Yagi slope

SLOPE STABILITY ENGINEERING VOLUME 1

This Page Intentionally Left Blank

PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON SLOPE STABILITY ENGImERING - IS-SHIKOKU’99/MATSUYAMA/SHIKOKU/ JAPAN/8- 11 NOVEMBER 1999

Edited by

Norio Yagi Ehime Universio,Japan

Takuo Yamagami & Jing-Cai Jiang University of Tokushima,Japan

VOLUME 1

U

A. A. BALKEMA/ R OTTERDAM BROOKFIELD/ 1999

The texts of the various papers in this volume were set individually by typists under the supervision of each of the authors concerned.

Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by A.A. Balkema, Rotterdam, provided that the base fee of per page is per copy, plus paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, USA. For those organizations that have been granted a photocopy license by CCC, a separate system of payment has been arranged. The fee code for users of the Transactional Reporting Service is: 90 5809 079 5/99

Published by A.A. Balkema, PO. Box 1675,3000 BR Rotterdam, Netherlands Fax: +3 1.10.413.5947; E-mail: balkema@ balkema.nl; Internet site: www.balkema.nl A.A. Balkema Publishers, Old Post Road, Brookfield, VT 05036-9704, USA Fax: 802.276.3837; E-mail: [email protected] For the complete set of two volumes, ISBN 90 5809 079 5 For Volume 1 , ISBN 90 5809 080 9 For Volume 2, ISBN 90 5809 08 1 7

0 1999 A.A. Balkema, Rotterdam Printed in the Netherlands

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Table of contents

Preface

XIII

Organization

xv

Special lecture Flow-type failure of slopes based on behavior of anisotropically consolidated sand K. Ishihara, YTsukamoto & S Nakayama

3

Keynote lectures The limit analysis for slopes: Theory, methods and applications Z Chen

15

Using limit equilibrium concepts in finite element slope stability analysis D. G. Fredlund & R. E. G.Scoular

31

Stability of geosynthetic reinforced steep slopes D. Leshchinsky

49

The mechanisms, causes and remediation of cliff instability on the western coast of the Black Sea M. Popescu

67

Design of slope stabilizing piles H. G.Poulos

83

1 Geological and geotechnical site investigations Geoenvironmental factors influencing the deterioration of shale in a rockslope A. M. Elleboudy

103

Weathering mechanism and slope failures of granitic rocks in Southwest Japan Effect of hydrothermal activities R. Kitagawa

109

Site investigation of weathered expansive mudrock slopes: Implications for slope instability and slope stabilization R.J. Mahuruj

1 15

-

V

Investigation of cut slope consisting of serpentinite and schist H. Kitarnura, M.Aoki, TNishikawa, TYarnamoto, M. Suzuki & TUmezaki

121

Using multibeam sonar surveys for submarine landslide investigations J. Locat, J.KGardner, H. Lee, L. Mayer, J. E. Hughes Clarke & E. Karnrnerer

127

Automatic measurement of pore water pressure in the hard-rock slope and the sliding weathered-rock slope - Field survey in mountainous region in Shikoku Island, Japan E.Tamura & S. Matsuka

135

Field measurement of suction in soil and rainfall in Kagoshima Prefecture R. Kitarnuru, K.Jomoto, K. Yamamoto, TTerachi, H.Abe & T Iryo

141

Application of acoustic emission method to Shirasu slope monitoring T.Fujiwara, K. Monrna & A. Ishibashi

147

Acoustic emission technique for monitoring soil and rock slope instability A. Kousteni, R. Hill, N Dixon & J. Kavanagh

151

Hydraulic fracturing as a mechanism of rapid rock mass slides S. Hasegawa & T Sawadu

157

Evolution of ridge-top linear depressions and a disintegration process of mountains K. Mokudai & M. Chigira

163

Geological characteristics of landslides of the soft rock type, Central Japan 7:Fujita

169

Study of configuration, scale and distribution of landslides S. Ueno

175

Geodynamics and spatial distribution of properties of sea cliff colluvium E. Dembicki & WSubotowicz

181

A mineralogical study of the mechanism of landslide in the serpentinite belt K.Yokota, R. Yatabe & N. Yagi

187

Detailed geotechnical study in Modi Khola Hydroelectric Project, Western Nepal VDangol & 7:R. Puudel

193

Local instability in saturated colluvial slopes in southern Brazil WA. Lacerdu

199

2 Soil slope stability analyses A new theory on instability of planar-sliding slope - Stiffness effect instability theory Qin Siqing

207

Ultimate state of a slope at non-linear unsteady creep and damage SA ElsouJiev

213

Application of FEM on the basis of elasto-viscoplastic model to landslide problems H. Fujii, S. Nishirnura, T.Hori & K. Shimuda

219

Coupled excavation analyses of vertical cut and slopes in clay T.Hoshikawa, 2: Nakai & Y Nishi

225

VI

Effects of a deep excavation on a potentially unstable urban hllside in San Marino G.Gottardi, G.Marchi, L.Tonni & F: Bianchi

233

Displacements of a slope in the Euganean Hills induced by quarrying S.Cola & RSirnonini

239

Stability evaluation of sliding failure along thin mudstone deposit due to excavation Y Nakarnura, J. Kojirna, S. Hanagata, K. Narita & YOhne

245

Appraisal of Bishop’s method of slope stability analysis G.L. Sivakurnar Babu & A. C Buoy

249

A convenient alternative representation of Taylor’s stability chart R. Baker & YTanaka

253

Influence of stress-strain curves on safety factors and inter-slice forces in FEM A. Mochizuki, J. Xiong & M. Mikasa

259

Slope stability analysis considering the deformation of slices YTerado,H. Hazarika, TYarnazaki & H. Hayarnizu

265

Slope stability analysis using a spring attached to inter-slice planes K. Kondo & S. Hayashi

27 1

Three-dimensional stability analysis of locally loaded slopes X.Q.Yang, S.X. He & 2.D. Liu

277

A lower-bound solution of earth pressure of cohesive backfill with inclined slope surface M. Luan, 7:Nian, C.E Lee, K.T. Law, K. Ugai & Q.Yang

28 1

Shear band formation and propagation in clay slopes L. E.Vallejo

287

Progressive failure analysis of slopes based on a LEM TYarnagarni,M.Taki, J.-CJiang & S.Yarnabe

293

Progressive failure analysis based on a method of non-vertical slices TYarnagarni,YA.Khan & J. -C.Jiang

299

Back analysis of unsaturated shear strength from a circular slope failure J. -CJiang, TYarnagarni & Y Ueta

305

A back analysis of MC-DP model parameters based on FEM and NLSSQP method T.Q.Feng, TYarnagarni & J.-C.Jiang

31 1

An FE analysis of anisotropic soil slopes and back analysis for its parameters T.0, Feng TYarnagarni & J.-CJiang

3 17

3 Rock slope stability analyses An upper bound wedge failure analysis method ZYChen, YJ.Wang,X.G.Wang & J.Wang

325

Stability analysis of rockfill dam and retaining wall constructed on dip bedrock S. S Chen & X.S. Fang

329

VII

Soil-water coupling analysis of progressive failure of cut slope using a strain softening model 333 TAdachi, E Oka, H. Osaki, H. Fukui & E Zhung A back analysis in assessing the stability of slopes by means of surface measurements S. Sakurai & 7:Nakayama

339

Numerical simulation of excavation of the permanent ship lock in the Three Gorges Prqject Y Zhang & K. Yin

345

Numerical simulation of the buckling failure in rock slopes I!Hu & H. -G.Kempfert

349

Fuzzy-based stability investigation of sliding rock masses NO.Nawari & R. Liang

355

Stability evaluation of discontinuous rock slope K. Kawarnura & M. Nishioka

36 1

Earthquake and seepage effects on the mobilised shear strength of closely jointed rock M.J. Pender

367

4 Effects of rainfall and groundwater Design chart for cut slope in unsaturated residual soils R. Subrarnaniam & E H.Ali

375

Factors affecting on water retention characteristic of soils K. Kawai, D. Karube & H. Seguchi

38 1

Suction profiles and stability of residual soil slopes E. C.Leong, B. K. Low & H. Rahardjo

387

Effects of perched water table on slope stability in unsaturated soils L. 7:Huat, E H.Ali, S. Mariappan & l? K. Soon

393

Field suction variation with rainfall on cut slope in weathered sedimentary residual soil L. 7:Huat, E H.Ali & S. Mariappan

399

Study of slope stability for Pleistocene cemented sandy sediments in Singapore (Old Alluvium) K. K. Poh, l? B. Ng & K. Orihara

405

Influence of pore water pressures in partly submerged slopes on the critical pool level E.N. Brornhead, A.J. Harris & l? D.J. Watson

41 1

Role of pore water and air pressures on slope stability in reservoir for pumped storage power plant TSato, N.Nishizawa, M. Wakarnatsu,I!Hiraiwa & I. Kurnazaki

417

Seepage characteristics of decomposed granite soil slope during rainfall S. Sasaki, S.Araki & K. Nishida

423

Relation between slope stability and groundwater flow caused by rainfalls M. Enoki & A.A. Kokubu

429

Vlll

Salient aspects of numerical analyses of rainfall induced slope instability C.-H.Wang

435

Centrifuge model tests and stability analysis on mobilizing process of shear strength of decomposed granite soil slope S.Yushituk & KOnitsuka

441

Centrifuge tests on slope failure during water infiltration H. G. B.Allersrna

447

Reinforcement’s effects in the tank-model prediction of slope failures due to rainfalls M. Shirnizu

453

Investigation of danger rainfall prediction system for natural and cut slopes H. Miki, A. Fujii & M. Furuta

459

Predicting ramfall-induced slope failures from moisture content measurement M. Nishigaki, A. Tohari & M. Kornatsu

465

Analytical study on the slope stability during ramfall and the rainfall indexes A. Togari-Ohta, TSugiyama, T Nara & S. Yarnazaki

47 1

Evaluation of critical rainfall with logit model I:Sugii, K.Yarnada & T Uno

477

Strategy for prevention of natural disaster due to slope failure R. Kitarnura, T Iryo, H.Abe, H. Yakabe & K. Yarnarnoto

483

Relationships between rainfalls and landslides after forest damages by typhoons S. Murata, H. Shibuya & K. Hayashi

489

Threshold rainfall for Beragala landslide in Sri Lanka

495

A K. Dissanayake, Y Sasaki & N H. Seneviratne

The importance of the groundwater regime studies of unstable slopes - An example of investigations on the landslide ‘Plavinac’, Yugoslavia G. Rasula & M. Rasula

50 1

Landslides induced by rainstorm in the Poun area of Chungchongbukdo Province D. Hun & K. Kim

509

Characteristics of Cretaceous granite slopes that failed during heavy rainfall TYarnarnoto, M. Suzuki, N. Matsurnoto & X Sehara

515

Seepage analyses of embankments on Tokaido-Shinkansen in long term rainfalls K. Kato & S. Sakajo

521

Instability analyses of embankments on Tokaido-Shinkansen in heavy rainfalls S. Sakajo & K. Kato

527

Chemical effect of groundwater from acid rain on slope evolution Z X u & R. Huang

533

Slope failures triggered by an earthquake and a heavy rain in Chiba S.Yasuda, XYoshida, I:Kobayashi & TMizunaga

539

IX

Numerical evaluation of the effects of drainage pipes TYamagami, K. Nishida & J.-CJiang

545

Effects of horizontal drains on ground water level and slope stability RCai & K. Ugai

55 1

5 Effects of seisrnicity Collapse of high embankment in the 1994 far-off Sanriku Earthquake KShioi & S. Sutoh

559

Slope instability of large embankments in residential areas caused by the Hyogoken-Nanbu Earthquake, 1995 T.Kamai, I:Kobayashi & H. Shuzui

565

Analysis of toppling failure of mountain slope caused by the Hyogoken-NanbuEarthquake TOkimura,NYoshida & NTorii

57 1

Stress condition and consequence of liquefaction on weathered granitic sands ZOkada, K.Sassa & H. Fukuoka

577

Effects of density, stress state and shear history on sliding-surfaceliquefaction behavior of sands in ring-shear apparatus G.Wang & K. Sassa

583

Real seismic-waveloading ring-shear test on the Nikawa landslide EWWang, K. Sassa & H. Fukuoka

589

Dynamic properties of fine-grained soils in pre-sheared sliding surfaces M.Yoshimine, R. Kuwano, J. Kuwano & K. Ishihara

595

Dependence of pore pressure generation on frequency of loading at sliding surface D.A. Vankov & K. Sassa

60 1

On-line earthquake response tests on embankments founded on saturated sandy deposits T.Fujii, M. Hyodo, I:Nakata, KYahuki & S. Kusakabe

607

Dynamic centrifuge tests of embankments on sloped ground and their stability analyses J. Koseki, 0.Mutsuo, K. Kondo & S. Nishihara

613

Evaluation of liquefaction potential for loose minefill slopes €? Kudella

619

Runout distances of earthquake-inducedlandslides I:Kobayashi

625

Evaluation of measured vertical and horizontal residual deformation at crest of rockfill dam under earthquake T. Okamoto

63 1

Displacements of slopes subjected to seismic loads R. L. Michalowski & L.You

637

Permanent displacement analysis of circular sliding block during shaking H. R. Razaghi, E.Yanagisawa & M. Kazarna

641

X

Dynamic analyses of slopes based on a simple strain-softening model of soil A.Wakui & K. Ugai

647

Slope instability due to rainfall and earthquake K. Shirnada, I3 Fujii, S. Nishirnura, ?:Nishiyarna & ir: Morii

653

Shaking table tests of concrete block retaining walls S. Mori, ir:Matsuyarna & ?:Ushiro

657

Shakedown analysis of soil foundations under varied loads M. Luan, Z: Cao & K. Ugai

663

Author index

669

XI

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang (c) 1999 Balkema, Rotterdam, ISBN 90 5809 0795

Preface

It is of a great concern to civil, geotechnical, and environmental engineers to overcome different problems caused by natural disasters, human errors and geo-environmental problems, whch are related directly or indirectly to the soil and rock properties. Although significant progress in the field of geotechmcal engineering has been made in past few decades, there are still a number of problems that arise in geotechnical analyses, designs, and specifications to prevent the possible damages due to unexpected disasters like landslides, debris flows, earthquakes, etc. So, figuring out these problems and tackling them very professionally are the main challenges at present-day world of geotechnical engineering. With this objective, the International Symposium on Slope Stability Engineering: Geotechnical and Geo-environmental Aspects - IS-Shikoku’99 was held at Matsuyama, Ehime from November 8 to 1I , 1999. The symposium was sponsored by the Japanese Geotechnical Society on its 50th anniversary under the auspices of the technical committee on landslides (TC-11) of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE) and the Japan Landslide Society. The aim of the symposium was to bring different professionals from different disciplines and backgrounds together into a place to broaden the knowledge and understand the problems all over the world from various perspectives. This symposium covers a broad range of topics such as site investigation, seismic effect, soil strength parameters, damage assessment, remediation techniques, land development, waste disposal, landslide hazard, simulation, analysis, etc on slope stability engineering. The main themes of the symposium are as follows: 1. Site investigation; 2. Stability analysis of soil and rock slopes; 3. Effects of seismicity and rainfall; 4. Design strength parameters of natural slopes; 5. Effect of land development; 6. Slope stability of waste materials; 7. Stability of landfills; 8. Stabilization and remedial works; 9. Reinforced steep slopes; 10. Probabilistic slope stability; 1 1. Landslide inventory and landslide hazard zonation; 12. Simulation and analysis of debris flow.

After reviewing the abstracts and manuscripts of 246 full papers from over 4 0 countries by the organizingcommittee, a total of 221 papers has been accepted for the presentation in the symposium and publication in the proceedings volumes. The chairman, on behalf of the organizing committee, would like to extend his deep gratitude to the special speaker, Prof. Kenji Ishihara, President of ISSMGE and the keynote speakers, Dr. Zuyu Chen, Prof. Delwyn G.Fredlund, Prof. Dov Leshchinsky, Prof. Mihail Popescu, and Prof. Harry G.Poulos. Thanks are also due to the professionals who made this symposium a grand success by submitting and presenting the papers in different topics in the field of slope stability engineering. All participants without whom the symposium would not have been a lively discussion forum are greatly acknowledged for their active participation. Special thanks from the chairman go to all the session chairpersons and to Prof. Yamagami, Prof. Mochizuki, Prof. Yatabe, Dr Jiang and the members of local and international advisory committee for their active involvement in accomplishing the symposium. Finally, the Ministry of Education, Science, Sports, and Culture that financially supported the symposium under the Grant-in-Aid for publication of Scientific Research Results is highly appreciated. Norio Yagi Chairman of the International Symposium on Slope Stability Engineering - IS-Shlkoku’99 Professor of Ehime University, Japan November 1999

XIV

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 905809 079 5

Organization

INTERNATIONAL ADVISTORY COMMITTEE Prof. T.Adachi, Japan Prof. K.Arai, Japan Prof. A.Asaoka, Japan Prof. R. Baker, Israel Dr R. K. Bhandari, India Prof. C. Bonnard, Switzerland Prof. E. N. Bromhead, UK Dr Zuyu Chen, China Prof. M.Chigira, Japan Prof. R.Chowdhury, Australia Prof. D. M.Cruden, Canada Prof. J. M. Duncan, USA Prof. M.Enoki, Japan Prof. R. M. Faure, France Prof. D.G. Fredlund, Canada Dr H.FuJita, Japan Prof. T.Furuya, Japan Prof. J. N.Hutchinson, UK Prof. Y. Ichlkawa, Japan Prof. K. Ishihara, Japan Prof. H. Kawakami, Japan Prof. Sang-Kyu Kim, Korea Prof. T. Kimura, Japan Prof. R. Kitamura, Japan Prof. Y. Kobayashi, Japan Prof. 0.Kusakabe, Japan Prof. W.A. Lacerda, Brazil Prof. K.T. Law, Canada Prof. C. E Lee, Hong Kong Prof. D. Leshchinsky, USA Prof. J. Locat, Canada Prof. M. Maksimovic, Yugoslavia

Prof. T. Matsui, Japan Prof. R. L. Michalowski, USA Dr H.Miki, Japan Prof. T. Mitachi, Japan Prof. S. Miyauchi, Japan Prof. H. Nakamura, Japan Prof. K.Narita, Japan Prof. M. Nishigaki, Japan Prof. H.Ochiai, Japan Prof. Y.Ohrushi, Japan Prof. H.Ohta, Japan Prof. K.Okada, Japan Prof. TOhmura, Japan Prof. S.Okuzono, Japan Prof. M. J. Pender, New Zealand Dr D. J. Petley, UK Prof. L. Picarelli, Italy Prof. M. Popescu, Romania Prof. H.G. Poulos, Australia Prof. S.Sakurai, Japan Prof. Y.Sasaki, Japan Prof. D.Schreiner, South Africa Prof. R. L. Schuster, USA Prof. H.Sekiguchi, Japan Prof. K. Senneset, Norway Prof. ETatsuoka, Japan Dr Gongxian Wang, China Prof. S.G.Wright, USA Prof. E.Yanagisawa, Japan Prof. S.Yasuda, Japan Dr H.Yoshimatsu, Japan

xv

ORGANIZING COMMITTEE

Chairman Prof. N.Yagi General Secretary Prof. T.Yamagami Secretaries Dr J.-C. Jiang Prof. A. Mochizuki Prof. R.Yatabe Members Dr S.Akutagawa Dr S. Hasegawa K. lshikawa E Kamada K. Koumura Prof. T. Muro H. Nishda Assoc. Prof. M.Ogura Dr H.Ohtsu

Prof. K. Sassa Dr N. Shimizu Y. Shono Dr A. Suemine M.Takeyama Prof. 1.Towhata Prof. K.Ugai M.Yamamoto A.YZiISIanaka

XVI

Special lecture

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami 8 Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Flow-type failure of slopes based on behavior of anisotropically consolidated sand K. Ishihara, YTsukamoto & S. Nakayama Department of Civil Engineering, Science University oj' Tokyo,Japan

ABSTRACT: Soil deposits in natural slopes are subjected to an initial shear stress as well as confining stress which are induced by the gravity. To evaluate effects of the initial shear stress on the behaviour of sand undergoing large deformation, a series of laboratory tests were performed, using the biaxial test apparatus, on saturated samples of Toyoura sand consolidated anisotropically under various Kc-conditions. The results of the tests were examined to determine the initial stress conditions distinguishing contractive and dilative behaviour in undrained application of shear stress. It was found that the major effective principal stress at the time of anisotropic consolidation is a parameter controlling dilative or contractive behaviour of the sand under otherwise identical conditions. Based on this conclusion, it was pointed out that the most appropriate way to normalize the residual strength of anisotropically consolidated sand is by the use of the major principal stress at consolidation. The outcome of the test results as above was used to address a method or criterion by which to identify whether or not a given sandy soil deposit under a slope will have a potential to develop the flow type failure with large deformation. Generally, it is a difficult task to determine the factor of safety for the slide triggering, because of uncertainty in quantitatively identifying the slideinducing external force to be applied to the soil element in addition to the gravity-induced shear stress. This external force could be seismic shaking or additional weight by rainfall. In contrast, the factor of safety for the flow slide can be determined rather easily primarily because the gravity-induced shear stress is the major driving force to be compared against the residual strength of the soils, and there is no need to identify other external forces. The aim of the present study is to indicate a basic concept for determining the residual strength for sandy soils that can be used to determine the factor of safety for flow type failure of slopes. In this type of analysis, no matter what is the slide-triggering driving force, the consequence is recognized as more important and there is no need to seek for the cause of the slide. The only force to be considered is the force induced by the gravity and this makes the analysis simple and straightforward.

INTRODUCTION In the conventional analysis of slope stability, a potential sliding plane is assumed and the shear stress expected to occur is compared against the shear strength that can be mobilized along the sliding plane. It has been customary to take up the magnitude of peak shear stress to define the shear strength. In the case of saturated loose sandy soils, the peak stress is mobilized at a relatively small shear strain of the order of 2 - 5%. Thus, even when the peak shear stress is passed over by some external forces, the resulting deformation may not be large enough, if there is no strain-softening taking place in the soils. In this case, cracking or small amount of deformation may be manifested on the surface of soil deposits and damage would be minor. However, if the soils are loose enough to induce strain-softening due to contractive nature of deformation, the shear strain of the order of 10 - 20% can easily be generated leading to flow type deformation. In terms of field behaviour, the soil in the slope is envisaged to move largely downstream giving rise to destructive damage there. Thus, the factor of safety against sliding of slopes can be defined in two ways, namely, (1) the factor of safety for triggering the slide against the peak strength, and (2) the factor of safety for the flow failure against the residual strength.

BASIC CONCEPT For the sake of simplicity, let a potential sliding plane be located in parallel to the surface of the slope as illustrated in Figure 1. Then, from the equilibrium of

3

Then, given the values of stress components, o, and z,, as above it is possible to locate a point B in the diagram of o, and 7, as illustrated in Figure 2. The direction of the line OB indicates the angle of obliquity of stress application, a , or the angle of stress mobilization. By drawing a half circle through the point B so that it is tangential to the line OB, it becomes possible to identify the points of the minor and major principal stresses o, and o3on the Mohr diagram. Then, from geometrical consideration, the following relations are obtained.

forces amongst the weight of a soil mass W, and normal and tangential forces N and S acting on the potential sliding plane, the stresses o, and T, are obtained as CT

N =-=y HCOS~CX

, e

... (1) S z, = - = y Hsina. coscx

e

where y is the unit weight of the soil, a is the angle of the sliding plane, and H is the height of the soil mass being considered.

o1= 0 , + (tan

( ~= 3 CT,

+

1

-lcos z, a

1 + (tana - -)za cos a

I

... (2)

Introducing Eq. (1) into Eq. (2), one obtains

o, = y H( l+sina) o3= y H( 1-sina)

1

... (3)

Thus, the ratio between the minor and major principal stresses is obtained as 1-sina KC= CT~/CT, =l+sina

... (4)

The relation of Eq. (4) is displayed in Figure 3. It is known that the majority of natural slopes consisting of relatively soft soils have an angle ranging approximately between a=O and a=45". Thus, the ratio, Kc, between the two principal stresses has a value between 0.2 and 1.0.

Figure 1. Forces acting on the soil element above a sliding plane in a slope.

Figure 3. Relation between Kc-value and angle of slope. Figure 2. Mohr circle to determine 0,and and 7,.

o3from o,

4

BACKGROUND OF LABORATORY TESTS

TYPICAL PATTERN OF DEFORMATION

When attempting to identify mechanism of failure of soils underneath sloping surface by virtue of laboratory tests, it has been a usual practice to subject a soil specimen to the stress changes which are similar to those expected to take place in the field. The principle of duplication of in-situ conditions as above would be executed in the laboratory tests by applying the principal stress CT, and C T ~under drained conditions and then by shearing the soil specimen under undrained conditions. It would be argued that the undrained conditions may not prevail in shallowly seated partially saturated soil deposits where sliding could frequently take place. However, the change in void ratio of the soil during large deformation leading to sliding may be deemed not so much appreciable that the constant volume condition may be maintained approximately to a tolerable level of accuracy. In addition, it may as well be assumed that, even though the soil is partially saturated, the deformation behaviour is considered to be represented approximately by that of a fully saturated sample, if its volume stays little changed. With the assumptions as above multiple series of triaxial tests were conducted by subjecting sand specimens to a stress system with varying Kc-values defined as

The typical pattern of undrained deformation of anisotropically consolidated specimens is schematically illustrated in Figure 4 in terms of stress path and stress-strain curve. In Figure 4 (a), the abscissa indicates the mean principal effective stress defined by p’=(0’,+20’,)/3 and the ordinate represents the shear stress defined by q In Figure 4, point A indicates an initial state of Kcconsolidation whereupon undrained shear stress application starts. When the specimen is loose, it shows an increase in shear stress, q, to a point B at peak strength and then a decrease down to a point C corresponding to the phase transformation. The bentover in the stress path takes place at point C and the shear stress increases to a point D where large deformation starts to occur without any change in the effective mean stress p’ and shear stress q. This state is called the steady-state. When the specimen is loose, the minimum shear stress is encountered, concomitant with fairly large deformation, at point C where the phase transformation take place from contractive to dilative behaviour. Thus, the residual strength should be defined by the shear stress qas which is mobilized at point C. The residual strength thus defined is called the strength at quasi-steady state. When the specimen is medium dense to dense, the stress drop does not appear and the shear stress at the phase transformation does not produce large deformation. In such a case, the residual strength should be defined as the shear stress mobilized at the steady-state, namely the point D. In the present study, attention will be drawn to the state of stress at the quasi-steady state, that is, the point C in Figure 4. No matter what is the strength at the steady state at point D, of practical importance in

Kc = C T ’ /~c T~ ’ , ~ where o ’ ,and ~ C T ’ ~stands ~ for, respectively, the effective major and minor principal stresses at the time of consolidation. After the specimens were consolidated anisotropically, they were subjected to shear stress under undrained conditions by increasing the major principal stress CT].

Figure 4. Typical stress-path and stress-strain relation for loose sand.

5

Figure 5. Stress path and stress-strain relation of anisotropically consolidated sand with Kc=0.5.

Figure 7. Stress path and stress-strain relation of anisotropically consolidated sand with Kc=0.7.

Figure 6. Stress path and stress-strain relation of anisotropically consolidated sand with Kc=0.6.

Figure 8. Stress path and stress-strain relation of isotropically consolidated sand with Kc=l .O. 6

loose sands would be the shear stress that can be mobilized at the point C in the state of phase transformation. In t h s context, the strength at the ultimate steady state is beyond the scope of the present study .

CONSIDERATION FOR TEST RESULTS It has been shown by Chern (1985), and, Vaid Chern (1985) that the relation between the void ratio and the minor effective stress at phase transformation G’,,is determined almost uniquely irrespective of the Kc-condition at the time of anisotropic consolidation. This conclusion has been proved to be valid as well for Toyoura sand as indicated by the data shown in Figure 9 where four test data are plotted for the cases of K,=0.5, 0.6 and 0.7. The specimens with an initial void ratio of ei=0.892 were consolidated to vertical stresses of o’,, =60, 70 and 12OkPa and sheared undrained in the triaxial compression mode.

OUTCOME OF TESTS The results of undrained compression tests on samples with void ratios ranging between 0.882 and 0.993 are displayed in Figure 5 where the shear stress q=(o,’-o,’)/2 is plotted versus the effective confining stress defined as p=(o,’+o,’)/2. The saturated samples were consolidated with a vertical stress of oI,’=196kPa and a lateral stress of o,,’=98kPa producing an initial state of Kc=0.5. It may be seen in Figures 5(a) and 5(b) that the dilatant behaviour is exhibited when the sample is prepared with a void ratio less than about 0.90, but otherwise the sample is contractive. It is to be noticed that the sample with e=0.912 has reached a steady-state with a shear stress of q=30kPa which is smaller than the initially applied shear stress of q=SOkPa. It is seen in Figure 5(b) that large deformation began to occur at an early stage of load application and continues further until an axial strain of 20% developed. The smallness of the shear stress at the quasi-steady state as compared to the shear stress at the outset would be regarded as a criterion for an unstable condition where flow-type deformation could be triggered if the peak shear stress is passed over by application of a slight agitation at the beginning. Another series of tests with the same initial lateral stress of 03,’=98kPa but with an increased Kc-value of 0.6 is demonstrated in Figure 6 for samples with various void ratios where the general tendency is seen to be the same as the results of the tests shown in Figure 5. Still other series of the tests with a further increased value of Kc are displayed in Figure 7 where it may be noted that the sample with a void ratio of 0.900 has reached a steady-state where the shear stress is about q=SOkPa which is much larger than the initial shear stress of q=20kPa. In such a condition, the flow type deformation would not be induced because of the gain in shear strength as compared to the initially applied shear stress. The last series of the tests with Kc=l.O are demonstrated in Figure 8 where it is apparently noted that the specimen with e=0.884 exhibits delative behaviour. In comparison amongst the cases of Kc=0.5 through 1.0, it is noted that the sample changes its behaviour from contractive to dilative with increasing Kc-values even if the void ratio is kept at a constant value of e=0.900. This means that, with an increasing degree of anisotropy at the time of consolidation, the sample becomes more contractive and susceptible to triggering of the flow failure.

Figure 9. Relation between void ratio and major principal stress G’,, at the state of phase transformation. The minor effective stress G ’ ~ , at phase transformation obtained in the tests was multiplied by a factor, ( 1+sin$,)/( 1-sin$,), to obtain the corresponding major principal stress, o’,,, and this value of is plotted versus the void ratio in Figure 9, together with the consolidation curve for the initial void ratio of 0.892. It was then possible to draw a curve amongst the data points to establish a correlation between the void ratio and as indicated in Figure 9. Note that there are some scatters in the data, but the scatters become less and less as the becomes large. It may be consolidation pressure o’,, seen in Figure 9 that for the two specimens with o’ ,=60 and 70kPa, dilative responses were observed throughout shear stress application, but for other two tests with o’ 120kPa, specimens exhibited contractive behaviour with limited deformation. 7

Figure 10. Plots of initial states of specimens in terms of void ratio and ollC to determine the Initial Dividng Line for anisotropically consolidated sand.

RESIDUAL STRENGTH OF ANISOTROPICALLY CONSOLIDATED SAND

Thus, the threshold condition differentiating between contractive and dilative behaviour would be obtained as marked in the diagram of Figure 9. In looking at the diagram in Figure 9, it is to be noticed that a unique set of curves are obtained for the consolidation and phase transformation, if the effective major principal stress, G’I c and G’ are used to plot the test data of Kc - consolidated samples. Thus, it may be mentioned that, the deformation behaviour of Kc consolidated sand is dominated by the effective major principal stress o’l. In order to examine the characteristic features of undrained deformation as above, the major principal stress c f I C at consolidation is plotted in Figure 10 for each of the test results with varying Kc-values. Note that each point in the figure indicates the void ratio and o’lc at initial stages before application of undrained shearing. It may be seen in Figure 10 that the Initial Dividing Line (ID-line) defined as a threshold curve differentiating between conditions of flow and non-flow can be established uniquely for anisotropically consolidated sample, if 0 ,1c is chosen as a parameter to indicate confinement of the sample at the initial state. Superimposed in Figure 10 is the quasi-steady state line established previously in Figure 9. According to the study by Kato et al. (1999), the QSS-line was shown to be determined uniquely also for anisotropically consolidated sand, if dIC is chosen as a parameter to indicate initial confinement.

It has been customary to define the residual strength, Sus, by referring to the minimum shear stress at the QSS which is mobilized at the state of phase transformation for sands exhibiting contractive behaviour. By denoting the deviator stress at this state by qs=o’1s-o’3s, the residual strength is expressed as (Ishihara, 1996, p. 268) sus =

4 M cos@ = -cos@ .p‘ 2 2 s s

... (6) M=- 6sin@,

3 - sin@,

where p’s is the confining stress at the quasi-steady state as defined by ps’=(o’Is+20’,,)/3 and M is a parameter related with the angle of phase transformation in the p’-q plot. When normalizing the residual strength, Sus, there are three methods that are conceived to properly represent the strength. In the previous study (Ishihara, 1993) dealing with isotropically consolidated samples of sands, the mean effective stress at the time of consolidation, p’c=(~’lc+20’3c)/3, has been used as a variable to represent the degree of confinement at the state of

8

consolidation. However, when dealing with the anisotropically consolidated samples of sand, it may not be convenient to utilize the mean effective stress p,'. The other options would be to adopt the confining stress fjC=(o',,+ci',,)/2 or to use the major effective confining stress o',,.The three options are summarized as follows. P'C'

-

Pc =

11 (a). Those data from denser samples exhibiting dilative behaviour are displayed with open circles and those shown by solid circles indicate that samples exhibited contractive behaviour. The boundary separating conditions of contractive and dilative behaviour is indicated by a vertical straight line in Figure 11 (a). It can be seen that the threshold initial state ratio differentiating between contractive and dilative behaviour remains almost unchanged with variation of Kc-values. Thus, it is considered appropriate to assume that the threshold initial state ratio, r,', takes a constant value which is equal to rc'= 1.2 for Toyoura sand. The same data set is expressed alternatively in Figure ll(b) now in terms of the Kc-value plotted versus the initial state ratio, ic, defined by Eq. (9). It may be seen that the threshold value of fctends to increase with an increasing value of K ~ = o ' ~ c / o ' , ~ . The other approach was adopted to arrange the data set in terms of the initial state ratio, rc=pc'/ps', defined by Eq. (8). The data plotted in Figure 1l(c) versus the Kc-value indicate as well that the threshold r,-value differentiating conditions between contractive and dilative behaviour tends to increase with increasing Kc-values. It is to be noticed in Figure 1O(c) that the value of r,=2.1 corresponding to Kc=l.O condition is approximately equal to the value of r,=2.0 determined in the previous study (Ishihara, 1993). Based on the observation as above, it may be assumed that the initial state ratio, r,', defined by Eq. (10) is to be taken as a fundamental parameter to indicate the threshold condition between the contractiveness and dilativeness of sand no matter whatever the anisotropic condition would be at the initial state. It may also be concluded that for Toyoura sand the threshold initial state ratio takes a value of r,'=1.2 for all the Kc-conditions employed in the tests. The relationship between rc', ?,and r, can be derived from their definitions as follows,

0' 1c + 2 d 3c

3

'

61, + d 3 c

... (7)

0' IC = d 1 c

~

Using the three confining stresses, the normalized residual strength is obtained variously as follows. sus - M -- -cos$, P'c 2

1

-

r,

1 i

I

... (9)

-

... (10) -

r rc'

1 9

+

C = - (1 2Kc)(2M + 3)

The ratio of the confining stress at the initial state to that at the quasi-steady state, rc, was introduced in the previous study (Ishihara, 1999, p269) as an important parameter to represent the degree of contractiveness in undrained loading on isotropically consolidated sand. It was referred to as the initial state ratio. The initial state ratio ?,and r,' are newly introduced in the present study as defined by Eqs. (9) and (10). In order to examine effects of Kc-consolidation on the value of the initial state ratio, the effective confining stress at the state of phase transformation was read off from all the test data such as those shown in Figures 5 through 8. The value of rc'=o,,'/ols' as defined by Eq. (10) was calculated first for all the test data on Toyoura sand and plotted versus the value of Kc =o,c'/~,c'as shown in Figure

... (1 1)

-

2M+3 = (1 + Kc)M+6 rc where M=

3(0' 1s-63s 1 - 6sin Qs +2d3, ) 3 -sin$,

(0'

The results of extensive tests in the previous studies (Ishihara, 1993) have shown that for Toyoura sand the value of M takes a value of 1.24 and Qs=31" . In the subsequent study, this value proved to be valid as

9

well for anisotropically consolidated samples of Toyoura sand with various Kc-values. Introducing this value into Eq. (1 l), one obtains

It has been known in the above that the threshold initial state ratio rc’=o,c’/oIs’takes a value of rc7=l.2, as demonstrated in Figure 11(a). Introducing this value, Eq. (12) can be rewritten as,

2=0.61(1+2Kc)

rc = 0.73( 1+ 2Kc)

rc‘

... (12)

-

% = 0.76( I + Kc) rC

TC =0.91(1+Kc)

1

. . . ( 13)

J

~

Figure 12. Relation between Kc-value and variously defined normalized residual strength.

Figure 1 1. Relation between Kc-value and variously defined initial state ratios. 10

magnitude of the residual strength is equal to or smaller than that of the shear stress induced by the gravity force. It is to be mentioned here that, no matter whatever may be the genetic cause of the slide, the gravity-induced shear stress would be the main force driving the soils mass moving downhills. If the soil deposit is in a loose state exhibiting the contractive behaviour with a residual strength which is smaller than the gravity-induced shear stress, then the soil mass would continue to move downwards leading to the flow-type of slide. As mentioned above, the degree of susceptibility to the flow slide depends also on the initial state of shear stress as expressed in terms of the Kc-values. Thus, it would be of interest to examine how the initial state will affect the potential for the flow slide if the soil is in the initial state under the slope as illustrated in Figure 1.

These relations are displayed in Figures 1 l(b) and

1 I(c). It may be seen that the relations of Eq. (13) are considered to hold true with a reasonable level of coincidence to mark the boundary lines differentiating between conditions of contractive and dilative behaviour of Toyoura sand, if the initial state ratio, rc and ?,are to be used to obtain the normalized residual strength through the use of Eqs. (8), (9) and (10). The values of the normalized residual strength can be determined for all the test data obtained in the present study based on the three expressions indicated by Eqs. (8) (9) and (10). The normalized residual strength obtained using Eq. (10) is displayed in Figure 12(a). Since the threshold value of rc’ is known to take a constant value of 1.2, the normalized residual strength is determined uniquely independent of the Kc-value. As indicated in Figure 12 (a), the normalized residual strength takes a threshold value of Sus/0’,,=0.24 which is the upper limit amongst a number of data corresponding to the condition fC 2 1.2. It is to be noticed that the test data indicated by open circles all belong to the state of phase transformation in dilative samples and the normalized residual strength in this region is not the minimum value of the strength. The ultimate strength in the region of fc51.2 needs to be determined by considering the ultimate state (steady state in dilating samples). The ultimate strength at the steady state in the dilative sand is generally higher and beyond the scope of the present study . The normalized residual strength Sus/p’, and Sus/pc determined by Eqs. (8) and (9), respectively, is also demonstrated in Figure 12. The threshold value of the strength bounding the upper limit of any of the strength values in contractive sand is obtained by simply introducing Eq. (13) into Eqs. (8) and (9), as follows. S u s / d I c= 0.24

0.48

1 ... (14)

s u s / Pc =

0.72 S,,/p‘ = ____ 1 + 2Kc

Figure 13. Residual strength versus the gravityinduced initial stress. For each of the results of the tests on loose samples with void ratios ranging between e=0.880 and 0.92 1, the value of shear stress qQsat the state of phase transformation was read off and its ratio to the initially applied shear stress qo was obtained as plotted in the ordinate of the diagram in Figure 13. The definition of qQsand qo is illustrated in the inset of Figure 13. Plotted in the abscissa of Figure 13 is the Kc-value in each of the anisotropically consolidated sample. Also plotted in the figure in the value of the slope angle, a, as obtained from the chart in Figure 3. It may be mentioned that if the ratio, qQs/qOis less than unity, there would be a potential for the flow-type slide being induced in the soil and otherwise the soil will be safe and free from being

1

The relations of Eq. (14) are also displayed in Figures 12(b) and 12(c) where it may be seen that the normalized residual strength as determined by E¶.( 14) could represent the upper limit of the strengths if the residual strength is to be normalized by p’, and P,. POTENTIAL FOR FLOW SLIDE As mentioned in the foregoing, the flow-type failure will be induced in loose sandy deposits, if the 11

Okuhara, students of the Civil Engineering Department, Science University of Tokyo. The authors wish to express their gratitude to these persons.

involved in the catastrophc slide due to flow-type deformation. Interpreted in this context, it may be inferred from the data in Figure 13 that , if the Toyoura sand exists in a slope with a void ratio of e=0.880 and 0.921, the slope with an angle of inclination greater than about 12.5” (Kc 50.65) would be considered to have a danger of being involved in the flow slide. It is to be noticed that the relation as shown in Figure 13 depends upon the density and material properties of sandy soils and more test data will need to be accumulated before any conclusion is drawn.

REFERENCES Chern, J. C. 1985. Undrained Response of Saturated Sands with Emphasis on Liquefaction and Cyclic Mobility. Ph. D. Thesis, University of British Columbia, Vancouver. Ishihara, K. 1993. Liquefaction and Flow F d u r e during Earthquakes. Geotechnique, Vol. 32, NO. 3 : 351 -415.

CONCLUSIONS

A series of undrained triaxial compression tests were conducted on saturated specimens of Toyoura sand with various densities to investigate effects of anisotropic consolidation on undrained behaviour distinguishing between contractive and dilative characteristics. The outcome of the tests indicated that the major at the time of anisotropic principal stress consolidation is a governing factor to uniquely determine the initial dividing line and quasi-steady state line in the plot of void ratio and confining stresses. This means that neither the mean principal stress defined by p’=(o’,,+2o’,,)/3 nor p=(o’1c+o’3c)/2is an appropriate parameter to specify the initial state of confinement in the consolidated sand. Based on the above conclusion, the residual strength of the sand normalized each to different initial p’ and Tj, was examined, with the stresses, i.e., o’],, result that the normalization by oYlcis most appropriate to define the normalized residual strength. It was also shown that the residual strength ~ a value of 0.24 as an upper normalized by o ’ ,takes lirmt beyond which the residual strength can not be defined because of the sand becoming dilative with increasing density. To evaluate whether the Kc-consolidated sand is susceptible to flow-type failure, the value of residual strength was compared with the shear stress applied at the time of the anisotropic consolidation for loose samples with a void ratio between e=0.880 and 0.921. The outcome of such assessment indicated that for a loose deposit of Toyoura sand, there would be a potential for the flow failure to be triggered, if the angle of slope becomes greater than 12.5” and otherwise there would be no danger for such catastrophic failure.

Ishihara, K. 1996. Soil Behaviour in Earthquake Geotechnics. Oxford University Press. Kato, S., K. Ishihara & I. Towhata 1999. Undrained Shear Characteristics of Saturated Sand under Anisotropic Consolidation. submitted to Soils and Foundations. Vaid. Y. P. & J. C. Chern 1985. Cyclic and Monotonic Undrained Response of Saturated Sands. Advances in the Art of Testing Soils under Cyclic Conditions, Proc. ASCE Convention in Detroit, Michigan: 120 - 147.

ACKNOWLEDGMENTS The laboratory tests described herein were performed by the help of Mr. T. Yoshimura and Mr. M. 12

Keynote lectures

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang (01999 Balkema, Rotterdam, ISBN 90 5809 079 5

The limit analysis for slopes: Theory, methods and applications Zuyu Chen China Institute of WaterResources und Hydropower Research, Beijing, People’s Republic of Chinu

ABSTRACT: The solution of a slope stability problem can be approached by its least upper bound and maximum lower bound. The limit equilibrium methods that employ vertical slices, such as those proposed by Bishop (1955), Morgenstern and Price (1965), imply a lower bound of the factor of safety. Those that employ slices with inclined interfaces, such the methods proposed by Sarma (1979), Donald and Chen (1997), give an upper bound approach to the stability analysis. In most cases the gap between the two bounds is very small and the rigorous solutions are indeed obtainable. However, care must be taken of the possible two directions of shear between the adjacent slices when the upper bound approach is used. The concept of upper bound and lower bound principles has been extended to wedge slide analysis. A number of case histories regarding the slope engineering of China’s hydropower construction, including those of the Three Gorges and Xiaolangdi projects, have been reviewed which indicated that an understanding of the Bound Theorems will help to obtain reliable and economical solutions to slope stability problems. 1INTRODUCTION

application of the theory to practical geotechnical problems possible. In this paper, the author wishes to give a general review of the theoretical background of the limit analysis method, demonstrate its accuracy, bring some critical issues that have not yet been discussed in literature and report its successhl applications in some important projects in China.

The limit equilibrium method, or in a broader sense, the limit analysis method (Chen, 1975), is an approach that has been extensively used in solving various practical problems concerned with slope stability analysis. In spite of its successfbl applications in geotechnical engineering for both soil and rock slopes there have been some critical issues needed to be discussed. The limit equilibrium method has been regarded sometimes as an empirical approach since some assumptions were introduced when establishing the governing equations and since the displacement of the soil or rock mass is not properly considered in the method. Another issue related to this method is that the method is well developed and understood. More work in updating the method seems not to be highly demanded. As a branch of applied science, Soil Mechanics and Rock Mechanics benefit from the recent developments in the Classic Mechanics and Computer Science. The former offers a theoretical background, such as the upper bound and lower bound theorems of Plasticity, which enables us to establish a modern system of limit analysis based on the traditional method of slices. The latter makes the

2THEORETICAL BACKGROUND 2.1 Fundamentals

The procedures of solving slope stability problems is similar to that for solid mechanics. For a specified load system, it is required to find a stress fielder,,, and its associated displacement field U,, which satisfy the following conditions (expressed in tensors). (1) Force equilibrium nq.,

=

*,

with the boundary conditions:

15

in which W, is the body force, T, the tractions in the boundary S and nl is the directional derivatives of the surface S. The force equilibrium conditions can be expressed in a formulation employing the virtual work principle.

I, crJ.i., dv =

W , . ri, dv

+IF,

U,

LJS

stability problems. However, rock mass is highly discontinuous, non-homogeneous, anisotropic and nonlinear, which exhibits complicated deformation behavior at failure, such as dilatancy, strain softening and large displacements, Finding the solution by some simplified methods is an approach actually employed by many practitioners in their consulting work.

(2.3)

where li is a compatible displacement increment field assigned on each force. The left side of (2.3) is sometimes called energy dissipation. (2) Compatible displacement filed A compatible displacement filed requires that the strain at any point follows the definition:

(3) Constitutive law The constitutive law relates the force equilibrium and deformation compatibility requirements and represents the material behavior. It includes both deformation and strength requirements.

where Cllk,is a matrix representing elastic or elastoplastic relationships expressed in tensors. For Eq. (2.6), Mohr-Coulumn' s failure criterion is generally employed, which states as ,r - o,,ig$ - c 4 0

(2.7)

or

where on and 'tr are normal and shear strength on the failure surface, while c and 4, shear strength parameters respectively. For rock and soil material, we also restrict the presence of tensile stress, i. e., 20

(2.9) FIG. 2.1 Slope stability analysis by an upper bound approach. (a) a general case; (b) the multi-slice failure mode: (3) the multi-block failure mode.

where 0 3 is the minor Principle stress at any Point of the media.

2.2 The upper bound and lower. borrnd theorems of Plasiiciiy

(1) The lower bound theorem The lower bound approach starts from the force equilibrium condition and states that any stress field that satisfies Eq. (2.1). (2.2) and (2.7) or (2.8) will

Satisfying all the conditions stated in Section 2.1 will lead to a real or rigorous solution to slope

16

r

2.3 Definition ofthe factor of safety

be associated with an external load that is lower than or equal to the real load that brings the failure.

Traditionally, the theorems of Plasticity employ a loading factor q that brings a structure to failure. Donald and Chen (1997) discussed the unique and monotonic relationship between the loading factor 7 and factor of safety F which, in order to bring the structure to failure, reduces the available shear strength parameters to new values as

(2) The lower bound theorem The upper bound approach starts from an increment of displacement, generally referred to as velocity U,, , in the plastic zone Q* and the slip surface r*.It states that the load calculated by (2.3) and (2.8) will be either greater than or equal to the real load associated with a real failure mechanism Q and r (Refer to Fig. 2.1 (a)). The left part of Eq. (2.3) consists of two parts, becoming

L o ~.zi,,JdQ+ , ~ IdD=dW;.Uldv+IT,zi,ds

C,

=CIF

tanp, = tanp, I F

(2.11) (2.12)

The minimum and maximum loading factors are directly related to the minimum and maximum factor of safety respectively. Therefore, all the statements related to the bound Theorems can be expressed in terms of factor of safety. In the following presentations, the subscription ‘e’ appeared for all variables would invariably mean that the related c and 4 values are reduced by (2.1 l), (2.12).

(2.10)

where D is the energy dissipation developed on the slip surface r. The limit analysis renders the solution by approaching the real ultimate load from lower bound and the upper bound, trying to find the least upper bound and the maximum lower bound. If the difference between the two bounds is small, we may conclude that the rigorous solution is actually obtained. The advent and rapid development of computers and the associated various numerical algorithms have enabled a practicable procedure to find the extreme for geotechnical problems and confirm that the two bounds are indeed very close. In explaining this concept, Pan Jiazheng (1980) summarized the following principles: (1) Among many possible slip surfaces, the real one offers the minimum resistance against failure ( Principle of minimum); (2) For a specified slip surface, the stress in the failure mass as well on the slip surface will be reorganized to develop the maximum resistance against failure ( Principle of maximum). The author has given a formal demonstration to Pan’s principle based on the Bound Theorems of Plasticity and Drucker’s postulates (Chen, 1998). In fact, Pan’s Principle is identical to the Bound Theorems but expressed in a more understandable way. Following the Bound Theorems or Pan’s Principles, performing slope stability analysis generally includes the following two steps: (1) For a specified failure mechanism, find a stress distribution that satisfies Eq. (2.1) with the constraints of (2.7) or (2.8), and search for a distribution that offers the maximum value of factor of safety. (2) Among all possible failure mechanism, find the one that has the minimum factor of safety.

2.4 Significance ofthe Bound Theorems Before proceeding with the details, we present the following three examples indicating that a proper implementation of the bound theory will help us find the solution in a very simple way with high accuracy. Further more, it will offer better understanding to some basic rock mechanics concepts which otherwise could hardly be well interpreted. Example I The upper bound approach used for solving structural problems. Fig. 2.2 shows an example taken from the textbook (Wang, et. al, 1992). The frame is subjected to a set of external load. Although modern Mechanics of Structure has provided well defined methods to obtain the ultimate external load that brings the structure to failure, use of the Bound Theorems could lead to the following very simple and direct solution. We know that the structure collapses in a failure mode that involves 4 hinges. Fig. 2.2 shows 4 possible such modes. For each of the failure modes, we assign a virtual rotation 8 and establish the equation for energy and work balance. For example, in mode (a), a virtual rotation 8 will cause the external vertical load 2P to do work with a magnitude of 10, and develop an internal energy dissipation 011 hinges 2,3,4. Equating the work and energy dissipation gives

which leads to 17

Similarly, the ultimate loads for mode (b), (c), (d) are P = M/21 ,P = 5 M/81, P = 5M/41 respectively. According to the upper bound theorem, the real ultimate load is the one that gives the lowest P, which is mode (b) with P = M/21. Performing the rigorous procedures of Structural Mechanics will give the same solution but in a much complicated way. This example indicates that if we are only interested in the ultimate loads and do not care about the failure process and the information about the stress and deformation during loading, there exists a straight forward and easy way to obtained the solution. This concept has been adopted to solve slope stability analysis problems as shown in the next example.

Examzple 2 A classical problem with the closed form solution. Fig. 2.3 shows uniform slope subjected to a vertical surface load. Sokolovski (1954) gave a closed-form solution with the assumption that the weight of the soil is neglected.-For this particular example in which c=98 kPa, $=30", the closed-form solution for the ultimate load T is 111.44 kPa. Associated with this load, we started with a four slice mechanism as shown in Fig. 2.3(a). Using Sarma's method, it is easy to find that the value of factor of safety is F=l.047. Sarma's method assumes that failure develops on both the slip surface and the inclined inter-slice faces. Therefore this solution can be regarded as the one that realizes Pan's principle of maximum. Following Pan's principle of minimum, we tried to find a failure mode that gives the minimum value of F as shown in Fig. 2.3(b) with a solution F,, =1.013. If the failure mass is divided into 16 slices, we obtained a failure mode almost identical to the one suggested by the closed-form solution as shown in Fig. 2.3(c), associated with F,], = 1.006. It is clear that with the theoretical support of the Bound Theorems, we are able to offer this example a solution for the ultimate load as accurate as the close-form solution.

FIG. 2.2 An example explaining a simple way to solve the ultimate loads using the upper bound theorem

FIG. 2.3 Example 2, an example describing the upper bound approach. (a) A four slice failure mode, initial estimate, F,=1.047; (b) Results of the optimization search, F,"=l.013; (c) Result of the optimization search using 16 slices, F,= 1.006.

18

Examule 3 An issue regarding the wedge failure analysis Fig, 2.4 shows the forces applied on the two failure surfaces of a typical wedge. When establishing the force equilibrium equations, we noticed that the resultant forces PI and P,applied on the two failure surfaces involve six unknowns, i.e., their components in XJ,Z .directions. The factor of safety adds one more. The number of available force equilibrium equations for the wedge block is three. Mohr-Coulumn failure criterion on the failure surfaces added another two equations. Therefore, two assumptions must be made to render the problem statically determinate. The traditional method presented in Textbook implies an assumption that the shear forces on the failure surfaces are parallel to the line of intersection of the two failure surfaces. Pan (1980) argued on the theoretical background of making such assumptions. H e believed that among all the solutions satisfiing force equilibrium equations. the real solution should be related to the one that gives the maximum factor of safety. It is after the observation of this critical issue Pan put forward his Principles of Maximum and Minimum. On a separate paper published in this Symposium Proceedings (Chen et. al. 1999), the author and his associates presented an example which showed that the factors of safety obtained by the conventional and the upper bound approaches were 0.870 and 1.136 respectively. This indicates that even in a very simple area of rock mechanics, there are still some fundamental concepts for which a critical study is needed.

Fig. 2.4 The wedge failure analysis, (a) Sketch; (2) Forces applied on the two failure surfaces: (3) Co-ordinate system.

Fig. 2.5 Search for the critical failure mode by the method of optimization, 1: the original estimated ; 2. the critical

To simulate this curve, we connect these points by either straight lines or smooth curves. Once this discretization mode is specified, factor of safety can be expressed as a function of x,,y,, x,, y,, ... .xi,,y,, In the upper bound method, the inclination of an interface 6, should also be included in the variable. We have

2.5 Numerical supports - the method of optimization

Use of the Bound Theorems or Pan's Principles essentially leads to a mathematical problem of finding the minimum of the factor of safety, which is associated with the input geometry of the failure mode, given the strength parameters for the material The method of optimization renders a powerfbl tool to find the minimum for geotechnical problems that involve complicated slope profiles and material properties. The task of an optimization operation is to find F,,, the minimum of the objective function F associated with the variable ZT=(z,,z2,...,z,J which represents the failure mode. In slope stability problems, the slip surfacey(x) is discretized by ni number of points A,, A2,,..., A,, (Fig. 2.5), whose coordinate values are ZI(i=l,2, ... m):

We start with an initial estimated failure mode, represented by A,,A2,....,A,, and 6,, 62,..., 6v,,which is associated with an initial value of F.Implementing the optimization routine, we eventually obtained a new mode represented by B',,B,,....,Bi,( refer to Fig. 2.5, n1=6 here), and a new set of 6,. 62,..., 6,, associated with the minimum value of F. A variety of optimization methods are available (Celestino and Duncan, 1981; Chen and Shao, 1988). Chen and Shao (1988) discussed the applications of the Simplex method, Negative gradient method and DFP method. While these methods on many occasions functioned well in finding the minimum factors of safety, they

(2.13)

19

sometimes suffered from not being able to find the global minimum. A random search technique was consequently developed (Chen, 1992; Greco, 1996) which greatly enhances the efficiency of the search.

The factor of safety will be obtained by solving the relevant boundary conditions based on the assumptions made for the distribution of p(x). (2) To satisfy (2.7), or (2.8), it is required that on the interfaces shear and tensile failure not occur, i. e.

3SIMPLIFIED LOWER BOUND APPROACHTHE METHOD OF VERTICAL SLICES 3.1 Theoretical back ground As a simplified approach, our profession has a long history of employing the method of slices to solve various practical problems of geotechnical engineering. Early approach divides the failure mass into a series of slices with vertical interfaces. The method proposed by Morgenstern and Price (1965), as well as by others (Bishop, 1955; Janbu, 1973), imply a lower bound approach since the solutions are associated with a force distribution satisfying Eq. (3.1) on the slip surface, and (2.7) or (2.8) on the interfaces. (1) To allow the satisfaction of Eq. (2.1) for each slice, the force and moment equilibrium equations are formulated as (Chen and Morgenstern, 1983) -dG _

dx

dP G = - p ( x ) sec t tan w y

dx

and d Gsinp=-y-(Gcosp)

dx

dw

d

+-(y G a p ) + 7-h d x t d x t

(3 4

in which dW . p(x) = -sin@: dx

dW

-a) +qsin@i -a) -7, --.seuy.singlj dx

(3.3)

G = the total interslice force; y, = y value of the point of application of the interslice force; a= inclination of the slice base; p=inclination of the interslice force; dW/& = weight of the slice per unit width; q= vertical surface load; q= the coefficient of horizontal seismic force, h, = distance between base and the horizontal seismic force, rt,= pore pressure coefficient (refer to Fig. 3.1(a)). Eq. (2.1) is obtained by projecting all the forces applied on a slice onto the line A-A' (Fig. 3.l(a)) which inclined at an angle of $e to the base of the slice. In that case the resultant of the normal force N and its contribution of the shear force on the base of the slice N tan$,, denoted as P , would be perpendicular to A-A' and not appear in Eq. (3.1).

FIG. 3.1 Slope stability analysis by the method of vertical slices, (a) the slope profile; (b) assumption for tan p ; (c) forces applied on a slice

[G' cosp' tanq:,, G'sinp'

20

+ cb,h] > F

(3.5)

G’>O

andf, (b) to be equal to the values of tanp at x=a and x=b respectively. J;,(x)is another function that has zero values at x=a and x=b. Fig. 3.l(b) shows an example that takesfix) as a sine function andf;,(x), a linear function that is zero at x=a and tan6 at x=a , where is the friction angle between the retaining wall and the soil. It is possible to find F (or P) and h from (3.8) and (3.9) by iterations. For details refer to Chen and Morgenstern (1983) or Chen and Li (I 998).

(3.7)

Among a variety of assumptions for p(x), we neglect those that produce results violating Eq. (3.5) or (3.7), and find one that gives the maximum factor of safety, according to the lower bound theorem. Solutions to the governing equations Chen and Morgenstern (1983) gave the solutions to the differential equations (3.1) and (3.2). They have been recently extended by Chen and Li (1997, 1998) to incorporate active earth pressure problems with the presence of a tension crack at the crown. The force and moment requirements take the form:

4SIMPLIFIED UPPER BOUND APPROACH THE METHOD OF INCLINED SLICES Theoretical background Sarma (1973) presented the method that employs slices of inclined interfaces. Therefore, the failure mode shown in Fig. 2.l(a) is simplified to a multiwedge system as shown in Fig. 2.1(b). We may understand the upper bound nature of Sarma’s solution in the following two ways. (1) Since both the slip surface and the interfaces are assumed to be in a state of limit equilibrium condition, the solution means a mobilization of maximum resistance against failure. Estimation for the external load is thus either higher than or equal to the real load, according to Pan’s Principle of Maximum. (2) While Fig. 2.l(a) is simplified to Fig. 2.l(b), Eq.(2.3) in the upper bound approach is approximated as

(3.9) where s(x) = sec yE(x)

(3.10) (3.11)

~ ( x=) [(sinp-cosptann)E-](nd{

(3.12)

G,,, = P,‘,- PE(b)

(3.13)

M,,, = P,,,h,,,- P[hCOS 6 + t(b)E(b)]

f

dW dx

(3.14)

where the first and second terms of the left side of (4.1) refers to the energy dissipation developed on the interfaces and slip surface respectively. In the following discussion we will demonstrate that Eq. (4.1) is equivalent to the force equilibrium equations given by Sarma (1979). Therefore the factor of safety obtained by Sarma’s method corresponds to an upper bound. It has been understood that for a material that obeys associated flow law and Mohr-Coulomb failure criterion, the plastic deformation produced by an increment in external load would incline at an angle $e to the shear band (Fig. 4.1 ), and the energy dissipation developed on the band is

i- 7, -h,dx

in which P is the value of G(x) at x=b, or active earth pressure at the vertical wall. P, is the water pressure at x=a, i.e. P,,=G(a). h is the distance between the point of application of the active earth pressure and the bottom of the wall, i.e., the value of o/-y,) at x=b; h , the distance between the point of application of the water pressure and the bottom of the tension crack, i.e., the value of o/-y,) at x=a;6 is the value of p at x=b, i.e., the friction angle at the wall Eqs. (3.8) and (3.9) involve an unknown F (or P) and an unknown variable p (x), Chen and Morgenstern (1 983) suggested introducing an assumption defining /3 (x) (Fig. 3.l(b)).

d D = (ccosp,, - usinpe)V

(4.2)

where U is the pore pressure applied on the shear surface (Donald and Chen, 1997). Let us examine a two block failure mode as ,f (x) is a linear function that allows the valueJ;,(a) 21

shown in Fig. 4.2. In Sarma’s approach, MohrCoulomn criterion applies on both the left and right bases of the blocks as well as on the interface. The normal force P and its contribution of shear force Ptan@on each of the faces forms a resultant Pwhich inclines at an angle @e to the normal of the bases. Establishing force equilibrium equation, according to Sarma’s concept, we have

formulated in a more efficient way by employing (4.5)’ the virtual work principle, with a set of virtual displacements, each inclined at an angle of &e to their respectively shear surfaces. (2) Since Eq. (4.5) is identical to (4.1) in this particular problem, the solution obtained by Sarma’s method would be identical to that obtained by the upper bound method described in Section 4. I .

FIG. 4.1 The plastic deformation V and the energy dissipation developed on a shear band.

w,+P,+Pi+c,,=0

FIG. 4.2 A two block failure mode explaining the equivalence between Sarma’s method and the energy approach.

(4.3)

And

Formulations of the upper bound solutions

w,+P,+Pi+c,,=0

A brief introduction to this method is given as follows. For details, refer to Donald and Chen (1997). As explained in section 2.1, we start the upper bound solution by establishing a velocity field. For a pair of adjacent slices, the velocity of the left and right slices V, ,V, and the relative velocity form a closed triangle. Therefore we have (Refer to Fig. 4.3 and Fig. 4.4)

(4.4)

for left and right slice respectively. In (4.3), W is the weight of the slice, C, is the shear force applied on the failure surface developed by cohesion. Now, we deliberately assign a set of virtual displacements V,, V,, y (Fig. 4.2)’ each inclined at an angle of @e to the shear surface. The work done V,, respectively is thus zero. P,, by P,,P,, on P,, Pi,as unknowns, disappear in the work and energy balance equation and Eq. (4.3) and (4.4) reduce to

< v,

Alel COS@^,^^ +Arc,.cos@J”,. + A,c, =

w,v, cos p, + wrvrcos p,.

COS^,,^,

sin(6,

(4.5)

where p is the angle between the weight vector and V The values V,., V, can be expressed as a linear function of V, , as will be given in the subsequent Section, and therefore are not unknowns. Eq. (4.5) remains only one unknown F which is implied in and is readily obtainable. We thus reach two conclusions: (1) Sarma’s method, which typically involves a procedure of solving Eq. (4.3) and (4.4)’ can be

- 8,)

v,.= v,sin(@,.- 6, )

(4.6)

sin(6, - 6,) v,= v,sin(6,. - 8,)

(4.7)

where 6 is the inclination of the interface with respect to the y axis. 8 is the angle of the velocity vector measured from the positive x axis. V, ,V, and V, of any slice can then be expressed as a linear function of the velocity of the left first slice V,. In general, the velocity of the wedge number k is determined by V=kV, 22

(4.8)

where

Fig. 4.4 Velocity compatibility between adjacent slices. The left slice moves downward to the right one.

Fig. 4.3 Velocity compatibility between adjacent slices. The left slice moves upward to the right one. To enhance the numerical efficiency, we usually discretize a slip surface by several nodal points which are connected by smooth curves, as shown in Fig. 2.l(c). The velocity at any point of the slip surface can be integrated by the following equation.

V

= E(x)V,

where T is the external surface load and q , the coefficient of horizontal seismic force. L is the length of the interfaces. In Chen and Donald (1997), as well as in Example 2, stability analysis with slopes containing weightless material were presented which indicated that the new method is capable of producing results as accurate as the closed-form solutions. In this paper, we give another example in which the weight of the soil material is not neglected.

(4.10)

where

E ( x ) = k exp[-

f cot(a -ro

-

p:

da

- Q ) -d<]

(4.11)

d<

The relative velocity on the interfaces is defined by

V, = -cosec(a

Example 4 A test problem with closed-form solutions -

4: - Q)E(x)V,da

Fig. 4.5 shows an example whose closed-form solution is available by Sokolovski (1954) who concluded that for a slope whose self-weight is not negligible, the ultimate load is associated with a curved slope surface and a critical failure mode designated in Fig. 4.5(b). With the parameters indicated in 4.5(a) and the theoretical solution of q=220.5kPa, we started at an initial guess of failure mode as shown in Fig. 4.5(a) and obtained F=1.065 by solving Eq. (4.13). The optimization process

(4.12)

Substituting (4.8) and (4.10) into (4.2), and following (2.10), we obtained the following equation calculating the factor of safety. V, is the velocity at x=x, . K accounts for the points on the slip surface where a or 4 changes abruptly. The subscripts 1 and Y refer to the variable at the left and right point of discontinuity.

23

,

FIG. 4.5 A closed-form solution for a slope whose self weight is not neglected. (a) The initial trial, F,,=l.O65, (b) The final solution, F,,,=l.O08

yielded a failure mode which is exactly the theoretical one as shown in Fig. 4.5(b), associated with the minimum factor of safety of F,,,=1.008.

8 =---&peJ 3z ' 2

use of Eq. (4.6) and (4.7) will produce positive values of V, or v/ In general, case 1 requires that the condition 8,- 8,> 0 be satisfied with a definition of eJ by Eq. (4.14) while Case 2 requires the condition of @, - 8,< 0 or 8, - 8)> - E , with a definition of Eq. (4.15) for 8/ , refer to Donald and Chen (1997).

On the two possible directions of shear between the adjacent slices In this section, we put forward an important statement which sometimes affects the results of the limit equilibrium methods of inclined slices. When establishing velocity field, one must examine whether the left slice moves in an upward or downward direction, with respect to the right one. Failure to do so will cause negative values of V,. or when (4.6), (4.7) are employed. Substituting these negative values into the work and energy balance equations, such as (2.10) or (4.1), means a violation of Drucker's Postulate. As a consequence, the calculation will lead to absurd results indicating that the bigger the cohesion value at the shear surface where the negative velocity develops, the smaller the factor safety will be obtained. Further investigation shows that this problem is related to the improper direction of v/ caused by a wrong direction of shear on the interface. Fig. 4.3 shows the velocity 7 which represents an upward movement of the left slice with respect to the right one. This case, defined as case 1, is most commonly encountered. In this case, BJ is defined as

z 8,=--6+p,, 2

(4.15)

Example 5 A simple problems explaining the need for considering two directions of shear To support this statement, let us examine a simple case shown in Fig. 4.6. The two-block system is pushed by a horizontal force at the right side. It is not difficult to find the critical load of P that brings the system into a state of limit equilibrium by establishing the following equation:

(4.14)

The symbol '+' in 'k'is associated with case 1, whereas '-' means case 2. For this example, the left block should move downward with respect to the right one since a,
However, if V, lies lower than V,, as shown in Fig. 4.4, and consequently 0,.-i o,, the left slice would move downward with respect to the right one. This case, defined as case 2, occurs when the base of the left slice is a weak zone having lower friction angle compared to that of the right one, or when the base exhibits an abrupt decrease of a. i.e., 4,. -i or a,. -i a , . It can be easily found that if a downward 7 is assigned and consequently, Q, is defined as

24

It has been understood that the shiplock may have two possible failure modes. (1) Landslide may take place along the whole or part of the slope. This may be caused by unexpected high ground water or by the inadequate shear strength of the rock mass especially due to the stress relief after the large amount of rock mass excavation. (2) The highly fractured rock mass may form random wedges whose stability must be carefully reviewed to ensure no hazardous instability triggered either during construction or operation. TABLE 5.2 c, pvalues obtained by Hoek-Brown Criterion n? RMR (3 c cp Rock Weather condition MPa kPa ( " ) Granite Moderately 25 57 50 60.01 41.4 Granite Slightly 25 77 100 199.5 57.7 Schist Slightly 17 57 50 57.8 37.7

FIG. 4.6 A two block system explaining the need for considering the shear direction between adjacent slices.

SAPPLICATIONS OF THE UPPER BOUND AND LOWER BOUND APPROACHES

The analytical results for Cross Section 20, shown in Fig. 5.1, are presented in Fig. 5.2 and Table 5.3. A tension crack 15 m deep filled up with water was assigned in the calculation. The horizontal anchor load 1000 KN/m and 30 m in length is applied on the slope where the cables pass through the slip surface. Since there exists a set of steeply dipping joints, vertical interfaces were employed in the upper bound method. However, the shear strength parameters of the interfaces are set to be equal to those of totally weathered rock, i.e., 4 ~ 3 5 ", c=5OkPu. From the results shown in Table 5.3, it can be seen that there is no substantial difference between the results obtained by Morgenstern - Price method and the upper bound approach. Morgenstern-Price sometimes gave larger factors of safety, compared to those of the upper bound method. This is because a relatively lower strength parameters were assigned to the interfaces in the upper bound method. Shear strength parameters suggested by the designers (Table 5.1) and by Hoek-Brown criterion (Table 5.2) are quite close for various types of weathering granite. However those for the schist intrusion deviate with each other quite a lot.

Examnle 6 Stability analysis for the shiplock slopes of the Three Gorges project The shiplock of the Three Gorges project assures the transportation through the Yangtze River and is therefore of utmost importance. It is located in the left abutment of the Complex with a total length of 6442 m in which 1607 m is covered with the main structure. The geology of the shiplock consists of early Sinian Period plagioclase granite. A schist vain intrudes transversely through this area. From the top to the bottom, the slope material transfers from the heavily, slightly, moderately weathered to fresh rock mass. Parameters for these rock types based on a comprehensive geological review are proposed and listed in Table 5.1. The shiplock slope is 160 m high and involves an excavation of 23.8 million m3 rock material. Refer to Fig. 5.1, above the elevation 161m, the slope ranges from 1.5:l to 1.1:l. The vertical cut 60 rn high below elevation 161 m is supported by two rows of prestressed cables, with a designed load of 3000 KN in general. Additional cables are installed where the wedge failure potential is of concern. Six levels of drainage tunnels are provided in both abutments (Fig. 5.1).

Example 7 Stability analysis for the Three Gorges dam

TABLE 5.1 Shear strength parameters for various types of rock based on a comprehensive geological study Rock No. Weathering cp c Unit weight kPa KN/m3 I Totally 35.050 25 200 26.5 Granite I1 Heavilv 45.0' I11 Moderately 52.4" 500 26.8 IV Slightly 1500 27 60.9' Schist V Slichtlv 150 26.8 35.0'

The bed rock of the power plants of the Three Gorges project rises near both abutments and consequently shortens the dam. Since the foundations of all the power plants are located at the same elevation, the dam units near the abutment will sit on a slope approximately 60 m high as shown in Fig. 5.3. It has been discovered that there exists a set of joint which dips in the same direction to that of the slope, presenting a very unfavorable condition to 25

Fig. 5.1

Cross section 20 of the Three Gorges Shiplock

FIG. 5.2 Critical slip surfaces obtained in local and overall stability review. Strength parameters: (a) from Table 5.1; (b) from Table 5.2, the Hoek-Brown failure criterion. Refer to Table 5.1 for rock layers I, 11, III,IV,V; refer to Table 5.3 for critical slip surfaces 1,2,3,4,5

the stability of the dam. Detailed geological explorations suggested some essentially interconnecting long joints as shown by line ABCHI in Fig. 5.4. The question raised by the designers are what the factor of safety is if the dam slide partly along OA, the concrete dam and partly along the joints and rock bridge. represented by BCHI, under the application of the reservoir water pressure, with the parameters shown in Table 5.4 . Using Morgenstern-Price method, we found it not difficult in obtaining a factor of safety which satisfies both force and moment equilibrium conditions. The result is F=2.79. When Sarma’s method was tried, we understood

TABLE 5.3 Factors of safety obtained by different approach for the Three Gorge Shiplock slope No. of the Sarma Morgenstern slip surface Designers Hoek- Price Brown Local Above 1 7.18 7.08 200m Above 2 5.33 5.89 5.80 151m Global 3 2.36 2.34 2.44 2.32 1.91 Vertical With 4 Wall cables 5 2.07 1.69 2.38 Without NOTE: Morgenstern-Price method adopted designers’ parameters (Table 5.1)

26

Fig. 5.3 Unit 3 cross section of the Three Gorges Dam

that for the part of failure mass which constitutes a continuous media of the concrete dam (OA in Fig. 5.4), optimization process must be introduced to determine the critical failure mode, just as we did for Example 2 and Example 4. Fig. 5.4(a) shows the critical failure mode associated with F=2.89, which is closed to that obtained by Morgenstern-Price method. However, the result is based on the understanding that at point A and C, the relative movement between slices take the direction defined by Case 2. If the issue about the two directions of relative movements between interfaces is ignored and along the slip surface, Case I was exclusively used, the optimization process eventually gave a failure mode shown in Fig. 5.4(b) with a minimum factor of safety F= 2.05. This result rather confused the designer until the idea of two possible directions of shear was introduced.

TABLE 5.4 Shear strength parameters used in stability analysis for the Three Gorges dam. Part of the slip surface OA ABCD HI

$ 47.7" 3 5 .O" 57.8"

c (MPa) 3 .O 0.2 1 .8

joints develops in this area, which dips into the slope with dip direction and angle of 280"and 71" respectively. The possible failure mode of this slope is consequently clear. Rock mass would slip along F236at the upper part and along a well defined clay seam between the bedding planes near the toe as shown in Fig. 5.6. The inclination of the interfaces would be 6=-20° based on the set of joints that dip into the slope. Very low shear strength parameters are assigned to the slip surface either on the weak seam or on F236,being c=o, $=11.5". For the rock mass near the toe where the slip surface exits, the parameters assigned are c=5OkPa, $=3 1.O". Heavy reinforcement including prestressed cables has been installed. In designing the reinforcement, it has been found that factors of safety were very sensitive to the analytical methods as well as the input parameters of interfaces as shown in Table 5.5. It can be found that Morgenstern-Price method gave a relatively low factor of safety being 1.08. Using Sarma's method, The F value ranges from 1.17 to 1.41 associated with different parameters on the inclined interfaces.

ExamAde 8 Stability analysis for the outlet slope of the Xiaolangdi project The outlet of the water discharge tunnels of the Xianglangdi Multiple-purpose Hydro-project creates a 60 m high slope which consists of severely adverse geological conditions. Fault F,,, passes through the crest of the slope which has a dip direction of 113" (Fig. 5.5). The dip direction of the bedding planes of the sandstone and shales ranges from 106" to 113", being very unfavorable. On the other hand, a set of

27

FIG. 5.4 Stability analysis for the Three Gorges dam and foundation at Unit 3 using the upper bound approach. (a) Taking case 2 at point A and C; (b) Case 1 is invariably used.

6CONCLUSIONS

TABLE 5.5 Factors of safety of the Xiaolangdi outlet slope F Method Shear strength parameters of interfaces c,( kPa) ‘p! Sarma 0 20° 1.17 3O0 1.38 50 20° 1.23 Morgenstern-Price

(p = 17.4’)

This paper has given a general review on the theoretical background and the numerical advances of the method of slices for slope stability analysis, which can be summarized as the following. The solution of a slope stability problem can be approached by its least upper bound and maximum lower bound. On most cases the gap between this two bounds is very small, such as shown in Example 6, 7 and elsewhere (Donald and Giam, 1992). The rigorous solutions are indeed obtainable. The limit equilibrium methods that employ vertical slices, such as those proposed by Bishop (1955)’ and Morgenstern and Price (1965), imply a lower bound of the factor of safety. A rational application of this method usually offers a safe solution to stability problems but is not always economical, especially when a rock slope is concerned as shown in Example 8. The limit equilibrium methods that employ slices with inclined interfaces, such as those proposed by Sarma (1978), Donald and Chen (1997), give an upper bound approach to the stability analysis. Use of powerful optimization routines has enabled the least upper bound being very close to the accurate answers. In rock slope stability analysis, this method is highly commended since its inclined interfaces offer better simulation to a jointed rock mass. Example 7 shows that a proper use of this method will give a good insight into the stability behavior of a rock slope for which both safe performance and economical issue are of serious concern. In performing the method of inclined slices, care must be taken on the possible two directions of shear between the adjoining slices. Using the energy approach proposed by Donald

1.OS

FIG. 5.5 Critical slip surface obtained by the Sarma method

The large difference in the F values might be attributable to the very low shear strength assigned on the slip surface. In making the final decision, we believed that the failure mechanism was clear in this particular problem. Employing Sarma’s method has considered the real condition of the discontinuities. The inclined interfaces represent a set of joints which are not thoroughly persistent. Therefore, giving a set of parameters such as c=SOkPa, @30° on the interfaces should be considered rational. The importance of the project requires that the reinforcement must be sufficient to ensure safe performance of this large project. On the other hand, the installation of prestressed cables presents a critical economical concern. A rational assessment of the stability of this slope depends partly on a good understanding to the analytical methods employed.

28

Celestino, T. B. and Duncan, 3. M., 1981. Simplified search for non-circular slip surface. Proceedings, 10th International Conference on Soil Mechanics and Foundation Engineering. Stockholtn. Vo1.3, pp. 391-394. Chen, W. F. 1975. Limit analysis and soil plasticity. Elsevier Scientific Publishing Co. , New York. Chen, Z..and Morgenstern, N. R., 1983. Extensions to the generalized method of slices for stability analysis, Canadian Geotechnical Journal, Vol. 20, No.1, 104- 109. Chen, Z and Shao, C. 1988. Evaluation of minunmum factor of safety in slope stability analysis, Canadian Geotechnical Journal, Vol25, No.4, 735-748. Chen, Z. 1992, Random trials used in determining global minimum factors of safety of slopes. Canadian Geotechnical Journal, Vol. 29, No. 2,225-233. Chen, 2.Y.and Donald, I. 1995. Comparison between the limit equilibrium and limit analysis method. 267-270. Proceedings of the 10th Asian Regional Conference on Soil Mechanics a n d Fo undation Engineering. 267-2 70. Chen, Z. Y.and Li, S. M. 1998. Evaluation of active earth pressure by the generalized method of slices. Canadian Geotechnical Journal, to be published in the August issue. Z. Y. 1995, Recent developments in slope stability Chen, analysis, Proceedings 8th International Congress on Rock Mechanics, Keynote Lecture, Vol. 3, 1041-1048, September 25-30, Tokyo. Chen, Z, Y., Xiaogang Wang, Yujie Wang and Jian Wang. 1999. An upper bound method for wedge failure analysis. Proceedings, International Sytnposium on Slope Stability Engineering. IS-SHIKOKOU’99, November 8- 1 1. Balkema. Donald, I and Chen, Z. Y. 1997. Slope stability analysis by the upper bound approach: fundamentals and methods.Canadian Geotechnical Journal, 34: 853-862. Donald, I and Giam, P., 1992. The ACADS slope stability programs review, Proc., 6th International Symposium on Landslides. Christchurch, Newzealand. Vol. 3, 1665- 1670. Duncan, J. M. et. al.1978, Strength, stress and bulk modulus parameters for finite element analysis of stress and movements in soil masses, Reprots No. VCB/GT/78-02, University of California, Berkeley. Chen, Z. Y., 1998. Demonstrations for Pan’s Principles of Maximum and Minimum. Journal of Qinghua University. No. 1, 6-13. (In Chinese) Greco, V. R. 1996. Efficient Monte Carlo technique for locating critical slip surface. Journal of Geotechnical Engineering, ASCE, 122(GT7):5 17-525. Hoek, E. 1990. Estimating Mohr-coulomb friction and cohesion values from the Hoek-Brown failure criterion. Int. J. Rock Mec. Min. Sci. 27:227-229. Hoek, E. and Bray, J. W. 1977. Rock slope engineering. The Institute of Mining a n d Metaf[urg,t Janbu, N.1973. Slope stability computation, Embankment Dam Engineering. 47-86. John Wiley and Sons. New York. Pan, J. Z., 1980. Satbility analysis and landslide assessment for structures. Water Resources Press, Beijing. (In Chinese). Sarma. K. S. 1979. Stability snalysis of embankments and slopes. J. Geotech. Am. Soc. Civ. Engrs, 105, GT. 12, 15 1 1 1524. Sokolovski, V. V. 1954, Statics of soil media, Fanslated by Jones, D. 1% andScholfield, A. N., 1960, London. Wang, R., Huang, W. B., Huang, Z. P. 1992. An introduction to Plasticity. Peking University Press. Wang, Y. J. 1998. Slope stability analysis by a threedimensional kinematic analysis method. Master of science thesis, China Institufe of Wafer Resources a n d Hydropower Research.

and Chen (1997), a criterion defining the two possibilities and the associated formulations for the calculation of factor of safety have been given. ExanipIe 5 and Example 7 show the importance of a proper consideration of this point in some rock slope problems. The traditional lower bound approach proposed by Morgenstern and Price (1965) and the upper bound approach proposed by Sarma (1 979) have been upgraded by the fully analytical and numerically more efficiently formulations as shown in Section 3 and 4. The concept of upper bound and lower bound principles has been extended to wedge slide analysis. It has been found that a problem of wedge slide analysis is actually statically indeterminate. That is, the number of the unknown forces applied on the failure surfaces exceeds that of available force equilibrium equations. The solution is therefore multiple in which both upper and lower bounds exist. It has been found ( Example 3 and Chen et. al. , 1999) that the two bounds become an identical value when the friction angles of both failure surfaces are zero and they diverge considerably when cohesion of the two faces are zero. More research work is needed to finally confirm the theoretical validity and significance of this statement. A number of case histories regarding China’s hydropower construction, including the Three Gorges and Xiaolangdi projects, have been reviewed which indicated that a better understanding of the Bound Theorems will help to obtain reliable and economical solutions to slope stability problems (Chen et. al. 1999). ACKNOWLEDGEMENT The draft of this paper is prepared for a presentation on a consulting meeting on large slopes organized by Golder Associates from August 6 to 8, 1998 in Vancouver. The author appreciates the support provided by Golder and the helpful discussions of the participants, especially the encouraging comments of Dr. E. Hoek. The author is indebted to Mr. Wang Jian for his help in editing the manuscript of this paper. The research work described in this paper is supported by China National Natural Science Foundation . REFERENCES Bishop, A. W. 1955. “The use of the slip circle in the stability analysis of slopes”, Geotechnique, 5 . No.l,pp.7-17.

29

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang (c) 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Using limit equilibrium concepts in finite element slope stability analysis D.G. Fredlund & R. E.G. Scoular University c?f Suskatchewun, Suskatoon, Susk., Cunudu

ABSTRACT: This paper reviews the development of finite element slope stability analyses and proposes that such a method can form a practical procedure for solving slope stability problems. Several slope stability methods have been proposed that make use of the finite element methods; these are summarized in this paper. The proposed finite element method is in a form that can be conveniently used in engineering practice. The procedure lends itself to present day numerical modelling techniques. The method has been updated to take advantage of recent advances in computer technology and algorithms. The combination of a finite element stress analysis with a limit equilibrium analysis provides greater certainty and flexibility regarding the internal distribution of stresses within the soil mass. The normal force along any selected slip surface can be calculated from the stress distribution that has been calculated using a linear and non-linear stress analysis. The overall factor of safety for a slope, when the finite element method is used, can be defined as the available shear strength of the soil divided by the resisting shear strength. The overall factor of safety is a combination of the local factors of safety within the slope. The resulting overall factor of safety retains the basic assumptions inherent to the limit equilibrium definition of the factor of safety. The local factors of safety are an expression of the stability of the soil mass at each point along the slip surface. The overall factor of safety computed using the finite element method shows good agreement with the factors of safety computed using any one of several limit equilibrium methods. The finite element method provides additional information regarding the potential performance of a slope; information not available when using traditional limit equilibrium methods. The results indicate that it is important to use the effective shear strength characterization of the soil when performing the slope stability analysis. The computed factor of safety obtained when using a total shear strength characterization of the soil, may not agree with the factor of safety computed when using the finite element stress analysis method. Key words: slope stability analysis, finite element, enhanced method, direct method, strength method, stress level method, factor of safety, local factor of safety.

the stresses in the soil mass. These stresses can subsequently be used to compute a factor of safety (Fig. 1). The complete stress state from the finite element analysis can be "imported" into a limit equilibrium analysis where the normal stress and the shear stress are computed corresponding to any selected slip surface. The objective of this paper is to demonstrate a procedure for combining a finite element stress analysis on a slope with the concepts of a limiting equilibrium method of analysis. The final method is called a "finite eIement method of slope stability analysis" and the results are compared to results obtained when using conventional limit equilibrium method of analysis.

1 INTRODUCTION Limit equilibrium methods of analysis have proven to be a widely used and successful method for the assessment of the stability of a slope. Limit equilibrium methods sum forces and moments related to an assumed slip surface passed through a soil mass (Fredlund and Krahn,1975; Fredlund et al., 1981). However, these methods do not utilize the stress versus strain characteristics of the soils involved. It is well known, and intuitively understood that the stability of a slope should be influenced by the stress versus strain characteristics of a soil (Kondner 1963). A finite element analysis utilizes a stress versus strain model for the soils involved to calculate 31

Figure 1. Illustration showing stresses that are "imported" from a finite element analysis into a limit equilibrium analysis.

2 BACKGROUND

surface. The normal and shear stresses fiom an elastic analysis were used to calculate an overall factor of safety. The formulation of Kulhawy (1969) was classified as an "Enhanced Limit Strength Method". A number of finite element slope stability methods have been proposed and the methods can be categorized as "enhanced limit methods" or "direct methods", as shown in Figure 2. Wright (1969) compared the factors of safety calculated using the "enhanced limit strength" method with factors of safety calculated using Bishop's Simplified method (1952). A slip surface was selected for comparative purposes that had a factor of safety of 1.O when using the Bishop's Simplified method. It was concluded that the factors of safety determined by the "enhanced limit strength" method (Kulhawy, 1969) were approximately 3% higher than those determined applying Bishop's Simplified method. Wright et al. (1973), using the "enhanced limit strength" method, showed that: 1) along one third of the slip surface, the local factors of safety are less than the overall factor of safety, 2) the factors of safety calculated by the finite element method using linear elastic material properties ranged fiom 0% to 4.5% higher than those calculated using Bishop's Simplified method, and 3) the factors of safety calculated by the finite element method using nonlinear elastic material properties increased with Poissonk ratio and are 2% to 8% higher than those calculated using the Bishop's Simplified method. Resdndiz (1 974) agreed with the concept of using the finite element method to calculate the stability of a slope; however, disagreed with points No. 2 and No. 3 of the results of Wright et al. (1973) because the factor of safety differences were too small. ResCndiz had developed a finite element method of

Bishop (1952) noted that the stresses from a limit equilibrium method of analysis did not agree with the actual stresses within an earth structure. Other researchers have confirmed this observation both with experimental evidence and with numerical modelling. La Rochelle (1 960) estimated the stress conditions in steep slopes using photoelastic tests on gelatine models. The results showed that stresses along a slip surface were over-stressed in the lower portion of the slip circle. Brown and King (1966) produced critical slip surfaces from a finite element stress analysis of slopes using a linear elastic soil model. The critical slip surfaces were produced by using the angle of obliquity, 8, along the slip surface Each critical slip sur(i.e., $equal to (45" + ~'h)). face represented a close approximation to an essentially circular shaped slip surface. Clough and Woodward (1 967) undertook a study to evaluate the effect of incremental loading with single step loading as it related to stresses and deformations. It was concluded that: l ) stresses and deformations in an embankment obtained fiom a direct application of the gravitational body forces on the complete structure were not completely accurate, and 2) changing Poisson's ratio interferes with the relationship between stresses and displacements, requiring a new analysis for each case. It was concluded that "meaningful stability analysis can be made only fi the stress distribution within the structure can be predicted reliably." Kulhawy (1969) developed a computer program to obtain an independent assessment of the normal and shear stress distribution along an assumed slip

32

I

Finite Element Slope Stability Methods

I

Direct methods

Enhanced limit methods (finite element analysis with

Load increase

to failure

a limit equilibrium analysis)

I Kulhawy 1969

Definition of Factor of Safety

Stress Level Zienkiewiczef a/ 1975

Strength & Stress Level Adikari and Commins 1985

C/(c' + o'tan4') AL]

Figure 2. Finite element approaches proposed in computing the factor of safety in a slope stability analysis.

slope stability analysis defined as an "enhanced limit stress-level" method" in 1972 (Fig. 2). This method used the maximum principal stress difference of the soil at failure to define the factor of safety. Analyses made using non-linear stress versus strain relationships led to factors of safety which in all cases were higher (i.e., differences as large as 30%) than conventional factors of safety (e.g., Ordinary method or Bishop's Simplified method). Zienkiewicz et al. (1975) also proposed a finite element method of analysis to compute the factor of safety by using the principal stress difference in the soil at failure to define the factor of safety. The method is an "enhanced limit stress - level method" (Fig. 2). Both the ResCndiz (1972) and Zienkiewicz et al. (1975) formulations are classified as "enhanced limit stress-level" methods. Naylor (1982) established two types of finite element slope stability methods, a "direct" and an "enhanced limit" method of analysis. The direct method used a finite element nodal formulation to define the slip surface and the factor of safety directly from the analysis. The proposed "direct" slope stability method defined the factor of safety either as the increased load necessary to cause failure, or as the reciprocal of the reduction in the strength properties required in order to achieve failure. These methods

have also been studied by Martins et al. (1981) and Tan and Donald (1 985). The "enhanced limit" slope stability methods are based on stresses calculated using a finite element analysis and combined with a limit equilibrium type of analysis along a prescribed slip surface, to define the factor of safety. The prescribed slip surface is the one defined by the lowest factor of safety and is found using a trial and error procedure. The stresses along the slip surface are computed using a finite element analysis and can either be used in a ''strength" method or a "stress-level" method. Farias and Naylor (1996) stated that when using the "direct" finite element method it is, "not easy to obtain a safety factor accurate to within the conJidence limits achievable by limit equilibrium methods". The authors noted that: 1) afine mesh is required, 2) a code capable of giving reliable results with the Mohr Coulomb elasto-plastic model for loading states close to failure is needed, and 3 ) it is usually necessary to carry out a set of analyses with c 'and tan+' progressively reduced by a factor which will become the safety .factor when .faillire is eventimlly reached. "Enhanced limit" methods require only one finite element analysis to calculate factors of safety for a slope with various combinations of c' and tand! 33

mal stress at the base of a slice is known. On the other hand, limit equilibrium methods, starting with Bishop's Simplified method (1955), have used an estimated factor of safety when computing the normal force at the base of a slice. The final factor of safety is found through an iterative process. The finite element method factor of safety is defined using the normal and shear stresses computed using a finite element analysis. Finite element numerical stress analyses have been available for many years. The finite element method, however, has not become popular for slope stability studies due to intense computational requirements and difficulties in assessing the stress versus strain characteristics of the soils. In addition, inexpensive and easy to use limit equilibrium methods have provided factors of safety that appear to represent failure conditions in the field in most situations. Microcomputers now have sufficient computational capacity to perform combined stress and limit equilibrium analyses. As a result, it is anticipated that the latter procedure will become more common in engineering practice.

Adikari and Cummins (1985) produced a finite element method that combine the "strength" and the "stress-level" methods as defined by Kulhawy (1969) and Zienkiewicz et al. (1 9 7 9 , respectively (Fig. 2). The Adikari and Cummins (1985) method produced factors of safety that were between the values obtained when applying the Kulhawy (1 969) and the Zienkiewicz et al. (1975) methods. It was noted that for near-failure conditions (i.e., as defined by Bishop's Simplified method, 1955), the value of the factor of safety calculated by the Adikari and Cummins (1985) method approached 1.O, while the value of the factor of safety calculated by the Zienkiewicz et al. (1975) method remained high. The factor of safety by the Kulhawy (1969) method also approached unity with the factor of safety being dependent on the percentage of the strength mobilization in the component materials. The main difference in results appears related to using the stresses on the principal plane (Zienkiewicz et al. 1975) rather than on the plane. By definition, failure does not occur on the plane of principal stress and therefore, the Zienkiewicz et al. (1975) method (or any stress-level method) is computing a factor of safety that must be higher than the factors of safety produced by a "strength" method. Duncan et al. ( 1 996) provided a summary of the limit equilibrium and finite element methods that have been proposed for slope stability analyses.

3.1 Procediire usedfor the finite elenienl analysis The enhanced limit (strength) finite element method proposed by Kulhawy (1969) was selected as the most appropriate method for slope stability analysis. The finite element stress-deformation software, Sigma/W (a proprietary product of Geo-Slope International Ltd., Calgary, Alberta, Canada), was modified to utilizes a search algorithm in order to assign and transfer calculated finite element stresses to a designed point on the slip surface (Bathe, 1982; Kralm et al., 1996). The calculated finite element calculated stresses are used to calculate the normal and shear stresses on the slip surface. The latter stresses are used to calculate local factors of safety at the center of the base of each slice as well as the overall factor of safety for the entire slip surface.

3 SUGGESTED STUDY FOR COMPARISON BETWEEN THE FINITE ELEMENT AND THE LIMIT EQUILIBRIUM METHODS OF SLOPE STABILITY ANALYSIS The finite element slope stability method proposed in this paper is of the "enhanced limit strength" type (Scoular, 1997). The finite element method uses the Kulhawy (1969) definition for the factor of safety combined with a finite element stress analysis of the slope. Stress analyses were done using Poisson's ratios equal to 0.33 and 0.48. For each stress analysis, the cohesion and the angle of internal friction of the soil were altered as the stability of the slope was computed. The selected values for cohesion, c', were 10, 20 and 40 kPa, and for the angle of internal friction, +; were 10,20 and 30 degrees. The finite element slope stability method produces an overall factor of safety that is an expression of the stability of the slope based on the calculated stresses within the slope. Slope stability problems solved using the finite element method have two important distinctions from limit equilibrium methods. First, the finite element slope stability equation is determinate; therefore, no further assumptions are required to complete the calculations. Second, the factor of safety equation is linear, because the nor-

3.2 DeJinitiori offactor of safety The overall factor of safety is defined in accordance with the finite element slope stability method described by Kulhawy (1969), and expressed as the ratio of the sun1 of the incremental resisting shear strengths, Sr, to the slim of the mobilized shear forces, S,, along the slip surface.

The resisting force for each slice is calculated in terms of the shear strength, z,at the center of a slice multiplied by the base length of the slice, p. The available resisting shear strength for a saturatedunsaturated soil (Fredlund and Rahardjo, 1993) can be written as: 34

Figure 3. Definition of the global and local coordinates for a rectangular finite element.

S, =zP=(c'+(D~ -U, >ta$+(ua

-U,

>ta@b > P

A common set of coordinates is used to identify the center of a slice along a slip surface with respect to the surrounding finite element. The global coordinates for the center of the base are calculated in order to determine the location of the base center within the slope, and to determine which element is associated with the center of the base. The local coordinates of the center of the base are then calculated within the element that encompasses the center of the base (Fig. 3). The global coordinates for the center of the base of a slice are related to the global coordinates of the finite element nodal points through use of the shape functions.

(2) The mobilized shear force, Sm, for each slice is calculated as the mobilized shear stress, zm, at the center of a slice multiplied by the base length, p. s r n

=

L P

(3)

The local factor of safety is defined as the ratio of the resisting shear force, S y , at a point along the slip surface divided by the mobilized shear force, Sm, at the same point,

(4)

x=< N

The resisting shear force, S y , and the mobilized shear force, Sm, are both calculated using the stresses computed in the finite element analysis. The normal stress, on, and shear stress, zm, can be "imported" as known values to the limit equilibrium analysis and the definition of both the overall and local factor of safety equations are linear.

>{XI

(5)

y = {Y) (6) Where x = global x coordinates for the center of the base of a slice; y = global y coordinates for the center of the base of a slice; {X) = global x coordinates for the element nodal points; {Y) = global y coordinates for the element nodal points; and = matrix of shape functions. The shape functions are defined in terms of the local coordinates (r, s). Since the global coordinates for the center of the base of a slice and the nodes are known, the local coordinates can be obtained by solving Equations (5) and (6), simultaneously. The shape functions for a rectangular finite element with four nodes are as follows (Bathe 1982):

3.3 Element identification corresponding to the base of a slice Each element must be checked to confirm that the center of the base of the slice is located within the element under consideration. Then the stresses calculated by the finite element analysis can be "imported" into the stability analysis. Once the element embracing the center of a portion along the slip surface is located, stress values from the Gauss points of the element can be transferred to the nodes of the element and consequently to the center of the base. The procedure is in accordance with the method described by Bathe (1982).

1 NI = - ( l + r ) ( l + s ) 4

N,

35

=

1 -(1 -r)(l + s )

4

( 7)

(8)

N, =

1 ( 1 - r)( 1 - s ) 4

-

(9)

1 4

(10)

N, = - ( 1 + r ) ( l - s )

be used to describe the change of a variable within an element in terms of nodal values. The finite element slope stability calculations require that stresses at the center of the base for each slice be within an element. This is achieved using the following procedure :

where r and s = local coordinates within the element. The local coordinates vary between -1 and +1 (Fig. 3). A knowledge of the local coordinates is crucial to identifying the element overlapping the center of the base of a slice. By definition, an element surrounds the center of the base of a slice if the following conditions are met: For a triangular element,

(0 5 r 21) and (0 5 s 21)

(1 1)

For a rectangular element, (-1 5 r 21) and (-1 5 s 21)

(12) The center of the base is outside an element if the local coordinates are not within the above specified ranges. The search continues until an element is found that satisfies these conditions.

{oIn= < N > {F)

(15)

where oIn= stresses at the element node; = matrix of the shape functions; and {F) = stress values at the Gauss points. The local Gauss point integration coordinates are (0.577, 0.577), however, when the local Gauss point integration coordinates are projected outward to the element nodes, the local coordinates become (1.7320, 1.7320) (Fig. 5). This projection is carried out for each element and the values for the stresses from each contributing element are averaged at each node. Accordingly, the values of ox, q,, and zxy can be computed at each node of the finite element mesh. The nodal stresses, ox, q,,and z,), of an element are transferred to the center of the base of a slice along the slip surface.

(o.)=< N >{oIn 3.4 Transfer of element stresses to the center of the base of a slice Calculated stresses are stored within the computer software relative to the Gauss points of an element. Stresses must be transferred from the Gauss points of an element to the nodes of the element and then to the center of the base of a slice. The local coordinates of a point within a finite element are defined in relationship to the global coordinates at the nodes of the element by using the shape functions, as per Equations ( 5 ) and (6):

(16)

where {c$ = stresses at the center of the base of a slice. The stresses, ox, q,,and zxy, can now be computed at the center of the base for each slice. 3.5 The normal and shear stresses at the center of a slice Once the stresses, a,, q,,and zxy, are known at the center of the base for each slice, the normal stress, o n ,and the mobilized shear stress, z, , can be calculated using Equations (17) and (1S), respectively (Higdon et al. 1976):

on

ox

=-

+ oy

+ 0,

2

- oycos 2 e

2

+ zxysin28 (17)

ox- oysin 28 2,

Y =

N,N,N,N,

>

>

(14)

where x and y = global coordinate positions within the element that are known as the center of base of a slice (Fig. 4); X and Y = global coordinate at the element nodes; and N I , Nz, N3 and N4 = the shape functions defined in Equations 7 to 10. The stresses from a fmite element analysis are stored at the Gauss points. The shape functions can 36

=

~xycos2e -

2

(18)

where ox= total stress in the x-direction at the center of the base;oy = total stress in the y-direction at the center of the base; zxy= shear stress in the x- and ydirection at the center of the base; and e = angle measured from the positive x-axis to the line of application of the normal stress. The above steps provide the necessary information required to calculate the stability of a slope using the finite element stresses. The calculated values for the normal stress, on, and the mobilized shear stress,, ,z at the center of the base of a slice are entered into Equations (2) and ( 3 ) to give the resisting shear force

Figure 4. Location of the center of the base along the slip surface within a particular finite element.

Figure 5. Gauss point projections to the nodes of a finite element.

4 PARAMETRIC STUDIES ON A SIMPLE 2:1 SLOPE

(strength) and the mobilized shear force (actuating shear), respectively. The local factor of safety is computed as the ratio of the resisting shear force to the mobilized shear force. The overall factor of safety is the sum of the shear force resistance values divided by the sum of the actuating shear forces along the slip surface.

A slope at 2 horizontal to 1 vertical is analyzed for 4 conditions (Scoular, 1997). The first case is a freestanding slope with zero pore-water pressures and the slope is referred to as a dry slope (Fig. 6). The second case is a free-standing slope with a piezometric line at three quarters of the slope height, and the slope is referred to as a wet slope (Fig. 6). 37

Figure 6 . Selected 2: 1 free-standing slope with a piezometric line exiting at the toe of the slope.

The third case is a slope partially submerged in water with zero pore-water pressures in the slope (referred to as dry) (Fig. 7). The fourth case is a partially submerged slope with a piezometric line at one half of the slope height (referred to as wet) (Fig.7). The partially submerged slope is covered with water to one half of the slope height, providing support for the slope and increasing the factors of safety. The cohesion of the soil was varied from 10 to 40 kPa and the angle of internal friction was varied from 10 to 30 degrees for each slope type.

slope is simulated by point loads equal to the weight of water on the slope. The analyses are performed using Poisson’s ratios of 0.33 and 0.48, and a Young’s modulus equal to 20,000 and 200,000 kPa. The results showed that the stresses change with a changing poisson’s ratio, but are constant for changes in the Young’s modulus. This observation is consistent with the observations of Matos (1982). 5 RESULTS OF THE FINITE ELEMENT SLOPE STABILITY METHOD

4.1 Limit equilibrium analysis

The local factors of safety differs along the overall slip surface (Fig. 8). Local factors of safety were computed for a 2: 1 (dry) slope with a cohesion equal to 40 kPa and an angle of internal friction equal to 30 degrees. While the local factors of safety differ along the slip surface, the overall finite element factors of safety fall within the range of the limit equilibrium factors of safety. The difference between the local factors of safety for Poisson’s ratios of 0.33 and 0.48, calculated using the finite element method, is reflected in Figure 8. The factor of safety computed by the limit equilibrium method and the finite element method appear to be very similar. The results appear to be within the limits of uncertainty associated with slope stability calculations. The finite element method incorporates the stress-strain characteristics of the soil when computing the shear strength and actuating shear force of the soil in the calculation of the factor of safety (Fig. 9).

The limit equilibrium analyses are performed using the General Limit Equilibrium method (GLE), (Fredlund & Krahn 1977) which provides a combined moment and force equilibrium solution. An empirical finite element interslice force function, based on an independent stress analysis (Fan et al. 1986) was used. The General Limit Equilibrium method along with a finite element interslice force function provides a method of comparison between the finite element based analysis and the limit equilibrium analysis. 4.2 Finite element stress analysis The finite element stress analysis was performed by “switching-on” gravity for the free-standing slope and for the partially submerged slope. The load of the water and the lateral support it provides to the

38

Figure 7. Selected 2:1 partially submerged slope with a horizontal piezometric line at mid-slope.

The factor of safety results computed using the finite element method (i.e., F3 corresponding to a Poisson's ratio of 0.33, F4 corresponding to a Poisson's ratio of 0.48) are compared to the factors of safety computed using the limit equilibrium method (GLE) and are shown in Tables 1 and 2. To assess the variations in the factor of safety by each method of analysis, the results are grouped according to cohesion and angle of internal friction. The factors of safety grouped according to cohesion, c', are plotted versus the stability number, [(pVtan&)/cl, (Janbu, 1954). The factors of safety grouped according to the angle of internal friction, +', are plotted versus

the stability coefficient, (c Y y H ) (Taylor, 1937), where p is the unit weight of the soil, H is the height of the slope, $'is the angle of internal friction, and c' is the cohesion. The factors of safety are grouped according to the soil parameters and plotted versus the stability number and the stability coefficient. The greatest difference in factors of safety is noticed at high angles of internal friction, at low values of cohesion and at the maximum values of Poisson's ratio. The factors of safety for the (dry) free-standing slope, when grouped according to cohesion and plotted versus the stability number (Fig. 10) show a

Figure 8. Presentation of the local and global factors of safety for a 2:1 dry slope.

39

Table 1. 2: 1 &ee-standing slope Soil

Parameters

kPa

degree

10 20 10 40 20 10 40 20 40

10 10 20 10 20 30 20 30 30

Dry

GLE Finite element hnction 0.669 0.882 1.131 1.260 1.370 1.615 1.794 1.892 2.356

F3 p=O.33

F4

0.662 0.867 1.125 1.230 1.352 1.639 1.765 1.884 2.324

0.672 0.874 1.151 1.239 1.368 1.696 1.775 1.918 2.339

GLE Finite element function 0.488 0.677 0.782 0.995 1.021 1.102 1.335 1.374 1.741

p = 0.48

Wet F3 p = 0.33

F4

0.456 0.634 0.745 0.930 0.969 1.077 1.260 1.287 1.627

0.467 0.647 0.755 0.953 0.988 1.101 1.293 1.312 1.661

p = 0.48

Figure 9. Shear strength and shear force for a 2: 1 dry slope calculated using the finite element method.

Figure 10. Factors of safety versus stability number for a 2: 1 dry slope as a h c t i o n of cohesion.

40

Table 2. 2: 1 partially submerged slope Soil CI

kPa

Parameters Dry qY GLE F3 degree Finite element ,U = 0.33 function

0.845 10 10 1.149 20 10 1.344 10 20 1.618 20 20 1.721 40 10 1.865 10 30 2.297 40 20 2.337 20 30 3.006 40 30 *n.s.a.: no solution achieved

0.843 1.115 1.425 1.586 1.722 2.08 1 2.385 2.268 2.970

Wet GLE Finite element function 0.649 0.886 1.050 1.318 1.322 1.482 13 0 0 1.783 2.303

F4 ,U = 0.48

0.827 1.OS5 1.422 1.575 1.691 n.s.a.* 2.368 2.204 2.899

F3

F4

,LI = 0.33

p = 0.48

0.635 0.874 1.046 1.314 1.296 1 SO5 1.774 1.763 2.260

0.641 0.880 1.068 1.343 1.316 1.530 1.795 1.786 2.274

Figure 11. Factor of safety versus stability coefficient for a 2: 1 dry slope as function of angle of internal friction.

Stability Number, [( yHtan4)lc'J Figure 12. Factor of safety versus stability number as a function of cohesion for a 2:l slope with the piezometric line at % of the slope height.

41

Figure 13. Factor of safety versus stability coefficient as a function of the angle of internal friction for a 2.1 slope with the piezometric line at % of the slope height.

Figure 14. Factor of safety versus stability number as a fimction of cohesion for a 2:1 dry slope % submerged with water.

nite element factors of safety and the General Limit Equilibrium factors of safety when the cohesion is 40 and 20 kPa. The difference between the factors of safety by both methods is constant at all values of cohesion until the angle of internal friction becomes equal to 30 degrees and cohesion becomes equal to 10 kPa (Fig. 13). The grouping of the factors of safety according to the angle of internal friction, plotted versus the stability coefficient (Fig. 15), shows the same pattern as for the (dry) free-standing slope (Fig. 10). The differences in the results are more pronounced as the cohesion become less than 10 kPa. The factors of safety for the partially submerged slope with a piezometric line at one half of the slope height were grouped by cohesion and plotted versus the stability number (Fig. 16). The results show close agreement between the General Limit Equilibrium method and the finite element method. The

slight divergence in the factors of safety when the cohesion approaches 10 kPa and the angle of internal friction approach 30 degrees. The factors of safety by the finite element method, with a high Poisson’s ratio, is greater than the General Limit Equilibrium solution. The slight divergence is evident when the factors of safety are grouped according to the angle of internal friction and plotted versus the stability coefficient (Fig. 11). It is also evident that at high values of cohesion, (i.e., c’equal to 40 H a ) , The factors of safety computed when using the General Limit Equilibrium method are greater than those from the finite element methods with either Poisson’s ratio value. The factors of safety for the (wet) free-standing slope with a piezometric line at three quarters of the slope height, are grouped according to the cohesion and plotted versus the stability number (Fig. 12). The results show a slight divergence between the fi-

42

Figure 15. Factor of safety versus stability coefficient as a function of internal fkiction for a 2: 1 dry slope % submerged in water.

Figure 16. Factor on safety versus stability number as a function of cohesion for a 2:l slope half submerged with a horizontal piezometric line.

same pattern of divergence is evident as was shown for the dry soil slope which is partially submerged (Fig. 14). However, the divergence is not quite as extensive. The same comments apply to the factor of safety versus the stability coefficient as shown in Figure 17. Plotting the factors of safety for the various slope conditions, (i.e., dry fi-ee-standing, wet free-standing and dry partially submerged), versus stability number on Figure 18, shows the ranking of slopes by factors of safety. The factor of safety can be estimated for a slope that is similar to one of these cases by calculating the stability number and selecting the appropriate value of cohesion and angle of internal friction. Both the General Limit Equilibrium method and the finite element method of slope stability produce factors of safety that are in close agreement. The advantage of the finite element method is that the stress-stain characteristics of the soil are used to de-

termine the stress state in the slope. If the limit equilibrium and finite element factors of safety are similar for a simple slope than results from the two methods can be interpreted in similar manners. This study then sets the stage for using the finite element method for situations where the limit equilibrium methods is known to not yield satisfactory results. The finite element method also produces graphs of the local factors of safety that can be combined with the shear strength-actuating shear force plots to help explain the best support mechanism for the slope. The close agreement between the factors of safety when using the limit equilibrium method or the finite element method, has historically favored the use of limit equilibrium methods. Examination of the critical slip surfaces reveals that while the factors of safety values are close, the location of the critical slip surfaces may be different.

43

Figure 17. Factor of safety versus stability coefficient as a function of the angle of internal fiiction for a 2:l slope half submerged with a horizontal piezometric line.

Figure 18. Factor of safety versus stability number as a h c t i o n of cohesion for a 2:1 slope, evaluated for dry, piezometric and submerged conditions.

6 ANALYSIS FOR THE LOCATION OF THE CRITICAL SLIP SURFACE

showed the deepest slip surface. For the partially submerged slope, the finite element method with a Poisson's ratio equal to 0.48, showed a considerably shallower slip surface.

The location of the critical circle changes depending on the situation being analyzed. The biggest change in location of critical slip surface was experienced for the (wet) free-standing slope (Figs. 19 and 20) and the (wet) supported slope (Figs. 21 and 22). In general, the finite element method slip surfaces go deeper than the limit equilibrium slip surfaces for the (wet) free-standing slope. The partially submerged slopes show that the limit equilibrium slip surfaces go deeper than the finite element method slip surfaces. For the free- standing slope, the finite element method with a Poisson's ratio equal to 0.48

7 CONCLUSION The finite element method of slope stability is a viable method of analysis that is now available for engineering practice. The use of the finite element method yields more detailed information on the stress state in the soil than is available horn conventional limit equilibrium methods. This information can assists engineers in the design of slopes and slope retaining structures. 44

Figure 19. Location of the critical slip surface for a slope with a piezometric line where the soil properties are c' = 40 kPa and 30".

4'=

Figure 20. Location of the critical slip surface for a slope with a piezometric line where the factors of safety are closest to 1.O.

the finite element method to slope stability problems, a better understanding is required regarding the effect of Poisson's ratio and the overall deformation model on the stability of slopes.

The value of Poisson's ratio can affect the calculation of the factor of safety as well as the location of the slip surface. With an increasing application of 45

Figure 21. Location of the critical slip surface for a half submerged slope where the soil properties are c' = 40kPa and qY = 30".

Figure 22. Location of the critical slip surface for a submerged slope where the factors of safety are closest to 1.O.

boundary conditions are being used and that a reasonable stress-deformation model is being used. With this assurance, soil structures can be better designed to account for a variety of stress conditions.

The finite element stress analysis provides input information for the calculation of the stability of a slope. Further research must be undertaken on the stress analysis in order to ensure that the proper 46

ACKNOWLEDGEMENTS

Leshchinsky, D. 1990. Slope stability analysis: Generalized approach. .Journal of' Geotechnical Engineering. ASCE 116(5): 851-867. Martins, J.B., E.B. Reis & A.C. Matos 1981. New methods of analysis for stability of slopes. Proc. lU[h In/. Conf.. Soil Mech. Found. Eng. 3: 463-467. Matos, A.C. 1982. The numerical influence of the Poisson ratio on the safety factor. Proceedings of' the Jth ltiterticrfiorial Confiretice on Nutmrical Methods in Geo-Mechanics 1 : 207-21 I . Morgenstern, N.R. & V.E. Price 1965. The analysis of the stability of general slip surfaces. Geotechniqzre I5( 1 ): 79-93. Naylor. D.J. 1982. Finite elements and slope stability. N u m e ~ i cul 1bfethorLs in Geomechanics. D. Reidel Publishing Company. ResCndiz, D. 1972. Accuracy of embankment deformations. Proceedings, ASCE Specierlly C'oiference on Perjormcrnce of Eurlh trnd Etrr/h-Supportecl Slriic/ures, Purdue University. West Lafayette, Indiana, 12-14 June, l(Part 1): 817836. Resendiz, D. 1974. Accuracy of equilibrium slope stability analysis. Jozirnd ofthe Soil Mechcinics arid Founcialion Division, ASCE I OO(GT8): 967-970. Scoular, R.E.G. 1997. Limit equilibrium slope stability analysis using a stress analysis. MSc. Thesis, (Jniversioq ? f Saskatchewm, Srrskatoon, Cunudu. Tan, C.P. & I.B. Donald 1985. Finite element calculation of dam stability. Proc. I llh Int. Conf.' Soil Mech. Found. Eng.. San Francisco, California 4: 2041 -2044. Taylor, D.W. 1937. Stability of earth slopes. Jozirnal of [he Boston Sociefy ofcivil Engineers XXIV(3): 337-386. Wright, S. G. 1969. A study of slope stability and the undrained shear strength of clay shales. Ph. D. thesis, University of Cd$ornicr cif Berrk1e.y. Wright, S.G., F. Kulhawy, & J.M. Duncan 1973. Accuracy of equilibrium slope stability analysis. ASCE. Journal of Soil Mechanics Foundation Division 99(SM10): 783-791. Zienkiewicz, O.C., C. Humpheson & R.W. Lewis 1975. Associated and non-associated visco-plasticity and plasticity in soil Mechanics. Gdotechnique 25(4): 67 1-689.

The authors want to acknowledge the initial discussions regarding the potential for using a finite element slope stability method that were held with Prof. Wong Kai Sin of Nanyang Technological University, Singapore. These discussions formed the basis for the study of this topic. The assistance of Dr. Fangsheng Shuai, Ms. Noshin Zaderzadeh and Ms. Brigitte Boldt-Leppin in assembling this manuscript is also acknowledged. The authors are also grateful to Geo-Slope International, Calgary, for the modifications made to their software in order that this study could be readily performed. REFERENCES Adikari, G.S.N. & P.J. Cuinmins 1985. An effective stress slope stability analysis method for dams. Proc. 11th Inl. Conj.. Soil Mech. Found Big. 2: 7 13-718. Bathe, K.J. 1982. Finite element procedures in engineering analysis: 200-233. Prentice-Hall. Bishop. A.W. 1952. The stability of earth dams. Ph.D. Thesis, University of London. Bishop, A.W. 1955. The use of the slip circle in the stability analysis of slopes. Geolechnique 5( 1 ): 7- 17. Brown, C. B. & I. P. King 1967. Automatic embankment analysis equilibrium and instability conditions. .Journd of' Soil Adechanics tmti Founcirition Division, ASCE. 93 (SM4): 209-2 19 Duncan, J.M. 1996. State-of-the-art: Stability and deformation analysis. .Journal of Geotechnicnl Engineering, ASCE 122(7): 577-597. Fan, K., D.G. Fredlund & G.W. Wilson 1986. An interslice force %nction for limit equilibrium slope stability analysis. Cariaclian GeorechriiccrlJournal23 (3):287-296. Farias, M.M. & D.J. Naylor 1996. Safety analysis using finite elements, Infogeo 96, Sa6 Paulo, Brazil. Fredlund, D.G. & J. Krahn 1977. Comparison of slope stability methods of analysis. Catieidicm Geotechnique 14(3): 429439. Fredlund, D.G., J. Krahn & D.E. Pufahl 1981. The relationship between limit equilibrium slope stability methods. Proc .f Tenth Internalional Confirence on Soil Mechunics und Foimdutions Engineering, Stockholm. Sweden 3: 409-4 16. Fredlund, D.G. & H. Rahardjo 1993. Soil mechanics jbr irnstirurcited soils. New York: John Wiley & Sons. Higdon, A., E.H. Ohlsen, W.B. Stiles J.A. Weese & W.F. Riley 1976. Mechcinics of ilfaterials New York: John Wiley & Sons. Janbu, N.1954. Stability analysis of slopes with dimensionless parameters. Harvard Soil Mechanics Series (46). Kondner, R.L. 1963. Hyperbolic stress-strain response: cohesive soils. .Joirrnal .f the Soil Mechanics and Foiindutions Division. ASCE 89(SMl): 115-143. Krahn, J., L. Lam & D.G. Fredlund 1996. The use of finite element computed pore-water pressures in a slope stability analysis. Landslides, Senneset (editor) 2: 1277-1282. Rotterdam: Balkema. Kulhawy, F.H. 1969. Finite element analysis of the behavior of embankments. Ph.D. Thesis, the University of California, at Berkley, California, U.S.A. La Rochelle, P. 1960. The short term stability of slopes in London clay. Ph.D. Thesis, University of London, London, UK.

.

47

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang (( ) 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Stability of geosynthetic reinforced steep slopes D. Leshchinsky University of Deluwure, Newark, Del., USA

ABSTRACT: To produce design of stable reinforced steep slopes, a framework for stability analysis is presented. Elements such as local, compound, global and direct sliding stability are ensured. Other stability analysis methods can be implemented using the presented framework as a generic template. To produce economical designs, a meaningful definition of factor of safety is introduced. It is applicable to slopes that are stable only due to the reinforcement tensile resistance. Furthermore, the phenomenon of progressive failure, comnion to reinforced earth structures, is addressed in the context of design. A hybrid type of stability analysis is employed. Peak shear strength dictates the location of the critical slip surfaces and hence sets the reinforcement layout. Residual strength is used to estimate the required force reaction of the reinforcement in case shear bands are fully developed along the traces of the critical slip surfaces. Also presented is an instructive parametric study. Finally, general guidelines about the selection of long-term geosynthetic strength and a comparison with a case history are discussed. 1 INTRODUCTION

2 DESIGN-OIRIENTED ANALYSIS

Soil is an abundant construction material that, similar to concrete, has high compressive strength but virtually no tensile strength. To overcome this weakness, soils, like concrete, may be reinforced. The materials typically used to reinforce soil are relatively light and flexible, and though extensible, possess a high tensile strength. Examples of such materials include thin steel strips and polymeric materials commonly known as geosynthetics (i.e., geotextiles and geogrids). When soils and reinforcement are combined, a composite material, the so-called 'reinforced soil', possessing h g h compressive and tensile strength (similar, in principle, to reinforced concrete) is produced. The increase in strength of the reinforced earth structure allows for the construction of steep slopes. Compared with all other alternatives, geosynthetic reinforced steep slopes are cost-effective. As a result, various earth structures reinforced with geosynthetics are being constructed worldwide with increased frequency, even in permanent and critical applications (Tatsuoka and Leshchinsky, 1994). This paper describes a design process for geosynthetic reinforced steep slopes. It includes the details of the various stability analyses used to determine the required layout and strength of the reinforcing material. It also details the relevant material properties, suggests a new concept related to the factor of safety quantifying stability, and addresses the phenomenon of progressive failure.

2.1 General Limit equilibrium analysis has been used for decades in the design of earth slopes. Attractive features of this analysis include experience of practitioners with its application, simple input data, useful (though limited) output design information, and results that can be checked for 'reasonableness' through a different limit equilibrium analysis method, charts, or even hand calculations. Consequently, extension of this analysis to the design of geosynthetics reinforced steep slopes, where the reinforcement is tangibly modeled, is desirable. The main drawbacks of limit equilibrium analysis are its inability to deal with displacements and its limited representation of the interaction between dissimilar or incompatible materials comprising the slope. Typically, adequate selection of materials properties and safety factors should ensure acceptable displacements, including safe level of reinforcement deformation. In principle, inclusion of geosynthetic reinforcement in limit equilibrium analysis is a straightforward process in which the tensile force in the geosynthetic material is included directly in the limit equilibrium equations to assess its effects on stability. However, the inclination of this tensile force must be assumed. Physically, its angle may vary between the as-installed (typically horizontal) and the

49

2.2 On the factor of safety in reinforced steep slopes Limit equilibrium analysis deals with systems that are on the verge of failure. However, existing slopes are stable. To analyze such slopes, the concept of factor of safety, Fs, has been introduced. In unreinforced slopes, Fs is used to replace the existing soil with artificial one, in which the shear strength is &, = tan-’(tan$/Fs) and cn, = c/Fs where $m and c,,, are the ‘design’ shear strength parameter of the artificial soil. Alternatively, these values represent the average mobilized shear strength of the actual soil. Employing the notion of Fs in limit equilibrium reduces the statical indeterminacy of the stable slope formulation via use of Mohr-Coulomb failure criterion. It also provides an object for minimization. Fs have little physical significance unless viewed in an average sense. The extensive experience with limit equilibrium analysis, however, has produced engineering database providing acceptable values of Fs. Extension of limit equilibrium stability analysis to reinforced steep slopes requires modification of Fs definition. Leshchinsky and Reinschmidt (1985), for example, applied Fs equally to all shear-resisting components, be it soil or reinforcement. This renders Fs that is even less physically meaningful then the one used in unreinforced slopes (e.g., symbolizing the same average reduction of strength of dissimilar materials that are attaining a limit equilibrium state simultaneously). Current federal design guidelines in the US (Elias and Christopher, 1997) define the factor of safety for reinforced slope as:

tangent to the potential slip surface. By using a log spiral mechanism, Leshchinsky and Boedeker (1 989) have demonstrated that for typical cohesionless backfill, this inclination has little effect on both the required strength and layout of reinforcement. Conversely, Lesliclinsky (1992) pointed out that for problems such as reinforced embankments over soft (cohesive) soil, the inclination of the reinforcing geosynthetic, located at the foundation and backfill interface, plays a significant role. The long-term value of cohesion used in design of manmade reinforced steep slopes (i.e., the topic of this paper) is negligibly small and hence, inclination has little effects. Therefore, the force can be assumed horizontal without being overly conservative. A potentially significant problem in limit equilibrium analysis of reinforced soil is the need to know the force in each reinforcement layer at the limit-state. Physically, this force may vary between zero and the ultimate strength when the slope is at a global state of limit equilibrium. Assuming the actual force is known in advance, as is commonly done in analysis-oriented approach, implies the reinforcement force is actually active, regardless of the problem. The designer then assumes the available ‘active’ force of each reinforcement layer to ensure that overall satisfactory state of limit equilibrium is obtained. The end result of such assumption may yield a slope in which some layers actually provide more force than their long-term available strength while other layers are hardly stressed. To overcome the potential problem of local instability, a rational methodology to estimate the required (Le., reactive) reinforcement tensile resistance of each layer is introduced via a ‘tieback analysis’ or internal stability analysis. Consequently, the designer can verify whether an individual layer is overstressed or understressed, regardless of the overall stability of the slope. Once this problem of ‘local stability’ is resolved, overall stability of the slope is assessed through rotational and translational mechanisms. The rotational mechanism (termed in this paper ‘compound stability’ or ‘pullout analysis’) examines slip surfaces extending between the slope face and the retained soil. The force in the geosynthetic layers in this limit-state slope stability analysis is taken directly as the maximum available long-term value for each layer. The translational analysis (‘direct sliding’) is based on the two-part wedge method in which the passive wedge is sliding either over or below the bottom reinforcement layer, or along the interface with the foundation soil. A new concept included in this paper relates to adequate definition of factor of safety of reinforced steep slopes. It suggests a rational and physically meaningful alternative to the conventional factor of safety used in slope stability analysis. In fact, this factor of safety can be measured in an actual structure.

Fs = Fsu + Mr / Md

(1)

where Fsu is the factor of safety for the unreinforced slope and Mr and Md are the resisting moment due to reinforcement and the total driving moment, respectively. Mr and Md are calculated for the same slip surface as Fsu. Such an approach yields an overall factor of safety whose physical meaning is difficult to interpret. Moreover, it treats the reinforcement as pure moment (i.e., only Mr resulting from reinforcement force is considered; actual force is not included in the equilibrium equations). Rather than extending the conventional definition of Fs, one can take advantage of the fact that reinforced steep slopes are stable solely due to the reinforcement tensile resistance. The full strength of the soil will mobilize along slip surfaces. By definition, ‘Fs’ for the soil alone in this case is unity everywhere along the slip surface (i.e., a plastic ‘hinge’ develops mobilizing the available strength of the soil). For this state, the required reinforcement force needed to restore a state of limit equilibrium can be calculated. As an example, see Figure 2 where a log spiral mechanism is used. The stability of the slope

50

now hinges on the reinforcement strength. Hence, the factor of safety can be defines as:

Fs = tavailable (4 trequired where tavailable is the long-term available strength and trequired is the strength required for stability (i.e., for a limit equilibrium state). This definition signifies a factor of safety with respect to the reinforcement available strength, a value that can actually be measured in a structure. The modified definition of Fs is based on the premise that the soil will attain its full strength before the reinforcement ruptures; i.e., the soil will attain an ‘active’ state exactly as assumed in design of retaining walls including those reinforced with geosynthetics. Geosynthetic materials are ductile typically rupturing at strains greater than 10% thus allow sufficient deformations to develop within the soil to reach active state. In reality, most of the deformation needed to develop the active state will occur during construction as the geosynthetic mobilizes its strength. It should be noted, however, that this ‘active state’ approach needs further verification if used with clayey backfill.

Figure 2. Log spiral slip surface and its statical implications.

Figure 1 shows notation and convention. Reinforcement is comprised of primary and secondary layers. Only the primary layers are considered in analysis. In practice, secondary layers allow for better compaction near the face of the steep slope and thus reduce the potential for sloughing. The secondary layers are narrow (typically 1 m wide) and are installed only if the primary layers are spaced far apart (e.g., more than about 0.6 m apart). At the slope face, the geosynthetic layers may be wrapped around the exposed portion of the soil mass or, if some cohesion exists, the layers may simply terminate at the slope face as shown in Figure 1. Steep slopes are defined as slopes inclined at angles for which they are considered unstable without reinforcement. For example, a slope would be considered steep if its inclination is larger than its angle of repose if granular backfill is used (i.e., i>$d where i and @d are the slope inclination and angle of repose, or design friction angle, respectively). Consequently, in steep slopes the force in the reinforcement is activated by an unstable soil mass. That is, the reactive force mobilized in each reinforcement layer has to restore a limit equilibrium state. In general, the following rational could have been used with any type of stability analysis. However, it is most convenient to use it in conjunction with log spiral stability analysis. This analysis produces the location of the critical slip surface and subsequently, the necessary reactive force in the reinforcement. The log spiral mechanism makes the problem statically determinate. For an assumed log spiral failure surface which is fully defined by the parameters xo yc

2.3 Internal stability analysis

Internal stability analysis (also termed tieback analysis) is used to determine the required tensile resistance of the each layer needed to ensure a reinforced mass that is safe against internal collapse due to its own weight and surcharge loading. In the context of retaining walls, this analysis identifies the tensile force needed to resist the active lateral earth pressure at the face of the steep slope. That is, the tensile force needed to restrain the steep slope from sliding along potential slip surfaces that emerge along the face of the slope. The reinforcement tensile force capacity is made possible through sufficient anchorage of each layer into the stable soil zone located behind the active zone.

Figure 1 . Notation and convention.

51

and A , the moment equilibrium equation about the pole can be written explicitly without resorting to statical assumptions (see Figure 2). Consequently, by comparing the driving and resisting moments, one can check whether the mass defined by the assumed log spiral is stable for the design values of the shear strength parameters: 4d and c d and the distribution of reinforcement force $. This check is repeated for other potential slip surfaces until the least stable system is found. That is, until the maximum required restoring reinforcement force is found. The terms K17 and K,, (see Figure 2) represent the seismic coefficients introducing pseudo-static force components. It is assumed to act at the center of gravity of the critical mass. No surcharge is shown in Figure 2 to simplify the presentation; however, inclusion of its effects in the moment equilibrium equations is straightforward. In this case, K h is also applied to the surcharge load, rendering a horizontal pseudo-static force at the crest, where the surcharge acts. Figure 3 illustrates the computation scheme for estimating the tensile reaction in each reinforcement layer. In STEP I, the soil mass acting against D, is considered. Note that D, is signified by a reinforcement layer wrapped around the slope face (see Figure 3), thus making it physically feasible for a mass of soil to be laterally supported, resulting in a locally stable mass. That is, D,is considered as a 'facing unit' (i.e., an imaginary facing element in the front edge of the reinforced soil mass) preventing slides of unstable soil above that tend to emerge through it. This facing is capable of providing lateral support through the development of tensile force in the geosynthetic. The moment equilibrium equation is used to find the critical log spiral producing max(t,J employing the freebody diagram shown in Figure 3 while examining many potential surfaces. The resulted tn counterbalances the horizontal pressure against 0,and thus, signifies the reactive force in layer n. That is, the resulted t, represents the force needed to restore equilibrium and hence stability. Note that D,7 was chosen to extend down to layer n. This tributary area implies a 'toe' failure that activates the largest possible reaction force. In STEP 2, the force against D,]-Jis calculated. extends from layer y2 to layer (n-1). Using the moment equilibrium equation, max(t,-J, required to retain the pressure exerted by the unstable mass against D,,-,, is calculated. When calculating t,,-/,the reaction t,,, determined in STEP I, is known in magnitude and point of action. Hence, the reactive force in layer (n-1) is the only unknown to be determined from the moment equilibrium equation. Figure 3 shows that by repeating this process, the distribution of reactive forces for all reinforcing layers, down to t l , are calculated while supplying the demand for a limit equilibrium state at each rein-

Figure 3. Scheme for calculating tensile reaction in reinforcement layers

forcement level. Application of appropriate factors of safety to the required reinforcement strength should ensure selection of geosynthetic possessing adequate long-term strength at each level. Note that cohesive steep slopes are stable up to a certain height. Consequently, the scheme in Figure 3 may produce zero reactive force in top layers. Though these layers may not be needed for local stability, they may be needed to resist compound failure as discussed in the next section. The outer-most critical log spiral defines the extreme surface as dictated by Layer I. In conventional internal stability analysis it signifies the extent of the 'active zone'; i.e., it is the boundary between the sliding soil mass and the stable soil. Consequently, reinforcement layers are anchored into the stable soil to ensure their capacity to develop the calculated tensile reaction tJ (see Figure 4). The 'stable' soil may not be immediately adjacent to this outer-most log spiral and therefore, some layers should be extended further to ensure satisfactory stability (see next section). Note in Figures 3 and 4 that the reinforcement layers are wrapped around the overlying layer of soil to form the slope face. However, in slopes that are not as steep (say, i<50 9, typically there is no wrap around

&-,

52

each reinforcement layer needed to ensure adequate stability against rotational failures. Internal stability analysis gives the required reinforcement strength at each level. In actual practice, however, specified reinforcement layers will have allowable strengths in excess of that required (Le., tj I t(allowab1e)jwhereas tallowable 5 tavailable and tavailable is the long-term available strength of the geosynthetics). The end result is that globally, the tieback analysis requires only m reinforcement layers extending outside the 'active' zone and into the stable soil. That is, the m layers are sufficient to maintain stability of the active mass as a whole. Internally, however, layers (m+l) through n are also needed to ensure local stability as implied in the scheme presented in Figure 3. To calculate the minimum number of layers, m, the following equation is used:

the face or any other type of facing. In this case, load transfer fiom each unstable soil mass to the respective reinforcement layer is feasible due to a 'coherent' mass formed at the face. This mass may be formed by soil arching, by a trace of cohesion and by closely spaced reinforcement layers. The end result is a soil 'plug,' in a sense similar to the one developed at the bottom of a driven open-end pile, that acts de fact0 as a facing unit thus making feasible the load transfer into the primary reinforcement layer. It should be pointed out that 'closely spaced reinforcement' does not necessarily mean closely spaced primary reinforcement layers; simply, thls 'plug' can be created by the combination of secondary and primary layers acting together to create a coherent mass. Since reinforcement layers, including primary and secondary layers, are spaced approximately 30 cm apart in practice, and since the secondary layers extend at least about 1 m into the slope, the contribution of secondary layers to the formation of a Yacing' should not be ignored. With time, surface vegetation and its root mat enhances this Yacing.' The end result of forming a coherent face is not just an efficient load transfer fiom the deeply unstable soil mass to the reinforcement, but also improved surficial stability and erosion resistance.

m

c

j = I

n

t(a1lowable

)j

c

tj

( 31

j=1

Note that m is the number of layers, counting from the bottom, capable of developing a total tensile resistance equal to (or slightly exceeding) the net total force obtained fiom the internal stability analysis. When m = n the compound stability degenerates to that introduced by Leshchinsky (1992). The m layers may contribute their full allowable strength simultaneously to global stability when compound stability of the reinforced system is examined. The assumption of simultaneous availability of reinforcement strength is commonly used in limit equilibrium stability analysis of reinforced slopes. Embedding the layers immediately to the right of the outermost log spiral obtained in the internal stability analysis, so that t&,l,able for layers I through m and t,

2.4 Compound (or pullout) stability analysis For a given geometry, pore-water pressure distribution and (#d and c d ) , the internal stability analysis provides the required tensile resistance at the level of each reinforcement layer. It also yields the trace of the outermost log spiral defining the 'active' soil zone, a notion commonly used in conjunction with analysis of retaining walls. In reinforced soil structures, the capacity of the reinforcement to develop the required tensile resistance depends also on its pullout resistance;. i.e.,. the length kchored into the siable soil zone. If the boundary of this stable zone is indeed defined by the 'active' one, then potential slip surfaces that are passing further into the soil mass than the outermost log spiral in Figure 4, outside or within the effective anchorage length, will never be critical. However, such potential surfaces may render reduced pullout resistance since the effective anchorage length is shortened. That is, the reduced tensile resistance capacity along these surfaces could potentially produce a globally unstable system. Consequently, a conventional slope stability approach is used to determine the required reinforcement length so that compound failures (i.e., surfaces extending into the unreinforced soil zone) will not be likely to occur. The term 'conventional' refers to the nature of the analysis in which global stability is sought (recall that internal stability, or tieback analysis, looks at local stability at the elevation Of each reinforcing layer)* The Objective Of the compound analysis is to find the minimum length of

Figure 4. Tensile reaction transferred into soil next to active zone.

53

for layers (m+I) through n can develop through pullout resistance, ensures that, in an average sense, the mobilized friction angle, $mob, along this log spiral is equal to, or slightly less than, (bd. The upper layers)I+‘( through n (see points A, B and C in Figure 5 ) are not needed for the global stability of the ‘active’ mass and therefore, from a theoretical view point could be ignored at points A, B and C. Note that the mobilized friction angle, (bf&,, represents the required angle to produce a limit equilibrium state while using the allowable reinforcement strength. Hence, when (bnzob < (bd, a fictitious situation is analyzed; i.e., the system is actually stable since the available soil strength, as expressed by (bd, is larger than needed, (b),,&, for a limit equilibrium state. Only when $,,lob = (bd is a limit equilibrium state achieved. At this stage of analysis, reinforcement layers I through m are lengthened to a test body defined by an arbitrary log spiral extending between the toe and the crest, to the right of the outermost log spiral (Figure 5). Each layer beyond the slip surface is embedded so that the calculated t(a/lo\vab/e)j can be developed; (b& for this surface will be smaller than (bd used in design (i.e., for this layout, the outermost surface from internal stability analysis is most critical). The upper reinforcement layer is truncated in a numerical sense (i.e., t,,, = 0), and the moment equilibrium equation for the arbitrary log spiral is used to check whether (bmob = (bd. If (br,lob = (bd than layer m is sufficiently long (see point D in Figure 5); otherwise, lengthen this layer and repeat calculations until satisfactory length is found. A satisfactory length implies that the critical log spiral passing through point D yields a stable system for the design friction angle, (bd; all feasible log spirals between this one and the one from the internal stability have (b,nob < (bd indicating they represent less critical mechanisms (note that the strength of layers I through m is available between these two log spirals). The process is repeated to find the required length of layer (m-1) (Figure 5). Since the layers above were already ‘truncated’, they no longer contribute tensile resistance to deeper slip surfaces. Once the process has been repeated for all layers down to layer 1, the length of all layers (curve DEFGH in Figure 5 ) required to ensure that (&job does not exceed $d for all possible log spiral failure surfaces is found. To be slightly conservative (and to avoid consideration of surfaces where only a fraction of the pullout resistance is available), all anchorage lengths may be specified beyond points D, E, F and G. This simplification is conservative since, contrary to the compound analysis procedure, it ensures the following: f(a/lol&le)f,l at point D (not zero resistance at D); ~(a//o)t~ab/e)m-l at point E (not zero resistance at E); and so on. Since the anchorage length of planar geosynthetic sheet is typically small (only a few centimeters) relative to its total required

length in practical problems, this simplification is reasonably conservative. In a theoretical sense, this simplification is not needed, however, it greatly simplify any computational procedure. Compound critical surfaces emerging above the toe are also possible and consequently, the procedure in Figure 5 should be formally repeated for slip surfaces emerging through the face of the slope. Subsequently, layers previously truncated are lengthened if necessary to ensure that (b,,job 5 (bd. Specifying a layout similar to the envelope ABCDEFG will contain, at least, m potential slip surfaces, all having the same minimal safety factor against rotational failure (see Figure 5). However, because of practical considerations, a uniform or linearly varying length of layers is specified in practice. As a result, the number of such equally critical slip surfaces is reduced in actual structure since most layers are longer, and typically, some are stronger than optimally needed. Finally, anchorage lengths are calculated to resist pullout forces equal to the required allowable strength of each layer multiplied by a factor of safety Fs.po. In these calculations the overburden pressure along the anchored length and the parameter defining the shear strength of the interface between soil and reinforcement are used. This parameter, C,, termed the interaction coefficient, relates the interface strength to the reinforced soil design strength parameters: tan(& and cd. The interaction coefficient is typically determined from a pullout test. The required anchorage length of layerj then equals t/ / (c~~,C,,[tay2((b&+cd]} where 4; signifies the average overburden pressure above the anchored length. Adding the anchorage length to the length needed to resist compound failure produces the total length required to resist tieback and compound failure. This length ensures that sufficient pullout resistance exists for all layers and therefore, sometimes termed Pullout Analysis. It considers compound failure developing in both the reinforced and retained soil.

2.5 Direct sliding analysis Specifying reinforcement layout that satisfies a prescribed (bd against rotational failure does not guarantee sufficient resistance against direct sliding of the reinforced mass along its interface with the foundation soil, or along any reinforcement layer. The reinforcement length required to ensure stability against failure due to direct sliding, L k , can be determined from a limit equilibrium analysis that satisfies force equilibrium; i.e., the two-part wedge method. Figure 6 shows the notation used in defining the geometry and forces in the two-part wedge analysis. First, an initial value of Lds is assumed. Then, for an

54

Figure 5. Length required to resist compound/pullout failure.

ussurned interwedge force inclination, 6, the maximum value of the interwedge force, P,,,, is found by varying 0 while solving the two force equilibrium equdions for the active Wedge A. This interwedge force signifies the resultant of the lateral earth pressure exerted by the backfill soil on the reinforced soil. Next, the vertical force equilibrium equation for Wedge B is solved considering the vertical component of the lateral thrust of the active wedge (i.e., Pnt,sin@. The reaction NU is obtained and the base sliding resisting force of Wedge B, TR,is calculated. When calculating TB, the coefficient Cd, is used (Cd, = the interaction coefficient between the reinforcement and the soil as determined from a direct shear test). If the bottom layer is placed directly over the foundation soil, two values of C d , are needed: one for the interface with the reinforced soil and the other for the interface with the foundation soil. At this stage, the actual factor of safety against direct sliding, Fs.ds, is calculated by comparing the resistiiig force with the driving force:

FWA

=-

TB P cos 6

(4)

This factor of safety corresponds to the assumed value of Lds. In case it is unsatisfactory, the value of L d s is changed and the process is repeated for Wedge A and Wedge B until the computed factor of safety against

Figure 6. Two-part wedge mechanism used in direct sliding analysis.

direct sliding equals to the prescribed value. The assumed value of 6 may have significant influence on the outcome of the analysis. Selecting s>O implies the retained soil will either settle relative to the reinforced soil and/or the reinforced soil will slide slightly as a monolithic block thus allowing interwedge friction to develop. Some reinforcement layers will typically intersect the interwedge inter-

Figure 5 . Length required to resist compound/pullout failure.

Figure 6. Two-part wedge mechanism used in direct sliding analysis.

stability calculations. Consequently, selecting a value of 6 in between (2/3)$d and $d should be viewed as a conservative choice.

face (especially if i < 70 "). However, the tensile resistance of these reinforcement layers is ignored in

56

compound failure analyses (Figure 5), this surface passes through both reinforced and retained soil and possibly, even through the foundation soil. As an approximation, one can use an averaging technique, considering the compound failure surface lengths in the reinforced soil and in the retained soil, to find equivalent values for & and cd to be used in analysis. The value of the equivalent $hd is used to define the trace of the log spiral passing through the reinforced and retained soils.

The techmque for incorporating seismicity into the force equilibrium analysis is shown in Figure 6. In a pseudo-static approach, however, large seismic coefficients may produce unrealistically large reinforced soil block, Wedge B. In this case, a permanent displacement type of analysis (i.e., Newmark's stick-slip model) is recommended. Alternatively, one may eliminate inertia fiom Wedge B, analogous, in a sense, to Mononobe-Okabe model used in analysis of gravity walls. Only the 'dynamic' effects on P are superimposed then on the statical problem. Finally, note that FSas is imposed when using 4 d and cd. In the context of limit equilibrium analysis, this may constitute a 'double taxation.' That is, if peak shear strength parameters are used, such a factor of safety is essential. However, if (bd and cd equal to or smaller than the residual strength values (see discussion later on progressive failure) then imposing Fs-ds is unnecessary.

3 DESIGN CONSIDERATIONS

3.1 General The presented approach is based on the state of limiting equilibrium. Such a state deals, by definition, with a slope that is at the onset of failure. Application of adequate safety factors should ensure acceptable margins of safety against the various failure mechanisms analyzed. It is implicitly assumed that the different materials involved (i.e., the geosynthetic materials and soils) will all contribute their design strengths simultaneously to attain a state of limit equilibrium. For materials having constant plastic shear strength after some deformation (e.g., soils), such an assumption is realistic. However, not all materials in the reinforced soil system possess this idealized plasticity. Consequently, the following guidance is provided for selecting material properties.

2.6 Commentary

No conventional factor of safety was used in the limiting equilibrium analysis. This is possible since the unreinforced slopes are considered unstable thus enabling the soil to mobilize its full strength (i.e., attain an active state). The presented approach assumes the foundation to be competent and therefore, deepseated failures were not considered. However, the computational procedure can be modified for slip surfaces that penetrate the foundation soil.

3.2 Progressive failure and soil shear strength

The approach can be modified to include any type of limit equilibrium analysis. In case of generalized approach, separation into direct sliding and compound stability is not needed. However, search routines in generalized methods must be capable of capturing critical surfaces of greatly different geometries. Furthermore, the problem may posses several minima thus complicating the search.

Slip surface development in soil is a progressive phenomenon, especially in reinforced soil where reinforcement layers delay the formation of a surface in their vicinity (e.g., Huang et al., 1994). Zornberg et al. (1998) discuss the elapsed time between failure initiation and complete collapse observed in centrifugal models of reinforced slopes. Clearly, this observation indicates a phenomenon of progressive failure implying that while the soil is about to reach its peak strength along portions of the slip surface, it has already passed the peak along other portions, perhaps reaching its residual strength. Leshchinsky et al. (1 995) recommended that the design values of 4 and c (i.e., 4d cd) should not exceed the residual strength of the soil. This would ensure that at the state of a fully developed slip surface, the shear strength used in the limit equilibrium analysis is indeed attainable all along the slip surface. Use of residual strength has clear cost implications in the design of reinforced steep slopes. The required strength of the reinforcement increases somewhat (see next section). However, the required

Possibility of surficial failure is ignored in the presented procedure. The presented approach can be modified to deal with this issue by assigning low or zero reinforcement strength at the face provided the geosynthetic is not wrapped around. However, for steep slopes, strict limit equilibrium analysis will indicate insufficient stability at the surface. The empirical concept of soil 'plug' is assumed to be valid for closely spaced reinforcement layers. In the strict sense of analysis, log spiral slip surface is valid for homogenous soil only. However, in the

57

determine the geosynthetic reactive force. In compound analysis use $residual in the limiting equilibrium equations to assess the required reinforcement strength along slip surfaces determined using $peak.

length of reinforcement increases significantly since much deeper slip surfaces are predicted. For compacted granular soil, an increase in length of 30 to 50% might typically be required. This additional length makes construction more difficult, especially if space constraint exists (e.g., widening existing embankment), thus rendering construction more expensive than just the cost of extra reinforcing material. Hence, this combined with what currently appears as overly conservative designed reinforced steep slopes create a need to introduce a less conservative design approach. It is an experimental observation that only one slip ‘surface’ develops during the shear of granular dense soil element (i.e., unreinforced soil in triaxial or plane strain tests). In these tests, Mohr circle at failure combined with Coulomb failure envelop indicates that the shear surface is inclined at an initial angle of (45”+ $ p e k / 2 ) to 03. As displacement continues, a shear band forms and the residual state of strength is reached. As an example, see Figure 7, reproduced from Yoshida and Tatsuoka (1997). Observing Figure 7 (unreinforced soil element), as well as measured traces of slip surfaces in centrifugal models of reinforced granular slopes presented by Zornberg et al. (1998), indicates a unique slip ‘surface’ within the shear zone. That is, there are no two different slip surfaces, one attributed to $peak and the other to $residual; instead, a rather narrow shear band is developed. Based on plane strain compression tests conducted on 12 different unreinforced sands, Yoshida and Tatsuoka (1 997) have demonstrated that the average inclination of the shear band (i.e., the ‘slip’ surface) is approximately related to $peak having a value that is slightly less than (45”+ $peak/2). This observation, however, is valid for medium to fine sand while the confining pressure is less than, say, 100 kPa. Zornberg et al. (1998) have demonstrated that a single ‘slip’ surface also develops in reinforced slopes. Via limit equilibrium backcalculations, Zornberg et al. (1 998) have shown that indeed their traced slip surfaces correspond well to $peak. Consequently, the following hybrid procedure is proposed for design when granular compacted fill is used:

It is entirely possible that the backfill in steep slopes will deform (during or after construction) mobilizing the soil beyond its peak strength. Therefore, the stability of steep slope may hinge then upon the strength of the reinforcement. Consequently, the reinforcement strength becomes critical to stability in case residual strength develops. Note that the hybrid approach recognizes that slip surfaces will initiate and have a trace based on the soil peak strength. However, possible development of progressive failure is also recognized and at this state, the ductile reinforcement should be sufficiently strong to keep the system stable. It should be pointed out that in a sense, Tatsuoka et al. (1998) proposed a similar hybrid approach, however, it was limited to seismic design of reinforced walls. The proposed procedure may result in significantly shorter reinforcement as compared to using &esidual. However, the required reinforcement strength will be somewhat larger than that computed by using $peak. If cohesive fill is used, extreme care should be used when specifying the cohesion value. Cohesion has significant effects on stability and thus the required reinforcement strength. In fact, a small value of cohe-

Use $peak and limit equilibrium analysis to locate the critical slip surfaces. These surfaces will be used to determine the required layout of geosynthetic layers (i.e., length and spacing). Note that in reinforced slopes there can be several equally critical slip surfaces. Use $residual along traces of the critical slip surfaces determined in ( a ) to compute the required geosynthetic strength. That is, in internal stability use $peak to locate the slip surface and the use $residual in the limiting equilibrium equations to

Figure 7 . Shear band in plane strain compression test (Ticino sand: Dr = 79%, DjO = 0.527 mm, at u3 = 78 kPa and ylllas = 13.3%). Photo courtesy of Professor F. Tatsuoka, University of Tokyo, Japan.

58

sion will indicate that no reinforcement at all is needed at the upper portion of the slope. However, over the long run, cohesion of manmade embankments tends to drop and nearly diminish (normally consolidated clay). Since long term stability of reinforced steep slopes is of major concern, it is perhaps wise to ignore the cohesion altogether. It is therefore recommended to limit the design value of cohesion to a maximum of about 5 kPu. It should be pointed out, however, that end-of-construction analysis must be also conducted if a soft foundation is present. In this case stability against deepseated failure must be ensured.

2. For clarity, a simple granular slope (c = 0) without water and seismic loads is depicted. 3. The weight of the sliding mass, W, and the required reinforcement force, treyujyed, are known in magnitude (from the solution of the moment equilibrium equation for $peak) and in direction.

Figure S. Approximate approach to consider the effect of residual strength.

where RF, is the reduction factor in the strength of geosynthetic due to consideration of residual strength along the slip surface while using peak strength in all calculations. In a sense, the assumption about the resultant inclination is similar to that used in the friction circle method (Taylor, 1937). However, unlike the friction circle, the 'accuracy' of this simplified approach has not been fully verified yet. Leshchinsky and Boedeker (1 989) have demonstrated that as the slope inclination approaches the log spiral degenerates to a planar surface (i.e., log spiral with a pole located at infinity). This plan is inclined at (45"+ $/2) when the reinforcement force acts horizontally. Observing Figure 8, one can realize that as the surface tends to be a plane, the approximation regarding A$ becomes accurate. That is, for a planar surface the problem is statically determinate and therefore, one can verify that the difference in Rp and R,. inclinations must equal to A$ = $peak - $resjdlral. Furthermore, geometry implies that the angle toequals to (45 "- $peak /2). Consequently, for granular vertical slope the reduction factor RF,. turns to:

The action line of R (i.e., the resultant force of the distribution of G and T along the log spiral) must coincide with 00' and simultaneously close the polygon to satisfy force equilibrium. Hence, the force equilibrium will be satisfied by virtue of the existence of an unspecified resultant R that will close the force polygon. The approximate procedure is implied in Figure 8. All elemental resultant forces due to o and T along the slip surface, dR,, at the residual strength, must be inclined at $residual to the normal; dRr no longer pass through the log spiral pole 0. At each location along the log spiral, the elemental resultant force at the peak strength, dR,, is inclined at $peak passing through the pole. Hence, at each point along the surface, the angle between dR, and dR, is A$ = $peak - $esidl,al. It is assumed that the resultant of all elemental dR,, R,, is also inclined at A$ to the resultant of dRp, Rp. This assumption allows for the construction of the force polygon (Figure 8). Consequently, using the force polygon in Figure 8, the results obtained for beak can be 'corrected' in a simplified way to adapt to the hybrid approach. That is:

3.3 Reinforcement force due to progressive failure The preceding discussion suggests using $peak to determine the location of each critical slip surface. Next, along these critical surfaces one should calculate the required reinforcement reaction to maintain a state of limit equilibrium using residual shear strength values. This process can be done using any limit equilibrium procedure, preferably a rigorous one. To be consistent with the presentation in this paper, the following modified approximate procedure is proposed. The general expression shown in Figure 2 implies that the critical results for the log spiral satisfy moment equilibrium explicitly. It can be argued that these results also satisfy the force equilibrium implicitly. To realize this, refer to Figure 8. Notice in this figure that: 1. For clarity, only one reinforcement layer is used (expansion to n layers is straightforward).

59

Close examination of RF,. reveals that it is relatively insensitive for reasonable range of values of to (between 20" and 50") while holding A$ constant. Furthermore, observing the results presented by Leshchinsky and Boedeker (1989), one can configure that toincreases as the steep slope flattens. The equations of RFr (Equations 5 and 6) imply that for 90" slope and constant A$, the largest value of RF,. is produced (within a reasonable range of both E0 and A$). Hence, it is practically sufficient to investigate the explicit value of RF,. for 90" slope and use it as an upper limit in evaluating the effects of progressive failure. Using typical values of $peak between 40" and 50" and A$ = 5" yields a narrow range of RFr between 1.24 and 1.28 (practically one would use 1.3). Unusual design values of @peak between 45" and 50" and A$ = 10" yields RF, of nearly 1.6. To avoid complication of design via introduction of complex concepts and involved analysis, it is practical to conduct the entire analysis using peak strength and then correct the needed strength reinforcement by invoking the multiplier RFr. For simplicity, in design guidelines the value of $peak can be limited to 45" while the correction factor is set to RF,. =1.40. Alternatively, the exact procedure can be followed as suggested.

3.4 Reduction factors related to geosynthetics The presented limit equilibrium analysis assumes that the geosynthetic will not mobilize its full strength before the full design strength of the soil is attained. Formally, there is no consideration of deformations. One can envision a scenario in which very stiff reinforcement will have its strength mobilized rapidly, potentially reaching its design value before the soil mobilizes its strength. This may lead to overstressing and subsequently, premature rupture of the reinforcement, violating the analysis premise that its tensile resistance will be available with the soil residual strength. The result might be local, or even global, collapse. However, since geosynthetics are ductile (typically, rupture strain greater than 10%), large strains will develop locally in response to overstressing thus allowing the soil to deform and mobilize its strength as assumed in the analysis and as needed for stability. Over twenty years of experience indicate that lack of stiffness compatibility is not a problem in structures based on limit equilibrium design. To ensure that indeed some overstressing of the reinforcement without breakage is possible, an overall

factor of safety for uncertainties is specified. This factor multiplies the calculated minimal required reinforcement strength at each level. Typical values for this factor range from F,,,=1.3 to 1.5. The strength of the factored reinforcement should be available throughout the design life of the structure. To achieve this, reduction factors for installation damage (RFjd), durability (RFd), and creep (RF,,) should be applied so that geosynthetics possessing adequate ultimate strength, tlrll,could be selected. That is, the specified geosynthetic should have the following short-term ultimate strength:

Table 1 gives preliminary values for geosynthetics reduction factors (Elias and Christopher, 1997). Note that for normal soil conditions in steep slopes (i.e., near neutral pH and no biological activity), degradation should not be a problem when using a typical reinforcing polymeric material. The values of RFjd and RFd are site specific. The creep reduction factor, RF,,., depends, to a large extent, on the polymer type and the manufacturing process. The term ultimate strength, tull, should correspond to the result obtained fiom the short-term wide-width tensile test, following, for example, ASTM D4595-86 procedure. Typically, the strength at 5% elongation strain in the wide-width test is reported as well. Some designers concerned with performance prefer to use this value as 'tu/,.' It should be noted that performance (i.e., deformations) of steep slopes is less critical than that of walls and therefore, the 5% 'limit' is unnecessary and overly conservative for most practical purposes. Finally, if seismicity is considered in the design, the reduction factor against creep can be set to one. Simply, since the duration of the superimposed pseudo-static seismic load is short, significant creep is not an issue. However, the designer should verify that the required seismic strength is no less than the required value for static stability where the creep reduction factor is high; the larger strength value from static and pseudo-seismic should prevail. 3.5 Other speciJied safety factors

The factor of safety against direct sliding, Fs-ds, ensures that the force tending to cause direct sliding of the reinforced soil block is adequately smaller than the force available to resist it. It is a straightforward adaptation of analysis from reinforced retaining walls or gravity walls. It is recommended to use Fsds=l .5 to 2.0 to avoid possible progressive failure as-

60

Table 1. Preliminary reduction factors.

(1

Leshchinsky provides these values for preliminary design. sociated with peak shear strength of soil,. If the design value of the soil shear strength used in analysis is lower than its residual strength, one can use Fs-ds= 1.0 to 1.3 since safety is already manifested in the reduced shear strength. With reference to direct sliding, note the coefficient C d , related to this mechanism. There are two direct sliding coefficients. The first signifies the ratio of shear strength of the interface between the reinforcement and reinforced soil and the shear strength of the reinforced soil alone. The second coefficient signifies a similar ratio but with respect to the strength of the foundation soil. This coefficient reflects a mechanism in which soil slides over the reinforcement sheet. Its value can be determined from direct shear tests in which the shear strength of the interface between the relevant type of soil and the reinforcement is assessed under various normal loads. Typically, C d , will vary between 0.5 and 1.0, depending on the type of soil and reinforcement. For granular soils and common geosynthetics used in reinforcement, C d , is about 0.8. In many cases the required length of bottom layer (i.e., see L g in Figure 9) may increase significantly as C d , decreases below 0.8. Factor of safety against pullout, F&,, multiplies the calculated required allowable tensile force of each reinforcement layer. Anchorage length then is calculated to provided pullout resistance up to this increased tensile force. Typically, Fs-povalue is specified as 1.5. C, signifies the interaction coefficient. It relates the strength of the interface between the reinforcement and soil to the shear strength of the reinforced soil or foundation soil. This coefficient reflects a mechanism in which the reinforcement is being pulled out from a confining stable soil. The required anchorage length is calculated based on Ci. The value Ci is normally determined from a pullout test. Typically, the value of Ci varies between 0.5 and 1.0, depending on the type of soil and reinforcement. For granular soils, the typical value of C,

61

is about 0.7. It should be pointed out that anchorage length for reasonably spaced continuous reinforcing sheets (i.e., 30 to 60 cm vertical spacing), is quite small relative to the total required length in the final layout. Consequently, the interaction coefficient may just be conservatively assumed in design. 3.6 Practical layout of reinforcement Two practical options for specifying reinforcement length are common in practice (see Figure 9). The first option simplifies construction by specifying all layers to have a uniform length. This length is selected as the longest value obtained from the internal stability analysis, the pullout/compound failure analysis, or the direct sliding analysis. The second safe option is to specify L g and L T at the bottom and top, respectively, where L g is the longest length from all analyses and LT is the longest length obtained from internal stability and compound/pullout analyses. Length of layers in between is linearly interpolated. This specification is more economical; however, it may result in misplaced layers at the construction site.

Figure 9. Practical layout of reinforcement.

Figure 9 shows primary and secondary reinforcing layers. In the stability analyses, only primary layers are considered. However, layers spaced too far apart may promote localized instability along the slope face. Therefore, secondary reinforcement layers should be used. Their width should extend at least l m back into the fill and their strength, for practical purposes, may be the same as the adjacent primary reinforcement. The vertical spacing of a secondary reinforcement layer from either another secondary layer or from a primary one should be limited to 30 cm. Secondary reinforcement creates a 'coherent' mass at the slope face, a factor important for local stability. Furthermore, it allows for better compaction of the soil at the face of the steep slope. This, in turn, increases the sloughing resistance and prevents surficial failures. If wrap-around is specified (necessary in slopes steeper than about 50°), secondary reinforcement can be used to wrap the slope face as well. It should be backfolded then at least I m back into soil, same as the wrapping primary reinforcement. 4 RESULTS AND CASE HISTORY 4.1 Typical results Figure 10, reproduced from Leshchinsky and Boedeker (1 989), shows the calculated required tensile force from internal stability analysis versus $peak and slope inclination. It should be noted that Leshchinsky and Boedeker (1989) used a variational technique to facilitate the generation of results, however, those results are identical to those produced using the scheme presented in this paper. This figure is limited to cohesionless slopes. The ordinate K represents the non-dimensional value of the calculated tj and, in a sense, is equivalent to K a in lateral earth pressures (K, is equivalent to Rankine's if horizontal reinforcement and to Coulomb's if the reinforcement is inclined). Notice that for reasonable range of $peak, the difference in required K as a function of assumed reinforcement force orientation at the slip surface is small. This difference is the largest for vertical slopes (practically, about 10%). The value of each tj can be back calculated from this chart following the rational presented in Figure 3 . That is, start with j = 1 and top layer to find tn for which H equals Dn, then go to j = 2 and layer n -1 to find tn-1 where H equals D,+Dn-I and t, is known, and so on. Alternatively, one can use this chart in an approximate manner. That is, the overburden pressure at the middle of a tributary area of a reinforcing layer can be calculated and then be multiplied by the tributary area and by the coefficient K obtained from the chart. Considering the potential for progressive

Figure 10. Calculated tensile reaction for cohesionless slopes

failure, the values of tj's determined from this chart have to be multiplied by RF, (i.e., typically, tj would be 20 to 40% larger to account for $residual). It should be pointed out that soil possessing low $ such as 15" or 20" is not likely to exhibit peak shear characteristics; it is presented in this and following figures for instructive purposes unless one uses the chart for a case where $design = $residual = $peak. Figure 11 show the outermost traces of critical slip surfaces obtained from internal stability analysis. This figure is for horizontal inclination of geosynthetic force (for traces when reinforcement is tangential, see Leshchinsky and Boedeker, 1989). Notice that for vertical slopes, the surfaces are practically planar inclined at angle of (45"+ +peak/2). Also notice that as $peak decreases, the slip surfaces become significantly deeper thus implying longer uniform required length of reinforcement. The impact of this phenomenon should be viewed in the context of the proposed progressive failure approach. No charts are shown for required length based on compound stability analysis. The results in this case will depend on the selected reinforcement strength. The interested reader is referred to Leshchinsky et

62

Figure 1 1 . Outermost traces of internal slip surfaces.

while Figure 12 (bottom) shows the conservative case where 6 = 0. Generally, it can be seen that as the slope flattens, the length of reinforcement increases. Also, the friction angle and the interwedge angle have significant effects on length. Notice that for 45" slopes combined with = 45", no reinforcethe ment is needed, however, if one uses $design < required length will increase. In this case, one could use lower Fsdsin lieu of smaller b.

al. (1995) to view some typical surfaces. In general, compound failure will not control the length in near vertical slopes provided the reinforcement is closely spaced and uniform in strength. However, this would not necessarily be the case if geosynthetic layers with variable length and/or strength is specified. Figure 12 shows the length of reinforcement required to resist direct sliding. It is constructed for strength related to peak shear strength, for direct sliding coefficient, Cds, equals one, and for a factor of safety to resist direct sliding, F,&, equals 1.5. Figure 12 (top) represents the case where full friction is developed along the interface of the two wedges (i.e., 6

=

+

4.2 Case history Fannin and Herman (1990) report the results of a field test of a well-instrumented full-scale slope.

63

One tested slope in which no intermediate reinforcement layers were used is adequate for comparison with the proposed progressive failure approach. The slope height was 4.8 m and its inclination was 1H:2V. The backfill soil was a uniformly graded medium to fine sand, compacted to a unit weight of 17 kn/m3. The plane strain residual internal angle of friction is reported to be 38". Unfortunately the peak angle is not reported. The layout of the uniformly spaced geogrids is shown in Figure 13. The force distribution in each geogrid layer was measured using load cells. Only the facing was constructed of a wire mesh, which is considered equivalent to wrap-around face. Following construction, the wall was surcharged with soil placed to a depth of 3 m. Since no details are given, it is assumed that the slope of the this surcharge fill was 2H:lV. The outermost internal failure surfaces using the approach presented in this paper are contained within the reinforced zone (Figure 13) for $residual = 38". Since $peak is unknown, the corresponding slip surface is not plotted, however, because $peak is larger than $residual, the critical slip surfaces would be even shallower (i.e., certainly contained within the reinforced zone). The long-term allowable geogrid strength is not reported, however, it can be verified that its value is much larger than the measured forces. Hence, all compound slip surfaces are also contained within the reinforced soil. Assessment of direct sliding reveals that Fs-dsfor the layout used is between 1.5 and 2.0. Since the actual layout is not the same as required in Figure 5 (i.e., not minimum length but rather uniform length), back-analysis using the presented design-oriented analysis can only suggest a probable range of feasible values. The probable range for each layer is between the required force against internal failure and compound failure (i.e., between the value needed to ensure local stability and global stability). The proposed approach in this paper specifies the maximum value of this probable range in design. Table 2 shows the comparison between measured values and those predicted using $residual = 38". The agreement exhibited in Table 2 is considered good. The total measured and calculated forces can be used, in an average sense, to realize whether the values suggested for RF, are reasonable. Repeating calculations for the problem for $peak = 43", one gets CtJ = 1 1.1 kN/m; for 4peak = 4 1", one gets Ctj = 13.3 kN/m. Considering the measured (actual) value of CtJ was 15.3 kN/m, the reduction for progressive failure would be RF, = 1.38 ($peak = 43") and RFr = 1.15 (@peak = 4 1"). If one considers the calculated value of Ctj = 17.0 kN/m, the corresponding RFr would be 1.53 and 1.28. Note that the proposed ap-

Figure 12. Required length to resist direct sliding as function of peak shear angle and slope inclination (assuming reinforced. retained and foundation soils possess same strength and density).

Figure 13. Configuration of Norwegian Wall.

proach recommends values between 1.2 and 1.4. The results of this exercise support the simplified approach of the hybrid approach using a reduction factor, RFr, to account for possible progressive failure along a surface determined by $peak. Fannin and Herman report only the total sum of forces for the surcharged case. The measured value is 22.2 kN/m whereas the calculated one ($residual =

64

Table 2. Reinforcement forces under self-weight loading.

Layer no. j I Elevation

liml

I

110.0

Superimposing on these critical slip surfaces the residual strength of the soil and solving the limit equilibrium equations provide an estimate of the required reinforcement strength in case progressive failure fully develops. It is recommended to ignore the cohesion value in long-term design of reinforced steep slopes. The proposed design procedure can be easily carried out using a computer program (e.g., Leshchinsky, 1997). The mechanism and analysis used can be replaced with other rigorous stability methods. Hence, this paper provides a conceptual framework for design of reinforced steep slopes. It is comprehensive and economical; experience proves it is safe.

38") is 21.1 kN/m. Calculating RF,. will produce similar trend to that of the self-weight case. Generally, this case history shows that use of $residual is justifiable. However, strain measurements by Fannin and Herman indicates the location of maximum force is shallower that that implied by $residual (i.e., implied by the trace of slip surface shown in Figure 13). Use of $peak will produce shallower surfaces while use of RF,. will correct the required reinforcement strength to account for a possible state in which residual strength is attained along that surface. 5 CONCLUSION A procedure for the design of steep slopes reinforced with geosynthetic materials has been presented. The analyses involved in the presented design process are based on limit equilibrium. These analyses ensure that the reinforced mass is internally and externally stable. A physically meaningful definition of factor of safety is introduced. It is applicable only to slopes having their stability hinging on the strength of the reinforcement. The presented design procedure includes recommendations regarding the selection of soil shear strength parameters and safety factors. Recognizing the limitations of limit equilibrium analysis, especially when applied to slopes comprised of materials posing different properties (i.e., soil and polymeric materials) and the potential for progressive failure, the following is recommended. The peak shear strength parameters of the soil should be used to determine the critical slip surfaces (i.e., the reinforcement layout).

REFERENCES Elias, V. and Christopher, B.R. 1997. Mechanically Stabilized Earth Walls and Reinforced Steep Slopes, Design and Construction Guidelines. FHWA Demonstration Project 82. Report No. FHWA-SA96-07 1. Huang, C.-C., Tatsuoka, F., and Sato, Y. 1994. Failure mechanisms of reinforced sand slopes loaded with a footing. Soils and Foundations, Journal of the Japanese Society of Geotechnical Engineering, 34(2), 27-40. Leshchinsky, D. 1992. Keynote paper: Issues in geosynthetic-reinforced soil. Proceedings of the Internutionul Symposium on Earth Reinforcement Pructice, held in Nov. 1992 in Kyushu, Japan. Editors: Ochiai, Hayashi and Otani. Published by Balkema, 87 1-897.

65

Leshchinsky, D. 1997. Software to Facilitate Design of Geosynthetic-Reinforced Steep Slopes. Geotechnical Fabrics Report, Vol. 15, No. 1, 4046. Leshchinsky, D. and Boedeker, R. H. 1989. Geosynthetic reinforced earth structures. Journal of Geotechnical Engineering, ASCE, 1 15(10), 14591478. Leshchinsky, D., Ling, H. I., and Hanks, G. 1995. Unified Design Approach to GeosyntheticReinforced Slopes and Segmental Walls. Geosynthetics International, Vol. 2, No. 5, 845881. Leshchinsky, D. and Reinschmidt, A.J. 1985. Stability of membrane reinforced slopes. Journal of Geotechnical Engineering, ASCE 111(1 l), 12851300. Tatsuoka, F. and Leshchinsky, D. 1994. Editors: Recent Case Histories of Permanent GeosyntheticReinforced Soil Retaining Walls, Proceedings of SEIKEN Symposium, held in November, 1992 in Tokyo, Japan, published by Balkema, 349 pages. Tatsuoka,F., Koseki, J., Tateyama, M., Munaf, Y. and Hori, N. 1998. Seismic stability against high seismic loads of geosynthetic-reinforced soil retainin structures. Keynote lecture, Proceedings of the 6 International Conference on Geosynthetics, Atlanta, Georgia, Vol. 1, 103-142. Taylor, D.W. 1937. Stability of earth slopes. Journal of the Boston Society of Civil Engineering, 24(3), 197-246. Yoshida, T. and Tatsuoka, F. 1997. Deformation property of shear band in sand subjected to plane strain compression and its relation to particle characteristics. Proceedings of the 141h International Conference on Soil Mechanics and Foundation Engineering, Hamburg, September, 237240, Balkema. Zornberg, J.G., Sitar, N. and Mitchell, J.K. 1998. Limit equilibrium as basis for design of geosynthetic reinforced slopes. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 124(8), 684-698. Zornberg, J.G., Sitar, N. and Mitchell, J.K. 1998. Performance of Geosynthetic Reinforced Slopes at Failure. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 124(8), 670-683.

a

66

Slope Stability Engineering, Yagi, Yamagami & Jiang fi 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

The mechanisms, causes and remediation of cliff instability on the western coast of the Black Sea Mihail Popescu Depurtnient of Geotechnicul Engineering, University of Civil Engineering, Buchurest, Romuniu

ABSTRACT: The large landslides along the Romanian shore of the Black Sea are well known instability phenomena. They are responsible for considerable economic losses each year and the severity of the problcm increased in recent years as increased scarcity of land forced utilization of inherently unstable areas. An important feature of these landslides is the presencc of a structured overconsolidated red clay underlying a loess layer at the ground surface. The sliding phenomena evinced by the red clay along the cliff of the Black Sea in Romania are developing cyclically, in time and space, with periods of attenuation and intensification. As the cliff front is unloaded by the sliding of the material previously fallen in, increasing shear stresses are developcd, causing clay dilatancy and its yielding by intense moistening. As the displacement of the sliding rnass increases, the mobilized shear strength of the red clay progressively decreases from its peak value to the residual one. The paper reviews the basic mechanisms involved in the instability phenomena of the Romanian shore of Black Sea. Back analyses of some slope failures in the iirea performed in order to asses the shear strength parameters mobilized along the sliding surface are presented and the results are compared with laboratory experimental data. Finally, the remedial works and associated design principles which take into account the causes, the extent and evolution of the landslide phenomena are discussed. slope to become unstable and the processes which triggered that movement. Only an accurate diagnosis makes it possible to properly understand the landslide mechanisms and thence to propose effectivc remedial measures. The computed value of the factor of safety is a clear and simple distinction between stable and unstable slopes. However, from the physical point of view, it is better to visualize slopes existing in one of the following three stages: stable, marginally stable and actively unstable. Stable slopes are those where the margin of stability is sufficiently high to withstand all destabilising forces. iWurginully stuble slopes are those which will fail at some time in response to the de stabilising forces attaining a certain level of activity. Finally, aclively zinsluble slopes are those in which destabilising forces produce continuous or internii ttent movement. The three stability stages provide a useful framework for understanding the causal factors of landslides and classifying them into two groups on the basis of their function: 1 . Prepurutory causal factors which make the slope susceptible to movement without actually initiating it and thereby tending to place the slope in a marginally stable state.

1 DEFINITION OF A LANDSLIDE; CAUSAL FACTORS AND REMEDIAL MEASURES Within the framework of the United Nations International Decade for Natural Disaster Reduction, the International Union of Geological Sciences has established a Working Group on Landslides (abbreviated IUGS WG/L) which is assisting the creation of a World Landslide Inventory. This has proposed a standard terminology for describing landslides; thus a working definition for a landslide is "the movement of a mass of rock, earth or debris down a slope" (Cruden 1991). The basis of the Inventory is the "Landslide Report", which includes aspects both of causes and of remediation for landslides. At the national and world centers, analysis of the landslide inventory data is expected to provide valuable information concerning their spatial distribution and their seasonalAong term patterns of behaviour. The successive movements of individual landslides will enable a more precise prediction of sites liable to failure in the future and their timing. "The processes involved in slope nioveinentc comprise a continuous series of events from cause to effect" (Varnes, 1978). When preparing a Landslide Report for a particular site, of primary importance is the recognition of the conditions which caused the 67

A particular causal factor may perform either or both functions, depending on its degree of acti\ it> and the margin of stability. Although it may be possible to identify a single triggering process, an explanation of ultimate causes of a landslide invariably involves a number of prcparatory conditions and processes. Based on their temporal variability, the destabilising processes J V : ~ ~ J be grouped into JIOWchanging (e.g. weathering. erosion) and fusi chcmging processes (e.g. esrihquake. drawdown). In the search for landslide causes. attention is oftcn fbcused on those processes within the slope system which provoke the greatest rate of change. Although slow changes act over a long period of time to reduce the rcsistancdshear stress ratio, often a fast change can be identilied as haviiig triggered movement. The IUGS WG/L Commission on Causes of‘ Landslides has prepared a short checklist of landslide causal factors arranged in four practical groups according with the tools and procedures necessary for documentation as illustrated in Table 1 . The format of the table lends itself to the creation of simple databases suited to much of the database management software now available for personal computers. The information collected can be coinpared with summaries of other landslides and uscd to guide further investigations and mitigative rncususes. Terzaghi (1 950) has written that “if a slope has started to move, the means for stopping niovenieiii must be adapted to the processes which started tlic slide”. Correction of an existing landslide or the prevention of a pending landslide is a function of a reduction in the driving forces or an increase in the available resisting forces. Any remedial measure iiscd must prokide one or both of the above results. The technical solution must be in harmony with the natural system, otherwise the remedial work will be either short lived or excessively expensive. In fact landslides are so varied in type and size, and always, so dependent upon special local circumstances, that for a given landslide problem there is more than one method of prevention or correction that can be successfully applied. The success of each measure depends, to a large extent, on the degree to which the specific soil and groundwater conditions are correctly recognized in investigation and applied in design. As many of the geological features, like the sheared discontinuities, are not well known in advance, it is better to put remedial measures in hand on a “design as you go basis”. That is the design has to be flexible enough for changes during or subsequent construction of remedial works. In order to help including relevant information in Landslide Report, the IUGS WG/L Comission on

able 1 A brieflist of landslide Lausal factooz -__ 1. GROUND-CSNDITION-S I ) Plastic weak rnatei ial 2) Sensitive material :3) Collapsible material :4) Weathered material ,S) Sheared material ;6) Jointed or fissured material :7) Adversely oriented mass discontinuities (including bedding, schistosity, cleavage) ,8) Adversely oriented structural discontinuities (including faults, unconformities, flexural shears, sediincntary contacts) :9) Contrast in permeability and its effects on ground water ( 1 @)Contrastin stiffness (stiff, dense material over pldbtic material) 2. GEO M0RP H(0LOC ICAL PROCESSES : I ) Tectonic uplift (2) Volcanic uplift (3) Glacial rebound (4) Fluvial erosion of the slope toe (5) Wave erosion of the slope toe (6) Glacial erosion of the slope toe (7) Erosion of the lateral margins (8) Subterranean erosion (solution, piping) (9) Deposition loading of the slope or its crest ( I @)Vegejat5io removal (byerosion, fore%t-fire,-drought) ~

3 PHYSICAL PROCESSES Intense, short period rainfall (2) Rapid melt of deep snow (3) Prolonged high precipitation (4) Rapid drawdown following floods, high tides or breaching of natural dams (5) Earthquake (6) Volcanic eruption (7) Breaching of crater lakes (8) Thawing of perinafrost (9) Freeze and thaw weathering (10)Shrink and swell weatherins of exgansLve soils

~-

-

(1)

-

4 MAN-MADE PROCESSES _ _ _ --( I ) Excavation of the slope or its toe (2) Loading of the slope or its crest (3) Drawdown (ofreservoirs) (4) Irrigation ( 5 ) Defective maintenance of drainage systems (6) Water leakage from services (water supplies, sewers, stormwater drains) (7) Vegetation removal (deforestation) (8) Mining and quarrying (open pits or underground gal er ies) (9) Creation of dumps of very loose waste (10)Artificial vibration (including traffic, pile driving, heavy _ __ machinery1 - ___ _

___

__ ____

-

___

--

-

2. Triggering causal jucfors which initiate mo\iement. The causal factors shift the slope from a marginally stable to an actively unstable state. 68

Table 2: A bt-ief list of landslide [syedjfinieastires 1. MODIFICATION OF SLOPE GEOMETRY I. 1. Removing material from the area driving the landslide (with possible substitution by lightweight fill) 1.2. Adding material to the area maintaining stability (counterweight berm or fill) 1.3. -Reducing general slope angle

the major categories. For example. while restrsint may be the principal measure used to correct a PHIticulx hidslide, drainage and modification 01‘ s ! ~ p e geometry. 10 s o x e degree and by nece Lit i l i d . Over the last s e ~ e r a decades l there has been a notable shift towards ‘“softengineering” non-.structui*ul solutions including classical methods such as drainage and modification of slope geometry but also some novel methods such as lime/cement stabilization, grouting or soil nailing. The cost of non-srructural reinedial measures is considerably lower when compared with the cost of structural solutions. On the other hand struct~ri~f solutions such as retaining walls involve opeiiing the slope during construction and often require steep temporary cuts. Both these operations increase the risk of failure during construction for oversteeping or increased infiltration from rainfall. In contrast. the use of soil nailing as a non-structural solulion to strengthen the slope avoids the need to open or al?er the slope from its current condition. Environmental considerations have increasingly become an important factor in the choice of suitable remedial measures, particularly issues such as visual intrusion in scenic areas or the impact on nature or geological conservation interests. This reporl is intending to discuss some problems related to causes and remedial measures of landslides along the Black Sea western shore in Romania as resulted from the work of the IUGS WG/L Commission on Causes of Landslides and the IUGS WG/L Commission on Landslide Remediation respectively, in the framework of the United Nations International Decade for Natural Disaster Reduction ( I 990-2000).

2. DRAINAGE__ _ ~ Surface drains to divert water from flowing onto the slide area (collecting ditches and pipes) 2.2. Shallow or deep trench drains filled with free-draining geoinaterials (coarse granular fills and geosynthetics) 2.3 Buttress counterforts of coarse-grained materials (hydro I og i ca I effect) 2.4 Vertical (small diameter) boreholes with pumping or self draining 2.5. Vertical (large diameter) wells with gravity draining 2.6. Subhorizontal or subvertical boreholes 2.7. Drainage tunnels, galleries or adits 2.8. Vacu~imdewatering 2.9. Drainage by siphoning 2. I0 Electroosmotic dewatering 2.1-!.LVege_etat con plantins (hydrolqg ical eff5cL) -3 .-RETA IN IN G - ~ T R U ~ TRU ES 3.1. Gravity retaining walls 3.2. Crib-bloch walls 3.3. Gabion walls 3.4. Passive piles, piers and caissons 3.3. Cast-in situ reinforced concrete walls 3.6. Reinforced earth retaining structures with strip/ sheet polymer/metallic reinforcement elements 3.7. Buttress counterforts of coarse-grained material (mechanical effect) 3.8. Retention nets for rock slope faces 3.9. Rockfall attenuation or stopping systems (rocktiap ditches, benches,fences and walls) 3 I O.Prgtec$veLock/concEE- blocks againsterosion 4,INTERNAL SLOPE REINFORCEMENT- 4 1 Rock bolts 4.2. Micropiles 4 3. Soil nailing 4 4. Anchors (prestressed or not) 4.5 Grouting 4.6. Stone or lirne/cement columns 4.7. Heat treatment 4.8. Freezing 4.9. Electroosmotic anchors 4.l~L~eg~,ti~n planting
2 SLOPE INSTABILITY MECHANISMS ALONG THE BLACK SEA WESTERN SHORE IN ROMANIA The eastern coast of Romania stretches approximately 2 10 km north from Constantza to south from Mangalia. Sarmat deposits are found at the cliff base while loessial collapsible soils form the cliff upper part. In some places the Quaternary loess reaches the beach. Starting from Mangalia towards south and continuing to Balcic and Varna in Bulgaria, the Sarmat is more frequently found on the beach. ‘The western edge of the Black Sea is a major seismic area where slope instability and landslides are common. Major landslides tend to occur throughout the Lower, Middle and Upper Sarmat (Miocene) sediments with the most spectacular large-scale failures tending to be of Neogene age. The large coastal landslides along the Black Sea shore in Romania are well known instability phe-

Landslide Remediation has prepared a short checklist of landslide remedial measures as given in Table 2. The measures are arranged in four practical groups, namely: modification of slope geometry, drainage, retaining structures and internal slope reinforcement (Popescu, 1996). The experience shows that while one remedial measure may be dominant, most landslide repairs involve the use of a combhation 01two or more of 69

nomena that evolve in time and space. There are many examples when the development of land has led to the reactivation or initiation of coastal landslides which have resulted in damage to property and services. An important feature of these landslides is the geological sequence including a red overconsolidated fissured clay underlying a loess layer at the ground surface. The underground water level is generally located at the base of the loess layer. The red clay is overlying a hard mar1 clay or limestone. The investigation of most landslides has shown that the basal slip surface is bedding - controlled and seated in the red clay layer. The cliff retreat follows cycles similar to those reported on the southern coast of England and on the northern coast of France (Hutchinson et al., 1991). Most prominent is the major cycle of a large, rapid landslide followed by slow erosion, but of importance is also the annual climate - driven cycle, causing large soil strength variations between spring, summer and autumn. In contrast to the longer time cycles of deepseated landsliding, the cycle of relatively shallow landslides tend to follow an annual, seasonal sequence. Loss of shear strength associated with swelling - shrinking cyclic events is responsible for many shallow failures that occur seasonally in culting slopes. Progressive slaking contributes to material weathering and increases its susceptibility to failure. Hard dried clods of red clay have been observed to rapidly and completely lose their shape due to slaking on immersion in water (Popescu, 1980). 'I'he geoinorphology of the landslides along the Romanian shoreline of the Black Sea suggests they comprise broadly a seaward system of compound landslides backed by a landward system of m~lltiple rotational landslides. The mechanism of rear scarp retrogression caused by successive landslips is illustrated by the cartoons in Figure 1. Continued erosion of the toe of the slopc results in a series of landslips. Each slide leeds to the removal of the lateral support of the main landslide blocks upslope, and progressively worsens the stability of the system. Each slope failure causes reduction of the lateral stress in its close vicinit3 which i n turn makes the red clay to meclianically expand and reduce its strength. Physical swelling is not possible in short term due to the low permeability of the clay. After a period of time, however, mater flows into the area, reduces the clay shear strength and causes further failure. Each slide leaves a steep rear scarp which rapidly degrades to a flattcr slope. The pile-up of debris on the rear of the main slide constitutes a loading which together with the generation of undrained porewater pressures, and the continuance of marine erosion at the toe, acts to destabilize the main slide, and cause further inovement. 70

Landslides in stiff fissured red clays are likely to be accompanied by volume increase at the failure surface. Field evidence shows that the equilibrium moisture content at the slip surface is gcncr~ally higher than that in the mass above or below it. l h c volume increase and associated moisture content increase at the failure surface are attributable to fhc folI owi ng factors : (1) mechanical expansion due to unloading by removal of the upslope lateral support; (2) shearing dilatancy where the mechanical behaviour of the red clay is brittle; (3) physical swelling due to water flow into thc areas undergoing mechanical expansion or shearing dilatancy. While mechanical expansion and physical s.ive1ling are always present in the mechanism of cliffrctreat by landsliding, the shearing dilatancy is restricted to the areas where the mechanical behaviour of the red clay is brittle (dilatant), i.e. the brittlenes index IB > 0. In the areas where 113 = 0, the clay mechanical behaviour is ductile (contractant). If3 is a function of the effective normal stress and the clay condition (intact or previously sheared), and consequently varies significantly along a slip surface as illustrated in Figure 2. Although for first - time shallow landslides the shearing dilatancy might be a major contributory factor of shear strength reduction by moisture content increase it does not play any important role for deep seated reactivated landslides. Due to the slow intermittent nature of ground movement along the Black Sea coast and the lack of precise monitoring information it was not possible to relate landslide activity with rainfall events. However, there did appear to be a close relationship between phases of increased landslide activity and periods of heavy or prolonged rainfall and inferred higher groundwater levels. 3 PROPERTIES OF THE RED CLAYS The red clays of the Doubrodjean Plateau are some of the most peculiar soils of Southern Romania. They are rigid, fissured, high plasticity clays. Bedding planes and fissures form natural zones of weakness in red clays. As with other lithologies, red clays that have been subjected to tectonic stress suffered interbed movement which resulted in smooth, sometimes polished structures. The existence of these ctslikensides)) is sometimes ignored by practicing engineers, particularly as these structural features may well be obscured by the weathering of the near surface material. The slickensides act as preferential flow paths often leading to the weathering and softening of material adjacent to the discontinuities. Randomly oriented stress release fissures occur as a result of a decrease in loading in red clays. Reduced stress following natural erosion, excavation or

fissured inaterid: red overcoilsolidated clay (1.6) adversely orieiited mass discoritinuities: slip surface - bedding controlled (1.8) wave erosion of the slope toe (2.5) intense, slxort period rainfall (3.1) prolonged high precipitation (3.3) shrink and swell of expansive red clay (3.10) loading of the slope at its crest: urban development (4.2) water leakage froin services (4.9

PREPAIUTOIiY CAUSAL FACTORS

1

1

TRIGGERING CAUSAL FACTORS

1.6, 1.8,2.5,3.1,3.10, 4.2. 4.6

2.5,3.3

I

Figure I Possible development and causal factors of landslides on the Romanian Black Sea shore

landsliding allows red clays to swell and hydratc, thus facilitating further weathering adjacent to the fissures. Uessication cracks result from summer

drying of red clays but these rarely penetrate more than 1 m. Because of their very high plasticity and activity 71

Figure 2 Cliff retreat mechanism and shearing dilatancy

as well as their liability to volume changes, red clays exhibit a thick zone of weathering which often is disguised by the loess cover. In the deep zone of weathering, the red clay is fractured into blocks of the ni-domain. Approaching the surface, the blocks gradually diminish in size (dm - and cm - domain) while in the subsurface zone they are reduced to ((crumbs))(mm - domain). Figure 3 summarizes the plasticity characteristics of the red clay in Casagrande plasticity chart. Red clay belongs to high plasticity clay CH group that correlates well with the clay fraction percentage (37-84 Yo)and high amount of montmorillonite (36-64 %) detected by mineralogical analysis of the clay fraction (< 2 p). Shear strength of the overconsolidated red clay varies from an initial peak to a residual value as failure occurs, and as the complex of discrete minor shears become linked into a smooth failure surface. Under low effective normal stress the progressive preresidual shear displacement is accompanied by soil dilatancy in the failure zone. If the shearing tlilatant zone is put in contact with a source of gravitational water the clay adjacent to this zone hydrates and swells leading to further decrease in soil shear strength. No shearing dilatancy and assocjated physical swelling are observed after attaining the residual strength state. 'Thus the shearing dilatarlcy cf-

f'ects are important only for first - time slides in red clays. Drained direct shear tests with stress reversal have been performed to examine the differenccs between peak and residual strength of red clay. Brittlenss index values as high as 0.6 - 0.7 have been recorded under effective normal stresses ranging between 100 - 300 kPa. Based on the assumption that the fully softened shear strength of the red clay can be represented by the average peak value of a remolded sample, drained direct shear tests on remolded samples haire been performed. The difference between the residual and fully softened shear strength is illustrated in Figure 4 for two typical red clays. The measured residual and fully softened strength effective friction angle values are 13.4' and respectively 20.5' for the red clay with plasticity index 42 % and clay fraction 37 %, while the corresponding values for the red clay with plasticity index 58 % and clay fraction 62 % are 11.5" and respectively 18.2'. These values compares well wiih studies of overconsolidated clays worldwide based on correlation with plasticity index. With the availability of the ring shear apparatus it became possible to undertake relatively quick and accurate residual strength testing enabling to obtain a large number of points through which the residual

72

Figure 3 Plasticity chart of the red clays

Figure 4 Residual and fully softened shear strength of the red clays

73

analyses are believed to be reasonable estimates of the average field strength of the red clay which forms the basal slip surface. In most landslips, the proportion of slip surface involving the upper loess layer is small and thus the back calculated shear strength parameters of the red clay are not very much affected by the values assumed for the loess shear strength parameters. Two dimensional static back analyses in ternis of effective stresses have been carried out for seiw'il sites wliere landslides occurred and relevant i nfbrmation was available. Figure 6 presents the d a a from a landslide in Constantza city area (Popt-scu et al., 1991). Both shear strength parameters h a w been simultaneously back calculated from the fo!lowing two requirements: (i) the safety factor was equal to unity, and (ii) the safety factor was niiiiimum for the given failure surface and the slope urlder comideration (Popescu, Yaniagami, 1994).

failure envelope can be drawn. This put into evidence the existence of a curved part of the strength envelope at low effective normal stress. Figure 5 shows the results of a series of ring shear tcsts performed on red clay samples at effective normal stresses less than 120 kPa. As the failure envelope is curved it appears that the assumption C'r = 0 is only applicable to tests carried out at very low normal stress and it is unrealistic when CDr' is obtained from the straight line section of the envelope. From the data presented in Figure 5 it results that the residual strength Parameters are C'r = 0 and @'r = 16.5' for shallow slips (0' = 30 kPa), C'r = 3 kPa and @'r = 12.5' for intermediate depth slips (U' = 70 kPa) and C'r = 5 kPa and @'r = 9.5' for deeper slips (0' = 110 kPa). As there is no unique it does not seem realistic to correlate the value of residual shear strength with the plasticity index. It is to be noted that the ring shear tests generally resulted in a lower value of the residual friction angle for deep slides corresponding to large effcctive normal stress when compared with the multiple reversal shear box. @Ir

Several factors concerning the investigated lmdslides introduced a degree of approximation into llie performed stability computations namely: (1) the slip surface is almost always known in only few points from its trace 011 ground surface and frnni slickensided surfaces and paleontoligical discoiitinuities found i n the borings; (2) the data con-. cerning the pore water pressure on the slip surf'dce are generally few and irnprecisc. Despite these uncertainties, the results of the stability back analyses are fairly consistent and agree reasonably well with the laboratory residual shcar strength data. The range of the back calculated shear strength parameters, resulted from foar investigated landslips, was c' = 3-15 kPa and respectively @'-10.2°-13.8", that draw attention on the effectiveness of drainage as a method of stabilization of landslides in red clays.

4 S1,OPE INSTABILlTY BACK ANALYSIS Post-failure investigation of landslides is potentially the niost fruitful means of advancing our knowledge in slope stability field. A landslide can reasonably be considered as a full scale shear test capable to give a measure of the shear strength mobilized at failure along the slip surface. In many cases, back analysis is an effective tool, and sometimes the only tool, for investigating the strength features of a soil deposit. However one has to be aware of the many pitfalls of the back analysis approach that involves a number of basic assuniptions regarding soil homogeneity, slope and slip surface geometry and pore pressure conditions along the failure surface. A position of total confidence in all these assumptions is rarely if ever achieved. Back analysis is of use only if the soil conditions at failure are unaffected by the failure. For example back calculated parameters for a first-time slide in a stiff overconsolidated clay could not be used to predict subsequent stability of the sliding mass, sincc the shear strength parameters will have been reduced to their residual values by the failure. The most important application of back analysis consists in proper design of remedial measures. It is generally assumed that the errors involved in the back analysis of a given slope failure will cancel-out by applying the back calculated shear strength in further limit equilibrium analyses of remedial measures and design new slopes in the same area. The scale of the landslides occurring along the Black Sea Romanian coast is such that the back

5 REMEDIAL MEASURES When designing landslide remedial measures it is of primary importance to recognize the conditions that caused the slope to become unstable. Landslide causal factors can be separated into two broad groups: preparatory and triggering. Three main preparatory factors have been identified for the vast majority of landslides along the Black Sea shore in Romania, namely (Popescu, 1996): the recession of the coastal cliffs, the construction and development activities in the area, and water suppiy/sewage network leakage. The primary triggering factor iniliating movement has been reported to be prolonged and/or intense rainfall. By considering various causal factors it was felt that the following approaches to stabilization are likely to have a positive effect: (1) Prevention of marine erosion by extending and 74

Figure 6 Example of a back analysed landslide in Constantza city area

ing variolis retaining works. Wave crosion at sea level tends to remove toesupporting laiidslide debris and steepen the slopc: profile, so leading to decreased stability. In order to protect the cliff toe against marine abrasion new sea defences consisting of cast-in-situ gravity retaining walls and precast reinforced concrete crib walls have been carried out as illustrated in Figure 7. Although very important. toe protection is rzre; sufficient to prevent further cliff - top recession or slope displacernsnt. Groundwater seepage from a

upgrading the existing sea defences along the ci iff toe. ( 3 ) Limiting the unfavourable effect of the groundwatedprecipitation conditions by providing appropriate drainage systems and monitoring the water supply network to identify areas of leakage where pipes need to be either repaired or rep 1aced. (3) Modification of the slope geometry by unloading its active ~ o n t ' and s loading the passive 2oncs. (4) Adding stabilizing h r c e to the slope by install75

Figure 7 Toe protection works against niarine erosion

taining walls. They are designed CO undertake the sloping ground thrust as well as to provide protection against marine erosion. which is the main cause of clifi retrogression in the area. 'The retaining walls provided with a special shaped "wave - breaking" face inighi be on spread foundation as illustrated 111 Figure 8 for Cosiinesti and Qlinip resorts area, where the liniestone bedrock is located near the ground surface, or on piled foundation as illustrated in Figure 9 for Mangalia resort area where the sound stiff mar1 layer is well bellow the sea level. In the areas of Constantza city and Eforie resort where the cliff height often exceeds 20-30 ni and the

boundary between the permeable loess top layei and the underlying impermeable red clay may cause oversteepening of the cliff top and softening of the lower cliff. Remediation engineering for the seepage problems of the parts of the coastal slope above wave height consists in a series of longitudinal and transversal open pit drains. In addition the whole slope is protected by planting trees viable in the near proximity of the sea. I n the area of Mangalia, Costinesti and Olimp rcsorls, where the apartment houses being located 011 the cliff top usually do not have more than two floors, the retaining works consist in 4-6 m high re76

Figure 8 Reta~ningnalls in Costinesti and Oliiiip area

zontal thrust diagrams corresponding to both situations and presented in figure 1 1b put into evidence that the resulting lateral forces are too large to be undertaken by the currently available retaining work systems The third option was to reduce the height of the apartment houses that would result in a corresponding decrease of the horizontal thrust within the sliding mass If the apartment house with groundfoor and 8-10 floors is taken as a comparison basis, a reduction in the house height by SO YO results in a 20 TOdecrease in the horizontal thrust as shown in Figure 1 l c The three design options presented in figure 11 are assuming that the apartment houses are on raft foundations A forth option was to build the apartment houses on piled foundations leading to a considerable decrease in the horizontal thrust to be undertaken by the retaining works In the 1950's an interesting innovation in slope stabilizing was carried out at the Black Sea coastal resort of Constantza Some 2 to 3 km of the coastal area, 30 to SO m high slopes and running at an angle of approximately 4S0, are composed of loess deposits mainly derived from Sarmatian sediments (shelly calcareous liniestones with a few shales). Smallscale slumping had caused problems to neighbouring housing developments, so a novel stabilization programme was undertaken The process entailed drilling vertical holes at horizontal distances of 5 to 8 m - the distance being de-

apartment houses being located on the cliff top might have groundfloor and 8-10 floors. the retaining works that should undertake large horizontal forces given by both earth thrust and house overload, consist of stabilizing piles bored through the sliding mass to the stable underlying material (Fig. 10). Distinct protection works against wave erosion are provided at the cliff toe. As the systematization plan of the city of Constantza required to place the apartment houses as marginal to the cliff edge as possible, diff'ereiit options have been considered as illustrated in Figure 11. In order to analyse these design options the back calculated shear strength parameters from slope failures in the area have been used to determine the internal horizontal thrust distribution within the sliding mass. Horizontal thrust distribution diagram provides information on the optimum location of the retaining works and the magnitude of the force that these works should undertake The first option was to place the apartment houses far enough from the cliff edge such as to provide the cliff slope with a minimum safety factor against sliding F = 1 3 The minimum distance between the cliff edge and the building front satisfying the requirement F =1 3 was found as large as 68 in (Fig 1 la) This was too large to be considered taking into accounl the city planing restrictions The second option was to level the cliff top by excavating the surfacial 6 m deep loess layer or to move the building front 10-12 m landward The hori77

Figure 9 Retaining walls in Mangalia area

termined empirically - over some 2 to 3 km of coast Natural gas mixed with oxygen was then ignited in the holes at a temperature of around 200°C This baked the surrounding sediments, “hardening” and increasing the strength of the cover The net-work of holes was then filled in and to date the hill slope has not moved (Stiinculescu, 1963\. ’The experiment was a “one-off’ and has not been repeated. Intensive housing development has occured in and around the slope with no evidence on any structural displacement being displayed. At the toe of the slope a new harbour development, with quays and jetties, has been finalised as Constantza is the main import/export harbour in Romania.

6 CONCLUDING REMARKS The causal factors that have contributed to the coastal landslides in the area of Constantza city have been grouped under two main headings: ( 1 ) preparatory and (2) triggering, as shown in the table

presented within Figure 1. By considering those factors which have contributed to the coastal land slides, a number of stabilisation approaches have been identified, as summarised in Figure 10. IJsing numbers selected from the checklists (Tables 1 and 2) provided by the IUGS WWL, rather than words, Landslide Reports can be compiled which are independent of language and thus more amenable to digital processing (Popescu, 1996). Much progress has been made in developing techniques to minimLe the impact of landslides along the Black Sea shore in Romania, although new, i n o x efficicn?, quicker and cheaper rnetlmls could well emerge in the future. Landslides may be corrected or controlled by one or any combination of four principle measures: modification of slope geometry. drainage, retaining structures and internal slope reinforcement. There are a number of levels ofei’fectiveness and levels of accepiability that may be applied in the use of these measures, for while one slide may require an iinmediate and absolute long-term correction. another may only require minimal control for a short period. 78

modification of slope geometry by reducing general slope angle (1.3) liirniting the urdavourable effect of precipitation/growndwater by appropriate drairiage system: surfixe drains (2.1) and shallow trench drains (2.2) planting the slope surface (2.11) preventing niaririe erosion by extending and upgrading the sea defence works: re t a b k g walls (3,I) a d protective rocMconcrete blocks (3.110) atldirig stabihhig force by passive piles (3.4) heat trcatriieIit (4.7)

I lLlOl)lFXCA?'ION OF SLOPE GEOMETRY DRAINAGE RETAINING STRUCTWS __ INI'Ii=RNAT,SLOPE REUVFORCEMENT ^ _ I _

Figure 10 Complex stabilization works i n Constantza city area

79

I

1.3 2.1,2.2, 2.11 3.1,3.4, 3.10 4.7

I

Figure I 1 Design options in building up apartment houses 011 the c!iff in Constantza city

80

Whatever the measure chosen, and whatever the level of effectiveness required, the geotechnical engineer and engineering geologist have to combine their talents and energies to solve the problem. Solving landslide related problems is changing from what has been predominantly an art to what may be termed an art-science. The continual collaboration and sharing of experience by engineers and geologists particularly in the framework of the United Nations International Decade for Natural Disaster reduction (1 990 - 2000) will no doubt move the field as a whole closer toward the science end ofthe artscience spectrum than it is at present. REFERENCES Cruden,D.M. 1991. A simple definition of a landslide. Bulletin IAEG, 43 :27-29. Hutchinson, J. N., Bromhead, E. N. & M. P. Chandler 1991. Investigation of landslides at St. Catherine's Point, Isle of Wight. Proc. Int. C'onf Slope Srahility Engg., Isle of Wight, 169-179. Popescu, M. 1980. Behaviour of expamive soils with a crumb structure. Proc. 4'" Ini C'017f' Expansive Soils, Denver, 1 : 1 5 8- 17 1 . Popescu, M. 1984. Landslides in overconsolidated clays as encountered in Eastern Europe. State-ofthe Art Lecture. Proc 4'" Int Symp Laiidslides, Toronto, 1 : 83-106. Popescu, M. 1991. Landslides control by means of a row of piles. Keynote Paper. Proc. Int. c'onf.. Slope Stability Engg., Isle of Wight, 361-366. Popescu, M., Chiroiu, M., Dragoniir, N. & A. Chiricii 1991. Instability phenomena and remedial measures along the North cliff of Constantza city. Ti.unspoi.tution Journul, 3-4: 7 1-79 (in Romanian with English and French summaries). Popescu, M. & T. Yamagami1994. Back analysis of slope failures. A possibility or a challenge ? Proc. 7'"Internutional IA EG Congress, 4737-4744. Popescu, M. 1996. From landslide causes to landslide reniediation. Special Lecture. Proc. 7"' h i . Symp. Lundslides, Trondheim, 1 :75-96. Stanculescu, I. 1'363. Sicherung der Gelanderutschung in Stadtgebiet von Konstantza, Wisscwschujiliche Zeitschrifi der Universitat Dresden, Heft 2. Terzaghi, K. 1950. Mechanisms of landslides. Geological Sociery of America, Berkley Voiume, 83-123. Varnes, D. J. 1978. Slope movements and types and processes. In: Landslides Analysis and Control. Ti.~~tn.s;i?"I.i~'tion Resecrrch Board Sjxciul Report. 176:11-33.

81

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami& Jiang (c) 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Design of slope stabilizing piles H.G. Poulos Cofley Geosciences Pty Limited, Sydney & University of Sydney, N. S.W ,Austruliu

ABSTRACT: This paper discusses a procedure for the design of slope stabilizing piles in which the resistance provided by the piles is assessed via an analysis of their response to lateral ground movements. The mechanics of such pile-soil interaction are discussed and it is shown that there are a number of modes of failure, involving yield of the soil and/or the piles themselves. For the ultimate case, a series of design charts are given to assist in the assessment of pile resistance. A conceptual approach for designing piles to limit slope movements is also presented. Finally, the application of the approach to two documented case histories is described. 1 INTRODUCTION One of the options for increasing the safety of potentially unstable slopes is to use stabilizing piles. Such piles have been extensively used in Japan (e.g. Ito and Matsui, 1975; Ito et a1 1979; Fukuoka, 1977; Broinhead, 1997), Europe (e.g. Sommer, 1977; Viggiani, 1981; Lippoman and Gudehus, 1985; Bandis and Tzaros, 1988) and North America (e.g. Merriani, 1960; Oakland and Chapman, 1984; Morgestern, 1982; Reese et al, 1992; Rollins and Rollins, 1992). Ito and Matsui (1 975) and Ito et a1 (1979,1982) have presented some solutions which illustrate the influence of various geometric parameters on the shear resistance generated by a pile in moving soil. Their solutions have formed the basis of some suggested methods of design (e.g. Popescu, 1991; Hassiotis et al, 1997). Model tests have been carried out in recent years to study more closely the effects of ground moveinents on piles (e.g. Poulos et al, 1995; Chen et al, 1997; Guerpillon et al, 1999), and these have helped to elucidate some aspects of pile behaviour. However, despite this work and the widespread use of stabilizing piles, methods of design are by no means well-established, and there remains an incomplete understanding of the mechanics of pile-soil interaction when soil flows past a pile or row of piles. The purposes of this paper may be summarized as follows: 1 to present a relatively simple framework for the design of slope-stabilizing piles

2 to describe an analysis which quantifies the response of piles to soil movements arising from slope instability 3 to discuss the mechanics of pile-soil interaction under lateral ground movements 4 to present a series of charts which inay be used for design purposes. Finally, application to two real cases is described, and comparisons are made between measured and observed behaviour of slope Stabilizing piles. 2 THE BASIC PROBLEM Figure 1 illustrates the basic problem being considered. A pile (which may be one of a number of piles) is located within a soil inass in which there is potential instability, with “unstable” soil to a depth of z, tending to slide over a deep layer of “stable soil”. The main issues are: i) to determine the forces and bending nioinents developed in the pile by moveiiient of the unstable soil to estimate the increase in stability of the ii) slope because of the presence of the stabilizing piles. The two issues are inter-related, since the increase in slope stability depends on the amount of shear force which can be developed by the pile at the level of the sliding plane and the position of tlie sliding plane will determine tlie shear force developed in the pilc.

83

3 DESIGN PROCEDURE FOR STABILIZING PILES The general design approach adopted follows closely that described by Viggiani (1981), Hull (1993) and Poulos (1995), and involves three main steps: 1 evaluating the total shear force needed to increase the safety factor for the slope (based on an analysis with no piles) to the desired value 2 evaluating the maximum shear force that each pile can provide to resist sliding of the potentially uiistable portion of the slope 3 selecting the type and number of piles, and the most suitable location in the slope. Step (1) makes use of the detailed results of the stability analysis. The actual safety factor Fa for the slope can be defined as follows:

where CR = sum of resisting forces along the critical failure surface; CFD = sum of disturbing forces along that surface. If the actual safety factor F" is less than the target safety factor, FT, the piles must provide an additional resistance AR, so that:

From equations (1) and (2), AR = CF,,(F, - F a )

(3)

This represents the stabilizing force, per unit width of soil, that must be provided by the piles, and can readily be calculated if CFD is extracted from tlie stability analysis results. It should be noted that the safety factor can also be defined in terms of the moments along the failure surface, rather than the forces e.g. Navfac (1986). The principle of the method is the same, regardless of the definition of tlie safety factor. For step (2), the most satisfactory procedure is to undertake an analysis in which the pile is subjected to soil movements which simulate tlie movement of a sliding mass of soil over a stable mass. Such analyses are discussed in the following section. Alternative approaches can be used to assess the relationship between safety factor and pile resistance, depending on the capabilities of the slope stability analysis used. These include: tlie inclusion of a lateral concentrated force within the soil, at the intersection of the pile and the critical sliding plane the inclusion of a stronger cohesive "lump" of soil, tlie strength of which can be related to the shear force developed by the moving soil acting upon the pile. a4

In both of these cases, the relationship between the factor of safety and tlie stabilizing force developed by the pile can be readily obtained. Guidelines for selection of the optimal location of piles in a slope are not well-established. However, there is evidence to suggest that, in order to be effective, stabilizing piles must have the following characteristics: they must be of relatively large diameter and relative stiffness they must extend well below the critical failure surface so that the failure surface is not merely shifted downwards below the pile tips with a factor of safety still less than tlie target value they should be located in tlie vicinity of tlie centre of the critical failure circle (or wedge, etc.) to avoid merely relocating the failure surface behind, or in front of, the piles. ESTIMATION OF SLOPE MOVEMENTS AFTER STABILIZING PILES INSTALLED In principle, it is possible to estimate the movement of tlie slope after stabilization by piles, if the following relationships can be estimated: 1 pile shear resistance (and hence improved factor of safety) versus soil movement 2 slope factor of safety versus soil movement. Figure 2 shows that tlie intersection of these two relationships gives the values of factor of safety and soil movement. Clearly, the larger the pile stabilizing force which can be developed for a particular soil movement, the smaller will be tlie resulting niovement of the slope. The first relationship can be established via a pilesoil interaction analysis, as outlined in Section 4 below. Unfortunately, there appear to be no wellestablished methods for estimating the second relationship and it would be necessary to adopt an enipirical approach. For example, it might be expected that such a relationship would take tlie following form:

F = 1.O

+ (F, - 1.O)e-""$

(4)

where F = factor of safety after stabilizing piles installed; Fo = minimum factor of safety which would result in no (or an acceptably "small") slope movement; ps= movement of slope after stabilization; k = an empirical coefficient. Unfortunately, there appears to be no systematic data which might enable the empirical coefficient k to be cstiniated. Tlie relationship betwcen pile shear resistance, V, and soil slope movement, p5,may be obtaincd from a pile-soil interaction analysis, as described in the following section. Tlie consequent factor of safety of

Figure 1. Basic problem of a pile in an unstable slope.

Figure 2. Conceptual approach for estimating slope movement after stabilization.

Figure 3. Model for piles in soil undergoing lateral movement.

the stabilized slope, F, can be obtained, e.g. from equation 2, as

ment, the following equation may be derived while the conditions of the pile-soil interface remain elastic:

(5) where CR and CFDare defined in equation 1, and CV = total shear resistance developed by piles per unit width of the soil, due to a specified slope movement Ps. An illustrative example of the utilization of this approach is given in Appendix A.

5 ANALYSIS OF THE PILE RESISTANCE It is assumed here that a pile in a potentially unstable soil mass is subjected primarily to lateral ground movements, although in general, there will also be a component of vertical ground movement acting on the pile. Thus, the basic problem is one of the response of a pile to externally-imposed lateral ground movements. Viggiani (1 98 1) has derived dimensionless solutions for the ultimate lateral resistance of a pile in a two-layer purely cohesive soil profile. These solutions, while being extremely valuable, are limited in the following respects: 1 they apply only to purely cohesive soils in which tlie cohesion of the unstable and stable soils is assumed constant with depth 2 they apply to the ultimate state only and do not give any indication of the development of pile resistance with soil movement 3 they are confined to a simplified representation of the distribution of soil movement with depth. A somewhat more versatile approach, which enables the above limitations to be overcome, can be developed by using a pile-soil interaction analysis in which the effect of soil moving past the pile can be considered at any stage of soil movement. Such an analysis has been described by Poulos (1 973), Poulos and Davis (1980) and Lee et a1 (1991) and makes use of a simplified form of boundary element analysis to obtain a solution. In this case, the pile is modelled as a simple elastic beam, and the soil as an elastic continuum. The basic problem is illustrated in Figure 3. The lateral displacement of each element of the pile can be related to the pile bending stiffhess and the horizontal pile-soil interaction stresses. The lateral displacement of the corresponding soil elements are related to the soil modulus or stiffness, the pile-soil interaction stresses, and the free-field horizontal soil movements. A limiting lateral pile-soil stress can be specified so that local failure of the soil can be allowed for, thus allowing nonlinear response to be obtained. By consideration of the compatibility of the horizontal movements of the pile and soil at each ele86

where [D] = matrix of finite difference coefficients for pile bending; [I]" = inverted matrix of soil displacement factors; KR= dimensionless pile flexibility factor = EI/EsL4; n =number of elements into which pile is divided; {Ap} = incremental lateral pile displacements; {Aps} = incremental free-field lateral movement; E1 = bending stiffness of pile; E, = average Young's modulus of soil along pile shaft; L = embedded length of pile. In addition, the horizontal and moment equilibrium equations, and the pile head and tip boundary conditions, may be expressed in terms of the displacements. After solving the resulting equations for the incremental displacements, the incremental pressures may then be evaluated from the equation of bending of the pile, and added to the existing pressures to obtain the overall pile-soil pressures. These values are compared with the specified limiting lateral pressures, and at those elements where the computed overall pressure exceeds the limiting value, the compatibility equation for that element is replaced by the pile bending equation which incorporates the condition that the lateral pressure increment is subsequently zero. The solution is then recycled until the computed lateral pressures nowhere exceed tlie limiting values. Allowance has also been made for limiting the bending moment within the pile itself to the yield moment, since nonlinear pile bchaviour can have a considerable influence on lateral pilc response (e.g. Kramer and I-Ieavey, 1988). A FORTRAN 77 computer program, ERCAP, has been developed to implement this analysis. Hull et a1 (1991) have described an alternative program, PALLAS (Piles and Lateral Loading Analysis) which uses a different formulation but gives cssentially similar results to ERCAP. Another alternative but similar analysis has been presented by Chow (1 986). The lateral response analysis requires a knowledge of the distributions of lateral soil modulus and limiting lateral pile-soil pressure with depth, and the free-field horizontal soil movements. For problems involving slope instability, a distribution of free-field soil movements such as that shown i n Figure 1 appears to be appropriate. This assumes that a large volume of soil (the upper portion) moves as a rigid body downslope. Below this is a relatively thin zone undergoing intense shearing in the 'drag zone'. The underlying 'stable zone' is stationary. The estimation of lateral soil modulus and limiting lateral pilesoil pressure will be discussed later in this paper.

6 MECHANICS OF PILE-SOIL INTERACTION Failure of a pile in a pile-reinforced slope will result from tlie interactions between tlie tliree components of tlie problem; tlie soil strength, the pile strength and tlie geometry of the problem. If tlie piles are also loaded by some external forces these too must be considered. Three modes of failure within the soil can be identified: 1 the “flow mode”, when tlie slide is shallow and tlie unstable soil becomes plastic and flows around tlie stationary pile 2 tlie “short-pile mode”, when the slide is relatively deep and the length of tlie pile in tlie stable soil is relatively shallow; the sliding soil carries tlie pile through the stable soil layer, and full mobilisation of soil strength in tlie stable layer occurs 3 the “intermediate mode”, when tlie soil strength in both tlie unstable and stable soil is mobilised along tlie pile length. Superimposed upon these three modes of soil failure is tlie consideration of tlie finite strength of tlie pile. Since failure of tlie pile in shear is unlikely, this leads to consideration of the “long pile” failure mode in which one or more positions along the pile are found to have attained the yield moment and then developed so-called “plastic hinges”. Tlie first attainment of tlie yield moment, My, (perhaps without fully mobilising the soil resistance) is possibly a more important practical consideration than the ultimate state of full mobilisation of pile strength, and will be considered here as the criterion for failure of tlie pile. More load could be taken by tlie piles but tlie pile itself is permanently damaged. Figure 4 illustrates the characteristics of pile behaviour for tlie flow mode, tlie short-pile mode, and tlie intermediate mode. The results are for a 15ni long steel tube pile with an external diameter of 0.5m and a wall thickness of 15mni. In the upper sliding zone, tlie soil is a clay with an uiidrained shear strength of 30 kPa, while in tlie lower “stable” zone, the undraiiied shear strength is 60 kPa. Tlie soil movement in tlie slide zone is assumed to be constant and no “drag” zone has with depth and equal to 0.41~1, been considered. The following observations are made from Figure 4: 1 the maximum shear force in tlie pile is developed at the level of the slide plane 2 for tlie flow mode, tlie maximum moment occurs below tlie slide plane, in tlie stable soil, and the pile movement is considerably less than the soil movement 3 for tlie short-pile mode, the maximum moment occurs well above tlie slide plane in the unstable soil, and tlie soil and pile movements are similar 4 for tlie intermediate mode, large moments are developed both above and below the slide zone, and

87

tlie pile head movement can exceed the soil movement. Figure 5 shows tlie dependence of tlie maximum shear force and bending moments (positive and negative) on tlie relative depth of tlie sliding unstable soil along tlie pile (z,/L). When the pile is elastic (i.e. does not yield), the maximum shear force is developed when z,/L is about 0.4, with tlie “interniediatc” mode being operative. However, for a yield moment of 0.94 MNm (representing a steel yield stress of 350 MPa), tlie “long pile” mode dominates over a wide range of values of z,/L, and tlie maxiinuin shear resistance is developed when z,/L is about 0.6. For three values of z,/L, Figure 6 shows the dcvelopiiieiit of the maximum shear forcc with increasing soil movement. In this case, for all modes of failure, tlie niaxiniuni shear is developed for a soil movement of about 60% of tlie pile diameter, or less. For tlie flow mode (z,/L = 0.2), a soil movement of only about 20% of tlie pile diameter is sufficient to develop tlie maximum shear force. Tlie pile response is essentially linear for ground movements of up to about 5 to 10% ofthe pile diameter. For a slide depth z, of 7.5ni, Figure 7 shows the effect of tlie embedment of tlie pile in tlie stable soil on tlie pile response. For enibednients of more than about 7.5111, tlic bcliaviour of tlie pile (flow mode) does not change, and it can be concluded that there is no benefit to be gained by increasing tlie pile length beyond this depth. It is interesting to note that the “critical” or “effective” length of tlie portion of the pile in tlie lower stable soil layer is (using the approach of Poulos and IHulI, 1989) about 7.4111. Thus, perhaps not surprisingly, for economical design, the pile length in tlie stable layer should not exceed tlie elastic critical length of tlie pile in that layer. Figure 8 shows tlie computed pile head movement as a function of tlie soil movement, for various depths of sliding soil. For shallow slide depths, where the flow mode is operative, tlie pile head movement stabilizes at a maximum value as tlie soil flows past tlie pile. However, for slide depths in excess of about 2.5177, the pile movement continues to increase with increasing soil movement, and may even exceed the soil movement for some slide depths (e.g. 6 to 911-1). Figure 9 illustrates the dependence of the niaximum shear force versus depth of slide relationship on tlie lateral soil movement p,. Also shown is tlie tlieoretical solution for tlie ultimate condition, derived from tlie equations of Viggiani (198 1). It can be seen that tlie numerical solutions tend to Viggiani’s solution as the lateral soil movement increases. For tlie flow mode of failure (z, 5 3111) and the short-pile mode (2, 2 13.5m), tlie ultimate condition develops at relatively small values of p5. However, larger movements are required to develop ultimate conditions for tlie intermediate failure mode.

Figure 4. Pile behaviour characteristics for various modes.

88

Figure 6. Effect of soil movement on maximum shear force developed on pile.

In general, it is found that the pile response is essentially linear for soil movements up to about 5% of the pile diameter. Ultimate conditions are developed in the flow and short pile failure modes when the soil 89

movement exceeds about 20% of the pile diameter. However, for the intermediate failure mode, soil movements in excess of 60% of the pile diameter may be required to develop ultimate conditions.

Figure 8. Pile head movement for different depths of soil movement.

Three important practical implications may be drawn from Figures 5 to 9: 1 the largest shear force occurs when the soil slide depth is between about 0.5 and 0.6 times the pile

length. The effect of yielding of the pile is to reduce the maximum shear force, especially for slide depths between about 0.25 and 0.9 times the pile length 90

where My = yield moment of pile section. The following characteristics can be noted from Figures 10 to 12: 1 as would be expected, the maximum shear resistance provided by the pile reduces as the pile yield inoinent reduces 2 the dimensionless pile shear resistance ( V ) decreases as z,/L increases (however, the actual value of V will generally reach a inaxiiiiuiii value for z,/L between about 0.4 and 0.6). The estimation of the ultimate lateral pile-soil pressure is discussed in the following section. An illustrative example of the use of the design charts is given in tlie Appendix.

2 the flow mode creates the least damaging effect of the soil movement on the pile; if problems involving protection of the piles are encountered, efforts should be made to promote this mode of behaviour 3 the intermediate mode develops the largest shear force and bending moment in the pile; hence, if the piles are being used to stabilise tlie slope, they should be designed so that tlie intermediate mode of behaviour occurs. This can be done by varying the depth of embedment of the pile in the stable zone in tlie analysis, until a maximum value of shear force is found. The soil failure mode will depend on the length, diameter and section of the pile, the strength and deformation properties of the pile material, the strength properties of the soils in the unstable and stable regions, the relative lengths of the pile in the unstable and stable regions, and the spacing between adjacent piles. It is possible to develop design charts which relate the resistance developed by piles to the above variables, as described below.

8 ESTIMATION OF SOIL PARAMETERS The key parameters required for a complete analysis of the lateral response analysis of a pile are: Young’s modulus of the soil E, limiting lateral pile-soil pressure pu Assessment of these parameters is usually made on the basis of: 1 correlation with strength properties of soil 2 correlation with insitu test data (e.g. CPT, SPT) 3 in-situ test measurements (e.g. via the pressuremeter of the dilatoineter) 4 interpretation of lateral pile load test data. A brief review of some correlations for E, and pU is made below.

7 DESIGN CHARTS FOR STABILIZING PILES The numerical analyses using ERCAP indicate that an ultimate condition is reached for ground movements in excess of about 60% of the pile diameter. As a design expedient, when it is not possible to carry out a complete site-specific analysis, useful design charts can be derived for the ultimate pile response to lateral moveiiieiits using the solutions of Viggiani (1 98 1). These solutions give the maximum shear force which can be developed by a stabilizing pile, regardless of the ground movements which act on the pile. Viggiani’s analysis considers a two-layer soil system in which the upper unstable soil layer can develop on ultimate lateral pressure (pUl)which is different from the value (pL,~) developed by the pile in the lower (stable) layer. Figures 10 to 12 give diinensionless curves for the maximum shear resistance V, for three values of pul/puz. In each case, the following dimensionless quantities are given: Dimensionless pile shear resistance:

8.1 Young’s modulus E, For clays, Young’s modulus E, is usually related o the undrained shear strength c,, as follows:

(7) Assuming a non-linear analysis is to be used, so that E, represents a secant modulus for relatively low load levels, the value of a1 typically lies between 150 and 400 (Poulos and Davies, 1980; Banerjee and Davies 1978; Decourt, 1991). For overconsolidated clays, Dccourt (1 99 1) suggests the following correlation with SPT value N: E, = 2 N (MPa)

V

-

V=-

(8)

For sands, it is customary to assume that the modulus varies linearly with depth, so that

P 1 dz , ,I

Dimensionless depth of sliding surface:

E, = N , , z

z, / L

where z = depth below ground surface. Typical values of NI, for saturated loose, medium and dense sands are 1.5, 5.0 and 12.5 MPdm respectively (Decourt, 1991). Kishida and Nakai (1977) relate E, to SPT value N as follows:

Dimensionless yield moment of pile section: -

M y =-

My

P I, 2 dz:

E, = 1.6N (MPa) 91

(9)

(10)

Figure 9. Influence of soil movement on shear development in a stabilizing pile.

Figure 10. Design curves for piles in two-layer laterally moving soil ultimate case: pu,-pu2= 0.5.

8.2 Ultimate lateral pressure p,,

large spacings or at very close spacings, the mechaIto and nism Of flow through the Piles Postulated is not the mode. In clay Soils, it usual to adopt a tota1 stress aPpoach in which pu is related to undrained shear strength as follOws:

It0 and Matsui (1975) have developed a theory for the flow of soil through a row of piles. The equations they have developed show that the limiting pressure py developed on a pile by the flowing soil depends on the strength properties of the soil, the overburden pressure, and the spacing between the piles relative to their diameter. Their equations are meant to apply for the portion of the piles in the unstable or moving soil. However, the equations are ,only valid over a limited range of spacings, since at

pit =

N~)Cil

(1 1)

where N, = lateral capacity factor. For a single pile, N, may be assumed to increase linearly from 2 at the 92

Figure 1 1 . Design curves for piles in two-layer laterally moving soil ultimate case: p , , , / ~=~1’.O. ~

Figure 12. Design curves for piles in two-layer laterally moving soil ultimate case: pl,Jpu2= 1.5.

ground surface to a limiting value of N, = 9 at a depth of 3.5 pile diameters or widths and beyond i.e.

N,

= 2(1+z/d) P

9

piles arranged parallel to the direction of soil movement the value of pu for the leading piles can be increased by up to about 40%, whereas “trailing” piles may have reduced pu values. Model tests by Guerpilon et a1 (1999) also imply that group effects may cause an increase in pile bending moments (compared to an isolated pile) and therefore (by iniplication) an increase in ultimate lateral pile-soil pressure. For piles in sands, the simplest approach is to use the suggestion of Broms (1 964) in which

(12)

where z = depth below ground surface; d = pile diameter or width. Theoretical studies by Chen and Poulos (1993) provide some indications of the influence of group effects on N,. Such effects may reduce N, if the piles are arranged in a line perpendicular to the direction of soil movement (typically by about 25% for piles spaced at 3 diameters centre-to-centre. For

I

P,, = a K % ,

93

(13)

Figure 13. Cross-section showing ground movements and location of shear plane.

Figure 14. Shear resistance of piles.

Figure 15. Displacement of pile with time.

where K, = Rankine passive pressure coefficient = tan2 (45 + $/2); $ = angle of internal friction of soil; ova, = effective overburden pressure; a = coefficient ranging between 3 and 5. 94

It is noted by De Beer (1 977) and Viggiani (1 98 1) that different values of the coefficients N, and a in Equations 11 and 13 may apply for the sliding and stable portions of the soil profile. Typically, the val-

ues in the stable soil have been taken to be those given in Equations 12 and 13 above, while the values in the sliding soil have been taken to be about half of those values. However, other than for the nearsurface effects, there appears to be no reason why such differences should exist. For example, if the sliding layer in a homogeneous clay soil is at a depth of 3 pile diameters, the average value of N, above the sliding surface (using Equation 12) would be about 5 , whereas below the sliding surface it would be 9. Thus, the near-surface effect would cause a reduction in pL,of about 45% compared to the case of deep embedment.

An analysis was also performed with inclined anchors located near the pile head. It was found that there was very little improvement in the shear resistance of the pile, despite the development of a substantial force in the anchor. Anchors were therefore not used in the pile wall design. The final design involved the use of two rows of 1.5m diameter piles with 13mm wall thickness, the first row at a centre-to-spacing of 2m, and the second at 4m spacing. The total cost of the remedial works was about C$2.38 million, of which almost half was for the supply of the steel piles. After construction, four slope indicators were installed in selected piles in the wall. Plots of deflection versus time for one of these piles are shown in Figure 15. A deflection of about 140m had occurred by the end of construction, with an additional deflection of about 30min in the ensuing year. In the slide mass downhill of the pile wall, there has been less than 20mm of displacement at the ground surface. Hence there are strong indications that the installation of the piles has been effective in improving the overall stability of the slope.

9 APPLICATION TO CASE HISTORIES

Beatton River Highway, Canada Polysou et a1 (1998) describe an example of the successful use of piles to stabilize a landslide 011 a section of highway in British Columbia, Canada. Construction of a highway remobilized a pre-historic landslide, causing ground movements of up to 5111. The sliding mass was 14oni wide by 2001n long, and movement occurred at a depth of 15-2oni. The method envisaged to stabilize the upper part of the slide mass and the highway fill was a pile wall, coilsisting of closely-spaced large diameter piles extending from ground surface at tlie toe of the highway fill to some depth below tlie shear toe. Figure 13 shows a cross section through the middle portion of the slide. Together with the slip surface deduced from slope indicator data and drill holes. The slip was essentially planar and was concentrated at a depth of about 1 1in, corresponding to the base of the pre-sheared very stiff clay with slicken sided shear surface. The design process involved the three stages set out in Section 3. It was decided that the stability of the upper portion of the slide was to be increased by 30% i.e. to raise the factor of safety to 1.3 on the weakest slip surface. It was deduced that such an increase in safety factor would require an additional shear resistance of 2.9 MN/m depth of wall. The ERCAP analysis was used by tlie author to analyze four types of steel pipe piles, with diameters of 1 to l S m , and wall thicknesses of 19 to 25mm. Young’s modulus of the soils was estimated via correlations with SPT values (Equation 8), while the ultimate pile-soil lateral pressures were taken as 9 times undrained shear strength for the clayey soils, 3 times the Rankine passive pressure for the gravel layer, and 20 MPa for the shale. Figure 14 plots the computed pile shear resistance versus pile length, for the four pile types considered. The maximum shear resistance increases as the pile diameter and yield moment increases, and reaches a maximum value for a length of about 24 to 26m.

Concrete pile in unstable slope Esu and D’Elia (1974) described a field test where a reinforced concrete pile was installed into a sliding slope. The slope consisted mainly of clay and the upper layer of 7.5m thick underwent lateral niovement. The test pile was 30m long, 0.79m in diameter and the bending stiffness (EI) was 360 MN.m’. The pile was instruinented with pressure cells along its shaft at depths of 5, 10 and 15ni below the ground surface and they were located on both the upstream face and the downstream face. An inclinometer was also installed inside the pile at the centre to measure the pile inclination and deflection. The measurements were carried out over a period of 8 months and the results showed that the stresses acting on tlie pile had increased gradually until the pile developed a plastic hinge at 1 lni below the ground surface. There was no information about the undrained shear strength and the ultimate soil pressure for the clay deposits. However, Maugeri and Motta (1991) analyzed tlie case and suggested that the undrained shear strength c,, might be 40 kPa, and the values of lateral ultimate soil pressure coefficient N, could be 3 and 8 for the upper moving soil layer and the lower stable soil layer respectively. Since their theoretical results compared fairly well with the measured results, these values were also adopted in the present analysis. To match the measured bending moment profile, two further assumptions regarding the soils were made in the present analysis: 1 the soil Young’s modulus E, increases linearly from zero at the surface to 16 MPa at the level of the pile tip (see Poulos and Davis, 1980)

95

Figure 16. Comparisons between the predicted and measured pile responses for test of Esu and D’Elia (1 974).

2 since the soil movement profile to cause the pile to yield was not reported, a uniform distribution of lateral soil displacement of 1 1Omm, from the

ground surface down to the sliding surface (7.51~1 below the ground surface), was assumed. The predicted and measured results are presented 96

in Figure 16. It can be seen that the measured bending moment profile is reasonably well predicted along the whole pile shaft, although the position of the maximum bending moment is predicted to be slightly higher than the measured. The shape of the shear force profile is seen to be very similar for both the predicted and the measured, and the value as well as the position of the maximum shear force is also in very good agreement (Figure 16c). Both the pile inclination and pile deflection profiles are in very good agreement between the predicted and the measured, as can be seen from Figures 16d and 16e. The pile portion above the position of the plastic hinge is seen to be affected significantly by the moving soil, with the pile head deflection greater than the soil movement at the surface, however, the lower portion of the pile remained essentially unmoved. Chow (1996) analyzed the same case using a method of analysis that is similar in principle to that employed herein. Chow used similar assumptions to those described above except that the Young’s modulus was taken to be 200 times the undrained shear strength. IHe obtained a similar measure of agreement with the measurements to that shown in Figure 16.

made of the ultimate lateral pile-soil pressure and the soil movement profile, the approach presented herein provides a reasonable method of designing slope stabilizing piles. ACKNOWLEDGEMENTS The author acknowledges the contributions to research in this area made by his colleagues and former colleagues at the University of Sydney, Dr T.S. Hull, Dr. C.Y. Lee and Dr L. Chen. Professor C. Viggiani kindly provided updated information on his equations, while Mr J. Sobkowitz provided detailed information on the Beatton River Highway case. REFERENCES Bandis, S.C. and Tzaros, S.C. 1988. Design of retaining concrete piles for stabilization of a slope at the Koutloumousi Monastery, Mount Athos, Greece. The Eng. Geol. of Ancient Works, Mons. and Hist. Sites, Ed. P.G. Marinos and G.C. Koukis, Balkeina, Rotterdam, I , 193-189. Banerjee, P.K. & Davies, T.G. 1978. The behaviour of axially and laterally loaded single piles embedded in nonhomogeneous soils. Geotechnique, 28 (3): 309-326. Broinhead, E.N. 1997. The treatment of landslides. Proc. ~nsh?. Civ. Engrs. Geofech. Enging, 125, April: 85-96. Chen, L.& Poulos, H.G. 1993. Analysis of pile-soil interaction under lateral loading using infinite and finite elements. Coniputers and Geotechnics, 15: 189-220. Chen, L.T., Poulos, H.G. & Hull, T.S. 1997. Model tests on pile groups subjected to lateral soil movement. Soils and Foundations, 37 ( I ) : 1-12. Chow, Y.K. 1996. Analysis of piles used for slope stabilization. lnt. Jnl. Nuin. Anal. Meths. in Geoinechs., 20: 635-646. De Beer, E. 1977. Piles subjected to lateral loads. Proc. Spec. Sess. No. 10, 9‘” lnt. Conf Soil Mechs. Fouridti. Eng., Tohyo: 1-14. Decourt, L. 1991. Load-deflection prediction for laterally loaded piles based on N-SPT values. Proc. 9’’’ PunAmerican Conf: Soil Mechs. Foirndn. Eng. Fukuska, M. 1977. The effects of horizontal loads on piles due to landslides. Proc. 10’‘’ Spec. Session, 9’’’ 1111. Con[ Soil Mechs. Foundn. Eng. Tokyo: 27-42. Guerpillon, Y . , Boutonnier, L.,Gay, O., Foray, P. & Flavigny, E. 1999. Modelisation physique et numerique de I’interaction d’un obstacle et d’un glesseineiit d’ epaisseur limitee. Proc. 12‘’’ Eur. Cot$ Soil Mechs. Foiindn. Eng. Amsterdam. Hassiotis, S., Chaineau, J.L. & Gunaratne, M. 1997. Design method for stabilization of slopes with piles. . J d Geol. crnd Geoenvir. Eng., A X E , 123, (4): 314-323. Hull, T.S. 1993. Analysis of the stability of slopes with piles. Proc. I I r i 1Asian Geol. Conj.‘,Singapore, 639-643. Ito, T., Matsui, T. & I-fong, W.P. 1982. Extended design method for multi-row stabilising piles against landslide. Soi1.s L U I ~ Foundations, 22 ( 1 ): 1 - 13. Ito, T. & Matsui, T. 1975. Methods to estimate lateral force acting on stabilising piles. Soils and Foundations, 18 (4): 43-49. Ito, T., Matsui, T. & I-long, W.P. 1979. Design method for the stability analysis of the slope with landing pier. Soils and Foundations, 19(4): 43-57. Kramer, S.L. & Heavey, E.J. 1988. Analysis of laterally loaded

10 CONCLUSIONS Piles provide a possible option for improving the stability of soil slopes. The interaction between the moving soil mass and the piles generates a shear force in the piles which tends to increase the factor of safety against failure. The maximum shear force developed in a pile is governed by a number of factors, primarily the shear strength of the soil above and below the potential slide plane, the depth of the slide relative to the pile length, and the structural strength (yield moment) of the pile. To be effective, stabilizing piles need to be of relatively large diameter and to have a high yield moment. The paper sets out a systematic approaih to the design of slope stabilizing piles, in which the shear force developed by each pile is calculated via consideration of the interaction between the pile and the moving soil. For general soil profiles, this interaction can be analyzed via a computer analysis such as ERCAP or that developed by Chow (1996). The dependence of the shear force on the soil movement can be computed from these analyses. For relatively simple two-layer soil profiles and ultimate conditions, the solution of Viggiani ( I 98 1) can be utilized, and design charts based on these solutions are presented in the paper. Comparisons between measured and predicted pile behaviour show reasonable agreement, and these indicate that, provided reasonable estimates can be 97

piles with nonlinear bending behaviour. Tramp. Res. Record 1/69, 70-74. Lee, C. Y . , Poulos, H.G. and Hull T.S. 1991. Effect of seafloor instability on offshore pile foundations. Can. Ceol. ,Jtil, 28 (5): 729-737. Lippoman, R. & Gudelius, G. 1985. Dowelled clay slopes: recent examples. Proc. I I"' It?/. Coi?f Soil Adech. Foundti. Etig., Sun Francisco, 3: 1269-1271. Maugeri, M. & Motta, E. 1991. Stresses on piles used to stabilize landslides. In Luiidslides. Ed. D. Bell, Balkema, Rotterdam: 785-790. Merriam, R. 1960. Portuguese bend landslides, Palos, Verdes Hills, California. Jtd. cfGeology, 68 (2): 140-1 53. Morgenstern, N.R. 1982. The analysis of wall supports to stabilise slopes. Applicutioti qf Walls to Latidslide Coiitrol Probletns. Ed R. B. Reeves, ASCE: 19-29. NAVFAC 1986. Soil mechanics. Design Manual 7.0 I , US Naval Facilities Eng. Command, Virginia. Nethero, M.F. 1982. Slide control by drilled pier walls. Applicatioti of Walls fo Latid.slide Coti/i.ol Proliletiis. Ed. R.B. Reeves, ASCE: 6 1-67. Oakland, M.W. & Chameau, J.L. 1984. Finite element analysis of drilled piers used for slope stabilization. ASTM, STP 835: 182-1 93. Polysou, N.C., Coulter, T.S. & Sobkowicz, J.C. 1998. Design, construction and performance of a pile wall stabilizing a landslide. Proc. Cat?.Geo,. Con6 Edmonton. Popescu, M.E. 1991. Landslide control by means of a sow of piles. Slope S/uhi/ily Etigitiecriiig. Thoinas Tel ford, London : 38 9 - 9 4 . Poulos, H.G. 1973. Analysis of piles in soil undergoing lateral movement. .Jiil. Soil Mechs. Foioidtis. Div., ASCE. Vol. 99, SM5: 391-406. Poulos, H.G. 1995. Design of reinforcing piles to increase slope stability. Ca17. Ceot. *JtiI. 32: 808-81 8. Poulos, H.G. & Davis, E.M. 1980. Pilefozmda/ioii ~1ti~1y.si.smid desigt?.John Wilcy and Sons, New York. Poulos, lH.G. & Null, T.S. 1989. The role of analytical geoniech an i cs in found at i on e i i g i n ee r i ng . Fo zmia/ioti Etigitieet.iti,q: Cin.ret71 Priiiciples uiid Pimlice. Ed. F.H. Kulhawy, ASCE, New York, 1: 485-499. Poulos, H.G., Chen, L.T. & Hull, T.S. 1995. Model tests on single piles sub-jectcd to lateral soil movement. Soils i i i d FOZiiiduliot7.s. 35 (4): 85-92. Reese, L.C., Wang, S.T. & Fouse, J.L. 1992. Use of drilled shafts in stabilising a slope. Stabili/y ~ i i i dPet:fi)riiiutice of Slopes atid Eiiibankinents - 11. Ed. R.B. Seed and R.W. Boulanger, ASCE, Vol. 2: 1318-1332. Rollins, K.M. & Rollins, R.L. 1992. Landslide stabilisation LISing drilled shaft walls. Ground A4ovet?zt~tsut7d S/ructzu~es. vol. 4, Ed. J.D. Geddes, Pentech Press, London: 755-770. Somnier, H. 1977. Creeping slope in a stiff clay. Proc. Spec. Session No. 10, 9'" In/. Conf Soil Adechs. Foiindti. Et7g. To/CJW:

113-1 18.

Viggiani, C. 198I . Ultimate lateral load on piles used to stabilise landslides. Proc. 10"' In/. CoiIf Soil Meclis. Fouiidti. Etigs. Stockholm. Vol. 3: 555-560.

APPENDIX A - ILLUSTRATIVE EXAMPLE The problem is shown in Figure AI, and involves a 22" slope consisting of a stiff clay layer (Clay I ) overlying another stiff clay layer (Clay 2), with a thin weak clay seam between them. It is assumed that sliding of Clay 1 on the weak clay seam may occur over a length of 30m, following cutting of a vertical 98

face in Clay I . For simplicity, it will be assumed that: 1 failure along the weak seam is governed by the effective stress strength parameters of the seam 2 failure in thin Clay 1 and Clay 2 will occur under undrained conditions 3 tlie water table is at the surface of Clay 2. An overall factor of safety of 1.4 is required for the slope, and if this is not achieved, then it will be stabilized by steel tube piles 10m long, 0.5m diameter, with a 15mm wall thickness. The yield moment of each of these piles is 942 kNm. If piles are needed, it is required to calculate the required spacing of the piles. It is also required to make an estimate of the movement of the stabilized slope. The factor of safety of the cut slope is computed first, using a simple planar failure mechanism along the weak clay seam. Using the parameters shown in Figure AI, the weight of the sliding mass, W, is W = 5 e 17030ecos22 = 2364.3 kN/m width of slope. The disturbing force along the slide plane is FD= Wesin 22 = 885.7 kN/m The resisting force is: R = W. cos 22. tan $ + cF 30 (where $ 5 = angle of friction of clay seam = 20');c = cohesion of clay semi = 5 kPa. R = 797.8 + 150 = 947.9kNlm. The factor of safety is therefore F R/FD = 1.070 This is less than the value of 1.40 required, and therefore stabilization with piles is required. For tlie calculation of the pile requirements to achieve the desired factor of safety, use can be made of the design charts in Figures 10 to 12. To estimate the ultimate lateral pile-soil pressures, use is made of Equation 12, with N, taken as 5 in Clay 1 and 9 in Clay 2. The ultiiiiate lateral pressures are therefore pk,1= 5 x 40 = 200 kPa in Clay 1, and pr12= 9 x 45 = 405 kPa in Clay 2. Thus, ~ ~ , l / pis, ~approximately l 0.5, and Fsure 10 can be used. Here, z,/L = 5/10 = 0.5, and M y = My/p,,IdzF2=942/200.0.5.5' = 0.377. From Figure 10, V = 0.60, and the inaxiniuni ultimate shear resistance which can be developed in the pile is V = V purd zs = 0.60 x 200 x 0.5 x 5 = 300 kN/pile. If a factor of safety of 2 is applied to this shear resistance, then tlie design pile shear resistance is 150 kN/pile. With pile stabilization, the shear resistance AR required (per metre width of slope) is given from Equation 3 as AR = Fr, (FT - F") = 886.7 (1.40 - I .07) = 292.6 kN/m (per metric width of the 30m length of slope.

If 3 equally-spaced rows of piles are used, as illustrated in Figure A2, then each row must contribute 292.613 = 97.5 kNlm. The required spacing sy across tlie slope is then

It is assumed in the above analysis that group effects are negligible. As indicated previously, group effects tend to increase the ultimate lateral pressure and hence the pile shear resistance. Ignoring group effects is therefore conservative from the viewpoint of slope stability. Having computed the required pile spacing, it is now required to estimate the slope movement that could be expected after stabilization of tlie slope. Following the procedure outlined in Section 4, it is necessary to estimate: 1 the relationship between pile shear resistance and slope movement, and from this, factor of safety of the slope versus slope movement from the viewpoint of the piles 2 tlie relationship between slope factor of safety and slope movement, from the viewpoint of the slope, for example from Equation (4). The first relationship has been computed via the program ERCAP. Tlie pile shear resistance versus slope movement relationship is shown in Figure A3. Tlie factor of safety with piles is given from Equation (5) as:

Table A l . Calculation of slope movement versus factor of safety for piles and for slope Factor of Slope movePile shear Factors of merit pS resistance safety (from safety (for MM kN pile viewslope) point) 0 0 1.07 I .50 5 22.3 1.12 I .48 10 44.8 1.17 1.46 20 89.5 1.27 1.42 50 186.8 1.49 1.32 100 246.1 1.62 1.20 140 266.5 1.67 1.14 200 28 I .4 1.70 I .08 250 286.6 1.71 I .05

Since the piles are spaced across the slope at 1.5m centre-to-centre, CR, CFv and CV are computed for a 1.5m wide “strip” of slope. Thus, CR = 1.5 x R = 1.5 x 947.9 = 1421.8kN CFD = 1.5 x F,, = 1.5 x 885.7 = 1328.5 kN Since there are 3 rows of piles along the 30m long slope, CV = 3V1, where Vl is the shear resistance of a single pile. Thus, F E 1421.8+3V,

1328.5

-

Vl 1.070 + 442.8

Table A1 tabulates the computed values of V1 for various slope movements and the consequent relationship between factor of safety and slope movement, from the point of view of the piles. This is plotted as Curve 1 in Figure A4. For the slope, it will be assumed (arbitrarily) that there is zero movement of the slope for factors of safety of 1.5, and that for a factor of safety of 1.05, the slope movement would be 0.25m. Thus, in Equation (4), F, = 1.50 and tlie exponent k is found to be -9.21. The resulting relationship between factor of safety and soil slope movement, from the viewpoint of the slope, is shown as Curve 2 in Figure

Figure A2. Arrangement of stabilising piles.

99

Figure A3. Computed relationship between maximum pile shear resistance and slope movement (from ERCAP Analysis).

Figure A4. Estiniation of movement of stabilised slope

A4. Curves 1 and 2 intersect at a slope movement of about 32mn1, and this would be the estimated slope movement for this configuration of piles. It should be noted that, from Figure A4, the computed factor of safety if the ultimate shear resistance of the piles is developed in excess of 1.70, which exceeds the design value of 1.40. This occurs because of the safety factor of 2 imposed on the computed ultimate shear resistance of the piles.

100

1 Geological and geotechnical site investigations

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Geoenvironrnental factors influencing the deterioration of shale in a rockslope A. M. Elleboudy Civil Engineering Department, Banha University, Cairo, Egypt

ABSTRACT : Rockfalls have been reported at the southwestern cliff of Mokattain plateau in the recent decades which endangered several buildings and damaged the main roadway bordering the western edge. Many gcoeiiviroiiineiital factors have led to rock deterioration and created unsafe condition for the traffic and structures in the vicinity of the cliff edge. An effort was inade to assess the factors that weaken and looseii the rock formation which is composed of lunestone interlayered with shale. Rehabhtatioii scheines for the damaged road and the affected structures near the cliff edge are demonstrated. Proposals for stabihzatioii of the rock slope through a iiuinber of feasible geotechnical solutions are discussed.

1 INTRODUCTION The author was involved in the gcotechnical Mokattaiii plateau since 1979 problems of (Ellebo~idy 1985) when a iiia-jor rockslide took place iiilioiit of' an iinportaiit hotel in the area and put it out of work (Fig. 1). This failure was l'ollowcd by several rockfalls at the western aiid southwestern cMfs that eiidaiigered several buildings aiid damaged the main roadway bordering the western edge. These failures had iieptivc impact on the public, land owners, local iiivcstoi-s. aiid thc urban devclopmciit of this special area which is privileged with its high altitude, open air, moderate weather, and its closcllcss to Cairo down town. Many geoeiiviroiiinental Factors contributed to rock deterioration aiid created an instability problem. N o satispactory solution has been iinplcineiitcd till now. The debate over the proposed solutioiis has delayed the execution of' any of them. This situation devaluated the properties aiid discouraged land owiiers aiid investors froin exteiidiiig their activities aiid dcvclopinciit projects. Thus, an effort was made to assess the gcoeiiviroiiineiital factors that weaken and looscn the rock inass at the edges and trigger the rockhlls in order to suggest the most suitable rchabhtatioii scheines aiid preventive measures.

Figure 1. Rockfall at the hotel locatioii

103

2 GEOLOGICAL SETTING Mokattain Mountain represents a notable plateau bounding Cairo south-eastwards with its highest point at an elevation of 2 131n above sea level. It is coinposed of thick succession of sedimentary ciirboiiates and argfiaceous rocks that belong mainly to middle aiid late Eoceiie. These include clayey inarl and shale layers interlayered with the basic limestone ineinbers. Near the top of this formation, limestone exists and servers as a cap. This layer is severely jointed and subjected to sluinpiiig aloiig cliffs. It is underlain by a thick shale member. The stratigraphic section is then coinposed of successive layers of hnestoiie and shale (El-Sohby & Elleboudy 1988). Jolliting is an important characteristic of the plateau. Some of the joint sets are closely spaced In a way that accentuates slumping aloiig the southern escarpineiit aiid in the vicinity of’ the faults. The iiitersectioiis between sets of joints occasionally give a blocky appearance foi- soine hnestoiie beds outcropping at Mokattain plateau. Faults have an important role 111 the developineiit of the present coiiliguration of the plateau. Moreover, they represent weak zoiies aloiig which inoveineiits caii be rejuvenated. They inaiiifcst vertical aiid horizontal displaceineiits. The layers of lunestone aiid shale show regional bedding direction slightly dipping towards the slope f x e .

3 THEPROBLEM Significant progressive deterioration of the rockslope has happened to the Mokattain plateau over the years. It was recently noticed after the urbaii developineiit of this area took place. At least four successive inajor rockfalls have occurred since 1960. A major rockfall occurred in 1979. The entire rock inass infront of‘ a f-jve-story hotel building has slipped taking with it a 50in wide lawn, and leaving the footing of the corner coluinii haiiging in the air. Aiier this incident the inaiii road bordering the western cliff started to deteriorate. Many parts of the road cracked and fell down the slope (Figs. 2,3). This deterioration was not given much attention at the design stage. The alternation in the physical and chemical properties of the rock inaterial due to exposure to uiiexpected geoeiiviroiiineiital factors that accelerated the dctc ri o rati o n was ii o t taken i i i to CO 11sidcr at io 11in the urban planning ofthe whole area. The initiation and propagation o f fractures was of particular

sigiiificaiice in the road surface breakdown and eventually led to major rockfalls along the edge of-’ the slope. The rate of slope deterioratioii and timing of consequent detachineiit of rock blocks and their separation froin the rock inass was difficult to predict quaiititavely. The rockfalls created a significant hazard to the road users aiid for pedestrians, thus it was closed waiting for a pragmatic solutioii to the problem. In a trial to assess the deterioration potential of the existing slope, the rating inethod suggested by Nicholson aiid Hencher 111 1997 was used. It included input parameters such as iiitact rock strength, inaterial weathering grade, discontinuity spacing, and discontinuity aperture. The input parameters of the rockslope was taken from previous research dolie by the author (Abouleid & Elleboudy & Hafez 1989) aiid applied to this criteria. Then it was converted to a rockslope susceptibility class after iiuinerical adjustments relating to adverse engineering, stress. aiid enviroiiineiital conditions. It gave a deterioration rating of ahiiost 60% which indicates a class of high susceptibility to Failure. The ciigiiieering classification of the rockslope deterioration inode was both blockfall and rockfall which preseiit a signilicant threat due to uiipredic t a b h t y aiid suddeii hill of large volume of materials. The lithostructural group was composite since the rock type was strong aiid weak strata represented by liinestoiie and shale respectively. They :ire subjected to diflkrciitial weathering leading to collapse of’overhangs with associated blockfall aiid occasional rockfall.

4 GEOENVIRONMENTAL FACTORS Most gcotechnical engiiiecrs 111 this country are used to build on sods and successf‘dly face the probleins encountered with different types of saturated and arid soils. However, the local experience with building on rocks is iiot as much since we don’t often have to build on inouiitainous areas. Morcovcr. when the urban developinclit ol Mokattaiii plateau has started decades ago. the designers did iio t visuahze the geoeiivu-onmental factors which should be taken mto consideration to achieve a safe and stable design for the long r~iii They thought that rocks with its high bearing capacity ,uid iicgligiblc compression would cause i i o problcin for low-rise structures even iicx the edge of the chf-f.It is true that the bcaruig capacity 104

Figure 2. Failure of the roadway pavement due to rockfdl of inost rocks with iniiiiin~undegree of induratioii varies between I400 kN/m’ and 7000 kN/m’ (Sowers 1976). However, inost surfdce rocks exhibit fdbric weaknesses and defects due to the destruction by weathering which reduces their strength (Hudson 1993). Moreover Peck (1976) stated that : “In coinparison to foundations o i i soil, those on rock L ~ S L I present L ~ ~ few difficulties if we exclude certain shalcs.” The dark gray fissile shale of Mokattain plateau consists of laminated heavily overconsolidated clay layers with seeins of sand, silt, and gypsum. The intersections of set of joints turned the top hnestoiic layer into a layer full of cracks aiid structural defects, or inore severely into separate blocks with random shapes (Fig. 4). The sewers and water supply networks were originally designed jli a primitive way relying on the low population of the area. Water loaded with carbonates from the dissolution of the liinestone itself, aiid suliltes and salts li-om defective sewer system percolates through the limestone cracks and joints to the uiidcrlyiiig shale. It reduces the shearing strength of both inarl and shale, and softens the shale. This process aloiig with the orientation of bedding planes when dipping towards the cliffs, create slip surfaces at the base of the lunestoiie blocks. Moreover. the expansive nature of the shale layers

Figure 3. Vertical crack in hnestoiie top layer 105

in close proximity of the slope area, added to the severity of the problem. Reviewing the above inentioiied Factors, it is obvious that the inost influential geoeiiviroiiineiital factor is the reinarkable change in moisture regime 111 such arid rocks. The seeping of water through shale layers towards the cliff greatly affected the integrity of the rock inass aiid altered the engineering properties of these water-sensitive layers. This fact was iiot clear at the design stagc. Hence, the urban planning lacked the necessary precautions against the adverse geoenvironinental conditions aiid resulted in Pacing this challenging pro blem .

5 REHABILITATION SCHEMES At the beginning, when the hotel rockfall occurred, a simple Llninediate solution was adopted. The structural members of the building were strengthened aiid rigidly tied together. The rock prolilc was raised by adding sand aiid boulders to bring it back up to grade. It was thought that replacing the f’alleii rocks by artificial enibanknient would substitute the lost lateral support. This solutioii did iiot improve stabhty, aiid the settlenient or tlie hotel continued. Thus, this solution failed to save the hotel or to stop further rockfall, and the hotel was abandoned. When rockfalls continued along the cM’f edge and endangered the main roadway and other buildings, a variety 01’ remedial ineasures were introduced to control the effect of the progressive deterioration aiid coinply with the eiiviroiinieiital planning requirements. It was clear that any solution should start with constructing a water tight, leakage-proof tanks, pipes, aiid sewer system to maintain the internal integrity of the shale layers aiid stop the seepage of water through the liinestoiie cracks. The repair strategy involved the following steps: - Removing the debris aiid scaling the cliff face froin loose rocks. - Exposing the surface of the hnestone aiid disclosing the pattern ofjointing. - Filli~igthe cracks aiid joints with cement mortar. - Treating the slots with grout injection. - Using rock bolts to preveiit the inoveineiit of the blocks that potentially would fail. - Placing a wire iiet above the surface of the roadway to restrict rockfall. The wire net should be anchored by grouted rods.

Figure 4. Detached lllnestoiic blocks at cliff edge is another important geoenvironinental factor that contributes to the problem. The shale exerts a rather high swehig pressure on the limestone bloclts upon the increase in inoisturc content (Ellcboudy 1985). The reinoval of the lateral confinement as a result of the preceding rockf:all encourages the expansion of shale in the lateral direction toward the cliff. Also, the increase of surcliargc load on the cliff edge due to construction of the road and tlie adjacent buildings enhances the inoveiiieiit in the horizontal direction towards the slope. The growth of gypsum crystals inay also add to the s w e h i g potential of shale. On the other hand, the seeping water inay dissolve the gypsum crystals aiid weaken the fabric of the shale strata. Thus, deterioration of shale, which includes progressive physical aiid chemical alternation of rock material, has the most adverse effect on the stability of the slope. Another important factor was the slope geometry. The high altitude and the steep angle contributed to the instabhty of the slope. Also, a stress factor, represented by the dyiiainic stresses imposed by blasting Ui limestone quarries

106

- Containing the upper loin of the cliff face with a wire mesh to reinforce the slope. - Coiistructuig a proper drainage system for the surface water to direct it away from the face of the slope. - Reducmg the slope angle by introducing benches and intermediate berms.

Foundations and slopes. 2 ; 1-21. Colorado, USA. Sowers, G.F. 1976. Foundation Bearing in weathered rock. Proc. Con$ on Rock Engineering for Foundutions und Slopes. 2 ; 32-42. Colorado, USA.

6 CONCLUSIONS The deinoiistrated rockfall problem is very challenging m inany ways. The plateau is high and steep, the cldf edge is long, aiid the treatinclit and iiiaiiiteiiaiice reyulreinents arc very costly. It was miportant to outliiie the most adverse gcociiv~oiiinental factors that threaten the stability of the slope in order to adopt the appropriate preventive measures. The proposed incasurcs will help i n controlhng the coiisequeiiccs oi deterioration of the 1-ockslopc by containment, 1 eiiif orcement, and protection. The p 1'0 p 0 scd 1-chd billt at10 11 pro lett 1s s t 111 under iiivcstigatioii by the authorities, and seekuig f o r government funds. Hopefully it will end the controversy over the best solution to the problem uid pi-ovide a safe aiid reliable treatment for the 1 ockf'lll

REFERENCES Aboulcid, A., A.M. Ellcboudy 8L H. Hal'cz 1989. Iinportmt aspects of Mokattam shale shearing strength. J O L ~ ~ I Iof'U ~ thr F u c i t l ~ ~ of' Engineering, Cniro Un Ellcboudy, A.M. 1985. Analysis 01' Mokattain 1-ockl'alls. Yroc. I I tli lnt. Conj: on SMFE. 4 : 232 1-2324. San Francisco, USA. El-Soliby, M.A. & A. M. Ellcboudy 1988. Instability of' iiatiiral slope in intcrbeddcd linestone and shale. Proc. 5th lilt. SJviip. on Lrii7dslitle.s. 12 1 - 123. Lausaniic, Switzerland. Hudson. J.A. 1993. Coiiiprelieiisive rock ciig in e e ring, 11rin cip les, 11r~ c tice Ce 11 je cts . New York: Pcrganion Press. Nicliolsoii, D.T. & S. Heiicher 1997. Assessing the potential for dctc ri o rat io 11 o 1' engineered rockslopes. Pi-oc. Int. Syinp. oii Enginec~riiig Ceolog?~ aiid the Eiivirontneiit. 1 ;9 1 1-9 16. Athens, Greece. Peck. R.B. 1976. Rock foundation for- striictures. Pi-oc. Colif: on Rock Engineering jbr

107

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami& Jiang @ 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Weathering mechanism and slope failures of granitic rocks in Southwest Japan - Effect of hydrothermal activities R. Kitagawa Faculty of Science, Hiroshimu Universig, Higashi-Hiroshima, Japan

ABSTRACT: This paper deals with the genetical relationship between the mechanism of decomposition of granitic rocks and occurrence of the slope failures distributed in Hiroshima and Shimane Prefecture with special reference to the effects of hydrothermal activities on the decomposition process of the granitic rocks. Decomposed granitic rocks have been strongly fractures and characterized by remarkable alteration to clay minerals at hydrothermal stage before weathering. The clay veins are generally developed in the granitic rocks, in particular in the decomposed parts. The existence of clay veins has significant effect upon occurrence of slope failures. The slope failures were often occurred in some areas where smectite formed by hydrothermal activity is formed remarkably in granitic rocks. 1 INTRODUCTION Studies of decomposed rocks are important to prevent the disasters such as the landslide and slope failures. Therefore,the decomposition of granitic rocks have been studied in various field such as pedology, geomorphology and civil engineering as well as in the fields of geological sciences. Nevertheless, the mechanism or process of the decomposition of granitic rocks have not been systematically explained yet. In the inner zone of southwest Japan, granitic rocks of Cretaceous to Palaeogene age are distributed widely and the rocks are characterized, in general, by common development of fractures and extensive alteration. The decomposition extends usually to the depth reaches more than hundred meters. While conducting the mineralogical study on the alteration mechanism of plagioclase in the granitic rocks, the author has found that clay veins or veinlets are commonly observed in the decomposed rocks (Kakitani and Kitagawa, 1977). These clay veins seem to have been formed by filling fissures and /or fractures developed in granitic rocks. Subsequent studies on the mode of occurrence, detailed constituent clay minerals and distribution of these clay minerals have revealed that clay veins are intimately associated with the post-magmatic activities, i.e., hydrothermal activities (Kakitani and Kitagawa, 1977; Kitagawa and Kakitani 1978a, b) . The constituent minerals of the host granitic rocks are, more or less, altered to clay minerals. It is to be noted that some clay minerals of the alteration mineralogical characteristics such as mineral species

and their paragenesis (Kitagawa, 1989). These facts suggest that the hydrothermal activities may play an important role on the decomposition. In addition, preferred orientations of fractures were formed under the regional stress field (Kitagawa and Okuno, 1983). On the other hand, many slope failures have been occurring in the granitic rocks during every rain and/or typhoon season. Some clay veins are often observed on the failured slopes of granitic rocks. Based on the mineralogical and geochemical studies of clay veins and clay minerals altered from plagioclase and geometrical analysis of fractures developed in the granitic rocks of Chugoku district, a systematic examination for the effect of hydrothermal activity on decomposition process of granitic rocks, will be described in the present, and also indicate that the existence of clay veins have the significant effect upon occurrence of slope failures in the granite regions.

2 MODES OF OCCURRENCE OF CLAY VEINS 2.1

Distribution of clay veins

The degree of the decomposition were roughly measured by the alteration degree of plagioclase in the granitic rocks. Clay veins develop considerably at the relatively more decomposed parts of the respective granitic rocks. The width of veins varies from one millimeter to one meter. In addition to the clay veins minerals, aggregates of clay minerals of replacement

109

(Lower I

upper P-t*

pari I

I

I

I

I

I

I

I

Figure 3 Schematic diagram showing variation of constituent clay minerals of clay vein plane are caused by the unloading (Hashikawa, 1985). The poles of the orientation of the microcracks were measured on both planes and results were plotted on the equal-area stereographic nets. As one example is shown in Figure lb. As seen in Figure, two district dominant directions have been confirmed. These directions are almost coincide with those of clay veins developed in the respective district.

Figure 1 Schematic diagrams of clay veins classified based on the characteristics of fractures.

2.3

Figure 2 Stereo diagram showing the prefered orientation of clay veins and microcracks in granitic rocks at one district, Hiroshima prefecture. origin which are aligned in certain directions resulting vein-like appearance will be also found. A continuous development of veins can be pursued more than several kilometers at least. These clay veins can be also pursued more than hundred meters in the vertical direction.

Constituent minerals of veins

The clay veins consist mainly of illite, smectite, interstratified mineral of mica and smectite, kaolin minerals associated with small amount of chlorite. Quartz is commonly associated with clay minerals and calcite and/or zeolite (laumontite, stilbite and heulandite) are occasionally found in the clay veins. Most of the clay minerals are composed of more than two kinds of clay minerals. It is to be noted that constituent minerals commonly change from the lower to the upper parts in the vertical direction of the veins. According to Kitagawa and Kakitani (1978a,b) and Kitagawa.( 1989), the main constituent mineral of the veins varies from illite to interstratified mineral of mica and smectite, smectite and kaolin minerals from the lower to the higher altitudes in the range between 400m and 800m (Figure 2).

2.2 Fractures developed in granitic rocks

3

Common developments of the clay veins in the granitic rocks may suggest that these fractures were formed in relation to the stress fields during the geological age as well as cooling process of the granitic rocks. Orientation of the fractures (clay veins) show in general certain preferred directions if the area is limited. Each district is characterized by two or three preferred orientations of the fractures (Figure la). Microscopic-microcracks developed in the constituent minerals of the host granitic rocks were measured on the oriented thin sections of parallel and perpendicular to the ground surface using an universal accepted that the microcracks developed on the vertical 110

CLAY MINERALS DERIVE FROM PLAGIOCLASE

Among the constituent minerals of the host granitic rocks, plagioclase is easily altered to clay minerals as well as biotite. In general, plagioclase alters to kaolin minerals under the weathering conditions in Japan (Nagasawa and Kunieda, 1970; Nagasawa, 1978). However, plagioclase in the granitic rocks of the district of the present study is often altered to illite, smectite and interstratified mineral together with or without kaolin minerals. Kaolin minerals, in general, are found mainly at the higher level, whereas illite and smectite at the lower level.

4 SLOPE FAILURES As typical examples, some districts where many slope failures were occurred are chosen to compare genetically the directions (strikes) between failured slopes and clay veins observed on the slope surfaces and/or their near outcrops. Each direction (strike) of clay vein and the strike of failured slope is indicated in Figure 3. As seen figure, both directions are similar to each other. Mite, smectite and kaolin minerals were formed in the failured materials (soils), in particular the dominant clay minerals is usually smectite.

Type 1 Total%,

Max:59.4%

Total:133, Max:22.6%

Figure 4 Strikes of the failured slopes and clay veins in the one district, Hiroshima Prefecture.

5 DISCUSSION One of the main purpose of this studies is to establish the significance’s of the hydrothermal activities on the decomposition of the granitic rocks. The clay veins observed in the decomposed granitic rocks have been distributed widely in Hiroshima and Shimane Prefectures. The complicated mechanisms of the decomposition process of the granitic rocks will be discussed from the two important view points, fracturing system related to the paleo-stress fields and clay mineralogy in relation to the formation conditions.

Type 5 Total:48, Max:45.8%

Figure .5 Histgram of strike of clay veins classified based on the mode of occurrence in one district.

shown in the figure, it is to be noted that one direction indicates bisectional direction of the other two. Moreover, the veins have characteristic conjugated features and accompanying slickensides occasionally. These facts strongly suggest that the veins are the shear fractures formed under the regional stress field of the district. Comparing fractures of clay veins with microscopic-fractures, it is suggested that both directions have been formed under the same stress field of the district.

5.2 Age of fractures

Concerning the formation ages of these fractures, KAr ages of illite obtained from clay veins will be 5.1 Fomtion mechanism of fractures useful. The data are taken from Ishihara et al. (1980) and Kitagawa and Kakitani (1981). The K-Ar ages First of all, it may reasonably be assumed that the clay of the host granitic rocks are also available (Kawano veins developed in the granitic rocks represent the and Ueda, 1%; Shibata and Ishihara, 1974). As is fractures which have been formed after the evident, the ages of clay minerals and those of granitic solidification stage subsequent to the ma,gnatic activity. rocks are identical with each other within the analytical Furthermore, a systematic fracturing pattern within error. The concordance in the ages indicates that the granitic rocks have been controlled by the stress fields clay minerals in the clay veins have been formed by of the representative district. the post magmatic activities of the host granitic rocks The fractures patterns of clay veins developed in of the respective districts. Therefore, fractures were the granitic rocks in Hiroshima and Shimane also formed just after the solidification of granitic Prefectures will be analyzed. The typical example of rocks. the analysis of the stress field is shown in Figure 2. In this district, the results of the orientation (strike) 111

5.3

Formation condition of clay minerals

The physic-chemical condition of the formation stage of clay minerals will be discussed based on the available data such as temperatures and sequence of mineral assemblages. Based on the results obtained by Kitagawa (1989), in spite of the previous researches on the formation of clay minerals under the weathering condition, present results strongly indicated the hydrothermal origin of the clay minerals. The decomposition of the granitic rocks can be represented by the amounts of clay mineral formation. It may be concluded that the decomposition of the granitic rocks is mainly the results of hydrothermal activities subsequent to the granitic activity as well as the weathering during the geological ages.

5.4 Relationship between slope falures and clay veins

As shown in Figure 4, the directions (strike) of slopes failured are almost same directions to the clay veins in each district. As shown in figure 4, both directions are almost same each other. These results strongly suggest that clay veins developed on the slope are one of the significance factors as to occurrence of slope failures. Smectite is mainly composed clay mineral in the veins developed in these districts. The typical profile of the slope occurred failure is schematically indicated in Figure 5. In these districts, strongly decomposed granitic materials (soils) are formed on the weakly decomposed or almost fresh rocks. On the slope some clay veins are developed as shown in Figure 5. Smectite was mainly and characteristically formed in the decomposed materials on the slope. Under the geological condition like this, the rain water saturate in the decomposed rock and expansion of smectite formed in both decomposed granite and veins with the water. Therefore, it is inferred that decomposed materials may easily separate from the clay veins and/or the boundary between decomposed materials and weakly or almost fresh rock, as shown in Figure S.

Figure 6 Schematical profiles of granite slope before and after slope failure. according to their geographical vertical positions. That is, the mineral sequence of illite---interstratified mineral----smectite-----kaolin minerals from the depth geological ages. To be noted that the clay minerals found in the host granitic rocks were formed during the same hydrothermal activity in more or less extend. The slope failures often occurred where smectite is mainly formed in the granitic rocks andor clay veins are composed mainly of smectite. Consequently, it is inferred that the hydrothermal activity has significant effect upon occurrence of slope failures.

6 CONCLUSION

Based on the results obtained in this study, the most possible decomposition process of the granitic rocks of the district will be explained: First, nearly vertical fractures and microcracks have been developed within the granitic rocks under the regional paleo-stress field of the respective districts after the solidification stage of the granite. The clay veins were formed filling the fractures by clay minerals from hydrothermal solution. The clay mineral species have been gradually changed 112

REFERENCES Hashikawa,K.( 1985) Studies on the planer fracturing of structures developed in the suficial part granite mass. Geol. rep. Hiroshima Univ. No.25, 1-37. Ishihara,S., Shibata, K,,Kitagawa, R. and Kakitani,S.( 1980)K-Ar ages of sericites from

the Chugoku district, Japan. Bull. Geol. Surv. Japan, 3 1,221-224. Kakitani, S. and Kitagawa, R.( 1977) Clay minerals in the veins and veinlets found in the granitic rocks of Hiroshima Prefecture. Mineralogical society of Japan, 13, Spec., 187-196. Kawano,Y. and Ueda,Y .( 1964) K-Ar dating on the igneous rocks in Japan (I), Jour. Japan Assoc. Miner. Petr. Econ. Geol., 51, 127-148. Kitagawa,R and Kakitani,S.( 1978a) The pale-green clay vein in the granitic rock at the Ondo-cho district, Hiroshima Prefecture. Jour. Clay Sci. Soc. Japan, 18, 1-10. Kitagawa, R. and Kakitani, S.( 1978b) The white clay vein in the granitic rock at the Hachihonmatsu district, Hiroshima Prefecture. Jour. Clay Sci. Soc. Japan, 1 8 , 3 1-39. Kitagawa,R.( 1989) Clay veins and clay minerals in the granitic rocks in Hiroshima and Shimane Prefectures, southwest Japan. -Effect of the hydrothermal activities on the decomposition of the granitic rocks-. Jour Sci. Hiroshima Univ. Ser.C, 8, 47-80. Kitagawa,R. and Kakitani,S.( 1981) K-Ar ages of mica clay minerals in clay veins found in granitic and rhyolitic rocks of Hiroshima Prefecture, Japan, Jour. Japan Assoc. Miner. Pet. Econ. Geol., 76, 176-179. Kitagawa,R. and Okuno, T.( 1983) Formation mechanism of clay veins found in granitic rock in Hi sashihi roshima district, Hiroshima Prefecture. Jour. Clay Sci. Soc. Japan. 23,45-60. Nagasawa, K. and Kunieda,K.( 1970) Geology and mineralogy of clay deposits in the Naegi district, Gifu Prefecture, Mining Geol., 20, 361377. Nagasawa,K.( 1978) A study on the formation and transformation of kaolin minerals, Rep. Earth Sci. Shizuoka Univ., 3, 17-33. Shibata,K and Ishihara,S.( 1974) K-Ar ages of biotites across the central part of the Hiroshima granite, Jour. Geol. Soc. Japan, 80,43 1-433.

113

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Site investigation of weathered expansive mudrock slopes: Implications for slope instability and slope stabilization Russell J. Maharaj Commonwealth Secretariat1 CFTC Expert, South Pacijc Applied Geoscience Commission, Suva,Fiji

ABSTRACT: This paper presents the results of a literature review and site investigations from Trinidad, West Indies, on the effects of weathering on slope instability in mudrocks and its implications for slope stabilization. The performance of mudrocks slopes decreases with weathering, through engineering time. In pyritic mudrocks, weathering produces acidic groundwater, which can lead to the precipitation of gypsum. Site investigations on slopes of these lithologies, from Trinidad, have shown that gypsum is commonly precipitated at geological contacts of intercalated and tectonically sheared pyritic and carbonate bearing mudrocks. Weathered carbonate rich mudrocks are fat clays, classified as CH, with in-situ densities of 16471900kg/m3, 52-92% clay, liquid limit up to 106%, clay activity up to 1.51, up to 88% montmorillonite, contains gypsum, free swell >10% and pH of 4-7.8. Weathered pyritic mudrocks are lean clays, classified as CL, with <40% clay, liquid limit of 40-50%, plasticity index of 22-24%, 18-34% montmorillonite, pH pf 67.5 and activity <0.80. The precipitation of expansive gypsum cause potential soil heave and slope instability on these slopes. Deccication of these soils is also significantly greater, lead to greater shrinkage, larger macropores and higher, negative soil suction. These increase potential groundwater infiltration during antecedent rainfall, and increase the susceptibility of these slopes and engineered facilities founded on them, to instability and failure. As a result, the characterization of these lithologies is very important during site investigations and selection and is useful for optimum ground control, remediation and improvement.

1 INTRODUCTION Mudrocks are common in the rock record and are frequently encountered in almost all civil engineering projects. Due to their high clay content, especially smectites, poor induration and sometimes overconsolidated nature, they are susceptible to high volume changes in response to wetting and drying (Taylor and Cripps, 1987). In addition, weathering of these rocks produce expansive clays and cause the development of hazardous ground conditions on shallow soils slopes. It is a well known that the performance of mudrocks slopes decreases with weathering, through engineering time. In construction projects, ground engineering problems often associated with these lithologies include soil and foundation expansion and shrinkage, frequently resulting in landslides. These all lead to failure of constructed and engineered facilities, incurring millions of dollars each year in

damage repair costs. In Trinidad and Tobago, damage repair costs, due to landslides exceeds TT $ l M each year. For a developing country, these costs are high, and can significantly impair financial allocations for developing projects within the domestic economy. To reduce the financial costs associated with landslides in weathered mudrocks, it is first necessary to characterise their geotechnical characteristics and engineering behaviour. This will assist in site selection for engineered facilities and guide the choice of methods for optimum ground control, remediation and improvement. Due to the variety of geotechnical problems frequently encountered in weathered mudrocks, considerable attention has been given to these material in the engineering literature. In this paper, the weathering characteristics and geotechnical behaviour of pyritidblack and glauconitic mudrocks are reviewed from significant publications in the geotechnical literature. The geotechnical implications

115

Figure 1A. Location of the study area; B- rainfall distribution and C- Thorntwaite soil moisture distribution index of weathering are discussed based on site investigations in weathered Tertiary pyritic, clacareous and glauconitic mudrocks from Trinidad, West Indies. Implications for slope instability and slope stabilization are presented. In addition, the strong geological control of mudrock properties and weathering are discussed. The study area is the Poole-Ortoire watershed/drainage basin, located in southeast Trinidad, between 10' and 10' 22' N and 61' and 61' 22' W, with an area of about 502 kmL(Figure la). It has a warm tropical climate, with a January-June dry season and a July-December rainy season. The study area has mean annual rainfall varying between 15002500 mm and variable soil mositure indices (Figure Ib and Ic). The depth to active deccication and heaving/active soil layers, varies between 1-2 m for zones 1 and 2 and 1-3m for zone 3 (Figure lc). Temperature varies from 17-35'C, with a mean daily range from 7-1 I'C.

2 METHODS Data were first obtained from a literature review. This was followed by site investigations of weathered mudrocks slopes. 23 hand-dug test pits were excavated to 3.5m deep and soils were described according to the Geological Society Working Party on Tropical Residual Soils (Anon, 1990a). Sample location, depth, surface elevation, slope, vegetation,

presence of gypsum crystals and bedrock were noted. 109 samples were collected from the 23 sites, sealed to prevent moisture loss and taken to the laboratory for testing. Soils were tested following guidelines of the ASTM (1 988). Granulometry; clay content; natural moisture; plastic, liquid limit and shrinkage limits; free swell and compaction were determined using Soiltest apparatus. Site investigation and laboratory data were then analysed in relation to mudrock weathering and slope instability. 3 GEOLOGY The study area is located on the Southern Lowlands and on the south flank of the Central Range and the north flank of the Southern Range Uplifts. The Central Range is a Late Cretaceous to Tertiary clastic and carbonate terrain. The Southern Range is a northeast trending line of upthrusted Miocene anticlines, while the Southern Lowlands is of late Tertiary to Pleistocene age. These rocks suffered intensive high angle normal faulting, overturned folding and thrust deformation, from the late Miocene to Pliocene. Contemporaneous southeast directed contractile deformation, tectonic transport and thrust deformation led to overturn folding and the development of a macroscopic asymmetrical synform in this part of the island (Kugler, 1959). The rocks of the study area are extremely diverse, varying from Lower Cretaceous mark and calcareous mudrocks, to Holocene alluvium. Black pyritic and

116

Figure 2. Geology of the study area. calcareous mudrocks are the most common lithologies, especially in the northern parts of the watershed. Black mudrocks containing pyrite include the Nariva, Brasso, Karamat, Moruga, Lengua and Morne L'Enfer formations. In addition, these formations also contain carbonaceous materials, including graphite and lignite. Formations with calcareous shales and marls include Cuche, Navet, Cipero, Brasso, Tamana and Lengua. Lengua formation is the only one with known gypsum. Glauconite is found in the Cuche, Brasso, Lengua and Morne L'Enfer formations. Together, these formations occupy more than 65% of the watershed area. Brasso and Lengua formations are the only ones with pyrite, carbonaceous and calcareous shales and marls. These mudrocks are highly weathered to produce stiff, acidic and expansive calcareous clays. Figure 2 shown the general geology of the study area.

4 MUDROCK WEATHERING Table 1 presents the geotechnical properties of pyritic and calcareous mudrocks. Mudrocks are generally very soft when weathered, but stiff and indurated in less weathered sections. They show low slake durability, as they disintegrate rapidly in the presence

of water and on continual surface exposure at landslide sites. They are usually iron stained, containing limonite and haematite, derived from the weathering of constitutent pyrite and glauconite. Iron staining is pronounced along stress relief cracks and discontinuities. Stress relief cracks are > 0.5 mm wide. Mudrocks contains numerous discontinuities, including joints, faults, bedding and lamination surfaces. These channel seepage, interflow and facilitate deep weathering. Typically grey-black calcareous and pyritic mudrocks, such as from Brasso and Moruga formations show yellow-red-brown limonite staining. These are common along shallow seepage zones, seen at landslide scarps. Seepage cause intense redbrown hematite staining of lower slopes. These stains suggest a high ferrous oxide content, which from these black mudrocks are derived from oxidised pyrite. The oxidation of pyrite is a complicated process. Ivarson (1973) notes that pyrite is oxidised in the presence of moisture to produce ferrous sulphate and sulphuric acid. Ferrous sulphate may become hydrated and react with water to produce limonite, which may oxidize to haematite. Ferrous sulphate may also combine with sulphuric acid and oxygen in soil air to produce ferric sulphate. Haematite is very abundant in weathered pyritic 117

Table 1. Properties of weathered calcareous and pyritic clays. Soil Properties Unified Classification Gravel, % Sand, % Silt, %O Clay, % Liquid limit, WI, % Plasticity index, PI, %O Shrinkage limit, SI, %O Skempton’s clay activity

Weathered BlacWyritic Mudrocks CL 1-10 20-60 10-15 <40 40-50 22-24

< 0.80

3

In-situ density, kg/m Rainv season moisture. % Dry season moisture, % Optimum moisture, %O Free swell, % Amorphous silica, YO Iliite, % Kaolinite, % Montmorillonite, % PH Calcium carbonate content,% 1 Unconfined compressive strength, kg/cm Cation exchange capacity (CEC), niilliequivalents/iOOg dry soil Saturated hydraulic conductivity, c d s e c

25-33 10-13

10-20 20-30 18-34 6.0-7.5 < 0.10 0.25-1.50

1 x10’7to i X io-*

mudrocks in the watershed, with between 5-16% of the soil mineral content. Further, haematite develops rapidly in excavations on exposure of limonitic soils with free air, evident from intense red-brown staining and also noted by Chenery (1952). Limonite staining is found in all weathered pyritic mudrocks, but in deeper, more saturated soil horizons. Since the above reactions lead to the formation of sulfuric acid, then soils weathered from strongly pyritic mudrocks should show strong acidity. In-situ measurements and wet chemical data show that the pH of these soils range from 4.0-6.5. Pyrite oxidation requires free air and water and therefore, is limited to shallow, more pervious weathered horizons. In the study area this is evident from the depth of soil staining and mottling, which is usually less than 3-4 m and particularly intense between 2.0-2.5 m deep. Seepage zones and discontinuity surfaces are the most common sites. Deeper layers will be oxygen deprived and possibly anoxic. Ferric suphate may be reduced further, with pyrite, to produce sulphur and ferrous sulphate. Sulphur produced may be oxidized to produce more ferrous sulphate and sulphuric acid (Garrels and Thompson, 1960 and Pye and Miller, 1990). In the watershed, diagenetic sulphur is abundant in Moruga and Morne L’Enfer mudrocks. Therefore, weathered soils in these mudrocks should be very acidic, confirmed by in-situ soil pH measurements (using a portable Soiltest pH meter) which show that weathered non-calcareous, pyritic mudrocks have pH’s between 4.0-6.5, while calcareous equivalents

Weathered Marls and Calcareous Mudrocks CI - CH 0 5 -22 1 0 - 18 52 - 92 65 - 106 46 - 71 12 - 19 0.679 - 1.51 1647 - 2010 31 - 4 3 1 2 - 18 23-31 1-9 1-3 20 - 35 8-35 20 - 88 4 - 7.8 0.2 - 12 1.25 - 3.25 20 - 80 1-2xIO.”

have pH‘s fiom 6.5-7.4 (Table 1). Wet chemical data from Ahmad and Jones (1969) and Government of Trinidad and Tobago (197 1) support these results, although they never gave reasons for such high acidity. Sulphuric acid produced by these reactions may enter seepage and react with other lithologies downslope. Inclusive of these are carbonate dissolution and gypsum formation within calcareous shales and marls. Evidence of carbonate loss was noted in these soils, which show that the percentage of CaCO, decreases rapidly from 10% at 1.0-1.2m deep to less than 3.3% in more shallow horizons. CaO and LOI (loss on ignition) percentage also show a similar trend. LOI reprsents free organic matter, which in these samples is largely derived from organic carbonates. These reaction may be more common and aggressive at faulted contacts and within intercalated pyritic and calcareous shales where acidic leachates can easily enter, e. g. Brasso formation. Such reactions in calcareous mudrocks with pyrite can cause a reduction in soil acidity due to the buffering action of calcite against sulphuric acid, e.g. a pH of 6.5-7.4 was measured in weathered calcareous and pyritic mudrocks of Brasso formation. Evidence of gypsum precipitation was found at two excavated sites, on unstable slopes, in the watershed, within the Upper Cipero formation, at a contact between acidic soils, pH 4-5, weathered from pyritic black shales and slighlty alkaline soils, pH 78, weathered from calcareous marls. At both sites, 3.0-4.5 m deep excavations of the weathering profiles in small hills cut during the beginning of the dry

118

season revealed euhedral crystals of gypsum, 1.5 cm long, 0.5-1.0 cm wide and 1 mm thick. These were found at 1.5-2.5 m deep. Immediately before and during the time of the study, rainfall was low which caused extensive development of deccication cracks on the cut surfaces. Careful removal of the outer 10 cm of soil from the cut surfaces revealed gypsum crystals. It is unlikely that this gypsum is the result of other processes, while the intense weathering of the shallow soil and bedrock horizons do not suggest that such crystals are of primary/bedrock origin. Adjacent weathering profiles also contained similar deposits. The occurrence of gypsum in relation to the above chemical processes have not been previously reported by former workers in Trinidad. Government of Trinidad and Tobago (1971) reports gypsum in soils weathered from non-calcareous clay shales (largely pyritic) in this and adjacent watersheds. While reasons for their occurrence was not given, analysis of the lithostratigraphy of their soil sample sites, with gypsum, show that they are found at tectonically shearedthrust fault contacts, of pyritic and calcareous mudrocks.

5 IMPLICATIONS FOR SLOPE INSTABILITY The precipitation of gypsum in tectonically sheared and intercalated mudrocks can lead to an increase in potential soil heave and increase the likelihood of slope instability under rainfall conditions. Since gypsum has a much higher swell potential than the original soil constituents, then the potential for long term slope instability is considerable. Site investigations have shown that the precipitation of this expansive sulphate in Trinidad is largely controlled by the presence and distribution of tectonic and geological contacts. Highly sheared lithologies, which are also highly weathered, are the most likely and favourable sites. This suggests a strong geological control on the precipitation of this expansive sulphate. Analysis of soil survey data from previous land capability studies (Chenery, 1952 and Government of Trinidad and Tobago, 1971) has aiso shown that slopes reported to have gypsum and also with a high landslide frequency and distribution are found within tectonically sheared and intercalated pyritic and calcareous mudrocks. This further supports the hypothesis that the precipitation of gypsum is geologically controlled. Based on the foregoing discussions, it is 119

plausible to infer the following regarding the identification of problematic slopes and unstable ground. Mudrock slopes which show all of the following combination of characteristics are the ones most likely to be affected by recurrent and long term slope instability. These include slopes which : 1. Have suffered intense tectonic shearing, 2. Contain intercalated pyritic and clacareous mudrocks, 3. Contain many discontinuities, 4. Are deeply weathered, 5. Are affected by seepage and interflow, 6. Are affected by significant deccication and shrinkage, 7. Receive high rainfall and 8. Suffer high seasonal soil moisture fluxes

6 CONCLUSIONS The weathering of pyritic mucrocks and the reaction; of derivative acidic leachates, with calcareous lithologies can cause the precipitation of gypsum. If both calcareous and pyritic mudrocks are present in adjacent areas, such as in faulted and sheared lithologies, then gypsum can be easily porecipitated. The precipitation of gypsum can increase potential soil heave, increasing the susceptibility of weathered mudrock slopes to failure during rainfall. Site investigations at excavated landslide sites, examination of the distribution of sites with reported gypsum and unstable slopes have shown that these sites have suffered intense tectonic shearing and contain intercalated pyritic and clacareous mudrocks. Precipitated gypsum can increase potential soil heave and expansion by up to 103% (Taylor, 1988). Ground heaving and landslides due the presence of gypsum is common at many road-sites in Brasso, Lengua, Nariva and Moruga mudrocks. Further site investigations are planned for unstable slopes in similar weathered mudrocks. These site investigations will be suplemented by in-situ and laboratory wet chemical analysis of soil constituents to determine soil chemistry and further geotechnical parameters. In addition, a programme of in-situ measurements of soil heave and shrinkage is also planned, for determination of the effective soil volume changes associated with seasonal moisture fluxes. These further investigations will assist in determination of in-situ behaviour of these weathered mudrock in this part of the island. Further, these data will be useful in selection of suitable slope

stabilization and remediation technologies for these and geologically similar areas.

ACKNOWLEDGEMENTS This work was supported by a Fellowship to the author funded by the Government of Japan and from research conducted at the Institute of Marine Affairs, Trinidad and Tobago. Field assistance by Peter Joseph and Hayden Chung are gratefully acknowledged. Writing of this paper was facilitaed by resources secured during tenure as a Commonwealth SecretariaVCFTC Expert at SOPAC, Fiji. The careful editing of the manuscript by Mrs. Penella C. Maharaj is gratefully acknowledged.

REFERENCES W a d , N.and Jones, R. L. 1969. Genesis, chemical properties and mineralogy of Caribbean grumusols. Soil Sci. 107: 166-174. Anon, 1990a. Tropical residual soils. Q. J Eng. Geol. 23: 1 - 101. ASTM, 1988. Annual Book ofASTMStandards. Soil and Rock, Building Stones; Geotextiles. Vol. 04.08. Philadelphia, ASTM. Chenery, E. M. 1952. Soils of central Trinidad. Trinidad, Government Printing Office. Garrels, R. M. and Thompson, M. E., 1960. Oxidation of pyrite in ferric sulphate solution. Amer. Jour. Sci. 158A: 57-67. Government of Trinidad and Tobago, 1971. Soil and Land Capability Study of Trinidad: Vols. 1-6. Trinidad, Government Printing Office. Hawkins, A. B. and Pinches, G. M. 1987. Cause and significance of heave at Llandough Hospital, Cardiff-a case study of ground floor heave due to gypsum growth. Q. J. Eng. Geol. 20: 41-57. Ivarson, K. C., 1973. Microbial formation of basic ferric sulphates. Can. Jour. Soil Sci. 53: 3 15323. Kugler, H. B. 1959. Geological map of Trinidad and geological sections, I : 100,000. 2 Sheets. Petroleum Association of Trinidad. Pye, K and Miller, J. A., 1990. Chemical and biochemical weathering of pyritic mudrocks in a shale embankment. Q. J Eng. Geol. 23: 365-381. Taylor, R K. and Cripps, J. C. 1987. Weathering effects: slopes in mudrocks and over120

consolidated clays. In: M. G. Anderson and K. S. Richards (eds), Slope Stability : 405445. New York, John Wiley. Taylor, R. K. 1988. Coal measures mudrocks: composition, classification and weathering processes. Q. J. Eng. Geol. 21 : 85-89.

Slope Stability Engineering, Yagi, Yamagami& Jiang (5-1 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Investigation of cut slope consisting of serpentinite and schist H. Kitamura, M.Aoki & T. Nishikawa I l b k m Geotech Company Limited, Yumuguchi, Jupur2

T.Yamamoto & M. Suzuki Depurtment of Civil Erigineeririg , Ymmguchi Uniwr yity, Uhe,Jupun

T.Umez& Department of'Ci\-il Engineering, Shirzshu UrziverJih; N u p n o , Japun

ABSTRACT A plan for the improvement of a public road was made regarding a hill which included slopes consisting of serpentinite and schist in the north of Ube-shi of Yamaguchi prefecture, Japan. In order to classify rock class for the stability analysis of these cut slopes, not only standard penetration tests, but also elastic prospecting, electric prospecting, and bore hole velocity logging were performed. Bore hole ring shear tests and direct shear tests were performed as well in order to evaluate the strength parameters of the weathered soils of both rocks. Based on these tests, an estimated classification of rock class of a cut slope was illustrated. The strength parameters of weathered soils used for a design of slope stability analysis was also proposed.

direct shear tests were performed on the weathered soils of both rocks. On the basis of these test results, a method of determining the relationship between rock class and P-wave velocity is suggested and a mode of estimating rock class of a slope is illustrated. The strength parameters of weathered soils used for a design of slope stability analysis are also proposed.

1 INTRODUCTION In a hill consisting of Sangun metamorphic rocks in the north of Ube-shi in Yamaguchi prefecture, Japan, a plan for the improvement of a public road was made. Due to the cutting of the slopes consisting of serpentinite and pelitic schist (hereafter called schist) in four steps, it became very important to examine the stability of the cut slopes. Furthermore, due to heavy rainfall during and at the end of the rainy seasons, cut slopes consisting of Sangun metamorphic in Yamaguchi prefecture have easily failed at not only very nearly this site but also other sites. The third author et al. have investigated the failed slopes and have described many properties of soils which were formed by the weathering of both rocks (Yamamoto et a1.1996 a & b, 1997 & 1998). Thus the weathered soils of Sangun metamorphic rocks have historically considered problematic. From the view point of the above, the examination of the following two issues in the cutting of slopes at the this site became necessary: 1) estimation the rock class of serpentinite and schist relating to the difference of the degree of weathering, and 2) determination the strength parameters of the weathered soils of serpentinite and schist. In order to address the first issue, not only standard penetration tests but also elastic prospecting, electric prospecting, and bore hole velocity logging were performed. In order to address the second issue, both in-situ ring shear tests and

2 IN-SITU GEOLOGY

As shown in Figure 1, the geology is composed of Sangun metamorphic rock consisting of serpentinite and schist which were formed during the Triassic period in Mesozoic (about 200 Ma year). In the narrow sense, Sangun metamorphic rocks are classified into Sangun-Renge, Suou, and Chizu metamorphic rocks according to formative year and process (Nishimura & Matsusato 1991). The Sangun metamorphic rock at this site is of Suou type. These serpentinite and schist are subjected to a penetration of granite and have hornfels structure. Namely, in the case of the schist shown in Photograph 1, a lot of biotite is observed. In the case of the serpentinite shown in Photograph 2, some serpentine have altered to olivine. Serpentinite e x i s t s only at the wedge of granite, and disappears in the north to the south direction in which schist is excelled. Areas of serpentinite and schist from a few meters to 10 meters wide are distributed alternatively in the 121

Figure 1. Investigated place and its geology.

Photograph I . Polarization - microscope photograph of schist under crossed nicols (qz, quartz; bt, biotite; pl, plagioclase).

Photograph 2. Polarization - microscope photograph of serpentinite under crossed nicols (ser, serpentine; 01, olivine).

east - west direction in a belt or a lens-like rock body. The boundary between both rocks inclines steeply in a northern direction. Most serpentinite observed at the outcrop is composed of hard massive rock. Serpentinite with a distinguishable foliated structure exists only at the edges of schist and ranges from about 10 meters to about 1 m width. Schist at the outcrop is altered to

weathered soil with a schistosity of 70 O in the northern direction.

122

3 INVESTIGATED ITEMS

As mentioned above, since this site has a very complex geology consisting of serpentinite and

Figure 2 (a). The distribution of N-value in depth on C line shown in Figure 1.

Figure 2 (b). The distribution of N-value in depth on E line shown in Figure 1. schist, it was thought impossible to understand its entire geology only by means of boring data. So, the following four in-situ tests were vigorously performed: 1)Standard penetration test (16 points) 2) Elastic prospecting (Total length:850 m) 3) Electric prospecting (Total length:850m) 4) Bore hole velocity logging (4 points) In order to obtain the strength parameters of the weathered soils, the following two shear tests were performed. 1)Bore hole ring shear test 2) Direct shear test Bore hole ring shear tests are said to be applicable to many soils and rocks such as clay, sand, and soft rock The details of the test apparatus and method have been described elsewhere (Yunoki et al. 1995 a & b). 4

RELATIONSHIP BETWEEN ROCK CLASS AND V,

As shown in Table 1, serpentinite and schist, and their weathered soils, respectively, were classified

Table 1. Rock class, average N-value and unit weight of weathered soil and soft rock. unit

Serpentinit

207

100 241

21.4 23.2

into C,, D, and D, classes according to N-value. Figures 2 (a) and (b) show the distributions of Nvalues in depth on C line and E line shown in Figure 1,respectively. Figure 3 represents the relationship between the P-wave velocity obtained by elastic prospecting (V,), and the P-wave velocity obtained by bore hole velocity logging (V,), for serpentinite and schist, and their weathered soils. As can be seen in Figure 3, no distinct relationship was observed between both velocities of both rocks’ P-waves because the test data are considerably scattered. Figures 4 and 5, respectively, show the (V,), and 123

Figure 3. Comparison of (V,), with (V,),. Figure 5. Variation of (V,), with geology and rock class.

Figure 4. Variation of (V,), with geology and rock class. Figure 6. Variation of resistivity with geology and rock class.

(v,), of serpentinite and schist, and their weathered soils according to rock class. It is seen in Figure 4 that the (V,), of both rocks and weathered soils increases when the rock class change in the order of D,-DD,-CL; namely, when the rock class becomes more conducive to slope stability. Furthermore, in case that the same rock class the (VJe of

serpentinite is smaller than the (V,), of schist. In contrast, it is found from Figure 5 that since the (V,),, of the C, class has become small, no distinct difference was dxerved between the (V,), of the C, and DH chsses. Bore hole velocity logging is

Figure 7. The distribution of estimated rock class for cut slope. 124

Table 2. Results of bore hole ring shear tests.

'eO

l4 '

14.1 , 18.0 3.0

Serpentinite Schist Schist Serpentinite Serpen-

D,

10

25.8

6.0

D, D,

35 50

17.0 26.5

13.0 25.0

D,

13

25.7

11.0

Table 3. Results of direct shear tests.

1

:i \

1 2

Serpentinite Schist

1 I

,

28.2 29.8

cd

(kN/m2) 7.0 7.0

Figure 8. Relationship between cohension and depth for weathered soils obtained from bore hole ring shear tests. the distinction between the D, and D,, classes. (V,& =2.0 km/s is a boundary value for the distinction between the D,, and C,- classes. On the basis of this, an estimated rock class classification of the cut slope (B line in Figure 1) was determined as shown in Figure 7.

1

Table 4. Strength parameters for a design. Rock class D, D,,

7

0'

C'

(kN/m3) 18.0 19.0

()

(kN/m2)

25'0 29.5

-

c'=D(Depth)

carried out by packing loose sand around the pipe, and this may affect test results. Figure 6 shows the relationship between the resistivity obtained by electric prospecting and rock class. As seen in this figure, the resistivity of both rocks and their weathered soils was very low, and the relationship of resistivity and rock class, for schist, is not so distinguishable as compared with that for serpentinite. As seen in the above results, the classifications of geology and rock class in areas with no boring data were determined as follows: 1) Because there exists no distinct difference of The (V,), between serpentinite and schist, and their weathered soils, both rocks were treated as the same rock class. 2) (V,),=l.O - 1.5 km/s is a boundary value for

5 STRENGTH PARAMETERS WEATHERED SOILS

OF

Table 2 shows the internal friction angle (,!I' and cohesion c' of weathered soils obtained by the bore hole ring shear tests carried out at each bore hole. Their N-values are also shown in this table. As mentioned before, bore hole ring shear tests could be applicable for various soils. This in-situ soil corresponds to the D, class. As can be seen in Table 2, in the case of weathered soils of serpentinite, @ ' ranged between 22.5 - 25.7" , and c' ranged between 3.0 - 11.0 kN/m2. In the case of weathered soils of schist,@' ranged between 17.0 - 30.2" and c' ranged between 1.0 - 25.0 kN/m2. 0 '=17.0" of weathered soil of schist at a depth=14.1 m of Bor.No.14 is remarkably small as compared to other values. Except for this (b '=17.0 " , (b ' values of weathered soils of serpentinite and schist existed within a comparatively small scattering. In contrast, c' values of both weathered soils existed over a wide range. In the case of weathered soils of serpentinite, average values of @ ' and c' were 24.6" and 6.0 kN/m2, respectively. In the case of weathered soils of schist, both average values were 27.2" and 9.0 kN/m2, respectively. Table 3 shows the strength parameters of block sampled specimens of weathered soils obtained by the direct shear tests under submerged conditions. As can be seen in Table 3, 0 of weathered soils of 125

serpentinite and schist are 28.2 and 29.8 , respectively. Thus these internal friction angles of both weathered soils obtained by direct shear tests are 2 - 4 ” larger than those obtained by the bore hole ring shear tests. Also, the levels cohesion of weathered soils obtained by direct shear tests range between those obtained by bore hole ring tests. Figure 8 represents the relationship between c’ obtained by the bore hole ring tests and the tested depth z. The straight line in this figure shows the relationship of c’(kN/m2) = z (m). This relationship has often been adopted in cases of determining c’ in the simple inverse analysis of a landslide. It is noticed in Figure 8 that 5 data among 9 data exist on or near this straight line irrespective of the kind of rock. Hereafter, it will be necessary to examine the reason why the data fit or not fit the relationship of c’(kN/m2) = z (m). As mentioned above, since no distinct difference was observed between the strength parameters of weathered soils of serpentinite and schist obtained by in-situ and laboratory tests, the strength parameters used for the stability analysis of the cut slopes were proposed according to D, and DH classes as summarized in Table 4. Namely, 6 ’is 25.0 and 29.5” for D, and DH classes, respectively. c’ (kN/m2) for both classes is given as the sampled depth (m). 6. CONCLUSIONS The relationships between rock class anf P-waqve velocity (V,) were investigated in the cut slopes in the Sangun metamorphic region in which serpentinite and pelitic schist are distributed in a complex way and show different degree of weathering. Also, the strength parameters of both rocks’ weathered soils used for a design of stability analysis were measured. The results are summarized as follow: Classification of rock class has a good correlation with the velocity of P-wave obtained by elastic prospecting, (Vp)e,but not with the velocity of Pwave obtained by bore hole velocity logging, (V,),. No distinguishable difference between the strength parameters of weathered serpentinite and schist soils were obtained by bore hole ring shear tests and direct shear tests. On the basis of this result, the internal friction angles of weathered soils of the D, and D, classes were determined as 25.0 and 29.5 , respectively. The cohesion (kN/m2) was given as the sampled depth (m).

126

REFERENCES Nishimura, Y. & Matsusato, H. 1 9 9 1 . h illustrated Book of rocks in Yamaguchi prefecture, Daiichi Gakusyusya Ltd. , 21-22 (in Japanese). Yamamoto,T.,Ohara,S, Nishimura, Y. & Sehara, Y. 1996a. Characteristics cut slopes consisting of Sangun metamorphic rocks which have failed due to heavy rainfall in Yamaguchi prefecture, Domestic Edition of Soils and Foundations, 36(1), 123-132 (in Japanese). Yamamoto, T., Takamoto, N., Nishimura, Y. & Sehara, Y.1996b. Saw-type slope failure in the Sangun metamorphic region, Tsuchi-to-Kiso (the Japanese Geotechnical Society), 44( 11)’ 9-12 (in Japanese). Yamamoto, T., Sehara, Y., Nakamori, K. & Morioka, K.1997. Landslide at the Sangun metamorphic Region the case of Ube - shi, Yamaguchi prefecture, Journal of Japan Landslide Society, 34(3), 41-50 (in Japanese). Yamamoto, T. 1998. Some geotechnical engineering properties of weathered soils on failed slope in the Sangun metamorphic region, Proceedings of the international symposium on problematic soils, ISTOHOKU ’98,537-540. Yunoki, M., Takano, M. & Rempo, M.1995a Study on residual strength tests by direct ring shear test, Proceedings of 30th Japan National Conference on Soil Mechanics and Foundations Engineering, 713-716 (in Japanese). Yunoki, M., Rempo, M., Takano, M. & Yagisawa, T. 1995b. Inspection tests of pore - pressure transition in soil-sampled by direct ring shear test, Symposium on method and application of direct type shear test, 283-290 ( i n Japanese).

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Using multibeam sonar surveys for submarine landslide investigations J. Locat Department of Geology and Geological Engineering, Lava1 University, Que., Canada

J.YGardner & H. Lee United States Geological Survey, Menlo Park, Gal$, USA

L. Mayer, J. E. Hughes Clarke & E. Kammerer Ocean Mapping Group, University of New Brunswick, Fredericton, N B., Canada

ABSTRACT: Multibeam sonar surveys have been carried out in areas where submarine mass movements have been identified. This technique couples various tools including the swath mapping system itself and differential GPS. After corrections for ship movement and tide, the resulting images provide a airphotograph-like picture of the sea floor which enable a detailed morphological analysis. The analysis of Saguenay fjord data will also show that this methodology can be use to precisely monitor landslide prone areas.

1. INTRODUCTION

2. MULTIBEAM SONAR SURVEY TECHNIQUE

The analysis of sub-aerial landslides must be done with an adequate knowledge of the morphology and stratigraphy, not withstanding the mechanical properties and pore water conditions. For submarine landslides, and until recently, most of the analyses had to rely on side-scan sonar and seismic surveys. A major limitation of these techniques was the complexity of integrating them into a homogeneous system whereby the inherent morphological distortions due to the data acquisition process would be corrected. This was particularily true for large landslides (Moore and Normark 1994, Schwab et al. 1991) For nearly a decade now, multi-beam techniques have been developed (Lee et al. 1991, Mitchell 1991, Li and Clark 1991, Prior 1993, Hughes Clarke et al. 1996) and, when coupled with differential positioning, can provide precise bathymetric information at such a density that a detailed map of the seafloor can be produced (Bellaiche 1993, Urgeles et al. 1997). This paper will focus on illustrating the use of such a technique for the geomorphological analysis of submarine slides. More attention will be given to the Saguenay Fjord where two surveys (1993 and 1997) were conducted over the same area of the fjord. At the same time, some examples, taken from various locations around the world, will be presented to illustrate the diversity and scale of subaquatic mass movements.

Multibeam techniques use an acoustic signal emitted from a series of transmitters mounted on the hull of a vessel (Figure 1). The greater the number of transmitters and higher frequencies will provide more precise bathymetric information. Bathymetry data from multiple sources can also be merged (Orange 1999). Since most of the examples provided herewith were obtained by means of EM1000, we will focus on this technique to illustrate the methodology (Hughes Clarke et al. 1996). The EMlOOO works at a frequency of 95 kHz, producing a fan of 60 sensors with 2.4" by 3.3" beam widths over a total angular swath sector of 150". While the sonar can operate in water depths ranging from as little as 3m to up to 1000m, this system is at its best for water depths between about 10 to 600m. The EM3000, a more portable and recent version of the EMlOOO system, can be used for water depths of less than 100m. The sonar is capable of resolving a water depth at an accuracy as little as 0.25%. The EM1000 can be mounted on a vessel a small as 8 m (Figure lb). The data is collected along a path (Figure lc) in order to cover all the survey area with an overlap percentage depending on the accuracy required. In most cases, an overlap of 150% is correct. The overlap assures a minimum of redundancy in the data and helps increase the precision of the measurements. The ship speed can be as high as 14

127

knots without loss of accuracy. Precise differential positioning, tide data and data correction related to ship movement are essential. In addition, the acoustic velocity is corrected by a series of acoustic profiles taken during the survey. If space permits, onboard post treatment can be completed for a quick production of the various maps. The overall aspect of data reduction and analysis has been presented by Hughes Clarke (1997).

movement illustrated hereafter are: rock avalanches, retrogressive slide, slides and debris flows. 3.1 Saguenay Fjord landslides and debris flows

Figure 1. Schematic deployement of a multibeam sonar survey with vessel types (a and b) and track pattern (c). Indications are given for major component, i.e. ship movement and position (S) with differential GPS.

3. MULTIBEAM SURVEYS: EXAMPLES The following examples are taken from various places around the world. The type of mass

The Saguenay Fjord was one of the first sites where a multibeam sonar survey was carried out to map submarine landslides (Couture et al. 1993, Hampton et al. 1996). It is located 200 km northeast of QuCbec City, Canada. The area provides a fairly quiet environment so that sea conditions are nearly perfect so as to ensure the best results. The same area was also re-visited in 1997 after a major flood event (Kammerer et al. 1998). The Saguenay Fjord survey covers the upper part of the fjord at water depths ranging from 0 to 225 m Figure 2). The water column is stratified with a surface freshwater layer of about 5m in thickness. At regular intervals, a sonic velocity profile of the water column was obtained for the first 75 m to take into account changes in tides and currents. The Saguenay Fjord region has frequent major earthquakes (e.g. 6.3 in 1988), the largest historic one occurring in 1663 (Locat and Leroueil 1988, Locat and Bergeron 1988, Syvitski and Schafer 1996) for which an equivalent Richter Scale of nearly 8 was given. It is believed that this earthquake triggered a series of major land and submarine slides, the largest sub-aerial one being the St. Jean Vianney slide totaling a volume of more than 200 millions cubic metres. At the same time, major submarine landslides took place in the upper reaches of the fjord so that a complex fan was constructed at the mouth of the Bras Nord (Figure 2b). From seismic and coring data, the fan appears composed of clayey debris flow deposits mantled by a thin layer (less than 2 m) of turbidite (with a typical sandy layer at its base) sediments derived mostly from the on-land St. Jean Vianney slide. Between 1984 and 1993, many seismic and sonar surveys had revealed the presence of other major submarine slide features (Locat and Bergeron 1988, Pelletier and Locat 1993) but a clear picture could only be assembled after a multibeam survey conducted in 1993 (Couture et. al. 1993). Results of the 1997 survey are used to detail the geomorphology of the fan complex. On the lower part of the Bras Nord we could map few slides as evidenced by compressive deformation at their base. A major retrogressive slide is also visible which extends on almost the total length of this part of the fjord, i.e. over about 6 km (Figure 2c). From seismic surveys, the depth of the failure plane would be at about 15-20 m, Figure 2d). The fan itself is cut by two channels a few

128

Figure 2. Morphological analysis of the upper part of the Saguenay Fjord, QuCbec, Canada, illustrating the use of sun-illuminated (from the east) multibeam sonar bathymetry from the 1997 survey. Failures are clearly seen along the edge of the fjord, as circular type failure while the centre of the Bras Nord shows retrogressive failures extending over few kilometres towards the north. Insert in b shows details of the fan complex, S1 and S2 are SEISTEK and 3.5 kHz seismic surveys of some landslide features; “a” refers to Figure 3.

129

Figure 4. Palos Verdes slide. “a”: plane view, “b” 3D view. The “x” points at the northwest extent of the detachment area (Source USGS). the variation in the thickness of the flood layer at about 5m. This example illustrates well the potential of this technology to make accurate pre and post measurements. If used in an active landslide area or a potentially unstable area, any future movements could be detected and calculated.

Figure 3. Evaluating 1996 Saguenay Fjord catastrophic flood deposit by comparing the two multibeam sonar surveys of 1993 and 1997 (Kammerer et al. 1998). In “a” the white color represent the 1997 bathymetry above the 1993. In “b” we show the three cross sections where both 1993 and 1997 depth profiles are compared.

3.2 Palos Verdes slide, California

hundred metres in width and flanked by escarpments which are about 10 m high. As indicated above, the second (1997) multibeam sonar survey provided an opportunity to test the reliability of the system (Kammerer et al. 1998). The vertical resolution of the system is about 25 cm for a depth of lOOm which corresponds to the maximum water depth in the area shown in Figure 3. As shown in Figure 3b, the 1997 survey was able to estimate

The Palos Verdes slide (Figure 4), off Los Angeles, had long been recognized on reflection seismic logs (Hampton et al. 1996). The slide took place along a steep escarpment and traveled a distance of about 10 km on the sea floor. The head scarp is about 500m high and the slope varies between 15-20’. The debris were dispersed over a wide area shown in figure 4b. From seismic records (Hampton et al. 1996) the thickness of the debris deposit varies from about 20 m in the lower part of the slope to less than lm, 10

130

preserved in the stratigraphic record (Nitttrouer 1999). One component of this study is to understand sediment stability and transport (Lee et al. 1999). In such a case, the detailed description of the morphology is an essential part of the analysis (Goff et al. 1999). The 3D bathymetry picture shown in Figure 5a represents the study area which can be divided into two parts. The northern part, located to the north of the anticline (a small sea mount in the middle on the slope), which present a regular slope with more or less regularly spaced gullies. The southern sector is characterized by a semi-circular feature which may represent the amphitheatre of a large sheardominated retrogressive failure (Fig. 5b, Gardner et al. 1999) or a large deep seated submarine failure (Lee et al. 1981, Lee et al. 1999, Orange 1999). The water depth range in this image is from zero to about 200 m near the shelf break and about 500m near the base of the slope. The slope itself is at an angle of about 3" to 6" and the slope break is at about 20 km from the shoreline.

3.4 Lake Tahoe rock avalanche

Figure 5. Humboldt Slide, Eel River Margin, California (see Gardner et al. 1999 and Lee et al. 1999 for discussion), a: swath bathymetry sun illuminated 3D map; b: Huntec seismic section with the location shown in "a". km away from the base of the slope, with an average thickness of 5 to 1Om. The image shown in Figure 4 appears to illustrate a process of continuing instability development towards the north-east. The nature of the material involved in the slide remains to be determined. According to the slope geometry and the blocky morphology still observable in the runout zone, the material should be made of stiff sediments.

Lake Tahoe is located at the boundary between California and Nevada. The lake is at an elevation of 1900m. The multibeam sonar survey of the lake was carried out in 1998 (Gardner et al. 1998). For this work, the EM1000 was mounted on a small vessel (8 m long, Fig. lb). Lake Tahoe, one of the deepest lakes in the United States, is located between two major faults, including the Sierra Nevada fault which is located about two kilometers west of the lake. Most rocks in the area were produced by volcanic activity. The landscape itself has been localy modified by glaciers. The headscarp of the slide is about 5 km wide and the debris reached a distance of up to about 10 km near the centre of the lake. Some lumps of isolated debris are of the order of 100 m in length. The north flank in the starting zone appears to be limited by strong lineament systems intersecting at an angle of about 130" (see arrows in Figure 6a).

3.3 Humboldt slide, Eel River margin, California The Eel River Margin example was obtained as part of a study related to a multidisciplinary effort aimed at understanding the process by which sedimentary strata are deposited, modified and ultimately

131

3.5 Canary Islands rock avalanches, Spain The Canary Islands submarine slides (Urgeles et al. 1997) were initiated along the flanks of the islands (Figure 7). The avalanche spreads from an elevation of about lOOOm above sea level to a depth between 3000 and 4000m with a run out distance at about 50 km. The La Palma rock avalanche is also partly visible on the left side of the Figure 7. These large scale mass movements involve very large volumes

(few cubic kilometres) and cover large areas of the sea floor (up to 2600 km2),and run-outs reaching 70 km (Urgeles et al. 1997). This type of mass movement is very similar to those reported by Moore and Normark (1994) for the Hawaiian Islands. This example also illustrates the coupling of land and marine elevation data.

4.DISCUSSION AND CONCLUSION

Figure 6 . Lake Tahoe debris avalanche (see Gardner et al. 1998 for details); a: plan view of the debris avalanche area, with the arrows pointing at lineament intersections, b: 3D view looking towards the west.

Recent multibeam sonar survey systems and their required software for data analysis now provide the engineering community with a powerful and reliable tool to map the sea floor with very high precision. With this technique, we can now really talk in terms of “submarine remote sensing”, as it now provides information nearly equivalent to aerial photography or radar images. In addition, the work carried out in Lake Tahoe has demonstrated that the system can be efficiently mounted on a small vessel thus showing that multibeam sonar surveys can be carried out in more restricted areas. The recently developed EM3000 is a portable system which will provide nearly a tenfold improvement in bottom morphology definition for water depths less than 100m. The experience of the Saguenay Fjord has shown that two surveys, conducted at a four year interval, were able to show morphological changes associated with flood deposits. At the same time, minute features revealed in 1993 were also observed in 1997. These results illustrate the monitoring

Figure 7. El Golfo debris avalanches off El Hierro Island (Canary Islands, Spain, Urgeles et al. 1997)

132

potential of this technique in submarine landslide prone areas. Finally, this limited compilation has also provided an opportunity to showcase the diversity and scale of sub-aquatic landslides and related mass movements.

5. ACKNOWLEDGEMENTS We would like to thank our supporting organizations including the U.S. Geological Survey, the Office of Naval Research (STRATAFORM project), the National Science and Engineering Research Council of Canada and the Fonds F.C.A.R. (Ministry of Education, Quebec). In addition, we like to thank Dr. M. Canals and Dr. R. Urgeles (University of Barcelona) for providing the example from the Canary Islands. We would also like to thank R. Sansfaqon and N. Doucet of the Institut Maurice Lamontagne at MontJoli, Quebec and P. C8t6, graduate student at Laval. REFERENCES Bellaiche, G., 1993. Sedimentary mechanisms and underlying tectonic structures of the nortwestern Mediterranean margin, as revealed by comprehensive bathymetric and seismic surveys. Marine Geology, 112: 89-108. Couture, R., Locat, J., Godin, A., Therrien, P., Messager, S., and Babineau, S., 1993. Relevks bathymetriques au fjord du Saguenay B l’aide de 1’Ccho-sondeurmultifaisceaux SIMRAD EM- 1000, Expedition B bord du F.G. Creed. Department of Geology and Geological Engineering, Laval University, Quebec, Canada, Report GREGI 93- 16, 1lp. Goff, J.A., Orange, D.L., Mayer, L.A., and Hughes Clarke J.E., 1999. Detailed investigation of continental shelf morphology using a highresolution swath sonar survey: the Eel river margin, northern California. Marine Geology, 154: 255-269. Gardner, J.V., Prior, D.B., and Field, M.E., 1999. Humboldt Slide - a large shear-dominated retrogressive slope failure. Marine Geology, 154: 323-338. Gardner, J.V., Mayer, L., and Hughes-Clarke, J.E., 1998. The bathymetry of Lake Tahoe, CalifroniaNevada. United geological Survey Open-File Report 98-509, 17 p. Hampton, M., A., Lee, H.J., and Locat, J., 1996. Submarine landslides. Reviews of Geophysics, 34:33-59.

Hughes Clarke, J.E., 1997. Data thinning for chart production purposes. In: Coastal Multibeam Training Course, Ocean Mapping Group, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, 26 pp. Hughes Clarke, J.E., Mayer, L.A., and Wells, D.E. (1996). Shallow-water imaging multibeam sonars: A new tool for investigating seafloor processes in the coastal zone and on the continental shelf. Marine Geophysical Research, 18: 607-629. Kammerer, E., Hughes Clarke, J.E., Locat, J., Doucet, N., and Godin, A., 1998. Monitoring temporal changes in seabed morphology and composition using multibeam sonars: a case study of the 1996 Saguenay rivers floods. In: Proceedings of the Canadian Hydraugraphic conference, Victoria. Lee, H.J., Brian, Edwards, B.D., and Field, M.E., 1981. Geotechnical analysis of a submarine slump, Eureka, California. Proceedings of the 13‘h Annual OfLshore Technology Conference, Houston, pp. : 53-65. Lee, H.A., Locat, J., Dartnell, P., Israel, and Wong, F., 1999. Regional variability of slope stability: application to the Eel margin, California. Marine Geology, 154: 305-321. Lee, H.J., Chough, S.K., Chun, S.S., and Han, S.J., 1991. Sediment failure on the Korean Plateau Slope, East Sea (Sea of Japan). Marine Geology, 97: 363-377. Li, C., and Clark, A. L., 1991. SeaMarc I1 study of a giant submarine slump on the Northern Chile Continental Slope. Marine Geotechnology, 10: 257-268. Locat, J., and Bergeron, M., 1988. Etude B rebours de glissements sous-marins, fjord du Saguenay, QuCbec. In: Proceeedings of the 41”‘ Canadian Geotechnical Conference, Waterloo, Ont., pp.: 338-346. Locat, J., and Leroueil, S., 1988. Physicochemical and mechanical characteristics of recent Saguenay Fjord sediments. Canadian Geotechnical Journal, 25: 382-388. Mitchell, N.C., 1991. Improving GLORIA images using SeaBeam data. Journal of Geophysical Research, 96: 337-351. Moore, J.G., and Normark, W.R., 1994. Giant Hawaiian landslides. Annual Reviews in Earth and Planetary Sciences, 22: 119-144. Nittrouer, C.A., 1999. STRATAFORM: overview of its design and synthesis of its results. Marine Geology, 154: 3-12. Orange, D., 1999. Tectonics, sedimentation, and erosion in northern California: submarine

133

geomorphology and sediment preservation potential as a result of three competing processes. Marine Geology, 154: 369-382. Pelletier, M., and Locat, J., 1993. Les glissements sous-marins dans la Bras Nord du fjord du Saguenay. In: Proceedings of the 4'h Canadian Conference on Marine Geotechnical Engineering, St. John's, Newfoundland, 2: 555-581. Prior, D.B., 1993. Submarine landslides: the value of high resolution geophysical survey for engineering. In: The royal Academy of Engineering Conference on: Landslides Hazard Mitigation with Particular Reference to Developing Countries,pp.: 67-82. Schwab, W.C., Danforth, W.W., Scanlon, K.M., and Masson, D.G., 1991. A giant submarine slope failure on the northern insular slope of Puerto Rico. Marine Geology, 96: 237-246. Syvitski, J.P.M., and Schafer, C.T., 1996. Evidence for an earthquake-triggered basin collapse in Saguenay Fjord, Canada. Sedimentary Geology. 104; 1-4, Pages 127-153. Urgeles, R., Canals, M., Baraza, J., Alonso, B., Masson, D. (1997).- The most recent megaslides on the Canary islands: The El Golfo debris avalanche and the Canary debris flow, West Hierro Island Journal of Geophysical Research, 102 (B9): 20.305 -20.323.

134

Slope Stability Engineering, Yagi, Yamagami & Jiang (01999 Balkema, Rotterdam, ISBN 90 5809 079 5

Automatic measurement of pore water pressure in the hard-rock slope and the sliding weathered-rock slope - Field survey in mountainous region in Shikoku Island, Japan E.Tamura & S. Matsuka Yonden Consultunts Compuny Incorporated, Kugawa, Jupun

ABSTRACT: It has been shown in general researches that one of the causes of the landslide is the rise of the pore water pressure. The rise of the pore water pressure causes initial rockslides and rockfalls in particular. We continuously measured the groundwater level and the pore water pressure in the slope of the rock and the slope of the weathered-rock slide in the mountain range in Shikoku which has an annual amount of rainfall from 2000mm to 3000mm. With regard to the disaster prevention of the landslide and the rockfall, we examined the start time and the disappearance time of the rise of the pore water pressure. The result of our research clearly shows the start time of the rise of the pore water pressure in heavy rain. Warning time of landslide is half a day or one and a half days after the stream flow had begun to increase or the beginning of the heavy rain. 1INTRODUCTION

has an annual rainfall of 2,250-2,75Omm. Rainfall is heavy in the rainy season and the typhoon season from

The rise of pore water pressure is regarded as a cause of landslides oaniguchi and Fujiwara, 1965). In the initial phase of rockslides and rock€& in particular, its involvement seems significant. However, there were performed not many studies in which the fluctuation of pore water pressure was observed in sites in relation to the occurrence of landslides. Higaki,K. et al. (1991) and Shiraishi,D.(1994) measured the pore water pressure at sliding surfaces and ascertained that landslides became active following rises in the pore water pressure, concluding that rises in pore water pressure cause landslides. In this study, the groundwater levels, pore water pressure in the rock slope and the sliding weathered-rock slope on a mountainous region in Shikoku Island were continuously measured, and the relation between the fluctuation of pore water pressure and the time elapsed was studied from a disaster-preventivepoint of view.

July to September.

2 GEOLOGICAL RAINF..

OF SLOPES AND

The geology of the central mountainous region in Shikoku Island is characterized by metamorphic rocks of the Sanbagawa Belt and sedimentary rocks of the Chichiiu Belt. The rock slope surveyed was located in the Chichibu Belt; the gradually sliding weathered-rock slope, in the Sanbagawa Belt. Landslides occurs frequently in these geologicalbelts. The area around the slopes surveyed 135

3 MEASUREMENT OF PORE WATER PRESSURE I N HARD ROCK SLOPE The hard-rock slope rested on the end of a ridge of a mountain range 1,ooOm high. The slope was 280-480 m above sea level and in a convex shape 2oom high (Fig. 1). The geology of the slope consisted of the strata of greenstone, slate, sandstone,and chert of the Chichibu Belt. These strata slanted downward by 15" and ran along the slope, as shown in Fig. 2. Underlying the strata was hard rock, which was 55 m deep in the upper part of the slope and 12 m deep in the lower part. The groundwater level was around the upper surface of the hard rock Vertical bores A-l,2,3, and 5 and a horizontal bore B1of a 76-mm diameter were made in the slope (Fig. 1).To measure the pore water pressure in the bedrock, a porewater-pressuregauge was set at the bottom of each vertical bore, and each bore was clogged above the gauge with bentonite and cement milk to isolate the groundwater(Fig. 3). The groundwater levels in the vertical bores were measured with water-pressure gauges. The horizontal bore was divided into three chambers with air-packers to measure the spouting-water pressure. Personal computers were used and data were collected Continuously. The measured pore water pressures were converted into groundwater levels. In the same bore, there were differencesof 1-6m between the converted water levels

Figure 2. Geological profile of hard rock slope. 136

and the measured water levels, the latter tending to be higher. The pore water pressure and the water levels in the bores changed under daily rainfall of 50 mm or more, presenting larger changes in the upper and middle parts of the slope and smaller changes in the lower part. There were observed time differences among the increase of the stream flow below the slope, and the increase of the groundwater levels and the rise of the pore water pressure in the bores in the middle part of the slope, while it was rainingcontinuously.Under the rainfallof 671 mm during the period of July 26-30, 1993, the stream flow increased first, then the water levels in the vertical bores and the spouting-waterpressure in the portion of the horizontal bore with the shallow section,and thereafter the pore water pressure in the vertical bores and the spouting water pressure in the portion of the horizontal bore with the deep d o n . The time Werence between the first event (for the surface water) and the second event (for the upper-stratum water) was 12 hours or so, and the time difTerencebetween the second event (for the upper-stratum water) and the third event (for the lower-stratum water) was 4-5 hours (Fig. 5). Besides, the relation between the starting times of

increase in the stream flow and the pore water pressure in the bedrock was studied. Data were collected fiom the stream and the bore A-2 in six cases of continuous rainfall of 50-600 mm (Table 1). According to the data of the table, although data are somewhat dispersed depending on the raining patterns and the water-saturated condition of the ground before the rains, the pore water pressure began to increase about 10 hours, and reached its peak 20-30 hours, after the stream flow had begun to increase (Table 1 and Fig. 9. T f i c on National Highway running by the survey area is regulated when continuous rainfall reaches 250

m. A tendency can be read from Table 1: at the point in time when rainfall reaches the level of 250 mm, (i) the stream flow already began to increase long before, (ii) the pore water pressure also began to rise a short while before, and (iii) it is 10hours or so before the pore water pressure reaches a peak. This suggests that the appropriate time zone to be wamed of landslides and mkMls is fiom the point of half a day after the stream flow’s increaseto the point of one and a half day after the same.

137

Figure 5. Automatic measurement of pore water pressure and groundwater levels in bores on rock slope.

138

Figure 6. Automatic measurement of pore water pressure in bed bedrock.

Figure 7. Automatic measurement of pore water pressure in sliding weathered-rock slope.

139

Tie

ous

Jul.

Oct. 7-8,

1993 Nov. 12-13, 1993

rainfall

Hourly

(mm) 671

(mm/h) (mm/d) 36 288

43

6

5

17

Almost no change

28

A low

126

12

88

41

55 ~

Jul. 25-27, 1994 Aug. 10-15, 1994

29

14

68 ~

-

27 _

461

42

281

7

18

36 22"

11

29

342

27

119

16

74

100 89"

58

84

area and a front _ No.7 typhoon

_

No. 13 typhoon

"*" Mark are the time period that each raintook to reach a rainfallof 250 mm. 4 MEASUREMENT OF PORE W m R PRESSURE IN SLIDING WEATHERED-ROCK SLOPE The sliding weathered-rock slope was composed of pelitic schist in the Sanbagawa Belt and located on the end of a ridge of a mountain range 1,OOO m high. The landslide was 40 m wide, 70 m long, and 5-7 m deep. The pore water pressure in the clay forming the slip surface was measured in the center of the sliding block A bore was made down to the slip surface. A vinyl chloride pipe was provided at the bottom of the bore and the upper portion of the bore was cemented so that underground water would enter the bore only from the clay of the slip surface. A water pressure gauge was set at the bottom of the bore to measure the water level in the bore continuously and determine the pore water pressure (Fig. 4). Under daily rainfall of 101)-300 mm, the pore water pressure increased rapidly at a time in the period from the point of half a day after the beginning of rainfall to the point of one and a halfdays after the same, and took seven days or so to decrease to the pre-rain level (Fig. 7). A similar phenomenon was observed in the study performed to measure continuously the ground water levels in a landslide area in Sanbagawa Belt in Tokushima Prefecture (Nishimura, k et al., 1997). Although the slope of the present study was not in ~ t u r a state l due to the measures taken to reduce the sliding displacement, it can be said that the time when the pore water pressure increases coincides generally with the time when the sliding displacement (XXLlrs.

5 CONCLUSIONS The main finding of the present study about the pore water pressure under heavy daily rainfalls of 100 mm or more are as follows: 1. In the non-sliding hard-rock slope, the pore water pressure began to rise about 10 hours, and reached a peak 20-30 hours, after the stream flow had begun to increase. 2. In the sliding weathered-rock slope, the pore water pressure increased at a time from half a day after the beginning of rainfall to one and a half days after the same, and the pressure took a week or so to retum to its normal level. REFERENCES Higaki, D. & Maruyama. K. & Yoshida, K. & Yoshimatsu, H. 1991. Pore-water pressure fluctuations in some landslide areas. Journal of Japan Landslide Society. 28-3 : 9-16. Nishimura, K. & Sakamoto, S. & Kawamura, M. 1997. Observation of groundwater levels with selfrecording water level meter; taking Owcita Landslide as example. proceedings of Chugoku-Shikoku Branch of Japanese Society of Applied Geology. 23-28. Shiraishi, K. 1994. Observation ofpore waterpressure on slip-su$ace for landslide control works. Proceedings of Japanese Society of Soil Mechanics and Foundation Engineering Symposium. Taniguchi, T. & Fujiwara, M. 1965. Investigation and analysk of landslides. Rikohtosho. 140

_

Slope Stability Engineering, Yagi, Yamagami & Jiang ((-1 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Field measurement of suction in soil and rainfall in Kagoshima Prefecture R. Kitamura, K. Jomoto, K.Yamamoto & T.Terachi Kugoshirna UniversiQ Japctn

H.Abe Chubu Chishitsu Company Limited, Japan

T. Iryo University of Western Ontario, Ont.. Canada

ABSTRACT: In Kagoshima Prefecture a non-welded part of pyroclastic flow deposits, Shirasu in Japanese, is widely distributed on the surface ground. The slopes composed of Shirasu and other volcanic products often fail due to the heavy rain in the rainy season every year. In order to prevent natural disasters due to slope failures our laboratory has started to measure the suction and rainfall at several points in Kagoshima Prefecture. In this paper the field measurement system of the suction in soil and the amount of rainfall are firstly introduced. The tensiometer is used to measure the suction in unsaturated soil. The data obtained at several measuring points are automatically filed in the data loggers and acquired by the personal computer in the laboratory by means of cellular phones. The change in suction and rainfall are shown with time. The hourly, dairy and monthly change in suction with time is discussed to predict the slope failure.

1 INTRODUCTION

introduced, and then some measuring results are presented and discussed*

Kagoshima Prefecture is located in the southern part of Kyushu Island, Japan, as shown in Fig.1. The surface ground in Kagoshima Prefecture is almost covered with the volcanic products such as pyloclastic flow deposits including pumice and falling ash, weathered igneous rock and so on. The non-welded part of pyloclastic flow deposits is locally called Shirasu in Japanese, which is classified into sandy soil. The density of Shirasu is smaller than popular silica sand because the particle is porous. Consequently Shirasu is easy to be eroded by the surface flow of rainwater. When heavy rains fall every rainy season, the slope failures often occur on the slopes composed of Shirasu on which thin surface humus layer is laid. It is qualitatively well-known that these slope failures occur due to the seepage of rainwater into unsaturated soil and the increase in water content, which brings the increase in self-weight of soil mass and the decrease in suction. But it is difficult to estimate the changes in water content and suction quantitative1y. Our laboratory started to measure the suction and rainfall in the field to make the seepage behavior of rainwater into surface ground clear (Kitamura et al., 1999). In this paper the field measuring system is

Fig.1 Location of Kagoshima Prefecture

141

2 FIELD MEASURING MEASURING POINTS

SYSTEM

AND

3 MEASURING RESULTS AND DISCUSSION

Figure 6 shows the change in suction and the amount of hourly rainfall with time obtained at the measuring point of Ijuin-twon in June 1996, where the suction is represented as the head of negative water pressure. The surface ground at this point is covered with the primary Shirasu layer of more than 10 m in thickness. In Fig.6 the absolute value of negative pressure (suction) is the largest at 20 cm in depth followed by those of 40 cm, 60 cm and 80 cm in order, which means that the water content increases with depth. The change in suction due to rainfall was initiated at 20 cm in depth followed by the change in suction of 40,60 and 80 cm in depth in this case that the ground is uniform and the ground water level is deep. The same behavior was obtained at some measuring points as shown in Figs. 7 and 8. Figure 7 shows the measured data obtained at Kokubu-city where the talus was formed by the slope failure of Shirasu. Figure 8 shows the measured data obtained at Tarumizu-city where the falling volcanic ash derived from Mt. Sakurajima deeply covers the surface ground with more than 1m in depth. Figure 9 shows the measured data obtained at Yoshida-town. Near this point the river is located and the ground water level is shallow. It is found out from Fig.9 that the head of water pressure of 80 cm in depth is always positive

Figure 2 shows the schematic field measuring system of suction and rainfall. The suction in unsaturated soil is measured by the tensiometer and the amount of rainfall is measured by the tipping bucket rain gauge. Four sets of tensiometer are installed into the ground of 20 cm, 40 cm, 60 cm and 80 cm in depth. The measuring data are filed in the data loggers and acquired by the personal computer. The sampling interval can arbitrarily be selected from lsecond to 60 minutes, which is now set to be 60 minutes for tensiometer and 10 minutes for rain gauge respectively. About 60000 data can be filed in the data loggers, which means that the data for more than 2 months can be filed. In the latest system the cellular phone is used to transmit the data filed in the data loggers as shown in Fig.3, where the sampling interval can remotely be controlled by the personal computer in the laboratory. Figure 4 shows the tensiometer which is composed of porous cup made of ceramic whose air entry value is about 250 kPa, acrylic pipe filled with de-aired water and pressure transducer at the top of acrylic pipe. Figure 5 shows the measuring points in Kagoshima Prefecture, where the remote measuring system is adopted in Kiire-town, Matsumoto-town and Izumicity.

Fig.2 Field measuring system

142

Fig.3 Remote system for data transmission

143

Fig.4 Tensiometer

Fig.6 Measured data obtained at Ijuin-town in June 1996

Fig.5 Measuring points in Kagoshima Prefecture because the ground water level is shallow. The water pressure of 20 cm is also positive when a rain falls, which means that the ground water level is easy to rise to be same as the ground surface in the rainy condition.

4 CONCLUSIONS The field measurement system for suction and rainfall is shown to investigate the seepage behavior of rainwater into ground in Kagoshima Prefecture.

Fig.7 Measured data obtained at Kokubu-city in April 1997

144

The measured data obtained at some measuring points are presented and discussed. It is found out that the suction is one of the basic informations for the water content in the ground and reflects the seepage characteristics of ground. Therefore the change in suction with rainfall should be continuously measured to analyze the mechanism of slope failure and prevent the natural disaster due to slope failure caused by the rainfall. This research was supported by the grant-in aid of scientific research (B) (Project No. 09555153) of the Ministry of Education.

REFERENCES

Fig.8 Measured data obtained at Tarumizu-city in May 1997

R. Kitamura, T. Iryo, H. Abe and H. Yakabe: Field measurement of suction on Shirasu ground, Proc. 1st Asian-Pacific Conference and Trade Exhibition on Ground and Water Bioengineering for Erosion Control and Slope Stabilization, 1999 ( to be appeared).

Fig.9 Measured data obtained at Yoshida-town in April and May 1996

145

This Page Intentionally Left Blank

Slope Sfabihty Engineering, Yagi, Yamagami& Jiang c,' 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Application of acoustic emission method to Shirasu slope monitoring T. Fujiwara & A. Ishibashi Nippon Koei Company Limited, R&D Center, Ibaruki, Japan

K. Monma Public Works Research Institute, Ministry of Construction, Government of Japan, Jupan

ABSTRACT: The Shirasu , that is widely covered on southern Kyusyu, characterized by gray soft rock derived from Pyroclastic flow sediment. In Shirasu area, slope stability is frequently disturbed by heavy rain, and Shirasu slope failures caused some deaths every year. It has become very important to predict these disasters. This paper on application of Acoustic Emission (AE)technique in the field of Shirasu slope failure prediction presents the findings on the real scale slope experiment.

1. INTRODUCTION Inherited nature of the topography, complicated geological structure and the relatively extensive rainfall makes Japan highly susceptible for slope failures. This is further accelerated with growth of urban fringe expanding into sensitive areas demolishing the natural balance of the mountainous and hilly region. Consequences are the increasing slope failures accounting for heavy losses to life and property. During the period between 1992 to 96 there were 2392 slope failures recorded killing 156 people. When compared to death toll with other types of slope tragedies, slope failures account for more than 60% of total destruction during the period mentioned above, Figure 1.

As at today, there are about 86,000 areas are legally designated as landslide prone areas of which 70% are further identified and categorized as high priority areas that require quick attention for proper preventive measures, Figure 2. Even though there are quite large number of places are recognized for quick action for appropriate counter measures, the response from responsible agencies is not sufficient. Due to the poor progress in the construction of anti-landslide facility, Ministry of Construction launched a program for improvement in warning systems that could prevent loss of life if sufficient, accurate and timely information could be provided to people who are living in questionable areas.

Fig.2 Fig.1 Death by Slope Disasters in the past Syears

147

Slope Failures and Preventive Measures

AE is long-awaited technology that could be combined with warning system to inform people living in a vulnerable area well in advance to reduce losses to a minimum. However, application of AE is considered questionable as not enough research works have been conducted on this aspect. Further, there are very few reports on real application of AE on real-world slope failure studies. 2. TEST SITE AND EXPERIMENT Slope failures that are occurring in Japan break out much higher speed when compared to other slope destruction. For this reason, experiments are mainly conducted in laboratories using models.

Subsequently, results are combined with few filed measurements to extrapolate experimental results to real-world situations. Hence, they face difficulties in applying to real-world situations.

2.1 Test Site To investigate the AE occurrence during a slope failure an experimental scale cutting slope was constructed in a Shirasu slope, and an experiment was carried out. Shirasu is a stratum widely found in southern part of Kyushu Island consists of sediments with the origin of pyroclastic deposits. This is one of the most vulnerable soil type for slope failures. The prepared experiment site is shown in Figure 3. The prepared slope was 5 meters wide and 6 meters in height. The material found in the slope is belonged to weathered Shirasu. In order to conduct the experiments the slope was made unstable by excavating at the bottom of the slope. AE measurements were started with the excavation and continued until the slope was collapsed, figure4. Three and half-hours were taken to the collapse from the time the excavation started, and AE mcasurernents for the whole period were recorded. 2.2 Equipment A PAC SPARTAN AT system was used for AE measurement. The frequency of the AE sensor was 6OkHz. Apart from AE sensor more equipment, an extensonicter and a tiltmeter was installed on the slope. The whole experiment was recorded in a video camera. Two AE sensors were mounted on wave guides, two meters long with a diameter of 2 cm. They were placed at upper and lower parts of the slope. For comparison, third AE sensor was placed on a stable slope.

Fig.4 Shirasu Slope Failure Experiment 148

3 . RESULTS AND DISCUSSION

3.1 Behavior of AE between Slope Failure Figure 5 shows AE measurements from the time of excavation until the moment of the slope failure. Black arrows pointed downward indicate excavations. Altogether five excavations were carried out before the slope failure. White arrow represents the AE observation of slope failure. During the excavations, high AE activity was detected, and exponentiaIIy decreased to zero once the excavation stopped except for the last one. After the 5th excavation, there was some AE activity, and this was rapidly increased 15 minutes before the collapse.

Fig.6 AE

Figure 6 shows AE occurrence of AE activities of the three sensors. Upper two graphs are for the collapsed slope and the lower one is for the reference sensor. The two graphs of the collapsed slope clearly showed that AE activity increased with the excavation. In contrast to this, there was no AE activity observed on the reference slope. Among the two sensor of the collapsed slope, the one placed at the lower part detected more AE activity than the one placed at the top of the slope. This shows that significant amount of energy was concentrated at the lower part of the slope. This suggest that sensor be installed on a wave guide and placed at the bottom or lower part o f a slope for easy detection of sensor activities.

Bchavior by Location

149

AE Count

Primary

Secondary

Tertiary

Fig.7 Comparison AE Behavior and Displacement

A reciprocal of AF, counts per sec

resembles each other and obviously shows similar behavior to that of a creep curve. Fukuzono have proposed a method to predict slope failure time using the strain per unit time at the tertiary creep stage. He has shown that reciprocal number of strain per unit time converges to zero at the tertiary creep stage. In this study, it was investigated whether failure time can be predicted using AE count. Figure 8 shows the failure time prediction by applying strain velocity to AE count rate. This shows that the failure time can be predicted accurately using AE count rate. In the case of AE observation, larger number of data can be obtained when the slope failure is beginning to start. This could provide finer information at the time of the failure. Therefore, failure time can be predicted more precisely by AE count rate than the strain velocity method.

4. CONCLUSION Findings and the conclusion of the present experiment can be summarized as below;

1. The applicability of AE was tested on a real slope and it was found that AE technology can satisfactorily be uscd in real-world slope failure monitoring. 2. Placement of sensors was experimented and it was found that for accurate and easy AE interpretation the sensors should place closer to the bottom of a slope. 3. Method to estimate slope failure time was proposed and the applicability of high accuracy was confirmed with obtained experiment results. REFERENCES

Fig.8 Collapse Time Prcdiction by AE

3.2 Collapse Time Prediction by AE If extensometcr observations are carried out during a slope failure, the strain data would shows a creep curve during a Failure. During this study, some attempt was made to formulate a methodology to predict the failure time during tertiary creep stage. Figure 7 compares changes of extensometcr observation with changes in the accumulated count of AE during the present experiment. These two

Sasahara,K. 1995 Evaluation of Soil Displacement by AE Parameter. Proceedings of 34'h Japan Landslide Society Conference (Japanese) :245-248 Fukuzono,T. 1981 Surface displaccmcnt velocity and acceleration in the slope failure. Proceedings of 36'h Japan Society of Civil Eng. Cod. (Japanese) : 302303

150

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Acoustic emission technique for monitoring soil and rock slope instability A. Kousteni - Department of Civil and Structural Engineering, Nottingham Trent University, UK R. Hill -Department of Chemistry and Physics, Nottingham Trent University, UK N.Dixon -Department of Civil and Structural Engineering, Nottingham Trent Universizj; UK J. Kavanagh - Transport Research Laboratory, Crowthorne, UK

ABSTRACT: This paper presents our recent research in Acoustic Emission (AE) monitoring used to assess slope instability and the factors controlling instrumentation design. These factors include wave-guide material type; the type of the backfill soil placed around the wave-guide, and the method of wave-guide construction. Both field and laboratory studies, undertaken by the authors, indicate that: i) the AE monitoring technique provides an early indication that small deformations are taking place during progressive failure; ii) even in “quite” material, such as clays, AE levels can be related to deformation rates and iii) the choice of wave-guide system is of fundamental importance (e.g. active wave-guides are best suited for the study of slopes formed in clay soils). Quantitative assessment of AE at an early stage of slope failure is still basic. Data is provided on the performance of wave-guide systems, and which will lead to a better quantitative assessment of field AE. The results of laboratory and field studies are discussed.

1.

2. can detect changes in the rate of movement; 3. provide information about the location of sliding surface; and 4. is portable for monitoring slope stability continuously. Such a system could provide an early warning of slope instability. Acoustic emission (AE) monitoring techniques have the potential to meet the above requirements. This paper presents recent developments and considers issues related to instrumentation design. Successful applications on field and laboratory studies are described. The work and results of the current research are discussed with the aim of quantifying the AE response of a wave guide and developing a reliable early warning monitoring system.

INTRODUCTION

Terzaghi, (1950) stated: “If a landslide comes as a surprise to the eyewitness, it would be more accurate to say that the observers failed to detect the phenomena which proceeded the slide”. The implication is that the smallest possible movements should be measured at the earliest possible time. The standard method for assessing the stability of slopes is by measuring ground deformations. At present, conventional surface survey markers, extensometers, or inclinometer tubes installed through the potentially unstable soil/rock are used to define the area of movement. Unfortunately the magnitude of the pre-failure movements which is of interest, is often of the same order as the accuracy of the above monitoring methods. These methods often require measurements taken many times and over a period of time to obtain trends, thus enabling the certainty of ground movement to be established. Therefore, there is a need of an instrumentation system which: 1 . is sensitive to small pre-failure slope deformations;

1.1.

Background information

Acoustic emission is a non-destructive technique which, since the 1970’s has been increasingly employed to monitor the stability of soil bodies. The main body of research into AE applications for soil

151

piles or soil reinforcement units). It is possible for the length of a wave-guide to be in excess of 30 m when used in field monitoring.

assessment has been carried out in the USA (e.g. Koerner et nl., 1981), Japan (e.g. Chichibu et al., 1989, Naltajima et al., 1991) and more recently at Nottingham Trent University (Dixon et al., 1997). When any material is stressed, it generates microseismic activity at locations of local instability. When soil is stressed, it responds by reorganising its constituent particles and changing their relative positions with the consequent frictional generation of stress waves. These micro-seismic stress waves, are referred to as acoustic emission. The associated stress waves propagate from the source of instability through the surrounding material and can be detected by suitable high sensitivity transducers. This is the main principle of the AE monitoring technique, which enables the detection of the occurrence of distress in soil before the development of significant movements. However, monitoring soils by using high frequency AE techniques, is affected by the high attenuation in soils. The attenuation of AE energy in soil is highly frequency dependent. According to Koerner (198 1) the attenuation coefficient (in dB/distance) in dry sands varies from 0.09 dB/cm at 500 Hz to 10 dB/cm at l6kHz. Since metals have a three to four orders of magnitude lower attenuation than soils, a metal wave-guide has been found very useful in conducting the signals from within the soil mass to the receiving AE sensor. Therefore, the use waveguides to monitor AE in soils, has became standard.

2.

Figure 1. AE field instrumentation

Preamplifiier and Filter: A preamplifier is used to amplify the low level signals from the sensor by 40 dB. The signal is filtered by a band pass filter with a bandwidth of 15 - 45 kHz. Hence the output signal consisted of waves with frequencies between 15 kHz and 45 kHz. This ensured that any low frequency background noise is not included in the recorded signal. Main Amplifier: The system can amplify the signal between 50 and 108dB. Data capture: An A-to-D board converts the analogue voltage to a digital value. The maximum sampling rate used is 1 MHz. By directly writing to the board, via the digital ports, it is possible to set the default to capture a stream of data including data points before any trigger time or voltage set by the operator. Data processing: A high-level programming language for data acquisition and processing was used. AE captured data are saved into binary files which can then be analysed.

AE MONITORING INSTRUMENTATION

The AE instrumentation components used for field monitoring and laboratory testing at NTU are shown in Figure 1. It is shown as a single channel system, the extension to a multi-channel system can be easily achieved. 2. I .

Components of monitoring system

Sensor: An AE Technology piezoelectric transducer with a resonant frequency of a 30 kHz has been used. The choice of 30 kHz resonant frequency is due to the need to minimise low frequency environmental noise and at the same time keep the frequency of the system as low as possible, to avoid high levels of attenuation. Wave-guide: Metal wave-guides can take the form of steel reinforcing rods, various metal instrumentation pipes, (e.g. aluminium iiiclinometer tubes) or construction units (e.g. tiebacks, anchors,

2.2.

Design of Wave-guide systems

In the present study a steel tube of 1.60 m length, 60 mm diameter and 6 mm wall thickness has been used. Steel threaded rings are used for connecting sections of the wave-guide. The choice of the steel tube AE wave-guide has the advantage that it can be easily fabricated to the required cross-section and length, and has a low ultrasonic attenuation coefficient. This wave-guide system transmits the emission generated by the frictional motion of the

152

soil particles which are in contact with or close to the wave-guide. It is possible to drive the wave-guide into the host soil for short distance. For larger slopes it is necessary to install the wave-guide in pre-drilled boreholes. This method requires a backfill material to improve the contact between the host soil and wave-guide. Depending on the backfill material two possible systems are formed: Passive and Active wave-guide systems. For passive systems the annulus around the waveguide has to be backfilled with low AE activity material (i.e. clay), so the installation does not introduce additional sources of AE into the waveguide. Any recorded AE signal is assumed to emanate from the deforming host soil. Driven systems can also be defined as passive, as a result of the wave-guide being in direct contact with the insitu material. Active wave-guide systems are installed when the monitoring site consists of cohesive material. As the emission levels generated are low, it is difficult to obtain quality AE data. Therefore, the annulus can be backfilled with granular soils such as sand or gravel which produce high AE levels. Although the recorded AE data will not relate directly to the stress state of the host soil, it may be possible to calibrate the system, such that the recorded AE signal can be related to the magnitude of the general ground deformations. It is this type of system which has been studied by the authors. 3.

FIELD AE MONITORING

Results from recent field studies are reported by Dixon et.al. and Kavanagh (1996, 1997). One of the case study areas was located on the north eastern coast of England at Cowden. At this location 20 meters high cliffs are formed of stiff cohesive glacial till. The failure mechanism of the cliffs was a rotational sliding which is triggered by marine erosion of the toe. Twelve steel tubing wave-guides and two inclinometer casings were installed into the coastal cliff section. Figure 2 shows the instrumentation array arrangement at November 1993. Part of the results that were obtained from a monitoring period of almost one year are shown in Figure 3. In this figure a comparison of the AE recorded data from 4 different wave-guides is made with displacement rates recorded by inclinometer 11.

Figure 2. Cowden instrumentation array It can be seen that there is a reduction in AE mean signal value between days 149 and 163 recorded by all wave-guides, which is accompanied by a reduction in the rate of increase of displacement recorded by the inclinometer. The monitoring method wasn’t continuous, but based upon periodic site visits and acquisition of AE data. Therefore, it is likely that much deformation-related AE was not captured because no operator was present when it was generated. However, under these conditions the correlation of displacement rates with AE was encouraging, and proved the good qualitative status of the AE monitoring technique. Unfortunately, at this stage, the signal could not be quantified to provide an independent measure of slope instability. One of the wave-guide design parameters was backfill type. Wave-guides 1, 5 and 12 were backfilled with sand, wave-guides 2, 6 with gravel and the rest of them with grout. The grout backfill produced the least AE, gravel appeared to be the next active and the sand backfill clearly produced the highest levels of AE (Figure 3b). The poor response of gravel backfilled wave-guides was a result of the gravel particles requiring greater displacements of the host soil to cause them slip. In addition, slippage would occur over a shorter period of time, but AE would be of much greater amplitude than for sand particles. 4.

CURRENT LABORATORY STUDIES

The aim of recent laboratory work has been to investigate the AE wave-guide response and quantify the AE levels with displacement. For the first stage of this work, the waveforms of the AE signals, propagating through a free surface wave-

153

guide were investigated to locate the AE source. For the second part the AE investigation of two granular backfills (gravel and sand) surrounding the waveguide were investigated.

breaks. This method was used because the generated signal mainly consisted of one event with short duration and was reproducible and consistent. The 0.3 mm pencil lead, of 3 mm length was broken at a constant angle, multiple times, at the five different locations, 0.36 m, 0.54 m, 0.72 m, 0.90 m, and 1.08 m away from the sensor. The signals were sensed and processed by the instrumentation described in section 2. The main amplifier was set to 50 dB. The A-to-D board was set to capture a stream of 400 data points including 50 pre-trigger points at a frequency of 237 kHz.

Figure 4. Experimental set-up

Figure 3 Displacement rate inclinometer 1 and AE mean signal value of four WG’s.

4.1.

A E source locution

Figure 5 . Arrival time of the 1st peak versus distance between source and sensor

In this study the histograms (waveforms in time domain) of the recorded signal were investigated. Different wave modes with different propagating velocities were identified in the signal. This identification is essential to locate the AE source. Two sections of 1.63 m length (6 mm wall thickness) steel tubes connected by a steel collar were used. The whole wave-guide body (two sections with the collar) was lifted from the ground and supported by three wooden blocks (Figure 4). This was to provide a free surface around the wave.. guide. The signal was generated in the form of a transient step force function by carrying out pencil lead

Analysis was focused only on the first part of each captured event. The reason being to identify the first two fastest modes, and not to complicate the study with other flexural modes or reflections. The arrival time of the first peak was plotted on a graph with respect to the distance between source and sensor. At each distance ten values of arrival time for the first peak from different pencil lead break records were plotted. Figure 5 shows a linear relationship between propagating distance and arrival times of the first peak. This is an indication of a constant velocity 154

difference between the fastest mode, which triggers the A-to-D board, and the flexural mode which arrives with higher amplitude. The pencil breaks were repeated with the transducer moved further away from the edge of the wave-guide to position B (0.40 m). This was to investigate whether reflections from the edge of the wave-guide would be included in the waveform. It was found that the slope of the line was similar to the above plot. This indicates that there is no interference of reflections in the first part of the waveform section that is under investigation, and that the results are consistent. The results of these tests show that it is possible to locate the AE source without using a second transducer. The recognition of the two fastest wave modes can be achieved, and hence the difference in their arrival times and the location of the source can be measured. It has to be noted that the above findings are at present only applicable for propagating distances less than 2 meters. 4.2.

Active wave-guide system

Two types of backfill soil were investigated: i) well graded sand and ii) medium size rounded gravel. A thick polythene sleeve with a diameter of 195 mm, and lenght of 1650 mm was used to contain the backfill material. The soil column was supported vertically by a steel frame. Before filling the sleeve with the soil, one section of 1.65 m (steel tube) wave-guide was inserted in the centre of the polythene sleeve (i.e. representing a wave-guide in a borehole filled with the backfill soil). The backfill soil then was placed between the wave-guide and sleeve. The transducer was fixed to the exposed top section of the tube. The AE instrumentation components were the same as in the previous experiment. The only difference was that A-to-D frequency was reduced to 150 kHz, and 1000 data were captured including the 100 pre-trigger points when a pre-set threshold was exceeded. The AE events were generated by a compression action, on the soil surrounding the wave-guide, achieved by using a G-clamp. The compression was applied at two different heights. The clamp was calibrated to produce controlled displacements of the soil cylinder surrounding the wave-guide (i.e. changes in diameter). The recorded AE events were assessed, by carrying out simple statistical analyses. The mean and standard deviation of the AE voltage response were plotted against cumulative displacements. This is

Figure 6. AE versus cumulative displacement of gravel backfill at propagating distance of (a) 565 mm (b) 1170 mm shown in Figure 6(a), (b) for gravel backfill and 7(a), (b) for sand backfill. It is obvious that the deformation of the gravel emits higher AE levels than the sand. There is a general trend of increase in the AE mean amplitude with displacement. The sand backfill behaviour seems to consists of sporadic releases of energy which results in the AE level dropping temporarily and then rising again to a new maximum value with increasing displacement. This phenomenon is the “Kaiser effect” in which AE levels are low until the material is stressed beyond that which it has experienced in the past. Kavanagh (1997) demonstrated this effect on sand in an isotropic compression tests. Measurements indicate that exact AE repeatability is difficult to obtain. This remains a topic for further research.

generates high magnitude emission over a short time scale. The relationship between displacement and statistical mean and standard deviation values of AE was as expected (the statistical values increase with displacement). However, additional studies are required in order to relate the displacement rate with the AE response. REFERENCES

Figure 7 AE versus cumulative displacement of sand backfill at propagating distance of (a) 565 mm (b) 1170 nini

5.

CONCLUSIONS

Results from field studies suggest that the AE technique can be used to detect and monitor prefailure deformations in soil slopes. The most promising area of research relates to the use of active wave-guide systems with the assessment of AE signal characteristics. The pencil lead break studies suggest that it is possible to locate the AE source using only one transducer. The two fastest guided-wave modes in the first part of the captured signal can be identified, and therefore the difference in their arrival times and hence the propagating distance of the signal can be estimated. The study of the two backfill types, gravel and sand, showed that the former backfill was “noisier” under small displacements than the latter. The sand backfill appears to generate low magnitude emission over a long time scale whereas gravel backfill

Chichibu A.K., Nakamura M., Goto T. & Kamata M., 1989. Acoustic emission characteristics of unstable slopes. Journal of Acoustic Emission, 8, 4, 107-112. Dixon N., Kavanagh J.G. & Hill R., 1997. Monitoring landslide activity and hazard by acoustic emission. Journal of Geological Society of China, Special Publication of the Proc. 3”d Sino-British Geological Conference, Taiwan, 39, 4, 301-327. Kavanagh J.G., 1997. The use of acoustic emission to monitor of a solid body. PhD. Thesis, Nottingham Trent University. Koerner R.M., McCabe W.M. & Lord A.E.Jr, 1981. Acoustic emission behaviour and monitoring Acoustic Emissions Geotechnical soils. Engineering Practice, ASTM STP 750, V .P. Drnevich and R.E. Gray, Eds., American Society for Testing and Materials, 93- 141. Nakajima I., Negilshi M., Ujihara M. & Tanabe T., 1991. Application of the acoustic emission monitoring rod to landslide measurement. Proc. 5th Conference on Acoustic EmissiodMicroseismic Activity in Geologic Structures and Materials, Pennsylvania State University, 505-520. Terzaghi K., 1950. Mechanism of landslides. Geological Society of America, Berkey, Application of Engineering Practice, S. Paige, Ed., 83-123.

156

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 0795

Hydraulic fracturing as a mechanism of rapid rock mass slides Shuichi Hasegawa Shikoku Research Institute Incorpora-arect,Takamatsu, Jupan

Tomihiro Sawada Suwu Soft Science Incorporated, rOkyo, Jupan

ABSTRACT: This paper presents a possible mechanism of rapid rock mass slides by hydraulic facturing of bedrocks. Large-scale rock mass slides along the Median Tectonic Line (MTL) in Southwest Japan are inferred to have been caused by hydaulic fracturing, based on texture of sliding layers. Past big earthquakes by the MTL might have trigged the rapid rock mass slides. 1.INTRODUCTION

The active fault planes are usually higt-angled, dipping north. The MTL have made the linear

The earthquakes are one of the most important landslides-inducing agents in seismic regions. As the Japanese islands are located in the CircumPacific seismic zone, numerous landslides caused by earthquakes have been reported. The Median Tectonic Line (MTL) contains highly active faults that have a potential danger of earthquakes in Shikoku, Southwest Japan (Osaka,1980). Large-scale rock slides occurred in the Early to Middle Pleistocene along the fault scarps of the Median Tectonic Line in Shikoku (Hasegawa,l991). This paper describes the geological characteristics on sliding surface of a typical rock slide masses in northern Shikoku, then disscusses a possible mechanism of rapid rock mass slide by hydraulic fracturing.

topographical boundary between the mountain and the plain in Shikoku. Geology along the MTL in Shikoku is shown in Fig. 1.

2. GEOLOGICAL SE'TTING The MTL separates the Ryoke granites and the Izumi Group from the Sanbagawa metamorphic rocks. It forms a active fault system with predominantly right-lateral displacement in the Quaternary in Shikoku and western Ki. The rate of right-lateral slip of the fault during the late Quaternary is estimated to be several meters per lOOOyears in Shikoku (Okada, 1980). The active faults of the MTL are inferred to cause magnitude 7 t o 8 class earthquakes on the basis of the fault lengths and the amount of displacement (Okada, 1992).

3. EXAMPLE OF ROCK MASS SLIDES

3.1 Shinyama rock mass slide In the northeastern part of Shikoku, the MTL is marked by striking contrast in topography between the northern Sanuki Range and the southern Yoshino River basin. The Ikeda fault runs ENE along the southern foot of the Sanuki Range (Okada,1968). The Shinyama hill is an isolated hill on the south of the Ikeda fault (Fig.2) . The hill is underlain by the alternated beds of brecciated sandstone and mudstone of the Izumi Group, which is a large-scale sliding rock mass with about 1.5km and 0.5km in width, and about 150m in thickness (Okada,1968 : Hasegawa,1993 : Fig.2,3). The sliding surface is observed at Loc.1, the southern foot of the Shikoku mountains (Fig.2) . At Loc.1, the sliding rock mass composed of the Izumi Group overlies on the debris flow deposits A (Fig.4). The sliding surface is undulated and gently dipping north. Clay-rich matrix brecciated layer is formed beneath the sliding mass. It consists of sandstone fragments with black clay-rich matrix and attains 20 -30cm in thickness. No distinct shear plane is observed in the matrix, or the bountary between the 157

158

Figure 4. Sliding surface of the Shinyama rock mass slide. (D:Debris flow depA (Dochu Fm.), SS:Sliding surface, CBL:clay-matrix brecciated layer, 1:Izumi Cp.)

ovelying mass and underlying debris flow deposits. The Shinyama mass can be restored on the open space at the mouth of the Aikurushi River about 45 km east of Shinyama, based on lithology, topography and slip rate of the Ikeda fault (Fig.2,3). This restoration suggests that the original sliding surface of the Shinyarna mass was very gently dipping less than 10" .

width, and over 180min thickness (Hasegawa, 1993;Fig.5,6). The sliding surface is obseved at LOc.2, where the type outcrop of the Gunchu fault was reported (Saito,1962). At h c . 2 , the sliding rock-mass composed of the Izumi Group overlies on the PlioPleistocen Gunchu Formation (Fig.7). The sliding rock mass consists of alternated beds of brecciated sandstone and mudstone, which is similar to those of Shinyama. The Gunchu Formation consists of harf-consolidated gravel and silt layes, and steeply dipping north. The sliding surface A is undulated, striking N70" - 80" E and dipping 50-60" S at the front, becoming horizontal at the seashore. The sliding surface A can be traced to the sliding surface B, which strikes N80" W and dips 3 2 " N. This indicates that the overlying Izumi Group is rootless. The sliding surface B cuts the reverse fault (probably sliding) plane C, which strike 80" E and dips40" S.

3.2 Miaki rock mass slide At the westernmost part of the MTL active fault system in Shikoku, the Iyo fault is marked by remarkable contrast in topography between the southern Shikoku mountains and the northern Matsuyama Plain, trending N50" E (Saito,1962 : Okada,1972). The Miaki mass is an isolated hill on the north of the Iyo fault (Fig.6). The hill is underlain by the alternated beds of brecciated sandstone and mudstone of the Izumi Group, which is a large-scale sliding rock mass with over 4km and about lkm in

159

Figure 5. Geological map of the Miaki rock mass slide.

Earrfiiddle Pleistccene deposits (Miaki Fm) P I i o f l e i s t c c e n e deposits (Gcmcho Fin Andesite & Rhyol i t e (Ishizuchi Gr.) @ Acidic tuff (Izuni Gr.) Mdstcne predcmimnt a l t e r m t i m (Izuni Gr.) 0Sandstcne predaninant a l t e r n a t i m (Izuni Gr.)

Figure 6. Geologic Profile of the Miaki rock mass slide.

The sliding surface A and B have accompanied black clay-matrix brecciated layer which attains 40 -50cm in thickness. This clay-matrix brecciated layer is quite similar to that of the Shinyama mass. It consists of sandstone fragments with black clay-rich matrix derived from the Izumi Group. Although destinct shear plane is obseved in the zone, boundarys between the overlying mass and the The Miaki sliding rock mass can be restored on the open space at Konokawa about lkm southwest of the mass. This restoration suggests that the original sliding surface of the Miaki mass was also very gentle dipping less than 10" (Fig.6).

4.CHACTERISTISS ROCKMASS

OF

THE

SLIDING

4.1 Sliding rock ~ x S Characteristics of the rock slide masses of the Izumi Group are as follows: 1) Original stratifications are roughly preserved, but sandstone beds are disrupted by fracturing to form polygonal-shaped fragments and mudstone beds are sheared parallel to the bedding. 2) Sandstone beds have many open fractures, some of which are filled with soils from the groundsurfaceand unconsolidated pebble bearing muddy materials, derived from the sediments of footwalls. 3 ) Beds beneath the footwalls have few fractures or 160

Figure 7. Sliding surface of the Miaki rock mass slide. (G:Gunchu Fm., SS:Sliding surface, CBL:clay-matrix brecciated layer, 1:Izumi Gp.)

shear planes, showing remarkable contrast with beds on hanging walls. 4) The surface layer of a rockslide mass has a texture similar to debris. 5 ) The masses have been displaced right-laterally by active fault of the MTL. 6) The masses are highly disected by erosion and are more displaced by the active fault, in case that the formative ages are older. 4.2 Sliding layer The sliding layers on the Quatenary sediments are composed of clay-matrix, brecciated layer. This sliding zone material named “clay-matrix brecciated layer (CBL)” has following characteristics. 1) Sandstone fragments are scatterd in clay-rich matrix.

2) h o s t fragments are matrix-supported, and have ramdom fabric. This texture resembles those of debis flow deposits. 3) Shear plains are seldom obseverd in the matrix. 4) Sliding surfaces are usually low-angled. 5 ) Some clay-matrix breccias have injucted into open cracks of the overliying sliding rockmasses. These evidence indicates that the rock-mass had slid rapidly by this clay-rich brecciated layer as lubricant layer and have not moved since having settled. This clay-matrix layers can be interred to be caused by hydraulic fracturing of the Izumi Group, judging from the sililarity of the texture. Sandstone layers have brecciated into fragments which are surrounded by clay material derived from mudstone. 161

5. MECHANISM OF ROCK MASS SLIDE

6. CONCLUSION

These rockslides have occurred at the fault scarp of the active fault of the MTL. These indicate that long-term gravitational deformation of rocks under the steep slopes prepared the starting materials for the large-scale rockslides. The steep slopes had been formed by faulting of the MTL before the time of the rockslides. Sliding surface are gentle (less than 10 ), judging from the restoatoin of the mass. These gentle sliding surfaces are very difficult to occur, where the bedding planes of the Izumi Group at the source area dip opposite to the slopes. Therefore, simple static slope stability analysis cannot be adopted. The texture of clay-matrix brecciated layers which were the lubricant layer during the sliding indicates that the clay-matrix brecciated zone acted as fluid. Injection at the front boundary of the Miaki mass also supports the extraordinary high pore pressure. We propose the dynamic formative process of the clay-matrix brecciated layer by hydraulic fracturing, based on above mentioned observation. The possible mechanism of rockslides is as follows: 1)The uplift by the fault activity and the opposite dipping structure of the Izumi Group had produced the large-scale steep slopes. 2) Grativitation deformation might have formed the creeping zone in the slope. 3) Groundwater had permeated into the mass along the creeping zone. 4)The tremor by a big earthquake by the active fault at the foot of the slope caused an extraordinary pore pressure in the slope. 5) The extraordinary pore pressure caused the shear failure of the atlernated bed of sandstone and mudstone. That is, the hydraulic fracturing occurred. 6) The hydraulic fracturing have propagated along the pre-exsisting creeping zone, and caused the slide. 7) The mass above the sliding layer had slid rapidly onto the unconsolidated sediments and had stoped after long - distance sliding. As this mechanism is inferred from geological evidences, theoretical and experimental study are needed. Nevertheless, the hydraulic fracturing is important agent of rapid rock mass slides, expecially in case of earthquakes.

This paper presents a posible machanism of rapid rock mass slides by hydraulic fracturing of bedrocks. Conclusions are as follows: 1)Large-scall rock mass slides along active faults of the Median Tectonic Line have clay-matrix brecciated layer as sliding surface. 2) The texture of the clay-matrix brecciated layers is inferred to have been formed by hydraulic fracturing of the bedrock. 3)The rock masses had slid rapidly from the fault scarp, using the clay-matrix brecciated layers as lubricant layer. 4)The hydraulic fracturing is important agent of rapid rock mass slides, in case of earthquakes.

ACKNOWLEDGMENT We thank to Dr. Seiichi Kanayama for useful comments on the manuscript, and Ms. Miki Kimura for typing the manuscript. REFERENCES Hasegawa, S., 1991. Large-scale rock mass slides along the fault scarp of the Median Tectonic Line in northeastern Shikoku, Southwest Japan. Landslides, D.H.Bell (ed.), Balkema, 119-125. Hasegawa, S., 1992. Large-scale rock mass slides and Quaternary faulting along the Median Tectonic Line on the southern foot of the Sanuki Range in Shikoku, SW Japan. Mem. Geol. Soc. Japan, No.40, 143-170. Hasegawa, S., 1993. Large-scale rock mass slides and Quaternary faulting along the Median Tectonic Line in Shikoku, SW Japan. Doctor Thesis of Univ., Tokyo: 219 Okada, A., 1968. Strike-slip faulting of late Quaternary along the Median Dislocation Line in the surroundings of AwaIkeda, northeastern Shikoku. Quaternary Res., 7, 15-26. Okada, A., 1972. Quaternary faulting of the Median Tectonic Line fault system in the northwestern part of Shikoku. Bull. Fac. Litel:, Aichi Pref: Univ., 23, 68-94. Okada, A., 1980. Quaternary faculty along the Median Tectonic Line of southwest Japan. Mem. Geol. Soc. Japan, 18: 79-108. Okada, A., 1992. Proposal of the segmentation on the Median Tectonic Line active faults system. Mem. Geol. Soc. Japan, (a). 15-30. Saito, M., 1962. The geology of Kagawa and northern Ehime Prefecture, Shikoku, Japan. Mem. Fac. Agri. Kagawa Univ., V01.10, 1-74.

162

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Evolution of ridge-top linear depressions and a disintegration process of mountains Kuniyasu Mokudai Kyoto University, Uji, Japan Masahiro Chigira Disaster Preventiofi Research Institute, Kyoto University, Uji, Japan

ABSTRACT: A formative process of upslope-facing scarps and ridge-top depressions has been investigated by the observation, description and measurement of these forms, and geological survey around a ridge in the Akaish Mountains, central Japan. The ridge is underlain by slate, of whch cleavage trends with a small angle with the ridge and &ps very steeply in the depth. The geomorphological features and the geological structure of these forms indicate that these forms were made by the valleyward bowing of slate and that such deformation is the incipient stage of hsintegration processes of a mountain that consists of rocks with steeply-&ppingfoliation.

1 INTRODUCTION

This paper describes and classlfies the morphological features of scarp topography in the southern part of the Akaish Mountains by means of interpretation of aerial photographs and ground survey. Based on the results, we infer the style of slope deformation in t h s area.

"Ridge-top depressions", "multiple ridges", and "upslope-facingscarps" have been documented in many mountainous areas including Japan (we call these forms as scarp topography). The scarp topography was sometimes attributed to periglacial processes (Kobayashi, 1956), but many recent stu&es attribute it to the gravitational deformation of mountains (Jahn, 1964; Zishnsky, 1966; Tabor, 1971; Nemcock, 1972; Matsuoka, 1985; Evans, 1987; Varnes et al., 1989). Moreover, Chgira (1992) and Chigira and Kiho (1994) reported gravitational deformation of rock mass that made scarp topography; steeply hpping foliation bowed valleyward, leaving scarp topography on the upper part of a mountain. The scarp topography has been called in various names, and its scientificrecognition and classification are not adequate as yet. Previous studies about scarp topography focussed mainly on large-scale features, and its detailed morphology has been scarcely described. In addition, its origins and historical development have not been fully studied in terms of the combination of surface morphology and internal geologic structure. Geomorphc processes caused by rock deformation are thus little known, while there are many stu&es on denudation processes of mountains. Understanding the features of scarp topography and its formative processes is very important to pre&ct slope movements or landslides.

2

GEOMORPHOLOGICAL OGICAL,SETTING

AND GEOL-

Study area is a ridge extending NE from the Mt. Yambushi upstream of the Abe River m g . 1).

Fig. 1.Index map of the survey area.

163

Two kdometers to the northeast of the Mt. Yambush is the Oya-kuzure, one the largest landslides in Japan. On t h s ridge and the upper parts of the nearby slopes, there is scarp topography whch consists of scarps and linear depressions aligning in three or four lines. The alignments trend subparallel to the ridge. The ridge is underlain by the Paleogene Setogawa Formation, which trend N-S and is mainly composed of sandstone, shale, and slate, with subordmate basalt, chert, and h e s t o n e (Sugiyama, 1995).

3 METHODS

To clarify the geomorphological features in the study area, we made a geomorphological map by interpreting aerial photographs (1:15000) and ground survey, paying attention to scarp topography. A unit of scarp topography consists of upper and lower h c k lines and a scarp in between. If the scarp inclines in the same kection with its surroundmg slopes, the unit is a downslope-facingscarp (Fig. 2). On the other hand, a unit with a scarp inclining in the opposite direction is an upslope-facing scarp. The scarp topography on top of a ridge is referred to ridge-top depression, because upslope or downslope could not be defined there. In order to characterize the alignments and morphology of scarp topography, we made profiles across of the ridge by using a tapemeasure and a hand level. Measured lines were approximately normal to the trends of scarp topography in a plan. We performed geological investigation by mapping and observation in the field, carefully dstinguishing stationary rock mass from creeping rock mass; almost all rock masses in elevations hgher than creek beds have crept (bowed downslope). 4 RESULTS 4.1 Geomophologcd features

Rgure 3 is a geomorphological map showing scarp topography, in whch many ridge-top depressions and scarps trend parallel or subparallel to the main mountain ridge. The survey area is dwided into two regions from a geomorphologicalpoint of view. The first area is around the peak of the Mt.Yambush. On the northeast side of the peak, there are some downslope-facing scarps trendmg NW, while on the southwest side of the peak, there are some ridge-top depressions parallel to the downslope-facingscarps.

Fig.

2.

Schematic sketch showing tei-minologyof scarp topography.

the

The second area is on the northeast of the first one, where the ridge top is narrower than in the first. In t h s area, there are upslopefacing scarps and ridge-top depressions aligned along several lines trendmg NE. m s is a different feature from those in the first area. Some of the scarps or the depressions are connected to each other. The top of the ridge in the second area widens toward the northeast. Figure 4 shows profiles across the ridge-top depressions and scarps along the lines shown in Figure 3. As is seen in Figure 4, top of the ridge is a wide gentle slope, and the scarp topography appears on the southeast side of the ridge almost exclusively. Scarp topography does not appear in the slopes on the other side of the ridge. The scarp topography has hgher scarps in hgher elevations. For example, along Line 3, the height of the scarp of a ridgetop depression is 10 m, while the height of the upslope-facing scarp on slope is about 1 m. In addition to the height change, scarp topography changes its sharpness according to elevations, the scarp tops are more rounded in hgher elevations than in lower elevations. 4.2 Geologcalstructure

The strata in the survey area consist mainly of slate with subordmate alternated beds of chert and slate, and greenstone. These strata strike N-Sand dip steeply to the west or east. The 164

Fig. 3. Geomoqhological map of the survey area. See Fig. 2 for legend.

slate has well-developed slaty cleavage whch is parallel to the beddmg planes in most parts with some exceptions. T h s slaty cleavage bowed to the east, downslope, in the surface parts of almost all slopes on the southeast side of the ridge from the Mt. Yambushi to the Oyakuzure (Fig. 5, Chigira, 1997). Consequently, the rock mass is fractured extensively by the shearing along the slate cleavage.

5

GEOLOGICAL STRUCTURE AND FORMATIVE PROCESSES OF SCARP TOPOGRAPHY

The scarp topography has not been formed by normal erosion processes, because the trend of the topography approximately parallels t h e contour lines, and its upper and lower knick points is clearly defined. On the contrary, the scarp topography has a n alignment andrelations with geologic structure, which indicate 165

Fig. 4.Proues across scarp topography along lines shown in Figure 3.

t h a t i t h a s been made by g r a v i t a t i o n a l deformation of rock (Fig. 6). Along the scarp topography, active tectonic faults could not be expected because it appears only around the ridge-top and because strata on one side of the ridge continue t o the other side across the topography. On the other hand, it is codrmed that the strata on almost all the southeast slope of the ridge bowed to the east. Moreover, such deformation could form a gravitational fault whch appear as an upslope-facing scarp, as has been observed in the landslide scar of the Aka-kuzure, 10 km west of the Mt. Yambushi (Chigira and Kho, 1994). Morphology and heights of scarp topography probably inhcate a period of its formation as follows. The top of a scarp is denudated gradually and its roundness is expected to

increase with time. In the survey, area, the roundness of a scarp in higher elevatioiis is larger than that in lower elevations as described before. This difference within an small elevation interval of about 40 m strongly suggests that the scarp topography in hgher elevations is older than that in lower elevation. In adhtion, the relative height of scarps in hgher elevations is larger than that in lower elevations. These geomorphological features suggest that slope deformation spread outwards from the top of the ridge. The shape of scarp topography also changes laterally along the ridge in the second area: scarp tops become more rounded to the northeast, inhcating older origin. Downslope-facing scarps in area 1, which form step-llke landform, are probably made by 166

Fig. 5. Geological map of the Survey area. Arrows inchmix the dixection of rock movement mfei-red &om the fold ayes made by the bowing of slaty cleavage

the translational slide to the northeast leaving ridge-top depressions on the southwest side of the Mt. YambusWs peak.

CONCLUSIONS

Ths study clarrfred geomorphological and geological features of upslope-facing scarps and ridge-top depressions on an ridge near the Mt. Yambush in the Akaish Mountains, whch is mainly underlain by Paleogene slate with steeply-hpping cleavage. Following results were obtained.

1. Upslope-facing scarps and ridge-top depressions trend parallel or subparallel to the ridge, being ahgned in several lines. 2. The top of a scarp in a higher elevation is more rounded than those in lower elevations. 3. The relative height of a scarp is larger for the scarps in hgher elevations. 4.The above two facts strongly suggest that the scarps and depressions in hgher elevations are older than those in lower elevations, indxating that slope deformation extended from the ridge top outwards. 5. The slope deformation is probably caused the

167

Matsuoka, N. 1985. Rock control on the dstribution of linear depressions on the main divide of Akaishi range, Southern Japan Alps. Geogz Re%Japan. 58 : 411-427. Nemcok, A. 1972. Gravitational slope deformation h g h mountains. International Geological Congress, 24th Montreal, Canada, Sec.lj: Proceedngs 131-141. Sugiyama, Y. 1995. Geology of the northern Setogawa Belt in the Akaish Mountains and the formation process of the Setogawa accretionary complex. Bd. Geol. S m . Japan. 46: 177-214. Tabor, R. W. 1971. Origin of ridge-top depressions by large-scale creep in the Olympic Mountains, Washngton. Geol. Soc.

Am. Bd.82: 1811-1822. Varnes, D. J.,Radbruch-Hall, D. H. and Savage, W. Z. 1989. Topographc and structural conhtions in areas of gravitational spreadmg of ridges in the western United States. U S GeoIogical Survey Professional Paper, 1496. Zishnsky, U. 1966. On the deformation of high slopes. Proc. Cong. Int. Soc. Rock Mechanics, 1st.2: 179-185. Lisbon. Fig. 6. Relationshp between scarp topography and geological structure.

valleyward bowing of slate separated by steeply-hpping cleavage. REFERENCE Chigira, M. 1992. Long-term gravitational deformation of rocks by mass rock creep. Engineering Geologv 32: 157-184. Chgira, M. & Kho, K. 1994. Deep-seated rockslide-avalanches preceded by mass rock creep of sehmentary rocks in the Akaish Mountains, Central Japan. Engheezing Geolow. 38: 221-230. Chigira, M. 1997. Large mass rock creep and possible landslides in the area from the Oya-kuzure to Yambush-dake. Heisei 9 nendo happyou kai kouen ronbun syuu. (Proceedngs of amual meethg of Japan Engneennggeology society) 89-91. Evans, S.G. 1987. Surface hsplacement and massive toppling on the northern ridge of Mount Currie, British Columbia. Geol. S m . Can. Paper. 87-1A.181-189. Jahn, A. 1964. Slopes morphological features Zeitresulting from gravitation. Geomorph.,Suppl. 5: 59-72. Kobayash, K. 1956. Periglacial morphology in Japan. Bid.PeuyglaqZy 4: 15-36. 168

Slope Stability Engineering, Yagi, Yamagami & Jiang (c 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Geological characteristics of landslides of the soft rock type, Central Japan

ABSTRACT: Many landslides of the soft rock type occur in Tertiary or Quaternary formations of the Japanese Islands, and are divided into three groups. Landslides of the first group, which are often large in scale, are found in the Neogene "Green Tuff" formations along the Sea of Japan side. Those of the second group mainly occur in scattered sedimentary basins of Neogene age, partly of Paleogene age, in the Setouchi area of the central Southwest Japan, and in the Pacific Ocean side of Northeast Japan. The third group is found in Quaternary sediments, or volcanic pyroclasts. The author discusses geological and geomorphologic characteristics of landslides of the second group, based on those of the Kobe Group of Paleogene age, Central Japan.

1 INTRODUCTION In the Japanese Islands, a large number of landslides belonging to the soft rock type are mainly distributed in the Neogene "Green Tuff" formations along the Sea of Japan side, which form typical landslide areas in Japan. Some characteristic landslides occur in scattered sedimentary basins of Neogene or partly Paleogene age in inland areas, and also in Quaternary unconsolidated sediments or volcanic pyroclasts. The landslides of the Kobe Group of Paleogene age, Central Japan, are typical ones in the Inner Zone of Southwest Japan, together with those of the Hokusho area in northern Kyushu. The author discusses geologic characteristics of landslides of the soft rock type, different from those of the "Green tuff" type. The Kobe Group, which mainly distributed in the Sanda Basin, north of the Rokko Mountains, Kobe in Central Japan, is one of the largest landslide areas in Southwest Japan. This Group consists of mudstone, sandstone and conglomerate of lacustrine origin, and is characterized by numerous tuff beds found in various horizons. Most of the landslide areas range from 5 to 10 in slope angle, though the Basin forms many hills of 10 to 20 in slope angle. It is clarified that many landslides occur in slopes with lower slope angle. On the basis of the fact that occurrences of landslides are generally controlled by geological factors, the author proposed the geologic control

of landslides. He pointed out that two kinds of main geologic factors, lithology and geologic structure of bed rocks, are closely connected with occurrences and movement of landslides. It is indicated that many landslides of the slow slide type occur in fine clastic sediments, such as mudstone and fine tuff, in every kind of basement sedimentary rocks.

Fig.1 Outline of geology of Kobe and its adjacent areas (based on Huzita and Kasama, 1983) 1: Alluvium and Quaternary sediments 2: Kobe Group 3: Basement rocks (pre-Cretaceous formations with volcanic rocks) (S): Sanda Basin 169

2KOBEGROUP The Kobe Group is mainly distributed in the Sanda Basin, north of Kobe in central Kinki District, which is a square area with about 22 and 16 km in the East to West and North to South directions (Fig.1). This Group is composed of mudstone, sandstone and conglomerate of lacustrine origin, and is characterized by numerous tuff beds found in various horizons. These tuff beds are useful as key beds in order to clarify the stratigraphic sequence and geology structure, though it commonly is difficult to distinguish them by naked eyes. The stratigraphy has been established by Huzita, Kasama and their group, who have been researching it since 1955, by means of tracing tuff beds in field and the petrographic study of tuff (Huzita et al, 1971; Huzita & Kasama, 1983). Generally, the Group is dips gently westward or toward the center of the Basin, except for several fault and flexure or fold zones. As the result, the Kobe Group in the Sanda Basin is divided into Arino, Yokawa and Ohgo Formations in ascending order. Each formation is 170 to 190 m’s’ thick, respectively, and shows sedimentary cycles changing coarse to fine clastic sediments. Fig.2 and Fig.3 show the modified stratigraphic sequences of the Kobe Group and the geological map of the Sanda basin, respectively. The fu-ino Formation unconformably overlies the basement rocks composed of rhyolitic to dacitic lava and pyroclasts of Late Cretaceous to Early Paleogene age, which are called by the Arima Group, and of pre-Jurassic clastic rocks. It is exposed the marginal area of the basin, particularly distributed its southeastern corner, and mainly consists of boulder to cobble conglomerate and sandstone with thin layers of mudstone and tuff. The Yokawa Formation, which is mostly widespread in central part of the Basin, conformably overlies the Arino Formation. Well-sorted and massive sandstone dominate the lower part, intercalating mudstone and two tuff beds, and partly containing pebbles derived from the basement rocks. The upper part, characterized by tuffaceous facies as a whole, is mainly composed of mudstone, sandstone and two remarkable tuff beds. The lower tuff is very conspicuous, hard and widely traceable, and is considered to be pyroclastic flow deposits. In the upper most part, thick sandstone beds with pebbles and mud balls are dominant. The Ohgo Formation, mainly occupied west side of the Basin, overlies the Yokawa Formation with slight disconformity, and is unconformably covered by the Osaka Group of Quaternary age, and several terrace beds. Thick massive and well-sorted

sandstone beds dominate the lower part, and include pebbles or mud balls, intercalating thin mudstone beds. The upper part is mainly composed of tuff and tuffaceous mudstone intercalating sandstone or conglomerate. Recently, Ozaki and Matsuura (1988) show that the Group is considered to be late Eocene to early Oligocene on the basis of the fission track age of tuff, and show new stratigraphy of the Group.

Fig.2 Compiled columnar section of the Kobe Group (based on Huzita and Kasama, 1983) 1: Tuff 2: Tuffaceous mudstone 3: Mudstone 4:Tuffaceous sandstone 5: Sandstone 6: Tuffaceous conglomerate 7: Conglomerate (well-sorted) 8: Conglomerate (poorly sorted angular gravels) 170

Fig.3 Geologic map of the Sanda Basin and distribution of landslides

1: Alluvium, low and middle terrace deposits 3: upper part of the Ohgo Formation 5: upper part of the Yokawa Formation 7: Arino Formation 9: fault The surround area with black line shows one 3 GENERAL REMARKS OF LANDSLIDES

Generally, the Sanda Basin shows hilly topography. The relative relieves are commonly small, showing below about 100 m. The inclination is also gentle, and most of the slopes in the Basin are between 5 and 20 in slope angle. According to Huzita and Kasama (1983), Fujita (1984 & 1994) and Ishida et a1 (1975, 1976, 1977 & 1985), main features of landslides of the Kobe Group are summarized as follows: By slope analysis (Fujita, 1984 & 1994), many landslide areas show 10 to 15 in slope angle, and it is clarified that many landslides occur in slopes with lower slope angle than with higher one. Then, landslide areas are so gentle and high in content of water that they mostly use as rice fields. Landslides of the Kobe Group are commonly found in found in mudstone or fine tuff beds. Its sliding mass is mainly composed of soft, light brown or gray colored, ill-sorted and massive debris deposits with angular to round cobble or

2: Osaka Group and high terrace deposits 4: lower part of the Ohgo Formation 6: lower part of the Yokawa Formation 8: Basement rocks (mainly Mesozoic Rhyolite) 1 0:landslide of the Fig.4 pebble, partly boulder, derived from mudstone, tuff and sandstone of the Kobe Group. The matrix mainly consists of viscous clay or silt, partly sand, including abundant clay minerals, such as montmorillonite. This is called a "debris and soil bed." On the other hand, some of the masses consist of weathered fine clastic rocks, partly coarse clastic rocks of the Kobe Group. The size of a sliding mass, which consists of "debris and soil bed," is generally 10 to 50 m in width, 50 to 300 m in length, 5 to 10 m in thickness. The average volume is estimated to be 4 x 104m3. Though a sliding mass is small in scale, a large new one is often formed, combining several sliding masses. A sliding mass composed of rock masses is usually large in scale, showing 300 to 500 m in width, 300 to 1,000 m, 5 to 30 m in thickness, and 5 x 106m3 in average volume. Most of the landslides show the slow slide type of movement. The displacement is usually less than 10 cm a year, but the movement is often continuous. Particularly, the movement of a 171

landslide composed of rock masses is very slow, namely the slow slide or creep type, and is continuous. Some landslides show the rapid slide one, but are commonly small in scale. A primary sliding surface is generally found on an unconformity plane between a "debris and soil bed" and each formation of the Kobe Group. It forms a soft clay layer with the thickness of 5 to 10 cm, and is very viscous and high content of water, including abundant montmorillonite. Some of the surfaces are formed in mudstone or fine tuff beds of the Kobe Group, and large-scale landslides often occur. The secondary one is often found within the bed, and smaller landslides occur. 4 GEOLOGIC CONTROL OF LANDSLIDES 4.1 Lithological Control On the basis of the fact that occurrences of landslides are generally controlled by geological factors, the author discussed the geologic control of He indicated that two landslides (Fujita, 1987). kinds of main geologic factors, lithology and geologic structure of the Kobe Group, are closely connected with occurrences and movement of landslides, and calls them the lithological and

structural control, respectively. Generally, it is indicated that many landslides of the slow slide type occur in fine clastic rocks, in every kind of bedrock of sedimentary origin. Fig.4 shows the geological map with the distribution of landslides of the slow slide type in the Ohgo area, which locates in the southern and central Basin. This area is well known to be one of the most typical landslide areas in the Kobe Group. On the map, the Kobe Group is divided into two kinds of lithofacies, namely fine clastic rocks composed of mudstone and fine tuff, and coarse clastic rocks composed of sandstone, conglomerate and coarse tuff. The former rocks are soft, weak and low in strength, and form many gentle slopes with large slope length. On the other hand, the latter are hard and high in strength, in comparison with the former ones. Therefore, the hard rocks form relatively steep slopes over 20 in slope angle, and landslides of the rapid slide or fall type occur. In general, they calls slope failures, and these are not shown in the figure, because of small in scale As Fig.4 clearly shows, most of landslides belonging to the slow slide type are found in soft and fine clastic rocks. From the fact, it is pointed out that fine clastic rocks show tendencies to form sliding surfaces, because of including abundant clay

Fig.4 Geological map and distribution of landslides in the Ohgo area 2: Landslide 3: Conglomerate and sandstone of the Kobe Group 1: Alluvium 6: Fault 4: Mudstone and tuff of the Kobe Group 5 : Mesozoic Rhyolite 0: Ohgo S: Kita-Sou0 H: Higashihata M: Mikage K: Kohda 172

Fig.5 Schematic cross sections of landslide areas (A) L1 L: Landslide ( LI: Old landslide, L2: Active landslide, L: Landslide of the rapid slide type) S: Soft rock SF: sliding surface H: Hard rock (B) SS: Sandstone (hard rock) MS: Mudstone (soft rock) C: Landslide of the rapid slide type (L3 type) L: Landslide of the slow slide type

-

minerals, particularly montmorillonite. Therefore, many landslides occur, and are often large in scale. They move on slopes slowly and continuously. In this area, the action of groundwater is closely related to form a sliding surface. Though the movement of groundwater is complex, two types of movement are proved. The first type is one of the shallow groundwater through relatively thin "debris and soil beds," 2 to 5 m under the ground surface. This type of groundwater is closely related to The second type shows groundwater rainfalls. moving in weathered strata of the Kobe Group about 10 m deep, and has a slight relation to rainfalls.

4.2 Structural Control The author proposed three structure type of landslides; the "Nagareban," "Ukeban" and "Yokoban" types (Fujita, 1987). Many landslides show the "Nagareban" type, whose sliding mass moves along the dip direction side of a bedding plane. On the other hand, landslides of the "Ukeban" type move toward reverse side of the dip direction of the plane, and the "Yokoban" type are the strike slide one. Fig.5 shows two schematic cross sections of landslide areas in this area. These sections indicate that soft and fine clastic sediments, mainly mudstone, form gentle and long slopes, and that most of the landslides occur on these slopes.

These belong to the "Nagareban" type, and are commonly large in scale. Particularly, sliding masses composed of rock masses belong to this type. These facts indicate that a main sliding surface forms along a bedding plane. Hard and coarse clastic rocks, mainly sandstone or conglomerate, form relatively steep slopes with short slope length, and a few landslides of the collapse type occur, showing the rapid slide type of movement, or sometimes the fall type. These are commonly small in scale, and belong to the "Ukeban" type. In this area, a small number of landslides belonging to the "Yokoban" type are found, and are commonly small in scale. In Fig.5, the upper figure (A) shows the relation between occurrence of landslides and bedding planes of sedimentary strata with low dips less than about 5 O . On very gentle and long slopes parallel to bedding planes, many landslides of the "Nagareban" type occur. Some of these old landslides are found on the end of slopes with about 5 in slope angle, and are stable at present. Present active landslides occur on relative steep slopes with about 10 in slope angle. Some small-scale landslides of the collapse type occur on slopes of the opposite side. These lanclslides show the movement rapid slide type, and most of them are distributed in central part of the Sanda Basin. On the other hand, the lower figure (B) shows typical cuesta topography, and landslides belonging to the "Nagareban" type occur on these slopes with 173

about 10 O in slope angle. Many landslides show this type, and move slowly and continuously. These landslides are mainly found around the central Sanda Basin. It is pointed out that the ridge in the upper figure was eroded out, and topography of the lower figure has been formed. Many landslide areas of the slow slide type form gentle slopes and are used as rice fields, because of keeping a large quantity of water. However, those of other types are difficult to be used as rice fields or farm, because of steep slopes.

ban'' type, which occur in coarse clastic sediments, in contrast to the former type. REFERENCES Fujita, T., 1984: Slope analysis of landslides of the soft rock type in Kinki, Southwest Japan. Proc. 3rd Inter. Symp. Landslides, Toronto, 2, 75-80. Fujita, T., 1987: Geologic features of landslides in Japan. Proc. China-Japan Field Workshop on Landslides, Xian - Lanzhon, 61-68. Fujita, T., 1994: Characteristics of landslides in Southwest Japan based on slope analysis. Proc. 7th Inter. IAEG, 3, 1415-1424. Huzita, K., Kasama, T., Hirano, M., Shinoda, T. & Tanaka, M., 1971: Geology and geomorphology of the Rokko area, Kinki district, Japan, with special reference to Quaternary tectonics. Jour. Osaka City Univ., 14, 71-124. Huzita, K. & Kasama, T., 1983: Geology of the Kobe district - Quadrangle series, scale 1:50,000. Geol. Surv. Japan, 115p. (in Japanese with English abstract). Ishida, Y., & Nishiura S., 1975: Studies of landslides of agricultural land in Kobe Group, Tertiary deposit (Part.1). Jisuberi (Landslide), 12(3), 17-23. (in Japanese with English abstract). Ishida, Y., Imamura, H., Abe A. & Tomoto S., 1976: Studies of landslides of agricultural land in Kobe Group, Tertiary deposit (Part.2). Jisuberi (Landslide), 13(3), 33-39. (in Japanese with English abstract). Ishida, Y., Kawahara, T. & Kunugi, Y., 1977: Studies of landslides of agricultural land in Kobe Group, Tertiary deposit (Part.3). Jisuberi (Landslide), 14(3), 15-21. (in Japanese with English abstract). Ishida, Y., Ozaki, E. & Sakane, I., 1985: Studies of landslides of agricultural land in Kobe Group, Tertiary deposit (Part.4) & (Part.5). Jisuberi (Landslide), 21(4), 18-28.; 22(1), 7-17. Ozaki, M. & Matsuura H., 1988: Geology of the Sanda district, with geological sheet map at 1:50,000. Geol. Surv. Japan. 93p. (in Japanese with English abstract).

5 CONCLUSION In Japan, many landslides of the soft rock type are found in Cenozoic formations. In Central Japan, the Kobe Group in the Sanda Basin is one of the most typical sedimentary formations of Cenozoic age, and includes many active landslides, which show the slow slide type of movement and are usually small in scale. The geologic and geomorphologic characteristics of the Kobe Group and the landslides are as follows: 1. The Kobe Group consists of three formations, and landslides are found in the Yokawa Formation, which is widely distributed and shows tuffaceous lithofacies as a whole. 2. The Kobe Group forms hills or hilly lands lower than 20 in slope angle. Generally, the landslide areas form gentle slopes between 8 O and 12" in slope angle. 3. Many landslides are composed of "debris and soil" beds, derived from the Kobe Group, including other basement rocks, mainly Mesozoic Volcanic rocks and partly Paleozoic rocks. Some landslides consist of rock masses. 4. As Fig.4 shows, most of the landslides occur in fine clastic sediments, namely mudstone or fine tuff. This fact indicates the lithological control of landslides. On the other hand, small-scale landslides of the rapid slide type occur in coarse and hard clastic sediments, namely coarse sandstone and conglomerate. 5. The fine clastic sediments are generally soft and weak, and include abundant clay minerals, such as montmorillonite. Accordingly, these easily form sliding surfaces for landslides. 6. As Fig.5 shows, many landslides are controlled by bedding planes of strata of the Kobe Group, and slide along the dip direction side of the planes. This is the typical structural control of landslides, and this type is called the "Nagareban" type. Generally, a sliding surface is formed along a bedding plane. 7. On the other hand, most of the landslides belonging to the rapid slide type show the "UkeO

174

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Study of configuration, scale and distribution of landslides S.Ueno OYO Corporation, Omiya,Japan

ABSTRACT: Configuration and scale of general landslides from the reality of existing landslides were studied, and as an example on study of landslides in the mountainous aria of Shikoku was given. The results of this study are summarized as follows: 1)As for the form of landslides, depth and width of landslides show a good correlation. 2)As for the scale of landslides, as a slope becomes steep scale of landslide becomes small. 3)In the mountainous area of Shikoku, the older geomorphic surface showed gentler slope and thicker weathered zone, and landslides are distributed over such place. 1 INTRODUCTION It is very important to understand configuration and scale of landslide, as well as dynamic condition, in an investigation of actual condition of a landslide and design of countermeasures. Even if whole structure of landslide cannot be identified, rational investigation and countermeasures can be programmed in early stage of landslides, if general tendency of landslides can be recognized by estimating one of configuration properties, namely as slide width, length, and depth, of landslide(Tab1e 1). For this purpose, it is necessary to clarify the relationship between each property from analysis of features of existing landslides. From this point of view, the author has been investigating the relationship between scale of landslides and configuration or slope angle, based upon 52 examples, in which actual conditions such as sliding extent or depth were known. In this process, the author came to recognize a specific relationship between scale of landslides and geomorphic surface condition. The author also carried out geomorphological analysis in a part of mountainous area in Shikoku, and studied dominating conditions in the scale and distribution of landslides.

2 CONFIGURATION AND SCALE OF LANDSLIDES 2.1 Configuration of Landslides The author defines the configuration properties of landslides from Figure 1 as follows: Width of landslide 0 : m a x i m u m width of landslide Depth of landslide@):maximum depth of slide plane in vertical direction Length of landslide(L):distance between the head and toe of landslide Slope angle(P):inclinationof line between the head and toe of landslide to a horizontal direction

Fig. 1 Terminology to define the form of landslide

175

Table 1 Na

Location

Geology

1 Ehime 2 3 4 5

6 7

8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49 50 51 52

Kochi Kochi Fukuoka Wakayama Kochi Fukuoka Kochi Kochi Kochi Kochi Kochi Kochi Kochi Kochi Kochi Kochi Kochi Kochi Kochi Kochi Ehime Hyogo Saga Saga Osaka Saga Saga Oita Saga Saga Saga Saga Saga Saga Saga Osaka Osaka Osaka Osaka Nara Hyogo Kochi Nagano Yamagata Hokkaido Nagano Nagano Nagano Toyama Osaka Akita

Geometric data measured for landslides

P(gr) P(gr) P(gr) P(sch) P( sch) P( sch) P( sch) P( sch) P(sch) P( sch) P(sch) P( sch) P( sch) P( sch) P( sch) P( sch) P( sch) P(sch) P( sch) P(sch) P( sch) M(ms,ss) M(ms,ss,tf) T(ms,ss) T(ms,ss) T(ms,ss)

,

T(ms) Utf) T(ms,ba) T(ms,ba) T(ms,ba) T(ms,ba) T(ms,ss,ba) T(ms,ss,ba) T(ms,ss,ba) Q(W) Q(CJ) Q(W) Q(c,s,g) P(S1) P(s1) M(wtf,dk) P(SP,Sl,SS) T (t f, cg ) T(ms,tf,tf) T(ms,tf,ba) T(ms,ss,dk) T(ms,ss,tf) T(ms,ss) T(ms,ss,tf) T(ms,ss,tf,tb) T(tf),Q(an,c,s)

Width W(m>

Depth D(m>

200 135 135 60 90 125 50 30 70 60 60 95 270 230 300 130 50 70 55 80

60 120 80 80 40 300 30 50

180 130 80

35 160 170 80 40 50 70 55 50 200 300 200 300 350 350 350 200 210 250 300 370

Length

Slope angle

B ("1 30 23 19 10 13 19 6 6 14 15 16 18 38 23 30 20 8 8 7 8 6 30 14 15 10 39 9 7 27 23 13 9 14 19 11 8 5 8 10 9 25 30 40 40 40 50 60 40 55 40 60 69

190 340 210 34 210 130 60 40 77 92 85 83 260 510 250 220 70 55 40 75 70 280 65 165 40

185 35 35 230 190 65 40 110 160 110 45 80 110

140 38 225 300 900 160 400 750 250 800 600 900 800

675

P: Palaeozoic, M: Mesozoic, T: Tertiary, Q: Quarternary, gr :green rock, sch: schist, sl; slate, sp: serpentinite, ms: mud stone, ss: sand stone, cg:conglomerate, tf: tuff, ba: basalt, dk: dyke, wtf: welded tuff, tb: tuff breccia, an: andesite, c: clay, s : sand, g: gravel

176

16 15 20 30 14 30 33 29 26 26 25 29 28 20 23 24 32 30 29 25 38 32 25 15 26 11 30 31 14 15 17 30 16 10 15 16 15 13 15 28 28 23 15 12 15 15 22 8 10 10 10 14

Ratios between each configuration property are defined as follows. Surface configuration ratio0;NV):ratio of length of landslide to width Transverse configuration ratio(W/D):ratio of width of landslide to depth Longitudinal configuration ratio(L/D):ratio of length of landslide to depth

From the analysis of transverse configuration ratio, the relationship between depth of landslide and width is shown in Figure 4. A good correlation was found, and the values of transverse configuration ratio(W/D) range within 4- 10. Especially, for the landslides with width grater than 2 1Om, W/D range within 5- 10, and correlation between W and D becomes better.

The values of surface configuration ratio, LMr, range within 0.5-3.0 from the result of analysis (Figure 2). However, in the case of landslides that have been active in long time, this value is often greater than 2.5 in Japan, because of expansion of landslide upward or downward. The Chausuyama landslide in Nagano (L=800m, L/W=4), and the Choujha landslide in Kochi (L=900mYL/W=4.5) represent such long and narrow landslides in Japan. In these landslides, the sliding block dose not move as a single block, because the sliding block is divided into several blocks, and each small block moves independently. So, for the unit sliding block, the value of LMr is supposed to fit within the range given here. For longitudinal configuration ratio, the values of L/D range within 4-15 as is shown in Figure 3. However, in some examples, the value of L/D exceeds this range because of same reason as surface configuration ratio.

Fig.2 Relationship between width and length of landslide.

Fig.4 Relationship between depth and width of landslide.

177

2.2 Scale of Lanaklides

The relationship between slope angle@) and depth of landslide(D) is shown in Figure 5. Most data spread lower than the solid line in this figure. This result shows that depths of landslide tend to be smaller in steep slopes. The author considers that, in steep slopes, because of erosion caused by small scale failure, thick unstable formation, such as weathered zone or talus cannot remain for long period in the process of weathering. The relationship between slope angle@) and transverse configuration ratio(W/D) is shown in Figure 6. From this figure, most data spread lower than the solid line in this figure. This result shows that both maximum and minimum value of transverse configuration ratio tend to be smaller, when slope angle becomes steeper. Considering this result along with the above mentioned relation between slope angle and depth, scale of landslide becomes smaller as the slope becomes steeper.

Fig.5 Relationship between slope angle and depth of landslide.

3.

GEOMORPHOLOGY AND DISTRIBUTION OF LANDSLIDES

In the topography with remarkable upheaval of ground, knick lines that correspond to the edge of the past geomorphic surface can be recognized in many cases.

Fig.6 Relationship between slope and transverse configuration ratio. In general case, several knick lines divide geomorphic surface, and geomorphic surface in higher elevation can be considered as older surface with smaller influence of present erosion. And focusing on the river bed profile, there are some steep zones (fast stream zones) corresponding with knick lines, and location of these zones is in a line with knick lines. An example of geomorphological analysis focusing on knick lines is shown Figure 7. River bed profile of this area is shown in Figure 8. In this profile, Yoshinogawa river and its branch are shown with the base point at Ikeda dam that is located 30km down stream from the study area, and the lower terrace along Yoshinogawa river is also mentioned. As is clearly shown in this figure, fast stream zone can be identified in branch river, and it is easy to compare each terrace to the past geomorphic surface. The relationship between distribution of landslides and geomorphic surface can be understood from classification of geomorphic surface with river bed profile. Geomorphic surface in this area can be classified into the following five types: Type 1:Gentle slope with peak that forms ridge distributed higher than EL. 700m. Type 1I:Surface with erosion by lower surface I11 distributed between EL. 500-800m. Type 1II:Surface that forms gentle slope from EL. 300-500m, on which many villages or paddy fields are located.

Fig.7 Geomorphologicalclassification map

Fig.8 Profiles of river bed of the Yoshinogawa River and its branch rivers Type 1V:Surfacethat is distributed between EL. 100400m and growing along river. The ancient river bed when surface IV was formed is the connection of terraces shown Figure 8. Type V:The newest geomorphic surface that is distributed along the main stream of Yoshinogawa 179

river. This surface corresponds to steep valley slope lower than EL. 2 0 0 4 and many rock outcrops are exposed. 4.

same with each other, weathered zone develops thicker in older surface, and larger landslide tends to occur in older surface. Landslides with similar scale tend to be distributed in the same surface.

WETHERING CONDITION AND GEOMORPHOLOGICAL SURFACE

Figure 9 shows the result of borings that were drilled on geomorphic surface III,IV, and V. Geology in this area mainly consists of metamorphic rocks with partly distributed sedimentary rocks in south area. From the result of boring on surface 111, thick layer of colluvial deposit about 20m is distributed in surface zone. Tuff breccia formation under colluvial deposit is weathered to depth about 35m and forms heavily weathered zone. From the result of boring on surface IVY the thickness of colluvial deposit is several meters. Crystallin schist under colluvial deposit is weathered to depth 23m and forms heavily weathered zone. From the result of boring on surface V, surface layer consists of terrace gravel that was river bed deposit when surface V was formed. Sandy schist layer is relatively fresh, and is not weathered to deep zone. As is shown above, thicker weathered zone is distributed in upper zone of slope, that was formed earlier, and it seems to have been caused by weathering in long term.

5.

3) If the slope angles of geomorphic surface are

REFERENCES D.Higaki 1992. Slope Evolution Processes of the Choja Landslide, Southwest Japan, Landslide 29(2): 12-19 N.Oyagi, H.Ikeda 1998. Landslide Structure and Regional Perspective on Sumikawa Landslide at Hachimantai Volcanic Area, Northern Honsyu Japan, Landslide 35(2): 1- 10 S. Ueno, H.Tamura 1992. Study of configuration, Scale and Distribution of Landslides, OYO technical report No 14: 1- 13 T. Kamai 1989. Movement Patterns of the Ogawamura-Sodechi Landslide in Nagano, Central Japan, Landslide 26(2): 1-8

CONCLUSION

Following are the result of this study. 1) About configuration of landslides, depth of landslide@) and -width of landslide0 show good correlation. And, transverse configuration ratio(W/D) ranges between 4-10. From this result, if width of landslide(W) observed, depth of landslide can be estimated, or, on the other hand, if thickness of unstable soil layer can be observed, surface extent of landslide can be estimated. These estimations can be utilized in planning of investigation or countermeasures. 2) From relationship between slope angle@) and depth of landslide(D), it is shown that if slope angle becomes steeper, the maximum of depth becomes smaller. It shows that in steep slope, unstable soil layer cannot remain for a long period, and large scale landslide is hard to form. 180

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Geodynamics and spatial distribution of properties of sea cliff colluvium Eugeniusz Dembicki & Wieslaw Subotowicz Environmental Engineering Faculty, Technical University of Gdaksk, Poland

ABSTRACT: In the paper three basic types of cliffs are presented and described, namely: slope wash, earth fall and landslipe cliffs. The spccial attention is paid to the slope wash cliff type and particularly to the geodynamics of its colluvium. Additionally, numerical kinetic model describing the process of internal alteration of colluvium into its homogeneous form is presented. Observed on cliffs landslides phenomena are strictly connected with its geological structure. Additionally, in the landslide development an important role plays presence of groundwater which mostly occurs on the cliff slope in the form of seepage springs. Long-term observations of the geodynamical behaviour of cliffs allowed the distinguishing of three main types of cliffs (Subotowicz, 1982), ( Fig. 2): A. Slope wash type B. Earth fall type C. Landslip type.

1. INTRODUCTION Along almost 500 kilometres of Polish coastline one can distinguish two main types of coast: cliffs and dunes (Fig.1). Cliff coast spreads out over a total distance of 100 km whereas dune coast covers 400 km. In both cases the coast can be divided into three basic elements: near-shore, beach and upper part of coast which in the case of the first type are cliffs (Subotowicz, 1982). The paper is devoted to the description of this coast element and particularly the properties and geodynamics of its colluvium.

2. GEODYNAMICAL TYPES OF CLIFF Cliffs of Polish coast are built of Pleistocene formations which are mainly represented by moraine clays and intermoraine deposits. The second ones consist of gravel, sands, silts and stagnant clays. Sometimes one can also meet formations of older age such as glacial detached blocks.

Slope wash cliff is characterised by sandy formations exclusively. Abrasive sea activity causes immediate slope wash of these formations. In this case, an inclination of a slope is very close to an angle of natural slope. Cliff colluvium is built of sandy cones. Earth fall cliff is forrned of soils with high strength parameters, such as loams and highly compressed

Fig. 2 Geodynamical types of cliffs. 1 - ,moraine clays; 2 - intermoraine sandy formations; 3 stagnant silts and clays. Age of formations Pleistocene.

Fig. 1 Scheme of Polish coast

181

clays. In this case, an inclination of cliff slope is usually almost vertical. Earth fall occurs due to abrasive sea activity undercutting a toe of cliff together with destructive activity of tree roots and frozen water in the cliff fissures. Landslip cliff is characterised by soil landslipes. The landslipes are related to differentiated geological structure and groundwater. As in previous cases the direct initiation of cliff development comes here from sea abrasion, however significant role in this process play so called land factors (e.g. geological conditions, flow of groundwater supplied additio-nally by leakage from water supply installations located in the nearest vicinity of cliff crest etc.). Both, sea and land factors cause that the cliff slope becomes more steep worsening global equilibrium conditions what finally may lead to a loss of cliffs stability and subsequently a landslide occurs which is usually of structural character. Such character is caused by the fact that potential failure surface initiating the landslide phenomenon runs along top of stagnant or moraine clays. The surface develops progressively upwards being tangent to the top of these deposits, forming cylindrical shear surface which becomes a border between soil masses displaced and the undisturbed subsoil. The displaced soil mass forms a colluvium which immediately after landslide starts to undergo its own geodynamical processes different from the rest of a matrix bed.

left to it there was much younger landslip denoted as Landslide I1 which occurred in 1986 forming younger colluvium. Thus both cliff parts represent two different kinds of colluvium characterised by different stages of dynamics process. These different phases of dynamics acting on the two colluvium caused changes in spatial distribution and in lithologic composition of individual layers. Such conclusion has been derived on the basis of exploratory borings and SPT (Standard Penetration Tests) tests analysis. The depth of boreholes was not exceeding 6 m. Additionally, in order to measure displacements of colluvium surface by standard survey methods near every boring the settlement points have been installed. The survey measurements were carried out in the period from 1994 to 1997, (Czarnecki, 1998). The borings and SPT tests analysis allowed also a determination of colluvium thickness and the depth and shape of slip surface. In both landslide cases colluvium was built of much less compacted soils comparing to the original subsoil. Due to high saturation of colluvium clayey soils were plastic or even highly plastic. In many cases such high saturation of colluvium prevented its drilling through thus the floor of it was being determined from SPT tests. It has been found that the border between natural subsoil and displaced masses of soil is reached at 35 blows on every 10 cm of driven drill rode.

3. BASIC ASSUMPTIONS OF INVESTIGATION PERFORMED The investigations of colluvium have been performed in the Jastrzqbia G6ra cliff (Fig. 1). The failure surface which had initiated landslide run along the roof of stagnant clays of varvedlike type called glacial-limnical clays (Fig. 3). They form cliff toe with well developed abrasive scar. The colluvium had been created due to displacement of two moraine clay layers separated by intermoraine sands. In both formations i.e. in intermoraine sands as well as in interstratified sandy and silty beds within clayey subsoil one can find groundwater. Displaced “en block” part of cliff which had become cliff colluvium preserved its original structure corresponding to undisturbed cliff subsoil only immediately after the landslide. In Fig. 4 is shown a landslide denoted as Landslide I which had developed on the turn of XIX and XX century. The colluvium formed due to this landslip process can be then recognised as old one. On the

Fig. 4 Overview of Jastrzqbia Gora cliff. 182

4. LITODYNAMIC AND GMNULOMETRIC CONDITIONS OF COLLUVIlJM DYNAMICS

Quarterly performed survey measurements have shown that the colluvium is being non-uniformly displayed in time. The colluvium movement is characterised by periods of different displacement velocities. The differences may range between 20-30 cm withir, three years observation period. Thcy are mostly caused by various configuration of colluvium subsoil and varying intensity of water supply. Additionally, zones of faster movements are located in the areas of relatively large colluvium thickness what causes smaller influence of a subsoil on the movement. It has to be noted that periods of higher movement activity of colluvium and worsening soils strength take place during spring periods and not in autumn-winter months. It means that dynamics of colluvium is much more influenced by groundwaters instead of rainfalls. Older Landslide I is characterised by thinner colluvium and higher plasticity of soils. It results from higher progress of colluvium homogenisation process comparing to the Landslide 11. The differences of a shape of failure surfaces can be also seen. The slip surface of older landslide is much flat and less declined whereas in the second case cylindrical shape of the surface is much classical. Czarnecki, 1998 has elaborated the numerical mo-del allowing the analysis of colluvium displacements and interpretation of the results obtained with regard to deeper colluvium parts. The numerical code incorporates soil resistance data provided from SPT tests. Typical data of this type are shown in Fig. 5.

Advanced dynamics of older Landslide I (see Fig. 6a cross-seclion A-A) has caused clear litodynamic stratificatiori within the colluvium area. Successive colluvium movement downwards cliff slope together with rainfall waters infiltrating into a subsoil and groundwaters caused that original layers of displaced "en block" soils underwent and continuously undergo the progressive process of alteration. The movement of individual layers (larger in the upper cliff part and smaller in the lower one) contributed to the decrease of thickness of original layers and to the formation of new ones. Subsequently, the new, qualitatively different colluvium subsoil has become homogeneous, (Wilski, 1997). However, it is not the arbitrary mixed structure but multilayered and flaggy spatial structure characteristic for gravitational flows, (Gradzinski et al., 1976). Such structure has been confirmed by both the description of soils drilled through the colluvium as well as by grain size distribution analysis. It has to be noted that the latter is an important feature allowing the assessment of grading, deposition and permeability of soils. These processes can indirectly serve for description of geological environment in which the deposits were formed. Sampling for the laboratory analyses was being done every 0.5 m of exploratory boring. The homogenisation of colluvium together with its lower border can be seen in Fig. 6 - cross-section A-A. The latter runs along slip surface localised on the roof of glacial-limnical clays. Lower colluvium part near abrasive scar can be subjected to the secondary landslip forming secondary colluvium consisting partially of older clayey subsoil (Fig. 6), (Czarnecki and Subotowicz, 1994). -

5 . INFLUENCE OF GROUNDWATER GEODYNAMICS OF COLLUVIUM

ON

Colluvium of both analysed landslides are highly saturated. Larger thickness of younger Landslide 11 colluvium and higher inclination of slope surface cause that groundwater table occurs quite deep within colluvium mass, sometimes several meters be-low the soil surface. In the case of Landslide I1 which is characterised by the essentially smaller volume of colluvium and little slope surface inclination ground-water table is situated much higher, not exceeding 2 m depth in the upper cliff part and reaching around 1 m going downwards.

Fig. 5 Diagram of soil resistance and displacement of the colluvium 183

Fig.6a Jastrzqbia Gora cliff colluvium - A - A cross-section.

Fig.6b Jastrzqbia Gora cliff colluvium - B - B cross-section. Locally, groundwater was found near colluvium surface (Fig. 6). There are three main sources of water supply. The first one is related to land supply coming from intermoraine aquifer. Its waters have direct contact with colluvium and occur in the form of seepage springs on the slope of landslide scar and consequently flow and infiltrate inside the colluvium. Second source are rainfall and melt waters, which also directly supply the colluvium. The third source are w-aters existing in cliffs undisturbed subsoil mostly in glacial-liinnical clays

and particularly in interstratified sandy and silty beds. They exist as confined groundwaters with its stabilised piezometric head at the colluvium level. They are hydraulically connected with colluvium waters and due to its confined character are source of additional supply. Continuous saturation of colluvium causes that its soils are permanently wet. It subsequently worsens strength parameters of these soils what induces dynamical gravitational processes.

184

6. SUMMARY

Dembicki E., Sobocinski G., Subotowicz W. and Czarnecki J. 1998. Spatial distribution of properties of Jastrzqbia G6ra cliff colluvium, (in Polish, Przestrzenny rozklad wlaSciwoSci koluwium klifowego w Jastrzqbiej Gorze), Iniynieria Morska i Geotechnika, 5 : 241 -248.

In the paper soil and water conditions of colluvium of Jastrzqbia Gora cliff and its influence on dynamics of cliff have been analysed. The colluvium soils are characterised by high saturation and are subjected to continuous dynamic process occurring in the form of permanent flow downwards the cliff slope. This process induces internal alteration of colluvium itself. It finally leads to the new qualitative structure of the homogenisation character, (Wilski, 1997). Grain size distribution and lithologic analyses performed, assessment of hydrogeological conditions existing within colluvium and SPT tests together with the measurements of colluvium movements were the basis for assumption to treat the colluvium as uniform liquid-plastic material, (Dembicki et al., 1998). The assessment of colluvium properties together with the above assumption served for construction of numerical kinematic colluvium model. The model has incorporated the assumption of uniform displacements of colluvium along its depth. It enabled making use of survey measurement of colluvium surface movements for verification of the model. They are dependent on soil resistance measured during in situ soil investigations in terms of SPT tests Fig. 5). The analysis presented can serve for better assessment of colluvium properties and its influence on the dynamics of cliff leading to the better understanding of the processes governing the behaviour of this coast structure. At this stage of analysis the interpretation of the influence of blows on the strength parameters of colluvium soils is not possible.

Gradzinski R, Kostecka A., Radomski A., Unrug R. 1976. Sedimentology, (in Polish, Sedymentologia), Wydawnictwo Geologiczne, Warszawa. Subotowicz W. 1982. Litodynamics of cliff coats in Poland, (in Polish, Litodynamika brzegow klifowych wybrzeia Polski), Ossolineum, Gdansk. Ter-Stepanian G. 1975. Theory of Progressive Failure in Soil and Rock Media, Proc. of the First Baltic Conf. on Soil Mechanics and Foundation Eng., Vol. 1, Gdahsk: 181-198. Wilski J. 1997. Homogenisation of colluvium on Jastrzebia Gora cliff landslides, (in Polish, Homogenizacja koluwium na osuwiskach klifu w Jastrzqbiej Gorze), Gdansk Technical University, Faculty of Environmental Engineering, Master Thesis.

REFERENCES Czarnecki J. and Subotowicz W. 1994. Genesis of Jastrzqbia G6ra cliffs landslides (in Polish, Geneza osuwisk klifu w Jastrzqbiej Gorze), Iniynieria Morska i Geotechnika, 5 : 248-25 1. Czarnecki J. 1998. Geodynamics of cliff coasts in Jastrzqbia Gora and Dqbno near Ustka. Gdahsk (in Polish, Geodynamika brzegow klifowych w Jastrzqbiej G6rze i Dqbnie k. Ustki), Technical University, Faculty of Environmental Engineering, PhD Thesis.

185

This Page Intentionally Left Blank

Slope Stab/lify Engineering, Yagi, Yamagami & Jiang G ) 1999 Balkema, Rotterdam, ISBN 905809 0795

A mineralogical study of the mechanism of landslide in the serpentinite belt K.Yokota, R.Yatabe & N.Yagi Depurtnzent of Environment and Construction, FUCUIQ of Engineering, Ehinic? University, Mutsuyuinu, Jupun

ABSTRACT; A Serpentinite is consisted of Magnetite, Brucite and Serpentine. It has been made from upper mantle matter and seawater at the deep sea floor. It has good coordination with basic rocks and sedimentary rocks. At the ground surface, Brucite is easily soluble into water, but Magnetite is stable. Therefore, at the border between Serpentinite and other rocks, many pores inner of weathered Serpentinite keep ground water channel. It affects other rock's weathering, and, some contact surfaces are made from different clayey layers. Serpentinite layers have larger residual strength and higher permeability than Montmollironite or Chlorite layers. When the layers of debris have loosen their stability, they sqush weathered Serpentinite layers, and they move slowly and creepy. The mechanism of landslide at the so-called Serpentinite zone is upper process.

1.INTRODUCTION

characteristics of Serpentinite's forming process and its characteristics of distribution. Then, we want to make clear of the mechanism of these characteristics of landslide at the areas of the so-called Serpentinite by the mineralogical method.

A Serpentinite has been valued as an ornament from its characteristic pattern, on the other hand, Serpentinite mountain's surface has been usually broken down and known fragile generally. We can see many landslide sites in the areas of the so-called Serpentinite. The characteristic profiles of Serpentinite's landslide have been worked up (Sokobiki et al. 1994). as below; 0 Serpentinite's landslide sites are distributed mainly along the tectonic lines, and there are complex geostructures around them. 0 Landslide topography is frequently at the border between Serpentinite and other rocks. There are few rock slides but many clay and debris slides. @ A gradient of the landslide site is comparatively gentle as 10 to 20. @ Many of the landslides still continue their slow and creepy movement. These features have been generally explained that Serpentinite is the intrusive rock and the surface of the landslides is formed from clay of Serpentine caused by faulty action and weathering. But these explanations do not give us positive proof about the characteristic of Serpentinite landslide's distribution and occurrence at the gentle slopes. It is considered that these features of landslide are caused by the

Fig. 1 Distribution of Serpentinites and sampling sites

187

2. I . Features of dislribution of landslide. Distribution of landslide sites has a distinctive feature as below; 0Landslide sites are rare inner of the Serpentinite's distribution area. @ Many landslide sites are at the border between Serpentinite and metamorphic rocks as green schist, and, Serpentinite and sedimentary rocks as black schist. . @ There are few landslide sites at the border between serpentinite and granite.

2.CHARACTERISTIC OF LANDSLIDE SITE The distributions of ultra basic rocks in Japan are showed in Fig. 1 (Miyashiro 1965). In Japan, we can find a Serpentinite as one of the ultra basic rocks along geotectonic lines. It has been considered, usually, that Serpentinite has been metamorphized from Peridotite whose main components are Olivine and Pyroxine. A Serpentinite is, generally, coordinated with green schist and black schist. And, it is often distributed with granite.

2.2.Minerals of slip surface

Tablc 1 Coinponetit minerals of so-called weathered claycy Serpentinitcand stress strength of them Sampling spot main I Str.strengtIi structure bedulace names I

In Table1 , the component minerals of weathered so-called Serpentinite by the X-ray analysis and residual strength by the ring shear test are shown. Minerals of' slip surface are consisted from Serpentine, Talc, Chlorite and Montmorillonite at Serpentinite landslide sites. Serpentinite has high shear friction about 30 , but Talc, Chlorite and Montmorillonite have low shear friction angles about 20 to 10 , and degree of decrease from peak strength to residual strength is large. Chlorite is one of the main minerals of weathered green schist. And Montmorillonite is one of the main minerals of weathered black schist.

3.WEATHERING SERPENTINITE

AND

OCCURRING

OF A

At the outcrop of the ground surface, weathered Serpentinite usually turn grayish blue or green, and it forms a striking contrast against other dark brown weathered basic rocks whose layers are found with coordination of Serpentinite layers. Engyoji

t "

1lC.SlS 2lC.SlS

Br.2 1L.SIT.S

Br. :boring core C.S.:cutting slope S.C. : swelling cutting slope L.S. : Landslide site

I 29.81

30.6

I 31.21 30.6

I

19.31

141

S. : Serpentine C, : Chlorite T. : Talc M. : Montmorillonite F. : Felspars

Fig.2. The propotion of Brucite at each sampling site 188

Chrysotile. Magnetite is one of the iron oxide and it is stable at the ground surface. Brucite is the only magnesium hydroxide mineral. It exists generally inner of the ultra basic rocks. And it is stable in the strong basic solution higher than pH 11. Serpentine is one of the magnesium hydrous silicate minerals and it is classified Anteigolite, Chrysotile and Rizaldite by the occurrence condition of temperature and pressure. In Fig.2, the proportion of Brucite, which is contained in respective serpentinite blocks in Japan, are illustrated. At the ground surface, Brucite is easily soluble into acid or weak basic water, but Magnetitc is nearly soluble. Therefore, Serpentinite is weathered easily and crashed into pieces quickly, and it keeps coarse-grained particles with Magnetite. Then, it has large residual strength and turns grayish blue or green. 3.2. A comparison with basic rocks In Fig.3, the metallic elements, which are leached from Serpentinite, Sanbagawa green schist, Sanbagawa black schist and Mikabu green stones in the acidic solution, are shown. Acid solution is H2C03 and pH6.3. Strikingly, leaching Mg from Serpentinite shows larger value than the others. And, prominently, leaching Fe from Serpentinite shows smaller value than the other rocks. Many other metalic elements are leached from the other rocks. Main minerals of basic rocks, as Pyroxene, Hornblende and Chlorite, have Mg2+,Fe2+,Ca2', A13+ and Fe3+in their crystal structures as anhydrous or hydrous silicate minerals. It seems that Fe and other elements are dissolved into acidic or basic solution with destruction of the crystal structure. Therefore, they are slowly weathered and reformed to clayey soils which have minute-grained particles and low residual strength. And they turn dark brown.

Fig*3'

3.3. A comparison with Peridotite rocks Olivine, which is a main mineral of ultra basic rock, has Mg2+and Fe2+ in its crystal structure as anhydrous silicate minerals whose names are Foresterite and Fairlite. The thin surface of weathered Peridotite turns reddish-brown, but inner of the Peridotite turns clear olive green. It seems that Fe is dissolved with destruction of the crystal structures. And it shows us that weathered Peridotite is not metamorphising to Serpentinite. We can find some slim, soft and straight white vein of fibrous the Chrysotile at the Peridotite outcrop. It has been reported that a Peridotite has some veins of Brucite and Chrysotile which keep fluidity of the upper mantle matter (Morimoto 989). The white vein the traces from which

components Of rocks and times

3. I . A Serpentinite We can observe, generally, a Serpentinite is basically consisted of some lumps of Magnetite with Serpentine and some veins of Brucite with 189

It is considered that Serpentinite has made from reaction between upper mantle matter and water at the deep sea floor suddenly with eruption or cracking the ocean crust. And it is considered that other basic or ultra basic rocks have gone hard slowly from lava of upper mantle matter with each condition respectively. The conceptual process is illustrated in Fig.4. (Arai 1992, Fujioka 1994, Ishizuka 1995 and Cannet 1995). It is considered that Serpentinite has good coordination with basic rocks at the sea floor, and many sedimentary rocks cover over the Serpentinite later.

Brucite has been dissolved into water at the ground surface.

3.4. A considervtion of the occurrence of Serpenlinite rocks These points of difference between Serpentinite and Peridotite, or, Serpentinite and basic rocks show us that Serpentinite has a unique occurrence condition and process compared with other basic or ultra basic rocks. A profile of mineral facies

A profile of rock facies

0:Olivine

T

SB

SB % SMS SB $ SMS T d SB SMS SB

Moho-discontinuity

4. WEATHERING AND DISINTEGRATION OF SERPENTINITE

H:Hornblendite C:Chlorite M:Magnetite B:Brucite S:Serpentinite

On the one hand, a large ultra basic rock body, which is consisted of Peridotite with Serpentinite, forms generally a high mountain. We can find that veins of Brucite and Chrysotile affect some cracks inner of the ultra basic rocks, and they affect some rock faults usually. On the other hand, some Serpentinite rock body is very fragile by the dissolution of Brucite into water and it breaks into pieces usually. And then, a mountain of ultra basic rocks has steep cliffs and gentle slopes. But weathered Serpentinite break into clayey pieces rarely at the outcrop, and it causes rarely landslide inner of the serpentinite areas.

4.1. The Primary Collapse with landslide In Fig.5, the coefficient of permeability of Serpentinite and other clayey soil at landslide site is shown. It shows that a Serpentinite has considerably larger coefficient of permeability than the others. At the border zone between Serpentinite and other rocks, when veins of Brucite with Chrysotile have dissolved into water from Serpentinite rocks, many pores are caused inner of the rocks, and they keep ground water channels. It affects other rock's weathering. In them, some contact surfaces are formed between weathered soft Serpentinite layers and other clayey layers as Chlorite and Montmorillonite. It has been cleared that Montmorillonite has the remarkable hydrophilicity and it expands with water. And it has been found that some Chlorite has been swelling at the outcrop with water. The two layers are contrary to each other. Weathered Serpentinite has the characteristics of high permeability and large residual strength. But, Chlorite and Montmorillonite have the characteristics of low permeability and small residual strength. If the stability is lost by some cause, the contact surface will affect collapse with landslide.

--,.------

A vain of B&S (yellow-white)

\L SMSMS SB SMSMS MSHSM SB MSHSM 00000 SB 00000 SMOMS SB SMOMS OOPOO SB OOPOO MOPOM SB MOPOM OPOPO SB OPOPO SMOMS SB SMOMS POPOP SB POPOP MSHSM SB MSHSM PPOPP SR PPOPP SMSMS SB SMSMS HPOPH SB HPOPH SerpentinisedPeridotite Peridotite (gray-blue) (01ive-green) IMSMSM SB MSMSM SMMMS SB SMMMS SMSMS SB SMSMS SMMMS SB SMMMS MSMSM SB MSMSM SBSBSB SB SBSBSB SMSMS SB SMSMS SMMMS SB SMMMS MSMSM SB MSMSM SMMMS SB SMMMS SMSMS SB SMSMS MSMSM SB MSMSM Weak Serpentinite Hard Serpentinite (blue-white) (black-green) Fig.4. Schematic diagram concerning genesis of Serpentinite 190

Table 2. Component minerals of landslide site's clay by X-ray analisis and stress strength of them

Fig.5. Permeability of landslide's clay

4.2. The secondory Landslide In Table 2, the minerals of deposit at landslide site, by the X-ray analysis and residual strength by the ring shear test, are shown. Minerals of slip surface are consisted from Serpentine, Talc, Chlorite and Montmorillonite. And they have the smallest residual strength. It has been reported that, at the Choja landslide site, many thin layers of Serpentinite and Slate are alternately with each other. They are few centimeters or several decimeters thickness. Main minerals of slate are Talc, Chlorite and Montmollironite. When slope collapse with other rocks should occur again and again, layers of debris containing many various rocks are formed. At the surface of the deposit, they keep a gentle slope caused by the characteristic of main mineral which have low friction angle. Inner of the deposit, some contact surfaces are formed between weathered soft

Ca:Calcite Tr:Tremolite M:Montmorillonite ss:slip surface Br.:Boring core Serpentinite layers and other clayey layers as Talc, Chlorite and Montmorillonite. One of the weakest contact surfaces becomes the slip surface at the location. When the layers of debris have loosen their stability, due to natural erosion by rivers or artificial cutting slop, they 191

squash weathered Serpentinite layers, and they move slowly and creepy. It is considered that clayey minute-grained Serpentinite layer is formed as the result of squashing weathered Serpentinite layer. It is considered that the mechanism of landslide at the so-called Serpentinite zone is upper process.

It is considered that the mechanism of landslide at the so-called Serpentinite zone is upper process.

REFERENCES

5. CONCLUSION 1. Landslide sites are rare inner of the Serpentinite's distribution area. Many landslide sites are at the border between Serpentinite and metamorphic rocks as green schist, and, Serpentinite and sedimentary rocks as black schist. . 2. Minerals of slip surface are consisted from Serpentine, Talc, Chlorite and Montmorillonite at Serpentinite landslide sites. Serpentinite has high shear friction about 30, but Talc, Chlorite and Montmorillonite have low shear friction angles about 20 to 10, and degree of decrease from peak strength to residual strength is large. 3. In acid solution, leaching Mg fkom Serpentinite shows strikingly larger value than the other rocks as green schist and black schist. And, leaching Fe from Serpentinite shows prominently smaller value than the other rocks as green schist and black schist. A Serpentinite is basically consisted of some lumps of Magnetite with Serpentine and some veins of Brucite. It is considered that it has been made from upper mantle maters and seawater, with ultra basic rocks, at the deep sea floor. And it has generally good coordination with basic rocks and sedimentary rocks. 4. At the ground surface, Brucite is easily soluble into water, but Magnetite is stable. Therefore, at the border between Serpentinite and other rocks, many pores inner of weathered Serpentinite, by leaching Brucite, keep ground water channel. It affects other rock's weathering. It is considered that the weathered contact surface will affect primary collapse with landslide suddenly. 5. At the landslide site, some boring cores show the many layers of weathered Serpentinite and other clayey soils, alternately, with each other. Clayey Serpentinite has considerably larger coefficient of permeability than the other clayey soil. When the layers of debris have loosen their stability, naturally or artificially, they sqush weathered Serpentinite layers. And then, one of the weakest contact surface become slip surface, and they move slowly and creepy. 192

Sokobiki H. et al, 1994. A study and property of Serpentinite landslide in Japan. The 33th Japan national conference on Japan landslide SOC. :7881. Miyashiro A. 1965. Metamorphic rocks and metamorphic belts, Iwanami Shoten. Morimoto 1989. Rock forming mineralogy. Tokyo University Publishing company. Arai S. et a1 1992. Petrology of peridotites as a tool of insight into mantle process, a review, Joint of Min.,Petro. And Econ. Geology, Vo1.87,pp.351363 Fujioka K. et al, 1994. Southerncross Cruise Preliminary Results-a Transect of Palau, Yap Tranches and Ayu Trough at the SouthernTip of the Phillipine Sea Plate-.JAMESTEIC J Deep Sea Res. 10:203-230. Ishizuka H. et al, 1995. Oceanic lower Crust and Upper Mantle Materials in Transform Fault Zone of WMARK. JAMESTIC JDeep Sea Res. 1 1:3752. Cannet M. et al, 1995. Thin crust, ultra-mafic exposures, and rugged faulting patterns at the Mid- Atlantic Ridge(22-24" N)., Geology.,231 :49-52.

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Detailed geotechnical study in Modi Khola Hydroelectric Project, Western Nepal I?Dangol Department of Geology, Tribhuvan University, Ghaiitughur, Kathmandu, Nepal

T. R. Paudel Modi Khola Hydroelectric Project, Nepal Electricity Authority, Tundikhel, Kuthmandu, Nepal

ABSTRACT: Detailed geotechnical study is very important for any infrastructure development works, especially for underground excavation in the geotectonically active parts like the Himalayas. This paper gives an account of the geotechnical study carried out for the Modi Khola HydroelectricityProject. It also describes the engineering geological problems faced during construction of tunnel and foundation works of various structures with assessments made to tackle the problems. As a result of the geotechnicalstudy,the project became safe and cost-effective.The advantageof self-supportingcapacity of rocks is used, which reduced a huge amount of cost in tunnelling. The formerly designed long and curved tunnel alignment from vertical shaft is changed to a straight and better alignment, which reduced the tunnel length by about 35.0 m. Previouslyfixed locationsof surge tank and penstock pipe at loose terrace and conglomerate deposit were shifted towards the bedrock by designing a 40 m high vertical shaft and about 4.45 m long pressure tunnel instead of an exposed inclined penstock. similarly, results obtained from various geotechnical tests granted a sound basis to decide the location and foundation of Powerhouse and Intake structures.

1 INTRODUCTION The MO&Khola Hydroelectric Project area is located in Western Nepal (Fig. 1). The construction site lies along the right bank of the Modi Khola - one of the major tributaries of the Kaligand& River. The Mod Khola is originated from the glacier cirque of the Annapurna Range. Total upstream catchment of the Modi Khola from the intake of the project is little above 500 km2. A concrete diversion weir (7.5 m high, 33 m long) diverts the 27.5 cumecs of water from the Modi Khola to a 154.8 m long Desanding Basin through a 30 m intake and 250.29 m long underground Box Culvert. Thereafter an open canal of 63 m length conveys the water to a Regulating Pondage of 26,640 m capacity. Then the water passes through 1507.1m long Headrace Tunnel of 3.15 m diameter, 41.25 m long Horizontal Tunnel of 4.24 m diameter, 37.96 m high Surge Tank of 5 m diameter, and 50.845 m long Vertical Shaft of 4 m diameter. After passing through 351 m long Pressure Tunnel of 4 m diameter and 90 m long Penstock Pipe of 3.2 to 2.77 m diameter, it reaches to the semiunderground Powerhouse (27 m x 14 m x 22 m) with a net head of 67 m and generates 14 M W electricity. Finally, the water runs down to the Modi Khola (Fig. 2) again through a 262 m long Tailrace Canal (Cut and Cover Box Culvert type). The main objectives of the geological and geotechnical investigationsfor the hydropower project were to obtain: 1.The necessary geological and geotechnical input for 193

evaluation of site and possible alternatives and for overall planning of the project, 2. A basis for evaluation of potential stability problems and judgement of geotechnical parameters for stability analysis, planning of reinforcement and treatments, 3. Classification of rockmass for support in the tunnel. 4. A basis for cost evaluation, and 5. Evaluation of unforeseen geological hazards in the construction site and recommendation for excavation through unstable zones. 2 GEOTECHNICAL INVESTIGATION The Project site (Fig. 2) lies in quartzitic terrain named as Naudanda Quartzite (Hirayama et al. 1988). It has

Figure 1. Location map of Modi Khola Hydroelectric Project.

Figure 2. Geological map of the Project area, showing locations of constructionfeatures. a sharp contact with the underlying Seti Formation and gradational contact with the overlying Balewa Formation (Paudel & Dhital 1996). The maximum thickness of the quartzite is about 1000 m in the Modi Khola section. The rocks of the Naudanda Quartzite are represented by medium- to coarse-grained, massive, white and green quartzite with intercalations of thinly foliated grey to greenish grey phyllites and massive dark green chloritic phyllite with mica schist. Surface mapping and subsurface investigations are carried out in the construction sites. Surface investigation comprised in-situ mapping and test of outcrops, surface mapping of old landslide scars, topographically depressed zones, active gullies and their interpolation to the subsurface structures. Detail geological map of the project site is prepared from the data obtained during construction of concrete structure and excavation of tunnel (Fig. 2). Generally, the rocks dip towards North West (N3Oo-35"E/25-30"NW) in the Project area. Two sets of joints are predominant. The bedding planes are slickensided with sandy clay infilling, while the joint planes are planar with plumose structure.

2.1 Headworks area

under stress and may create the problem of water tightness and unequal settlement. Due to the unfavourable geological condition for foundation works of diversion weir and sluice gate, essential treatments were carried out. The spongy silty clay part at the foundation elevation was removed and replaced upto 1.5 m by sand with jute membrane at the lower part (P1.2) to stop the sand boiling. Considering the low bearing capacity of deposited material, heavy concrete structures was to be designed for the Desanding basin and its side spillways so that it can withstand giving minimum load at its sloping walls. 2.2 Tunnel Area The Headrace Tunnel pass through greenish to white quartzite and highly weathered, soft phyllitic schist, chloritic schist and kaolinite band. The inlet portal is affected by a fault. The portal and about 300 m length of tunnel alignment runs through an old stabilized landslide area. The rockmass in this area is composed of fully decomposed saturated swelling clay fault gouge, breccia, kaolinite mass with altered schist layers and fractured rock fragments. Such a rockmass has zero

Geologically, the Headworks area lies totally in old terrace of the Modi Khola. The structures are designed on alluvial deposit, taking into consideration of the geotechnical parameters accordmgly.The alluvial deposit of the Modi Khola is composed of irregularpoorly sorted sequence of boulders, gravels, sand and silt. A quartzite rock cliff is exposed on the left bank of the river (Pl. 1). The bore hole drilled during detail design stage shows that the bedrock is far below the foundation level. An anticlinal fold axis passes through the river at this site. Foundation works in such geological condition is not favourable for heavy concrete structures in river channel. The engineering property of quartzite bedrock, spongy soil and boulders can not be compared and such inhomogenous material act differently

Plate 1. Out crop of bedrock (quartzite)on the left bank and diversion weir under construction. 194

3 GEOTECHNICAl FINDINGS AND CONSTRUCTION WORKS

3.1 Relocation of Surge Tank and Pressure Tunnel In the original design, the Surge Tank was located at the slope surface just at the interface of the quartzite beds and the conglomerate deposit. The conglomerate is composed mainly of gravel, boulders, pebbles and sand produced from granite, gneiss and quartzite, cemented by calcareous matrix and clay. Most of the part of this conglomerate is hard and compact, but it is loose at top and often at its depth too. It is normally unsorted and inhomogenous. The bedrock is no more continuous in the tunnel excavation line due to NW dipping of rock. As a result, about 300 m long Headrace tunnel, upstream from portal was designed to be located through the conglomerate deposit. Considering the geological problem, two exploratory drill holes were sunk to findout the subsurface condition of rock and thickness of overburden above the bedrock. From these two borehole interpretation, the bedrock line was traced. Consequently, it became obvious that the original Surge Tank location and last 300 m of Headrace Tunnel was on the loose terrace conglomerate deposit lying unconformably over the bedrock, which is geologically unfavorable for hydropower tunnel. Then the location of surge tank was shifted on the bedrock about 340 m upstream from its

Plate 2. Foundation treatment of the sluice gate using jute membrane. stand up time. In these reaches, excavation was done with heading and benching method. The steel ribs installed became buckled (inwardly bended upto 20 cm) due to high stress from right slope. After 325 m length, slightly weathered, thick bedded,jointed, strong to very strong massive green quartzite appeared in the tunnel. Therefore, only 50 mm thick plain shotcrete and spotbolts are used for initial support. 2.3 Powerhouse and tailrace area

A semi-underground Powerhouse and 270 m long cut and cover box culvert type Tailrace canal is designed on the terrace deposit along the right bank of the Modi Khola (Pl. 3). The alluvium exhibits mainly two cycles of deposition. The first cycle consists mainly of dark gray to ash colored silty sand with fine aggregates. Few boulders of granite, gneiss, limestones and calcareous sandstones are also interspersedwith in it. The secondcycle is composed of irregular sequence of boulders gravels, sand and silty clay. The alluvial deposit as a whole is non-cohesive, brownish in color and the sediments are poorly sorted. The opencut excavation at the cutslope of 1:0.5 was far higher than the internal friction angle of alluvial deposit. Therefore slope stability problem was faced in the tailrace part. From the geological condition observed, the expected bedrock might have deeply eroded and buried by the alluvial deposit of the first cycle in the past. The dipping of bed rock towards the hill also limits its continuation towards the Powerhouse. From Engineering classification of soil, the soil found at the foundation, level of powerhouse falls in Poorly graded sand silt mixtures with fine aggregates (SM). Obviously, this type of deposit is not competent for foundation of Power house, where the vibrating load is high. Desirability of foundation for this type of soil is 3 to 7, (where 1 is for excellent and 14 for unacceptable). Recommendation to shift the Powerhouse at about 40 m upstream towards the slope in the same alignment is given, where competent bedrock of quartzite is confirmed.

Plate 3. Power house site on the alluvial deposit. 95

original location. The last 450 m tunnel profile is lowered by about 45 m along the bedrock and designed as Pressure Tunnel introducing a 40 m high vertical shaft. A vent adit of 2.5 m diameter and 68 m length is added for the ventilation of surge tank. About 40 m length of vent adit was designed to be located on the conglomerate deposit. Since the diameter of adit was small, no problem was faced during excavation. Since this adit is to use only for ventilation purpose, there remains no geological problem in future also.

3.2 Pressure Tunnel Excavation through Shear Zone A 76.5 m long work Adit No. 2 (PI. 4) for the excavation of Pressure Tunnel was designed just below the Pokhara-Baglung road. The massive bedrock outcropped at the Portal and the orientation of bedding and joints shows a very favorable condition for tunnel excavation. But, at the end of Adit and further in the Pressure Tunnel, a major shear zone was to cross along the upstream part from junction. At the junction area, thinly foliated, soft mica schist layers were appeared.The orientation of these weak layer is almost parallel to the tunnel alignment. As a result, the weak zone continued for a long distance. On further excavation, a major shear zone composed of fully decomposed soft fault gouge and shattered fault breccia collapsed at upstream face chainage of 26 and 41 m. Since the Pressure Tunnel alignment is 7-10 m below the river bed level, high rate of ground water inflow further made the condition worse. The slid material was piled up at the face and consolidation grouting was started to stabilize the collapse. The grouting was done by injecting the cement milk at the ratio of 1:l (cement:water) through 3 to 8 m long perforated GI pipes. Cubes from the collapsed material was made and tested in the laboratory. After consolidation grouting in the perimeter and above the crown, heading and benching method is followed for further excavation. Heading by steel arch installation above SPL at 30 to 50 cm spacing and lagging behind with steel bars was done in the first stage. In the second stage full section excavation was done by erecting the post and struts with concrete foundation at 30 to 50 cm spacing. After excavating 14 m in the shear zone following the heading and benching method; horizontal Probe Hole Drilling was started to find out the width of the shear zone. Core samples of fractured quartzites were obtained from about 18 m onwards from the drilling face so that the width of the shearzone was found to be about 32 m. About 300 bags of cement grouting in the perimeter and spiling bars at 20 cm spacing was required per meter length of tunnel in average. Steel ribs support with 75 to 100 mm thick fibre reinforced shotcrete was used throughout the weak zone. On the basis of experience from the Modi hydropower, tunneling methods in unstable sqeezing

Plate 4. Work adit 2 for the pressure tunnel excavation..

rockmass can be suggested to overcome the problems encountered at other projects in similar situations. Provisions of compressible packing between rock and the support to allow deformation under controlled condition and final lining of the tunnel after sufficient time has elapsed through completion of excavation so that all the movements have died down, is an important consideration in the context of tectonically active zones.

3.3 Assessment for Permaneizt Support in the Tunnel The major discontinuities, and their infilling, opening, spacing, persistency, weathering, roughness and alteration of joint surface (Table 1) provide very important clues in malung permanent support in the tunnel.The quartzite bedrock is sufficiently strong but the major discontinuitiesare very prominent and intersectingwith one another. Moreover, the Headrace tunnel alignment N36"E and N48"E is nearly parallel to the bedding orientation of N30"-35"E/24"-30"NW. Intersection of bedding plane by south dipping prominent joint (N1O0E/58"SE) has resulted maximum possibility of block failures along the left wall and crown of Headrace tunnel. The analysis of stereographic projection of bedding plane, joints and shear planes (Fig. 3) shows many unstable condition on crown and walls (Kwon & Choi 1998).

196

Table 1: Orientation and characterestics of discontinuities in the Headrace Tunnel.

Tunnel Chainage Location 99- 120 120-130 330-400 400-440 HRT 400-440 from 440-500 Inlet 500-600 600-660 660-690 0-200 0-200 200-360 200-360 360-390 Adit - 1 390-530 Upstream 530-55 0 550-600 600-660 660-705 705-795 705-795

BeddingJJoint Bedding Bedding Joint Joint Bedding Joint Joint Bedding Joint Bedding Joint Bedding Joint Joint Joint Joint Joint Joint Joint Bedding Joint

Orientation

In filling

N 25'E/35"NW N 27"E/37'Nh 125 "/60°NE 12/70 SE N 45'E/23'NW N 45"E/85 SE 200/44 SE N 3l0E/35NW N-S/62E N 3O0E/24NW N 20°E/65 SE N 27"E/28 NW 78 "E/74"SE N95/6SW 220/66SE 42/72 SE 175/66 NE 340/60NE 90/70 "S 45 '/35N W 330/65NE

Clay Clay Sandy clay

The support system primarily guided by rock mass quality (Q-value) of rock calculated during excavation. Further, subjective judgment of evaluating parameters also exist under consideration according to the field condition, purpose of tunnel and safety factor. Minor modification in the support as recommended by Q-system is carried out in the Headrace and Pressure Tunnel. Steel rib support at 1 m to 1.5 m spacing is provided at the major weak zones and in the remaining part the support pattern is primarily the combination of shotcrete and rockbolts where the rockmass appears in Poor to Fair class.The rockbolt spacing and length is determined from the formula given by Hoek & Brown (1980):

L=2+0.15 BESR

Sandy clay Clay Clay Sandy Clay Sandy Clay Sandy Clay

Sandy Clay Silt + clay Clay

Spacing

2-3 m 2-3 m 30-100 cm 2-3 mm 50-100 cm 50-150 cm 3-5 mm 100-200 cm 40- 100 cm 50- 100 cm 20-50 cm 100-200 cm 3-5 mm 40- 100 cm 60- 100 cm 2-5 mm 20-60 cm 100-300 cm 5-1 0 mm 50-100 cm 30- 100cm 5- 10 mm 50-100 cm 40- 100 cm 3- 5 mm 50-150 cm 200-300 cm 2-6 mm 100-150 cm

Roughness Slickensided Planar Planar Smooth Undulated Smooth Planar Undulated Planar Slickensided Smooth Slicken sided Rough/Planar Roughhight Rough/Planar RoughPlanar Smooth Smooth Smooth Planar Smooth/Planar

112 -1/3 P=

2Jn

. 98.1 kPa

(3)

3Jg

Considering these situation, the permanent support system for the underground waterways are recommended after modification on the basis of subjective judgement of actual field condition. The Pressure tunnel, Vertical Shaft, Surge Tank and Upper Pressure Tunnel are concrete lined taking the design and hydraulic elements in consideration. In the remaining underground waterways, the final support system is recommended as follows:

(1)

where, B is Tunnel height. The spacing of bolt is 1/2 of the bolt length and the diameter of rockbolt is 20 to 25 mm. The support pressure (P) is calculated from

p=-

Opening

100-RMR gb 100

where g = rock density and b = tunnel height Permanent support pressure is calculated taking the average value of Joint set number (Jn), Joint roughness and Q value of rock from the following formula (Speers 1992). 197

Figure 3. Stereonet analysis of discontinuities of a) Head Race Tunnel-1 and b) Head Race Tunnel-2

In the concrete lining sections, the rock bolts and consolidation grouting will be reduced and instead, backfill grouting will be required; while in the shotcrete lining sections, rockbolt number and consolidation grouting will be increased. The rockbolts and shotcrete applied as an initial support will be the part of final support and required number of rockbolts and shotcrete layer should be added in shotcrete lining sections. High water pressure test was camed to decide the grouting pattern and locations

The geological problems observed during the study can not be generalised for other hydropower projects, however, the experience gainedtackling various problems may help to solve the similar problems in other orojects. The geological and geotechnical parameters taken into consideration in various hydropower projects of Nepal under construction would be a great advantage for other hydropower projects proposed in the country. REFERENCES

4 CONCLUSIONS The detailed geotechnical investigation for the Modi Khola Hydroelectric Project helped to relocate a few major structures, previously designed in geologically unstable sites to safe sites with competent bedrocks. It also helped to reduce the cost in support measures. Present geological and geotechnical study in hydropower project incorporates the geotechnicalparameters taken during design and their deviation in particular construction site. The engineering geological problems in construction site sometime requires certain modification of structures for which a geologist works in close contact with design engineer. The role of geologist in makmg decisions is very important. Hydropower development in Himalayan region requires a high level expertise in geological and geotechnical fields. The geological study in coming years should be confined to particular specific purpose rather than in generalized forms.

198

Hirayama, J., Nakajima, T., Shrestha, S.B., Adhikary, T.P., Tamrakar, J.M. & G.R. Chitrakar 1988. Geology of the southern part of the Lesser Himalaya, West Nepal. Bull. Geol. Sum. Japan, 39(4): 205-249. Hoek, E. & E T . Brown 1980. Underground excavations in rock. Institute of mineralogy and metallurgy, London. Kwon, K.O. & K.D. Choi 1998. Review report on construction works in view of geotechnical and civil engineering, Modi KIzola Hydroelectric Project. Unpubl. Report., Kathmandu, Nepal. Paudel, L.P. & M.R. Dhital 1996. Geology and structure of the area between Pokhara and Kushma, Western Nepal Lesser Himalaya. Bull. Dept. Geology, Tnbhuvan Univ., 5: 47-60, Kathmandu, Nepal. Paudel, T.R., Dangol V. & R.H. Sharma 1998., Construction phase engineering geological study in Modi Khola Hydroelectric Project, Parbat district, western Nepal. JOUKNepal Geol. Soc., Spec. Issue, 18: 343-355. Speers, C.R. 1992. Support for tunnels subjected to changing rock loads: a comparison of design methods. In: ‘Tunneling and underground space technology’, 7( 1): 25-32.

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Local instability in saturated colluvial slopes in southern Brazil Willy A. Lacerda COPPE, Federal University of Rio de Janeiro, Brazil

ABSTRACT In the southern coast of Brazil annual rainfalls range from 1000 to 6000 mm. Thick colluvial mantles cover the residual soil on the sea-side of a long (2.000 km) mountain range. Their thickness range from a few meters to about 30 meters, and some of them are permanently saturated. They present a marked influence of rainfall and phreatic levels on the rate of movement, as superficial and in depth measurements indicate. However, local artesian conditions, often unpredictable, initiate local instabilities that can trigger landslides of the upward mass. Two cases are shown, and a simulation of local artesianism is presented, aiding in the . understanding of the observed phenomena. 1. INTRODUCTION Thick mantles of colluvial soil cover the hillsides of an appreciable portion of the “Serra do Mar” mountain range along Brazil‘s southeastern coast. Due to the high annual rainfall, typically in the range of 1500 to 3000 mm a year, and up to 6000 mm a year in some locations, they present a permanent phreatic level. Their movement is conditioned by the position of the water table, which in turn is related to the rainfall. These masses are usually long, 300 to 500 meters in length, with thickness varying from 5 to 30 meters, and widths of 100 to 200 m. They have been studied in length, and some papers describe their behavior and mitigation measures employed (Eacerda, 1997, Lacerda & Sandroni (1985), Teixeira & Kanji (1 970)) They move along a pre-existing shear surface, permanently wet, and the shear strength along this surface is at the residual value. Since these soil masses were originally composed of the weathered granitic-gneissic parent rocks (and also weathered diabase dikes, very abundant) with a predominance of sand and silt particles, their residual effective friction angle is not very low, and is found to be in the range of 26 to 30 degrees (Silveira & Lacerda, 1992; Pinto et a1 1993).

2. INSTABILITY DUE TO WATER LEVEL FLUCTUATION Borda (1 996) analyzed the instrumentation data of a deep (10 to 20 m thick) colluvium in a granitic/gneissic environment, with may faults and pegmatite and diabase dikes crisscrossing the mountain range. It is situated at a distance about 200 kilometers west from the city of Rio de Janeiro, at seaside, along the Rio de Janeiro-Santos highway. The slope was extensively instrumented by piezometers, water level indicators and inclinometers. Raingages were read at a distance less than 1 km from the site The period of observation was from September 1987 to December 1993. Average annual rainfall during the observation period was 2200 mdyear. The history of the movement goes back to 1978. The initial history of this period can be seen in Sandroni (1982). Up to 1980 total horizontall displacements of 3040 cm were read at the middle of the slope, and of 80 cm near the foot. Deep horizontal drains were installed just above a highway that crosses the lower third of the slope, and a large rockfill berm was placed at the foot, and anchored walls were built just below the highway. The slope was continuously monitored, and the period from 1987 to 1993 was more intensely studied. During that period 16 piezometers and water level indicators and 18 inclinometers were read on a weekly basis. 199

Figure 1 - Section of the deep colluvial slope (Borda Gomes, 1996) (Lacerda, 1997). In Figure 3 the horizontal displacement of a typical inclinometer was plotted. It can be seen that a “jump” in deformation occurs when the accumulated 25-day rainfall exceeds about 200 mm; the position of the piezometric lines was then 1,5 to 2 m higher than the minimum level. This indicated that at a certain critical elevation of the piezometric line the velocities of deformation read by the inclinometers increased abruptly, for example, from less than 0.02 inm/day to 0.13 mmlday. Nevertheless, piezometer installed at different depths at the same location showed that both in the paper by Sandroni as in the study reported the direction of flow was predominantly parallel to the slope, but in some places bent downwards or upwards, irrespective of the position (upper or lower elevations). These local anomalies could be explained by the mechanisms described in the following sections.

Figure 2 - Typical inclinometer graph (Borda Gomes, 1996) Initial inclinometer and monument readings of the 1987 - 1993 period showed velocities of movement at the surface up to 20 mdmonth, and the sliding surface was clearly indicated at a depth between 5 and 22 meters, at the contact colluviudresidual soil Figure 1 shows a profile of the instrumented slope, with an extension of 450 m, and figure 2 is a typical inclinometer graph, showing distinctly the slide surface at a depth of 21 meters. The analysis of rainfall data showed best agreement when 25 day accumulated rainfall was plotted against piezometric elevations, and these results can be seen elsewhere

3. LOCAL INSTABILITY DUE TO IMPERMEABLE VERTICAL BARRIER

AN

The slides of Soberbo Road in Rio de Janeiro have been extensively studied (Soares et al, 1988; Lacerda & Schilling, 1992). Figure 4 shows a partial plan of the slide. Section C-Cl along zones C, B and D is shown in Figure 5. The branches of this complex slide present a colluvial layer on top of the residual soil. The thickness of the colluvium lies between 6 and 10 meters.The water table is very 200

Figure 3 - 25-day accumulated rainfall and inclinometer horizontal displacements against time (Borda Gomes, 1996) close to the surface, except at the lower range, when it appears at the surface. At this point a thick diabase dike was found, which presents a barrier to the groundwater flow. The position of the diabase dykes found while perforating long (80 m) horizontal drains is noted in Figure 4, which also shows the position of piezometers, inclinometers and superficial marks. The accumulated movement of the superficial marks can be seen to increase as the diabase dyke is approached, as the arrows in this Figure show. Two piezometers and a water level indicator were installed besides most of the soundings, and they are shown in the Figure 5 as positions A, B and C. The arrows in this figure indicate the direction of movement of the flow lines at the interval between two piezometers. They are seen to bend upwards near the diabase dikes. The position of the more impermeable dikes influence the flow lines, as Figure 5 shows. Thus, artesian pressures can be observed just above the dikes, as shown. In the Soberbo Road case artesianism was indeed observed, the water level of the deepest piezometer rising more than one meter above ground elevation. Of course, the ground was very wet, with rivulets of water springing at the surface. The local stability of the colluviuni is then

decreased just above the obstacle to flow which the diabase dikes represent, as indicated by the schematic Figure 6. Indeed, superficial horizontal movements were larger at this location, as already discussed, and a succession of cracks and the inclination and displacement of small trees and inclinometers showed the signs of this instability. 4. INSTABILITY DUE TO HIDDEN SPRINGS Artesianism is not always caused by the obstruction of flux. Water recharge by means of concealed springs connected to water bearing fractures in the underlying rock can alter significantly the flow pattern in its neighborhood, and a suitably located piezometer would show artesianism. Local artesianism can initiate landslides in upper colluvial layers, and has been observed in some cases in Brazil, in the Author’s experience. In order to simulate this situation Borges and Lacerda (1 986) made Finite Element analyses of a slope with an initial low water table (Fig. 7), and then applied a fountain with a piezometric pressure above ground level, as Figure 8 shows. The arrow indicates the direction of flow, and the water level is 20 1

Figure 4 - Plan view of the Soberbo Road landslide (from Lacerda & Schilling, 1992) significantly altered to a position close to the slope surface. If a cut were made in this slope at the dry season, it would eventually fail during the wet season, and, even without a cut, the slope would certainly show signs of instability. The observation of some slides in natural slopes just after a very heavy rainy period showed springs of water near the crown of the slide, inside the slided mass.

5. CONCLUSIONS The movement of infinite type colluvial masses are strongly dependent on the position of the phreatic level, and follow the equations of the infinite slope equilibrium equations. In this case the velocity of downward movement of the mass is reasonably the 202

Figure 5 - Flow conditions along Section ACDE (From Schilling, 1993)

Figure 7 - a) Seepage along a slope with an impermeable base parallel to the slope; b) Seepage pattern of the same slope affected by spring in localized fracture of the underlying rock (Borges & Eacerda, 1986)

Figure 6 - Idealized flow lines past the diabase dike same along the entire extent of the colluvium. The first case is a typical example, however local anomalies of flowlines could be explained by the presence of dikes or springs, as the latter part of the paper shows. Flux restrictions or the existence of covered springs are also a cause movement initiation, and in

this case local instabilities due to upward deflection of the seepage direction. Portions of the colluvium mass affected by these phenomena exhibit slides of the circular shape type, which in turn leads to loading of the lower part and to the unloading of the foot of the upper part of the colluvial mass, in both

203

(1988) - Mechanism of Movements in Colluvial Slopes in Rio de Janeiro - 5th International Symposium on Landslides, Lausanne, V01.2, 121 1-1216 Pinto, C. S., Gobara, W., Peres, J. E. E., e Nader, J. J. (1993) Properties of residual soils, (in Portuguese), Solos do Interior de 5'60 Puulo, ABMS, USP-Sgo Carlos. Siio Paulo, Vol.1, 95142 Teixeira, A.H. & Kanji, M.A. (1970) Stabilization of the Landslide at elevation 500 of the Serra do Mar of the Anchieta Highway (in Portuguese) Proc. 4th Brazilian Conference on Soil Mechanics and Foundation Engineering, ABMS, Rio de Janeiro, Vol. 1-1, IV-33 to IV-53

cases propagating the movement. These occurrences are illustrated by the two last cases.

6. ACKNOWLEDGEMENTS The author thanks the PRONEX program of the National Research Council (CNPq) and FINEP for the partial funding of this research., and Mr. Luiz de Franqa for the Figures.

7. REFERENCES Borda Gomes, D. (1996) Correlation among rainfall, movements, piezometric levels and Factor of Safety in colluvial slopes in tropical regions, MS (in Portuguese) COPPE-UFRJ, Rio de Janeiro, 186p Borges, M.S.N. & Lacerda, W.A. (1986) On the internal drainage of cut and fill slopes (in Portuguese), Proc. 8th Brazilian Conference on Soil Mechanics and Foundation Engineering, ABMS, Port0 Alegre, Vol. 1, 17-33 Eacerda, W.A. (1991) Mass Movement Phenomena in Tropical Soils. IX Pan-American Conference on Soil Mechanics, Vifia del Mar, vol 4 19071925 Lacerda, W.A., & Schilling, G.H. (1992) Rain induced creep-rupture of Soberbo Road Landslide, Landslides, ed. D.H. Bell, Balkema, Proc. 6th Int. Symposium on Landslides, Christhurch, vol 1,45-152 Lacerda, W.A. & Silveira, G.C. (1992) Shear strength and compressibility characteristics of residual and colluviai soils of the Soberbo hillside, RJ (in Portuguese) 1st Brazilian Conference on Slope Stability - 1st COBRAE, ABMS, Rio de Janeiro, vol2 445-462 Lacerda, W.A. (1997) Stability of natural slopes along the tropical coast of Brazil, Symposium on recent developments in Soil and Puvement Mechanics, June, COPPE-UFRJ, Rio de Janeiro, Ed. Balkema, 17-40 Sandroni, S.S. (1982) Forecasting the behavior of slopes, examined from case histories (in Portuguese) 7th Brazilian Conf. On Soil Mechanics and Foundation Engineering, ABMS,, Olinda - Recife, vol 1, 74-97 Schilling, G.H. (1993) - Instrumentation and Analysis of the movements at the Soberbo Road hillside, Alto da Boa Vista, Rio de Janeiro, MS Thesis, (in Portuguese) COPPE-UFRJ, Rio de Janeiro, Soares, M.M., Pedrosa, M.G.A., & Lacerda, W.A.

204

2 Soil slope stability analyses

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

A new theory on instability of planar-sliding slope - Stiffness effect instability theory Qin Siqing Institute of Geolog); Chinese Acudemy ($Sciences, Beijing. People’s Republic of’ China

ABSTRACT: A cusp catastrophe model is presented for instability of planar-sliding slope. The discrimination formula for rapid and slow landslide is given and the stiffness effect instability theory is established.

1 PRESENTATION OF THE PROBLEM According to the traditional limited equilibrium method of rigid body, the safety factor of slope is defined as the ratio of sliding force and anti-sliding force, to evaluate the stability of slope. However, there is a great shortcoming in this method. To be understood easily, we take the instability of planarsliding slope as an example to explain it. In order to guarantee the uniformity of sliding, we assume that the upper part rock mass above sliding plane is rigid body, sliding plane is composed of two kinds of media with different strength, the sliding force is

not a fixed value, so it is not reliable to evaluate slope stability, neglecting the evolution of the slope evolution, merely according to the safety factor for one certain state.

Figure 1. Curve of sliding plane medium, simultaneously reaching the peak value of strength where, Fa,,,,= limited anti-sliding force by limited equilibrium method of rigid body; z,,and % =the peak value of anti-shearing stress for medium 1 and 2, respectively; L , and L, =the length of medium 1 and 2,respectively. There is a defect in the above mentioned method . Observing the curve of anti-shearing stress and sliding displacement, we can find this method is proper in the condition that the deformation of two media simultaneously reaches the peak value of strength (Fig.1). But in fact, it is hardly possible for the two media to reach peak simultaneously (Fig.2), so we can not calculate anti-sliding force with equation (1). We have met two strange cases in practice: landslide with safety factor more than 1 is unstable and landslide with safety factor less than 1 is stable. I think the anti-sliding force by equation (1) is the reason. Otherwise, it is the safety factor for one certain point by the limited equilibrium method of rigid body. In Fig.2, anti-shearing stress varies with the creep-sliding displacement U , and the safety factor is

Figure 2. Curve of sliding plane medium, not simultaneously reaching the peak value of strength On summary, when tracing the failure reason of the limited equilibrium method of rigid body sometimes, we should pay more attention to the defect of theory itself, rather than only consider the unreasonable values of parameters of rock mechanics. To evaluate the stability of this kind of slope rightly, the new theory is needed to develop. Obviously, landslide is an unconsecutive and catastrophic process, and it is more rational than any of the mathematical tools to describe successive

207

phenomenon for landslide to be described by the catastrophe theory (Thom 1972), which can reflect the dynamic instability process of slope. In view of this, a simple mechanical model is presented to solve the instability problem for planar-sliding slope, and a new theory on instability of slope - the stiffness effect instability theory is proposed by a cusp catastrophe model in the paper, with which the mechanical mechanisms of slope instability are explained.

where, G,=shear modulus; u*=critical displacement of unstable point; z,,,=residualanti-shearing strength. The constitutive equation for segment with the strain softening property (Qin 1993) is (31 h where,G,=initial shearing modulus; u,=displacement at the peak value of stress (Fig.4). It is easily known u,=221,, slope is equal to -G,e-'lh, at the turn point of the curve, by the equation (3). = G, ~ e - " ~ l i c

2 THE CUSP CATASTROPHE MODEL 2. I Mechanical model

Supposing the sliding plane as non-uniform weak intercalation, upper part rock mass above the sliding plane as rigid body (Fig.3), e s l o p e angle, psliding plane dip angle, H=vertical height of upper part rock mass, h=layer thickness of weak intercalation, mg=weight of upper part rock mass @gravity acceleration). Figure 4. Curve of two media

2.2 Cusp Catastrophe model In the system shown in Fig.3, the overall potential energy is equal to the sum of strain energy and sliding potential energy. The total potential energy is Figure 3. Mechanical model of instability of planar sliding slope Due to the sliding force caused by weight of rock mass, there is a creep displacement U for the rock mass to slide along the weak intercalation. At some segments of weak intercalation, media, such as locked patch, show elasticity or strain hardening because of high strength of media or smaller shearing stress, whose capability to resist deformation adds up with the increasing deformation; But at the other segments, because of the broken media, muddying action of water or great shearing stress, media are with strain softening property after the peak stress value, whose ability to resist deformation declines with increasing deformation. To simplify the analysis and focus on the physical essence of instability, assume the weak intercalation is composed of two media with different mechanical properties, one is elastic, the other is with strain softening property. The constitutive equation for the elastic segment of weak intercalation is

208

where, I,, l,=the length of sliding plane with strain softening and elastic property, respectively, I,+ l,=H/sinp. According to the catastrophe theory, we can choose U as state variable to make cusp catastrophe theory analysis by the equation (4). Above all, according V'=O,the equilibrium surface equation is expressed as - G A ue-lIIu" +---u--mgsin/3 Gel, (5 1 h h Apparently, this above equation is balancing condition of forces. The cusp is solved by the smoothness property of the equilibrium surface, V "=0 at cusp, that is

v'

and further, we can get u=u,=2u,

(7)

That is, the displacement value at cusp is exactly one at turn point of the constitutive curve of medium with strain softening property.

softening property is not more than 1. The smaller is the stiffness of medium with elastic property and the greater is the stiffness of medium with strain softening property, the more possible is for slope system to cause catastrophe. The necessary catastrophe condition depends on internal properties of system because the stiffness ratio depends on geometric dimension and material characteristic of system. If media of weak intercalation are wholly hardening (the medium with strain softening property is not exist) or one segment is with elastic property and the other is with ideal plasticity, that is analogous to k+co, landslide will not happen. When across the left branch of bifurcation set, b
Make Taylor extension with reference state u l , for the equation ( 5 ) , neglecting the forth order item and more, substituting (6) into ( 5 ) , we can obtain

Carry out variable substitution for equation (8), in order to transform it into typical form of cusp catastrophe. The equilibrium equation is

where,

x=( U-U I)/ul

(10)

U*

Jz

= uI[1--(1-

k)”’] 2 When control variables meet

(1 8)

k=G,l,e’lG,l,

(13)

2(k- 1)3+9(1+k-kg?
~mghsinplG,l,u,

(14)

, show that, although slope is in limited equilibrium state ,owing to action by internal and external factors, very small change of those factors also results in very small change of equilibrium state, which is corresponding to slow landslide in nature.

Parameter k is stiffness ratio, which is the stiffness of medium with elastic property divided by the stiffness at turn point of constitutive curve of medium with strain softening property; 5 is called as geometric-mechanical parameter, in relation with weight of rock mass, geometric dimensions of system and mechanical parameters of medium. From equation (1 1) and (1 2), control variables a and b are determined by stiffiiess ratio k and geonietricmechanical parameter 6,that is to say, bifurcation set that is possible to take place catastrophe is decided by mechanical system characteristic itself and is irrelevant to external action. Substitute equation (1 1) and (12) into equation of bifurcation set,

3 COMPARISON WITH THE TRADITIONAL STABILITY ANALYSIS METHOD We can change equation (1 6) as

For rapid landslide, h
&

uo[l + k + ---(13

k)’”]

The stability factor, defined by ratio of anti-sliding force and sliding force at certain deformation U , is

(16)

This equation is the sufficient-necessary mechanical criteria for instability of planar-sliding slope. Apparently, only when a20, system can cut across bifurcation set to result in catastrophe, the unstable necessary condition is

k< 1

0.5 e 2

-

)

mgh sin p

We get 2(k-1)’+9( 1 +k-ka2=0

(19)

K=G1

“

e-‘i

’“o

+ kC,l,ue-’

mgh sin p

(22) z/L u , [ l + k + - - -(1-k)3’’] 3 It is easily known the stability factor only depends on k and ulu,. that is to say, K is relevant to creepsliding deformation U and varies as increase U .

(17)

That is to say, the stiffiiess ratio of the stiffness of medium with elastic property and that with strain

209

When slope evolves to critical state, u=u*, substitute equation (1 8) into (22), we can obtain the critical stability factor as follows

[1 -

fi _ - (1 - k)1/?][edl(l-k)”2 + kl

KL =

(23) 1+k

+ &(l-

k)3/2 3 We know from equation (23), KL is only relevant to k. Values calculated with equation (23) are listed in Table 1.

K K,

0.0 0.819

0.2 0.4 0.6 0.8 0.895 0.947 0.979 0.996

1.0 1.0

It is clear that K, is the smallest at k-0 and KLwill add up when k increases. This explains rapid landslide will take place when anti-sliding force is more than sliding force and some condition is met. But this condition can not be given with the limited equilibrium method of rigid body, for which, landslide will occur when stability factor is less than 1 and the effect of stiffness ratio is not considered. It is analogous to condition k=l and is a special example. The happening condition can be got for different stiffness ratio by equation (1 9), whose expression is

[I - f i (1 -k)l’?][eJ’(1-”“2

+ kl


1+ k

+ &(I 3

- k)3”

[I - & (1 __ k)”?][e\/2(’”’‘2 +kl 2 (1 - k)j/z l+k3 and which is listed in Table 2.

to understand why landslide (slow landslide) possibly takes place when the stability factor calculated by this method is more than 1. We can also see that even if K,<1, but is not less than certain degree, the rapid landslide can not occur, such as k 0 , O.82
4 INSTABILITY MECI4ANISM OF SLOPE It is generally thought that slope instability has great relationship with water’s action. Acted by water, shearing modulus of medium with elastic property, becomes lower and its anti-shearing force also decreases at the same time, so the stress borne by media with strain softening property correspondingly adds up and its peak strength value become lower by water’s action. This coupling interaction easily make medium deform into the phase of strain softening after peak strength value.

(24)

0

k

0.0 0.2 0.4 0.6 0.8 0.9 0.819 0.895 0.947 0.979 0.996 0.999

70

2.279 1.595 1.299 1.137 1.043 1.015

Figure 5 . Steepening of inclination of the softening segment of quartzite deformation curve with the increase of pore water pressure (numerals on the curve are pore water pressure, in Mpa)

We can see that when k
When it turns to the phase of strain softening. water’s action makes stiffness add up (Fig.5) and at the same time also makes stiffness of medium with elastic property decrease, this easily causes stiffness ratio less than 1 to result in slope instability. This process can directly be understood through the senses, the greater the stiffness of medium with

K‘

-

-

-

-

-

-

210

strain softening property, that is, the steeper the curve T-U after peak strength value, that shows its bearing capability decreases quickly at certain deformation, and the elastic segment (locked patch) will have to undertake larger load, and also bearing capability of locked patch decreases by action of water, the locked patch will break for the reason not to undertake the higher shearing stress, this will lose its original equilibrium state to cause landslide.

5 CONCLUSION The problem, such as the slope with safety factor more than 1 is unstable, but less than 1 is stable, is reasonably explained. It is pointed out that there is great shortcoming for the limited equilibrium method of rigid body. It is possible to make physical forecasting of landslide and explain the cause of rapid landslide with the theory presented in this paper. To be sure, the above mentioned model and theory are not too perfect, such as the form of constitutive equation needs to develop further. But the author believes that the concept and method proposed in this paper will have vast developing prospect along with deeper research on the theory. REFERENCES Qin, S. Q. 1993. An introduction to nonlineur engineering geology. Chengdu: Southwest University Press of Traffic. Saunders, P. T. 1980. An introduction to catastrophe theory. Cambridge: Cambridge University Press.

21 1

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami& Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Ultimate state of a slope at non-linear unsteady creep and damage S.A.Elsoufiev Odessa State Universiy, Ukraine

ABSTRACT: Non-linear deformation and ultimate state of a slope under vertical Ioads are considered. Constitutive equations of a non-linear unsteady creep and a damage (the development of internal defects) are introduced. Critical strains and time as well as the mode of fracture and ultimate load are found according to the criterion of infinite rate of strains for a hardening body and the scheme of the perfect plastic media. Some simple engineering formulae are proposed. The problem of a wedge penetration is also studied.

1 INTRODUCTION

should be solved together with boundary conditions

The complications in soils behaviour do not allow to assume a single rheological law for all the earths. Great difference between the properties of a sample and an element of a material in a structure makes difficulties in the usage of the Media Mechanics methods. In this situation it is convenient to apply to objects’ strength computation comparatively simple constitutive equations with the determination of their parameters from the data on the structures mechanical behaviour.

‘c(+~) =

rd(d(r2ee)/rdr)/dr- d2~e/d02= d(r&y/&)/dr.

Here ye = d ( 2 ~ r+) ~$ - an equivalent strain, o - a function of time t, p - an exponent of the hardening law. The experiments (Elsoufiev, 1982)show that (2.4) is valid at a monotonous loading while the equivalent strain does not diminish. At stepwise or interrupted stress change equations (2.4) may be used for the parts in which the equivalent stress is not less than on the portions before it, if the time is calculated from the beginning of the new loading. The correlation of (2.4) with test data is better for unsteadier creep. When the influence of time is negligible expressions (2.4) turns to be the constitutive equations of the plasticity theory. Basic law (2.4) may be easily generalized for quasi-brittle rupture(see below) that takes into account a damage (the development of internal defects) that induces the third parts of creep curves, the growth of materi-

~

= O, doe/d0

+

2T = O

(2.3)

The stresses are linked with the strains by the rheological law (Elsoufiev 1978)

For a slope under loads P, in polar co-ordinates r, 8 (Fig. 1) static expressions for stresses Gr, zro ‘I: -

(2.2)

Strains E F -Q,y subdue to the compatibility equation

2 MAIN EQUATIONS

a(ror)/dr -k

o, oe(-h)= o, oe(k)= -p.

(2’1)

213

the similar way the cases m >2 and m <2 may be studied, when with consideration of the symmetry demands we have respectively

als volume, the fall of critical strains and time for not enough plastic media and other effects.

3 SOLUTIONS FOR ELASTIC HARDENING AT CREEP BODIES

AND The constants D1, D2 can be found from (3.2) as above. At p = 1 we have the result of 3.1 at h = n/2. For practical purposes it is interesting to establish the dependence of yo,/P-value on angle 0. From (3.6) and well-known formulae of tensor transformation we have for m = 1,2,4 respectively

3.1 Elastic solution The common solution may be received by superposition method when we have (Fig. 1)

the

z = Co(cos20-cos2h), 0 0 = Co(20cos2h-sin20) - p/2,

CTy(

1) = -(2Pcos40)/ny, oy(2)= -(Pcos30)/2y,

or= C~(20cos2h+sin28)-p/2+(Acos0+Bsin0)/r, (3.1) CTy(4)= - (o.4P(cosh2d~0)"4cos30 )/y. where The corresponding diagrams C T ~ = F(0) are constructed in Fig.2 by solid, dashed and interrupted by points lines and we can see that with the increase of m-value the distribution of the stress becomes more even.

-

CO = (p/2)(sin2~ 2hcos2~)-'

and constants A, B can be found from integral static conditions h

Psinh = -Irorcos0d0, Pcosh -Srorsin0d0 -h -h which give

(3.2)

A = -Psinh(h+O.Ssin2h)-', B = -Pcosh(h-O.Ssin2h)-'.

3.2 Non-linear solution.for the case p-0 = z =O and from the Here as in 3.1 we suppose first static equation (2.1) we find

or=f(0)/r

(3.3)

and according to rheological law (2.4) we have E, = -E@ = Q(t)r-"g(0),

(3.4)

wherein m = p-', g = f" and function SZ is linked with a.Putting (3.4) into compatibility expression (2.3) we find g"+ p2g = 0.

Fig.2

(3.5)

denotes the second Here p = dm(2-m), and derivative by 0. The solution of (3.5) depends on the m-value. If m = 2 g = C0 + D and due to the symmetry condition C = 0 and constant D may be found from (3.2). For the case of h = rc/2 we find
214

In order to appreciate the results we compute for the case m = 1 the distribution of oyalong axis y under the concentrated load as well as under the centres of the stamp and uniformly distributed load on the length (-1,l) where we have respectively GU/q=4(iiY)in,oy/q =(2/~)( 1+2(~/1)~)( 1+ ( ~ / 1 ) ~ ) - ~ / ~ ,

os/q= 2(tan-'(l/y)+(y/l)/( ~+(y/l)~))/n.

Here q = P/21 and from Fig.3 where by solid, dashed and interrupted by points lines the diagrams Oy= =F(y/l) are constructed we can see that at y>41 these Curves practically coincide. AS with the growth of non-linearity the stress distribution becomes more uniform we can expect that solution (3.6) can be valid at least in the above shown limit.

Sokolovski 1969 integrated (3.8) for p = 1/3, y
Fig.4 Here we integrate (3.9) by the finite differences method at boundary condition CD(0) = 1. Then we integrate expression dWdy = -CD at border demand 8(n/4) = 0 which also gives condition 8 = h at y = 0. Firstly we considered the case p = 1 when we have the rigorous solution (see 3.1) which in the new variables here is (upper sign refers to h > n/4)

Fig.3 3.3 The non-linear solutiorzfor the case P = 0 Here we suppose that the strains and stresses do not depend on r (Sokolovski 1969) and putting representation

cos28 = (1 - CD +cos22h)((2 - cD)cos2h)-I The calculations by a computer reveal good agreement with these formulae . It allows to use the scheme above for other p-values. In Fig.5 diagrams y = y(8) are shown for different h which practically coincide for 1-1 = 1,2/3, 1/2 and 1/3.

into (2.3) and (2.1) respectively we derive

that at p = I gives the solution of 3.1 at P=O. Fulfilling the operations in (3.8) we find the second order differential equation that is shown only in a common form i n the Sokolovski‘s book, 1969. Replacing in it CD = -d8/dy we receive

+ 1 - 2/Y), (3.9) tan2y(dCD/dy) = 2@(1-@)((@-1)/p where Fig.5

215

Here we again suppose z’= 0 that gives z“’=O and with consideration of (2.1),(2.2)-the following result

When function ~ ( 0 is) known the z,-value may be found from the equation following of (2.1), (3.7) and boundary condition (2.2) for cig as

h dxe/zedO+ 2 ( d ~ / d 0+ l)cot2y, p = 4!zesin2~d0 0 that in combination give for (h2d4) the equation

h

maxx,

=x,l= z,(O)

From Fig.4 where the latter expression is shown by the interrupted by points line we can see that this solution may be used at least as the first approach.

8

p=4~,l!sin2~exp(-2!( l+dy/d0)cot21yd€l)d8 0 0

(3.10) 4. PENETRATION OF WEDGE INTO SOIL AND CONNECTED WITH THIS TASK PROBLEMS

Computations show that for p-values above diagrams z,= F(h) are near to the solid line in Fig.4. It may be explained by the absence of p in (3.10) and the vicinity of curves in Fig.5 (for h equal to n/4 and n/2 the straight lines coincide at all p). That allows to use the solid curves for practical purposes. In order to use the criterion of infinite strains at fracture (Carlsson 1966) we write similar to (3.4)

Here we suppose as everywhere in Soil Mechanics compressive stresses to be positive and use the Mohr’s diagram for the ultimate state (Fig.6),. where cp is an angle of repose and c - the cohesive factor.

Here e - the Neper’s number, a - a damage factor and E = As at 8 = 0 ci, = 00, then E, = €0 = 0, E = = y/2 and according to the criterion dddt +m we have from (3.1 1) the critical values (denoted by *)

Fig.6

As E = E* acts under angle n/4 to the line 8 = 0 the destruction should begin on the line OH (Fig. 1). In order to get simple engineering formulae we put (3.1 1) at a = 0 into (2.3) which gives

Fig.6 allows to find many important formulae. In particular we have for main stresses

((rn-l)(~,)’”~3~~2 + ~(T~)”’-’)(T,’ + 42) = C2.

0 3

(3.12)

=(,ic

where C2 is a constant. According to the symmetry demand ~ ’ ( 0 = ) 0 and taking this condition for the whole wedge we get from (3.12) (zJn-’(z/, + 42) = = C2/4 which at m = 1 gives the solution of 3.1. To exclude C2 from (3.12) we differentiate it as follows

+42))(z”+4z)z ’+4(Q2(m( 1)z

1 k sincp) rt cxcoscp

(4.1)

01

and construct the simple fields of slip lines that are inclined to the planes of maximum and minimum stress action under angles n/4 -t 9/2. Another field of this kind consists of straight lines r with the same origin and inclined to them curves described by equation

+ 4(Q2) (z, ’+4z’)=O.

r = r0exp(8tancp).

216

(4.2)

From Fig.6 we can also derive

o, = Hexp(20tancp) - c/tancp.

much bigger its value for an ideal plasticity, where cp = 0, c = zyi- the yielding limit at shear. (4.3)

We construct the field of slip lines at the wedge penetration as in Fig.7 and suppose that A 0 is a straight line. From the Figure we compute that it is inclined to the horizon AK by the angle h - v and we

Fig.8 Fig.7

At v = 2h - n/2 we find from (4 6 ) the ultimate load for a slope (Figl), and if v = n/2 we have the well-known so-called second ultimate load for a foundation with depth h in the soil with the weight of its unit 6

have for the segment KE lcosh - h = llsin(h-v), and from the equality of triangles AOG and GKD for the material of constant density we compute h’tanh=( 1I)’sin( h-v)(cos(h-v) + sin(h-v)tank). (4.4)

P,, = (6h + c/tancp)(I+sincp)e”t””’P(1-sincp) - c/tancp.

From geometrical considerations we find 11 = al, where a = (1 - sincp)exp(-vtancp)/coscp, and h = Il(acosh - sin(h - v)). Putting the latter expression into (4.4) we derive the formula linking angles h and v as

5 CONCLUSION In the same manner other problems for a non-linear soil at unsteady creep can be solved: a strength of a thin layer at tension or compression; the stability of retaining wall, as well as of cylinder, sphere and cone under internal and external pressure; a flow of a material between two foundations, inclined rigid plates and in a cone; the bearing capacity of piles and sheets of piles; propagation of cracks and plastic zones near stamps edges etc..

(4acosv + sin2v)tan2h - 2(a2 - C O S ~ V+ 2asinv)tanh - sin2v =O.

(4.5)

Now we find the ultimate load. In triangle AOB = 0 = 0 and from (4.1) qn(1 - sincp) = cxcoscp, but from (4.3) o,,,= H - c/tancp, and so H = c/(l 01

sincp)tancp. In the same manner for triangle OCD where 03 = p., 0 = v we find from (4. l), (4.3)

REFERENCES

p+= H( 1 + sincp)exp(2vtancp) - c/tancp

Carlsson, R. 1966. Creep induced tensile instability. J. of Mech. Eng. Sci. 7, 2: 218-229. Elsoufiev, S. !978. On one scheme of determination of ultimate creep strains. Strength of Muter. 10. Elsoufiev, S. 1982.The use of simplified rheological rules for describing the processes of deformation and fracture of materials.Sov Mut.Sci. 13,1:62-65 Sokolovski, V. Theoiy ojplasticity. 1969.(In Russ.).

and with consideration of H-value we derive finally

p. = c(( 1+sincp)exp2vtanv/( 1-sincp) - l)/tancp.

(4.6)

Lastly of static conditions we find P, = 2lp,sinh and from diagrams PJ21c = F(h)in Fig.8 we can see that P, increases with the growth of h and cp. It may be

217

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Application of FEM on the basis of elasto-viscoplastic model to landslide problems Hiroaki Fujii, Sin-ichi Nishimura & Kiyoshi Shimada Faculty of Environmental Science and Technology, Okayama UniversiQ Japan

Toshio Hori WESCO Incorporated, Hyogo, Japun

ABSTRACT : This paper discusses the applications of FEM on the basis of the elasto-viscoplastic model to landslide problems. Fluidity parameter y which governs the time dependent behavior of landslide, is determined from the comparison of the calculated displacement of landslide with the measured in the Site. Concluding remarks are as follows: 1)The fluidity parameter identified from five typical landslide Sites is within the range of 1* 10-5+7*104(day-’);2)The effect of dewatering method was proved by the proposed method; 3)Using this model, it may be possible to make predictions on the future trend of deformation.

The viscoplastic strain rate is expressed by the next equation based on the excess stress model and the associated flow.

1 .Introduction The numerical method is discussed to predict landslide behavior in this study. Particularly, the finite element method based on the elasto-viscoplastic model (E-VP FEM) is described here. By E-VP FEM, we can analyze the rheological (time dependent) deformation behavior of landslide. E-VP FEM is applied to some actual landslide Sites in this paper. The measured displacement of the landslide surface is compared with the calculated one. Then, the fluidity parameter y that is one of the parameters constituting the elasto-viscoplastic model and governs the deformation velocity of ground is identified in some landslide Sites. Finally, the range of value of the parameter was grasped roughly in the actual landslide Sites.

y :fluidity parameter, @ ( F ):flow function, F : yield function

0 :stress vector,

Mohr-Coulomb’s failure criterion is used as a yield function here, and it is defined as follows. F

(0’ - 0 ’ )

=

2

1

- C’ . cos$’ - (0; + 0;). sin$’

C’ : cohesion based on effective stress, : internal friction angle based on effective stress, 0; ,D; : maximum, minimum, effective principal

2. Elasto-Viscoplastic model’)’2)

stress,

2.1 Basic concept qf Elasto- Viscoplastic model

0, ,o3:total stress

( o ; , ~=;(0, ) - U , o3- U ) , u :pore water pressure

The behavior of the soil is assumed to be elastoviscoplastic in this researchh the elasto-viscoplastic theory, the strain rate is obtained by (i= ke + iVp ) as

In this research, the following simple function is assumed concerning @ . That is,

(x> 0) -+ (I+))

summation of the elastic strain rate€, and the visco-

. Here, the time differentiation plastic strain rate ivp of stress vector is obtained by the next equation according to the elastic strain rate. D : elasticity matrix ci = D i e

= 1,

(x< 0) + (@(x))= 0

It can express viscoplastic behavior of the landslide well enough. It is shown by the following examples.

219

2.2 Meaning of 7 and flow of the analysis 6 ’ measurement velocity

Pt

c

A Paleozoic 210m 120m 22.5

0

Site geology length width

A decision method of y has not been established yet. Therefore, it is decided by the trial and error, so that the analytical and measured value agree with each other well in this research. Here, the measured values are obtained from the inclinometer and the extensometer in the actual landslide Sites. The analytical values are compared with the measured in many places of landslide Site and corresponding y is determined at each point. The range and the difference of y in the various points are considered and the representative of the landslide Site is determined. The representative in the objective Site is used as an analytical parameter. Finally, the history of the landslide and the prediction of the future displacement can be discussed according to the result of analysis.

(mm/Y)

33.4 inclinometer

5-12

I

B

”

C

Tertiary

600m 320m 19.6 19.6 23.4 extensometer 4003,300 70m

30m 17.6

D Mesozoic 18Om 90m 19.6 P ,:unit weight(kN/m’), C

80-100

7.8

17.4

0

26.7 inclinometer

”

10

:cohesion(kPa), d, :internal friction angle(- )

3. Application to Site A3’landslide Figure- 1 Inclinometer (Site-A) 3. I Analysis condition

The outline and the movement situation of the landslide in Site A are shown in Table-1. The position of inclinometer 12, 11, and I3 in the landslide block is shown in Figure-1. As for the landslide activity of Site A, there is no information about the initial movement. Here, it is assumed that the initial movement was caused, when the tail of the slope was cut for the improvement of the highway. The cut spot is coincide with the end of the sliding surface. Various investigations and the measurements were started 4,00Oday( = 11years) after the landslide start based on the assumption. The horizontal displacement is used for the comparison of the analytical with measured.

Figure-2 Element division chert Table-2 Parameter of Site-A Pt E v c’ Surface Sliding Base rock

19.6 23.1 22.5

17,640

6’

0.31

9,800

I’

-

-

24.6 33.4 45.0

4,900,000 0.25 9,800 0 ,:unit weight(kN/m3), E : modulus of elasticity(kPa), v : poisson’s ratio, c : cohesion(kPa), d, : internal friction angle( )

3.2 Modeling qf stratum a n d n i t e elements The finite element model is shown in Figure-2. The stratum classified into three layers, “Surface”, “Sliding”, and “Base” as shown in Figure-1. The material parameters of these layers are shown in Table-2. The horizontal displacement corresponds to the surface and the sliding surface are used for analysis. The positions of the bore holes for the inclinometer I2, I1 and I3 are given in Figure-1. The highest water level of the past during the measurement period is shown in the figure.

point

‘y

t=O I2 : surface 43.2 cm

: sliding

measurement

‘U

4000 7

8ooo average fitting 7

0.92

0.71

Y

0.75

1.1 XlO-’

1.1 XlO-’

7.9 ’1

1.14

0.45

0.50

I1 : surface 42.4”

1.05

0.67

0.82

1.2X10-5

8.4 ’1

1.09

0.94

0.77

0.8X 10”

I3 : surface 22.2 1’

1.04

0.96

1.18

1.2X lO-’

1.10

0.79

0.80

1.0X10-5

: sliding : sliding

220

calculated displacement ( = 1 x IO-’)

6.2”

3.3 Analvsis result and considerations

The value o f y which corresponds to the measurement is within the range of (0.8-1.2) X 10-5(day-') according to an analytical result. Table-3 gives the analytical and measured results of the displacement velocity and identified y -values in the six points. Fig~re-3~ shows ) the relation of the surface displacement of I2 point and the elapsed time in the case that y =1.O* 10-5(day-').Here, the displacement obtained by this analysis can be divided into the elastic component and viscoplastic component. In Fig.3, the analytical displacement is added to the measured one so that the measured and analytical are coincide with each other at the 4,000 days. According to the result, the analysis predicts the surface displacement of I2 point well, while on the sliding surface the analysis a little underestimates the displacement velocity. Almost similar results are obtained in I1 and I3 points. From the analytical result, ~ = l . o * l O (day-') -~ is adopted as a fluidity parameter in Site A. 3.4 Prediction qf displacement

The deformations of slope on the t=5,050 day and t=l1,362 day after are shown in Figure-4. In the figure, the dotted and solid lines mean the initial and deformed states respectively, and the displacement scale is extended 50times.

Figure-3 I2 point displacement

4. Application to Site B * C * D landslide 4.1 Outline of Site B -C -Dlandslide

The outline of the landslide and the movement Site C *), Site D9' are situations of Site B5),6)37), shown in Table- 1. Site B : The displacement had been measured by the extensometer during 1989-1990. Due to the dewatering well or bore hole in the measurement period, the displacement velocity measured by the extensometer decreased as follows. At the head, from 2 . 5 d d a y to 0.70mm/day, in the middle part, from l.lmm/day to 0.43mm/day, and in the end part, from 9. lmm/day to 5 . 0 4 d d a y . Site C : Small-scale cutting was conducted in the vicinity of the center in the landslide block. The displacement of extensometer about six months after construction, is accumulated in the tensile direction. The displacement velocity is 0 . 2 2 d d a y at the landslide head and it's 0 . 2 8 d d a y in the middle part.

Figure-4(a) A-Site displacement

Figure-4(b) A-Site displacement 22 1

Site D : The displacement shown in Figure-5 is obtained by the inclinometer in the landslide block in Site D. 4.2 Modeling of Site B -C *D We divides into three zones of "Surface", "Sliding" and "Base", and Table-4 shows the material parameters of each zone. The finite element mesh is also shown in the figure. 4.3 Fluidity parameter 7 of Site B .C *D

The highest ground water level of the past was used in the analysis. The time-horizontal displacement relationship is shown in Figures-6, 7 and 8. Adopted values as the representative of yin the figures are 7*10-4(day-1)in Site B, 2*10-4(day-')in Site C and5*10-5(day-') in Site D. The result of analysis correspond to each Site is described as follows. Site B : The parameter y is identified to be 1.2*10-3 (day-'), 7.1 *10-4(day*')and 9.5*10-4(day-')from the measured displacements at the head, middle and end zones respectively. According to Figure-6, the analysis underestimates the displacement compared with measured in the head and end zones, while in the middle zone, calculated displacement agrees well with the measured, y =7* 1O-'(day-') is adopted as a representative value. Site C: The parameter y is identified to be 1.9* 1OU4 (day-') and 2.2" 10-4(day-') from the measured displacements respectively. According to Figure-7, an analytical result when we use y =2* 1O-'(day-') that is the average value of above-mentioned values. The calculated displacement agrees well with the measFigure-6 B-Site displacement ured, though the observation period is shorter than other Sites. Site D: The parameter y is identified to be 5.0* 10-4 and 1.4*1O-4(day-') from the measured displacements of the surface and the sliding surface respectively. In Figure-8, the former value 5.0*10-4(day-') is used. In this case, measured displacement of the sliding surface exceeds the calculated and varies widely. On the other hand, the calculated and the measured displacements of the surface are corresponding well. Here, y =5 * 1O-4(day-') obtained by the measured displacement on the surface is adopted as a representative value. Figure-5 D-Site Inclinometer 222

4.4 Dewatering effect in Site B

Table-4 Parameter of sliding layer (B,C,D) Site

An analytical result in the head of landslide, the middle zone, and the end zone is shown in Figure-9. An analytical value of the displacement velocity at any point roughly agrees with the measured. In this calculation, it is assumed that groundwater level decreases to the sliding surface after the drain con-

parameter of sliding layer o t ( l < ~ / m ~c) ~ a $) ( " I

displacement( mm/y) -?.zoo ,_- -

19.6

7.8

17.4 extensometer 80-100

0

26.7

inclinometer

the landslide behavior caused by the change of the pore water pressure is predictable. It is extremely difficult to evaluate the effect in the design stage. Currently, the evaluation of the improvement effect is based on the observed ground water level in the bore holes or the observed volume of drained water. It is clarified the displacement measurement is more effective for the evaluation of the construction effect.

5. Conclusions The representative y of the each Site is shown Table-5. The value of y of Site A or D whose landslide is not active is small. On the other hand they of Site B or C whose landslide is active are larger than Site A and D. The obtained finding is surnmarized as follows. (1)Site A, on the assumption that various measurements were started 4,000 days( % 11y) after the initial movement took place, we have compared the analytical value which is calculated by the material parameters obtained from the conducted laboratory soil tests and the identified parameter from the measurement value of inclinometer 12, I1 and I3 in the hole points. It turned out that the fluidity parameter of this Site is y=l*lO-'(day-'). The calculated displacement of the surface in each point was adjusted to the measured to identify the fluidity parameter y here. (2)The fluidity parameter obtained by four typical landslide which include Site A is within the range of 1*10-5-7*10-4(day'1). Moreover, there is great possibility that landslide is affected by geological features. The older the geological features age is, the smaller y is. The characteristic of yis clarified by investigating deferent types of landslide cases and accumulation of the identification. (3)As for B Site, the effect of the dewatering against the landslide is confirmed by comparing the calculated displacement after the dewatering construction with the measured one by the extensometers. Thus, the landslide behavior after construc-

Figure-9 B-Site drainage

223

10

5) Ryousuke Amiki, Hiroyuki Nakamura, Kazumi

tion is predictable by comparison of the measured and the calculated displacement. (4)The analytical technique shown in this study, EVP FEM is based on the comparison of various measured data with the calculated and some kinds of ordinary soil tests. The proposed method seems to be practical to analyze a lot of types of landslide area. However, the method of deciding the fluidity parameter y which governs the visco-plastic behavior of landslide, depends heavily on the observation of landslide movement. Some problems remains to establish the better prediction method as follows. 1) Many of the measured displacement always change the pattern by the influence of rainfall. The accumulation of an analytical case with the technique to consider variable pore water pressure. 2) The method of identify the initial movement of landslide is necessary considering the geological property of the Site.

-Table-5 Site A

The Parameter y of A,B,C,D Site landslide velocity length width ( d y )

Paleozoic 210m 120m

B

I!

C

Tertiary

D Mesozoic -

I

5-12

day-’ lllI17/y lX10-5 3 x 1 0 - ~

600m 320m ~ o o ~ 3 70X01~ O4 2 x 10” 70m

30m 80-100

11Omi 9Omi

10

2X104 7 X 10” i5X1O4 1 x 1O4

References 1) Yoshiaki Yamada : Finite element method of plasticity, Science & Technology publisher inc., pp. 26-28,pp.96- 1 OO,pp.283-285,1988. 2) 0wen.J & Hinton : Finite Elements in Plasticity,, Theory & Practice, 1980. 3) Hiroaki Fujii, Toshio Hori, Kiyoshi Shimada, Shinichi Nishimura: Some considerations concerni -ng precipitation and amount of movement on landslide area, Ground EngineeringVol. 10-1,pp 13-24,1992.(Geotechnical engineering society Chugoku branch thesis report collection) 4) Hiroaki Fujii, Shinichi Nishimura, Toshio Hori, Kiyoshi Shimada : Application of FEM on the basis of Elasto visco-plasticity model in a certain landslide area, Ground Engineering,vol. 1 1-1,pp. 11 - 1,pp. 11-23,1993.(Geotechnical engineering society Chugoku branch thesis report collection)

224

Itou : Measurement result and the predict of Pore water pressure on a certain landslide area, Landslide Academy research & lecture thesis collection of 1990 term,pp.244-247,1990. 6) Tatsuo Iinuma, Masatate Funazaki, Tsuyosi Yauchi : Geographical & geological features consideration to large-scale landslide, Landslide Academy research & lecture thesis collection of 1991 te1-m~pp.33-36,1991. 7) Hiroyuki Yoshimatsu, Michio Takeshita, Ryousuke Ichikawa : Measures worker and the construction effect of Kuchisakamoto landslide in 6. Pref.,Landslide Academy research & lecture thesis collection of 1991 term,pp. 149152,1991. 8) Susumu Hoshino, Tamotsu Yoshida : The meas -urement of the displacement on Rikushinai Landslide in Hokkaido Furubira-cho,Landslide, vo1.7-3,pp. 1520,1971 9) Masabumi Yuube, Norio Yagi, Ryuuichi Yatabe, Meiketu Enoki : Characteristic of behavior of the Chichibu belt Kitaobiutiki district landslide and landslide clay, landslide Academy research & lecture thesis collections of 1991 term,pp. 114117,1990

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Coupled excavation analyses of vertical cut and slopes in clay T. Hoshikawa & T. Nakai Department of Systems Management and Engineering, Nagoya Institute of Technology,Japan

Y. Nishi Deparhnent of Civil Engineering, Nagoya Institute of Technology,Japun

ABSTRACTS: Soil-water coupled analyses of vertical cut and slope excavations are conducted to investigate the behavior of an excavated ground in clay. In this paper, an elastoplastic model for clay named the tij-clay model (Nakai & Matsuoka 1986) is extended to one which can describe the behavior of over-consolidated clay. To take into consideration the influence of stress history including over consolidation, the subloading concept (Hashiguchi 1980) is introduced into the model. Employing this model, finite element analyses are carried out on normally and/or over consolidated grounds. The difference of time dependent behavior of excavated ground between normally and over consolidated states has been discussed on the basis of numerical results. 1 INTRODUCTION

In recent years, there are many cases of excavation closely neighboring to other structures in urban areas. Hence, it is necessary to consider not only the stability of excavated slopes but also the settlement of ground surface and the deformation of surrounding ground. The stability of slopes is usually analyzed by using the theory of rigid-plasticity. On the other hand, ground deformations are predicted using elastic finite element analyses in many practical problems. In excavation problems, it is very important to take into consideration the process of the excavation (Nakai et. al., 1995, Nakai et. al., 1996). Elastoplastic analyses, however, should be conducted to consider the excavation process on the mechanical behavior of grounds. Nakai & Matsuoka (1986) proposed an elastoplastic constitutive model for clay named the t,-clay model. This model is based on the tij-concept (Nakai & Mihara, 1984), can describe the deformation and strength characteristics of normally consolidated (NC) clay. The validity of this model has also been confirmed by using many laboratory test results. Nakai et al. (1996) discussed the influence of the construction history on the earth retaining wall. Model tests and elastoplastic finite element analyses were conducted on sandy ground. It was indicated that the settlements and earth pressures on the retaining walls are very much influenced by the excavation procedure. Also it is necessary to carry out elastoplastic analyses in order to predict the behavior of ground under excavation accurately.

In practice the ground conditions in many geotechnical problems are considered to be under over-consolidated (OC) state. In order to simulate the behavior of OC ground, the previous model has been extended to one which can describe the behavior of OC clay as well as NC clay. In this extended model, the subloading concept by Hashiguchi (1980) is introduced. Then, soil-water coupled finite element analyses are performed for different excavation times in order to investigate the change of deformation on the excavated slopes and vertical cuts with time.

225

2 ELASTOPLASTIC

MODEL

WITH

SUB-

LOADING CONCEPT Nakai & Matsuoka (1986) proposed an elastoplastic constitutive model, named as the t,-clay model for normally consolidated clay. The yield function of the t,-clay model has been deduced by assuming that a linear stress-dilatancy relationship is satisfied in the tij-space.

Where t, and X are mean stress and stress ratio respectively according to the tij-concept. The value of t, at reference state on normally consolidation

line (NCL) is denoted as tN0.a and Cp = C,-C, are the soil parameters. Now, total strain increment is composed of elastic and plastic component as follows (2) The elastic strain increment of clay is assumed to follow isotropic Hooke's law (3)

Where E, is Young's modulus and v, is Poisson's ratio for elastic component. It has been assumed that the plastic strain increment satisfies the associated flow rule not in the ordinary stress space but in the tii stress space. Thus it can be given as d ~ =; A - d f d tiJ

Figure 1. Explanation of t,, and t,,, on the subloading surface and normal yield surface in tN-tsplane.

The proportionally constant A of Equation 4 can be evaluated from the consistency condition df=O.

(9)

(4)

The above is the outline of the tjj-clay model. Now, we extend this model by introducing the subloading surface concept (Hashiguchi 1980). According to this concept, Equation 1 is modified as Equation 5.

In the above Equation, the evolution rule of G can be defined as Equation 10. In this Equation, the scalar U should satisfy Equation 11, since the subloading surface approaches the normal yield surface monotonically with increase in plastic strain.

(5)

Where G is the inverse of over consolidation ratio in accordance with the tij-concept and defined by Equation 6.

d G = + m for G = O dG=O for G = l dG 1

We adopted the following function for U for definiteness, which is monotonically decreasing function of G. Where, t,, is given by Equation 7. It is the value of t, on NCL and can be obtained from present stress state (e.g. at P in Fig. 1). On the other hand, the mean stress t,,, corresponds to the volumetric strain and is expressed by Equation 8. The mean stresses tN1 and tNlein the tN-t, plane are shown schematically in Figure 1.

Substituting Equations 10 and 12 in Equation 9, the scalar A of Equation 4 can be obtained as

Thus, the formulation of the subloading tjj-clay model is complete. Due to the presence of the second term in the denominator of Equation 13, the 226

proposed model can express some features of overconsolidated clay. Namely, it reduces the magnitude of strains and increases the strength compared to those of normally consolidated clay (because 0 < G s 1). This model can describe not only the strain hardening and softening but also positive and negative dilatancy, which are typical features of the over-consolidated clay. For normally consolidated clay (G=l), the second term of the denominator in Equation 13 disappears and the present model coincides with the original tjj-claymodel.

3 ANALYSES OF EXCAVATION PROBLEMS Figure 3 shows the assumed excavation process of the clay ground. CASE 1 and 2 are slope excavation of ground. CASE 3 is the vertical cut of ground. Normally consolidated ground is assumed in CASE 1. Over-consolidated ground in CASE 2 and 3 are formed in such a way that a uniform load of q=98kPa is applied on the surface of ground and unloaded under drained condition. In the excavation process, ‘gradual’ excavation (tE=10,000hr:A-series) and ‘instantaneous’ excavation (t,=O:B-series) are assumed for each case. The ground material of these analyses is assumed as the Fujinomori clay, which is used in previous section (see Fig. 2). All these finite element analyses are carried out using the subloading tij-clay model and the soil parameters of Table 1. The coefficient of permeabillity (k) used in these analyses is O.GxlO~”m/hr.

Figure 2. Laboratory tests vs. model prediction for clays with various OCR. Now, we will show an example to verify the performance of the proposed model. Figure 2 shows the comparison between the observed results of conventional triaxial compression tests at constant mean stress on Fujinomori clay with various over consolidation ratios (OCR=1,2,4 and 8) and calculated ones by the proposed model. It can be seen from this figure that the proposed model can predict well the deformation and the strength characteristics of clay (stiffness, peak strength, dilatancy and so on) depending on the OCR. Soil parameters of Fujinomori clay used in these calculations are listed in Table 1. An additional parameter ‘ a ’ of Equation 12 is required for the proposed model, and the remaining parameters are the same as the original model.

h /(1 +e,,) K. /( 1+e,)

0

a V

a

5.08 X 10-’ 1.12 x 10-2 33.7 O 0.7 0.2 0.25

I ,

t,=10,000hr (-

t,=0hr

---

Slope excavation NC

I

n;:::E e: OC (q=98kPa)

CASE1-A

CASE2-A

CASE3-A

CASE1-B

CASE2-B

CASE3-B

I

In order to consider the influence of the migration and dissipation of pore water pressure, coupled analyses based on Biot’s theory are carried out under plane strain condition. The mesh of Figure 4 is used for CASE 1 and 2, while the mesh in Figure 11 is used for CASE 3. The boundary condition is the same for both meshes. The bottom boundary is

Figure 4. Finite element mesh of slope excavation

227

Figure 5. Computed contours of principal stress ratio for NC ground

Figure 7. Computed displacement vectors for NC ground

Figure 6. Computed contours of deviatoric strain for NC ground

Figure 8. Computed contours of principal stress ratio for OC ground 228

assumed to be fixed, and the lateral boundaries are assumed to be free only in the vertical direction. The ground water level is assumed at the ground surface, and the dissipation of pore water is allowed at the top of the grounds. The initial stresses in the grounds are calculated from the effective unit weight (y’= 0.93tf/m3) and the coefficient of earth pressure at rest (&,=0.47). To prepare the over-consolidated ground in CASE 2 and 3, the grounds were loaded with overburden stress q=98kPa and then unloaded. The excavation procedure is simulated by removing l m thick layers one by one from top to bottom.

3.1 SLOPE EXCAVATION Figures 5 to 7 show the computed contours of principal stress ratio, deviatoric strain, and displacement vectors respectively for CASE 1 (normally consolidated ground). Here, figures (a) correspond to ‘gradual’ excavations and figures (b) correspond to ‘instantaneous’ Though the region with high stress ratio firstly develops just behind the top of slope in the case of ‘instantaneous’ excavation (see Fig.S(b)), the region moves with time to the toe of slope and the surface of excavated ground in the same way as the region for ‘gradual’ excavation. We can see from Figure 6 that though the region with large deviatoric strain distributes along the circular zone from top to toe of slope ground in figure (c), such region is not so clear in figure (a) even if the elapsed time from the beginning of excavation is the same. The computed patterns of displacement in Figure 7 depend on the elapsed time.

Figure 9. Computed Contours of deviatoric strain for OC ground

Figures 8 to 10 show the computed contours of principal stress ratio, deviatoric strain and displacement vectors for OC ground (CASE 2). We can see from these figures that deviatoric strain in OC ground are less than NC ground, but the contours of stress ratio and deviatoric strain qualitatively show the same trend. 3.2 VERTICAL CUT The excavation of vertical cut is simulated by removing the rectangular domain ABCD from the original mesh (see Fig. 11). The behavior of overconsolidated ground under vertical cut is shown in Figures 12, 13 and 14. As shown in Figure 12(b) in CASE 3-B, high stress ratio area concentrates in the vicinity of the vertical cut at the completion of excavation. With increase of elapsed time, it progresses toward the excavated surface. In the case of ‘gradual’ excavation (CASE 3-A, Fig. 12(a)) the stress ratio distribution shows the same trend as that of ‘instantaneous’ excavation after t=10,000 hours from beginning of excavation (CASE 3-B, Fig. 12(c)). It is also noticed from Figure 14 that under

FigurelO. Computed displacement vectors for OC ground

Figure 11. Finite element mesh of vertical cut

229

Figure 12. Computed Contours of principal stress ratio for OC ground

Figure 13. Computed contours of deviatoric strain for OC ground

Fig U re 1 4. Coin p u t ed d i sp 1ace m e n t vectors

for OC ground

‘gradual’ excavation the vertical face deforms almost horizontally. The ‘instantaneous’ pattern in Figure 14(b) is very similar to the ‘gradual’ one in Figure 14(a). But the vertical displacements increase only as t approaches to 10,000 hours under ‘instantaneous’ excavation. That is due to the migration of pore water after excavation. Such tendency can be seen in the distribution of deviatoric strain in Figure 13. CONCLUSIONS An elastoplastic constitutive model (tij-clay model)

has been extended to one, which can describe the behavior of both normally and over consolidated clay and is named subloding tij-claymodel. The numerical simulations of slope excavations and vertical cuts have been performed using the

above-mentioned extended model. In order to investigate the time depended behavior of the excavated ground, the computed results of the ground behavior for ‘instantaneous’ and ‘gradual’ excavation have been compared. It is shown from the calculated results that the deviatoric strains in ‘instantaneous’ excavation are larger than those in ‘gradual’ one for every case. It is also found from these comparisons that the behavior of ground is different depending on the excavation procedure even if the elapsed time from the beginning of excavation is the same. Thus, we can conclude that the simulation of excavation should be conducted using coupled analysis and appropriately considering the excavation process.

230

ACKNOWLEDGEMENTS The first author acknowledges the financial support of the Japan Society for the Promotion of Science (JSPS). REFERENCES Hashiguchi, K., 1980. Constitutive equations of elastoplastic materials with elasto-plastic transition, J. Appl. Mech., ASME, Vol. 47, pp. 266-272. Nakai, T., Kawano, H. and Hashirnoto, T., 1996. Prediction of earth pressure and settlements due to excavation: influence of wall deflection process and wall friction, Proc. of Geotechnical Aspects of Underground Construction in soft Ground, Vol. 1, pp. 127-132. Nakai, T. and Matsuoka, H., 1986. A generalized elastoplastic constitutive model for clay in threedimensional stresses, Soils and Foundations, Vol. 26, NO. 3, pp.81-98. Nakai, T. and Mihara, Y., 1984. A new mechanical quantity for soils and application to elastoplastic constitutive model, Soils and Foundations, Vol. 24, NO. 2, pp.82-94. Nakai, T., Xu, L. M., Kawano, H. and Hashimoto, T., 1995. Influence of construction history in excavation, Proc. of 10'" Asian Regional Conference on Soil Mechanics and Foundation Engineering, Vol. 1,329-332.

231

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & JiangO 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Effects of a deep excavation on a potentially unstable urban hillside in San Marino G-Gottardi, G. Marchi & L.Tonni DISTAR7; University of Bolognu, ltuly

E Bianchi Engineering Service,FuenTa, Ituh

ABSTRACT: The paper reports the geotechnical engineering aspects of a deep, complex excavation into an urban hillside in the Republic of San Marino for a multi-storey building. The soil to be excavated was principally a highly over-consolidated, pliocenic silty clay and slickensided slip-surfaces - formed during historic iandslips in it - were positively identified during site investigation. The new permanent excavation, inore than 100 m long, progressed in front of a retaining wall of contiguous bored-piles of 800-1000 mm diameter. During and after construction ground movements in the hillside were monitored by three inclinometers which detected the re-activation of earlier landslip surfaces and other, smaller but deep-seated movements. The relevant topography and soil stratigraphy, coupled with congested urban development, are quite common in San Marino and the surrounding region (Marche and Romagna, Central Italy) and, therefore, achieving a satisfactory and safe construction and monitoring methodology for deep excavations in them is of considerable economic importance.

1. INTRODUCTION The paper reports the geoniorphological and geotechnical aspects of a deep, complex excavation into an urban hillside in the Republic of San Marino for the construction of a new shopping centre. The Republic of San Marino is an independent State, located in Central Italy, contained between Marche and Romagna regions (see map in Fig. 1). A multi-:torey commercial building over an area of 10000 in- had to be constructed in the circled area at the bottom left corner of Figure 1. The basement level of the new building was planned to be at a depth of 7.5 m with respect to the previous surface level (with an estimated amount of excavated soil of 100000 m3) and up to a maximum of 13 in below the dual carriageway, heavy traffic road, running immediately above the hillside and leading to the main city centre. Excavation work started in September 1997 and ended only in May 1998, after the construction of a contiguous bored-pile wall, incorporating three tiers of reinforced concrete waling beams restrained by ground anchors. From the start of excavation, clear evidence of soil displacements (concentrated along the bedding plane discontinuities of the existing formation) appeared in front of the excavated cuttings. Furthermore, small, but alarniing, cracks appeared in the major road

pavement. Causes of displacements, their monitoring and the prediction of possible further movements which might develop during and after completion of the excavation work, were all studied intensively. According to vertical cracks and local failures of preexisting masonry walls and to records of continuous road pavement repairs in the past, shallow slope movements had already occurred, well before excavation work started. The main question was therefore whether the new, but closely similar, soil movements were to be simply related to the stress level reduction induced by the excavation or, on the contrary and more worrying, to the activation of a major deep-seated slope movement (Bertuccioli et al., 1992). 2. GEOLOGICAL SETTING The area shown in Figure 1 is a typical example of the geologically complex situation of the Northern Apennines towards the plane borders (Colleselli & Colosimo, 1977) and is characterised by the general outcropping of Pliocenic formations, locally overlain by more recent alluvial deposits. The older sediments essentially consist of bluegrey silty clays deposited in 10-40 cm-thick, subhorizontal layers, sometime with the insertion of

233

Figure 1. Map of tlie area investigated and relevant outcropping geological formation.

very thin arenaceous sub-layers. In the area investigated, they reveal a main NE-S W direction strike and a dip angle between 10” and 15”, as shown in tlie geological section A-A’ sketched in Figure 2. The undisturbed stiff “bedrock” is usually topped by a softened and weathered shallow layer, a Sew metres thick, essentially made of the same material. The dashed area of Figure 1 is where the more recent alluvial deposits of the local Torrent Ausa outcrop: they are soft brown silts and clays, with organic matter and gravelly-sandy lenses. The construction site is located beside the rivulet named ”Fosso del Rio”, at the junction between

outcrops of the T. Ausa alluvium and the Pliocenic clayey formation. 3.SITE INVESTIGATION AND GEOTECHNICAL PROPERTIES Figure 3 shows a general plan of the construction site. The main dual carriageway road is shown at the top; the dashed area represents the area occupied by the building under construction, which is maxiinally 13 m lower than the current road level. The site investigation for design purposes basically comprised ten cone penetration tests, five

Figure 2. Schematic geological section along A-A’.

234

Figure 3 - General plan of the construction site.

12 in-deep boreholes and two open standpipe piezometers. Undisturbed samples from borings and fi-om specifically dug trenches were used for the determination of standard physical and mechanical soil properties. On such basis two stratigraphic units can be easily identified, both belonging to the same geological formation and essentially made from the same material: a highly overconsolidated, strongly anisotropic, pliocenic silty clay of medium plasticity (classified as CL, with average activity index 1.2). Howcvcr, the top layer (Unit A) shows clear evidence of a strongly weathered material, i.e. a higher water content and a considerably lower undrained shear strength. As regards tlie geotechnical parameters, the alluvial material where present - can be considered as part of the same stratigraphic unit. Such shallow layer is between 4 and 5 i n thick and is separated from the underlying, much stiffer, deeply fissured and stratified clay (Unit B) by a transition layer a few centimetres thick. Shear strengths laboratory (direct shear and Ltiiconsolidated-uiidrained triaxial) tests were performed on Unit B soil only, obtaining average peak (cp = 70 kPa and @p = 25”) and residual (& = 19”) parameters. However it should be kept in mind that the material is strongly anisotropic, not only because densely stratified. but also because of the frequent silty-sandy lenses on the bedding planes which tend to influence the overall available shear strength. During excavation, slickensided slipsurfaces (which had developed during historic landslips), were clcarly identified both along the two units interface and within the Unit B, in correspondence of the bedding planes. Little information is available on the piezometric levels, but they are probably rather low and related

to Unit A only. In fact, due to the very low permeability of the clayey soils, perched water tables - fed locally through the coarser upper alluvial deposits - are likely to form. A secondary minor groundwater circulation through the many fissures and silty lenses is also possible in the clayey “bedrock”, as detected during the excavation work.

4. THE DEEP EXCAVATION The new permanent excavation, more than 100 in long, progressed from north to south in front of a contiguous bored-pile wall (800-1 000 min diameter by 15-18 m long). The wall was supported by three tiers of reinforced concrete waling beams restrained by 40 ni long x 600 kN ground anchors, inclined of 25” with respect to the horizontal and spaced, typically, at 2 m centres horizontally and 3 m vertically. A schematic section of the designed situation (X-X’ in Fig. 3), throughout the slope and normal to the wall, is shown in Figure 4. Twelve benchmarks (BMn in Fig. 3) were positioned on the top edge of the pile wall in order to monitor the horizontal displacements. Since October 1997 some indication of soil movements appeared on the face of the excavation as relative displacements, up to 10 cm, either on the two units interface or within the clayey “bedrock”, in correspondence of the silty lenses, showing tlie same average inclination of the existing bedding planes (see Fig. 2). This situation, together with the numerous previous records of shallow slope movements. induced the contractor to ask for advice and install three 20 in-deep inclinometers behind tlie pile-wall (labelled In in Fig. 3), in order to measure with time and excavation progress - the

235

Figure 4. Section X-X’: measured displacementsand possible slip surfaces. displacements within the soil mass and detect any reactivation of earlier landslip surfaces and other, possible, deep-seated movements, the pile wall had not been designed to accommodate. 5 . MONITORING OF DISPLACEMENTS

The three inclinometers were installed on 3 1 October 1997, read monthly until June 1998 and again in January 1999. Inclinometer I1 showed immediately (after the first two readings) a total displacement of 6 mm at a depth of 6 m, at the interface between Units A and B; however in all subsequent readings, movements at every depth appear to halt. Inclinometer 12, the more northern located, displayed some deep movement at a depth of 9 m and, subsequently, of 12 m, i.e. well within Unit B; however the main displacements were concentrated in the first 5 m, with a maximum integral value at the inclinometer head of 21 mm. Virtually nothing happened after April. Inclinometer I3 is situated along the mean section X-X’and all the relevant incremental readings since late October 1997 are reported in Figure 5 . Again early data show a possible shallow slip surface at a depth of 5 m, which progressed until April and then practically stopped. It is interesting to note a much deeper movement, occurring within the “bedrock”, which advanced until last May and achieved a maximum value of 7 nun; the last readings seems to suggest that also those movements have now ceased. The integral displacement at the inclinometer head has been 37.1 mm so far. The inclinometer readings are in good agreement with benchmark measurements, which were carried

out in the same period. They also show initial displacements of few tens of millimetres, essentially normal to the wall axis, and, afterwards, the same decreasing trend from May onwards. BM6, the benchmark which moved most, exhibited a total horizontal displacement of 48 mm, from late October 1997 till mid May 1998. In Figure 4 the I3 readings plot, together with the total horizontal displacements as measured from the benchmark BM5 at the top of the pile wall in the same period, have been superimposed on section XX’. These information, together with the cracks position in the main road pavement and record of relative displacements on the face of the excavation, enabled us to draw possible slip surfaces (labelled from 1 to 3) for subsequent slope stability analyses. In order to better understand all these data, the excavation progress and the ground anchors installation should be also taken into account: in fact about 80% of the excavation work was quickly completed by October 1997; then it stopped until the end of March and resumed to end in June 1998. Again only one tier of ground anchors was installed by 1997 and the whole set completed in mid-April. Some tendons were equipped with a load cell, which, from the data available so far, have shown an essentially constant trend with time starting from the initially given value of 600 kN. As specifically the middle ground anchor was regards section X-X’, installed first, in December 1997, and subsequently the other two in March 1998; the final situation was reached at the end of April. Therefore the soil displacements were clearly detected at various depths only after October 1997, i.e. when most soil had already been excavated. The shallow movements could well be interpreted as the

236

Table 1. Factors of safety (FS) from limit equilibrium stability analysis. Slip surface Before excavation After excavation without ground anchors After excavation with ground anchors

Figure 5. Inclinometer I3 incremental readings. reactivation of previously developed slip surfaces, whilst the deep-seated displacements might, on the contrary, be related to the soil deformations induced by the stress level reduction and concentrated - in a strongly anisotropic material - on the weaker layers. All movements tend anyway to cease after the excavation work completion and the ground anchors installation.

6. STABILITY ANALYSES In order to better investigate the causes of the measured soil displacements and predict possible further movements, two separate analyses were performed. The first applied standard limit equilibrium methods to the slope stability analysis of section XX', taking into consideration the following three slip surfaces (see Fig. 4): surface 1 essentially corresponds to the two units interface, surface 2 is the expression of shallower movements recorded both by the inclinometer and on the face of the excavation, finally surface 3 concerns the whole slope and is related to the deep-seated movements which developed within the Unit B. For each slip surface the factor of safety towards slope instability was calculated with reference to the original soil profile (before the excavation) and the final situation (end of works), with and without the ground anchors. For the inclined concentrated forces applied

1 1.38

2 1.52

3 2.27

1.16

1.28

1.64

1.21

1.32

1.66

by the ground anchors, the load cell measurements were used. The stability calculations were carried out assuming homogeneous and isotropic soils in Units A and B, with the following soil strength parameters: (PA = 16" and (PB = 20" and no cohesion. Results are reported in Table 1. FS is generally greater than unity, significantly increasing with the slip surface depth. Of course the most severe situation everywhere is after the end of excavation and without the ground anchors, which, however, do not seem to have a great effect on the overall stability. It is interesting to observe that the existence of a perched water table in the Unit A would substantially reduce the factor of safety of surface 1 (to 1.06 with a water level at -2 m from the soil surface), which can even become less than unity (0.99 when the water level coincides with the soil surface). A second analysis using a 2D finite element code was aimed to verify what could be the order of magnitude of the strains induced by the stress level decrease, due to the excavation, in a strongly anisotropic material and whether such soil deformation could concentrate in thin levels of a silty-sandy nature. Therefore a much simplified situation was considered: a steep, 9 m-deep slope, progressively excavated in an elasto-plastic homogeneous material (Fig. 6). A marked anisotropy was introduced as a layer with no cohesion and an inclination of 10" with respect to the horizontal, like the existing bedding planes. Such model provides, as a consequence of the unloading phase, total horizontal displacements up to 10 cm and relative movements concentrated in correspondence of the silty interface; these relative displacements tend to progressively reduce, moving from the face of the excavation towards inside the soil mass, for a length of about 5 m, in good agreement with what observed on site. 7. CONCLUSIONS The geotechnical engineering aspects of a deep, complex excavation into an urban hillside in the Republic of San Marino were presented. The soil to be excavated was principally a highly over-

237

Figure 6. Horizontal displacemeiits induced by the excavation of a 9 in-deep slope (FEM analysis). consolidated, stiff, silty clay, overlain by a few metres-thick layer of the same material, but softened and weathered. The particular interest of this case-history is in the analysis of the possible causes of the soil movements which had been detected during the excavation work, both on the cutting face and on the pavement of the major road running immediately above the hillside. Previous shallow slope iiioveinents had already occurred and question arose whether the new displacement evidence was to be related to the reactivation of an ancient deep-seated slip surface or, more simply, to the stress level reduction induced by the excavation. The displacemeiits of the bored-pile wall top edge, through topographic surveys, as well as the soil movements behind the wall, through the installation of three inclinometers, were continuously monitored and carefully kept under control during the excavation. Total displaceinents greater than 30 nim were measured at the surface level, mostly before the ground anchors installation and, now that work is completed, they appear to be substantially attenuated. Such important observation. together with the results of the relevant limit equilibrium slope stability analysis which provided factors of safety well above unity and increasing with depth, would suggest that major slope movements are unlikely to occur in these circumstances. The deep-seated displacements, measured by the inclinometers within the stiff clay, could be better interpreted (as well shown also by the schematic finite eleinent analysis performed) as the soil strains resulting from the considerable stress level reduction caused by the excavation of a highly overconsolidated material.

Those strains, in a strongly anisotropic material, tend to concentrate on the weaker layers, like the bedding planes or the silty lenses trapped within the clayey matrix. On the other hand, surface evidence like the road pavement cracks are to be related to much shallower slope movements (also measured by the inclinometers), probably situated at the two units interface. Slope stability analyses have confirmed that the actual factor of safety is considerably lower in this case and can be further reduced by the possible creation of a temporary perched water table. However, these shallow slope movements had already occurred previously and were just reactivated by the major excavation work: once the wall was completed and all the ground anchors installed, they clearly stopped. Such topographic and stratigraphic situation, coupled with congested urban development, is quite coinnion in San Marino and the surrounding region and similar deep excavations have often to be realised. It is hoped that the results of this study can help to achieve a satisfactory and safe construction and monitoring methodology.

REFERENCES Bertuccioli P., Distefano D., Esu F., Federico G. (1992). Initial deforinatioiis of high cuts in overcoilsolidated jointed clay. Proc. 6" ISL, Christchurch, vol. 11, pp. 1265-1270. Colleselli F., Colosimo P. (1 977). Coinportaiiiento di argille plio-pleistoceiiiche in una faiesia del litorale adriatico. Riv. It. Geot., vol. XI, N.1, pp. 5-22.

Slope Stability Engineering, Yagi, Yamagami & Jiang (( 1999 Balkema, Rotterdam, ISBN 905809 0795

Displacements of a slope in the Euganean Hills induced by quarrying

ABSTRACT: The paper concerns the evaluation of stability conditions of a landslide which occurred behind a marl and limestone quarry located in the Euganean Hills, Northeastern Italy. The limit equilibrium conditions of the landslide is evaluated. Then, an analysis of the displacements induced by the excavation together with their backward-propagation effect on slope movements is performed using the finite element method. The influence of some recent drainage works on the overall stability is also briefly discussed. stability are probably of less importance compared the intensive quarrying activity performed during the last decades. The influence of human activity on the stability conditions of a landslide, located in the south eastern area of the Euganean Hills and involving the colluvial cover, is analyzed and discussed in this paper using both limit equilibrium and finite element method. The effects of some drainage works, carried out recently in the most sliding zone, are also briefly commented.

1 INTRODUCTION The Euganean Hills rise isolated in the Venetian alluvial plain, covering an area of about 120 km2 and reaching an altitude of 600m above mean sea level. They are composed of sedimentary and eruptive rocks, the former composed of limestone and mar1 and the latter by basalst, ryolithes, trachytes and latites (Piccoli et al., 1975). The marl and basalt formations are normally covered with layers of weathered clay materials. These colluvial materials, having sometimes a thickness of up to several metres, show a precarious equilibrium also on gently conformed slopes. A recent census of landslide movements singled out about 140 unstable areas, corresponding to about 4% of the total surface of the hills (Dal Pra et al., 1995a,b). For example, during 1997 more than 60 landslides of various size and importance were recorded (Mazzucato, 1998). These landslides are due to anthropic as well as natural causes. Since about 2000 years, the morphology of the Euganean Hills has been intensively modified by several types of human activities, among which the most important is probably represented by open quarries of mark and trachytes. The former are generally excavated from the toe of the slopes whereas the latter from the volcanic outcrops. These excavations involve sharp variations of the profiles of the hills. Terracing for agricultural purposes, construction of new roads, changes of river paths or of the surface drainage system also create alterations of the original profiles of the hills, but their effects on slope

2 LANDSLIDE CHARACTERIZATION Figure 1 shows a general view of the landslide area. Features to note are: extension of the quarry and of the unstable zone; position of tension cracks and of damaged houses (Ravarotto house, S. Lucia Chapel, ect.); location of water springs, irrigation wells and drainage well; in-situ instrumentation such as piezometers and inclinometers; section A-A and B-B both considered in the analyses. 2.1 Brief history of the landslide The quarrying activity was undertaken in the early 1960s and continued until about 1986: at that time the scarps reached an height of about 60 m with a slope of 20". During 1976, some small sliding movements involving the colluvial sheet were observed behind the top of the excavation front. Again, in 1985 a larger failure with an extension of about 1000 m2 occurred at the eastern border of the quarry. Thereafter, it was decided in 1985 by the

239

Figure 1. General view of the landslide area.

altimetric shape of the limestone bedrock supporting the colluvial deposits.

Mine and Quarry Regional Department to suspend the excavation works and the scarps were reprofiled, as shown in the cross-section of Figure 2. At the same time, the owners of some properties located at the eastern border of the area, where the rock outcrops emerge forming the Rusta Hill, complained about damage (i.e. cracks, fissures, wall rotations, etc.) occurring to their houses. The presence of tension cracks at the ground surface was also observed. Therefore an area of approximately 20,000 m2 was suspected to be active including a transitional sliding area around the quarry involving the whole detrital layer. The movements, occured along slightly sloping surfaces (8’- 10’) and continued at variable rate depending on hydrological site conditions. The possibility that quarrying works might influence the stability of the entire area, has been and is still being debated. On the basis of the limit equilibrium analysis carried out since then it appeared that no significant interaction between excavation and slope movements would have occurred or would occur.

2.3 Structural setting Two types of sedimentary soft rock formations characterize the investigated area: the “Scaglia Rossa” (marly limestone) and the Euganean Marl, whose emergences, having thickness of about 50 m, can be observed in the quarrying zone. The soft rock deposits slope in a east by south east direction with a dip angle of 25-30”. On the basis of the in-situ investigations two crosssections were reconstructed as shown in Figure 2 (section A-A) and Figure 3 (section B-B). Section A-A was selected along the maximum slope direction whereas section B-B intersects the zone of quarrying. The thickness of the colluvial sheet does not exceed (about) 16 m in section A-A or 30 m in B-B. For section B-B the ground surface and the bedrock are counter-sloping in the proximity of the border of the quarry.

2.2 In-situ investigations 2.4 Laboratory tests

In order to characterize the nature and the extent of this larger sliding movement, boreholes and geopyhsical tests were carried out in 1986. Some results have been already reported (Aquater, 1986, Favaretti et al., 1991). These investigations were performed mainly with the aim to provide the plano-

Due to the nature of the overconsolidated detrital materials, mostly composed of weathered trachytic elements (with dimensions up to several decimeters) in a clayey matrix, extensive undisturbed sampling was not allowed. Nevertheless, some samples were

240

Figure 2. Cross section along the maximum slope.

Figure 3. Cross section intersecting the quarrying area.

taken and subjected to geotechnical laboratory tests, especially to determine shear strength parameters to be used in limit equilibrium analysis. Atterberg limits were determined both on the detrital cohesive matrix and on the altered marl. For the matrix plasticity index ranges from 10% to 29% whereas for the marl from 20% to 29%. Liquid limit lies in the range between 30% and 59% for the cohesive matrix and between 43% and 53% for the altered marl. Residual shear strength was determined on a cohesive fraction under 0.42 min by using Bromhead's ring shear apparatus. Figure 4 shows the results of the shear tests: note the higher values due the clayey fraction composing the matrix of the detritic colluvium (25"-3 1") compared to those of the altered marl (16"-2 1"). Deforniability of colluvial material was estimated from some triaxial tests carried out on undisturbed samples as suggested by Soranzo (1988). The average value of the elastic Young's modulus at stress levels compared to those acting in-situ were approximately equal to 2035 MPa.

2.5 Hydrological conditions The ground water flow is relatively poor in the whole area and confined in the detrital materials resting above the impermeable marly bedrock. On the basis of the geophysical investigations the presence of an underground valley, delimited by two watersheds having an East West direction was noted. This was also confirmed by the presence of some water springs located at the interface detrital cover/marly bedrock in the southern part of the quarry. The ground water condition was monitored throughout the observation by piezometers and wells, whose position is reported in Figure 1. Figure 5 gives the results of the water level measurements in the period December 1985 to May 1986 and, for some wells, during 1998. These latter measurements were taken in order to veri@ the efficiency of drainage system constructed in 1997, consisting in a large well with sub-vertical microdrains departing radially from it. More particularly, the Casagrande piezometers S2

24 1

Figure 4. Residual friction angles.

Figure 6. Displacements observed in inclinometers I1 and 12.

3 LIMIT EQUILIBRIUM ANALYSIS

Figure 5. Ground water level measurements.

and s3 are located along the B-B section whereas wells W I and w2 are along section A-A. No pore pressure was measured in piezometer S 1. on compar~sonwith the measurements taken in early Spring 1986 and 1998 the influence of deep drainage on the pore pressure can be appreciated.

The limit equilibrium analyses were carried out along A-A section (maximum slope) and along B-B section (intersection with the quarry). The Bishop simplified method was used considering residual strength of altered mar1 (20") as the minimum resistance parameter influencing the stability of the slope (Trevisan, 1998). Two types of pore pressure conditions were assumed: phreatic surface corresponding to the maximum levels measured in piezometers and wells or coinciding with the slope (i.e. fully saturated soils). In both cases the safety factor resulted greater than the unity, approaching the instability condition in section A-A when the phreatic surface reaches the ground level. Therefore, it was presumed that the NEE'lipping movement occurred prevalently WSW direction as confirmed by inclinometric measurements.

2.6 Slope displacements 4 FINITE ELEMENT ANALYSIS

In the two boreholes S4-I1 and S5-I2 inclinometers were installed. Figure 6 reports the displacements, ranging from 2 mm to 11 mm with a SW direction, measured from 24'h April to 25th May 1986. Despite the limited period of observation, it appeared that the sliding surface lies around 14 m below ground level for I1 and 18 m for 12. Note that I1 is located close to the most damaged buildings.

In order to evaluate the effect of excavation on slope movements, numerical analyses were carried with BEFE (Beer, 1986). The material models used for sedimentary bedrock and detrital sheet were linear elastic and elastic-perfectly plastic respectively. In this context, for the detrital materials it is assumed that the effect of lithic elements present in the matrix with relatively small percentage do not influence significantly the deformability of the detrital cover.

242

Figure 7. Contours of horizontal (a) and vertical (b) displacements.

Elastic modulus for sedimentary rock was assumed as suggested by Meigh (1976). On the basis of site and laboratory investigations and on the above considerations, the following parameters were selected: * Detrital material: Young's modulus E=20 Mpa; Poisson's ratio ~ 0 . 3 0Friction ; angle @=20"; Sedimentary bedrock: E=200 MPa; ~ 0 . 3 0 . The mesh is composed of 8-node isoparametric finite elements. Boundary elements were used at the vertical and horizontal borders of the mesh. Figures 7a and 7b show the horizontal displacement contours spaced at intervals of 0.04 m and the vertical displacement contours at 0.01 m, It can be observed that the swelling of the marly bedrock induces a general heave of the whole area especially in the zone close to the quarry. Small vertical settlements, between 0.02 and 0.04 m, are calculated at the ground level in that zone where some tension cracks were observed in the field (see Figure 1). In the same zone horizontal displacements at the ground, ranging from 0.01 to 0.02 my were determined in the direction of the quarry. From numerical analyses, it appears that stress relief due to the excavation propagated backwards up to the upper border of the landslide. Even though the calculated displacements are characterized by small values, they should be taken into account if the landslide is in a residual condition along with preexisting sliding surfaces. In other words, the landslide was probably so close to limit equilibrium conditions that the stress variation due to the lateral excavation behaves as external perturbation inducing movements towards new stable slope configurations.

5 CONCLUSIONS A back-analysis of a landslide in the Euganean Hills, involving detrital materials, carried out with the limit equilibrium and finite element method was presented in the paper. On the basis of the results of the limit equilibrium analysis it seemed that no significant interaction between the landslide and the quarry could take place. The advantage of using a finite element approach was given by the possibility of considering the effect of excavation due to mar1 and limestone quarrying not only on the overall stability but also on slope displacements. Therefore, it was shown that the influence of the excavation back-propagates, even though with small movements, up to the upper border of the landslide, about 400 m far from the crest of the quarry. Although the calculated displacements are characterized by very small values (2-4 cm), these are probably not negligible when shear stress levels on pre-existing sliding surfaces are very close to failure conditions. Finally, on the basis of the last observations of the displacements and pore pressure measurements, the slope seems to be stabilized by the drain system recently constructed in the most damaged zone of the landslide. REFERENCES Aquater, (1 986). Versante Ovest Monte Rusta - Condizioni di Stabilita, Regione Veneto, p. 36.

243

Beer G. (1 984). BEFE - A combined Boundary-Finite Element Computer Program. Advances in Engineering Sofiare, 6, No. 2. Favaretti M., Previatello P. & Soranzo, M. (1991). Stability analysis of landslides occurred close to a mar1 and limestone. Proc. of the Sixth Int. Symp. on Lanslides, Vol. 1, pp. 397-402. Mazzucato A. (1998). Studio sulla franosita dei Colli Euganei. MSc Thesis, University of Padova. Meigh A. C. (1976). The Triassic rocks, with particular reference to predicted and observed performance of some major foundations. Rankine Lecture. Geotechnique, Vol. 26, NO. 3, pp. 391-452. Piccoli G., Sedea R., Bellati R. & Di Lallo, E. (1975). Note illustrative della Carta Geologica dei Colli Euganei. Societa Cooperativa Tipografica, Padova. Dal Pra A., Di Lallo, E., Passuto A., Sedea, R. & Silvano, S. (1995a). Le frane nei colli euganei. University of Padova, Mem. Sci. Geol. Vol. 47. Dal Pra A., Di Lallo, E., Passuto A., Sedea, R. & Silvano, S. (1 995b). Carta della franosita dei Colli Euganei. Cartografia SELCA, Firenze. Soranzo, M. (1988). Results and interpretation of multistage triaxial compression tests. Advanced Triaxial Testing of Soil and Rock. ASTM, STP 977, pp. 353-362. Trevisan A. (1998). Analisi di un movimento franoso nei colli Euganei Sud-occidentali. MSc Thesis, University of Padova.

244

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Stability evaluation of sliding failure along thin mudstone deposit due to excavation Y. Nakamura - AICO Company Limited, Japan J. Kojima - Tokai Technology Center,Japan S.Hanagata - Wakachiku Construction Company Limited, Japan K. Narita & Y.Ohne -Department of Civil Engineering, Aichi Institute of Technology,Toyota,Japan

ABSTRACT: This paper concerns the mechanism of sliding failure along a thin layer of mudstone deposit due to excavation. Some laboratory tests were carried out on both undisturbed and reconstituted samples of the mudstone material to know its shear strength characteristics, especially on the relation among strength values of the peak, residual and normally consolidated states. Stability evaluation was then conducted by use of FEM and a conventional limit equilibrium approach in order to discuss accuracy and reliability of the estimated behavior of the clay slope as compared to that observed in the field during excavation. 1 INTRODUCTION

2 OUTLINE OF SLIDING FAILURE

A large scale sliding failure happened to occur in a project of land improvement due to excavation. A thin layer of mudstone deposit of 5 to 10cm thick lies beneath deposits of clay and gravel mixture of

The sliding failure now under consideration took place in a project of land improvement of about 32.5ha in area. The land has a topography of gentle slope hill formed near a river, of about 40m in height, as illustrated in a plan view in Figure 1 and in the cross-sectional view of A-A in Figure 2a) . The profile of the hill is geologically composed of a Tertiary mudstone deposit of Neogene period as a bedrock, Tertiary deposits of porcelain clay and sand gravel overlying the bed, and a talus deposit of Quaternary on the hillside. A big sliding failure of soil block of 150m wide, 120m long and 8 to 10m deep took place immediately after the excavation of a part of talus and porcelain clay deposit, along a thin flat layer of mudstone deposit inclined with a very low angle of 2 to 3 to the horizontal. This mudstone deposit of 10 to 20cm thick lying beneath the porcelain clay differs a little from the bedrock deposit, containing some kind of carbide, and a thin layer of chocolate color alterated clay of 5 to 10cm thick is considered to be a potential slip surface in this sliding failure. The sliding took place just after excavating the clay deposit in 5 to 7m, and a large deformation was observed, as indicated by displacement vectors of point survey in Figure 1, in the horizontal and vertical direction of the order of 50cm to 150cm in the duration of two months until a countermeasure construction is completed by replacing a part of soil near the toe of the slope with crashed stone, as

about 10m thick, and a big slide took place through this thin mudstone layer immediately after excavation of talus and clay deposit, accompanying large horizontal and vertical deformation of the order of 50cm to 150cm. Field investigation and survey conducted after failure revealed that the mudstone deposit lies with a very low angle to the horizon and is considered to have some latent sliding planes which had been a cause of instability of the existing clay slope before excavation. This paper concerns the mechanism of sliding failure along a thin layer of mudstone deposit due to excavation. Some laboratory tests were carried out on both undisturbed and reconstituted samples of the mudstone material to know its shear strength characteristics, especially on the relationship among strength values of the peak, residual and normally consolidated states. Material tests were also conducted on the clay deposit in order to estimate stress-strain behavior of slope during failure and lateral earth pressure acting in the field to promote sliding. Stability evaluation was then conducted by use of FEM and a simple conventional approach of limit equilibrium in order to discuss accuracy and reliability of the estimated behavior of the clay slope as compared to that observed in the field during excavation.

245

shown in Figure 2c) . The land slide is thus characterized by a very flat and straight slip of a soil block on along a polished latent sliding plane.

Table 1. Physical properties of mudstone Density of solid particle: Natural water content: Content of Sand: Silt: Clay: Liquid limit: Plastic limit: Plastic index:

2.7 1g/cmj 52.8% 4.2% 30.6% 65.2% 116.3% 31.1% 85.2

3.1 Repeated loading direct shear test In order to investigate the relationship between the peak and residual strength of the material, direct shear test was conducted on undisturbed samples by applying shear force repeatedly from one side to the other several times until the ultimate state of shear failure is reached. The test was done under CD condition: The sample was first submerged in a week to be saturated state and consolidated in 24 hours under a constant vertical pressure, and then 6mm in horizontal loaded repeatedly up to direction under a drained condition at the rate of O.Olmm/min.. Figure 3 shows an example of shear stress and deformation relation curve in a repeated loading under a vertical pressure of CI ~=200kPa.It is seen that shear stress gradually decreases nearly at a constant rate and tends to converge to a certain ultimate state as the repeated loading proceeds. The relation curves of shear stress and deformation are again plotted in Figure 4 by taking as usual the total absolute shear deformation on the abscissa. Point of interests noticed in this figure is the fact that the shear deformation until the peak strength is reached is significantly smaller as compared to that after peak to the ultimate state.

*

Figure 1. Plan view of sliding failure

Figure 2. Cross sectional view along A-A

3 SHEAR STRENGTH CHARACTERISTICS OF ALTERATED MUDSTONE DEPOSIT Laboratory shear strength tests were carried out on both the undisturbed and reconstituted samples of the alterated mudstone deposit to know its peak and the ultimate residual strength values. Some physical properties of the mudstone material are summarized in Table 1.

Figure 3. Stress-deformation in repeated loading 246

Shear stress and deformation curves obtained in the test are hyperbola in shape as usually observed in a normally consolidated clay and the maximum shear stress at a large deformation was defined here as the completely softened strength. Failure line thus determined for the reconstituted sample is drawn in Figure 5, indicating very small cohesion intercept, similarly as normally consolidated clay, and rather large angle of friction as compared to the residual strength of the undisturbed samples. 4 FEM ANALYSIS

In order to discuss stress and deformation behavior and safety against sliding along the thin mudstone deposit, a FEM elastic analysis of excavation is conducted on the cross section presented in Figure 2a), which was obtained through site investigation after failure. The solution of a simple self weight analysis for the model with the original ground surface before excavation is superposed with that by an inverse load due to excavation. Deformation parameters used in the analysis, some of them were determined from the results of triaxial tests, are taken to be 5MPa for the thin mudstone layer and 10 25MPa for overlain clay and gravel mixture. Figure 6 shows distributions of the local factor of safety (Fs) obtained at elements along the surface of the thin mudstone layer for the original configuration before excavation. The factor FS is defined here as a ratio of the radius of the stress circle at failure to that at the present state and was evaluated for three different cases of strength values ( c , @ ) presented in Figure 5; i.e., 0 Peak and @ Residual strength of the undisturbed sample, and @ NC (normally consolidated) strength of the reconstituted sample, respectively. Also shown in Figure 7 is distributions of FS calculated for the configuration after excavation and filling of banks on the gravel layer. Distributions of the maximum acting along the thin mudstone shear stresses z layer before and after excavation are also plotted in Figure 8, together with the change in stress circles before and after excavation at two representative elements of No.10 and No.20 below the toe of the first and the second step of the excavated slope, respectively. Discussions associated with these figures are summarized in the following. 1)Distributions of FS before excavation in Figure 6 are rather flat in shape for every case of ( c , @ ) under consideration. This suggests equal potential of sliding along the base, though the lowest value of FS appears near the toe of the original slope in the case of residual strength. 2) Distributions of FS after excavation in Figure 7

Figure 4. Shear stress vs. total deformation

-

Figure 5. Comparison of failure lines Failure lines are drawn for the peak and the residual strength in Figure 5, where the latter is defined here by the shear stress at deformation of 200mm. It should be noted that the undisturbed samples have a certain small amount of cohesion component in the peak strength, which is supposed to be constituted with its stress history in the field, but it disappears by a large shear deformation in the residual state.

mbl

3.2 Direct shear test on reconstituted samples Direct shear strength tests were also carried out on the reconstituted slurry samples of the mudstone to compare the strength value obtained above with that at compIetely softened state. The slurry sample of under 0.42mm was consolidated in a week with its self weight and cut out and set in the shear box for a CD test under a specified vertical pressure.

24

demonstrate locations of higher potential of sliding near the toe of the first and second step of the excavated slope. The value of FS becomes below unity in the case of residual strength along two sections (1) and (2) near the above toes, where tension cracks were observed in the time sequence as the 1st (1) and the 2nd (2) slide in the field. 3)Distributions of T: mar in Figure 8, together with the change in stress states at No.10 and No.20 elements before and after excavation, suggest the occurrence of different patterns of failure along the

slip plane: i.e., failure at No.10 element is largely dependent on the loss of confining pressure, not at least on the increase in shear stresses, and that at No.20 is mainly caused by an increase in shear stress accompanied by a significant unbalance of overburden weight due to excavation and filling. 4)Stability analysis was conducted by use of a limit equilibrium method for two composite sliding planes, which start in circles from the points where tension cracks were detected, running along straight surface of the mudstone layer, and passing through in circles again near No.10 element, as illustrated in Figure 7. The values of safety factor for the 1st small and the 2nd large sliding planes obtained in three cases of ( c , @ ) are listed in Table 2. Very low safety in the 1st slide, irrespective of strength values, suggests higher potential of a local sliding failure and is considered to be a threshold of the overall big failure due to excavation. Table 2. Safety factor based on limit equilibrium

0Peak 1st 2nd

Figure 6. Distribution of FS before excavation

1.13 2.03

@Residual 0.35 0.75

@NC 0.61 1.23

Although much more discussion is still required on the mechanism of progressive nature of sliding failure, for instance presented by Bjerrum 1967 and Burland et al. 1977, some useful suggestions were supplied in this paper on the stability evaluation of sliding along a thin weak mudstone deposit.

5 CONCLUSIONS FEM analysis can be a practically useful tool for evaluating stability of sliding failure along a thin mudstone deposit due to excavation, together with the residual strength obtained in the repeated loading direct shear test. Distributions of local factor of safety roughly indicate the position of higher potential of sliding and stress circles at elements along the failure plane suggest different patterns of failure, which are supposed reasonable to interpret sliding failure observed in the field.

Figure 7. Distribution of FS after excavation

REFERENCES

Figure 8. Stress change before and after excavation 248

Bjerrum,L. 1967. Progressive failure in slopes of over-consolidated plastic clay and clay shales, Proc ASCE, 93-SM5: 3-49. Burland,J.B. et al. 1977. A study of ground movement and progressive failure caused by a deep excavation in Oxford Clay, Geotechnique, 27-4: 557-591.

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Appraisal of Bishop’s method of slope stability analysis G.L.Sivakumar Babu & A.C. Bijoy Department of Civil Engineering, lndian Institute of Science, Bangalore, India

ABSTRACT: The stability of slopes is a major problem in geotechnical engineering. Of the methods available for the analysis of soil slopes such as limit equilibrium methods, limit analysis and numerical methods such as FEM and FDM, limit equilibrium methods are popular and generally used, owing to their simplicity in formulation and in evaluating the overall factor of safety of slope. However limit equilibrium methods possess certain disadvantages. They do not consider whether the slope is an embankment or natural slope or an excavation and ignore the effect of incremental construction, initial stress, stress strain behavior etc. In the work reported in this paper, a comparative study of actual state of stress and actual factor of safety and Bishop’s factor of safety is performed. The actual factor of safety is obtained by consideration of contours of mobilised shear strains. Using Bishop’s method of slices, the critical slip surfaces of a number of soil slopes with different geometries are determined and both the factors of safety are obtained. The actual normal stresses and shear stresses are determined from finite difference formulation using FLAC (Fast Lagrangian Analysis of Continuaa) with MohrCoulomb model. The comparative study is performed in terms of parameter Ac+ (= yH tan@). It is shown that actual factor of safety is higher than Bishop’s factor of safety depending on slope angle and Lc+.

1 INTRODUCTION The stability of soil slopes is a common problem in geotechnical engineering and is a topic of considerable interest to engineers as well as researchers. Limit equilibrium methods, more popularly Bishop’s simplified method provides a simple means of evaluating the likelihood of failure in many types of soils. These methods do not consider whether the slope is an embankment or natural slope or an excavation and ignore the effect of incremental construction, initial stress, stress strain behavior etc and is likely that these methods predict the stability conservatively. In many situations, it is often advantageous to know the margin of safety so that this information could be used in the event of additional stability measures. In the work reported in this paper, a comparative study of actual state of stress and actual factor of safety and Bishop’s factor of safety is performed. The actual factor of safety is obtained by consideration of contours of mobilised shear strains. Using Bishop’s method of slices, the critical slip

surfaces of a number of soil slopes with different geometries are determined and both the factors of safety are obtained. The actual normal stresses and shear stresses are determined from finite difference formulation using FLAC (Fast Lagrangian Analysis of Continua) with MohrCoulomb model. 2 LITERATURE REVIEW

Duncan and Dunlop (1969) superimposed upon the finite element configuration of slope, the critical circular slip surface from which the limit equilibrium solution was evaluated. From finite element solutions, the mobilised shear strength along the failure surface was averaged and compared with the assigned value. The ratio was taken as the factor of safety against failure. Their results exceeded those of limit equilibrium by more than 20 % for a homogeneous and normally consolidated slope. Lo and Lee (1 973) analysed the behaviour of slope of a strain softening material. The residual factor based

249

on Skempton’s concept was calculated. Their results show that the limit equilibrium solutions overestimated the actual factor of safety when peak strength was used and underestimated when the residual strength was considered. Limit equilibrium methods have certain disadvantages (Wright et al, 1973, Duncan and Dunlop, 1969. Lo and Lee, 1973, Deschamps and Leonards, 1992) such as; a) the nature of arbitrary assumptions employed with regard to the determination of normal stresses and shear stresses which are determined without due consideration to the stress strain characteristics of soils and b) the factors of safety being one and the same for all slices. Wright et a1 (1973) made a detailed study of these factors and examined the variations of normal stress and factors of safety along the potential failure surface as well as the overall factor of safety using finite element method. The distribution of normal stresses by both the Bishop’s simplified method and finite element calculations assuming linear elastic for the material of the slope were determined. It was observed that variations were small. Variation of local factors of safety along the potential failure surface assumed by the Bishop’s method were studied and noted that along one-third to one-half of potential surface length, the factors of safety calculated were less than the average values for the slope, according to linear elastic theory. A comparative study of average values of factor of safety was made and it was shown that the values calculated from line of safety stress distributions were marginally higher, varying from 0 to 4.5 % depending on the value of parameter hc,+(= yH tan$/c). Deschamps and Leonards (1992) carried out a detailed study of slope stability analysis considering a simple wedge problem, comprising a slip surface with two planar segments and one interslice plane and determined the bounds of all possible solutions satisfying equilibrium and limiting shear strength and showed that these bounds were greater than those determined from conventional limit equilibrium analysis. In this paper, calculation of actual factor of safety and its comparison with the limit equilibrium methods particularly, Bishop’s modified method is carried out in the following manner.

comparatively smaller (Fig. 1(a)). These contours define a locus of points, which can be considered as the actual potential failure surface. The maximum levels of strain are at the toe and decrease towards top and variations in strain levels are due to the overburden at different levels and hence the above assumption is considered to be in order. Fig.1 (a)shows a typical actual failure surface as defined by strain contours and Bishop’s critical slip surface. In order to calculate the stresses and strains in slopes, finite difference scheme using FLAC (Fast Lagrangian Analysis of Continuaa) is employed and Mohr-Coulomb model is adopted for modeling material behavior. Fig. 1 (b) shows the distribution of resultant displacements that are essentially along the actual failure surface. The soil parameters considered are treated as effective and hence results are applicable to end of construction as well as long term stability of slope. Incremental construction with 12 lifts is considered for each slope.

Fig. 1(a)Typical actual failure surface as defined by strain contours and Bishop’s critical slip surface

3 ACTUAL FACTOR OF SAFETY Slopes on account of their geometry have induced shear strains and the corresponding shear stress within the soil mass on account of self weight. The contours of the shear strain define a continuous band of strain concentrations within the zone of overstress. Out side this zone, the strains are 250

Fig. 1 (b) Distribution of resultant displacements in the soil slope

4 PRESENTATION OF RESULTS Fig.:! (a) and 2(b) show the variation of shear stress, shear strength and Fig.2(c) shows the variation of local factor of safety along the slip surface for 1:l slope of 6 m height with c = 10 kN/m2 and @ = 37’ and bulk density of 18 kN/m’. It can be observed that local factors of safety calculated along the Bishop’s failure surface and the surface defined by maximum shear strain are marginally different. The average factors of safety are also given for comparison. The correspooding Bishop’s factor of safety is 1.76 and is less‘rhan the actual factor of safety. It can also be observed that at the toe, local factors of safety are less than the average values of actual factor of safety. The letters ‘a‘ and ‘b‘ in figures denote the slip surfaces as per maximum Fig.:!(c) Variation of local factor of safety along shear strain and Bishop’s failure surface respectively. failure surfaces( 1: 1 slope of 6 m height with c = 10 kN/m2, $ = 37’ and yb , 18 kN/m3). The letter ‘c’ denotes the Bishop’s factor of safety and is determined from conventional slope stability program. The above approach is extended to a number of soil slopes of different heights and slope angles and actual and Bishop’s factors of safety are determined. Factors of safety obtained by Bishop’s method and factor of safety along the Bishop’s failure surface are given for comparison. The results are examined in terms of a dimensionless parameter Ac$ (= yH tan4/c), where y is the unit weight, H is the height of the slope, 4 is the angle of internal friction and c is the cohesion. As indicated earlier, Wright et a1 (1973) also used the above parameter for slope stability analysis. Figs. 3 and 4 shows the variation Horizontal distance from the toe along the slip surface in r~ of factors of safety with Fig. 3 and Fig.4 present Fig.2(a) Variation of shear stress along failure results for I : 1 (V:H) and 1.5:1 slopes respectively. surfaces, (1: 1 slope of 6 m height with c = 10 kN/m’ Results clearly show that the actual factors of safety and 4 = 37’ and Yb, 18 kN/m3). are more than Bishop’s factor of safety varying from 10 to 48 % depending on the slope angle and LC$

Horizontal distance from the toe along the slip surface in m

Fig.2(b) Variation of shear strength along failure surfaces.

Fig.3 Variation of actual factor of safety with A,, for I : 1 slope 251

Fig.4 Variation of actual factor of safety with XC$ for 1S:l slope

5 CONCLUDING REMARKS In this paper, a critical examination of actual factors of safety in slope stability analysis is undertaken. An approach to evaluate the actual factor of safety in terms of shear strains for soil slopes is suggested. It is shown that the actual factors of slopes are more than Bishop’s factors of safety to the extent of 10 to 48% depending on the slope angle and kC+. REFERENCES Deschmaps, R.J. and G.A. Leonards (1992). A study of slope stability analysis. Stability and performance of slopes and embankments - 11, Vol.l, Geotech STP: 3I(Eds. R.B. Seed and R.W. Boulanger) 267-291. Duncan, J. M. and P. Dunlop (1969). Slopes in Stiff figured clays and shales. JI. Of SMFE, ASCE 5, N0.2,467-492. Lo, L.Y. and C.F. Lee (1973). Stress analysis and slope stability in strain softening materials, Geotechnique, 23 (I), 1-1 1. Wright S.G., Kulhawy, F.H. and Duncan, J.M. (1973). Accuracy of equilibrium slope stability analysis, Journal of SMFE, Vol. 99, No. 10,783791.

252

Slope Stability Engineering, Yagi, Yamagami & Jiang (c) 1999 Balkema, Rotterdam, ISBN 90 5809 0795

A convenient alternative representation of Taylor's stability chart R. Baker Technion-lsruel Institute of Technology.ffctifu,Isruel

Y.Tanaka Kobe University, J q a n

ABSTRACT': The evaluation of slope stability using a notion of safety factor with respect to strength usually

requires iteration as long as the strength envelope is defined by more than one strength parameter. Use of Taylor's stability chart provides a classical example of this situation. Practically performing this type of iterations using Taylor's stability chart is time consuming and not convenient, particularly in the range of small slope inclination where the stability number varies considerably with the friction angle, Utilizing the information in Taylor's stability chart, it is possible to construct a design chart resulting with a safety factor with respect to strength, which avoids the need for iteration. The key to this representation is the use of a non-dimensional parameter h = c/(y H tan$ ) which represents essentially the ratio of cohesive to frictional forces. In this representation, the parameter h and the slope inclination $ are the two independent parameters. It is believed that the new stability chart provides a convenient tool for practical slope stability calculation using Taylor's approach. 1. INTRODUCTION Taylor's stability chart, Taylor (1937), is still the main tool for analyzing homogeneous slope stability problems. Taylor's original derivation was based on a modification of the friction circle assumption. This assumption can not be justified rigorously; however, as noticed by Taylor himself, results obtained on this basis are practically identical with results based on the assumption that slip surfaces are log-spirals. The log-spiral assumption can be justified on the basis of the upper bound theorem of plasticity, Chen and Liu (1990). Alternatively, using a variational approach, it can be shown that slip surfaces yielding the minimal safety factors are log spirals in homogeneous problems, Baker and Garber (1 978) and Baker (1 98 1). Consequently, Taylor's results have rigorous theoretical support and it is expected that his chart will continue to be used extensively in practical applications. Taylor presented his result in terms of mobilized friction angles. This presentation makes it necessary to use iterations in order to calculate a safety factor for a given slope. In the present work we derive an alternative representation of Taylor's results in which safety factors can be established directly, without iterations. The wide-spread use of Taylor's results is expected to make such a representation a useful design-aid.

2. TAYLOR'S STABILITY CHART Taylor's stability chart is a set of functions : SN = SN [P I@rnl where S N = C and d- = tan-' Y HF are the stability number and a mobilized friction angle respectively;(c, @ } are the Mohr-Coulomb strength parameters cohesion and angle of internal friction; y is the unit weight, F is the safety factor with respect to shear strength, and {H, P } are the slope's height and inclination respectively. We use the convention that quantities written to the right of the vertical bar " 1 " are considered as constant given parameters; i.e. SN[f31@,] is a system of functions depending on p, each one of which corresponds to a different constant value of the mobilized friction angle. The functions SN[P ($rnJ are obtained by specifying the general two dimensional function SN[P, @m] to a constant value of $rn. The functions SN[P I@,,] are shown in Fig. 1. The stability chart shown in this figure was obtained by Baker (198 l), and it represents results for log-spiral slip surfaces (i.e. strictly speaking this figure is not Taylor's chart). However, for all practical purposes the results shown in Fig. 1 are the same as those obtained by Taylor, and we will refer to Fig. 1 as the Taylor's stability chart (the angles along the right vertical coordinates in this figure are the given values

surfaces passing through the toe of the slope (the region CDEFC), and situation in which the critical conditions are realized on "deep" slip surfaces passing below the toe (the region ABCFA). It is noted that the present definition of shallow and deep solutions differs from the one employed by Taylor. Taylor's classification is related to the depth of the lowest point on the slip surface, while the present classification is related to the location of the starting point of the slip surface. The utility of the present classification is related to the fact that the functions SN [p $I], have a slope discontinuity along this boundary (see Fig 1). The end points C and F of this boundary occur at (approximately), {8=52.5", (9m=O, S N ~ 0 . 1 8 )and { f ~ ( 9 ~ = 1 0SN ", = 0). 4. Point E corresponds to the limiting situation in which $ = Qm= 90" and SN = 0. (9 values larger then approximately 50" are obviously not realistic, however (9, depends also on F and if F < 1, it can have any value in the range 0 5(9m 590".

Figure 1. Taylor' s Stability Chart It is instructive to note the following features of Figure 1: 1, The two dimensional function SN[p, (9m] is defined only for p ~(9,,,, and it satisfies the limiting relation SN[p I(9 ,] = 0. Considering the definition of Taylor's stability number, it is clear that the only physically significant case in which SN can be equal to zero is if the cohesion c is equal to zero. Consequently SN = 0 can be realized only in cohesionless materials, and in that case the definition of the mobilized friction angle implies that the safety factor is given by F = tan[@]/tan[p]. Consequently, for c = 0, Taylor's stability chart is consistent with the result usually obtained on the basis of the infinite slope approximation in cohesionless material. 2. Ta'ylor have shown that for (9, = 0 the horizontal line BC in Fig. 1 represent situations is which the critical conditions are realized for infinitely deep slip surfaces. In such situations the height of the slope is negligible compared with the depth of the slip surface, and the slope's inclination does not affect the stability number if the slope inclination is less then approximately 52.5'. In order to eliminate this obviously unreasonable result, Taylor postulated a rigid bed-rock at some finite depth Df, and incorporated the effect of Df in his stability chart. Baker (1981) has shown that infinitely deep critical slip surfaces occur only if (9m is identically equal to zero, (i.e. critical slip surfaces have finite depth for all finite values of @,,,). Figure 1 shows that SN depends on ((9m = l", and critical slip surfaces associated with ( 9 m = 1" have a finite depth. It is noted that the small (but non-zero) compressibility of water implies that even for un-drained conditions (9m is not identically zero, and the "singularity" associated with (9, P 0 is not physically significant. In the present work we choose to consider the completely homogeneous case which does not include the effect of Df. 5 . The dashed line CF in Fig 1 represents the boundary between situations in which the critical condition are associate with 'khallow" slip

3. TRANSFORMATIONS OF TAYLOR'S REPRESENTATION For the present purpose it is convenient to "invert" Taylor's stability chart, representing it as a system SN = SN[vm IS], where of functions tan 4 vm= tan[4,,,1= as shown in Fig.2.

?r-]

[vm

Figure 2. The functions SN I@] The "concentration point" A in Fig 2 corresponds to the horizontal line BC of Fig 1, and the dashed line AB in this figure is the boundary between deep and shallow solutions in the "coordinates" (SN, q m }. Consider any one of the functions SN [ q m I@] shown in Fig. 2, and define the non-dimensional uarameter h as:

Physically h represents the ratio of cohesive to

254

frictional forces. The definition of h implies that SN h q,,,and this relation plots as a straight line through the origin in the coordinates (SN, q)m>as shown in Fig. 3. Inspection of Fig 3 shows that for each pair ( h, p} the intersection point A between the functions SN = h q,,,and SN = SN [v,,,lp] can be obtained by solving the non-linear equation SN [ q m l B ] = A q m . Solving this equation yields qy,=q, [A, 4, and it is possible to define a function GI [A,p] as =

Figure 3. The basic transformation

The value of h does not depend on F (Eqn. l), and

Figure 4. The stability chart G [ hI p]

255

knowledge of G1 [A,B] = F/tan[@]makes it possible to calculate F without iterations (in essence solving the non-linear equation SN [qmlp] = h q,,,replaces the conventional iteration process). Figure 3 shows that h = 0 is associated with SN = 0. SN = 0 implies that c is equal to zero, and in that case the safety factor is given by F = tan[$] / tan[P]. Introducing this result into the definition of G1 [A, p] shows that this function satisfies the limiting relation G I [ h=O, p] = l/tan[p]. Figure 3 shows also that G1 [h I p] = 1/ q mincrease monotonically with h. Consequently, when h is small, the functions G1 [h,p] start at a large value (l/tan[P] ), and continues to increase with h, while large p values result with small values of G1. It is convenient therefore to normalize the functions G I [h I p] with respect to their values at h= 0, and define G [hIj3]-as:

i.e. G represents the relative magnitude of safety factors in comparison with the limiting case of a cohesionless slope (subtracting the constant value of 1 from the ratio F [$, c] / F [$Ic=O] is not essential, and it is introduced for plotting convenience only. The definition of G guaranties that G [h=0, f3] = 0 for all values of (3 (except f3 = 90" where G [h,f3] is not defined). Figures 4 show the functions G [LIB] plotted in two different ranges of h values. Numbers along the top and right hand side of this figure are slope inclinations f3. The dashed lines OA in Figs. 4 represent the boundary between deep and shallow failure mechanisms (solution points below those lines correspond to slip surfaces below the toe).

Figure 5. Steep slopes 256

Figures 4 are the main result of the present work, and in the following section we discuss various features of those figures. 4. RESULTS AND DISCUSSION a. The main advantage of the representation shown in Figs. 4 is that it allows evaluations of safety factors without the need for iteration. In order to illustrate the utility of this figure consider a 10m slope, with an inclination of 1 to 4 (f3-14"), c = lOkPa, $=25" and y = 20 kN/m3 (these conditions are typical of many clay embankments of small water reservoirs in Israel). For this input information Eqn. 1 gives h = c / (y H tan[$]) = 0.1 1; interpolation in the first one of Figs 4 gives G[h=O.11, p=14"] = 0.43, and using Eqn. 2 results with F = (G+l) tan[$]/tan[p] = 2.67. It is noted that this result was obtained directly (i.e. without iterations). b. Consider the limiting case of c = 0. The definition of ( (Eqn. 2) shows that that c = 0 implies h=O, and excluding the limiting case of p=9Oo (which is considered below), Figs 4 show that G[h=O, f3] = 0. When G is equal to zero, Eqn. 2 yields the classical result F = tan[$]/tan[f3] which is known to be valid for the limiting case of c = 0. For the present purpose the important point is that there is no need to use Figs. 4 in the vicinity of h=O where all the functions G [Alp] merge together, and when c is small enough it is possible to calculate the safety factor directly as F = tan[$ ]/tan[ f3]. c. The representation in Figs. 4 is not useful when (3=90" ( G [h, p=90"] CO for all values of h except h=O where G [h=O, f3=90"] = 0). -+

Figure 6. Limiting behavior of G[h I p] when h is large Therefore in this particular case it is convenient to present results in terms of the functions G I [Alp] 3 F / tan[@]as shown in Fig. 5. Figure 5 makes it possible to evaluate safety factors without iterations in the limiting cases of vertical and nearly vertical slopes. d. Consider the limiting case of $=O, which is associated with h-. 03. Figure 6 illustrates behavior of the functions G [Alp] h is large; showing that for such conditions G [hip] a[P] h. It can be shown that

REFERENCES Baker R. and Garber M. (1978), Theoretical analysis of the stability of slopes. Geotechnique. Vol. 28, NO. 4, pp. 395-41 1. Baker R. (198 l), Tensile strength, tension cracks and stability of slopes. Soils and Foundations. Vol. 21, NO. 2, pp. 1-17.

=(

Chen W.F. and Liu X.L. (1990), Limit Analysis in Soil Mechanics (Developments in Geotechnical Engineering Vol . 52). Elsevier Oxford, New-York, Tokyo.

where SN[pI$=O] is ihe limiting line ABCD in Taylor's stability chart (Fig. 1). The validity of this result is illustrated by the dotted lines in Fig. 6. It can be verified that in general G [ h l p ] a[P] ~ h, so using the approximation G [LIP]= a[P] h (which is valid only for large values of A), results with a conservative estimate of safety factors.

Taylor D. W. (1937 ), Stability of earth slopes. Jour. of Boston Soc. of Civil Eng. Vol. XXIV, No. 3, pp. 197-246.

Figures 4 and 6 make it possible to evaluate G [h, p] for all pairs {A, p) (except p- 90" when the analysis should be done in terms of the functions G, [A, p] given in Fig. 5). As a result, it is possible to calculate safety factors for all input variables {c, $, p, y H} without the need for iterations. It is noted that the presentations in Figs. 4, 5 and 6 contain the same physical information as the classical stability chart of Taylor (Fig. l), expressed in a different (hopefully more convenient), way. Consequently, the results presented in those figures suffer from the same limitations as the original presentation of Taylor (i.e. no external loads, constant strength parameters, and dry or fully submerged slopes).

257

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang 6 1999 Balkema, Rotterdam, ISBN 905809 0795 I

Influence of stress-strain curves on safety factors and inter-slice forces in FEM A. Mochizulu & J.Xiong nepurb?ient of

Cilil

Engineering,

U n i l v i \it\ of

rokushinin, Japun

M. Mikasa Soil nrid Foumlotion Engineering Centei J q m i ~

ABSTRACT: The use of Limit equilibrium methods (LE-methods) over the past sixty years has proven them to be reliable for evaluating potential danger of a slope. Recently, modeling the stresses and strains that dcveIop within a slope has been an important area of research in civil engineering. The FE-method has been used, however, this method has not been proven to be a reliable method for evaluating the degree of dangcr of a slope. In thiy paper, the safety factor and inter-slice forces of a slope, which are obtained from the LEmethods including two new methods presented by the authors, are compared to those obtained from the FEmethod. It is found that the safety factors obtained using the FE-method are in a range between values obtained from the Bishop method and Modified Janbu method. This result shows that stress-strain curves influence the safety factor of a slope even if soils have the same strength. Distributions of inter-slice forces and normal forces obtained using the FE-method are similar to those obtained using the LE-methods.

1 INTRODUCTION

Up to the present, however, the FE-method is yet to be proven for accurate evaluation of the degree of danger of a slope. In this paper, inter-slice forces acting on slices of potential slip surface and safety factors arc evaluated using the FE-method and LEmethods. In the FE-method three types of stressstrain curves with the same strength were employed in order to investigate the influence on safety factors.

Fellenius et al. (1936) presented the original limit equilibrium method (LEM) for slope stability analysis which, today, is known as the ‘Swedish method’. Following this, several methods based on the limit equilibrium of forces have been developed. At present, the M&P-method is regarded as being the most reliable. Mochizuki et al. (1986) presented the Advanced LE-method and Modified Janbu method. Both methods are able to provide accurate results with less computation than the M&P method. One failing of the LE-methods is the fact that displacements in a slope are not considered. In a number of situations it is necessary to assess potential danger of slope failure based on each stage of slope deformation from stable to unstable states. As an alternative technique, the FE-method has been used since 1970. Penmun et al. (1973) employed the FE-method successfully to evaluate the displacements in dams. Following this, a number of studies concerning the FE-method have been carried out. These studies were discussed in J. M. Duncan’s paper (1996) entitled ‘State of Art: Limit equilibrium and finite-element analysis of slope’. With regard to assessing potential danger of a slope using the FE-method, Ugai (1993, 1995) presented results showing that the safety factors obtained using 2-D and 3-D FEM were almost the same as those of thc Swedish method in 2-D and 3-D systems respectively.

2 INTRODUCTION OF TWO NEW LEMETHODS AND COMPARSION OF RESULTS 2.1 The Modified Janbu method arid Advanced LEmethod. Figure 1 shows inter-slice forccs acting on a slice in a soil mass on a potential slip surface. Neutral porewater pressure due to seepage flow, water table, or consolidation etc., are regarded as external pressures acting on each surFace of slices in both methods. The force, N, acting in a normal direction to a potential slip surface is assumed to be acting at point m, where the vertical line from the center of gravity of a slice crosses the potential slip surface. For seismic force, a lateral seismic coefficient, LY,~,is included in the quasi-static coefficient method. The Modified Janbu method (referred to in this paper as the MJ-method) employs formulas for the

259

assumed, and D in Eq. (4) is neglected as in Janbu’s guide in his original method.

safety factor of a slope from equilibrium of interslice forces for both horizontal and vertical directions in addition to momentum equilibrium of the forces at point tn. Height of the thrust line (h, in Fig.1) is assumed to be 1/3 of a slice height in the MJ-method. The derivation process of the MJmethod is basically the same as that of the Generalized Janbu method (Janbu 1973). Referring symbols are shown in Fig. 1.

=

-H tan P, - M h , / b + E[(h, - h, )/b - tan a ]

/b+(l-c)tana]+U(c -E)/cosa -< tanaj+D

-~,w[h,/b

Here, D

=

-AV(l-

(4)

<)+ M(
h,=h,s,/3

Boundary conditions at both ends of a potential slip surface are shown in Eq. (6):

The suffix of symbols in Eq. (6) denote slice number. Thus, a safety factor of a potential slip surface can be obtained when F , on the left-hand side of Eq. (31) coincides with the assumed FJ on the right-hand side of Eq. (3-2) under the conditions presented in Eq. (6). The safety factor using the Advanced LE-method (referred to as the ALE-method) can also be obtained by solving Eq. (3). Here it is assumed that the direction of “total surplus thrust force, F, on a slice surface coincides with that of the thrust line, instead of using Eq. (5). Here, totul surplus thrust force is a vector composed of AV and A H , as shown in Fig. 3, and calculated using Eq. (7).

(l A V H , A H : inter-slice forces U,E: water force due to water pressure h,hl: height of the action point of E,H E / , i l : distance to the action point of U,N

Fig.l

Forces acting on a slice

‘I

The safety factor of a slice is defined by Eq. (1).

Here, Sfrepresents the potential resistance force and T represents mobilized shear force on the slip surface. This has the same magnitude as the sliding force with an inverse sign. By considering equilibrium of €orces in directions parallel and normal to the potential slip surface, Eq. (2) is obtained:

Eq. (9) can be obtained following the conditions of Eq. (8).

cb + (W - AV -U coscr ) tan 4 M= ~J(cos2a+sincrcosatan4/Ij,j

- M - K,W

- (W

- AV)tancx

(2)

Differentials of inter-slice forces A H and AV in the above equation are shown in Fig 1. Taking ZH=O into consideration for all slices, Eq. (3) can be presented as follows: F,=A/,z[( AE+K~~W)COS a +(W-A I/)sin a ]

(3-1)

[cb+(W-AV-Ucosa)tan@] [cosa + sin a tan $ / F , ]

(3-2)

A=C

The angle B,is defined by Eq. (lO), though the angle in the MJ-method is defined as the angle from the horizontal. Smooth transference of surplus thrust forces was assumed for each slice in the ALEmethod, rather than assuming V/H= 2 f(x) (Morgenstern and Price, 1965).

-

2.2 Comparison of solutions obtuined using LEmethods

Momentum equilibrium of forces around point m will give Eq. (4) with respect to V when Eq. (5) is

260

Table 1 presents known and unknown conditions, and degree of redundancy for each LE-method. As the Infinite Slope method is the only one”’ with a statistically determinable system, it follows that

ccrtain assumptions must be introduced in the other methods. It should be noted that the Generalized Janbu method, the MJ-method, the M&P-method'r2 and the ALE-method have the same number of unknown conditions. They also have the same number of known conditions, with the exception of a condition of 2 A H =O in the M&P-method. Taking the above into account, it can be said that all these analysis methods are based on the same fundamental principle. Table 2 presents assumptions introduced into each method. The degree of redundancy coincides with numbers of assumed conditions. The Swedish method is thought to have a comparatively large crror in the safety factor because some inter-slice forces are neglected in the formulas. Figure 2 shows the differences of thrust lines and safety factors by varyingf(x) and /1 in the M&Pmethod obtained by Whitman (1967). Fig.3 shows the same solutions obtained using the ALE-method and MJ-method. The obtained safety factor is almost the same as, or slightly larger than, that of the M&Pmethod with a similar thrust line of slice forces (see Fig. 2 (1) and (2)).

obtained using the LE-methods wcre compared to those obtained from the ALE-method in the bottom line of the table. Table 1 known-unknow conditions and degree of redundancy of the LE-methods stabil~tycomputation In-sliSwedishl Blshop ;hape~tslipsurlace P C C number oi slice I n n known concls. 1. Force acts on slice n n 1 (1) 2. Boundary conds. 2 2 (1) Vi, Vn+l=KI 2

w

N T

v

H (5) AV (6) AH (7) h, ?umberof unknowns 6 -ond. of sedundancy 5. Equilibrium of slice , '1)horizontal direction )r slip surface direction 1 '2)vertical direction or iorrnal to the slip surface lirection 1

'3) moment 7. Equilibrium of inter slice force (1) 2 AH=O 1 (2) 2 AV=O 1 3. Total equilibrium (I) H=O (2) v=o (3) M=O 3 . Strcngth formula (1) Coulomb formula 1 10. Formula of safety factor ( I ) F=MR/MD (2) F=S/T 1 ( 3 ) Fl=I;,= ...=F,, , ,ootalof formulas 6 Iegreeofwdundancy 0 n-sl infinite slope P: plane

Fig. 2 Solution by the M&P method Table 3 shows safety factors of the slip surface from the LE-methods, including those of the two new methods. The safety factor obtained using the Swedish method has the smallest value. The M&Pmethod provides a safety factor that has a range between the value calculated using the Bishop method and that of the ALE-method. Due to the assumption that V=O and H=O, the Swedish method tends to estimate smaller normal forces for steep slopes, which results in a low safety factor. Computations by the Bishop method, which assumes that A V d , result in a value of the safety €actor between those given by the Swedish method and the MJ-method. The ratios of the safety factors

NC NC n n

n

n

n

n

-

2 2 2

2 2 2

2 2 2

2 2 2

1

n

i

n

n

n n n-1 n-1

n n -

3. Safety factor (1) F 1.Total strcngth (1) s 5. Forcc acting on slice (1) (2) (3) (4)

GJ MBP MJ ALI

NC NC n n

_ I

-

I

n

n

-

-

511-1

6n

i

n

n

n

n 11 n n n n n n n-1 n-1 n-1 n-1 'n-3) 711-1I 711-1 7nI

n

n

-

-

n

n

n

n

-

n

n

n

n-1 6n n-i

n-1 6n n-1

n

1 -

-

(1)

n

n

I -

3i1+1 2n-2 C. cricular

n n-1 n-1 n-1 5n , 6n 6 n - 1 n n-1 n NC. non-cricular

The safety factors given by the Swedish method and the Bishop inethod were 12% and 6% lower respectively than those given by the ALE-method. Bishop noted that the safety factor given by his simplified method was about 5% less than that from his rigorous method (Bishop, 1955). Whitman et al. (1967) reported that the Bishop method is subject to errors of 7% or less compared with the M&Pmethod. Judging from the rate of F/F,, in the table, the ALE-method provides almost the same solution as that of other methods.

:*1:T h e Wedge method is also statistically determinable. '''2:One of the features of the M&P-method is that slope shape, slip surfacc, thrust liiic etc. can be replaced with appropriate fiinctions. T h i s enablcs problems of the slope to be treated in a morc gciieralizcd manner. 'This point, however, is not a condition s h o w n in the table.

26 1

Fig. 3 Distribution of surplus thrust forces and inter-slice forces Table 2 Assumptions used in the LE-methods shape of slip circular

method Swedish

number of assumptior n-1 n-1 total 2n-2

assuming

v=o H=O

Bishop Original Janbu

M&P

total Modified Janbu

circular & non-circular h,=h,/3 4dvanced Limit circular & Equilibrium non-circular V/ H=-tan /3

Here, rigidity Go,, is E / 2 ( 1 i’ ? I ) , and Rf is a constant for adjusting stress-strain curves of a numerical model to those of test results. Table 4 shows model parameters for thrce cases of different stress-strain curves with the same strength parameters, c and d. Case 1 and 3 havc the smallest and thc largest slope stress-strain curves respectively. The same slope as shown in Fig. 2 was adopted in the analysis. Stress-strain curves represented by the parameters in Table 4 are shown in Fig. 4. The slopc was meshed by 222 isoparametric elements with 250 nodes. Eq. (13) shows the definition of the safety factor used in the FEmethod (see Fig. 5).

n n-1

circular V=O circular & assumed non-circular relevant ht circular & V= f(x)H: non-circular n-1 of f(x)

I

n-1 1 n n-1

n- 1

Table 3 Safety factors obtained using the LE-methods F, F

FE,,

1.43 0.88

F, 1.54 0.94

F,, 1.63 1.0

F, 1.63 -

FMKP 1.53-1.66 0.94-1.02

Case

met hod

1

c, ci, p,

3 RESULTS FROM THE FE-METHOD COMPARED WITH SOLUTIONS OF LEMETHODS

E,, (kgf/cm’)*

N Rf

In slope stability analysis the basic process involves evaluation of T and o N(or N in Fig.l), which are mobilized shear forces acting on a potential slip surface and normal stresses, respectively (see Fig.1). The potential resistance force on slip surface Sf is a On this basis, the FE-method is €unction of o,,,. considered to be valid for evaluating T and oN, instead of using a LE-method. In the FE-method a hyperbola-type model was adopted for describing the stress-strain relationship of soil. For simplicity, a Poison’s ratio of 0.4 is used, assuming only volume shrinkage during shearing. Elastic moduli in the model are defined by Eqs. (11) and (12).

262

2

3

c=0.044 kgf/cm2(=4.3kPa), 0 =32‘ 2.0 t/m‘ (=19.6kN/m’) 21 9 500 3,000 0.421 0.420 0.421 0.8 0.8 0.9

Fig4 Stress-stain curves for Casel,2 and 3

Table 5 presents safety factors obtained using the FE-method. Results from the ALE-method are also shown in the table. Ratios of FFE/FAare shown in the bottom line of the table. Case 1, with the gentlest slope of the initial stress-strain curve, gives the smallest safety factor, which coincides with that of the Bishop method. The greatest safety factor is given by Case 3, showing almost the equivalent safety factor as that of the ALE-method. It is shown that the safety factors differ due to the difference of stress-strain curves. Fig. 6 shows the distributions of safety factors that are defined by Eq. (1) for each slice. In Case 2 and 3, the safety factors have the largest value at the toe of a slope and reduce further away from the toe, showing a feature of progressive failure of the slope. However, in Casel, the value of the safety factor is greatest near the top of the slope.

Case I?, r F,JF,,

Fig. 5

1 1.54 0.94

2 1.63 1.0

3 1.64 1.01

F, 1.63 1.0

Fig.7 Inter-slice force obtained using the FE-method

The definition of safety factor

Fig.8 Inter-slice forces obtained using the LE-methods method were compared with those of the LEmethods (Figs. 7 and 8). In the solution of Case 1, inter-slice forces and their differentials show similar distributions to those obtained from the LE-methods. However, solutions of Case 2 and 3 show some differences from those of the LE-methods. It is

Fig.6 Safety factor distributions obtained using the FE-method Next, inter-slice forces H and V and their differentials AH and A Vobtained using the FE263

The present paper has shown that the FE-method is also practical for assessing the potential danger of slopes.

supposed that the tension zone of the potential slip surface in Case 1 would yield. In Case 2 and 3 the potential slip surface will move as a soil mass, then values of +H and -I/ will not yield in the slice near the top of the slope. Distributions of small magnitude of +H in Case 2 and 3 is also one of the features of the FE-method. Figure 9 shows a comparison of distributions of normal stress o N(=N/AZ) on the slip surface with those of the LE-methods. The n, calculated using the FE-method is more scattered, showing larger values than those obtained from the LE-methods. The stresses near the toe are obviously greater than [hose obtained from the LE-methods. However, the FE-method gives safety factor valves in a range bctween those of the Bishop method and ALEmethod.

ACKNOWLEDGEMENTS: The authors would like to express their gratitude to Hirofumi Yumioka, who is master student of civil engineering in Tokushima University, for his help with the analysis.

'3: In the LE-methods, the solution is obtained assuming the safety factors of slices arc all the samc, while in FE-method, the safety factors of slices differ from each other.

Fig.9 Comparison of 0 obtained using the FE-method and the LE-methods 4. CONCLUSIONS (1) The condition, equilibrium equations and degree of redundancy made in LE-methods including two new methods were clarified in Table 1 and 2. Comparison of the safety factors provided by the LE-methods was shown in Table 3. (2) The FE-method was employed for evaluating stresses and safety factors under conditions of soils having the same shear strength but different stressstrain curves. The safety factors presented by the FE-method were in a range between those of the Bishop method and ALE-method (about the same as the Modified Janbu method). It should be noted that the safety factors depended on stress-strain curves of soils. (3) Inter-slice forces H and V and their differentials AH and A V obtained from the FE-method showed similar distributions as those of the LE-methods.

264

REFERENCES: Fellenius, W. (1936), Calculation of the Slability of Earth Darns, Second Congress on Large Dams, pp.445-462. Bishop, A.W.(1955), The Use of the Slip Circle in the Stability Analysis of Slopes, Geotechnique, Vo1.5, pp.7-17 Morgenstern, N. R. and Price, V.E. (1 9 6 3 , The Analysis of the Stability of General Slip Surface, Geotechnique, Vol. 15, pp.79-93. Whitman, R.V. and Bailey, W.A. (1967), Use of Computers for Slope Stability Analysis, ASCE, SM4, pp.475-498. Spencer, E. (1968), Effect of Tension on Stability of Embankments, ASCE, SM5, pp.1159-1173. Janbu, N. (1973), Slope Stability Computations, Embankment-Dam Engineering, John Wiley & Sons, pp.47-86. Mochizuki, A., Mikasa, M. (1986), Two New Slice Mcthods for Slope Stabillity Analysis, Journal of Geotechnical Engineering, No. 370, IU-5, pp. 261-270. Poulos, H. G., Booker, J. R., and Ring, G. J. (1972), Siinplified calculation of embankment deformations, Soils and Found., 'Tokyo, 12(4). pp. 1-17. Penman, A., and Charles, A. (1073), Constructional deformations in rockfill dam, J, Soil Mech and Found. Div., ASCE, 99(2), pp.139-163. H.Ida, K. Ugai, and T. Hagiwara. (1903), Analyses of 3dimensional slope failurc by FEM and the column method, The 28th Japan national conference on soil mechanics and foundation engineering, Kobe, No.799, pp. 2145-2148. K. Ugai, and D. Leshchinsky. (199S), Three-dimensional limit equilibrium and finite element analyses: a comparison of results, Soils and Found.,Vol.35, No.4, pp. 1-7. J. M. Duncan. (1996), State of art: limit equilibrium and finite-element analysis of slopes, Journal of geotechnical engineering, Vol. 122, No.7, July, 1996. ASCE, pp. 577-596.

Slope Stability Engineering, Yagi, Yamagami & Jiang (c) 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Slope stability analysis considering the deformation of slices 'r'.Terado - TechrzicdResearch L a ~ o r a t o Japan r ~ Foundation Engineering Company Limited, Tokyo,Japi~i W. Hazarika -Department of Civil Engineering,M & u - uNutiorzal College of Technology,Kyoto, Japan T.Yamazak_l- Technology Section, Japan Fottndation Engineering Company Limited, Tokyo,Japan H. fliayamizu - Retired Faculty Chiha Institute of Technology,Japan

ABSTRACT: With the aim of developing an analysis method that can give a uniquc solution for slopc stability problcms, finitc elemcnt formulation is incorporatcd in the existing mcthod of slopc stability analysis using sliccs and a new numerical method is devised. in this mcthod, it was considcrcd that thc nodal displaccmcnts develop along the sliding surface. Also, the shear force and the normal forcc acting on the slopc arc considcrcd a s the nodal forces on an element. A relationship is dcrivcd rclating the two forccs so that thc ~ o h r - C o u l o m b critcrion is satisfied. ~ i g h rcl~ablevalues ~y of the global factor of safety and thc external nodal forcc could bc o ~ t ~ ~ i from n c d thc present method of analysis comparcd to the cxisting slope stability analyses, which arc bascd on thc mcthod of sliccs. Howcvcr, concerning the nodal disp~dcementstwo C ~ S C Swcrc obscrvcd: 1) whcn thc slopc docs not fail, the valucs arc closc to those that conventional FEM givcs and 2) whcn therc is a failurc, dcpcnding on the valucs of the global safcty factor, the dispIa~mcntmagnitudes diffcr grcatly from thc convcntional onc.

1 INTRODUCTION Thcrc arc many circumstances in natural slopcs, compacted embankmcnts and excavations where thc civil enginccr must invcstigate the stability of a slope by performing slopc stability analysis. Such analysis should, therefore, be as inscnsitive as possiblc, to 'a priori' conditions. Existing rncthods of slope stability analysis using sliccs (Bishop 1955, Janbu 1957) arc bascd on the limit equilibrium thcorern, however, most of them rcndcr a statically i n d e t c ~ i n a t esystcm. Thereforc, in order to obtain a unique solution it is ncccssary to introducc an additional condition, Since varictics of conditions can be imposcd, dcpcnding on thc reasonableness of the imparted conditions, therc may be significant differences in the results. Thus, it is not possiblc to obtain rcliablc rcsults from thc analyses based on the method of sliccs. The reason why the mcthod of sliccs rendcrs statically indeterminate system can bc attributed to the fact that only the force and the moment acting on thc slices arc considered with total disregard to the deformation developing in the sliccs. In this research, in order to do away with the necessity of additi(~na1 constraints, thc displaccmcnt and thc dcformation of the sliccs arc takcn into considcration. In othcr words thc slicc or thc portion of thc split slicc is considercd as a planar elcmcnt of a finitc clcmcnt assembly. I n this casc, since the forcc and thc momcnt cicvclopcd in each slice automatically forms thc cquilibrium, they naturally satisfy the analysis condition of thc convcntional rncthods of sliccs as well. In addition duc to thc abscncc o f any additional conditions a 265

statically dctcrminatc systcm, and hcncc a uniquc solution can bc obtained. It is also possiblc to improvc the accuracy of thc rcsults by making the sizc of thc planar clement smallcr. Sincc no stress analysis is pcrformcd for thc lower stable formation (bclow thc failcd mass) of thc slopc, it is important to handlc thc discontinuous displacement that dcvclops bctwccn thc nodcs o f thc movablc sliccs and thc stablc formation. Normally, such discontinuity is takcn carc of by introducing joint clcmcnt in such boundarics. H o u w w , since thc forcc in thc nodc acting in thc dircction of thc slopc is d e t e r ~ i n e dby thc forcc acting pcrpcndicui~to thc slope, hcncc, it is not ncccssarily that thc problcm of d ~ s c t ~ n t i ~ u displacement ous can bc gottcn rid o f by the usc of joint clement. In the present method, it was assumed that the nodal displacements develop along the sliding surfacc. The shear force acting along the slopc and the normal force acting at right anglc to the slope are considcred as thc nodal forces. A rclationship is derived, by introducing a factor of safety betwecn thc two forces, so that the Mohr-Coulomb critcrion is Kojima et. a1 1997, satisfied ( ~ a y a m i1996, ~ Terado ct. a1 1998). Thus, a ncw analysis method is developcd, based on the finite element method, by considering the slices thcmselves or thc portions of the split slices a s planar elements. The nodal displacements, the global factor of safety and other parameters were calculated using the dcvelopcd method.

Figurc 1. FEM discretization of a slope nodal displacement and the nodal forcc of a typical nodc k (Fig. 2) should satisfy thc conditions (a) and (b) statcd below. (a) Sincc nodal displacement develops along the slip surface, the displacement in the x direction U2k-l and the displaccment in thc y direction u2k is rclatcd by the following relationship: u2k

=

u2k-l

tanek

(2)

Hcrc, 8k is thc angle of inclination of thc slip surfacc with respect to thc position of thc nodc. (b) The forces acting between thc movablc slicc and the stable formation undcrncath act on thc nodc a s external nodal forccs. The rcaction forcc Nk acting pcrpendicular to thc slip surfacc and thc shear forcc Tk acting parallcl to thc slip s u r f x c obey thc relationship as in thc cxisting rncthods of slopc stability analysis using mcthod of sliccs.

Figurc 2. Displaccmcnts and forccs acting on a typical node

Tk 2 FINITE ELEMENT FORMULATION SLOPE STABILITY ANALYSIS

FOR Here, c k is the cohesive force at the node calculated from the distributed cohesion at the slip surface, Pk is the nodal force due to the pore water pressure generated inside the movable slice, @kis the angle of internal friction, and Fs is the global factor of safety. Conditions (a) and (b) render four unknowns: U2k-1, U2k, Nk and Q. However, since we have two additional equations (Eqs. 2 & 3), ultimately w e are left with only two unknowns: u2k-land Nk. Thc external forces, F2k-1 and F2k, acting at the node k in the x direction and the y direction respectively can be calculated from thc forces Nk and Tk (see Fig. 2).

Figure 1 shows a typical finite element discretization for a slopc stability problem using slices. As shown in the figure, the failure mass is broken into a series of vertical sliccs. Each slice is again sub-divided into planar triangular elements. If Kij is the stiffness of each node of the planar element, thcn FE formulation givcs the following relationship between the nodal force Fi and the nodal displacement uj:

In Eq. (l),in general, if Fi is unknown, Uj is known or the vice versa. Therefore, the number of unknowns and the number of equations are equal and hence a unique solution can be obtained. However, for the sclected problem rcprcsentcd in Figurc 1, thc

(4)

266

3 NUMERICALPROCEDURE

(5) 3.1 Finite element model Here w k is the force component acting on the node k due to the self weight of the movable slice. The forces F2k-1 and F2k can be divided into a known part and an unknpwn part. The known parts arc newly referred as F,,-, and F,, , and can be written as follows:

Numerical calculations wcrc pcrformcd for thc slopc shown in Figure 3. Thc wholc slopc was dividcd into 10 movable slices, and a finitc clcmcnt asscmbly was formed using each slicc as an clcmcnt. Thc triangular sliccs were takcn as triangular clcmcnts, while thc quadrilateral sliccs wcrc trcatcd as fivc nodcd quadrilatcral elements. In addition, thc fifth nodc of the five noded quadrilateral clcmcnt is madc to coincide with the ccntcr of gravity of thc quadrilateral slicc. For each clement thc following paramctcrs wcrc adopted. Young's modulus, E = 50 Mpa Poisson's ratio, Y = 0.35 Average unit wcight, p = 17.0 kN/m3 Distributcd cohcsion, c = 12.0 kPa The angle of intcrnal friction, $k = 16.3".

Thc unknown parts G2k-1 and G2k bccomc,

3.2 Method of analysis It is worthwhile mentioning here some of thc important points to be considcred while performing the slope stability analysis using the developed theory. A movable slice remains stationary unless the slopc fails. At that moment, the minimum valuc of displacement at cach nodc does not ncccssarily bccomc zcro. Even though movement occurs in all parts of a movable slicc, in ordcr to yield the rcsults to the safe side, thc nodc at thc lowest part (node 28 in Fig. 3) of the failed mass was assumed to bc fixed. Also, thc value of global safety factor Fs should bc obtaincd from thc calculation. However, Fs appears in many parts of the modified vcrsion of Eq. (I), and hence a trial and error m e t h d was adopted by rcpcating the calculation using various values of Fs. Thc correct valuc of Fs was assumcd as thc onc that is obtaincd whcn the displacement at the bottom nodc (node 28) of thc failed mass becomes equal to zcro.

Now, Eq. (1) is modified so that it satisfies the conditions (a) and (b). Denoting k as the node number of each node of the slip surfacc in the right hand side of Eq. (I), and then using Eq. (2), the CXpreSSiOn ( K i 2k-1 Uzk-l+Ki 2 k u2k) bccomcs (Ki2k-ltKi2ktanC)k)U2k-1.

Thc

CxprCSSion

(Ki2k-l+Ki2ktanOk) is then substituted into Eq. (l),and a new Ki 2k-1 is calculated. In addition, thc following condition is introduccd: K i 2 k = 0 for all i . Thcn, transfcrring G2k-1 and G2k from the left to the right hand side of the Eq. (l), and rcplacing all U 2 k by Nk, the following rclations can bc obtaincd:

Eq. (1) thus can be modified as above which yields a unique solution by rcndcring the number of unknowns and the numbcr of cquations equal. Morc cvcr, the weight of the planar clcmcnt wk,which acts as an external forcc o n the rnovablc slice is considered as thc resultant of the forccs Nk and Tk acting betwccn thc movable slicc and the fixed layer underneath. Thus, it represents a condition that is similar to thc forcc boundary condition considcrcd in the convcntional method of sliccs. I n the above derivation, since it was assumcd that thc valuc of Tk in Figure 2 is positive, the nodal displaccmcnt u 2 k - 1 should havc a ncgativc valuc.

Figurc 3. FEM mcsh of thc slopc undcr considcration

267

Tdblc 2. Nodal forcc and displacements for Casc I1 Nodc Reaction Displaccmcnt Displaccrnent Nos. forcc, Nk in x dircction in y dircction (kN/m) (cm) (cm)

4 RESULTS The numerical analyses were performed for two cases: Case I. Neglecting the pore water and Case 11. Considering the pore water.

1 4.1 Slope without pore water Table 1shows the results of the analysis for the case I where the presence of the pore water in the slope was neglected. The corresponding global factor of safety Fs was 1.08 for this calculation. Tablc 1. Nodal force and displaccments for Casc I Nod e Reaction Displaccmcn t Displaccm cn t Nos. force, Nk in x direction in y direction (kN/m) (cm> (cm)

1 2 5 8 11 14 17 20 23 26 28

124.0 937.1 2024.4 2582.2

-14.18 -15.07 -14.72 -12.75

-10.84 -9.56 -7.72 -5.45

3240.6

-9.80

-3.33

3572.7 3539.4 3200.6 2500.7 1658.3

-6.67 -3.74 -1.57 -0.30 0.00 0.00

-1.72 -0.68 -0.17 -0.01 0.00

241.5

2

117.8 941.1

-14.82 -15.82

-11.33 -10.04

5

2029.5

-1571 -13.97

-8.24 -5.97

8

2564.8

11 14 17 20 23 26 28

3208.9 3543.5 3527.6 3206.7 2527.7

-11.08

-3.76

-7.84 -4.69 -2.21 -0.65

-2.02 -0.85 -0.24 -0.02

1696.3 263.3

-0.13 0.00

0.00 0.00

cases is the same and thcrc is a critical point in thc failure surface at which thc rcaction attains thc maximum valuc. In thc abovc calculation using the modificd finitc element formulation, thc valucs of thc cohcsion and thc friction anglc changc according to thc valucs of thc global factor of safcty uscd. This rcsults in thc differencc of the magnitudcs of thc displaccmcnt and the external force shown in Tablc 1 and Tablc 2 from thosc given by thc convcntional FEM analysis cvcn whcn the slope is stablc. This factor should bc notcd while interpreting thc rcsults.

0.00

It is clcar from thc x and y dircctional displacemcnts that dcpcnding on thc forces Nk and Tk acting bctwccn thc movablc slicc and fixcd formation the magnitudc of thc displaccmcnt varics. Thc negativc valucs of all thc x dircctional displacemcnts imply that thcrc was nothing wrong in the assumption of thc direction of thc forcc Tk.

4.2S h p e with pore water Tablc 2 shows thc rcsults for thc Casc 11, whcrc thc porc watcr insidc thc elcmcnts is considcrcd. In this casc, thc global factor of safcty, Fs is 0.937. For this valuc of Fs, practically thc slopc will fail and hcncc thc numcrical valucs shown in Tablc 2 can not bc obtaincd as it is. Howcvcr, thc cohcsion c and thc friction anglc & wcrc recalculated (dividing cach by thc abovc valuc of Fs) and thc rcsults obtaincd using thcsc ncw valucs arc shown in Tdbk 2. Thc rclation bctwccn thc rcsultant displaccmcnt and the reaction forcc along thc failurc surfiicc is shown in Figurc 4 for thc two casts considcrcd in this rcscarch. It can bc sccn that thc trcnd for both thc 268

Figure 4. Variation of the reaction force with displaccmcnt

5 CONCLUSIONS This rescarch has established that the use of the Finite Element Method in the slope stability analysis using slices yields a unique global safety factor without imposing any additional conditions. In addition, this has also made clear some points regarding displaccments of the nodes of the movable slices, which was one of the drawbacks of the existing slope stability analysis based on method of slices. When the global factor of safety is greater than 1.0, the results are not much different from the conventional method. When the global factor of safety is smaller than 1.0 attention should be paid, as in that case fairly large difference exists between the results obtained and conventional method. Regarding the magnitude of the force that develops between the movable slice and the stable formation, it is seen that the present method gives more accurate results as comparcd to those from the existing methods of slices. Furthermore, even while using a value of Young's modulus for the elements different from that used in the reported calculations, no differences of the valucs of the global safety factor and the force developed between the failed mass and the stable formation underneath were found. However, the magnitude of displacement showed an inverse relation to the values of the Young modulus.

REFERENCES Bishop, A.W. 1955. Thc use of slip circle in thc stability analysis of earth slopes. Ge~tecIzni~ue, 5: 7-17. Hayamizu, H. 1996. A ncw analysis mcthod for slope stability evaluation. In Teclznology and Constructiorz: (Rcscarch Report of Japan Foundation Enginccring Co. Ltd., Tokyo): 54(2): 76-8 1. Janbu, N.1957. Earth pressure and bearing capacity calculation by generalized procccturc of sliccs. Proceeding of the 4th International Conference of Soil ~ ~ c h a ~ and ~ i cF~Iundati~>i~ s Engi~~eering~, London: 2 : 207-212. Kojima, Y., Yamazaki, T., and H. Hayamizu 1997. Slopc stability analysis incorporating slice e ~ ~ deformation - Part 1. ~ ~ ~ ) of cthee 32nd Annuul Coizference of .lupane.se Geotechnical Society. 3: 1871-1872. Lane, P.A. and Griffiths D.V. 1997. Finitc clcmcnt slope stability analysis - why arc cnginccrs still drawing circl cs . Proceedings of the Sixtlz ~ ~ ~ t e ~ n a~,~ym~~o.siurn ti~)na on urnerica1 ~ ~ ) d einl ~ s Geomeclzanics. Montrcal, Canada: 589-593. Tcrado, Y., Yamazaki, T., and H. Hayarnizu 1998. Slopc stability analysis incorporating slicc ~eformation- Part If. P i - ~ > c e ~of ~ ~the ~ g33rd ~s Annual Coizfirencc of Jupuncse Ck~teclinicul S>ciety. 3: 1707-1708.

269

~

~

~

~

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang ic) 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Slope stability analysis using a spring attached to inter-slice planes K. Kondo Public Works Department, Aichi Prefecrural Governmenr,Nugoya, Jupun

S. Hayashi Faculiy of Bioresources, Mie UniversiQ Japan

ABSTRACT: A new slope stability analysis method is proposed by using springs attached to the inter-slice planes based on the limit equilibrium method(LEM), and an evaluation of this method on typical soil failure problems is discussed. The subject of slope stability analysis using the slice method based on LEM, involves determination of the inclination angles of the inter-slice forces related with a statically indeterminate problem. In the method proposed, the inter-slice forces including these angles and the overall safety factor can be determined logically by deformations of the vertical slices, which are obtained from the stress-strain relation of the soil and the limit equilibrium condition. Results obtained by this method satis@ the force and moment equilibrium conditions on each slice and the whole slope. This method can be applied to most soil failure problems, even on a non-uniform ground surface. 1 INTRODUCTION The slice method based on the limit equilibrium principle is the most common method for slope stability analysis. Various slice methods have been proposed by Fellenius( 1936), Bishop( 1954), Janbu ( 1955 ), Morgenstem-Price( 1965 ), Spencer ( 1967,1973) and others. However, owing to the statically indeterminate nature of the problem, most of these methods have done nothing but analyze by only using groundless assumptions regarding inter-slice forces. For example, the Morgenstern-Price method (MPM) and Spencer method( SPM) have been based on a determinate state by using an additive of unknown value( Sarma,1979, Imaizumi et al., 1988) They satisfy the force and moment equilibrium conditions on each slice and the whole slope, and assume all acting inclination angles of inter-slice forces( these hereafter will be called internal angles) to be set as usually parallel to each other as shown in Figure 1 ( a ) . In an actual slope, the internal angles depend on the locations, as shown in Figure 1 ( b ) . As a. matter of course, the results of slope stability analyses are under the influence of the internal angles. Therefore, the appropriateness of results obtained from the conventional methods such as the MPM and SPM is not ascertained. The bearing capacities whose correct values have already been known, are analyzed using conventional methods, and are high in errors( Hanssen, 1966). This fact also indicates that the appropriateness of

Figure 1 Situation of internal forces the conventional methods is not clear, even for the slope stability analysis. By the way, soil failure phenomena such as those on a slope, footing and back-fill of a wall, are caused mainly by soil shear failure. From the standpoint of mechanics, thou h these failures result from the same phenomena? Yamaguchi, 1990) , the slice methods are not usehl for soil failure phenomena on the footing and the back-fill of a wall. The analysis of these requires other methods, because of the inability to determine the internal angles with reasonable accuracy by the conventional slice methods. It has been desired that these phenomena can be dealt with uniformly by using one method (Imaizumi et al., 1986). 27 1

effective inter-slice force, Wi the self-weight of slice, U1 and PI the total pore water pressure on the base plane and on the left side inter-slice plane respectively, QI the surcharge force, br the width of the slice, 61’the internal angle of Zl’, Q I the inclination angle between the tangent to the base plane and the horizontal, w r the inclination angle of Qj, I sec Q I ) and SOZI( C I ~ b~ ( NI’.tan q5 the mobilized shear strength owing to the cohesion and friction angle on the base plane, LI and hrl vertical distances of the acting position of Zl’ and P,from the base plane respectively, Iiu, h’,Iv and IQ horizontal distances of the gravity center and the acting position of NI’, lJl and Qi from the left side inter-slice plane respectively, hQ vertical distance of the acting position of Ql from the acting position of NI‘, where cnll’=clYFs, tan q5 )?I1 ’=tan q5 I YFs, Fs the overall safety factor, cI’ and @ I ’ the cohesion and the friction angle in terms of effective stress on the base plane, du= ( b I - h )tan a I , dL=h tan a By considering U * , whose direction is the mobilized friction angle, dn,,‘, measured upward from the base plane and considering 8 * , the sum of the virtual work, wl, of the z-th slice can be obtained as follows l?II

Figure 2 Several forces acting on a slice The aim of this paper is to propose a new slope stability analysis method by using the slice method based on the limit equilibrium principle, and to discuss an evaluation of this method for typical soil failure problems. This method is capable of determining the internal angles reasonably, and even results in accurate solutions for the problems of bearing capacity and earth pressure. Therefore, this method can be widely applicable to soil failure problems.

WI

= U*.

el

-cos( x I + 61 ’ ) cos! T6I-1’ 1 -sin x I -cos q5 1n1 sin q5 ini -cos x I cos x I -cos( x l - w l )

Rr., =

2 NEW LIMIT EQUILIBRIUM FORMULAS FOR SLOPE STABILITY

Ij T

In the slice methods such as MPM and SPM, to derive the limit equilibrium formulas, the force and moment equilibrium conditions are usually employed in each slice. However, the principle of virtual work can also make the derivation of the same formulas as equivalent as the SPM. That is, the force and moment equilibrium formulas using the principle of virtual work can be derived from considering a virtual deformation without rotation, U * , and a virtual rotatory deformation, 8 * , respectively. Figure 2 shows the several forces involved in the derivation of formulas. The acting position of the effective force, NI’, normal to the base plane of the i-th slice is defined as the origin of the orthogonal coordinates, and the coordinates of the acting positions of several forces are defined as shown in Figure 2 In this figure, the definition of each variable of the i-th slice is as follows: Zj’: the left side

RM =

where x i included in the above equation is q5 ml‘- Q i. Eq. ( 1 ) must satis@ the following relational equation concerning the principle of virtual work:

wi

=

0

(2)

Since U * and 8 * are not zero, and Eq. ( 2 ) has to be satisfied for all slices, the equilibrium formula of the whole slope is written as follows:

=o 272

Figure 4 Deformation of slices in the SSM Figure 3 Model of the SSM planes. The plastic springs, N, normal to the base plane and the sliders parallel to the base planes are attached to the base plane. As for the deformation of slices, the following are assumed: 1 )The slices are assumed to move basically parallel to the base and inter-slice planes. The rotational movement is not considered here. 2)The moving direction of slices is employed to a dilatancy angle while being in a plastic state on the inter-slice plane. The base plane is dealt with in the same way. 3)Soil mass is assumed to be isotropic.

where i1 is the number of slices. Eq. ( 3 ) which is as equivalent as an equation in the SPM, has the generality of the slice method. From now on, this new formula will be useful as a general formula of the vertical slice method, because it is impossible to derive it clearly and quickly from the principle of virtual work. 3 INTERNAL ANGLES

6

I’

3 2 Dejbrmation of slice based on the model

The subject of the slope stability analysis using the slice methods such as the SPM and MPM, deals with how to determine internal angles This problem is caused due to the lack of a number of mechanical conditions as compared with the number of unknown values Accordingly, to add the new conditions, the new slope stability analysis method utilizes springs attached to the inter-slice planes ( Kondo, Hayashi, 1997b ) This method hereafter will be called the SSM (Slice Spring Method) The SSM adopts a new limit equilibrium formula as mentioned above, and is equivalent to the SPM The SSM utilizes springs to determine the internal angles which are impossible to determine reasonably by the SPM or others Initial trial forces, namely, the horizontal inter-slice forces, ZH~’,and NI’ are determined by the SPM Then the actual internal angles are yielded by a deformation of the slices caused by action of the springs etc, introducing the stress-strain relationship attached to the inter-slice planes

In the SSM, the deformations of slices are obtained from applying two forces (Zm‘,N‘) to spring-H and spring-N, respectively Considering the usual slope rising to the right side, each slice being a base plane in the limit equilibrium state moves downward to the left, shrinks with Zm’ and then moves downward to the left side along the slip surface Shrinking upper slices also slip downward to the left side on the slip surface following the lower moving slices If the inclination angles of slip surfaces are all the same, namely, a linear slip surface, a relatively vertical deformation between the adjacent slices does not occur However, since the inclination angles of slip surfaces usually become steep at upper sides of the slope, a relatively vertical deformation between the adjacent slices occurs due to a difference in the inclination angle of the base plane between the adjacent slices Furthermore, Ni’ caused by @,I’ ( 2 1 , ZI’, etc which are acting on the slice, bring a sinking normal deformation to the base plane into the slices The difference of the sinking deformation between the adjacent slices also yields a relatively vertical deformation As mentioned above, two kinds of vertical deformation, which are caused by both moving of the slices along slip surfaces and normal sinking of the slices to the base planes, yield the relatively vertical deformation, V I , as shown in Figure 4 This figure

3.1 Model of SSM

Figure 3 shows the model of SSM to express the characteristics of the soil mass as an elasto-plastic body. Regarding the slices as a rigid body, the horizontal elastic springs, H, and the vertical elastoplastic springs, V, are attached to the inter-slice 273

indicates that point. P, which is stationary before the moving of slices, moves to different positions( Pi, P2) after this movement, and then by these deformations the relatively vertical deformation,,1'1 occurs 3 3 b?rilml acting arigk of rrzter-slice force

6w

unique internal angle, can be derived from Eq ( 6 ) regarding k as the unknown variable While k, in the SPM needs to be assumed, the SSM does not ~ , can be provided need to assume k and 6 ~which by an iterative calculation of the conditions of Eqs ( 3 ),( 5 ) Namely, the SSM is also different from the SPM in the usage of the scaling factor In the SSM, Rs derived from the force equilibriand k derived from both the um equation using 6,' moment equilibrium equation and Eq ( 6 ) , are determined by calculating both Eq ( 3 ) and Eq ( 5 ) with iteration until Fs and each 6,' converge During iteration, once transforming the inter-slice plane to a plastic state, 61'are the imposed angles on the plastic state as follows

In the SSM, the virtual acting angles of inter-slice forces (these hereafter will be called virtual internal angles, ~ D I) , are calculated before determining the internal angles, 6 Calculating 6D~ requires ZfIl' and NI', which are obtained from the SPM assuming all the internal angles to be parallel Just after determining these forces, the action of the springs ( H,N) diminished upon applying the forces ( ZH~ ',NI') to these springs ( H,N ) respectively, yield V I as mentioned above Before determining 6 ~the~ , virtual internal shear force, ZDV~, needs to be obtained from both 1'1 and the stress-strain relationship where 7b: the shear resistance force on the interof the spring-V as follows slice plane, Zvl: the vertical internal force. 1'

where g the tangential spring constant of the spring-V, ml=( dl+dI -1 )/Hi, HI the vertical length of the left side inter-slice plane, (dl+dl+i) the horizontal length between the midpoints of adjacent slices By determining ZDr.1, dol can be given as shown in Eq ( 5 ) , using ZH!'obtained from the SPM

Details concerning the derivation process of 11, are referred to in the paper by Kondo & Hayashi, 1997a. 3.4 Computing Method of

8I '

The internal angles 6 i ' satisfying the limit equilibrium conditions are obtained from Eq. ( 6 ), which includes 8~ and the limit equilibrium in Eq.( 3 ) concerning slope stability derived from the principle of virtual work.

where k is the scaling factor. In the SPM, the internal angles, 6 are derived from Eq. ( 7 ) with iteration regarding 8 as the unknown variable. t a n 6 I'

=

kl

*

tan8

(7)

where 8 : the scaling factor, kl: function that describes the manner in which the internal angle varies across the slope. Usually, kl is taken as 1.0 owing to the inability to determine these angles individually. On the other hand, in the SSM, the 274

4 VERIFICATION OF SSM

To verify the SSM, the bearing capacities of which the correct values are already known and of which the results from using the conventional vertical slice methods have much error, are computed using the SSM. At the same time, computing by the SPM is also performed to compare with the SSM. A ground is considered for the bearing capacity problem in which the parameters are given as c=l, @ soil unit weight y =0, footing width B=l and V ( Poisson's ratio) 4 3 . Namely, the value of Nq is computed. The ground is divided into 5 slices as shown in Figure 5 . The bearing capacity value must be optimized for the geometry of the slip surface on Fs set to 1.0 (the tolerance is 10-4 ) . The method of optimization employed is a quasi-Newtonian method similar to that of Arai et al. ( 1985 ) . To search for an optimum geometry, the vertical 10cations of slip surfaces are taken as variables along the inter-slice planes. Also, the slip surfaces located at the mid-vertical plane on the active and passive earth pressure wedges are moved along the rupture line of each wedge, and the tip of the rupture line on the ground is moved along the ground surface. The computed results are shown in Figure 5 comparing with those by others ( Hansen, 1966). The SPM gives 9.5 as the value of Nq and causes an error of -45.6% as compared with the correct value( 18.4) by Prandtl (Prandtl, 1921 ) . Though the SPM is known as an accurate method for slope stability analysis, this method gives rise to much error because of being obliged to assume all the internal angles to be parallel to each other( in this case, 6 T'=l.26" ) . Contrarily, the SSM gives 19.6 as the value of Nq, and causes an error of only 6.5% as compared with the correct value. This error is the

Figure 5 Nq30" and slip surface shape obtained from several methods same as the one obtained from GLEM( Enoki, et a1 , 1991 ) , and much less than the one obtained from the SPM Moreover, the internal angles on the mid-vertical inter-slice planes of the active and passive wedges are known as horizontal, because of being in an active failure state under the footing, and being in a passive failure state adjacent to the footing Eventually, with these internal angles set to horizontal as the boundary condition (this hereafter will be called the horizontal boundary condition), the SSM still yields a more accurate value( 17 9, error=-2 7% ) Figure 6 draws the bearing capacity values of Nq obtained from the SSM where the ground is divided into 6 slices with correct values( Prandtl ) (Kondo, Hayashi, 1997b) Results of the SSM are computed on the condition that v (Poisson's ratio) is given at 0 3 Figure 6 shows the values obtained from both conditions of the horizontal boundary and without them Values of Nq by the SSM agree well with the correct values by Prandtl Errors of these values without the horizontal boundary conditions are about 1% in c,6'=10"and 10% in $'=40" Given the horizontal boundary conditions, errors become less than 4% on the whole The examination above by means of analyzing the bearing capacity indicates that the results obtained from the SSM are appropriate and the SSM can be verified

Figure 6 Nq by SSM

ified by analyzing a model slope using the SSM (Kondo, Hayashi, 1998 ) . At the same time, computing by the SPM is performed to compare with the SSM. Once anchor force is introduced into a slope, the internal angles are supposed to change partially at and around the slice with the introduced anchor force. It is impossible for the conventional slice methods to properly estimate the change of these angles due to anchor force in the design of anchor works to stabilize a slope. Therefore, the necessary anchor force, in other words, the safety factor and the slip surface to determine the position of an anchor body, may not be able to be estimated properly. On the other hand, the SSM is supposed to be able to estimate these properly, because of considering the slice deformations due to anchor forces and then determining the internal angles based on these deformations. Figure 7 shows the model slope in which the parameters are given as @'=25.0",c'=9.982kN/m2, 7 =17.64kN/m3 and v =0.3. In the analysis to determine the necessary anchor forces in which the safety factor is 1.500, the directions of the five anchor forces are assumed to be normal to the ground surface, and then the anchor is acting position, L, measuring from the left side inter-slice planes and is varied simultaneously to the upper side of the slope. An optimization method which is the same as that in the above chapter is employed. The computed results of slip surface shapes are shown in Figure 7. Accompanied with increasing L, the tops of slip surfaces have been moved toward the center side of the slope, and the toe of these have moved toward the opposite side of the slope. Figure 8 indicates the difference and variations of the necessary total anchor forces by the SSM and

5 APPLICATION TO ANCHOR WORKS

A basic characteristic of anchor force variation depending on the acting position of the anchor is clar275

6 CONCLUSIONS

The slice method is convenient for the actual problems because of its ability to deal with several problems in which conditions are complicated. However, the conventional slice method cannot estimate the internal forces properly, so that when the anchor works and bearing capacity problem where the internal angles vary widely depending on the surcharge force, the conventional slice method has much error. The proposed method( SSM) can estimate the internal forces properly. While the SSM cannot deal with a ground whose soil parameters are not uniform, it can deal with a non-uniform ground surface which is difficult for the limit analysis and slip line methods to analyze. Therefore, the SSM is capable of wide application to soil failure problems.

Figure 7 Slip surfaces depending on acting location

REFERENCES

Figure 8 Necessary anchor forces depending on acting location (Fs=1.500) SPM These forces increase with increasing L. The tendency of its variation is linear in the SSM as compared with a curved line in the SPM The line of discontinuity at L=l Om is generated by changing the slice acted upon by the anchor forces accompanied with increasing L. The necessary anchor forces by SSM are smaller than those by SPM The difference between the two methods increases with increasing I,, and is 2% at L=OOm and becomes 29% at L=l 2m, which is indicated as a percentage divided by the values of SSM The verification of SSM carried out in the above chapter can provide the results of SSM better than the results of SPM Therefore, there is little difference between the SSM and SPM in the case where the force acts on the lower part of the slope, but the results by SPM are overestimated in the case where the force acts on the upper part of the slope In such cases, a method capable of estimating the effects of inter-slice forces such as the SSM should be utilized

Arai. K. and Tagyo, K. 1985 : Determination of noncircular slip surface giving the minimum factor of safety in slope stability analysis. Soils and Foundations. V01.25, No. 1. pp.43-51. Enoki, M. , Yagi, N., Yatabe, R. 1991 : Generalized limit equilibrium method and its relation to slip line method. Soils and Foundations, Vo1.3 1, No.2, pp. 1-13. Hansen, J. B. 1966 : Comparison of methods for stability analysis, Danish geotechnical institute, Bulletin No.2 1 pp.5-9. Imaizunu, S. and Yamaguch. H. 1986: Bearing capacities of shallow foundation calculated by the method of slice. Soils and foundations, V01.26, No.2, pp.143-150 (in Japanese 1. Imaizumi. S.; Yamaguclu, H.,Oohasl~i,K.. 1988 : Stability annlysis by the generalized slip surface. Tsuchi-to- Mso, Vo1.36, No.5, pp.55-60 ( in Japanese). Kondo, K. and Hayashi. S. 1997a : Slope stability analysis using the springs attached to the interslice plains, Journal of Geotechnical Engineering, ,JSCE, No.561lIII -38, pp.33-46 ( in Japanese). Kondo. K. and Hayashi, S. 199% : Evaluation of the SS method on typical soil failure problems, .Journal qf Geotechnical Engineering, J Y E , No.5821III -3 1, pp. 137-149 ( i n Japanese) . Kondo. K. and Hayashi. S. 1998 : Analytical study on the location of anchor works to stabilize a slope, Journal qf The Japan Society qf Erosion Control Engineering, Vol.50, No.5. pp.12-20 ( i n Japanese) . Morgensteni. N. R. and Price. V. E. 1965 : The analysis of the stability of general slip surfaces, Geotechnique, 15. pp.79-93. Prandtl, L. 1921 : Uber die eindringungsfestigkeit plastischer baustoffe und die gestigkeit von schneiden, Z. Anyew. Math. Mech.. Vol. 1. No. 1. pp. 15-20. Sarma, K.. 1979 : Stability analysis of embankments and slopes. .Journal of the Geotechnial Engineering Division, .,ISCE, GT12, pp.1511-1524. Spencer. E. 1967 : A method of analysis of the stability of embankments assuming parallel inter-forces. Geotechniqu 17. pp. 1 1-26. Spencer. E. 1973 : Thrust line criterion in embankment stability analysis. Geotechiiique. 23, No. 1. pp.85-100. Yamaguchi. H. 1990: Soil mechanics, Gihoudou- shuppan pp. 197( in Japanese ) .

276

Slope Stability Engineering, Yagi, Yamagami & Jiang cc) 7999 Balkema, Rotterdam, ISBN 90 5809 079 5

Three-dimensional stability analysis of locally loaded slopes X.Q.Yang& S.X.He Hubei Polytechnic University, Wuhan, People’s Republic of China

Z. D. Liu Wuhun Universify of Hydraulic and Electric Engineering, People’s Republic of China

ABSTRACT: Stability analysis of locally loaded slopes is a complex three-dimensional research topic. Based on limit analysis theory and three-dimensional failure mode, corresponding calculation method of local limit surcharge on top surface of slope is proposed. By use of energy safety factor, some relations between slope general stability and local stability are revealed for locally loaded slopes in this paper. 2.1 Smaller local surcharge

1 INTRODUCTION Many practical geotechnical problems involving local surcharge on top surface of slopes require reasonable stability analysis evaluation. When the local surcharge is smaller, it does not influence slope general stability. When the local surcharge is bigger, it is proved by many geotechnical engineering practices that dimension and location of the local surcharge will control slope failure state, and local three-dimensional slope failure will be easy induced. Because of complexity of problem, beneficial influence of two end failure surfaces is neglected, and the slope with local surcharge is analysed by means of two-dimensional methods, assuming the surcharge of an infinite extent, this may lead to a very conservative design. Based on limit analysis theory (Chen 1975) and some research results reported in literatures( Baligh 1975. Hovland 1977 and Michalowski 1989), and combined with energy safety factor(Yang et al. 1977 a,b), the paper gives out a further study about the three-dimensional stability problem of slope with local surcharge.

When the local surcharge is smaller, it does not influence slope general stability. In such the circumstances, the surcharge can be neglected, and corresponding slope with no local surcharge can be used to study the slope general stability, as shown in Figure 1.

Figure 1. General stability analysis of slope The slope general stability analysis can be regarded as a two-dimensional stability problem,. for certain failure angle p, external force work rate W ~ . , I done by weight of failure soil mass is expressed as follo~vs:

2 LOCAL SURCHARGE ON TOP SURFACE OF SLOPE Internal dissipative work rate J;,,,,, produced by failure soil mass sliding along failure surface AD can be obtained:

There is a slope with an infinite extent, its top surface is horizontal, slope height is h. and slope angle is (9O”-~).Soilmass’s unit weight is r, cohesion and internal friction angle are C and p respectively. If the soil mass satisfies Mohr-Coulomb yield criteria and obeys associated flowing rule, then slope stability analysis will be detailed under two kinds of local surcharge conditions in the following sections.

W,,,; = ChV cosiplsin p

(2)

According to definition method of energy safety factor (Yang 1997 b ),the energy safety factor FS, of 277

Figure 2. local stability analysis of slope

the slope general stability can be gotten: FS I

w =-=--. ,,,I

.

W,YI

2c

mode of total three-dimensional sliding soil mass is shown in Figure 2(b). Based on some geometry relationships, weight W, of total three-dimensional failure soil mass can be expressed as follows:

cos p

rh (ctgp - tgE) s i n ( p - p) sin p

In order to calculate FSI,,,,,, making dFS,/dpO, then critical failure angle p,,. has a following relationship:

w,= 1 rBH -

(ctgP - t g E )

-

1 ; I-H 3

I

=. sin ,8

(ctgfl

-

tgE)

(5)

Then external force work rate done by the W, and local surcharge on top surface of the slope can be obtained :

Formula (4) coincides with failure angle derived by literature (Hunt 1986). For vertical slope (FO"),its =45 p/2. Putting p,, obtained by formula (4) into formula ( 3 ) then corresponding FSjlllll, of the slope general stability can be gotten. O+

1

1

2

3

- tgc)

i r , z = [-I-BH '(ctgp - t g E ) - ; r H 3 *(ctgp

+ 41bIC'

sin( p

-

sin ,8

p)

(6)

Just shown in Figure 2(b), area S, of bottom failure surface GEFK can be derived as follows:

2.2 Bigger local surcharge

If rectangular surcharge on top surface of slope is uniform, when the local surcharge is bigger, local three-dimensional failure of slope is easy induced. as shown in Figure 2, corresponding failure angle p can be calculated by use of the relationship tgpH/(g+b+HtgE). Under such the circumstances. sliding velocity V of the total failure soil mass is shown in Figure 2 (a) and angle between velocity 'I and sliding tangent GG'(or KK') of bottom failure surface GEFK is equal to 9.At the same time, GE and KF are sliding tangents of two end failure surfaces AEG and DFK respectively. so angle between Vand GE(or KF) is also equal to p. Based on the construction of kinematically admissible velocity field. such field has to comply with the kinematical boundary conditions and compatibility conditions, it can easy be conjectured that angle between GE and GG'(or KF and KK') must be equal to p. corresponding lower-bound length EF of the three-dimensional failure soil mass should satisfy the relationship B=I+2HtgpIsinp. If AE and DF. two failure lines exposed on the slant slope surface, are vertical to the line AD, then GA and KD must be two failure lines exposed on top surface of the slope. According to above demonstrations. then the failure

np-H s,= H ( B s isin? p

tgq)

And area S, of end failure surface AEG(or DFK) can also be gotten:

H2

s, = -{

+ 2(ct@-tg&)'

4

4 sin' pco? pco? E I

1

COiE

sin-p

- _ _ _ _ -, [

cos?E

-~

2

sin' pcos?E

I

-(ct&-

tg&)'l2}?

Then internal dissipative work rate M', produced along velocity discontinuity surfaces GEFK, AEG and DFK can be expressed as follows: W,,,' = C(S, - + 2 S 2 ) V c o s p

,

'

q c t g p - &E)?

cos2&

2 I sin2Pcos2& cos4&

(9) Corresponding energy safety factor FS, of the local three-dimensional stability has following relationship:

278

-

1

[T r-BH'(ctgp-tg~)-

1 ~

J

I

r-H5*-(ctg,8-tgs)+y sinp

bI ]

2(ctgP- tgE)? H(Bsinp- H tgp) H ' +--E 2 sin' P C O4S ' ~ C O S ~ E+ COS'€ sin' p

In above formula(lO), making FS2=1,then limit rectangular uniform surcharge q,, can be obtained as follows:

q,, =

c

H(Bsinp- Htgq) H' 4 +-[ sin' 2 sin' pcos'qcos

2(ct@ - tgs)? +

COS?€

2 sin'pcos?E

'E

1 COS4€

If I / b - + x , i t means the surcharge with an infinite extent, Putting B=I+2Htgp/sinp into the formula( 11 ), then formula (12) can be derived:

(1)When the local surcharge is smaller, it does not influence the slope general stability, then energy safety factor of the slope with no local surcharge can be obtained by formula (3): FS,,,,,,,=1.54, its PC,=45"+p/2=6Oo. (2)When the local surcharge is bigger, local three-dimensional failure will be induced, then qilllllll=148.88kPa can be calculated through trial and error by formula ( I I ) , PC,=59.04O and H=5 m corresponding to the q,,,,,,,,can be obtained respectively(3) Putting &=59.04" and H=5 m into formula (IO), then q=46 kPa corresponding to FS2,,,,=1.54 can also be gotten by trial and error. Example I1 :Some vertical cohesive slope (c=Oo), there is a rectangular uniform surcharge on its top surface, its g=lm, b=2m, and I/b+x,other known parameters are same as that of example I . Please give out q,,,,,,,and its 3/, q,,,,,,,=36.53kPacan be calculated through trial and error by formula (12), &,=59.04" and H=5m corresponding to the q,ll,,lll can be obtained respectively. Example 111: Some vertical cohesive slope (FO"), its top surface is horizontal , corresponding h=5 m , r=18 kN/m', C=20 kPa and ~ 3 0 " .There is a rectangular uniform surcharge on top surface, its g=O, b=2m, and I=4m. Please give out q,,,,,, and its

P',.

(1)When the local surcharge is smaller, it does not influence the slope general stability, then energy CHcosq rH2 safety factor of the slope with no local surcharge can --(ctgPtgs) (12) be obtained by formula (3): FS,,,,,=1.54, its 2h = hsin psi@ - p) ~cr=450+p/2=600. (2)When the local surcharge is bigger, local threeTo locally loaded slope, local three-dimensional dimensional failure will be induced , then failure soil mass could be slided out either from toe q,,,,,,,=99..54kPacan be calculated through trial and of the slope or from the slope surface, so it often error by formula (11)- ,8,,=61.93" and H=3.75 m needs to calculate through trial and error by putting corresponding to the qrllnln can be obtained respectivedifferent values of H=cx h(a< I .O) into formula (1 1) ly. or formula (12), in which the selected value q~lmln is (3) Putting &=61.93" and H=3.75 m into formula called limit rectangular uniform surcharge, and the (10), then q=43 kPa corresponding to FS21,1n=1 .54 can failure angle corresponding to qllllllll is named critical also be gotten by trial and error. failure angle ,8, of the local three-dimensional failure Example I\/: Some slant slope ( F I O O ) , its top soil mass. surface is horizontal , corresponding h=5 m , r=18 It can be proved that failure surface corresponding kN/m', C=20 kPa and ~ 3 0 " There . is a rectangular to FS2,,,,,,derived by formula (10) is identical with uniform surcharge on top surface, its g=O.12m, b=2 failure surface corresponding to q,,,,,,,calculated by m, and I=4m. Please give out q,,,,,, and its p,,. formula (1 1). (1)When the local surcharge is smaller, it does not influence the slope general stability, then energy safety factor of the slope with no local surcharge can 3 CALCULATION RESEARCHS be obtained by formula (3): FS,,,,,,=2.12, its pcr=(90"Et p)/2 =5 5". Example I : Some vertical cohesive slope (~0"). its (2)When the local surcharge is bigger, local threetop surface is horizontal, corresponding h=5m, dimensional failure will be induced, then q,,,,, ~=18kN/m', C=20kPa and ~ 3 0 " . There is a =172.46kPa can be calculated through trial and error rectangular uniform surcharge on top surface, its by formula ( l l ) , ,8,,=54.77" and H=4 m g=lni, b=2m, and I=4m. Please give out qLllnln and its corresponding to the qlllnln can be obtained respectiveP' I ly. 279

Figure 3. local failure as distance g increases

(3) Putting ,3i ,= 54.77" and H=4 m into formula (1 O), then q=42 kPa corresponding to FS2,n,n=2. 12 can also be gotten by trial and error. According to above calculation results, some understanding can be summed up as follows: (1)To locally loaded slope, there are general failure surface and local failure surface, When the local surcharge is smaller, for examples q646kPa in example I , q G 3 k P a in example 111 and g 642kPa in example 1V. energy safety factor of slope general stability is smaller than that of slope local stability, then the stability will be controlled chiefly by slope general failure surface. As increasing of the local surcharges, energy safety factor of slope general stability is bigger than that of slope local stability, then the stability will be controlled chiefly by slope local failure surface. (2) When the stabi~ityi s control chiefly by general failure surface, the slope should be reinforced along its entire length. When the stability is controlled chiefly by local failure surface, the slope should be reinforced locally, some active reinforcing techniques such as soil-nails and bolts et al. in-suits suppo~ing systems can be adopted to restraint the local failures, other passive supporting techniques such as retaining structures et al. can also be adopted. @)By comparison between example I and example 11, it is clearly indicated that assuming the surcharge with an infinite extent will lead to a very conservative design for locally loaded slope. (4) By comparison between example I and example 111, it is shown clearly that q,,,,,, of local surcharge will increase rapidly as distance g increases. ( 5 ) By comparison between example I , example 111, and exampleIV, it is also shown clearly that the local three-dimensional failure soil mass induced by local load easy slides out from slope surface as distance g decreases or as angle F increases. 4 CONCLUSIONS Based on energy safety factor and local threedimensional failure mode. some relations between 280

slope general stability and local stability for locally loaded slope are detailed in this paper, corresponding local limit surcharge yu,,l,,tcan be given out by formula (1 1). I t should be noted here that the local threedimensional failure mode suits to a smaller distance g. As the distance g increases, local three- dimensional failure mechanisms will change and approach failure inechanisms of shallow foLindations gradualfy, as shown in figure 3. When the distance g exceeds certain critical value, local surcharge on top surface will have no any effects on the slope stability.

REFERENCES Baligh, M. M. & A . S. Azzoiiz 1975. End effects on stability of cohesive slopes. J. Geotech. Engng Div. Am. 101 (1 1): 1105-1117. Chen, W.F. 1975. limit analysis and soil plasticity. New York: Elsevier. Wovland, H.J. 1977. Three-dimensional slope stability analysis of locally loaded slopes. J. Geotech. Engng Div. Am. 103 (9): 971-986. Hunt, R.E. 1986. Geotechnical engineering analysis and evaluation. New York: McGraw-Hill. Michalowski, R.L. 1989. Three-dimensional analysis of IocaIiy loaded slopes. Geotechnique 39 (I): 27-38. ~ang,X.Q.,H~,S.X.&G.L.Chen1997. Research about stability of slurry trench excavation i n soft clay. I n J.X. Yuan(ed.), computer methods and advances in geomechanics: 1903-1908. Rotterdam: Balkema. Yang, X.Q., Liu, Z.D.&S.X. He 1997.A new definition method of safety factor and its application. In J.X. Yu~n(ed.~.coinp~ter methods and advances in geomechanics: 1625-1630. Rotterdam: Balkema.

Slope Stability Engineering, Yagi, Yamagami & Jiang (01999Balkema, Rotterdam, ISBN 90 5809 0795

A lower-bound solution of earth pressure of cohesive backfill with inclined slope surface M. Luan & T. Nian - Depurtment c?fCivil Engineering and State Key Luborutor-y ( ~ C o a s t u l and Oflyhore Engineering, D u l i m University of Technology, People’s Republic of China

c.

E Lee & K.T Law - Depurmzent of Citil ancl Stmc~turulEngineering, Urzi~~ersip of H m g Koizg, People’s Republic of China

K.Ugai - Departnient of Civil Engineering, Gunmn Universitv, Kiryu, Japan Q.Yang - Department of Ciiil Engineering. Dalian Vniiw-sityof Techology, People’s Rejmh/ic oj‘Chinu

ABSTRACT: Rankine’s theory of earth pressure cannot be directly employed to the backfill with an inclined surface. For this practical case, it seems that there is no analytical solution available. In this paper, a theoretical solution of active and passive earth pressures of cohesive backfill with an inclined surface is developed on the basis of the lower-bound theorem of limit analysis. First a statically-equilibrium stress field of the slope ground consisting of cohesive soils is constructed from elasticity theory. Then it is enforced to not violate the Mohr-Coulomb yield condition. According to the lower-bound theorem of limit analysis, two extreme values of lateral stress which respectively correspond to active and passive earth pressures will be found and expressed in the superposition form. Based on numerical computations conducted for different combinations of key parameters related to the problem, and the computed results useful for engineering practice are given in tabular form.

1 INTRODUCTION While analyzing stress conditions in the limitequilibrium state attained under self-weight in semiinfinite mass of cohesive soil, Rankine (1857) presented following analytical formulae for calculating lateral active and passive earth pressures of cohesive backfill on retaining wall with a vertical and smooth back and horizontal surface of backfill, p , = CT, = p k ,

pP

=O

P

- 2cJka

= p k P + 2J ~ kP

where p , and y,, are respectively the active and passive earth pressure given by Rankine’s theory, y is bulk unit weight of soil, z is the depth to any soil element on the vertical back of the retaining wall from the level ground surface, c and qJ are cohesion and internal friction angle of backfill soil, k, and kp are respectively the active and passive earth pressure coefficients based on Rankine’s theory with the following expressions

k,

=-1-sin4 = tan;(:

1 + sin 4

-

$)

In the case of active state of limit equilibrium based on Rankine’s theory, the depth of surface tension cracks zo may be found by equating oa to zero as

A graphical method was presented by Terzaghi (1943) for obtaining the lateral earth pressures of cohesive soil in the case of backfill inclined at an angle a to the horizontal. This method becomes rather tedious for solving practical retaining wall problems, since several Mohr’s circles of stress need to be drawn for several points along the back of the retaining wall to determine the lateral active and passive earth pressures profile. At present, it seems that there is no theoretical solution available. In this paper, an analytical procedure for solving this problem is developed on the basis of the lowerbound theorem of limit analysis. Numerical calculations are made for different combinations of related key parameters of the problem, e.g., friction angle 4 of soil, inclination angle a of backfill surface slope and non-dimensional ratio c / p of cohesion to vertical self-weight stress. The computed values of active and passive earth pressure coefficients are given in tabular form for direct applications in engineering practices.

28 1

2 FUNDAMENTAL AND FORMULATION Shown in Figure 1 is a typical differential soil strip element with the height of z and width dx cut from the inclined earth slope. The bottom of the element is designated to parallel to the slope surface. According to equilibrium conditions of forces, when q=O, notice that the self-weight dW of the soil strip element is given by dW = y t d x , normal reaction force dN = dWcosa and shear force dT = dW s i n a along the bottom surface can be expressed respectively as CW = ytdxcosa,

(4)

dT = p d x s i n a

(5)

r=yirsinacosa

Their relevant principal stresses will have the following values

/7\

The stress field ( ox,oz,zn) or ( oI,oj) obtained in this way is an equilibrium one which fulfills both the equilibrium conditions within the soil domain of slope and the stress boundary conditions. In accordance with the concept of limit analysis, this stress field will be a statically allowable stress field if it everywhere doesn't violate the yield condition such as Mohr-coulomb criteria. According to the lower-bound theorem of limit analysis, the limit load corresponding to the statically allowable stress field will be a lower-bound estimation of its real ultimate load. Mohr-Coulomb failure criteria can be expressed in the form of principal stresses as

Notice dx = dl cosa , the average normal stress o = dN/d/ and shear stress z = d'/dl acted on the soil strip bottom surface may respectively be written as o=pcos2a,

expressions of the vertical stress o,and shear stress z, satisfying the equilibrium conditions with the lateral stress ox as an unknown variable,

+

E

(oI--o3 (oI+~,)sin4 + c cos 4

(8)

By substituting Equation 7 into Equation 8, the following relation can be formulated,

Figure 1. Stress state of soil in slopes.

Solving this equation yields two limit values of horizontal stress ox in the statically allowable Figure 2. Stress analysis of wedge.

stress field

Referring to Figure 2, in order to determine the lateral stress ox and shear stress vertical stress oz, 2, of soil in the slope in the limit-equilibrium state, the stress condition acted on the inclined cross section of the differential element under consideration is analyzed for obtaining the interrelationship among various components of stresses, o=

z=

+

+ ox)+ t (oz- ox)cos 2 a rxzsin 2a

(Uz

-

(oz- ox)sin2a + zn cos2a

Substituting the expressions of normal and shear stresses (i.e., o and z) given by Equation 5 into above equations and rearranging lead to following 282

ox

==

[

]

l+k' 2sin2a p P-+ 2c tan 4F 2kp cos2$

Further simplification of this equation will give two principal values of lateral stress o x ,i.e., horizontal components o and cr, of passive earth pressure p , and the acfive earth pressure p , . Referring to Figure 2 and Equation 6, it can be observed that the passive and active earth pressures of backfill with inclined surface on the retaining wall will be parallel to the slope surface and have the following values

Table 1. Comprehensive active and passive earth pressure coefficients values ( k,", k i ) for various combinations of 4 , a and c / p .

They can further be expressed in the superpositiontype form

in which 2sin2a c o s a + cos2@ ca tan$!-

2 cos a cos @

(1 1 4

where ca is a factor that is dependent on the nondimensional ratio of the cohesion and self-weightinduced vertical stress of soil,

vertical and smooth interface, two principal values of lateral earth pressure in infinite slope obtained above will be the active or passive earth pressure of backfill with an inclined surface on retaining wall. The optional sign in the above equations (e.g., Equations 10 and 11) will take the upper and lower sign respectively for passive state and active state of limit equilibrium. The first and second items in the right side of Equation 10 respectively stand for earth pressures caused by the self-weight and cohesion of cohesive backfill on retaining wall. ky and kc are respectively referred to earth pressure coefficient due to the contributions of soil self-weight and cohesion. Setting p , in Equation 10 to be zero and making a series of simplifications will yield a quadratic equation with respect to tension-crack depth zo, y 2 z," - 4 c y t a n @ z o- 4 c 2 = O From this equation, the same value of the tensioncrack depth zo as given by Equation 3 will be obtained. It may be noted that the depth of the tension crack is independent of backfill slope angle. Especially, for the cohesionless backfill and inclined slope surface, i.e., c=O and a g o , the above formulae will be reduced to

It is supposed that the effect of the left-side soil mass of any cross section in infinite slope on the right-side soil is replaced by a rigid retaining wall with a

283

Table 2. Active earth pressure coefficients (kay,kac)for various combinations of

4, a

and c / p .

Friction angle

&20"

&30"

which is the solution of Rankine's theory of earth pressure for cohesionless backfill with inclined surface. Furthermore for the cohesionless backfill 284

Table 3. Passive earth pressure coefficients (kp.,,kpc)for various combinations of (s , a and c / p Friction angle

630"

6-40"

and horizontal surface, i.e., c=O and a=O, (13)

which is Rankine's formula of earth pressure for cohesionless backfill with level surface. Equation 10 can be further expressed in the comprehensive form as

three items of passive earth pressure coefficient increase with increasing values of 4. in which 4 CONCLUSIONS where k,’ and k i are the comprehensive values of active and passive earth pressure coefficients respectively. Active earth pressure and passive earth pressure given by numerical calculations are linearly distributed along the depth z.

3 NUMERICAL RESULTS AND ANALYSES According to Equations 11 and 15, numerical values of comprehensive or branch active and passive earth pressure coefficients are computed for various combinations of relevant key parameters such as soil friction angle 4, inclination angle a of backfill surface slope, and non-dimensional ratio c / p of cohesion and self-weight-induced stress of soil. The corresponding results are presented in ta)ular form and given in Tables 1-3. The negative k, values in Table 1 show that tension develops within the soil behind the wall leading to surface tension cracks in the soil. If the tension cracks are filled with water, hydrostatic pressures will develop on the wall. Subsequently, the tension components of active earth pressure in Equation 10 should be removed. Tables 1-3 together with Equation 10 or Equation 14 can be used for calculating earth pressures of backfill on retaining wall with inclined cohesive backfill (y-c-q5 type soil). For given values of friction angle 4 and surface slope a of backfill, with the increase of the non-dimensional ratio c / p , both the branch value k,,, due to soil self-weight and comprehensive value k,* of active earth pressure coefficients decrease while the branch value k,, due to cohesion increases. However all the branch values (i.e., kpyand kd) due to self-weight and cohesion of soil and comprehensive value kpc of passive earth pressure coefficient increase with increasing values of c./ For given values of non-dimensional ratio c / and ~ friction angle 4 of soil, the branch value kay due to self-weight and comprehensive value k,’ of active earth pressure coefficients increase while the branch value k,, resulting from soil cohesion substantially decreases with the increase of backfill surface slope inclination a. At the same time, all the branch values kpy and kpc arising from self-weight and cohesion of soil and comprehensive value k i of passive earth pressure coefficients decrease with increasing values of a. For given values of a and c/p, two branch values and comprehensive value of active earth pressure coefficients decrease, while all

286

Analytical expressions (see Equation 10 or Equation 14) of active and passive earth pressures of cohesive backfill on retaining walls with inclined surface of backfill are developed based on the concept of lower-bound theorem of limit analysis. Combined with numerical calculations, both the branch values and comprehensive values of active and passive earth pressure coefficients for various combinations of relevant key parameters, such as soil friction angle 4, backfill surface slope inclination a and nondimensional ratio c/yz of cohesion and self-weight vertical stress, are given in tabular form (see Tables 1-3). The active and passive earth pressures of cohesive backfill on retaining walls with inclined surface can be conveniently achieved by the proposed formulae for practical applications. ACKNOWLEDGEMENTS The financial support from the Trans-Century Training Programme Foundation for the Talents offered by the Ministry of Education of China for this study is gratefully acknowledged. REFERENCES Terzaghi, K. 1943. Theoretical Soil Mechanics. New York: John Wiley & Sons, Inc. 35-41.

Slope Stability Engineering, Yagi, Yarnagarni& Jiang 0 1999Balkerna, Rotterdam, ISBN 905809 079 5

Shear band formation and propagation in clay slopes Luis E.Vallejo Department of Civil and Environmental Engineering, University of Pittsburg, Pa., USA

ABSTRACT: Stiff clays in the ground are highly overconsolidated, with lateral pressures several times greater than the present overburden stress. When a cut is made in deposits of stiff clays, the resulting stress relief causes the clay near the cut faces to exhibit large lateral movements towards the face of the cut. Such movements lead to the concentration of stresses in regions close to the toe of the cut, resulting in the formation of what is referred to as “shear band” or “toe crack” at the base of the cut. The present study presents the results of laboratory and theoretical investigations designed to understand the mechanics of formation and propagation of a shear band in vertical cuts in clay. Laboratory tests on simulated vertical slopes in clay containing a small shear band (crack) at their toe indicated that the shear band did not propagate in its own plane when subjected to a combination of normal and shear stresses. Instead, the shear band or toe crack propagated in the form of a secondary crack that developed an angle with respect to the plane of the shear band. This study also presents a way to obtain the critical height of a cut in clay considering a failure surface that is made of a shear band of small length at the base of the cut, a secondary crack at an angle with the plane of the small shear band, and a tensile crack at the top of the cut.

1 lNTRODUCTION The stability of a vertical cut made in a homogeneous clay layer has been a subject of great interest to geotechnical engineers. Fig. 1 indicates the failure mechanisms used by geotechnical engineers to obtain the critical height, H, at which the cut fails. The first two mechanisms (I and 11) assumes the failure to take place in a clay which is saturated and has an angle of internal friction, 4 , equal to zero; a cohesion, c , equal to the undrained shear strength, cLl; and a unit weight, y , equal to its saturated value. The third mechanism (HI) assumes the failure to take place in a clay that have both, cohesion (c) and friction to resist failure. Mechanism (I) is due to Coulomb (1 773) who calculated the cut to fail when the height, H , reached a value equal to (4cu/y ). Mechanism (11) is due to Taylor (1948) who calculated the height at failure, H , to be equal to (3.83cJy). Mechanism (111) is due to Lohnes and Handy (1968). Mechanism (111) assumes a tensile crack in the upper section of the cut. This tensile crack joints a plane failure surface that starts at the toe and is inclined at an angle (45 + @2) with the horizontal. The height at failure, H ,can be obtained

(a),

Fig. 1 Interpretation of the failure of a cut in clay.

287

from Eqs. (1) and (2).

F i g . 2 Shear band f o r m a t i o n i n a c u t i n clay.

cause the walls of the crack to slide in the plane of the crack. This is a sliding mode and represents the mode IT type of cracking. Cracks can propagate in materials as a result of one or a combination of the two modes. In the study conducted by Palmer and Rice (1963), they indicated that even in the absence of gravi~tionalinduced driving shear stresses, the magnitude of strain energy stored in a stiff clay deposit plus the existing lateral earth pressures can cause a shear band or toe crack formed right after a cut was made in the stiff clay to propagate inside the slope. In the analyses presented by Palmer and Rice (1973) and Bjerrum (1967), the propagation of the shear band was assumed to take place in a self-same manner, “analogousto direct shear test conditions.’‘ Thai is, an initial horizontcrl cmck at the base of vertical cut made in a horizotita? ground wotitd advance into the intact material of the excavation I?orizontciIly (mode I1 type of crack propagation using the terminology of fracture mechanics) . Field work conducted by Biirland et al. (1977),indicates that the self-same manner of propagatio~iof a crack under mixed-mode type of loading (mode I plus mode II) indeed occur in in a cut in Oxford clay containing a shear band at the toe of this cut. However, Hutchinson (1972) found that horizontal notches at the toe of chalk cliffs in England did not propagate inside the slope following the direction of the plane of the notches. Hutchinson (1972) established that the notches propagated in the form of secondary failure surfaces that extended from the tip of the notches in a direction equal to 67 degrees with the horizontal plane of the notches. Therefore, there is field evidence contrary to the assumption advanced by Palmer and Rice ( 1973) that shear bands in slopes propagate following the direction of their own planes. The purpose of this study was to conduct a laboratory study to clarify the shear band propagation mechanism in slopes.

The above mentioned mechanismsdo not consider the shear band or closed crack that develops at the toe of the cut when the excavation is completed. The introduction of this toe crack in the stability analysis is vital for our understanding how vertical cuts in clay fail.

2 SHEAR BAND DEVELOPMENT IN VERTICAL CUTS IN CLAY Stiff clays and shales in the field are highly overconsolidated, with lateral pressures several times grater than the present overburden. In London Clay deposits, Skempton (1961) measured lateral stresses that were in some instances equal to 2.5 times the vertical overburden stresses. When a cutting is made in stiff clay deposits, the resuIting stress relief causes theclay near the cut face to exhibit large lateral movements (elastic rebound) towards the face of the cut. Smith and Redlinger (1953) described how a 3 inch wide cut i n the Fort Union shale closed in about 24 hours. Such movements in open cuts in stiff clay will lead to: (a) the formation of a “shear band” or “toe crack” at the base of the cut (Bjerrum, 1967) (Fig. 21,and (b) concen~rationand re-orientation of stresses in the region close to the toe of the cut.

3 SHEAR BAND PROPAGATION The propagation mechanics of the shear band which forms at the toe of a cut immediately after it is made in a layer of stiff clay has been the subject of various studies (Christian and Whitman, 1969; Bjerrum, 1967; Palmer and Rice, 1973). Patmer and Rice (1973) made their analysis of shear band propagation iii slopes made of stiff clay using fracture mechanics principles. According to Linear Elastic Fracture Mechanics (LEFM) theory, a crack or fissure in clay can be stressed in three different modes (Broek, 1984). Normal stresses to the crack walls give rise to the mode I type of cracking. In this mode I, the displacementsof the crack surfaces are perpendicular to the plane of the crack. In-plane shear stresses

3.1 Laboratory study involving shear bands in simulated clay slopes To better Linderstand how shear bands propagate at the base of slopes, a laboratory and a theoretical study using the principles of LEFM theory were carried out. The laboratory study involved the use of

288

the shear stress (T) on the plane of the closed crack were equal to 78 kPa and 45.7 kPa respectively. The closed toe crack propagated in the clay sample in the form of a secondary crack the extended from the tip of the pre-existing toe crack and deviated from its original horizontal direction. This secondary crack was inclined at an angle c( equal to 70 degrees from the horizontal direction of the original toe crack (Fig. 3) . This finding is contrary to the Bjerrum (1967) and Palmer and Rice (1973) assumption that states that when a shear band or closed toe crack at the base of a slope is subjected to a combination of normal and shear stresses, it will propagate in a direction that follows that of the plane of the shear band.

a prismatic clay sample containing a cut and a preexisting toe crack as shown in Fig. 3. The sample of clay that simulates a vertical cut in a horizontal clay deposit, was subjected to stresses similar to the ones a vertical slope will experience in the field. This was done using the Plane Stress Direct Shear Apparatus (PSDSA) described in detail in articles by Vallejo (1987, 1991). The sample of clay with the planar dimensions shown in Fig. 3 and a thickness equal to 3.18 cm was subjected in the PSDSA to a combination of normal, on , and a lateral normal stress, oh . The normal stress, o n ,simulates the gravity stress acting on the slope material, and the lateral normal stress, o h ,simulates the lateral earth pressures. One can also obtain the shear stress, T , acting on the clay in a direction parallel to the plane of the crack (Fig. 3). This shear stress is obtained by dividing the known lateral force (oh x 5.13 cm x 3.18 cm) by the area on which it acts (8.76 c m x 3. 18 cm). The prismatic clay sample used in the experiment was cut from a larger clay sample prepared by conso~idatin~ a soft mass of kaolinite clay in an oedometer 30 cm in diameter (Vallejo, 1987, 1988, 1989). The water content of the clay sample used for the crack propagation experiment was equal to 27%.

3.2 Theoretical evaluation To evaluate the laborato~results shown in Fig. 3, the maximum tangential stress criterion of LEFM theory developed by Erdogan and Sih (1963) is used. According to this criterion, the tangential stress, o0 , in the material located in the vicinity of

a crack subjected to a mixed mode type of loading (normal and shear stresses) can be obtained from the following relationship (Ingraffea and Heuze, 1980) (Fig 4)

In the equations above r is the radius between the tip of the crack and a point in the clay surrounding the crack where the stresses are being measured, 0 is the angle that the radius r makes with the axis of the crack (Fig. 4), and KI and KII are the stress

F i g . 3 L a b o r a t o r y e x p e r i m e n t of shear band p r o p a g a t i o n i n a c u t i n c l a y .

During the experiment, the normal stress, oil , applied to the clay sample was equal to 40 kPa and was kept constant ~hroiighoLitthe experiment. The lateral stress was gradually increased until the toe crack propgat4 in the sample. The application of the 40 kPa on stress to the clay sample caused the toe crack to doso. T/ZecIostJdroe c*rt~kpropagated in the sample when the lateral norinal stress (Oh ) and

Fig*

289

Stresses near

Of

shear

The solution of Q. [7] gives the angle of propagation of the shear band or closcd cruck .The theoretical value of the angle of crack propagation,

intensity factors for an open crack under mode I and mode II type of loading. These stress intensity factors are given by (Ingraffea and Heuze, 1980)

KI

=

KII

=

1.1215 0, ( T

c ) I I2

a , is equal to 70.5 degrees. The angle of crack propagation in our simulated slope experiment was equal to 70 degrees (Fig. 3). Thus, LEFM theory has proved very effective for the interpretation of the laboratory results on the propagation of shear bands. The theoretical findingsare also close to the field findings by Hutchinson (1972) of notch propagation in chalk cliffs in England. Hutchinson found the horizontal notches at the base of the cliffs to propagate at 67 degrees with the horizontal. Thus, the laboratory and field values of crack propagation are validated by the maximum tangential stress criterion of fracture mechanics. If the crack remains open, the angle of crack propagation, a , can be obtained from the following equation

[41

and 1.1215 T ( T c ) 1I2

~51

where on is the normal stress that acts perpendicular to the plane of the open crack (Figs. 3 and 4) and T is the shear stress that acts parallel to the crack, and c is the length of the crack in Figs. 3 and 4. Erdogan and Sih (1963) have proposed the hypothesis that crack extension in brittle materials takes place in a direction in which o8 , given by

sina + (KII/K1) ( 3 cos a

Q. 1 11 ,reaches its maximum value. That is, crack extension will take place in a radial direction from its crack tip and that the direction of crack growth is nonizul to the direction of the maximum tangential stress o8 (Fig. 4). Hence the direction of crack

-

1 ) =0

181

Using Q. [ 81, Fig. 5 was developed and shows the values of a for different values of the ratio (I
also eqiial to the ratio (do).

propagation taking place when 8 reaches a value equal to a is can be obtained after differentiationof o8 with respect to 8 (d o8 / d 8 ). If this is done the following relationship is obtained from which to obtain a (Ingraffea and Heuze, 1980)

KI sina + KII ( 3 cos a - 1 ) = 0

161

where a is the value reached by 8 when crack propagation takes place (Figs. 3 and 4).

3.3 Direction of crack propagation. The direction of crack propagation, cx , can be obtained by using Fq. 161 . @. 16) applies to an opcv7 crctck. That is the stress intensity factors KI and K 11 apply when the cmck is open. If the cmck close.~as was the case of the laboratory experiment depicted in Fig. 3, the stress intensity factor K I becomes equal to zoro (Broek, 1984), and Elq. 16) can be written as F i g . 5 Angle of p r o p a g a t i o n of a s h e a r band assumed open.

290

4. CRITICAL HEIGHT USING FRACTIJRE MECHANICS APPROACH The critical height for a vertical cut in clay with a shear band of sincrll length at the toe of the cut, as well as a tensile crack at its upper surface can be obtained very easily from a stability analysis of the failing soil geometry shown in Fig. 6. This geometry is very similar similar to that shown in Fig. 1 (mecanism 111). The only difference between the mechanism 111 of Fig 1 and that shown in Fig. 6 is the angle that the lower failure surface males with the horizontal. For mechanism III of Fig. I , this angle is equal to (45 + $12). For the failing geometry depicted in Fig. 6 this angle is equal to a . Values of this angle a can be obtained from the plot shown in Fig. 5. From a simple slope stability analysis of the geometry depicted in Fig. 6 a relationship to obtain the critical height H of the cut can be obtained. This relationship is the following:

H=

4c -I, y sin 2 a - 2cos2a tan@

2. A shear band at the toe of a vertical clay cut is subjected to a combination of normal and shear stresses (mixed mode type of loading) and propagates in the form of a secondary crack that grows from the tip of the shear band. This secondary crack is inclined with respect to the direction of the plane of the shear band. 3. The maximum tangential stress criterion from LEFM theory predicted very well: (a) the type of stresses (tensile) that caused the shear band to propagate, and (b) the direction of propagation of the shear band under the mixed-mode type of loading. This result indicates the usefulness of LEFM theory for understanding crack propagation in clay slopes. 4. The critical height of a vertical cut with a shear band or toe crack was influenced by the value of the shear and normal stresses acting i n a direction parallel and normal to the shear band.

6 REFERENCES Coulomb, CA. 1773. Essai sur line application des regel de maximis et minimis a quelques problems de statique relatifs a I'architecture, Mein. Muth. Phys., 7:343 Bishop, A.W. 1967. Progressive failure-with special reference to the mechanism causing it. Proc.Geotcch. Conf:,Oslo, 2: 142-150. Bjerrum, L. 1967. Progressive failure in slopes of overconsolidated plastic clay and clay shales. J Journal qfthe Soil Mechanics and Foundutions Dillision, ASCE, 93: 1-49. Broek, D. 1984. Elcinentary Enginrwing Fracture Mcchunics. Martinus Nijhoff Publishers, Boston. Burland, J.B., Longworth, T.I., and Moore, J.F.A. 1977. A study of ground movement and progressive failure caused by a deep excavation in Oxford clay. Geotcchnique, Vol. 27 (4):557-591. Christian, J.T., and Whitman, R.V.1969. A one dimensional model for progressive failure. Proc. Selmth Int. Con$ Soil Mech. und Found. Eng., Mexico, 2541-545. Erdogan, R., and Sih, G.C. 1963. On the crack extension in plates under plain loading and transverse shear. Journal qfBasic Eng., ASME, 85: 519- 527. Hutchinson, J.N. 1972. Field and laboratory studies of a fall in Upper Chalk cliffs as Joss Bay, Isle of Thanet. Stress-Strain Behaviour oj'soils, Parry, R.H.G., ed., G.T. Foulis and Co., London, England, 692-706. Ingraffea, A.R., and Heuze, F.E. 1980. Finite element models for rock fiacture mechanics. Znt. Journal jbr Numericul Methods in Geomechanics, 4( 1): 25-43. Lohnes, R. A., and Handy, R.L. 1968. Slope angles in friable loess. J. of Geology, 76(3):247-258.

191

The depth of the tensile crack, z, can be obtained from Eq. I 2 1 and the vaule of a from Fig. 5 .

F i g . 6 F a i l u r e mode of a c l a y c u t w i t h a s h e a r band and s e c o n d a r y and t e n s i l e cracks.

5 CONCLUSIONS 1. When a cut is made in a stiff clay, a shear band or toe crack develops at the base of the cut as a result of a relief of the lateral stresses that acted normal to the face of the cut.

29 1

Palmer, A.C., and Rice, J.R. 1973. The growth of slip surfaces in the progressive failure of overconsolidated clay. Pi-oc. ofrhe Royal Sociqy of Lnnihn, A332: 527-548. Sltempton, A.W. 1961. Horizontal stresses in an over-consolidated Eocene Clay. Proc. Fiflh [}It. Conf:on Soil Mech. unrl Found. Eiig., Paris, 1:351-357. Smith, C.K., and Redlinger, I.F. 1953. Soil properties of Fort Union Clayshale. Proc. Third Irir. Conf.‘ on Soil Mmh. mid Found. Etig., Zurich, 1: 62-66. Taylor, D.W. 1948. Firnhrni~nrcrlsqfSoil Mr.chcmics.New York: Wiley. Vallejo, L.E. 1987. The influence of fissures in a stiff clay subjected to direct shear. Gootechniyue, 37( 1): 69-82. Vallejo, LE. 1988. The brittle and ductile behavior of clay samples containing a crack under mixed mode loading. Thcoi-cticul and A pplicd Fi-ucrurc. Mr.chunic.s, 10: 73-78. Vallejo, L.E. 1989. Fissure parameters in stiff clays under compression. J ou rn(iI of Gmtc.ch . E H ,~ . ASCE, Vol. 115 (9):1303-1317. Vallejo, L.E. 1991. A plane stress direct shear apparatus for testing clays. Gcwtc.cl?nicul Etiginocring Congress 1991. McLean, F.G., Campbell, D.A., and Harris, D.W., eds., ASCE’Special Geotechnical Publication No. 27(11): 85 1-862.

292

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Progressive failure analysis of slopes based on a LEM Takuo Yamagarni & Jing-Cai Jiang Depnrhnent of Civil Engineering, UniversiQ of Tokushirnu, Japan

Masakazu Taki Fukken Conzpaizy Limited, Consulting Engineers, Hiroshinza, Jupnn

Satoiu Yarnabe A ruig Limi Company Limited, Hyog o, J c p n

ABSTRACT: A new method for progressive failure analysis of slopes is presented, based on the variable local factors of safety in the limit equilibrium approach. A local factor of safety is defined at the base of each slice, and used to account for the progressive, local failure along a slip surface. It is also used to approximately simulate the softening behavior of soil. The introduction of local factors of safety results in an increase of the number of unknowns. In order to render the problem determinate, simplifying assumptions are simultaneously made of the interslice forces and the line of thrust which are separately used in the Morgenstern-Price method and the Janbu method. Two different techniques called AILC and AGLC are devised to deal with the local factors of safety in the failure zones. The results of case studies show that the proposed approach can simulate the actual behavior of progressive failure. 1 1NTRODUCTION

In this paper, a slope stability analysis method considering progressive failure is developed based on the limit equilibrium approach. A local factor of safety is defined at the base of each slice to represent progressive failure. Although the number of unknowns increases due to the local factors of safety, the problem can be easily made determinate through introducing simplifying assumptions. The softening of soil can also be taken into account in terms of local factors of safety. Limit equilibrium equations are derived using the slice method. In an actual slope, local yielding or failure initiated at some points gradually develops, and finally leads t o overall slope failure. This phenomenon is known as progressive failure (e.g. Skempton, 1964; Bjerrum, 1967; Bishop, 1971). The stress or strain levels are non-uniform along the slip surface, so the factor of safety varies from place to place as well. Therefore, the local factors of safety have to be used to express the progressive failure within the framework of the limit equilibrium method. A single value factor of safety, however, is assumed along the whole slip surface in conventional limit equilibrium methods. Hence it is impossible to deal with progressive failure using such existing methods. Law and Lumb (1978), Srbulov (1995), Chugh (1 986) put forward limit equilibrium analysis considering progressive failure respectively. However, all these methods are quite limited. Law and Lumb do not take into account the interslice forces. In Srbu-

lov's method, the number of equations is one more than the number of unknowns, which makes the conditions redundant. Chugh considers the variations of the factor of safety (8, and stipulates the characteristic hnction g(x) [F=g(x)T where T is the unknown scalar factor], but he fails to explain how to determine it. On the other hand, FEM (e.g. Lo and Lee, 1973; Potts ef al., 1990; Rowe, 1991), Discrete Element Method (Chang, 1992), Discontinuous Deformation Analysis (Huang & Ma, 1992) are all effective methods for progressive failure analysis due to their available stress and strain fields. Nevertheless, these methods are complicated and the amount of computation required is quite large. Furthermore, the initial stress state and pore water pressure are difficult to determine in practice. Therefore, they have not been widely used. In this paper we propose two different techniques to treat the local factors of safety after local failure has occurred at some location: the AlLC method and the AGLC method. The former permits a local factor of safety to have a value less than unity, while the latter does not. Once local failure takes place, the locally failed zone is in limiting equilibrium, that is, the local factor of safety of the zone becomes equal to unity. Therefore, the latter method seems preferable from a physical standpoint, while the former still has a mathematical significance. The following abbreviations are used in the main body of this paper: L.F.S. = Local factor of safety L.Fs.S.= Local factors of safety 293

Table I The numbers of unknowns and equations The number of unknowns

The number of eauations ~~~

Nonnal force N at base of slice Location of nonnal force N Shear force 5' at base of slice Nonnal force E at interslice Location of interslice force E (line of thrust) Shear force X at interslice Local safety factor F a t base of slice An unknown parameter Total number of unknowns

11

n n n- 1 n- 1 n- 1 n 1 7n-2

Horizontal force equilibrium for each slice Vertical force equilibrium for each slice Moment equilibrium for each slice Definition of local safety factor F (F=RIS. R shear strength at base of slice) Location of normal force N (middle of base) Relation between interslice forces X and E [X=;1f(x)q Location of interslice force

11- 1

Total number of equations

7n-2

n n n n n

n- 1

O.F.S. = Overall factor of safety 2 STATICALLY DETERMINANT SOLUTION

b,

= M,-, + 0

As the slope stability problem is highly indeterminate, some simplifying assumptions are necessary to make the problem determinate In the present analysis, the assumptions used in the Morgenstern-Price method (1965) and the Janbu method (1957) are employed simultaneously, namely one is the relations between shear force X and normal force E on the interslice faces, and the other is the acting points of normal force E i e the line of thrust. A typical slope, which is divided into n slices, is illustrated in Fig 1. The forces acting on a slice are also shown in this figure For such a slope, the numbers of unknowns and equations are summarized in Table 1 We can see clearly from Table 1 that the numbers of unknowns and equations are in corrspondence; namely, the problem becomes determinate. As for the detailed solution procedures, refer to our companion paper (Yamagami, Yamabe, Jiang & Khan, 1999). The basic equations from which the solutions can be obtained are as follows (see Fig. 2).

L

[ALf(x)- 41 E,-,L, + e x + -b,2

L, + Kzx

1,

where b,;x,-x, I and M,=E, (yt,-yJ,M, denotes a moment of E, about the rightmost point of the base of the z-th slice

(a) Potential sliding mass

(b) Forces acting on an infinitesimal slice Fig. 2 Diagram for formulation

Fig. 1 Forces acting on a slice 294

in Fig.3. If the L.Fs.S. lie below or equal unity at a portion of the slip surface, this means that local failure has occurred on that portion. Even under this situation, no sliding as a whole will take place along the slip surface unless the O.F.S. is smaller than unity. It is true, however, that as long as the soil mass above the slip surface is in equilibrium, the factor of safety should be equal to unity on the locally failed zone. The reason for this is that the shear forces become equal to the shear strengths on the failed zones. Then, is a result wrong in which L.Fs.S. are less than unity, e.g. those in Fig.3? The answer is of course not. In short, the method of analysis addressed so far has allowed values of L.F.S. below unity, while it meets all the equilibrium conditions for the entire sliding soil mass. This approach, as will be briefly discussed below, can be justified. Hereafter, we call this method AILC: Analysis of Instantaneous Loading Condition. In the meantime, it is also necessary to establish an approach in which once local failure takes place on some part of the slip surface during the solution process, the factor of safety for that part is kept at unity. Hereafter we call this type of analysis method AGLC: Analysis of Gradual Loading Condition, and will explain its details in the following section.

Slice number (b) Local factors of safety

Fig.3 Simple example problem

AGLC From Eq.[l] a value of El is determined with a known value of El-). Substituting this value into Eq.[2] yields an equation which contains F; as the only unknown, enabling us to solve for P', iteratively. Solving the two equations for each slice thus provides local safety factors as well as the location of the thrust line, interslice forces, and so forth. The result of an illustrative example is given here to demonstrate how the above procedure yields the solution Fig.3 (a) shows the configuration of a homogeneous slope, a given slip surface and division of slices. The soil parameters used are y=19.6kN/m3, cp=ci=2.56kPa, friction angle at peak strength $p = 27.6" and friction angle at post-peak residual strength $i= 23.4.6' ($1l$~=0.85). Fig.3 (b) illustrates the distribution of L.Fs.S. together with the overall factor of safety. It can be seen from Fig.3 (b) that a local failure zone where the L.Fs.S. are lower than unity appears though its overall factor of safety is 1.129. This indicates that local failures may have already occurred at some locations even if the slope is safe as a whole. Conventional single value factor of safety analyses do not represent this essential phenomenon.

In a stable slope, in which local failure has occurred at some location, shear stresses must be equal to shear strengths, i.e. the local factor of safety is inevitably equal to unity over the failed zone. An analysis method that satisfies this condition has been named as AGLC. In the following we propose an iterative procedure of the AGLC which starts with the solution of AJLC. The slices i to m in Fig.4 are assumed to have L.Fs.S. less than or equal to unity as the result of the AILC. In other words, let's suppose that the part poq. of a given slip surface AB has locally failed as the result of AlLC. Suppose also that the L.F.S. of slicej is the smallest of all the L.Fs.S.. In the schematic figure the locally failed slices occur continuously, but

3 DEFINITIONS OF AILC AND AGLC Fig.4 Schematic diagram illustrating a situation immediately after solution of kdLC has been obtained

The preceding procedure provides the L.Fs.S. distribution along a given slip surface just as can be seen 295

this is not a prerequisite. They may appear at discontinuous locations without loss of generality.

First step The iterative procedure starts with making the factor of safety for slicej that has a minimum factor of safety equal to unity. That is to say, computation is made of the AILC on condition that c=l.O. More specifically, starting with the first slice the procedure of AILC described before is performed, and when arriving at slicej, the factor of safety 6 is made equal to unity, followed by the subsequent procedure. It is essential that we treat the L.F.S. for slicej as known (l.O), whereas the rest of L.Fs.S. are all unknown. Nothing else is otherwise different from the original AILC. And when the last slice is reached, a check is made of the boundary condition (En=O)at the rightmost end; if the condition is not satisfied, the process is repeated until a converged solution (the first converged solution) is obtained.

Fig.5 Schematic diagram showing a situation in which the first converged solution has been attained at the end of the first step

Secorid Step Fig.5 shows schematically a situation in which the first converged solution has been attained. Assume that the slices above a part p q of the slip surface have failed as the result of the First Step. The part p q does not necessarily coincide with the initial failure zone poqcj(slices i-n) in Fig.4. There might have occurred discontinuous failure zones as well at this stage; however, causing no problems at all. Here, pay attention to the slice having the smallest factor of safety again, e.g. slice k. This time we conduct a similar computation of AILC on condition that fi;=l.O and Fk=l.O. Consequently, a new set of L.Fs.S. will be obtained as a converged solution. The third iteration is done in order to obtain the solution in which, beside the two slicesj and k, a third slice, e.g. slice I, retains a factor of safety of 1.0. Ob viously, slice I possessed a minimum factor of safety less than unity at the end of the second iteration process (see Fig.6). In this way, it is the AGLC method that renders each factor of safety equal to unity one by one for the slices in locally failed zones. The iteration processes are continued until no slices having factors of safety smaller than unity exist. Hence, all the L.Fs.S. are greater than or equal to unity when a solution for the AGLC is attained. We may encounter a case where a converged solution cannot be obtained even after all the L.Fs.S. have become equal to unity. This case suggests that the O.F.S. is less than unity and implies that complete failure will take place along the slip surface under consideration. The AGLC thus fails to provide the solution for this case; only the AULC may solve these types of problems.

Fig. 6 A schematic diagram illustrating the second converged situation

4 CASESTUDY

The Selset landslide (Skempton and Brown, 1961) is employed to show how the proposed method works. This landslide has been also solved by Law and Lumb ( I 978) with their progressive failure analysis method. Hence we omit showing the pre-slide slope profile here. Fig.7 illustrates the conditions employed for the analysis and the results obtained. As seen at each base of the slice in Fig 7(a), ru values are different from one slice to another. These values have been read fiom the original flow net profile, while the r,, value is a constant of 0.35 in Law and Lumb’s analysis. It is quite interesting as can be seen in Fig.7 that both AILC and AGLC have predicted almost the same 0. F. S., but the distributions of L. Fs. S. are totally different. The result of AGLC is, of course, physically much more reasonable. 5 CONCLUDING REMARKS Within the framework of the limit equilibrium approach, a progressive failure analysis method has 296

zone to be less than unity. In the AGLC method, however, they are kept at unity based on an iterative procedure starting with the solution of the AILC method. Physically, the AGLC method is rational, and indeed it has turned out through case studies that this method provides highly accurate solutions. The AGLC is, nevertheless, not available for a situation in which the overall factor of safety will fall bellow unity, i.e. complete failure is anticipated to occur. The AILC method still holds for the situation. It has also turned out that locations where local failures take place and overall factors of safety predicted by the AILC method approximately coincide with those from the AGLC method. The proposed method should be expanded in the hture in order that it may search for the critical slip surface that has the minimum overall factor of safety. With regard to this, a possible way is to use the AILC method in search of the location and shape of the critical slip surface. And then the AGLC is applied to the critical slip surface so as to obtain detailed solution. This is the subject for our fbture study.

(a) Thrust lines for AILC and AGLC for Selset slope

ACKNOWLEDGEMENT The authors would like to thank Dr. D. Leshchinsky, Professor of Delaware University, for his kind review and advice on the main parts of this paper.

(b) Local factors of safety f?om AILC and AGLC

Fig. 7 Selset slope failure NOTES: The main contents of this paper were presented at the Special Sino-Japanese Forum on Performance and Evaluation of Soil Slopes under Earthquakes and Rainstorms, June 28-29, 1998; Dalian, China.

been presented. This method, a variable local factor of safety analysis method, completely satisfies the equilibrium of forces and moments. Occurrence of local failure along a slip surface and its progress are recognized on the basis of the local factor of safety defined at the base of each slice. Softening can be simply handled through the use of local factors of safety. Furthermore, the overall factor of safety has been used to evaluate the overall stability of the sliding soil mass. Introduction of the local factors of safety resulted in an increase in the number of unknowns, thereby making the problems highly indeterminate. However, simple assumptions from the Morgenstern and Price method and the Janbu method could equalize the number of unknowns and that of equations or relationships available. In other words, the analysis has been rendered statically determinate. Two different treatments are developed for the local factors of safety after locally failed zones have occurred: the AILC and AGLC methods. The AILC method allows the local factors of safety of the failed

REFERENCES Bishop, A.W. 197 1. The influence of progressive failure on the choice of the method of stability analysis. Geotechnique. 21 (2). 168-172. Bjerrum; L. 1967. Progressive failure in slopes of overconsolidated plastic clay and clay shales. ASCE Journal of Soil Mechanics and Foundations. 93 (SM5). 3-49. Chang, C.S. 1992. Discrete element method for slope stability analysis. ASCE Journal of Geotechnical Engineering. 118 (12). 1889-1905. Chugh, A. K. 1986. Variable factor of safety in slope stability analysis. Geotechniqe. 36 (1). 57-64. Huang, A. B. & Ma, M. Y. 1992. Discontinuous deformation slope stability analyses. Proc. Sfahilify and Performance of Slopes and Bmhankments- D. 1. 479-492. danbu N. 1957. Earth pressures and bearing capacity calculations by generalized procedure of slices. Proc. 4th ICXMIX Lolldon 2. 207-2 12.

297

Law K. T. & Luiiib P. 1978. A limit equilibrium analysis of progressive failure in the stability of slopes. Canadian Geotechnical Jozirnal. 15. 113- 122. Lo K. Y. & Lee C. F. 1973. Analysis of progressive failure in clay slopes. Proc. 8th ICSMFE. Mockba. 1. 25 1258. Morgensteni N.R. & Price V. E. 1965. The analysis of the stability of general slip surfaces. Geofechnique 15 (1). 79-93, Potts D. M., Dounias G. T. & Vaughan P. R. 1990. Finite element analysis of progressive failure of Carsington embailluiieiit. Geotechnigue. 40 (1). 79- 101. Rowe P.W. 1991. A reassessment of the causes of the Carsington embankment failure. Geotechnigue. 41 (3). 395-42 1. Skeiiipton A. W. 1964. Long-term stability of clay slopes. Ceotechnigzie. 14 (2). 77-102. Srbulov M. M. 1995. A simple method for the analysis of stability of slopes in brittle soil. Soi1.s and Foundations. 35 (4). 123-127. Yaniagami, T., Yamabe, S. Jiang, J.-C., & Khan, Y. A. 1999. A promising approach for progressive failure analysis of reinforced slopes. Pi-oc. ofInt. Sym. on Slope Stability Engineering: Geotechnicnl and geoenvironmental Aspects ('s'-S'hikoki~'99), Yagi N.et al. Eds, Rotterdam: Balkema.

298

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Progressive failure analysis based on a method of non-vertical slices Takuo Yamagami & Jing-Cai Jiang Department of Civil Engineering, University c?f’ Tokushima, Japan

Younus Ahmed Khan Gracluare School of Engineering, Universify of Tokushima, Japan

ABSTRACT: An approach of progressive failure analysis of slope stability is proposed based on a method of non-vertical slices within the limit equilibrium framework. Variable factor of safety is defined along a shear surface and the local safety factors are calculated. Simplifjring assumptions about the inter-slice forces and their points of action made this method determinate. Force and moment equilibrium equations are derived from the equilibrium conditions and the Mohr-Coulomb failure envelope. The softening behaviors of the soil materials are also included in the method. To evaluate the ultimate stability of a slope an overall factor of safety is introduced. The method is presented with two case studies safety for the entire failure surface; i.e. the factor of safety is the same for all locations along the shear surface. However, in an actual slope stress or strain levels vary along any slip surface, and the nonuniform distributions of either stress or strain level inevitably cause local failures along the surface. Therefore the single value factor of safety is unable to define these failure surfaces. So, the local factors of safety have to be introduced to express this nonuniform distribution of local stress levels during progressive failure within the limit equilibrium framework. Finite Element Method (e.g. Lo and Lee, 1973; Potts, et. al., 1990; Rowel, 1991), Discrete Element Method (Chang, 1992) and Discontinuous Deformation Analysis (Huang and Ma, 1992) are all effective methods of progressive failure analysis. But due to the complicated nature and large computation procedures, these methods have not widely been used so far. There are number of limit equilibrium methods considering progressive failure, for example, Law and Lumb (1978), Chugh (1986), Srbulov (1995), Yamagami and Taki (1997). However, these methods are not so satisfactory except, that of Yamagami and Taki (1997). Yamagami and Taki have satisfied all equilibrium conditions in their method satisfactorily to make the problem deterministic. In an accompanying paper, two different techniques called AILC (Analysis of Instantaneous Loading Condition) and AGLC (Analysis of Gradual Loading Condition) are devised to deal with the local factor of safety in the locally failed zone (Yamagami, Taki, Jiang & Yamabe, 1999). Furthermore, an approach

1 INTRODUCTION A limit equilibrium method of non-vertical slices for slope stability analysis considering progressive failure is developed. In this method, variable factor of safety is defined along a shear surface to represent the nature of progressive failure. The required assumptions are made in order to get the solution of the method. The equilibrium equations are derived using the static equilibrium of non-vertical slices and MohrCoulomb failure criterion. There are many instances, where local yielding or failure initiated at some points along the shear surface develops which finally leads to the failure of the slope as a whole. This process is called as progressive failure (e.g. Skempton, 1964; Bjerrum, 1967; Bishop, 197 1). In geotechnical engineering practice, slope stability analysis of artificial and natural slopes is usually performed by the limit equilibrium method. In limit equilibrium analysis certain assumptions are made to solve the problems using static equilibrium and failure equations. The commonly used procedures are those of Bishop (1955), Morgenstern and Price (1965), Spencer (1967), Sarma (1973) and Janbu (1973). These conventional limit equilibrium methods are generally regarded as best available for stability analysis, but they will not result in the true progressive failure mechanism. A complete method should satisfjr force and moment equilibrium. Multiple wedge methods have proved capable of satisfjring all these needs and the approach of Sarma (1979) is widely accepted. All these methods assume a single value factor of 299

for progressive failure analysis of reinforced slopes with vertical slice have been developed and presented in a companion paper (Yamagami, Yamabe, Jiang & Khan, 1999). All of these methods of progressive failure analysis are based on the vertical slices. Therefore, progressive failure analysis using nonvertical slice needs to be considered. This paper presents a simple limit equilibrium method of progressive failure analysis using nonvertical slices. Here, the analysis is based on the AILC (Yamagami, Taki, Jiang & Yamabe, 1999) technique where, the local factors of safety are allowed to be less than unity in stable slope. 2 METHOD OF ANALYSIS

2 1 Necessary ussirmptrons In this method, the body of mass contained within the assumed slip surface and the ground surface is divided into n non-vertical slices (Fig 1) Now, we have the following 7n-3 unknowns n number of the normal force N, n number of the shear force T, n-1 number of the inter-slice force E, n-1 number of interslice force X,n- 1 number of the points of application of the E forces given by Z , n number of the points of application of the N forces and n number of the local factors of safety I; On the other hand, we have the following 4n number of equations n number of horizontal force equilibrium equations, n number of vertical force equilibrium equations, n number of moment equilibrium equations and n number of Mohr-Coulomb failure criterion equations for each slice In order to get the solution of the proposed method, the number of required assumptions are 3n3 We assume 17-1 acting points of E forces and another ii acting points of N forces at the middle of the slope base Another n-1 assumptions are made about the relationship between X and E forces, i e X= A. f(x)E This type of relationship is considered here to introduce one extra unknown, A. to equalize the unknowns to the number of equations as proposed by Morgenstern & Price (1965) in their method Therefore, the actual number of assumptions is reduced to 3n-2

Figure 1. (A) Division of non-vertical slices and (B) forces acting on an inclined slice. where, c; , 4 i are the strength parameters li is the length of the slice base Ni & ui are the total normal force.and pore pressure acting on the base of the slice and Fi is the safety factor of the slice Resolving the forces vertically and horizontally we have, 7,’sin a, + N, cos a, = - El+1 sin 6,+, + X,+ I cos6,r, +E, sin 6, - X i cos.6, (2) T c o s a , - N I sina, =KIT+ E,-, cos6,+,+ X i , ,sin6,+,

-E, cos 6,- X,sin 6

(3)

From equations (1) & (2),we get, 2.2 Resolving eyiruiions

Considering a failure surface as shown in Figure 1, the mass contained within the slip surface and the free ground surface is divided into n non-vertical slices. Since we define a local factor of safety (I;,) at the base of each slice, we get the following expression from the Mohr-Coulomb equation:

By combining the equations (2), (3) and (4) for eliminating T, and NI,we have,

I?,+,A1 = E , A2 + Xi+,A3 - XIA4 + A5- A6 300

(9

where,

A1 = m, sinS,,, +m,cosS,,, A2 = m, sin 6, + m,COSS, A3 = m, COSS,,, - m,sin 6,+, A4 = m, COSS, - m,sin 6,

A5 = (m,sina, -m,cosa,) 14~1,tan @,

c,b,

+ ym,

A6 = K,W;m,

m,= mz =

s i n a , tan@,

I;;

+ cos a,

cosa, tan@,

E

- sin a ,

Wi= weight of the slice Ki = horizontal Earthquake acceleration b; = horizontal length of the slice base 6i & & + I are the inclinations of slice interfaces with y-axis ai= angle between the slice base and x-axis. Therefore, we obtain a recurrence equation (6) of inter-slice forces. 1 A1

E,,, =-[EiA2+X,,,A3-XlA4+A5-A6]

where, (xgi, ygi) is the center of gravity of the slice and d, is assumed to be half of the base length (I,). Z,+] andf(x) must be optimized in the present analysis (Yamagami, et. al. 1999) A value for E,+,is determined from equations (6) and (7) with a known value of E,. Substituting this E,+,value into equation (9) yields an equation which contains F, as the only unknown. By solving the equation (lO), with for example the Secant method, the moment equilibrium for individual slice is satisfied and the value of <(i = 1 . . . r?) in sequence can be obtained. The complete solution must satis@ the boundary condition, E,,+,= 0. 2.3 Cnlculatiori procedures

For any slope, the above mentioned equations are applicable to find a solution for safety factor calculation. The calculation procedures for a slope, which is divided into n non-vertical slices numbering 1 to n from left to right, are as follows:

(6)

Step I: 1. Assume A. = A. 1 & A.2 for Secant method 2. Start with A.1 Step 11: 1. i=l, setting Ei and Xi to zero 2. Assume two initial F values, Fit and Fi2 for Secant method 3. Start with FI1 4. Calculate E,+1and X1+lfrom equations (6) & (7) 5 . Find N, value from equation (4) 6 . Find moment value M,,[Al, F,,] from equation (9) 7. Putting another initial F (=F12)value and recalculate M1,[~1,Fi,1 8. Find F,.,,, from the Secant method as,

To solve this equation, we assume, as mentioned before, the relation between normal force E and shear force X, which is similar to that of Morgenstern-Price method.

where, A is an unknown parameter, and .f(x)is a known hnction. Considering moment equilibrium(M, = 0) about the left corner-point, C (xb;, ybi) of the base of the slice, we obtain,

<,I- E,Mr,(AL E,) c-,,,,= 6Mi,(A1, M,, (A4 e,)- M,,(AI,
If (F,-ne~\..~-F,-ne~\)>tolerance, then recalculate M,[A,F,]with this F,.,,, and find next F,-,,, until (F1-nea-l-FI-nea )< tolerance, is satisfied SO, F, = Fi.,,,, if (Fi-nem-1-F1-nas)< tolerance Here, F,-new-l is the immediately previous value of F,-,,, and tolerance is1 O'6 9. Calculating the processes from 2 to 8 of step-11,

Now putting the value of Xi.] from equation (7) into equation (8), we have the following equation of moment equilibrium:

301

The local factors of safety are calculated using the calculation procedures discussed in the previous section. If slices whose F<1 emerge, the peak strength of such slices is then replaced by the residual strength. The calculation is continued until the peak strength of all the slices with F<1, are replaced with residual strength.

for n numbers of slices we find the values of F1, FZ,F3, . . . . F,. Now, check the boundary condi=O; usually En+lf 0. tion, 10. Recalculate the processes from 1 to 9 of step11, with A.=A.& and we will get another set of F values. 11. Then, reiterate the processes from 1 to 10 of step-I1 with A..,value until the boundary condition =0) is satisfied. A value is found from the Secant method as follows,

2.5 Optimization of f(x) and Z if ( A. new-l - A. new)
In the Morgenstern-Price method, f(x) is taken as an arbitrary function, for example, a constant (e.g. 1) or half sine and so on. In the Janbu method, Z is assumed usually to be 1/3 of the slice height. However, many studies have indicated that f(x) and 2 in this method must be optimized to obtain a complete converged solution. The boundary condition can be reached by optimizing the following equation:

I'Il+l

2.4 Considering softening The softening can not be defined with the amount of deformation or strain in the limit equilibrium analysis. In this study, it is assumed that the soil resistance will drop abruptly to the final residual value (as Law and Lamb, 1978) immediately after reaching the peak value (Fig. 2). Peak ,strength (Rp) and Residual-strength (Rr) are expressed as,

Rp = c ' , l + N t a n @ ,

1'

= F2m[a>f(x, 1,

-+

f (',),

"'>

f

('n)7

1'

> 2'

minimize(= 0)

7

"'

1

> z~l

(13 )

The Nelder-Mead simplex method for non-linear programming is applied to solve the equation (1 3). 2.6 Overall safety factor

For evaluating the safety factor of the slope as a whole, we define the overall safety factor, Fc,,.era,lby the ratio between the sum of the mobilized shear forces (T, and TP) and the sum of the available shear strengths along the entire slip surface. Therefore,

Rr = clr I + N tan @ r

where, m is the number of slices with residual strength among the total slices (n). 3 EXAMPLE SOLUTIONS

Here, we present solutions of the two illustrative examples. Figure 2. Schematic diagram of softening. (after Law & Lumb, 1978) The softening processes are included by the following iterative procedures: a. At the beginning, every slice is assigned with the peak strength.

3.1 Example I :Simple homogeneoirs slope

Figure 3 illustrates the geometry and strength properties of a slope problem with no pore pressure. The slip surface for this case is non-circular. Yamagami & Taki (1997) solved this problem considering progressive failure with vertical slices. The solutions including no softening as well as softening process are presented. Figure 3b shows the 302

Figure 4. Solution of Selset landslide (example 2) distributions of local factors of safety along the slip surface. The Morgenstern & Price method provided a single value factor of safety of 1.20 for the case of no softening, where the proposed method showed an overall factor of safety of 1.25. To demonstrate the effects of the softening behavior of the soil, we consider several cases with residual strengths (Figs.3~& 3d). For these cases, we find the overall factor of safety gradually decreases with strength. 3.2 Example 2 :Selset Landslide This is a failed valley slope of the River Lune, near Middleton-in-Teesdale in Yorkshire, which is analyzed by Skempton & Brown (1961). A number of researchers have analyzed this slip surface for example, Law & Lumb (1978) and Chang (1992). Figure 4 depicts this slide with the calculated results. For this case the slip surface is circular. In the present approach, the calculated overall factor of safety is 0.98. We used the strength parameters, c=8.6 kPa & $=32.0° and unit weight of the material(y) =21.8 kN/m3. Here, we find that the local safety factors of about two-third of the slip surface are below unity.

Figure 3. Solution of a simple homogeneous slope (example 1)

303

4 CONCLUSIONS

A method of progressive failure analysis considering non-vertical slices within the limit equilibrium approach has been proposed. This method hlly satisfied the force and moment equilibrium conditions. The method became statically determinate with the inclusion of simple assumptions from the Morgenstern & Price method and Janbu method. By defining the local factors of safety, local failures along a slip surface and softening behavior of the soil materials have been taken into account. The locally failed zone has been treated with the AILC technique. The overall factor of safety judged the safety factor of the slope as a whole. Finally, the method provided acceptable solutions of the two example problems. This method should be treated with AGLC technique for locally failed zones of the slope. Moreover, it might be extended for the slopes with reinforcing elements. So our hture research is aimed to these possibilities.

der clay at Selsct, Yorkshire. Geotechnique, 11:4:280293. Srbulov: M.M. 1987. Limit equilibrium method with local factors of safety for slope stability. Canadian Geot. J.. 24:652-656. Yamaganii, T. and Taki, M. 1997. Limit equilibrium slope stability analysis considering progressive failure. Proc. Intl. Symposizim on Deformation and Progressive IG+htre in Geomechanics (edited by Asaoka, A. and et.al), Nagoya, Japan, 7 19-724. Yamagami, T., Yamabe, S., Jiang, J.-C. & Khan, Y. A. 1999. A promising approach for progressive failure analysis of reinforced slopes. Proc. of Inter. Svmp. on Slope Stability Engineering: Geotechnical and Geo-environmental Aspects (IS'-Sliikokzr '99), Yogi, N. et. al. eds., Rot terdam, Balkem a. Yamagami, T. Taki, M., Jiang, J.-C. & Yamabe, S. 1999. Progressive failure analysis of Slopes Based on a LEM. Proc. of Inter. Symp. on Slope Stability Engineering: Geotechnical and Geo-environmental Aspects (ISShikoku '99). Yogi, N.et. al. e h . , Rotterdam, Balkema..

REFERENCES Bishop, A.W. 1955. The use of slip circle in the stability analysis of earth slopes. Geotechnique, 5: 1:7- 17. Bishop, A.W. 1967. Progressive failure-with special reference to the mechanism causing it. Panel discussion. Proc. Geotech. COTIFO~l0,2:142-150. Bishop, A.W. 1971. The influence of progressive failure 011 the choice of the method of stability analysis. Geotechniqzte, 21:2:186-172. Bjerrum, L. 1967. Progressive failure in slo es of overconsolidated plastic clay and clay shales. 3"Terzaghi Lecture, .J. Soil Mech. Found. Div., ASCE, 93:SM5:3-49. Chang. C.S. 1992. Discrete element method for slope stability analysis J. Geot. Eng. Div., ASCE, 118:12:1889-1905. Chugh, A.K. 1986. Variable factor of safety in slope stability analysis. Geotechnique,36: 1:57-64. Janbu, N. 1954. Application of composite slip surfaces for stability analysis. Proc. European Con$ On Stability of Earth Slopes, Stockholm,3 :43-49. Janbu, N. 1954. Stability analysis of slopes with dimensionless parameters. Hanrard Soil Mechanics Series, No.46. Law, K.T. and Lumb, P. 1978. A limit equilibrium analysis of progressive failure in the stability of slopes. Canadian Geot. .I., 15:113-122 Lo, K.Y. and Lee, C.F. 1973. Analysis of progressive failure in clay slopes. Proc. gfh.ICSMFE, Mokba, 1.1:251-258. Morgenstern, N.R. and Price, V.E. 1965. The analysis of the stability of general slip surfaces. Geotechnique, 15:1:7993. Potts, D.M., Dounias, G.T. and Vauglian, P.R. 1990. Finite element analysis of progressive failure of Carsington embankment. Geotechnique,40: 1:79-101. Sarma, S.K. 1979. Stability analysis of embankments and slopes. J. Geot. Eng. Div., A X E , 105:GT12:1511-1524. Sarma, S.K. 1973. Stabilty analysis of embankments and slopes. Geotechnique, 23:3 :423-433. Skempton, A.W. 1964. Long term stability of clay slopes. 4h Rankine Lecture, Geotechnique, 14:2:77-102. Skempton, A.W. and Brown, J.D. 1961. A landslide in boul-

304

Back analysis of unsaturated shear strength from a circular slope failure Jing-Cai Jiang & Takuo Yamagami Depurmient of Civil Engineering, Uni\wsitv of Takwhimu, Jupatz

Yasuhiro Ueta HLInshin Consultunts Comnpuny Lini ited, Osuki, J u p n

ABSTRACT: A back analysis method is described to determine three unsaturated strength parameters (c’, 4’, 4”) in Fredlund’s failure criterion. This method is based on two essential conditions which take full advantage of the information provided by a slope failure in a unsaturated zone. A back calculation procedure is constructed by combining these two conditions with the Bishop factor of safety equation with Fredlund‘s failure criterion. Application of the proposed method to a hypothetical slope failure illustrates that a unique and reliable solution of (c’, bb) can be back calculated quickly. The back analysis method proposed has the potential to determine the magnitude of (c’, 4”) from an actual slope failure as long as the suction distribution along the slip surface at failure is known. internal friction, 4 - angle of internal fi-iction associated with suction of soil, U , - pore air pressure, U , pore water pressure, (on-u.) - net normal stress state variable on a failure surface at failure, (U,-U,) - matric suction on the failure surface at failure. Eq.[l] can easily be combined with the conventional limit equilibrium methods to carry out stability analyses for unsaturated slopes. The unsaturated strength parameters (c’, $b) in Eq.[l] are usually determined by triaxial compression tests and/or modified direct shear tests (e.g., Gan et al., 1988; Tadepalli, Rahardjo & Fredlund, 1992; Abramento & Carvalho, 1989; Vanapalli et al., 1996). However, laboratory testing is not a practical method as it requires costly laboratory equipment, expert test techniques and long test times. In addition, the difficulties in undisturbed soil sampling from an unsaturated soil also greatly limit applications of laboratory testing. Back analysis is an effective tool for obtaining shear strength parameters for design of landslide control works because it avoids many of the problems associated with laboratory tests. However, all existing back analysis techniques to determine strength parameters are only available for slope failures under saturated conditions. Some being used to back calculate both c and $) (e.g. Nyugen, 1984; Yamagami & Ueta, 1986, 1992) and others being used to estimate the magnitude of 4 only by assuming a value of c or vice versa. The objective of this paper is to present an effective and quick method for determining the unsaturated strength parameters from a slope failure. The basic idea of this method is based on two fundamental

1 INTRODUCTION

In engineering practice, it is often encountered that the groundwater table in a slope is deep and/or only a shallow slope failure is possible due to particular geological and geographical conditions (for example, a slope overlying a relatively shallow strong layer of soil or rock). In such cases, when slope failures occur slip surfaces will be located in an unsaturated zone. Therefore, it is necessary to consider the effect of unsaturation of soil on slope stability. In other words, an unsaturated strength criterion, instead of the Mohr-Coulomb model for saturated conditions, should be adopted in order to evaluate reasonably the stability of slopes in unsaturated zones. An effective failure criterion for unsaturated soil (Fredlund, 1979) is expressed as (see Fig. 1).

where c’ - effective cohesion,

4’- effective angle of

Fig. 1 Failure criterion for unsaturated soil 305

conditions (Yamagami & Ueta, 1986, 1992), which take full advantage of the information provided by a slope failure. The back calculation procedure for (c', b', $b) is described in detail by applying these two conditions to the Bishop safety factor equation with Eq.[11. Finally, an illustrative example problem is presented to demonstrate the effectiveness of the back analysis method. 2 BASIC IDEA OF BACK ANALYSIS

2 1 7ivo Essential Conditionsfor Back Analysis

Two essential conditions suggested for back analysis of strength parameters (Yamagami and Ueta, 1986, 1992) are presented here for the sake of completeness Since the aim of this paper is to develop a simple and quick back analysis method for the unsaturated strength parameters, we assume the slope in question to be homogeneous in strength In other words, c', 4' and +'' are back calculated as an average of the strength parameters along a failure surface The Bishop method for unsaturated conditions is employed in this paper and the factor of safety equation is written as follows (Fredlund, 1987)

>- =

hrd + W tan@+ ( U ,

-

u,,)d tan@b}/ma

Y'Wsina

[21

where m,=cosa+sinatan$'/F, W is the weight of a slice, d=Icosa is the width of the slice ( I is the length of the slice base), and a is the inclination of the slice base to the horizontal. Back analysis of strength parameters is carried out based on a known or assumed failure surface within a slope. As an actual failure surface reflects the most critical conditions, its factor of safety should be the smallest of all admissible slip surfaces in the vicinity of the failure surface. That is to say, a solution (c'o, tan$'o, to be back analyzed should make the factor of safety of the failure surface minimum. The value of the factor of safety of a failure surface is usually taken to be F p l . 0 . Substituting the known value ofF=Fo (=1 .O)into Eq.[2], we have -u,,)dta~~+~) F, C W sin a c {crd+Wtanbr+(u, mcr

some point on the relation surface. In Fig.2, maximum values of the strength parameters, crmax,tan$',,, and tan$',,,, limit ranges of variation of c', tan$' and tan$'. In other words, a solution (c'o, tan4'0, tan+") to be back analyzed should meet the inequalities of O
=

c31

where W, d, and m, are evaluated from the information of the failure surface. Eq. [3] indicates the relationship between c', tan$' and tan$b, representing a 3-D surface, egf in c'-tan$'tan$b space, as shown in Fig.2. This surface will be called the "relation surface" hereafter. Note that the c'-tan$b relationship is linear when tan+' in Eq.[3] keeps unchanged (constant). The required strength parameters satisfying Eq.[3] is corresponding to

As Eq. [4b] is implicit in tan$',,, an iterative procedure, e.g. the Newton-Raphson method, is necessary to obtain a solution of tan$',,, . To summarize the above descriptions, the two essential conditions for back calculation of the strength parameters are yielded: I). Strength parameters to be identified must satisfy the relation surface shown in Fig.2, i.e. the crtan$'-tan$b relationship of Eq.(3); 11). Strength parameters to be identified must satisfy that the factor of safety of the failure surface is the minimum among any admissible slip surfaces close to the failure surface. These two conditions take full advantage of the information provided by a slope failure, and are essential for any back analysis procedure of strength parameters. Based on the above two conditions, we will first show that when a parameter among (c', $b) is given through experimental or empirical means, the other two strength parameters can be determined by Yamagami and Ueta's back analysis (1986) of c and 4 for saturated conditions. Then, a procedure, which is able to back calculate three unsaturated strength parameters simultaneously, is presented. $I,

306

2.2 Application of Yamagamiand Ueta s method In this section, a similar method to that proposed by Yamagami and Ueta (1986) is applied to dealing with back calculation problems where one of (c’, $I, $b) is given. Since one parameter is known, say =$I0 is assumed to be known here for convenience. As the Bishop method is employed, a circular failure surface is illustrated in Fig.3. In order to explain the back analysis procedure, a number of trial slip circles are also chosen in the vicinity of the failure surface (Fig.3). For computational convenience, all trial slip circles are constrained to pass through the two ends A and B of the failure surface. Substituting $‘=$‘ointo Eq. [3] and re-arranging the terms of the equation, we have $I

t:c’d +

( U , - u,,)d

tan bb =

w(hosin a

tm4i) [5]

--

ma

ma

This equation indicates the relationship between c‘ and tan$b, which can be represented by a straight line PQ on the relation surface, as shown in Fig.2. In the present case, the condition I) means that strength parameters (c’o, tan$”) to be identified must satisfy the c‘-tan$b relationship shown in Eq. [5]; corresponding to a point on the line PQ in Fig.2. Next, we consider the condition 11) which requires that the factors of safety, F,, of trial slip surfaces should be greater than Fo, i.e. F, 2 F,

For any trial slip surface, the factor of safety, F,, may be expressed as:

Y

where the overlined symbols indicate that they are evaluated from the trial slip surface in question.

Fig.4 Restriction of ranges of variation of (c‘, tan$”) It is of interest to note that the factor of safety, F,, in Eq.[7] is considered to be a knction rather than a constant in the present analysis, varying with the parameters c’ and tan$b. Application of the Yamagami and Ueta back analysis (1986) has shown that when (c’, tan$b) change along the line PQ in Fig.2, the F,-c‘ and relationships for a trial slip circle above the failure surface (such as AO’B in Fig.3) can be illustrated by a curve a1a2in Fig.4 (a) and by a curve dldz in Fig.4 (b), respectively. On the other hand, the F,-c’ and relationships for a trial slip circle below the failure surface (such as A0‘’B in Fig.3) can be represented by a curve blb2 and a curve ele2, respectively (Fig.4). From Fig.4 we can see that satisfaction of the condition 11) signifies that values of c’ and tan$b cannot be beyond the ranges AB and DE, respectively. In other words, the required c’o and tan$bo should satisfy the follow inequalities (see Fig.4). c; d c ’ o 5 c;/ tan$bIStan$bo 5 tan+bn

P I P I

Eqs.[8a] and [Sb] indicate that application of the two essential conditions to a pair of trial slip surfaces resulted in reduction of possible range of the required c’ and tan$b. It has been shown that when the above procedure is performed with respect to an appropriate number of pairs of trial slip circles close to the failure surface, the range of variation of c‘ and tan$h can be restricted to an extremely narrow zone in

Fig.3 Circular failure surface and trial slip circles 307

which a required solution of (c', tan$b) exists. 2.3 An efficient and Aysternatic back analysis procedure Similarly to the method by Yamagami and Ueta (1986), the back analysis procedure described in Section 2.2 can be performed more efficiently and systematically by applying the following calculations. 1) An appropriate number (n) of trial slip circles are separately chosen above and below the failure surface (but in the vicinity of it). Their radii are denoted by ri and ri* (i=l, 2, ..., n), respectively (see Fig. 3 in which only two trial circles on each side are shown for simplicity). 2) Values of c;~.,. and tan$',,,,,, are calculated respectively using Eqs.[4a] and [4c] on the basis of the failure surface information. Note that $' =$I0 is assumed to be known in the present case. 3 ) The range of O-C',,,,~ is divided into (m)equal parts, and the value of c' at a dividing point is represented by c', ('j=l, 2, ..., m+l) where c'l=O and c;+, =c ',a.r. 4) Substituting c' = c', into Eq.[3], values of tan$';. (j=l, 2, ..., m+l) corresponding to c; are calculated. The pairs of (c;, tan$'j) so calculated certainly meet the condition I), i.e. Eq.[3]. 5) Using the above (c;, tan$'j), j=l, 2, ..., m+l, computations of Ft by Eq.[8] are carried out for each trial slip surface, and the results are recorded. 6) For the trial slip surface with the radius r1, a value c ' ~of c' at the point of intersection of the Ft-c' curve with the line of Ft=Fois obtained from the results in step 5 ) (see Fig.5). Also, a value (tan$")l of tan$' at the point of intersection of &tan$' curve with the line of Ft =Fois determined in the same way. The above procedure is repeated for each trial slip surface. 7) Accor$ng to the obtained values of c'i (C*'i), tan$'; (tan$' ;) associated with r,(r*,)(i=1,2,, . . ,n), r-cr and r-tan$" relationships can be drawn schematically (Fig.6). The point of intersection of the r-cr curve with the line of r=ro (radius of the failure circle) corresponds to a required solution of c'. And the point of intersection of the r-tan$" curve with the line of r=ro yields a solution of tan$', as illustrated in Fig.6.

Fig. 6 An efficient and systematic procedure It has been shown that when c' or tan$' is given as a known value, similar back calculations can be constructed to determine (tan$', tan$') or (c',tan$'). 2.4 Verification An illustrative example problem is presented here to verifl the effectiveness of the back analysis procedure described in section 2.3. The example has a configuration with a height of 5.Om, an inclination of 1:2 and a lower groundwater table, as shown in Fig.7. The distribution of suction is assumed to be (ua-u,)=4.9H (kPa), in which H (m) denotes the height from the groundwater table. In order to obtain a failure surface, a search using the soil parameters of ct=4.9kPa, $'=loo, $'=6' and y=17.64 kN/m3 has been carried out by combining Eq.[2] with the conventional repeated trials. The obtained critical circle and the corresponding minimum factor of safety are also shown in Fig.7. By assigning a known value to one of (c', $', $'), the other two parameters are back calculated according to the information shown in Fig.7. When $'= $'o=lO' is given, the results of (c1=4.91kPa, $'= 6.24') are obtained by the efficient and systematic procedure (see Fig.8). In addition, 10.1', $b= 6.03') and (c'=5.0 kPa, $'= 9.85') are back calculated respectively by giving c'=c'0=4.9kPa and $b= $'o= 6.0'. It can be seen from these results that in each case the back calculated strength parameters agree with the assumed values quite well. Stability analyses for the slope shown in Fig.7 are performed using the back calculated strength parameters. As a result, the critical slip surfaces and the associated minimum factors of safety obtained from the above three situations are almost the same as those shown in Fig.7. ($I=

3. BACK ANALYSIS PROCEDURE FOR DE-

TERMINING(c', Fig.5 points of intersection of the Ft-c' curve with the line of Ft =Fo

4', 4')

It has been indicated that when one of the three parameters c', $' and $' is given as a known value, a similar back analysis to the Yamagami and Ueta 308

Fig.7 Critical slip surface of a hypothetical slope (H: vertical distance from the water table)

Fig. 8 Back calculation results based on T-c' and r-tan$b relationships ($'=$'0=1Oo) method (1986) can be applied to determining the other two strength parameters uniquely. Based on this fact, a procedure is presented here to back calculate three unsaturated strength parameters simultaneously where the following condition is used:

number of equal parts (tan$;, j=1, 2, . . .m)where tan$'l=O and tan$k+l=tan$lmax. 3)Regard each value of tan$; to be a solution of tan$', i.e. tan$'o = tan$;, and back calculate (c), tan$") by the procedure described in the previous sections. Eliminate back calculated values of (c', tan$b) which are beyond O - C ' ~ , and 0- tan$b,,,. 4) Search for the critical slip surfaces and the minimum factors of safety using each group of (c), tan$:, tan$") obtained in 3). 5 ) Take such values of (c), tanb;, tan$bj) as a required solution which give the critical slip surface that is most close to the failure sudace. While the above procedure is described in terms of tan$', similar back calculations can also be carried out in terms of c' and tan$b separately. If the range of 0-tan$',, is divided sufficiently small, the above-mentioned back calculation procedure can result in a sufficiently accurate solution of strength parameters. However, such computations require long computer time. An optimization approach is constructed to enhance the efficiency of back calculations. In order to explain the approach, a value of tan$' is chosen between 0 and tan+',,, first, and then c' and tan$b can be back calculated by giving tan$'o = tan$'. Usually, three parameters (c', tan$', tan$b) so obtained are not a required solution. Therefore, the critical slip surface located using these parameters differs from the failure surface. It is obvious that the magnitude of difference between the locations of the critical slip surface and the failure surface depends upon the chosen value of tan$'. In other words, difference between critical slip surface and the failure surface can be regarded to be a fknction of tan$'. In searching for critical slip surfaces, it is convenient to constrain them to pass through the two ends A and B of the failure circle (Fig.9). Thus, the difference between a critical slip surface and the failure circle can be represented by the distance DR (Fig.9) between their centers. DR varies with tan$', being a hnction of tan$'. The minimum value of DR, DRmm (=O), corresponds to a required solution of unsatu-

Required strength parameters (c'o, $'o, 4'0) should satisfy that the critical slip surface searched by do, and $"o must be identical with the failure surface, and the associated minimum factor of safety must be equal to FO(=1 .O). $Io

By considering the above condition, the back calculation procedure for determining (c', $', +b) is described as follows. 1) Calculate values of,,, 'c tan$',,, and tan$bma,using Eqs.[4a]-[4c] on the basis of the failure surface information. 2) Divide the range of 0-tan$',,, into an appropriate

Fig.9 Optimization problem for back analysis 309

rated strength parameters. The golden section method is employed to solve the above optimization problem. Details of this are described in the following. A value of tan$',,, is calculated, then 6m=O and 6, =tan$'maxare denoted. The following two values of tan$' are calculated by the golden section method: 61=6,+0.382 (6nSm), and 62=6,+0.618 (6n-6m). (c'l, tan$"') and (~'2,tan$'J are back calculated by giving tan$'o = 61 and tan$'o = 62, respectively. Two circular critical slip surfaces are located using the obtained (~'1, 61, tan$") and (c'z, 62, Then, DRI and DRz, differences between the two critical slip surfaces and the failure circle, are obtained. If DRl DRz, assume 6,=61 and 6, =6n; and if DRI =D&, assume 6,=61 and 6, =62. Repeat steps from 2) to 5 ) until the difference between 61 and 62 does not exceed a prescribed tolerance. The average value, 6 (tan$'), of the final 61 and 62, and the corresponding c' and tan$" are taken as a required solution of the three strength parameters. Of course, the above solution procedure can also be performed in terms of c' or tan$". 4. EXAMPLE PROBLEM

Based on the critical slip surface, the minimum factor of safety and the distribution of suction shown in Fig. 7, three unsaturated strength parameters are back calculated by the back analysis method described in the preceding section. The results obtained from the procedures in terms of c', $' and $" are summarized in Table 1. Their average values and the correct solution of (c', $', $") are also shown in this Table. It can be seen from Table 1 that in all cases the back calculated values of (c', 4") are in good agreement with the assumed parameters (correct values). This indicates that the proposed back analysis procedure can provide sufficiently accurate results of unsaturated strength parameters. $I,

5. S U M A R Y A back analysis method for determining the unsaturated strength parameters (c', 4') in Fredlund's failure criterion, has been presented. This method is based on the two simple and rigorous conditions which take full advantages of the information provided by a slope failure. It is an extension of Yamagami and Ueta's (1986, 1992) back analysis of (c, $) for slope failures in saturated conditions. The back analysis procedure for (c', $', 4") was suggested by applying the two essential conditions to $I,

310

Table 1 Back calculation results Cases in terms of $'

1 correct solution I

5.0

I

10.0"

1

6.0"

I

the Bishop factor of safety for unsaturated conditions. Application of the proposed method to a hypothetical back analysis problem indicates that the back calculated strength parameters agree well with the correct values of (c',$I, 4'). Future research planned is to carry out laboratory failure tests for model slopes to further verifL the accuracy of the back analysis method. In addition, the same idea will be combined with factor of safety equations for noncircular slip surfaces for back calculation of unsaturated strength parameters. REFERENCES Abramento, M., & Carvalho, C. S., 1989. Geotechnical parameters for the study of natural slopes instabilizatioii at 'Serra do Mar'. Proc. the 12th Int. Con$ on Soil Mechanics and Foundation Engineering, Rio de Janeiro, 3. 15991602. Fredlund, D. G. 1979. Second Canadian Geotechnical Colloquium: Appropriate concepts and technology for unsaturated soils. Canadian Geotechnical Journa, 16. 121-139. Fredlund, D. G. 1987. Slope Stability Analysis Incorporating the Effect of Soil Suction, Slope Stability (Ed. by M.G. Anderson and K.S. Richards), John Wiley & Sons, Ltd., 113-144. Gan, J. K. M., and Fredlund, D. G., and Rahardjo, H. 1988. Determination of the shear strength parameters of an unsaturated soil using the direct shear test. Canadian Geotechnical Journal. 25. 500-5 10. Nguyen, V. U. 1984. Back calculations of slope failure failures by the secant method. Geotechnique. 34(3). 423-427. Tadepalli, R., H. Rahardjo, and Fredlund, D. G. 1992. Measurements of matric suction and volume changes during inundation of collapsible soil. Geotechnical Testing Journal, GZJODJ. 15 (2). 115-122. Vanapalli, S. K.; Fredlund, D. G. Pufahl, D. E. and Clifton. A. W. 1996. Model for the prediction of shear strength with respect to soil suction. Canadian Geotechnical Journal. 33. 379-392. Yamaganii, T. & Ueta, Y . 1986. Back analysis of average strength parameters for critical slip surfaces. Proc. Int. Symp. on Computer and Physical Modelling in Geotechnical Engineering (A. A. Balkema). Bangkok, 53-67. Yamagami, T. & Ueta, Y. 1992. Back analysis of strength parameters for landslide control works. Proc. 6th International Symposium on Lanhlides (A. A. Balkema). ChristChUrCh. 1. 619-624.

Slope Stability Engineering, Yagi, Yarnagarni & Jiang 0 1999 Balkerna, Rotterdam, ISBN 90 5809 079 5

A back analysis of MC-DP model parameters based on FEM and NLSSQP method T.Q. Feng Sun Brain Plan Company Limited, Tokushima,Japan

T.Yamagami & J.-C. Jiang Department of Civil Engineering, University of Tokushima,Japan

ABSTRACT: This paper presents a possible method to back analyze the parameters of MC-DP model by incorporating FEM into a minimization method NLSSQP. The NLSSQP method is capable of solving Nonlinear Least Squares problems with constrained conditions by means of Sequential Quadric Programming method. The model parameters are estimated by minimizing a norm of the difference between observed and calculated values at specified observation points. Although only MC-DP model is investigated in this paper, there is no necessity to prescribe the constitutive model; any model can be used as a subroutine program. The proposed method is applied to an excavation performed in a homogeneous and isotropic slope. The results indicate that the proposed method can provide convergent and accurate solutions. 1 INTRODUCTION The parameters of constitutive models are conventionally determined using two ways such as laboratory tests and in situ tests. With the development of the measuring instruments and techniques, the results of laboratory tests and in situ tests become more and more reliable. However, in some cases such as large-scale natural slopes, it is extremely difficult to quantitatively estimate the mechanical properties of soils by tests. This difficulty is mainly due to the complex and non-homogeneous geological conditions of the ground. It is not surprising that material properties largely scatter from place to place, although soil formation seems to be identical. Therefore the real behaviors of structures such as displacements often differ from the predicted ones, even after a carefid investigation. In order to avoid these difficulties, some researchers proposed back analysis methods, and these methods have been more and more frequently used in the estimation of the model parameters. For example, the strength parameters (c' and +') of failed slopes have been successfblly back analyzed by combining limit equilibrium method and optimization techniques (e.g. Nguyen, 1984;Yamagami & Ueta, 1989, 1990). These methods, however, can not be applied to the slopes without failure slip surfaces; in fact there is no effective back analysis methods so far for the stable slopes. But if the stable slopes are subjected to loading (e.g. excavation), a sophisticated numerical analysis method such as finite element method (FEM) can be used to back analyze the soil's

parameters on the basis of displacement measurements (Sakurai, 1990). One important and difficult task in FE analyses is the choice of constitutive models for soils. An elastic and transversely anisotropic model was assumed for rocks and applied to cut slope problems (Sakurai, 1990); however, the elastic model is not applicable to soils, because it is well known that the soils usually present elasto-plastic behavior. So it is essential to employ elasto-plastic model for soils. The problem is that there are more material parameters in elasto-plastic model than in elastic model. In back analysis, there are mainly two types of errors: one is the system modelling error which can be evaluated by the goodness of fit of the calculated results to the observed data; and the other is the error corresponding to parameter uncertainty. An increase in parameter number generally improves the system modelling error, but it also increases the parameter uncertainty and vice versa. Therefore it should be recognized that increase in parameter uncertainty reduces the prediction reliability which is the most important aim of the back analysis. Thus, a complex model may not give better prediction. So one should choose the most appropriate model depending on the quality and quantity of the given information for prediction purpose. In the present paper, a simple but practical model called MC-DP elasto-perfect-plastic model (Tanaka, et al., 1996) is employed in which Mohr-Coulomb failure criterion is used and Drucker-Prager model is taken as plastic potential functions. There are only four parameters (E, v , c' , 41' ) to be back analyzed. 31 1

K: the number of the time steps; N: the total number of the data.

It should be noted that there is no necessity to prescribe the constitutive models; any model can be used as a subroutine program. So the proposed method can be applied not only to the homogeneous and isotropic soils discussed in this paper, but also to various types of soils. The other important task in back analysis is to solve minimization problems. So far, there are several minimization methods available (e.g. Luenberger, 1973). Many methods, however, suffer fiom non-uniqueness and instability solutions. The solutions obtained are very much affected by the set of initial values in the optimization schemes and sometimes, different schemes give different answers. The present paper introduces a minimization method (NLSSQP method), which is capable of solving Nonlinear Least Square problems with constrained conditions by using Sequential Quadric Programming method. This method is applied to an excavation in a fictitious slope. The convergent solutions by the proposed method are very close to the correct values.

3. NLSSQP METHOD

2. MINIMIZING FUNCTION

The constitutive parameters are estimated by minimizing a norm of the difference between observed and model calculated values at specified observation points. The observation data can be related to the calculated values at the specified points by the following relationship: U* = ~

( xe) : + r(x)

(1)

where U*:field observation data vector; U: calculated results vector by FEM based on the employed physical model with a chosen parameter vector; x: model parameter vector to be estimated; 8: known input data vector, e.g. soil profile, loading conditions and boundary conditions; r(x): error vector. The most comprehensive function to be minimized in the parameter value estimation procedure is given as:

Equations (2) and (3) are commonly called Least Square problem. Due to the complexity of the constitutive relationship, the relation between r(x) and x is usually nonlinear and non-convex as well; therefore the problem described above is a Non-linear Least Square (NLS) problem. There are some methods available such as quasi-Newton method for the optimization of NLS problems. The quasiNewton method, however, can not be used to solve the NLS problems with some constrained conditions. In fact, it is very common in geotechnical engineering that most model parameters have definite ranges which can be known by experience or laboratory tests in advance. Although in some cases, it is difficult to determine such ranges, it is clearly understood that the parameters are at least positive. Hence we usually need to solve the NLS problems with some constrained conditions. In order to solve such problems, this paper employs NLSSQP method (Takahashi et al., 1987), in which Sequential Quadric Programming is used to solve Nonlinear Least Square problems with constrained conditions. It is the authors' opinion that NLSSQP method has so far been the only method to be capable of solving NLS problems with constrained conditions. The .details will be described in the following. First let's see the following nonlinear least square problem: Constrained conditions:

and the objective function is:

Denoting the Lagrangian multiplier vectors of constraints g(x)SO and h(x)=O by A. andp , the Lagrangian hnction is defined by: 1

where

f(x) = r(x)T 2

rj(x) = u l

'('1

L(x,h,p) = -r(x)Tr(x)+hTg(x) +pTh(x) 2

1 N=PxK

=

~ l l r ( x ) l ~ = 2 c ( r ('~))'

(3)

The Hesse matrix corresponding to x is given as:

(4)

V,,L= J(x)TJ(x)+$rj(x)V2rj(x)

J=1

-U,

j=l

P: the number of the observation points; 312

(8)

m

+ChiV2gi(x)+$,pjV2hj(x) j= 1

(9)

i=l

Step 4: Let xk+l=xk+ a kdk. Step 5: Renew the matrixes of 4 and ck to produce Ak+,(DGW Equation) and Ck+l(BFGS Equation).

where J(x) stands for the Jaccobi matrix of r(x). The B matrix in SQP method can be expressed as:

Then the algorithms of NLSSQP method can be described briefly as follows:

Step 0: To set up initial x,,,the matrix of A,,, C,and parameter 6 >O, LL) '(0,0.5), z E(O,l), k=O. Step I : When the xk, Ak,Ck are known, we can solve the following QP problem with respect to d.

h(Xk) + Vh(xk)d = 0

(13)

The solution of this problem is dk by which we can determine the searching direction. Correspondingly, Lagrangian multiplier vectors of constraints g(x) 5 0 and h(x)=O become 2- k + l and p k + l respectively. Step 2: If (xk, 1 k,l, p k + l ) satisfy Karush-KuhnTucker (K-K-T) conditions, then stop; otherwise, go to step 3 to judge the convergence. Step 3: To determine a k in the following procedure (Line Search): Step 3. I : Let Y k,1=1 and j=1. Step 3.2: Regarding the following line search evaluation fkction:

then let a k= Y kJ7and go to step 4; otherwise, go to Step 3.3. Step 3.3: let Y kJ+l=z Y 4, j=j+l, then go to Step 3.2.

Step 6 : Let k=k+l, go to Step I 4. MC-DP MODEL

The constitutive models of soils (from simple linear elastic ones to very sophisticated elasto-plastic ones) have been developed for several decades and a great deal of achievement has been acquired. Generally, elasto-plastic models can simulate the behaviors of the soils better than elastic ones do, but the number of the model parameters increases correspondingly. An increase in parameter number generally improves the system modeling error, but also increases the parameter uncertainty. Therefore, it is essential to employ an appropriate constitutive model that can provide reasonable results. Considering this point, this paper employs an elastic-perfectly-plastic model (Tanaka et al., 1996; Oettl, et a1.,1998). The MohrCoulomb failure criterion, which coincides with experiment data very well, was adopted in this model; and the non-associated flow rule is assumed in which Drucker-Prager model was taken as plastic potential fhction. So a mixed model (MC-DP model) was produced. The Mohr-Coulomb failure criterion and Drucker-Prager plastic potential function are given in Equations (21) and (22), respectively.

313

0;

+o;

f=--------

2

+ T2,

/(o;+o$ 4

0;

a=---

5 . BACK ANALYSIS PROCEDURES

sin $' +

- c'

The determination of the mechanical properties from the measured values of displacement is referred to as a back analysis. The proposed method belongs to indirect back analyses in which the FEA is one of the subroutine of NLSSQP. The flow chart of back analysis for determining model parameters is briefly given in Figure 1. The convergent solutions have been obtained when Karush-Kuhn-Tucker (K-K-T) conditions are satisfied (Takahashi et al., 1987). Note that the number of the measured values should be large enough in order that optimization techniques can be adopted to determine the unknowns.

cos$' = 0

+o; 2

sin cp +

where c' represents effective cohesion; $' is effective angle of internal friction and cp represents angle of dilatancy. ox',o,', and z,' are stress components. The stress-strain relation then can be expressed as follows:

d o = [Del--(1~

L

where 2(1-v) _ _ (1-2v)

_

2v_ (1-2v)

2(1-v) _ _ (1-2v)

0

0

~

[Del =-

E 2(1-v)

~

2v _ _ 0 _ (1-2v)

Figure 1. The flow chart of back analysis

_ 0

6. NUMERICAL EXAMPLE 1

and r represents a coefficient; when stress state is at elastic zone r=l; at perfectly plastic zone r=O; in other cases O
An excavation performed in a homogeneous and isotropic hypothetical slope is taken into consideration in this paper. The finite element mesh and six observed nodal points are shown in Figure 2.

Figure 2. FE mesh and the observed points

314

This excavation was done in the slope in 5 stages. The height of the original slope is 20 m at 1:l. The height of the cut slope is 10 m with the slope of 1: 1. The initial stresses are determined by elastic analysis in which self-weight is handled as loading force. The boundary conditions for the displacements are described as follows: there are only horizontal restrictions at left and right sides (i.e. AB and CD in Figure 2). There are both horizontal and vertical restrictions at bottom (i.e. BC). For the sake of simplicity, - we do not take into account the pore water pressure. The constrained conditions for the parameters to be back analyzed are handled as: c'> 0

(25)

As we do not have in situ observed horizontal displacements, which are usually taken by inclinometer, the observed data are then produced from forward FEA. The material parameters used in the forward FEA are regarded as correct values (see Table 1). The corresponding output of horizontal displacement of specified points is taken as observed values for the following back analysis. The model parameters are back analyzed by optimizing the norm of the difference between observed and calculated displacements at the specified observation points. Table 1. Material parameters Property Cohesion (c) Angle of internal friction ($) Young's modulus (E) Poisson's ratio (v) Density (y)

Value 9.00 KNm-2 32.00' 7 140 KNm-2 0.30 22.3 KNm-3

Table 2. Four sets of initial values Property

c (KNm-2)

4(0) E(KNin-') v

7. RESULTS

case 1

case 2

case 3

15.50 38.00 5130 0.22

4.50 25.50 5540 0.22

15.00 42.00 12000 0.35

case 4 7.49 24.70 10300 0.35

AND DISCUSSIONS

The back-analyzed results of four cases are listed in Table 3. We can see that the present procedure could back analyze the reasonable constitutive parameters, which provide the good approximation of measured displacements. Like other optimization methods, the present method also needs to do trial computations with different initial values till the convergent solutions are obtained. Therefore, the computation time may be quite long if the initial values are given improperly and may be quite fast if the initial values are set properly. Nowadays, with the development of the fast, small size computers, the computation time is no longer the most difficult problem. From table 3 we can conclude that the back-analyzed values having the smallest error can be taken as the final back analyzed results. For example the results of Case 4 can be chosen as the best one. Figure 3 presents the comparison of the displacements between the observed and computed values at the end of the excavation. It is shown that the values of Case 4 and Case 2 are nearer to the observed values compared with Case 1 and Case 3. The development of the displacements of nodal point 41 1 with construction process is given in Figure 4. In this figure, we can see that the displacements of Case 3 meet the observed ones better than other cases do. This does not mean that the back analysis results of Case 3 are the best one, because this figure represents only one point other than all the points. Due to the limited space, we do not list the results of all the observed points. Table 3. Back analysis results Property

case 1 correct values initial results C (KNm-') 9.00 5.50 9.01 38.00 31.10 32.00 No) E(MNm-2) 7140 5130 6900 V 0.30 0.22 0.31 4.74 Errors( x 10-4) Number of cycles 5

As it is well understood that the back analysis results depend closely on the initial input material parameters. As we do not know whether the solutions with the input initial values are convergent or not in advance, we first set the initial values arbitrarily. If the solutions are not convergent, then we need to change the input initial parameters till the convergent solutions come out. The following four sets of initial values can provide convergent solutions (see table 2). 315

case 2 initial results 4.50 4.71 25.50 31.80 5540 6940 0.22 0.31 1.36 6

Attention, however, should be paid to the large number of the parameters associated with the complicated models, which may lead to the instability of the solutions. This is another topic of the authors’ interests (Feng et al., 1999).

Table 3. (Continued) Property

case 3 correct values initial results C (KNm-’) 9.00 15.00 5.29 No> 32.00 42.00 33.80 E(KNm-*) 7140 12000 7240 v 0.30 0.35 0.30 Errors(x 1(Y4) 5.35 Number of cycles 7

case 4 initial results 7.49 6.83 24.70 31.00 10300 7120 0.35 0.30 1.06 11

REFERENCES Feng T.Q., Yamagami, T. & Jiang J.C., 1999 A finite element analysis for transversely isotropic soils and the determination of model parameters by means of back analysis. International symposium on slope stability engineering: Geotechnical and Geoenvironmental aspects. IS-Shikoku’99, Japan. Luenberger D.G., 1973. Introduction to linear and nonlinear programming. Addison-wesley Publishing Company. Nova R., 1986. An extended Cam clay model for soft anisotropic rocks. Computers and Geotechnics, 2: 69-88. Nguyen, V.U., 1984. A technique for the back analysis of slope failures. Proceedings of the Fourth Australia-New Zealand Conference on Geomechanics, Perth: 6 17-622. Oettl, G., Stark, R.F. & Hofstetter, G., 1998. A comparison of elastic-plastic soil models for 2D FE analyses of tunnelling. Computers and Geotechnics 23:19-38. Sakurai, S., 1990. Numerical analysis for the interpretation of field measurements in geomechnics. Numerical Methods and Constitutive Modelling in Geomechanics, CISM courses and lectures No.3 1I, Edited by C.S. Desai/G. Gioda, Springerverlag: 35 1-407. Schmidt, R.J. Wang D.Q. & Hansen A. C., 1993. Plasticity model for transversely isotropic materials. Journal of Engineering Mechanics, ASCE, 119(4): 748-767. Takahashi, S., Yamaki, N. & Yabe, H. 1987. Some modifications of sequential quadratic programming method for constrained optimization. TRU Mathematics. 23(2):28 1-295. Tanaka, T., Ugai, K., Kawamura, M., Sakajo, S. & Ohtsu, H. 1996: Three dimensional elastic-plastic finite element analysis for foundations. Maruzen Co. Ltd., Japan (in Japanese). Yamagami, T. & Ueta, Y., 1989. Back analysis of average strength parameters for critical slip surfaces. Computer and Physical Modelling in Geotechnical Engineering (eds. A. S. Balasubramaniam et al.) Balkema: 53-67. Yamagami, T. & Ueta, Y., 1990. Back analysis of failed slopes in heterogeneous soils. Proceedings of the Tenth Southeast Asian Geotechnical Conference: 2 13-2 16.

Figure 4. The comparison of horizontal displacement at Nodal point 41 1

8. CONCLUSIONS

A back analysis method for determining the soil parameters has been proposed by incorporating FEM into NLSSQP method. This method has been applied to an excavation in a hypothetical slope. The solutions obtained were very close to the correct values in case the solutions were convergent; and the computations were quite fast. Correspondingly, the solutions with the smallest error could be regarded as final results. The proposed method belongs to indirect back analysis methods. The advantage of this method is that there is no necessity to prescribe the constitutive models. Hence this method is not limited to the homogeneous and isotropic problem discussed here; it can also be used to solve more complicated cases (for instance, elasto-plastic and anisotropic condition) if the constitutive relationships are available. 316

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

An FE analysis of anisotropic soil slopes and back analysis for its parameters T.Q. Feng Sun Bruin Plan Coinpany Limited, Tokushimu, Japan

T.Yamagami & J.-C. Jiang Depnrtnient of Civil Engineering, University oj'Tokushimu,Jupun

ABSTRACT: A finite element analysis has been implemented by employing an elasto-plastic model for anisotropic soils proposed by Nova (1986). Owing to the complexities of the anisotropy, the number of model parameters increases in comparison with that of isotropic soils. Also, these parameters are quite difficult to be determined by laboratory tests, because it is hardly possible to acquire the specimens of high quality for representing the anisotropy of geotechnical materials. At present, there are few acceptable methods proposed for the determination of the parameters of anisotropic models. In the present paper, an attempt has been made for the determination of the model parameters by combining FEA with an optimization method. The proposed procedure is illustrated through a cutting in an orthotropic slope. The results indicated that the present procedure is applicable for transversely isotropic soils 1 INTRODUCTION

the model parameters (Sakurai, 1990; Feng et al. 1999). A very important task in FE analyses is the choice of constitutive models. A complex model is not always preferable to a simple one due to its large number of parameters, which may leads to parameter uncertainty. Thus the final goal of our research is to develop a rational method in which the constitutive models should be implemented in a simple and proper manner to present the anisotropy of the geological materials. As a first step, a simple and practical model (Nova, 1986) dealing with the anisotropy of soils, is introduced into the present paper. It is the authors' opinion that this model is the most suitable for FE analysis because it is extended from a well-known Cam-clay model (Burland, 1967) and there is a small number of parameters compared with other models. These parameters are to be back analyzed by a minimization method in which NLSSQP method is combined with FEA. This procedure has been successhlly applied to isotropic soils (Feng et al. 1999). Its effectiveness is also illustrated in the present paper through a fictitious excavation performed in a transversely isotropic slope.

In the numerical analyses of soil behaviors, it has been generally assumed that the .properties of soils are isotropic. However, this assumption does not appear reasonable for the natural slopes, which exist broadly in the mountainous regions of Japan. The mountainous regions of Japan consist of very complicated, heterogeneous and anisotropic geological materials varying from soft soils to hard rocks. It is, therefore, essential to take into account the anisotropy of the geological materials. In order to present the anisotropy of the soils, some researches have been done in the past decade (e.g., Oda & Nakayama, 1989; Sakurai, 1990). Oda and Nakayama (1989) introduced a fabric tensor to express the anisotropy of the discrete particles. Sakurai (1990) described the anisotropy of the soils only in elastic behavior. It has been well understood that most geological materials present elasto-plastic rather than elastic behavior. At present, however, there are no generally accepted elasto-plastic constitutive models that can be used with confidence to simulate the nonlinear response of anisotropic materials under a variety of loading conditions, because it is either difficult or costly to determine the parameters used in anisotropic models by laboratory tests. The difficulties exist in that it is nearly impossible to obtain the specimens of high quality through samplings in mountainous areas. A back analysis substituted for laboratory tests has become an available method for the determination of

2. CONSTITUTIVE RELATIONS OF TRANSVERSELY ISOTROPIC SOILS To start with, the transversely isotropic soils are taken into consideration in which the axis of symmetry is normal to the bedding plane. We shall define a cartesian frame where one axis y coincides 317

In plane strain condition, the elastic matrix for transversely isotropic materials is known as (Zienkiewicz, 1977)

with the symmetry axis, and cofisequently, the plane of isotropy is the plane (x, z) as shown in Figure 1.

n(l-nv:)

[Del =

J

T lnv2A,

AlA, where A, = l + v , ,

X

0

nv2Al 1-v: 0

A, = 1-v, -2nv;

0 0

mA1A2 (7)

Figure 1 . A cartesian coordinate system for transversely isotropic soils

If the soils are isotropic, the yield surface may be expressed by a hnction of the state of the stress dij and the plastic history of the material through hardening variables, k, which is a hnction of plastic strains, ePhk f = f(oij,k(&)) If the material is orthotropic, the yield function and in general all mechanical properties depend on the orientation of the principal axes of the stresses which are inclined to the orthotropy axes with angles 8,. Since the strain history may change the initial anisotropy of the soils, 8, will be in general hnctions of the plastic strains. Thus

Then the elasto-plastic stress-strain relationship can be expressed as (3)

Dep]represents the elasto - plastic matrix

where H is referred to as hardening parameter and is written as

E,, v , are associated with the behavior in x-z plane and E,, G2,v along y direction; perpendicular to the x-zplane. Hence, there are 5 elastic parameters such as m, n, E2,Y , and v 2 . There has been no effective testing techniques for them so far; and they will be back analyzed in the present paper. 3 . YIELD FUNCTION FOR TRANSVERSELY

ISOTROPIC SOILS In order to present the elasto-plastic matrix (i.e., equation (4)), one needs to choose a yield function f and a potential hnction g. In the following, we shall employ the associated flow rule. Although it is widely accepted nowadays that the associated flow rule is not valid for geological materials (e.g., Lade and Duncan, 1975; Lade and Musante, 1978), the associated flow rule will be, as a first step, assumed here for the sake of simplicity. For anisotropic materials, Nova (1 986) proposed a constitutive model by generalizing the yield hnction of the modified Cam Clay model (see Burland, 1967). The model for anisotropic materials was investigated through triaxial compressions for soft sedimentary rocks (e.g., Nova, 1986). Although the quantitative agreement between experimental data and predicted values, as reported by Nova, was not always satisfactory, this model, however, gives an overall picture of the behavior of sedimentary rocks. In the following, the derivation of the yield hnction for anisotropic materials is briefly described. The yield hnction of the modified Cam-clay model is given by the expressions

where p' = -(G; 1 +20;) 3

q = 0;- 0 ; 318

M =strength parameter; pc= initial mean effective stress. Equation (9) can be expressed in a generalized formulation

where

4. FINITE ELEMENT FORMULATION

The finite element method follows a conventional elastic-plastic formulation except that the stress components corresponding to local x-y coordinate system must be transformed into those of global XI-y' system as shown in figure 2.

p2=2M2/9, k= pc /2, 6, is the Kroneker delta. Equation (12) holds for an isotropic material. A generalization of equation (12) to orthotropic conditions was given by Nova (1986) who followed Hill's ideas (1950). The generalized equation may be expressed by the following equation Figure 2 . Two sets of coordinate systems

C..11'sz..~.. - 3k2 = 0 IJ IJ where C,, is a quadruple tensor whose components are linked to the anisotropic characteristics of the material. In plane strain condition, the quadruple tensor Cllrsis given by

The relation of elasto-plastic matrix between the two coordinate systems can be given as

in which [D',,] is an elastic-plastic matrix corresponding to XI-y' global coordinate; [D,,] represents the elastic-plastic matrix associated with x-y local coordinates; [T] is a transformation matrix and may be expressed as

Equation (15) is the yield fimction for anisotropic materials. To obtain the elasto-plastic matrix of equation (4), it is still necessary to define the fimctions k and 8 Nova (1986) pointed out that it is very difficult to choose a suitable expression for 8 I because few experimental findings have been achieved so far. Therefore 8 I is not taken into account in this paper as a first approximation. A possible expression for k( E Phk) may be assumed as follows

,.

-cos2 e

sin2e

- 2 sine cOse

[T]= sin28

cos2e

2sin€Icose

-

sine cose

- sine cos0

(19)

cos28 - sin28

where 8 is the angle between the x-y and XI-y' coordinate systems (see Figure 2). The basic governing equilibrium equation, based on the principle of virtual displacement, is given by

in which A. represents the volumetric compressibility. (17), there are 5 plastic paIn equations (15) rameters (i.e, Q , p , y , p , l.). Since y may be linked to 0: (see Nova,1986), the number of plastic parameters then reduces to 4.

-

where [BIT is the strain-displacement transformation matrix; and { U )= j[Nr{Afb}dV+ /[N]T{Af,)dS v S

(21)

where [NI =displacement interpolation matrix; { A f,}=body force vector; { Af,}=external load vector. 319

5. DETERMINATION OF THE PARAMETERS BY MEANS OF NLSSQP METHOD

The constrained conditions for the parameters are prescribed as

There are 10 parameters in this model (i.e., m, n, E,, v ,, Y , ,U, a , P , ;L and 8 ). These parameters are conventionally determined by laboratory tests. However, these tests cannot be carried out successhlly because it is hardly possible to acquire specimens of high quality for representing the behavior of anisotropic soils. This does not imply that the authors underestimate the value of laboratory tests. On the contrary, we believe that the researches should be contributed to the essential development in tests, since the intrinsic properties of anisotropic soils may be revealed only through a wealth of test data. This paper does not contribute to this aspect, while focussing on the determination of the parameters in terms of an optimization procedure, in which NLSSQP method is employed. The NLSSQP method is capable of solving Nonlinear Least Square problems with constrained minimization conditions by means of Sequential Quadric Programming method. With regard to the details about the optimization method, the readers are referred to the related papers (e.g., Takahashi, et al., 1987; Feng et al., 1999).

O
6. NUMERICAL EXAMPLE

A cutting made in a fictitious slope of transversely isotropic soils is investigated in the following sections. The finite element mesh and six observed nodal points are shown in Figure 3 . Due to lack of the observational data of practical projects, we need to do a forward FEA to produce them. The properties of the soils and the model parameters listed in table 1 are regarded as real solutions. The initial stresses are determined by elastic analysis in which self-weights are handled as loading forces. The boundary conditions for the displacements are described as follows: there are only horizontal restrictions at left and right sides (i.e. AB and CD in Figure 3). There are both horizontal and vertical restrictions at bottom (i.e. BC). For the sake of simplicity, we do not take into account the pore water pressure.

0 < v1 < 0.5;

0 > 0;

m>0;

E2>0

0 < v2 < 0.5

a>0;

p o

Table 1. Material parameters. Property n m Young's modulus (E,) Poisson's ratio (v,) Poisson's ratio (v,)

Value 0.50 0.09 7000 KNm-' 0.30 0.30 45.00" 2.50 1.35 1.oo

8 a P

P A.

0.03 20.0 KNm"

Density ('yJ

Theoretically speaking, all the 10 parameters and density yt ought to be evaluated. As the excessive number of parameters , however, may lead to unstable solutions, some parameters can be determined by tests in advance. For example, the value of density yt can be easily obtained by routine tests. Also the values of A. can be determined by performing a compression test since it is affected little by anisotropy. In addition, the value of 0has no influence on'the shape of the yield surface for 8 =O" and 8 =90", and is of minor importance for other values of 8 (Nova, 1986). So the value of 0is assumed to be 1.0 in the present example. As a result, only 8 of them are herein left for back analysis. Like some other optimization methods, the present procedure also needs to set up a group of initial values. Here four groups of initial values are taken into investigation as listed in table 2. Table 2. Four groups of initial values Property case 1 n 0.20 m 0.03 E, (KNm-') 10500 VI 0.21 v2 0.21 20.00 8 (0) a 1.25 P 1.15

Figure 3. The finite element mesh and the observed point number

320

case 2 0.37 0.05 5500 0.20 0.20 20.00 1.90 1.15

case 3 0.70 0.10 9000 0.35 0.35 70.00 3.20 1.45

case4 0.80 0.20 11000 0.20 0.20 70.00

1.50 1.10

7. RESUL,TS AND DISCUSSIONS The back-analyzed parameters are listed in table 3, and the corresponding horizontal displacements are given in figure 4. The displacements back analyzed are generally approximate to the observed values, especially those of case 4 meet the observed values very well (see figure 4(b)). It is very common that the back-analyzed values of parameters having the smallest error, which is a norm of the difference between observed and model calculated displacements at specified observation points, can be taken as the final results (Yamagami et al., 1992; Feng et al., 1999). Here, the results of case 4 can be chosen as the final values of the parameters. It is worth noting that the value of the angle between local and global coordinate systems (i.e., 8 ) can be well optimized to the real value in the four cases. This means that the present method can predict accurately the values of 8 , which is difficult to be determined in practice. Hence, this method is worth hrther studying. However, some values (e.g., a , y in case 3) are not convergent towards correct values, which leads to a larger errors (i.e., 1.027X 103 in case 3 ) . To avoid such discrepancies, the simplest way is to choose the results with smallest errors.

Figure 4. The comparison between observed and computed values at the end of excavation

Table 3. Back analysis results Property correct values n 0.50 m 0.09 E, (KNm-,) 7000 v1 0.30 v2 0.30 45.00 0 (") ff 2.50 P 1.35 Errors(x w 4 ) Number of cycles

8. CONCLUSIONS

case 1 initial results 0.20 0.45 0.03 0.08 10500 7180 0.21 0.35 0.21 0.27 20.00 44.73 1.25 2.60 1.15 1.39 0,0802 18

case 2 initial results 0.37 0.52 0.06 0.12 5500 6340 0.20 0.30 0.20 0.38 20.00 45.45 1.90 2.29 1.15 1.45 0.0800 28

case 3 initial results 0.70 0.60 0.10 0.09 9000 6220 0.35 0.24 0.35 0.34 70.00 45.39 3.20 3.30 1.45 1.50 1.0270 4

case 4 initial results 0.80 0.51 0.20 0.09 11000 6910 0.20 0.29 0.20 0.31 70.00 44.60 1.50 2.33 1.10 1.29 0.0 120 30

A finite element analysis has been implemented by introducing a constitutive model for the transversely isotropic geotechnical materials. The significance of introduction of this model is that some materials such as sedimentary rocks enjoy an intrinsic or structural anisotropy due to their formation process. However, this model has not been widely used so far due to the complexities of determining the model parameters by laboratory tests. An attempt has been made in the present paper to employ a back analysis method in which FEM was incorporated into NLSSQP method. The proposed procedure has been verified using an example of excavation in a stratified slope. The values of the parameters back analyzed were very close to the correct values. Correspondingly, the solutions with the smallest error could be regarded as final results. Since the study on the constitutive relations of anisotropic geological materials are insufficient at the present stage, various attempts, including laboratory tests and back analyses, should be made in order to predict more accurately the behaviors of heterogeneous and anisotropic slopes existing broadly in Shikoku of Japan.

Table 3. (Continued) Property Correct values n 0.50 m 0.09 E, (KNm-,) 7000 0.30 V1 v2 0.30 0 (") 45.00 ff 2.50 P 1.35 Errors(x l(Y4) Number of cycles

321

REFERENCES Burland, J. B., 1967. Deformation of soft clay. Ph. D. Thesis, University of Cambridge. Feng, T. Q., Yamagami, T. Jiang, J.C., 1999. A back analysis for parameters of MC-DP model by combining FEM with NLSSQP Method. International symposium on slope stability engineering: Geotechnical and Geoenvironmental aspects. ISShikoku'99, Japan. Hill, R. 1950. The mathematical theory of plasticity. Oxford University Press, London, England. Lade, P. V. & Duncan D. M., 1975. Elastoplastic stress-strain theory for cohesionless soils. Journal of Geotechnical Engineering Division, ASCE, V01.101, No.GT10: 1037-1053. Lade, P. V. & Musante H. M., 1978. Three dimensional behavior of remoulded clay. Journal of Geotechnical Engineering Division, ASCE, Vol. 104, No.GT2: 193-210. Nova, R.,1986. An extended Cam clay model for soft anisotropic rocks. Computers and Geotechnics 2: 69-88. Oda, M. & Nakayama H. 1989. Yield Function for Soil with anisotropic fabric. Journal of Engineering Mechanics, ASCE, Vol. 115, No. 1: 89-104. Sakurai, S., 1990. Numerical analysis for the interpretation of field measurements in geomechnics. Numerical Methods and Constitutive Modelling in Geomechanics, CISM courses and lectures No.3 11, Edited by C.S. Desai/G. Gioda, Springerverlag: 35 1-407. Takahashi, S., Yamaki, N. & Yabe, H. 1987. Some modifications of sequential quadratic programming method for constrained optimization. TRU Mathematics. 23(2):28 1-295. Yamagami, T., Mori, K., Ueta, Y. & Yasutomi, H., 1992. Design and construction control of a large embankment with reinforced earth walls. Proceedings of the International Symposium on Earth Reinforcement Practice. IS-Kyushu'92, Japan: 443-448. Zienkiewicz, 0. C. 1977. The finite element method. Published by McGRAW-HILL Book company (UK) Limited: 93-134.

322

3 Rock slope stability analyses

This Page Intentionally Left Blank

Slope Stabhty Engmeenng, Yagi, Yamagami & Jiangco 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

An upper bound wedge failure analysis method Z.Y.Chen, Y. J. Wang, X.G. Wang & J.Wang China Institutue of Water Resources und Hyclsopor~wResecisch, Bei jing, People's Republic of' China

ABSTRACT: The solution to a wedge failure of a rock slope is normally obtained by employing force equilibrium analysis (Hoek, 1976). It has been found that the problem is in fact statically indeterminate and some assumptions were made to render the analysis tractable. A new method based on the upper bound method of plasticity has been proposed by which Pan's postulates( 1980) can be numerically performed. More than 80 potentially unstable wedges in the Ship-lock slopes of the Three Gorges Project were evaluated, compared with the traditional approaches. It has been found that for material that has no friction angle, the new method gave exactly the same answers as those from the textbooks. However, for wedges with cohesionless material, the textbook answers can be as low as 60 percent of the upper bound solutions. This means that the currently available wedge failure method may be too conservative if failure potential is assessed on the ground that cohesion of the material are not considered. This is certainly an area of much needed firther research. 1 INTRODUCTION Wedge failure is a common collapse mode found in rock slopes. In this case, the sliding mass falls along two well defined weak planar structures either with or without a tension crack at the crown (Figure 1). Hoek and Bray (1 977) discussed the conditions upon which a typical wedge failure may take place. In general, a wedge failure may occur if the line of interaction of the two slip planes daylight at the slope surface. The limit equilibrium method is generally used to find the factor of safety for this kind of failure mode. The procedures are well documented in textbooks (e.g. Hoek and Bray, 1977). However a detailed study of these procedures will come to the fact that the problem is statically indeterminated. When establishing the force equilibrium equations, there are generally two unknown force vectors on the two failure surfaces, which involve a total of six components in the x,y,z co-ordinate axes(Figure 1). The value of factor of safety to be searched adds one more. The numbers of available force equilibrium equations for the wedge block are three. MohrCoulumn failure criterion on the failure surfaces would provide another two equations. Therefore, two assumptions must be made to allow the problem statically determinate. The traditional method presented in Textbooks actually implies an

assumption that the shear forces on the failure surfaces are parallel to the line of intersection of the two failure surfaces. To understand the effect of the assumption made in the conventional method, let us examine an example that has a symmetric geometry and material properties with respect to the line of intersection. Main parameters are shown in Table 1. Cohesion of the two failure surfaces is set to zero. Figure 2 gives the factor of safety associated with different values of the angles between the line of intersection and the shear forces applied on the failure surfaces, which is represented as p. It is apparent that the case p=O" corresponds to the conventional method which assumes that the shear forces on the two failure surfaces are parallel to the line of intersection. It can be found that the conventional method gave a value of factor of safety F = 0.87. However F can be as large as 1.136 at p =39". The question thus arises is what the true answer to F would be and in what cases the deviation between different assumptions regarding the directions of the shear forces can be of significance and caution must be exercised to select appropriate answers. In this paper we would investigate the theoretical background regarding this issue and try to establish a new analytical method that is based on the upper bound theorems of Plasticity.

325

Figure 2. Factors of safety for different value of p Figure 1. The wedge failure analysis

where W is the weight vector of the wedge. The subscripts r and I refer to the right and left failure surfaces respectively. Now, we assign a velocity V that inclines at angles q,,,qerto the left and right failure surfaces respectively. According to the virtual work principle, we have

Table 1. Parameters for an example of symmetric wedge Surface Dip direction Dip angle Left 120" 65" Right 240" 65" Crest 180" 0" Slope 180" 90" Unit weight = 27KN/m3

w + P,,,V + P,,,V + C,,,V + c,,y= 0 2 AN APPROACH BY THE VIRTUAL WORK PRINCIPLE

(4)

Since the work done by the frictional forces P on V is zero, the work and energy balance equation becomes

Let us examine the forces applied on the two failure surfaces that constitute the wedge. Each force comprises two components. The first component, designated as P (Figure lb), is a resultant of the normal force N and its shear resistance N tanq,, . P inclines at an angle qeto the normal of the failure surface. The second component designated as C is the shear resistance force contributed by the cohesion, whose magnitude is c ',,A . The subscript e involved in the strength parameters defines the factor of safety F, which reduces the available shear strength parameters c ' and 4' to the new values of c', and $'c by the following equations to bring the wedge into a state of limiting equilibrium.

where y is the angle between the weight vector. Equation ( 5 ) involves only one unknown, the value of F, which is implicitly involved in the shear strength parameters with the subscript e and can be solved by iterations. The velocity V that inclines at angles qel,q,,, to the left and right failure surfaces respectively can be uniquely determined by solving the following equations:

ck = c ' l F

(1)

V, . N,

tan 4; = tan 4; / F

(2)

V,'

Considering force equilibrium for wedge leads to

W + ?,e

+ Pr,, + C/,c+ Cr,e = 0

+ Vy- N, + V, . N ,

+ Vy' + Vz2= 1

=

sin ye,,,

(7)

(8)

where the components of V in x, y, z directions are designated as (V,,Vy,V,) . (N,,Ny, N,) is the directional component of the normal of the failure

(3)

326

term in Equation (9) does not exist. On the other hand, for problems which concerns factor of safety rather than the external ultimate load, T* is zero, performing the upper bound statement would be the determination of the minimum values of F involved in the following equation

surface. IVI is the magnitude of I?

3 THE THEORETICAL BACKGROUND 3.1 Pan s postulates of maximum and minimum The value of factor of safety obtained by the procedures described in Section 2 is one of many possible solutions that satisfy Equation (3). It is different from the one obtained by the conventional method introduced in the textbook, which assumes Pie,Pr,eparallel to the line of intersection. Perhaps Pan was the first one who challenges the conventional approach. In his book (Pan, 1980), he put forward the famous postulates in China as follows: (1) Among many possible slip surfaces, the real one offers the minimum resistance against failure ( Principle of minimum); (2) For a specified slip surface, the stress in the failure mass as well as on the slip surface will be reorganized to develop the maximum resistance against failure ( Principle of maximum). Pan tried to find the maximum values of F in Equation (3) among all the two possible extra unknowns. However the mathematics was too complicated to be approached in the time when his theory was advocated. It is now possible to demonstrate that the procedure described in Section 2 is actually the maximum value of F based on the upper bound theory of Plasticity. The procedures described in Section 2 actually gave the maximum factor of safety of 1.136 for the example shown in Figure 2.

L.

= WV*

The second term D,,refers to the energy dissipation developed on the slip surface, based on the reduced shear strength parameters c and For a Mohr-Coulomb material the yield surface is given by @Ie.

where z and G are shear and normal stress on the failure plane respectively, U is the pore pressure. The associative flow rule thus requires that the normal velocity V, and tangential velocity y, obey the following relationship

This implies that for a Mohr-Coulumb material the plastic velocity is inclined at an angle of 4Ie to the failure plane. The energy dissipation developed on a unit area of the failure surface can therefore be determined by the expression.

dD = zy,+ oV, = (zcos 4; + o sin 4; )V = (c‘cos 4; - U sin 4: )V

(13)

3.2 The Upper bound theorem of Plasticity The upper bound theorem of Plasticity as applied for soil mechanics is discussed in detailed in Chen’s textbook (Chen, 1975) and can be stated as follows:

If an increment in compatible plastic deformation V* (called velocity) and strain filed E,; are assigned to a failure mechanism R*bounded by a failure surface P, then the external load T* determined by the following work-energy balance equation will be either larger or equal to the true load T that brings the structure to failure. (9) The first and second terms refer to this energy dissipation developed in the failure mass and on the failure surface respectively. In wedge slide the failure mass is a rigid body, therefore the left first

Now it is not difficult to find that: (1) the velocity determined by solving Equations (6), (7), (8) is exactly the plastic velocity determined by MohrCoulumb associate flow law which obeys (12); (2) Equation (10) is identical to (5). Therefore, the solution obtained by the procedure presented in Section 2 is an upper bound, or in other words, a solution that offers the maximum resistance. Use of the bound theorems of Plasticity to Geomechanics is not new. Chen, W. F. (1975) gave a comprehensive review on its fundamentals and applications to solving bearing capacity, earth pressure and slope stability problems. Sloan (1988, 1989) used finite elements and linear programming to approach both upper and lower bounds for the determination of bearing capacity on both uniform and layed foundations. Donald and Chen (1997) presented an upper bound slope stability analysis method which employed a multi-wedge failure mechanism. Optimization was followed to find the

327

velocity field that offered the minimum factor of safety, which according to the upper bound theory would be either equal or slightly higher than the true answers of the problem. The method presented herein belongs to the same theoretical framework, but is particularly applicable to wedge analysis. It is also not difficult to demonstrate that for material with $',=O, the method described in Section 2 will give identical results to those obtained by the conventional method.

4 CASE STUDY - THE THREE GORGES SHIPLOCK SLOPES In evaluating the stability of potential wedge failure of the shiplock slopes of the Three Gorges project, we performed some 80 wedges. Some of them exhibited quite large difference between the results obtained by the conventional method and the upper bound method described herein. The following is a typical example. Example Stability analysis for the No. 4 Wedge of the shiplock slope of the three Gorges Table 3 shows the result for No. 4 Wedge based on a different combination of parameters. Geological and strength parameters are shown in Table 2. We found that: (1) When the friction angles of both failure surfaces are zero, the two methods gave identical results; (2) Great discrepancy was found for cases where the cohesion of both surfaces is zero. Table 2 Parameters of Wedge No. 4 of the Three Gorges shiplock slope DiD direction DiD angle 345" 76" left right 130" 80" crest 21" 0" slope 21" 90" Height = 32.1 m Unit weight = 27 KhJ/m3

5 CONCLUSION It hzs been found that the limit equilibrium method involved in a wedge failure analysis is in fact statically indeterminate. The conventional method (Hoek and Bray, 1977) introduced an assumption that the shear forces on the failure surfaces are parallel to the line of intersection of the two failure surfaces. This paper presents a new method based on the

upper bound method of plasticity and Pan's 'Theory of maximum-and minimum'. This method gives the maximum possible factor of safety among all statically admissible stress fields. More than 80 potentially unstable wedges in the shiplock slopes of the Three Gorges Project were evaluated, compared with the traditional approaches. It has been found that for material that has no friction angle, the new method gave exactly the same answers as those from the textbook. However, for wedges with cohesionless material, the textbook answers can be as low as 60 percent of the upper bound solutions. This means that using currently available wedge failure method may be too conservative for cohesionless materials. Further experimental research is certainly much needed to justify the issue raised in this paper. Table 3 Factors of safety associated with different strength parameters for Wedge No. 4 of the Three Gorges shiplock project Friction c=O KN/m2 c=25 KhJ/m2 c=50 KN,/m2 angle U.P. L.M. U.P. L.M. U.P. L.M. O0 0.982 0.982 1.97 1.97 5" 0.285 0.172 1.176 1.15 2.154 2.142 10" 0.573 0.346 1.405 1.328 2.361 2.317 15' 0.872 0.526 1.661 1SO8 2.591 2.497 2OQ 1.184 0.715 1.942 1.697 2.846 2.685 1.516 0.916 2.25 1.898 3.129 2.886 3l0 1.953 1.18 2.665 2.16 3.154 3.150 *L.M. stands for the conventional limit equilibrium method, and U.P., for the upper bound method proposed in this Section. 5

O

REFERENCES Chen, W. F. 1975. Limit analysis and soil plasticity. Elsevier Scientijk Publishing Co., New York. Donald, I and Chen, 2. Y. 1997. Slope stability analysis by the upper bound approach: fundamentals and methods. Canadian Geotechnical Journal, 34: 853-862. Hoek, E. and Bray, J.W. 1977. Rock slope engineering. The Institute of Mining and Metallurgy. Pan, J. Z., 1980. Stability analysis and landslide assessment for structures. Water Resources Press, Beijing. (In Chinese). Sloan S. W. 1988, Lower bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 12, 6 1-67. Sloan S. W. 1989, Upper bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 13,263-282. 328

Slope Stability Engineering, Yagi, Yamagami& Jiang 0 1999 Balkerna, Rotterdam, ISBN 90 5809 079 5

Stability analysis of rockfill dam and retaining wall constructed on dip bedrock Chen Shengshui & Fang Xushun Department of Geotechnical Engineering, Nanjing Hydraulic Research Institute, People’s Republic of China

ABSTRACT: Modified Janbu’ s general slice method is used to calculate the stability of the downstream shell of rockfii dam along the dip bedrock, the in - situ direct shear test are carried out to determine the shear suen,oth between rockfill and the bedrock. Results show that the stability safety factor does not meet the desired value. As a result, a concrete gravity retaining wall is used to cut the long dip bedrock, and modified Coulomb theory is used to analyses the stability of gravity concrete retaining wall along the dip bedrock and the soft intercalated layer in the bedrock again. Results show that the stability of the retaining wall is sufficient. and k d m k surface is one of key factors to determine the stability of the downstream shell of rockfill dam along the dip k d m k surface. Tnus, an in-situ dimt shear test is carried out to m m the shear stren,&. The curve of shear stress and dsplacexmt, and the shear stren-a index between the n8mkfZI and weak warherd quarti! sandstone and strong h e r e d gmxteprphyry are shown in Fi,.ure 2. and Fi,.ure 3 respectively. It is found that the shear mn,& betwen rockfill and tedrcck is obviously less than that of mkfill itself ( G x n & Guan 1 5 9 ) . ’Therefore, the interface of downstream shell and k d m k b e c m of the mt p b l e slide plane. The stabdity analysis of downstream shell along be$rock suface is irnplemnted by rmm of d e d Janbu s general slice mthd. In the mthd, the following assqtions are made (see Fi,oure 2):

1 INTRODUCTION A lOOOMW pumped storage hydro - plant will be built in %a, the major dam of upper reservoir constructed on the dip bedrock is a remforced concrete face rockfill darn. The average gradient of bedrock surface is about 1 : 1 . 5 , and the maximum height is

about 270111, see Figure 1 . Therefore, the stability of downstream shell is one of key problems. As a result, two kinds of type of downstream shell is chosen at preliminary design stage, one is that the downstream shell is all rockfill, the other one is that a gravity concrete retaining wall is built to cut the long downstream shell in order to increase its stabllity. In what follows, the stability of downstream shell of two kinds of type is discussed respectively. Figure 2 Forces applied on soil slice

It is wll known that the shear strength between mkfill 329

1.slide plane has saT1z: safety factor; 3 . 3 CITES ~ pint of vertical load AW and sLide plane

is also the acting pint of reactive force AN; 3.?he push E is linear distribution, and the distance between its acting pint and the bottom of soil slice equals 1 3 Based on the esphbrium of force and rrmmx, the following expsiions can be obtained for i soil slice: - w

- ( p + t)Axtga when the width of soil slice is srr!all enough, then

where t = AT/a?G,p = y z , y is the unit wight of

(1)

soil,

hi and h i + l is the distance betwen acting pint of push f a E and the bottomof soil slice, U is the pressure of pore water. As a result, the expresson of stability safety factor F , can be given: F

3

2

[ cllz

+ (pAz + AT - u h ) t g 4 ~[ (1 + $ a ) / (

1+

Figure 3 . Direct shear test results (benveen tuff rock-fill and weak weathered quartz sandstone)

F)]

-

( p ~ +z ar)tga , = I

(3)

?he iteration m t h d will be q l o y e d to calculate the stability safety factor F,. In the calculation, the acting force E and T betven soil slices are obtained from lower position to uppx position, different from Janbu’ s general slice IrEthd. Moreover, the simpl5ed Bishop’ s mthod is employed to a n a l p the stability of mkfill, the slide plane in rockfill is detemdned by t d and m.In above calcularion, the shear strengh between rock-fiu and w a k weathered quartz sandstone or granite - porphyry is used respectively for merent bedrock (see E , - 3 and Fi,a 3 ) , the inm~ockingforce of mkfill c = W a , internal Figure 4. Direct shear test results firction angIe $ = 4P. It is worth to indicate that the seep(between tuff rock-fill and strong weathered granite-porphyry) age force applied on tedmk surface and rockfill is not considered in the calculation. ?he calculation result shows that the safety factor is 1.34, less than 1.50 requested by 9m,the average height is about 28.9m, the total lengch of the Chinese design code of earth and mm darn. ?he axis of retaining wall is about 4 1 3 . k . As a result, che combined slide plane of typical section campnding to stability of downstream shell tlansfers into the stabil~tyof retainhg wall. It is well known that the stability of retainthe rninimm safety factor is show in F i m , 1. ing wall contains the following two aspects: I. ?he stability of retaining ~+aLlalong the kdrcck 3 WILITY ANALYSIS OF REc4TMNG MI?vL Considering the long and steep k d m k surface of downstream shell, a gravity concrete retaining wall is sugested to M d in order to increase the statxlity of downstream shell and d u c e the volunx: of midill. The distance betwen axis of ~tainingwall and axis of mjcx damis about 1&, the maxirrmm height of retaining wall is about 62.

SLlIface; 3,. ?he stability of

retaining wall along the softintercalated layer in k h x k . Figure 4 gives three typical Sections that mml the stability of retaining wall along the k d m k surface. Figure5 is a typical section, it indicates the disolbunon of faults and soft inferabed layers in becjtrock.

330

3.1 stability d y i s qf retauwzg ud &ng beasock srqfpace Generally, for ' L' type retaining wall, the connecting line BC of wall top and wall toe can be approximately regarded as the wall back (Guang 1996). According to Coulomb theory, the angle between direction of active soil pressure E, and normal direction of BC plane equals to the internal friction angle of rockfill. As for slide plane AB, it can be determined based on the principle that the active soil pressure E, induced by rockfill reaches the maximum. Thus, the following expressions can be obtained from Figure 4:

J 1 + tg(a

+ $)ctg( 4 - a ) ] - tg($ -13) + ctg( $

-a)

1

(7)

Where G is the rockfill weight of slide mass AI3C (D) , 6 is the angle between slide plane AI3 and horizontal plane. It is worth to note that the obtained by above expressions less than the dip angle of bedrock surface for section 3 , therefore, the interface of bedrock and rockfid becomes of slide plane. Accordingly, the direction of acting force applied on slide plane is determined by the friction angle between rockfii and bedrock surface. Now, the active soil pressure E, induced by slide mass ABC(D ) can be calculated by means of vector mangle method. Moreover, the lirmt equrlibrium theory of rigid body can be used to calculate the stability Figure 5 Sraoilip anaihsis o i r m i n i n g nail along becrock surhcs safety factors of retaining wall. In stability analysis, the unit wei&t of rockfii and concrete are 31.5kN/ Table 1 Stabdity analysis results m3 and 23,5kN/rn3 respectively, the internal friction angle of rockfii 4 = 42", the friction angle between rockfill and bedrock $ = 33.1' , the cernendng power 1 34609.8 6.42 3.93 between concrete retaining wall and bedrock c = 2 30479.7 8.11 1.75 GOOkPa, the hction factor f = 0.8 . Consider that the 3 9772.8 10.8 6.50 dip contact face of retaining wall and the bedrock is possible tensile stress zone, only the cementing power tion 3 have an excessive safety factor. As a result, and friction force of horizontal contact face between the toe slab length of retaining wall may be reduced in reraining wall and bedrock are considered. The active order to reduce the volume of concrete. soil pressure E, and stability safety factors F,, Fo against sliding and overturning of retaining of above 3 . 2 Stability analysis of retaining waLL along s o j Intkree typical sections are listed in table 1 . It is found tercalated layer and fault in Bedrock that the stability safety factors of retaining wall along bedrock surface are lager than 3 . 0 requested by (31nese design cede, especially , the section 2 and secFi,me 5 indicates that interconnected Fig, F4 faults ~~

331

~~

and St20, St21 soft intercalated layers exist in the foundation of retaining wall, therefore, it is necessary to analyses the deep slide stability of retaining wall along faults and soft intercalated layers. At first, on the basis of Coulomb theory, the active pressure E, applied on wall back HI is obtained. In the calculation, fault F19 is redarded as slide plane of slide mass AHI. For conservative aim, the direction of acting force R applied on slide plane AH is determined by the friction angle $ r of fault FI9. Then, the active soil pressure E, is regarded as external force, the stability analysis of retaining wall along the soft intercalated layers and faults is canied out. The stability analysis of retaining wall along fault F19 and F1 is implemented by means of equivalent safety factor method (Lu 1984) . In the calculation, block DBE and EBC are assumed in limit equilibrium state, the weight of block MDEJKL is assumed as the external load, the cohesion and friction angle of fault FI9 and F4 c = 30kPa, $ = 17.7",the unit weight of bedrock is 24. 5kN/m3 . Calculation result shows the stability safety factor F, = 3.44. Therefore, the stability of retaining wall along fault F19and F1 is sufficient. Conventional Limit equilibrium method is used to calculate the stability of reraining wall along soft intercalated layer St20and Sbl . In the calculation, HD or HF plane is assumed in critical unjoint state. The shear stren,gh of soft intercalated layer Stzo and St21is determined by in - situ test, the cohesion and friction angle c = 30kPa, 4 = 15.6". Consider that the dip angle of soft intercalated layer of Sb0 and St21has

obvious influence on the deep slide stability of retaining wall ,the 3", 5" and 8" dip angle of soft intercalated layers are chosen to cany out the sensitivity analysis. Calculation results are listed in table2. It is found that the stability increases with increasing depth of soft intercalated layer, and the stability safety factor F, = 1.30 when the dip angle of soft intercalated layer St20reaches 8", less than 1 .50 requested by Chinese design code of earth and rockfiu dam. As a result, the anchoring measures should be taken to ensure the deep slide stability of retaining wall. Table 2 D e e ~slide stabilitv safetv factor Slide type Dip angle Safety factor 3" 2.05

HD-DE

HF- FG

4

5"

1.67

8"

1.30

3"

5"

2.93 2.19

8"

2.08

CONCLUSIONS

Based on above analysis results, the following conclusions can be obtained: 1 . The shear stren,gh between rockfill and bedrock surface is less than the shear stren,gh of rockfill itself, the dip bedrock surface conn-ol the stability of downstream shell of rockii dam. 2. The stability of proposed concrete reraining wall along bedrock surface is sufficient. However, the deep slide stability of retaining wall along shallow soft intercalated layer does meet the requested value when its dip angle a = 8". Thus, the anchoring engineering measures must be taken.

REFERENCES

S.S . Chen

& B . H. Guan (1999). Study on shear snen,& between rockfill and bedrock surface. NHRI Rport. F. N . Guang ( 1996) Design of Retaining Wall. Chinese Hydropower Press. S . S . Lu (1984) Rock Mechanics and Engineering. Hohai University Press.

Figure 6

Srabilip analysis ofreramng n a i l along iauirs and soft layer

332

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 7999 Balkema, Rotterdam, ISBN 90 5809 079 5

Soil-water coupling analysis of progressive failure of cut slope using a strain softening model T.Adachi, EOka, H.Os& & H.Fukui Department of Civil Engineering, Kyoto University,Japan

E Zhang Department of Civil Engineering, Gifu University,Japan

ABSTRACTS: In the present paper, based on an elasto-plastic model with strain hardening and strain softening (Oka, and Adachi, 1985), a finite element analysis of soil-water coupling problem is conducted to investigate the progressive failure of a cut slope in a model ground. The mechanical behaviors of a cut slope, such as the change of excessive pore-water pressure, the redistribution of stress in ground due to strain softening, the propagation of shear band and the progressive failure are discussed in detail. It is found that a soil-water coupling analysis based on an elastoplastic model with strain softening can simulate the progressive failure of a cut slope. 1 INTRODUCTION It is commonly known that soft sedimentary rock can be linked to many geotechnical engineering problems, such as the instability of cut slopes and foundations. Generally speaking, the mechanical behavior of soft sedimentary rock is elasto-plastic, dilatant, strain hardening-strain softening and time dependent. From a physical point of view, soft sedimentary rock has an unconfined compressive strength of 1-10 MPa and its mechanical behavior is between the behavior of soil and rock. Cementation plays an important role in its shearing strength. Compared to other geological materials formed in the same epoch, the void ratio is relatively large and a special structure formed during sedimentation. Its mechanical behavior during shearing is largely dependent on the confined stress and the pore-water pressure. The cementation existed in the structure, deteriorates due to the breakdown of the structure. Various processes, such as large shearing deformation, cyclic drying-wetting or stress release cause such a breakdown. The softening behavior of soft sedimentary rock becomes a very important factor in the long-term stability of cut slopes It is known that progressive failure of cut slopes is usually caused by the following two factors, namely, (a) the deterioration of the structure of geologic materials due to the swelling and the weathering during and after the cut of the slopes, and (b) a reduction in the apparent shear strength due to the dissipation of negative pore-water pressure caused by rapid excavation of the cut slope. In general, there

333

are two types of time-dependent behavior, one is due to the interaction of free water and soil skeleton and the other is brought about by the inherent viscous characteristics of soil skeleton. Yoshida et al. (1991), Adachi and Yoshida (1993) discussed the softening behavior of soft sedimentary rock and the instability of cut slopes. Adachi et al. (1 994) proposed an elasto-viscoplastic model that can describe the aspects of time dependency, such as strain rate dependency, creep and stress relaxation, but also the strain softening of geologic materials. In the present paper, a finite element analysis was carried out to investigate the instability of a cut slope, using the strain softening model. In the analysis, Biot type solid-fluid mixture theory with effective stress concept were adopted in order to take into consideration soil-pore water interaction. Long term stability and progressive failure of cut slope have been studied due to strain softening and time dependency due to the dissipation of pore water pressure with small permeability of soft rocks. 2 ELASTOPLASTIC MODEL WITH STRAIN SOFTENING Oka and Adachi (1985) proposed an elastoplastic model with strain softening, using a strain measure expressed as dz = (de,,de,,)"'

(1)

It is assumed that plastic potential function is expressed by the relation as

where dz is an incremental strain measure. The stress history tensor is expressed by introducing a single exponential type of kernel function, namely,

where zis a material parameter which expresses the retardation of stress with respect to the time measure and a;/ is the effective stress tensor. The total strain increment tensor is composed of the elastic and plastic components: d E q = dE,f

+ d&T

where Sq is the deviatoric stress tensor and omis the mean stress and M is the parameter that controls the development of the volumetric strain. omb, the plastic potential parameter, is determined by isotropic consolidation tests and takes the value of the pre-consolidated stress. The following relation expresses a boundary surface, which defines the normally consolidated and overconsolidated region as shown in Figure 1:

(31

The plastic strain increment is given by the nonassociated flow rule as,

fb= i + g , n l n [ ( o , n +b)l(o,, +b)]=O (11) Based on this relation, the value of M in equation 10 can be determined based on the boundary surface:

where & is the plastic potential function, fy is the yield function and H is a positive function describing the strain hardening-softening characteristics. The subsequent yield function is defined by

L,= q ' - K = O ,

7' =

.,/-/U:,

(5)

where S*,, is the deviatoric stress history tensor, b is the plastic potential parameter that represents the extensive. o',,~is the mean stress history. K is the strain hardening and softening parameter and is given by the following evolution equation:

In the case of proportional loading, it can be integrated as Figure 1 Plastic potential and boundary surface y p = jdyP

Combining Equations 4, 5, 6, 8, 10 and 12, the following equation for the plastic strain increment tensor can be derived:

where 8,is a deviatoric plastic strain tensor. G' and h f fare the strain hardening-softening parameters. For the yielding function defined in Equation 5 , the following Prager condition should be satisfied, dfy = d 7 * - dK = 0

(8) A = M;' IG'I(M; - q*)' , q,, = SV/(o,,, +b)

The loading condition is given by the following relations:

8 parameters are involved in the model and they can be determined with the conventional triaxial compression tests. Detail description of the determination of these parameters can be referred to references (Oka and Adachi, 1985)

0 if f J= 0, dfy > 0 loading = 0 if A = 0, dfy = 0 neutral = O if f,= 0 , d&, < 0 unloading #

334

3 FINITE ELEMENT ANALYSIS OF PROGRESSIVE FAILURE I N CUT SLOPE OF MODEL GROUND In this paper, a soil-water coupling finite element analysis based on the model introduced in section 2 is conducted to analyze a progressive failure of a cut slope in a model ground of soft rock. For strain softening material, when it is subjected to a shearing force, it will firstly exhibit strain hardening. After it reaches a peak value, strain softening will occur and if the shearing deformation continues, it will finally reaches a residual state. In a boundary-value problem such as an excavation, a stress concentration will occur, which often results in a localized softening zone. In this case, because of the strain softening, the stresses around the zone will redistribute to satisfy the equilibrium equation. For this reason, the strain-softening zone will develop gradually due to the redistribution of the stresses. If the development of the zone stops, an overall failure of ground will not occur. However, if the zone develops to such an extent that the surround ground cannot bear any more stress shifted from the softening zone, then an overall failure will occur and it is called as progressive failure. Table 1 shows the material parameters of the ground.

stress field of the model ground is a gravitational field with a value of K0=0.43. In the calculation, the excavation of the slope is completed within one month, simulated by releasing the initial stress with 500 steps (0.2%/step, 6000 sec/step). After the completion of the cut slope, 30000-step calculation with a time interval of 6000 seclstep is conducted to simulate the dissipation of the excessive pore-water pressure caused by the excavation of the slope.

Table 1 Material Darameters of model ground Young' modulus E (MPa) Poisson Ratio v Density y' (g/cm3) Permeability k (cdsec) Strain-softening parameter G ' (MPa)

0.33 1 .O 1O-'

45.2

Residual stress ratio M'f b (MPa) omh - (MPa)

1.oo

M ,"

0.87 16.0 1.25

z

0.025

Figure 2 Comparison of stress-strain-dilatancy relations obtained from theory and FEM

Figure 2 shows a comparison of stress-straindilatancy relations of the model ground in conventional triaxial compression and extension condition obtained from the theory and the finite element analysis. It is found that the calculated relations agree well with the theoretical ones, which implies that the finite element analysis is convincible. Figure 3 shows the finite element mesh adopted in the analysis of the cut slope. The size of the ground is 1000 m in length and 360 m in depth. The height and the slope gradient of the cut slope are 150 m and 5:l respectively. The numbers of the node and 4node isoparametric element are 1120 and 1053 respectively. In the soil-water coupling analysis, an excessive pore-water pressure is taken as the unknown variable. The boundary condition is given as: (a) for displacement, it is fixed at the bottom in both x, y directions and is fixed at the vertical boundaries in x direction; (b) for excessive porewater pressure, the ground surface is the drainage boundary and the others are impermeable. The initial

335

Figure 3 Finite element mesh

In order to fully study the process of the progressive failure, the following two points are discussed, (1) Overall changes of the field quantities such as plastic strain, excessive pore-water pressure and stress state (2) Time history of stress, strain, strain rate and dilatancy of individual element.

3.1 OVERALL VIEW OF CHANGE IN FIELD QUANTITIES IN PROGRESSIVE FAILURE Figure 4 shows the change of the distribution of stress-history ratio. In Adachi-Oka's model, the failure state or the residual state is described by the equation as

Figure 5 Change of plastic shear strain

Figure 4 Distribution of stress-history ratio with time In'the residual state, the cohesion or the cementation of the geologic material tends to be zero and only the frictional strength that depends on a confining stress remains. In this case, the stress-history ratio will be the same as the stress ratio and takes the value of In the figure, t=O means the time immediately after the completion of the excavation. At the beginning, the value of q* is kept as a constant of about 0.80. 4.67 years after the completion of the excavation, it increases abruptly at the toe of the slope and then the phenomenon propagates to other regions. 5 month later, a failure band formed from the toe to surface, in which the q* reaches to the residual value. Finally an unstable block appears in slope, taking the band as its boundary connecting the stable area of ground. Figure 5 shows the change of the distribution of plastic shear strain. Similar to the stress-history ratio, shear strain develops very quickly in a zone at the time of 4.67 years. The propagation of the shear zone in which a large shear strain occurs takes the same form as the failure zone shown in Figure 4.

336

Figure 6 Change of excessive pore-water pressure Figure 6 shows a change of distribution of excessive pore-water pressure with the time. At the time immediately after the completion of excavation, a large excessive pore-water pressure developed in the

ground, resulting in an apparent shear strength that keeps the slope stable. After 4.67 years, it dissipated gradually and the failure zone shown in Figure 4 began to develop due to the loss of the apparent shear strength. At the moment, the excessive porewater pressure reached its minimum value. When the shear zone formed, strain softening occurred and a dilatancy develops in some area, resulting in an increase of excessive pore-water pressure as shown in Figure 6. From Figures 4-6, it is clear that because of the dissipation of an excessive pore-water pressure due to excavation, the ground of cut slope lost its apparent strength and a strain softening occurs in some area. Then a redistribution of stress leads to a start of the propagation of the softening zone, resulting in the formation of the failure band and the shear zone. The failure band develops gradually and finally a global failure in cut slope happens.

Figure 8 shows the change of stress ratio with time and the stress-strain relations. It is also known that the stress ratio increased very slowly but did not change for a long time, meanwhile the plastic strain was very small. When the ratio reached its peak value, strain softening occurred and the plastic strain developed very quickly, resulting in a sharp reduction of the stress ratio. It is also found that the time when strain softening occurs is different for different elements, showing a clear propagation of the softening zone. In group A, the softening propagated from inner to outer, while for group Byit propagated from the lower to the up part. In both cases, the softening started from the shear band.

3.2 TIME HISTORY OF FIELD QUANTITIES IN THE ELEMENTS In order to clarify the mechanism of the progressive failure, the time history of field quantities such as stress ratio etc. in individual element is studied in detail. Two groups of elements located in the shear zone, one is grouped along a horizontal line and the other is grouped along the slope surface, are considered. Figure 7 shows the change of stress-history ratio with time in the elements. Obviously, the stresshistory ratio kept as constant for a long time and then increased abruptly to the failure line. Figure 8 Time change of stress ratio and stress-strain relation

Figure 9 Relation of strain rate with time

Figure 7 Change of stress-history ratio with time

337

Figure 9 shows the relation of strain rate with time. It is found that although the strain softening occurred at different time for different elements, the creep failure that is usually marked by an acceleration of strain rate occurred at the same time in all elements, implied that the global failure does not depends on a single element, but depends on the deformation of surrounding ground. Figure 10 shows the stress and stress-history path of element 423. The stress at the end of excavation has already excceed the residual line, while the stress history is under the line, showing that it is stable at the moment. Then the stress history and the stress move towards the failure line and finally they reached the line and failed.

Figure I1 shows the time history of the stress ratio, the stress-history ratio, the volumetric strain and the excessive pore-water pressure of element 423. The figure gives a clear description of the change in these valuables. The strain softening of the element always accompanied with dilatancy, resulting in an increase of excessive pore-water pressure and an acceleration of the strain rate 4 CONCLUSION Based on the numerical analysis of progressive failure in a cut slope conducted in this paper, the following conclusions can be obtained (1) A cut slope of soft rock may remain stable for a long time after the completion of a rapid excavation. Sometime, however, a failure band may forms abruptly in the slope and then slope may fail overwhelmingly at a few months. (2) The propagation of the shear zone in cut slope takes the same form as the propagation of the failure zone. (3) The progressive failure in a cut slope is caused by the redistribution of a stress due to the stain softening. (4) Before a global failure of cut slope, an acceleration of a strain rate, and an increase of a negative excessive pore-water pressure that has dissipated long time before, can be observed in a localized area. ( 5 ) By conducting a soil-water coupling analysis, it is possible to simulate the time dependent behavior of geologic materials due to pore water-soil interaction. (6) The progressive failure of cut slope can be simulated with a soil-water coupling analysis based on an elasto-plastic model with strain softening.

Figure 10 Stress and stress-history path

REFERENCES Adachi, T., and Yoshida, N., 1993. Analysis of excavation in clay shales with high KO stress states, Proc. Int. Symp. on Application of Computer. Mathematics in Rock Mechanics and Engrg, Xian, China, pp835-842. Adachi, T., Oka, F. and Zhang, F., 1994. An elastoviscoplastic constitutive model with strain softening and its application to the progressive failure of a cut slope, AMD-Vol. 1 83/MD-Vo1.50, Material Instabilities: Theory and Applications, ASME, pp.203-217. Oka, F. and Adachi, T. 1985. A constitutive equation of geologic materials with memory, Proc. 5th Int. Conf. on Numerical Method in Geomechanics, Balkema, V01.1, pp.293-300. Yoshida, N., Morgenstern, N., and Chan, D. H., 1991, Finite-element analysis of softening effects in fissured, overconsolidated clays and mudstones, Canadian Geotech. Jour., Vo1.28, pp.5 1-6

Figure 11 Change of stress and strain in element 423 338

Slope Stability Engineering, Yagi, Yarnagarni& Jiang 0 1999Balkerna, Rotterdam, ISBN 90 5809 0795

A back analysis in assessing the stability of slopes by means of surface measurements S.Sakurai Hir-oshimuInstitute oj Technology, Jupun

T. Nakayama Kohe University, J q m n

ABSTRACT: This paper deals with a back analysis method for assessing the stability of slopes which can determine not only a sliding plane, but also the strength parameters, such as cohesion and internal friction angle, by using displacements measured at the slope surface alone. This method makes it possible to use a GPS surveying for monitoring the slopes. The method is based on a concept of strain-induced anosotropic damage of geomaterials, and formulated by finite element method. Furthermore, taking into account the critical strain of geomaterials, the strength parameters can be determined, so that a factor of safety is easily evaluated by this method.

1INTRODUCTION The stability of slopes is in general assessed by a factor of safety. In this method, strength parameters such as cohesion and internal friction of angle of concerned geomaterials are most important. The laboratory tri-axial tests on small specimens which have been most commonly used may be adequate for either soils or soft rocks. However, the strength parameters of hard rocks are difficult to obtain by using a small specimen in a laboratory. This difficulty is because the strength of hard rocks entirely depends on joints and joint systems existing in rock masses. Therefore, the effect of joints on the strength of rocks must be taken into account. For this purpose, in-situ tests such as direct shear test may be useful, but it is costly. As an alternative for the in-situ tests, field measurements by using extensometers and inclinometers are carried out during the excavation of soils and rocks. The objectives of the field measurements are first to monitor the stability during excavation of the concerned structures like tunnels and slopes. The idea of monitoring arises because the real behavior of structures under excavation quite often differs from the one predicted at the design stage. In such a case that the real behavior differs, the original design must be modified. This evaluation and modification of the initial design, then, is the second objective of field measurements. In this process of evaluation and modification, the question of how to design parameters such as cohesion and internal friction angle arises.

This paper addresses the question of how to monitor the stability of slopes and how to assess the strength parameters, cohesion and internal friction angle. A back analysis is described which can determine the location of sliding planes, and can evaluate the cohesion and internal friction angle from field measurement results. Since displacement measurements are most commonly carried out, the field measurement results are usually displacements. This proposed method is also used for interpreting the measurements results of GPS surveying.

2 MODELING OF ROCKS It is assumed that the concerned rocks are highly jointed, so that the continuum mechanics approach can be adopted. The constitutive equation adopted in the back-analysis is based on the concept of staininduced damage (Sakurai et al, 1998). The straininduced anisotropic damage is defined in such a way that the geomaterials start to yield as the shear strain along the slip plane reaches a certain level, the slip planemay occur along the direction of the maximum shear strain. However, slip does not occur completely unless the maximum shear strain becomes quite large, Therefore, in this paper we call it a “potential slip plane.” When the principal stress directions are known, the direction of a potential slip plane is determined, considering the Mohr-Coulomb’s failure criterion. The conjugate slip plane is also defined as shown in Fig. 1. The constitutive equation expressed in the

339

local coordinate system x’ - y ’ is shown for twodimensional plane strain condition in Eq.(l):

Fig. 2 Parameter m (= U E )versus shear strain. Fig. 1 Conjugate slip planes under a triaxial compressive stress condition.

11-Y

Y

0

1

0

! (2)

It is noted that there are two ways for the cause of displacement in slopes. One is due to the reduction of stress caused by excavation. The other is due to the reduction of strength of soils and/or rocks. In other words, in the second case the displacements occur as the parameter of m decreases, even though there is no excavation. This type of decrease of the parameter m may be caused by weathering. However, it should be noted that no matter what cause may be the increase of shear strain causes the reduction of the parameter m (see Fig. 3).

1 2(1+ where E and Y are Young’s Poisson’s ratio, respectively. The the ratio of shear rigidity to Young’s anistropic damage parameter d is follows:

modulus and parameter m is modulus. The then defined as

where Y is Poisson’s ratio. Laboratory experiments show that the parameter m is expressed as a function of the maximum shear strain in the following general form. One of the results for sand is shown in Fig. 2. It is worth mentioning that Young’s modulus remains almost constant, while shear modulus decreases as a function of shear strain. Eq. (2) can be transformed to a global coordinate system as follows:

7

U )

Fi m

Fig. 3 Relationship between increments of parameter m and shear strain. In this study, the finite element method is adopted. When the parameter m decreases in a certain increment, say Am (see Fig. 3), the external forces acting at each nodal point, which are the equivalent to the reduction of m values, can be represented by the following equation:

(4) (5)

where [ T] is a transformation matrix.

340

. .. .

where [ B ]is a matrix connecting strain in an element with displacements at nodal points of the element.

{cr} is stress induces by gravitational force.

Sakurai and Hamada (1996) demonstrated that the constitutive equation shown in Eq.(l) can simulate well three different types of deformational modes of slopes, that is (1) elastic, (2) sliding and (3) toppling.

3 PROPOSED METHOD FOR PREDICTING A SLIDING PLANE A method for determining a sliding plane from displacement vectors measured at the ground surface is proposed. Though the method may be extended to a three dimensional case, a two dimensional case is illustrated here.

Fig. 5 Application of the proposed method for predicting a sliding plane from the ground surface displacements displacement vectors as the measuring value, a sliding plane is predicted by using the proposed method. It is obvious that the predicted sliding plane falls exactly within the assumed damaged zone. This means that the proposed method is well applicable to accurately predict a sliding plane from surface displacements alone.

4 BACK ANALYSIS PARAMETERS

OF

STRENGTH

As already mentioned the stability of slopes is usually assessed by the factor of safety. The determination of factor of safety generally requires strength parameters such as cohesion and internal friction angle. These strength parameters are difficult to evaluate at the design stage because there are many Consider the displacement of vectors measured along uncertainties involved in geological and the surface of slopes, as shown in Fig. 4. It is To geomechanical characteristics of geomaterials. assumed that we can find the edge of the sliding plane overcome these difficulties, field measurements are at point A, considering displacements of the ground surface. A sliding plane starts from the point A carried out for the monitoring of slope stability during its excavation. Monitoring displacement parallel to the displacement vector ul, until hitting measurements by using extensometers, inclinometers point B on a straight line which is perpendicular to the slope surface and passes through point E located and surveying are commonly used. The question is at the center of the two measuring points @ and 0. however how to determine the strength parameters From point B, the sliding plane stretches parallel to from the measured displacements. There are two different approaches available to the displacement vector u2 until hitting point C. After that we repeat the same procedure as before answer this question: (1) a non-linear back analysis in until arriving at the last point D. the determining strength parmeters directly from In Fig. 5 w e demonstrate the adequacy of the displacement measurements, and (2) a linear back proposed method. In this figure the displacement analysis in which the moduli of deformation such as vectors u1-ul0 were obtained by the finite element Young’s modulus and shear modulus, is firstly method assuming a damaged zone indicated as the obtained, and the strength parameters are then shaded zone in the figure. In this damaged zone, determined from the back-analyzed deformation decreases. Considering these the parameter m

Fig. 4 Schematic diagram for the procedure of the proposed method.

34 1

moduli by considering the correlation between the strength and deformability of geomaterials. This paper uses the second approach. Sakurai (1983) demonstrated that there exists a good correlation between the strength and deformability of geomaterials like soils and rocks. The ratio of uniaxial strength to Young’s modulus is defined as “critical strain”, which is a function of Young’s modulus. It is a great advantage for the critical strain that there is no scale affect, so that if Young’s modulus is known, critical strain can be immediately evaluated. Once the critical strain together with Young’s modulus are known, uniaxial strength can be evaluated by the definition of critical strain, and cohesion of the materials can be obtained by assuming the internal friction angle. The procedure of this back analysis is as follows:

(1) The parameter mi and m (see Fig.3) are determined by a back analysis of the displacement vectors measured at the ground surface. In this back analysis, m; and m may be determined as to minimize the following equation:

2

Fig. 6 The relationship between critical shear strain and shear modulus.

(5) Cohesion c is then determined by the following equation assuming the internal friction angle q5 :

(6) The factor of safety can then be calculated by a conventional limit equilibrium method. The procedure of this back analysis is illustrated in Fig. 7.

(7) Uirn

i=l

where U; and uic are measured and computed displacements at measuring point i , respectively, and N is the total number of measuring points. (2) Since Young’s modulus E has also been determined by the back analysis, shear modulus G can be evaluated by

G G = mE

(8)

(3) The critical shear strain y , is determined by the following equation (Sakurai et al, 1993):

Sheor Hodu I U S

(a) Relationship between shear modulus and critical shear strain

where E , is the critical strain and Y is Poison’s ratio. The critical shear strain y, is plotted in relation with shear modulus G, as shown in Fig. 6. Thus, from this figure the critical shear strain can be evaluated from shear modulus determined by Eq. (8). I

0

following equation:

( The definition of shear strain is y ,

>

I

(4) Shear strength zccan then be determined by the (b) Shear strength

=

Fig. 7 Schematic diagram for critical shear strain and shear strength

‘A

)

342

5 CONCLUSIONS (1)To represent the deformational behavior of slopes, the parameter m, whose physical meaning is the ratio of shear modulus to young’s modulus, was proposed. Considering this parameter a constitutive equation has been proposed. (2) A method for determining the location of a sliding plane has been described. This method requires the displacements at the ground surface alone be known. This means that this method can be used for interpreting the results of GPS surveying being carried out during the monitoring of slopes.

(3) A back analysis method for evaluating the strength parameters such as cohesion and internal friction angle from measured displacements have been described. In this method, the parameter m, together with the critical strain plays a key role. It is a great advantage that according to this method, the strength parameters can be evaluated by displacement measurements which are commonly carried out during monitoring of slopes. Once the strength parameters are obtained, the factor of safety can easily be evaluated. REFERENCES Sakurai, S., I. Kawashima and T. Otani, 1993. A criterion for assessing the stability of tunnels, EUROCK’93, Lisboa, 969-973 Sakurai, S. and K. Hamada, 1996. Monitoring of slope stability by means of GPS. Presented at the 8th Intl. Sympo. Deformation Measurements, Hong Kong, June 25-28. Sakurai, S., A Hiraoka and K. Hori, 1998, Straininduced damage of rocks, Proc. 3rd Intl. Conf. on Mechanics of Jointed and Faulted Rock, Vienna, 21-27

343

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami 8 Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Numerical simulation of excavation of the permanent ship lock in the Three Gorges Project Yongxing Zhang & Ke Yin Chongqing Jianzhu Universiv, People’s Republic of China

ABSTRACT: According to the characteristics of rock mass slope of the permanent ship lock in the Three Gorges Project, it is simplified to be orthotropic. Based on the characteristics of unloading, the law of mechanical parameters changing with the degree of unloading caused by slope excavation is presented in this paper. The software of unloading nonlinear finite element analysis of rock mass excavation named UNLOAD has been programmed. Numerical simulation of excavation of the rock mass slope of the permanent ship lock has been done by this program. The results are consistent with the in-situ observed data. There are differences of several orders of magnitude between these results and those of other past researches. 1 INTRODUCTION The permanent ship lock is one important part of the Three Gorges Project. It is also one of the biggest navigation buildings over the world. Its characteristics are: (1) Huge dimension The total length of the lock is 1617m, and the effective lock room dimension is 280mX34mX5m. The ship lock is located in a trough valley excavated deeply in granite rock mass. (2) Obvious anisotropy There are many kinds of structural planes in the bedrock that is mainly composed of granite. The structural planes include dikes, faults, joints and cracks. These structural planes, especially those have large inclinations, make the rock mass anisotropic. (3) High initial stress Because of complex geological conditions, the initial stress is up to 10Mpa. After rock mass excavation, the initial stress-unloading area is wide, and the secondary stress field is induced in the new rock slope. The deformation of rock mass is relatively large. (4) Obvious horizontal unloading The river valley topography of the Yangtze River makes the rock inass unload in the East, West and South directions, which mainly occurs in the Huangling anticlinal plagio-granite. The dominating unloading direction is perpendicular to the axis of the lock slope. It is typical rock mass unloading and natural unloading is coupled with artificial unloading.

The main problem in past analysis of rock slope stability or stress-strain relationship is that the value of deformation obtained from computation or lab test is much less than that from in-situ observation.

For examples, in-situ gaps of cracks in rock mass of Lian Zi Ya precipice, which is in the Three Gorges of Yangtze River, are over 2m, but results of past computations and lab tests are only about 3cm. The actual deformation of the slope of Jin Chuan Open Mine is already over 5m, but results of past computations and lab tests are only about 20cm. Obviously, these results can not correctly represent the mechanism of slope deformation and damage. The main reason of above problems is that there are many joints, cracks and the existence of initial stress in rock mass, which make the stress-strain relationship different for loading and unloading. The rock mass deformation of unloading is much larger than that of loading. When tensile stress appears in rock mass, the difference is even more evident. In past research it is assumed that the constitutive relationships under loading and unloading condition are the same. The relationships are also thought to be the same when rock mass is subjected to tensile and compressive stresses. Generally, the mechanical parameters used are obtained from loading mechanical tests as well. According to the actual situation of the high rock mass slope of the permanent ship lock in the Three Gorges Project, the mechanical characteristic of unloading with slope excavation is studied in this paper. The numerical simulation has been done for excavation of the high rock mass slope of the permanent ship lock.

345

2 MECHANICAL CHARACTERISTIC OF SLOPE EXCAVATION AND UNLOADING In the geological history a sequence of architectonic actions have made various joints and cracks in rock mass of the ship lock, so the strength of rock mass is much less than that of the rock. In the tests for the in-situ deformation curve or strength of rock mass, or when rock mass being excavated, the stress-strain curve of rock mass is a continuation of the architectonic loading and unloading curve, as shown in Figure 1. Because of the architectonic actions, it is assumed generally that the initial state of stress is at point a in the figure. Due to unloading in rock mass, the stress-strain relationship will advance along the unloading curve abc into the tension region. As to loading in rock mass, it will be along the curve ab'c' to the compressive strength of the rock mass, point c' . It is seen in the figure that the initial modulus of loading is much larger than that of unloading, and the strength point c' is the residual strength of rock mass. In 1986, in-situ tests were done for studying the mechanical characteristic of the bedrock of the dam in San Dou Pin. The method of flexible plates was used at all test points. The stress-strain relationship curve was obtained from the tests, just as shown in Figure 2. The results of these tests indicate that the slope of the unloading curve decreases rapidly with the stress reducing to low level. In rock mass excavation, the stress is usually unloaded to low level and there are relative large tensile regions appear, so it is important to study the stress-strain relationship under condition of unloading and to tensile stress. Chongqing Jianzhu University and Ge Zhou Ba College of Hydraulic and Electric Engineering, in order to study thoroughly the unloading mechanical characteristic of rock mass with tensile regions, have done some mechanical tests with similar models.

The test simulation material is a mixture of barite powder, gypsum and water. There are many class 111, IV and V structure planes in the rock mass slope of the permanent ship lock. For analyzing the influence of the various structural planes on the strength of rock mass and deformation behavior, the engineering dominant structural planes have been considered in these tests. These structural planes have large inclinations and are the most important influence factor of anisotropy and unloading characteristic in rock mass of the slope. The special triaxial test equipment was designed for the tests. Thus, the actual unloading condition of slope excavation can be simulated, in order to achieve the nonlinear constitutive relationship and corresponding mechanical parameters. According to the past geological research, the loading paths of these tests are based on principle of architectonic movements in this area, which started from the structural system of the rock mass formed by the sixth tectonism (Movement of the Himalayas). The loading and unloading paths of triaxial tests are keeping with the actual plane strain problems. The error is about 20% when 3D problem is simplified to a plane one. Therefore, the result of the tests is very useful in engineering, and it is the basis of nonlinear mechanical analysis of the permanent ship lock and research of anchorage methods.

Figure 2. Stress-strain curves of the tests with flexible plates

Table 1. Unloading modules of horizontal deformation of slightly weather and fresh granite rock mass. (E0=40GPa, o ,=lOMPa) (unit: GPa) <30 30508090100% "load % 50% 80% 90% 100% Figure 1. Diagram of stress-strain curve of unloading and loading tests

E 26 18 E'/E 0.65 0.45 "Tensile stress

346

12 0.30

3.2 0.08

0.4 0.01

0.25 0.006

iterative steps. Thus, they can represent the unloading characteristic of the rock mass. The process of deformation to damage of the rock mass slope can be simulated by this method. The conventional programs of finite element method can not be used directly in computation and analysis of unloading nonlinear rock mechanics. We have expanded and developed ADINA, a wellknown standard structural nonlinear FEM program. It was used in computations of Jin Chuan Open Mine slope and Qian Mu Rock Tunnel, where there are plentiful observation data. The order of magnitude and tendency of computation results are consistent with in-situ values. However, the program used is expanded from others, so the amount of manual work is very large. One specific program for unloading nonlinear excavation has been programmed by the authors, named UNLOAD. Results computed by this program are the same as that by the expanded one, but manual work is reduced to the least amount.

The horizontal deformation modules of slight weathered granite rock mass in different unloading period are shown in Table 1. E, is the initial “loading” modulus, which formerly was used in almost all cases, no matter what condition rock mass was under; E, is the “unloading” modulus. It is shown in the table that the horizontal deformation modulus of rock mass decreases with the increase of amount of unloading, this phenomenon is more apparent in the region of tensile stress. Moreover, for any particular stress the unloading modulus is less than the corresponding loading one.

3 COMPUTATION METHOD OF ROCK MASS EXCAVATION AND UNLOADING The degrees of unloading are different in different regions of rock mass as it is excavated. The unloading mechanical parameters used should be consistent with the unloading condition in the rock mass. The excavation can be approximately simulated by the following steps: (1) The rock mass in computational area is considered as an anisotropic continuum. The stress field and unloading forces on the excavation boundary are computed firstly. (2) Without changing the parameters of the rock mass, the stress field of the rock mass slope is computed when it is acted with the unloading forces from the first step. Comparing this stress field with that of step 1, the rock mass after excavation of the slope can be divided into several regions with different degrees of unloading. (3) According to unloading mechanical characteristic of the rock mass, the unloading mechanical parameters are determined in corresponding regions with different unloading degrees. When the unloading forces are applied in opposite directions, the initial displacement and stresses of rock mass are computed, and the quality of rock mass is degraded by excavation and unloading. (4) The unloading regions computed above will expand continuously. The unloading regions can be determined again by the same way, and the iterative process will last until satisfactory accuracy. In the computation of the rock mass slope of the permanent ship lock, according to the degrees of natural weathering, the rock mass of the slope is classified into strongly weathered, less weathered, slightly weathered and fresh. The results of computation show that after excavation of the rock mass the depth of strongly degraded region is about 5m, and that of the influence region where the quality of rock mass is degraded by excavation is about 20m. Then there are over ten computational regions, in which the corresponding macro mechanical parameters used are different in different

4 SIMULATING THE EXCAVATION OF HIGH SLOPE OF THE PERMANENT SHIP LOCK 4.1 Comparing and analyzing the results of computation and observation In the past analysis, the observation data in one particular period were compared with computation results, which were the total value of deformation. Thus, the comparison is worthless obviously. In this paper where the observation points locate and when the observation start as well as the corresponding excavation elevation are paid enough attention. Then the computation results at same time and excavation elevation are compared with the corresponding observation data. The UNLOAD program was used in the stepwise computation of three observation points in the high slope of the permanent lock: TP40GP02, TP41GP02 and TP42GP02. The excavation level of every computation step is based on the observation data of the three points. The comparison between observation data and computation results is shown in Table 2. It indicates that the displacement computed by unloading nonlinear program UNLOAD is consistent with that of observation. Thus, the abovementioned model and parameters of unloading nonlinear rock mechanics can represent the actual rock mass condition of the high slope of the permanent lock. 4.2 Predicting the deformation of high slope of the permanent ship lock Results of Computation are shown in Table 3 when 347

the permanent lock is excavated completely to its design altitude in the simulation computation. We also computed the deformation of the same sections with the elastic-plastic Drucker-Prager criterion with corresponding tensile strengths, in which the usual isotropic deformation parameter (E=3 5Mpa) of less weathered and fresh granite rock was used. The results are equal to those of other past research. The horizontal displacements of the top of the lock room, which are computed by UNLOAD and traditional method respectively, are both shown in Table 3. It indicates that there are different orders of magnitude between results of these two computations. If the loading mechanical parameters of rock mass are used in computation, the results show that terminal horizontal displacement of the rock mass in this section without supporting is about 4cm. However, the computation results of UNLOAD program show that the corresponding displacement depends on the tensile strength of rock mass, and it is over lOcm at least.

5 CONCLUSIONS 1. Because of many structural planes with large inclinations and nonhomogeneous behavior to a certain extent, the rock mass in this area is obviously anisotropic. In order to simulate the behavior of the rock mass, it is suitable to choose an orthotropic model in computation. 2. The natural condition is changed with excavation of the rock mass slope of the permanent lock, large unloading and tensile regions appearing. The rock mass characteristics of unloading are different from those of loading. Only when the mechanical parameters be considered as degrading Table 2. Comparison between computation results and observation data. (unit: mm) Obser- Computation result ObservaAltitude vation (r ,*=2.2 cr t=l .5 tion point (m) Value MPa MPa TP40GP02 +170 17.38 15.10 18.2 TP41GP02 +185 24.33 26.60 30.8 TP42GP02 +200 22.88 20.05 21.0 *Tensile strength used in computation.

continuously in the computation process can the results be consistent to the actual situation. 3. The research shows that macro mechanical parameters should be adopted in simulation computation of excavation of rock mass slope, and the anisotropy should be considered. Thus, the results of computation can reflect that of observation. The results of unloading computation show that without supporting the tensile strength of rock mass of the permanent lock decrease gradually, and the largest displacement is over lm, but only 4cm in usual computation. 4. The results of computation indicate that according to the present design plan there will be several large tension regions after excavation. These regions are mainly concentrated under the two walls of the lock rooms and in the middle partition wall. This is unfavorable to maintain the lock gates. 5. The largest unloading displacement is about 14cm during excavation. It occurs in one very short period. This displacement is hard to be controlled by any past reinforcing methods. Therefore, initial lateral pressure should be applied beforehand or promptly during excavation. This can prevent rapid development of the unloading process and stop more quality degrading of the rock mass that may cause too large displacement and even make the slope collapse. REFERENCE Ha, Q.L. & G.L. Liu 1996. Research of engineering geology in unloading rock mass of rock slope. Beijing: Chinese construction industry. Ha, Q.L. & J.L. Li 1996. Research of macro mechanical parameters in unloading rock mass of rock slope. Beijing: Chinese construction industry. Ha, Q.L. & Y.X. Zhang 1998. Research of unloading nonlinear rock mass mechanics of rock slope. Beijing: Chinese construction industry.

Table 3. Horizontal displacements of the top of the lock room with different tensile strength. (unit: mm) - 1 , -

I

Unloading 14.82 15.95 21.37 56.00 72.00 4.06 4.06 4.06 4.08 4.11 Loading *Tensile strength used in computation.

348

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Numerical simulation of the buckling failure in rock slopes Y. Hu & H.-G. Kempfert Institute of Geotechnics, University of Kassel, Germany

ABSTRACT: The buckling of slope in jointed rock is a special failure mode. In this paper, a numerical method is presented simulating the buckling failure process of rock slope. The calculation model is based on the geometrically nonlinear theory and implemented by using finite element method. The discontinuity behavior is simulated using "joint element". A calculation example is illustrated for a slope in an open pit mining. 1 INTRODUCTION

It is well-known that the geological structure and strength of the rock discontinuities as well as its orientation with respect to the slope face are the essential factors to the failure of rock slope. The preexisting weak planes or discontinuities with unfavorable orientation are usually the failure surfaces of an unstable rock slope, whereas in soils it appears generally in the form of a circular arc. The pure sliding is predominately the failure mode in rock slope engineering. However, it was reported in the literature that the buckling failure of rock slope can occur if the rock mass contains one or more throughgoing discontinuities approximately parallel with the rock surface, see e.g. Fig. 1. This failure mode appears in sedimentary rocks containing slabs separated by bedding planes, and also in jointed rocks. In general, the buckling failure may occur in the rock slopes, if the slope dips more steeply than the internal friction angle of the discontinuities parallel to the slope. The basic boundary conditions may be described as follows: a) Major discontinuity set is parallel to slope face; b) The spacing of discontinuity set is relatively small; c) The discontinuities have a low friction angle smaller than slope angle. Kutter (1974) as well as Hock Lk Bray (1977) described and discussed the buckling failure of the

a) photograph of the buckling

b) three hinge buckling model Figure 1. A buckling failure of sandstone strata in an o en it coal mine and modeling, from Cavers 98

6 17.

349

rock slope qualitatively. For plane slope, Cavers (1981) assumed four possible failure modes of single slab lying on the slope and formulated two simple approaches to the analysis of buckling failure of rock slabs. Hu & Cruden (1992) reported the buckling of beds in the sedimentary rocks occurring on steep underdip and dip slopes in the Highwood Pass, Alberta, Canada. The observation and the analysis of the four buckling sites indicated that the bedding thickness is an important parameter determining the modes of buckling. The corresponding mechanical models were proposed for predicting the initiation of the observed buckling behavior. In these approaches, however, only the critical state at failure is referred to and the failure procedure can't be simulated. In this paper, a numerical method is presented simulating the process of buckling failure in rock slope. A calculation example i s given for the buckling failure of a rock slope in an open pit mining. 2

MODELING OF JOINTED ROCK

As a simplified way, the jointed rock can be approximately seen as a continuum material, see e.g. Zienkiewicz & Pande (1977), if the dimension of building is much smaller than that of joint spacing. In the replacement material, the real spacing of the discontinuities exists no longer (dT1, d7.2, d7.3, compar. Fig. 2 a) and b)), and each point in this new material behaves mechanically same, whereas the orientation (striking and dip angles of the discontinuities ( ~ t 7 . 1 , P7.l Ct7.2, P T ~ aT3, , p.1.3) remains. This represents the deformation and strength anisotropy. The influence of discontinuities in elastic stage (kN,T1, kS,TI ,~N,Tz, kS,T2, kN,T3, kS,T3) is taken into consideration using the average values for rock mass (EF,UF). The analysis using this modeling lead normally to conservative results. Separate treatment of joints becomes necessary, if the joint opening or large sliding along joints occurs. In these cases, a combined modeling seems to be computationally economical. That is, the discrete modeling is applied to the area where the joints should be individually considered, whereas the other area of the jointed rock is simulated using the homogeneous model, see Hu (1997).

Jointed rock is essentially a discontinuous system. In general, there are two ways modeling its stress-strain behavior. To represent the hndamental behavior, a rock mass containing three families of discontinuities (joints) is illustrated in Fig. 2 a).

Figure 2. Modeling of jointed rocks.

350

Compared to this procedure, the distinct element method was specifically developed for discontinuum analysis in rock mechanics about thirty years ago, see e.g. Cundall (1988). Here, jointed rock mass is represented as an assemblage discrete blocks. All joints in rock mass are individually treated and viewed as interfaces between distinct rock blocks. The corresponding contact forces and displacements at the interfaces are determined through a iterative procedure using the principle of mechanics. For many years, however, it was seen as not-yet-proven numerical technique and has not been applied so extensively as conventional continuum analysis technique. In the recent years, the theoretical further refinement and the development of the software related to this method were made. More and more rock engineering projects are analyzed using this technique. In the near future, it may become a generally recognized tool in the analysis of rock engineering as the continuum technology.

{f?(t+At)}: { f"(t+At)}: (F'(t+At)}:

This equation can then be converted into a finite element formulation:

[KL,tl :

linear stiffness matrix referred to the configuration at step t; [KN,~]: nonlinear stiffness matrix referred to the configuration at step t; {Rt(t+At)}: total force applied at step t+At referred to the configuration at step t; { Ft } : equivalent internal force vector at step

FORMUALTION OF THE APPLIED MODEL

3

body force vector at step t+At; total surface traction vector applied at step t+At; total concentrated load vector applied at step t+At.

{ AFtVp} :

For the analysis of the buckling failure of rock slope presented in this paper, the continuum model is applied with the special treatment for some key joints. In order to investigate the buckling phenomena, the geometrically nonlinear theory is used. Arising from the updated Lagrangian formulation and the elasto-viscoplastic theory, the controlling equation can be written to:

equivalent visco-plastic force vector at step t+At referred to the configuration at step t.

Upon the finite element equation (2) a finite element program has been developed for analyzing the deformation and stability of buildings in jointed rock. In addition, "joint element" has also been implemented in this program which makes the separate treatment of some key joints possible. 4 NUMERICAL CALCULATION EXAMPLE

W(t + At) -

'I

4.1 Details of the problem

i,,, ~ ( A E , ) ' (a(t)}dV(t) + *

Fig. 3 shows the cross section of an open pit coal mine as well as the planed excavation procedure. The slope is located in a geological fold and covered by two rock slabs being 0.6 m thick, respectively. The dip above the fold is 50" and below the fold 70". The total height of the slope comes to 49 m. The discontinuities between the two slabs as well as between the underlying slope surface and the slab below have the same mechanical behavior as that of three cross joints. It is assumed that the tension strength perpendicular to the joints is zero. The geometrical and mechanical parameters of the jointed rock are given in Table 1.

7

~ ( A E . [D] . {AE jdV( t) L t ,

6

: (As,> :

PI

:

(A?-it}: {o(t)) : (Acvpt): {Au} :

(1) variationof; incremental linear strain vector referred to the configuration at step t; elastic matrix; incremental nonlinear strain vector referred to the configuration at step t; incremental linear strain vector referred to the configuration at step t; incremental visco-plastic strain vector referred to the configuration at step t; incremental displacement vector at step t+At;

351

Figure 3. Details of the problem,

COSS

section of an open pit coal mine with the rock slope.

Figure 4. Computation cross section and FE-mesh. 4.2 Computation cross section and FE-mesh Table 1. The geometrical and mechanical parameters of the jointed rock rock:

y = 25 kN/m3; E = 10000 MN/m2;

Fig. 4 illustrates the chosen computational cross section and FE-mesh. Apart from the area of slope surface, 8-node finite element elements were used for other area in the cross section. The rock slabs and joints on the slope surface were separately considered using finite elements and joint elements, so that the possible sliding and opening along the parallel and cross joints can be well simulated. The excavation was divided into 5 part excavations in the numerical simulation, see Fig. 3. Totally 6 calculation steps are necessary. In the first step the

U = 0.2.

parallel joints: a = 180"; p = 50"/70"; c = 0; cp = 26"; y~ = 12" cross joints:

a = 180"; p = 50"/30"/20"; c = 0; cp=26"; y ~ = 1 2 "

352

Figure 5 . Relative sliding of the second slab to the slope surface.

Figure 6. Opening of the second slab to the slope surface.

primary stress state before the construction was determined. The following 5 steps simulated the 5 step excavations. The designed FE-mesh consists of 1274 nodes, 189 elements as well as 58 joint elements.

round the fold and increases from 5.7 mm to 27 mm at the last two stages. From the development of the relative displacement, it can be concluded that the slope is in the critical state of buckling failure. Any minor disturbance may trigger the massive slab slide. Fig. 7 gives the total displacement arising from the excavation with the reference to the primary state.

4.3 Calculation results

In Fig. 5 and 6, the sliding as well as opening of the second slab relative to the underlying slope surface are illustrated for the excavation down to 45 m and 49 m, respectively. The relative sliding of the slab part above the fold appears toward the bottom while the slab part below the fold toward the top. It comes to ca 1.9 mm at the excavation depth of 45 m and increases drastically to 8.25 mm at 49 m. At the same time, the opening of the parallel joints occurs

5

CONCLUSIONS

The numerical method using the geometrically nonlinear theory and the discrete modeling of joints has been applied for simulating the buckling failure of rock slope in an open pit mining. The calculation example illustrates the gradual failure process in the course of the excavation until the critical state.

Figure 7. Total displacement with the reference to the primary state.

REFERENCES Cavers, D. S. 1981. Simple methods to analyze buckling of rock slopes. Rock Mechanics 14. Cundall, P. A. 1988. Conceptual, analytical and numerical modeling. Key address in 29'h U.S. Sym. on Rock Mech., Minneapolis, Minnesota. Hoek, E., Bray, J. W. 1977. Rock slope engineering. 2'ld ed. London: The Inst. of Mining and Metallurgy. Hu, X.-Q., Cruden, D. M. 1993. Buckling deformation in the Highwood Pass, Alberta, Canada. Can. Geotech. J. 30. Hu, Y. 1997. The buckling failure analysis of a cavern in jointed rock. Proceedings of the 36'h US Rock Mechanics Symposium (CD-ROM), NYRocks'97, Columbia University, New York. Kutter, H. K. 1974. Mechanisms of slope failure other than pure sliding. Rock Mechanics, International Center for Mechanical Sciences, Course and Lectures No. 165, L. Miiller ed. New York: Springer. Zienkiewicz, 0. C., Pande, G. N. 1977. Time-dependent multilaminate model of rocks - A numerical study of deformation and failure of rock masses. Int. J. Num. & Anal. Methods in Geomech., Vol. 1.

354

Slope Stability Engineering, Yagi, Yamagami & Jiang (c) 1999 Balkema, Rotterdam, ISBN 905809 0795

Fuzzy-based stability investigation of sliding rock masses N.O. Nawari & R. Liang Civil Engineering Depurtment, Universig of Akron, Ohio, USA

ABSTRACT: Stability of rock sliding surfaces is governed not merely by the shear strength of rock alone, but also by various rock defects, such as jointing, cracks, fissures and other possible weaknesses. In bedded or foliated rock, cut by joints, there are many possibilities for a block mass movement along weakness planes and a large variety of behavioral modes are exhibited. The appreciation of modes of failure in such cases has usually ill defined boundaries. Gravity, tectonic, weathering and erosion brought about by the environment are factors contributing eventually to the instability of rock slopes. Such factors are generally difficult to quantify with the present approaches. In this paper a new procedure to estimate the risk of instability of sliding rock masses will be presented using fuzzy-safety techniques. This will enable to solve the difficulties mentioned above in quantifylng the noisy geological and environmental data. The application of this method in the practice will be illustrated by numerical examples.

1 INTRODUCTION Rock slope stability analysis and design are rarely free from uncertainty. Uncertainty in a design situation emerges whenever information pertaining to the situation is deficit in some respect. It may be imprecise, incomplete, fkagmentary, unreliable, ambiguous, vague, contradictory or deficit in some other way. For example, the real behaviour of rock, soil and soft rock-hard soil near failure remains unknown in most cases because of the diversity of complex factors affecting the behaviour. Unexpected loading conditions, or unseen deficiencies in soil or rock continuum are likely to cause the geotechnical structure (tunnels, dams, natural slopes, waste deposits,. ..etc.) to behave other than usually assumed (modelled as linear or idealised non-linear) and it is not practical in most cases to conduct even a single full scale test of these massive geotechnical structures. Conventionally, in the construction of the mathematical models of these ambiguous systems, the imprecision is standardly modelled as a random process (classical stochastic model). This conventional probability theory require idealised assumptions such as the independent of evidence and the mutual exclusiveness and exhaustiveness of

hypotheses. Other uncertainties, especially those involving description and, judgmental opinions, as well as those based on very scarce information have never been incorporated satisfactory in the probability theory (Klir, 1988, Kosko 1992). In other words, uncertainties of geotechnical parameters (geological materials and structures, boundary conditions, loading, ground water, ...etc.) can not be adequately described with probabilistic models. Rock slope failure represents one of the most complex geotechnical problems that can not be grasped and analysed totally by any conventional mathematical models. This is due to the diversity of factors affecting the stability of the slope. Factors such as variation of geological formations, hydrogeology, tectonic forces, vegetation, rainfall, erosion, temperature fluctuation, frosts effects, ...etc. are difficult to include in safety analysis computation. Difficulties stem from the vague, incomplete, and ambiguous terms and concepts concerning these parameters. It is more rational to describe these factors in the manner of fuzzy variables. Presented in this paper is a new approach to estimate risk and safety of rock slope stability employing methods of fuzzy quantification, synthetic fuzzy evaluation, and

355

computation with imprecise and uncertain parameters utilizing the concept of fuzzy variables and fuzzy preference functions. 2 THEORETICAL SETTING

The essential theoretical backbone for the fuzzybased slope stability investigation will be stated below: 2. I Tlzejkzzy variable:

The preference fiinction of a fuzzy variable A, (AA) is a mapping from % (real number line) to the unit interval [0, 13 and is defined as a ,,class" with a continuum of grades of membership (Nahmias, 1978). Let X be a set of objects, called the universe of discourse, whose generic elements are denoted by Xi . Then if A is a subset of X with hA(Xi) is the grade of membership of Xi in A, A is completely characterised by the set of pairs: A = ((h~(x)/X):X E x,L*(X) E[0,1] 1 (1) 2.2 Fuzzy Relations

A fuzzy relation R is a fuzzy set in a Cartesian product X x Y of universe of discourse X and Y (Zadeh, 1971, 1973). R(x,y) is the membership value of (x, y) in R. Fuzzy relations generalize ordinary relations. As such, they can be composed: let R and S be two fuzzy relations on X x Y and Y x Z respectively, the membership function of the fuzzy relation R o S, on X x Z is defined by: S O S ( x ,z ) = SUP min (All ( x ,Y ) , ( x , 4) (2) YEY

Note that in (2), a product or other algebraic operations could replace "min". R can be interpreted as a fuzzy restriction on the value of a variable (u,v) ranging over (X x Y), i.e. R acts as an elastic constraint.

2.3 The Extension Principal:

Owing to this principle, any mathematical relationship between non-fuzzy elements can be fitted to deal with fuzzy entities. This principle will be stated below and its main applications will be seen later. Let AI, ..., A, be fuzzy sets over XI, ... X,. respectively, their Cartesian product is defined by: A ~ ... X XA,, = J ~ i n A ~ i ( x i ) / ( x , , . . . , x " ) (3) x,x.,.x X" i = l , 1 1 Let f be a mapping f : XI x.. .

x X, + Y . The fuzzy image B of AI, ..., A, through f has a membership function: AB( y ) = sup min AA8(xi) (4) x I,... X " E X I X ...X X , i=',n under the constrain y = f(x1, - .. x,). 3 APPLICATION EXAMPLE

Rock slope failure is generally governed by the intercalated change in lithologies and the related change in discontinuities such as faults, bedding planes and joints. The stability of rock slope is conducted to evaluate the possibility of slope failure in terms of plan sliding, wedge sliding and toppling. The first computation model for the slope investigation will be based upon the Direct Sliding Block Method(DSBM) (Nawari et. al., 1997b). This method assumes an admissible collapse mechanism of the sliding rock blocks and satisfies the conditions of statics and kinematic, (i.e. staticskinematic correct solution for the stability analysis). The second computation model deals with the quantification of subjective excitation conditions. This practical example concerns the determination of the safety of cut along a highway alignment passing through a rock formation. The characteristic values of rock properties and geometry are given in figure.1. The failure mechanism can be approximated by three sliding blocks as shown.

The governing equation at the limit state is given by

r

where

356

1

Figure 1: Jointed Rock Slope

4r = where, dCi = Cohesion force; 1; = Length of the block along the sliding surface; dui= Porewater pressure along the sliding surface of Block(i); dUi-,,i = Porewater pressure along the left side of Block(i); dUi,i+l = Porewater pressure along the right side of Block($ dWi = Weight of the sliding block(i) (including applied load); cpi = Friction angle along the sliding surface of Block(i); Vi-l,i = Friction angle along the left side; (Pi,i+l = Friction angle along the right side of Block(& 0; = Slope of the sliding surface in Block(i); a i,i+1 and ai-l,i = inclination of Qi,i+l and Qi-l,i from the horizontal; dQj = Resultant from normal and shear forces along the sliding surface of Block(i); dQij = Vectorial difference (dQi.l,i - dQi,i+l) with unknown inclination pi; dQi-l,i = Inter-block force from left inclined with the angle Oi-1,i against the horizontal; dQi,i+l = Inter-block force from right inclined with the angle oi,i+lagainst the horizontal; T = Fictitious disturbing shear stress; The safety measure is then adequate when T 2 0. Now, all design parameters in equation 5 will be considered as fuzzy variables and the computation of the fictitious disturbing shear stress T will be determined using the extension principle. The fuzzy variables are defined using linear and non-linear functions (equations 7-9) and are summarized in table 1.

;il

L(Q = L((a, - x) / U ) R(Q=L((x-a,)/v)

xIa,, u>o a, Ix, _a, -v

In case of non-linear functions, the reference hnctions L(<) and R(<) are given by the following relations:

(9) Table 1. Definition of the Fuzzy Variables

1

Variable

1

Function parameters

1.3 b3 [m] y [ ~ \ ~ / m ~20] 22 $["I 5 ~] c[M\T/~ 44

1.35 21

0.35 3

0.35 2

23 6 45

4 5 3

3 4 2

The results of the computations are depicted in Figure 2. In the fuzzy failure event, there is no unique precise limit state surface to provide a crisp portioning of strict dilapidated and survival sets. hstead a family of limit state surfaces will be

(0.8/0.6), (0.2/0.7), (O.UO.8) } hw3 = ((UO), (0.910.l), (0.5/0.2) } h~1= A, = CON(K3) = ((0.16/0.7), (0.25/0.8), (0.81/0.9), (14) } hm = {(0.4/0.7), (0.5/0.8), (0.9/0.9), (1/1) The total effect on the degree of danger of slope failure will be determined using the following equation: G = ( W I A K1) V (W2 A K2) V (W3 A K3) (10) If the measure of safety is defined using the index (13), then the interaction between consequence (K) and the index (13) is to be considered. Theses interplaying actions will be described using the following approximate reasoning relations: if K is significant, then 131 is very significant = {(O.O4/n), (0.64/(n-0.5)), (l/(n-1)) >. if K is medium, then 132 is significant = ((0.2/n), (0.8/(n-0.5)), (l/(n-1)) >. if K is small, then 133 is also small = {(l/n), (0.8/(n-0.5)), (0.2/(n-l)) }. where n = safety index (considered safety level ). Now, fuzzy relations between (K1, Bl), (K2,132) and (K3, 0,) can be constructed. These relations will be denoted by RI, R2 and R3. Further, a relation between RI, R2 and R3 will be created to estimate the entire interaction: R = R1 v R2 v R3 A subjective measure of risk of failure (S) will be built using the fuzzy composition: S=GoR W n n-.5 n-1 0.0 0.2 0.64 1.0 0.1 0.2 0.64 0.9 0.2 0.2 0.5 0.5 0.3 0.16 0.2 0.2 0.4 0.16 0.64 0.8 S = 0.5 0.16 0.64 1.0 0.6 0.16 0.64 0.8 0.7 0.16 0.4 0.4 0.8 0.16 0.5 0.5 0.9 0.16 0.64 0.9 1.0 0.16 0.64 1.0

>

1. -10

-15

U

-5

,

'

5

0

\

10

b 15

Figure 2. Safety Grade for the Rock Slope introduced to reflect the real structural environment (Nawari & Hartmann, 1997a, 1998): (a)- Safety state (I): absolute safe (b)-Safety state (11): safe (c)-Safety state (IQ: more or less safe (slightly damaged) (d)-failure state (I): partial collapse (require maintenance) (e)-failure state (n): absolute collapse. Now, we can assess the slope stability as more or less safe (Safety state III) (see figure 2). The area under the curves in Fig2 varies from negative to positive having almost equal values. Performing conventional Factor of Safety analysis in this problem results in FS=1.19. In the second model, consideration of the climatic conditions, tectonic activity, vegetation and unexpected loading in the safety evaluation will be made. As a first step for the system identification, the causes or actions which affects the safety of the rock slope system will be described using fuzzy variables (see Table 2): ile 2. Fuzzy Variables for the synthetic analysis

snow, frost, TemDerature) 2 Tectonic activity 3 \Vegetation and

significant

II

medium small

II

simificant very significant

II

The preference functions for the fuzzy variable in Table (1) are defined below: Awl

It is now necessary to find ftom S a subset S,(n), which represent the risk assessment. The selection of Sm(n) will be as considered as a fuzzyfied process. For example, if the maximum value in every column is selected, then results S m (n) = ((0.2/n), (0.64/(n-0.5)), (l.O/(n-1)) (12)

= {(0.4/0.7), (0.5/0.8), (0.9/0.9), (1/1) }

Aw2 =

{(0.1/0.2), (0.2/0.3), (0.8/0.4), (1/0.5),

358

1

Journal of Rock Mechanics, Vo1.34, No.3 14, pp.516, 1997.

From Eq.( 1l), if one specifies the largest g a d of membership as a diffzification criteria, one gets the safety index (n-1). This represents the influence of the subjective, vague and experience wise disturbing actions. For example, if n is chosen to be T (as defined in Eq.5), then due to climatic and geological factors we must reduce T by one. This result would changing the state of safety in our example from safety state III (more or less safe) to failure state I.

Zadeh, L. A.(1965). Fuzzy sets and systems, Proc. Symp. System Theory, Polytech. Inst. Brookl, , pp. 20-37. Zadeh, L. A. (1971). Similarity relations and fuzzy ordering. Inf. Sci, vo1.3, pp.177-200. Zadeh, L. A. (1973). Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Trans. on Systems, Man and Cybernetics, Vol. SMC-3, pp. 28-44,

4 CONCLUSIONS Rock slope stability analysis is associated with inherent uncertainties, which arise in the reduction of actual site conditions to a representative analytical model, and in the determination of physical properties of the subsurface formations. Not all these uncertainties can be considered adequately within the probabilistic safety concept. The fuzzy model presented is a more reliable procedure for mapping the slope failure potential because it is based upon the incorporation and managing of uncertainties through a combination of objective and mostly explicitly expressed data and from information that is eminently subjective.

REFERENCES : Klir, G.J. and Folger, T. (1988). Fuzzy Sets, Uncertainty, and Information. Prentice-Hall, Englwood, Cliffs, New Jersey. Kosko B. (1992). Neural networks and fuzzy systems. Prentice Hall-Englewood Cliffs. Nahmias, S. (1978). Fuzzy variables. Fuzzy sets and systems I, pp.97-110. Nawari, 0. and Hartman, R. (1997a). Determination of the Characteristic values with respect to the new European Codes in Civil Engineering using Fuzzy Modeling. (in German) Journal of “Die Bautechnik” 74, Heft 4, pp.227-232, Berlin, April. Nawari, 0. and Hartman, R. (1998).Fuzzy Logic Concept in the Limit States of Geotechnical Structures. The XI Danube-European Conference, 25-29 May,, Porec, Croatia, pp.855-862. Nawari, O., Hartman, R. and Lackner, R. (1997b) Stability Analysis of Rock Slopes with the Direct Sliding Blocks Method”, International 359

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang (0 7999 Balkema, Rotterdam, ISBN 90 5809 079 5

Stability evaluation of discontinuous rock slope K. Kawamura & M. Nishioka Department of Civil Engineering, Kanuzawa Institute of Technology,Ishikawu, Jupun

ABSTRACT : In Japan, the evaluations of many dangerous discontinuous rock slopes have been urgently carried out from view-points of geography, geology, slope conditions and the risky aspects of present slope location, etc, in each local region since Toyohama Tunnel in Hokkaido largely failed in 1996 and consequently a number of passengers suddenly died. However this evaluation method is not now perfect, because the contents of it cannot clearly determine both the influcnce zone and the degree of rock block falling on the road nearby the toe of dangerous rock slope. The purpose of this paper is to propose an original procedure for drawing up a road hazard map along the toe of dangerous rock slopes. The map will be based on the analyses for both the possibility and the extended length of each rock block falling from the Distinct Element Method with taking the Image Processing Method into consideration.

1 INVESTIGATED ROCK SLOPES The discontinuous rock slopes investigated for the risk analysis are located in about 250m between Sosogi Tunnel to Hase-no Tunnel in the traffic road Route No.159 along the Sea of Japan in the Noto Peninsula, Japan. There, rock slopes which consist of rhyolite, volcunic brecciu and tuj"-brecciu in geology have slope angles of 40 to 50 degrees on average and can be especially found either large or small dominant discontinuities in site by site, as shown in Photograph 1. Topically, the 50m near the Wajima side entrance of Hase-no Tunnel can be recognized as the most dangerous zone of rock block falling and sliding highly possible to occur in the near future.

2 2.1

the road$ is very important in practical engineering to exactly predict a path and an arrival distance of rock block falling. This prediction has been carried out under the following conditions: 1. The direction range of rock block falling may

he generally indicated to be about 45" each zone to both wings under the condition of a flat surface on rock slope. 2. As a general rule, a risky rock block may

SIMULATION OF ROCK BLOCK FALLING

Puth of rock block fulling

On the occasion that dangerous rock block of discontinuous rock may fall down toward

Photo.1 Near entrance of Hase-no Tunnel

Fig.1 Path of rock block Palling mainly fall down along the nearest valley line on rock slope surface, except that it is also possible to jump over a low ridge line in case of a shallow valley line. 3. The actual path of rock block falling along discontinuous rock slopes in the past may be registered as a path again in the future. Figure 1 shows each predicted result of falling path of dangerous rock block according to the above-mentioned rulc. It can be determined that the topical rock blocks on the most dangerous discontinuous rock slope are highly likely to fall down along either Path 1 or Path 2 in this figure.

dangerous discontinuous rock slope can be counted from the distribution of dominant discontinuous planes, such as the cracks and the fissures, and each size is also able to be determined from several clear photographs of rock block induced into the Image Processing Method. The simulation of rock block falling is carried out with the Distinct Element Method under the following conditions:

Table 1 Input data for the Distant Element Method

I Vertical elastic modulus (kN/m2) Lateral elastic modulus (kN/m2) Coefficient of viscosity (kN -s/m2) Internal friction angle

2.2 Simulation by using the Distinct Element Method

4

(sec)

362

I 26.0 X 1 O6 1

ks

9.0 X 1O6

r)

41.8 35.0

("1

Cohesion C (kN/m2) Unit weight y (kN/m3) Time interval A t

The section of rock slope, along which the most dangerous rock blocks may probably topple and roll down along either Path 1 or Path 2 of Figure 1, can be shown in Figure 2. Each rock block consisting of

kn

0.0 23.5 9.5

x m5

10 3 (m)

be demonstrated that almost all dangerous rock blocks will fall down along Path 1 and soon stop by the small dam below the rock slope which was constructed in order to protect against the mud outllow and also store it. However, although almost all rock blocks will probably stop over this dam, a few large blocks will jump over it and arrive at Route No. 249 road. That is, the rock block falling along Path 1 makes the downward road much dangerous. While if along Path 2, their behavior may be predicted to be more serious than Path 1, because several large rock blocks falling will not only easily jump over the steel nets on retaining wall which was constructcd in order to protect against the falling, but also they come to Route No. 249 road. Especially, it is highly possible to destroy the steel nets by the large impact of dangerous rock falling, so that this falling energy through Path 2 Table.2 Investigation sheet for rock slope stability

Fig.2 Simulation rcsults

That is, a simulation has been continued until either dangerous rock block behaviors stop perfectly or the falling rock block arrives at a road lower down. Both the distribution of dangerous rock blocks divided by some dominant discontinuous planes of the Image Processing Method and the input data of the Distinct Element Method for the material characteristics determined based on comparing a few results of actual cases with the simulations of rock block falling can be indicated i n T a b l c l ~

more than lOOm

height of

rock slope

2.3 Sim it La t ion result s An example of simulation results by the Distinct Element Method is shown in Figure 2, where it can

363

50m to lOOm 30m to 50m

10 7 4

7/(10)

% 1 Risk for rock block falling and rock slope sliding EZZ3 Any possibility for rock block falling and jumping in near future Any possibility for rock block falling and arrival in near future 5 q Any possibility for rock block falling and arrival in near future % 2 Effective action of protector structure against falling and sliding No expectant structure IlTTrmOl A part of expectant structure Effective structure % 3 Integrated judgement for road hazard Needful to urgently make measure for road safety Needful to make measure for road safety E -Needless to make measure and only observation for road safety % 4 Examples of unsafe degree of dangerous rock blocks and slopes, Ha, Hb, Hd, * ,Hn --- Needful to urgently make measure against dangerous rock block falling and sliding

ma

--

mx ;_3

Needful to make measure in near future against dangerous rock block falling and sliding Needful to make measure in future against rock block falling and sliding Needful to observe behavior

Fig.3 Road hazard map

364

will be not able to be decreased because there is not the same small dam as Path 1. Path 2 is assumed to be more dangerous.

3

and to predict the influence of damage by rock block falling and slope sliding. Conclusions obtained from this study are summarized as follows: 1. An original road hazard map, which is based on not only several results for any possibilities of rock block falling and rock slope sliding determined from the conventional investigation method but also results of an arrival length and a falling path of dangerous rock block obtained by simulation of the Distinct Element Method, can be proposed in engineering practice. 2. It is possible from a proposed road hazard map to comprehensively evaluate the road safety while simultaneously taking both the danger of rock block falling and the effectiveness of structure in order to protect against rock block falling and slope sliding. 3. It is easy by using a proposed road hazard map to select a extreme dangerous road position, where either the hard protection measure of any structures should be constructed in the near future or the soft protection measure of traffjc control rapidly carried out against rock block falling and rock slope sliding.

ROAD HAZARD MAP

A road hazard map against rock block falling of the most dangerous slope area can be concretely illustrated in order to maintain a safe road. Making a road hazard map is based on adding the results of conventional investigations, which have been composed of the position and the size of dangerous rock block, the unsafe conditions of discontinuous rock slope surface, the possibility of slope sliding and the other of Table 2, to the original simulation results of an arrival length and a falling path of dangerous rock block falling determined from the Distinct Element Method. This simulation can fully consider the effective actions of structures, such as the shade of reinforced concrete and the steel net, in order to protect against rock block falling. In this paper, a road position where there is any possibility for dangerous rock block either falling or passing is defined as increasing the degree of safety by one rank. This road hazard map can illustrate the unsafe degree by three bands shown in Figure 3, in which the first band described on the mountain-side can indicate any possibilities of dangerous rock block falling and discontinuous rock slope sliding. The second band, in other words, the central band demonstrates an improved and effective structure in order to protect against rock block falling and rock slope sliding. Finally, the third band on the sea-side is examined to show an integrated hazard judgement while taking both the first and the second bands into consideration. It is easy from this proposed road hazard map to not only keep a road safe but also to make i t possible to carry out meaningful measures against rock block falling and sliding in the case of extreme danger.

4

5 ACKNOWLEGMENT The authers are grateful to Ishikawa Prefecture Civil Engineering Office for their valuable data and comments in this study.

6

REFERENCES

Kawamura,K. and Ogawa,S. (1989). Topographical consideration for landslide prediction. 12th I C M F E V01.3 1587-1590 Kawamura,K. ,Murayama,H. and Kondo,H.( 1997). Applicability of Distinct Element Method t o failure prediction of discontinuous rock slope based on an actual slope failure. Proc. .!SCE, NoS68/ -39 175185 (in Japanese) Kawamura,K. and Ogawa,R. (1997). Slope failure in major Tertiary mud-stone zone. Proc.

CONCLUSIONS

Dejbrmation and Progressive Failure Geomechunics in IS-Nagoya 701-706

This paper proposes a valuable road hazard map from the practical views of how to keep a road safe 365

in

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang (o 1999 Balkema, Rotterdam, ISBN 905809 079 5

Earthquake and seepage effects on the mobilised shear strength of closely jointed rock

ABSTRACT: This paper continues a long-standing interest of the author on the shear strength parameters for closely jointed rock masses. Greywacke (an indurated sandstone of Mesozoic age in which the unweathered rock material is very strong and hard) is one of the principal basement rocks in New Zealand. Because of the complex tectonic history of NZ these greywackes are closely jointed. In a previous paper the Casagrande resistance envelope for greywacke slopes in the Wellington area was estimated from the back analysis of existing stable slopes. As this envelope lies well below the estimated Hoek-Brown failure envelope for the rock mass, the effects of seepage and earthquake loading are investigated herein. It is found that earthquake effects are more severe than seepage; in fact, an earthquake with a peak ground acceleration at about the maximum expected in the region is likely to move the mobilised shear strength curve out to the estimated Hoek-Brown failure envelope.

1 INTRODUCTION This paper continues work reported earlier (Pender & Free 1993, Pender 1990) in which back analysis of existing slope height - slope angle data was used to obtain a lower bound on the shear strength envelope of a closely jointed rock mass. The particular slopes are those around the city of Wellington in New Zealand in which the rock type is greywacke a highly indurated sandstone of Mesozoic age. The standard method for assessing the strength of a geotechnical material is to recover a sample and test it in the laboratory, or, alternatively, conduct in situ tests. In the case of a closely jointed rock mass neither of these approaches is feasible; consequently back analysis is used to give some indication of the shear strength properties of the rock mass. The slope height - slope angle relation (GrantTaylor 1964), is shown in Figure 1. Two limiting cases are evident in this figure, an upper limit for the best material and a lower limit for the material near the Wellington Fault. As the context of this paper is stability analysis, there is a temptation to consider all the points on Figure 1 as the result of slope instability. However, Grant-Taylor emphasises that other mechanisms, for example erosion, are likely to be responsible for at least some of the points in the diagram. Therefore, it seems reasonable to assume that the upper bound of all the points in Figure 1 is a contour of constant factor of safety. The upper bound curve leads to the highest values for the mobilised

shear strength of the rock mass that can be obtained by back analysis of the data. The majority of the work reported in this paper was based on three points along the upper bound curve in Figure 1 : a 17 m high slope at 75", a 72 m high slope at 60", and a 188 m high slope at 45". Preliminary back analysis shows that it is not possible to model these three combinations of slope height and angle with a single linear c and @ failure envelope. The mobilised shear strength curve obtained (Pender & Free 1993) for a dry rock mass when under static conditions is plotted in Figure 2. Clearly the rock close to the Wellington Fault cannot be expected to stand as well as material remote from the fault, as near the Wellington Fault the rock is likely to be more closely jointed with interlocking much reduced. Unlike the upper bound in Figure 1, the data for slopes near the Wellington Fault can be matched reasonably well with a single set of MohrCoulomb shear strength parameters: c = 30kPa and @ = 26". As this friction angle is considered too low for a typical closely jointed rock mass, the heights of the slopes adjacent to the Wellington Fault must be controlled either by the properties of the fault zone or by a gradual surface deterioration of the rock. The Hoek-Brown failure criterion is, in principle, capable of describing rock masses such as those in closely jointed Wellington greywacke. The modified version of the criterion (Hoek at a1 1992), used herein, assumes that a closely jointed mass has zero cohesion; it is expressed in terms of principal stresses and has the form: 367

Figure 1. Wellington slope-height slope-angle data.

Figure 2. Mobilised shear strength curve for dry Wellington greywacke under static conditions and the estimated HoekBrown failure envelope.

The parameters a and mnb depend on the intensity of jointing in the rock mass. A basic input parameter is the unconfined compression strength, oc, of the unweathered rock; for NZ greywacke this is frequently well in excess of 100 MPa. However, in the earlier paper it seemed more appropriate to use a smaller value of 50 MPa. (It is of interest that independent work on the shear strength properties of greywacke rock masses (Read et a1 1999) found that a value of 60 MPa for the unconfined compressive strength was needed to achieve a reasonable HoekBrown failure envelope.) Using the guidance given in the Hoek et a1 (1992) paper, and the comments of Hoek (1998), values were chosen for the parameters a and mb (0.5 and 1.2). The corresponding MohrCoulomb failure envelope for the rock mass, obtained after calculations outlined by Hoek et a1 (1992), is plotted in Figure 2 along with the mobilised shear strength curve for the Wellington slopes. In passing, it is of note that the shear and normal stresses in the rock mass are a very small fraction of the assumed unconfined compression strength for the intact rock. The previous back analysis (Pender & Free 1993) was done on the assumption that the slope is dry and that there is no earthquake acceleration present; this gives a lower bound on the mobilised shear strength curve. There is the possibility that inclusion of other effects on the slope might go some way to spanning the gap between the two curves in Figure 2. The rainfall in Wellington is such that seepage is likely to be a significant effect on slope behaviour. Similarly, as NZ is in a seismic region the effect of accelerations on slope stability is a legitimate question. The relevance of these two classes of action is thus investigated in this paper. The conclusions reached

are that water pressures will not explain the difference between the two curves in Figure 2, but earthquake shaking may be the key to understanding the observed slope-height slope-angle data. This does assume, of course, that the estimated Hoek-Brown failure envelope is appropriate for the rock masses, perhaps the greatest assumption of the whole paper and the one that is most difficult to verify. 2 TERMINOLOGY 2.1 Closelyjointed rock masses A rock mass is described as closely jointed when the joint spacing is small in relation to the scale of the project in question. The cuts in the greywacke slopes in and around the city of Wellington provide a good example. In these rock masses, and at many other locations throughout NZ, the joint spacing is a small fraction of a metre. It is, therefore, very much smaller than the scale of the cut slopes which are up to several tens of metres high. Furthermore, at many locations there is no clearly defined characteristicjoint direction (notwithstanding that plotting a large number of joint directions may indicate other than random joint orientations). As the individual joints do not seem to have great continuity, a particular joint cannot exert a dominant effect on the rock mass behaviour. The behaviour of the mass is thus a consequence of the combined action of a large number of individual joints. At stress levels of interest in slope stability assessment, the strength of the intact rock between the joints is usually so high that failure of the mass is controlled, in a complicated way, by the joint system. This comment restricts the consideration herein to

368

I

Normal stress (MPa)

f

I

Normal stress (MPa)

Figure 3. Mobilised shear strength curve with, along with the curves from Figure 2.

Figure 4. Mobilised shear strength curve with a pseudo-static horizontal acceleration of 0.4 g, along with the curves from Figure 2.

hard rocks that are unweathered or only slightly weathered. However, many of the concepts developed are also valid for slopes in weathered rock and soil. Assumptions about the type of failure mechanism are also required. In closely jointed media it seems appropriate to assume that the material is approximately homogeneous, i.e. there are no clearly defined joint planes or joint sets which control the form of the failure mode. With this assumption of homogeneity it is necessary to search for the critical case of each type of failure mechanism. If, for example, a circular failure mode is under investigation then a search has to be made until the critical circle is found.

(1988). These provide a method for generating mobilised shear strength curves both for dry and saturated slopes. For slopes subject to earthquake accelerations the logarithmic spiral approach of Prater (1979) is adapted to the back analysis. 3 EFFECT OF SEEPAGE

2.2 Resistance envelopes und mobilised shear strength curves A further point of terminology needs clarification. As originally formulated (Casagrande 1950) the resistance envelope refers to one particular slope geometry. This relation tells us nothing more than the stress combinations required to satisfy equilibrium in the slope. The envelope of a number of separate resistance envelopes gives a better bound on the failure envelope for the material in the rock slope. Herein the term resistance envelope is confined to information derived from a single slope geometry and the term mobilised shear strength curve is used when information gained from the back analysis of slopes with different geometries is combined. It should be noted that the mobilised shear strength curve is not the failure envelope of the rock mass, it will have more curvature than the actual failure envelope, but may approach the failure envelope from below. The stability charts of Hoek and Bray (1981) have been replotted as resistance envelopes by Baikie 369

There is little information about the water conditions in the steep slopes in Wellington greywacke. It is not common to see water seeping out of slope faces around the city. Furthermore water was not a particularly difficult problem during the construction of the Terrace Tunnel in the late 60’s and early 70’s or during the construction of the investigation drive several years earlier. SimilarIy most of the prebored holes for piles on the Shell Gully structures for the Wellington Urban motorway were dry. The topography of the Wellington region, with roughly parallel ranges of hills separated by steep sided valleys, means it is unlikely that the highest slopes will ever be completely saturated. Finally, as pointed out by Grant-Taylor, the higher less steep slopes are mantled by a layer of weathered greywacke having a low permeability, so water falling on the slopes will runoff rather than infiltrate the unweathered and closely jointed rock mass below. These comments provide another perspective on the assumption in the earlier back analysis that the rock masses are dry, which was made to give a lower bound on the mobilised strength curve. Using the curves developed by Baikie the effect of having the slopes completely saturated with water is easily investigated. The resulting mobilised shear strength curve is plotted in Figure 3. This diagram shows that seepage through the slopes, even when the slopes are fully saturated, gives rise to only a

modest change in the mobilised shear strength curve which remains far short of the estimated HoekBrown failure envelope in Figure 2. Clearly, then, seepage will not explain the difference between the two curves in Figure 2.

about slope deformations during and after these earthquakes. Thus we cannot reach a definite conclusion that they are responsible for the existing slope configurations. Current assessment of the earthquake risk in the Wellington region suggests that peak ground accelerations in the 0.6 to 0.8g range could occur for a major earthquake on the Wellington fault. It is apparent from Figure 4 that a peak horizontal acceleration in the 0.6 to 0.8g range would scale the mobilised shear strength curve into the proximity of the estimated Hoek-Brown envelope in the figure. Although less frequent, horizontal accelerations of this magnitude will have a more severe effect on the slopes than 0.4g. Once again we are hampered by lack of information about slope damage during large earthquakes. The pseudo-static analysis discussed in this paper indicates the stresses that will be generated during earthquake loading. However, the above two paragraphs indicate that we cannot decide if the geometry of the greywacke slopes around Wellington is defined by relatively infrequent major earthquakes or a series of more frequent events with a smaller peak ground accelerations. In particular we need information about the long term effect of the earthquake accelerations on the slopes. If the earthquake causes loosening of the rock mass then long term deterioration may follow. The pseudo-static calculations have been done with horizontal acceleration only; in reality vertical accelerations will accompany the horizontal. This will be another effect on the mobilised shear and normal stresses. Another possibility would be to combine earthquake and seepage effects to further expand the mobilised shear strength curve. This has not been considered herein as the simple addition of the two effects is most unlikely. A closely jointed mass behaves as a very dense medium, thus, when saturated, any shearing, and even more so any loosening, of the rock mass will lead to a short term reduction in water pressures.

4 EARTHQUAKE EFFECTS

The Hoek and Bray charts do not include inertia forces in the slope generated by earthquake accelerations. Prater ( 1979) presents a pseudo-static approach, although he uses a logarithmic spiral rather than a circular failure surface, to assess the effects of horizontal and vertical accelerations in the slope. Prater does not include a vertical tension crack at the top of the slope, which is incorporated into the Hoek and Bray charts. However, Baikie has investigated this and found that it is not of great significance for slope inclinations 60" or less. For given values of friction angle and cohesion Prater tabulated values of the horizontal acceleration coefficient, k,,, which will just have a slope of a certain height and angle at limiting equilibrium. In the work herein the range of the tabulated values was extended by coding in Mathcad the expressions given by Prater. One thus obtains from Prater's equations a range of linear c, Cp failure envelopes corresponding to the limiting equilibrium of a particular slope configuration at a given horizontal acceleration. The resistance envelope for the particular geometry is then obtained by plotting the linear failure envelopes and sketching an inner envelope to them. These steps, with a horizontal acceleration of 0.4g, lead to the mobilised shear strength curve plotted in Figure 4. From this it is apparent that the demands on the slopes of earthquake accelerations of this level are considerably more severe than those of water seeping through the slope.

5 DISCUSSION It is clear from Figures 3 and 4 that a psuedo-static horizontal earthquake acceleration of 0.4g has a more severe effect on the Wellington slopes than seepage. Even so we are still some way short of being able to conclude that the mobilised shear strength curve for kh = 0.4 in Figure 4 is the failure envelope for the Wellington greywacke rock masses. The following points preclude this: The earthquake shaking of the slopes is a transient process, whereas the above calculations have been done in a pseudo-static manner. The horizontal acceleration of 0.4g used in the calculations is thought to be representative of the peak ground acceleration to which slopes in the Wellington region will have been subjected a number of times in the past. Unfortunately we have no direct information

6 CONCLUSIONS The following conclusions are reached: Extending the Casagrande resistance envelope concept to encompass different slope geometries, means that the lower bound on the shear strength properties of the rock masses is also extended. It appears that earthquake loading with a peak ground acceleration of the magnitude that could be expected in the Wellington region in a major event would mobilise shear strengths approaching the estimated Hoek-Brown failure envelope in Figure 2. The effects of pseudo-static earthquake loading at

370

the level of 0.4g are much more demanding of the shear strength behaviour of the jointed rock masses than seepage under fully saturated conditions. In as much as the pseudo-static analysis performed herein tells us nothing of the deformations in the slope, it is not possible to conclude definitely that earthquake shaking can account for the observed slope height - slope angle relation. Although the this paper extends the mobilised shear strength curve obtained by Pender and Free (1993), there is still considerable uncertainty about the actual shear strength properties of the closely jointed greywacke rock masses in Wellington. The actual unconfined compression strength of unweathered greywacke gives what seems an unreasonable Hoek-Brown rock mass failure envelope. Herein a smaller value (5OMPa) was used. The range of shear and normal stresses in the slopes associated with the mobilised shear strength curve is a small fraction of the assumed unconfined compression strength of the intact rock material.

7 REFERENCES Baikie, L. D. 1988. Casagrande resistance envelopes for rock and rockfill slopes having circular slip surfaces. Canadian Geotechnical Journal, 25: 42-49. Casagrande, A 1950. Notes on the design of earth dams. Jour. Boston Societ), Civil Engineers. 37: 405-429. Grant-Taylor, T. L. 1964. Stable angles in Wellington greywacke. New Zealand Engineering. 19: 129-130. Hoek, E. & J. W. Bray 1981. Rock slope engineering. London: Institution of Mining and Metallurgy. Hoek, E., D. Wood, & S. Shah 1992. A modified Hoek-Brown criterion for jointed rock masses. Proc. Eurock’92: 2092 13. London, Thomas Telford. Hoek, E. 1998 Reliability of Hoek-Brown estimates of rock mass properties and their impact on design. Int. J. Rock Mech. Min. Sci. 35( I): 63-68. Pender, M. J. & M. W. Free 1993. Stability assessment of slopes in closely jointed rock masses. Proc. Eurock’93: 863-870. Balkema: Rotterdam. Pender, M. J. 1990. Stability of slopes in closely jointed rock masses. NZ Road Research Unit Bridge Design and Research Seminar, RRRU Bulletin 84: 1 15-126. Wellington: RRU. Prater, E. G. 1979. Yield acceleration for seismic stability of slopes. Jnl. Geotechnical Engineering, 105(GT5): 682-687. Read, S. A. L., L. R. Richards, & N.D. Perrin 1999. Applicability of the Hoek-Brown failure criterion to New Zealand greywacke rocks. Proc. 9”’ Congress of the ISRM, Paris.

371

This Page Intentionally Left Blank

4 Effects of rainfall and groundwater

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 7999 Balkema, Rotterdam, ISBN 90 5809 079 5

Design chart for cut slope in unsaturated residual soils R. Subramaniam KTA Tenugu Sdn Btid, Mulaysia

EH.Ali Civil Engineering Department, University of Malaya, Kualu Liinzpur,Malaysia

ABSTRACT : In the past, tlie effects of soil suction , rainfall and conductivity of soil were not considered in the coiiveiitioiial slope stability analysis that were carried out using parameters based on saturated condition. The analysis when linked to shallow failure, deep ground water conditions or climatic fluxes, should however be extended to incorporate unsaturated soil mechanics. This study has been carried out in view of partial saturation with other related parameters involved in the stability of slopes in residual soils using a combination of seepage and slope stability programs.

1 INTRODUCTION The relatively steep cut slopes in residual soils are initially stable aiid partly saturated. The partial saturatioii of the soil allows the negative pore pressure (matric suction) to exist aiid develops an apparent cohesion, which in iiiajority of the cuts is the predominant stabiliziiig factor. The rain initiates the absorption of water by the surface layers causing the degree of saturation to increase. The saturation zone advances to greater depths. The advancing saturation front alters tlie hydraulic gradient and the hydraulic Conductivity thus changing the flow patterns and the distribution of moisture content in the soil.

3. To use the predicted hydrological condition (steady state and transient state analysis) as input to a physically based two diiiiensional (2D)slope stability sub model (SLOPEIW) to study tlie changes in factor of the safety of slopes based on the various parameters determined above. 4. To apply the combined seepage and slope analysis to arrange a slope form aiid antecedent condition for the production of design chart for partially saturated soils which summarizes the effect of a particular storm event on slope stability.

2 DEVELOPMENT OF SLOPE STABILITY CHARTS

This project has been carried out in view of tlie partial saturation with other related parameters involved in tlie stability of slopes in residual soils. The following objectives have been o u t l i d .

1. To identify tlie different hydrological, physical, geometrical aiid strength parameters that affect tlie stability of slopes in unsaturated residual soils. 2. To produce a physically based coupled dimensional (2D)dynamic slope hydrological condition (transient) model controlling stability due to various parameters identified above using tlie available SEEP/W software.

Standard approaches to stability analysis usually simplify consideration of the hydrological condition to that of a static, fixed grouiidwater level. Stability analysis procedures are then used to determine the factor of safety for the slope, given the distribrrtion of positive pressures along the slip surfaces. Soil suctions are generally ignored in such analysis, being assumed zero. Many researcher have produced chart that enable the stability of simple slopes to be assessed without the necessity of coiiipletiiig detailed calculations. They are a1v ~tscfu!fgr prcliiiiinary aiialysis and enable

375

the designer to quickly assess the sensitivity of a problem to changes in different input parameters.

This output model is later used as input to SLOPE/W programme for stability analysis.

The main objectives of this exercise is to :-

2.3 Results 2.3.1 Factor of Safety vs Permeability (ks) for various slope heiglits(H)

To find the critical condition where the landslide could occur or the combination of permeability of the soil and the rainfall intensity which will be critical.

- ~ (Figure I), the factor of For a fixed qs = 1 ~ 1 0 m/s safety tends to decrease with the increase of permeability of the soil. For all the various heights ranging from 20 meters to 50 meters, the factor of safety seems to decrease with increasing saturated ~ the factor of conductivity. For qs = l ~ l O -m/s safety is the lowest at permeability value of ks = 1x10-7 m/s and increases at ks = 1 ~ 1 0 m/s ‘ ~ and 6 1x10- m/s. or qs = 1 x 1 0 - ~m/s, the lowest value is obtained at ks = 1xlOb8 m/s. This signifies that the lowest factor of safety is achieved when the infiltration rate is alinost or equal to the permeability of the soil. However the lowest value is obtained at qs = 1xl 0p6 m/s wliicli means the liiglier the permeability the lower is the factor of safety.

To find a linear relationship between the f ctor of safety and the diinensionless factor tan $ for unsaturated residual soils.

t

To establish a design chart for approximation of preliminary design. Determination of the critical condition Before the slope stability charts are produced a table is formed to study the different rainfall intensity and conductivity f~inction. The critical case is to be found and to be used for the development of slope stabilitp charts. The following parameters are identified as these values represent the comnion values for residual soils at the Kuala Lumpur - Karak highway project and these values can also be used at other residual soils in Malaysia (Othman, 1989).

9s = I ~ I o - M ~ ,O - ~ , 1 x 1 0 - ~ni/s for a duration of 24 hour. 1% = MO-~M , O-~M , O-~ H = 10, 20, 30, 40, 50,60 meters = 1:1,2:1, 3:2 tan p C’ = 0, 5 , 1OltPa = 20,25, 30, 35,40 degrees $b Q, = 0, 0.25, O$O, 0.75, 1.00 Yb = 18 kN/ni’

Figure 1 Factor of Safety vs Permeability (lts) for various slope heiglits(H)

2.3.2 Factor of Safety vs Heiglit(H) for various rainfall intensity (qs)

2.2 Procedure A homogeneous slope model is developed with the respected parameters using tlie SEEP/W programme and the various iiifiltratioidrainfall intensities is used as input to run the transient condition. A typical initial condition is simulated with the groundwater table to be at 10 meters perpendicular distance from the toe of the slope. A maximum suction value of 100 1;Pa is fixed to siniulate tlie site condition.

2-

For a ixed saturated permeability of the soil, ks = 1x10- m/s (Figure 2), the factor of safety seems to decrease with increasing slope heights. When the rainfall intensity is close or equal to the saturated permeability the lowest factor of safety is achieved, whereas there is not much changes in factor of safety when the rainfall intensity (qs) is M O - ~m/s or 8 1xl0- d s ) . Again when the saturated permeability (ks) is l ~ l O m/s, - ~ the factor of saftty tends to drop also with tlie increase in height. The difference between the threc different rainfall intensity do not

A transient analysis is carried out and the respective profile changes in tlie suction are then observed.

376

Figure 2 Factor of Safety vs Height(H) for various rainfall intensity (9s)

Figure 3 Factor of Safety vs Saturated Permeability seem to be big when compared to when ks = 1 ~ 1 0 (ks) ~ ~for various slope angle (tan p) d s . However when ks = ~ x I O -m/s, ~ the various rainfall intensity tends to be close to one another. The soil can only infiltrate the maximum value of ks = 1x10-8 m / s and the excess water acts as surface runoff.

2.3.3 Factor of Safety vs Saturated Permeability (ks) for various slope angle (tan 0) For a fixed rainfall intensity (qs = I X ~ Om/s) - ~ and height (H = 50 meters) as in Figure 3, the factor of safety tends to decrease with increasing saturated permeability . The drop in the factor of safety is very much greater for slope 1V:lH compared to slopes 3V:2H and 2V:IH. The lowest factor of safety is obtained when the rainfall intensity is close or equal to the permeability of the soil. However the drop in the fact r of safety whe the rainfall intensity is (qs 9/ = 1x10- m/s and 1x10- m/s did not vary much for each slopes.

Figure 4 Factor of Safety vs slope angle (tan various rainfall intensity (qs) 2.4 Discussion

1

2.3.4 Factor of Safety vs slope angle (tan various rainfall intensity (9s)

p)

p) for

In the computation of the data for the development of stability charts it has been assumed that the slope is homogeneous and constructed of a single material with effective stress strength parameter c’ and 4’. The critical condition qs = ks is chosen when ks = l x 10-6m/s because of its high permeability and the duration of rainfall intensity is fixed at 24 hours as determined from the analysis. The ks = 1x 10-6 m/s was found to give the lowest safety factor during the sensitivity analysis for the slope of Kuala Lumpur Karak Highway.

for

For a fixed height (H = 50 meter) and saturated -6 permeability (ks = 1x10 m/s) as in Figure 4, the factor of safety tends to decrease with increasing s!ope angles. However when qs is less than or more than the saturated permeability, the difference is not very much. The critical condition occurs when qs = ks and the worst case is for slope 2V: 1H.

The range of the parameter are as follows:= 2:l , 1:1, 3:2 tan p = 0.0,0.25,0.50,0.75, 1.00 c’/yH = 0,0.015,0.030 pore water pressure = SEEP/W Heads

o9

377

An accurate and extensive general solutions is made possible by these factors:-

For a simple soil profile and specified shear strength parameters, it had been found that to a closer approximation, the factor of safety, (F) varies linearly with the magnitude of the tan 6b

2.4.1 Dimensionless iiuiiiber c’/yH

(dimensionless value of rate of change in shear strength with respect to suction). A typical example of this linear relationship is given iii Figure 6

For a given value of tlie dimensionless number c‘lyH, the factor of safety depends only on tlie geometry of the section, expressed as tan p, 011 the pore-pressure given by SEEP/W and on the aiiyle of shearing resistance,$’ aiid suction resistance, $B for unsaturated residual soils.

F

=

f + s.tan

--------(1)

where f and s are termed the stability coefficient for a particular slope and soil properties, tan $b .is the rate of change in shear strength with respect to suction (ua - U*).

To reduce the amount of computation cn!y three(3) values of c’/yH have been used that is 0.0, 0.015, 0.03. Considering that tlie cohesion intercept in terms of effective stress is gradually somewhat lower than the cohesion intercept in total stress, these values have been selected as represeiitiiig the range coiniiioiily encountered in effective stress analysis and also a range within which a linear interpolation can be used without significant errors. Tlie intermediate values for c’lyH can be interpolated as shown in Figure 5 for a particular slope angle and strength value. It should however be renieiiibered that for cross sections of natural slopes or wide embankments some errors inay be iiicurred due to the neglect of tension cracks whose effect on stability becomes more pronounced at higher values of c’lyH. For these problems, a modified analysis is generally required.

Figure 6 Linear relationship between factor of safety and dimensionless tan $b value for = 30 degrees and c’/yH = 0.005 for various slope angle Linear relationship between F and tan$b for a givcn value of c’lyH, tan p as shown in Figure 6 can be described in t e r m of two parameters, f. and s where geometrically, f is the intersection with factor of safety (F) axis of me describing the relationship between F aiid tan 4 and corresponds to the v 1 of tlie factor of safety for zero suction value (4 = O)., and s is the slope of this line. Since the slope of this line is always positive (Fredlund. 19 4), the factor of safety increases with increasing $ value. whilst all other parameters being held constant and inay be expressed in tlie form of equation (1 ).

2.4.2 Factor of safety (F) varies linearly with the magnitude of tlie tan $b

6

4

These two parameters f and s are determined from tlie fitting curve passing through all or near all the b respective points where $ /$* = 0.0. 0.25. 0.50, 0.75. 1.00 for various 4’ values process using the blicrosoft EXCFL programme \\it11 an a\ erage standard error. R- value of 0.9 (Fredlund. 1994). Figure 5 Linear relationship between factor of safety and dimensionless number c’/yH for a particular = 30 degrees and = 15 degrees for various slope angle

The values of the stabilit) coefficients f and s Lire then plotted against tan 0.the tangent of the slope angle. for varying $‘ bet\veeii 30 degrees to 40 degrees. Figures 7. 8, 9 shoib the f m d s coefficients 370

for values c‘h{H = 0. and also for three different heights. H = 0 - 20m. 21 - 4Om. 41 - 60111 respectively. The presentation and tabulation of the results are greatly simplified by the use of these stability coefficients, which also have the advantages of giving an immediate picture of the influence of suction on the factor of safety. To calculate the factor of safety of a section whose c’lyH lies within the range covered by these figures, it is necessary only to apply the equation ( 1 ) to determine the factor of safety of the two nearest values of c’lyH and then perform a linear interpolation between these values for the specified c’lyH as the factor of safety(F) is also linearly increasing with dimensionless value c’lyH.

Figure 8 Stability coefficients for c’lyH = 0 and H = 21 - 4 0 m

Figure 7 Stability coefficients for c’lyH = 0 and H = 0-20m Figure 9 Stability coefficients for c’lyH = 0 and H 41 - 6 0 m

3 CONCLUSION

The following conclusion can be derived from this study:1) Eiig]1er suction values give higher factors of safety.

=

2) The factor of safety for unsaturated soil seems to be increasing with a dimensionless value tan+b .

379

3) A linear relationship can be obtained for the factor of safety of unsaturated residual soil. F=f

+ s tail 4'' -------(I)

Where F = factor of safety. f aiid s = the stability coefficient = is the rate of change in shear strength with respect to suction ( Ua - Uw). Hence tlie factor of safety for a particular slope can be deteriiiiiied from the coiiibinatioii of stability coefficients obtained from tlie stability chart.

4 ACKNOWLEDGMENT Special thanks to the authors colleagues Mr. Low Tiaii Huat and Mr. Saravaiiaii Mariappaii for their kind assistance in helping to write this paper.

REFERENCES

1. Affeiidi, A ( I 996). Field aiid laboratory study on unsaturated residual soils in relation to slope stability analysis, P1i.L). thesis, University of Malaya. Unpulished. 2. Fredlund, D.G and Raliardjo, H. (1993). Soil Mechanics for Uiisaturated Soils. John Wiley & soils. 3. Morgentern, N (1963) Stability Charts for earth slopes during rapid drawdown, Geotechnique, vo113,pp121-13 1. 4. Othmaii, M.A., (1990). Highway cut slope instability problems in West Malaysia, P1i.D. thesis, Uiiiversity of Bristol, unpublished.

380

Slope Stability Engineering, Yagi, Yamagami & Jiang e) 1999 Balkema, Rotterdam, ISBN go 5809 079 5

Factors affecting on water retention characteristic of soils Katsuyulu Kawai Deparhnerzt of Citd Engineering, Kohe University,Japan

Daizo Karube & Hitoshi Seguchi Graduate School qf Science und Technology,Kobe University, Japun

ABSTRACT: The mechanical behaviors of unsaturated soil are strongly influenced by the suction value and the pore water distribution. The water retention curve is provided as the relationship between the suction and the moisture content and widely used in the analyses for an unsaturated soil medium such as the unsaturated seepage flow. However, since the water retention curve essentially shows hysteresis loop, the moisture content is not uniquely determined even if only the suction is specified. Void ratio also affects the degree of saturation. Therefore, some physical quantity considering the volume change of unsaturated soil element has to be introduced in the expression of water retention characteristics. In this paper, a new expression of water retention characteristics of unsaturated soil is presented, in which the initial void ratio of the soil is introduced as a variable in the mathematical expression of water retention characteristics. 1. INTRODUCTION Slope failures are often connected with the rainfall and statistically analyzed with the total amount and/or the intensity of the rainfall. It is well known that the mechanical behavior of unsaturated soils in the slope is much influenced by the water retention characteristic of the soils. The water retention characteristic is conventionally represented by the “water retention curve” provided as a unique relation of the suction value and the degree of saturation of the soil. Some models describing its relation have been proposed and used in the analyses. However, in actuality, the values of degree of saturation are different in the drying and wetting processes. Since the relation of suction and degree of saturation draws a sort of hystresis loop depending on the loadinghnloading process of suction stress, the degree of saturation is not uniquely specified for a suction value. Vachaud et al.’) examined the hysteresis loop of water retention curve using the soil column method. Nakano’) 3 , proposed the water retention model, which can express the hysteriesis loop in the relation of the suction and saturation degree, considering the geometrical shape of soil pore. The exponential function is employed to express the distribution of pore size after the expression of energy distribution in the classical statistical mechanics. However, there would be of much difficulty in specification of parameters in the practical use of it. Toll )‘ pointed out the similarity between the 381

hysterisis loop in the water retention curve and the loading/unloading response of saturated soils. He introduced “Virgin Drying Line (VDL)”, defined as the relationship between the water content and the suction value for an initially saturated normallyconsolidated soils under the drying process without applying any external stress, and proposed a simple model. Toll’s model can rationalize the volume change of the soil by separating the volume change of water from it. However, a question whether VDL can be uniquely defined for a soil has been left. In this paper, a series of laboratory tests, i.e. oedometer tests for compacted soils and triaxial tests for reconstituted soils, are carried out to obtain the water retention curves. And possible factors effecting on the water retention characteristic is discussed by fitting it to the relationship between the suction stress and the degree of saturation obtained from experiment. Then, new model that contains the effect of void ratio is introduced. 2. EXPERLMENTAL METHOD 2.1 Soil S’ecinieri The soil specimens used in the experiment are No.5 clay and Catalpo clay which are on the market. Their material properties are summarized in Table.2.1. Table.2.1 Material properties of clays

!

No.5 Catalpo

1

Gs

2.7 2.7

1

wp 29.6% 20.3%

I

WL

43.0% 33.5%

I

1,

13.4 13.2

]

The grain size of Catalpo clay is finer than that of No.5 clay. 2.2 Experimental procedure Uedometer test on compacted soils The powder of No.5 clay is mixed with water and clay specimens are prepared around prescribed water content. Clay specimens are compacted statically in the oedometer test apparatus. The initial conditions of thus prepared clay specimens are summarized in Table 2.2. The experiments are carried out as follows. Under the condition of the constant vertical pressure of 196 Wa, the suction stress is changed by means of applying air pressure directly to the compacted soil specimen of which boundaries are set to be permeable. Namely since the pore water pressure is measured, the suction value can be calculated as, s = zc, -U,, (1) in which s is the suction, zi, is the pore air pressure and U, is the pore water pressure. Thus, the suction stress is increased from 196 to 492 kPa and then reduced to 0 kPa under the condition of constant vertical pressure of 196 kPa in the experiment.

Trimial test on reconstituted soils Slurry paste of clays is prepared and preconsolidated in the container. Thus obtained reconstituted clay materials are trimmed in the shape of the diameter of 35 mm and the height of 80mm. The reconstituted clay specimens are set in the triaxial test apparatus and air pressure is applied in the same manner with the oedometer test. The stress paths chosen in experiment are summarized in Table 2.3. The suction stress is applied as shown in the table under the condition of constant confining pressure.

382

1

c d e

1.62 1.59 1.20 0.99

1

Water

Degree of

30.2 17.5 23.1 30.4

50.5 29.7 52.0 82.9

Confining Pressure Suction (Wa) (&a) IAl 19.6 1 0-+490+0 1 B 19.6 0-392-+49+245 C 19.6 0+294+49-+245 ID1 98.0 I 0-490-49 I E 19.6 0+490+0 F 196.0 0+490-0 Test-A, B, C, D: No.5 Clay; Test-E, F : Catalpo Clay

2.3 Experimental Results Fig. 1 shows the experimental results obtained from oedometer tests for compacted clay specimens. And changes of water content, void ratio and degree of saturation with the suction stress are compared. In the process of suction increase, the change of void ratio with suction is not seen. But the water content decreases with the increase of suction and seems to converge into a certain constant value in all cases. On the contrary, in the process of suction decrease, the void ratio drops at the low value of suction. It is called “collapse” phenomenon and is seen more conspicuously in initially higher value of void ratio. F i g 2 shows changes of water content, void ratio and degree of saturation obtained from triaxial tests

for reconstituted soils. The effect of suction stress history on the water retention characteristics can be examined from Fig.2. The water retention curves obtained in the loading process of suction (with increase of suction) are different from those obtained in the unloading process of suction (with decrease of suction). But the water retention curves in the unloading process of suction gradually converge into the curves of specimen applied higher suction stress. Fig.3 shows influence of confining pressure on water retention property of soil. The results obtained from Test-A and Test-D for No.5 clays are compared. It appears that the degree of saturation in the case of Test-A more rapidly decreases with the

increase of suction stress than that in the case of Test-D. However, its difference is quite small. Moreover, since the drainage of pore water is hard to be made under higher confining pressure in the experimental practice, its difference due to the confining pressure cannot be immediately accepted as a mechanical property of unsaturated soils. In fact, the experimental results obtained from Test-E and Test-F for Catalpo clays do not show dependency on the confining pressure as shown in Fig.4. Therefore, it would be concluded that the confining pressure does not influence the water retention characteristics of unsaturated soils.

383

Fig.5 Application of Brooks and Corey's model

Fig.6 Relation of air entry value and void ratio

3. THE EFFECT OF VOID RATIO ON THE FORM

OF WATER RETENTION CURVE In order to examine the effect of void ratio on the water retention curve, a model proposed by Brooks and Corey is applied to the water retention curves from experiments and the fitting parameters employed in the model are considered. The Brooks and Corey's model is expressed as,

in which S,is the normalized degree of saturation, S, is the degree of saturation, Slo is the degree of is residual saturation when the suction, s + C O , s, the suction at saturation and a is the fitting parameter and s, is generally called the air entry value in drying process or the water entry value in wetting process. Experimental data are plotted on the bi-logarithmic plane of S, and s with assuming the value ofS, and a straight line is drew so as to best fit experimental data by using the least square method. Such trial and error are made and fitting parameters of s, and a are determined. And simultaneously the air entry value and the water entry value are also estimated. Fig.5 shows a example of data fitting lines (solid lines) by Eq.(2), in which s , ~and s,, in the figure are the air entry value and the water entry value, respectively. The

Fig.8 The Capillary Model

384

Fig.7 Relation of water entry value and void ratio

air entry value and the water entry value corresponding to the value of void ratio are different in each test. Since each entry value corresponding to the void ratio can be specified for each of all tests, the dependency of s, and s, on the void ratio is summarized as shown in Fig.6 (air entry value) and Fig.7 (water entry value). It is found that each entry value can be expressed by a power fknction of the void ratio as shown in the figures. In order to examine the void ratio dependency, a capillary model as shown in Fig.8 is introduced. From equilibrium of forces, the suction value is expressed as, 2T s = zi, -74," = ___ ( 31 r in which T is the surface tension, Y is the radius of the capillary tube. If the sectional area of the capillary tube per a unit surface of the model shown in Fig.8 can be regarded as being equivalent to the void ratio, Eq.(3) means that the suction stress becomes smaller as the void ratio becomes larger. Actually, the experimental results shown in F i g 6 (drying process) and Fig.7 (wetting process) are consistent with it. The suction value is expected to be in inverse proportion to the square root of void ratio. However, the pore structure in real soils is much more complicated. It would not be suitable that such a simple model shown in Fig.8 is directly applied to quantitative prediction of suction stress in the real soils. In this paper, the power law is used in the expression of water retention curve to consider the void ratio dependency. First, the idea by Toll is employed here. He introduced the "equivalent void ratio" which was defined as, e," = w.G, = e . S , . (4) The effect of void ratio on the water retention characteristic of soils can be considered if one employs the equivalent void ratio instead of the degree of saturation as in Eq.(2). Then, the following expression is presented.

Fig9 Water retention curve in terms of equivalent void ratio

Fig. 12 Relation of

0:

and Sro

Fig. 10 Theoretical drying curves from saturated state

Fig. 11 Theoretical drying curves from unsaturated state

Fig. 13 Predicted and experimental wetting curves

Fig. 14 Theoretical wetting curves from unsaturated state

(5)

in which e,is the equivalent void ratio and e,, is the equivalent void ratio at residual state (s + a). When one compares Eq.(5) with Eq.(2), he becomes aware that both expressions have the same parameters, i.e., CL and s,. Therefore, these fitting parameters can be determined by the same manner as shown in Fig.5 and then the fitting curves are obtained as shown in Fig.9. The equivalent void ratio at residual state, e,,, is uniquely specified from S,,and the water content at the residual state in the drying process. However, in the wetting process, it is necessary to assume a proper value of equivalent void ratio at the residual state (s -+ a) for each case The water retention curves in the drying process are drawn in Fig. 10 in terms of the equivalent void ratio. Two cases in which the initial void ratio is different are considered, i.e. 0 and 0. The broken line in the figure indicates the air entry value, which is obtained from Fig.6. If the suction is applied to initially saturated soils, the water retention characteristics of the soils are expected to change along the curves shown in Fig.10. The

385

suction works so as to compress the soil mass as the external force until the suction reaches the air entry value. The drainage begins when the suction reaches the air entry value and the remarkable compression of soils occurs. However, after that, the amount of compression of soils gradually reduces with the increase of suction and finally the void ratio reaches its residual value, ewe. Fig. 11 shows the case that the suction is applied to initially unsaturated soils indicated by “P” in the figure. Likewise, the suction at first works so as to compress the soils as the external force until the suction reaches to the water retention curve of initially saturated specimen in this case. Then, the drainage occurs along the water retention curve as shown in the figure. The timing when the drainage begins is different depending on the initial void ratio as indicated by 0and 0in Fig. 10. On the other hand, in the wetting process, the equivalent void ratio at the residual state cannot be specified uniquely. It is different in each wetting process even for the same soil. And the water entry value shows void ratio dependency as indicated in Fig.7. Then, to address this problem, considered is the shape of water retention curve in the wetting process. As seen in Fig.1 and Fig.2, the gradient of

3) M. Nakano. 1976. Pore volume distribution and curve of water content versus suction of porous body: 2. Two boundary wetting curve. Soil Science. Vol. 122. No.2: 100-106. 4) D. G. Toll. 1995. A conceptual model for the drying and wetting of soil. Proc. 1st Int. Con$ on Unsaturated Soils.Vol.2: 805-8 10

the water retention curve becomes smaller as the degree of saturation is lower. Since the gradient of the curve is governed by the parameter, a, the relation of a and the degree of saturation at residual state (S,, = e,, / e ) is examined. Fig. 12 indicates the relationship between a and S,, . It is found that there is a unique linear relation between CL and S,,independent of soil properties. Then, once a is specified, S,, and ew, can be estimated using the linear relation shown in Fig.12. Fig.13 shows the performance of above mentioned approximation method that makes it possible to draw the water retention curve in the wetting process. Experimental data shown in Fig.2 are used and compared with the theoretical curves. Good agreement between them can be seen. Fig.14 shows the theoretical water retention curves in terms of equivalent void ratio. Two cases in which initial void ratio is different are drawn in the figure. Once initial state of the soil indicated by “P” in the figure is given, the water retention curve considering void ratio dependency can be predicted fiom Eq.(5) as shown in the figure. 4.CONCLUDING REMARKS The main conclusions described in this paper are as follows, 1. The void ratio dependency of the water retention curve is quantitatively examined throughout laboratory experiments. It is shown that the air entry value and the water entry value are also influenced by the void ratio. 2. The model proposed by Brooks and Corey is introduced and the influence of void ratio on the water retention curve is quantitatively examined based on the model. It is found that the parameter that effects on its gradient has a linear relation with the degree of saturation in the wetting process. 3 . The idea of the equivalent void ratio by Toll is adopted to express more realistic water retention characteristics of soils and a new model to rationally predict the water retention characteristics of soils is proposed. REFERENCES 1) Vachaud. G. and Thony. J. L. 1971. Hysteresis during infiltration and redistribution in a soil column at different initial water contents. Water Resources Research. Vo1.7. N o . 1 : 11 1-127. 2) M. Nakano. 1976. Pore volume distribution and curve of water content versus suction of porous body: 1. Two boundary drying curves. Soil Science. Vol. 122. N o . 1: 5-14.

386

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Suction profiles and stability of residual soil slopes E.C. Leong, B. K. Low & H. Rahardjo NTU-PWD Geotechnical Research Centre, Nanycrrzg TechtzologicalUniversity, Singapore

ABSTRACT: In the tropics, many residual soil slopes stand at a very steep slope angle. The stability of these very steep slopes is attributed to the suction or negative pore-water pressures within the soil. Measurements of suction within a slope showed that the suction in the surface soils can change drastically due to climatic conditions. As the pore-water pressure condition in the slope is never a constant, it is very difficult to account for suction in slope stability analyses. Hence in practice suction is often not considered in slope stability analyses. The paper attempts to illustrate how suction may be accounted for in the stability of residual soil slopes through limit equilibrium analysis. Suction profiles, typical of residual soil slope conditions found in Singapore, will be used in the analyses.

1 INTRODUCTION The relief of Singapore island can be divided into the central hilly region of igneous rock formation in Bukit Timah, Bukit Panjang and Bukit Mandai, the western region of sedimentary rocks forming a succession of northwest trending hills and valleys, and the relatively flat eastern region of sand and gravel deposits. The igneous rock formation is known geologically as the Bukit Timah granite formation and the sedimentary rocks as the Jurong sedimentary formation. Each formation occupies about onethird of Singapore’s land area. The upper strata of these formations are highly weathered where weathering depth may vary from several metres to tens of metres. The groundwater table in these soils is usually quite deep, thus most of the residual soils are in an unsaturated state. Most of the island’s steepest slopes are found in the ridges of the Jurong sedimentary formation. Singapore lying in the tropics is uniformly hot and humid throughout the year, with an average mean temperature of 27OC and average daily humidity of about 85%. Rain falls throughout the year but is heavier in the months of November, December and January. Most of the rain falls as sudden showers, with rainfall of more than 50 mm per day. The average annual rainfall is about 2400 mm. Not surpris-

ingly, a number of landslides occurred during the months of November, December and January (Pitts 1983, Tan et al. 1987). The factors affecting slope instability due to rainfall are: slope geometry, groundwater condition, soil properties, rainfall pattern and slope surface conditions (Leong & Rahardjo 1997a). In this paper, emphasis is placed on the effect of rainfall duration and intensity on soil suction profiles and hence its effect on slope stability. A typical slope geometry found in parks and along highways in the Jurong sedimentary formation is selected for the study. 2 SLOPE INSTABILITY DUE TO RAINWATER INFILTRATION To evaluate slope instability due to rainwater infiltration, two processes need to be examined. One process is the change in pore-water pressure conditions in the slope due to movement of rainwater into the slope. The other process is the change in shear strength of the soil due to the increase in pore-water pressure and hence its effect on the factor of safety against slope failure. Specialized computer programs are available to evaluate the factor of safety for the slope taking into account the reduction in suction during rain. The most commonly adopted approach

387

is to use a finite element program for transient seepage to obtain the pore-water pressures in the slope during rain and to incorporate the pore-water pressures in a slope stability evaluation using limit equilibrium analysis (e.g. Fredlund & Barbour 1992, Alonso et al. 1995, Sun et al. 1995). Nowadays with the improvement in desktop computing power, it is possible to formulate and solve the problem using a spreadsheet program. Such an approach is adopted for the present study. 2.1 InJiltration In this study, the process of rainwater infiltration is treated in one dimension only. The transient onedimensional water flow into unsaturated soils can be solved using Richard's equation:

2.2 Limit equilibrium analysis A number of limit equilibrium methods are available for slope stability analysis mash 1987). Fredlund and Krahn (1977) found that differences between factors of safety obtained from Bishop's simplified method (satisfying moment equilibrium only) and Spencer's and Morgenstern and Price's methods (satisfying both force and moment equilibrium) are less than 0.4% for the cases that they had analysed. The limit equilibrium method adopted for this study is the Bishop's simplified method for noncircular slip surfaces. Details of a spreadsheet formulation for slope stability analyses can be found in Low & Tang (1 997) and will not be elaborated here.

3 SOIL PROPERTIES AND SLOPE GEOMETRY

where 8, = volumetric water content, t = time, z = vertical ordinate, k, = unsaturated permeability and h = hydraulic head. A widely used solution of Equation 1 in terms of the depth of the wetting front zw was proposed by Lumb (1 975). The depth zwto which a wetting front will penetrate into a slope in time t is given as:

The Jurong sedimentary formation consists mainly of interbedded layers of mudstone and sandstone which are highly folded and faulted. The top portion of the formation is generally weathered to residual clayey or sandy silts. The weathered depths can extend to 40 m and is generally deeper in the faulted areas and in the mudstone region. The groundwater table can generally be found as shallow as 1.5 m from the ground surface in the low lying areas and can be deeper than 10 m in the hilly areas. The saturated permeability k, of the Jurong formation residual soils ranges from 10-4m / s to 10-9m/s depending on the depth and degree of weathering. Typical unit weight y of the residual soils ranges from 17 to 20 kN/m3. The shear strength z of the Jurong formation residual soils may be described using the extended Mohr-Coulomb envelope (Fredlund et al. 1978):

(3)

where D = diffusion term, k, = saturated coefficient of permeability, n = porosity, Sf = final degree of saturation and So = initial degree of saturation. However, this solution is based on the restrictive assumption that unsaturated permeability is constant with depth and is valid only for the case where the rainfall intensity exceeds the saturated permeability of the soil. Equation I can be recast in finite difference notations and implemented in a spreadsheet. To solve Equation I , the soil-water characteristic curve and permeability function of the soil are required. The infiltration rate is dependent on both the rainfall intensity and the permeability of the soil at the soil surface. Using this approach, the pore-water pressures at various depth can be obtained at different rainfall durations. The pore-water pressure conditions in a slope can be determined at different vertical sections of the slope.

where c' = effective cohesion, (T, = normal stress, ua = pore-air pressure, $' = effective friction angle, U, = pore-water pressure and $b = angle defining the increase in shear strength for an increase in matric suction (ua - U,). The value for 4' ranges from 20' to 40'. The value for c' is quite variable ranging from 0 to about 50 kPa. Typical $b angle for Jurong fonnation residual soils ranges from 20' to 30'. Typical cut slopes in the Jurong formation can be found in parks and along highways. These slopes have a height of about 10 to 15 m with a slope angle between 20' and 30'. The slope geometry selected for this study is shown in Figure 1 with the groundwater table (GWT) at the level corresponding to the toe of the slope. It was assumed that the slope consists of homogeneous residual soil of the Jurong sedimentary formation. The Jurong formation resid-

300

ual soil properties used for the study are y = 18 kN/m3, k, = 10-5d s , c' = 5 kPa, and 4' = $b = 26". The soil-water characteristic curve and permeability functions used are given in Equations 4 and 5, respectively. Details of the form of Equations 4 and 5 can be found in Leong & Rahardjo (1997b, 1997~). (4)

Figure 2. Rainfall intensity - duration plot for return periods of 1, 10 and 100 years. groundwater table is assumed to remain constant at all times during rainfall.

In the above equations, (U, - U,) is in kPa and y, is in kN/m3. The saturated volumetric water content 8s used in Equation 4 was 0.4. Equations 4 and 5 were used together with Equation 1 in the infiltration analysis at sections 1 to 4 of the slope. The porewater pressure conditions in the slope were determined by interpolations from the four sections and together with Equation 3 were used in the factor of safety calculation using limit equilibrium analysis. Section 11

Figure 1. Slope geometry and groundwater condition. 4 RAINFALL CONDITIONS In the tropics, rainfall of high intensity is of short duration and rainfall of low intensity is of much longer duration. In Singapore, the relationships of rainfall intensity and duration for return periods of 1, 10 and 100 years are shown in Figure 2. The chart is normally used for surface drainage design (ENV 1992). The rainfall intensities selected for the analyses were 8 mm/h, 16 mm/h and 61 mm/h or approximately 0.22kS, 0.44k, and 1.69k, (where ks is saturated permeability of the soil), respectively. The rainfall intensities correspond to rainfall duration of 10h, 5h and l h respectively for a rainfall return period of 1 year as shown in Figure 2. In all cases, the

5 INFLUENCE OF INITIAL SUCTION PROFILE The suction or pore-water pressure profiles in the slope are affected by the position of the groundwater table and the climate (Leong and Rahardjo 1997a). The deeper the groundwater table, the higher is the suction at the ground surface which can increase to even higher values due to evaporation and evapotranspiration. With rainwater infiltration, the upper part of the ground may lose part of or in the extreme case all of its suction. Such changes in the suction profiles have been observed in Singapore residual soil slopes (Lim et al. 1996, Rahardjo et al. 1998). Two initial suction profiles for the residual soil slope were used in the analyses. The initial suction profiles at Sections 1 to 4 of the slope are shown in Figure 3. Suction profile A represents the typical pore-water pressure condition in a slope during the dry season. Suction profile B represents the typical pore-water pressure condition in a slope during the wet season. The suctions are highest at Section 1 and lowest at Section 4 as the ground surface at Section 1 is furthest from the groundwater table compared with the other sections. The changes in suction profile at various times under a rainfall intensity of 16 mm/h (0.44kS)are shown in Figures 4 and 5 for initial suction profiles A and B respectively. It can be observed in Figure 4 that the suctions at Sections 1 and 2 did not change any further after 3h of rainfall. The depth of influence is less than 2 m. At Sections 3 and 4, the situations are very different. At Section 3, the suction decreases with rainfall duration reaching almost zero suction after 18h of rain. The reduction is much faster at Section 4 where the profile reaches almost zero suction after 6h of rain. In Figure 5 , the reduction in suction is more rapid. The suctions reduce to zero in all sections after a certain rainfall duration. Similar to that of initial suction profile A, the suctions reduce the fastest at Section 4

389

Figure 3. Initial suction profiles A and B.

Figure 4. Changes in suction profile with time for rainfall intensity, i suction profile A.

=

16 mm/h, starting with initial

Figure 5 . Changes in suction profile with time for rainfall intensity, i suction profile B.

=

16 mm/h, starting with initial

390

and slowest at Section 1. Using these suction profiles at different rainfall duration, a limit equilibrium analysis of the slope was conducted using Bishop’s simplified method with a non-circular slip surface. The factors of safety with rainfall duration are shown in Figure 6. Also shown in Figure 6 is a dash line indicating the factor of safety of the slope if pore-water pressures above the groundwater table are assumed to be zero at all times. For initial suction profile A, the slope will show a reduction in factor of safety but it will not reach the factor of safety of the slope where zero pore-water pressures were assumed zero above the groundwater table. Not all the suctions in the slope were diminished by the rainfall even after a long rainfall duration. For initial suction profile B, the factor of safety of the slope reduces with rainfall duration reaching the factor of safety of the slope without suction consideration after 27h of rain. The results indicate that initial suction profiles play an important role in slope stability during a rainfall event. The results also provided explanation for the role of antecedent rainfall in slope instability due to rain.

6 INFLUENCE OF RAINFALL INTENSITY Some researchers have suggested that if the rainfall intensity exceeds a critical value, slope failure will occur. The influence of rainfall intensity on slope stability was studied using three different rainfall intensities, 8 m d h , 16 mm/h and 61 m d h , with initial suction profile B. The factors of safety for the different rainfall intensities at different rainfall duration are shown in Figure 7. For the rainfall intensity of 8 m d h , the factor of safety reduces very slightly at the initial stage and does not change any further. The critical slip surfaces at various times for 8 mm/h rainfall intensity are shown in Figure 8a. For the rainfall intensity of 16 m d h , the factor of safety reduces as the rainfall duration increases, reaching a constant value that is above the factor of safety for the case where the pore-water pressures are assumed to be zero above the groundwater table. The critical slip surfaces for this case, shown in Figure 8b, indicate that the critical slip surfaces become shallower with the increasing rainfall duration. For the rainfall intensity of 61 mm/h, the decrease in factor of safety is more rapid, decreasing to the factor of safety for the case where the pore-water pressures were assumed to be zero above the groundwater table (Figure 7). The change can be more clearly observed in the progression rate of the critical slip surfaces in becoming shallower with the increasing rainfall duration as shown in Figure 8c. The results in Figure 7 seem to indicate that there is a critical rainfall intensity dependent on the initial suction profile, below which the stability of the slope will not be affected.

7 CONCLUSIONS Figure 6. Factors of safety versus rainfall duration for different initial suction profiles.

In this paper, a way of accounting for suction in the stability of residual soil slopes through limit equilibrium analysis has been illustrated. The formulation can be implemented in a spreadsheet and does not require any specialized computer program. The analyses showed that initial suction profile plays an important role in the stability of residual soil slopes during rain. In some cases, the suction profile does not diminish significantly even after a long rainfall duration. The analyses also showed that for an initial suction profile, there exists a critical rainfall intensity, below which the stability of the slope will not be affected even after a long rainfall duration. ACKNOWLEDGMENTS

Figure 7. Factors of safety versus rainfall duration for different rainfall intensities.

The work described in this paper is part of a research project funded by the National Science and

391

Technology Board, Singapore, Grant No. NSTB 17/6116.

Figure 8. Critical slip surfaces at different rainfall durations for different rainfall intensities.

REFERENCES Alonso, E, A. Gens & A. Lloret 1995. Effect of rain infilitration on the stability of slopes. In E. Alonso, & P. Delage (eds), Proc. 1st Int. Con$ on Unsaturated Soils, Paris, France, 1:24 1-249. Rotterdam: Balkema.

ENV 1992. Code of practice on surface water drainage/ Drainage Dept., 4th Ed., 1st reprint. Singapore: Drainage Dept., Ministry of Environment. Fredlund, D.G. & S.L. Barbour 1992. Integrated seepage modelling and slope stability analysis. In R.N. Chowdhury (ed.), A generalized approach for saturated/ unsaturated soils: 3-35. Rotterdam: Balkema. Fredlund, D.G. & J. Krahn 1977. Comparison of slope stability methods of analysis. Can. Geotech. J., 14 :429-439. Fredlund, D.G., N.R. Morgenstern & A. Widger 1978. Shear strength of unsaturated soils. Can. Geotech. J., 15:3 13-321. Leong, E.C. & H. Rahardjo 1997a. Factors affecting slope instability due to rainwater infiltration. Proceedings 2nd Japan National Symp. on Environmental Geotechnology, Kyoto: 163-168. Leong, E.C. & H. Rahardjo 1997b. A review on soilwater characteristic curve equations. J. of Geotechnical and Geoenvironmental Engineering, ASCE, 123(12):1106-1117. Leong, E.C. & H. Rahardjo 1997c. Permeability functions for unsaturated soils. J. of Geotechechnical and Geoenvironmental Engineering, ASCE, 123(12):1118-1126. Lim, T.T., H. Rahardjo, M.F. Chang & D.G. Fredlund 1996. Effect of rainfall on matric suctions in a residual soil slope. Can. Geotech. J., 33:618-628. Low, B.K. & W.H. Tang 1997. Probabilistic slope analysis using Janbu’s generalized procedure of slices. Computers and Geotechnics, 2 1 : 12 1- 142. Lumb, P. 1975. Slopes failures in Hong Kong. Quart. J. Engineering Geology, 8:3 1-53. Nash, D. 1987. Chapter 2: A comparative review af limit equilibrium methods of stability analyses. In M.G. Anderson & K.S. Richards, Slope Stability: 11-75. John Wiley & Sons Ltd. Pitts, J. 1983. The form and causes of slope failures in an area west of Singapore island. Singapore J. Tropical Geography, 4(2): 162- 168. Rahardjo, H. & E.C. Leong 1997. Soil water characteristic curves and flux boundary problems. Unsaturated Soil Engineering Practice, ASCE Geotechnical Special Publication No. 68:88-1 12. Rahardjo, H., E.C. Leong & S.K. Tang 1998. Assessment of rainfall effects on stability of residual soil slopes. Proc. 2nd Int. Con$ on Unsaturated Soils, Beijing, China, 1: 280-285. Sun, Y . , M. Nishigaki & I. Kohno 1995. A study on stability analysis of shallow layer slope due to raining permeation. In E. Alonso, & P. Delage (eds), Proc. 1st Int. Con$ on Unsaturated Soils, Paris, France, 1: 3 15320. Rotterdam: Balkema. Tan, S.B., S.L. Tan, T.L. Litn and K.S. Yang 1987. Lanslide problems and their control in Singapore. Proc. 9th Southeast Asian Geotechnical Con$, Bangkok, Thailand, 1 :25-36.

392

Slope Stability Engineering, Yagi, Yamagami L3 Jiang 0 7999 Balkema, Rotterdam, lSBN go 5809 079 5

Effects of perched water table on slope stability in unsaturated soils Low Tian Huat, Faisal Haji Ali, Saravanan Mariappan & Phang Kam Soon Civil Engineering Department, University of Malaya, Kuala Lumpur, Malaysia

ABSTRACT: Instability is an extremely important consideration in the design and construction of man-made slopes and natural slopes. Slope failures and landslides are influenced by geologic topographic and climatic factors. In tropical region, most of the slope failure occurs during severe rainfall. Rain water infiltrates into the slope and reduce the soil matric suction and the strength of the soil. Perched water table may also develops depending on the permeability of the soil layers in the slope and the rate of infiltration. In the paper, effect of perched water table, which occurs after severe rainfall and underlying of impermeable layer were studied. The effects of perched water table on factor of safety of slope were analysed by varying the permeability ratio of soil layers, thickness of impermeable layer, position of impermeable layer, number of impermeable layer and orientation of impermeable layer. 1 INTRODUCTION

Tropical countries like Malaysia experiences warm and wet climatic conditions throughout the year. Most of the highlands are covered with tropically weathered residual soils. Significant infiltration into residual soils can cause slope instability. Many constructions of roads and highways are carried out especially on undulating terrain that mainly consist of residual soils. Recently, slope stability problems had gained attention from both public and local authorities after a few cases of serious landslides occurred and caused losses in properties and even lives. A huge amount of money had to be spent on slope remedial works yearly and giving rises for the need of thorough and detail research on slope stability. Most of the slope failures occurred during rainy seasons. Many researchers found that rainfall infiltration is the triggering factors of most landslides (Affendi, 1996; D.G. Fredlund 1993). The slope failure basically caused by the reduction of soil suction during prolong period of rainfall and reduced the shearing resistance. Most of the sedimentary residual soils in Malaysia are not homogeneous. The nonhomogeneity also caused by the weathering process. They usually overlaid by one or more layer of soils. Due to the different characteristic of the soil layers, ground water condition and seepage flow would be too and their influences to slope

stability become unpredictable. Perched water table would probably built up when these nonhomogeneous soil strata are exposed to prolong period of infiltration which is common for the climatic condition in this region. 2 METHODOLOGY

In this study, the water flux and seepage on slopes were simulated first by using a water seepage (SEEPN) software (refer to Figure 1 for typical output). The output from S E E P N was then exported to a slope analysis (SLOPEN) software to find the safety factor of slope (refer to Figure 2 for typical output). Before using S L O P E N , the moisture condition for transient analysis from S E E P N has to be clearly defined. The output at different interval of time was combined with S L O P E N to make it possible to determine the factor of safety of each interval of time. For all cases, Bishop method of analysis were chosen for the stability check. In the analyses, the strength parameters for soils has been defined as follow: Unit weight (y) Angle of friction (phi) Cohesion (C)

= 18 kN/m3

= 20° = 20 kN/m’

The strength parameters were used to study the effects of perched water(for both the permeable and impermeable strata).

393

Under this type of rainfall intensity perched water table can be generated in most of the cases. Thus the effect of perched water table under these specified parameters can be studied carefully. The effect of the permeability ratio (ratio of permeability of a permeable stratum to impermeable stratum) was also studied. The critical ratio that causes perched water table was determined. The parameters chosen were as below: 2.1 x 10-4m/s and for sloping surfaces was i) 1.05 1 0 - ~dS. Thickness of impermeable layer was 2m and ii) it was modelled at 4m below top surface. iii) Height of slope was 8m. Permeability of impermeable layer had been iv) selected as 1 x 10.' m/s. The ratios were defined in the range of 30000 to 100000.

Figure 1. Typical output from S E E P N

In the study few possible cases were considered:

I) 2) 3) 4) 5)

Effect Effect Effect Effect Effect

-

of position of impermeable layer. of dipping of impermeable layer. of thickness of impermeable layer. of number of impermeable layer. of rainfall intensity

Verification of the SEEP/W program

Figure 2. Typical output f r o m x O P E / W

Before the parametric study, verification of the suction values was carried out by comparing the measured suction values in the laboratory hydrological model (Figure 3) with the simulated suction values by the S E E P N program. Figure 4 shows one of the typical variations of with time. The difference of the lowest simulated and measured suction is just 2 kPa. However, there is a time lag of about 100 minutes between the simulated and measured suction values. The rainfall pattern agrees well with the drop in suction. The trend in recovery of the suction values for the simulated and site values are also found to be almost the same. The initial difference of the suction values might be due to the hysteresis effect of the soil water characteristics of the sample used. .

Figure 3 Laboratory Hydrological Model Parametric Study The pattern of rainfall chosen was constant rainfall with intensity 2.1 x 1 0 ' ~m / s for all cases. The duration of rainfall was 12000 sec (3.333 hrs).

Figure 4 comparison suction value. 394

of simulated and measured

3 DISCUSSION Rainfall intensity for all the cases was specified for horizontal surface as well as dipping surface. The water flow into the slopes will be much more complicated as the interference of water flow from horizontal and dipping surface will happen. So, fluctuation is expected. The conditions that cause slopes to become unstable and the factors that initiate the slip failure should be able to be identified. These factors are by the geological structure and hydro-geological conditions of the slope. Generally in all cases the safety factor drops as the perched water table starts to build up. The drops are not very large i.e., not more than 20 %.

Figure 6. Effect of position of impermeable strata (distance referring to the top of the slope)

3.3 Effect of Dipping of Impermeable Layer Cases with dipping layers generally have safety factor with sloping bed dipping backward (Figure 8). This is because the dipping backwards enables more water to accumulate above impermeable layer. The effect of perched water table is more significant as it is easier to form as safety factor drops earlier compare to model with dipping bed gradient same direction with dipping surface.

3. I EfSect of Permeability Ratio of Permeable Layer to Impermeable Layer By varying the permeability ratio, it will affect the seepage and water content in the slope and hence the stability of the slope. From the results shown in Figure 5 , it is clear that safety factors drop at certain interval of time when perched water table starts to build up. The perched water table starts to build up earlier for higher permeability ratio and this causes safety factor drop earlier. This is true because the higher ratio means the permeable layer with higher hydraulic conductivity, which allows water to infiltrate into the soil faster. Generally perched water table starts to build up from interval time 6000 sec to 8000 sec.

3.2 Effect of Position of Impermeable Layer By varying the position of impermeable layer, the time to build up perched water table seepage infiltration and water content will be affected. From graph (Figure 6), the safety factor of slip surface starts to drop at time 6000 sec. This means perched water table starts to build up at this time. Generally the effect of position of the impermeable strata is not significant.

Figure 7 Typical profile showing the impermeable stratum

Figure 8. Effect of dipping of impermeable soil layer on slope safety factor. (negative in the figure indicates dipping backwards)

Figure 5. Effect of soil permeability ratio on slope safety factor (Permeability of 1 X lo-' m / S for impermeable stratum was used as datum) 395

3.4 ESfect of Number of Impermeable layer. As the number of impermeable layer increases the safety factor drops accordingly as shown in Figure 9. In all the three cases shown in Figure 7, the safety of factor seems to drop after a critical duration i.e., about 4000sec. This is due to the build-up of perched water table in the slope.

to be considered carefully. If the rainfall intensity is more than the permeability of the soil, surface runoff needs to be specified.

Figure 10 Effect of rainfall intensity on factor of safety

4 CONCLUSIONS Figure 9. Effect of number of impermeable strata on slope safety factor.

From the studies carried out, the following conclusion can be summarised:

3.5 EfSect of Rainfall Intensity Figure 10 clearly shows that for rainfall intensity of 1 x 10-5 m/s or less the factor of safety remains constant as no perched water table build up. For rainfall intensity 5 x 10-5 m/s and 5.2 x 10-5 m/s there are only slight drops i.e., not more than 2 %. The drop of safety factor becomes more significant for higher rainfall intensity. Rainfall intensity of 1 x 10-4m/s records a maximum drop of 4.4% while rainfall intensity of 2.1 x 10-4 m/s records a maximum drop in factor of safety. Generally the safety factor starts to drop at time 6000 sec or 7000 sec. The reading is constant for set of data with lower rainfall intensity, as for lower rainfall intensity the effect of perched water table is not significant. The safety factor for rainfall intensity 2.1 x 10-4m/s shows fluctuating trend before perched water table starts to build up because seepage of high rainfall infiltration is more complicated and difficult to predict. Interference of water flow from horizontal and slope surface is another contributing factor. The permeability of the soil also plays an important role in this study because when the rainfall intensity is lower then the permeability of the soil, the infiltrated rain water can dissipate fast into the slope and does not cause perched water table to build up. But, when the rainfall intensity equal to or more than the soil permeability value, perched water table will start to form. In the analysis, the flux boundary condition needs

i) ii) iii)

iv)

Factor of safety will drop lower for slope with higher ratio of permeability. When perched water table is formed, it decreases the factor of safety. Further rainfall does not seem to lower the safety factor. Cases with impermeable stratum dipping backward generally gives lower safety factor compares to cases with impermeable stratum dipping forward. As the number of impermeable layer increases the safety factor will drop. The drop in safety factor is rapid after the critical duration.

REFERENCES Affendi, A (1996). Field and laboratory study on unsaturated residual soils in relation to slope stability analysis, Ph.D. thesis, University of Malaya. Unpublished. Fredlund D.G. , “Slope Stability analysis incorporating the effect of soil suction”, 1987, Slope Stability, John Wiley & Sons Ltd. Fredlund, D.G and Rahardjo, H. (1993). Soil Mechanics for Unsaturated Soils. John Wiley & sons. Morgentern, N (1963) Stability Charts for earth slopes during rapid drawdown, Geotechnique, vol13,pp 121- 131. Othman, M.A., (1990). Highway cut slope instability

396

problems in West Malaysia, Ph.D. thesis, University of Bristol, unpublished T.H. Low F.H. Ali, R. Subramaniam, “Parametric Studies of Slope Stability in Unsaturated Residual Soils” 13‘h. Southeast Asian Geotech. Conference, Taiwan, 1998, pp 117-122.

397

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang 6 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Field suction variation with rainfall on cut slope in weathered sedimentary residual soil Low Tian Huat, Faisal Haji Ali & Saravanan Mariappan Civil Engineering Departnzent, Uiziversity of Malaya, Kualu Lumpur, Muluysiu

ABSTRACT: Most residual soils especially in slopes are in unsaturated condition and therefore matric suction is an important factor to be considered in the design or analysis of slopes. The suction has an important bearing on water entry, structural stability, stiffness, shear strength and volume change. The soil matric suction, the water content and the solute content and how they vary with time are often the most important variables in soil engineering design. The field instrumentation for automatic continuous measurement of soil matric suction, rainfall and other slope instability related parameters are presented in this paper. Description of the selection. fabrication and installation of the instrumentation are discussed. 1 INTRODUCTION

Construction activities in hilly terrain covered by residual soil frequently confront geotechnical engineers with slope instability problems. Failures in both natural and cut slopes in residual soils of Peninsular Malaysia are usually brought about by rainfall during the monsoon season. The upper layer of the residual soil profile is always partially saturated , but invariably has a relatively high permeability to infiltrating rainwater. This obviously causes the pore water regime to be governed largely by rainfall pattern. The mechanism of slope failure is that the infiltration of rainwater causes a reduction of matric suction in the unsaturated soil, resulting in a decrease in the effective stress. This in turn reduces the shear strength to a point where equilibrium can no longer sustained in the slope. Good correlations between rainfall intensity and frequency of landslides have been reported by some researcher from Hong Kong, Japan, United State and NewZealand. The instrumentation is attempted to study the change of soil matric suction with the rainfall on a cut slope along the link road of The Kuala Lumpur International Airport (KLIA) Malaysia. The cut slope mainly consists of two types of weathered sedimentary residual soil, i.e., weathered sandstone and shale. These residual soils come in alternate bedding which is almost vertical. The weathered sandstone bed basically is the thicker bed and the study is concentrated in one of these beds. The soil consists of very fine sand and silt. The slope is

covered by different types of synthetics (biodegradable) and non synthetic covers ( poly-jute) after hydro-seeding to prevent erosion . Instrumentation is carried out on every berm with respect to different weathering grades of soil. 2 ROLE OF SUCTION IN SLOPE STABILITY The principle of effective stress for unsaturated soil was first used by Terzaghi (1923) and proposed by him in the first International Conference on Soil mechanics in 1936. Numerous researchers have carried out work since then in order to confirm. But the validity of the principle for unsaturated soil mechanics has been questioned by Jennings and Burland (1962). Following an extensive research program on unsaturated soil conducted in Imperial College the shear strength of partially saturated soil was hypothesised ( Bishop, 1959) to be a function of an effective stress defined as:-

where cf and 0 are the effective and total stresses respectively, ua is the pore air pressure and uw is the pore water pressure. is a function that depends on the saturation with value 1 at 100% saturation and 0 for completely dry soil. Fredlund and Morgentern (1987) showed from a stress analysis that any two combination of the

x

399

system is set in such that when there are rapid changes (in terms of percentage change of suction value) the 10 minutes interval would be utilised, or else, the 30 minutes interval is used. The recorded data are downloaded from the data logger direct to a portable notebook computer through an RS232 interface. An automatic logging tipping bucket rain gauge is installed at the study site. The rain gauge records rainfall events on a real time basis. The clock of the data logger for the tensiometers and moisture blocks and the rain gauge recorder are always synchronised. Figure 1 shows the schematic arrangement of the instrumentation at the study site. The infiltration characteristics of the soil are deduced by using a sprinkler system installed at the site. A V- Notch fixed with a flow meter is used to measure the surface run-off in a control section in the study (refer to Figure 2). Besides, an infiltrometer P-88 from Geonor (refer to Figure 3) is used to obtained the infiltration capacity at the site for the comparison with the sprinkler system.

three possible stress variables (0 -U,), (0 -U,,,) and (U,-U,) can be used to define unsaturated soil. The equation for unsaturated shear strength ‘I: is written in terms of the stress state variables for an unsaturated soil and is an extension of the form of equation used for saturated soils

where, = effective cohesion = total stress Ua = pore air pressure UW = pore water pressure = effective angle of friction 0’ (u,-uw) = matric suction = gradient with respect to changes in (ua-u,) 0 C’

0

when

(0 -U,)

is held constant.

The factor of safety for slope stability analysis using method of slices can be derived using shear strength equation [2] above. The shear force mobilised at the base of slice can be written as:S, =OR { c’

+ (0 -U,)

tan$

+ (Ua-U,)

tan$

}

[3]

Where = the shear force mobilised on the base of S, each slice. F = the safety factor = the sliding surface of the slice. p 3 INSTRUMENTATION

Figure 1. Instrumentation Layout of the study Site.

20 numbers of tensiometer and 20 numbers of moisture block and a rain gauge are installed on the slope to monitor the changes of matric suction with respect to rainfall. The tensiometers and moisture blocks are installed at different depths. At each berm, 4 numbers of tensiometers and moisture block are installed i.e., with depth of OSm, l m , 3m and 3m. An automatic data acquisition system is designed to record the output from tensiometers and moisture blocks. Automatic data acquisition system solves the problems of reliability, access and safety which are difficulties associated with manual data recording and allows continuous monitoring. The data acquisition system is supported by a solar powered set and specifically designed for low power consumption. The logging intervals are achieved by prescribing the appropriate interval during the set-up process. Two time intervals are adopted in this study, i.e., 30 minutes interval and 10 minutes. The

Figure 2. Field Infiltration Sprinkler System

400

5 INSTALLATION OF INSTRUMENT SENSORS In this study, normal coring tools cannot be used because the soil is brittle and hard (various weathering grades of weathered sandstone). A special in-house designed motorised auger is fabricated for the installation purposes. The motorised auger consists of two motors with ?hand % horse power. The quarter horse power motor is fitted at the top of the machine to push the auger into the slope as the half horse power motor is used to rotate the auger. Both the motors are fitted with a speed controller. During installation, four sand bags are placed at the base of the augering machine and the speed of the motors are properly controlled to prevent the auger machine from being pushed up when drilling through hard layers. The set-up is shown in Figure 5. The auger used in this study is designed to suit the soil condition at the study site. The most suitable distance between the flights is determined to be 25mm in order to ease the process of augering. Due to the difficulty in fabricating long auger, 2 or 3 lengths of short extension flights are jointed together. After the hole has been augered, a special tool is used to remove the residual from the hole. Precaution needs to be taken because an intimate contact with the soil is necessary in order for the tensiometer and moisture block to function properly. Moisture blocks are inserted into the bored hole using a fabricated tool in the form of a long rod with a modified tip. The soil is tamped firmly after placing the blocks and bentonite is placed at the surface of the hole in order to prevent the hole from becoming an abnormal water passage. All the wire leads are inserted into a poly-pipe and are buried in a shallow trench in the ground. The wires are connected to the data logger situated at the midway between the berms. The adverse tropical climate and vandalism are major concerns in the installation. The tensiometers and moisture blocks installation are protected by lockable steel security cages grouted to the slope. The data acquisition system is contained in a lockable steel hut. All the transducers for the tensiometers are protected from sunlight by wrapping them with a double layered foam rubber on the inside and aluminium foil on the out side.

Figure 3. Infiltrometer 4 MATRIC SUCTION MEASUREMENT

In this study, matric suction of the soil is measured using jet-fill tensiometer and moisture block (Soil Moisture Corporation U.S.A). Moisture blocks are used because tensiometer can only measure matric suction below 1 bar of negative pressure while moisture block can measure more than 4 bar. The matric suction obtained from the tensiometer is the difference between the gauge reading and the head of the water in the stamp. The longer the tensiometer, the lower the suction it can measure. In this study the tensiometer is installed perpendicular to the slope surface to reduce the head of water ( refer to Figure 4)

Figure 4. Sensors Layout for each berm.

6 DISCUSSION The accuracy of the moisture block when the suction is below 1 bar is not as good as tensiometer. To overcome the limitation of both the devices, both the tensiometer and moisture block are installed at the same depth for comparison and cross checking purposes.

Figure 6 shows a typical suction variation with rainfall (one month duration) for one of the berm at the study site. It is clearly shows that as the depth increases, the matric suction reduces. During the time interval of 14000 to 24000

40 1

Figure 7. Typical High Rainfall Intensity from The Study Site Figure 5. Special Fabricated Augering Machine As shown in Figure 6, high rainfall intensity with short duration may not play an important role in the instability of slope. Prolong rainfall even with low intensity could be significant.

7 CONCLUSIONS

Figure 6. Typical suction variation with rainfall for on e-month duration. minutes, there was no rainfall occurred. All the four tensiometers experiencing increments in matric suction. When the rain started to fall, matric suction did not reduce immediately. Due to the infiltration of rain water into the ground after rainfall, the matric suction reduced slowly for all depths even without any rainfall after the rainstorm. From Figure 6 , the time interval of 0 to 13000 minutes, suction of the 3.0m depth tensiometer gives very low suction values. This is mainly due to the cumulative rain water during the raining period. From the field infiltration test, the water infiltration rate is 2.31 x10-6m/s.From Figure 6, it is clearly shown that during heavy rainstorm, the suction drops very fast and also recovers fast. One of the reasons- is that the rainwater infiltrate nto the slope through quartz veins in the soil. Figure 7 shows one of the typical high rainfall intensity patterns at the study site. The rainfall intensity at the site can be very high, i.e., 1. 3 x 104m/s.

402

The automatic data logging system for monitoring tensiometers, moisture blocks and other devices has been detailed. The desired attributes of the system have been reasonably achieved and the advantages of a fully electrical installation are credited to its flexibility and continuity of data obtained. Installation method which creates much less disturbance helps to obtain more accurate data from the instruments. Generally as the depth increases, matric suction reduces. But, in some circumstances, due to the flux condition, this can be the other way round. Heavy rainfall intensity may necessary cause instability to slope but prolong rainfall can be significant. Geological features like quartz vein could be significant in slope instability because it increases the rainwater infiltration. 8 ACKNOWLEDGEMENT Acknowledgement is due to the Road Section, Public Work Department, Malaysia for providing part of the research grant. REFERENCES Abdullah, Affendi M.L. & Ali Faisal, "Field Instrumentation for Slope Stability in Residual Soil ". GEOTROPIKA 92' Johor Bahru, Malaysia.

Anderson , M.G. & Burt, T.P. “Automatic monitoring of soil moisture conditions in a hillside spur and hollow”, Journal of hydrology, V01.33,1977,~~27-36. Bishop, A.W. and Blight, G.E. (1967) “Effective stress evaluation for unsaturated soils” Jour. Soil Mech. & Found. Engg. Div., ASCE 93 (SM2), pp. 125 - 148. Fredlund D.G. “Appropriate concepts and tecnology for unsaturated soils”. Second Canadian Geotechnical Colloquim, Canadian Geotechnical Journal, No. 1 6 , 1979, pp 121-139. Fredlund,D.G., ”Slope stability analysis incorporating the effect of soil suction”, Slope Stability : Geotechnical Engineering and Geomorphology, Edited by Anderson,M.G., and Richards, K.S., John Wiley and Sons, Chichester,1987, ppl13-144. Rahardjo.H, Loi, J., and Fredlund, D.G.,” Typical matric suction measurements in the laboratory and in the field using thermal conductivity sensors”, presented at Indian Geotechnical Conference (IGC-89), Vol. 1, Visakhhapatnam, December 1989.

403

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang C) 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Study of slope stability for Pleistocene cemented sandy sediments in Singapore (Old Alluvium) K. K. Poh, F! B. Ng & K.Orihar-a Koso-Jihun Singupore Pte Limited,Singupore

ABSTRACT: This paper describes the methodology in the design of the 10 to 20m high cut slope in Old Alluvium which is Pleistocene cemented sandy sediments in Singapore. Also described are the measures taken to improve the safety margin of the cut slope and proposed monitoring program to verify the design assumption and concept. The project is in the initial construction stage and some of temporary cut slopes have been constructed. Based on the monitoring results and field observation, the slopes designed according to the above methodology (analysis and assumption) are found to be adequate. 1 INTRODUCTION

2 GEOLOGYAJVDOCCURANCE

Over a kilometer of cut and cover tunnel is currently being constructed in the northeastern part of Singapore using open cut excavation. Because o f ‘ space constraint, it is necessary to design steeper slope based on the best estimate of the soil properties and ground water condition.

The Old Alluvium is alluvial fan or piedmont plain deposits formed in the period of Pleistocene (10,000 to 1 million years ago), which is found lying on the eastern part of Singapore.

Due to the high permeability of the Old Alluvium, drained analysis is carried out for the design of temporary cut slope. Nevertheless, short term undrained analysis is also conducted as a check.

The Old Alluvium consists mainly of lightly cemented to cemented coarse quartz-feldspar sand. It is heavily weathered near the ground level to the greater depths. 3

Drained shear strength and groundwater conditions of the slope are critical parameters in the drained analysis. Drained shear strengths were determined by consolidated undrained triaxial tests with porewater measurement on undisturbed samples, and design values were then determined by statistical method after consideration of safety margin. Seepage analyses were carried out using two-dimensional FEM seepage programme to estimate the groundwater levels both at transient and steady state.

SOIL PROPERTIES

;

> i

I I

I

5

Gmii1 Size Distr ih U tion

Figures 1 and 2 show the distribution of grain size and clay/silt content in the Old Alluvium. The Old Alluvium is divided into sandy and clayey layers. Stiff clayey layers are present as lenticular bodies (Tan et a1 1980).

)

1

The stability analyses were then carried out using 5 Modified Bishop method. During the construction, , groundwater levels are monitored by piezometers to I verify the design information.

405

There is no significant difference in the grading curves of sandy layers. The silt/clay contents in the sandy layers range from 15 to 35% with an average of 25%. There are little clayey layers in the present site, with clay content as little as 10%.

Figure 1. Grading Curves of Old Alluvium

Figure 2. Silt/Clay Contents in Old Alluvium

Figure 3 . P - q’ Plots

Permeability

Figure 3 presents the p-q plots of sandy soils for OA 1(N
The coefficient of permeability of the sandy soil - ~ as obtained from range from I x ~ O -to~ l ~ l O idsec in-situ rising head permeability tests. The permeability values estimated based on Dzo are one or two order higher than from field tests. This may be due to cementation of the Old Alluvium. UrzdruiriedShear Stsergth

4 SEEPAGE ANALYSIS

Undrained shear strengths were obtained from laboratory unconsolidated undrained triaxial tests on undisturbed soil sample. The undrained shear strength was correlated to SPT N-values, and the average line of Cu/N = 6N (Wa) was used in design.

To determine the phreatic surface, seepage analysis was carried out using a two-dimension FEM seepage programme. The computer programme “Soil2F” developed by Kiso-Jiban is used in the seepage analysis.

Efft’ctive Shear. Strerigth The effective shear strength parameters vary in a wide range. To simplify the ground for analysis, the Old Alluvium was divided into sub-layers according to SPT N-values.

406

Goveniirig Eqircrtrons The governing equation of seepage flow in saturated/unsaturated soil is written as follows. For simplicity, the equation for one-dimensional vertical flow is given as follows :-

Figure 4. Phreatic surface of a single slope by FEM seepage analysis

Figure 7. simplified phreatic surface for design Figure 5. Phreatic surface of a single slope with subsoil drain by FEM seepage analysis permeability. The boundary condition of the seepage analysis are defined as follows:(a) constant head at 3 to 5H from edge of slope (b) constant head at base of slope From the seepage analyses, it is noted that at steady state, a residual water head will form near the toe of the slope. Figure 4 shows the lowering of ground water level in a one-step slope. Figure 5 shows the water level when subsoil drain is provided at the base. The residual water head will drop below the base when drain is provided.

Figure 6. Phreatic surface of two step slope with subsoil drain at toe by FEM seepage analysis

Due to the relatively high permeability of the Old Alluvium, water level will reach almost steady state in about 30 days, which is approximate time required for excavation. 0 : unsaturatedregion a = [I : saturated region

Figure 6 shows the lowering of ground water level for two-step slope. Water level will reach almost steady state in about 90 days.

Where z is the vertical co-ordinate t is the time k is the permeability of soil \v is the pressure head S, is the specific storage coefficient 8 is the volumetric water content

Based on the above study, a standard simplified approach is proposed for determining ground water profile or phreatic surface for stability study of other slopes. Figures 7a and 7b illustrate the approach.

The seepage at transient and steady state were: studied based on initial groundwater table and soil I

2. a rise in groundwater level due to rainfall

Generally, the following assumptions are made :1. a residual water head at the toe of each slope

407

ground. However, there is a difficulty to determine unsaturated soil parameters and local rain fall data. In our case, we assumed phreatic surface before excavation close to the slope although seepage analysis shows lower level. Preferably, the monitoring shall coininence over a suffjcient period of time prior to the actual excavation in order to assess the rise in ground water level due to heavy rain. 5 SLIP CIRCLE ANALYSIS

Figure 8. Toe failure due to residual water head

Analysis Modified Bishop's method was used in the slope stability analysis and the minimum safety factor of 1.2 was used. The slope stability analyses were carried out under the following conditions:a) Stability of slope was studied under drained condition and also checked under undrained condition. b) Tension crack was assumed to be filled with water to the ground level for undrained analysis. No tension crack was assumed for drained case. c) Surcharge load of 15 kN/m2 to 30 kN/m2 was also considered depending on construction equipment. Adverse combination of loads are considered for slope of more than one-step. d) The phreatic surface was determined by seepage analysis and modified slightly. Equi-potential line determined by seepage analysis was not used in the stability analysis. Phreatic surface and linear increment of porewater pressure was used in the analysis for safe design.

Measures to intprove safety iiiai-gin af slope Figure 9b. Undrained analysis Figure 9a, 9b. Results of slip circle analysis The residual water head can be determined by seepage analysis and verified by monitoring the drawdown of ground water level, The rise in groundwater level can be assumed by seepage analysis which allows seepage by rain fall into

408

To improve the safety margin of slopes, subsoil drains were proposed to be provided at the base of slopes. There was a case that slope toe was eroded due to residual water head (seepage force) and subsequently partial slope failed. Figure 8 shows toe erosion due to residual water head. The residual water head will be lowered when subsoil drain is provided. This lowering of water head is not considered in design to allow for possible rise in Water level due to rain, O r other reasons.

Piezometers and Observed Ground Water Levels

Figure 13

Figure 10

Ground Water Levels versus Time

Figure 14

Figure 11

Comparison with Seepage Analysis

Figurc 15

Figure 12

409

Figure 15 presents the comparison of observed ground water levels and water levels from seepage analysis (transient state).

Turfing may also be provided to protect the slope from surface erosion. Piezometers may also be provided at suitable location to check the actual phreatic surface and to confirm the design. 6 RESULTS

The comparison of ground water level, between the observed and analysis is good, indicating a permeability ranging from l x 10‘ to l ~ l Om -d ~s.

AND VALIDATION

Monitoring results from piezometers are only available at sections A and B at the present stage of construction. The slope at section A and B are typically one-step slope of 8m height, with a gradient of 1 (vertical) : 1 (horizontal). At the moment, subsoil drain has not been installed.

7 CONCLUSION As the constructed slopes are stable and predicted phreatic surfaces are reasonably close to the monitored, the following conclusions are made :-

The stability of the slope indicates that the design approach is adequate. Figures 9a and 9b show the result of slip circle analysis for the slope.

Section A Two piezometers, GWC( 1) and GWC(2), were installed at section A. Figure 10 shows the slope and the observed lowering of water level at the section. Figure 11 presents the graph of ground water and excavation level versus time for the piezometers. There is an abrupt change of pressure head at GWC( 1) just before the excavation reaching the base. The reduction of overburden probably had caused dilatancy of the ground, and thus the build u p of negative pore pressure. The water level finally stabilized at lm above the toe level Figure 12 shows a comparison of the observed ground water level and the results of seepage analysis (transient state). The trend line of ground water lowering compares reasonably with the results from seepage analysis. Based on the comparison, the permeability of the soil at section A corresponds to a permeability of 1x10-*d s .

1) the phreatic surface at transient and steady state can be determined by two dimensional FEM program 2) simplified approach can be used for one-step slope. For two-step slopes, verification will be carried out with monitoring results. 3 ) rise in phreatic surface of ground water may be estimated by seepage analysis. However, unsaturated parameters and local rain fall data are required. 4) the permeability of Old Alluvium is estimated to be varied between lx 10-6to 1 ~ 1 0m/s ‘ ~ based on monitoring results. 5) Piezometers are usehl tools for observing the changes in phreatic surface during construction and comparing with it to design.

REFERENCES 1.

Orihara, K. and Khoo, K.S. (1998). “Engineering Properties of Old Alluvium in Singapore and Its Parameters for Bored Pile and Excavation Design.” Thirteenth Southeast Asian Geotechnical Conference, Taipei, pp 545550.

2.

Tan, S.B., Loy, W.C. and Lee, K.W. (1980). Engineering Geology of the Old Alluvium in Singapore.” Sixth Southeast Asian Conference on Soil Engineering, Taipei, pp 673-684.

3,

Scott, R.F. (1 965).Principles of Soil Mechanics pp 63-77, Addison-Wesly Publishing Company Inc.

At Section B One piezometer, GWC(3) was installed at section B. Figure 13 shows the slope and the observed lowering of ground water level at the section. Figure 14 presents the graph of ground water and excavation level versus time for the piezometer.

41 0

Slope Stability Engineering, Yagi, Yamagami & Jiang v 1999 Balkema, Rotterdam, ISBN 905809 079 5

Influence of pore water pressures in partly submerged slopes on the critical pool level E. N.Bromhead, A. J. Har-ris & I? D. J.Watson School of Cil-ilEngineering, Kiii\q\ton Uni\wsity, Kingcton upon 7‘harne.s UK

ABSTRACT: Variation in the external water level of a partly submerged slope causes changes in stability which show up in the Factor of Safety computed by limit equilibrium methods. This paper considers the computation of stability in partly submerged slopes, and shows that several alternative procedures give essentiallythe same result. In many cases, there is some critical level for submergence at which the Factor of Safety is a minimum. This is shown to be not a fixed location or level for a given slope, but to vary according to the response of pore water water pressures inside the slope to the changing external water level. For example, in cases of declining water level where water flows out of the slope, both the critical pool level and the minimum factor of safety are different to the case where the water level is rising, and pore water pressures in the slope are lagging behind. The implications of this to slope engineering is discussed.

INTRODUCTION

Rather than to consider the arbitrary extremes of pore water pressure response to loading which go under the titles “drained loading” and “undrained loading”, the Authors prefer to split the problem into two parts: the imposition of the load itself, and the pore water pressure response. The pore water pressure response at any time may be made up fiom elements of steady seepage, with elements of unsteady seepage arising from either (or both) soil compressibility or the emptying of soil pores. What really counts in conventional limit equilibrium slope stabilityanalysis are the resulting pore water pressures, and not the mechanisms which give rise to them. Water loads on the face of a slope can improve stability. Both the horizontal and vertical components of water loading on the toe of a slope act to decrease the overturning forces and moments. In the early stages of submergence of a slope, for example, in the first impounding of a reservoir, the increased support for the slope fiom the reservoir water load may be more than offset by the effect of rising piezometric pressures in the slope. In such cases, the factor of safety of the slope against sliding may be found to be a minimum at some critical reservoir level. This level is known as “the critical pool level”. Factors controlling the critical pool level are discussed below. An analogous effect may be observed when the water level is drawn down, but the critical external water levels for impounding and drawdown may not be the same, especially if the pore water pressures in the slope lag behind the external water level.

In Bishop’s paper of 1955, a method of dealing with partly submerged slopes was introduced. This was of particular importance in connection with embankment dam stability. It was recognised then, as now, that a critical stability condition could arise on drawdown. Indeed, it was also recognised that critical conditions could occur during impounding. Thus there is an apparent paradox that both filling and emptying a reservoir gives rise to potential stability issues.Although this has been recognised for decades, the partly submerged case is a comparative rarity. The Authors have found that engineers often have a “blank spot” in respect of this aspect of slope stability, and even where the principle is understood, the detail of the procedure to solve the problem is poorly covered. An increasingly widespread use of computer s o h a r e appears to have had surprisingly little impact on the understanding of slope stability analysis in general, but in this area at least, it has probably reduced awareness ofthe problem. Since some software does not make provision for the partly submerged case, the situation can only worsen. The procedure which Bishop set out for dealing with these cases, discussed below, is only one of a set of strategies for handling reservoir loading within limit equilibrium methods generally. The alternative procedures can have advantages when dealing with water retaining embankments with different external water levels on both sides - a case which Bishop’s method handles only with difficulty. 41 1

The four alternative procedures are considered individually below. The explicit procedure

An explicit procedure is to add the forces and moments arising out of the external water loads on to the individual slice force components. For a completely satisfactorysolution, a method which handles additional horizontal forces explicitly is required. This requirement is a surprisingly difficult one to meet, and many methods do not fblfil it (e.g. Bishop’s iterative method). If the horizontal load transfer is not carried out correctly, the effect of the water load is usually underestimated. Figure 1 shows how the forces fiom the reservoir water load are applied to the top surface of slices which are submerged by the “downstream” and “upstream” water levels. The vertical force component is naturally easiest to deal with, because the weight of water acting on a slice is simply added to the slice self weight component. As always in slope stability analyses based on a slices method, the pore water pressures are treated as a completely independent set of variables. Some sofbvare will assume that pore water pressures underneath the external water level are hydrostatic, but this is by no means always the case, and a more general situation is indeed better catered for when no such assumption is made. An outstanding instance of the assumption not being appropriate is the case of a lined reservoir, with a drain immediately underneath the impermeable liner. Methods in which the explicit representation of water loads can be made include those by Maksimovic (see Bromhead, 1986, 1992), Sarma (1973) and Janbu’s Generalised Procedure of Slices (1983).

Figure 2. Adding the wedges through the external water zones. Pore water pressures inside the slope are handled independently. surfaces must be extended to the level of external water at the toe and head of the slip if appropriate (Figure 2) It is essential to include hydrostatic pore water along the slip surfaces at these locations. A method which uses inter-slice forces is de rigeur, but these forces must be horizontal, at least in those parts of the slip surface extended through the water. The vertical loads of water are added to slice weights where appropriate. Wedges through the water at the toe and head of a potential slide are shown shaded in Figure 2, with the force diagram for the toe wedge also shown inset. Slip surface extensions through the water are shown dashed. The force polygon with the slip surface through the “water” gives the correct horizontal resultant acting at the position of the toe. A similar result is found at the head of the slide. Problems which can arise when using this method usually relate to the inability of some methods to cope with zero shear strength. One reason for this might be accidentally rotating the interslice forces in between slices which consist wholly or largely of water, implying that the water can sustain shear! Such a problem arises, for example, when injudicious use is made off(x) functions in Morgenstern and Price’s (1965) method. The method is particularly sensitive tof(x) = 0 (no inclination) and this is worse in some computer codes than others. For small slip surface extensions, and good codes, the problem may not arise at all, but for sensitive codes and long, especially curved, slip surface extensions, it may prevent a solution from converging.

Figure 1. Adding the water load forces to each slice. The pore water pressures are handled independently. Strengthless soil zone procedure In this method, the external water loads are represented by soil layers devoid of strength but having selfweight, with a unit weight equivalent to that of water. The slip

Figure 3. Treating the water load as end forces to the whole slip. Once again, the pore water pressures are handled independently.

412

Pre-calculated end forces procedure In this procedure, end forces are applied to the slip surface at the toe and head, computed from the depth of submergence (Figure 3). This method replaces the slip surface extensions of the “strengthless soil zone” method, and therefore works in methods which fail when strengthless soil is input. It is, however, imperative that the end forces are not rotated (implying shear!) as can easily be overlooked. Such a problem arises, for example, when injudicious use is made of f(x) hctions in Morgenstern and Price’s (1965) method and is related to the problems noted above for the strengthless soil procedure. Some software can handle this procedure, with varying degrees of completeness, simulating a “waterfilled tension-crack”. In cases where this can be done, it is almost certain that it will only be permitted at the slide head - and not at the toe. Problems can also arise with programs which judge the direction of failure from the relative heights of the ends of the slip surface. In this case, the external water forces may cause sliding in a direction which is “downstream” but “upslope” with respect to the inclination of the slip surface (see slip surface xy on Figure 3). Whereas at first sight this may seem an improbable slide surface, the combination of the nett imbalance in water thrusts, a pre-existing (tectonically) sheared zone on this alignment, taken together with some seismic acceleration in the appropriate direction (from y to x), could cause this to be the critical slide surface.

Bishop k procedure The procedure outlined by Bishop is one where the forces from the external water load are omitted from the analysis. To do so without effect on the computed factor of safety, a set of internal force and moment components which exactly equilibrate the external water loads are also removed. Figure 4 shows this for the whole slope and for sample slices. Consider slip surface abcde and the possible sliding of soil above it. The external water load acts along af

Figure 4. Slope submergence handled via Bishop’s method.

413

at the toe of the slope. The linef c is at the level of the external water. Bishop noted that the hydrostatic pressures along af were exactly counterbalanced by: (a) a set of pore water pressures along abc such that the piezometric head at every point on abc is the pressure head rising up to the linefc. and (b) the forces and moments due to the self-weight of a body of water shaped like the polygonal figure abcfa. The forces along af can be removed from consideration, provided that forces equivalent to (a) and (b) above are also removed. This is done, for example in the slice illustrated, by modifying the pore water pressures and the slice weights. The water weight and moments are removed by taking only the submerged unit weight in the dark shaded part of the slice. Pore water pressures are modified by only considering the piezometric heads above the linefc. In effect, this reduces the piezometric heads on the illustrated slice from the total shaded area down to the light shaded area. Segments of the slip surface below the external water (say, for example, from a to vertically belowjj may end up with zero pore water pressure after modification. Of course, if the pore water pressures in this zone are not hydrostatic with respect to the external water level, then the modified pore water pressures may be non-zero positive (in the case of greater-thanhydrostatic pore water pressures) or even negative (when the pore water pressures are less than hydrostatic, for example, because there is downward flow). Apparently negative pore water pressures come about where the piezometric line dips below the external water level line projected into the slope. This is seen in the curved slip surface xy in Figure 4.Of course, there are situations where the pore water pressures are genuinely negative, for example in deeply desiccated clays in arid regions, or in newly-placed clay fills in low height embankments. This is not such a case, but is one where the pore pressure modificationwhich in an integral part of Bishop’s procedure creates the apperance of a negative pore water pressure. It is essential to use the resulting pore pressures after modification without further adjustment. Some software will, for example, take zero pressures when negative pore water pressures are indicated. This is conservative in ordinary engineering practice, but can be misleading in dealing with submergence as well as in back analysis (Chandler, 1977). Problems arise when the external water is high on one side of an embankment (Figure 4), and the method deals with two water levels with difficulty, if at all. Different water levels are normally dealt with by a variation of the “End force” method, at least for the higher of the two external water levels, or occasionally by use of the “strengthless soil zone” method.

TEST CALCULATIONS Effects of part submergence on pre-selected slip surfaces The above procedures have been tested with a variety of methods implemented as computer codes. Both codes written by one of the Authors and codes produced by others have been tried. Within the limitations of each implementation, and the quantum nature of the method of slices, they all provide equivalent answers. A consistentdifficultywas found with some codes when the slope was entirely submerged. To analyse this case with many computer codes is possible, when the following practice is followed: (a) Consider only the submerged unit weight in the slope (b) Operate only with those pore water pressures which are different from hydrostatic with respect to the external water level. A series of calculations was also made with varying external water levels on a simple test slope to examine the “critical pool” effect. This test slope in indicated in Figure 5 , which shows the simple geometry used in the analyses. The height of the slope was taken as lOm, and the slope angle was l(V) to 2 (H). While this is comparable to many earthworks slopes, it is obviously a small scale problem compared to many earth dams and valley slopes submerged by reservoirs. However, for purely frictional soil with a constant angle of shearing resistance, the slope height does not enter into the problem, and the same answers would be obtained for a lOOm high slope. Scale does enter into the equation when the soil properties contain appreciable cohesion. For a given slope angle in a soil which is partly or wholly cohesive, the initial factor of safety decreases with increasing slope height, but the negative effects of part submergence become progressively less important as the proportion of cohesion rises, since they are essentially an effective stress effect. Two slip surfaces through the test slope were considered: a shallow slip surface, slip 2, and a deeper

seated slip surface, slip 1. Both of these slip surfaces are slip-circles, and the analyses have been done with an implementation of Bishop’s (1955) iterative method, coded by one of the Authors. All of the strategies listed above, with the exception of the “end force” strategy can be employed in this code, and selected cases have been analysed for comparison purposes. The majority of the analyses have been carried out using Bishop’s procedure. The selected cases provided identical results. The end forces procedure is available within a computer code implementation of Morgenstern and Price’s method. This models the slip surface less accurately as a circle (although probably more realistically in practice) as a series of wedges. Certain of the deep slip surface cases were modelled. In addition, this code permits the other strategies to be adopted. There were differences between the base results obtained by the Morgenstern-Price procedure and Bishop’s method, so that they never yielded identical results, although they were close enough for practical purposes, especially when enough slip surface points were used. A further complexity with the Morgenstern Price method is that the results are influenced by the interslice force assumptions made. However, the results satisfied the Authors that the different strategies produced the same effect within a given code. Even the differences between codes were at the level of small changes in the second decimal place for the numerical value of the Factor of Safety. Slip 2 does not extend to the crest of the slope, and thus becomes totally submerged by the higher external water levels. The changes in factor of safety are shown in Figure 5 , expressed as a ratio between the Factor of Safety for the submerged case, and the Factor of Safety without submergence (Fsub/ F ,). Four different piezometric distributions have been considered, labelled cases A to D inclusive. Case A ignores pore water pressure change inside the slope. This situation could arise with a perfectly lined reservoir,

Figure 6. The results: for the shallow slip (2) above, and for the deep slip (slip 1) below. Results are plotted for different reservoir elevations and the cases shown in Figure 5.

Figure 5. Different cases analysed. Water pressure conditions inside the slope vary, and the effect is calculated for a deep slip (slip 1) and a shallow slip (slip 2). 414

analysis. The unit weight of soil in the slope was taken as twice the unit weight of water, and the soil was considered to be non-cohesive. As a result, the fullysubmerged results should be the same as the unsubmerged result without pore water pressure, and indeed, the Factor of Safety ratios for cases B & C did return to 1.O when the slip was fully submerged. Case D started with a lower factor of safety for the base case than did cases B and C, and ends up, when fully submerged, with a higher factor of safety ratio. Cases B, C and D represent very similarpore pressure conditions for the small shallow slip, and thus the stability analysis results are very close. For the deeper slip, there is more separation between the results for all cases, in effect because the pore water pressure conditions are more clearly different. The deep slip is never fully submerged in these test analyses, but the results are explicable using a similar logic for the shallow slip. The base case is never (except for case A) a “no pore pressure” case, and so the fully submerged result will never be the same as the unsubmerged case. Total stress analyses (using cuonly as a soil property) do not appear to exhibit the critical pool effect. Quite simply, as the effect as the external water level rises is an interaction between the increasing load (which increases stability) and the corresponding rising pore water pressures (which decrease stability), the total stress analyses which are subject only to the first of these can only show a rising factor of safety with impounding. These calculations did not attempt to address the question of the location of the critical slip surface for different degrees of submergence. This provides a degree of further complexity which obscures the simplicity of the interactions found. However, experience suggests that there are two classes of field situation which can be clearly distinguished.In the first of these, similar to the model analysed here, the position of the critical slip surface is constrained only very loosely by the slope geometry, materials and pore pressures. In such a situation, the critical slip surface does change as the external water level rises. In addition, the critical pool effect tends to be accentuated and caused to occur at lower externalwater levels. A second class of problems is encountered when the slope contains an internal structure which constrains the slip surface to follow a definite path. Examples of this include pre-existing shears, or where the critical slip surface location runs along thin weak layers. In these problems the critical slip surface position does not change on submergence.

o r where the bank is of clay and operates undrained in respect of the reservoir filling so that it is modelled using total stresses, and any pore water pressure effects are ignored. It was found that for this case there was no critical pool effect, but that the imposition of reservoir load acts always to increase stability. Slip 2 (the shallow one) increased in stability as the depth of complete submergence increased. This was the result o f the increase in pressures acting on the slope face as the submergence depth increased. The base result for the evaluation of Fo was no submergence and no pore water pressure in the slope. Case B could occur in a variety of field situations. A good example would be a dam with a rockfill upstream shoulder, where the permeability of the shoulder was such that the water level in the rockfill was at all times equal to the external water level. Both on impounding and drawdown the same conditions would apply. In case B, the piezometric levels rose with the reservoir level, such that the water levels in the slope were always the same as the external water level. The base result for the evaluation of Fo was no submergence and a piezometric line level with the toe of the slope. This case demonstrated a critical pool effect, shown on Figure 5, occurring when the external water level was between 40 and 50% or the slope height. Cases C and D, respectively for water flowing-into and out of the embankment, correspond crudely to the piezometric conditions expected when filling or emptyinga reservoir where the piezometric equalisation lags behind the reservoir level change. Another field situation modelled by Case C is the flow through a homogeneous embankment to a toe drain, where we are consideringthe upstream slope. Ofcourse, the shape of the top flow line (shown in a variety of positions as the water level was progressively raised) is grossly oversimplified, even for the situation where an idealised homogeneous soil is taken, but the intention of the demonstration was to identify general principles only. Steady state conditions corresponding to Case D are the flow of groundwater towards a river or pond, where the external water level is lower than that in the surrounding ground. Critical pool effects were also noted in both of‘these cases. The analyses of the deep slip exhibited greatest clarity, and the the three cases B to D exhibit different critical pool levels, as well as different percentage reductions in stability, demonstrating clearly that the critical pool effect is caused by pore water pressure change in the slope and not by the external loading which followed the same sequence for all analyses. The shallow slip case was less clear because of additional effects, but showed a critical pool effect for water pressure cases B, C and D. The base result for the evaluation of Fo with cases B and C pore water pressures was the same as for case A, because the slip surface did not dip below the toe of the slope. Case D, however, did have pore water pressures in the base

Eflects of submergence on the critical slip surface In none of the cases investigated did the critical slip s d a c e mode, or even the factor of safety for the critical slip surface, change on part submergence. For Case A

415

Slopes subject to the critical pool effect may suffer stability problems both on impounding and on drawdown, and the critical pool levels for the two situations will differ slightly, as the water pressure regimes on filling and emptying of a reservoir will differ appreciably.

and Case By with a soil exhibiting non-cohesive characteristics, the critical slip surface is always an extremely shallow slip sub-parallel to the slope face and located above the external water level. As the water level rises, the length of this surface shortens, but its factor of safety remains unaltered. Deeper slip surfaces may have reductions in their factor of safety against sliding, but riot to a value which is as little as the critical factor of safety for shallow sliding. With the extremely simplified pore pressure distributions shown in Cases C and D, the same effect is also shown. It is, however> clear that particularly with Case D, the effect of the external water level in the slope could have some effect on the stability of even shallow slips with toes immediately above the external water level. For example, if the phreatic surface was a convex-upwards curve, then it could approach ground level above the external water level, and thus have some effect on the critical slip surface. Non-homogeneous slopes, where due to materials or geology the critical slip surface lies well within the slope, have not been investigated specifically, but experience shows that there the part-submerged Factor of Safety does reduce with submergence. There does not appear to be a simple rule for this, and each case must be treated and analysed independently.

REFERENCES Bishop A. W. (1955). The use of the slip circle in stability analysisof earth slopes. Gkotechnique 5, 717. Bromhead E.N. (1986, 1992). The stability of slopes (1st or 2nd edition), Blackie Academic and Professional, Glasgow. Chandler R.J. (1977). Back analysis techniques for slope stabilisation works: a case record. Gkotechnique 27, 457-466. Janbu N. (1973). Slope stability computations. In Embankment Darn Engineering, Casagrande Memorial Volume, Hirschfield E., Poulos S. Eds. John Wiley, New York, pp. 47-86. Lauffer, H., Neuhauser, E. and Schober, W. (1967) Uplift responsible for slope movements during the filling of the Gepatsch Reservoir.Proc 9th Congress on Large Dams, Istanbul, 669- 693, Maksimovic M. (1970). A new method of slope stability analysis.Private communication. Morgenstern N.R. Price V.E. (1965). The analysis of the stability of general slip surfaces. Gkotechnique 15, 79-93. Sarma S. (1973). Stability analysis of embankments and slopes. Ggotechnique23,423- 433.

Ground deformations on submergence The limit equilibrium method makes no allowance for ground strains. However, on submergence, some potential slide mechanisms in a slope need to mobilize a greater proportion of the available shear strength. It is impossible to visualize this without imagining some correspondingground strains, leadingto settlementand possible shearing (if the soil material has brittle stressstrain characteristics). A mechanism similar to this was invoked to explain slope deformation due to flooding by Lauffer et al. (1967) in slopes adjacent to the Gepatsch Reservoir.

CONCLUSIONS Partly submerged slopes with varying reservoir levels can be analysed with equal validity making use of a variety of procedures implemented within the limit equilibrium method. Some of these procedures may be available in stabilityanalysis sofhvare not explicitly designed to cater for the partly submerged slope case. Where the pore water pressures in the slope vary as the reservoir level is changed, a minimum factor of safety may be found at a critical reservoir level, termed the critical pool level. Critical pool levels depend on the piezometric distributionswithin the slope. A critical pool level is more easily found for a specific individual slide mechanism: the critical pool effect may not exist for the slope as a whole.

416

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Role of pore water and air pressures on slope stability in reservoir for pumped storage power plant T. Sat0 & N. Nishizawa Department of Civil Engineering, Gifu UniversiQ,Jupan

M.Wakamatsu & Y. Hiraiwa Tokuru Construction Cornpuny Limited, Nugoya, Japan

I. Kumazaki Chubu Electronic Power Company Incorporuted, Nagoya, Japan

ABSTRACT: Pore water and air pressures were measured at a slope of a reservoir by using a special waterproof filter to prevent from water or air invasion into sensor chamber. The observations revealed that air entrapment takes place at pressure of much greater than A.E.V. and suction starts to decrease earlier than the time when water table rises above the elevation of the installation once air entrapment occurs.

on infiltration rate into unsaturated soil. Despite of the investigations, lots of unknowns still remains with respect to the effect of air entrapment onto slope stability. The purposes of this study are: ( I ) to offer an example for measuring pore water and air pressures in field; (2) to give a good understanding on measured values; and (3) to show air entrapment effects on slope stability, especially on failure due to suction decrease near the surface.

1 INTRODUCTION Fluctuation of water table sometimes accelerates the increase of damages to slope stability. Several instability factors have been reported, such as decrease of soil strength, increase of pore water pressure, progress of weathering, etc. There have been no field measures to show good understandings of slope instability induced by water table fluctuation. A top reservoir of a pumped storage power plant was chosen as a case study for investigations of pore water and air pressure changes to show a good performance of instability due to water table fluctuation. The site locates at the northeast edge of Aichi prefecture, Japan. Soil type is mainly composed of granite. Water content varies as water taljle rises and Ialls. Measurements of TDR(Time Domain Reflectometry) reveal that soil does not become fully saturate condition even when water tablc rises above the ground surface. The degree of water saturation varies from 60 to 80 percent at submerged condition. Soil pore contains air even after the surface is submerged. Entrapped air builds bubble that tends to move upwards into atmosphere with buoyancy. This easily happens in pore with large radius. At this moment, pressure of the entrapped air is no longer the same as the atmosphere. Former researchers had already reported that air entrapment causes an reduction of infiltration as compared with the case where air is allowed to smoothly escape from soil pore as water enters into soil (Christiansen 1944, Horton 1940). Youngs and Peck( 1964) and Peck( 1965a, 1965b) observed fluctuation of air pressure and escape of air bubbles in bounded column. The studies, however, focussed

2 FIELD MEASUREMENTS 2.1 Pore water pressure Three types have been proposed for measuring negative value of pore water pressure in soil. Type 1 is the use of manometer displaying water potential inside soil as height of water surface. Type 2 uses sensor instead of manometer. This shows a good response to soil-water pressure change. Type 3 is a pressure meter applicable to the negative. Filter selection is important to detect hydraulic potential of water affected from capillary. Large amount of A.E.V. (air entry value) is recommended for preventing from air invasion into sensor chamber. Pore pressure meter of which filter is replaced by a ceramic is installed in the slope. A.E.V. is 200kPa with considering fluctuation of water table from 846 to 868 meters above the mean sea water level (M.S.L.). Tension meter is also installed to find out capillary potential near ground surface. The pressure meter applicable to negative value is illustrated in Fig.1. Air is removed from the filter by putting it into boiled water before installation.

417

Figure 1. Device for pore water pressure. Figure 2. Device for pore air pressure.

Figure 3. Layout of gauges at a reservoir slope. 2.2 Pore air pressure

because pore water and air pressures simultaneously detected this month.

A waterproof filter called as Bio-filter is applied. This enables air to pass through it. Water can not invade into the chamber containing air pressure sensor. An apparatus is displayed as Fig.2. This is originated from water level gauge equipped with the filter fixed by a holder. The space bounded among Bio-filter, filter holder and sensor is as small as possible since responsibility to a small volumetric change is improved. It amounts to 34 cm3, which is a little too large to measure.

are

3 RESULTS 3.1 Pore water pressure

2.3 Layout Pressure meters are installed as Fig.3. P1, P3, P4 and P5 are Type 3. T2, T3 and T4 are Type 2. Pore air pressure is installed at the point of A, of which elevation is the same as T2. Measurements by P1, P3, P4 and P5 started in Oct. 1995, T2, T3 and T4 in Aug. 1996 and pore air pressure in Oct. 1998. The paper addresses to the observations within Dec. 1998 418

Figure 4 shows results of pore water pressure and reservoir water table. Unit of pressure is expressed by gauge pressure that is different from absolute one. The figure implies that the pressure inside slope changes dependently on the elevation of water table. P3 and P4 similarly behave with good response to water table fluctuation, but P5 does not respond when water table falls below 861 meters above M.S.L. 3.2 Tension ineter Measurement of tension meter is shown in Figure 5. Behavior within the positive value shows a good

Figure 4. Results of pressure gauges.

Figure 5. Results of tension meters.

increases dependently on water table. Air entrapment takes place at this moment. Reservoir water table had never risen above the elevation of the pressure gauge until Dec. 9. Once pressure gauge is submerged, air can not escape from the chamber since the bio-filter prevents from water invasion. The increase results from air invasion into the chamber surrounded by waterproof filter. The pressure is no longer the same as atmospheric once the entrapment happens. The measurement is for air in the chamber, but the same situation is expected in entrapped air in soil pore.

response to water table fluctuation. On the other hand, changes become slow once the pressure turns into negative. This comes from capillary force acting at the soil-water interface. Rapid increase is also seen after the increase of negative value. 3.3 Pore air pressure

Results are described in Figure 6. Air pressure is recoverable until Dec. 9. Residual pressure is generated in a couple of days later and it gradually

41 9

Figure 6. Results of a pore air pressure gauge.

Figure 7. Pore water of T2 and air pressures of A. 4 DISCUSSIONS

4.1 Air entrapment Air pressure recoverably changes even when pore water pressure turns into positive value until Dec.9. Once air entrapment occurs, the measurements describe the residual value larger than the atmosphere. The residual air pressure is kept at a constant until pore water pressure reaches to a minimum value. According to Fig.6, the residual 420

value tends to gradually increase as water table fluctuation goes on. Air entry value (A.E.V.) of this soil is estimated as 10 cmH,O from laboratory measures of water retention characteristics. The entrapped air pressure increases from 20 cmH,O on Dec. 10 to 50 cmH,O on Dec.24. The difference results from exchange of air and water in addition to effect of the waterproof filter. Laboratory tests are conducted at a slow speed enough to smooth exchange of air and water. Rapid rise and fall of water table induces air entrapment

Figure 8. Suction change at air-water interface.

inside the slope. Once air is entrapped, it does not escape from the soil even when air pressure attains A.E.V. because water is applied to overburden pressure. Youtigs and Peck( 1964) declared that the maximum value of air pressure is about A.E.V. plus overburden water pressure above the depth of considering point. Their estimate meets with the measurements in Fig.6. The iiiaxiiiium value of air pressure appears at the peak of water pressure. Air and water pressures are theoretically the same at air-water interface in the equilibrium condition. Figure 7 shows that the generating air pressure is a little less than the water pressure. The difference ranging from 5 to 17 cmI3,O may come from displacement due to elasticity of the Bio-filter. Nolie of exact relationships can be seen between the difference and pore water pressure.

suction due to water table rises. Suction dissipation suddenly takes place after water table rises. At this moment, air is replaced by water. Air escapes and water invades into soil pore. Suction dissipates at different value before and after air entrapment takes place. Once entrapment occurs in the chamber, rapid dissipation takes place at lower elevation of water table. Before Dec. 9, dissipation starts at 863 meters above M.S.L. After Dec.15, suction decrease arises at lower level of water table less than 862 meters above M.S.L. and the amount becomes large. One of the reasons is residual pressure of entrapped air in the chamber. Microscopic investigations may be required to well understanding on the mechanism of air replacement by water in soil pore.

4.2Suction chungeJ

Diagrams are displayed in Figs.9, 10, 11 and 12 to show the relationships between reservoir water table, pore water and air pressures. The vertical axis describes gauge pressure. Focus is on the rises of reservoir water table, of which elevation is given on the horizontal axis. The switching point, where pore water pressure turns into the positive (hydrostatic condition) from the negative (capillary condition), increases as the elevation of the tension meter decreases. This implies that air smoothly escapes from the shallow rather than the deep. Differences between the hydrostatic pressure line and the measures are the pressure generated by air entrapment at each depth. The results of T4, of which depth is 120 cm below the surface, describes that switching point arises much later than the other two. The difference from

Pressure difference at air-water interface is defined as suction. In engineering practices, air pressure is assumed to be alniost the same as atmosphere. The physical meaning of suction corresponds to the negative value of capillary pressure. Once entrapment occurs, air possesses pressure differing from atmosphere. Figure 8 shows suction defined as difference between pore air and water pressures. Rapid fall down and rise up in water table induces suction change. Soil-water capillary is an important factor for suction increase generated at water table draw down. On the other hand, air pressure induced by entrapment in soil pore mainly takes an effect on suction increase when water table rises. Important things happen after growing up

4.3 Air-water exchnage

Figure 9. Relationship between T2 and water table.

Figure 11. Relationship between T4 and water table.

Water table (M.S.L.m) Figure 12. Relationship between A and water table.

Figure 10. Relationship between T3 and water table.

355-366. Horton R.E.( 1940). An approach towards a physical interpretation of infiltration capacity. Soil Sci. Soc. Am. Proc. 5,399-417. Peck A.J. (1965a). Moisture profile development and air compression during water uptake by bounded porous bodies: 2.Horizontal columns. Soil Science 99, 327-334. Peck A.J. (1965b). Moisture profile development and air compression during water uptake by bounded porous bodies: 3.Vertical columns. Soil Science 100,44-51. Youngs E.G. and Peck A.J. (1 964). Moisture profile development and air compression during water uptake by bounded porous bodies: 1 .Theoretical introduction. Soil Science 98, 290-294.

hydrostatic pressure is also as big as the other two. Air is replaced by water in conjunction with drastic change of water pressure at this moment. This is one of reasons for slope instability. 5 CONCLUSIONS Pore water and air pressures were simultaneously measured at a slope of a reservoir to find out suction decrease effects on slope stability. A special filter was applied to water level gauge for preventing from water invasion into the sensor chamber. The conclusions of this study are as follows, (1) Field measurements reveal the possibility of air entrapment in slope when water table rapidly rises, (2) Entrapped air builds up pressure much greater than A.E.V. estimated from laboratory tests for water retention characteristics, and (3) Air replacement with water takes place at slope inside later than the near ground surface and it accompanies a drastic decrease of water suction. REFERENCES Christiansen J.E.( 1944). Effects of entrapped air upon the permeability of soils. Soil Science 58? 422

Slope Stability Engineering, Yagi, Yamagami & Jiang ((-1 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Seepage characteristics of decomposed granite soil slope during rainfall S.Sasaki Depu r tnz ent of En viromnen rul and Civil Engineering, Wukuyuma Nurionu1 Col1eg e cf Technology, Goho,Jupu n

S.Araki Osako Ojjke of Dn iya ConsLil tunt, Jupan

K. Nishida Depurh?ienrof Civil Engineering, Kaiuui Uizivei-sity,Suitu, Jupan

ABSTRACT: This paper deals with the relationship between seepage parameters of undisturbed decomposed granite soil and degree of weathering, and examines the seepage characteristics of natural slope in a decomposed granite soil area during heavy rainfall. The severely weathered sample contains much confined water evaluated at pF4.2 than the slightly weathered sample does. Especially, the confined water affects not only on the soil water characteristic curve with hysteresis but also on the relationship between hydraulic conductivity and volumetric water content. It has demonstrated that the water flow pattern in slope during rainfall can be clarified by means of the seepage analysis depending on the seepage parameters

1.INTRODUCTION The disasters such as natural slope failure and ground collapse take place during rainfall on every year in the decomposed granite soil region of Japan. In examining a weathering zone in detail, it is often seen to take place the several layers, which are different in the degree of weathering. The reason why the soil collapses is closely connected with the peculiarity of the soil. The decomposed granite soil has already used a: ; a material for embankment constructions. However , slope failure due to rainfall is caused in this soi 1 region and the following property peculiarities haw : been pointed out: (I) Soil particles are easily broken and deformation due to collapse occurs during water permeation. (2) A physical property of soil varies with the degree of weathering. Accordingly, this soil is referred to one of problematic soils in Japan. Many investigators have already clarified the relationship between degree of weathering and the

physical properties of compacted

decomposed

granite soil and also many data relating to the soil have been applied for the embankment design or slope analysis. However, it is found that the natural slope failure due to the heavy rainfall takes place mainly the region in which the decomposed granite soil is distributed. Therefore, it is important to investigate the seepage characteristics and mechanism both on undisturbed sample and on natural slope of the decomposed granite soil regions during rainfall. But, in this case, it has been stated that the informations of seepage parameters have not been fully collected yet for the practical seepage analysis of natural slopes. Because it is difficult to examine the pore water pressure of the specimen collected in undisturbed state on slope of decomposed granite soil. In this study, the relationship between degree of weathering and seepage parameters such as hydraulic conductivity and soil water characteristic curve are examined for undisturbed decomposed granite soil specimens and moreover the seepage

423

mechanism is clarified for the natural slope during rainfall by applying the numerical analysis

The samples of undisturbed decomposed granite soil with different degree of weathering were obtained from a cutting slope. In order to examine the soil fabric effects on the seepage characteristics of decomposed granite soil, a large undisturbed specimen (length 3Omm, section 13 0 x 13 Omm) were prepared by means of the nail sampling method (Nishida, 1986). The ignition loss of samples was adopted as a criterion of the degree of weathering and the coefficient of permeability in saturated state was determined by the constant head permeability test at a definite hydraulic gradient (1). The confined water content at pF4.2 was measured by making use of the pressure membrane method. The physical properties of samples are shown in Table 1. It is shown in this table that the degree of weathering increases with the increment of sample number depending on the values of ignition loss. In Table 1, the water content at pF4.2 of the severely weathered sample is also larger than that of the slightly weathered one. This fact suggests that much water should be held within or around the

\

No.1 2

3

4

2.675 2.617 2.676 2.732

1.192 1.269 1.514 3.750

It is important to evaluate the confined water content as water content at pF4.2 in the estimation of seepage parameters of decomposed granite soil. Photos. 1 and 2 show the photomicrograph of the

2 .EXPERIMENTAL PROCEDURE

Physical Specific Ignition Properties Gravity loss Ps (%) Sample

weathered soil particles depending on the soil fabric,

Dry Density (glcm3) 2.166 2.145 1.876 1.291

soil fabric of samples. The specimens were prepared after infiltrating the methylmethacrylate into the sample of the diameter of 6 cmxlength 5cm. The slightly weathered sample is given as Photo. 1. It shows the flat surface of feldspar without the existence of intragranular voids. On the other hand, Photo.2 of the severely weathered sample shows porous soil fabric which correspond to intragranular voids.

3.RESULTS AND DISCUSSION The soil water characteristic curves for the samples of different degrees of weathering are given in Figs. 1 and 2, which are measured by the pressure plate

method. In order to measure the volumetric water content in undisturbed sample, the experiment was done for a large sample with the length lOcm, diameter 14cm. The experiment of pressure plate method carried out by using a n apparatus shown Fig. 3 equipped with neutron ray radiation equipment (15'Cf 1.85MC').

The measurement of volumetric water content

Water Content a t pF4.2 (cm3/cm3) 0.040 0.040 0.040 0.130

424

Coefficient of Degree of Permeability Weathering (cm/s) 6.00X 10.' 4.77 4.59 2.50

Slightly Weathered

Fig.2 Soil water content characteristics sapmles

of

Fig.3 Layout of experimental appratus

has been done periodically under a definite air pressure by means of the air pressure control system,

Fig.1 Soil water characteristic curves of samples

after the sample is h l l y saturated The first hysteresis loop that means the difference between drainage and infiltration process for the severely weathered sample is remarkably revealed in comparing with the slightly weathered one. For the second hysteresis loop in these figures, the difference in degree of weathering can be found. The phenomenon suggests that water should be held tightly within or around the soil particles. In examining the seepage phenomenon of an undisturbed sample, it is important to estimate the amount of confined water for the analysis of soil water characteristic curve.

425

?)/.

:suction (kPa)

'$ cr : critical suction(kPa)

h , A,B,C constants 8 :volumetric water content(cm3/cm3) 8 ssaturated water content(cm3/cm3) 8 r:residul volumetric water content (cm3/cm3) In Eqs. (1) and (2),Se was caluculated by using the equation defined by (3). In these equations, 8 r is the volumetric water content at pF4.2 shown in Table 1.Water content at pF4.2 is not involved in permeation. The evaluated values from Eqs. (1) and (2) are shown in Fig.4. It is clear that the values evaluated in Eqs. (1) or (2) fit relatively well the measured values for the slightly weathered sample. On the other hand, the difference between values calculated by both equations is remarkable for the severely weathered sample. From these data, it is useful to estimate the soil water characteristic curve making use of Eq. (2), which has been ascertained for the various kinds of compacted soil. The relationship between by hydraulic

Fig.5 Relationship between relative permeability and volumetric water content

The shape of the curves is expressed by Eqs. (1) (Brooks et.al.1966) and (2) (Matsukawa et. a1.1983) which have been derived experimentally.

Se = (8- 8 r/O s- 8 r) where, Se : effective degree of saturation

conductivity and volumetric water content for the representative samples in Table 1. is plotted in Fig.5. The difference is appeared between compacted and disturbed samples. At first, the hydraulic conductivity of compacted sample varies in smoother paraboratic curve, comparing with that of one. Especially, it is seen that for the severely weathered samples, the sudden drop of the hydraulic conductivity can be seen at volumetric water content because of the presence of macro pore as shown in Photo.2. In order to analyze the seepage properties of decomposed granite soil layer, the failed slope in Masuda City was adopted as a model slope for seepage analysis by FEM. In the numerical analysis, it is reasonable to choose the multi- layered model which is consisted of layers of the different degree of weathering and the pressure head @ = 0 kPa is given along the slip surface of the layer as an initial condition.

(3)

426

Fig.6 The seepage analysis o f FEM

427

Volumetric Water Content 8(cm3/cm3)

A B

Suction$ (KPa)

A 11.3 B 10.9

Relative Permeability Kr Saturated Volumetric Water Content 0 s(cm3/cm3) Residual Volumetric Water Content 0r(cm3/cm3) Specific Moisture Capacity C($) (llcm) Coefficient of Permeability Ks(cm/s)

0.339 0.365 0.413 0.445 0.460 0.374 0.381 0.413 0.461 0.50 1.3 2.7

0.5 0.5

A B

0.003 0.015 0.05 0.007 0.014 0.06

0.15 0.29

A B

0.46 0.50

A B

0.10 0.20

A B A B

7.3 x 10.4 9.9 x 10-4 2.0 x 10.3 7.0 x 10-4

11

5.8 8.9

0.4 0.3 1.00 1.00

A: Slightly weatherd sample B: Severely we athered sample

4. CONCLUSION

The behavior of water stored within a soil layer during rainfall is expressed in Fig.6 obtained by applying the physical parameters of Table 2. As the results, the magnitude of flow vector in slightly weathered lower layer is larger than that in severely

1.The seepage parameters such as soil water characteristics curve and hydraulic conductivity are dependent on the degree of weathering. 2.It is reasonable to understand that from the results

weathered upper layer and the values increase toward the slope toe. Moreover, it can be understood that the ground water level rises gradually until the surface of slope and the high water pressure is generated in a localized portion at

of seepage analysis, the increment of water pressure due to rainfall causes the slope failure.

REFERENCES

the toe of slope. Another simulation result for examining the

Nishida, K. 1986. Engineering properties of weathered residual soil, Kashima Publish Company,

factors relating to the water pressure generation described above is shown in Fig.6, which was calculated by assuming the inverse rainfall pattern. It is realized from the result that the water level is

Tokyo. Brooks, R.M.& Corey, A.T. 1966. Properties of porous media affecting fluid flow. A.S.C.E.: 61-88. Matsukawa,S.&Souma, K. 1983. New experimental equation describing the soil moisture characteristic curves (desorption curve),J.S.I.D.R.E., No.104:31-

lower, comparing with the carrier of real rainfall pattern state. As a result, for the factors affecting slope failure, it can be pointed out that the water stored at the interface of different weathered layers contributes greatly to the generation of high water pressure.

38. Nishida, K., Aoyama,C. 1985. Weathered residual soil properties & failure mechanism of slope. Proc. Ivth International conference field workshop on landslides, Tokyo: 289-294. 428

Slope Stability Engineering, Yagi, Yamagami & Jiang (c i 1999 Balkema, Rotterdam, ISBN go 5809 0795

Relation between slope stability and groundwater flow caused by rainfalls M.Enoki & A.A. Kokubu Department of Civil Engineering, Tottori University, Jupan

ABSTRACT: In this paper, slope failure due to rainfall is analyzed considering some simplifications concerning the stability analysis, infiltration and seepage parallel to the base rock. Then, the conditions required for the slope to fail are obtained. Accuracy by means of field tests in the determination of the parameters that arc required for stability analysis, that is, permeability. strength parameters, etc. is very difficult to attain. This is principally owing to field tests and measurements involving only a small portion of the slope. The degree of influence of the error in the measurement for cach parameter is investigated through a sensitivity analysis. Furthermore, permeability of the slope is investigated by means of tests based on the actual velocity principle and the apparent velocity principle. Slope failures of such proportions are the aim of this investigation. Sliding of the mass of soil of the slope takes place along a base rock, which has high shear strength and low permeability. In every case, slope failure is sliding of thin layers along a base rock. The cause of failure of natural slopes is generally infiltration of rainwater which reaches the base rock and make the surface layer fail. The aforementioned characteristics makes the process of failure of natural slopes different from that of landslide which involves slow sliding of an extremely large mass of soil. Concerning landslide problems, the infiltrated rainwater cannot reach the base rock because of the magnitude of the depth of the soil layers overlying the base rock. The water that reaches the base rock has a different origin which is not explained in this paper.

1 INTRODUCTION Nearly all slope failures occur during o r after a precipitation. Slope failure is a common natural disaster in mountainous regions and the most dangerous type of sliding due to the quick movement of the mass of soil. Japan, being a mountainous country with an annual precipitation of approximately 1800 mm, suffers frequently from this kind of natural disasters during rainy seasons. The distribution of dimensions of failed slopes in Japan is shown in Figure 1. Numerous invcstigations carried out in this country led to the conclusion that the representative slope failure has the following dimensions: length L = 10 m, depth of failure H = 0.5 m and width W = 15 m.

2 MECHANICAL STUDY OF SLOPE FAILURE CAUSED BY PRECIPITATION 2.1 Meclzuiiism of' slope fuilure cuused by precipitutioii

10 Length L (m)

1

From laboratory and field observations. the mechanism of slope failure was disclosed as follows: a. Infiltration process (Figure 2-a): After a given precipitation begins, infiltration phenomenon commence in the form of Wetting Front (WF). The volume of flow of the WF and its descending velocity arc conditioned by rainfall intensity and ca-

2

Depth of failure H (m)

Figure 1. Distribution of dimensions of failed slopcs if Japan.

429

pacity of infiltration of the soil b Seepage flow along the base rock (Figure 2-b) A few moments after the WF reaches the base rock, a seepage flow along it is generated The height of the groundwater table at any point along the base rock depends on the rainfall intensity, the permeability along the base rock, the distance of the point from the top of the slope and the inclination of the slope c Slope failure (Figure 2-c) If the height of the groundwater table at one point along the base rock is large enough, pore pressure at that point on the base rock grows too large to support the overlying soil, consequently slope failure occurs 2 2 II!filtr~cftlon yr.oce.s.s

During the infiltration process for any position of the WF, the hydraulic gradient is unit This is derived from the fact that for a given column of soil subjected to the wetting front, both upper and lower ends are at atmospheric pressure Also, the effects of suction are neglected, otherwise the hydraulic gradient takes a value different from unit Then the infiltration velocity I' is I' k, where k, is the vertical permeability If rainfall intensity is larger than k, then infiltration velocity takes the value I' = k, . If rainfall intensity is smaller than k, infiltration velocity is I' - R where R is the rainfall intensity Therefore, the infiltration velocity is I' = min (R,k,) The time required for the WF to reach the base rock may be expressed as

where I I , is the effective porosity of the soil and H the depth of the soil layer overlying the base rock

S

The height of the groundwater table at a distance .s measured from the top of the slope is s I'

HI, = HI,,+k, sin [I where H,, is the depth of the ground water table at s - 0, fl is the inclination of the slope, Kh is the permeability along the base rock and i' is the infiltration velocity

For infinite slopes there have been many slice methods to analyze the stability of slopes However, one of the authors has already clarified that every slice method is not valid (Enoki et a1 1992), though the explanation I S omitted here Moreover, it is obvious that the closer a safety factor obtained by arbitrary slice method gets to one obtained by an analysis method for infinite slopes, the more slender the slipping mass becomes Generally, for a slope of thickness N and length L , the ratio of H/L of actual slipping masses is about 0 1, then, an analysis method for infinite slopes is along used here For a given seepage of depth H,, the base rock, the pore pressure ZI on the base rock is as follows I[-

y ,, H,,, cos:

P

(3 1

Therefore, the depth H,,,at the instant of failure is

where, H is the thickness of surface layer of slope, ,8 is the angle of slope, yis the unit weight of the , the strength parameters mass of soil, and @(/, c ~are of soil. 3 CONDITIONS FOR SLOPE FAILURE

Figure 2. Process of failure in slopes due to precipitation.

General description of the failure condition: For a given rainfall of intensity R and period 7: two conditions for the slope to fail are required, that is 1. The wetting front must reach the base rock, which means that Equation 5 is satisfied

430

Table 1 Sensitivity analysis for each parameter of the slope Slope parameters

2. The pore pressure due to the seepage flow along the base rock must be large enough to make the mass of soil of the slope slide along the base rock. Assuming the slope length to be L , from Equations 2 and 4, the following equation is obtained.

rr(c111)

I,(I l l )

r: ,,(ClldS)

Coefficients

50 10 2x102 0 64

10 -1

y (g/cm') Y w (dC11l3)

2

1 1 1

1

-1

tall/ tan d<,

0 84

6 25

1

5 25

SlnB

These two conditions of slope failure are summarized in Figure 3. In Equation 6 the values of slope parameters affect the required rainfall intensity i ; therefore sensitivity of the potentiality of failure to every parameter of the slope must be evaluated. This analysis is explained in the next section.

Standard Ialues

Relatn e dispersion 12 1

4 02 0 0 11 0 35

0 15

From one measurement of permeability to another, the range of dispersion may be ten times or more For this reason, it has a high relative dispersion in the term drh: The same strong influence of vertical permeability k,, on Equation 5 is expected. The terms tan/ and tan dcjhave a low relative dispersion, but in turn, their coefficients are large. These coefficients becomes larger for closer values of / and @(,. Therefore, it can be concluded that k,,, tan / and tan d',are the most sensitive terms in Equation 6 or in other words, in the term d d r .

4 SENSITIVITY ANALYSIS

The sensitivity of the principal slope parameters are analyzed and shown in Table 1 Every parameter of Equation 6 and their standard values are shown in the first two columns In the right part of the table, the corresponding coefficients and relative dispersions in the term ddr. are shown Standard values of the parameters are representatives of nearly all slopes that have failed in the mountainous areas When measuring permeability, field tests are generally more adequate than laboratory tests performed on samples Sample represents only a very small portion of the slope, in addition to this the sample is in many cases disturbed However, because of the hardships founded in carrying out field tests in natural slopes, generally the scale of the tests is relatively small Therefore, the uncertainties that appear in the measurement of permeability are still unavoidable.

5 INVESTIGATION FOR PERMEABILITY 5 1 fiield tests f i ir!filti.ntiori ~ 5 1 1 Ring test c?f nypnr.erit velocity

The procedure of this test is as follows A metal ring is set on the ground surface (Figure 4), sweet water is poured inside the ring by means of a Mess cylinder in a way that all the time a film of water appears on the surface ground By means of this procedure the soil immediately below the ring is subjected to a saturated flow The rate of flow of the supplied water is measured by means of a stopwatch The permeability is calculated as follows

k,,= A (2 / (A A t )

(7)

where A t is the time necessary to pour the volume of water A Q and A is the cross-sectional area of the ring The intrinsic characteristics of this test, makes Equation 7 valid for only a short period of time. That means that only at the beginning of the test, the flow of water is one-dimensional. With elapsing time the flow of water becomes three-dimensional, therefore, the accuracy of Equation 7 decreases. Moreover, the unsteady flow of water is subjected always to the effect of suction which is not considered in Equation 7. A good point of the test is its simplicity and readiness to perform.

Figure 3. Conditions of slope failure.

43 1

Figure 4. Ring test of apparent velocity for a soil layer. Figure 5. Ring test of actual velocity for two soil layers (Layer 1 and Layer 2). 5.1.2 Ring test of actual velocity Tests for infiltration based on the actual velocity principle are not dependent of the three dimensional spreading of salty water, because only the actual velocity along the known flow line is measured to calculate the permeability of the layers. This is an advantage when compared with the ring test of apparent velocity which is affected by the spreading of the flow of water and the effect of suction. Layered deposits usually consisting of a mixing of two or more types of soils with erratic soil grain properties are common characteristics founded in the field. Because of this, the weak point of the test is the difficulties founded in the positioning of sensors.

The test procedure is similar to that of the ring test of apparent velocity. The principal differences are as follows: 1. Sensors that are sensible to salty water are placed beneath the ring, at depths corresponding with the border line between two layers. 2. Sweet water is poured in the ring until the saturation of the layers of which the permeability will be measured is attained. 3. Supply of sweet water is replaced suddenly by salty water. By means of the sensors shown in Figure 5 , the flow of salty water is detected and the time to cover the corresponding depths of the layers are recorded by a stopwatch. The steady flow of salty water is not subjected to the effect of suction because of the saturation of the mass of soil carried out in the preceding step. Therefore, the hydraulic gradient for the flow of salty water may be considered as unit in the calculation of permeability. The permeability of layer 1 is calculated as follows k,, = H,.nel IT, where H I is the depth of layer 1, neI= /VT)is the effective porosity of layer 1 and T, is the time required for the flow of salty water to cover the distance H p Permeability of every layer is calculated in the same way. In the proposed formula of k,, the flow of water is assumed as a block of uniform height leaving behind soil in saturated condition though actually infiltration under saturated condition is not possible. Also, the voids distribution of the soil is assumed as homogeneous but actually it is not. If the voids distribution of the soil is assumed as homogeneous, the velocity of the flow according to Darcy’s law vd and the average actual velocity v,, are related as follows v,, = vJn,, where ne < 1. If the actual case of inhomogeneous voids distribution were considered, the average actual velocity is less than the actual velocity or in other words the maximum velocity of the flow.

5.2 Field tests for permeability along the base rock Two vertical holes separated a distance d that range from 50 to 100 cm are perforated on the slope surface (Figure 6). Hole A is filled with sweet water, with the purpose to establish a steady flow between holes A and B. Sweet water is replaced by salty water which is detected in hole B by means of a sensor. Then the permeability along the base rock is as follows

(v,

kh= d n,l (i A t )

(8)

where A t is the time for the salty water to cover the distance d and i = (h2- h,) I d is the hydraulic gradient. This test is also based on the actual velocity principle, therefore it has the same advantages and disadvantages of the ring test of actual velocity. To obtain conditions of steady flow in the field are extremely difficult. For this purpose, a large amount of water and a long duration test would be required. Due to the distance from water sources, precariousness of the approach roads etc, the amount of water is generally restricted. Because of this, tests of permeability along the base rock are usually performed under the conditions of unsteady flow.

432

Figure 6. Actual velocity test (Seepage along the base rock) for a soil layer (Layer 2). 5 3 Pimcrpnl dffewmxs hetweeii the ring test of nppnrwit wdocrtj)arid the mig test of nctiinl ~wlc)cif~ Intending to explain the differences between the ring test of apparent velocity and the ring test of actual velocity, the voids distribution of soils may be made alike to a model pipe This model assumes the voids distribution of soils as pipes of different sizes aligned parallel to each other As for permeability tests based on the apparent velocity principle, the rate of flow through each one of the pipes as a whole is measured in order to calculate the coefficient of permeability In other words, the apparent permeability of the mass of the soil is calculated On the contrary, for permeability tests based on the actual velocity principle, instead of rate of flow, the maximum velocity of the flow along the known flow line is measured For this purpose, salty water etc may be used as tracer The larger the diameter of the pipe, the larger the velocity of the flow, therefore, the calculated value of permeability is larger than the apparent 5 4 Resiilts rzrl .slope.s

Figure 7. Portions of slope showing the values of k,, and kh for every kind of test.

phoon 5 as shown in Figure 8 Because of this natural disaster, 80 families of a village had to take rehge and numerous houses were destroyed. Location of the slope failure, contour lines representation, geometry of the slope as well as its strength parameters are shown respectively in Figures 9, 10 and 11 The characteristics of permeability are shown in Figure 7 Rainfall intensity during the precipitation of Typhoon 5 is shown in Figure 12 From the rainfall pattcrri of Figure 12, rainfall intcnsity is lcss than thc capacity of infiltration of the soil. Bccausc of this I’ = R must bc uscd in the first condition of slopc failurc, Equation 5. According to

of permenhrlrty tests tamed orrt in nnfii-

Figure 7 shows observational data obtained from field tests performed on natural slopes of ‘Egoouchi’ and ‘Taka no Su’ district, Hiroshima prefecture Subscripts meanings are as follows v vertical infiltration, b base rock, a ring test of actual velocity, r ring test of apparent velocity and s permeability tests performed on samples Units in cm/s The dispersion for the values of kh and k, is evident as it was already mentioned in section 4 6 APPLICATION OF FAILURE CONDITION

The conditions of slope failure, Equations 5 and 6, were applied to a natural slope located in ‘Taka no su’ district, Hiroshima prefecture, in which slope failure happened on July 27, 1993 during the Ty-

Figure 8. Slope failure in ‘Taka no su’.(July 27, 1993)

433

this cqiiation and the rainfall pattcrn indicated in Figurc 12, thc WF rcachect thc basc rock on July 27 at 18 h. Thcn, application of thc sccond condition of slopc failurc indicatcs that the slope failed during thc intcrval lrom 18 to 19 h. The slopc failurc caused dcbris flow, and it attacked the villagc on July 27 at 20 h.

Figure 12. Rainfall pattcrn for ‘Taka no su’ area

7 CONCLUSIONS The mechanism of slopc failure presented in this paper assumes both infiltration and sccpage along the basc rock as proccsses of steady flow, although these processes arc unsteady. For cvcry case, sliding of thc mass of soil is assumcd to occur along a base rock of low pcrmcability. Morcovcr, actual finitc slopcs arc assumcd to lx iiifinitc. Ttic conditions of slopc failurc are C X ~ J C S S Cb~y iiicans o f cquations that rclatc failurc with thc pattcrn of tlic prccipitation, gcomctry o f thc slopc and its strcngth paramctcrs. Thc rcsult of thc thcorctical analysis shows a good agrccmcnl with thc practical c;isc prcscntcd in this papcr. From thc rcsults of thc scnsitivity analysis, pcrmcability along thc basc rock has a marked influence in the conditions of slope failure. For this reason, determination of pcrmeability along the base rock by means of large scale field tests that improve the accuracy of the measureinents should be developed.

1 :1,500,000

Figurc 9. Location of slopc failures.

I :25,000

Figure 10. Contour lincs.

REFERENCES Enoki, M., Ikeda, Y. & Kokuhu, A.A. 1998. Mechanism of slopc surface failure caused by precipitation. The First Asia-Pacijic Corlferetice otid Exhibition. Enoki, M., lketla, Y. & Terauchi, K. 1YY8. Field tests related 10 slopes stabilily. Proc. of the 53lh aritiual cotlfererice ofthe .Iapati Society of Civil Etigiricers. (In Japanese) Enoki, M. & Ikcda, Y. lYY8. Theorelical analysis of slope failure due 10 precipitation. Proc. ofthe 53th aririual cot!& o f f h eJaporz Sociefy of Civil Eizgirieers. ( I n Japanese) Enoki, M. & Kokubu, A.A. 1998. Using of tracer in the analysis of tlie pipe diainelcr distribution of soils. Proc. ofihe 53th atitiuol cotiferetice o/ [tie.Inparr Society of Civil Etigitieers.

Figure 11. Geometry and strength parameters of the slope.

434

Slope Stability Engineering, Yagi, Yamagami & Jiang (U 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Salient aspects of numerical analyses of rainfall induced slope instability C.-H.Wmg Department of Civil Engineering, Tiunjin Univel-sif?!People’s Republic of China

ABSTRACT: This paper outlines principally some salient aspects of numerical analyses of rainfall induced slope instability problem, while discussing on diverse ideas as well as different techniques presented in literature. Suggestions are given, concerning with the following aspects: (1)infiltration and evaporation as transient boundary conditions; (2)simulation of the effects of vegetation; (3)assessment of initial stress condition; (4)definitions of factor of safety. problems will be of great significance. It is this topic the writer tries to address. This paper outlines four important aspects of the numerical analysis of rainfall induced slope instability. They are: (1)infiltration as flux boundary condition; (2)effects of vegetation on slope stability; (3) initial ground stress condition; (4)definitions of the factor of safety.

1 INTRODUCTION Rainfall induced slope instability is one of the most sophisticated geoenvironmental problems and has been increasingly the focus of the interests of researchers from multidiscipline. Conventionally used slope stability analysis methods such as limit equilibrium methods are incapable of solving so complicated problems as they, by nature, can not take so many complex factors into analysis of the problem. On the other hand, numerical methods are now taking an increasingly important role in analysing slope stability problems, as they can also by nature, simulate the behaviour of slopes under complicated conditions (Cai et al. 1998, Fourie et al. 1999, Ng & Shi 1998). Though numerical methods, especially finite element methods, are most promisingly used at present for analysing andor predicting the behaviour of soil dopes under transient infiltration conditions due to rainfalls, some old difficulties do still exist and new problems merge in conducting these analyses. The numerical analysis of rainfall induced slope instability include mainly three subjects. The first is how to represent the rainfall as a transient boundary condition, i.e. to describe properly the nature of rainfall such as the intensity, duration, pattern, distribution and direction, to the slope to be analysed. The second is how to represent the existing status of slopes, which include the shape, materials, initial conditions such as initial stress field, initial ground water table, and so on. The last is how to present properly the results of the analyses, i.e. to select a rational way to define degree of safety of slopes. A comprehensive understanding of the correct and efficient ways of application of the methods to these

2 INFILTRATION AS BOUNDARY CONDITION Infiltration is the direct reason for the seepage and changes in stress and strength condition of soil body. Infiltration due to rainfall is now commonly considered as a boundary condition prescribed on to surface of slopes. There have been misunderstanding and difficulties in taking infiltration as a boundary condition, which needs to be examined to conduct the analysis successfully. To prescribe a variable value, e.g. an external load or a displacement, as a boundary condition, generally in numerical techniques, is to decompose it into normal and parallel components to the boundary surface. For example, in conventional seepage analysis, water pressure or pressure gradient at a boundary is easy to apply in this way provided that these values are known. Unfortunately, a boundary condition involving infiltration due to rainfall can not be so easily set, which is a problem that is being overlooked. 2.1 Capacity of Infiltration There must be a limit capacity for a soil layer at the surface of a slope to actually intake flowing water.

435

It is wrong to set an amount of water flow velocity to a surface just without caring about whether this amount is within the limit capacity of the boundary. The capacity for a surface to let water to come in is determined by many factors such as soil type, porosity and degree of saturation of soil, water viscosity, permeability of soil and so on. Though at present an exact solution of the capacity is not generally available, the rate of infiltration due to rainfall could be set within the limit value of permeability as the infiltration can, for practical use, be best regarded as under zero or very small water pressure condition. In some analyses, boundary values of infiltration were set as rainfall intensity that were much greater than that the infiltration rate could have reached, i.e. coefficient of permeability of soils (Zaradny 1993, Cai et al. 1998). In fact, the part of such an infiltration intensity that surpasses the capacity will build up a mass of water on the boundary, and subsequently alters the boundary condition. There will be changes not only in quantity but also in type of boundary condition when an effective rainfall intensity is greater than the capacity of infiltration of ground surface. If a boundary is capable of maintaining the part of rain water that is over the amount of infiltration, the type of the boundary condition will change from Neumann condition to Derichlet condition. That is to say, water pressure should be then exerted on the area where a water flow was once allowed with a velocity value. If the boundary is not be able to maintain the additional water, the additional water will be definitely spread under the action of its gravity. This process is even more difficult to simulate. For a horizontal surface that is near the initial part of infiltration boundary, there will be a newly generated seepage boundary, be either Neumann type or Derichlet type, according to the volume of additional water and surface conditions. Here some difficult problems may be encountered and need to be answered. What is the range of the newly generated boundary? How can one to distribute the additional water over this range? Which type of boundary condition should be for this range? All these problems are of importance in analysing the state of seepage in unsaturated soil slopes, and may be difficult to be incorporated into a computer code.

2.2 Directions of infiltration The issue of the direction of infiltration rises from three aspects: slope surface gradient, permeability and direction of rainfall. In dealing with rainfall on non-levelled slopes surface, the formal way to supply rainfall intensity is to decompose the total effective rainfall intensity I; (Equ.1) into two components, i.e. a normal component I,, (as infiltration) and a tangential one I , (as 436

runoff) to the surface as shown in Figure l(a), which have been used in numerous literature (Fredlund & Rahardjo 1993, Yagi et al. 1985). This could be right in case where effective rainfall intensity is greater than the capacity of infiltration.

(4 (b) Figure 1 Direction of infiltration on slope surface Unfortunately, from simple tests and field observations it can be seen that the infiltration takes place in almost vertical direction for some materials with high permeability, e.g. sand, gravel, as shown in Figure l(b). That is to say, the surface runoff and inflow are not simply determined only by the slope gradient or surface direction but also some other factors such as soil permeability and its anisotropy and sometimes even the direction of rainfall. Though the mechanism is not quite clear at present, it is true that the traditional way of applying boundary condition is no longer valid in such a situation. The way to set up a boundary condition under such circumstances will have a great influence on the results of numerical analysis, especially in analysing unsaturated soil slopes with high permeability under a prolonged rainfall with low intensity. 3 EFFECTS OF VEGETATION

Vegetation effects on slope stability include interception and evapotranpiration, reinforcement, exerting forces to slope and absorption of chemicals of soil. Stability analysis of vegetated slopes is necessary to include these effects, but now little attention has been given to this issue in numerical analyses. 3.1 Incorporation of Interception Interception by vegetation can significantly reduce the mount and delay the time of rain water fallen on the ground surface. Knowing this is very usefil in conducting transient seepage analysis in determining the factor of safety that changes with the process of rainfall. The effective rainfall intensity is given as

where I ; is the effective intensity of rainfall directly to the surface of a slope, q is the intensity of rainfall, I , is the rate of interception, and t is time. In Equation (l), the term of interception rate may become zero when the capacity of total interception is reached, and all rainfall intensity will be effective.

If the rate of interception is equal to the rainfall intensity, there will be no infiltration. This is quite true in heavy forested slopes in tropical areas. 3.2 Simulation of reinforcement

A quasi-suction is only for seepage calculation, and it should not be included in metric suction in determining unsaturated soil strength. All the last three methods need the knowledge of root distribution. If the root distribution can be assessed, the second will be the best and should be the first choice.

Roots are natural fabric materials while strengthening soil. The strength increase due to root system can be determined experimentally and statistically in relating to root intensity or a distribution function (Zaradny 1993). As roots are arbitrarily distributed, it is nearly impossible and unnecessary to represent every root with elements, a simple yet economical way to take the reinforcement effects in numerical analysis is to add an increase to soil cohesion (Wu 1997), and sometimes also to soil hctional angle. At where tension is of importance, an increase in tension strength of soil should be considered, for use of tension failure criterion. Root reinforcement may be practically negligible where root system are quite shallow distributed as the critical slip surface may be deeply seated in a slope or where bed rock surface is covered with a thin soil layer and roots can hardly penetrate across soil-rock interface, because it is more likely to such slopes the most part of slip surface is at the interface.

One of the advantages of finite element methods over limit equilibrium methods is that finite element methods give stress results that can be used in calculation of factor of safety and in examination of failure mechanism of soil of particular interests. Such stress results can be affected by initial ground stress condition as in stability analyses soils are necessary to be mechanically nonlinear materials. Therefore, how to simulate initial ground stress condition is a vital aspect to finite element analyses of slope stability problems. All slopes have undergone a complicated geological process that can not be mimicked from its very beginning stage. Generally speaking, the initial condition of a slope is referred as a state that is just prior to new changes to the slope conditions.

3.3 Simulation of hydraulic effect

4.1 Total or net stresses

Living roots draw water from unsaturated soils. The water uptake flow process affects the water balance of under ground water. There are four possible ways in all to simulate this process in finite element analysis, i.e. to prescribe a negative flux boundary, to add an element sink, as add a quasi-suction to soil mass or set an increase in permeability of soil. To prescribe a negative part flux flow of water is a simple way when the information of spatial distribution of roots is not available. This negative flux of boundary condition should be regarded as to have included evapotranspiration as well as evaporation of pore water directly from soil surface. Add an element sink of water is the most direct way to take this effect into calculation. The sink is dependent on factors such as root distribution, mean root conductivity and soil type, and can be roughly assessed using a root distribution fimction (Zaradny 1993). To add a quasi-suction and to add an increase in water conductivity are two indirect ways to simulate the phenomena based on the relationship between water conductivity and metric suction of unsaturated soil. Both methods have the side effect that they do not distinguish the direction of water flow, i.e. they may result in an acceleration of water flow inward as well as upward. So under general conditions, the two methods should be used where only upward flows exist.

There are two methods in current practice in setting up the initial ground stresses. One is to specify stress values to an element according to its vertical position (either at gauss points or nodes of elements). This is referred as the direct method. The other is apply material gravity and other loads already exerted on a slope prior to any new changes is made to the slope, conduct an initial step of calculation, then set the horizontal stress results to be (the coefficient of lateral pressure at rest) times of vertical stress to achieve static equilibrium at rest. The direct method can be best used in where the shape and soil condition are both relatively simple (Zou et al. 1997). For most natural slopes with complicated geometry, large error may be introduced in this way, as secondary stresses may have been resulted from structural geological movements and from other possible geoenvironmental influences, and as a consequence, the stresses at a point can not be determined simply by its position. In analysing a reinforced natural slope, Mastui et al. (1995) adopted a technique to assess initial ground stresses. In the analysis, an original ground was assumed to be horizontal, then an excavation analysis was taken to simulate an erosion process to form the existing natural slope. This is a simple yet useful measure to get initial ground stresses provided that the so called original ground could be represented with rational geotech437

4 JNITIAL, STRESS CONDITIONS

nical parameters. Unfortunately the authors failed in giving clear information about what was the difference between parameters of original ground soils and those of existing natural slope. This issue has not been able to be shed on lights yet, and, therefore, need for further investigations. In order to simulate the process of formation of existing slope, excavation is usually mimicked by cutting off elements from the top of the slope to its bottom from initial ground element mesh, whereas embanking is simulated by adding elements from the bottom to the top of the slope from the initially levelled ground mesh. Both ways are exposed to an unconditional use of the presently available parameters rather than parameters before or after a slope has been formed. This is to say that soil parameters remain unchanged in both stages of the simulating the formation of a slope and analysing the behaviour of the existing slope. Another severe shortcoming to these methods for simulation initial ground stress condition is that when the simulation is finished, some elements may be already failed before a stability analysis is taken, while the existing slope was supposed to preserve static equilibrium according to the direct methods. Can stresses of the failed elements be simply set to values that meet requirement of the static equilibrium, as in the direct method? This is a key problem that needs investigation.

4.2 Initialpore pressure distribution Initial pore pressures include pore water pressures and pore air pressures. Their initial distribution has an unusual influence on the results of seepage analysis and stress analysis. Pore air pressures are generally set to nullity where pore air is assumed to connect with atmosphere, which is widely accepted. However, at where the pore air is enclosed from atmosphere, a determination of initial pore air pressure becomes a necessity to numerical analysis. Such an issue may be concerned in dealing with deeply seated organic unsaturated soils, in where gases may be generated in chemical andor biochemical processes. Waste deposit slopes covered by a clay barrier is more likely the case. Pore water pressures have tremendous effects on soil strength of both saturated and unsaturated soils. For the propose of analysing slope stability due to rainfalls, an initial state of pore water pressure distribution must be linked with the permeability of unsaturated soils. There have been several ways to prescribe the initial pore water pressure condition. Yagi et al. (1985) considered a capillary rise h in determining the seepage characteristic curve for initially unsaturated sand, and set the initial potential value to be a give value. Vargas et al. (1990) used a constant moisture

or pressure head through the unsaturated soils as the initial pore water pressure condition in a series of transient seepage analyses due to rainfall. Spierenburg et al. (1992), in analysing slope stability during infiltration into a dike, assumed a linear negative initial pore water pressure head above phreatic surface until a suction head had reached 1.0 my and above this level, soil suction is assumed to be constant up to the top surface of the dike. Ng & Shi (1998) conducted an analysis steady state seepage in unsaturated soil slope under specific hydraulic head boundary condition, and its pore water pressure result were then used as an initial condition in subsequent transient seepage analyses. This seems the most reasonable way to set up initial ground condition, like the indirect method in determining net or total stress of soils. In analysing the effects of horizontal drain on the stability of unsaturated soil slopes, Cai et al. (1998) assumed an initial degree of saturation distribution that was 61.7% at the crest of a slope and linearly increased to unity at the height of the initially assumed ground water table. This method is most feasible as the degree of saturation is easy to assess and applicable in setting initial pore water pressure based on the relationship between soil moisture and suction. For shallow slopes, assumption of constant negative pore water pressure may not introduce severe errors, as it was demonstrated by Fourie et al. (1999). It may be seen from above examples of setting initial conditions to the seepage and stress analyses that the ways are quite diversified. This situation reveals the badly needs for making filed measurement of initial state of slopes for stability analyses. Only with comprehensive measurements and back analysis techniques, can we improve the theory of applying initial ground conditions for geotechnical numerical analyses. 5 DEFINITIONS OF FACTOR OF SAFETY By nature, finite element stress analyses do not link directly their results to the value of factor of safety for a slope. The factor of safety of a slope can be calculated by using the stress results from finite element analysis. There are many methods to calculate the factor of safety, but not all the methods are suitable for use based on the stress results of finite element analysis. A rational definition of factor of safety should reflect the basic mechanism of slope stability, not be in conflict with basic rules in mathematics and mechanics, and be easy to use in practice. Although there have been a number of ways to define the factor of safety for finite element analysis, they are exposed to severe shortcomings. In this section, several main definitions of factor of safety are discussed, as to make it clear that how they can be used in particular situations. For brevity, yet

preserving generality, the discussion is limited in two dimensional cases. Among the definitions of factor of safety in literature, the following one seems to be most popular (Yamgami & Ueta 1988, Zou et al. 1994, Shi 1998, Farias & Naylor 1998). For the convenience in choosing shear stress and compute the shear strength in practical calculation, Equation (2) is widely used in its difference form .

i=l

i=l

where is the line of slip surface, x and z are horizontal and vertical co-ordinates of a point on the slip surface, respectively, zand zj . are the shear stress and shear strength at point (x,z), respectively where Alli is a segment line in the slip surface, i denotes the number of segments in the slip surface and n is the total number of the segments (Fig. 2). Although Equation (2) is widely used, it has an illness in physical meaning when used with noncircular slip surface. Both the sliding forces and the potential resistant forcesq are summed up numerically rather than geometrically. To add the vectors by their numerical value without caring about their directions is in conflicting with mathematically and mechanical principles. As it can be seen in Figure 2 there are differences among the directions of sliding and antisliding forces and between their resultant vectors. So Equation (2) can be used free from illness only with circular and translational slip surfaces.

Figure 2 Directions of sliding and antisliding forces In avoiding this illness, another way is to calculate the overall factor of safety through integration of local factor of safety along the slip surface, i. e.

In Equation (3) there is no illness as that in Equation (2), but in practical use of this definition, another numerical difficulty may be encountered. Infinity of local factor of safety can be resulted in at some points or some areas in soil body where the shear stresses happen to be zero. Another definition of local factor of safety is the inverse of the stress level (Matsui & San 1990)

whereo, ando, are maximum and minimum principal stresses of at a point on the slip surface, respectively, and f denotes the stress difference at failure condition according to Mohr-Coulomb's criterion. One can also see from above that this method has the same numerical problem as in Equation (4). Furthermore, this definition of local factor of safety does not mean the real shear stress level on the slip surface. Ge (1987) suggested a method called main-sliding direction method, for calculating factor of safety. In this method, all forces are summed up in the main sliding direction which is determined by the resultant sliding force vector (Fig, 2), and the factor of safety is given by n

Sinai +zli COSai)Ali

Z
\

I

COS~~>AZ~

i=l

where a , i s the angle between direction of ith force and the main-sliding direction ,o,.is normal stress. This method is free from above illness, but it involves an equivocality about the role of normal stresses in stability as they appear in both sides of sliding and antisliding forces. The confusing feature prevented the method from being widely recognised. Recently, Wang et al. (in prep.) suggested a weighted method similar to that used in calculating the factor of safety with respect to moment equilibrium in general limit equilibrium method (Fredlund & Rahardjo 1993). The definition is given as

(3) where FsLis the local factor of safety at print (x, z) in the slip surface and is defined as

Fa =--z P xi

(4)

where w(x,z) is a weight function and is same for both shear stress and shear strength and at point (x,z) along the entire slip surface. Other symbols are of same meanings as above. The weighted function w(x,z) acts as the arm of force in limit equilibrium 439

method and can be determined by the distance from a reference point to the point (x,z) along the entire slip surface. For translational slip surface, the function is always set to unity. For a circular slip surface it is the radius of the circle. For a noncircular slip surface, the reference point is the intersect of two lines normal to the slip surface at its upper and lower end segments. The factor of safety can be calculated with moments in one direction with this technique. 6 CONCLUSIONS Four salient aspects in numerical analyses of slope stability under rainfall condition are summarised and analysed in this paper. The key issues that are now not well established or generally overlooked at present are discussed and emphasised on with regard to further studies and applications. Completely solving of these problems may take great efforts and may not be achieved within a short step forward. But without a comprehensive understanding of these complex problems and without a firm engineering judgement about the applicability of methods and results of presently numerical analyses, application of the results can be dangerous. Through the discussion of problems raised in this paper, it is clear that great improvement should be made in numerical techniques in analysing rainfall induced slope instability by solving these problems. REFERENCES Cai, F. et al. 1998. Effects of horizontal drains on slope stability under rainfall by three-dimensional finite element analysis. Computers and geotechnics, 23(4): 255-275. Farias, M.M. & Naylor D.J. 1998. Safety analysis using finite elements, Computers and geotechnics, 22(1): 165-181. Fourie, et al. 1999. The effect of infiltration on the stability of the slopes of a dry ash. Geotechnique. 49 (1): 1-13. Fredlund, D.J. & Rahardjo, H. 1993. Soil mechanics for unsaturated soils. New York: Wiley. Ge, X.-R. 1987. Finite element analyses of rock engineering problems using micromachine CP. In Proc. of the first national symposium on computatioal geomechanics, Southeast Jiaotong University Press (in Chinese). Matsui T.& San K.-C 1990. A hybrid slope stability analysis method with its application to reinforced slope cutting. Soils and foundations. 30(2):70-88 Ng, C.W.W. & Shi, Q. 1998. A numerical investigation of the stability of unsaturated soil slopes subjected to transient seepage. Computers & geotechnics, 22(1): 1-28. 440

Shi, H.-T. 1998. Nonlinear finite element analyses of stability of complex slopes. Thesis submitted to Tianjin University for the degree of Master of Engineering (in Chinese). Spierenburg, S.E.J. et al. 1992. Slope stability during infiltration. In. Pande & Pietruszcak (eds), Numerical models in geomechanics: 3:2499-2503. Rotterdam: Balkema. Vargas,E.A. et al. 1990. Saturated-unsaturated analysis of water flow in slopes of Rio De Janeiro, Brazil. Computers and geotechnics, 10(3):247-261. Wang, C.-H. et al. (In prep.). A parametric analysis of rainfall induced instability of unsaturated soil slopes. Submitted to the 8th international symposium on landslides. 2000. Cardiff. Wu, T.H. 1997. Slope stabilizaion. In Morgan & Rickson (eds), slope stabilization and erosion control: 221-264. E & FN SPON Yagi, N. et al. 1985. Slope failure mechanism and prediction method due to rainfall. In Proc. of the 5th international conference and workshop on landslides. 209-2 14. Tokyo. Yamagami, T. & Ueta, Y. 1988. Search for critical slip lines in finite element stress fields by dynamic programming. In Proc. of the 6th international conference on numerical methods in geomechanics. 1347-1352. Innsbruck. Zaradny, H. 1993. Groundwater flow in saturated and unsaturated soil. Rotterdam: Balkema. Zou, J.-Z. et al. 1994. Search for critical slip surfaces based on finite element method. Can. Geotech. J. 32:233-246

Slope Stability Engineering, Yagi, Yamagami& Jiang 0 1999Baikema, Rotterdam, iSBN 90 5809 079 5

Centrifuge model tests and stability analysis on mobilizing process of shear strength of decomposed granite soil slope S.Yoshit ake Nihon Kensetsu Gijutsu Company Limited, Saga, Japan

K.Onitsuka Department of Civil Engineering, Saga Universify,Japan

ABSTRACT :Centrifuge model tests were performed on slope models made from undisturbed and statically compacted decomposed granite soils with and without rainfall to clarify its characteristics of slope failure. From the tests, shallow sliding type of failure of undisturbed and compacted granite soil are observed in the centrifuge model tests, independent of the case with and without rainfall. It can be observed that the local failure occures initially at the toe and gradually reach the top of the slope and finally result in failure of the slope. In order to explain such a failure state for decomposed granite soil slope, a new stability analysis method is proposed. It considers the variation of shear strength coefficients(c,,cbm) with the increase in deformation under low confining pressure. A proposed slope stability analysis can explain the failure pattern or failure occurrence phenomenon of the decomposed granite soil slope very well. tion of the strain or deformation is necessary than the critical equilibrium method in which the strength mobilized along the sliding surface is assumed to be the peak strength without considering the magnitude of the deformation. The shear strength is not constant during the shear process, and varies with the change in the magnitude of the deformation (Hayashi, 1982, Onitsuka and Yoshitake, 1987, Yoshitake and Onitsuka, 1990). Stability analysis is done with consideration of the variation in the shear strength coefficient and its results are compared with the centrifugal experimental results.

1. INTRODUCTION

Natural and man-made slopes of decomposed granite soil are stable under normal dry condition, but are sometimes unstable under wet condition such as a rainy season. Most failures are shallow sliding failures of 1.0m to 2.0m depth. Such shallow failures is one of the characteristics of decomposed granite soil slopes. Shallow sliding type of failure of the decomposed granite soil slope was observed in the centrifuge model tests with and without rainfall. For the stability analysis of the decomposed granite soil, therefore, it is necessary to consider the shear and strength characteristics, including the effect of soaking, under low confining pressure. In addition, it is the general pattern for the failure of the slope of decomposed granite soil that the failure occurs firstly at the toe of the slope, and progressively develops toward the upper part of the slope. In order to explain such a failure state, an analytical method with considera-

2. SAMPLES AND TEST PROCEDURE 2 . 1 Sample

The samples used in this study were obtained from two sites in Saga prefecture. Sample A was obtained by pressing a CBR mould with a cutting edge into the natural decomposed granite soil slope. Sample B was obtained by a nail sampling method for the cen-

441

Table 1

larger than that of the prototype.

Soil properties

MOBILIZING PROCESS OF SHEAR STRENGTH COEFFICIENTS ( c rn , C$ rn ) WITH INCREASE IN SHEAR DISPLACEMENT Shear strength coefficients(c,, + m ) can be obtained from the relationship between normal stress o and The observed shear stress ‘1:. changes in the values of shear strength coefficients(c,, + m ) can be used to describe the mobilizing process of shear strength as a function of shear displacement D . Linear relationships are observed for each particular shear displacement D . Thus, different values of shear strength coefficients can be obtained at every stage of shear displacement, e.g. at the primary, failure and residual states. Fig.l(undisturbed specimens) shows the variations of shear strength coefficients with increase in shear displacement for unsoaked and soaked conditions under both low and moderate confining pressures. For the undisturbed specimens, the cohesive component coefficients( c r n ) increase to the peaks value at small shear displacement. After that, it decreases gradually with increase in shear displacement and gradually approaches a constant value. The frictional component co3.

trifuge model test. Properties of these samples are shown in Table 1. Direct shear test The consolidated constant normal stress direct shear tests were carried out on both undisturbed and statically compacted soils. The range of the normal stress is from 1.96 to 17.6(kN/m2) under low confining pressure and from 19.6 to 294(kN/mZ) under moderate confining pressure. Tests were carried out under unsoaked and soaked condition wi.th strain control(O.Eimm/min). (Onitsuka and Yoshitake, 1988). 2.2

2.3 Centrifuge model tests Centrifuge model tests were performed on slope models of both undisturbed and compacted unsaturated soils with and without rainfall. The undisturbed soil slope model were prepared with after various inclinations, a , setting the sample mass in the container. In the case of the compacted slope model, decomposed granite soil was compacted from five to seven equal layers of 2cm. In the case of without rainfall, the centrifugal force is gradually increased till the failure of the slope occurs. In the model test under rainfall, the rainfall begins after the centrifugal acceleration become to 9O(G). Details of test procedure have already been presented elsewhere(Y0shitake and Onitsuka, 1992, 1994) The failure patterns of the slope and its seepage characteristics were investigated. In order to make the slope failure and make clear the failure state, the slope gradient of the compacted slope is somewhat

Fig.1 Influence of soaking on the variation of shear strength coefficients 442

efficients ( b m ) increase gradually with shear displacement and gradually becomes constant regardless of the soil conditions. It can be concluded that, therefore, the cohesion component mobilizes maximally at a small shear deformation, while the friction component mobilizes maximally only at quite large shear deformation. In case of compacted specimens(figure not shown), the cohesive component coefficient also increases to the peak value at small shear displacement and remains constant after taht. As shown in Fig.1, the mobilizing process of shear strength coefficients is not affected by soaking. In addition, the decrease in shear strength due to soaking depends mainly on the decrease in cohesive component coefficients. In particular, the degree of decrease in cohesive component coefficients is great under low confining pressure. On the other hand, the frictional component coefficients are unaffected by soaking. Fig.2 shows the relationship between the degree of decrease in shear strength due to soaking (the ratio of peak strength of soaked specimen to that of unsoaked specimen) and confining pressures. The degree of decrease is nearly constant under moderate pressure. Under low confining pressure, it becomes large, particularly, when the confining pressure is less than about 20 ( k N / m 2 ) (Onitsuka and Yoshitake,l988). It is necessary to consider the degree of decrease in shear strength, espesially under low confining pressure for the slope stability analysis of surface failure.

CENTRIFUGE SLOPE MODEL TESTS 4.1 Slope Failure without Rainfall The centrifuge model tests were conducted to investigate the failure characteristics of the decomposed granite soil slope without rainfall. For undisturbed decomposed granite soil slope, sliding surfaces are not obserbed clearly. The slope failure pattern was a slide at the top of the slope. Shallow sliding type for all kinds of slopes was observed in the centrifuge model tests. In case of the compacted slope model, a sliding surface can be clearly observed by centrifugal tests. The sliding surface is close to a circular in the shape as shown in Fig.3. The failure pattern in the compacted slope is similar to that occurred in the undisturbed slope of the decomposed granite soil. That is, the sliding surface occurs in the shallow surface layer. In order to make clear the process of the failure for the slope of the decomposed granite soil, the photographs are continually taken on compacted slope during the centrifugal model test. An example of the failure process is shown in Fig.4, in which the slope gradient is 45" and the height is 14cm. The failure process is observed as follows: 1)settlement occurs in the whole model slope and a little movement forward is found in the toe of the slope(centrifuga1 acceleration: 90G); 2)cracks oriented in parallel to the slope occur in the vicinity of the toe, and quite swelling occurs in middle of the slope(94G); 3)cracks in both the toe and top slope develop to the middle of the slope, and the slid4.

Fig.2 Ratio of peak strength of soaked specimen to that of unsoaked specimen

Fig.3 Failure state of the slope(Compacted slope model, without rainfall ,inclination of slope : 60' )

443

tial state(void ratio, water content) and the slope gradient on the slope failure. As shown in Fig.5, three types of failure states were observed. The first type occurs as a straight line from the top to the middle of the slope in Fig.5 (a). As shown in Fig.Fj(b) for the large void ratio, the sliding surface is in a little deeper position from the toe to the top with a shape of the circular. It is clear that the effect of the initial viod ratio is large on the failure state of the slope. In the case of high rainfall intention for a low gradient of a slope as shown in Fig.5(c), the decomposed granite soil in the shallow layer runs of along the slope, like a debris flow.

SLOPE STABILITY ANALYSIS

5.

Fig.4 Process of slope failure (compacted slope, sample A)

ing seems beginning in the shallow layer of the slope(96G); 4)the shallow surface layer in the slope slides down and failure occurs(97G). Above observation makes clear that the failure process for the slope of decomposed granite soil develops progressively in the following order: firstly, deformation occurs in the vicinity of the toe, then the deformation increases, finally failure occurs in the shallow surface layer. 4.2 Slope Failure Under Rainfall The failure state of the slope for undisturbed decomposed granite soil under rainfall shows a straight line of the sliding surface from the top to the middle of the slope. This failure state i s almost the same as that without rainfall. The failure of the slope under rainfall occurs before seepage develops for all slope models. Next, centrifuge model test was performed on the slope model of the compacted decomposed granite soil under rainfall. The purpose is to investigate the effects of the ini-

Relationships between shear stress and shear displacement were obtained from direct shear test. As mentioned above, variation of shear strength coefficients can be expressed in terms of shear displacement. In the analysis using the finite element method, the stressstrain relationship is needed. Hence, the concept of relative displacement which is correspondent with strain is newly introduced. For example, in the case of low confining pressures for undisturbed samples, the maximum cohesional component is mobilized at shear displacement of 2.0mm. It is called as maximum shear displacement, D,,,, . The concept of relative displacement was proposed based on the maximum shear displacement, Dcmax , responsible for the relative displacement, D r e , is defined as the ratio of shear displacement D to D c m a x , D r e = D / D c m a x . The analysis of decomposed granite soil slope was done by finite element method considering the variation of the shear strength coefficients with increase in relative displacement. Nonlinear secant modulus method was adopted in the stability analysis. The following equation is used to judge whether the local failure occures. local safety factor F ~ , Fr.

sinq5,*(a l t a 3 ) / 2 t c m * c o s 4 m = ( 0 1-

444

a3)/2

Type of slope failure state

The analysis is done considering of the variation of the shear strength coefficients with relative shear displacement obtained from direct shear test. The value of deformation modulus 10000(kN/m2) and poisson's ratio is 0.30. Fig.6 shows the variation of the shear strength coefficients in approximately linearized form with respect to the relative displacement. The analysis results are shown in Fig.7 (a),(b). Fig.7(a) shows the distribution of the deveioped relative strain. Fig.7(b) shows the distribution of local failure elements with F ~ < 1 . 0 .The relative strain develops from the initial stage in the analysis, and a sliding surface gradually develops from the toe of the slope as shown in Fig.'l(a). From Fig.7(b), it can be observed that the local falure occurs at the toe of the slope at the initial stage. Finally, failure occurs when the local failure elements reach the top of the slope. This gradual slope failure pattern is correspondent with the centrifuge model test results. Next, in the case of undisturbed' decomposed granite soil slope model, the value of deformation modulus is 15000(kN/mZ) and poisson's ratio is 0.28. The analysis results using relative displacement are shown in Fig.8(a)(without rainfall) and (b) (under rainfall). From Fig.8(a), the local failure elements develop initially at the toe and gradually reach the top of the slope and finally result in failure of the slope. In the undisturbed decomposed granite soil slope, the local failure elements develop in the relative shallow position comparing to the slope of compacted decomposed granite soil. As shown in Fig.8(b), the distribution and developed state of local failure elements under rainfall are almost

Fig.6 Simplified shear strength coefficients with relative displacement the same as those without rainfall. The distribution of local failure elements under rainfall shows a relative deeper position. Therefore, the stability analysis which considers variation of shear strength coefficients, especially under low confining pressure, can explain the failure pattern of the decomposed granite soil slope very well. 6. CONCLUSIONS

The centriguge model tests were performed on both undisturbed and statically compacted decomposed granite soil with and without rainfall to study slope failure characteristics. The failure characteristics of the decomposed granite soil slope were also simulated by a new stability analysis, which is a finite element method considering variation of shear strength coefficients with the increase in relative displacement. The following results are summarized. 445

1)For both undisturbed and compacted decomposed granite soil, the cohesional component mobilizes maximally at the initial stage during the shearing. On the other hand, the frictinal component gradually increases with increase in the shear displacement and become constant. 2)Shallow sliding type of failure of the decomposed granite soil slope was observed in the centrifuge model tests with and without rainfall. 3)The slope failure of decomposed granite soil always occurs before the all part of slope is soaked. This indicates that the strength obviously decreases in the surface part of the slope(overburden pressure is small) due to soaked. 4)A proposed slope stability analysis, especially under low confining pressure, can explain the failure characteristics of the decomposed granite soil slope very well. REFERRENCES l)Hayashi,S.(l982):A study of three-dimensional friction rule of soils, Dr. Eng. Thesis, Kyushu University.(in Japanese). 2)0nitsuka, k. and Yoshitake, S . (1987):Consolidation on the variation of strength parameters, displacement, c , q~ with shear Proc. of JSCE, Vo1.382, III-7, pp.265-268(in Japanese). 3)0nitsuka, K. and Yoshitake, S . (1988): Shear characteristics of decomposed granite soil compressible under low pressure, Proc. J.S.C.E., V01.400, III-10, pp.141150(in Japanese). 4)Yoshitake, S . and Onitsuka, k . (1990):Factor's influence strength parameter behaviour of decomposed granite soil, Residual soil in Japan, pp. 105-110. 5)Yoshitake. S . and Onitsuka, K. (1992):A study of slope failure of decomposed granite soil due to rainfal1,Report of the 26th Japan Annual meeting on Soil Mechanics and Foundation Engineering,JSSMFE. pp.1873-1874(in Japanese) 6)Yoshitake, S and Onitsuka, K. (1994):Stability of decomposed granite soil slopes, Proc. Int. Conf. Centrifuge 94, Singapore, pp.599-604.

Fig. 7(a), (b) The distribution of the developed relative strain y R and the local failure

Fig.8(a), (b) The distribution of the local failure

446

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Centrifuge tests on slope failure during water infiltration H.G. B.Allersma Deljt Universityof Technology,Netherlunds

ABSTRACT: A description is given of centrifuge tests for investigating the behaviour of slopes of embankments during water infiltration. The stability of embankments during infiltration has to be known in order to predict the degree of safety provided for the protection of land fiom flooding. Tests have been performed for investigating tlie failure mechanism and for verifying assumptions of tlie mechanisms in calciilation tnetliods. Tlie phenomena are relatively simple to simulate in a centrifuge and reproduction of the test was good possible. Fiirtliertiiore, the phenomena could be made visible in detail and it was possible to manipulate the water table in tlie embankment.

1 INTRODUCTION

Centrifuge research is a method with world wide acceptance for investigating the behaviour of soil structures. A large variety of geotechnical problems can be modelled by this technique (e.g. Kitnura et al. 1998). A powerful application is tlie validation of calculation methods and tlie visualization of mechanisms. Furthermore, several geotechnical problems are currently not susceptible to any solution by mathematics, so that experimental research is the only possibility for gaining insight into a particular geoteclinical phenomenon. I n a centrifuge, even in a small model, it is possible to obtain a good ratio of shear stresses to cohesion. This circumstance allows small scale tests to be performed on clay models. Furthermore, tlie stress dependent behaviour of sand can be scaled correctly. It is usual to validate calculation mctliods by predicting ttie behaviour of real scale problems. However, in reality, tlie geometry is often rather complicated and tlie soil characterization contains several uncertainties, so that tlie validation has to be carried out on a complex problem. In centrifuge models, however, a start can be made with simple configurations, and the soil parameters are under much tighter control, so that a better connection with the theory is obtained. Because tlie models can be reproduced accurately. differences in behaviour arising from slight changes in the construction procedure can be made visible. For tnechanistn studies, a small centrifuge is preferred, because models can be built in a short time and several tests can be performed thanks to tlie low costs of operation. Tlie applications of centrifuge research to slope stability engineering in the Geotechnical Laboratory of

447

tlie University of Delft are devoted to tlie behaviour of embatiktiients for the protection of tlie land from floods. 'I'he resistance of dikes to tlie infiltration of water are of interest in the prediction of the degree of safety provided. I n 1953, several dihes protecting tlie low lying areas of tlie Netherlands against tlie sea were breached during a heavy storm in combination with spring tides. It appeared that for several dikes, damage was riot sustained in tlie first instance by the mechanical forces of tlie waves on the sea side, but, rather, on tlie land side. Tlie sea had reached such a high level that it flowed over tlie top of tlie dikes as a result of tlie wave action. Tlie water infiltrated into the dike because tlie top of tlie dike arid the slope on the land side were not covered with a waterproof layer. Water flow in tlie soil reduced tlie stability of tlie slope on the land side, causing failure of tlie dike. Centrifuge tests have been performed to gain more insight into tlie mechanism causing failure. Clay dikes that were made higher by sand were tested in a previous test prograin (Allersnia et al., 1994~).In a later test program niore attention was paid to homogeneous dikes of sand that were covered with a clay layer. I n a centrifuge model, tlie cohesion attributable to capillary action exhibits tlie same ratio to the shear stresses as pertains i n the prototype problem. Because tlie capillary rise of tlie water is also in good correspondence n i t h the prototype dimensions, tlie warer flou tliroiigh ttie dike can be made visible by means of tracers and tlie mechanism of failure can be visualized. The aim of this test program was to investigate tlie mechanism leading to slope failure of pure sand dikes and sand profiles covered with clay, during water infiltration.

Fig.:! Test box with an air lift to simulate the effect of wave overtopping. Fig. 1 The University of Delft geotechnical centrifuge.

Furthermore, methods were tested that could improve tlie stability, and tlie effect of homogeneity was examined. When the mechanisms of failure are known, there is a better possibility of designing methods that improve the stability. I n many cases, new methods can be tested relatively simply i n a centrifuge model to investigate the effect. Examples are the use of drains to improve the stab i I i ty during in fi I trat ion.

2 TEST FACILITIES 2.1 The cenlrijuge The tests are performed in a small geotechnical centrifuge (Fig. 1). This device has been developed at the Ceotechnical Laboratory of the Faculty of Civil Engineering of the University of Delft (Allersma, I994b). The design goal was to obtain a device that is flexible and cheap in operation. The centrifuge, which has a diameter of 2.4 metres, contains two swinging platforms to carry the samples. With tlie present motor power, samples with a weight of more than 3OON and a volume of 15x40~40 cm can be accelerated up to 150 times earth’s gravity. I n most cases, the weight of the model containers is less than 200N, so that the tests can be conducted by one person. This makes the centrifuge very convenient i n use. An advanced electronic system, containing a single-board 1BM PC compatible computer (486 central processor, 66Mhz), is installed i n tlie spinning part of the centrifuge for the purpose of controlling the tests. The computer can be accessed in a normal way via slip rings. A link with the mechanical devices is made by means of an analogue to digital converter with a 16 channel multiplexer, two voltage controlled outputs of more than 5 amps each and two 16 bit counters. A special feature is that several plienomena can be measured by using the video images of the on-board camera. Digital image processing is used to visualize and digitize automatically the surface deformation of clay and sand sainples (Allersma, 199 I ) . I n this test program, the 448

course of the tests could be analyzed in inore detail by subtracting images of the tests taken at the end of different time steps. Several devices have been developed in order to perform tests in flight (Allersma, 1994a). I n this test program, a computer controlled water circulation system has been used to manipulate the course of the test.

2.2 In,jlight test equipmerit Water is circulated by means of an air lift (Fig.2). I n this technique, air is injected into water confined within a plastic tube. The advantage of this system is that the water supply can be controlled very smoothly from zero to the maximum flow and the device is very simple and cheap to build. The flow rate is detected by a small turbine, the rotational speed of which is converted to a voltage via an optical sensor. A maximum flow of about 10 I/min can been obtained at I OOg.

3 WATER INFILTRATION TEST The tests were performed in plane boxes with transparent walls separated by 50 mm (Fig.2). The dimension of the box was 360x400 min. The model of a dike was located on a metal platform. The space left under the platform was used as a water reservoir. An air lift driven by compressed air was used to circulate the water. The tests were performed at XOg. At this gravity, dikes with a height of approximately 2 to 7 meters could be simulated in the test box. The water was supplied at the top of the dike through a small box with holes. A filter at the bottom distributes the water evenly and prevents erosion of the top layer through fast running water. I n reality, during wave overtopping, the water infiltrates not only into the crest, but also into the slope of the dike. It was found, however, that the infiltration pattern did riot change significantly if tlie water was supplied at tlie crest only. During centrifuge tests. a video camera was focused on the model. Thanks to the transparent boundaries it was possible to watch the groundwater behaviour i n the soil.

Since the capillary rise is only a few inm at 80 g a phreatic line could be created in the small model. The water table in the sand layer was visible as a result of the difference in contrast between wet and dry sand. The stream lines are visualized by means of a tracer. The tracer consists of grains of potassium permanganate, which are inserted into the sand during preparation. As soon as the groundwater flowed around the grains, coloured stripes representing the streamlines of the water flow became visible. Owing to the higher g level, the pseudo cohesion induced by the capillary forces (36 cm water at 1 g) could be ignored. On the other hand, the flow rate of the pore water in the dune sand during tests at 80 g was still low enough (maximum flow rate in the test series was 0.01 6 m/s) to keep the Reynolds number (the estimated max. value was 1.6) below the value indicating turbulence (Goodings, 1984). If the flow can be assumed to be steady state and laminar, the flow rate of the water varies linearly with the acceleration of the centrifuge. Additional tests have shown that Darcy's law is valid at the acceleration level employed. The slopes are made of dune sand, which is characterized by Unit weight 16 kN/m3 Permeability 0.01 cm/s 0.1 m m DlO D50 0.2 iiim Friction angle 36"

3.1 Dike qfpure sand I n Fig.3, a number of test stages are presented where a dike of pure sand is infiltrated by water. If a homogeneous dike of sand with a critical slope is infiltrated in the centrifuge, the failure of the dike started in all cases near the toe owing to seepage-induced local instability. The initial failure of a homogeneous dike appeared to be a surface phenomenon. Even in the case of a critical slope, the test did not show a Bishop like shear band mechanism. The local instability proceeds with increasing water flow, which results finally in a total failure of the embankment. I n Fig.3c a slope with a smaller angle is shown after failure. Also in this case failure starts near the toe. 111 Fig.3d the stream lines are made visible by a tracer. The seepage is clearly visible, which explains the erosion of the sand. I n accordance with the exception more water can be infiltrated if the slope angle is smaller. It was found that the mechanism is not significantly influenced by density and particle size.

3.2 Sand dike with clciy In this case a dike is constructed with a sand body to which a clay layer is applied to prevent erosion of the sand by wirld and rain. Usually grass is growing on the clay layer. Because the clay layer has relatively poor contact with the subsoil. the clay becomes dry. This

Fig. 2 Different stages showi11g the bellaviour o f a dike of pure sand during water infiltration.

449

drying process can cause small cracks in the clay layer. If water runs over the slope, infiltration occurs via the cracks. In Fig.4 a test is performed on a sand dike covered with a clay layer. In this test the water is infiltrated at the crest only. The stream lines are made visible by a tracer. If the sand slope is covered with a clay layer, the first visible sign of failure is the crack in the clay layer (Fig.4~).The crack is caused by the fact that the clay layer is lifted up, so that the friction between clay and the sand slope is reduced strongly. A crack appears as a result of tlie inherent weight. The moment of uplift of the clay layer can be deduced from the curvature of the visualized stream lines. It appeared that the location of the crack in the clay layer was dependent on the thickness of the layer. The larger ttie thickness of ttie clay layer, the closer the crack comes to the crest of the dike. This tendency is shown in Fig.4d. In practice tlie crack is mostly located at the transition between slope and crest.

Fig.5 Centrifuge tests to examine the effect of a drain at the toe of the embankment.

The influence of a drain close to the toe of the dike is tested in Fig.5. This is a typical demonstration of how centrifuge modelling can be used to examine alternative constructions. It should be pointed out that it is almost impossible to make such a comparison in field tests. As was expected more water was required to cause failure. The stream lines show clearly that water is discharged via the drain. The practicability of a drain as a solution is a matter for debate. Dikes have to be reliable for hundreds of years. whereas there can be no certainty of the drain continuing to work well for such a long time. For the same reason, the use of geotextile for dikes has not been common to date. Fig.4 Moment of cracking of a clay layer covering a sand dike; the stream lines are visualized by means of a tracer.

450

Fig. 6 Effect of a heterogeneity during infiltration

I n Fig.6, the effect of a heterogeneity i n the sand body is visualized. This test was performed as a response to critical remarks that only liomogeneous sand bodies could be tested. The stream lines of the groundwater flow are made visible by a tracer. It was found that a heterogeneity can have a positive effect on the stability.

deformation of the dike was measured by digital image processing (Allersnia, 1996). For this purpose, labels were placed at the slope of the dike. The labels are monitored by a video camera mounted on a fixed point 30 metres distant. The deformation of the dike body could be visiialized easily by subtracting two images. taken at different time steps. A typical example is shown in Fig.7. It can be seen that in the field tests almost tlie same mechanism is visible as i n the centrifuge tests, i.e. failure does not occur along deep shear bands. Rather, the clay layer slides over the sand surface, so that a crack is formed at the transition between slope and crest. After that, the water infiltrates the sand body via the crack, which causes a gradual erosion of the dike body. I n practice, the water siipply by wave overtopping is given i n litres/s/ni. In the field test, about 1 litre/s/m was supplied. I n the centrifuge tests the water infiltration at failure varies between 0.1 and 0.3 I/s/m. There are no accurate measurements available from practice. In the design rules, the permitted quantities lie between 0.1 and 10 I/s/m. depending on tlie protection of the slope. The data show that there is a realistic agreement between the tests.

4 CONCLUSION The small geoteclinical centrifuge was very convenient for investigating the behaviour of slopes of embankments during water infiltration. I11 a relatively short time a large number of test conditions could be investigated, were the costs are very reasonable. The niotnent of failure of a sand slope during wave overtopping is dependent on the degree of saturation and the slope angle of the sand body. Critical slopes with an angle of 36" show failure if the phreatic line has reached the soil surface at a height of 1/3 of the slope. Noncritical slopes can be completely saturated before failure occurs. It appeared that the failure of sand slopes during water infiltration is initiated by seepage-induced local instability. This is i n contradiction to some theoretical hypotheses, which assume that failure starts with a slip circle mechanism, as is supposed in the failure mechanism of Bishop. I n the centrifuge tests, the behaviour of a clay layer covering a sand slope could be visualized. It appeared that tlie clay layer is lifted up by the water pressure. Due to reduction of friction between clay and sand the self weight of the clay causes tensile cracks. Infiltration of the water into the cracks results in progressive failure of the slope. A similar mechanism could be observed in a field test. This agreement is a satisfying demonstration that centrifuge tests are a very realistic simulation of practice. The centrifuge tests can be used to examine the effect of alternative constructions. A typical example is tlie visualization of the effect of a drain. Moreover, tlie effect of a heterogeneity can be visualized, so that conclusions can be drawn about tendencies in practise. It is believed

F i g 7 Deforniation of a real eriibanknient during water i nfi Itration.

The centrifuge tests could be compared with field tests. I n this test a real dike with a height of 6 metres was infiltrated by water. The construction of the dike was comparable with a sand Fig.7 Deformation of a real dike during water infiltration. covered with a clay layer. The water was supplied over some length via holes i n a large tube at the crest of the dike. The water ran over the slope, so that some proportion infiltrated into the sand body. The surface

451

that a small centrifuge is valuable tool for testing new ideas i n geotechnical engineering.

ACKNOWLEDGEMENT The research described is assisted by several graduate students from different countries, they are: I.A.G. Ligtenberg (the Netherlands), 0. Mareschal (Belgium). Many thanks are expressed to the technicians of the laboratory for their assistance in this project.

REFERENCES Allersma, H.G.B., 199 I : Using image processing in centrifuge research. Proc. Int. Conf. Centrifuge9 1, Boulder, Balkema, Rotterdam, pp. 55 1-558. Allersma, H.G.B., 1994a: Development of miniature equipment for a sinall geotechnical centrifuge. Transportation Research Record no. 1432, Inovation in Instrumentation and Data Acquisition Systems, National Academy Press, Washington, D.C.,pp. 99- 105. Allersma, H.G.B., 1 9 9 4 ~ : The University of Delft geotechnical centrifuge. Proc. Int. Conf. Centrifuge94, Balkema, Rotterdaqpp.47-52. Allersma, H.G.B., I.A.G. Ligtenberg, B.A.N. Koehorst, 1994d: Sirnulation of failure of dikes by water infiltration by waves. Proc. Int. Conf. Centrifuge94, Balkema, Rotterdam, pp. 289-294. Allersma, H.G.B. 1996: Using digital image processing in field measurement. Geotechnique 46(3), pp.561-563. Goodings, D.J., 1984: Relationships for modelling water effects i n geotechnical centrifuge models. Proc. Symp. Application of Centrifuge Modelling to Geotechnical Design, Manchester: 1-24. Kimura, T., 0. Kusakabe, J.Takernura, 1994: Editors Proceedings Centrifuge 98, A.A. Balkema, Rotterdam.

452

sfabil‘fy EngineerW yagi, Yamagami & Jiang U 1999Balkema, Rofferdam, ISBN 90 5809 079 5

Reinforcement’s effects in the tank-model prediction of slope failures due to rainfalls Masayoshi Shimizu Faculiy o j Engineering, Tottori Universih;Jupurz

ABSTRACT: In 1983, heavy rains caused senous disasters including slope failures in San-in Regon, Japan. Using undisturbed samples taken at a slope that failed, tnaxial and unconfined compression tests were conducted. Results say that not only physically dscontinuous plane such as a crack but also non-uniformity of mineral composition can form weak planes. It was verified that the rain in 1983 is the heaviest by Characterizing hourly rainfall data from 1976 to 1997 in two ways: one is using R-T diagram and the other based on the tank model method. One of conclusions is that, although reinforcement techmques adopted as countermeasures for disasters in 1983 are effective up to present, the effectiveness would be verified by possible record-brealung rains.

1. INTRODUCTION One purpose of this paper is concerned with mechanical view of slopes. It is crucial to assess mechanical properties of geomaterials for examining the mechanical stability of a slope. Geomaterials have to be tested in the undisturbed conditions. In 1983, heavy rainfalls caused many serious disasters including slope failures in Shimane Prefecture, San-in Regon, Japan. Slopes that failed in 1983 have been reinforced. The main purpose of this paper is to examine the effectiveness of the reinforcement. The reinforcement would be effective unless reinforced slopes fail in a rain heavier than or equal to the rain in 1983. Whether a rain is heavier than another rains or not has to be examined through the characterization of rains by an objective manner. The duration of raining T and the amount of the rain R during T are important factors characterizing the rain in relation to disasters due to rains. In this sense, a rain can be characterized in the R-T diagram. Another way of characterizing rains is utilizing a tank model. The tank model was originally developed as a method for predicting discharge in hydrology and it is used for that purpose. The tank model, however, was used to predict the occurrence of disasters such as slope failures due to rains by Michiue & Kojima (1981) and the effectiveness of the method has been verified (Shimizu & Sugimoto, 1984a; Shimizu, 1988). In the tank model method, a parameter, ‘storage height’ St, representing the height of the water in tanks is used as an index with which the occurrence of disasters is predicted. A rain can be characterized by

453

t h s parameter St. For two purposes of this paper, i.e. the examination of the effectiveness of reinforcement of slopes and the assessment of mechanical properties of geomaterials of a slope, a failure that hlled 13 people at a site in Hamada City, Shlmane Prefecture, in 1983 is studied as a representative case. The first half of this paper describes geographical, geological and geotechnical conditions based on the investigation and researches previously made by the authors . Geotechcal researches include biaxial tests on undisturbed samples of the soil taken on the failure surface and uniaxial compression tests on specimens cored from rocks that have fell down the slope at the failure (Shimizu & Sugimoto, 1984b). The second half discusses the characterization of hins on the basis of analyses of hourly rainfall data observed at a meteorologcal station in Hamada City from 1976 to 1997.

2. DESCRIPTION OF THE SLOPE 2.1 Outline Figure 1 shows the plan of the site where four slopes failed on the 23rd July 1983. The biggest slope failure occurred at 12:30. The debris attacked houses at the foot of the slope and killed 13 people. The section of the slope is shown in Figure 2 with geologcal information. The investigation of the site showed that the thickness and volume of the sliding mass, which had fallen down, were about 20m and 15,000m3, respectively. The inclination of the slope’s surface was

3. STRENGTH OF UNDISTURBED SAMPLES 3.1 Samples Three kinds of samples were taken: undisturbed block-samples of heavily weathered and soft diorite, which were taken at the point indicated by the mark 0 in Figure I , rock masses of rhyolite having fallen down in the debris, and Physical and mechanical properties of these samples will be described separately in the following. 3.2 Weathered diorite rocks Some of the undisturbed samples were taken in the way. that the author had employed for taking undisturbed samples of weathered granite (Shimizu, 1983) and some with many cracks in the way developed by Nishida and Aoyama (198 1). In the latter way steel nails 15 cm in length were forced into the ground so that they surround an area to be a block sample. The rock of the ground was so soft that nails could be forced into with hammer. X-ray diffraction patterns were examined on two fractions of one of undsturbed samples (Figure 3). The sample A is a fraction of the white part that is rather uniform in color and texture. The sample B is a fraction of the part that appears relatively black. Minerals common to both samples are quartz and chlorite; the peak for feldspar is not high. The peaks of 28=8.8O and 17.6', observed only for the sample B reflect the existence of black mica and montmorillonite, respectively.

Figure 1: Plan of the site.

Figure 2: Section and geologCa1 Profile m

Of

the 'lope

w. over 30". At the investigation on August 2, 1983, water was flowing with a murmur from the point marked with X in the figure. However on November 5 , no water flew. From the measurement of the water table in bonngs dug at four points in different height, the groundwater surface was supposed to be as shown in the figure. From these observations, we can assume that the levels of groundwater's surface arose as well as its pressure on the sliding surface to much higher level than those before the failure, which led to the loss of the stability of the slope. 2.2 Geological features of the slope The slope comprises masses of crystalline schist, rhyolite and diorite. All the masses are heavily weathered with cracks in particular along faults. The thickness of the mass having fallen makes us suppose that the weathered mass had developed as thick as more than 20m. The weathering has deteriorated diorite rocks to be clayey soft-rocks and crystalline schist and rhyolite rocks to be fissured.

Figure 3: X-ray diffraction patterns of the dioritic sample. Triaxial compression tests were conducted on undisturbed samples. Specimens of cylindrical form, 5 cm in diameter and 10 cm in height, were prepared by the following way: at first sample blocks were frozen with liquid nitrogen, and cylindrical specimens for triaxial tests were cored by using a boring machine.

454

The coring bit of the machine is a special one designed for coring weathered granite soft rocks (Shimizu, 1990). Each specimen was photogaphed both before and after the triaxial test (Figure 4). The comparison of photos could help us to examine the effects of the tone of color and the existence of cracks upon the mechanical behavior in triaxial tests. The tone of color seems to retlect the non-uniformity of mineral composition as pointed out in the reference o f Figure

3.3 Rhyolite rocks The blocks ot' rhyolite that we took in the debris deposit had Fallen from the upper part of the slope; they had been separated by existing cracks. Each block

I

3.

Figure 5 : Stress-strain relationships.

Figure 6: Effective stress paths.

itself appeared intact without clayey material although they have flow texture. Blocks were cored to be cylindrical specimens, 3 cm Figure 4: An example of photos taken before (left) and in diameter and 7 cm in height, by using a boring after the test (right) machine. The direction of the coring was varied so that the direction of the flow texture, p, varies (See the Tnaxial tests were conducted under the conditions of figure inserted in Figure 7). Unconfined compression consolidation-undrained (CU) with measurement of tests were conducted on specimens that have different pore pressure. Figures 5 and 6 show the effective values of p. Results are shown in Figure 7, in which stress paths and stress-strain relationships, the unconfined compression strength qu and the secant respectively. Young's modulus E, are plotted against the angle p. E, We observe in these figures two distinctive types of was determined from the secant corresponding to qJ2. behavior: one is strain-hardening but less rigid type for This fi,we shows that both qu and E, take relatively specimens No. 3 , 3 and 5 ; the other is strain-softening low values for p higher than 65". The direction of and relatively rigid type for specimens No. 1, 4 and 6. failure planes for all the specimens were also in this The observation of photos showed that the strainhardening type is for specimens of which failures occurred along preexisting cracks or plane parts of black-color tone, and that the strain-softening type corresponds to specimens in which failure planes were neither coincident with preexisting cracks nor with black-colored plane parts. Different values of strength parameters, Cp' and c', were determined between two different types: and c'=58 kPa for No. 2, 3 and 5 ; and Cp'=39" and c'=66 kPa for No. 1, 4 and 6. This difference in the value for strength parameters, especially, for $', as high as about loo, reflects not only the existence of cracks but also the non-uniformity of mineral composition. As a conclusion, physical discontinuity, for example, due to cracks and non-uniformity of Figure 7: Unconfined compression strength qu and mineral composition such as micaceous composition secant Young's modulus Es versus the direction of form 'weak planes', which reduce inacroscopic shear flow texture p for rhyolite rock samples. strength. 455

range of angle, which indicates that the direction of the flow texture of rhyolite can be the mechanically weak direction. According to the Deere,s classification which is used to classify rocks from the relationships between E, and qu, the data shown in Figure were plotted in the lowest end for intact igneous rocks.

According to meteorobY~warm O r stationay fronts and typhoons Cause h e a y rains in Japan. A rain would be characterized with the consideration of these meteorological causes. However, the detailed data on these causes other than records of rainfalls are not available particularly for disasters several decades ago; records of rainfalls have been provided as fundamental records for long years. 5.1 R-T diagram

4. REINFORCEMENT OF SLOPES

A usual way of characterizing a rain is to use the duration of raining and the amount of rain. A rain will continue for some duration of time and stop; after stopping, it may rain again. Therefore, the duration and the amount depend on whether we include the duration ofthe stopping in that of the rain or not. The definition of a rain depends on how to treat the time-duration, AT, during wtuch the raining was stopping. BY setting a value of AT, the raining with the intemption less than AT or equal can be defined as a rain. Suppose that it rains for some time, stops for the duration longer than AT and rains again; in this case the raining is w w d e d to comprise WOrains. Analyses were made using data on hourly rainfalls, observed at a meteorological station, locating Hamada CW, S h h a n e Prefecture, from 1976 to 1997. Figures 8 (a) and (b) show the results, in which the relationships between the duration of raining, T, and the amount of rain, R, during the duration T. The figure (a) corresponds to the case when and (b) AT=12 hours. Only rains of R more than 150mm are shown for clearness. Figures 8 (a) and (b) show that the rain from July 22, 1983 was record-breaking in the examined range of Years that Precede with regard to the amount R. If the rain is counted as the same rain as that from July 20, the amount R will be more than 500 mm. The a m u n t R of the rain recorded from July 15, 1988 exceeded that of the rain of 1983. This rain caused floods and broke banks along two rivers in Hamada City but did not cause serious slope failures other than river banks. By comparing figures (a) and (b), we see that it rained before and after this rain for the time as long as about 10 days. Another rain of July 7 or 8, 1997 caused disasters 5. CHARACTERIZATION OF RAINS due to slope failures in mountainous area. This year, fortunately, disasters were rather insignificant so that This section discusses whether the rainfall in July no one died. 1983, which caused serious disasters in San-in Region, was really record-breaking or not, comparing with 5.2 Tank-m~delmethod rainfalls that we experienced before and after that time. The tank n d e l used for analyses is the Same as that It seems that the tern 'record-breaking' is too often used in previous studies (Figure 9; Shimizu, L9xx). used without proof for rainfalls having caused Parameters 9i (i=1,2,3) represent the rate of disasters. Whether a rain was record-breaking or not discharges; Pi (i=l,2,3) the rate of vertical percolation has to be examined by defining or characterizing the or infiltration into ground; S, (i=1,2,3) the height of rain in an objective or quantitative manner. Here two water or storage height in tanks; a, (i=l to 4) and bi methods of characterizing rains are examined: one is (i=1,2,3) are coefficients to control the discharge and based on the duration and amount of a rain and another Percolation; and L, (1'1 to 4) the height of outlets. For on the concept of the storage height used in the tankmodel method. In the district, as well as the main slope that failed to kill 13 people, indicated as @ in Figure 1, another slopes failed, too, or became unstable. In particular, the slope in the west of the main slope, tension cracks were observed. Countermeasures were adopted to prevent further loss of human lives and estates of inhabitants in the district. As stated in the preceding section, the main slopefailure occurred due to the rising of the groundwater's level and therefore its pressure. The most appropriate countermeaSure for possible failure in future was considered to keep them low even in heavy rains. For this purpose, borings for drainage were dug at ten different vertical levels, and 7 or 9 at a level. Total number of borings reached 80. Usual level of groundwater could be lowered by two to one meters. Boring tubes were fixed in retaining walls constructed on the slope surface at those ten vertical levels. In 1999, more than 15 years after the failure, a bamboo forest develops in the surrounding area outside the area where borings were dug, but no inside the area. Considering that the bamboo can grow only in wet conditions, the cowtemeasure is effective in the sense that it could keep the groundwater level low. This c o u n t e m e a u e can be regarded as an indirect reinforcement for the main slope. As for the slope in the west of the main slope, concrete frames were constructed on the surface to make the slope more stable. In 1999, a grove mainly of bamboo is growing so that the frames can not be viewed. This direct type of reinforcement appears to be also effective.

456

Figure 9: The tank model used for analyses.

Figure 8: R-T diagrams for rains from 1976 to 1997. our purposes, the total height of storage St(=SL+S2+S3) is of importance. The intensity of rainfall r to be input is hourly rainfall. Table 1: Values of coefficients for the tank model. Discharge Percolation Height of outlets coefficients coefficients 1h o u r lhour mm a l a2 a3 a4 bl b2 b3 L1 Lz L3 L4 .15 .10 .05 .01 .12 .05 .01 15 60 15 15

Figure 10: Variations of total storage height St with time in selected years.

Whether slope failures occur or not depends on not only the level of St but also the duration in which the level continues. From this point of view, Figures 11 (a), (b) and (c) were prepared. The proportion of the In Figure 10, the variation of S, with time is shown duration in which S, exceeds a certain value X, only for particularly selected years; the years in which T(S0X) to the total time T (=a year) is plotted against the high amount of a rain R was recorded were to the value X. All the years from 1976 to 1997 were selected (see Figure 8). examined; for clearness three figures are provided for In the previous studies, the critical storage height SIC every several years. For the comparison, the data for was determined to be 157mm in Hamada City the year 1983 is shown in all the figures. (Shimizu & Sugimoto, 1984a; Shimizu, 1988),. The We can see in these figures that how much more value was determined on the basis of the criterion that heavily it rained in 1983 and in 1988 than in other we could predict 85% of those slope-failures which years. Comparing these two years, however, the rains would fail due to the rain in which S, exceeds StG. In in 1983 was heavier than those in 1988 because, for this regard, the level of St=157mm is shown in the example, the time proportion for which St exceeds figure with a dotted line for each year. At a glance, this 150mm reaches 0.3% in 1983 and 0.15% in 1988. level was reached in 1983 and 1988.

457

Rains in Hamada City, Shimane Prefecture, Japan, from 1976 to 1997 were characterized in two ways. One way is to use R-T diagram, where T is the duration in which a rain continues and R is the total amount of the rain during T. The other is to use a parameter for the tank model, the total storage height st.

Through these two ways of characterizing rains, it was verified that the heavy rains in 1983, which caused serious disasters in San-in Region, Japan, was record-breaking. After that year, in 1988, so heavy rains attacked this regon that rivers' banks broke and flood occurred, however tremendous disasters dld not occurred in slopes other than river banks. Although the rain of 1988 was really so heavy that the amount of rain R was the highest in the examined years, the duration in which St was higher than the critical value was shorter comparing with the rain of 1983. Slopes that failed or deteriorated due to the rain in 1983 were reinforced by direct or indirect techniques. Up to present, 1999, the reinforced slopes have been kept stable. Although the effectiveness of reinforcement can not be denied, we have to continue to observe their stability because we have not yet experienced a rain heavier than the rain in 1983 in the sense that S, in 1983 has not been exceeded. ACKNOWLEDGMENTS The Author sincerely thanks Mr. T. Inoue, Engmeer of Shimane Prefecture, and Mr. A. Tsumiya, Engineer of WESCO, Co., Ltd. for their help in field investigation. Mr. N.Sugmoto, Engmeer of Muramoto Kensetsu Co. Ltd., former student of Tottori University, is also acknowledged for his co-operation in conducting laboratory tests and investigating the site.

REFERENCES

Figure 11: Characterization of rains from 1976 to 1997. T(SPX)/T vs. X

6. CONCLUSIONS Results of triaxial and unconfined compression tests on undisturbed samples of weathered diorite and

rhyolite rocks showed that not physical but also weak planes to mineralogical discontinuity deteriorate macroscopic shear strength.

Michiue, M. and Kojima, E. 1981. study of forecast for occurrence of land slides due to heavy rain storm. Reports of Faculty of Engineering, Tottori University, 12:167-178. (in Japanese) Nishida, K. and Aoyama, C. 1990. Evaluation of permeability of residual soil. Residual Soils in .Japan. JSSMFE. 133-136 Shimizu, M. and Sugimoto, N.1984a. Application of a method for predicting occurrence of slope failures due to rain falls, Report of Faculty of Engineering, Tottori University. 15: 130-140. Shimizu, M. and Sugimoto, N. 1984b. Strength characteristics of strongly weathered rocks taken at a slope-failure site. Proc. of the 31st Annual Conference of Civil Engineering. JSCE. 3:633-634. (in Japanese) Shimizu, M. 1987. Weathering and strength behavior of granite Soils. proc. Of8th Pun-American conf: on sMrE3 2: 141-152. Shimizu, M. 1988. Prediction of slope failures due to heavy rains using a tank model. Lundslides. Proc. of' (he Fdth lnt. Symposium on Lundslides. Balkema. 77 1-776.

458

Slope Stability Engineering, Yagi, Yamagami & Jiang k-' 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Investigation of danger rainfall prediction system for natural and cut slopes H. Miki, A. Fujii & M. Furuta Soil Mechanics Division, Public Works Research Institute, Ministry of Construction, Tsukubu, J n p n

ABSTRACZIt is difficult to predict both the quantity of rain that must fall for a cut and natural slope to collapse under its effects and when the collapse will actually occur. This means that under present conditions, warning and danger rainfall levels are established by referring to the relationship between past rainfall records and disasters in the surrounding area to empirically set rainfall criteria for closing roads. In the past, the authors have conducted studies based on a series of field monitoring results to determine wheather it is poscsible to quantitatively evaluate stability and danger rainfall levels at specific slopes based on the rainfall permeation and the destabilization mechanism. This paper proposes a survey and analysis system that can quantitatively evaluate the danger rainfall level of a specified slope: a task formerly very difficult to perform to a degree adequate for practical use.

(1) Slope survey : The actual state of the slope is surveyed in order to obtain the analysis model and basic parameters necessary to perform a stability evaluation. The items surveyed are the shape of the slope, seepage properties, and mechanical properties, and these are tested by means of both in-situ experiments

1 PURPOSE OF THE STUDY Because of the extreme difficulty in predicting the quantity of rainfall that may cause the failure of a natural or cut slope and when such a collapse will occur, the establishment of rainfall levels to serve as standards for closing roads is now generally done based on experience with reference to the relationship between past rainfall records and disaster records in the region where the road is located. The authors have drawn on a series of monitoring results to conduct a study to clarify to what extent it is possible to quantitatively evaluate the rainfall that will cause the failure of a specific slope (referred to hereinafter as the "danger rainfall") based on the rainfall seepage and accompanying dmtabilization mechanism. This paper introduces a proposal for a survey and analysis system that can be used to perform the hitherto difficult feat of quantitatively evaluating the danger rainfall of a specific slope and illustrates typical examples of the application of the proposed system.

r

I-

In-situsurvey -y- Soil testing 7

Monitoring

Rainfallgauge

oil mdsturemeter

Sampling Moisturecontent n-situ seepagetesting testing

ore pressuremete

Analysis precision improvement

Purp0se:recreatethesite Resultconfirmationofthe usefulness of theanalysis method

2 STUDY OF THE NATURAL AND CUT SLOPE DANGER RAINFALL PREDICTION METHOD

t

emage tlow analysis Purpose:clar/ficationofthe rainfallquantityqrior tothe failure Result failure at Xmm of cumulativerainfall

2.1 Overall Procedures Figure 1 is a flow chart of the proposed a natural and cut slope danger rainfall prediction method. The basic overoil evaluation procem is divided into three stages.

I

t

Figure 1 Slope dunger rainfall setting process

459

I

Stabilityanalysis Purpose:clarificationofthe degree of saturationprior to the failure Resultfailure at satur ationof X %

and laboratory experiments using specimens obtained at the site. (2) Slope monitoring :This monitoring is performed to clarify the rainfall seepage properties on the slope at the site in order to obtain information needed to bring the analysis model and parameters established tentatively in stage (1) closer to actual conditions at the site. It is vital to perform the monitoring using appropriate methods in order to improve the precision of the analysis because the data obtained through this monitoring b information directly related to the establishment of the parameters of the seepage model. The monitoring is performed by installing soil moisture meters, pore pressure meters, water level indicators, and other monitoring instruments to measure changes continuously in water content, the water level, etc. (3) Slope analysis and danger rainfall forecasting : Danger rainfall forecasting is performed through both seepage flow analysis and stability analysis. Seepage flow analysis can be used to forecast changes in the degree of saturation of the interior of a slope under the effects of rainfall of various intensities by developing a slope seepage model that represents the response and behavior of the actual slope related to rainfall seepage. Stability analysis can forecast the stability of a slope under various seepage states by developing a slope stability mechanical model based on the relationship between the saturation and strength of the slope obtained based on laboratory soil experiments. By performing a failure simulation based on the results of the above two kinds of analysis, it is possible to link the state of the rainfall to the degree of stability of the slope in order to set the danger rainfall at which the slope may fail.

figure 2 Example of a detailed topographical clwifiation

topographical maps and records of past disasters. At the site, more detailed visual observations focussed on the natural and cut slopes selected by the above procedure are carried out to estimate the latent danger of a failure of the slopes and the form of failure likely to occur. Then traverse lines are established on the natural and cut slopes which are assumed to be at the highest risk of failure in light of their geological and topographical nature, vegetation conditions, disaster occurrence history, and spring water situation and with reference to the same conditions on nearby natural and cut slopes. (2) Internal slope exploration : After the traverse lines are determined, the geological structure of the interior of the slope is investigated using the following exploration methods. a) Hand sounding staff(Figure 3) : A steel rod with a diameter of about 5mm that can be inserted into the ground manually. It is a good method that provides test results in a few seconds for sites with the weathered layer lem than lm. It has a small slit at the end that allows the user visually check the soil at the insertion depth after pulling it out. It is a method used to perform a simple survey in order to determine whether or not the weathered layer is deeper than lm.

2.2 Proposal of Practical Slope Survey Technology Because the geological structures of natural and cut slopes are very inhomogeneous, it is very difficult to correctly verify their internal geological structures. This research project was a study of the application of various kinds of survey technologies in order to ebzabliih survey methods that are simple and can be used to obtain information with the maximam possible practical precision. The slope survey is divided into the following three StageS.

(1) Preliminary survey : The interpretation of topographical maps and photographs completed before entering the site focuses on topographical classification and vegetation. The first step is the classification of the slope into detailed topographical features such as the valley top, knick line, and failed ground(F4gure 2) in order to estimate the form of the failure and at the same time prepare for a field survey centered on those natural and cut slopes that are assumed to be at high risk of failure while referring to

Figure 3 Hand sounding 6 h f f Figure 4 Simple penetration test device

460

Figure 5 Example of a summary of the state of the the state of the interior of a slope

b) PWRI type simple penetration test(Figure 4) : A

seepage properties. These are seepage testing, pF testing, etc. The specimens used are ones obtained by block sampling or other undisturbed specimen collection method must be used. Because the results of these tests are seriously effected by disturbance of the specimens. c) Soil tests related to strength : These tests are performed to confirm the strength-related properties of the soil. The test items include box shear testing, triaxial compressive testing, and so on. A study of the failure mechanism of a natural and cut slope must account for the fact that it is almost impossible to account on the internal friction angle component of the soil cover and that a major cause of failure is a reduction in strength caused by soil moisture. For this reason, the test must be done at a low confining pressure of l.0kg/cm2 or less, and if possible, at a confining pressure of 0.2kg/cm2. The box shear test method is recommended because it permits this to be done with ease. These teshs should also be done using undisturbed specimens.

rod with a diameter of 16mm and a cone on its tip is equipped with detachable 5kg weight The weight is dropped from a height of 50cm to push it into the ground to investigate the penetration resistance of the interior of ground. It can investigate the ground down to a depth of about 3m, and because it can obtain specific and continuous strength information in a relatively short time, it is an extremely useful method of investigating a natural and cut slope. c) Physical exploration : Other new exploration technologies developed to quickly obtain data regarding the ground over a wide area include the underground radar method, electromagnetic wave reflection method, and the specific resistance exploration method. Since it is difficult to convert data obtained by these methods into actual strength constants, it is necessary to use them in conjunction with a direct test such as the PWRI type simple penetration test An actual survey begins with a simple hand sounding staff survey followed by the use of more detailed survey methods considered necessary in light of the results of the simple survey. The data obtained is recorded on a single diagram to summarize the interior condition of the slope(Figure5). (3) Soil quality tesbs : Soil quality tests are performed in order to confirm the properties of each soil layer categorized using the exploration technologies described above. The soil quality tests include in-situ tests done at the same time as the slope interior exploration and laboratory soil tests of specimens of soil taken from the site. a) Soil testing related to basic properties of the soil specimens : The soil testing is done to confirm a fundamental categorization of the soils. The tests performed include wet density testing, dry density testing, specific grain testing, moisture content testing, and grain size analysis. These are the tests that can also be done to the disturbed specimens. b) Soil testing related to seepage : Tests are performed to confirm properties related to the soil's

2.3 Proposal of a Practical Slope Monitoring Method

The following precautions are observed in order to continuously metss changea in saturation inside a slope and the deformation of the slope in order to obtain stable long-term data. a) Soil moisture meters (Tensiometers)(Figure6) : A soil moisture meter is a device with a porous cup filled with deaerated water on itS. tip (made of unglazed porcelain to allow a little water to pass through) that is also equipped with a sensor to measure the suction (force that draws water) by sensing the force the moisture adsorbs from the area where the cup presses tightly on the soil. The data obtained is represented by the unit gkmH20 (pF value = log10(suction value)). If a model of soil moisture meter that can also measure positive pressure is selected, it can be substituted for a pore pressure meter. Hut because a meter of this kind is not as sensitive as a pore premure meter, it is better to also install a separate pore pressure meter when it is necessary to obtain real-time water p r m u r e fluctuation data. 46 1

A soil pressure meter is installed by drilling a vertical hole with a hand auger etc., inserting the meter in the hole, and pouring in slurry so that the cup adheres closely to the soil. This must all be done carefully to prevent any damage to the cup on the tip. Accurate evaluations can be performed by installing this meter at the end of the slope where rainwater is likely to collect or at a location where the weathered layer is deeppigure 7). A data logger records data at intervals ranging from 15min. to lhr. In s l o p suscep tible to severe dryness, the deaerated water inside these meters is exhausted and they stop working in between one month and one week. As necessary, maintenance workers have to replace the deaerated water. Although not done in this case, it is possible to track the seepage of a slope in real time by installing telephone lines to transmit the data to an office. b) Pore pressure meterpigwe 8) : Pore pressure meter measures the water pressure generated when a water level appears in the soil and converts the pressure to data. These meters can be installed any locations where water level will certainly appear because this meter basically does not respond where a water level fails to appear. The model of pore pressure meter selected must perform extremely precise measurements because it will be installed to detect the failure of shallow layers. Pore pressure meters are installed in boring holes and, as in the case of soil moisture meters, at locations where rainfall collects easily. As in the soil moisture meter case, the measurements are done at short intervals of time so that the process of seepage can be tracked closely. One good feature of this type of meter is that it requires less maintenance than a soil moisture meter. Because there are some slopes where a water level does not appear, this meter is installed after confirming to the greatest degree possible that a water level exists. c) Miscellaneous instruments : Because the data obtained with soil moisture meters and pore pressure meters is closely related to the rainfall, a rainfall gauge

Figure 6 k%oil moisture meter

is installed close to the other measurement locations to measure the rainfall. The installation of inclinometers, extensometers, and other instruments are useful to measure the deformation of a slope. But they are not necessarily required where the main object is to gain an understanding of the seepage properties of the slope. The data obtained using the aforementioned monitoring techniques is summarized by plotting them on a common time axis(Figure 9).

2.4 Analysis and Prediciion Method

The results of the in-situ survey and monitoring described above are reflected in an analysis model and seepage flow and stability analyses are performed to predict the danger rainfall. The following sections present methods of reflecting the various kinds of data obtained from the in-situ survey and monitoring in the analysis model. a) Seepage flow analysis : Seepage flow analysis is done to investigate the behavior of moisture that seepage a slope following a rainfall. The slope shape, weathered layer depth, moisture properties curve, the specific coefficient of permeability, coefficient of permeability, rainfall, etc. obtained from the site are entered into the analysis program in order to find changes in the water content (degree of saturation) at various points inside the ground. As explained in Section 2.1, in order to increase analysis precision, it is important to add the rainfall data obtained by the rainfall gauge to the analysis model and repeatedly perform analysis while making fine adjustments to the input parameters until the soil moisture content output by the analysis model conforms as closely as possible to the data from the soil moisture meter that has been buried in the slope in order that the analysis model closely resembles the actual slope. b) Stability analysis : Stability analysis is performed to investigate the relationship between a slope's stability and the increase in the moisture content of the slope caused by rainwater seepage.

Figure 7 Example of instrument installationlocations

462

Figure 8 Pore preasure meter

Figure 9 Example of a aummarization of monitoring results

The slope 6hape that basically serves as the analysis model is a stratification model consisting of the bedrock and weathered layer. The calculation performed by the analysis model treats the weathered layer and bedrock layer as an infinite slope. The incline and weathered layer depth of the slope may be entered as the maximum inclination and the maximum depth of the slope. And the cohesiveness, internal friction angle, and wet density are obtained by using relationship with the saturation found from the results of the soil test and varying the saturation in 10% steps as it is entered. c) Overall evaluation : Because the stability analysis clearly shows the state of the moisture (degree of saturation) of a slope where the safety factor of the slope is less than 1.0, the seepage analysis model is used again to study what kind of rainfall conditions must be provided for the corresponding saturation to be achieved. Rainfall intensity between 5 and 30mdhr may be consecutively applied because simple consecutive rainfall more readily clarifies the failure conditions.

tions that closely resemble the actual site can be obtained by finely adjusting the parameters. The approximation method is to increase or decrease the coefficient of permeability, pF curve, specific coefficient of permeability etc. to an extent that does not deviate sharply from the actual test values that were initially entered. And this definition is performed by focussing on the decline and recovery of the pF value and the delay between the rainfall and the rise in the saturation. b) Stability analysis : Figure 12 presents the results of providing the relationship between the saturation of the slope obtained experimentally with c ,cl) ,y t to

3 EXAMPLE OF AN APPLTCATION OF T€ESYSTEM

This section of the paper introduces a case where the above danger rainfall establishment system was applied to a natural and cut slope facing a national highway in Yamanashi Prefecture. Figure 10 shows the site layout The survey revealed that it is a steep slope with an average gradient of 4Odegrees and that it6 top is almost completely covered with thick deposits of collapsed soil and that bedrock is exposed at its bottom. a) Seepage flow analysis :Figure 10 also illustrates a FEM mesh modeled basedon information obtained from an insitu survey. Figure 11 defines the soil moisture changes on the slope obtained by monitoring and the soil moisture changes in the slope model obtained by analysis by superimposing the two results on a single axis. It reveals that a model indicating soil moisture fluctua-

Figure 10 site condition6 and seepage flow analysis no del

Figure 11 Similarityof monitoring resdts and analytical results

463

calculate the safety factory by varying the saturation for the model of the site shown in the upper right part of the figure. As the saturation rises, the safety factor against failure gradually declines until the safety factor falls below 1.0 at a saturation level of 80%. From this graph, it can be concluded that the slope will fail at a saturation of 80% or more.

safety factor below 1.0. And at a rainfall intensity of 5mm, the safety factor will stop declining at 1.3, a result of the fact that at this intensity, the rainfall seepage and L\e drainage of moisture from the bottom of the slope are balanced, maintaining the saturation at a constant level. In this case, it is possible to predict that when rainfallof 20mdhr continues, the failure could occur at the minimum cumulative rainfall level of 340mm and at a rainfall intensity of S m d h r , the safety factor stops declining at 1.3. This is because of the fact that at this intensity, the rainfall seepage and the drainage of moisture from the bottom of the slope are balanced, maintaining the saturation at a constant level. And results of the above study for a number of other slopes indicate that this is a plausible result. 4 CONCLUSION AND RECOMMENDANTIONS

R g w e 12 Saturation and safety factor decline of the slope

c) Overall evaluation : The next step was the introduction of a hypothetical rainfall to set the danger rainfall of the slope. Figure 13 shows a summary of the cumulative rainfall - safety factor (calculated from the degree of saturation) relationship. This shows that the cumulative rainfall that would cause failure varies according to rainfall intensity. As an overall trend, the higher the rainfall intensity, the more rapid the rise in the degree of saturation and the lower the cumulative rainfall required to reduce the

The proposed danger rainfall prediction system for natural and cut slopes that feeds back rainfall seepage monitoring results for analysis purposes can be used to quantitatively predict the danger rainfall of a specific slope. Future research themes may include the development of simple soil survey methods to be used to accurately mess the strength properties of soil, the continued study of failure predicting based on the use of monitoring instruments, and research on ways to apply these to actual road management.

Figure 13 Cumulative rainfall - safety factor relationship

464

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Predicting rainfall-induced slope failures from moisture content measurement M. Nishgaki, A.Tohari & M. Komatsu Department of Environmental Design and Civil Engineering, Okayama Universio,Japan

ABSTRACT: This paper presents the results of a series of laboratory slope failure experiments conducted to examine the effectiveness of monitoring moisture content to predict the occurrence of rainfall-induced slope failure. Numerical seepage analyses were also conducted prior to the experiments to identify the hydraulic response of the model slopes to the simulated rainfall. The changes in moisture content and pore-water pressure were monitored during rainfall infiltration and at the initiation of failures. The experiments showed that moisture content of soil slope increased to the saturated value at the time of failure. This indicated the possibility in predicting the critical time of failure initiation by monitoring the change in moisture content. Upon advantages of moisture sensing instruments over pore-pressure measuring instrument, therefore, monitoring of moisture contents during rainfall is more effective and more reliable than that of pore pressures to predict failure occurrences. The results of precise monitoring of moisture contents in the field to predict the rainfall-induced slope failures are encouraging. A series of small-scale experiments on rainfallinduced slope failure were conducted to examine the effectiveness of monitoring the changes in moisture content to predict the occurrence of rainfall-induced slope failures. This investigation forms part of a program of studies at Okayama University into the development of method of predicting the occurrence of rainfall-induced slope failures.

INTRODUCTION Rainfall-induced slope failures are among the most dangerous and destructive natural hazards that affect humans and human works. Worldwide, especially in the tropical slope areas during high rainfall intensity, these mass movements have claimed untold numbers of casualties and millions of dollars in property losses every year. Recently, there have been some attempts to find the ways to predict rainfall-induced slope failures. Sammori, et a1 (1996) investigated the effect of soil thickness on slope failure initiation, and pointed out the possibility of predicting the initiation of rainfallinduced slope failures by monitoring soil thickness and physical soil properties. However, this approach only applies to soil slopes with uniform thickness. Predicting the occurrence of slope failures may also involve monitoring the change in pore-water pressures of the soil during rainfall. Nevertheless, the present-day devices for measuring soil suction still show some limitations, and require special care and regular maintenance when used for a long-term measurement activity (Rahardjo et al. 1998). Therefore, considering the practical limitations of the above-mentioned methods, the findings of an effective and reliable monitoring method for predicting failure time are of major importance to mitigate loss of life and property.

2 SOIL PROPERTIES

Two different types of soil were used in the experiments, namely river sand and residual granite soil. The properties of the soils determined by laboratory experiments are summarized in Table 1. Table 1. Properties of soils used in experiments Soil type D,, D,,JD,,, I Density of I K, (mm) particles, (cds)

I

River sand Residual granite soil

465

I

I

0.175 0.157

7.14 4.63

p, (gr/cm’> 2.69 2.70

0.064 0.0072

I

Figure 1. Overview of experimental apparatuses induced in each of model slopes by simulating the rainwater infiltration into the model slope. The rainfall intensity was set at 100mm/h for all experiments. The measurements focused on the changes in moisture content (0) and pore-water pressure just prior to slope failure. Prior to each experiment, the process of infiltration into the model slope was analyzed using a finite element method, UNSAF code (Nishigaki, 1987). Each analysis used the initial pore-water pressure in the slope as the initial boundary conditions, and the respective SWC curves shown in Figure 2.

3 EXPERIMENTAL APPARATUSES

The basic apparatus consisted of a landslide tank in which one-meter high model slopes could be constructed, and brought to failure by the simulated rainwater infiltration. The geometry of the model slopes was chosen not to confine the development of failure surface and the occurrence of slope failure. The model slopes were instrumented with porewater pressure transducers (P1-P8) and moisture sensors (Amplitude Domain Reflectometry type: ADR I-ADR4). The instruments were mounted in custom fitting at certain points on the vertical section of the model slopes, and were connected to a microcomputer-based data acquisition system as illustrated in Figure 1. Each of the instruments was logged at approximately 60 seconds intervals.

4 EXPERIMENTAL PROGRAM In the experiments, two homogenous model slopes were constructed under the specific properties summarized in Table 2. The changes in the initial hydrologic condition, and the instability were Table 2. Properties of experimental model slope

1 Exp. I No 1 2

I

Soil type Sandy soil Residual granite soil

I

I

Slope angle (") 45 35

I Average I Porosity I fl

0.081 0.17

Figure 2. Soil-water characteristic curve of river sand used in Case 1.

0.454 0.342

466

5 EXPERIMENTAL RESULTS 5.1 Failure process The results of transient seepage analyses demonstrated the simulated rainwater infiltration had introduced the developments of groundwater level in the slopes and the formation of seepage face near the toe of the slopes (Figures 3 and 4). As far as the prediction of slope failure is concerned, the development of seepage face can be indicative of the generation of the instability of the slope.

Figure 5. Change in moisture content with time during experiment 1. 5.2 Case I : moisture content at failure Detailed moisture content measurement records for all moisture sensors are shown in Figure 5. The records showed two phases of significant increase in moisture content. The first phase was associated with the ingress of the wetting front by which the soil reached about 50% degree of saturation. This saturation condition lasted until the groundwater level was developed in the slope. The increase in groundwater level had resulted in the next phase of increase in moisture content and saturation. Moisture sensor ADRl indicated that the moisture content of the soil near the toe of the slope reached the saturated value at failure. This clearly suggested that saturation of the toe of the slope contributed to failure initiation.

Figure 3. Level of groundwater at the time of failure in experiment 1. Experimental evidences indicated that the development of seepage face at the area near the toe of the slope resulted initially in the generation of tension cracks just above the saturated soil. In sandy soil slope (Case l), the tension cracks introduced instability to the whole portion of the slope. In contrast, in residual granite soil slope (Case 2), tension cracks only induced local instability on saturated soil portion. Therefore, the experiments have demonstrated the critical influences of seepage face development on local and overall instability.

Figure 4. Level of groundwater at the time of failure in experiment 2.

Figure 6. Variation of pore-water pressure with time during experiment 1.

467

5.3 Case I : Pore-wuter pressure at f d u r e

increase in groundwater level indicated by ADR3 and ADR4 resulted in the next Occurrence of slope failure.

Pore-water pressure records frorn all transducers are shown in Figure 6. The advancing rainwaterwetting front resulted initially in sharply increased pore-water pressures near the surface of the slope. The pore pressures were then constant and finally increased slowly again in response to the rise in groundwater level. In contrast, pressure transducers located near the bottom part of the slope (P5 and P7) initially displayed no pore-water pressure increase until the arrival of advancing groundwaterwetting front, when there were sharp increases to zero. Transducers located near the slope surface (PlP3) showed pore-pressure increases to positive values prior to the occurrence of slope failure. This gave the indication that the development of seepage face was responsible for failure initiation.

Figure 8. Variation of pore-water pressure with time during experiment 2. 5.5 Case 2: Pore-water pressure at failure Pore-water pressure records are given in Figure 8. Pressure transducers located at the bottom of the slope (P5 and P7) indicated the appearance of initial groundwater table. The changes in pore-water pressure in response to rainfall infiltration commenced with the generation of significant increase in pore-water pressures near the surface of the slope. Pore-water pressures then increased slowly during the ingress of wetting front and rise in groundwater level. Then, seepage face developed in the area near the slope toe as indicated by the development of positive pore-water pressure at P1 and P2. Further increase in groundwater level enlarged the seepage face area, which was believed to initiate two subsequent failures.

Figure 7. Change in moisture content with time during experiment 2.

5.4 Cuse 2: Moisture content at fuilure

6 DISCUSSION

Variation of moisture content with time is presented in Figure 7. Moisture sensor ADRl located 30 cm above the base of the tank initially indicated the existence of a nearly saturated area. Moisture content in the most parts of the soil slope increased slowly throughout the experiment. The first significant increase occurred in the near slope surface area of the slope as displayed by moisture sensor ADR2. This increase suggested the rise in groundwater level and development of seepage face during which a slope failure initiated. Moisture sensor ADR2 showed the soil failure involved nearly saturated soil slope. The next

The experiments have demonstrated the possibility in predicting failure initiation by monitoring the changes in either moisture Content or pore-water pressure during rainwater infiltration. Precise monitoring of moisture contents and pore pressures in relation to failure initiation consistently indicated that moisture content of soil approached saturated value, while pore-water pressure reached zero value at failure initiation. Instruments for the monitoring of negative pore pressure (suction) have suffered from a number of disadvantages. The present-day instruments are restricted to measuring a very low suction, and

468

require special care and maintenance for long-term monitoring program. In contrast, long-term monitoring of moisture content has been possible by the present-day moisture-sensing instruments. This advantage of moisture sensing instrument over suction measuring instrument suggests that monitoring of moisture content during rainfall is more effective and more reliable to predict the occurrence of slope failures compared with that of pore pressure. However, in order to observe properly the changes in soil moisture content, it is so preferable that soil is initially at low moisture content. The general profile of variation of moisture content with time due to rainwater infiltration, inferred from the experiments, as shown in Figure 9 suggests two phases of significant increase in moisture content. Referring to this Figure, the initiation of second increase in moisture content (Profile 11) may be used for early warning towards the occurrence of slope failure. Knowledge of the value of saturated moisture content of soil and the rate of moisture increases will assist one to estimate the critical time of failure. The experiments reported in this Paper indicated that the development of seepage faces at the slope surface were responsible for the initiation of slope failures. This clearly illustrates the importance of precise monitoring of moisture contents in seepage face area to predict failure time. The use of numerical analysis would help to determine the location where the seepage face will develop. The conclusions drawn from this study are that direct monitoring of the change in moisture content

provide a higher possil$ity in predicting slope failure occurrences during rainfall. The advantage of moisture sensors for long-term measurement would tend to recommend this predicting method over other available method. Field experiments to investigate further the application of this method are desirable. REFERENCES Abraham, L. W., T. S. Thomas, S. Sharma & G. M. Boyce 1995. Slope srability and stabilization methods. New York: John Wiley and Son. Fredlund, D.G & H. Rahardjo 1993. Soil mechanics for unsaturated soils. New York: John Wiley and Son. Nishigaki, M 1987. Unsaturated seepage analysis (UNSAF), Okayama University, Japan. Rahardjo, H., E.C.Leong, G.M. Gasmo & S.K. Tang 1998. Assessment of rainfall effect on stability of residual soil slopes. Proc. 2"" Znt. COT$Unsaturated Soils, Beijing, 2 7-30August 1998: 280-285. International Academic Publisher. Sammori, T., Y. Okur, H. Ochiai & H. Kitahara 1996. Seepage process in sloping sand layers and mechanism of landslide-Effects of soil thickness on landslide initiation by laboratory and numerical experiments. Proc. 7"' Znt. Symp. Landslides, Troizdlzeim, 17-2I Juni 1996:13511356. Rotterdam: Balkema. van Genuchten, M. Th. 1989. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Am. J. 44: 892-898.

Figure 9. General variation of pore-water pressure and moisture content with time at failure (under the effect of rainwater infiltration)

469

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami L? Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Analytical study on the slope stability during rainfall and the rainfall indexes A.Togari-Ohta East Japan Railway Company,Japan

T. Sugiyama & T. Nara Railway Technical Research Institute, Tokyo, Japan

S.YamaZaki Kyushu Railway Company,Japan

ABSTRACT: In order to ensure a safe rail-transportation during rainfall in Japan, the operation control is performed to limit a speed of train or to suspend a train operation, comparing the measurements of rainfall with the assigned rainfall indexes. The combination of an hourly rainfall and an accumulative rainfall is mainly applied for the operation control as the rainfall indexes at present. Aiming at clarifying scientifically that these rainfall indexes can catch up the instability due to rainfall within the adequate timing, we performed the analytical investigations for relationship between stability and rainfall indexes. By two differentconceptual simulations, so as the saturated-unsaturated seepage analyses and the stability analyses of limit equilibrium method, we obtained the time-dependent series of safety factors as stability. With comparing the calculated safety factors and the rainfall indexes on a time-series, we succeeded to educe the characteristics of the interested rainfall indexes for the instability at the patterned rainfalls. using for engineering and practical fields. Additionally, we also investigate the effectiveness of an antecedent rainfall, which is not reflected to the present operation control. We, herein, report the results of analytical investigations and the conclusion from these results.

1 INTRODUCTION Railways are obligated to ensure a safe and steady transport as mass transport. The geotechnical and meteorological conditions in Japan, however, tend to induce collapses of embankments or cuttings even along railways, during Typhoons or heavy rainy season. In order to keep a safe transportation away from a disturbance of disasters due to rainfall, the construction works for disaster prevention must be done at the places judged as danger spots. At the same time, the operation control must be performed by the rainfall indexes or the detecting sensors against collapses as countermeasures. Although the occurrence of disasters becomes relatively decreasing by the effects of advancement of disaster-prevention technology, more developing countermeasures for safe transportation becomes necessary, because a speed-up and a high-frequency of train are required by public. Rainfall indexes are applied for the operation control during rainfall and the combination of an hourly rainfall and an accumulative rainfall is widely used as rainfall indexes for railway in Japan. On these background and requirement, we perform the analytical investigations to ensure the relationships between stability of earth structures and rainfall indexes, aiming at clarifying it scientifically and

2 OBSERVATIONS OF PAST COLLAPSES DUE TO RAINFALL The past cases that the collapses of embankments or cuttings occurred along the railways sites are classified by the types of the measured rainfall. Herein we observe how the antecedent rainfall would influence the collapse phenomenon. 2.1 Procedure of analysis The used data are based on the actual collapse cases which caused at the embankments or cuttings along the railways after 1975 (Sugiyama et al., 1995). These include 67 cases of embankments and 119 cases of cuttings. As amounts of rainfall, the data of AMEDAS provided by Japan Meteorological Agency are used for all the cases. For classification, we set four types of rainfall. The definition is follows; * type I : no or less than 50mm as antecedent rainfall,

471

antecedent rainfall and also to imply the influence with disasters due to rainfall. One of these rainfall indexes is an effective rainfall. We investigate analytically the relation and consistency between the stability of railembankments during rainfall and the rainfall indexes including an effective rainfall and practically used rainfalls. As the first step of procedures, we set the embankment-model for numerical analysis with the data from actual sites of railway, and then, perform the saturated-unsaturated seepage analyses with the data of patterned rainfall. As the next step, embankment-models are remodeled with the moisture distributions obtained by the former analyses, and then perform the stability analyses with assumed shear strength of soils. The calculated rainfall indexes of the patterned rains are compared with the time-dependent series of safety factors obtained as results of these two different-conceptual numerical analyses to educe the characteristics of the rainfall indexes for stability at the each patterned rainfall.

*typeI1 : the antecedent rainfall is more than 50mm but less than the accumulative rainfall of the collapse’s occurrence, *type111-1 : the antecedent rainfall is more than the accumulative rainfall of the collapse’s occurrence, and the time interval between the antecedent rainfall and the following rainfall is less than 24 hours, *type111-2 : the antecedent rainfall is more than the accumulative rainfall of the collapse’s occurrence, and the time interval is more than 24 hours, An antecedent rain means to have fallen within 10 days before the collapse occurred. 2.2 Occurrence frequency of collapses for classified types Failure of cuttings can be distinguished into two types; one is shallow failure whose slip surface goes through a relative shallow depth with a relatively linear shape, and the other is deep failure whose slip surface goes relatively deeply with a rather circular shape. The classification of the interested 186 past cases is shown in Figure 1. The past cases of type I and I1 occupies about 80 96 of all for the both of embankments and cuttings, thus, it is figured out that the rest of 20% can be judged to depend on the antecedent rainfall. This result implies that some past collapses should be analyzed with the antecedent rainfall, and thus, represents the influence of antecedent rainfall noticeably.

3.1 Procedures of analyses

n u m b e r inside:occurrence of collapse

embankment (67 data)

39

cu ttingshallow

32

cuttingdeep (59 data)

30

0%

20%

4 4

20

6

20

40%

60%

6

5

17

80%

3

100%

Figure 1. Occurrence frequency of collapses.

3 NUMERICAL ANALYSES FOR STABILITY AND RAINFALL INDEXES From the hereinabove results of the classification for the 186 past cases, we can clarify that the 20 96 of these can be collapses influenced by antecedent rainfall. Several studies and practical applications have been attempted for setting the rainfall indexes which have possibility to present the influence of an

472

For analyzing slope instability due to rainfall, an infiltration of rain water into a ground or soil material of earth structures is essential phenomenon to be in interest. Here, we apply the saturatedunsaturated seepage analysis which can treat a permeability of an unsaturated domain to get hold of the distribution of soil moisture inside of slope. The embankment-model for this seepage analysis is set up with the profile data based on the standard cross section for Shinkansen. For setting the soil moisture property for this model, p F tests and permeability tests are done with the samples taken from railway sites. As the rainfall data, we adopt eight patterns of rainfall, of which total amounts are all set to be 400mm. After the series of moisture are obtained, the stability of slope can be calculated at the selected time-point by Janbu’s Simplified procedure of a limit equilibrium method of slices. The embankment-models are remodeled at the selected time-points by setting the layers for several ranks of saturation degree to reflect the moisture distributions obtained at the former seepage analysis. The shear strength of soil generally tends to vary depending on its moisture content. Using the data of triaxial compression tests of unsaturated soil samples, we assume the variation of cohesion of soil due to saturation degree while the constant value of an internal friction angle. As results of a series of stability analyses, we obtain the time-dependent series of safety factors as stability. An hourly rainfall, an accumulative rainfall, a 24-hour’s

rainfall, and two effective rainfalls with 24 and 72 hours’ half-life periods are also calculated for the adopted patterns of rainfall as the interested rainfall indexes.

TZ = 0.69 - 1311

(3)

where k is a coefficient of unsaturated permeability with an arbitrary water content, k, is a coefficient of saturated permeability, K, is specific coefficient of permeability, and n is a coefficient. These parameters for the approximate equation of (I),@), and (3) are obtained by the least squares methods using soil test data, shown in Table 2. (3) Rainfall data: patterned and measured rainfalls The eight patterns of assumed rainfalls and the practical rainfall are adopted as rain data for the analyses. The variations of eight patterned rainfalls are set as; * 40mm/h pulse (40mm/h X 10 hours) rainfall, 10mm/h pulse (10mm/h X 40 hours) rainfall, 100mm/h pulse (100mm/h X 4 hours) rainfall, * double pulses I (300mm+100mm) rainfall with interval of 14 hours, double pulses I1 (100mm +300mm) rainfall with interval of 14 hours, * equal-double pulses (200mm+200mm) with interval of 14 hours, - increasing intensity (increased linearly form Omm/h to 30mm/h for 26.3hours) rainfall, decreasing intensity(decreased linearly from 30mm/h to Omm/h for 26.3hours) rainfall. The total amounts of patterned rains are all set to be constant value of 400 mm, which has been obtained as the maximum daily amount of rainfall with 70years-probability in the district of Tohkai, Japan. The rainfall intensities of patterned rain are set to be varied as 0 to 100 mm/h due to the variation of each patterned rainfall. As a practical rainfall data for the analysis, it is selected a series of rains measured in Shizuoka Prefecture from August 15‘hto 31” , 1983, of which maximum hourly rainfall is 62 mm/h and total amount is 600 mm. (4) Shear strengths of soil For the stability analysis, we need to set shear strengths of soil material inside an embankmentmodel. Based on the moisture distribution obtained the seepage analysis, several layers are set due to ranking of the saturation degree inside embankment-model. Every rank holds the individual property of moisture and water content on which the

3.2 Targets and conditions of analysis The target of this series of analyses is to reflect the moisture situation into the stability analyses for embankment models with a standard profile and property along a railway under the patterned rainfall. The analytical conditions are the follows. (1)Profile of embankment-model The external form of embankment-models for both of the seepage analysis and the stability analysis is referred to the Standard of Design for Shinkansen (RTRI, 1992). The embankment-model is shaped as the only half profile of embankment because of symmetry. The height of embankment is set to be 6.0 meters , the gradient of embankment slope to be l(vertica1): 1.5(horizontal), the half width on crest to be 5.35 meters. (2) Soil moisture property and permeability The parameters of the soil moisture property and permeability for the seepage analysis are set on the base of representative or average data from saturated permeability tests and pF tests. The samples for these tests were taken from the railway sites of commercial lines or used for the past experiments of a slope failure. The parameters are shown in Table 1. Since the seepage analysis concerns not only saturated domain but also unsaturated domain, the soil moisture characteristics and the unsaturated permeability should be defined before the analyses. For soil moisture characteristics, the $ ,,,-8 relation is defined by Brooks & Corey equation (Brooks et al., 1966) as;

-

where 8 is a volumetric water content, 8 is a saturated volumetric water content, B is a minimum volumetric water content, $ is a pressure head, $ c r is a limit suction pressure head, and h is a coefficient. The unsaturated permeability is defined using Irmay equation (Irmay, 1954) and Nishigaki assumption (Nishigaki, 1983) as; Table 1. Parameters set from soil tests Darameter coefficient of saturated permeability (k,J soil gravity (G,,) void ratio (e) dry unit weight ( P d) saturated volumetric water content ( 0 b) minimum volumetric water content ( 0

k,?

value 3.6 X 10” cm/s 2.65 0.698 1.30 g/cm3 0.41 1 0.180

Table 2. Parameters set for approximate equations Parameter value Coefficient ( A dry ) :for drying process 0.35 Coefficient ( A wet ) :for wetting process 0.60 limit suction pressure head ($ cr) -2.80 cm Coefficient for Irmay’s Equation (n) 3.7

473

values of cohesion and wet unit weight of soil are dependent. Using the existing data of triaxial compression tests on unsaturated soil samples taken from the actual railway sites, we assume the valuables of cohesion of soil depending on saturation degree of soil’s ranking. The internal friction angle of soil is assumed to be constant of 30 degree, because the relation between waterlmoisture content and this value has not been clarified enough yet. The assumed shear strengths of soil due to ranking of saturation degree are listed in Table 3.

(a) Patterned rainfall : 40mmh pulse rainfall

3.3 General concept of an eflective rainfall The concept concerning to an effective rainfall has been recognized on the base that a slip movement of ground relates to a groundwater level rising due to rainfall. The effective rainfall, which is used herein, is defined by Suzuki et al.(Suzuki et al., 1981). 3.4 Results of analyses (1) Patterned rainfalls The analyses are carried out for all eight patterned rainfalls. For representatives cases of patterned rainfalls, the time-dependent changes of safety factors are shown with rainfall indexes in Figure 2. The rainfall indexes examined herein are an accumulative rainfall, which is applied to conventional railways, a 24-hour’s rainfall, which is a rainfall cumulated for 24 hours before an arbitrary time and applied to Shinkansen, and two effective rainfalls with a halt-life period of 24 hours and 72 hours. The followings are considerations against the four representative patterned rainfalls for relations of safety factor and rainfall indexes. (a) Patterned rainfall :40mmlh pulse rainfall As the characteristics of this patterned rainfall, it is found out that the safety factor takes a minimum in nine hours after rainfall-stop. At the point of timing of a peak value, only an accumulative rainfall and a 24-hour’s rainfall are realized to keep enough consistency with safety factors. An effective rainfall tends to start to go down at the very time of rainfallTable 3 . Cohesion (c) of soil and saturation degree (S,) rank of S, representative c (kPa) wet unit weight value of S, (kN/m3) 100 % 100 % 1.961 16.10 100 - 90 % 95 % 2.452 15.94 80 - 90 % 85 % 3.334 15.60 70 - 80 % 75 % 4.315 15.27 65 % 5.394 14.94 60 - 70 % 55 % 7.257 14.59 50 - 60 %

(b) Patterned rainfall : 10mmh pulse rainfall

(c) Patterned rainfall : double-pulses rainfall

(d) Patterned rainfall : decreasing intensity rainfall

--

_.

... . .

hourly rainfall effective rainfall ( M = 2 4 h ) effective rainfall ( M = 7 2 h )

-a c c u m u l a t i v e rainfall - - - - 2 4 - h o u r ’ s rainfall safety factor

Figure 2. Change of rainfall indexes and safety factor for patterned rainfalls.

474

relatively long half-time periods, however, can be recognized to be better than the others at the point that their peak values occur during the second pulse-rain when factor of safety has not begun to recover yet. In addition, the tendency that the minimum factor of safety occurs after rainfall ends is the common phenomenon for all other patterns of double-pulse rainfalls. Thus, when the rainfall similar to this pattern would occur practically, all examined rainfall indexes have difficulty to satisfy to get hold of the appropriate timing of change of the instability. (d) Patterned rainfall :decreasing intensiy rainfall The characteristics shown for effective rainfalls are distinctive, namely, the shorter a half-life period becomes, the earlier a peak amount of effective rainfall tends to appear. The tendency of decreasing factor of safety seems relatively stronger at the immediate after rainfall starts, and then, because a intensity of rainfall becomes linearly smaller, the ratio of decrease becomes flatter and the factor of safety reaches at a minimum three hours after a rainfall ends. Therefore, the rainfall index which can hold the consistency of a factor of safety with their limits is only an accumulative rainfall not the other rainfall indexes. However, for the decreasing and recovering tendencies an accumulative rainfall has much difficulty to follow the safety factor. (2) Practical rainfall Picking up the period including antecedent rainfalls enough to be concerned, a series of analyses is carried out with the selected practical rainfall data. Figure 3 shows the results of rainfall indexes and a safety factor. There is not seemed the significant differences between the examined rainfall indexes for this practical rainfall, concerning the decreasing tendency of safety factor and the timings when the peak and the minimum appear. The accumulative rainfall has also difficulty to hold the recovering tendency of safety factor as recognized for

stop, while a safety factor not to start to increase at that time. An effective rainfall, however, can follow better than the others in regard to the recovering tendency of a safety factor. (b) Patterned rainfall :10mmlh pulse rainfall At this pattern a safety factor tends to start to decrease at the very time of rainfall-start and to recovery just after rainfall-stop. On the other hand, all examined rainfall indexes take their peaks at the time of rainfall-stop, and those except an accumulative rainfall tend to start to decrease after rainfall-stops. Thus, since the value of a safety factor does not recovery enough to reach at the beginning value in twelve hours after rainfall-stops, there is not any difference to be recognized between the examined rainfall indexes except an accumulative rainfall which takes a zero value at that time. (c) Patterned rainfall :double-pulses rainfall I The accumulative rainfall becomes zero due to the interval period of the over twelve hours without any rainfall before the second pulse-rain of 100mm. For both half-life periods to be set here, the effective rainfalls take non zero values. Additionally, for 24hours’ half-life period the effective rainfall during the first pulse-rain becomes bigger than one during the second pulse-rain, while for 72-hours’ half-life period the effective rainfall during the second pulserain becomes bigger than one during the first pulserain. The safety factor decreases gradually during the first pulse-rain and the ratio of its decrease becomes slightly smaller during the interval after the first pulse-rain’s end. After the second pulse-rain starts, the safety factor once indicates to recover, then starts to decrease again at the time around the end of the second pulse-rain, and eventually takes the minimum value when it spends more than twelve hours after rainfall completely ends. That is the reason why all rainfall indexes can not catch up the timing to cause the minimum factor of safety. The 24-hour’s rainfall and effective rainfalls with

Figure 3. Changes of safety factors and rainfall indexes in the case of the practical rainfall.

475

Table 4. Consistency between a change of safety factor and rainfall indexes. comparison with F, at a consistency of peak timings comparison with F, after Patterned rainfall beginning of rainfall with F, niin rainfall-end Rainfall index R R24 Rc24 Rc72 R24 Rc24 Rc72 R R24 Rc24 Rc72 40mm pulse o o o o ~ o x x x x A 100mm pulse O O O O x x x x x x x n 10mm pulse O O O O O O O O x ~ n equaldoublepulse x 0 0 0 x x x x x X 0 double pulse I x O O O x x x x x x n O double pulse I1 n O O O O A n n x x n O increasing intensity 0 0 0 0 0 0 0 0 x x A 0 decreasing intensity 0 0 0 0 0 X x x x A 0 0 practical 0 0 0 0 0 0 0 o x x a o ovcrall A O O O n n n n x x n O R: accumulative rainfall, Rc24:effective rainfall with 24-hours’ half-life period, RZ4:24-hours rainfall, F,: safety factor, Rc72:effective rainfall with 72-hours’ half-life period, 0: relatively good consistency, A: rather consistency, X : no consistency (difference of peak timings is less than 3 hr.(O), or more than 6 hr. (X), otherwise (A).)

o O

characteristics of an effective rainfall and an accumulative rainfall, while it tends to recover earlier than an effective rainfall and a safety factor.

the patterned rainfalls. The interested practical rainfall includes the non-rainfall interval of 36 hours, however, in case that the interval would be shorter, the minimum factor of safety could be expected to appear during the following rainfall, then an accumulative rainfall might be not able to hold the existing consistency with safety factor.

5 CONCLUSION We succeed to educe the characteristics of the examined rainfall indexes for the stability in the patterned rainfalls through the numerical analyses. Shown in Table 4, the engineering judgements are obtained, and then, an effective rainfall is recognized to hold the most consistency to stability. On the other hand, resulting from our verification, even an effective rainfall might miss at the timings to catch up an instability, it is necessary to remark such points for applying to a practical operation.

4 COMPARISON O F RAINFALL INDEXES BASED ON STABILITY OF EMBANKMENT We herein verify the consistency between the time-dependent change of safety factor and examined rainfall indexes for all patterned rainfalls. For this verification, we aim at (1) the consistency between the decreasing tendency of safety factor and the time-dependent change of rainfall amount at the beginning of rainfall, (2) the consistency of timings when a safety factor take a minimum and when the peak of rainfall indexes appear, (3) the consistency between the recovering tendency of safety factor and the decreasing tendency of rainfall indexes. This result for engineering judgement is listed in Table 4. From the general judgement in Table 4, an effective rainfall is realized to have the most consistency with the tendency for time-dependent change of safety factor. Since an accumulative rainfall keeps a cumulative value for 12 hours continually after rainfall ends, it can catch up the timing of a minimum safety factor to appear some hours after rainfall ends. However, because it must be zero 12 hours after rainfall-end, it can not follow the recovery tendency of safety factor. By the same reason, in case of a series of rainfalls with any antecedent rainfalls and interval period of more then 12 hours, an accumulative rainfall may be caused to count as bigger value for the antecedent rainfall than one for following rainfall even a safety factor becomes smaller than after antecedent rainfall. A 24-hour’s rainfall seems to show the middle

REFERENCES Brooks, R.H., and Corey A. T., 1966 Properties of porous media affecting fluid flow, ASCE, IR(92), pp.61-88. Irmay, S. 1954 The determination of the hydraulic conductivity and diffusivity of unsaturated soils, Soil Science, ~01.113, 110.4,pp.264-276 Nishigaki, M., 1983 The considerations on permeability characteristics of soil moisture in saturated and unsaturated domains, Journal of Japan Society of Soil Mechanics, vo1.23,no.3, pp.165-176 (in Japanese) Railway Technical Research Institute (RTRI), 1992 Design standard and its explanation for railway structures - Earth structures, Maruzen (in Japanese) Sugiyama, T., Okada, K., Muraishi, H., Noguchi, T., Samizo, M., 1995 Statistical rainfall risk estimating method for a deep collapse of a cut slope. Soils and Foundations 35-4 Suzuki, M., Kobashi, S., 1981 Correlation between the occurrence of collapse and the rainfall. Shi-Sabo 121 (in Japanese)

476

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Evaluation of critical rainfall with logit model T. Sugii & K.Yamada Chubu University, Aichi, Kusugui, Jupun

T.Uno Giju University, J q u n

ABSTRACT The critical rainfall that triggers slope failure has been evaluated based on the history of slopes, disregarding the properties of the slope. In this paper, a statistical method of evaluating the critical rainfall considering the properties of the slope is proposed. The strength of slope (the resistance potential) is evaluated with a logit model. The results showed several significant characteristic factors that affect the slope stability. The rainfall intensity and the effective rainfall corresponding to the resistance potential determined the rainfall threshold. Management of the slope and traffic control could be controlled based on the LM (Logit Model) line and the curves of rainfall intensity and effective rainfall.

1 INTRODUCTION

cumulative rainfall and effective rainfall, as shown in Fig.1.

In the past, decisions on critical rainfall have been based on the history of the slope or data of the neighboring area. However, critical rainfall should consider the influence of many characteristic factors of the slope such as the gradient of the slope, as well as the permeability, cohesion and water retention curve of the soil that affect slope stability. This paper proposes a method of evaluating critical rainfall considering properties of the slope with a logit model. The logit model is a regression model (Domencich et al., 1971). In the previous study, it was clarified that river levee stability could be evaluated with a logit model (Uno et al., 1991), which could identify characteristic factors for levee failure and express the probabilities of failure. It can also incorporate qualitative factors, too. In this paper, slope properties are evaluated as a function of “resistance potential” obtained by calculation using the logit model (Sugii et al., 1998). The critical rainfall to trigger slope failure is decided by the resistance potential, the effective rainfall and the rainfall intensity with a logit model again. The effective rainfall is an index expressing the antecedent rainfall, and the modified cumulative rainfall.

Fig.1

Indexes of rainfall

(1) Rainfall intensity (Hourly rainfall): R, Rainfall intensity R, is defined as the amount of rainfall in one hour. In this paper, it is the amount of rainfall from one hour to the next using AMeDAS(Automated meteorological data acquisition system, JMA). (2) Cumulative rainfall: RA This is the amount of rainfall intensity from a certain time until the present time, and is defined as:

2 INDEX OF RAINFALL

There are three kinds of index used to indicate rainfall at present. They are rainfall intensity, 477

R , = C R I I= R I i+ R I , + * - * - . . + R I , (1) where RI, is the rainfall intensity of the previous i hours (3) Effective rainfall R , When cumulative rainfall is used, the starting time of rain is an important issue Effective rainfall is a modification of cumulative rainfall considering the antecedent rainfall It is given by the half-life,T

P, =

z,) (7)

where P, is the probability of slope failure, Z, is damage potential function and C are unknown parameters estimated by the maximum likelihood method R,, is the effective rainfall, and RI is the rainfall intensity The dummy variable, C ,,, however, is a constant that is affected by unknown factors If P, is regarded as 0 5 , the critical line of R,\ and R, is given by equation (8) Substituting equation (7) into (6) gives

where a , = 0 5(l-')

1 1 + exp(-

'

(3 1 T is dependent on the period of antecedent rainfall If a, is equal to 1, R , corresponds to the cumulative rainfall As a, approaches infinity, R,\ becomes equal to the rainfall intensity The half-life is not defined at present The data used for this study consists of cut slope data for the last 10 years, therefore, T is set as 12 hours in this paper

If RI exceeds equation (8), it is supposed that slope failure occurs. Thus, we can predict whether slope failure will occur. When the probability of slope failure, P,, is greater than 0.5 (50%), it is judged that slope failure will occur. Fig.2 shows the critical line estimated by the logit model using 14 slope failures and 70 no-failures. By using the logit model, the critical line can be decided objectively. But the critical rainfall is not independent of many characteristic factors of the slope. It is necessary to define the critical rainfall appropriate to the properties of slopes.

3 CRITICAL RAINFALL DISREGARDING THE SLOPE PROPERTIES

In the debris flow, the critical rainfall is evaluated using rainfall intensity and effective rainfall. Rainfall intensity is concerned with the permeability of the slope, effective rainfall done with strength of its soils. Though the critical line for judging the rainfall that triggers slope failure is decided empirically, its line is estimated by following the logit model in this paper. 3.1 OUTLINE OF LOGIT MODEL

Slopes are regarded as randomly selected samples. For the n th slope, the damage potential fimction is denoted by U,. If U, is greater than 0, the slope collapses, but if it is less than 0, there is no collapse. The function is defined by U, = V, (deter min istic part) + E, (random part) (4) where V, is expressed by the characteristic factor of the slope, and F consists of unknown factors and random errors in the data. The probability of collapse, therefore, is P, = Prob(U, > 0) = Prob(V, = h o b ( - E, < V,)

+E,

Fig2 Critical line by logit model

> 0)

(5)

4 METHOD STABILITY

where Prob(, . ,) is the probability that satisfies the conditions in the parentheses. When the Gumbel distribution is applied to the random part, P, is

OF

EVALUATING

SLOPE

In this section, the logit model is reformulated to evaluate the properties of the slope. In order to 478

evaluate the stability of many slopes easily, the logit model is used The probability of non-collapse concerning slope stability is given by 1 (9) ’sn 1 + exp(- v,

done “Upheaval types”. In the case of containing category of unknown as in Table m , they are classified into “Recognized water flowing and seeping out (Recognized spring)” and “Others”. In the same way as these, categories are modified. Modified categories are shown in Table JY. Table V shows the coefficients of correlation among the properties of the slope. The coefficient of correlation between classification stratum and weathering is the highest.

where

v,

=B,] + P , X , ,

+P2Xn3

+ . a * +

BkXk

(10)

P,, is the probability of non-failure, V, is the resistance potential, [3 is an unknown parameter estimated by the maximum likelihood method and X,, is a characteristic factor of the slope. The probability of non-collapse, Psn, increases with the value of resistance potential, V, The larger V, is, the more stable the slope is. This model of evaluating slope resistance is called as “Resistance potential model” in this paper.

Failure proporno n

Number Number s of of stable failure slopes slopes Mountain Hill Plateau A l l ~ i 1 ~fan 1 Bench

4.1 SELECTION OF CHARACTERISTIC SLOPE VARIABLES AND DATA CATALOG

Upheaval t\ pe Scdimentar

t’pe

72 169 5 4 46

(%)

40 86 4 1 3

36 34 44 20 6

Many possible characteristic slope variables are shown in Table I. TableIII Fail U re proportions (Spring) Table I

Characteristic slope variables Chsrnctcristic rlopc variahlcs I Numher I Slope 1 Backgr I

proportion

Arti1ic.i

Unrecognized

Others

Unhionm

Table L e n g h of slope

Xn3 Shape of slope X,,,Utih/;ltion of upper field x,,,Classificatron I stratum x,,,Weathering Xn6 Degree of fissuring X,,- RecogniLed fault X,, Recognized spring X,,, Slope protection I\ ork x,,,,LengtIi of slope

1

~

1

X,,,? 1 Degree of slope X,,,, I Width of berm

479

1 85

100

31

IV Modified categories

X,,,1 Topography

Where “ A ’ shows a qualitative variable and “B” does a quantitative variable. The numbers of categories is 70. We selected thirteen characteristic slope variables as following description. Tables II and Ill show the failure proportions of each category of topography and spring (the water flowing out of the slope). Both of topography and spring are classified into two categories, respectively. In variables of topography, plateau, alluvial fan and bench are defined as “Sedimentary type”, others

0 190

Categories x,,=O x,,k=1 Sedimentary type

Uphea\.al

Developed

Uiidel eloped

Sods

Rocks

h pe Flat Noi1-flat

I Weathered Existence Others Recognized Others Recognized Others protection except Others planting Unit (in)

1 Fresh

1:11 Unit (111)

Table V Coefficients of correlation

TableW Parameters for rainfall model t-value constant Effect rainfall Rainfall intensity

i, Resistance potential of slope Hit ratio 0.99 / Likelihood of inodel

4.2 RESISTANCE POTENTIAL BY LOGIT MODEL

------Alternative specific dummy constant Topography (sedimentary Qpe) Shape of slope (flat type) Height of slope

Hit ratio

Parameter

t-value

0 0I

3 76 2.20 1.89 1.93

I BII

4.28 -1.74 2.10 I-0.06

0.92 / Likelihood of model

intensity are positive variables that affect slope failure. The parameter of resistance potential is negative. From analyses, the LM line is obtained as 1 {0.0039R,\, - 0.66V, + 0.088> (12) 0.0573 where R,\, is the effective rainfall, R, is rainfall intensity, V, is resistance potential. The safety factor of critical rainfall is determined by the probability of slope failure, P, as in equation (8). In this case, P, is regarded as 0.5, because it is considered that slope failure will occur when P, exceeds 0.5 (50%). Equation (12) is called as LM line in this paper.

RI

A resistance potential model is formulated using the selected variables in Table V . Parameters, fi k, estimated by the logit model are shown in Table VI.

0.93

-

5.1 DECIDING THE LM LINE FOR THE CRITICAL RAINFALL

0.67

The LM line shows the dangerous combination of effective rainfall and rainfall intensity for a slope with a certain resistance potential. The dangerous combination of R,\, and R, is decided by the resistance potential, V,. The plane in Fig.3 shows the relations among effective rainfall, rainfall intensity and resistance potential. When the relation between effective rainfall and rainfall intensity exceeds this plane (LM lines), slope failure will occur.

Other variable factors in Table VI are rejected by the t-test. With parameters B ,), P ,, fi and /3 ,,, the resistance potential of the slope, V,, can be evaluated. The greater V, is, the greater the probability of nonfailure, P,,, is. Therefore, the positive parameter, fi k, affects slope stability, and the negative one fi affects instability. V, = 4.28 - 1 . 7 4 ~ ,+, 2 . 1 0 -~0~. 0~ 6 ~ ~ ; (1 1)

It is clear that the value of V, indicates the relative stability of the slope. Sedimentary type of topography and height of slope are negative parameters, causing slope instability. But a flat type slope is a positive parameter, improving slope stability.

5 MODEL OF EVALUATING RAINFALL CONSIDERING RESISTANCE OF SLOPE We combine the resistance potential given by equation (1 1) with the rainfall model by equation (7). Rainfall data for the slope failure period were obtained from AMeDAS. The logit model is formulated with rainfall intensity, effective rainfall and resistance potential as the variables of equation (7). Estimated parameters are shown in Table W . The parameters of effective rainfall and rainfall

Fig.3 Effective rainfall, rainfall intensity and resistance potential

480

Since the two slopes are located near each other, the same rainfall data are observed by AMeDAS. The resistance potential of the failure slope (No.57) is evaluated as 2.016, and that of the non-failure slope (No.57) is 3.584. LM lines are calculated using equations (13) and (14), respectively. The LM lines of slope No.57 are given by R =--(0.0039R1\,- 2.2774) I 0.0573

(13)

The LM lines of slope N0.60 are given by 1 0.0573

R , = -----(0.0039R,

LM lines are shown on the plane. Solid lines present the same resistance potential lines. The figure shows that the greater the resistance potential is, the greater the effective rainfall and the rainfall intensity are. If the resistance potential of the slope, V,, is evaluated as 2.0 by the resistance potential model in equation ( l l ) , the LM line is given by the intersection of the plane of resistance potential equal to 2.0. This LM line is shown in Fig. 4, and is drawn in the horizontal plane with equal resistance potential. Therefore, it is easy to evaluate the critical rainfall by using the two indexes of effective rainfall and rainfall intensity as shown in Fig. 4. 6 SLOPE STABILITY MANAGEMENT WITH CRITICAL RAINFALL

7 CONCLUSIONS

This paper presents a method to evaluate critical rainfall with a logit model. The conclusions are summarized as follows: (1) The characteristic factors for evaluating the strength of the slope are identified from various properties of the slope according to the logit model. (2) It is clarified that the critical rainfall can be defined using the strength of the slope as well as effective rainfall intensity. (3) A method of predicting slope failure against rainfall considering the stxength of the slope is propose d.

Table w1 ProDerties of selected slooes No 57 No 60 Num ofslope Non-Failure Failure Shape of slope Height of slope Resistance potential of slope

Sedinientap t>pe

x.7 ,=1

XA,, ,=1

Flat t j pe

Flat t> pe

xj7 2=1 xi, ,,=17 6(m) V,,=3.5 84

X61, 3= 1 xhi\,,=43 7(m) V6,=2.016

(14)

s,

The case of slope stability management for rainfall with equations (1 1) and (12) is presented in the next example. Two slopes are selected in the neighboring area and equations (11) and (12) are calculated. However, the two slopes are not used in the formulation of those equations. The properties of these slopes are shown in Table w1.

Sediinentap t>pe

1.3306)

Where R, is the effective rainfall and RI is rainfall intensity. Figs.5 (a) and (b) show the snake curves of rainfall and two LM lines of equations (13) and (14), respectively. In the case of No.57, the rainfall is always less than the LM line as in Fig. 5 (a), so slope No.57 does not collapse. Since slope No.60 is not stable, the LM line is shifted down to the left, therefore, the rainfall intensity exceeds the LM line. It is estimated that the slope failure in N0.60 occurs at the time exceeding the LM line. The exact time of slope failure in slope N0.60 is not observed, but it is clear that the slope failure can be predicted from Figs. 5(a) and 5(b). According to this method, it is easy to manage the slope against rainfall considering the strength of the slope. If the resistance potential (equation (1 1)) and LM line (equation (12)) are obtained beforehand, and if the snake curve approaches the LM line using and R,, slope failure can be predicted, and countermeasures should be taken.

Fig.4 Decided LM line

Topographr

-

ACKNOWLEDGEMENT The authors thank Japan Highway Public Corporation, and Mr. Y. Kato for his assistance

481

Report of Grant-in- Aid for Scientific Research (No.07555446), 1997. Japan Meteorological Agency: Rainfall intensity data in Gifu and Nagano Regions, automated meteorological data acquisition system (AMeDAS), 1976-1983. M. Suzuki: Prediction of slope failures by monitoring rainfall (review) (in Japanese), Proc. of Symposium on Forecast and Prediction of Landslide, Japan Landslide Soc. and Soc. of Erosion Control Eng., pp.31-42, 1991. T. Uno, T. Sugii and M. Hayashi: Logit model for river levee stability evaluation considering the flood return period, Structural safety, Vol. 14, pp.81-102, 1994. T. Uno, H. Morisugi and T. Sugii: Identifying dangerous levee location, Proc. 9th Asian Conf. ISSMFE, pp.441-444, 1991. T.A. Domencich and D.MacFadden: Urban Travel Demand (A Behavioral Analysis), North-Holland, Amsterdam, Ch.5, 1975. H. Morisugi: Estimation and testing of disaggregate behavioral modeling (in Japanese), in: the Research Committee on Infrastructure Planning (Eds.), Theory and Practice of Disaggregate Behavioral Modeling, JSCE, pp.121-147, 1984.

Fig. 5 (a) LM line for slope No.57 and the snake curve.

Fig. 5(b) LM line for slope No,60 and the snake curve. contribution in collecting data and arrangement part of this work.

assisting

REFERENCE T. Sugii, K. yamada and T. Uno: Evaluation of rainfall considering resistance of slope (in Japanese), Porc. 53rd Annual Japan National Conf. on JSCE., pp.450-451, 1998. T. Uno and T. Sugii: Evaluation of critical rainfall considering characteristics of slope (in Japanese),

482

Slope Stability Engineering, Yagi, Yamagami & Jiang (c) 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Strategy for prevention of natural disaster due to slope failure R. Kitamura & K.Yamamoto - Kagoshima University,Japan T. 1170- Univer-sih)of Western Ontario, Ont., Canada H.Abe - Cliubu Chishitsu I'ornpany Limited, Japan H.Yakabe -Diva Con.s~rlta~it Cornpany Limited, Japan

ABSTRACT: In Kagoshima Prefecture a non-welded part of pyroclastic flow deposits, Shirasu in Japanese, is widely distributed on the surface ground. The slopes composed of Shirasu and other volcanic products often fail due to the heavy rain in the rainy season every year. The mechanism of slope failure is qualitatively known, but can not quantitatively estimated at present. In this paper the strategy to establish the prevention system for natural disaster due to slope failure caused by heavy rain is proposed based on the combination of current field measured data with those obtained by the laboratory soil tests and the numerical models. The field measurement apparatuses for the suction in soil and the amount of rain fall, the unsaturated-saturated permeability testing apparatus and the numerical models to simulate the seepage behavior of rain into unsaturated soil are firstly introduced. And then the method to qualitatively estimate the risk of slope failure is explained where the measured data are processed and used to calculate the safety factor of slope by means of the numerical models. Finally the synthetic system is proposed to apply for the disaster prevention in Kagoshima Prefecture.

1 INTRODUCTION In Kagoshima Prefecture, which is located in the southern part of Kyushu Island, Japan, there are a lot of volcanoes such as Mt. Sakurajima, Mt. Kirishima, Mt. Kaimon etc. Consequently most of the surface ground is covered with various volcanic products. The non-welded part of pyroclastic flow deposits is locally called Shirasu in Japanese that is classified into sandy soil and forms steep slopes. In the rainy season (June - September) the slope failures often occur due to heavy rainfall on such steep slopes. In this paper the strategy to establish the strategy to establish the prevention system for natural disaster due to slope failure caused by heavy rain is proposed based on the combination of current field measured data with those obtained by the laboratory soil tests and the numerical models.

2 FIELD MEASUREMENT It is qualitatively known that the slope failure due to heavy rainfall is caused by the increase in water content which brings the increase in the self-weight of soil mass and the decrease in suction related to the apparent cohesion in soil. But the seepage process of rainwater into soil is not made clear quantitatively.

Our laboratory started to measure the suction and rainfall in the field to investigate the seepage process in Kagoshima Prefecture (Kitamura et al., 1999a, 1999b). The data is filed at intervals of one hour for suction and ten minutes for rainfall in the data loggers, and acquired by the personal computer. This system can be remotely controlled through the cellular phone by the personal computer in the laboratory. Figure 1 shows an example of obtained data, which are processed to be the change in suction and rainfall with time.

3 NUMERICAL. MODELS A numerical model for seepage of water into soil element was proposed based on the mechanical and probabilistic consideration on the soil particle scale (Kitamura et al, 1998), where this model is called the model for voids. The water void ratio, water content, unsaturated-saturated permeability coefficient, degree of saturation and suction can be obtained by using this model. In model the grain size distribution curve is only needed to obtain the above physical quantities. Figure 2 shows an example of moisture characteristic curves obtained by this model. A numerical model for seepage of

483

Fig. 1 Change in suction and rainfall with time in the field measurement of suction and rainfall, and the numerical simulation. The in-situ test such as the cone penetration test should be carried out to identify the layer composition of slope. As the laboratory tests, the permeability test, water retention test, and the shearing test should be done for undisturbed sample. The permeability test and the water retention test with the grain size analysis are needed to prove the validity of model for voids. The shearing test such as the triaxial compression test and the direct shear test on unsaturated soil are needed to prove the validity of numerical method to relate the suction to apparent cohesion. The field measurement of suction and rainfall should be done to prove the validity of numerical simulation of seepage of rainwater into soil by the seepage model. Once the numerical models and method are proved 4 LABORATORY SOIL TESTS to be valid, the rainfall data are only needed to A permeability testing apparatus was tried to calculate the safety degree of slope. Figure 7 manufacture in our laboratory to prove the validity shows the procedure to achieve the proposed of the numerical model for voids (Abe et al., 1999~). strategy. Figure 6 shows the arrangement of this apparatus. 6 CONCLUSIONS The air and water circuits can be controlled The strategy for the prevention of natural disaster independently. The moisture characteristic curves due to slope failure is proposed in this paper. The are simultaneously obtained from one specimen by system to measure the suction and rainfall in the this apparatus. field has been established and the data are filed every day at several field measuring points. The 5 STRATEGY FOR PREVENTION OF NATURAL system for laboratory tests on saturated soil are also DISASTERDUE TO SLOPE FAILURE established. The validity of numerical methods is The strategy is composed of three parts, which are now checked by the field measuring and laboratory the in-situ and laboratory tests, the field

water into ground was also proposed, in which the calculus of finite differences was used (Fukuhara et al., 1995). This model is called the seepage model. Figure 3 shows an example of simulation result for the infiltration test where the contour lines of water content are presented with time. A numerical method to relate the suction to the apparent cohesion was proposed by Kitamura & Yamada (1997) based on the mechanical and probabilistic consideration on the particle scale. Figure 4 shows an example of the relation between the suction and apparent cohesion. This relation was applied to calculate the safety factor of slope where the infinite slope stability analysis is used. Figure 5 shows an example of the relation between the safety factor and apparent cohesion.

484

Fig. 2 Moisture characteristic curves

Fig. 3 Simulation result for infiltration test

485

Fig.6 Schematic arrangement of permeability testing apparatus

486

I

1

I

Sampling of soil from slope

Permeability test & Water retention test

Undisturbed sample

Numerica1

Disturbed sample I

>

Grain size analysis

Numerical experiment

I

Shearing test on

Numerical experiment to obtain the relation between suction and apparent cohesion

No

>

Improvement of numerical model and soil test

Yes\/ Numerical seepage model

I

Comparison I

II

I

I

In-situ infiltration test Improvement of numerical method

I

and shearing test

Numerical simulation of infiltration test I

Comparison I

slope by surveying, sounding and in-situ cone penetration test

Improvement of seepage model and in-situ test condition

2 Yes V

Numerical simulation Measurement of suction and rainfall

Improvement of

Slope stability analysis

/

No

es

>. numerical simulation of infiltration

~

Safety factor

Nn

487

>

Improvement of slope stability analysis

test data. The in-situ test should also be developed to promote the accuracy of identification of the geological condition of slope in the near future. This research was supported by the grant-in aid of scientific research (B) (Project No. 09555153) of the Ministry of Education.

REFERENCES

S. Fukuhara, R. Kitamura and T. Muranaka (1995): A numerical experiment by seepage model, Proc. of 50th Annual Conf. of JSCE, Part IIIA, pp.182183, (in Japanese). R. Kitamura and M. Yamada (1997): Slope stability analysis for Shirasu taken account of cohesive component, Proc. Sympo. on Geotechnical Engineering for Prevention of Slope Failure due to Heavy Rain and Earthquake, pp.77-80, (in Japanese). R. Kitamura, S. Fukuhara, K. Uemura, G. Kisanuki and M. Seyama (1998): A numerical model for seepage through unsaturated soil, Soils and Foundations, Vo1.38, No.4, pp.261-265. R. Kitamura, T. Iryo, H. Abe and H. Yakabe(l999a): Field measurement of suction on Shirasu ground, Proc. 1st Asian-Pacific Conference and Trade Exhibition on Ground and Water Bioengineering for Erosion Control and Slope Stabilization,(to be appeared). R. Kitamura, H. Abe, T. Iryo, K. Jomoto, K. Yamamoto and T. Terachi (1999b): Field measurement of suction in soil and rainfall in Kagoshima Prefecture, Proc. Int. Sympo. On Slope Stability Engineering(IS-Shikoku'99), (to be appeared). H. Abe, R. Kitamura, K. Jomoto, M. Seyama and H. Shikata (1999~):Permeability and water retention tests on unsaturated soil, Proc. 34th Japan National Conf. on Geotechnical Engineering, (to be appeared), (in Japanese).

488

Slope Stability Engineering, Yagi, Yamagami & Jiang (( 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Relationships between rainfalls and landslides after forest damages by typhoons S. Murata, H.Shibuya & K. Hayashi Depurhnent of Civil EiizineeriiigVKLmiunioto Institute of Techiiologj! Jupun

ABSTRACT: Many severe disasters occurred by heavy rainfalls during rainy and typhoon season in Kyushu. We investigated many disasters and rainfalls. As a result, we found the relationships between rainfalls and degrees of disasters in Kyushu. Furthermore, big forest damages occurred by typhoons and bulky trees were blown down. After the typhoons, many landslides occurred in the areas of forest damages and those landslides occurred by weaker rainfalls than those which caused the former disasters. And most of landslides were overlapped with the areas of forest damages. Therefore, these landslides were caused by the influence of the forest damages due to the typhoons. These slopes and mountains in the areas of forest damages have changed to different situations and strength of ground decreased severely after the typhoon.

1 INTRODUCTION We have had many sediment disasters, landslides and debris flows, caused by rainfalls in Kyushu. Therefore, i t is needed to find a method of mitigation of disaster. It is widely known that there are some relations between rainfalls and sediment disasters. However, those relationships are not yet found exactly. At first, we examined about those relationships using AMeDAS data of the Meteorological Agency. And then, we discuss sediment disasters after typhoons. We had big typhoons in 1991 and 1993 and bulky trees were suffered severe damages. Some damaged trees were completely overturned from their roots and others were bent like an arch and broken at the middle of their trunks. At the same time, the ground was disturbed by the overturned trees and the strength of ground were decreased. Therefore, it was worried that landslides would occur by rainfalls more easily than before the typhoons. After the typhoons, many landslides occurred by the weaker rainfalls than those which caused the former disasters in the areas of forest damages. These landslides show that the strength of ground was extremely decreased. Those subjects were described in this paper.

2 RELATIONSHIP BETWEEN RAINFALLS AND SEDIMENT DISASTERS Typical examples of rainfall which caused severe disasters in Kumamoto Prefecture are shown in Figures 1 and 2. Figure 1 shows an example of heavy

rainfall in the late rainy season. This rainfall had a lot of antecedent precipitation before the disaster and this point is a distinguishing character of this rainfall. On the other hand, Figure 2 shows a example of heavy rainfall which had not antecedent precipitation1 before the disaster and the heavy rainfall happened only on the day of disaster. Since both rainfalls caused severe disasters, antecedent precipitation before the disaster is not so important for the occurrence of the disaster. We can easily realize that disasters occurred by the intensive rainfall within a short period of time.

Figure 1 Hourly rainfall hyetograph observed at Aso Otohime in Kumamoto, July, 1990 Most disasters occurred while the intensive rainfall continued for several hours and when the maximum hourly rainfall happened. Therefore, relationships between the hourly rainfalls and the amount of rainfalls before the disaster were already pursued by several researchers. However, these relations are not complete 489

Figure 2 Hourly rainfall hyetograph observed at Manotaniyama in Kumamoto, May, 1988 and have to be improved by the new data. Then we pursued to find new relations about the hourly rainfalls and the amount of rainfalls before the disaster. Data used in this research are rainfalls of big disaster occurred in Kyushu during the past 50 years and rainfalls of rainy season in 1998 in Kumamoto Prefecture. The rainfall of rainy season in 1998 gives special data, because the total rainfall in one week was more than 1,000 mm in several places. If this rainfall was concentrated in one or two days, we could imagine that sever disaster occurred in everywhere. However, only small disasters occurred in several places in Kumamoto, because the rainfall dispersed during one week. So the rainfalls give the lower level of the occurrence of the disaster. As times of antecedent precipitation before the maximum hourly rainfall, 3, 4, 5 , 6, 12 and 24 hours are selected. And relationships between these antecedent rainfalls and the maximum hourly rainfall are plotted in Figures 3(a), (b), (c), (d), (e) and (9. It become clear from these figures that 12 or 24 hours as the antecedent precipitation are better to estimate a degree of disaster. For example, if w e had a antecedent precipitation of 12 or 24 hours, we could estimate a degree of disaster for the next intensive rainfall.

3 FOREST DAMAGES DUE TO TYPHOON NO. 19 AND LANDSLIDES DUE T O RAINFALL AFTER THE TYPHOON Typhoon No. 19 went through northern part of Kyushu on September 27, 1991 as shown in Figure 4. The typhoon brought very strong wind and its maximum wind velocity was 60 m/sec. The typhoon caused big forest damages in wide areas in Kyushu Island Bulky

Figure 3 Relationship between antecedent precipitation and maximum hourly rainfall

trees were also blown down by the typhoon in Oguin Town, Kumamoto Prefecture. Most blown-down trees were Japanese cedars, which were planted artificially

490

Figure 4 Courses of Typhoon No. 19, 1991 and No.13, 1993 and aged 30-40 years. Some damaged trees were completely bend like an arch. The rest of them were broken down a t the m i d d l e of their trunks o r overturned form the roots. At the same time, the ground was disturbed by the overturned trees and the strength of the ground decreased. After the typhoon, many landslides and debris flow occurred in Oguni town and other places by the rainfall. Especially, the severe disaster occurred in Tsuetate village, a hot spring resort. This village is located on narrow places in the village and surrounded by steep slopes, 40m-50m high. People have often suffered from damages by floods of the Tsuetate River which flows through the center of the village. These steep slopes were undamaged for a long time. Therefore, people only worried about a flood at that time. The rain which began from June 13 continued as a typical rain in the rainy season and the accumulative rainfall became about 200mm by the time of the disaster as shown in Figure 5. The rainfall became heavy from early morning and continued until the afternoon. Many landslides occurred between 1O:OO am and 12:OO am as shown in Photo 1. The first small landslide and rockfall occurred around 9:OO am. Most people evacuated t o s a f e t y places before the occurrence of severe landslides. A big landslide occurred at 11:lO am. And two people were killed by the landslides. These landslides occurred during a day time so that the occurrence of landslides and rockfall, etc. were actually observed. 4 COMPARISON OF RAINFALLS BETWEEN THIS TIME AND JULY 1990 Distinctive feature in this rainfall was that the rainfall continued for six hours from 6:OO am. to 12:OO am. However, this rainfall was not distinctive in comparison with the former ones which caused severe

Figure 3 Relationship between antecedent precipitation and maximum hourly rainfall

491

Figure 5 Hourly rainfall hyetograph observed at Tsuetate in Kumamoto, 1993

Figure 6 Hourly rainfall hyetograph of the day of landslide at Tsuetate on June 18, 1993 Photo 1 Landslides of Tsuetate on June 18, 1993

Figure 7 Hourly rainfall hyetograph observed at Tsuetate on July 2, 1990

Photo 2 Forest damages of Tsuetate due to typhoon No.19. 1991 disaster. And landslides usually do not occur by this magnitude of rainfall. The rainfall was investigated in details to verify the cause of these landslides. Figure 6 shows the rainfall of the day when the disaster occurred. The cumulative rainfall until the occurrence of the first rockfall and landslide was about 100 mm and the hourly rainfall was about 30 mm. On the other hand, Figure 7 shows the rainfall on July 1990. There was no landslide in this area at that time, although the cumulative rainfall was 150 mm and the

Figure 8 Relation between landslides and areas of forest damages 492

hourly rainfall was about 45 mm. If the ground situations of these slopes were the same as in 1990, the landslides would not occur at 9:OO am. These slopes and mountains suffered from the damages by blowndown trees which caused by Typhoon No.19 (Photo 2). T h e areas of forest damages and the places of landslides were illustrated together in Figure 8. Many landslides were overlapped with the areas of forest damages. Therefore, these slopes and mountains have changed to different situations after the typhoon. And these failures were caused by the influence of the forest damages due to Typhoon No.19.

5

FOREST DAMAGES DUE T O TYPHOON N 0 . 1 3 AND LANDSLIDES DUE TO RAINFALL

Typhoon No.13 went through the southern part of Kyushu on September 3, 1993 as shown in Figure 4. T h e typhoon caused severe forest damages in Sakamoto Village, Kumamoto Prefecture. Bulky trees were also blown down by the typhoon. Most blowndown trees were Japanese cedars, which were planted artificially and aged 30-40 years. Some damaged trees were bent and others were completely overturned. The rest of them were broken down at the middle of their trunks. At the same time, the landslide occurred in many places as shown in Photo 3. These landslides occurred due to the rainfall carried the typhoon. The rainfalls were timely measured by the Aburatani Dam station located in the center of the forest damaged area. The hourly rainfalls on the day of typhoon are shown in Figure 9. However, this rainfall was not so strong. There were stronger rainfalls on August 1 and 18 before the typhoon. The ground was disturbed by the overturned trees and as a result the strength of the ground decreased. Therefore, it is

Photo 3 Landslides of Sakamoto Village on September 3, 1993

Figure 9 Hourly rainfall hyetograph observed at Aburatani Dam on September 3, 1993 clear that these landslides occurred by the influence of blown-down trees caused by the typhoon.

6 ANOTHER LANDSLIDE IN SAKAMOTO VILLAGE A big landslide occurred in Sakamoto Village on July 15,1998 as shown in Photo 4. This area suffered from forest damages by the Typhoon No.13, 5 years ago as shown in Photo 5. The bulky blown-down trees and some landslides are seen in the photo. The landslide was overlapped completely with the area of forest damage as shown in Figure 10. The rainfall was measured by the rain recorder of Highway Office station located at only 600m from the failure place. There were a lot of rain from July 7 to 9 in this area, but it did not rain on the day when the failure occurred as shown in Figure 14. Therefore, this landslide did not occur directly due to the rainfall. Thess slopes and mountains have changed to different situations after the typhoon. And this landslide was caused by the influence of the forest damages due to Typhoon No.13. After the failure, we found that a lot of water flowed out from the middle of the slope as shown in Photo 8. 493

7 CONCLUSIONS Conclusions are summarize as follow: 1. When w e m a k e a relationship between the antecedent precipitations and the maximum hourly rainfalls, as antecedent precipitation 12 or 24 hours is better for estimation of the degree of disaster. 2. The ground was disturbed by the overturned trees and the strength of the ground decreased by typhoons. Slopes and mountains suffered from forest damages areas have changed to different situations after the typhoon. Therefore, the landslides occur due to more small rainfall in those areas, so we have to pay attention to weaker rainfalls for several years in future.

Photo 5 Forest damages of Ayugaeri in Sakamoto Village due to Typhoon N0.13~1993

3. Rainfall permeated into the ground and reached the non-permeable layer, then concentrated and flowed in the permeable layer. After that, groundwater act on a slope and the pore water pressure in the weathered stratum went up, then the landslides occurred. It is estimated that the groundwater may gathered not only in the failure area but also in other areas. ACKNOWLEDGMENTS We obtained information regarding rain record, photo, map etc., from Kumamoto Local Weather Station, Oguni T o w n , S a k a m o t o T o w n , K u m a m o t o Prefecture, Kikuchigawa Branch in Ministry of Construction, Japan Highway Public Corporation and Kyushu Power Electric Co. Ltd. The authors express their sincere acknowledgments with many thanks.

Figure 10 Relation between landslide and areas of forest damages

REFERENCES Murata, S. & Shibuya, H 1994. Failure of Sabo dams and rockfall prevention walls caused by the heavy rainfalls of Kumamoto in 1990and 1993, Int. Conf Landslides Slope Stability and the Infra-Structure, Malaysia, 257-263.. Aboshi, H. & Sokobiki, H. 1972. Failure of natural slopes in Masa area, Conf 7”” Soil and Foundation Engineering, 507-5 10.

Photo 6 Flow of groundwater from landslide surface Rainfall permeated into the ground and reached nonpermeable layers, and then concentrated and flowed in the permeable layers. This groundwater acted of the slope from behind and the pore water pressure in the weathered stratum went up, then the failure occurred. It is estimated that the groundwater gathered not only in the failure area but also in other areas.

494

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Threshold rainfall for Beragala landslide in Sri Lanka A. K. Dissanayake & Y. Sasaki Department of Civil and Environmental Engineering, Hiroshima University,Japan

N.H. Seneviratne Department of Civil Engineering, University of Peradeniya, Sri Lanka

ABSTRACT: Particularly during the monsoonal rainy seasons, landslides occur very frequently in the central highlands of Sri Lanka causing numerous problems. In order to study the appropriate instrumentation in understanding the mechanism of rain induced landslides, a research study was undertaken to monitor the Beragala landslide, which is particularly significant because of the possible disruption it causes to the national transportation system in the southern part of the central highland. This paper describes the results of the field monitoring carried out at this landslide and the stability analysis with respect to the variation of ground water levels. Both the piezometric levels and surface movement observations showed that the one-week cumulative rainfall causes the instability of the landslide at Beragala. The threshold value of the one-week cumulative rainfall at which the landslide becomes unstable was estimated to be 310mm. Outcome of the results showed that the selection of appropriate monitoring techniques are indispensable in understanding the mechanism of landslides and thereby to provide both economical remedial measures and warning systems to mitigate the sliding induced disasters. experiences 3000 to 2000mm annual rainfalls, which covers the entire hill country. Almost all the landslides occur within these two climatic zones in the central highlands due to the heavy precipitation. Beragala landslide area belongs to Badulla district in the central highlands of Sri Lanka, which is in the intermediate climatic zone. The landslide is situated on the southern slope of Ohiya-Idalgashinna-Haputala ridge at an elevation of about 1200m above mean sea level (MSL). This landslide is on a scarp slope and its location is shown in Fig.1.

1. INTRODUCTION

Because of the great damage that landslides cause to the forest growth, farmlands, communication systems, engineering constructions, infrastructure, such as supply systems, roads, railway lines, etc. and buildings, they are attracting increasing attention in many countries in the world (Ng., et al., 1998 and Bhandari, et al., 1994), and have become a serious economic problem. In Sri Lanka, many landslides occur in residual terrain of the central highlands, particularly during rainy seasons, which present difficulties in understanding the behavior and mechanism due to the inherent heterogeneity of the soil involved. The central highlands of Sri Lanka starts from an elevation of about 270 m above Mean Sea Level (MSL) and nearly 22% of the land area is covered with hilly or mountainous terrain, embracing well over one million hectares, spread over seven districts. Predominantly, Precambrian crystalline rocks underlie ninety percent of the Sri Lankan land area, including the entire hill country. (Cooray, 1994). According to the annual precipitation experienced, Sri Lanka has been divided into three climatic zones. The Wet Zone that covers nearly one third of the area of central highlands and southwestern sector of the island receives above 3000mm annual rainfall, The Intermediate Zone

Fig. 1 Location of Beragala landslide 495

This slide is of major national significance as the sliding area encompasses two major motor ways A4 and A16, which connect the capital, Colombo, with outstation cities of Wellawaya and Haputale respectively. Beragala landslide crosses Beragala-Hali Ela (A16) road just after the 1st kilometer post from Beragala junction.

geotechnical investigations were done at Beragala landslide area under Second Road Improvement Project. Following the consultant's report, the Road Development Authority of Sri Lanka has undertaken the stage 1 of the remedial work in 1992, focusing mainly on improving the drainage of the area. This work consisted of constructing a 500m long surface diversion drain which has been built using 0.9m diameter hume pipes and a 4m deep trench drain of length 50m by the side of the road A16. These drains had been designed to collect the surface water from the area above the road and to discharge them safely into a stream far away from the slide. In addition, three horizontal underground drains have been constructed across the road A16 to relieve the artesian pressure in the area. At the time when this project began in July 1995, several cracks at the joints of hume pipes of the surface diversion drain, which was spanning across the sliding area, were visible and water stagnant could also be seen at places along this diversion drain caused by sinking of hume pipes. Some catch pits in the sliding region have been damaged due to ground subsidence. Water was leaking from several places along the surface drain and it was obvious that this drainage system has been badly maintained since after the construction. Nevertheless, the water coming out of the horizontal drains, which relieve the artesian pressure of the slide above the road A16, has been discharged on to the lower part of the sliding area. Further, the water flowing in the diversion drain has been tapped for watcring vegetable cultivation in the lower slope of the slide below the road A16 by farmers living in that area. These illegal tappings supply water for several unlined wells dug on the landslide through out the day. Because of the above reasons, the ground water level has been increased in the area down slope; a marshy area could be observed in the middle of the slide between the roads A4 and A16 and a stream originates from there. Because of these evidences of instability of the area, it was decided to reinvestigate the state of the slope, focussing mainly on the surface movements and subsidence as the data of the complete geo-exploration and topographical surveying of the area was available (RDA, 1989).

Fig. 2 Cross section of Beragala landslide showing the soil profile and borehole locations Soil layer 1

2

I

3 4 5

6

Y

Description

1 I

Bed rock Weathered rock Dense top soil Colluvium Soil mixture with SPT>15 Top soil with SPT<15

I

kN/m3 21.0 20.5 19.0 20.0 18.5 18.0

1

Deg. 45.0 40.0 27.5 27.5 25.0 21.0

1

I

1

C' KN/m' 0 0 10 20 10

1

5

1.1 History of Bcragala landslide

The area above the road A16 (Fig. 2) had been under tea cultivation over the years. Subsequently, a part of this area came under vegetable cultivation and small holdings of the original tea estate, which are in and around the sliding area, have been badly maintained since 1970s. The land on the upper slope has been replanted in early 1970s after clearing of land. Several years before the first failure of the slide, a stream had been diverted into the landslide area, towards the Beragala junction, for watering the vegetable cultivation below the road Al6. Following a heavy rain in June 1986, the first major slide at Beragala took place depositing debris on the road A4 and the area below. Sincc then the area above the slide has been creeping continuously, badly affecting the road Al6. After this event. due to the poor water retention as a result of ground cracks and subsidence, Vegetable cultivation was partially abandoned. However in May 1987. the slide recurred causing severe damages to both roads A4 and A16 and made these roads impassable for several weeks. In 1958. because of the possibility of recurrence.

1.2 General geology, topography, subsoil conditions and the climatic variations in the vicinity of the landslide Beragala landslide area is underlain by the Precambrian rocks, which consist of quartzite, charnockite, charnocketic gneisses, biotite gneisses and granulitcs rock types (Cooray, 1994). Charnokites encountered at the site area are sparsely jointed while the quartzites are highly jointed. Biotite gneisses fall in between. Majority of joints is near vertical having a strike direction of NS to N20E and N O W to N80W.

496

The strike of the rock foliation trends in N50W to N70W with North-Easterly dips of 30 to 40 degrees (RDA, 1989 and Bandara, et al., 1994). Two welldeveloped sub vertical joint sets occur approximately in the east-west and north-south directions. The combination of the foliation and these two major joint sets has produced a step like morphology on the surface of the bedrock. Therefore, it can be observed steep escarpments alternate with less steeply sloping benches; the latter covered with colluvium and talluvium of varying thickness. The general topography of the landslide area is shown in Fig. 3 (Loganathan et al., 1992). The cross section along the major upper centerline of the landslide area shows that the southern slope of OhiyaIdalgashinna-Haputale ridge above the landslide area rises to an elevation of 1680m above MSL. The upper part of the slope, which runs from the level of 1200m above MSL to the ridge of the slope, inclines about 40 degrees to the horizontal whereas the lower slope below 1200m contour, where the landslide encounters, is inclined only about 20 degrees. The surficial slope just below the road A16 has even been much lowered down to 15 to 12 degrees due to the landslide activities that have taken place in the recent past.

Table 1. Gravel and boulders of different sizes are encountered between ground level and the top of the bedrock. The upper part of the bedrock is usually weathered. The bedrock has been encountered, in general, between 20 to 25m below the ground surface with exception of areas near the road A5 and estate bungalow where some outcrops of the bedrock are visible. Beragala landslide area is located in the Intermediate Climatic Zone, where the annual rainfall receives is in between 2000 to 3000mm. Monthly variation of the rainfall at the site, for a ten-year period starting from 1987, is shown in Fig. 4. It indicates that the landslide area receives heavy monthly rainfall of about 500mm in average during the months of April and November. In addition, it has been observed that the ground water level also varies between the ground surface and several meters below the ground level during the rainy periods. (RDA, 1989)

Fig. 4 Monthly rainfall at Beragala landslide since 1987 2

INSTRUMENTATION OF THE SLIDE

The stability of the slope can be checked by measuring the slope movements within a potential landslide area as a failure is characterized by relatively large displacements and displacement rates, which increase with time. Therefore, Beragala landslide was instrumented, basically to observe the surface movements and subsidence as the data on detailed exploration was available from an investigation done at the site in 1988. The surface movements were measured by deploying Extensometers. Ten constant tension type extensometers were setup within 300m distance along the centerline of the slide as shown in Fig. 3. Continuous recording of surface movements with time was made for 75 weeks starting from November 1995. The first extensometer was installed at a stable location above the crown of the landslide close to estate bungalow, where an outcrop of the bedrock was visible (extensometer No. 1 as shown in Fig. 3). The movements of the other extensometer

Fig. 3 General topography of Beragala landslide area Many gullies and toppled boulders remaining down the slopes in the vicinity of Beragala landslide show evidence of intensive land degradation, which has taken place over the years. Many landslides and rock falls were reported, since early 1 9 7 0 ' in ~ ~this area. According to the geotechnical investigation done at Beragala landslide site in 1988 (RDA, 1989), the subsurface soil profile has alternating silt and silty clays down to the bedrock level of which the thickness varying from 0 to about 20m (Fig. 2). The geotechnical properties of these layers are given in

497

points were calculated relative to this extensometer. As shown in Fig. 3, fifty concrete markers were installed on the slope, close to road A16 in May 1996, because this area seemed to be critical during the visual inspection of the slide. In October 1996, another 25 numbers of markers were positioned below the road A16 to enhance the intensity of data in that region. Precise leveling was carried out monthly of these markers with respect to the fixed points located well away from the sliding area, starting from May 1996. The rainfall for the site during the period of monitoring was obtained from a measuring station situated at the adjacent tea estate approximately 30 m perpendicularly away from the extensometer line between 4th and 5th extensometers. Apart from above data, the piezometric pressure observations made in the previous investigation in 1988 at Beragala landslide were also utilized in this study. 3

movements of extensometers and the one-week cumulative rainfall (Fig. 5) than with 2 and 3 weeks cumulative rainfall. This observation shows that the landslide had reactivated on the 57th week with weekly rainfall of about 400mm. The horizontal displacements of greater than 2mm of individual extensometer on respective weeks along the centerline of the landslide and the positions of the boreholes 2, 4 and 5 are shown in Fig.6. The extensometer Nos. 4 to 7 show consistently increasing movements during the respective weeks where as the movements have almost ceased at the extensometer No. 8. The extensometers 7 and 8 are located below the road A16 whereas the other instruments are located above this road. Since this stretch of the landslide undergoes large deformations during the rainy periods, it was considered as a critical section for stability analysis.

FIELD OBSERVATIONS AND ANALYSIS OF DATA

The use of extensometers, in surface movement observations, started in November 1995 and continued for 75 weeks, which includes a complete weather cycle. The cumulative movements of each extensometer with respect to the extensometer No. 1 and cumulative rainfall, during the monitoring period, are presented in Fig. 5. These data show that, even after a complete weather cycle (i.e. after 55 weeks), the average rate of surface movement is only 75 mm per year and also indicates that the movement of the slide increases with the increase of rainfall intensity.

Fig. 6 Horizontal displacements of extensometers along the centerline of the slide Monthly subsidence of the ground at Beragala landslide was observed using precise leveling since May 1996 and carried out uninterruptedly until October 1996. There was no significant subsidence of the ground observed until about five months after the commencement of the measurements. Markers were surveyed again in the 8th month (Jan.’97) and in the 13th month (Jun.’97) and the observations are shown in Fig. 7.

Fig. 5 Variation of cumulative movement of extensometers with weekly rainfall Analysis of the variation of weekly cumulative movements of extensometers against the 1, 2 and 3 weeks rainfall at Beragala landslide showed that a better COrrelatiOIl exists between weekly CUmUlatiVe

~

498

i 7 Subsidence ~ . Contours at Beragala landslide

These observations also indicate that the landslide has reactivated during 5th and 8th months probably after heavy rainfall periods in November and December 1996. The sliding area, especially just below the road A16, has undergone a considerable amount of subsidence 0f up to 45 cm during the period of 5th month to 13th month. This observation also confirms the fact that the area around road A16 is more susceptible to failure during heavy rainy periods. It is also clear from these figures that the upper centerline of the landslide has shifted to the left of the proposed centerline. This may be due to the alteration of the drainage after the stabilization measures in 1992. The piezometric pressure variation observed during the period of August to November 1988 also showed a better correlation with one-week rainfall as presented in Fig. 8. The fact of increasing the piezometric heads during the rainy spell between October 9th, 13th and October 30th to November 13th illustrates the above argument. The almost constant piezometric levels during the period after November 15th may be explained by the fact that the time elapsed between rise and reduction of pore pressures in the sliding area. Further, the continuous accumulation of water in the landslide area is less than the accumulation of water during the period between October 9th and 13th.

by 1.6m, l.lm, 2.3m and 0.9m at boreholes 2, 4, 5 and 8, respectively due to 310mm weekly rainfall above the “normal” ground water level, which prevails most of the time during a complete weather cycle as found by the previous investigation in 1988.

Fig. 9 Piezometric pressure relations with weekly rainfall

4

STABILITY ANALYSIS OF THE SLOPE

A computer program based on Spencer’s procedure was adopted in computing the factors of safety of the slope for several ground water conditions corresponding to different weekly rainfalls as found by using the relations shown in Fig. 9. The sub-soil profiles and their geotechnical properties, as shown in Fig. 2 and Table 1 respectively, were used for the stability analysis of the slope. The boundary conditions were imposed considering the surface movement observations as mentioned earlicr and thus, the stability of the lower (below the road A16) and upper (above the road A16) slopes were analyzed separately and the critical shear surfaces found from this analysis are given in Fig. 10.

Fig. 8 Variation of piezometric pressures along the centerline of the landslide Linear relations with reasonable accuracy were found between piezometric pressure and one-week rainfall at Beragala landslidc at each borehole as shown in Fig. 9. Almost all the piezometers indicate good linear relations with the cumulative rainfall except the piezometer at BH8-7.35m. Gradients of the trend lines are varying between 0.0031 to 0.0077 m per millimeter of weekly rainfall. These gradients were utilized in determining the ground water profile at the sliding area for various weekly rainfall intensities. For instance, the ground water level rises

Fig. 10 Critical Failure surfaces at Beragaja landslide (R = Radius of the Circle, Fs = Factor of safety)

499

only in monitoring the movement, but also in determining the critical sections for stability analysis. 3. A shift of the subsidence zone is probably caused due the alteration of the drainage patterns after stabilization. Therefore, it can be concluded that the conventional precise leveling technique provides useful information, although it is time consuming. It further concludes that the monitoring of surface movements is indispensable in understanding the mechanism and discussing the stability of landslides. 4. Observations show that the slope above the existing landslide becomes unstable during heavy rainy periods. It also showed that the 1-week cumulative rainfall has a good correlation with the variation of the surface movements. 5. The stability analysis of the slope at Beragala landslide shows that the circular slide at the toe of the landslide becomes unstable at low intensity of weekly rainfall of about 210mm. The studies also showed that the whole slide becomes unstable after the total failure of this toe slide. Therefore, it was recommended to offer priority to this slide in the stabilization work of the landslide area. 6. It was also estimated a threshold value of 3lOmm weekly rainfall, which could trigger the landslide at Beragala; a value of which might be used to implement an early warning system to mitigate disaster due to sudden collapse of the slide.

The factors of safety of the slope for different ground water levels corresponding to the weekly rainfall of 250, 300, 350, 400, and 450 mm respectively, were calculated and are plotted in Fig. 11.

Fig. 11 Variation of safety factor with weekly rainfall (Failure profile : NC- Non Circular, C- Circular) From this analysis, it was found an exponentially decaying relation between the safety factor of the upper circular slide and the weekly rainfall. Utilizing this relation, a threshold value of one-week rainfall of 310 mm was estimated, which could trigger the failure of the upper slope. In fact, the recurrence of the landslide was observed when the weekly rainfall was about 400 mm as shown in Fig. 5. It was also found that the circular slide at the toe of the landslide becomes unstable at a low weekly intensity of rainfall of about 210mm. The stability analysis further showed that the whole slide becomes unstable after the collapse of this toe slide. Therefore, this fact was brought to the notice of the relevant authorities in Sri Lanka and an immediate attention to stabilize this critical slope prior to any other counter measuring work was recommended.

REFERENCES Bandara, R.M.S. and Kumarapeli, K.A.D.S.P. 1994. Mharagala debris flow cuin rock full, Proc. National Symposium on Landslides in Sri Lanka, 83-88 Bhandari, R.K and Thayalan, N. 1994. Landslides and other mass movements including failures of ciittings in residual soils in Sri Lanku, Proc. National Symposium on Landslides in Sri Lanka, 73-82. Cooray, P.G., 1994. Geological fuctoi.s affecting landslides in Sri Lanku, Proc. National Symposium on Landslides in Sri Lanka, 15-22. Ng, C.W.W and Shi, Q. (1998) “A numerical investigation of unsaturated soils slopes subjected to transient seepage” Journal of Computers and Geotechnics, Vol. 22, No. 1, 1-28 Loganathan, N., De Silva, S and Thurairajah, A. 1992. Strength correlation fuctors for residual soils, Journal of Geotechnical Engineering, ASCE, Vol. 118, NO 1, 593-610. Road Development Authority (RDA) of Sri Lanka, 1989. Phase I report, Asian Developtneizt Bank Fiinded Second Roud Improvement Project.

5 CONCLUSIONS The detailed geotechnical investigation at Beragala landslide in Sri Lanka was carried out to identify the mechanism and thereby to propose economical remedial measures. Following conclusions were made after the analysis of the field observations and the stability of the slope. 1. The observed surface movement during a complete weather cycle was 75 mm before the slide was reactivated. The small value of the movement is due to poor rainfall during the first 55 weeks. After the heavy weekly rainfall of 400 mm in November 1996, the landslide has reactivated and the extensometer observations and subsidence measurements showed a surface movement of about 700 to 800 mm per year, subsequently. 2. Use of the extensometers in landslide observations is also a very effective technique not 500

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

The importance of the groundwater regime studies of unstable slopes - An example of investigations on the landslide 'Plavinac ', Yugoslavia Goran Rasula Jaroslav Cerni Institutefor the Development of Wuter Resources, Belgrade, Yugoslavia

Mladenka Rasula CIP Institute.for Transportation,Departmentfor Geotechnics, Belgrade, Yugoslavia

ABSTRACT Many unstable slopes with active or partially soothed sliding processes are limiting factors in urban planning, and urban, traffic and other development on the Danube river bank (right). Because of complex lithological structures, neotectonics, erosion and other current geodynamical processes in the area, a multidisciplinary approach to investigations is required and particularly needed for any local remedial or protection measures. Our numerous papers on engineering-geological investigations on unstable slopes clearly show that we have not enough experience in the determination of groundwater table fluctuations, although its presence is one of the key active factors in slope stability. During 1997, the engineering-geological and hydrogeological investigations performed for the purpose of planning and developing the lands of the "Zlatni Breg" Ekonomija (Golden hill Farm estate) located in the central part of the "Plavinac" landslide, near Smederevo included a detailed groundwater table study after which geotechnical conditions for planning the land development and adequately and rationally protecting it were established. This paper puts an emphasis on the hydrogeological activities and methodology of a reliable, quality determination of the groundwater regime in the landslide body as a basis for geotechnical modelling of slope stability, all for the purpose of planning the farm estate development, i.e. preparing optimum measures of protection. Key words: hydrogeology, engineering geology, landslides, groundwater regime, slope stability, protection measures 1 INTRODUCTION

protection measures of the level of a detailed design were to be planned in order to arrange and develop the land on an area of about 3 1 hectares.

For the purpose of determining geotechnical parameters for local land development, vineyard raising, construction of access communications, subsidiary buildings, an optimum irrigation system and drainage systems in the overhumid zones in the area of Golden hill farm estate near Smederevo, which is fully situated in the central part of the "Plavinac" landslide, a program of specific, dedicated, hydrogeological and engineering geological investigations, in the office and in the field, was first defined and then implemented in due time. The main approach was to first identify all ground stability disturbing processes bearing in mind its planned use, and then to briefly refer to the groundwater regime and balance in the wide surrounds of the landslide. In the final phase the ground stability was to be modelled using different groundwater tables, and

2 MAINPOINTS The central section, precisely the Golden hill farm estate lies in the west end of the urban area of Smederevo, south of the old Smederevo Ironworks on an area of 3 1.5 ha, 21 ha of which are under plantations of pear trees, apple trees and vineyards and 10 ha under auxiliary buildings, communications and the park with a very interesting historical museum building, the old villa of the Obrenovic dynasty. The estate extends between Bratstvo i Jedinstvo St. in the north, at altitude of 115 m above sea level, Goricka St. in the south, at about 190 m above sea level, Timocka St. at the east, 115-190 ni above sea level 501

used to touch the Smederevo-Belgrade road (Goranska St.) while today its bank is moved by about 60 m towards the river stream centre. Morphology in the area of the Old Villa shows a ground leap of 2-5 m, sloped at about 30' that cannot be noticed on the topographic plan of 1941. Moderate continental climate is evident. Average annual amount of precipitation (19491995 records) is 665.8 mm, maximum 916 mm (1954), and minimum 447 mm (1950). In the dry months only (July, August) the minimum monthly precipitation is 4 mm (July, 1958), and maximum 194 mm (August, 1975). Average annual air temperature is 11.3"C. The lowest temperatures of 0,06-2OC on average occur in winter months (January, February), while they are maximum 20.9-21.2OC in summer months (complete records).

3 CAUSES OF INSTABILITY IN THE INVESTIGATED A'REA

Fig 1. Situation map of the investigated area

Based on the analyzed properties of the ground from the aspects of geomorphology, engineering geology, hydrogeology in the wide zone of the investigated area, the causes of the "Plavinac" landslide formation were determined and found to be still causes of stability disturbance, though occasional and localized. In the period before the completion of the hydroelectric power plant of "Djerdap" the Danube river used to undermine the shore belt by permanent linear erosion. As the labile balance was thus disturbed and the toe of the slope taken away, sliding processes were actuated both occasionally and continually with a regressive up slope tendency to an altitude of 175 m above sea level. With regard to geology, frequent alternating of loessoid clays and dusty sands as well as coal clay beds are evident (Fig.2) which caused local fragmentation of sedinients and which, due to geomorphologic and neotectonic processes made disturbances of the slope stability easier. The landslide was activated to a major extent after the Bucharest earthquake. The hydrogeological properties of the ground with three fully separated aquifers (Fig.2), where the first aquifer groundwater plays the most active role in water saturation of the ground in surface and subsurface colluvial deposits down to the depth of about 10-I5 m constitute one of the main factors of adverse strain, particularly in wet periods. Inappropriate human activity also partly

and Nevesinjska St. in the west, at about 125-190 m above sea level. The entire investigated area lies in the body of the "Plavinac" landslide (Fig.1). In order to make a comprehensive review of the soil engineering geological and hydrogeological characteristics, a broader district was investigated encompassing the land lying eastward, i.e. the western flanks of the adjacent "Provalije" landslide around the Cir Antina fountain. With regard to geomorphology the investigated area lies on a relatively gentle slope (from 129 m in Goricka St. down to 70 m along the bank of the Danube river). Watched along the south-north line first comes a steep cut inclined at 1:2 (in the zone of a loess cap on Zlatni breg). South from the park the slope is inclined at 1:5, while in the park itself at the location of the Old villa of the Obrenovics the inclination is 1 :10. The inclination of the rest of the investigated area, the farmland zone north of the villa to Bratstvo i Jedinstvo St. is 1:15 (Fig.2). The stretch below the estate northern boundary, at the Danube side (on which numerous unplanned private housing projects and other buildings have been built) is much steeper and shows evident scars of active sliding (toe of the landslide). A comparison of the topographic plans of 1941 with those of 1976 shows that the section of the Danube river opposite the "Plavinac" landslide 502

contributed to ground instability such as: extensive unplanned (wild) housing, construction of sheds md other buildings, private water intakes, sump pits for waste and other waters, drains for runoff and faecal waters in the wide surrounds of the farm estate.

that any extremely high groundwater rise in this aquifer can almost in a nick of time activate the whole landslide or some of its parts. For this reason additional hydrogeological investigations and quantification of groundwater regime and balance was started in the wide surounds of the investigated area.

4 THE CONCEPT AND METHODOLOGY OF APPLIED INVESTIGATIONS After a preliminary study of the basic geological documents and detailed reconnaissance in the wide investigated area and pursuant to the terms of reference for the farm estate development and preservation of the "Old villa of the Obrenovics" museum and its grounds (the park), the following study and investigations were first designed and then realized: * Desk-top study of the available documents in order to define the programme and schedule of field work. * The field work included: engineering geological ground mapping (wide surrounds of Golden hill farm estate); an expert inspection of the Old villa building (detailed in the basement); detailed hydrogeological mapping, a questionnaire on the use and yield of all the existing wells; preparation of a cadastre of all observation water structures, for the six selected wells, tests were carried out in order to identify filtering parameters of their aquifers and set water intake rules, regulate the groundwater levels and specify ground remedial measures and requirements for future drainage and irrigation systems; at all registered water structures a systematic observation of the groundwater table fluctuations and daily observation of the amount of precipitation on the farm were started. * The desk top and laboratory work included: a detailed study of the past engineering geological and hydrogeological investigations, an engineering geological map; a detailed hydrogeologicalhydrodynamic study of groundwater fluctuations in the determined aquifer environments, particularly in the first phreatic aquifer and correlation with the observed daily amounts of "in situ" precipitation this becoming the base for a geotechnical analysis of soil stability. A summary of the results of past investigations is given as a general statement that tlic ground in the farm estate is in a so-called tranquilized state and that any possible future disturbance of its stability may be associated with the sliding plane which lies at the average depth of about 10 m (in the first phreatic aquifer floor) and

5 HYDROGEOLOGY OF THE TERRAIN A detailed analysis of the available documentation and additional hydrogeological investigations designed to the purpose down to the relative depth of about 138 m pointed to three characteristic aquifer complexes (Fig. 2): a) The "first phreatic aquifer" located in the surface and subsurface complexes in colluvial loessoid sands and clays to the depth of about 10 m and depths to the groundwater table of 0.90 m (at the lower sections around 125 m above sea level) to about 4 m (on higher ground at 150-155 m). Replenishing conditions in the first aquifer are directly related with vertical balance parameters (precipitation, evaporation, evapotranspiration, humidity, temperature etc.) as well as with inflows from the background (from hypsometric higher loess deposits while drainage, depending on ground morphology is in form of gravity percolation to lower ground sections. In the wide investigated area, this aquifer drains through numerous dug out and drilled wells that serve as water supplies in households mostly for garden, vineyard and courtyard watering). b) The free level phreatic aquifer is formed in the complex of the so called roof sands that occur mostly at the depths of 15-30 m (Fig. 2). In the higher ground sections (south of the park) these sands lie at the depth of 34-78 m (thicker than 30 m) while in the lower grounds, below the level of 125 m they lie at the depth od 17-45 m (thickness about 25 rn). In the lower ground sections this aquifer practically blends with the first aquifer (borehole Sb-19) and because of a pronounced sliding process, waters from both of the aquifers percolate by gravitation and diffuse downwards towards the shore belt of the Danube (without visible springs, filtration springs or pools). The depths down to this aquifer table measured on the highest ground sections (borehole Sb-34) amount to about 69 m while on the lower ground (well Sb-29) they are about 25 m. Water is replenished at the expense of infiltration from the "first aquifer" in shallow subsurface complexes and particularly from the loess deposits in the

503

Fig. 2 Hydrogeological and engineering-geological yroJile of the wide investigated area

504

Fig 3. Comparison between groundwater table diagrams of the 'tfirst aqufer" and precipitation in the period of investigation background. The aquifers are drained, in addition to gravity percolation towards the Danube stream, by intense water intake in local wells in the wide investigated area wherefrom water is taken for household water supply systems. c) A subartesian aquifer is formed within the so called floor sands at the depth of over 75 m below the surface. Groundwater observations show that the groundwater table varies between absolute levels of 76 m (Sb-18) and 79 m (Sb-23). In the course of the preliminary investigations the thickness of this aquifer was determined only in two boreholes in the coastal belt of the Danube (Sb-29 and VB 4) where it was about 10 m while in the Sb-18 borehole it exceeded 20 m and its floor has not been located with precision. This aquifer is replenished with infiltrated water from the shallow aquifers in the wide investigated area (Sumadija hinterland) of the general N and NW direction of migration. The aquifer is drained practically in the whole wide investigated area. It is evident that the absolute groundwater levels of the first aquifer in the zone of the farm estate lie between 149.76 m above sea level (in the park south of the Old Villa) and 117,93 m (in the zone of water intake wells at the lowest part of the estate - along Bratstva i Jedinstva St.). One may say that the piezometer profile practically follows ground morphology (Fig. 1 and Fig.2.). In the same period the groundwater table in the deeper phreatic aquifer (within roof sands) ranged from 124.20 m above sea level (SB-23) and 98.06 m (Sb-28). The subartesian aquifer (within floor sands) has the most gently falling piezometer line and its groundwater table varies between 79.29 m above

sea level (Sb-23) and 72.92 m (Sb-29) - (Fig.2). Continuous systematic observation of groundwater table in all three aquifers is performed on more than 40 registered water structures with simultaneous daily recording of the amount of precipitation on a local pluviograph stationed in the estate. Groundwater observations are so programmed that the retardation period and the infiltration rate particularly in the zone of the "first aquifer" are determined with the highest possible reliability after any intense precipitations. Data from trial pumping in selected wells were analyzed on a full hydrogram using original hydrodynamic software programme for trial pumping data processing MVAS 17 (Jaroslav Cerni Institute, Belgrade). Transmissivity coefficient values for the "first aquifer" vary within the limits of T=5 x 10-6- 7 x 10-' m2/s and T = 1.2 x 10-4m2/s for the deeper aquifer (Sb-29). Effective porosity varies within the limits of E = 0.002-0.05. It is evident that the yields of both phreatic aquifers ("first aquifer" to the depth of about 10 m and the deeper phreatic aquifer to the depth of about 30 m) are very small the average one being about 0.1 l/s/well. On the other hand, a preliminary hydrodynamic model was formed to analyze primary and basic hydrogeological prerequisites for selecting a drainage system in order to monitor and control groundwater table on the basis of the identified filtration parameters of the "first aquifer".

505

6 GROUND STABILITY AS A FUNCTION OF THE "FIRST AQUIFER" GROUNDWATER TABLE

to Bratstvo i Jedinstvo St. (1 15 m).

* Slide "B" extending from the youngest front scar in the Old villa zone (at the level of about 150 m) to Bratstvo i jedinstvo St. (1 15 m). In addition to the hydrogeological parameters of the existing water structures in the wide surrounds of the Farm estate, a need appeared in the course of 1997 to adopt values for the physical-mechanical parameters of the lithological environment derived from preliminary investigations (1 986). The standard for an analysis of the impact of groundwater table fluctuations on stability is the limit state of the balance Fs=l and the average observed groundwater levels in the period (May-June, 1997). For different conditions of the first phreatic aquifer groundwater table, the values of safety factor Fs is giving in Tab 1. On the basis of a stability analysis and with a view to all preliminary hydrogeological observations the definite conclusions and recommendations have been made.

Extensive hydrogeological investigations were conducted for a reliable separation of characteristic aquifer complexes down to the investigated depth of 138 my and were followedby a specific quantitative analysis of the "first aquifer" groundwater table. The aim was to determine conditions for possible active monitoring and control of the "first aquifer" groundwater table in particular for the purpose of preserving the existing conditional ground stability (by appropriate geotechnical measures of protection) on the one hand and design optimum and rational hydrotechnical amelioration measures for ground development and raising of new plantations in the estate on the other hand. A six-month analysis of fluctuations of the first aquifer groundwater table indicated risky sudden rising of the table after abundant precipitations (about 1.7 m at Sb-2, Fig.3) with an approximate 7-day retardation period. Thanks to this, guidelines were established for an approach to a concrete targeted geotechnical analysis of soil stability. With regard to earlier landslide engineering geological investigations and hydrogeological properties of the colluvial complex in the first aquifer, conditions were considered for preserving ground stability by maintaining groundwater table at the given optimum depth. A quantitative geotechnical analysis of slope stability was done, first of all, in the narrow zone of the investigated area from which the toe of the landslide was excluded. A calculation was made by Janbu modifying method that depends on the type of the slide planes that were considered to the depths of 10-15 m: * Slide "A" extending from the loess plateau cut at the level of 175 m (the front scar zone)

7 FINAL COMMENTS The results of the conducted engineeringgeological and hydrogeologic works and study in the wide surrounds of Golden hill farm estate have been used to prepare the main geotechnical plans for a detailed design for the estate development in order to raise vineyards and orchards on the area of 31 ha. This paper puts an emphasis on contributions that the groundwater regime determination of quality and quantity, an interactive implementation of hydrogeological experience and a good communication with geotechnical modelling of soil stability have for modern and rational approach to solving concrete problems of unstable slope protection and rehabilitation.

Tuble I . The average groundwater level at the depth from 1 to 4 m below the ground surface

"A" Slide Fs= 1

Fs = 0.758

y,=2 1.O kN/m3 Fs = 0.696

Fs = 0.908

Fs = 0.870

Fs = 1.135

Fs = 1.095

Fs = 1.473

Fs = 1.352

y7=19.6 kN/m3

The average groundwater table is at the Around level For the groundwater table (1 - 2 m of higher than average) after one day of intense precipitation of > 130 d m 2 For the groundwater table 2 m below the average Fully drained surface permeable soil complex ('first aquifer')

"B" Slide Fs= 1

506

REFERENCES 1. Todorovic T., Cvetkovic T. et. al., 1986: Synthetic report of geotechnical investigation of Plavinac-Provalije zone in Smederevo, “Kosovoprojekt”, Belgrade, Yugoslavia 2. Rasula G. et al., 1997: Report of engineeringgeological and hydrogeological investigations for designing and developing the lands of the Golden hill Farm estate near Smederevo, “Jaroslav Cerni” Institute for the Development of Water Resources, Belgrade, Yugoslavia

507

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami8.Jiang 0 1999 Balkema, Rotterdam, ISBN 905809 079 5

Landslides induced by rainstorm in the Poun area of Chungchongbukdo Province Daesuk Han & Kyeongsu Kim Korea Institute of Geology,Mining m d Materials, Tccejon, Korea

ABSTRACT: A rainstorm occurred on 12th August 1998 causing over 120 landslides in the Poun area of Chungchongbukdo Province; the maximum hourly rainfall was as much as 91 mm. The landslides, most of which were classified into debris and mud flows, caused loss of life, injury of people, and property damage. Seven typical cases, Kumgulri, Waisujong, Jangiaeri 1, Jangiaeri 2, 2nd Uhamri, 2nd Jukjonri, and Sokaeri are discussed in the paper. Based on the results of field checking on the landslides and laboratory investigation on the soils taken from some of the landslide sites including the above mentioned cases, most of the landslides occurred in the areas having a slope angle greater than 30" and composed of the thin colluvial soils overlying granite saprolite. The landslide deposits were classified into SC-SM, SM, and SP-SM according to the Unified Soil Classification System.

1 INTRODUCTION A project entitled Geologic Hazard Investigation was carried out during the period from January to December, 1998 for the middle region of the Republic of Korea; the region included parts of Chungchongbukdo and Chungchongnamdo Province, encompassing about 3080 km2. This paper deals with the Poun area of Chungchongbukdo, a northern part of the study region. The area encompasses about 137 km2, lying between 36'25" and 36'3 0 ' N. Over 120 natural slopes in the Poun area suffered rapid failures due to the rainstorm occurred on 12th August 1998; the maximum 24-hour and one-hour rainfalls were 409 mm and 91 mrn, respectively. The most abundant type of landslide that formed during the rainstorm was debris flow, mud flow being the next abundant one. The landslides caused loss of life, injury of people, and property damage. This paper focuses on the flows that occurred at Kumgulri, Waisujong, Jangiaeri 1, Jangiaeri 2, 2nd Uhamri, 2nd Jukjonri, and Sokaeri.

The terrain was divided into areas of five units, 0-5", 5-15', 15-30", 3040", and >50' slope. Based on the slope classification map constructed using the units, the distribution of terrain angles for the study area (Figure 1) was prepared. According to the figure, the natural slopes of the study area are steep, more than 50% of the land area being steeper than 15' and about 40% being steeper than 30".

Figure 1. Distribution of terrain angles for the study area. 2 TOPOGRAPHY AND GEOLOGY 2.2 Geologic setting 2.1 Topographic setting The land of the study area is rugged, with a number of mountains exceeding 250 m above the sea level. 509

As illustrated in Figure 2, the rock types in the study area are phylIite and Hwanggangri Formation @ebble bearing schist) of Ordovician age, Jurassic

Figure 2. Geologic map of the study area with the locations of raingauge stations and landslides. granite, and the rocks of Cretaceous age comprising Tongjungri Formation (conglomerate, sandstone and shale), tuff, porphyries, and acidic dyke. Of the rock types, the most predominant one is the medium to coarse grained granite which occupies about 54% of the land area. In the granite terrain where the landslide events took place, colluvium is commonly in a loose state, thus being of high permeability; it varies in thickness from 0.2 to 1.5 m. In general, the colluvium directly overlies the saprolite defined here as the weathering product of granite that was decomposed andor disintegrated in-situ to the consistency of a soil, while retaining the original rock structure that is still largly intact. The thickness of the saprolite rarely exceeds 3 m. The residual soil of granite is normally not found beneath the colluvium at the landslide sites having a slope inclination greater than 30"

and 3) Waisokri. Their locations are shown in Figure 2. Figure 3 shows the hourly rainfall records at the

Figure 3. Hourly and cumulative rainfalls at the Pounup station on 12th August 1998.

3 RAINFALL

On 12th August 1998, a rainstorm occurred in the Poun area of Chungchongbukdo Province. Hourly rainfalls were recorded by the automatic raingauges installed at the three stations, 1) Pounup, 2) Suhan, 510

Pounup station. The distributions of hourly rainfalls at the Suhan and Waisokri stations, which are located 2 km southwest and 6.5 km southeast of the

Pounup station respectively, are very similar to that of the Pounup station. The 24-hour and maximum one-hour rainfalls at the three stations are listed in Table 1 for comparison.

colluvium (about 30-cm thick) and the granite saprolite (about 1.5-m thick) overlying on the highly to moderately weathered granite; the slope inclination of the flow-material source area, which is located near the ridge, was measured at 30". Large amounts of runoff were infiltrated into the permeable colluvium and the granite saprolite of medium permeability, the infiltration elevated pore pressures enough to cause flow failure of the soils. The soil-and-water mixture began to move downslope, scouring the existing drainage channel (Figure 4). The source materials, combined with the scoured material, moved rapidly along the channel and destroyed two houses located near the mouth of the channel (Figure 5 ) , a life being lost. The flow materials finally spread into the nearby paddyfield. The distance from the source head to the paddyfield was about 300 m; the total damaged area was estimated at 1.4 ha.

Table 1. Rainfall records on 12th August 1998 in the Poun area. Location No.

Raingauge Station

1 2 3

Pounug Suhan Waisokri

Rainfall, mm 24-hour

Max. 1-hour

409 400 395

91 78 87

4 LANDSLIDE EVENTS The field investigation on 120 landslides, which were undertaken during the period from 18th August to the end of November, 1998, revealed that most of them were flows. The flows were grouped into the three types as defined in Table 2. Table 2. Classification of the flows occurred in the Poun area. Group

Mode of slope failure

1

Failure started at source head; the soil-andwater mixture rapidly moved downslope, scouring the existing drainage channel. Flow generated by semi-planar failure that started at source head and emerged at the toe of the slope, the lower part of the slope being entirely scoured or flow generated by the semi-circular slide, the toe of which emerged from the face of the slope, the lower part of the slope being partly scoured. Failure started at tomb site, the mode of failure being similar to that of the group No.2.

2

3

Figure 4. Scoured channel in the Kumgulri landslide.

The numbers of landslide occurrence for the group Nos. 1, 2: and 3 arel2, 87, and 11, respectively. Seven typical cases of the flows, Kumgulri, Waisujong, Jangjaeri 1, Jangjaeri 2, 2ndUhamri, 2nd Jukjonri, and Sokaeri are briefly discussed in this chapter.

Figure 5. Homes destroyed by the Kumgulri flow. 4.2 Waisujong landslide

4.1 Kumgulri landslide

The Waisujong landslide also belongs to the group 1 in Table i.The landslide started at the six source areas having a slope inclination that ranges from 30

This flow belongs to the group 1 in Table 2. The flow formed as a result of failure of both the thin 51 1

to 35" and comprising about 1-m thick colluvium. Though the topographic and geologic conditions somewhat differ from those for the Kumgulri landslide, the failure mechanism was the same as that described in the preceding paragraph. At the mouth of the existing drainage channel, two homes were carried away and three cattle sheds were damaged; fortunately, nobody was either killed or injured, but 20 cattle were killed. The nearby paddyfield was covered by the flow materials, the damaged area being about 0.7 ha. The distance from the source head to the paddyfield was about 700 m and the total damaged area was predicted at 3.0 ha. Figure 6 shows the panoramic view of the Waisujong landslide. Figure 7. Houses destroyed by the Jangjaeri 1 flow.

Figure 6. Panoramic view of the Waisujong landslide that damaged two homes and three cattle sheds.

Figure 8. Jangjaeri 2 landslide.

4.3 Jangjnevi 1 and 2 landlsides

The Jangjaeri 1 landslide belongs to the 1st case of the group 2 in Table 2. The saturated colluvium (50cm thick) and granite saprolite (about 80-cm thick) of the upper part of the slope (32 to 35") moved along the surface of highly to moderately weathered granite in the manner of semi-planar failure, scouring the lower part of the slope. The flow materials destroyed a house completely and another one partly (Figure 7); they farther moved along the alleys of the village, damaging several fences and houses. A life was lost and several people were injured; the total damage area was estimated at 1 ha. The Jangjaeri 2 landslide (Figure 8) belongs to the 2nd case of the group 2 in Table 2. The semi-circular failure of flow type first occurred in the upper part of the slope (45") comprising the saturated colluvium (about 25-cm thick) and granite saprolite (about 1.2m thick) and then the soil-and-water mixture partly scoured the lower portion of the slope, finally damaging an area (about 0.3 ha) of the farm land located in front of the slope. The semi-circular slide surface was analyzed using a stereographic projection method as shown in Figure 9.

51 2

Figure 9. Stereographic projection for the grid points on the slide surface of the upper part shown in Fig. 8.

4.4 Landslides at 2nd Uharnri and 2nd Jukjonri

4.5 Sokaeri landslide

The 2nd Uhamri landslide belongs to the group 3 in Table 2.There were two tombs at the site shown in Figure 10; one of them was carried away by the landslide, while the other remained undamaged except that the flat part of its front side moved away. The thickness of colluvium and the slope inclination around the tombs were measured at 1.2 m and 25 to 30", respectively. All the saturated colluvial soils moved downslope together with the underlying weathered and fractured granite and acidic dyke, damaging several fences and barns. The total damaged area was estimated at 0.3 ha.

The landslide, which belongs to the group 1 in Table 2, started at the source area having a slope angle of 35" and composed of the 50-cm colluvial soil together with the underlying granite saprolite (about 1.5-m thick). The saturated soils moved downslope, scouring the nearby drainage channel. The flow materials destroyed only a home (Figure 12); the total damaged area was estimated at 0.5 ha.

Figure 12. Home destroyed by the Sokaeri landslide.

Figure 10. Damaged tomb-site. Note that the right (arrow mark) remains, while the left is missing.

5 LABORATORY INVESTIGATION 5.1 Shear strength

The 2nd Jukjonri landslide also belongs to the group 3 in Table 2. The flow-materials source area neighboring a tomb and comprising the thin colluvium (about 10-cm thick) and the completely weathered acidic dyke (about 90-cm thick) was subjected to a semi-circular failure. The soil-andwater mixture moved rapidly downslope, partly scouring the lower portion of the slope ranging in inclination from 30 to 35". A home was damaged (Figure 11) and three people were injured. The total damaged area was predicted at 0.4 ha.

The undisturbed samples, which were taken from the sites of the seven landslides described in the preceding chapter, were subjected to shear strength test. The measurement on the samples was accomplished by means of an ELE direct shear box machine. The specimen size used for the test was 60 mm square and 20 mm thick; the normal stresses applied to each of the three specimens were 20, 34, and 53 kN/mz, while the loading rate was 1.06 mm/min. The shear strength parameters are presented in Table 3. Table 3. Results of the shear box test on the soils from seven landslide sites. Sample Location

Soil Type

"USCS

Kumgulri Waisujong Jangjaeri 1 Jangjaeri 2 2nd Uhamri 2ndJukjonri Sokaeri

Colluvial SP-SM << SP-SM << SC-SM SP-SM SC-SM SM **CW Colluvial SM
"

"Unified Soil Classification System. * *Completely weathered.

Figure 1 1. Home damaged by the 2nd Jukjonri flow. 513

Shear strength c,kPa 2 1 5 3 4 2 2

0 31" 34" 33" 34" 31" 32" 32"

5.2 Landslide deposits

saprolite, both of which generally were of high to medium permeability. The shear strengths of the 6 colluvial soils (Table 3) are quite similar, the internal fnction angle being 31 to 34" and the intercept cohesion being 1 to 5 kPa. As can be seen in Figure 13, 53 percent or more of the grains of the landslide deposits from the site Nos. 1 to 6 are larger than 2 mm in diameter, whilst 87 percent of the grains of the landslide deposit from the site No. 7 is smaller than 2 mm in diameter. Judging from the definitions of Varnes (1978), the landslides of Kumgulri, Waisujong, Jangjaeri 1, Jangjaeri 2, 2nd Uhamri, and 2nd Jukjonri are debris flows and the Sokaeri landslide belongs to mud flow. Based on the gradation analysis on 50 landslide deposits, 45 of the 50 landslides are debris flows, the rest being mud flows; the flow deposits are classified into SC-SM, SM, and SP-SM according to the Unified Soil Classification System Considering all the available information, it is concluded that the granite terrain in the Poun area, which is steeper than 30°, is more liable to become unstable than the terrain of phyllite, porphyries, etc. under the weather condition that hourly rainfall of more than 40 mm occurs consecutively for several hours.

The samples of landslide deposits, which were collected from 50 landslide sites, were tested for their grain-size distribution and Atterberg limits in accordance with ASTM D 422 and ASTM D 4318, respectively. Of all the grain-size distribution curves constructed based on the test results, seven typical ones are presented in Figure 13. Their liquid limits and plasticity indexes ranged from 21.5 to 32.5% and from non-plastic to 7.9%, respectively.

7 REFERENCES Figure 13. Grain-size distribution curves for the landslide deposits of Kumgulri, Waisujong, Jangjaeri 1, Jangjaeri 2, 2nd Uhamri, 2nd Jukjonri, and Sokaeri. 6 DISCUSSION AND CONCLUSION The intense rainstorm on 12th August 1998 in the Poun area, which was associated with a slowmoving trough of low pressure, caused over 120 landslides. One-hour rainfalls of more than 40 mm occurred consecutively from 3 up to 7 o'clock in the morning; the 4-hour rainfalls ranged from 233 to 247 mm depending on location. It has been reported that most of the landslide events took place during the hours mentioned above. As mentioned in the chapter No. 3, the terrain angles of the seven landslide sites vary from 25 to 45'; according to the slope analysis on the 120 landslides, 10, 95, and 15 of them occurred in the mountains with the slope angles of 15 to 30°, 30 to 50°, and X O " , respectively. The analysis on the relationship between the geologic units shown in Figure 2 and the 120 landslides reveals that 109 of them occurred in the granite terrain composed of the relatively thin colluvial soil (0.2 to 1.5 m thick) and the underlying granite 514

American Society for Testing and Materials1 980, Annual Book of ASTM Standards, Section 4 vol. 04.08. Davis, G.H. 1984. Structural geology of rocks and regions: 68-8 1. New York: Wiley. Han, D. et al. 1998. Geological hazards investigaion. KIGAM Research Report KR-98(C)-03: 18-70. Head, K.H. 1982. Manual of soil laboratory testing v01.2. London: Pentech. Johnson, A.M. & J.R. Rodine 1984. Debris flows. In D. Brunsden & D.B. Prior (eds), Slope instability: 257-357. New York: Wiley. Keefer, D.K. & A.M. Johnson 1983. Earth flows: Morphology, mobilization, and movement. Geological Survey Prof. Paper 1264: 1-41. US Goverment Printing Office, Wahsington. Kim, O.J. et al. 1977. Geological map of Bouen sheet (scale 1:50,000). Korea Research Institute of Geoscience and Mineral Resources. Kim, D.H. & B.J. Lee 1986. Geological map of Chongsan sheet (scale 1:50,000). Korea Institute of Energy and Resources. Varnes. D.J. 1978. Slope movement types and processes. In R.L. Schuster & R.J. Krizek (eds), Landslides: Analysis and control. Transportation Research Board Special Report 176: 11-33. US National Academy of Science, Washington. Zaruba, Q. & V. Mencl 1976. Engineering geology: 163-197. Amsterdam: Elsvier.

Slope Stability Engineering, Yagi, Yamagami& Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Characteristics of Cretaceous granite slopes that failed during heavy rainfall T.Yamamoto & M.Suzuki Departnient of Civil Engineering, Yamugiichi UiiiLvrsity, Uhe,Japan

N.Matsurnoto Graduate School of Science and Engineering, Yiinia
Y. Sehara 7hkiwa chiku K o g y Compcrtiy L im ired, Uhe, Jupun

ABSTRACT: 215 slopes consisting of cretaceous granite-namely, Hiroshima granite, older Ryoke granite, and younger Ryoke granite-failed due to rainfalls during the years 1978 to 1997 in Yamaguchi prefecture, located at the west end of Honshyu in Japan. Case or field investigations of the slopes were made in order to examine the features of the failed slopes and the physical and mechanical properties of surface soils in relation to granite type. 1 INTRODUCTION

southern region of Yamaguchi prefecture, while Ryoke granite is distributed only in the southeast (Nishimura & Matsusato 1991). 215 slopes consisting of granite failed due to heavy rainfalls during and at the ends of the rainy seasons of 1978 - 1997 in Yamaguchi prefecture Case investigations were performed on 192 failed slopes consisting of the above three kinds of Cretaceous granite during the years 1978 to 1994 (Yamaguchi prefecture 1994). In addition, field investigations were conducted on 23 slopes that consisted of the above three types of granite that failed

Granite formed in the Cretaceous period in the Mesozoic is widely distributed in Chugoku district of Japan. Granite distributed in Yamaguchi prefecture, located at the west end of the Chugoku district, are classified into three kinds: namely, Hiroshima granite, older Ryoke granite, and younger Ryoke granite. All three types are notably weathered, and the weathered soil they form is well known as masado (the decomposed granite soil). As shown in Figure 1, Hiroshima granite is distributed in a belt through the

Figure 1. The distribution of Cretaceous granite in Yamaguchi prefecture and the location of slopes failed during the years 1978 to 1997. 515

Figure 2. Frequency distribution of dimensions of failed granite slopes.

during the years 1994 to 1997. Physical tests, permeability tests, direct shear tests, and compaction tests were conducted on the surface soils (masado) sampled from these slopes.

2 FAILED SLOPES AND RAINFALLS 215 slope failures occurred in the locations shown in Figure 1. The closed circles indicate the slopes at which case investigations were made, and the double circles indicate the slopes at which field investigations were made. All of 192 failed slopes were classified by inclination, height, and depth for each type of granite. The results are shown in Figures 2(a), (b), and (c). It was found from Figures 2 that irrespective of the kind of granite, the dimensions of the failed slopes generally ranged between 40-49 degrees in inclination, 5.0-9.9 m in height, and 1.00-1.49 m in depth. 96 slopes were found to have failed due to plane slips. Figures 3(a) and (b) represent the amount of rainfall

516

Figure 3. Rainfall amounts over at two week period and a single day prior to slope failure.

preceding failures of slopes consisting of Hiroshima granite and Ryoke granite, respectively. The two curv~sin both figures were obtained by Aboshi (1972) and Ohara (1988) ,who investigated numerous failed slopes in Yamaguchi and Shimane prefectures. As can be seen, most of the slopes consisting of Hiroshima granite failed at a rainfall accumulation of 40-230 mm

Place

Slope N 0.

Mine A

I

Mine B

I(1)

Yanai B Yanai C Kaminoseki A' Kaminoseki B'

I I 1 I

Kind of granite

Younger Ryoke

Dimensions of Inclination Height (degree) (m) 35.3 -

48 45 31 50

14.9 4.8 7.5 14.6

failure Width (m) 130.0

-

11.5 5.0 66.0 18.0

Depth (m) 2.0 -

Type Amount of Rainfall (mm) Date of One Two failure day weeks Toppling 15.0 352.0 August 22, 1993 1987

Surface Circular

134.5

241.0

1.5

-

-

July 27,1993 June-August, 1995

1.8 1.0

Surface Surface

173.0 177.0

325.5 325.5

July 28, 1993 July 28, 1993

-

during 1 day rainfalls and 100-500 mm during two weeks rainfalls. In contrast, most of the slopes consisting of Ryoke granite failed at a rainfall accumulation of 100-190 mm during the one-day rainfall and at an accumulation of 180-600 mm during the two weeks rainfalls. This difference may be explained as follows. As shown in Figure 1, since Hiroshima granite is more widely distributed in Yamaguchi prefecture than Ryoke granite, the amount of rainfalls needed to cause slope failure in areas of Hiroshima granite is more widely dispersed than the amount for failure in Ryoke granite areas. Furthermore, the slopes consisting of Hiroshima granite failed under smaller rainfall accumulation that did slopes consisting of younger and older Ryoke granites.

occurred due to toppling and circular slip, respectively. Furthermore, as seen in Table 1, the slopes I (1) and (2) at Kumage failed during one day rainfalls of 0 and only 1.0 mm respectively. Both slopes are located in geological discontinuity positions, in which biotite-rich granite interpenetrates into Sangun metamorphic rock (Nishimura & Matsusato 1991; Yamamoto et al. 1996).

The results of the 23 field-investigated failed slopes are summarized in Table 1. Among them, 13 slopes are consisted of Hiroshima granite, and 4 of older and 6 of younger Ryoke granites. Rainfall accumulation on the failed slopes consisting of Hiroshima and Ryoke granite are indicated by closed symbols in Figures 3(a) and (b), respectively. As can be seen in Table 1, with the exception of slope I at Mine and slope I at Yanai B, for which the dimensions of failure were much larger, all the failed slopes had dimensions similar to those shown in Figure 2. All failures occurred due to surface slips, with the exception of the failures of Mine A and Yanai C slopes, which

(1) Hiroshima granite Hornblende contained in quartz diorite at Mine B altered into chlorite due to weathering. Aplite at Ube interpenetrated as a dyke into Sangun metamorphic rock. Biotite granite at Hofu had an equi-granular texture, and a large amount of alkali feldspar, some of which had been altered into muscovite.

3 PROPERTIES OF ROCKS Table 2 summarizes the minerals composing the three kinds of granite sampled at each location. The properties of rocks are described below for each type of granite.

(2) Older Ryoke granite In the biotite granite at Oshima, the gneissic structure, which is a typical structure in old-age Ryoke granite, was observed. Garnet, a mineral typically contained

517

Yanai A Oshirna Hirao Kurnage Yanai B Yanai C Kaminoseki A Kaminoseki B

Garnet biotite granite Biotite granite Biotite granite Biotite granite Biotite granite Biotite granite Younger Ryoke Muscovite-biotite granite Biotite granite Muscovite-biotite granite Muscovite-biotite granite Older Ryoke

Quartz, Plagioclase, Alkali feldspar, Biotite, Muscovite, Chlorite, Garnet Quartz, Plagioclase, Alkali feldspar, Biotite, Apatite, CNorite Quartz, Plagioclase, Alkali feldspar, Biotite, Chlorite Quartz, Plagioclase, Alkali feldspar, Biotite Quartz, Plagioclase, Biotite, Muscovite, Garnet Quartz, Plagioclase, Biotite, Chlorite Quartz, Plagioclase, Alkali feldspar, Biotite, Muscovite, Garnet Quartz, Plagioclase, Biotite, Muscovite, Chlorite Quartz, Plagioclase, Alkali feldspar, Biotite, Muscovite Quartz, Plagioclase, Alkali feldspar, Biotte, Muscovite, Chlorite

Table 3. Physical properties and soil classification of surface soils.

minerals such as chlorite were produced by the weathering of hornblende or biotite.

in Ryoke granite, was observed in garnet biotite granite at Yanai A.

(3) Younger Ryoke granite Unlike older Ryoke granite, the gneissic structure was not observed in younger Ryoke granite. Garnet was observed in biotite granite at Kumage and in muscovite biotite granite at Yanai B. As shown in Table 2, all three kinds of granite were composed primarily of quartz, plagioclase, alkali feldspar, biotite, and a little muscovite. Also, clay

4 PROPERTIES OF SURFACE SOILS 4.1 Physical properties Table 3 shows the physical properties of surface soils sampled from each slope, and the soils’ classification according to the Japanese Unified Soil Classification

518

Figure 5(a). Internal friction angles, ((b ,),, and ((b & for each surface soil.

Figure 4. The change of coefficient of permeability k with void ratio e for each surface soil.

System. It can be seen in Table 3 that Ryoke masado samples had much lower finer content (FJ and were all classified as NP,while Hiroshima masado samples had comparatively higher F, content and all showed I,, values. Both Ryoke masado samples were classified as S-M (sand with silt) or SM (silty sand), and almost all Hiroshima masado samples were also classified as SM or SM, with the exception of a ML (silt with low liquid limit) at Mine and a CL (clay with low liquid limit) at Onosaka B. Masado samples at Mine B, C and Onosaka B consisted of enriched hornblende, which is easily altered to clay minerals by weathering. In contrast, since the enriched acidic-rich granite at Kumage and the aplite at Ube contained enriched biotite, their I,, values were low in spite of their comparatively large clay content (FC,;J.

4.2Permeability Constant head permeability tests were performed on three kinds of disturbed masado. Figure 4 shows the change of the coefficient of permeability k with the void ratio e. It is found from Figure 4 that each masado is characterized by a unique change in k with decreasing e. The higher the content of color minerals such as biotite and hornblende, the smaller the coefficient of permeability of masado. That is, with the exception for Kaminoseki A masado, Hiroshima masado has a larger coefficient of permeability as compared with both Ryoke masado. Similar results have been obtained by Matsuo et al. (1970).

Figure S(b). Cohesion, (c,), and (c,), for each surface soil.

4.3 Strength parameters Direct shear tests using a direct shear test apparatus were performed on several disturbed masado specimens ( b ,=60 mm, h=20 mm) under both natural and submerged conditions. Figure 5(a) shows the relationship between the under natural internal friction angle ( (b,),, and ((b,) and submerged conditions, respectively, for three kinds of masado. Figure 5(b) shows the relationship between the cohesion (c,)" and (c& under natural and submerged conditions, respectively. It can be seen from Figure 5(a) that although no distinct difference of (6d),, was observed among the various kinds of masado, the decrement of the internal friction angle of Hiroshima masado due to the submergence was larger than that of older and younger Ryoke masados. It can also be seen from Figure 5(b) that the cohesion of

519

5 CONCLUSIONS

Figure 6. Relationship between P each surface soil.

dmax

and M, for

almost all masado samples decreased remarkably, or disappeared due to submergence. The same results showing that the strength parameters of masado decrease remarkably due to submergence have been obtained by Onitsuka et al. (1985).

The conclusions of the present study are as follows: Most slope failures during rainfall occurred due to plane slips of comparatively small magnitudes irrespective of the kind of granite involved. Namely, 96 slopes among 215 failed slopes failed due to plane slips of 0.5-0.8 m in depth. The slopes consisting of Hiroshima granite failed with a small amount of rainfall as compared with those slopes consisting of older and younger Ryoke granites. Though most Hiroshima masado were classified as ML, SM, or S-M, all Ryoke masado were classified as SM or S-M. The degree of decrease of the internal friction angle (5, and the cohesion c, of the surface soils by submergence were larger for Hiroshima masado than for either type of Ryoke masado. Older Ryoke masado has lower degrees of compaction and a lower coefficient of permeability level than either younger Ryoke masado or Hiroshima masado. REFERENCES

Aboshi, H. 1972. Heavy rainfalls and failures of masado slopes, Seko-gijutsu, 5 (11): 39-49 (in Japanese). 4.4 Compuctionproperties Lambe, T. & Whitman, R.S. 1979. Soil mechanics, SI version. John Mley & Sons:147. Compaction tests were performed on three kinds of S. & Nishida, K. 1970. The properties of Matsuo, masado according to the A-b method (the dry and decomposed granite soils and their influence on cycle method) by the Japanese Society of Geotechnical permeability, Soils and Foundations, 5(1):93-105. relationship Engineering. Figure 6 shows the Nishimura, Y. & Matsusato, H. 1991. An illustrated between the maximum dry density p dmax and the Book of rocks in Yamaguchi prefecture, Duiichi mole ratio of each oxide M, given by Eq.4.1 for each Gakusyusya Ltd. :21-22 (in Japanese). masado. The mole ratio increases with the increase of ahara, S. 1988. Investigation of prediction procedure colored minerals such as biotite and hornblende. It was of occurrence for ground disaster by heavy observed that the maximum dry density decreases with Report on important area study(1) in rainfalls. the mole ratio value. In particular, the the increase in research expenses on Ministry of Education p ,,,,,=1.55-1.60 g/cm3 of older Ryoke masado rich in (No.62601529):1- 17 (in Japanese). biotite are very small compared with the p dmax=1.80Onitsuka, K., Yoshitake, S. and Nanri, M. 1985. 1.90 g/cm3of biotite-poor Hiroshima masado. Mechanical properties and strength anisotropy of decomposed granite soil, Soils and Foundations, M, = A1,0, / (Na,O f K,O 9-CaO) (44 25(2):14-30. Yamaguchi prefecture 1994. Tables of results of It is known that a micaceous sand will often have a investigation on slopes failed due to heavy large void due to little interlocking (Lambe & rainfalls during the years 1978 to 1994 (in Whitman 1979). Therefore, our test results reflected Japanese). the fact that, in the case of earthworks using masado in Yamamoto, T., ahara, S., Nishimura,Y. & Sehara, Y. Yamaguchi prefecture, although the degree of 1996. Characteristics of cut slopes consisting of compaction of Hiroshima masado is high, the Sangun metamorphic rocks which have failed due compaction of Ryoke masado is not achieved to heavy rainfall in Yamaguchi prefecture, satisfactorily. Domestic Edition of Soils and Foundations, 36(1):123-132 (in Japanese).

520

Slope Stability Engineering, Yagi, Yamagami 6: Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Seepage analyses of embankments on Tokaido-Shinkansen in long terrn rainfalls K. Kato R&D Ceizter,TechnicalResearch and Development Division, Central Japan Railway Company,Nagoya, Japan

S.Sakajo Numerical Analysis Section of Geo-mechanics,Kiso-jiban Consultants Company Limited, Tokyo,Japan

ABSTRACT:The sensitivity of seepage soil properties was studied in the seepage analysis of the seven embankments on Tokaido-Shinkansen. It is obvious that the un-saturated soil property is the key of success of saturated and unsaturated seepage analysis. However, the consistent analytical study based on soil properties obtained from in-situ has never been studied. Re-evaluation of seepage soil parameters was discussed in the present study. The computed results were compared with the observed water pressure in the embankments.Finally, the authors have proposed a procedure to determine the various un-saturated seepage soil propertiesfor Tokaido-Shinkansen.

1 INTRODUCTION JR Tokaido-Shjnkansen is between Tokyo and Osaka. At

many portions of the line, embankment structures are constructed for the railway foundations, which have been faced with damage due to heavy rainfalls. The embankment height varies from 3 m to 10 m. Eispecially, small scale slope failures have occurred on the line in Shizuoka and Aichi Prefecture. On the other hand these days, the computer facilities have been advanced very much and many sophisticated softwarecan be applicable using high speedy computers. Now is the time to start to simulate the seepagebehavior and assess their stability in rainfall using the these computer software. In this study, a saturated and un-saturated seepage analysis on -finite element analysis is emplyed, which was proposed by Prof. Nishigaki (Akai,Ohnishi,Nishigaki, 1977). The used rainfall records for a long term are two kinds. One is one month in April 1998. Another is one month in August 1998( except for G site ) (Central JR. and Kisojiban ConsultantsCo., Ltd., 1999).

2 SEVEN EMJ3ANKMENTS ZNVESTIGATIONS

AND

SOIL

Fig. 1 shows embankments and foundations at seven sites of A, B, C, D, E, F and G. The characteristics of these embankments can be described as follows. The embankment at A site was constructed with mud stone fractures from a nearby tunnel excavation. This kind of material is not easy tc! define the seepage properties because of the complicated composite mixtures of soils. It seems hke silt gravel. The initial water table is rather

low, where a river is existing beside this embankment. The embankment at this site has cut off walls on their right and left sides of the embankment. The embankment at B site is made of loam mixed with gravel from Mt. Fuji. The strength of the embankment is rather week. This soil of the embankment at C and D sites were constructed with clayey circular gravel. However these gravel contain little clay. Therefore, it is d%cult to evaluate the seepage properties. The E embankment was constructed with the residual soils of sand and mud stone from a nearby tunnel excavation. The embankment at E site is about 3m high. The embankment at F site was made of sand with clay. The embankment at G site was contains sand. The embankment at B, C and E sites used a structure of retainingwall. The embankment at B site has the walls at the right and left sides of the embankment. The embankment at C site has one at its left side and the embankment at E site has one at its right side. These embankmentsdiffer from each other in size and soil. The G embankment was selected near from Toyohashi and Mikawa-Anjo area, Aichi prefecture. The others were selected from Shizuoka prefecture. The heights of embankmentsvary from 3 m to 10 m. The constitution soils of these embankments are from silt clay to gravel. Their soil profiles were made by the boring results (Radway T e c h c a l Research Institute, 1997a; Central J R and &so-jiban Consultants Co., Ltd., 1998). A set of soil investigations was conducted to obtain soil properties. Standard penetration test (SPT) was conducted to evaluak the soil profile and the basic strength of the embankments. Un-disturbed tube and biock samples were obtained for the laboratory tests for

521

Fig. 1 Embankment models for the seven sites measuring soil strength and soil seepage properties, respcctively. TA-axial compression tests were conducted to riieasurc soil strength. Tlie CD test was applied for sand soils and CU test was applied to clay soils. As

scepagc properties of soil, coefficient of pernieability and pF curve of soil was measured. From the results of the boring data, the following classifications ~ a i be i obtained. The embankment at A

522

site is silt gravel, which is residual soil from tunneling but it was found to be gravel. The embankment at B site was classified as gravel clay but it was found to be clay. The embankments at C and D site were classifiedas clay gravel but they were found to be silt. The embankment at E, F and G site arc classified as sandy soils but they were found to be sand. These reasons would be explained at the next section. The W, and the W, are the observation wells of pore water pressures in this figme. The computed poic water pressures were compared with these observed valucs. (Central J R and IGso-jiban Consultants Co., Ltd., 1999).

3 MEASURED AND USED PROPERTIES OF SOILS

SEEPAGE

The soil properties for the saturated and un-saturated seepage analysis are the coefficient of permeability at saturated state ks, the volumetric water content in saturated state 6's and the residual volumetric water content Br. To obtain these parameters, permeability test and pF test were conducted using block samples. These test results are shown in Table 1. The coefficient of permeability at unsaturated state ku can be obtained by h a y ' s equation. :

where, the @isvolumetric water content and the n

canbe defined as n = O.69-1.311og1& The permeability test is free water head test. pF test is conducted with tension meter for pF value of 0.0 to 2.0 and centrifuge test for pF value of 2.0 to 3.0. The maximum suction was applied up to 1Om because embankment height is 6 to 7 m w w a y 'lkchcal Research Institute, 1997a;199713). These results do not match with soil classifications. For example, the soil at the distance of E section was classified as sandy clay from boring data but the measured coefficient of permeability ks was 7.78 X 10" (cm/sec), which was like a clay. The values of 0 s and 8 r from pF tests were 48.9 and 40.6 respectively,which were rather large values corresponding to the clay soil. All the pF curves from @ to 0are shown in Fig. 2. The 0, 8 and 0 is for silt gravel, sandy gravel and sand. The 0, 0, @ and @ are for gravel clay and clay gravel. Therefore,these values must be re-evaluated through comparing the numerical simulation with the observation.

4 SlMULATIONS AND RESULTS To assess the measured seepage properties, many

trial

numerical

simulations were

Fig. 2 Un-saturated seepage soil properties

D E F G

clay gravel sandy clay sandyclay sand

1.20X 10-5 7.78XIO-j 1.13X10-3 1.OOX 10-3

39.8 30.6 48.9 40.6 41.1 23.5 26.0 20.5

@ @ @

a

conducted and these properties were changed into 4 categories, 1)gravel, 2) silt, 3) silt clay and 4) sand as shown in Table 2. Then, the last seepage analyses on h t e element methods were conducted for long term ramfall (Central JR and &so-jiban Consultants Co., Ltd., 1999).

523

Fig. 3 Simulated results at the seven sites

The retaining walls were modeled as a concrete material in the seepage analysis. However, the cutoff walls are not modeled in the analysis because of the a c u l t judgement for the seepage properties. Fig. 3 shows the simulated results for long term radaUs. The computed relationshps between pore water pressure and r d d time can be seen in these figures compared with the observations. At A OyJ and B (W,) sites, the computed pore water pressures can fit with the observed ones

524

Fig. 4 Patterns of water lines in embankments at the moment of the heaviest rainfall

525

F

sand

G

sand

1.13X10-3

41.1 1.OOX 10-3 26.0

23.5 20.5

@

0

very well for the one month. Thzse pore water pressures are very sensitive due to the very large permeabhty. At C (WJ site and D (W,) site, the computed pore water pressures are flat against the r d a l l time because of the low permeabdity at these sites, whch are similar to the observations although there is a gap between the both values at C site. At E (WJ, F (WJ, and G (Wd sites, the computed results could explain the observations very well. From these computed results at E, F and G, the sand embankments could rise the water line much hgher than the others. It inhcates that the embankments at E, F and G are very dangerous for the real r d a l l s . From the above tlungs, it can be concluded that the computed results explained the observations very well and the seepage properties are very important in the seepage analyses. Fig. 4 shows the patterns of water lmes at the moment of the heaviest rainfall. These figures show the characteristics of the above seepage properties very well. One can see the veiy h g h water h e in the embankments at E, F and G . The others have very low water h e s in the embankments. From these figures, it can be also concluded that the seepage properties are very important in the seepage analyses.

M. S.Suzuki at Shizuoka Shinkansen Structure InspectionCenter of Central Japan Railway Company.

REFERENCES Akai, K, Ohnishi, Y and Nishigaki, M. 1977, Finite element saturated and un-saturated seepage analysis, Journal of Japanese Civil Engineering Society, V01.264, pp. 87-96 ( in Japanese ). Central JR and Kiso-jiban Consultants Co., Ltd. 1999. Report on the stabilityanalysis of the embankments of JR Tokaido-Shinkansen Line 309km and other 6 locations ( in Japanese ). Central J R and &so-jiban Consultants Co., Ltd. 1998. Report on Soil Investigation results for embankments on Tokaido-Shinkansen in Shizuoka StructuralInspection Center. Sakajo, S. and Kato, K 1999, In-stab&@Analyses of

Embankments on Tokaido-Shmkansen in Heavy hnfalls, IS-Shikoku ( under submitted ). Railway Technical Research Institute, 1997%Report on Soil Investigation and permeability test results of Toukai-dou Sin-kan-sen at 309kmZOOm ( in Japanese ). Railway Technical Research Institute, 1997b, Research on evaluation procedure of railway slope damege for rainfalls ( in Japanese ).

5 CONCLUSIONS The followingconclusionsare developed: 1)The consistent analytical study based on soil properties obtained from in situ has never been studied. 2)The measured seepage properties were be reevaluated through comparing the numerical simulationwith the observation. 3)Then, a set of seepage properties was proposed for the embankmentson Tokaido-Shinkansen. 4)The computed results could explain the observations very well. 5)The seepage properties may effect on the iise of water lmes in the embankment. T h s would be related to the safety of embankment is long term r d a l l s . 6)The embankments at E, F and G sections are very dangerous for the real rainfalls. The other embankments are not dangerous in the actual rdalls. 7)The seepage properties are very important in the seepage analyses.

ACKNQWLEGEMENTS The authors would like to show sincerer appreciation to

526

Slope Stability Engineering, Yagi, Yamagami& Jiang

1999Balkema, Rotterdam, ISBN 90 5809 079 5

Instability analyses of embankments on Tokaido-Shinkansen in heavy rainfalls S.Sakajo Numerical Anulysis Section of Geo-Mechanics, Kiso-jiban Consultants Compuny Limited, Tokyo, Japan

K. Kato R&D Center, Technical Research and Development Division, Central Japan Railway Company, Nagoya, Japan

ABSTRACT : The authors studied in-stability of embankments on Tokaido-Shinkansen due to heavy rainfalls. At first, a set of seepage and stability analyses of a model embankment was carried out. Then, a set of seepage and stability analyses of the seven real embankmentswas conducted.From these results, it was found that the safety of embankments might be deeply related with the seepage properties. The used seepage properties in the present study were re-evaluated through the numerical simulations of pore water pressures in the embankments by the long term rainfall. Stability analysis was a circular stability analysis based on a limit equilibrium method. The analytical results of the embankments showed the importanceof the seepage soil properties on the stability analysis.

1 INTRODUCIlON

properties were assessed through the numerical simulations of embankments at many different locations on Tokaido-Shinkansen. (Kato and Sakajo, 1999). The authors attempted to investigate the importance of these seepage properties for the safety evaluations of these embankmentson Tokaido-Shinkansen.

Several numerical procedures are now available for the stability analysis of slopes in rainfall. For example, The first author has proposed a procedure of slope stability analysis coupling seepage analysis on finite element method (Yoshimaru,Sakajo and Ugai, 1997; Ugai, Cai, Sakajo and Wakai, 1999). In this procedure, the stability analysis proposed by Ugai (Ugai, 1990; Tanaka, Ugai, Kawamura, Sakajo and Ohtsu, 1997) is employed, which could be the most rational evaluation method for several countermeasure works like piles in slope, because it can consider the critical state deformation of piles and ground in their resistance. This method also can be applied to embankment as an artificial slope. In this procedure, a saturated and un-saturated seepage analysis on finite element analysis is employed, which was proposed by Nishigaki (Akai, Ohnishi, Nishigaki, 1977). Therefore,saturated and un-saturated seepage soil properties can be required in this analysis. To increase computational accuracy, seepage lines coordinates in the seepage analysis results are transferred to the stability analysis. However, in the present study, a circular stability analysis based on rigid plasticity is used, which is simpler than the that on finite element method and can be applicableto the ground without piles. The strengths of soils are not only important but the seepage properties of soils are also important, for the safety evaluation of embankment in rainfall. However, seepage properties of soils are not well investigated usually. Therefore, it seems that there are yielding many bad simulations using in-realistic seepage properties. The authors conducted a set of soil investigations to measure the seepage properties at in situ and then these

2 SOIL INVESTIGA?rlONS AND EMBANKMENTS ON TOKAIDOSHINKANSEN The 7 different embankments were chosen from Tokaido-Shinkansenand their soil profiles were made by the boring results (Nishio et al., 1998; Kanda et al, 1998; Railway Technical Research Institute, 1997a; Central JR and Kiso-jiban Consultants Co., Ud.,1998). These embankments differ from each other in size and soil. A set of soil investigations was conducted. Standard penetration test (SP") was conducted to evaluate the soil profile and the basic strength of the embankments. Undisturbed tube and block samples were obtained for the laboratory tests for measuring soil strength and soil seepage properties, respectively. Tri-axial compression tests were conducted to measure soil strength. Table 1 shows the soil characteristics and their strength of soils of embankments. The c denotes and the 6 denotes cohesion of soil and frictional angle respectively. The CD test was applied for sand soils and CU test was applied to clay soils. As seepage properties of soil, coefficient of permeability and pF curve of soil was measured.

527

Table 2

Table 1 Soil classificationand unit weight, strengths of embankments

(site)

1

A B C D E F G

1

The used soil classifications and seepage classdkation gravel silt siltclav silt clay silt clav sand sand sand

(cdsec)

1

1.22X 10-' 1.00X10-3 1.06X10-5 1.06X 10-5 1.20X10-' 1 l.00X10-3 1.13X10-3 1.00X10-3

(%) (%) 48.9 19.2 80.5 64.0 38.3 21.4 39.8 I 30.6 26.0 20.5 41.1 23.5 26.0 20.5

curve

0 @ @ 1 ?' $ 1

0 @

0

were conducted using block samples. The permeability test is falling head permeability test. pF test is conducted with tension meter for pF value of 0.0 to 2.0 and centrifugemethod for pF value of 2.0 to 3.0. Suction was applied up to 10 m because the maximum embankment height is around 10 m (Rdway Techrucal Research Institute, 1997a;199713). However, these seepage properties obtained fkom tests were re-evaluated by the numerical simulations of seepage behavior in long term rainfall (Central JR and Kiso-jiban ConsultantsCo., Ud., 1999; Kato and Sakajo, 1999). These re-evaluated seepage properties are tabulated in Table 2. The used pF curves from @ to 0are shown in Fig. 1. The 0, 8 and 0is for sand and gravel. The 0, @ and @ are for silt and silt clay silt clay. The computed results using the above seepage properties could explain the observed pore water pressures very well.

4 INFLUENCE OF SEEPAGE PROPERTIES ON SAFETY OF A MODEL EMBANKMENT AT E SITE A 5 m high model embankment was assumed to show the influence of soil properties on safety. This is a simplified embankment at E site, which consists of two soil layers. The embankment slope was set 1.0 to 1.5. Rainfall intensity was set 10 mm/hour. The total rainfall was set 800 mm. It can be said a kind of heavy rainfall. Fig. 2 shows the cross section of this model embankment. Table 3 shows the used seepage parameters for three cases. Fig. 3 shows the computed water lines for this embankment at the moment that 30 hours passed for the three cases. The water line does not change at all for CASE-1. However, the water line went up to 4 m for CASE-2 and it reaches to the embankment top For CASE-3. This implies that the coefficient of permeability influenced the change of water line very much. Fig. 4 shows the change of water lines for CASE-3 at the moments that 0, 10, 20 and 30 hours passed. From this figure, it was found that there was significantchange of water lines with time passing. At the initial stage, water line goes up near the slope of embankment by

Fig. 1 The used pF curves

3 USED SEEPAGE PROPERTIES OF SOILS Necessary soil properties for the saturated and unsaturated seepage analysis are the coefficient of permeability k, the maximum volumetric water content 6's and the minimum volumetric water content Br. To obtain these parameters, permeability test and pF test

528

Table 3 The used seepage and strength properties CASE CASE-1 CASE-2 CASE-3

ki (cm/sec> 7.78X1Op6 LOOX 10-3 1.00X10-3

9s

Or

(%) 48.9 48.9 26.0

%

pF-curve

40.6 40.6 20.5

0

Fig. 2 The cmss section of model embankment with a height of 5 m

Fig. 3 The computed water lines for this embankment at the moment that 30 hours passed Fig. 5 The pore water pressure change and rainfall time

Fig. 4 The change of water lines for CASE3 at the moments that 0,10,20 and 30 hours passed rainfall. Then, the water line goes up at the center of embankment.This may yields the non-linearity of safety change. Fig* shows the Pore water pressure change Of the three cases at the two points, 1) under the embankment shoulder and 2) at the center of embankment on the ground surface level. The pore water pressures at the two points W, ( under the embankment shoulder ) and w2 ( at the center of embankment ) do not change for CASE-1. CASE-2 and CASE-3 show a similar increase of pore wa-ter pressures, where the rise of water line at

fig. 6 The relations of safety factor and rainfall time W, is much faster than W, at the initial stage. However, the rise of water line for CASE-3 is faster than that for CME-2, because of the differenceof the pF curves. Fig. 6 shows the relations of safety factor (S.F.) and

529

Fig. 7 The safety and rainfall time relations elapsed time. Safety factor of the embankment is around 1.7 at the beginning and it decreased to be 1.2 by the rainfall. For CASE-1, the safety factor does not decrease but it decreases for CASE-2 and CASE-3. For CASE-2,

a significant drop of safety factor happens at the moment that 25 hours passed since start of rainfall. On the other hand, a significant drop happens at the moment 20 hours passed since start of rainfall. This is correspondingto the

530

Fig. 8 The patterns of water lines

differencebetween CASE-2 and CASE-3 in Fig. 5. From above things, it can be said that the seepage properties of soils may influence the safety of railway embankment very much. The permeability is the primarily important and the pF curves are the secondary important.

5

INFLUENCE OF SOIL PARAMETERS ON SAFETYOFREALEMBANKMENTS

It is not easy to judge the safety for the long embankments of various soils along TokaidoShinkansen. The safeties of the seven real embankments were computed for the heavy rainfalls. Rainfall intensities(R.1.) were 10, 20, 30, 40, 50, 00 and 70 mmhour. The total rainfall was 800 mm. The computed safety and rainfall time relations were shown in Fig. 7.

531

The patterns of water lines corresponding to the minimum safety are shown in Fig. 8. The computed safety in rainfall corresponds to the seepage analysis (Kato and Sakajo, 1999). From Fig. 7 and 8, it was found water line rising does not change at the sections of A, B, C and D site. On the other hand, it was found the water line goes up at the sections of E, F and G site. The former sections keep very safe in the rainfall but the latter sections become very dangerous at E, F and G site in the end of the rainfall. Especially, the safety of the sections at F and G site becomes less than 1.0. The section at A site belongs the same group with B, C and D site fiom the water line change and safety change with rainfall. However, the section at A site has very permeable embankment and foundations and the others have not permeable embankment made of silt and clay. It was seen that the water line change looks similar although the mechanism of water flow is different. It can be explained by the difference of seepage soil properties in Table 2 and Fig. 1. From these things, it can be said that the safety might be deeply related with the seepage properties.

6 CONCLUSONS The authors studied in-stability of embankments on Tokaido-Shinkansendue to heavy rainfalls in the above. The following conclusionsmight be developed: 1)The seepage properties on Tokaido-Shinkansencan be classified into four types. 2)A 5 m high model embankment at E site could show the importance of the seepage properties on the safety evaluation. From this result, it was found that permeability and the un-saturated seepage properties of soil might be primarily and secondarily important on the analysis. 3)From the seepage and stability analyses of the seven model embankments, it was found that the safety might be deeply related with the seepage properties. 4)It was also found that the sandy embankments at E, F and G site are more dangerous in the heavy rainfall than the other embankmentsat A, B, C and D site. 5)The gravel embankment at A site is very safe because of the large permeability. 6)The silt clay embankments at C and D site are very safe because there are very few rain penetrations into the ground similarly as the silt embankment at B site.

REFERENCES Akai, K., Ohnishi, Y. and Nishigaki, M. 1977, Finite element saturated and un-saturated seepage analysis, Journal of Japanese Civil Engineering Society, V01.264, pp. 87-96 ( in Japanese ). Central JR and Kiso-jiban Consultants Co.,Ltd. 1999. Report on the stability analysis of the embankments of JR Tokaido-ShinkansenLine 309km and other 6 locations ( in Japanese ). Central J R and &so-jiban Consultants Co., Ltd. 1998. Report on Soil Investigation results for embankments on Tokaido-Shinkansen in Shizuoka Structural Inspection Center. Kanda, H., Suzuki, S., Nishio, A. and C h h m a , T. 1998, Field measurement of the pore water pressure in the embankment of Tokaido-Shinkansen (2), Proc. of the 33 rd annual conference of JGES, pp.321-322 ( in Japanese ). Kato., K. and Sakajo., S. 1999, Seepage analysis of embankments on Tokaido-Shinkansen in long term rainfalls, IS-Shikoku ( under submitted ). Nishio, A, Kanda, H., Fukuyama, F., Kokubo, M. and Fukuda, K., 1998, Field measurement of the pore water pressure in the embankment of TokaidoShmkansen (l),Proc. of the 33 rd annual conference of JGES, pp.319-320 ( in Japanese ). Railway Technical Research Institute, 1997%Report on Soil Investigation and permeability test results of Toukai-dou Sin-kan-sen at 309km2oOm ( in Japanese ). Railway Technical Research Institute, 1997b, Research on evaluation procedure of rainfall slope damege for rainfalls ( in Japanese ). Tanaka, T., Ugai, K., Kawamura, M., Sakajo, S. and Ohtsu, H., 1997, Three dimensional finite element analysis in geomechanics,Maruzen. ( in Japanese ). Ugai, K. 1990. Availability of shear strength reduction method in stability analysis, Tsuchi-to-kiso, Journal of JGES, Vo1.38, No.1, pp.67-72 (in Japanese). Ugai, K., Cai, F., Sakajo, S. and Wakai, A. 1996. Evaluation of slope safety in rainfall, Journal of land slide. Vo1.35, No.1, pp.19-23 ( in Japanese). Yoshimaru, T., Sakajo, S. and Ugai, K 1997, Effect of un-saturated seepage properties of slope stability in rain fall, Proc. of symposium of JGES on geotechnid engineering to protect the slopes from rainfall and earthquake damages, pp.99-102 ( in Japanese ).

ACKNOWLEGEMENTS The authors would like to show sincerer appreciation to Prof. Ugai at Gunnma University for his discussion. He is the co-researcherof land sliding in rainfall.

532

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN go 5809 079 5

Chemical effect of groundwater from acid rain on slope evolution Zemin Xu & Runqiu Huang Depurtment of Hydrogeology and Engineering Geology, Chengdu University of Technology, People’s Republic of China

ABSTRACT. Taking a railway slope located in Chongqing acid rain region as an example, the paper investigated the chemical effect of acid groundwater on slope evolution. Based on this research result, model experiments on the prevention and control measures against corrosion of acid groundwater on slope rock and soil were carried out. The results demonstrated that the corrosion of acid groundwater on the slope rockmass was very intense. Both minerals easily dissolved and a great deal of minerals hard to dissolve such as feldspar and laumontite were corroded on a large scale and the total corrosion amount amounted to 30 t or so per year. Since occurred mainly along the discontinuities, the corrosion had an important influence upon the mechanical and hydraulic properties of the rockmass. Model experiments showed that the neutralizing barrier formed by mixing the sand clay covering the slope with a proper amount of limestone could effectively contain the corrosion of acid groundwater on the slope rockmass.

1 INTRODUCTION In the rocky slope evolution process from stable to unstable state, as well as complete failure, groundwater from rain is the most active inducing factor The effect of groundwater may be summarized into chemical or long-term effect and mechanical or short-term effect. The former covers the changes in structure, strength, as well as porosity and so on of rockmass caused by corrosive groundwater and the latter means that during rain or rainstorm the large margin elevation of slope groundwater level causes slope failure, that is, landslide The long-term effect causes gradual change of slope and short-term brings about the sudden change. Oabviously, the latter is based on the former and the sudden change would not appear without necessary gradual change The chemical effect of groundwater on slope evolution shows mainly in the following two aspects A, it makes the loose layers covering rocky slopes become thicker and thicker with time, and under proper condition these loose accumulations separate themselves from the rockmass and cause shallow landslide or mud-rock flow B, it causes the decrease in JRC and JCS, and the increase in aperture, which lead to the profound change of rockmass strength and deformation

property. At the same time, the effective porosity of rockmass will be gradually elevated and the storing and conducting water capacity strengthened. Thus, the stress field and stability of rockmass will become more and more sensitive to the fluctuation of slope groundwater and under proper condition a heavy rain or a long time rain may induce rockmass landslide. That is why the researches on the effect of groundwater on slope evolution is of importance to the prediction, prevention and control of landslide. The former relevant researches were focused on the mechanical effect of groundwater and although the existence of chemical effect has been realized for a long time, the researches about it have been few as yet. The difference in research degree maybe results from that the chemical effect is not only a very slow process and not evident enough to attract wide attention, but also highly complicated and very difficult to study. In contrast, mechanical effect is rather apparent and the natural phenomena that most of landslides occur during rain season have attracted close attention. Taking some railway bed slope as an example, the paper investigated a method of estimating effect of the groundwater from acid rain on slope evolution and a corresponding measure of containing the effect.

533

2

EFFECT OF ACID GROUNDWATER ON SLOPE EVOLUTION

Some railway slope is located in Chongqing suburbs. It is mainly made of sandstone and mudstone and is covered by a layer of sand clay of l m thick. The strata incline down to outside and angle of inclination is 10"-15". In the backside of the slope there is a tensile fracture zone forming in 1960's. The fluctuation of the groundwater and slope deformation are sensitive to rain and during rain seasons, tensile fractures develop and the deformation of the slope aggravates, which seriously threatens the security of the railway. It has become clear that rain is the most important factor inducing the slope deforming, which should be contributed to the long-term corrosion of groundwater on the fracture and pore system of the slope rockmass. The slope groundwater stems from rain and recharge amount from regional groundwater is small (Figure 1). The groundwater discharges in the way of a serious of springs, whose chemical composition was given in Table 1 . Congqing is a famous acid rain region in china and the pH of rain is usually below 5 (Table 1). Table 1 showed after the acid rain had seeped through the slope body, not only its acidity was neutralized but also the element concentrations were apparently raised by way of corroding the various minerals in the rockmass. Under a SEM, it was found that minerals hard to dissolve, such as feldspar and laumontite, were dissolved intensely along cleavage seam and seams around mineral grains and honeycomb-like mineral skeleton and a great deal of secondary quartz and clay minerals were left over (Figure 2). The study of rock casting thin sections using polarizing microscopes found that the

F i g r e 1. H-0

corrosion along discontinuities such as microfractures was intense especially. The observation about corrosion phenomena was easy, but the evaluating quantitatively these complex phenomena was relatively difficult. Based on mass balance reaction modeling theory (Plummer et al. 1977, 1980, 1983, 1993; Katz et al. 1995), the corrosion intensity of acid groundwater on the slope rockmass was estimated. 2.1 Equilibrium specintiori cnlciilntioii

Equilibrium speciation calculations were made to provide saturation indices (So of minerals that may be reacting in the system The Sl of a specific mineral is defined as (Plummer et al. 1993) 5'1 = lg-

UP K,.

where IAP is the ion activity product of the mineralwater reaction and K,is the thermodynamic equilibrium constant. Calculated values of the saturation indices of gypsum, calcite and dolomite were presented in Table 2.

Table 2. Results of saturation indices calculation Mineral iiaiiie

rain water

spring \\ ater

gypsuin

-1.5

-0.59

calcite

-CO

1.11

doloinite

-CO

1.90

stable isotope diagram of the slope groundwater

Table 1 The analytical data of the water pH SiO, Ca" Mg" K' c1 DS DIC 6 "U%") "S(%") Rain 4.3 0.020 0.045 0.013 0.025 0.029 0.135 0.604 -12.83 -3.97 Spring\vater 7.35 0.149 6.600 0.810 0.132 1.109 1.480 3.829 -18.41 5.2.3 All concentrations of cleiiietits and species are 111 iiimol/l; DS denotes total dissoh ed sulfur. DIC denotes total dmoh cd inorganic carbon; the Ialues of Ca' , Mg' , Na-, K , C1 and DS of the rain after Zhilal Shen et a1 ( 1992 )

534

Figure 2

SEM photograph of corroded minerals and minerals left over

2.2 Pln~isihlephases

2 3 A4ns.s halarsce reaction niodeliiig

Plausible phases refer to constituents that enter or leave the aqueous phase during the course of waterrock (soil) interaction. The determination of plausible phases is the basis of mass balance reaction modeling. By way of comparing the chemical composition of rain and spring water, analyzing the mineralogy and microstructure of the slope rock and clay by X ray diffraction, casting thin section ( that is, rock samples being impregnated with a red resin prior to sectioning) and SEM observation, the plausible phases of the slope water-rock system were selected (Table 3).

The chemical evolution of the water along the flow path were constrained by the relationship of conservation of mass that was represented by the following equations 0 calcite +

0 dolomite +

a ,o

=

1777

(2)

(3

(3)

a gvpvp’um = A 1771s 0 calcite + 0 laumontiv + 0 iioloniite + 0 g ’ p u i n

a dolomite = a NaCl =

=

illrc;r

n7T4fg n7TCl

0 poias,iurn icld5par + 0

illlie

=

ll?TAk

(4) (5) (6) (7)

Table 3 Selected plausible phases for mass balance reaction modeling feldspar potasslulll

Phase

laumol~tltc

Composition

CaSi ,AI20,? KSi,A10,

calcite doloinite

gypsum Sodiuiii clilonde

Carbon dioude

llllte

CaCO, CaMg(CO,),

CaSO, NaCl

CO?

KAISi-020(OH)I

535

quart/

SiO?

results of the mudstone from XRD, the phase was pyrite. The corrected mass balance reaction models were following where o P is the number of moles of yth mineral entering (positive) or leaving (negative) the solution, b , , is the stoichiometric coefficient of kth element in the yth mineral, A indicates a difference (final value minus initial value), nrT,kis the total molality of the kth element in solution. Considering the dissolving process and carbon isotope equilibrium, there were the following relationships modeling results were showed in Table 4

24

Esiinzniion qf fotnl m m m t of niim.cils cor.roded

2.5

The preliminary modeling results were obtained from the mass balance reaction model consisting of equation (2)-equation (10)

The total discharge rate of the slope groundwater per year (0t/a) was calculated using the following equation

L x a n m m v 1 oj 17?0dtdI?lgresrdt

Comparing the above relevant a , with the saturation indices in Table 2 indicated modeling results were reasonable from one aspect The sulfur isotope data in Table 1 offered relevant information for examining the modeling result The examining be carried out on the basis of equation (11) (Hummer et a1 1993)

where Q f ( t ) is the discharge hnction with time of ith spring. The total corrosion amount (M t/a) was defined as P

M

= 1 x 10 - " x

113)

QC a I , n 7 , , P- 1

where Y is the total number of reactant phases and the molal mass ofyth phase. The total corrosion amount calculated using I' 077T J7w,,l,f +, < , a,$ , , ~ 7 9 "equation 1 > (13) equaled to 38.93 t/a, of which the P-1 cements such as laumontite accounted for 99.05% or = ( b 3 byr 5 ) so. According to this result, the estimated corrosion (m, 5 depth per year was about 3mm. Because the main (11) phases of mass transfer were aluminosilicate where h,,, is the stoichiometric coeficient of sulfur minerals, the corrosion amount of 3 8 . 9 3 did not in the y t h phase, 6 ''SI, is the sulfur isotope denote that so amount of mass was bought out from composition in per mil of the yth phase, inTSand 6 the slope, but the amount of the minerals whose "S, denote the total molality of sulfur in solution structure were destroyed. and the average isotopic composition, in per mil, of The above research results showed that the total dissolved sulfur, respectively corrosion of acid groundwater to the slope rockmass The calculated ~ ~ " Sfor I J final water equaled to was very intense. Since occurs mainly along the 18 92%0, but the corresponding measured value was discontinuities, the intense corrosion action will only 5 23 %o, which indicated that in addition to speed up the slope evolution process from stable to gypsum other phase containing sulfur existed in the unstable state, as well as complete failure. water-rock system According to the analyzing nip is

),,8,f,d

Table 4 Results of the mass balance reaction modeling ~ l isea a

I1

~ a iiio u lit i t e 5 390

ssiuill Calcite feldspar 0 134 0 24

Dolomite

Gypsum

0827

0098

536

chlonde 108

diovde 2 158

Illite -0 027

Quart' -22 02

3

minerals to dissolve easily were corroded, the concentration of every ion of the four leaching fluids had an apparent rise. Except the sand clay the pH of the leachates amounted to 7 or so. Because modeling the corrosion of aluminosilicate minerals such as feldspar was hardly possible, the ion concentration margin of the leachate from the sandstone was relatively lower.

PREVENTION AND CONTROL MEASURES

It was clear that if seepage water was neutralized prior to entering the slope rockmass, the corrosion action may be effectively contained. Since the slope rockmass was covered by a sand clay layer of 1 m thick, the sand clay may be changed into a neutralizing barrier by mixing it with some additive. Considering the neutralizing effect, cost as well as availability, limestone was chosen as additive.

3 2 Modeling experiment or7 tiei4ti*aImrighariwr

3.1 Modelirig experinient OH corroding capacity of acid izliti OH the slope rock and clay

Acid rain was modeled by adding hydrochloric acid into distilled water and the modeling experiment on conoding capacity of acid rain on the slope rock and clay was made using a leaching column. Water-rock interaction time was controlled within 20 hours by circulating leaching The sand clay, weathering and fresh mudstone, as well as fresh sandstone from the slope were leached respectively. The fresh mudstone and sandstone were ground to pass a lcm sieve. The results were given in Table 5 . Table 5 demonstrated the corrosion of acid rain on the slope rocks was very intense. Although the modeling water-rock interaction time was far shorter than the real that, and in the course only part of the

According to carbonic acid equilibrium theory, when the action between water and CaCO; gets balance in a open system, the pH of the solution is equal to 8 4, which indicates that limestone has the capacity of neutralizing acid water Moreover, as a natural material it is not only inexpensive but also may be obtained easily So, limestone was chosen as additive Limestone was ground into broken stone of 2cm in diameter to increase interaction time The sand clay was mixed with limestone at some fraction to turn it into a neutralizing barrier Mudstone and sandstone were ground to pass a lcm sieve Simulating experiment was conducted in a leaching device (Figure 3) The interaction time of waterbarrier and water-rockmass was controlled within 20 hours

Table 5 Chemical composition of acid rain and leaching fluids (mg/l) ca ?+ M ?+ Na' K' c1 SO,? HCO, CO,? 1 OS6 060 2 7 11 7 33 3 1086 281 4 3016 212 5 8 1 1 221 1. acid ran, 2. sand cla!.

CO? pH TDS 5 11 255 1443 535 599 000 1051 42 33 1 3 2558 348 1413 41 98 4545 000 1583 5 95 1197 1918 417 2367 1239 10023 0 0 0 122 7 10 183 52 3716 526 6839 2099 7592 000 844 7 1 201 11 2575 391 1841 2099 7226 000 422 73 115 54 3. weatheniig mudstone. 4, Fresh mudstone. 5. sandstone. TDS denotes total dlssol\ed sollds

Figure 3. Experimental model of neutralizing barrier

537

Table 6. The comoosition of leachate _.

Number Na' K Ca?' Mg?' C1- SO:HC0,- CO:- CO? pH TDS 0 0.86 0.60 5.11 2.55 14.43 5.35 5.99 0.00 10.54 4.2 33.33 259.65 1 7.51 1.36 71.03 15.07 11.43 38.28 223.77 0.00 21.51 7.10 257.79 2 10.35 1.86 59.23 20.40 21.01 39.92 209.93 0.00 10.12 7.10 0:acid rain (input ivater); 1, leachate from neutralizing barrier; 2, leachate from roclunass

Table 7. The composition of leachate Number

NaK Ca?' 4.12 2.42 71.12 15.63 1.77 61.51 1. leachate froin neutralizing barrier: 1 2

Mg" C1' SO:HCO,' CO? pH 8.81 74.31 31.28 123.51 0.00 7.72 9.50 78.25 31.69 114.22 0.00 7.52 2, leachate from rockinass

The comparison of the compositions of acid rain and leachates from the barrier and rockmass were presented in Table 6. The neutralizing barrier not only elevated the pH of acid rain from 4.3 to 7.1 but also raised its TDS by about 7 times. The concentrations of all the ions increased apparently, especially HC0;- and Ca". Comparing Table 6 with Table 5 , these changes obviously stemmed from limestone, but from sand clay. So, the neutralizing effect of the barrier was striking. After passing through the neutralizing barrier, the seepage water from acid rain lost basically the capacity to corrode the rockmass. Having penetrated the rockmass, the increase margins of ion concentrations were all little, and even those of Ca2+, HCO; and TDS were negative. That is why the effect of neutralizing barrier was conspicuous. In order to confirm further the above conclusion a dilute solution whose pH was 4.2 was compounded by adding hydrochloric acid into running water and a repeated experiment was conducted. The result was given in Table 7. The concentration changes trend of Na*, Ca?' and HCO; and the change in TDS indicated in Table 7 were basically consistent with that shown in Table 6. It became clear that after passing through the neutralizing barrier, the seepage water from acid rain lost basically corrosiveness and the neutralizing barrier made of limestone could prevent effectively the slope rockmass against corrosion. Considering slope property, neutralizing barrier is suitable to those covered by weathering clay layer; In light of geographical condition, it is proper not only in acid region but also most of areas where chemical weathering are intense and soil acidity are strong, such as vast southern china. 4

SUMMARY AND CONCLUSION

Groundwater originating from rain plays an important part in slope evolution and deformation. Its effect may be divided into mechanical and chemical two aspects.

538

TDS 255.83 255.46

The chemical effect of groundwater from acid rain on some railway bed slope located in Chongqing suburbs was investigated and a corresponding prevention and control measure were studied. The results demonstrated that the corrosion of acid groundwater on the slope rockmass was very intense. Both minerals easy to dissolve and those hard to dissolve, such as potassiuni feldspar and laumontite, were intensely corroded. The porosity of rockmass was obviously raised. The corrosion took place along the discontinuities and was the most important factor causing the rockmass strength decaying. The total leaching amount of the slope amounted to 30 t per year or so, which meant the structure of about 30 t minerals, especially the cements such as laumontite, were destroyed. The corrosion depth was about 3mm per year. The experiments indicated that the neutralization barrier made of the slope sand clay and limestone could effectively lowered the acidity and corrosive capacity of the seepage water from acid rain and prevent the rockmass against corrosion.

REFERENCES Pluinmer L. N. 1977. Defining reaction and mass transfer in parts of the floridan aquifer. l ? b w resoiiiw.~resenrcli. Ibl. 13. Xo. 5. Plummer L. N. et al. 1980 The iiiass balance approach :application to interpreting the chemical evolution of hydrological systems. .lii/ericnii journnl oj science. I bl. 280 Pluinmer L. N.et al. 1983. De\clopiuent of reaction models for ground-water system. Geochimicn e l Cos~rocl7iii/icn .Icm Tbl. 17 Plurmner L. N. et al. 1993. Geochemical modeling of the Madison aquifer in parts of Montana Wyoming and South Dakota. Ilhter resoiirces rcseni-ch. Ibl. 26. NO. 9 Younger P. L. 1992. The hydrogeological use of thin sections: estimates of groundwater flow and transport parameters. Qiiorter!v Jouri7ol of Ei7gineeriiig Geolo
Slope Stability Engineering, Yagi, Yamagami & Jiang GJ 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Slope failures triggered by an earthquake and a heavy rain in Chiba S.Yasuda, Y.Yoshida, T. Kobayashi & T. Mizunaga Tokyo I l m k i Universig, Suitnnia,J u p n

ABSTRACT: Slope failurcs during thc 1971 hcavy rain and 1987 Chibaken-toho-oki carthquakc in Chiba were studicd by aerial photo survcy. Slopes failed during thc second trigger wcrc thc slopcs saved from the failure during thc first triggcr. Laboratory tcsts for thc failcd soil showcd that cohcsion dccrcascd with weathering. It was concludcd that thc soils of the slopcs arc scnsitivc to wcathcr and tend to fail during rains or earthquakcs.

1 INTRODUCTION In Japan, slope failures occur frcqucntly because there arc many big carthquakcs and hcavy rains. Morcovcr, soils or rocks of slopcs arc weak and sensitivc to slidc bccausc they arc young and tend to wcathcr. Sharp fluctuation of tcmpcraturc and moisturc accclcratcs thc wcathcring of thc soils and in rocks. Tcmperaturc is ovcr 30°C and under 0 summer and in wintcr, respcctivcly. Rainfall continues during about 2 month in rainy scason but no rain falls in dry scason. Thcrcforc the study on dccrcasc of strcngth of soils and rocks due to wcathcring sccms to be important. Rccently, many slope failurcs occurred during a heavy rain and an carthquakc at almost samc slopcs in Chiba. It scemcd that thc soils of the slopcs arc scnsitivc to wcather. Thcn, thc authors studicd thc soil and topographical conditions of thc failcd slopes, and conductcd laboratory tcsts to ciemonstratc thc dccrcasc of strcngth duc to wcathcring.

"c

2 TOPOGRAPHICAL AND GEOLOGICAL Fig. I Location of the arca studicd

CONDITIONS OF THE STUDIED AREA Figurc 1 shows thc arca studicd. Thc arca is in and around Naruto and Matuo towns, mrhich arc about 60 km wcst of Tokyo, in Chiba Prcfccturc. Shimofusa Tcrrdcc is formcd bchind Kujyukuri lowz land. Height of thc tcrracc is several tcns mctcrs. Figure 2 shows a cross section of thc tcrracc at thc sampling sitc shown latcr. The tcrracc is composed mainly of dcnsc and ccmentcd sand laycrs named Narita Sand which was dcposited in Plcistoccnc. Surface soils of Narita Sand are fairly wcathcrcd. Top of thc terracc is covered with a thin layer of loam.

3 SURVEY OF FAILED SLOPES DUE TO TWO TRIGGERS

3.1 Slope failures during earthquake

U

heavy ruin and an

Slope failurcs occurred at about 7760 sites in Chiba Prefecture due to the heavy rain on September 6 to 8 in 1971. Most failures were shallow slides of Natira Sand. In 1987, Chibaken-toho-oki earthquake, with a 539

Fig.2 Soil cross section at the sampling site (Sambu Construction Work Office of Chiba Prcfecture Government) different. Therefore, it can be concluded that surface sand of slopes had been weathered and sensitive to failure before two disasters. Some slope failed during the 1971 heavy rain and remaining slopes failed during the 1987 Chibaken-toho-oki carthquake.

magnitude of 6.7 on the JMA scale occurred about 10 krn southeast Kujyukuri low land. Many terrace slopes failed. Most of failures were shallow slides of Narita Sand again. 3.2 Survey of failed slopes by aerial photoes

Locations of failed slopes during the 1987 Chibakentoho-oki earthquake were investigated and plotted on maps by Chiba Prefecter Government. However, locations of failed slopes during the 1971 heavy rain were not clear. Then, aerial photo survey was carried out for both disasters to find the locations with a same accuracy. Aerial photos used were taken in the following years: a) 1971 heavy rain: 1970 (before the disaster, 1/20,000) 1972 (after the disaster, 1/13,000) b) 1987 Chibaken-toho-oki earthquake 1986 (before the disaster, 13,000) 1988 (after the disaster, 12,500) Figure 3 shows the locations of failed slopes during two disasters. As shown in this figure, many slope failures occurred on terrace slopes which are the boundary between Kujyukuri lowland and Shimofusa Terrace during the 1971 heavy rain. Slope failures occurred also on almost same line of terrace slopes during the 1987 Chibakn-toho-oki earthquake. Volume of slid mass is also similar. However, locations of failed slopes were slightly different. This means that slopes which had been saved from failure during the 1971 heavy rain, failed during the 1987 Chibaken-toho-oki earthquake. From topographical points of view, terrace slopes are not curved in this area. Topographical conditions of failed slopes during the two disasters were not

3.3 Effect of failure of neighbor slope

In detailed survey of Failed slopes, several interesting locations where failures during the former disaster affected the failures during the latter disaster, were found. Figure 4 s h o w the dctailcd map of these locations. At Site No.1 and 3, east and west slopes failed during the heavy rain, then central slope failed during the earthquake. At Site No.2 east slope failed at first, then west neighbor slope failed. Neighbor slope also failed at Site No.4. In these sites, the central or neighbor slopes must be sensitive to failure during the earthquake because side friction of these slopes had been lost due to the Failures of neighbor slopes during the heavy rain.

4 RING SHEAR TESTS TO STUDY THE DECREASE OF STRENGTH DUE TO WEATHERING 4.1 Sampling and weathering procedures As mentioned above, typical pattern of slope failures was shallow slide of a surface weathered soil layer. It seemed also that the soil named Narita Sand is sensitive to weather. Then, decrease of shear strength of the Narita Sand due to weathering was tested by a ring shear test apparatus. Undisturbed samples of Narita Sand were taken at the site shown in Figs.2 and 3. As the slope had failed

540

Fig.3 Locations of failed slopes during the heavy rain and the earthquake

Fig.4 Detailed map of the interesting sites

541

and inner diameter are 2.5cm, 15cm and 10cm, respectively. In this district, heavy rain falls in June and July but no rain falls in winter. Moreover, it’s very hot in summer though snow falls in winter. Then two procedures to weather the specimens were selected: cyclic drying and wetting, and cyclic freezing and thawing. In the first procedure, specimens were dried in a drying furnace with the temperature of 60°C for 22 hours and wetted by a spray for 2 hours as shown in Fig.6. This procedure was repeated for prescribed numbers of cycles. In the second procedure, specimens wcre frozen with -20°C for 3 hours and thawed with 40°C for 3 hours as shown in Fig.7. Numbers of cycles were selected as 0, 1, 4, 16 and 64. Confining pressure was not applied during these processes because only surface soil layer must be weathered. Figure 8 shows volume change of specimens during the weathering processes. Specimens swelled up to 16th cycle. Especially, the volume changed rapidly up to fourth cycle. The volume change by drying and wetting was larger than that by freezing and thawing.

Fig.5 Grain size distribution curve of the samlpe

4.2 Ring shear tests Shear strength of the weathered specimens were tested by a ring shear test apparatus. Water content of the specimen were adjusted as natural water content in situ, then vertical pressure of 50, 100 or 200 kPa was applied. Torsional shear stress was applied with a speed of 0.183 degrees/minute, up to 50 degrees under drained condition. Torsional shear strcss, torsional angle and vertical displacement were measured during the tests. Torsional shear stress increascd with torsional angle, then decreased slightly after a peak strength. The peak strength was induced at several degrees of torsional anglc. Figures 9(a) and 9(b) show the change of peak strength and residual strength,

Fig.6 Procedure of drying and wetting

Fig.7 Procedure of freezing and thawing surface soil only was excavated to the depth of about l m at the middle height of the slope. Then undisturbed samples were taken by block sampling technique. Figure 5 shows grain size distribution curve of the sample. As shown in the figure the sample was silty sand with 27.6 % of fines. Samples were trimmed for specimens. Height, outer diameter 542

Fig.8 Volume change of specimens during weathering process

Fig.9 Change of pcnk and residual strengths with repeated number oi':;~ks for drying and wetting respectively, with repeated number of cycles for dried and wetted specimens. Figures 10(a) and 10(b) show test results for the specimen weathered by freezing and thawing. Both peak and residual strengths decreased up to fourth cycle. This number of cyclc is similar as the number in which volume change occurred, as mentioned above. Reduction of the strengths for the specimens weathered by drying and wetting were more sevcrc than that weathered by frcczing and thawing. As mentioned above, volume change during the drying and thawing was larger than that during the freezing and thawing. Therefore, it can be said reduction of peak and residual strengths is attributed to the swelling of the specimen, because cementation of particles decreases with the swelling. Figures 11 and 12 show relationships between vertical pressure and peak strength for the two series of tests. Change Of angle Of internal friction, d , and cohesion, C , from zero cycle to 64th cycle, derived from these figures are: a) weathered by drying and wetting: c=15 kPa-0 kPa, #=35' -311' b) weathered by freezing to thawing: c=15 kPa-5 kPa, 4=35" -33"

Fig. 10 Change of peak aiid residual strengths with repeated number of cycles for freezing and thawing

Fig. I 1 Relationships betweell vertical pressure and peak strellgth for dried and wetted specimen Therefore it can be said that the main reason of decrease of strength is attributcd to the loss of cohesion. In general, the loss of cohesion causes 543

Denki University. Their cooperation and assistance are gratefully acknowledged. REFERENCE Yasuda, S., T. Kobayashi, T. Mizunaga & K. Yamamoto 1999. Decrease of shear strength of two types of soils during the cyclic drying-wetting and freezing-thawing, Proc. of the 34lh Annual Convention of the Japanese Geotechnical Society (in press, in Japanese).

Fig. 12 Relationships between vertical pressure and peak strength for frozen and thawed specimen shallow slide because the strength of surface soil is controlled not by internal friction but cohesion. This must be the reason why shallow slides occurred during the heavy rain and the earthquake as mentioned beforc. The authors has been conducted same tests for Kdntoh Loam which is volcanic ash soil (Yasuda et al., 1999). Test results showed that not cohesion but internal friction decreases due to weathering for the Kanto Loam. It is interesting that the mechanism of decrease of strength due to weathering is different between the Narita Sand and the Kdntoh Loam.

5 CONCLUSIONS Slope failure sites during the 1971 heavy rain and 1987 Chibaken-toho-oki earthquake in Chiba were studied by aerial photo survey. Laboratory tcsts to demonstrate the decrease of strength due to weathering were also carried out. Based on these studies, following conclusions were derivcd: 1) Type of the slope failures during both disasters was shallow slides. 2) Surfdcc sands of the slopes had been wcathered and sensitivc to failure before the two disasters. 3) In this soil, cohesion decreases with weathering and bring shallow slides.

ACKNOWLEDGMENTS Boring data shown in Fig.2 are provided by Sambu Construction Work Office of Chiba Prefecture Government. Great support was given by the office and Nihonkohatsu Co. Ltd. in the sampling of the Narita Sand. Ring shear tests were conducted with the assistance of Messrs. S. Imura, Y. Uno and K. Yamamoto who were former students at Tokyo

544

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Numerical evaluation of the effects of drainage pipes Takuo Yamagami & Jing-Cai Jiang Department of Civil Engineering, Universityof Tokushima,Japan

Kenji Nishida Obayashi Corporation Technical Research Institute, Tokyo,Japan

ABSTRACT: An evaluation method is presented for the effectiveness of horizontal/semi-horizontal drains to reduce ground-water pressures in soil slopes. A system of horizontal/semi-horizontal drains is commonly used to enhance the stability of slopes in which ground-water is the main cause of instability, this is the usual case for almost all landslide slopes in Japan. Despite its quite frequent use, no design guidelines have been established. In this paper ground-water behavior is solved by the 3D-finite element saturated-unsaturated seepage analysis. One dimensional linear finite elements are incorporated into the 3D-finite element groundwater system to simulate the influence of the drains. An experiment was conducted on a model sandy ground in a metal tank in which perforated drainage pipes were installed. The observed results were compared with the numerical ones, and good agreements were obtained, indicating the usefulness of the proposed method. approach (Cai, et al. 1998) has been presented in which pressure heads are simply forced to zero along drainage pipes. This treatment however dose not seem to reflect the real state of seepage flow. Drainage effects may vary widely according to the size and perforation ratio of each pipe. The scheme of zero-pressure head along the pipe however, cannot take into account the above fact. Regardless of the type of pipe, it will yield the same result. On this point, the present method discretizes a drainage pipe as one-dimensional finite elements with a hydraulic conductivity, thereby enabling us more flexible treatment. An experimental investigation was made for verification of the proposed method, based on a small scale model sandy ground with some model drainage pipes. Good comparisons were obtained between the predicted and the measured values, demonstrating that the proposed method can be used with confidence for design purpose as long as soil grounds are concerned.

1 INTRODUCTION Fans of perforated drainage pipes are installed almost invariably in Japan to improve the stability of landslide slopes. To the authors' knowledge however, a rational design method has not yet been developed for this type of stabilizing measure. The choice of drain length and drain spacing for systems of drainage pipes are usually chosen on the basis of engineering judgement by the engineers in charge. This is unavoidable, in one sense, because of Japan's natural ground conditions. Mountainous regions in Japan, where usually landslides take place, consist of very complicated, unsystematic and heterogeneous geological materials varying from soft soils to hard rocks. It is thus quite difficult to treat the groundwater behavior quantitatively. These circumstances have hindered progress in the theoretical aspects of the design criterion for drainage systems. We must nonetheless make efforts to overcome this difficulty. Thus, the goal of our research is to develop a rational design method which will adapt to the actual situations mentioned above. And as the first step toward this goal, ground conditions in this paper are restricted to soil systems only, without discontinuities with regard to seepage flow. This paper presents a 3D-finite element representation of the effectiveness of drainage pipes, provided that the ground consists of soils amenable to an integrated saturated-unsaturated seepage analysis. The key to success of the proposed method is how to numerically model the drainage pipes. An

2 NUMERICAL MODEL A three-dimensional saturated-unsaturated finite element technique is employed to simulate transient seepage for ground-water flow systems including drainage pipes. The soil system is treated as a continuum, without hydro-geological discontinuities which may become preferred flow paths, encompassing flow in both saturated and unsaturated 545

zones. The governing equation for this system is

for the pipe flow: divkB($)6(9+x3)+q=CB($)-3s at

as

The Galerkin method has been applied to this equation for the finite element formulation. In Eq.(6), if the pipe under consideration lies in a saturated zone, then the pipe is also assumed to be saturated ; and if it is in an unsaturated zone, then the pipe may be, either. It is how to determine adequately the saturatedunsaturated seepage characteristics for the pipe flow that is the biggest problem. There is no existing testing method to determine these properties. We have thus established an empirical approach that was attained through trial and error. In the approach, soilwater characteristic curve and unsaturated hydraulic conductivity are respectively defined in a bilinear form as shown in Fig.2. For the saturated flow in the pipe, required property is the hydraulic conductivity only, and this value has influential effects on the computed results. Therefore, how to determine an adequate value of the hydraulic conductivity is of great importance. About this essential point a brief discussion will be given later. Complete solutions are provided by the simultaneous treatment of the 3D-model governing the equation of the ground-water system, Eq.( I), and the governing equation for the pipe flow, Eq.(6), with appropriate boundary and initial conditions. In the finite element formation, 8-node isoparametric and one-dimensional linear elements are used for the

- CC(4) + as,]- = 0 at

where xi : the spatial coordinate, k,( 4 ) : the relative hydraulic conductivity, $ : the pressure head, ki,' : the saturated hydraulic conductivity, C( 4): the specific moisture capacity(=a B / a $I), (Y : a = l ( $20), a = l ( 4 < 0 ) , S, : the specific storage, t : time. But descriptions of the formulation of finite element technique based on this equation are omitted . here, because it is well-documented elsewhere. One-dimensional finite elements are used to represent the flow in the drainage pipes. Fig.1 illustrates schematically part of a drainage pipe installed in a drilled hole. It is clear that water flows predominantly in one direction in the pipe, taking in neighboring water through perforations or slits on the peripheral wall of the pipe. Now suppose that water is incompressible and no pipe deformation occurs during drainage, then the continuity equation of saturated-unsaturated seepage in the pipe can be expressed as

aeB

-div?+q =-

at

where v : the velocity, q : the flow rate into the pi e per unit length of it from surrounding ground, 8 E: : volumetric moisture content. Eq.(2) can be rewritten as

34

-div?+q =CB($)-

at

(3) Fig. 1 Drainage pipe in a drilled hole

where CB( 4) : the specific moisture capacity (= a B B/ a y5 ) for the flow in the pipe. We assume here the following equation of motion, that is Darcy's law, for the flow in the pipe for both saturated and unsaturated conditions :

v =kB($)I

(4)

where

+

where k,"( ) : the relative hydraulic conductivity (0 S k,"( 4)5 1 ). Then we can finally obtain the governing equation

Fig.2 Unsaturated properties for drainage pipes

546

ground-water system and for the flow in the pipe, respectively. In what follows, the numerical model mentioned above is named LE (Linear Element) model ; whereas the existing model is called PP (Prescribed Pressure) model in which the pressure head is prescribed to be zero. Even in the PP model, nodal flow rate is zero for the nodes located in an unsaturated zone. 3

EXPERIMENTS

A test tank used is shown in Fig.3 ; the size of which is 190cm wide , 9Scm high and 40cm deep. The front face of the tank is made of a transparent acrylic (resin) plate. On the rear, steel plate are attached 60 manometers to measure pore water pressures along the inside surface of the rear plate. Toyoura sand was used in the tank to make a model ground which measured 1S0.5cm wide, 64.Scm high and 40cm deep as shown in Fig.3. The specific gravity of the sand was 2.65 and the dry density was 1.Sg/cm3. Sufficiently strong, pervious wire screens were vertically installed on both sides of the ground.

In the ground four perforated metal pipes imitating horizontal or semi-horizontal drains were placed. The outside and inside diameters of each pipe were 8mm and 6mm respectively. Perforations were made over the whole length of the pipes. Each pipe was protected on the outside by wire gauze stocking. Arrangement of the pipes on the front and rear faces are shown in Fig.3. The rear side ends of the pipes protruded penetrating through the steel plate and were put in a plug. The water tables on both sides of the ground were gradually raised from the bottom up to a height of S5cm and this final condition was kept for 24 hours, followed by the following two types of experiment : 1) The first case (Case 1) : Drainage was performed for 2 minutes after pulling out the four plugs simultaneously. The water tables were kept at the height of S5cm during this experiment. 2) The second case (Case 2) : First, one water table was lowered down to a height of 4.5cm, while the other was kept at the initial level. The water level variation with time is given in Fig.4. Then, the four plugs were pulled out at an elapsed time of 10 minutes, without changing the levels of water table on both sides. Under this condition drainage was conducted for 2 minutes.

Fig3 Experimental apparatus

547

4.1 Case I

4 NUMERICAL PREDICTIONS AND EXPERIMENTAL OBSERVATIONS Unsaturated seepage characteristics for the sand, i.e. the pressure head-volumetric moisture content and the pressure head-relative hydraulic conductivity figures are shown in Fig.5. These characteristics are obtained from Kohno and Nishigaki's research(Kohn0 and Nishigaki, 1981). The hydraulic conductivity k" is 2.04 X 10-2cm/sec for saturated condition. The specific storage S, is zero assuming that the sandy ground will not deform at all. Unsaturated seepage characteristics for the flow in pipes are shown in Fig.6. As seen in the figure, the same form is assumed for both relations, with a porosity of n= 1.O. The largest value available is preferable for C1 in reflecting the actual behavior ; however an excessive value of C I causes a numerical instability. Thus we need some experiences to manage to deal with this problem. The finite element mesh division is shown in Fig. 7 ; the total number of elements is 560 and that of nodes is 825. This seems like a rather coarse mesh division.

Fig.8 shows the locations of the free surfaces on the inside surface of the rear steel plate at the end of the experiment of Case 1, where a free surface means a line connecting points of zero water pressure head. The hydraulic conductivity kB for drain pipes are unknown in advance. Thus, a parametric study has been done in which three different values were used for kB as shown in Fig.8. Table 1 lists total volume of drained water from the mouth of each pipe. The LE model with kB=lOOcm/sec has yielded the best

Fig.6 Unsaturated properties for drainage pipes

Fig.4 Water level variation with time (Case 2) Fig.7 3D-finite element mesh (A view from steel side)

Fig.8 Comparison of numerical and experimental free surface locations at the end of Case I (120sec, Steel side)

Fig.5 Unsaturated properties for sand

548

Fig.9 Free surface locations at the end of Case 1 (120sec, Vertical sections including drainage pipes)

solution among the competitors in the light of the locations of the free surfaces. On the other hand, the LE model with kB=40cm/sec is considered to be preferable based on the out-flow amount of water. Fig.9 shows the locations of the free surfaces in vertical sections including drainage pipes.

4.2 Case2 Fig.10 shows the transition of the free surface locations, on the same surface as that in Case 1, from the beginning up to the time immediately before the start of drainage from the pipes. The final conditions in Fig.10 become the initiaI ones for the following drainage analysis. Fig.11 shows the locations of the free surfaces at the end of the experiment of Case 2. Table 2 lists the same kind of data as Table 1. Again, the LE model with kB=lOOcrn/sec has yielded the best result regarding the locations of the free surfaces, and also from the viewpoint of the discharged amount of water. Fig. 12 shows the locations of the free surfaces as in Fig.9.

Fig. 10 The transition of free surface locations from the beginning up to the time immediately before the start of drainage from the pipes of Case 2 (Steel side)

Judging from the discussions above synthetically,

kB of 100cm/sec seems to be the most desirable for the pipes used here. In this way, a promising method of determinin an adequate value of the hydraulic conductivity kT3 for any drainage pipe is to perform a well-controlled, high quality experiment, together with a parametric study such as that shown in this paper. Back analysis procedure is recommended to identify the adequate value.

Table 1 Comparison of numerical and experimental total volume of drained water from each pipe in Case 1 (Unit : cm3) No.1

No.2

No.3

No.4 Total

420

1750

1980

2120

6270

72

2829

1265

2495

6661

LE model (kB=100cm/sec)

283

2432

2058

2566

7339

LE model (kB=SOcm/sec)

338

2141

1831

2221

6531

LE model ( k ~ = 4 0 ~ ~ /366 ~ ~ ~2097 )

1786

2152

6401

Experimental PP model

Fig. 11 Comparison of numerical and experimental free surface locations at the end of Case 2 (120sec, Steel side)

549

Fig. 12 Free surface locations at the end of Case 2 (1 20sec, Vertical sections including drainage pipes)

5 CONCLUDING REMARKS

REFERENCES

A new attempt has been employed for the evaluation of the effects of drainage pipes based on the 3Dfinite element seepage analysis, on the premise that the proposed method is valid only for soil slopes. Numerical simulations were made of experimental results on the model ground in a tank, and good comparisons were obtained. It has been also known that the existing approach, i.e. the PP model is much less accurate than the proposed one, the LE model. This is because the PP model cannot take a variety of drainage pipes into consideration. Horizontal andor semi-horizontal drains are installed in almost every case as a controlling measure for landslide movements in Japan. Nevertheless, a rational design method has not been established for this kind of stabilizing works. In order to improve this situation, the present study has been done ; but this is not sufficient because it is of only use for soil slopes. Therefore, we must develop the proposed method into a more versatile one which may be adapted to strongly heterogeneous formations with flow channeling.

Cai, F., K. Ugai, A. Wakai and Q. Li : Effects of horizontal drains on slope stability under rainfall by threedimensional finite element analysis, Computers and Geotechnics, vo1.23 , pp.255-275, 1998. Kohno, I. and M. Nishigaki : An experimental study on characteristics of seepage through unsaturated sandy soil (in Japanese), Proceedings of the Japan Society of Civil Engineers, No.307, pp.59-69, 198 I .

Table 2 Comparison of numerical and experimental total volume of drained water from each pipe in Case 2 (Unit : cm3) No.1

No:2

No.3

No.4

Total

30

1510

1490

1240

4270

PP model

1

2364

737

701

3803

LE model (kB=]OOcm/sec)

2

1700

141 1

1177

4290

LE model (kB=’jocm/sec)

2

1849

1239

1026

4116

1747

1180

975

3904

Experimental

LE model ( k ~ = 4 0 ~ m / ~ ~2~ )

550

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Effects of horizontal drains on ground water level and slope stability Fei Cai & Keizo Ugai Department of Civil Engineering, Gunnza University,Kiryu, Japan

AEISTRACT: The effects of the horizontal drains on the ground water level are predicted by 3D FE analysis of transient water flow through unsaturated-saturated soils. The slope stability is evaluated with the global safety factor, obtained by 3D elasto-plastic shear strength reduction FEM, where the pore water pressure is obtained from the transient water flow analysis. The numerical results of a typical slope show that the ground water level is effectively lowered with the horizontal drains installed, and that the steady-state pressure head is independent of the hydraulic properties of soils. The slope stability increases with the length of the horizontal drains, and lengthening the horizontal drains is more effective than making the spacing smaller and increasing the drains number in a group when the length of the horizontal drains is shorter than the critical length.

1 INTRODUCTION

2 MODELING WATER FLOW IN SOILS

The horizontal drains are an effective measure to lower the ground water level and to increase the slope stability. The effects of the following parameters, i.e. the length, spacing, and direction angle of the horizontal drains, on the ground water level and slope stability are the factors concerned in the design of the horizontal drains . In the present paper, the effects of the horizontal drains on the ground water level in a typical slope with upstream water level of 14m and down stream water level of 5m are predicted with 3D FE analysis of transient water flow through unsaturated-saturated soils. The slope stability is evaluated with the global safety factor, obtained with 3D elasto-plastic shear strength reduction FEM, where the water pressure is obtained from the above-mentioned transient water flow analysis. The conventional elasto-plastic FEM is modified to predict the global safety factor of slopes, whose definition is identical to that of the conventional limit equilibrium methods (Ugai & Leshchinsky 1995). The shear strength of the unsaturated soils is expressed with the Bishop’s effective stress equation (Bishop 1959). Three sets of hydraulic characteristic parameters of van Genuchten model (van Genuchten 1980) are used to investigate their influences on the ground water level and the slope stability.

2.1 Fitnabmenfa1flow equation

The Darcy’s law has been shown to be valid for the water flow through unsaturated soils as well as the flow through saturated soils (Richards 193 I). The main difference is that the hydraulic conductivity is assumed to be constant for saturated soils, while it depends on the pore volume occupied by water for unsaturated soils. Based on the mass conservation and the Darcy’s law, the differential equation governing the water flow through unsaturatedsaturated soils is given by:

where K ( 0 ) is the hydraulic conductivity, 8 is the volumetric moisture content, 0 is the pressure head, z is the elevation head, t is time, and c(B) is the specific moisture capacity.

2.2 Hydraulic characteristics Equation (1) includes two soil parameters that must be determined: the hydraulic conductivity and the specific moisture capacity. These parameters under unsaturated conditions are dependent on the 551

volumetric moisture content, which is in turn related to the pressure head. A widely used representation of the hydraulic characteristics of unsaturated soils is the set of closed-form equations (van Genuchten 1980). The soil-moisture retention, specific moisture capacity, and hydraulic conductivity are given by:

s, = (8 - 8,)/(8,

- 8,) = (1

c(8) = U (n - 1)(& - 8,)

+I U

sym (1 -

@/'I

rm

Sk'"')'I

respectively, where

m

=

1 - 1/M

n>l

(5)

and S, is the relative degree of saturation, and 9, and Ss denote the residual and saturated volumetric moisture contents, respectively. K, and K,are the saturated and the relative hydraulic conductivity, respectively. a , n, and nz are empirical parameters of the hydraulic characteristics. The hydraulic hnctions are determined by a set of five parameters, 6, , 9,, a , n, and K,. 2.3 Numerical approach

The FE formulation for the transient water flow through unsaturated-saturated soils can be derived by the Galerkin principle of weighted residual:

d@

D@+E-=Q df

where, D is the seepage matrix, E is the capacitance matrix, and Q is the flux vector. The time derivative can be approximated with Crank-Nicolson algorithm. Because the hydraulic conductivity and specific water capacity are fbnctions of the volumetric moisture content, Equation (6) is highly nonlinear and is solved by an iterative method.

sliding surface as the conventional limit equilibrium methods (Ugai & Leshchinsky 1995). The global safety factor of slopes, defined in the shear strength reduction FEM, is identical to the one in the limit equilibrium methods. The reduced strength parameters ck and 4; replace the shear strength parameters c' and #' of the MohrCoulomb's failure criterion. Stresses and strains are then calculated in the slope by the elasto-plastic FEM. The initial F is selected to be so small that the soils of the slope are under elastic condition. Then the value of F is increased step by step until the global failure of the slope finally develops, which means that the FE calculation diverges under a physically real convergence criterion. The global safety factor at failure lies between the F, at which the iteration limit is reached, and the immediately previous value. The detailed procedure can be seen elsewhere (Ugai & Leshchinsky 1995). For unsaturated soils, the water phase occupies only parts of the pore volume, while the remainder is covered by air. Bishop (1959) introduced a x -factor to account for the fact, and suggested an equation for the effective stress of unsaturated soils. The shear strength of unsaturated soils is then calculated as:

where zJ is the shear stress at failure, c' is the effective cohesion, CT is the total normal stress, U , is the pore-air pressure, U", is the pore-water pressure, @' is the effective friction angle, and x is a parameter with the value between zero and unity, depending on soil type and the degree of saturation. The x -factor can roughly be replaced by the relative degree of saturation. The shear strepgth obtained from the hypotheses are in good agreement with the experimental results. When the degree of saturation is larger than 50%, there is a better correlation between the predicted and measured shear strength for unsaturated soils (Oberg & Sallfors 1997, Vanapalli et al. 1996).

4 EFFECTS OF HORIZONTAL DRAINS An idealized slope with the height of 10m and the gradient of 1: 1.5 is analyzed with a mesh, as shown in Figure 1. The initial ground water level is supposed to be 14m in the upstream and 5m in the downstream. The slope and the ground are assumed to be composed of the same soil. Three sets of the van

3 FE ANALYSIS OF SLOPE STABILITY The shear strength reduction FEM can analyze the slope stability under a general frame. The numerical comparison shows that this method can yield nearly the same safety factor and the corresponding critical 552

Figure 1. Typical slope and FE mesh Table 1. Hydraulic properties USS Soil tvne GCL 1.060 7.087 a (m-') 1.395 1.810 n 0.049 0, 0.106 0.469 0.304 0, 1.516 18.29 K,( 10'4cm/s)

Table 2. Mechanical properties Parameter Young's modulus Poisson's ratio Unit weight Effective cohesion Effective friction angle Dilatancv angle

BLS 2.761 3.022 0.044

Figure 3. Time histories of pressure head linearly increases to unity at the height of the initial water level for each type of soil. The initial moisture content has not influence on the pressure head in the steady state. The effects of the horizontal drains on the slope stability are predicted with the shear strength reduction FEM, in which the pore water pressure is obtained from transient water flow analysis. In order to compare the effects of hydraulic characteristics on the slope stability when the horizontal drains are installed, it is assumed that mechanical parameters of GCL, USS, and BLS are the same, as shown in Table 2, in spite of these soils with different grain characteristics and micro-structures.

0.375

63.83

Value 98.1 MPa 0.3 17.66 kN/m3 7.85 kPa 25" 0"

4.1 Effects of horizontal drains length

Figure 2. Contours of pressure head (m) Genuchten model parameters of the hydraulic characteristics for the Glendale clayey loam (GCL), the Uplands silty sand (USS), and the Bet Degan loamy sand (BLS), as shown in Table 1, are used to investigate their effects on the ground water level and the slope stability (van Genuchten 1980). The initial relative degree of saturation is assumed to be the same, i.e. Se=0.617, at the slope crest, and 553

The horizontal drains are installed at the height of the lower ground surface. The spacing is 10m, i.e. S=5m as shown in Figure 1 , when the effects of the length are analyzed. The pressure head along the horizontal drains is specified as zero. The length of the horizontal drains, L, from the slope toe is changed to clarify its effects on the ground water level and on the slope stability. The pressure head contours for the cross section show that the ground water level is effectively lowered with the horizontal drains installed(Figure 2). The numerical results show that the steady-state phreatic surface (the zero pressure contour) is independent of the hydraulic properties of soil for the homogeneous slope. However, the time histories of the pressure head on appointed points from the steady-state without the horizontal drains to the steady-state with the drains of L=15m are dependent on the hydraulic properties, and can not be

Figure 4. Pressure head versus length

the length of the horizontal drains, but it does not increase further when the horizontal drains are extended beyond the critical length, as shown in Figure 5. This is because only the pressure head of the zones along the slip surface influences the slope stability. Figure 6 shows that the discharge of the horizontal drains, Q, can be normalized with the saturated permeability, Ks. It implies that the other hydraulic parameters have no influence on the discharge. The normalized discharge almost linearly increases with the length of the horizontal drains. 4.2 Effec fs of hosizontnl drains syncirig

Figure 5. Safety factor versus length

The relationships between the pressure head and the spacing of the horizontal drains (L=7.5m and L=l5m) are shown in Figure 7. For all three types of soil the ground water level is definitely lowered only in the zones in the extent of the horizontal drains with the spacing becoming smaller. Figure 7 shows again that the steady-state pressure head in homogenous slope is independent of the hydraulic properties of soil. When L=7.5m7 the slope stability increases a little with the spacing becoming smaller. In contrast, when L=l5m, the slope stability comparatively more increases with the spacing becoming smaller (Figure 8) By comparing the rate of the increase in the safety factor in Figure 5, it is shown that lengthening the

Figure 6. Discharge versus length normalized with the saturated permeability, Ks, as shown in Figure 3. Figure 4 indicates the relationships between the pressure head and the length of the horizontal drains. These relationships are the same for all three types of soil. It is shown that the rate of the decrease in the ground water level at the points B and C becomes smaller and smaller when the horizontal drains are extended beyond a critical length, i.e., the distance between the slope toe and the slope shoulder. The slope stability increases with the increase in

Figure 7. Pressure head versus spacing 554

horizontal drains is more effective to lower the ground water level and increase the slope stability when the length of the horizontal drains is shorter than the critical length. Figure 9 shows that the discharge of the horizontal drains with different spacing also can be normalized with the saturated permeability. The normalized discharge almost linearly increases with the length of the horizontal drains whether L=7.5m or L=l5m. 4.3 Eflecfs of horizontal draiia directiori Figure 8. Safety factor versus spacing

Figure 9. Discharge versus spacing

Figure 10. Pressure head versus direction angle

The horizontal drains are installed in a group in the horizontal plane for easy construction. It is assumed that the group consists of three horizontal drains, and only half of the group is analyzed due to its symmetry. The direction angle, i.e. the angle between the drains is assumed to be 0", 30°, 45", and respectively. When the length of every horizontal drains in the group L=7.5m, the spacing is assumed to be 15m, i.e. S=7.5m. When L=15m, the spacing is assumed to be 30m, i.e. S=15m. The relationships between the pressure head and the direction angle of the horizontal drains (Figure 10) show that for all three types of soil, the direction angle influences slightly the pressure head. When the direction angle is 30 degree, and the length reaches the critical length, the ground water level is the lowest, and the pressure head decreases only 10% further. This implies that the ground water level is slightly lowered firther with the increase in the number of the horizontal drains in a group if the length of the drains in the group is the same. This is because the ground water level has been lowered with installing the horizontal drains with the direction angle of zero degree and the other drains in the group are installed in the region with the lowered ground water level. The direction angle of 30" obtains the maximum increase in the safety factor whether L=7.5m or L=15m. The increase in the safety factor for the spacing of 30m and the length of 15m is larger than that for the spacing of 15m and the length of 7.5m. Under these conditions, the total length of the horizontal length is the same. This implies that the lengthening the horizontal drains in the extent of the critical length is more effective than increasing the number of the horizontal drains in the group in order to lower the ground water level and to increase the slope stability. The discharge increases a little with the number of drains in a group, and the direction angle of the drains almost does not influence the discharge, as shown in Figure 11, where the discharge ratio with the 555

drains in a group when the length of the horizontal drains is shorter than the critical length.

REFERENCES

Figure 1 1. Discharge versus direction angle direction angle of 90" includes the seepage flow through the toe of the slope. 5 CONCLUSIONS The 3D FE analyses have been conducted to investigate the effects of the horizontal drains on the ground water level and the slope stability, where the effects of the length, spacing, and direction angle on the ground water level in a typical slope are predicted with 3D FE analyses of transient water flow through unsaturated-saturated soils. The slope stability is evaluated by the global safety factor, based on the elasto-plastic shear strength reduction FEM. From the calculated results, the following conclusions are obtained: 1. The procedure proposed in the present paper can be used to determine the length, spacing, and direction angle of the horizontal drains, and 3D analyses can give more realistic results than 2D ones. 2. The effects of the horizontal drains on the ground water level, in turn, the slope stability under steady-state are independent of the hydraulic properties of soil for homogenous slope. However, the time histories of the pressure head from the steady-state without drains to the steady-state with drains are influenced by the hydraulic properties. 3. The ground water level is effectively lowered due to the drainage effect of the horizontal drains. The slope stability increases with the increase in the length of the horizontal drains, but the rate of the increase in the safety factor of the slopes becomes smaller and smaller when the horizontal drains are extended beyond a critical length, i.e., the distance between the slope toe and the slope shoulder. 4. In order to lower the ground water level and increase the slope stability, lengthening the horizontal drains is more effective than making the spacing smaller and increasing the number of the horizontal

Bishop, A.W. 1959. The principle of effective stress. Plrblicnfion 32. Oslo: Norwegian Geotechnical Institute. van Genuchten, M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. SoiI Sci. Soc. Anzer. J. 44: 892898. Oberg, A.L. & G.Sallfors 1997. Determination of shear strength parameters of unsaturated silts and sands based on the water retention curve. Geotech. Testing J. 20(1): 40-48. Richards, L.A. 193 1. Capillary conduction of liquids through porous mediums. Physics 1: 3 18-333. Ugai, K. & D.Leshchinsky 1995. Three-dimensional limit equilibrium and finite element analyses: a comparison of results. Soils Foz~rzd.35(4): 1-7. Vanapalli, S.K., D.G.Fredlund, D.E.Pufah1, & A.W.Clifion 1996. Model for the prediction of shear strength with respect to soil suction. Cm. Geofech.J. 33: 379-392. Zienkiewicz, O.C. & R.L.Tayor 1989. The Jinite elenienf niefhod, 4th edn. London: McGraw-Hill.

556

5 Effects of seismicity

This Page Intentionally Left Blank

Slope Stability Engineering, Yagi, Yamagami & Jiang (01999Balkema, Rotterdam, ISBN 905809 0795

Collapse of high embankment in the 1994far-off Sanriku Earthquake Y. Shioi Huchinolze institute of Technokogv,Aomol-i,Japan

S.Sutoh East Japan Passenger Ruilway Company Limited, Morioku, Jupuii

ABSTRACT: A study using the sliding circle mcthod indicated that a high railway embankment, in Hachinohe, collapsed in the 1994 Far-off Sanriku Earthquake due to strong vertical seismic motion. Combined with other types of structural damage, this information should prove useful in evaluating the stability of other embankments.

1 THE 1994 FAR-OFF SANRIKU EARTHQUAKE The 1994 Far-off Sanriku Earthquake occurred in northeastern Japan at 21:19 on December 28, 1994, heavily damaging structures in the city of Hachinohe, 200 km west of the epicenter (Figure 1). The Far-off Sanriku Earthquake measured 7.5 in magnitude on the Japan Meteorology Agency (JMA) scale and put forth a very strong motion with a maximum acceleration of 675 gal (Figure 2). Table 1 gives the maximum values of acceleration recorded at Hachinohe Port Construction Office, Hachinohe Meteorological Observatory and Hachinohe Institute of Technology (HIT). This quakc occurred 20 days before the 1995 Hyogoken Nanbu (Hanshin) Earthquake that ravaged the city of Kobe. The largest aftershock occurred 10 days after the main shock with a magnitude of 6.9 and with nearly the same level of acceleration (Table l), 80 km southwest of the epicenter (Figure l), heavily damaging area of Hachinohe

Table 1. Maximum accelerations of the main shock and aftershock of the Far-off Sailriku Earthquake Observa- Seismo Max. main Max. aftershock accel. -graph shc ___ ;k ac el. tory UD EW NS UD EW NS PortConst SMAC 675 470 132 552 295 140 Office -B2 Meteorol. JMA87 95 94 363 499 488 602 Observa. > > JEPH. 300 300 192 627 292 186 I. GL-1 m 4B3 JEPT. 56 149 __ 69 174 102 109 G1-20 m 4B3

1

I

1

Figure 1. Important sites in the 1994 Far-off Sanriku Earthquake

only lightly affected by the main shock. The main shock evidenced such phenomena as damage due to the vertical component of seismic force and effectiveness of ground improvement for soil liquefaction, similar to the Hanshin Earthquake. The seismic measures for water supply in Hachinohe, after the 1968 Off Tokachi Earthquake were functioned efficiently and became a standard methods for repair and reconstruction works after a great earthquake, including the Hanshin Earthquake.

1

2 VERTICAL SEISMIC FORCE PHENOMENA While the damage in Hachinohe was relatively small compared to the Hanshin disaster, several types of damage

559

Figure 2. Corrected main shock acceleration record of the 1994 Far-off Sanriku Earthquake, Hachinohe Port Construction Office, the Ministry of Transportation

Figure 5. Comparison of damaged and undamaged masonry lanterns

Figure 3. Cracks in columns at Hachinohe city hall

cracks, the building should have collapsed under alternative load. A viaduct side column (Figure 4) lying on a border between terrace and sedimentary ground suffered buckled reinforcing bars at the top and coarse aggregate cut finely on the shear face. A comparison of damaged and undamaged masonry lanterns at a Shinto shrine 011 a hill in central Hachinohe (Figure 5 ) showed those damaged with ashlars heaped and plastered upon each other. Another in slender type was connected firmly part to part by other means. Had horizontal force predominated, undamaged lantern should have been toppled and the damaged ones with stable shape remained sound. A tall stone monument at the same shrine rotated only slightly, with the top stone plate remaining sound (Figure 6). Had horizontal force alone operated here, force should have exceeded 0.6 g corresponding to the frictional resistance between the massive footing and the ground, breaking the plate. Figure 7 shows a comparison of a leaped natural stone monument and a small masonry tower, set on rocky ground at another shrine. The former was plastered to footing with concrete mortar and parts of the latter was

Figure 4. Railway viaduct column breakage were very difficult to explain in terms of conventional horizontal seismic force alone, in both cases. Geologically, the Hachinohe area consists of tertiary and Pleistocene (Dilluvium) terraces covered by thick loam and Holocene (Alluvium) soft sediment on Paleozoic formations. Most of damage occurred, interesting enough on terraces compared to Holocene ground, as detailed below.. The columns of the city hall, built on a low hill, shows cracks (Figure 3). Intermediate columns had X shaped cracks, while end columns, which carried a comparatively light load, remained sound. If horizontal force caused these

560

Figure 9. Embankment collapse in the 1994 Far-off Sanriku Earthquake

Figure 6. Shape and rotational deviation of monument structure

Figure 10. Collapse of high railway embankment

Figure 7. Comparison of leaped natural stone monument and a small masonry tower

Figure 11. Embankment collapse in the 1968 Off Tokachi Earthquake not. A masonry lantern and small towers on the stairway to the same shrine remained sound (Figure 8). Had even a small horizontal force been acting, these towers should have been toppled.

3 RAILWAY EMBANKMENT DAMAGE 3.1 Overview

Figure 8. Masonry lantern

011

stainvay to shrine

Although it is surmised that vertical seismic force predominated in damaging embankments and cut slopes observed in the Far-off Sanriku Earthquake, it is difficult to prove. A typical railway embankment collapse occurred on Holocene ground near Hachinohe (Figure 9 and 10). This

56 1

Figure 12. Completed rehabilitation works embankment had evidence of severe slope sliding (Figure 11) in the 1968 Off Tokachi Earthquake, which had a magnitude of 7.9, a relatively long period, and a maximum acceleration of 233 gal. The embankment was repaired using sheet piles at the slope end and gabions implemented over the slope. The top of the collapsed embankment remained positioned almost the same (Figure lO), but gabions at the slope end were thrown several tens meters, suggesting that a strong, abrupt force acted on the embankment. To restore the embankment and enable trains to pass as soon as possibility, a rehabilitation plan (Figure 12) was quickly implemented. Repair work was completed in 3 days working 24-hour shifts and the first train passed through slowly at midnight December 31, 1994. Other railway damage was mainly railbed misalignment and settlement, with similar heavy darnage not occurring elsewhere nearby. About 1.5 km away, however, a similar road embankment slide (Figure 13) was seen along an old small basin. No marked damage was seen to houses or

Figure 13 Collapse of road embankment near railway embankment

other structures in nearby residential areas. Interestingly, while the maximum aftershock had the same level of acceleration as the main shock (Table l), it did riot produce the same degree of damage. Train operation continued under careful observation after the railbed had been inspected. The aftershock mainly damaged houses in eastern Hachinohe that were located on relatively firm ground, even so, damage was not great. 3.2 Collapsed embankment Case study After the collapsed embankment had been repaired, East Japan Passenger Railway Co. Ltd. conducted a surveys and analysis series to examine the mechanism of damage. The rehabilitation plan was based on a triangle block analysis (Figure 14). The soil survey provided the geological section (Figure 15) at the center of collapsed bank and soil coefficients required for analyses, which were conducted using the waves of the Far-off Sanriku and the Off Tokachi Earthquakes (Table 2).

Figure 14. Loads adopted in the triangle block analysis

562

Seismic Comp Top of slope wave onent Acc.ga1 Dsp.cm Tokachi EW 325 6.3 Sanriku EW 678 10.9

Figure 15. Geological section at center of collapsed embankment

Slope end Acc.gal Disp.cm 260 5.3 403 7.9

1

Table 5. Safety factors of circle sliding in embankment and in embankment and ground in the Off Tokachi and the

As a result, one dimensional response analysis shows the acceleration and displacement of the top and end of slope (Table 3). Two dimensional analysis with an EW component is shown in Table 4. The sliding circle method using finite element method (FEM), gives the safety factors in the embankment itself and in the embankment and ground in Table 5. Shioi calculates the safety factors along a assumed sliding line for the horizontal and the vertical forces (Figure 16).

wave

minimum

Sanriku EW+UD

0.76 0.73

minimum 0.85 0.77

seismic force. In these cases, many similar slides should have been easily found all over on the same ground nearby and their lateral movements of collapsed embankment must have been great. The safety factors for a vertical force 1 g in Figure 16 is nearly 1.0 and the forces are so great as 1 g or 2 g which mean a phenomena of leaping upward, observed in large earthquakes, although this motion have not yet been recorded. This motion appears to have been extremely short as was the impact from other phenomena discussed. In pile driving, the impact acceleration was some tens or hundreds gs and some hundreds of microsecond. If 1 g is a critical value to slide, these phenomena are due to the strong impact of a vertical force that barely generates embankment failure but the amount of its works (force x distance) is not so large. This presumption can explain the difference in failure between the two earthquakes, the sliding of road embankment, the lack of marked damage of structures nearby and embankments, and railbed settlement. Despite the small safety factor for the horizontal force, the lack of further damage to neighboring embankments by the maximum al'tershock appears to indicate that vertical force predominated in the Far-off Sanriku Earthquake.

3.3 Discussion Except one dimensional analysis, values calculated for the Far-off Sanriku Earthquake are so great enough to excite slope collapse in embankment due to the Off Tokachi Earthquake and previous heavy rain Actual sliding through the base ground involved a great vertical displacement and a small horizontal movement of main embankment. The values of safety factor in the Sanriku Eq. in Table 5 and Figure 16 are too small even for a small horizontal Table 2. Surface and base accelerations in the Off Tokachi and the Far-off Sanriku Earthauakes Base acc. Seismic Component Surface acc. wave (gal) (gal) NS ' 232.7 Tokachi EW 180.6 Eq. NS 431.3 Sanriku

4 CONCLUSION

Seismic Comp Top of slope wave onent Acc.ga1 Dsp.cm NS 213 4.2 Tokachi 220 5.5 Eq. EW Sanriku NS 249 3.8 Eq. EW 280 8.8 UD 152 0.4

Slope end Acc.gal Disp.cm 235 3.9 5.4

~~

1

1

1

!:

325 ,

A series of case studies for collapse of the railway embankment in the Far-off Sanriku Earthquake, led to the following conclusions. 1. There is a possibility that the collapse of railway embankmeiit occurred mainly due to the vertical impact of the seismic wave in the Far-off Sanriku Earthquake. 2. The hypothesis of strong impact wave with a great acceleration and a very short period can explain clearly the mechanism behind damage to neighboring structures.

,

8.8 0.4 4.2

563

Figure 16. Calculation of safety factor for sliding circles to various seismic coefficients

3. These analyses suggest the importance of examining the stability of embankments under vertical seismic force with horizontal force added.

To prove the existence of such impact wave in large earthquakes, Hachinohe Institute of Technology is exploiting a special minute seismograph because existing apparatus can not record such impact wave with very short period.

REFERENCE Disaster survey committee for the 1994 Far-off Sanriku Earthquake 1995. Disaster survey report for the 1994 Far-Ofi Sanriku Earthquake. Japanese Geotechnical Society 1994. Disaster survey report for the 19Y4 Far-OfiSanriku Eurthquake. Morioka Branch, East Japan Passenger Railway Co. Ltd. 1996. Disaster record (technicul version) for The FurOff Sanriku Earthquuke. Shioi, Y 1996. Phenomena influenced by vertical force in the Far-off Sanriku Earthquake, Proc. 51st Conf: Jupun Society of Civil Engineers, Nagoyu, Oct.1996.

564

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Slope instability of large embankments in residential areas caused by the Hyogoken-Nanbu Earthquake, 1995 Toshitaka K m a i Department of Civil Engineering, College of Science and Technology,Nihon University,Tokyo, Japan

Yoshiyuki Kobayashi Graduate School of College of Science and Technology,Nihon University,Tokyo,Jupan

Haruo Shuzui Nippon Koei Company Limited, Japan

ABSTRACT:The Hyougoken-nanbu earthquake triggered numerous instances of slope instability in the gentle slopes of residential areas between Nishinomiya and Kobe cities. These cities have developed on the alluvial plain and southern slope of the Rokko Mountains. The slopes consist of the semi-consolidated clay, sand and gravel of the Lower Osaka group, Plio-Pleistocene. Urban development, such as, housing, road and lifeline construction has been continuing since the 1920’s in this region. The crests of the hills have been removed and the valleys have been filled by cutting soil and industrial waste, and many valleys have been filled artificially. The following four types of landslides were found in this areas: A) Slide associated with high-speed flows (0.9%) B) Creep and slide in artificial valley fill (53.3%) C) Creep and slide of embankments caused by liquefaction in alluvial deposit (at the toe of slope) (10.7%) D) Slide on steep slopes (small-scale slope failure) (35.1%) Soil strength for B- and the C-type slides was investigated by simplified penetration tests. Most of the artificial embankments in the residential areas were insufficiently compacted and had low mean N-value of below 5. However, no marked contrasts in soil strength were found between cases of unstable embankments and stable cases. Rather, differences in the shapes of embankments, their depth, width, the inclination angle of the base, transverse form, etc. seem to be key factors in determining slope instability. Consequently, based on studies of artificial geomorphological changes in residential areas in the past, we can identify embankments are likely to be unstable following an earthquake. Many large cities in Japan have ground conditions almost identical to those of the Hanshin district; and thus have potential for future landslide disasters. Clearly, there are geological aspects for all government development plans, not only geotechnical engineering for surveying ground conditions, but also importantly in providing information to residents. Earthquake hazard mapping for slope instability in urban region is urgently needed.

I INTRODUCTION A disastrous earthquake shook the southern part of Hyogo prefecture and the eastern part of Osaka, Japan on 17 January 1995. Its epicenter was about 50 km east of Osaka. The magnitude of 7.2 placed this event among the strongest earthquake in densely populated areas of Japan in the last 70 years. The earthquake was due to a dextral movement along the Rokko active fault system, and caused 1 1 km rupture (Fig.1). The earthquake killed about 5500 residents and involved great property loss. During the earthquake, two main types of landslides occurred: landslides in the mountainous slopes of the Rokko Mountains, and landslides in the hillside urban districts between Nishinomiya and Kobe cities on the southern slope of the Rokko Mountains. In the latter case, landslides occurred in areas that have been covered by artificial materials. These landslides caused serious damage, injured 34 people and destroyed a few thousand houses at the time of the earthquake.

Figure 1. Index map of the disaster district.

565

Beyond causing serious damage to the lives and people living in the Hanshin district, these landslides also revealed the weaknesses of urban development in Japan over the past half century. This paper describes the landslides which occurred in the residential areas; including their distribution, classification, movement and the serious problems in the urban environment which they caused.

southern part of Takarazuka to the west end of Kobe. The geological details of two typical landslides in Nishinoniiya were prepared using drillings and the Swedish sounding method. The N-values of land filling material was measured by simplified penetration tests for eighteen representative landslides in the eastern part of the region. Simplified penetration test results can be converted into N-value for SPT based on the experirnental results on abundant soil materials.

2 GEOLOGIC SETTING

4 DISTRIBUTION OF LANDSLIDES

The Hanshin District, between Osaka and Kobe cities is one of the most important, densely populated areas in Japan. Takarazuka, Nishinomiya, Ashiya and Kobe cities are located together on the alluvial plain and hills of the southern slope of the Rokko Mountains. The Rokko Mountains’ elevation is 100-900m above sea-level, and mainly consist of: Rokko Granite, Quartz Diorite, small patches of Palaeozoic sedimentary rocks (Tamba Group) and Cretaceous-Paleogene volcanic rocks. The hills of the piedmont area consist of overlying strata, which are members of the Lower 0s ak a G ro LIp , P 1 i o - P 1e ist oc en e : se m i -conso 1id ated clay, sand and gravel. Plio-Pleistocene sediments have filled the Osaka Basin with a thickness of more than l000m (confirmed by deep drilling in the northeastern part of Osaka). The highest peneplain elevation of the Rokko Mountains is 800-900m. This means that the vertical displacement of the surface of the basement between the Rokko Mountains and Osaka is about 2000m, most of which accumulated in the Quaternary Period. The Quaternary tectonic movenients in this district are clearly visualized by the active fault system in the southern side of the Rokko Mountains, that is the stepwise vertical displacements of 200-3OOm along the large faults with NE-SW and E-W trends. The average movement rate of each fault is in order of 0.1 mm/yr, but the total amount of displacement between the Rokko Mountains and the alluvial plain is about 1 mni/yr.

4.1 Landslide concentration regions Fig.2 shows the distribution of landslides in the Rokko Mountains and in the urban district. Numerous shallow landslides in residual soil occurred in the Rokko Mountains. The Rokko Granite in the mountains is strongly sheared by several fault movements. This granite is deeply weathered which has caused many previous slope failures. These landslides have sometimes caused debris flow and damage to downstream areas. In July, 1938, this district suffered from one of its heaviest rainfdls, many landslides occurred in the Rokko Mountains, and debris flow damaged the urban district. Fortunately, due to the occurrence of recent earthquake in the dry season, no debris flow was caused by the landslides. During 1995 earthquake, more than two hundred landslides occurred in the gentle hillsides slopes of residential areas on the southern slope of the Rokko Mountains. They directly affected the urban conimunities, and caused more serious problems in this district. As shown in Fig.2, landslides in the gentle slopes of residential areas were distributed mainly in two separate regions: The eastern region was from Nishinoniiya City to the eastern part of Kobe City, and the western region was the middle part of Kobe City. 4.2 Influence of urbanization

3 FIELD INVESTIGATION The strong ground shaking caused by the earthquake, created many cracks at the ground surface. These cracks were classified based on their. characteristics such as opening width, height and sense (tension, cornpression and strike-slip). Both compressional cracks, pressure ridges in toe of slopes, and tensional cracks, scarps in upper part of slopes can be used as clear markers to indicate the toe and head of a landslide. Distortion of roads and buildings were also effective in determining landslide area in the slope. We mapped the distribution of cracks and landslides on topological maps with a scale of 1/2,500, and then, compiled these, to maps with a scale of 1/1,000. The prepared map nearly covers the entire the Hanshin district; the

The original hillside landform has been changed completely due to urban development in this district. The crests of the hills have been removed and the valleys filled by cutting soil and industrial waste, with many artificial slopes and valley fills have been formed in the hillside. Now, i t is difficult to distinguish the original landform. Urbanization has continued since 1920’ s, from the hillside which consists of the Osaka Group (semi-consolidated clay, sand and gravel). However, in the hills that consist of the Kobe Group, Miocene marine sediments, and mountainous slope of the Rokko Mountains, major development has taken place since 1970. Remarkable progress has been made in construction methods and management systems in recent decades. Therefore, in order to clarify the effective factors in the occurrence of disaster, not only geology 566

Figure 2. Distribution of major landslides caused by the earthquake. Geologic map is modified from Huzita & Kasama, 1982 and Huzita & Kasama, 1983.

Figure 3. Four types of landslides and their occurrence ratio in the Hanshin urban district.

567

such as the Miyagiken-oki earthquake (1978) in Japan (Tamura et al., 1978). The largest one of this type was the Morikita-cho landslide in Kobe City that had a long and narrow shape along the original valley (300m in length and 150m in width), thirty or forty houses were moved by this slide. The slip surface of landslides formed in artificial fills consists of loose material of silt, sand and gravel. A high ground water level is usually found in this filling material. This type of landslide was moved frequent in the hillside that consisted of the Osaka Group. Both the heads and toes of the B-type landslides were clear, tension cracks were usually found at the head of the original valley, and compression cracks and an uplifting area were formed at the end of the landslides. However, the landslide mass remained in its source area; that means no collapse were occurred and compared to A-type landslides, the total strain of this type was very small.

and geomorphology, but also the quality of construction in urban development should be take into account. By comparing the topographical maps of different ages, we can reveal the age of urbanization in each area. The topographical maps from 1888 show the original landscape of this district. Many small valleys, ponds, marshes and rice fields are shown on this map, but today, most of this area is covered by houses. This contraction extended from the area surrounding railway stations (located on the alluvial plain), to the upper part of the hillside after 1920. Development on the hillside consisted of the Osaka Group was almost completed in 1960. Most recent landslides occurred i n the area with artificial landform changes. It is thought that the loose and uncompacted material of filling slopes with poor drainage systems are responsible to the occurrence of the landslides.

5 TYPE OF LANDSLIDES 5.3 Landslides caused by liquefaction in alluvial deposit, C-type

The following four types of landslides were found in the gentle slopes of the residential areas (Fig.3):

Distribution of the C-type landslide was limited to the Shukugawa area. In this area, due to the erosion of terrace deposit, a gentle slope was formed between the terrace surface and the alluvial plain. This gentle slope consists of artificial embankment, old landslide mass and talus deposit (recent slope deposits). At the lower part of slope, these sediment partially covers of the alluvial plain (mainly consists of loose sand). Sand boiling in the inland district was discovered only in this area. It is thought that ground liquefaction took place in the alluvial loose sand underlying the slope deposits, and caused the collapse of the toe of the slope. The the landslide moved down due to the failure at the toe area.

A) Slide associated with high-speed flows B) Creep and slide in artificial valley fill C) Creep and slide caused by liquefaction in allu vial deposit (at the toe of slope) D) Slide on steep slopes (small-scale slope failure) Distribution of occurred landslide of types A, B, C and D was 0.9,53.3, 10.7 and 35 % respectively. Normally landslides occurred in the youngest material and on steep slopes. 5.1 Landslides associated with high speed flow slide, A-type

5.4 Landslides on steep slopes, D-type

A-type landslides have occurred in two locations: the Nikawa landslide in Nishinomiya and the Takarazuka golf course landslide in Takarazuka. These landslides were characterized by high mobility. The landslide mass of both slides mainly consisted of artificial filling material with high water content. This material settled on the steep valley side, with about 20-30 deg. of its original slope angle (base angle of embankment) , and the bank faced the valley with no retaining wall (embankment slope angle of 20-25 deg.). These embankments collapsed instantaneously during earthquake, and the associated high speed flow (partially changed to %surge€)caused fatal damage to the residential areas in the valley side. In the Nikawa landslide, 34 people were injured by the rapid motion.

D-type landslide mainly occurred in the steep slopes of the terrace scarp and artificially cutting slopes in the urban district. This type is a small-scale and a shallow slope fdilure comparing to A, B and C-types. The largest one of this type was the Satsukigaoka-cho landslide in Nishinomiya City that had a rectangular shape on the terrace scarp (60m in length and 70m in width) , an old people’s home was moved by this slide. Despite to its small size, this type of landslide was dangerous due to its rapid movement. 6 SOIL STRENGTH (N-VALUE) OF EMBANKMENTS

5.2 Landslides in artificial valley fill, B-type Investigations as to the extent of damages due to the earth q u ake re vea 1ed that 1an ds 1 i des in art i f i c i a 1 em bankment (B- and C-type) occupies the majority of slope instability that occurred in the urban region of

B-type landslides were found conimonly in the urban district. Similar types of earthquake-induced landslides have also been reported in previous research, 568

generally at low levels of between only 2-5.(Fig. 4 ). 2. Soil compaction was still ongoing in surface layers of embankments (limited within 2m from ground surface). N-values reduce from the middle levels down to the base levels of the embankment (Fig. 5). 3. Allowing for the accuracy of the tests, no marked differences were found in soil strength between the sliding unstable embankments and the stable ones . 4. A weak, low N-value layer often forms at the bottom of the embankments. This layer develops at ground surface before formation of the embankment. 5. The embankments were confirmed as having a shallow ground water level. Figure 4. Frequency of N-value in embankments by

7 ASSESSMENT OF SLOPE INSTABILITY OF LARGE EMBANKMENT

simplified penetration tests.

The results of field investigations on artificial valley fill landslide suggest that the bottom shape of embankment, that is, the shape of the valley before artificial filling is a primary factor behind embankment landslides. Despite large displacements by landslides, the N-values in some embankments (i.e., Nishi okamoto in Kobe city) was relatively high (5- 15).In these cases, a slip surface probably developed along the weak bottom layer of embankments. Although, Morikitachou embankment in Ashiya city was destroyed by the earthquake, the adjacent Kounandai embankment in Kobe city was safe despite the fact that the two embankments had similar N-value and mass scale (volume). Topographical deference be-

Figure 5. The N-value distribution in Higashi-ashiya embankment Kobe. Soil strength (N-value) of the artificial filling material was measured by simplified penetration tests in the eastern part of the region. The main geotechnical characteristics Of the filing soil found in this survey are as followers.

Figure 6. Topographical deference between the two embankments. The Morikitachou embankment is semicircular in shape, the Kounandai embankment has a V-shape cross section.

1. The average N-value of embankment soil was 569

tween the two embankments suggests that there was a clear difference in earthquake ground motion. Although the cross section of the Morikitachou embankment is semicircular in shape, the Kounandai embankment has a V-shape cross section (Fig.6). As the driving force for landslide is not so great, landslide can be easily controled by the presence of an internal resistor for distortion in embankments (i.e., foundations of large buildings). The Higashi-ashiya embankment in Ashiya city was stable despite its very low N-value (below 5). Distortion in this embankment was reduced by the foundations for an apartment building situated in the center of the slope. This suggests that how the land is used on an embankment can also be a factor controlling landslide. These results show that based on topographical research and field studies, it is possible to objectively assess the slope instability of an embankment. Using GIS methods, it is not very difficult to survey the topography of valley before embankments created, including the inclination of valley floor and valley cross sections. Based on these methods and such research, it will be possible to make landslide avoidance maps with assessments of slope instability.

5. The geological aspects of all government development plans should considered not only in terms of geotechnical engineering for surveying ground conditions, but also importantly in providing information to residents. The work of preparing landslide avoidance maps for urban regions, especially in Tokyo and Yokohama, is a necessary first step in mitigating future disasters. ACKNOWLEDGEMENTS We express our appreciation for useful discussion to Mis. Chikako Jinbo of Central Research Institute for Construction Technology. Particular thanks are due to the menbers of Ohta georesearch Inc., Mr. Hidemasa Ohta, Mr. Yoshitaka Hayashi and Mis. Mayunii Furuta, for their support in the field survey. This research work has been financially supported in part by the scientific research grant of the Ministry of Education (No. 1 1680475).

REFERENCES Huzita, K. & Kasama, T. 1982. Geology of the Osakaseihokubu District. Quadrangle Series, scale 1 : 50,000, Geol. Surv. Japan. (in Japanese with English Abstract) Huzita, K. & Kasama, T. 1983. Geology oftlie Kobe District. Quadrangle Series, scale 1 :50,000, Geol. Surv. Japan. (in Japanese with English Abstract) Kaniai, T., Suzuki K. & Isobe, I. 1995. Landslides in the Hanshin Urban Region caused by the Hyougoken-nanbu Earthquake 1995. Jour. Ja pan Soci. Engineering Geology 36- 1 :47-50. (in Japanese) Kamai, T 1995. Landslides in the Hanshin Urban Re gion Caused by the 1995 Hyogoken-Nanbu Earthquake, Japan. Landslide News 9: 12- 13. Kamai, T., Suzuki K. & Isobe, I. 1996. Landslides in gently sloping residential areas caused by the 1995 Hyougoken-nanbu Earthquake. Bill. Geol. Surv. Japan 47:175-200. (in Japanese with En glish Abstract) Okimura,T. 1995. Characteristics of Slope failures caused by the Hyougoken-nanbu Earthquake, Landslides caused by the Hyougoken-nanbu Earthquake. Cornniitteeon Landslides and Slope failures caused by the Hyougoken-nan bu Earth quake, Japan Landslide Society: 1-31 . (in Japanese) Tamura, T. , Abe, T. & Miyagi T. 1978. Housing Construction in Hillside and Earthquake Disas ter. General Urban Research 5: 1 15-13 1. (in Japanese)

8 CONCLUSIONS The following main conclusions can be made on the basis of the research presented in this paper. 1. Artificial landform changes in urban region tend to be at great risk of landslide. Many cities in Japan have ground conditions almost identical to those of the Hanshin district, where there is a danger of landslide disasters. 2. The following four types of landslides were found in residential areas on gentle slopes. A) Slide associated with high-speed flows B) Creep and slide in artificial valley fill C) Creep and slide caused by liquefaction in alluvial deposit (at the toe of slope) D) Slide on steep slopes (small-scale slope failure) Normally landslides occurred in the youngest material (artificial material) and on steep slopes. 3. Soil compaction was still ongoing in surface layers of enibankments. (in B- and C -type slides). The N-value of embankment soil is generally at low levels, and this reduces from the middle levels down to th base levels of the embankments. 4. The shape of a valley before formation of artificial fills, that is, the topography of an embankment, is a primary factor behind embankment landslides. Based on topographical research and field surveys, it is possible to objectively assess the slope instability of an embankment. 570

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Analysis of toppling failure of mountain slope caused by the Hyogoken-Nanbu Earthquake Takashi Olumura, Nobuyuki Yoshida & Nobuyuki Torii Reseurch Center for Urban Sqfety arid Securig, Kobe University,Japan

ABSTRACT: The Hyogoken-Nanbu Earthquake, Japan, of Jan. 17, 1995, induced a lot of slope failures or collapses in the Rokko Mountains, near Kobe. A field investigation carried out immediately after the earthquake and its showed that in the most location the outcrop after collapse exhibited marked discontinuous faces and the debris was not soils but rock fragments. It can be deduced that rock blocks were detached form base rock along well-developed joint systems due to seismic forces and brought to collapse, and it is not unreasonable to consider that most such collapse occurred in a toppling mode. This research presents a limit equilibrium analysis of toppling failure of mountain slope due to earthquake and discusses the effects of seismic acceleration on slope stability and its failure mode through an example analysis and a case study. I n the example analysis, the relationships between seismic acceleration and the critical angle of friction are presented. From these relationships, the magnitude of seismic acceleration sufficient for slope to collapse can be determined and the mode of collapsing can also be evaluated, provided that the friction angle of slope material is known. From the analysis of mountain slope collapsed in a toppling-dominated mode caused by the Hyogoken-Nanbu Earthquake, it was suggested that the strength of the slope material and the seismic acceleration are conjectured. 2 . L I M I T EQUILIBRIUM TOPPLING FAILURE

I . INTRODUCTION Due to the Hyogoken-Nanbu Earthquake in January 17, 1995, it is said that slope failures or collapses took place about 750 locations in the kokko Mountain System in Iiyogo Prefecture, Japan. A field investigation carried out immediately after the earthquake and its showed some characters of slope failures or collapses . For example, 1 ) their scales almost were small, 2 ) they almost took place in steep slope, 3 ) they almost took place in the convex and linear slope, 4 ) in most locations the outcrop after collapse exhibited marked discontinuous faces and 5 ) the debris was not earth but rock fragments ( Okimura, 1996) . In these, 4 ) and 5 ) are especially characteristic and it can be deduced that rock blocks were detached from base rock along well-developed joint systems due to seismic forces and brought to collapse, and it is not unreasonable to consider that most such collapse occurred in a toppling mode. In this paper, a limit equilibrium analysis is presented for toppling failure by introducing the coefficient of seismic acceleration into the analysis. An example analysis is first performed to grasp the influence of the coefficient, type and inclination of slope and shear strength ( friction angle) on the slope stability. Next an actual collapse of mountain slope is anaiyzed and the strength of the slope material and the seismic acceleration are conjectured.

ANALYSIS

OF

2.1 Prelimin~rrj. Toppling failure involves the forward rotation of columns or blocks of rock about some pivot point. In this paper, toppling failure of rock blocks on an inclined stepped surface due to earthquake is analyzed using the method proposed by Hoek and Bray ( 1981 . Figure 1 shows a model for limit equilibrium analysis of toppling on a stepped base rock.

Figure 1. Modei for limit equilibrium analysis of toppling on a stepped base rock

571

The slope consists of a system of rock blocks dipping at (90- d, ) underlain by the base rock with an overall inclination of 0 . The inclination of the surface of rock blocks is 0 1 for the low portion and 02 for the upper portion. From the geometry, the constants a,, b,, and cn €or the n-th block are obtained as:

where xn,x,\.t is the width of each block. When the equilibrium of the block system is disturbed and the blocks start to move, they are classed into three groups of behavior: ( 1 ) a set of sliding blocks in the toe region, ( 2 ) a set of stable blocks at the top, and ( 3 an intermediate set of toppling blocks. Under a certain geometry, the toppling zone extends down to the toe and the group of sliding blocks may be absent. Forces acting on the n-th block is shown in Figure 2. The forces R,, and S,, act between the block and the base rock, and the forces P,,, Q,,, P,).Iand Q.-I act between the adjacent blocks. As the body force of each block, seismic effect is also taken into account in terms of the coefficient of horizontal seismic acceleration, kt,. When the block under consideration is one of the toppling group, the application points of all forces on the block are determined, and the following relations are satisfied on the sides of the block at the limit condition (shown in Figure 3 ) .

Figure 2. Forces acting on the n th block

Figure 3. Toppling of the n th block

Thus, R, and S,, are expressed as:

From the equilibrium condition for moment, the force Pn.l,,,sufficient to prevent toppling is obtained as:

Figure 4. Sliding of the n th block where M,, and L,, are the distance from the block the application point of force for the M th block, angle of friction, Y, is the height of the block, weight of the block and ki, is the coefficient of seismic acceleration.

bottom to 4 is the W,, is the horizontal

When the block under consideration is one of the sliding group, the following condition is met at the base ( shown in Figure 4 ) . S,=R, tan 4j

[91

572

However, the magnitudes and points of application of all the forces on the sides and base of the block are unknown. Here, an assumption is made that just like for the toppling case, conditions for limit equilibrium are satisfied on the sides of the block; that is, Equations [ 6 I and [ 7 1 are applicable. Then, using Equation [ 91 the force, Pn.t.>, sufficient to prevent sliding is obtained as: P,i.l., =P, { W,tan 4 cos 9 - sin 4 - kt, (cos d, +sin tan 4 1 I / ( 1-tan' 4j )

[ 101

2.2 Analisis procedure Define that nl is the uppermost block of the group of toppling blocks and that n? is the uppermost block of the group of sliding blocks. The analysis is to determine the critical value of @ for the limit equilibrium of a system of rock blocks.

1: Assume a value of 4 which satisfies the condition that 4

>

(

4" +tan.'ks)

.

2: Find the uppermost block of a group of blocks which satisfies the condition that x,JY,,< tan ( (1, +tan"kl,) , and set it as nl. The blocks higher than the nl are in a stable state.

3 Staiting with this n-th block, calculate P,,l I and P,,I , using Equations [ 8 1 and [ 10 I , and comparc. with each other If P.I, is greater than P,,I,, the block is about to topple and P , I IS set equal to P,I, If P , , I ,is smaller than P,,I , the block is about to slide and P,, I is set equal to P,,I 4 : Repeating this procedure for the ( n-1) -th block and all the lower blocks, nz may be determined. Note that the critical condition of nz and all the lower blocks is in a sliding state. If the condition which P,>.I., is smaller than P , > I is \ not satisfied for any block, there are no sliding blocks and toppling extends down to the block 1.

Figure 5. Two type models in example analysis

Table 1. Analysis condition for example analysis 5 : If POis greater than zero for the block 1 at the toe, the

slope is unstable for the assumed value of 4 . Thus, the calculation should be repeated assuming a larger value of cp. On the other hand, if P,, is smaller than zero, the calculation should be repeated with a smaller value of Cp . When PI)becomes very small, 4 is set as the critical value for the limit equilibrium, O L . In this study, the calculation is repeated until the condition that /Pi11 < 0.1 ( k N ) is satisfied. 6: In this study, the 4 1 is determined for a given value of kl,, and the stability of slope is evaluated by comparing it with the friction angle of the slope.

2.3 Example anal.ysi.7 In this example, two type of model slope are considered as shown in Figure 5. In model type A ( the slope inclination changes at the middle block ( Block 5 ) , while in model Type B the slope inclination changes at the uppermost block (Block 10) . Table 1 shows analysis condition for example analysis. Total six slopes are analyzed as seen from the table; and for each slope, the critical angle of friction for limit equilibrium is calculated for values of the coefficient of horizontal seismic acceleration from 0.0 to 0.5. Figure 6 shows the relationships between horizontal seismic acceleration, kh, and the critical angle of friction for limit equilibrium, @ I . For a given k,,, regardless of the model type, as the inclination of rock blocks ( 4 increases,

10 OL tends to increase. For instance, in the case of kh equal to 0.1, OL is zero for Slope 1, 24 for Slope 2 and 41.5 for Slope 3. This suggests that, Slope 1 remains stable even if the friction angle of the slope is zero, while Slope 3 will topple or slide if the friction angle of the slope is sinaller than 4 1.5 . It can be said that, the larger the inclination of rock blocks is, the more likely the slope fails. Both the model types show a similar tendency for kl, smaller than 0.2 but as light difference beyond it. O L can be obtained even for kh equal to 0.5 for Slope 1 but not for kl, greater than 0.32 for Slope 4, which suggests that Slope 4 is more susceptible to toppling or sliding than Slope 1. Figure 7 shows the behavior type of each block at the . limit equilibriumFrom this figure, a tendency can be that; for limit equilibrium for Slopes 1, 2, 3, 4, 5 and 6,

573

Figure 6. Relationships between ki, and qh

Figure 7. Behavior type of each block at the limit equilibrium ( a )

574

- f) )

Table 2. Analysis condition for collapsed slopes

the slope ( 6 ) , the inclination of rock blocks ( 4 ) and the overall inclination of base rock ( [3 are known. The behavior of each block, moreover, can be seen from the relationships between ni and nz.

2.4 Analysis of’ collupsed slopes

Figure 8. Location map of two slopes observed slopes 1, 2 and 3, the blocks higher than the middle block remain stable, the middle block and its neighbors topple, and those lower than the middle block slide. As kt, increases, the toppling group extends upward and downward. On the other hand, for Slopes 4, 5 and 6, toppling starts at the uppermost block and extends downward as ki, increases. Once toppling takes place in these slopes, no blocks remain stable. In the case of applying this analysis to an actual case of collapsed slope, the magnitude of seismic acceleration (ki,) for bringing the slope to the limit state can be determined from the relationships between kt, and @ I as presented in Figure 6, provided that the friction angle of

The analysis presented in the previous section is applied to an actual case in which mountain slope collapsed in a toppling-dominated mode caused by the Hyogoken-Nanbu Earthquake. The collapsed mountain slopes are located near Koininegahara checkdam in the upper stream of Sumiyoshi River in Kobe City ( denoted as Nos. 1 and 2 in Figure 8 ) . The collapse surfaces of these slopes were found markedly discontinuous and stepped along well-developed joint systems, and rock fragments at the toe of slope contained boulders as large as 1.5m in diameter. The longitudinal profile of two slopes is shown in Figure 9, respectively, which was determined based on a field survey or from topographic maps with a scale of 1:2,500. The slope consists of weathered granite with highly-developed joints, and analysis condition for collapsed slopes is given in Table 2. The analysis procedure is the same as in the previous example, and the critical angle of friction for limit equilibrium is computed for a given seismic acceleration. Figure 10 shows the computed relationships between the horizontal seismic acceleration and the critical angle of friction for limit equilibrium. In the case of horizontal seismic acceleration equal to zero, the critical angle of

Figure 9. Longitudinal profile of two slopes

575

discusses the effects of seismic acceleration on slope stability and its failure mode through an example analysis and a case study. 2. In the example analysis, the relationship between seismic acceleration and the critical angle of friction are presented. From these relationships, the magnitude of seismic acceleration sufficient for slope to collapse can be determined and the mode of collapsing can also be evaluated, provided that the friction angle of slope material is known. 3 . Froin the analysis of collapsed slope, it was suggested that, for the Slope 1 all the blocks were in the toppling mode while for the Slope 2 upper thee blocks were in the toppling mode and two blocks from the toe were in the sliding mode.

Figure 10. Relationships between kil and 6 I

REFERENCES Okimura, T., 1996. The Hyogokcn-Nanbu Earthqtiake and Slope Disaster -Mountain Slope Failure-, Landslide Control Techniques, 23-2, pp.38-44. ( i n Japanese) Hock, E. and Bray, J.W., 1981. Rock Slope Engineering. Inst. Min. Met. London. 358p.

Figure 1 1 . Behavior type of each block at the limit equilibrium friction for limit equilibrium is 27.5 ' for Slope I and 42.9 '' for Slope 2. As the seismic acceleration increases, the critical angle of friction for each slope approaches 44.7 " . From this, it can be said that, if the both slopes had the same friction angle, Slope 1 would be more stable than Slope 2 for a low level of seismic movement. Considering that the distance between these two slopes is only about 230111 and that both the slopes consist of the same type of Rokko granite, it inay be assumed that the two locations experienced almost the same magnitude of seismic movement. Hence the critical angle of friction and horizontal seismic acceleration given by the intersection of the two curves in Figure 10 could correspond to the friction angle of the material of both slopes and the seisinic acceleration acted, respectively; and these are read out from the Figure as 44.7 '' and 0.28, respectively. Figure 1 1 shows the behavior type of each block at the limit equilibrium. This figure indicates that all the blocks topple in Slope 1 and that in Slope 2 the upper three blocks topple and the lower two blocks slide.

3. CONCLUSIONS 1. This study presents a limit equilibrium analysis of toppling failure or mountain slope due to earthquake and

576

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Stress condition and consequence of liquefaction on weathered granitic sands Y. Okada Graduate School of Science, Kyoto Universiy, Uji,Japan

K. Sassa & H. Fukuoka Disaster Prevention Research Insrirure,Kyoto UniversiQ Uji,Japun

ABSTRACT: This paper presents the results from a series of the undrained speed-controlled ring shear tests, carried out on weathered granitic sands taken from a landslide source area caused by 1995.1.17 HyogokenNanbu earthquake. The stress condition which marks the onset of contractive deformation and the consequence of liquefaction through collapse behaviour are examined. Though all normally consolidated specimens have not exhibited liquefaction but the newly proposed sliding-surface liquefaction, the collapse behaviour before the stress paths reaching the failure line has been obtained from all tests. These collapse points in stress space can be bound by the straight line passing through the origin (collapse line). And the steady state line from the ring shear tests shifts downward compared with that from the triaxial compression tests, it is interpreted as the ultimate estimate of steady state line, "ultimate steady state line."

1 INTRODUCTION

the liquefaction through collapse behaviour are conducted by the undrained speed-controlled ring shear tests.

Among some types of landslides, liquefactioninduced landslide is one of the most hazardous landslides. Geo-disasters by liquidizing landslides were recently caused also in Japan, for example, Otarimura debris flow (1996), Harihara debris slidedebris flow (1997), and Sumikawa reactivated landslide (1997). As the responsibility for socioeconomic losses of landslides is increasing, it is more and more important to reveal the liquidizing mechanism of landslides. After the catastrophic earthquakes of 1964 in Niigata, Japan, and Alaska, United States, the extended laboratory tests on the liquefaction behaviour have been conducted (Castro 1969, Poulos 198lj. Collapse line by Sladen et al. (1985) and critical stress ratio line by Vaid et al. (1985) as for the triggering stress condition of liquefaction, and steady state line by Poulos (1981) as for consequence of liquefaction were proposed. But it was almost entirely conducted by using the triaxial test, the shear behaviour along the sliding surface especially after the long shearing have not been investigated. In other words, remarkable concepts were proposed by many researchers using the triaxial test, but the investigations by the ring shear test which can closely simulate the stress condition along the sliding surface are really limited. In this paper, an investigation and examination about the stress condition and the consequence of

2 RING SHEAR APPARATUS

Apparatus employed in this study is the fifth version in a family of the ring shear apparatuses developed by Disaster Prevention Research Institute, Kyoto University (DPRI Ver.5) in 1996 (Sassa 1997). DPRI Ver.5 is considered to be improved intelligent type because of satisfying criteria of the simplicity of both construction and operation, and the capability of complete undrained testing to investigate pore pressure generation before and after the failure or the collapse of soil. After the pioneering work by Bishop et al. (1971), the ring shear apparatus is widely used to study the mechanical behaviour of landslide motion (Tika et al. 1996) especially in residual state. For the purposes other than the measurement of the residual strength, it has all the disadvantages of the shear box, such as high local concentrations of the strain and the uncertainty about the direction of the principal stresses as the test proceeds. But it is the most powerful tool to reproduce the stress condition along the sliding surface of the landslide in situ for very long shear displacement, the extended laboratory tests by means of the ring shear test were performed (Sassa 1988, Sassa et al. 1996).

577

Figure 1. Schematic figure of the shear box of the ring shear apparatus Ver.5. The soil specimen is set in the donut-like (circular) shear box made of steel. The outer diameter of shear box is 18.0 cm and the inner diameter is 12.0 cm, thus the area of the sliding surface is 141.37 cm’. The nominal specimen height after initial consolidation is around 6.0 cm and the sliding surface is located at around the middle of the specimen. Rubber edge is pasted along the upper surface of the lower half of the shear box (Fig. 1). And it was turned on a lathe to completely remove unevenness and designed for preventing the leakage of water and specimen in the process of consolidation or shearing. The constant contact force at 1.4 kN between the rubber edge and the upper half of the shear box is supplied during the test. Before each test, rubber edge was covered by Teflon spray and silicon grease was laid on it for the complete undrained condition.

Silica sand No.8 is the construction material for industrial use. It consists of weathered silica sand. It is almost angular sand with 92 through 98 percent of quartz and a little amount of feldspar and has a mean diameter D,, = 0.057 mm, a uniformity coefficient of Uc = 10.2, and specific gravity of Gs = 2.63. 4 TEST PROCEDURE It is said that air-pluviation method provides a more uniform specimen (Gilbert et al. 1988) and yielded the specimens of the lowest resistance to liquefaction (Mulilis et al. 1977). Since airpluviation is difficult for the donut-shaped shear box, the oven-dry specimen was poured into the shear box from the top of the upper shear box by a cup as close as air-pluviation. To make saturated specimens, CO2gas was supplied into the specimens to expel air for about 1 hour first, and then de-aired water was percolated for around 12 hours. For checking the degree of saturation of the specimens, pore pressure parameter B,, in the undrained direct shear condition (Sassa 1988) was measured.

3 PROPERTIES OF SPECIMEN

B, = AuIAo

The soil specimen employed in this study is Osakagroup coarse sandy soils and Silica sand No.8. Osaka-group coarse sandy soils widely distributed in the Knasai area was sampled from the source area of Takarazuka Landslide, which was triggered by 1995.1.17 Hyogoken-Nanbu earthquake. The depth of the sampling point was approximately 4 m. Osaka-group is a lacustrine and marine deposit of weathered granitic sands in the Pliocene to the MidPleistocene (Ichihara 1996). It is an angular sandy soil made up of 77 percent of quartz and 23 percent of feldspar, and has a mean diameter D,, = 0.9 mm, a uniformity coefficient of Uc = 5.2, and specific gravity of Gs =2.6 1.

where U = pore pressure; and CT = normal stress. The specimens were consolidated at 50 kPa of normal stress, and then the generated pore pressure was measured when the additional 50 kPa of normal stress was applied under undrained condition. In this study, the specimens with B, value larger than 0.95 were adopted as the fully saturated specimens. Normal stress was decreased to 50 kPa under undrained condition and then certain initial normal stresses for each test were applied and the specimens were consolidated. The specimens were sheared up to 10 m of shear displacement at the 1.0 d s e c of shear speed. During shearing, the data of normal stress, shear resistance, pore pressure, shear displacement, and

578

(1)

Figure 2. Collapse line on stress paths of normally consolidated Osaka-group coarse sandy soils. vertical displacement were measured at very high frequency. And it should be mentioned about the rubber edge friction between the gap. In this study by the ring shear tests, obtained shear resistance includes the real shear resistance of soils and the rubber edge friction. Thus, after the undrained ring shear tests, the shear box was changed into the drained condition. And by decreasing normal stress gradually to almost 0 kPa, a clear failure line was obtained for each test. Assuming zero cohesion of sandy soils, the value of the intercept (shear resistance at 0 kPa of normal stress) was interpreted as the rubber edge friction. These values were subtracted from the measured shear resistance for each test. The conducted test numbers and test conditions are listed in Table 1.

5 STRESS CONDITION OF LIQUEFACTION THROUGH COLLAPSE BEHAVIOUR As for liquefaction phenomenon, Bishop et al. (197 1) pointed out that the mobilized peak internal friction angles were considerably smaller than the maximum angle of shear resistance based on the Mohr-Coulomb criterion. Sladen et al. (1985) put it forward the collapse line in the stress space (p-q diagram) by using the triaxial compression test. The stress points of peak shear resistance when the specimens at a certain void ratio were collapsed fell on the straight line. Hence the collapse line reached the steady state stress point of the specimens at a certain void ratio. As the void ratio is getting smaller, the collapse line shifts its position upward in the stress space. Meanwhile, Vaid et al. (1985) proposed the critical stress ratio line by the triaxial test. This line is passing through the origin and independent of initial void ratio. When the stress path reaches a certain stress ratio of shear resistance divided by effective normal stress, in other words, the stress path is trying to cross the critical stress ratio line, the

579

specimens collapse into liquefaction. The controversy of which line shows the real undrained shear behaviour of sandy soils has not been resolved. Besides very few investigations have been conducted by means of the ring shear test. In order to investigate the collapse behaviour by the ring shear test, the specimens of Osaka-group coarse sandy soils (Test RO1 through R07) were normally consolidated at different initial normal stress from about 103 kPa through 628 kPa. Relative density varies from 80.4 to 96.1. Figure 2 shows the effective stress paths of these tests. All stress paths reached almost the same failure line on the way to the final stress points and effective normal stresses at steady state were as small as around 20 kPa. It means liquefaction was not generated but slidingsurface liquefaction (Sassa et al. 1996) was yielded from all tests. In the ring shear test, the shear deformation is concentrated at around the sliding surface and it seems difficult to whole liquefy. Although the postpeak loss of shear resistance was small and the pore pressure in Test RO1 and Test R 0 2 showed the small turnaround into decreasing, the collapse behaviour of sandy soils was observed from all tests. Each collapse point (circles in Fig. 2) before the stress paths reaching the failure line fell on the almost straight line passing through the origin (collapse line as for ring shear test). Based on the test result, when the stress paths reached a certain stress ratio of the temporal peak shear resistance divided by effective normal stress under the failure line, the specimens collapsed and the stress path moved to the failure line with shear resistance decreasing. The collapse line in this study which was from the undrained speed-controlled ring shear tests on normally consolidated Osaka-group coarse sandy soils is harmony with Vaid's critical stress ratio line. However, as to the speed controlled ring shear tests on normally consolidated Silica sand No.8 (Test RS 1 though RS5), effective stress paths (Fig. 3) did not show the temporal peak shear resistance before

Figure 3. Effective stress paths of normally consolidated Silica sand No.8.

Figure 5. Negative dilatancy region and grain crushing dominant region of Silica sand No.8.

Figure 4. Negative dilatancy region and grain crushing dominant region of Osaka-group coarse sandy soils.

GRAIN

to the final stage under steady state condition. In the first stage pore pressure considered to be generated entirely by negative dilatancy, and in the second stage by negative dilatancy plus grain crushing (grain crushing dominant). The relationship of excess pore pressure ratio, r,,(t)expressed as the ratio of excess pore pressure increment to initial effective normal stress, d o ' (Popescu et al. 1997) versus shear displacement of Test RO1 through Test R07 is presented in Figure 4 and that of Test RSl through RS5 is in Figure 5.

As to Figures 2, 3, effective stress paths of Osakagroup coarse sandy soils and Silica sand No.8 could be divided into two parts. The first region is from the beginning to the stress path reaching the failure line and failed, and the second is from what time the stress path went left-downward along the failure line

where uo= initial pore pressure. In Figure 4, excess pore pressure ratio, ru(t)of Osaka-group coarse sandy soils was positively increased just from the beginning of shearing.And at around 4 mm of shear displacement, some of them

reaching the failure line and the collapse points ware not able to be observed. Although the shape of effective stress paths were similar to those on Osakagroup coarse sandy soils and pore pressure was monotonically increased without decreasing, no collapse line was defined on Silica sand No.8.

6 NEGATIVE CRUSHING

DILATANCY

AND

580

Figure 6. Ultimate steady state line compared with steady state line and quasi steady state line. showed the temporal peak and the others showed the very small increase of excess pore pressure ratio. And then from around 10 mm of shear displacement excess pore pressure ratio was re-increased. From 1 m to 10 m of shear displacement, excess pore pressure ratio was almost constant for each test and this final value was proportional to the initial effective normal stress. Though there was the scatter of about 0.1 as for excess pore pressure ratio, the generated excess pore pressure ratio at 4 mm and 10 mm of shear displacement could consider to be independent of initial void ratio or initial effective normal stress. Accordingly it should be noticed here that the negative dilatancy region when effective stress path moved under the failure line and the grain crushing dominant region when effective stress path moved left-downward along the failure line could be demarcated by the shear displacement of 4 mm and 10 mm respectively for Osaka-group coarse sandy soils. From Figure 5 on Silica sand No.8, the negative dilatancy region could be also finished at 7 mm of shear displacement. And the emphasis should be placed on the complete coincidence of the excess pore pressure ratio from 5 tests at different relative density. Grain crushing dominant region might be from about 15 m of shear displacement and the find excess pore pressure ratio under steady state condition was in order of initial effective normal stress. From these results, it was revealed that negative dilatancy region and grain crushing dominant region of each specimen could be demarcated by the certain values of shear displacement respectively. And excess pore pressure ratio under steady state condition was affected by initial effective normal stress.

7 CONSEQUENCE OF LIQUEFACTION THROUGH COLLAPSE BEHAVIOUR It is stated in the definition of the steady state by Poulos (198 1) that the steady state is achieved only after all particle orientation has reached a statistically steady state condition and after all particles breakage, if any, is complete, and that these conditions normally can be attained only at larger strains - well beyond those that can be reached in the triaxial tests. Nevertheless the widespread concept of steady state line and the subsequent of quasi steady state line proposed by Alucon-Guzman et al. (1988) are mostly based on the test results by using the triaxial test and examinations about steady state have been scarcely conducted by means of the ring shear test. Figure 6 compares steady state line from the ring shear tests with quasi steady state line and steady state line from the triaxial compression tests (Okada et al. 1998). As to the triaxial compression test, a sliding surface would be theoretically formed in the cylindrical specimen with the angle of (45 + $72) degrees from the vertical direction, and effective normal stresses on a theoretical sliding surface at quasi steady state and steady state conditions are calculated by the following equation assuming internal friction angle at quasi steady state and steady state conditions as 3 1 degrees.

(3) where U ' = effective normal stress on the sliding surface; p:, = p ' at quasi steady state or steady state; and ' = internal friction angle at quasi steady state or steady state.

+

581

Of evidence is that the steady state line from the ring shear tests was located under the other two lines from the triaxial compression tests and the inclination of the steady state line from the ring shear tests was steepest of all three. Since the ring shear tests (Test RO1 through R07) all generated sliding-surface liquefaction, much generation of excess pore pressure was due to grain crushing. Thus effective normal stresses at steady state by the ring shear test were obtained after possible grain crushing was finished. Accordingly it could be considered that the steady state line which is completely conformity with the original definition by Poulos (1981) was obtained ultimately. In this sense, the steady state line from the ring shear tests after long shearing should be interpreted as "ultimate steady state line." There is a controversy on which of quasi steady state strength or steady state strength from the triaxial tests should be used as residual strength, but the authors emphasize that the ultimate steady state line from the ring shear tests should be concerned in relation to some practical problems considering residual strengths of soils. 8 CONCLUSIONS

1. As to the speed-controlled ring shear tests on normally consolidated Osaka-group coarse sandy soils, the collapse line was obtained as the criterion for liquidization phenomenon. 2. Effective stress paths of normally consolidated Osaka-group coarse sand soils and Silica sand No.8 could be divided into two regions of the negative dilatancy region and the grain crushing dominant region. And these regions could be demarcated by shear displacement from the viewpoint of the relationship of excess pore pressure ratio versus shear displacement for each normally consolidated specimens. 3. Steady state line from the ring shear tests on Osaka-group coarse sandy soils obtained after finishing grain crushing as much as possible should be treated as the real steady line, and it was interpreted as "ultimate steady state line." REFERENCES Alarcon-Guzman, A., G. A. Leonards & J. L. Chameau (1988): Undrained monotonic and cyclic strength of sands. ASCE Journal of Geotechnical Engineering Division, Vol. 114, No. 10, pp. 10891109. Bishop, A. W., G. E. Green, V. K. Garga, A. Anderson & J. D. Brown (1971): A new ring shear apparatus and its application of the measurement of the residual strength. Gkotechnique, Vol. 2 1, No. 4,pp. 273-328.

Castro, G. (1969): Liquefaction of Sands. Ph. D. Thesis, Harvard Soil Mechanics Series, No. 81. Harvard University, Cambridge, MA. Gilbert, P. A. & W. F. Marcuson (1988): Density variation in specimens subjected to cyclic and monotonic loads. ASCE Journal of Geotechnical Engineering Division, Vol. 114, No. 1, pp. 1-20. Ichihara, M. (1996): The Osaka group layer and Chinese loess layer (in Japanese). Tokyo: ChikujiShokan . Mulilis, J. P., H. B. Seed, C. K. Chan & J. K. Mitchell (1977): Effect of sample preparations on sand liquefaction. ASCE Journal of Geotechnical Engineering Division, Vol. 103, No. GT2, pp. 91108. Okada, Y., K. Sassa & H. Fukuoka (1998): Comparison of shear behaviour of sandy soils by ring-shear test with conventional shear tests. Environmental Forest Science, Proceedings of IUFRO Div. 8 Conferences, Kyoto, Kluwer Academic Publisher, pp. 623-632. Popescu, R., J. H. Prevost & G. Deodatis (1997): Effects of spatial variability on soil liquefaction: some design recommendations. Giotechnique, Vol. 47, NO. 5, pp. 1019-1036. Poulos, J. (1981): The steady state deformation. ASCE Journal of Geotechnical Engineering Division, Vol. 107, No. GT5, pp. 553-562. Sassa, K. (1988): Motion of Landslides and debris flows - Prediction of hazard area -, Report of Grant-in-Aid for Scientific Research by Japanese Ministry on Education, Science and Culture (No. 61480062). Sassa, K., H. Fukuoka, G. Scarascia-Mugnozza & S. Evans ( 1996): Earthquake-induced-landslides: Distribution, motion and mechanisms. Special Issue for the great Hanshin Earthquake Disasters, Soils and Foundations, pp. 53-64. Sassa, K. (1997): A new intelligent type dynamic loading ring shear apparatus. Landslide News (Japanese Landslide Society), No. 10, PP. 33. Sladen, J. A., R. D. D'Hollander & J. Krahn (1985): The liquefaction of sands, a collapse surface approach. Canadian Geotechnical Journal, Vol. 22, pp. 564-578. Tika, T. E., P. R. Vaughan & L. J. L. J. Lemos (1996): Fast shearing of pre-existing shear zones in soil. Gkotechnique, Vol. 46, No. 2, pp. 197-233. Vaid, Y. P., J. C. Chern & H. Tumi (1985): Confining pressure, grain angularity, and liquefaction. ASCE Journal of Geotechnical Engineering Division, Vol. 11 1, NO. 10, pp. 1229-1235.

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rofterdam, ISBN 90 5809 079 5

Effects of density, stress state and shear history on sliding-surface liquefaction behavior of sands in ring-shear apparatus Gonghui Wang Graduate School of Science, Kyoto Universir)! Uji,.Inpm

Kyoji Sassa I1 isci.5 ter Presention a i d Re.,eu rch I n s titu re, Kyoto Uni rsi 9, U ji , J upa n

ABSTRACT: The concept of sliding-surface liquefaction was proposed by Sassa in the studies of landslides triggered by the Hyogoken-Nanbu earthquake through undrained ring-shear tests. In the present research, to make a further understanding of sliding-surface liquefaction, a series of tests was conducted on silica sands in ring-shear apparatus to study the effects of initial density, stress state and shear history on sliding-surface liquefaction behaviour. The tests on different initial relative densities showed that undrained shear behaviour was affected greatly by initial density. While the tests on different initial shear stress proved that initial drained shear stress had some influences on static liquefaction resistance and the resulting deformation after failure, but no effect on steady state shear strength. Repeated shear tests on the same sample showed that with increase of repeated shear times, the peak shear strength and the steady state shear strength become greater. 1 INTRODUCTION

tremendous ring-shear tests on different samples under different loading conditions (static load and cyclic load) to study the effects of these factors on sliding-surface liquefaction behaviour, and had made this phenomenon widely understood. However, most of the studies were on the mechanism of slidingsurface liquefaction, with some emphasis on the relationship between grain crushing and pore pressure generation, etc (Wang 1998). The evaluation of sliding-surface liquefaction susceptibility of a soil element under a certain stress state and the evaluation of post failure behaviour that could be connected with the potential resulting disaster were less studied. And even more, there is no research concerned with the failure of re-activate field slopes. In practical situation, a slope could have suffered several times of failure, it means that the soils within the sliding zone may have repeatedly suffered shear failure arid grain crushing. This kind of slope should be paid more attention, because the stability factor is small (usually considered as l.O), when triggered by some factors (such as earthquake, rainfall, etc.). Therefore, it is necessary to make the behaviour of the soils within the shear zone of this kind of failure clear. The data presented in this research is to aid understanding of the effects of initial relative density, previously mobilized drained shear stress, and shear history on the undrained shear behaviour in ringshear apparatus. These constitute the main purpose of the present research.

Liquefaction landslide is always characterized by high-speed movement and long run-out distance, so it is usually accompanied by tremendous hazards. To predict the potential of this kind of failure and mitigate the disasters, it is necessary to have a good understanding of its mechanism. In the studies of landslides triggered by the Hyogoken-Nanbu earthquake through undrained ring-shear tests, a new concept “sliding-surface liquefaction” was proposed by Sassa et al. (1995), which could reasonably interpret many initiated high speed landslide phenomena. Sliding-surface liquefaction is a special kind of liquefaction, it differs from the normally known Liquefaction (namely mass liquefaction) (Sassa 1995). Mass liquefaction is a process during which the soil losses a great number of its strength due to the generation of excess pore pressure, and shows the behaviour of liquid. Sliding-surface liquefaction is a phenomenon that liquefaction only takes place along the sliding surface. With increasing of shear displacement, accompanying the grain crushing, pore water pressure builds up gradually, and shear resistance decreases slowly, finally reaches a certain value, known as the steady state strength (Sassa et al. 1996, Sassa 1997). Therefore, Sliding-surface liquefaction can take place even in medium or dense soil structure; it is a localized liquefaction limited in the shear zone both in laboratoryand in the field. Recently, Sassa and colleagues had carried out

583

Figure 2. Shear stress-shear displacement curve in ring shear test.

Figure 1. Grain size distribution of silica sand no. 8

(W. 2 SAMPLE CHARACTERISTICS Silica sand no.8 (abbreviated as S8) was selected as the sample. S8 is a kind of sand material for building made from silica sandstone by grinding, comprised of sub-angular to angular quartz. S8 has a mean diameter of D,, = 0.057 mm, uniformity coefficient of U , = 10.2, maximum void ratio of 1.657 and minimum void ratio of 0.852, and specific gravity of 2.63. Figure 1 shows the grain size distribution of S8. The permeability coefficients range from 0.001 to 0.01( c d s ) when the void ratios vary from 0.9 to 1.3.

3 TEST APPARATUS AND TEST PROCEDURE 3.1 Ring-shear apparatus Two new sets of almighty intelligent ring-shear apparatus (DPRI Ver.5, DPRI Ver.6) were developed and improved by Sassa and colleagues. In the present research, DPRI-6 was employed. The shear box for DPRI-6 is very large, of 250cm in inner diameter, 350cm in outer diameter and 15cm in height. The detailed information on ring-shear apparatuses could be referred to Sassa (1997). Corresponding to the shear stress control, there are three kinds of rotating gear with final speed of I0mdsec (Low), 30cdsec (Medium) and 21dsec (High). In this study, the Low gear was selected. 3.2 Test procedure The oven-dried sample was set into the shear box by means of dry deposition (Ishihara, 1993). Sample was saturated with aid of carbon dioxide and deaired water. In all the tests, full saturation was ensured by using B,, parameter (proposed by Sassa, 1988) with B, 2 0.95. The sample was normally consolidated. After consolidation, initial mobilized drained stresses corresponding to those of a given slope were applied Undrained shear stress was subsequently applied at a loading rate of 0.098 kPa/sec. Transducers were

scanned at an interval of 1 second before the peak shear stress; after that, the sampling rate was increased to 20 sampleshec. To observe the generation of pore pressure accompanying the shear displacement, the samples were usually sheared to a large displacement of 10m. 4 STATIC LIQUEFACTION RESISTANCE AND BRITTLENESS INDEX Static liquefaction refers to these liquefaction resulted from monotonically increasing of static loading. The criterion for the analysis of liquefaction susceptibility of sand under a certain condition (stress state and density) had been made clear (Castro 1969, Castro & Poulos 1977). Considering that both in the field and in the laboratory, liquefaction can only occur when shear stresses under undrained conditions are greater than or equal to those required to initiate liquefaction, Kramer & Seed (1988) proposed a new concept of static liquefaction resistance to evaluate the liquefaction potential at a given site, that was defined as the increase in shear stress under undrained conditions required to initiate liquefaction, and formulated as:

,.

where r = peak undrained shear strength, r = previously mobilized drain shear stress, as shown in Figure 2. A parameter “Brittleness index” was proposed and used by Bishop (1967) with which to relate postrupture behaviour. It was defined as: Where T , is the residual undrained shear strength, usually referred to as the steady state shear strength. A greater brittleness index indicates a greater reduction in shear strength that may be associated with larger deformation after the initiation of liquefaction. In this paper, we will use R, to evaluate the liquefaction susceptibility and Z, to analyse the postfailure behaviour of liquefied soil in ring-shear tests. 584

Figure 3. Ring shear test on very loose sand showing mass liquefaction phenomenon. (a) and (b): Variation of pore pressure and shear resistance in relation to shear displacement for the tests with shear displacement being 10 m and 3 cm, respectively; (c): Effective stress path. (B, = 0.99, D,. = 63.3%, = 196 kPa.)

5 TEST RESULTS 5 . I Muss liquefuction and sliding-su@uce liquefulctian behavior To make a good understanding of the distinction between sliding-surface liquefaction and mass liquefaction, test results were presented to show their unique characteristics. The results of two tests on loose sands showing the behaviour of Inass liquefaction during undrained shearing are illustrated in Figure 3 (S,, and Soo3), Both of these two tests were carried out under the same initial stress state and initial density. S,, was sheared to 10m. So,, was a complementary test of S,,, and its purpose was to observe the undrained shear deformation of soils. Two vertical slices of lcm width made from Toyoura standard sands with different color were made inside the samples. After undrained sheared to 3Cm, the shear box was opened and the shear deformation was observed, which confirmed the character of mass liquefaction. Figures 3a shows the variation of pore pressure in relation to shear displacement for

Figure 4. Ring shear test on dense sand showing sliding-surface liquefaction phenomenon. (a): Effective stress path; (b): Variation of pore pressure and shear resistance in relation to shear displacement. (B,,=0.99, D, = 9 1.2%, CT =I96 kPa.)

test of S,(),and Figure 3b for test of S,,,,. As shown, immediately after the undrained shear stress was applied, shear displacement was generated. Accompanying the increase of shear displacement, pore pressure built up quickly within limited shear displacement range (about 1cm), and shear resistance decreased remarkably. This period is usually known as the collapse period, mainly due to the failure of metastable structure. It could be seen that test S,, and S,,, behaved almost the same. After that, pore pressure built up gradually with the shear displacement, and as a subsequence, shear resistance decreased slowly (Fig. 3a). Figure 3c shows the effective stress paths and failure line. The failure line was measured after the undrained shear test was stopped by means of reducing the normal stress at a very slow unloading rate while keeping the shear box rotating at a constant speed under drained condition. From this figure, it could be seen that after undrained shear stress was loaded from 0.0, with increasing of shear stress, stress path extended towards but did not reach the failure line with a final point, known as the steady state point. Mass liquefaction occurred only in the very loose sands. Because all the tests were carried out under 585

normally consolidated state, there were limited tests showing mass liquefaction, while most of them showed sliding-surface liquefaction. Figure 4 shows the results of a test on dense sands, in which typical sliding-surface liquefaction phenomenon occurred. This sample was made through tamping method. After saturated, sample was normally consolidated. Figure 4a illustrates the variation of pore pressure and shear resistance in relation to shear displacement; Figure 4b shows the corresponding effective stress path. As shown in Figure 421, in the initial period after shear stress was applied, with increase of shear displacement, pore pressure built up gradually, but after point “L”, it decreased due to the dilatancy of dense sands. After the peak shear strength was reached (Point F in Figs. 4a,b), sample failed, and thereafter, pore pressure built up gradually with shear displacement, finally reached about 110 kPa. The shear resistance decreased slowly consequently, and finally fell to about 60 kPa. The pore pressure ratio (pore pressure / normal stress) was about 0.56. As shown in Figure 4b, upon increase of shear stress, the effective stress path extended left downward due to the pore pressure generation. After point “U’, the path went right-upward accompanying further shearing, showed a turn point. After failure point “F”, the path fell downward along the failure line until a small shear resistance. This is a typical stress path of sliding-surface liquefaction. The generation of high pore pressure is due to grain crushing in the shear zone. The undrained shear behaviour in triaxial apparatus as that before the point “F’ in Figure 4b was described as limited liquefaction (Castro 1969). Due to the limitation of triaxial apparatus in shear displacement, the behaviour after “F” was not obtained and not made clear until undrained ringshear apparatus was developed. Obviously, the prerequisite for this kind of liquefaction is that enough shear displacement could be offered for the completely grain crushing.

Figure 5 . Results of tests on samples with different initial relative density. (a) and (b): the variation of shear resistance and pore pressure in relation to shear displacement for these tests, respectively. results. As shown, both the samples tested at relative densities of 76.0% and 74.1% exhibited transient period of dilative behavior with decreasing excess pore pressure and increasing shear stress after a period of limited liquefaction. Thereafter, with the increase of shear displacement, excess pore pressure was built up gradually, and shear resistance decreased subsequently, finally, dropped down to a certain value respectively, which is usually much less than the peak value of shear resistance, this means that the soil was liquefied. The increase in shear stress under undrained conditions required to initiate liquefaction in samples tested at 63.3, 74.1,76.0 and 91.2% relative density was progressively greater. This means that the static liquefaction resistance increases with increasing relative density. It could be found easily (in Fig. 5a) that steady state shear resistance becomes greater with increase of relative density also. In the liquefaction potential analysis based on triaxial test results, it has been pointed out that, at relative densities greater than those corresponding to the steady state line, the soil will exhibit dilative behaviour, and there will be no potential for liquefaction. However, the test results presented here shows that, provided that shear stress is enough to initiate the failure of soil, liquefaction could be resulted in, no matter the soil is denser or looser than that of steady state line.

5.2 Effects of initial relative density As widely known, void ratio plays an important role for the liquefaction. To study the influence of soil density on shear behaviour in ring-shear apparatus, a number of tests were conducted on sands with initial normal stress being 196.0 kPa and shear stress being 0.0. Relative density was selected as the parameter to expressed the density. Figure 5 presents the variation of shear resistance (Fig. 5a) and pore pressure response (Fig. 5b) in relation to shear displacement for samples with different relative densities. Two of them (D,.= 63.3% and D,.= 91 2%)had been presented in detail in the proceeded section, therefore, emphasis will be focused on the description of another two tests

5.3 Effects of initial drained shear stress

To study the influence of initial drained shear stress 586

Figure 7. Test results of three shear times. (a): effective stress paths; (b): variation of shear resistance in relation to shear displacement; S 1, S2, S3: final shear strength for the first time, second time, and third time, respectively.

Figure 6. Results of tests on sample at different initial drained shear stress. (a): effective stress paths; (b): variation of shear resistance in relation to shear displacement. on the following undrained shear behaviour of sands, a series of tests was conducted on sands under different initial drained stresses. Initial drained shear stresses were 0.0, 26.3, 58.0, 70.2 and 99.7kPa respectively, while the normal stresses were kept the same, 196.0kPa. Duiing test, after the normal stress was applied and sands were normally consolidated, initial drained shear stress was loaded, and then switched the shear box into undrained condition and increased the shear stress until failure. Theoretically, all the tests should be performed under the same relative density, but due to the difficulties in making samples and effect of initial shear stress, there were still little differences between their initial relative densities among the tests presented here. Figure 6 shows the results of tests on different initial shear stresses. Figure 6a presents the effective stress paths for these tests; and Figure 6b is the variation of shear resistance in relation to shear displacement. From Figures 6a, b, i t could clearly be seen that with increase of initial shear stress, the peak shear strength become greater. However, the differences between the peak strength and initial shear stress were approximately 54.8, 26.3, 15.6, 11.3 and 3.8 for the tests at initial shear stress of 0.0, 26.3, 58.0, 70.2 and 99.7kPa respectively, namely the static liquefaction resistance becomes smaller with increase of initial drained shear stress. It should

587

be noted that the static liquefaction resistance for the test on initial drained shear stress of 99.7kPa is just a very little proportion of the initial shear stress (about 3.8%). This means that a soil that have been subjected to high initial drained shear stress is easier to suffer from sliding-surface liquefaction because a very little change in shear stress under undrained condition could initiate sliding-surface liquefaction. This result showed a good consistent with other studies on mass liquefaction (Castro 1969, Castro & Poulos 1977, Kramer 1988). Although the tests on sands with different initial shear stresses showed different peak shear strength and different static sliding-surface liquefaction resistance, it could be seen easily (Figs. 621, b) that the final liquefaction resistance was approximately the same. The little differences between their values may be due to the little differences between their initial relative densities. As described above, denser sand will have greater steady state strength. Therefore, i t could be concluded that initial shear stress has no influence on the steady state strength. Figure 6 presents another phenomenon that is, the peak shear strength ( i- ,) becomes greater with increase of initial shear stress while the steady state shear strength ( T ,) is the same. Therefore, the brittleness index (In) becomes greater consequently ( I , for these five tests were 1.42, 1.75, 2.19, 2.53 and 3.5 1 at initial shear stress of 0.0, 26.3, 58.0, 70.2 and

study the sliding-surface liquefaction behaviour in ring-shear apparatus. Through changing the initial density and shear stresses, shearing the same sample repeatedly, the effects of initial density, initial drained shear stress and shearing history on the undrained shear behaviour of sands were analyzed. The conclusions could be drawn as follows. 1. Mass liquefaction could only happen in very loose sands, while sliding-surface liquefaction could take place even in medium or dense state. 2. Initial shear stress has no effect on the steady state shear strength. With increase of initial shear stress, the static sliding-surface liquefaction resistance decreases, while brittleness index becomes greater. It shows that a steeper slope is more prone to suffer from the sliding-surface liquefaction failure with rapid deformation. 3. With increase of repeated shear history, the static liquefaction resistance and residual shear strength become greater, namely soils become difficult to suffer from liquefaction failure.

99.7kPa respectively). It shows that the soil liquefied at a steeper slope will suffer from larger progressive deformation, namely greater run-out distance. 5.4 Efsects ofrepeated shear history Considering that failure could happen on a pre-failed slope or along an existed sliding surface, repeated shear tests on sands were performed to study the shear behaviour of soils that have even experienced prefailure. During test, sand was normally consolidated and sheared (under undrained condition with a given drained initial shear stress) to about 10m. Then, unloaded the loading and turned the shear box into drained condition, re-consolidated the once sheared sample, and performed the test under the same condition as that of the first time for the second and third time. The effective stress paths for three times of tests on the sample subjected to an initial shear stress of 70.2 kPa were presented in Figure 7a. Figure 7b shows the corresponding variation of shear resistance in relation to shear displacement. As shown in Figure 7a, for the first shear time, after undrained shear stress was applied, accompanying the excess pore pressure generation, effective stress path extended leftwards remarkably before reached the failure line. After reached the failure line, due to grain crushing, excess pore pressure continued to build up until reaching the steady state. Focusing on the effective stress path for the second time, we can find that, although accompanying the increase of undrained shear stress, the excess pore pressure was built up, but it did not lead to the quick failure. After the stress state reached the failure line, with increase of shear displacement, shear resistance decreased slowly accompanying the built-up of pore pressure. For the third time, it could be seen that once the undrained shear stress was applied and increased, negative pore pressure was generated due to the dilatancy. When shear stress was increased to a certain, the sample failed, and then shear strength fell to the failure line, thereafter, dropped down along the failure line towards 0 point with increase of shear displacement. From Figures 7a, b, it could be seen that with increase of repeated shear times, the steady state shear strength and the peak shear strength became greater. It indicates that with increase of shear times, it becomes difficult for the liquefaction failure to occur, because the collapse of metastable structure and the grain crushing are tending to be finished with increasing of repeated shear times.

REFERENCES Bishop, A.W. 1967. Progressive failure-with special reference to the mechanism causing it. Proc. Geotechn. Conf., Oslo, Norway 2, 142-1 SO. Castro, G. 1969. Liquefuction ofsands. Ph.D. Thesis, Harvard University, Mass. Castro, G. & S.J., Poulos. 1977. Factors affecting liquefaction and cyclic mobility. J. Geotech. Eng. Div., ASCE 103, 50 1 -5 1 6. Ishihara, K. 1993. Liquefaction and flow failure during earthquakes. GPotechnique 43(3):349-45 1. Kramer, K. L. & H. B . Seed 1988. Initiation of soil liquefaction under static loading conditions. J . Geotech. Engrg., 114: 4 12-430. Sassa, K. 1988. Geotechnical model for the motion of landslides. Special Lecture of 5th International Symposium on Landslides, “Landslides”, 1. Rotterdam: Balkema. 37-55 Sassa, K. & H. Fukuoka. 1995. Prediction of rapid landslide motion. Proc. X X IUFRO World Cong., Finland. Sassa, K., Fukuoka, H., Scarascia-Mugnozza, G. & S.Evans 1996. Earthquake-induced-landslides: Distribution, motion and mechanisms. Special Issue for the great Hanshin Earthquake Disaster, Soils and Foundations, 53-64. Sassa, K. 1997. A new intelligent type of dynamic loading ring-shear apparatus. Landslide News. No.10, pp.33. Wang, F. W. 1998. An experinzentul study on grain crushing and excess pore pressure generation during-shearing of sandji soils-A key factor for rupicl landslide niotion. Ph. D.Thesis. Kyoto University.

6 CONCLUSIONS A series of tests was conducted on silica sands to

588

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Real seismic-wave loading ring-shear test on the Nikawa landslide EW W a g , K. Sassa & H. Fukuoka Disaster Prevention Research Institute, Kyoto University,Uji,Japan

ABSTRACT: By employing an undrained cyclic-loading ring-shear apparatus, a series of tests to reproduce the sliding behavior of the Nikawa landslide was conducted. Test sample was taken from the landslide. The initial stress condition acting on a soil element in the sliding surface was applied on the sample. Based on the monitored seismic-wave records, the input seismic wave was synthesized to obtain the seismic stress acting on the sliding surface. The most remarkable result is that the pore pressure generation and the acceleration of shear displacement continued after the main shock. Combining with the grain crushing at the shear zone in the drained ring-shear test, the mechanism of this landslide is interpreted as that the main shock triggered the failure of the slope, then shear displacement caused grain crushing in the shear zone, and resulted in residual excess pore pressure generation and sliding-surface liquefaction.

1 INTRODUCTION

granite. The Osaka-group layer and terrace deposit distributing on the slope overlaid on it. Above the old slope surface, landfill was consisted of the Osaka-group layer, and the landslide occurred in the landfill. Test sample was taken from the landslide mass just above the sliding surface by excavating the landslide debris, namely the same materials (Osakagroup coarse sandy soil) where the sliding zone was formed. To investigate the depth of groundwater table, some boreholes were drilled immediately after the occurrence of the landslide. The ground water table existed in 6-7 m below the ground surface near and outside of the landslide area in three boreholes from February to March 1995. As an example of rapid landslides induced by earthquakes, the Nikawa landslide was studied by Sassa et al. (1996), with an undrained ring-shear apparatus, DPRI-3. In that study, normal stress was kept as constant, and shear stress was applied as a sine wave of 0.1 Hz with the amplitude increasing cycle by cycle. In undrained condition, dense sample was sheared and effective stress path was obtained. Basing on the study, a concept termed as "slidingsurface liquefaction" was proposed. Sliding-surface liquefaction can take place even in medium-dense or dense soil layer because grain crushing in the shear zone results in potential of volume reduction and generation of excess pore pressure. It is of great geotechnical significance to perform a test using a real earthquake record to investigate

The January 17, 1995 Hyogoken-Nambu earthquake in Japan killed more than 5,500 persons, destroyed about 200,000 houses, and triggered many disasters of landslides. The Nikawa landslide is one of the largest geo-disasters of the earthquake. It destroyed 11 houses and killed 34 persons. According to Sassa et al. (1996), the landslide volume was 110,000 120,000 m3. The moving distance was 175 m. No observation data of the sliding speed is available. However, it is believed that it was a high-speed landslide, because no one could evacuate from the destroyed houses and all 34 residents were killed. The landslide occurred on a gentle slope, and moved for a long distance to the nearby residential area. Figure 1 shows the plan of the landslide area before the landslide occurred. The sliding direction of this landslide is about 60"NE. Location of borings and excavation pits PI and P2 for observation and sampling point S1 are plotted. Standing ground water was observed at secondarily moved debris. Although January in this area is very dry, the Osakagroup layer composing the slope retained ground water. The ground water table was confirmed by ground water level monitoring in them later. Figure 2 is the A-A' section shown in Figure 1. It is drawn based on the ground surface survey, boring investigation and the ground water monitoring at the boreholes. The average angle of the sliding surface was about 20". The base-rock of the slope was

589

Figure 1 Plan of the slope before the Nikawa landslide occurred and the outline of the landslide area (from Sassa et al. 1996). courtesy of the Japan Railway Technical Research Institute. There are two important factors in the input seismic wave. One is the peak ground acceleration, and the other is wave shape. Concerning the peak ground acceleration, an attenuation equation (Eq. 1) proposed by Fukushima & Tanaka (1992) was employed. 10gA=0.42Ms-log(R+O.O25~10~~~~’)-0.0033R+1.22 (1)

where A is the average of two peak horizontal acceleration in cds’, Ms the moment magnitude and R the distance from an observatory station to the fault rupture in km. Eq. (1) is for the horizontal acceleration, because vertical acceleration also attenuates following the same law, the correction of the vertical acceleration was also processed with this equation. According to the Active Faults Map in Urban Area published by Geographical Survey Institute of Japan (1996) and Lrikura & Fukushima (1995), the distance from the active fault, the Koyo active fault, to the JR Takarazuka Station and the Nikawa landslide are about 7 km and 0.5 km, respectively. The peak acceleration for the moment magnitude ( M s ) value for the Hyogoken-Nambu earthquake is 7.0. By calculation, the peak ground acceleration at the Nikawa landslide was about 1.4 times to that at the JR Takarazuka Station. Fukushima & Tanaka (1990) also found that, in

Figure 2 Geological section along A-A’ line in Figure 1 (from Sassa et al. 1996). the sliding behavior of landslide triggered by earthquakes. For this purpose, an improved undrained ring-shear apparatus, DPRI-5, which is possible to load real seismic wave, was developed in 1995 (Sassa 1997) and used in this study.

2 INPUT OF SEISMIC LOADING Theoretically, it would be the best to use a seismic record monitored at the landslide site, but it did not exist. -4mong seismic records monitored in the earthquake, the seismometer at the JR Takarazuka Station is the nearest one from the Nikawa landslide site. Therefore, the real seismic wave monitored at the JR Takarazuka Station was used in this study by

590

Figure 4 Loading stresses on the sample. (a): Normal stress, (b): Shear stress consisted of landfill was assumed to be 140% of that measured by seismometers at the JR Takarazuka Station. Considering the two factors, 2.0 (1.4~140% = 2.0) was selected as the amplifying coefficient of the peak ground acceleration. Concerning the wave shape and loading magnitude, through the procedure shown in Figure 3 (Fukuoka et al. 1998), the seismic wave acting on the soil element in the sliding zone was calculated. Here, we use the following values based on the field investigation. H = 14 m, 8 = 20°, 'yl = 17.6 kN/m3, E = 20.6 kN/m3, respectively (Kawasaki Geology Corporation 1995). The pore pressure table above the sliding surface was assumed to be about 7 m (at least), because the ground water table outside the landslide area was 6-7m below the ground surface. Accordingly, the initial normal stress 0,was 236.1 kPa, the initial shear stress T, was 85.9 kPa, and the initial static pore pressure U, was 60.6 kPa. Eventually, the dynamic-loading stress input was obtained as shown in Figure 4. The seismic wave lasts for 40 seconds. The main shock distributed between 4 second and 7 second. After the seismic wave is over, the stress state of the soil element returns to the initial stress state at the slope.

Figure 3 The synthesizing procedure from seismic loading to normal stress and shear stress. (a) Transfer the horizontal acceleration (EW and NS) components to the horizontal slope direction. (b) Transfer the horizontal component along the slope direction and the vertical component (UD) to the components (NR and SH) along the sliding surface. (c) Sum the initial stress according to the selfweight (w)and the increments of normal stress (Ao) and shear stress (AT) acting on the sliding surface by multiplying acceleration and mass of the soil columns.

3

general, the mean value of the peak ground acceleration for loose soil was 140% times of the average value. The seismic measurement system was set in stiff layer at the JR Takarazuka Station. While, as described previously, the Nikawa landslide mass was consisted of landfill of the Osaka-group coarse sandy soil. So the peak acceleration in the landslide

SAMPLE PREPARATION PROCEDURE

AND

TEST

Grains greater than 4.75 mm are about 7% of the sample. They were eliminated after dried in oven, considering the size of the shear box. The physical properties of the sample are shown in Table 1. The seismic loading simulation test on the Nikawa

591

Table 1. Physical properties of the Osaka-group coarse sandy soil. Specific gravity, G,y Minimum void ratio, ernin Uniformity coefficient, U,

0.50 mm landslide was performed by following procedures. 1) Weigh and set the dry sample in the shear box with free-fall deposition method, and then saturate it. The degree of saturation is confirmed by B D value, a pore pressure coefficient in direct shear state. The BD value at this test was 0.99, means a high degree of saturation was achieved. 2) Consolidate the sample at the initial normal stress, 0,and then apply the initial shear stress, z, at drained condition. 3) Apply the initial pore pressure U , from the upper drain line of the shear box to simulate the ground water condition. The relative density of the sample was 121.2 percent. 4) Change the shear box to undrained condition and load the seismic-wave loading of normal stress and shear stress simultaneously. S ) Keep on the shearing with the shear box in the undrained condition, until the steady state of the tested sample is reached.

Figure 5 Time-series data of the simulation test on the Nikawa landslide. B, = 0.99, Dr = 121.2 percent (a): Normal stress (kPa); (b): Pore pressure (kPa); (c): Shear resistance (kPa) and shear displacement (x100 mm).

4 TEST RESULTS AND ANALYSES Figure 5 shows the time-series data of monitored parameters of normal stress 0,pore pressure U , shear resistance z and shear displacement. In Figure 5a, the monitored normal stress is almost the same as the control signal. Figure 5b shows the variation of pore pressure. During the main shock (4-7 second), the excess pore pressure changed rapidly as a response to the loaded stresses. The low boundary of pore pressure curve indicated the built-up of pore pressure during the main shock. It is noticed that pore pressure is built-up to a certain value after the main shock. Figure 5c shows the variation of shear resistance and shear displacement. During the main shock, the sample failed because the loaded shear stress exceeded the shear strength of the soil. Shear displacement was observed. However, it was so small during the main shock that almost invisible in this figure. The mobilized shear resistance changes rapidly, while the maximum value did not decrease so much during the main shock. It is quite remarkable that the shear displacement accelerates through the whole process after failure. It is apparently resulted from the decrease of shear resistance to a certain low value, reasonably

corresponding to the tendency of pore pressure builtup after the main shock. This is the same phenomenon observed in the previous research in the 0.1 Hz cyclic-loading ring shear test for the same soil sample. Figure 6 shows the stress path obtained in the simulation test. ESP means the effective stress path, while TSP means the total stress path. Because of possible delay of pore pressure measurement during the period of high frequency, some stress points distributed above the failure line. Although it is difficult to follow the process of both stress paths with this figure, referring to the time series data, it is reasonable to describe the stress path as following. At first, the stress path reached the peak strength failure line ($I,) = 39.6') and the soil failed. The state of shear zone became to residual one. With the progress of shearing after failure, the effective stress path turned to the residual failure line ($Ir = 35.5'). Shearing under a high effective stress should cause the grain crushing and then result in the generation of excess pore pressure. Thereafter, with the generation of large excess pore pressure, the effective stress path descended along the residual failure line to a very low effective stress level. The

592

Figure 6 The stress path for the simulation test on the Nikawa landslide. ESP: Effective stress path, TSP: Total stress path B, = 0.99, Dr = 121.2 percent residual excess pore pressure ratio defined as Eq. (2).

rilr(t) = ( ( u ( t ) - uo) - A o ( t ) B ~ ) / o o ’

Figure 7 The relationship between residual excess pore pressure ratio and the shear displacement. apparent friction angle is 6.3”. The grain crushing process went to close, until the effective stress became small enough that grain crushing can not take place any more. This is somewhat different from the usual liquefaction, in which the stress path instantaneously reduces to a very low stress level without reaching the peak strength failure line. It is consistent with the phenomenon of “sliding-surface liquefaction”. In it, the excess pore pressure, which caused by grain crushing in the shear zone during shearing is important. The grain crushing makes volume reduction potential, and results in the builtup of excess pore pressure. To examine the concept, the built-up of residual excess pore pressure with shear displacement is presented here, and the grain crushing property of the sample is investigated later. Figure 7 shows the changing process of the

(t)).r,, ( t ) was

(T,,~

(2)

where, u(t) is the monitored pore pressure, uo is the initial pore pressure, do ( t ) is the applied normal stress increment, and oo’ = o, - uo is the initial effective stress. B, is pore pressure coefficient in direct shear state. The residual excess pore pressure ratio is independent for the initial pore pressure and the loaded normal stress, and has the maximal value of unity. It is shown that, although there is possible measurement delay of pore pressure between the shear displacement of 0.2 mm and 3 mm, the increase trend of r,, ( t ) with shear displacement is clearly observed. Especially, after 10 mm, it is convinced that, the excess pore pressure is generated with the increasing of shear displacement. When the shear displacement exceeds 1000 mm, the excess pore pressure ratio reaches about 0.8. Slidingsurface liquefaction occurred with the progress of shear displacement.

5 GRAIN CRUSHING PROPERTY OF THE TESTED SAMPLE After the simulation test, drained constant-speed ring-shear test was carried out on the same kind of sample to investigate the grain crushing property of the tested sample. Under a normal stress of 196 kPa, and shear speed of 3 m d s e c , the sample was sheared for 42 m in drained condition. In order to investigate the state of grain crushing in the shear zone, the sheared sample after the drained test was excavated and the cross section was exposed. Figure 8 is the photograph showing the cross section of the sheared sample in

593

6 CONCLUSION The mechanism of the Nikawa landslide was investigated. Dynamic loading synthesized from the real seismic-wave was loaded in this test. Results presented that shear displacement started during the main shock, but it was very small. The major phenomenon representing the rapid motion of the landslide occurred after the main shock. After the main shock, shear displacement increased rapidly, pore pressure was built-up continually and shear resistance reduced to a very low value. Through confirmation of the grain crushing process in the shear zone after the drained shear test, it is concluded that the sliding-surface liquefaction is caused by grain crushing. Figure 8 Photo of the sample after drained shear. A trench cut in the shear box. Pins show the upper and lower boundary of the graincrushing zone.

ACKNOWLEDGEMENTS We would like to express our special thanks to Japan Railway Technical Research Institute, for providing the real seismic record at the JR Takarazuka Station. REFERENCES

Figure 9 Grain size distribution analysis results for the original sample, sample at the shear zone, samples at the upper part and the lower part of the shear box after sheared for 42 m under 196 kPa normal stress, shear speed = 3 m d s e c . the sample box. It is clearly observed that a graincrushing zone, which was finer and denser than the upper and lower sample, was formed at the shear zone. The pins show the upper and lower boundary of the grain-crushing zone. Then, the samples in the shear zone, and that at the upper part and lower part of the shear box were taken out, and grain size distribution analyses were conducted on them. Figure 9 is the result comparing to the original sample. The samples at the upper part and lower part have just the same grain size distribution as that of the original one, while that in the shear zone was much finer. It is indicated that grain crushing only took place in the shear zone. Based on this result, it is reasonable to estimate that the built-up of pore pressure is resulted from the grain crushing in the shear zone. It is confirmed that, because of the grain crushing occurred in the shear zone, sliding-surface liquefaction happened.

Fukuoka, H., F.W. Wang & K. Sassa 1998. Ring shear test with real seismic loading. Proceedings of 1998 Annual Con. of the Japan Society of Erosion Control Engng., JSECE Publication. Sapporo, 25:98-99 (in Japanese). Fukushima, Y. & T. Tanaka 1990. A new attenuation relation for peak horizontal acceleration of strong earthquake ground motion in Japan. Bull. of the Seis. Soc. of Am., 80(4):757-783. Fukushima, Y. & T. Tanaka 1992. Revised attenuation relation for peak horizontal acceleration using a new data base. Prog. and Abs. of Seisrn. SOC,Japan, 2: 116 (in Japanese). Geographical Survey Institute of Japan 1996. Active Faults Map in Urban Area: Northwest part of the Osaku area. Irikura, K. & Y. Fukushima 1995. Attention characteristics of peak amplitude in the Hyogoken-Nambu earthquake. J. of Natural Dis. Sci., 16(3):39-46. Kawasaki Geology Corporation 1995. Field Investigation Report on the Nikawa Landslide. Sassa, K., H. Fukuoka, G. Scarascia-Mugnozza. & S. Evans 1996. Earthquake-induced-landslides: Distribution, motion and mechanisms. Special Issue for the great Hanshin earthquake disasters, Soils and Fdn. 53-64. Sassa, K. 1997. A new intelligent type dynamic loading ring shear apparatus. Landslide News (Japan Landslide Society), 10:33.

594

Slope Stability Engineering, Yagi, Yamagami L? Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Dynamic properties of fine-grained soils in pre-sheared sliding surfaces M.Yoshimine - Tokyo Metropolitan University, Japan R. K U W ~-O University of Tokyo, Japan J. K U W ~- O Tokyo Institute of Technology,Japan K. Ishihara - Science University of Tokyo,Chiba. Japan

ABSTRACT To evaluate the seismic stability of slopes containing pre-sheared surfaces, a series of cyclic loading tests on samples with pre-sheared surface were conducted with a dynamic ring shear apparatus. The effects of the dynamic loading such as the number of cycles and fiequency were examined. It was also attempted to find if the dynamic behavior of soil with pre-existing shear surface is correlated with physical properties of the tested materials. 1 INTRODUCTION Slopes of clay and weak mudstone often contain shear surfaces at residual strength which were created by previous landslides or tectonic movements. For evaluating the stability of such slopes during earthquakes, dynamic properties of materials with pre-existing shear surfaces at or close to residual strength should be known. For this purpose, high speed shear tests have been conducted on clayey materials by means of ring shear apparatus (Skempton, 1985, Lemos et al., 1985, Tika et al., 1994 and Tika and Hutchinson, 1999). Based on the relationship between shear resistance of slip plane and the rate of displacement derived from these experiments, Lemos et al. (1994) proposed a method to calculate the displacements of slopes induced by earthquake loading. Although these previous studies addressed dynamic and cyclic properties of pre-existing shear surfaces, only monotonic loading tests have been conduced and cyclic loading tests have not been performed. To directly observe the cyclic behavior of of fine-grained soils in pre-existing shear surface, a dynamic ring shear apparatus was manufactured (Ijuin et al. 1987, Kuwano et al. 1991) and a series of cyclic loading tests on pre-existing shear surface have been carried out. This paper reports on the results of these tests.

15cm and 2cm, respectively. The torque arm and the load cell for torque-measurement fix the rotation of the loading head and the upper half of the specimen. During displacement-control and monotonic loading tests, the electric motor and the gear system rotates the lower half of the specimen. A shear surface is created at the middle height of the specimen. In case of load-control cyclic tests, the pulley is lifted up by air pressure and fixed to the base platen. Then the gear system is disconnected, and the cyclic load is applied to the lower half of the specimen by air pressure in torque cylinder through the wire-pulley system. This mechanism enabled soil samples to create shear surfaces at residual state in one direction. Then cyclic load was applied on the shear surfaces successively. In the ring shear testing, setting adequate gap between upper and lower rings is necessary for precise measurement of vertical load and torque on the shear surface. The gap controlling system of the Imperial College - NGI type ring shear apparatus (Bishop et al., 1971) is not suitable for dynamic loading, because it is impossible to keep normal stress on the shear plane constant due to the fluctuating vertical friction between upper ring and specimen. To overcome this limitation, the gap is adjusted using the screw on the loading head as shown in Fig. 1. This system is superior also for monotonic loading providing that residual state is achieved and the height of the specimen is constant.

2 THE RING SHEAR APPARATUS 3 TESTED MATERIAL AND TEST PROCEDURE The outline of the dynamic ring shear apparatus used in this study is shown in Fig. 1. The outer diameter, inner diameter and height of the specimen are 20cm,

Sixteen materials were obtained from some sites of landslides in natural or manmade slopes and tested. 595

Table 1. List of ring shear tests ~

Li,qu,id Plasticity limit index

Normal ( < 2 p ) stress

Residual shear strength, T, (kPa) [ Rate of displacement ( m d m i n ) ]

Dynamic strength, q, ( H a ) [ Sinusoidal loading ] [Earthquake]

applied on the residual slip surface to examine the effects of the nuniber of cycles, then sinusoidal loading with increasing amplitude were applied to examine dynamic strength characteristics. Finally, the behavior of the shear plane under earthquake loading was studied. Before each steps of dynamic loading, it was made sure that the slow residual strength, ~ ~ ( 0 .mdmin) 01 ,was achieved by applying monotonic load. During the final stage of consolidation and the monotonic and dynamic shear process, the gap between upper and lower rings was kept constant around O.lmm. The test results are also summarized in Table 1.

The physical properties of the materials are summarized in Table 1. Some of these materials were sampled near ground surface, and therefore they might not be exactly the same as the materials causing the landslides in the field. After processing the natural materials through the sieve to remove particles coarser than 2mm, distilled water was added to make the water contents around the liquid limit. Then the material was poured between outer and inner rings and consolidated under the target vertical stress of 49 to 490kPa, but mostly in the range of 98 to 294kPa. Only normally consolidated specimens were tested. First, specimens were sheared at constant rate of 0.01mndniin until residual strength was attained. Very smooth and clear slip surface was created for all of the materials. Second, the shear rate was gradually accelerated up to 300mdmin to study the rate effects during monotonic loading. Third, sinusoidal loading with fixed amplitude were

4 TEST RESULTS AND DISCUSSIONS 4.1 Slow sesidid stsength Secant residual friction angle at shear rate of 0.01 596

Figure 1. The dynamic ring shear apparatus Figure 3. Effect of displacement rate on residual strength

m d m i n is displayed in Fig. 2. Skempton (1964), Voight (1973), Kanji (1974), Lupini et al. (1981), Skempton (1985) and Tika et al. (1999) pointed out that the residual friction angle of clay decreases with increasing plasticity index or clay fraction. Fig. 2(a) and (b) indicate the same tendency, although the measured residual friction angle was somehow larger than the previous studies. Stark and Eid (1994) reported that the residual friction angle was a function of liquid limit, clay fraction and overburden pressure. The same trend may be seen in Fig. 2(c), though more scatters were detected. 4.2 Rate effect in monotonic loading Fig. 3(a) shows the shear rate effect on residual strength. Generally, shear resistance increases with higher speed, but in some cases the resistance dropped with increasing the rate of displacement, especially when the rate reached 300 mndmin. It should be noticed that the shear resistance of Kalabagh clay at high rate of displacement was less than half of the slow residual strength. Skempton (1985) and Tika et al. (1996, 1999) also reported such “negative rate effects” especially for Kalabagh soils. Pore pressure on the slip surface was not measured in this study. Skempton (1985) pointed out that “intermediate soils” that had clay fraction of 20 to 30% could exhibit negative rate effects. The same trend may be seen from Fig. 3(b).

Figure 2. Slow residual strength

597

Figure 6. Dynamic stress versus displacement

4.3 Effect of the nuniber. of cycles in a'yriuinic loading tests A typical example of the result of sinusoidal loading test with fixed amplitude was shown in Fig. 4. Before all of the cyclic loading, including sinusoidal and earthquake loading described below, initial static load equal to 70% of the slow residual strength (q, = xr x 0.7) was applied to the shear surface. Hence, the movement during cyclic loading was observed mostly only in the same direction as the initial static loading. Fig. 4 shows that the deformation was negligibly small when stress level was smaller than a threshold value. Sudden increase in plastic deformation started when stress level became larger than the threshold value in each cycle. Another prominent feature of the behavior of residual slip surfaces shown in Fig. 4 is the fact that displacement in one cycle was nearly constant for any cycles. This means that the number of cycles did not influence the cyclic behavior, i.e. no hardening or softening occurred during cyclic loading on residual slip surfaces.

Figure 4. Sinusoidal loading test (fixed amplitude)

4.4 DeJinition of Dynamic strength Fig. 5 shows a typical example of the sinusoidal loading tests with increasing amplitude. Based on the finding that the cyclic stress - displacement behavior was not much affected by the previous cycles, peak stress of cyclic loading (to+ tc.yc) and displacement in each cycle was plotted in Fig. 6 (a). One may see from this figure that when the cyclic stress level reached to -Some level, the stressdisplacement curve became nearly flat and large

Figure 5. Sinusoidal loading test (increased amplitude)

598

4.6 Dynamic strength characteristics Cyclic loading test results were summarized in Fig. 9. In this figure, the ratio of dynamic strength to slow residual strength was plotted against clay fraction of each material to see if the dynamic behavior of pre-existing shear surface is correlated with the physical properties of the tested materials. The dynamic response of materials that had larger clay fraction was more ductile and the ratio of dynamic strength to slow residual strength tended to be higher, but scatter of data was considerably large. From Fig. 9, it may be seen that, in general, the dynamic strength was 1.2 to 2.0 times larger than the slow residual strength. 5 CONCLUSIONS Sixteen materials, ranging from low plastic silt to very high plastic clay, were tested by means of dynamic ring shear apparatus. In the first series of the tests, sinusoidal cyclic stress with fixed amplitude was applied on pre-existing shear surface in the specimen at residual state. It was found that the number of cycles showed almost no influence on the stress-displacement behavior, i.e. no hardening or softening occurred during cyclic loading. Sinusoidal cyclic stresses with increasing amplitude were loaded on the shear surfaces to study the relationship between dynamic stress ratio and the magnitude of deformation in one cycle. The increase in the loading frequency from O.1Hz to 1.OHz resulted in the increase in the dynamic strength by 5

Figure 7. Earthquake loading test (Hachinohe EW)

deformation developed. This stress level, zd, was defined as the dynamic strength in this study. In addition to the sinusoidal loading tests, EW and NS components of acceleration record acquired at Hachinohe Port during Tokachi-oki Earthquake, Japan (1964) was used. Due to the fiequency limitation of the pneumatic loading system, the time scale was four times as the reality. Fig. 7 is an example of earthquake loading tests. The dynamic strength for earthquake loading was defined in the same manner as sinusoidal loading tests as shown in Fig. 6 (b).

4.5 Frequency and random loading efects Fig. 8 (a) shows the frequency effect in sinusoidal loading. It may be seen that, in the majority of the cases, dynamic strength of residual shear surface increased around 5 to 20% when the frequency of sinusoidal loading became 10 times in the range of 0.1Hz to 1,OHz, though opposite frequency effects appeared in some cases. Dynamic strength against the earthquake loading (four times extended in time scale) was nearly the same level as 1.OHz sinusoidal loading as shown in Fig. 8 (b). The relationship between the frequency effect and physical properties of the material was hardly detected as shown in Fig. 8 (4.

Figure 8.

599

Effects of frequency and random loading on dynamic strength of residual slip surfaces

Figure 9. Dynamic strength characteristics and physical property of tested material

to 20%. In addition, the dynamic response to the random loading simulating earthquakes was examined. Using these test results, it was attempted to find if the dynamic behavior of pre-existing shear surface is correlated with the physical properties of the tested materials such as clay fraction. Though scatter of data was very large, it seemed that the higher the clay fraction, the larger the ratio of dynamic strength to slow residual strength. In most of the cases, the dynamic strength was 20 to 100% larger than slow residual strength.

ACKNOWLEDGMENT The ring shear tests on the material No. 8 to 16 (Table 1) were performed by Mr. Y. Kamegai (Chubu Electric Power Co.), Mr. K. Sat0 (Tokio Marine and Fire Insurance Co., Ltd.) and Mr. K. Amano (Shimizu Corporation).

REFERENCES Bishop, A.W., G.E. Green, V.K. Garga, A. Andresen & J.D. Brown 1971. A new ring shear apparatus and its application to the measurement of residual strength. Gkotechnique 2l(4): 273-328. Ijuin, R., K. Ishihara & J. Kuwano 1987.Residual strength and dynamic strength of pre-existing sliding surface. Proc. 42nd Annual Con$ of JSCE 3: 148-149 (in Japanese).

600

Kanji, M.A. 1974.The relationship between drained friction angles and Atterberg limits of natural soils. Gkotechnique 24(4): 671-674. Kuwano, J., K. Ishihara, R. Kuwano & M. Yoshimine 1991. Dynamic strength of cohesive soils from landslide sites. Proc. 1st Young Asian Geotechnical Engineers Con$: 207-216.Bangkok. Lemos, L.J.L., A.W. Skempton & P.R. Vaughan 1985. Earthquake loading of shear surfaces in slopes. Proc., 11th Int. Con$ Soil Mech. And Found. Engrg. 4: 19551958. Lemos, L.J.L., A.M.P. Gama & P.A.L.F. Coelho 1994. Displacements of cohesive slopes induced by earthquake loading. Proc., 13th Int. ConJ Soil Mech. And Found. Engrg. 3: 1041-1045. Lupini, J.F., A.E. Skinner & P.R. Vaughan. 1981. The drained residual strength of cohesive soils. Gkotechnique 31(2): 181-213. Skempton, A.W. 1964.Long-term stability of clay slopes. Gkotechnique 14(2): 77-102. Skempton, A.W. 1985. Residual strength of clays in landslides, folded strata and the laboratory. Gkotechnique 35(1): 3-18. Stark, T.D. & H.T. Eid 1994. Drained residual strength of cohesive soils. J. of Geotech. Engig., ASCE 120(5): 856871. Tika, TH. E., P.R. Vaughan & L.J.L. Lemos. 1996. Fast shearing of pre-existing shear zones in soil. Gkotechnique 46(2): 197-233. Tika, TH. E. & J.N Hutchinson. 1999. Ring shear tests on soil from the Vaiont landslide slip surface. Gkotechnique 49(1): 59-74. Voight, B. 1973. Correlation between Atterberg plasticity limits and residual shear strength of natural soils. Gkotechnique 23(2): 265-267.

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Dependence of pore pressure generation on frequency of loading at sliding surface D. A.Vankov & K. Sassa Landslide Section, DPRI, Kyoto UniversiQ Uji,Japan

ABSTRACT: This paper presents results of series of shear stress controlled and shear displacement controlled cyclic tests, conducted by an advanced model of ring shear apparatus, with different frequencies of loading. It was found that frequency of loading has an effect on shear displacement in shear stress controlled tests. Due to large shear displacement, mechanism of pore pressure generation was strongly affected by type of loading.

2 APPARATUS EMPLOYED

1 INTRODUCTION

A ring shear apparatus (DPRI-4) was used in present investigation. In addition to ordinary advantages of a ring shear device, such as limitless shear displacement, clear location of shear zone, etc, this apparatus has following features, which were important in carrying out our investigation: 0 Possibility of applying reversible cyclic shear stress; 0 In a cyclic loading test, either shear stress controlled or shear displacement controlled modes are available; 0 Undrained condition with pore pressure measurements along shear zone provided; 0 In a cyclic loading test, a frequency of loading up to 5 Hz can be produced; 0 Large shear box (approximately 2000 cm') enabling testing of coarse grain soils. The structure of this ring shear apparatus was described in details by Vankov & Sassa (1 998).

Extensive field investigations conducted after the 1995 Hyogo-ken Nanbu earthquake (Kamai 1995; Sassa et a1 1996), revealed that many landslides occurred on very flat slopes in urban and residential areas. These landslides usually formed in sandy soils. Some of them were reported to have moved several days after the main seismic shock. Generally, all houses and structures constructed on these landslides were not completely destroyed by the movement and no casualties were reported. However, since all these houses and structures should be rebuilt, they created substantial financial damage for owners. The mechanism movement in these landslides was not clear. However, it was suggested by the second author, that pore pressure generation might play a decisive role in landslide occurrence and movement. Therefore, the mechanism of pore pressure generation in sandy soils at potential sliding surfaces should be investigated in detail. Frequency of loading is one of possible factors affecting pore pressure generation at direct shear state. Completion of this task requires a series of basic experiments, for obtaining primary dependencies, however the sample condition as well as stress state at potential sliding surface should be reproduced with accuracy. It is believed by the authors, that an advanced ring shear apparatus is the most suitable device for studying the process of pore pressure generation at the sliding surface.

3 EXPERIMENTAL OUTLINES

3.1 Sarizple properties The soil used in our investigation was a coarse-grain sandy soil belonging to the MiddleUpper Subgroup of Plio-Pleistocene Osaka Group (Osaka Formation) widely distributed in the Kansai Area. The Osaka group consists of loose sedi-

601

Therefore, in extreme cases, these sandy layers could be completely saturated and during loading they would be in an undrained state. The same state should be provided during experiment. The high degree of saturation is necessary for obtaining correct data. Samples were saturated with help of carbon dioxide and back pressure. For checking of degree of saturation before cyclic test we used B, : the pore pressure coefficient in the direct shear state, which was devoted as:

ments made of gravel, sand and clay, and is divided into three subgroups, Lower, Middle and Upper. The Lower Subgroup is clearly distinguished from the others due to the absence of marine deposits. Differences between the Middle and Upper Subgroups are not so clear. Geomorphologically the Osaka Group forms hilly lands and uplifted areas. The sampling site was at the headscarp of the Takarazuka Landslide, triggered by the 1995 Hyogoken-Nanbu earthquake. The landslide was described in details by Sassa et al. (1996). The depth of the sampling point was about 4 meters. Totally more than 1000 kg of soil were taken by machine excavation. Results of the grain-size distribution analysis and basic physical properties are summarized in Table 1. The mineral composition analysis was carried out visually and shows that the investigated soil consisted mostly of quartz and feldspar, probably albite. Both of these minerals, being interacted with water are chemically passive, i.e. they are unlikely to change their physico-mechnical properties.

B, =-

Au (1)

AD

where Au and Ao are increment of pore pressure and total normal stress respectively. Xia & Hu 1991, reported that value of back pressure has significant influence on the liquefaction resistance of sands. They even suggested, that in liquefaction tests the back pressure technique should not be used to enhance the degrees of saturation of the tested sand. The observed phenomenon of the effect of back pressure can be summarized as: the higher the applied back pressure, the higher the liquefaction resistance of the sand. The goal of this research is not to simulate field conditions but to obtain principal dependencies of pore pressure generation on the rate of loading. In such cases back pressure technique could be used. Another sensitive aspect, is the moment of checking saturation degree, i.e. before or after consolidation of the sample. Measurement of pore pressure response before consolidation is rather common among geotechnical researchers (Drnevich 1972, Ladd 1977, Mulilis et a1 1977, Novak & Kim 1981, Towhata & Ishihara 1985, Figueroa et a1 1994, Boulanger 1995, Hatanaka et a1 1997). However, it was established by preliminary tests that in ring shear apparatus pore pressure response parameters after consolidation are substantially less (sometimes lcss than 50% of initial value) than before consolidation. Based on this fact, all BD parameters were measured after consolidation.

3.2 Saiizple preparation The procedure of preparation of samples for the tests was as follows. The sandy soil was dried at 105°C for 48 hours. Then it was removed from the oven and cooled. After that soils were dispersed by means of a rubber hammer and sieved through a sieve with a diameter of 4.0mm. The soil finer than 4.0mm diameter was used in the experiment. During field observations, it was concluded that sandy layers are sometimes confined between clayey ones and partially saturated. The permeability of clayey layers seems to be very low.

___Table 1. Basic properties of investigated soil. Parameter Value Grain size, mm 12% -2.00 2.00-0.84 36% 33% 0.84-0.42 0.42-0.25 7% 0.25-0.105 8% 0.105-0.074 2% 0.0742% Coefficient of uniformity (D60/D10) 5.55 1.17 Maximum void ratio Minimum void ratio 0.66 Specific gravity (g/cm') 2.61

Table 2. Parameters of SSC-tests. No f BD e 0'0 (Hz) (kPa) 1-s 0.01 0.95 0.77 220 2-s 0.05 0.95 0.74 213 3-s 0.10 0.98 0.75 201 4-s 0.50 0.96 0.72 210 5-s 1.00 0.97 0.71 206 6-s 2.00 0.96 0.67 199

602

U()

(kPa) 106 69 84 85 103 108

A (kPa) 52-58 52-58 52-58 52-58 52-58 52-58

Table 3. Parameters of SDC-tests.

1-d 2-d 3-d 4-d 5-d 6-d 7-d 8-d 9-d

0.01 0.02 0.04 0.08 0.10 0.20 0.30 0.40 0.50

0.95 0.97 1.00 0.97 1.00 0.95 0.96 0.95 1.00

0.68 0.68 0.67 0.66 0.66 0.67 0.67 0.67 0.67

200 200 192 195 182 204 202 169 202

47 50 57 63 68 39 47 51 56

1.00 0.98 0.98 0.98 0.96 1.00 0.92 0.86 0.76

Figure 2. Effective stress path for 4-s test

f -loading frequency, BD-pore pressure parameter in direct shear state, e-void ratio, 0'0-initial effective normal stress, UOinitial pore pressure, A-amplitude of shear stress, A*- amplitude of shear displacement.

3.3 Test program A series of shear stress controlled tests (hereafter SSC-tests) and shear displacement controlled tests (hereafter SDC-tests) has been conducted. The test parameters for SSC-tests and SDC-tests are given in Table 2 and Table3. All samples were subjected to reversible cyclic loading. Liquefaction was believed to have occurred when the pore pressure was not less than 95% of the total normal stress at all stages of loading.

Figure 3. Time series data for 6-d test

4 TEST RESULTS AND DISCUSSION Representative test data are plotted in Figures 1, 2 (SSC-data, time series and effective stress path, respectively), and Figures 3, 4 (SDC-data, time series and effective stress path respectively). In both types of test pore pressure gradually built-up and subsequently reached the value of total normal stress. Due to a decrease of effective normal stress the amplitude of shear displacement increases (SSC-test), and shear resistance decreases (SDCtest). When a sample reached liquefaction state the amplitude of shear displacement obtained its maximum value (SSC-test), and shear resistance 350 , , 500 300

250

m

200

4

100

& 7

200

0

m

2 3

-

000

w

-1 00

3

150

v)

'

100

3

50

-200 I

0 -50

-100

decayed to almost zero (SDC-test). This mechanism is almost the same for all tests conducted. In order to analyze whether the frequency of loading has any influence on pore pressure generation, the number of cycles required to liquefaction was counted and total dissipated energy required to liquefaction was calculated. Total dissipated energy per area of shear plane required to liquefaction, was calculated by means of following equation:

4 00

300

-

Figure 4. Effective stress path for 6-d test

300

' 0

3

4 00

-500 2

4

6

8

10

12

14

16

18 20

22 24

26 28 30

Time (sec)

Figure 1. Time series data for 4-s test

Where z is shear resistance, I is shear displacement, n is number of points recorded to liquefaction. 603

energy decreases abruptly, while in SDC-tests W decreases much more gradually. In terms of the absolute value of total dissipated energy required to liquefaction a large difference is observed at low-frequency range of testing, as loading frequency increases the difference is decreases. This effect is an outcome of variance in shear displacement during testing. In SDC test shear displacement is servo controlled by the apparatus and its amplitude is always the same. However, during SSC test shear displacement is dependent on the values of applied shear stress and shear resistance. At the beginning of tests, when shear resistance of a sample is large, shear displacement is almost equal to zero. As pore pressure is gradually built-up, under cyclic loading, shear resistance of the sample decays due to the decrease of effective normal stress and shear displacement gradually increases. During the final stage of testing, when pore pressure approaches the value of total normal stress, shear resistance drops almost to its zero value and shear displacement depends solely on the frequency of loading. The lower frequency is, the greater shear displacement becomes. In Figure 7 total dissipated energy is plotted versus cumulative shear displacement required to liquefaction. For both groups of points (SSC and SDC tests), linear trend lines were drawn and the value of the coefficient of correlation was calculated. For SSC tests the coefficient of correlation obtained, was very high (0.992), while for SDC test this parameter demonstrates a total absence of any correlation (0.064). This supports our idea, that value of total dissipated energy is controlled by shear displacement. From Figure 8 it is obvious, that most of energy dissipates while shear displacement is developing, because of the remaining shear resistance. On the

Figure 5. Dependence of number of cycles required to liquefaction (N) on frequency of loading (0in shear stress controlled (SSC) and shear displacement controlled (SDC) tests. It can be seen, from Figure 5 , that different types of test provide different tendencies, in terms of the number of cycles required to liquefaction. In SSC-test the number of cycles required to liquefaction increases with increasing loading frequency. However, SDC-tests demonstrate a different tendency, it appears that with increasing loading frequency there is no significant changes in the number of cycles required to liquefaction. The latter statement is in agreement with conclusions of other researchers, who reported an absence of influence of the frequency of loading on the dynamic behavior of sand (Wood 1982). Dependence of total dissipated energy required to liquefaction on loading frequency has similar trend for both types of testing. With increase of loading frequency, total dissipated energy required to liquefaction decreases as it shown in Figure 6. However, the character of the trend is different for SSC and SDC tests. In SSC-tests as the loading frequency increases total dissipated

Figure 6. Dependence of total dissipated energy required to liquefaction (W) on frequency of loading (0in shear stress controlled (SSC) and shear displacement controlled (SDC) tests.

Figure 7. Total dissipated energy required to liquefaction versus cumulative shear displacement in SSC and SDC tests. 604

nal friction angles are different from each other for SSC and SDC tests (Figures 2, 4). For SSC test it is 33O, while for SDC it is 31”. Therefore, sample exhibit more resistance to shearing during stress-controlled tests. The peak failure line for the same soil tested under monotone loading in drained condition inclined at 34”. During monotone shearing grain crushing certainly takes place. Although method of determination of friction angle has precision of about O.5O-l0, it could be stated that its value in SSC test is closer to that of monotone loading, than in SDC test. This is one more indirect evidence of possibility of grain crushing during stress controlled test. Therefore, we can assume, that if shear displacement starts, it can lead to liquefaction within the first 2-3 cycles. If dynamic load has a low-frequency spectra with magnitude large enough to induce shear displacement of about 2-4 mm, it could trigger grain crushing along the sliding zone with subsequent pore pressure generation. It is very probable, that there is a certain treshold value of shear displacement for given soil in a given stress condition. If shear displacement overcomes this threshold value, pore pressure will start to build-up, which ultimately will lead to liquefaction. Verification of this idea requires additional studies.

Figure 8. Time series of total dissipated energy (W) and shear displacement (1) for 4-s test other hand, a shear displacement reaches its maximum value, shear resistance is almost equal to zero, thus very small amount of energy is dissipated.However, during SDC-test shear displacement was constant and about 1 mm amplitude. Since shear resistance has highest values at first cycles, the largest amount of energy dissipated durins the first cycles (Figure 9). Therefore, the mechanism of pore pressure generation for different types of loading is different, from the standpoint of such criteria as total dissipated energy. It was also mentioned above, that absolute values of dissipated energy in each test vary significantly (Figure 6). These differences could be explained on the basis of grain crushing phenomena. The necessary condition for grain crushing is movement of particles, i.e. shear displacement. It is very likely, that during large shear displacement grain crushing occurred. This would lead to an increase of dissipated energy and pore pressure generation because of volume shrink in the shear zone due to comminution of crushed particles. This phenomenon is called “sliding surface liquefaction” (Sassa 1996). The fact that the number of cycles required to liquefaction increases with increasing of loading frequency (for SSC-tests), supports this explanation. It also should be noted that values of inter-

5 CONCLUSIONS After a series of shear stress-controlled and sheardisplacement controlled tests with different frequencies of loading were performed on sandy samples the following conclusions could be drawn: Frequency of loading has direct influence on magnitude of shear displacement in shear stress-controlled tests. With increasing of loading frequency, shear displacement increases. Due to increase in shear displacement, the value of total dissipated energy increases in the same manner. For shear displacementcontrolled tests the value of loading frequency has little effect on value of total dissipated energy. Liquefaction within first few cycles is possible under low frequency of loading due to grain crushing and comminuting along sliding zone.

REFERENCES Boulanger R.W., Seed R.B. 1995. Liquefaction of sand under bidirectional monotonic and cy-

Figure 9. Time series of total dissipated energy (W) and shear displacement (1) for 6-d test 605

clic loading I/ Journal of Geotechnical Engineering Division. 121:870-878. Drnevich V.P. 1972. Undrained cyclic shear of saturated sand. Journal of the Soil Mechnics and Foundations Division, Proceedings of ASCE. 98: 802-825. Figueroa J.L., Saada A.S., Liang L., Dahisaria N.M 1994. Evaluation of soil liquefaction by energy principles. Journal of Geotechnical Engineering. 120(9):1554-1569. Hatanaka M., Uchida A., Ohara J. 1997. Liquefac tion characteristics of a gravelly fill liquefied during the 1995 Hyogo-ken Nanbu earthquake. Soils and Foundations. 37(3): 107-115. Kamai T. 1995. Landslides in Hanshin Urban Region Caused by 1995 Hyogoken-Nanbu Earthquake, Japan. Landslide News. 9: 1213. Ladd R.S. 1977. Specimen preparation and cyclic stability of sands. Journal of Geotechnical Engineering Division, Proceedings cf ASCE. 103(6): 535-547. Mulilis J.P., Seed H.B., Chan C.K., Mitchell J.K., Adanandan K. 1977. Effects of sample preparation on sand liquefaction. Journal of Geotechnical Engineering Division, Proceedings ofASCE. 103(2):91-108 Novak M., Kirn T.C. 1981. Resonant column technique for dynamic testing of cohesive soils. Canadian Geotechnical Journal. 18: 448-455. Sassa K., Fukuoka H., Scaraccia-Mugnozza G., Evans S. 1996. Earthquake-InducedLandslides: Distribution, Motion and Mechanisms. Soils and Foundations (special issue on Geotechnical Aspects of the Junuary 17 1995 Hyogoken-Nambu Earthquake53-64. Towhata I., Ishihara K. 1985. Shear work and pore water pressure in undrained shear. Soils and Foundations. 25(3):73-84. Vankov D. A., Sassa K. 1998. Dynamic Testing of Soils by Ring Shear Apparatus. Proceedings of 8‘” Congress of IAEG, Vancouver, Canada, (1):485-492. Wood D. M. 1982. Laboratory investigation of the behaviour of soils under cyclic loading: a review. in the book “Soil Mechanics-Transient and Cyclic Loads”, edited by Pande and Zienkevich:5 13-582. Xia H., Hu T. 1991. Effects of Saturation and back Pressure on Sand Liquefaction. Journal of Geotechnical Engineering. 117(9):1347-1362. 606

Slope Stability Engineering, Yagi, Yamagami & Jiang k j 1999 Balkema, Rotterdam, ISBN go 5809 0795

On-line earthquake response tests on embankments founded on saturated sandy deposits T Fujii Fukken Company Limited, Hiroshimn, Japun

M. Hyodo, Y.Nakata & K.Yabuki Deparbrient of Civil Engineering. Yhiaguchi Uni\wsity, Ube,J c p a n

S. Kusakabe Okunzuru Conipuny Limited, Tsukubci, Japun

ABSTRACT River dykes and road embankments are frequently damaged during earthquakes. The liquefaction of foundation, the behavior of which is not yet well realized. is considered to be the main cause of the damage. Based on the results of past studies, the foundation of an embankment was divided into three zones to examine the failure modes. One-dimensional on-line earthquake tests, which were conducted by a combination of element tests and computer earthquake response analyses, were performed for such zones of actual river dykes damaged during earthquake. The cumulative horizontal displacement values obtained by the tests were compared with the measured enibanknient-crest settlement data, which showed that the liquefaction sliding failure under the toe of slope of such an embankment is found to be the most detrimental of all failure modes. 1 INTRODUCTION Numerous river dykes and road embankments suffered severe damages in the 1994 HokkaidoNanseioki Earthquake and the 1995 HyogokenNanbu Earthquake. Since rivers have long embankments and small breakage of embankments may be permitted where such failure dose not cause a disastrous overflow, it has long been a cherished desire of engineers to establish a method of predicting the magnitudes of deformation of river dykes under earthquakes. The liquefaction of fourdation, the behavior of which is not yet well realized, is LuA3deredto be the main cause of the damase. Based on the results of past studies, the foundation of an embankment was divided into three zones to examine the failure modes. Considering the embankments of the ShiribeshiToshibetsu River struck by the I994 HokkaidoNanseioki Earthquake, the authors performed onedimensional on-line earthquake tests which were a combination of element tests and computer earthquake response analyses under the boundary conditions of failure modes in the three zones of each embankment. The crest settlements of the river embankments, measured in the field, and the cumulative horizontal displacements of their foundations obtained by the on-line earthquake response tests were compared to find which failure mode contributes most to such crest settlement.

2 CLASSIFICATION OF FAILURE MODES According to the study by Koga and Matsuo with a shaking table (1990), different typical modes of earthquake behavior were observed in three zones; i.e., a zone directly under an embankment, a zone under the toe of slope, and a zone of the horizontal glL.:iid, In the horizontal ground, the exce~sf-?rewater pessure ratio rose close to 1.0 to causc liquefactioa in the ground. In the zone directly under the embankment, although the excess porewater pressure ratio rose to less than 0.6, residual deformations in both the vertical and horizontal directions were built up. In the zone under the toe of the slope, though the pressure ratio did not reach 1 .O, the deformation in the horizontal direction was large, forming a circular slip surface, as is shown in Fig. 1. Thus three liquefaction failure modes were identified in the horizontal ground (Zone I>, circular slip under the toe of slope (Zone IQ, and shakedown directly under the embankment (Zone 111). Fig. 2

Fig. 1. Result of shaking table test

607

Fig. 2. Classification of failure modes shows the failure modes, condition of elements, effective stress paths, and stress-strain relations. To verify the validity of the above zoning and classification of the failure modes, on-line earthquake response tests were carried out.

3 OUTLINE OF ON-LINE RESPONSE TEST

EARTI-IQIJAKE

Fig. 3 shows the concept of the on-line earthquake response test (Kusakabe et al. 1990). A system of lump mass on the ground is modeled. and earthquake ground motion is input from the base of the layers to be examined. The equation o l motion of the lump-mass model is solved by a computer to find corresponding displacements in the ground. Then, shear strains equivalent to the corresponding displacements are applied to specimens under coinputer control to measure shear stresses automatically, and shear stresses are used for the calculation of the corresponding displacemcnts of the next step. This process is repeated for the

duration of an earthquake. In this way, the continuously changing non-linear shear stress response in the ground during an earthquake are obtained directly from element tests of specimens, and they are processed on-line by a responseanalyzing system to simulate the behavior of the ground. For cyclic loading tests, the simplified simple-shearing tester developed by Kusakabe (1 999) is available. 4

TESTRESULTS

The embankments of the Shiribeshi-Toshibetsu River struck by the 1994 Hokkaido-Nanseioki Earthquake developed, at their top surfaces, crest settlements of over 2 meters. Fig. 4 shows the cross s e c t i o n ( N o . 1 s e c t i o n ) o f t h e most s e v e r e l y damaged embankment. Soil investigation carried out after the earthquake revealed the N values of the alluvial sand layers As, and AsZto be as low as 3-7, suggesting their liquefaction during the earthquake. In this study, therefore, the layers As, and As2 were 608

Fig.3. Conceptual flow for on-line testing

Fig.4. Section of damaged river dyke treated as the on-line layers the other layers were treated as non-linear elastic bodies. Fig. 5 shows that each zone of the two-dimensional section was replaced by a one-dimensional lump-mass model. For the initial shear stress acting on and around the toe of the slope due to the dead weight of the embankment, the static circular slip analysis was performed to calculate the average shear stress, which was applied to the model in advance of the testing. Toyoura sand of such relative density as

Presents a liquefaction strength curve overlapping that of the undisturbed sand in situ, as is shown in Fig. 6 was used in the tests. The other conditions for the tests and analyses were also set up based on the results of the soil investigation. The acceleration waveforms recorded by the Suttsu Observatory were modified by taking into account the damping over distance to obtain the input earthquake motion, which was an input from the bottom of the layer AC2. Fig. 7 shows the input acceleration waveform and the corresponding mass acceleration waveforms in Zone I. The period of the waveform was prolonged in the upper liquefaction layers rn, and m?. The amplitude of the waveform was amplified in the clay layers m6 and m,, damped in the liquefaction layers m4, m3 and m2, and again amplified in layer m1. Fig, 8 and Fig. 9 show the effective stress paths and the stress-strain relationships, respectively, of the on-line layer As2 in the zones. In Zone I, the effective stress reached almost zero and the shear modulus decreased rapidly, indicating the occurrence of liquefaction. In Zone 11, the effective stress did not reach zero due to the initial shear stress but reached a steady state when it approached the phase-changing line. Simultaneously. the shear strain began to develop rapidly, indicating the occurrence of sliding failure with a liqued flow. In Zone 111, the effective stress decreased by only 30% or so and reached a steady state without reaching the phase-changing line, and although there occurred vertical strain of a few percent, it hardly increased after the effective stress had reached a steady state. Figs. 10 (a) and ( b ) s h o w t h e calculated magnitudes of settlement of the embankment in Zones I1 and 111. The magnitude of settlement of

Fig. 5. On-line testing model

609

soil by the thickness o f soil was regarded as equivalent to the crest settlemcxt of the embankment, assuming that sliding failure crvies the soil within the circular slip surface uniformly. In Zone 111, the settlement was calculated from the vertical strain in soil multiplied by the thickness of soil. Zone I does not appear here because no residual shear strain or vertical strain occurred. It is apparent from these figures that large settlement occurred in the on-line layers in both Zones I1 and 111. The Zone I1 settlement picked up rapidly about 10 seconds after the startup to reach over 60 cm, whereas Zone 111 exhibited a settlement growing rapidly i n the first 10 seconds or so, progressing slow thereafter. and reaching a mere 10 cm or so finally. In Fig. 10 (a), the cumulative curves terminate at around 20 seconds after the startup, because the strain-measuring range of the tester was 25%. If the test had been continued up to 40 seconds, it should have presented considerably large settlements. The above results are consistent with those of the shaking table test mentioned earlier, proving the validity of the classification of the failure modes made in the present study. Zone I1 of the sliding failure which was liquefied exhibited the largest strain, which seemed to be the main cause of the heavy crest settlement of the embankment.

Fig.6. Cyclic shear strength

5 COMPARISON OF DEFORMATIONS

Fig. 7. Input acceleration

acceleration

and

responding

each layer was calculated by multiplying the strain obtained in tests by the thickness of the layer, and all the settlement magnitudes of the layers were summed to obtain the magnitude of settlement of the embankment. In Zone 11, the shear displacement calculated by multiplying the residual shear strain in

The above tests indicated that the failure mode most detrimental to an embankment was the sliding failure under the toe of the slope (Zone 11). Accordingly, further damaged (No. 3 and 5 sections in addition to No. 1 section) and undamaged (No. 2 and 4 sections) embankments of the River were chosen, and on-line earthquake response tests for their Zones I1 were carried out. In Fig. 11, the cumulative horizontal displacement values obtained by the tests are compared with the crest settlement values of the embankments measured in the field. Although the values of displacement obtained by the tests are not in such so good agreement with the measured values of settlement, the former well reflect the trend of the latter. One factor contributing to the underestimation of the settlement by the tests would be that the survey of the ground deformation was carried out several days after the earthquake, allowing later subsidence due to the dissipation of pore water pressure. a d d i t i o n a l p e r m a n e n t deformation over time. and so on. Another factor is that the soil properties of the ground would have changed under the influence of the earthquake hampering the accurate estimation of the input acceleration based on the liquefaction strength and daniping over distance. It was assumed in the present study that sliding failure with a circular slip 610

Fig. 8. Effective stress paths

Fig. 9. Stress-strain relations

Fig. 10 Cumulative

61 1

settlement

Kusakabe, S., Morio, S., Okabayashi, T., Fujii T. and M. Hyodo (1999). Development of a simplified simple shear apparatus and its application to various liquefaction tests, Journal of Geotechnical Engineering, No. 617, m-46,pp.299-304.

Fig. 11 . Comparison between results of on-line tests and results of measured in situ of crest settlement surface occurred in the soil directly under the damaged embankments. However, the embankments should also have been subjected to the effects of the nearby liquefaction. In addition, although no damage was reported for the No. 2 and 4 embankments, the above tests suggested that some horizontal displacement occurred. When these factors are taken into account, it can be said that the cumulative horizontal displacement values obtained by the on-line earthquake response tests are in fairly good agreement with the crest settlement values measured in the field. 6 CONCLUSION In this study, the foundation of an embankment was, on the basis of the results of past studies, divided into three zones for the examination of failure modes, and a liquefied sliding failure occurring under the toe of slope was ascertained being the most detrimental failure mode, though other modes, should of course, be considered together with it since actual failure involves multiple factors and modes. The approach taken in this study proved itself to be a feasible method for estimating the earthquake crest settlement of river dykes.

REFERENCES Koga, Y. and Matuo 0.(1990) . Shaking table tests of embankments resting on liquefiable sandy ground, Soils and Foundations, Vol.30, No.4, pp. 162174.

Kusakabe, S., Morio, S . and Arimoto, K.(1990). Liquefaction phenomenon of sand layers by using on-line computer test control method, Soils and Foundations, yOl.30, No.3, pp. 174-184. 612

Slope Stability Engineering, Yagi, Yamagami& Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Dynamic centrifuge tests of embankments on sloped ground and their stability analyses Junichi Koseki - Institute of Industrial Science, University of Tokyo,Japun O S ~Matsuo U - Public Works Research Institute, Ministry of Construction,Jupan Koichi Kondo - Nugushimu Dam Construction Office, Ministry of Construction,Jupan Satoshi Nishihara - Geo-TechnologicalAnalysis Division, Chuo Kaihutsu Corporation,Japun

ABSTRACT: Dynamic centrihge tests were performed on model sandy embankments with a height of 20 cm, which were prepared by compacting Edosaki sand having a mean diameter of 0.17 mm on a rigid slope ending with a flat base layer. After adjusting the oil table used as pore water, a centrihgal acceleration of 40 or 50 G was applied t o the model, and it was shaken horizontally with 20 cycles of sinusoidal waves at 100 Hz.Limitequilibrium and pseudo-static stability analysis assuming a circular failure plane was conducted on the tested models, in which combined effects of excess pore pressure generated in the submerged portion of the embankment and inertia force during shaking were considered. In general, with increase in the crest settlement, the calculated safety factor decreased irrespective of the oil table. On the other hand, different relationships between these values were obtained for cases with different degree of compaction.

1 INTRODUCTION The 1993 Kushiro-Oki earthquake caused severe damage to road embankments constructed on sloped ground in hilly area. Based on survey results conducted after the earthquake, it was estimated that the damage was induced by reduction in the shear strength of the fill material which was partly submerged in the ground water, as typically shown in Figure 1 (PWRI, 1994). However, it has not been fully understood how the ground water affects the seismic behavior of embankments on sloped ground. In the present study, to investigate the effects of the ground water on the seismic stability of embankments on sloped ground, a series of dynamic centrifuge tests were performed with changing the ground water level in the embankment and some other configurations.

2 TESTING PROCEDURES A typical cross-section of the tested model is shown in Figure 2. In a rigid soil container having inner dimensions of 800 mrn in length, 200 mm in width and 300 mm in depth, a rigid original slope that ends with a rigid flat base layer was made with gypsum. Then, embankment was filled by using a fine sand

613

retrieved from Edosaki Town, Ibaraki Prefecture, Japan, having a mean diameter of 0.17 rmn and uniformity coefficient of 2.0. In several layers having a thickness of about 2 cm, the embankment was compacted at an optimum water content of 19 % to a specified degree of compaction, D ("A), defined as:

where pd is the dry density of the embankment, and Pdmax is the maximum dry density of the sand that was determined to be 1.588 glcm' based on standard compaction tests. In total, seven models as listed in Table 1 were tested. The inclination a: of the original slope was set to 35 degrees in cases 2-5 through 2-7 and to 30 degrees in other cases. The embankment was made to have crest width of 200 mm and the same slope inclination as the original slope. In case 1-3, the embankment was compacted relatively heavily to the D value of 85 %, while in other cases the D values were set about 80 %. It is to be noted that, as shown in Figure 2, the actual model configuration was slightly modified according to the rotational radius of the centrifuge. In cases 1-3 and 1-4, the whole sand box was put in a larger box in order to apply a partial vacuum to the embankment. Under this condition, silicone oil

Figure. I Cross section of road embankment at Higashi-Arekinai, Shibecha Town along National Highway Route No. 272 damaged by the 1995 Kushiro-oki earthquake (PWRI, 1994) mm, lower: WL=80 mm) .

+ \A& 5-- DV

I

I

A

s

1 : Displacement gage (DV) I 0 : Horizontal accelerometer (A) : vertical accelerometer (AV) i 0 : Pore pressure gage (P)

: Oil level (upper: wL=160

- ---

of colored sand

_------

\

c _ _ / - - c

----I

Original

L I

160

W

N

0

O

N P-

'"80AU,

, 60

1

a

I

@

, 60 ,

140

I

160

i

I @

a

Unit inmm (R: rotational radius)

Figure. 2 Cross-section of model embankment having a slope inclination a equal to 35" which is 50 times as viscous as water was injected from the bottom of the embankment to submerge it up to a specified height, WL, measured from the base layer. After setting the sand box to the rotor, a centrifugal acceleration of 50 G was applied, and several steps of horizontal shaking were conducted by using 20 cycles of sinusoidal waves at a frequency of 100 Hz. On the other hand, in cases 2-5 through 2-9, the same silicone oil as used in cases 1-3 and 1-4 was poured i n t o the o p e n space at t h e side of t h e embankment. By applying a centrifugal acceleration to the model, the embankment was submerged to the specified height, WL. After stopping the rotation, excessive silicone oil that was left in the open space was expelled. A centrifugal acceleration of 4 0 G

614

Table

2-5 2-6 2-7 2-8

2-9 __

Clonditions of model embankments Slope I Oil* tablein I Centrihgal inclination, embankment, acceleration, n,/ WL / amplitude of al existence of base shaking degree of acceleration in compaction, oil table in open space each step, abase** D 30°/85.2% 80mmiyes 50/6.9,14.5,18.6C 30"/ 79.2% 1 6 0 d yes 50/ 6.8,13.3G 35"/79.8% 160mm/no 40/ 13.1, 12.6G 35"/ 81.4% 80mmlno 40/ 12.5, 12.6G 35'/80.9% Odno 40/ 13.8, 14.3G 30"/ 80.2% 40/ 10.9, 12.2G 801nm/ no 307 79.4% O m m / no 40/ 14.2, 14.3G

L -:I . 311

** by 2o cycles ofsinusoidal waveS at

Hz

Applied case 1-3

Degree of compaction, D about 85%

Submerged region

Unsaturated region

beIow oil

above oil

table

table

c=O,

c=3.9kPa, 4 =35" c=2.9kPa, 4 =33"

(5 =45"

1-4 and 2-5

Base layer

.

'

through 2-9

'

Figure. 3 Circular failure plane assumed in the stability analysis was reapplied quickly in order to maintain the submerged condition in the lower part of the embankment, and several steps of horizontal shaking were conducted by using the same input form as in cases 1-3 and 1-4. It should be noted that lowering of oil table in the embankment during the process of reapplying the centrifugal acceleration could not be prevented in cases 2-5 through 2-9. By monitoring the pore pressure gages installed in the embankment, attempts were made to evaluate the oil table at the time of shaking. However, accurate evaluation was not successfully made, due possibly to effects of partial suction in the unsaturated layer. For simplicity, lowering of the oil table was neglected in the following analysis.

3 STABILITY ANALYSIS

Based on the modified Fellenius method assuming a circular failure plane as shown in Figure 3 , which is one of the Iimit-equilibrium and pseudo-static analyses, a factor of safety F, of the model embankment was evaluated as:

where kh is the horizontal seismic coefficient; r is the radius of t h e failure plane; Wi, b, and Li are the weight, the horizontal width, the bottom arch length of i-th soil block, respectively; hi is the vertical distance between the mass center of the i-th soil block and the center of the circular failure plane; fi i is the average angle of the partial failure plane at t h e bottom o f the i-th soil block measured from the

about 80%

c=O, (5 =42"

horizontal direction; and U; is the pore pressure acting on the bottom of the i-th soil block that is evaluated as a summation o f the hydrostatic pressure U,; and the excess pore pressure dui induced by shaking. In the present study, values of c and 4 , cohesion and shear resistance angle of the embankment, were determined as listed in Table 2 based on triaxial test results on specimens with 5 cm in diameter and 10 in height, which were prepared by compacting the sand in a mold in the same way as employed to prepare the embankment. By neglecting the amplification in the response acceleration of the embankment, the value of kt, was determined from the amplitude of the base shaking acceleration abase as

where nE is the centrihgal acceleration applied to the embankment (either 50 G or 40 G). Further, the value of Au; was determined by dividing the submerged region of the embankment into several sub-regions and by assuming a uniform distribution of the excess pore pressure ratio A U ~ O , ~ ~ ' within each sub-block, which was assigned based on the maximum excess pore pressures measured by pore pressure Sages installed in the embankment. The initial effective overburden pressure o,~' was calculated one-dimensionally. For cases 1-3 and 1-4 having free oil table in the open space at the side of the embankment, effects of hydrostatic oil pressure applied to the slope surface in the submerged region were also considered in the analysis.

4

RESULTS AND DISCUSSIONS

Typical r e s p o n s e s o f t h e m o d e l embankment recorded during shaking are shown in Figure 4. Generation of excess pore pressure during shaking was observed i n the submerged portion o f the

615

. .. .

-.

... : Before first shaking . After first shaking

1Not observed Figure. 5 Residual deformation of embankment after the first shaking step in case 2-5

Figure. 4 Recorded responses in the first shaking step of case 2-5

embankment, and the crest settlement accumulated mostly during shaking. These behaviors suggest that the combined effects of the excess pore pressure and the inertial force should be considered in analyzing the stability of model embankments under the present testing conditions, It is also seen from Figure 4 that the excess pore pressures did not reach their maximum values simultaneously. Further, horizontal response accelerations were not the same as the horizontal base acceleration, and vertical response acceleration measured at the crest was much larger than the vertical base acceleration. However, these behaviors were not considered in the stability analysis. Residual deformation of the embankment in case 2-5 observed after the first shaking step is shown in Figure 5 . The whole embankment deformed largely by the shaking, and a failure plane having a relatively small radius was formed near the slope surface. Similar failure planes were formed in cases 2-5, 2-6

Figure. 6 Relationships between horizontal seismic coefficient and normalized crest settlement

616

and 2-8, in which the embankment was partially submerged without having a free oil table in the open space at the side of the embankment. Because these failure planes did not cross the crest in these cases, it was estimated that the crest settlement was caused mainly by s h e a r d e f o r m a t i o n o f t h e w h o l e embankment. N o t e also that no failure plane was formed in other cases. Therefore, in the present study, the F, values evaluated by assuming a circular failure plane should be regarded as an index indicating the relative extent of the combined effects of the inertia force and the excess pore pressure as well as those of

Figure. 7 Relationships between horizontal seismic coefficient and safety factor

Figure. 8 Relationships between safety factor and normalized crest settlement

different initial configurations and densities, which may be correlated with the extent of the damage although they do not directly reflect the actual failure mechanism. To investigate a possible link with the amount of residual crest settlement measured at the shoulder (DV in Figure 2), the F, value was evaluated by assuming a failure plane crossing the lines a-a’ at the crest and b-b’ at the toe of embankment, as shown in Figure 3 , which mobilize a relatively large failure zone including both the crest shoulder and the lower part of the embankment. Figure 6 shows relationships between t h e horizontal seismic coefficient kh that was calculated from the base shaking acceleration using Eq. (3) and the crest settlement induced by each shaking step that w a s n o r m a l i z e d by d i v i d i n g w i t h t h e i n i t i a l embankment height (=200 mm). At nearly the same value of kh about 0.3, the normalized crest settlement was larger for the cases having higher oil table (i.e., with larger value of WL). When cases with the same oil table are compared, it is seen that embankments having a steeper slope (Le., with a = 3 5 O as shown by solid symbols in the figure) showed larger settlement. On the other hand, the embankment in case 1-3 that

was compacted to the D value of 85 YO showed smaller settlement than those compacted to the D value of about 80 %. Relationships between the kh and the F, values are shown in Figure 7. At nearly the same value of kh, embankments having higher oil table yielded smaller F, values With the same oil table, embankments having a steeper slope yielded smaller F, values. Further, in cases 1-3 and 1-4 having free water table in the open space at the side of the embankment, the F, value was reduced with the increase in the khvalue Consequently, as shown in Figure 8, relatively unique relationships were obtained between the F, value and the normalized crest settlement. In general, the F, value was reduced with the increase in the normalized crest settlement. On the other hand, at the same F, value, the normalized settlement was smaller for the embankment in case 1-3 that was compacted to the D value of 85 % than those compacted to the D value of about 80 %. Such different relationships may be caused by difference in the residual deformation behavior of embankments compacted at different degrees of compaction and subjected to cyclic loading, which was not considered in evaluating the F, value.

617

these values were obtained for cases with different degree of compaction. Further investigations on procedures to evaluate the seismic coefficient and the excess pore pressure and those on possible scale effect are required in order to employ the above relationships in designing actual sandy embankments.

It is also seen from Figure 8 that the normalized crest settlement in the second shaking step was sometimes smaller than that in the first shaking step in spite of the reduction in the F, value. This may be caused by the change in the embankment configuration and possibly by the change in the oil table in the embankment due t o the previous shaking hstory, which were not considered in evaluating the F, value. Figure 8 may be used t o roughly estimate the amount of seismically induced crest settlement of actual sandy embankments from the F, value obtained by the stability analysis under the same conditions as employed in the present study; i.e., strength parameters of the embankment material are determined from relevant triaxial compression tests; combined effects of the excess pore pressure and the inertial force are considered in the same way as in the present analysis; and the embankment configurations with respect to the slope angle, crest width, and the degree of compaction are similar to those in the present model tests. However, further investigations are required to determine horizontal seismic coefficient that is equivalent t o the actual irregular seismic motion, to estimate the distribution of excess pore pressure rationally, and to check if there is a scale effect on the behavior of the tested models.

REFERENCES Public Works Research Institute. 1994. Report on the disaster caused by the Kushiro-oh Earthquake of 1993, Repoyt of PWRI, Ministry of Construction, Japan, Vol. 193, pp.158-170 (in Japanese).

5 CONCLUSIONS

The results of the present study could be summarized as follows. 1) For model sandy embankments compacted to 80 % or 85 ?40 of the maximum dry density, excess pore pressure was generated in the submerged portion by shaking. The crest settlement accumulated mostly during shaking. These behaviors suggest that combined effects of the excess pore pressure and the inertial force should be considered in analyzing the stability of model embankments under the present testing conditions. 2) The major failure mode of the model embankments was overall deformation, while a failure plane was also observed near the surface of the embankment slope for submerged cases without free water table at its side. Therefore, safety factors obtained by assuming a larger circular failure plane should be regarded as an index which may be correlated with the extent of the damage although they do not directly reflect the actual failure mechanism. 3) With increase in the crest settlement induced by each shaking step, the calculated safety factor decreased in general. Different relationships between 618

Slope Stability Engineering, Yagi, YamagamigJiang 0 1999 Balkema, Rotterdam, ISBN go 5809 079 5

Evaluation of liquefaction potential for loose minefill slopes €? Kudella Institute of Soil Mechanics and Rock Mechanics, Universityof Karlsruhe, Germany

ABSTRACT: Uncompacted embankments of certain fine sands exhibit a spontaneous liquefaction potential, which cannot be evaluated based on undrained shear strength alone. A novel procedure for stability analysis has been developed, based on Hill’s stability criterion and a hypoplastic constitutive law. With given relative densities, assumed initial stress states and variations of perturbation directions, stability or instability of slope sections can be assessed. Catastrophic landslides observed in the past could thus be explained.

1 INTRODUCTION

1.2 Conventional failure analysis

1.1 Spontaneous liquefaction

Usually, stress equilibrium analyses are performend for risk assessment of embankments. Characteristic shear strength values are taken from undrained triaxial tests with undisturbed or reconstituted samples. These tests typically exhibit a raise of porewater pressure and a deviatoric stress peak before reaching a plateau with a lower - or even zero - shear resistance (Ishihara 1993).

The East German open-pit lignite mining has left large areas of refilled sandy mining deposits behind embankments of up to 70 m height. During the next decades, the groundwater table will rise again to its original level creating an artificial lakeland. Some of the prevailing sands exhibit significant liquefaction potential when inundated. The most important factors which contribute to this behaviour are: Extremely inhomogeneous, mainly loose packing due to ”moist dumping” without densification; Unknown stress state due to the dumping process, including residual shear stresses; Uniform grain size distribution and rounded grain shape; Insufficient drainage due to small grain size. Prior to inundation, the unsaturated material is stable due to capillary forces. Quite a number of catastrophic landslides have been observed already, involving up to 12 Mio. m3,claiming a number of lives and causing great material damage (Warmbold & Vogt 1994). Sometimes, large moving loads or stabilization measures can be identified as so-salled ”initials” triggering spontaneous liquefaction events. Great efforts are made to minimize danger before the land is rendered to public use. Common techniques are vibrofloatation and compaction by blasting (Raju & Gudehus 1994). There is urgent need for a rapid and economical evaluation procedure for the remaining liquefaction risk and also for quality control of stabilization measures.

For different initial stress levels, deviatoric stress peaks can be connected with an ”instability line” in the p-q-diagramm (Lade 1992) or a ”collapse surface” (Sladen e.a. 1995), and have been compared with results calculated for special constitutive laws (Doanh e.a. 1997). According to the experts opinion, either the undrained peak strength c , , ~= a‘ tan pupor the steady state strength c,, = CT’ tan pIL,(Poulos e.a. 1985) or any value in between is introduced into conventional slope failure mechanisms. This approach, however, cannot capture the problem for the following reasons (Gudehus 1993): e

a

Q

Q

Mechanical histories in reality are far different from the triaxial test regime, and they vary with the soil element’s position in the slope; For a soil skeleton with overcritical void ratio, brittle failure may propagate from weak points where the peak has been passed; Clearly defined slip surfaces are not observed; Residual strength cannot be determined confidentially in most triaxial tests due to restricted deformation capacity or early bifurcation.

That means that any evaluation of slope stability requires a high portion of empirical judgement. Coinci619

1998), but it seems justified as long as only the inundated soil body after macrovoid breakdown is considered. The following properties are implied:

dence of calculation and observation may be incidential.

1.3 Stability concept e

0

Effective stress principle and rate-independence hold; The soil state is characterized only by grain pressures and void ratio;

e

Characteristic limit void ratios (critical, upper and lower limit e,, e, and e d ) decrease with mean pressure;

e

Proportional strain paths lead to proportional stress paths independent of the initial state;

The stress rate tensor can be written (v. Wolffersdorff 1996): as

Figure 1: schematic energy cases (left = stable, right = instable) Our novel stability evaluation approach uses a consistent energy-based definition of stability (Hill 1958). A system in static equilibrium is unstable, if a small perturbance of the actual state exists for which an excess second order work will be released as kinetic energy and accelerate the initial motion (see fig. l a as an example). If a soil element of volume V under external dead loads cij is subjected to a monotonic initial deformation gradient, say gij = dvi/dzj in an arbitrary direction, the excess second order work reads (Drucker

1964):

The criterium only gives a yes-or-no-answer for the actual state: A 2 E 2 0 means stability and A2E < 0 instability. It cannot answer questions about the future system behaviour after non-vanishing deformations or about the amount of necessary energy to transform the system from one equilibrium state to another (fig. lb). For evaluation of the actual state, the second order energy can be summarized over a set of elements under infinitesimal deformations forming a kinematic chain (fig. lc).

2 CONSTITUTIVE LAWS

For non-symmetric$ deformation gradients, the corotated stress rate d.has to be transformed into the initial configuration a’: but in most cases, the simplification 8/is sufficient. The factors HI,H2, H3 describing the incremental stiffness depend on mean pressure and relative density. The derivation is explained elsewhere in detail.

a’

N

The equations require 8 constants as material parameters: critical friction angle (pc),granulate hardness (h,), minimum, critical and maximum void ratio at zero pressure ( e d o , e d , eio) and three exponents ( a ,b,72). They can all be referred to granulometric properties and be determined on reconstituted samples using laboratory element tests and standard index tests (Herle 1997). 2.2 Partial saturation

Eq. (2) describes the effective stress development only. Due to field data, degrees of saturation in the order of S,.= 0 , 8 ...O, 95 are reached after inundation. Using Boyle-Mariotte’s law p G + $& = 0 and assuming that the pore gas fraction V, is distributed in the pore liquid forming isolated bubbles, the gas pressure (initial atmospheric plus hydrostatic pressure, p positive) rate can be expressed as

2.1 Hypoplasticity

For calculation of the stress rates in eq. ( l ) , a hypoplastic soil model is used which has proved it’s ability to predict the pre-failure stress-strain-relation of the soil under changing stresses and densities (Gudehus 1996). It holds for so-called ”simple grain skeletons” where the stress transfer can be characterized by the mean values of grain contact forces alone. It’s applicability has been questioned with regard to macrovoids and pseudo-grains of moist minefill sands (Herle e.a. 620

Capillary effects can be accounted for by a further constitutive law (Gudehus 1995), but they can be neglected for fine sands. In that case the generated gas pressure is transferred totally to the pore water, and we thus expect a pore pressure increase for contractive and a drop for dilative deformations.

3 STABILITY ANALYSIS 3.1 Stability criterion Combining eqs. (2) and (3) with eq. (1) and omitting small terms, the stability criterium for an unsaturated soil element finally reads

The lower the relative density, the wider the range of possible stress states with instable deformation paths. As the second term for the pore pressure is always positive, a low degree of saturation always stabilizes the grain skeleton. One of the advantages of the above criterion is that no time integration of the constitutive equation is required. For the same reason, however, it can only provide a snapshot-like criterion for the actual state.

Figure 3: critical void ratios for different angles 6 and horizontal pressures

3.2 Single soil element

has to be satisfied and determines the unknown initial dilatancy v (or contractancy if it is negative). Fig. 3 shows ”critical” (in the sense of A’E = 0) relative densities for a certain set of hypoplastic parameters and full saturation. There are also kinematic constraints for 6: an initial strain direction 6 > ,O cannot accelerate in the long term, even if it produces excess kinetic energy at the beginning. The following general rules can be deduced from the analysis of single soil elements: 0

0

Figure 2: definition of strain and stress directions in a slope

e

For the analysis of an embankment, the above criterion can be applied to a number of soil elements each representing one material point. If we assume that the trigger deformation acts in a plane strain cross section, the equations are considerably simplified. The deformation gradient is defined with an angle of dilatancy v and an arbitrary angle 6 according to fig. 2. The most unfavourable combination of both, giving a minimum A’E for each soil element, can be found by variation.

+p

The greater the mobilized degree of friction in the initial state, the higher the liquefaction risk; A steep slope angle is a sufficient, but not necessary condition for liquefaction.

The disadvantage of this single soil element consideration is that the critical deformation directions of neighbouring elements are not kinematically compatible as the kinematic chain of fig. lc. 3.3 Coherent deformation.jields The velocity profile for the initial perturbation can be chosen in such a way, that the deformations of adjacent soil elements are fully compatible. The simplest deformation mode is the constant-volume shear of a triangular region below the water table (Raju 1994) which was later extended to contractant shear (Kudella 1995). Dilatancy v and the angle of shear base 6 = ?9. are constant for all material points (comp. fig. 2 and 4 4 . As a kinematic chain like the one of fig. l c acts, the excess energy can now be summarized over

In practice, there are static constraints for v: As the vertical stresses cannot differ much from the dead load of the overlying soil mass, the condition of zero total stress rate b,, = 0 = b;,

Liquefaction is at first to be expected for shear directions coinciding with the directions of maximum shear stress;

i ~

e(1 - S?.) 62 1

finitesimal deformation (kinematic chain) can indeed replace the real initials. Global instability arises, if a kinematically possible coherent deformation field (fig. 4) can be found yielding A’E < 0 . Because this field is not necessarily the most critical mode, the criterion is a sufficient, but not necessary condition for liquefaction. A’ E > 0 as a condition for stability is thus on the unsafe side for the coherentfield-consideration.

Local instability may still arise, if the decisive deformation field yields A’E < 0 only in an isolated region or for directions which are not globally compatible (fig. 5a). Such modes may be identified using the single-element-consideration. In terms of safety, this case refers to fig. l b and remains unclear without further time integration. Global failure is not necessary, contractant deformation causes local pore water increase, but may stop again at a new equilibrium state.

Figure 4: kinematically possible velocity fields

Global stability is surely demonstrated only if

the whole wedge. For steep slopes, a stability minimum for 0 < f l c r Z t < @ can always be found.

A 2 E > 0 results for all directions and for every single point. As a condition for stability, the

Another option is a circular section reminding of a slip circle, leading to slightly higher critical densities (fig. 4b). The geometric boundaries of the mechanism have to be varied until a stability minimum has been found. However, there is still an infinity of other possible velocity fields of that kind.

single-element-consideration is on the safe side as the decisive deformations, though incompatible, represent a lower limit of A’ E.

3.4 Local arid global instability

Fluctuations of void ratio e may initiate local instability which evolves into global instability. The remainig open question is therefore, whether void ratio mean values can describe reality or whether a statistical density fluctuation should also be accounted for in the model. 3.5 Parameter variation The analysis uses the computer program STABIL which carries out the necessary variations of deformation field geometry. Slope geometry, initial density and hypoplastic material parameters are supplied as input data. The program calculates a field of A’Evalues and shows them grafically according to fig. 6.

Figure 5 : schematic representation of so-called local and global instability A strong argument for Hill’s stability criterion can be drawn from calculations of liquefaction onset using time integration. It has been shown by detailed calculations that, if an initial deformation field with A’E < 0 exists for the whole slope while also kinematically possible, all perturbations will cause the slope to fail. With time, the deformations are directed into the critical direction, and the same steady state flow pattern will be approached independently of the initial perturbation’s specific direction, magnitude or location (fig. 5b). The simultaneously acting in622

Figure 6: distribution of A’E, typical result plot of stability analysis

1,o 1

o,201 0.4

1.0

or undisturbed sampling. Apart from costly ground freezing technologies, no sampling method for extremely loose sands under water can provide reliable undisturbed densities. The derivation of relative densities from CPT results needs careful calibration and experience. For an objective interpretation CPT data and comparative cone pressiometer sounding data can be combined with a calculation model (Cudmani & Osinov 1999). Many attempts have been made to measure the insitu stresses directly (Wehr e.a. 1995). Results show that horizontal stress ratios can be as low as Kmor as high as I< = 1 , 5after densification. Shear stress components cannot be measured as yet; a limited numerical variation of empirical stress distributions makes more sense. It is also promising to extend the calculation program by a statistical distribution of initial state parameters, as has already been tried with success for settlement analysis (Nubel & Karcher 1998).

I

0,2

0.4

0,6

7

0,8

inundation ratio H,.,kRIk

,

-

-

1 -___I___?

Figure 7: critical relative density for parameter variation

4.2 Case studies

Non-constant void ratio distributions can be accounted for. The realistic assumption of the initial stress state is one of the crucial factors. Depending on a preselected horizontal stress ratio ( K a 5 I( 5 K O ) and the slope angle ,O the program derives a set of combined equilibrium stress fields. Alternatively, it would also be possible to use initial stresses from FE models. By variation, the influence of the different input parameters on liquefaction risk can be separated (fig. 7):

1

AZE

A2%:rder

enerav distribution

0

' h 6 = 3 5 42" decisive shear direction

1

Figure 8: cross section of the embankment showing the distribution of 2nd order work

4.1 Identification of state parameters

A back-calculation has been made for 37 documented landslides which happened since 1960 in the East German mining areas. Although a single set of hypoplastic parameters was adopted, most of them could be well justified. The reported in-situ densities lie in between the back-calculated critical values for the limiting horizontal stress ratios Kmand KO. The case study presented here refers to a site where first spontaneous liquefactions were reported in the 70s a few years after ceasing of groundwater lowering. Slope inclination at that time was about 30". To increase stability the slope was flattened to an average angle of 6,3" (fig. 8). The deposit consisted of 27 m thick very loose silty fine sand. Soil parameters were taken from frozen specimens. The measured average in-situ void ratio was e = 0,87 with a recorded maximum of e = 0,97, and the average saturation was S, = 0,8. As the water will rise 19,8 m above slope toe in the year 2030, stability was further increased by blasting in the lower part and by vibratory rollers in the upper part. This technique creates a so called "hidden dam" parallel to the slope and the later shoreline, a defined region densified to e = 0 , 7 6 which obstructs the undensified soil mass from flowing out into the lake in case of liquefaction.

In-situ densities can be measured using radiometric combination sounding, cone penetration testing

Back calculation using STABIL proves that the steep original slope with an assumed water level of 5 m

e

e

o

high influence: slope inclination p, horizontal stress ratio K , hypoplastic exponent n and relative density I D ; medium influence: inundation ratio H,k/Hk,degree of saturation S,,critical friction angle cpc and hypoplastic granulate hardness h,; low influence: slope height Hk and for other hypoplastic parameters.

The calculated critical water level corresponds to observations. An active horizontal earth pressure is more critical because of the higher mobilised shear resistance. Low saturation stabilizes, but full saturation should be assumed if no data are available. The risk of global liquefaction rises with increasing slope angle, but with the single-element-consideration also slopes with less than 15" can liquefy under certain void ratios and initial stress states.

4 BACK-CALCULATION AND PREDICTION

623

Gudehus, G. 1993. Spontaneous liquefaction of saturated granular bodies. Modern approaches to plasticity, ed: Kolymbas, Elsevier, Amsterdam, pp. 691-714, 1993 Gudehus, G. 1995. A comprehensive concept for nonsaturated granular bodies. Unsaturated Soils, eds. Alonso & Delage, Balkema. Gudehus, G. 1996. A comprehensive constitutive equation for granular materials. Soils and Foundations, 36(1): 1-12. Herle, I. 1997. Hypoplastizitat und Granulometrie einfacher Korngeriiste. PhD thesis, Veroffentlichungen des IBF der Universitat Karlsruhe, I42

Figure 9: critical void-ratio prior to and after construction of the hidden dam for several K values must have liquefied for void ratios above ecrit = 0,74. For a representative cross section of the 6O-slope no instable coherent deformation fields were found. But using the single-element-consideration, local instability is possible for void ratios of e = 0,7 to 1,l and horizontal stresses between active and at-rest earth pressure (fig. 9). This instability occurs with sliding directions, however, in which global flow-out of the slope is not possible (6 >> p,fig. 8) as in fig. 5a. Significant contractant perturbations, like for example saturation sagging, will nevertheless produce pore water overpressure and thus diminish static resistance. Prior to compaction, stability of the embankment was given d u e to capillary effects and horizontal stresses probably well above K, (see range of in-situ state in fig. 9). But following the analysis, safety for future flooding can not be guaranteed without compaction. T h e hidden d a m improves the overall stability as it balances the negative 2nd order work of the uncompacted soil mass to some extent (fig. 8). The stabilizing effect of densification is further improved by simultaneously increasing the horizontal stress to a .&-state. A stable behaviour can thus be predicted for the highest water table in the year 2030.

REFERENCES Cudmani, R., Osinov, V. 1999. The cavity expansion problem for the interpretation of cone penetration and pressiometer tests. submitted to Can. Geotechn. Journal Doanh, T., Ibraim, E., Dibujet, Ph., Matiotti, R. 1997. Static liquefaction: performances and limitations of two advanced elastoplasticity models of loose. NLUII.Methods in Geoinechanics, eds: Pietruszcak & Pande, Balkema. Drucker, D. C. 1964. On the postulate of stability of material in the mechanics of continua. Journal de Mkcan ique, 3(2) :236-249

Herle, I., Wehr, W,, Gudehus, G. 1998. Influence of macrovoids on sand behaviour. 2nd. Int. Cont on Unsaturated Soils, Beijing. Hill, A. 1958. A general theory of uniqueness and stability in elastic-plastic solids. Joinrn. Mech. Phys. Solids, 61236-249 Ishihara, K. 1993. Liquefaction and flow failure during earthquakes. Gkotechnique, 43(3):35 1-415 Kudella, P. 1995. Stabilitatsberechnung von setzungsflieflgefahrdeten Kippenrandboschungen. Geotechnik, 19(1):7-15 Lade, P.V. 1992. Static instability and liquefaction of loose fine sandy slopes. Journal of Geotechnical Engineering, 118(1) Nubel, K., Karcher, Ch. 1998. FE simulations of granular material with a given frequency distribution of voids as initial condition. Granular Matter, 1 : 105-112 Poulos, S.J., Castro, G., France, J.W. 1985. Liquefaction evaluation procedure. Journal of Geot. Eng. Div. ASCE, 1 1 1(6):772-792 Raju, V. & Gudehus, G. 1994. Compaction of loose sand deposits using blasting. In Proc. XIII ICSMFE, New Delzli, 1 145- 1 150 Raju, V. 1994. Spontane Verflussigung lockerer granularer Korper - Phanomene, Ursachen, Vermeidung. PhD thesis, Veroffentlichungen des IBF der Universitat Karlsruhe, 134 Sladen, J., d'Hollander, R., Krahn, J. 1985. The liquefaction of sands, a collapse surface approach. Canadian Geotechrzical Journal, 22:564-578 Warmbold, U. & Vogt, A. 1994. Geotechnische Probleme und technische Moglichkeiten der Sanierung und Sicherung setzungsflieflgefahrdeter Kippen und Restlochboschungen in der Niederlausitz. Suijace Mining, 7:22-28 Wehr, W., Cudmani, R., Stein, U., Bosinger, E. 1995. CPT, shear wave propagation and freeze probing to estimate the void ratio in loose sands. Int. Symp. on Cone Penetration Testing, Linkoping, (2):35 1-356 von Wolffersdorff, P.-A. 1996. A hypoplastic relation for granular materials with a predefined limit state surface. Mechanics of Cohesive-Frictional Materials. l(3): 251-271.

624

Slope stability Engineering, Y'Si, Yamagami 8,Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Runout distances of earthquake-induced landslides Yoshimasa Kobay ashi Hiroshima Institute of Technology,Japan

ABSTRACT: Cases of earthquake-induced landslides in Japan are described. Items such as name, date, location, causative event, volume, area, thickness, drop height H, attained distance L, Fahr-boeschung WL, velocity, composition,references, etc. of investigated landslides are given. Fahr-boeschungs or WL ratios, which correspond to net coefficient of friction, are variable depending on size, geology and other factors. Moisture content is one of the important factors for triggering and for increasing runout distances of slides. Volume is another important factor affecting the runout distance. Volcanic areas are particularly susceptible to debris avalanches. The timedistance relationships of some of the slides are reproduced, and the maximum velocity is found to reach about 5 to 50 d s .

I lNTRODUCTION Landslides have caused many fatalities in past destructive earthquakes. It is hence desirable to understand their characteristics. In particular, prediction of the runout distances of slides is important for mitigating this kind of hazard since they often reach unexpectedly long causing disaster. However, the data base for this category of hazard is relatively poor. I have hence tried to collect data of well-documented earthquake-induced landslides in Japan mainly in the recent past. The information will be usehl for preventing disaster as well as in preparing land-use planning. In the following, case histories are first described briefly, then based on the cases the correlations between the runout distances and volume or other factors are examined. Estimated velocities of landslides if available are given for reference. Lessons are extracted fkom the experiences described in this article.

2 CASE HISTORIES 2.1 Bandaisan volcano(1888) Volcano Bandai erupted on the 15' of July, 1988 and caused a well-known giant debris avalanche amounting to 1.5km3 on the northern flank of the volcano. It attained the distance of 11.4km, covered an area of

3.5km2 devastating farmland and houses with toll of 477 lives. Sekiguchi et a1.(1993) divide the process of the activity into 5 stages as follows: 1) Ascent of magma and expansion of the edifice starting around the 8' of July accompanying marked tremors and noise at 7:OO on the 15', 2) eruption of the first stage with a phreatic explosion below Kobandai peak. 15 to 20 strong explosions occurred and the last one broke the north flank causing a rock avalanche. An avalanche valley was formed by this event and debris buried the villages in the northern foot of the mountain causing great hazards. It formed also hummocks along the flowed-down course, 3)relative quiescence at around 8:50, 4)a small explosion at around 9:30 caused a slide of Kobandai. Fan-shape cleavages and a pressurized zone were formed by this slide, and 5)cease of eruptions around 16 hr. The avalanche valley is 1.2km wide and 3km long. The sizes of hummocks located on the extension of the avalanche valley mostly range 70 to loom, and the maximum is 300m in longer diameter. This slide was extraordinary since it accompanied a volcanic explosion and undoubtedly gaseous content had some effect on the mobility of the rock mass. This type of slide is relatively rare but cannot be ignored, since in volcanic areas similar phenomena can occur occasionally as exemplified by the slide at Mt. St. Helens in 1980. 625

2.5 Nahzgi(1974) The off Izu Peninsula earthquake of the 9“’ of May, 1974 (M 6.9) caused a Shirohatayama slide at a fishermen’s village Nakagi and took 27 lives by burying 19 houses. The rock type is volcanic breccia and tuffaceous sandstone underlain by pumice tuff. Short drifts had been driven into the latter for storage and their effect on the stability of the slope was argued after the event. Seepage of ground water was observed at the outcrop of pumice tuff after the slide, which suggests the base rock was saturated on the earthquake. The slide was rapid, and after destroying the village a part of the soil mass flowed into the bay.

2.2 N e b u b a ( 1923) A rock avalanche was triggered by the 1923 Kanto earthquake of September 1, 1923, and it rushed into the village of Nebukawa, south of Odawara, and demolished the village killing 300 to 400 people. This is the most catastrophic case among earthquakeinduced landslides in modernized Japan (Kobayashi, 1985). The source area of the avalanche is supposed to be 3.5 km upstream of the Shiraito river along which the rock mass flowed down. The volume is estimated at 1 to 3 million m3. 2.3 Dedo-Nishime(1964) In the Niigata earthquake of June 16,1964 (M 7.5) a 7 m high railway embankment failed as long as 150 m and the soil deposited flat on one side of the railroad covering paddy field up to 115m from the foot of the slope (Tada et al., 1964). From the fluid-like appearance of the deposit the fill material is presumed to have liquefied during shaking or sliding. According to an eyewitness account by a farmer, the soil in the embankment broke through the mid-slope surface and the higher part of the embankment dropped vertically down on that portion. The deposit was 1.0 to 1.5 m thick at 50 m and 0.3 to 0.5 m thick at 90 m from the railroad, respectively. Patches of the slope-surface with grass on them were scattered overriding the rice field giving little damage to rice plant below. At this site the railroad crosses a buried valley of 10m deep unconsolidated silt and clay deposits including thin sand lenses. This subsurface may have been responsible to strong shalung of the site.

2.6 Mitaka-Iriya(1978) In the near Im-oshima earthquake of Jan. 14, 1978 (M 7.0) many slides were triggered including the present one. This slide of about 10,000 m3 took place at a slope with 110 m relative height with maximum width of 200 m, slope length of 120 to 200m, and the depth 2-3m. A characteristic feature of the slide is its speed estimated at 1 5 d s or more, and the slid mass stopped after climbing some height on the opposite bank. Seven people who could not flee died by the slide. This is a slide of recent pyroclastics along a bedding plane. Although the size of the slide is not large, this type can be dangerous because its speed is high and its runout distance is relatively large.

2.4 Shiriuchi(l968) The Tokachioki earthquake on the 16* of May, 1968 (M 7.9) caused a number of slope failures of railroad embankments of the Tohoku line of Japan National Railways. It is noteworthy that this earthquake was preceded by a heavy rainfall amounting to 150 mm in total till the previous day of the event. Among others a failure between Shiriuchi and Mutsu-ichikawa stations is a typical flowslide with liquefaction of material (Yamada et al. 1968). Slope surface of the embankment 15m high failed as long as 80 m and the surface soil slid 80m from the slope end over a paddy field. T h s location was underlain by soft ground containing peat of 1 to 2 m thickness. On the day of investigation on June 17, there still remained pools of seepage water at the foot of the slope suggesting ground water played an important role in this slide.

2.7 Nashimoto-West and East( 1978) In the same earthquake as above, two slides took place at Nashimoto along the Amagi-pass road. The slides amount to 19,000 and 15,000 m3, respectively. The former buried a bus and 3 passengers died. At this location cutting was made in 1971-72 to widen the road into the rock mass of volcanic breccia or tuff breccia as high as 30m or more on the mountainside and several meters on the valley side, respectively. The slope was unstable since then and failed repeatedly; e.g. by a 94.5 mm daily precipitation of Oct. 9, 1976. On the earthquake the western part of the slope was being reconstructed after a failure while closing one of the lanes. The west slide was 50 m high, 120 m wide and 10 m deep in the maximum. The east slide was 53 m high, 110m wide and 7 m deep in the maximum. The basic cause for these slides is undercutting of layers sub-parallel to the original ground surface.

626

2.8 Kotobukiyama(l978) A part of the slope of a fill for residence area in Kotobukiyama, Sliroishi city failed during the Miyagiken-oki earthquake of the 1 2 of~ June, 1978 (M 7.4). The size of the slide was 120m wide, 230m long involving 16,000m2 residential area. One person died buried by the slide. The failed mass flowed about lOOm fi-om the foot of the slope and is estimated at 80,0001n3 in volume. The site is underlain by pumice tuff and the fill material is provided by sand from the same rock. The fill thickness ranges up to 25m in the maximum. The slide is rather fluid-like and is 5 to 6 m in the deposited area. The groundwater table measured in 1976 had been less than 10 m from the surface. This suggests an effect of soil liquefaction on the present slide.

3 RUNOUT DISTANCE VERSUS VOLUME AND TYPE OF LANDSLIDES It is well known that there is a general tendency that larger landslides exhibit lower net frictions or smaller Fahrboeschungs H/L (Scheidegger, 1973). I have compiled data for the cases described in the foregoing sections(Table1 and Fig.1). They e h b i t a similar tendency as usual except that some smaller slides have extraordinary low net frictions; the latter group belongs to those where materials liquefied. Those with volume larger than 106m3 are debris avalanches at Bandai, Ontake and Nebukawa. They have in general smaller net frictions than other slides. It may not be by chance that all of them were in volcanoes. In particular, the Nebukawa debris avalanche was very likely facilitated by light loaniy soils involved.

2.9 Ontake(1984) The Western Nagano Prefecture earthquake of the 14'h of September, 1984 (M 6.8) triggered a giant rock slide which turns into a debris avalanche and flowed down along the Denjogawa canyon as long as 8 km or more. 15 people were killed by this debris avalanche. The volume is estimated at 36x106m3. According to eyewitness account it took about 6 minutes after the onset of the main shock to reach the 8-km point, Yanagase, giving an average speed of 2Ods. The slide occurred on the south-eastern slope of Volcano Ontake in two steps, the first in the foot of the slope contains about 10% volume and the second in the upper part of the slope about 90%. The slid mass fell into the Denjogawa canyon and flowed down in the canyon leaving little deposit till the canyon meets the Nigorikawa canyon about 5 km downstream. In the farther stretch than the confluence with the Nigorikawa the quantity of deposit grew rapidly and there were also huge hummocks. Whether the debris were dry or wet was actively argued. Relevant lnformation is that mud was found sticking to ground and trees where the debris flowed through; that the quantity of water contained in the debris of 36x106m3is estimated at 7.7x106m3and it is not sufficient to saturate the whole debris. One of the hypothesis is that only the lower part of the mass was saturated facilitating slide while the upper part remained dry. Another category of hypotheses assumes mechanism for facilitating dry debris avalanches (e.g. Kobayashi, 1994).

Table 1. Volume and Fahrboeschung WL of earthauake-induced landslides year 1888 1923 1964 1968 1974 1978 1978 1978 1978 1984

event

name

voiume(m3) WL

Eruption Bandaisan Kanto Nebukawa Niigata Dedo-nishime Tokachi Shiriuchi IzuPen. Nakagi Izu-oshima Mitaka-inya Izu-oshima Naslimoto W Izu-oshimaNashimoto E Miyagiken Kotobukiyama Naganoken Ontake

1 . 5 ~ 1 0 ~ 0.070 1 . 0 ~ 1 0 ~ 0.15 1 . 8 ~ 1 0 ~0 ,047 3 . 4 ~ 1 0 ~0.15 1 . 7 ~ 1 0 ~0.37 l.0x105 0.30 1.9~10' 0.83 1 . 5 ~ 1 0 ~0.73 6 . 0 ~ 1 0 ~ 0.12 3 . 6 ~ 1 0 ~0.12

note: H is the dropped height, L the horizontal distance of slide

4 VELOCITY OF MOVEMENT

Debris avalanches are in general rapid phenomena and their velocity is an important factor of concern. However, estimation of the velocity is difficult because very few were measured in field in real events and it is in general hard even to collect data for simulations. Nevertheless, I have tried simulations of the slides based on limited evidence; only three cases so far; the Nebukawa, Mitakairiya and Ontake cases. Based on a simple simulation incorporating hction and air-drag resistance Kobayashi (1985) estimated the velocity-distance relationship of the Nebukawa debris avalanche as shown in Fig.2 to fit the eyewitness account that it reached Nebukawa village about 3-5 minutes after the main event. If the estimation is true the maximum speed attained 40 to 50 m/s in the fulst third of its travel. 627

Fig.1 Net fhction of landslides versus volume

Fig.2 Velocity-distance and travel-time-distancecurves for the Nebukawa debris avalanche in the Kanto earthquake 1923 under the effect of gravity and friction as well as air turbulcnce . Next example is for the Mitaka-iriya slide in the1978 Lzu-oshima earthquake. Assuming the friction angle of sliding plane between 11 and 16 degrees, Kobayashi (1981) estimated the speed as shown in Fig.3. It ranges between 5 and 15 m/s depending on the assumed f?iction angle. The last example is for the Ontake debris avalanche in 1984. Kagawa and Kobayashi (1987) conducted a computer simulation to reproduce the debris avalanche by representing the debris by a number of spherical masses flowing down on a three dimensional canyon topography and obtained a result as shown in Fig.4.

The left panel is a bird eye’s view of the trajectories of rock masses on the three dimensional topography, the central one locations-time of rock masses ( upper line: leading rock mass; lower line: average rock masses), and the right one is the instantaneous average speed of rock masses and time. 5

CONCLUDING REMARKS

Relatively a few number of cases are available at the present moment, but even in such a limited situation it is possible to draw some lessons from experience.

Fig3 Velocity-distance curves for the Mitaka-iriya landslide in the Izu-oshima earthquake 1978.

Fig.4 Computer simulation of the Ontake debris avalanche in the Western Nagano Prefecture earthquake 1984. Left: bird eye’s view of the trajectories of rock masses; Center: locations of the leading (top) and average rock masses; Right: velocity-travel time of average rock masses. From Fig.1 showing examples of net hction or WL of earthquake-induced landslides, it is evident that it can be lower than 0.1; one is in case of a large debris avalanche and another is the case affected by liquefaction. The data of speed of earthquake-induced landslides

are more limited, and only three examples could be discussed. In these examples the values range between 5 and 50 m / s depending on conditions including the size. Larger slides seem to have greater speed and tend to be more dangerous. It is important to collect more data on this relevance 629

to make a more concrete recommendation to prevent slope hazards by earthquakes. REFERENCES Japan Scientists Association (1978) Report of the 1978 Izu-oshima -kinkai earthquake, p.76(in Japanese). Kagawa, T. and Y. Kobayash (1987) Simulation of debris avalanche of Mt. Ontake induced by the Western Nagano Prefecture earthquake, 1984. Proc. Japan National Symp. Rock Mechanics, 3 19-324 (in Japanese). Kawakanii, F., A. Asada and E. Yanagisawa (1978) Damage to embankments and earth structures due to Miyagiken-oki earthquake of 1978, Soils and Foundations 26-12,25-3 l(in Japanese). Kobayashi, Y. (1984) Back-analysis of several earthquake-induced slope failures on the In1 peninsula, Proc. 8WCEE, similar contents also in Annuals of Disaster Prevention Res. Inst. Kyoto Univ.24 B1(198 l), 401-410. Kobayashi, Y. (1985) A catastrophc debris avalanche induced by the 1923 Great Kanto Earthquake, Natural Disaster Science, 7,l-9. Kobayashi, Y. (1994) Effect of basal guided waves on landslides, PAGEOPH 142,329-346. Scheidegger, A. E. (1973) On the prediction of the reach and velocity of catastrophic landslides, Rock Mechanics 5,23 1-236. Seluguchi, T., K. Haraguchi, J. Iwahashi, T. Otani, Y. Inazawa and M. Tsusawa (1993) Study of topography forming process in the 1888 eruption of the Bandai volcano, Report of Geodetic Survey Inst. Japan D1No.308, 150-160 (in Japanese). Tada, Y., M. Saito, M. Ihara, T. Matsunami, T. Muromachi, T. Fujiwara, C. Ueda, Y. Kobayashi, Y . Sat0 and H. Uezawa (1964) Survey report of Niigata earthquake, Report of Railway Res. Inst. 448, 92p. (in Japanese). Yamada, G., T. Takayama, T. Muromachi, T. Fujiwara, Y. Sat0 and Y. Kobayashi (1968) Survey report of Tokachioki earthquake, Report of Railway Res. Inst. 650, 137p., (in Japanese).

630

Slope Stability Engineering, Yagi, Yamagami Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Evaluation of measured vertical and horizontal residual deformation at crest of rockfill dam under earthquake Toshiro Okamoto Geotechnical and Eurthquake Engineering Department, Abiko Laboratory, Central Reseurch Institute of Electric Power Industry,Jupun

Abstract: Many data have been collected concerning the deformation of completed rockfill dams under strong earthquake from all over the world, in this study some data, especially horizontal deformation and recently observed data are added to evaluate the effect of magnitude, compaction, gradient and so on. In this study settlement and horizontal deformation ratios are defined to be the values of crest deformation / dam height, and the relation among deformation, acceleration and duration are evaluated by regression analysis. Then the influences of performance and dam structure are studied.

was conducted, so its data is included herein. Table 1 is their summary.

1 INTRODUCTION

It is more necessary for seismic design to take account of seismic behavior and structure function in Japan especially after Hyogo-ken Nanbu earthquake, it needs the study of earthquake input motion and evaluation method of stability taking in account of the function appropriate to the kind of structures. Also the design of rockfill dam should be reflected by dam function evaluation according to seismic behavior. It may be said generally that rockfill dam has high seismic resistance, however measured deformation should be analyzed rationally to lead to the design taking account of dam function.

3 SETTLEMENT AND HORIZONTAL DEFORMATION 3.1 Settlement ratio and base acceleration Settlement ratio E ,is defined and introduced to be crest settlement S, / dam height H (Bureau et.al, 1985). According to Fig. 1, it found that the data distributed in some region between settlement ratio and base acceleration. 3.2 Settlement ratio and crest acceleration Fig.2 shows the relationship between settlement ratio and crest acceleration and it found that the distributed region seems to be wide comparatively as well as Fig. 1. Fig. 1 and 2 shows that the maximum E , is less than 1% and most of E ,are less than 0.5%, and no poundage function damage of leakage increment were reported about soil core type dams listed in Table 1 or Fig. 1 and 2. The maximum settlement in Fig. 1 and 2 is 80 cm in Matahina dam and is less than 1.Om and the more, which was observed in earth fill dam with large damage of poundage function by earthquakes (Tani, 1982). On the other hand, Cogoti and Minase of CFRD type dams leaded to increased leakage though their E , were less than 0.5%, so it found that E , related dam function of poundage are deferent between soil core type and concrete facing type of rockfill dam.

2 INVESTIGATION METHOD AND MAIN RESULTS Technical Research Center of Japan Development, 1982, Bureau et.al, 1985, Kondou, 1990, Finn et.al, 1995 collected many data and evaluated them. As the recently observed data this study includes the following, namely Anderson dam by Morgan-Hill Earthquake (1984) (Bureau, et.al. 1985) and Loma Prieta E. (1989) (Tepel, et.al. 1996), Matahina dam by Edgecumbe E. (1987) (Gillon, et.al. 1989), Ambuklao dam by Philippines E. (1990) (Japan Society of Civil Eng. 1993), and Los Angels dam by Northridge E. (1994) (Bureau, et.al. 1996). Los Angels dam is zoned earthfill dam replaced San Fernando dam, but its data seems to be valuable because gentle design, performance and observation

631

Table 1 Measured deformation and dam characteristics dam

I

nation :earthquake . (Magnitude)

rest residicrest resit lam base ;crest accerel. laccerel. e t t h e n 4 horiz. del Ab (gal) IAc (Pal) v (cm) ISh (cm) 7.6 5.1 *loo ___ Malpasso jPeru i 1938.10.10 . . . --60 (8.3) '190 Cogoti /Chile 1Illapel 1943 3 1 5 --Miboro :Japan 1Kita-Mino 1961 (7.0) *200 1 j 11.4 13.9 Minase !Japan fNiigata 1964 (7.5) 55 I --72.8; 300.2 LaVillita IMexiccj 175.10.11 (5.5) 2 2.5 ; 40.8; 191.6 LaVillita :Mexico (75.11.15 (6.5) 2 2.5 5 j 2.5 371 17 i LaVillita :Mexico 179.3.14 (7.6) 11 4.5 60 LaVillita ;Mexico 181.10.25 (8.1) 338 85 j 125 450 32 ; 11.5 60 (8.1) LaVillita \Mexico j85.9.19 0.54 j --148 52.9; 130.1 Infiemillo ;Mexico j75.11.15 (5.5) 148 7.55 j 12.9 105 355 Infiemillo ;Mexico j79.3.14 (7.6) 148 10.6 I 10.7 125 1 303 1nfiemillo:Mexico j85.9.19 (8.1) 5.7 j --Namioka [Japan 1Nihon-kai Chubu 83 (7.7) 223 79 j 50 j --105 Makio j Japan iNaeano-kenSeibu 84(6.8' *400 1 '750 410 j 630 1.5 0.9 Anderson :USA jMorgan-Hill84 (6.2) 3.9 j 2.4 Anderson !USA ILomaPrieta89 (7.1) 78 j 421 1 26.8 86 Matahina i ~ e wzeallvnajEd~ecumbe1987(6.3) 324.7/ 764.e 80 --- I --40 9 129 AmbuklaoiPhilippin$85.4.24 (6.3) --129 68 28 AmbuklaojPhilippinej1990 Ruzon (7.8) '200 8.89 I 3.81 46.5 270 I 600 LosAngels \USA ;Northridge 1994(6.7)

type

Refference

1) Okamoto,S.,Yoshida,N. and Nakayama,K( 1961) : On the behavior of dams during earthquake, J. of Japanese society of Large Dam, No.26,33-48 2) Committee of damage investigation by Niigata earthquake, Japanese Society of Civil Enginerring (1966) Report of damage investigation by Niigata earthquake 3) Noguera, Larrain,G.(1979) : Seismic behavior of some Chilean earth dams, 13th Intem. Congress CECRD of Large Dam CECRD 4) Nose,M. and Baba,K.(1981) Dynamic behavior CECRD of rockfill dams, Proc. of Dams and Earthquake CECRD Conference, Institute of Civil Engineers, London, CECRD 5) Rom0,M.P. and Resendiz,D. (1981) Computed and observed deformation of two embankment CECRD dams under seismic loading, Proc. of Dams and Earthquake Conf. Institute of Civil Engineers, London, 267-274 IECRD 6) Arrau.L.. 1barra.I. and Noguera.G.(1985) : CECRD Performance of Cogoti dan under seismic loading, CECRD Concrete face rockfill dams-Design Construction CECFDl and Performance, ASCE, 1-14 7) Bureau.C., Volpe.R.L., Roth,W.H. and Udaka, T.( 1985) Seismic analysis of concrete face rockfill dams, Concrete Face Rockfill Dams - Design, Construction and Performance, ASCE, 479-508 8 ) Ohne,Y.( 1985) : Behaviorof Makio dam under earthquake, Specialty session, 20th Symposium of Soil Enginerring, Japanese society of Soil Engineering, pp 47-54 9) Construction Department of Mexico United Ministry of Electric Power(1985) : Prompt report on structure behavior of Jose Ma Morelos and El Infemillo Hydrolic Power Station by 1985/9/19 and 20 earthquake El Infemillo Hydrolic Power Station by 1985/9/19 and 20 earthquake 10) Matsumoto,N., Takahashi,M. and Sato,F.( 1985) : Repairing the concrete facing of Minase rockfil Sv observed at abutment dam, 15th ICOLD, vol N 203-225 11) Sawada.T (1986) : Behavior of fill dam under earthquake- example of Namioka dam by Nihonkai Chubu earthquake, J. of JSIDRE. Dec 37-40 Anderson 25 25 Matahina 2.5 2.3 12) Tamura,C (1986) report of damage investiAmbuklao 1.75 1.75 gation by Mexico Earthquake, J. of Japanese Ambuklao I 75 1.75 Society of Large Dam, No. 116,40-5 I 13) Uzu,N (1987) : Dictionary of earthquake, Asakura Library, 372-374 * : estimated 14) Gil1on.M D. and Newton,D J.(1989) : EarthCECRD : Center Earth Core Rockfill Dam, CECFD : Center Earth Core Fill Dam, quake Effects at the Matahina Dam, New Zealand IECRD : Inclined Earth Core Rockfill Dam, CFRD Concrete Facing Rockfill Dam proc of discussion session on influence of local conditions on seismic responce, 12 th I C on S.M.F E , 37-46 15) Kondou,N( 1991) : Research on behavior of rockfill dam basing long-term observation result, doctor thesis 16) Matsumoto,N., Yasuda,N. and Shougoku,Y.(1991) Behavior of dams by Loma Prieta earthquake, J. of Dam Technology, NoS6, 19-33 17) Tepel,R.E., Nelson,J.L and Hosokawa,A.M (1996) Seismic responce of eleven embankment dams, Santa Clara county,Califomia, as measured by crest monument surveys,ldth annual USCOLD Lecture Senes, Seismic design andPerformancc o f Dams , 185-199 18) Japan Society of Civil Engineers( 1993) : Reconnaissance Report on the July 16,1990 Luzon Earthquake, the Philippines 19) Bureau.G , Ine1.S , Davis C.A and Roth W H( 1996) Seismic responce of Los Angels dam, CA During the 1994 Northndge earthquake,l6th annual USCOLD Lecture Series. Seismic design and Performance of Dams ,281-295

I

I

: :

I

3.3 Horizontal deformation and acceleration Fig. 3 and 4 indicate horizontal deformation ratio, it can be recognized that horizontal deformation ratio relates acceleration, however the correlation is lower. Fig.5 shows low correlation between horizontal deformation and settlement. After completion some dam showed the horizontal deformation to upstream side not to downstream side not by earthquake (Japanese Association of Electric Civil Engineering, 198l), and some data of earth dam showed horizontal deformation to upstream side by earthquake (Tepel,

R.E., 1996). The reasons are not clear, but the following factors can be listed, crest center or top slope of observation position, difference of slope gradient between upstream and downstream, foundation shape and embankment height difference between upstream and downstream side, earthquake input direction and wave.

632

Fig.4 Horizontal deformation ratio and crest acceleration

Fig. 1 Settlement ratio and base acceleration

Fig5 Crest settlement and horizontal deformation

Fig.2 Settlement ratio and crest acceleration

Fig.6 Effect of Magnitude on the relation between Settlement ratio and base acceleration

4 ANALYSIS OF FACTORS AFFECTING

DEFORMATION Fig.3 Horizontal deformation ratio and base acceleration

4.1 Earthquake characteristics Magnitude M is known in each dam. The longer duration the larger M, and cyclic number increase when the duration is longer. Now the data classified to 8 2 M , 8 > M 2 7 and 7 >M, and the results are showed in Fig.6 and 7. It found that the deformation occurred by small acceleration if M 2 7.

633

Fig.7 Effect of Magnitude on the relation between settlement ratio and crest acceleration

Fig.9 Effect of performance or dam structure on the relation between settlement ratio and crest acceleration @no damage under construction and first filling (Matahina) @rock foundation (La Villita) @no local settlement (Namioka) According to the results of Fig.8 and 9, it found that the data of each case distribute in some different region. However for most of “easily deform” case, which are satisfied the above-mentioned conditions, they suffered the bigger earthquakes of M 2 7 , so it is not clarified whether the deformation depends on magnitude or the above-mentioned condition of performance and dam structure. So further analysis is needed.

Fig.8 Effect of performance or dam structure on the relation between settlement ratio and base acceleration

5 REGRESSION ANALYSIS

4.2 PerJomnce and dam structure As the other factors except for earthquake characteristics, compaction of performance and slope gradient, and foundation ground of dam structure has some possibility to affect the measured deformation by earthquake. Concerning compaction, most of dams embanked by compaction after 1965, but before 1940 compaction was not applied (Cook,J.B., 1984, Yamamura, 1995). And the compaction and slope gradient clearly affect the deformation of rockfill dam due to the results by shaking table tests (Okamoto,S. et.a1,1972). Now collected data are classified by the following conditions to “easily deform” case and “hardly deform” case. Dams in ( ) means that they don’t satisfy the condition. asufficient compaction (not dumped) (Malpaso, Cogoti, Minase, AmbuMao) Blower gradient than 1: 1.8 (Malpaso, Cogoti, Minase, El Infernillo)

5.1 Effect of duration Bureau et.al, 1985 suggested ESI (Earthquake Severity Index) which is defined to AD2 (A: foundation base acceleration, D: duration =7(M4.5)1.5 ). Japanese Association of Electricity (1987) applies widely the relation log D=0.3 1M-0.774, and the relation between settlement ratio and D calculated by its equation are shown in Fig. 10. Good relation is obtained except for Matahma dam data, but its correlation is comparatively low. 5.2 Regression analysis ESI depends on the simple estimation method of Newmark, 1965. Now fundamental relation E = 1 * A” D” is introduced to clarify the affecting degree of acceleration and duration by regression analysis. D is estimated by the equation of Japanese Electric association (1987). Replacing E v1 , A, , D, to 2, , XI, Y,, here i means each data, and N is the number of the data. Generally N should be more than 60 to get generalized relationship, so it needs 100 years and

634

-

Constants are as follows.

,) m= ( c z , x , c Y , ~ - C Z , Y ~ C X ~ Y/ 1 C X i 2CYi2 ( C X i Yi)2 1 n = ( C Z Y , C X , ~ - C Z ~ X ~ C X ~/ YJ 1cx,“Cy,”- ( C X i Y , ) 2 1 I = ( 1 / N ) C l o g E v i - m * (1,”) * C log&n * (1,’” ) C logD, Final relations are followed. E .=7.79X 10 -74,0.5 * D’ E v = 1 . 1 9 X 1 0 - 9 A , 1 . 8 3 . D0.84 4, and A, are base and crest acceleration each other. The ratio of the POW ers of base acceleration and duration is almost 1:2, and this result is similar to ESI, however the crest settlement depends highly on the crest acceleration.

-

Fig. 10 Effect of duration on settlement ratio

6 EVALUATION BY EIDI 6.1 Inntroduction of EIDI The relation obtained by regression analysis

Fig. 11 EIDI for base acceleration of rockfill dams in Japan without deformation by earthquake

Fig. 13 EIDI for crest acceleration of rockfill dams in Japan without deformation by earthquake

Fig. 12 Relation between EIDI for base acceleration and settlement ratio more. This analysis is basing on the restricted number and the result depends on the character of each data. Z,=log E v i - ( 1 /” C log E ,, Xi=logA, - ( 1 /N ) C log A, Yi=logDi - ( 1 /N ) C logDi

Fig. 14 Relation between EIDI for crest acceleration and settlement ratio 635

REFERENCES

indicated average relation among settlement, acceleration and duration. And then it can be recognized that if the settlement is larger than the relation by regression analysis, other factor will affect the deformation, which are seem to be especially compaction and / or gradient and so on. So new index EIDI (Earthquake Induced Deformation Index) is introduced, EIDI= A"' * D". For base and crest acceleration, EIDI,= & o . 5 3 D 1 , 3 g EIDI,= 3D0.s 6.2 Evaluafion by EIDI According to the results of regression analysis, /EIDI=7.79X 10 - 7 0 r 1.19X 10 E however E should be 0 if EIDI is small. Then the EIDI in non deformation case is evaluated by calculating A" * D" for the data without deformation measured in Japan, and the relation between E and EIDI is evaluated by least square method for the data with larger EIDI than it. Fig. 11 and 12 show the results of EIDI without deformation and the relation between E and EIDI with deformation. The average re1ation is E = 2 . 2 2 x 10 - 6 (EIDI, - i,ooo) It found that the performance and dam structure don't affect the settlement ratio. Fig. 13 and 14 are for crest acceleration. The average relation is E =1.67X 10 (EID1,- 2 x 1 0 ') Fig. 14 can evaluate the effect of the performance and dam structure on the deformation. Table 2 indicates the correlation coefficients when each relation is linear, and the settlement of Matahina dam is 10.2cm. And it found that the coefficient in applying EIDI, is bigger.

-',

-'

Table 2 Correlation coefficient

CON CLUSI ON Recent data of measured settlement and horizontal deformation of rockfill dam are collected. Applying the regression analysis settlement ratio relates acceleration and duration. Introducing EIDI settlement ratio is more rationally recognized, and EIDI for crest acceleration can evaluate the effect of performance and dam structure.

Bureau.G, Volpe,R.L., Roth,W.H. and Udaka,T. (1985) Seismic analysis of concrete face rockfill dams, Concrete Face Rockjill Dams - Design, Construction and Pe$omzance, ASCE, 479-508 Bureau, G., Inel, S., Davis, C.A. & Roth, W.H. (1996) :Seismic response of Los Angeles dam, CA during the 1994 Northridge earthquake, Seismic design andpei$omzance of dams, USCOLD, 281295 Cooke, J.B. (1984) Progress in rockfill dams, J. of Geotechnical Engineering, Vol. 110, No. 10, 1383-1414 Finn, W.D., Ledbetter, R.H. & Marcuson, W .F. (1995) The Evolution of Geotechnical Earthquake Engineering Practice in North America : 1954-1994 (State of the Art Paper), 3rd International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, 88 1909, Vol. II Gil1on.M.D. and Newton, D.J.( 1989) : Earthquake Effects at the Matahina Dam, New Zealand, proc. of discussion session on influence of local conditions on seismic response, 12th I. C. on S.M.F.E., 37-46 Japanese association of Electric Civil Engineering ( 1981) Recent Fill Dam Engineering Japanese Association of Electricity ( 1987) :Technical Standard of Seismic Design of Nuclear Power Plant (JEAG 460 1) Kondou, N. ( 1990) :Research of Rockfill Dam based on long-term.Observation, doctor thesis Newmark, N.M. (1965) :Effects of Earthquakes on Dams and Embankments, Rankine Lecture, Geotechnique, No. 15 Okamoto, S., Tamura, J. and Katou, K. (1972) About failure of rockfill dam by vibration, 12th meeting of Japanese Earthquake Engineering, 2326 Research Center of Japan Development (1982) Seismic Design of Dams Tani, S (1982) :J. of Japanese Large Dmz, No.140, 32-50 Tepel, R.E., Nelson, J.L. and Hosokawa, A.M. ( 1996) : Seismic response of eleven embankment dams, Santa Clara county, California, as measured by crest monument surveys, 16th annual USCOLD Lecture, design and Per$orm.mce of Dams, 185199 Yamamura, T. ( 1995) :J. of Japanese Electric Civil Engineering, No.259, 17-26,

636

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Displacements of slopes subjected to seismic loads Radoslaw L. Michalowski & Liangzhi You Departnzent of Civil Engineering, Johns Hopkins University,Baltimore, Md., USA

ABSTRACT: Geotechnical structures, such as slopes, subjected to earthquake loads, are often designed using quasi-static design loads. The displacement-based design method was suggested in the nineteen-sixties, with a relatively simple one-block translational mechanism. However, the most adverse failure pattern known for uniform slopes is the one where the soil mass rotates as one rigid block, separated from the stationary soil by a failure surface. A scheme for calculating displacements for the rotational mechanism will be shown. Yield accelerations for slopes will be calculated, and expected displacements for seismically loaded slopes will be computed.

I

LNTRODUCTION

Recent earthquakes in the U.S. and Japan have renewed interest in the analysis of displacements of earth structures subjected to seismic loads. A rigid sliding-block method was suggested more than 30 years ago, and, even though this method is only approximate, it is still widely accepted today. Originally this technique was used for a translational mechanism (Newmark 1965, Goodman and Seed 1966), but later it was adapted to a rotational failure pattern (Chang et al., 1984). This paper briefly reviews the rigid block technique as applied to rotational failure, and gives a practical means for its application to earth slopes. Similar considerations have been the subject of research in recent years (e.g., Ling & Leshchinsky 1995, Cai & Bathurst 1996). Results directly applicable in engineering practice are presented in this paper.

2

during shear has been experimentally proved and it is also the consequence of the normality rule in modeling effort. Whereas the dilatancy predicted by the flow rule associated with the Mohr-Coulomb yield condition is larger than the dilatancy seen in experiments, the normality rule is the reasonable flow law to be used in perfectly plastic models. It was found out earlier (Chen 1975) that the rotational mechanism of slope collapse is the most adverse of all known collapse patterns. A kinematically admissible failure mechanism for a uniform slope is shown in Fig. 1. The failure surface is a log-spiral

where ro is the log-spiral radius related to angle 80, and cp is the angle of internal friction of the soil. Velocity discontinuity vectors along the failure surface BC are all inclined at cp to that surface, assuring kinernatical admissibility of the deformation process. Block ABC rotates about point 0, and the moment of the block weight about 0 can be calculated as the moment of block BCO about 0 minus moments of AB0 and ACO

ROTATIONAL MECHANISM OF SLOPE FAILURE

M 7 L l

It is a common practice to assume that slopes collapse along failure surfaces that separate a moving rigid block of soil mass from the base soil at rest. Commonly assumed circular surfaces in frictional soil are not admissible, since they do not allow for the dilation of soil during shear. Dilation of granular soils

=

r d (fl - f 2 - f3)

where y is the specific weight of the soil. Analogously, the moment of an inertial force caused by horizontal shaking can be calculated as

f; - f a 637

(3)

where k is the coefficient representing horizontal acceleration as a fraction of the gravity acceleration. Coefficients f i are given in the Appendix. The moment of the resisting shear on BC about point 0 is

fl - f 2 fl" - f2"

3.1

- fi

The yield accelerations were calculated from eq. (6), and an example of results (for the soil with ip = 30") is shown in Fig. 2. The geometry of the failure surface was optimized where the minimum of k, was sought with angles Bo and Bh being variable.

where c is the soil cohesion. If the acceleration coefficient reaches its critical value k,, then the three moments must be in limit equilibrium

3

- f3

SLOPE DISPLACEMENTS Critical acceleration

Critical acceleration for uniform slopes now can be derived directly from eq. ( 5 )

Figure 2: Yield acceleration for homogeneous slopes (soil internal friction angle cp = 30").

3.2

Acceleration of rotating block

If the ground acceleration exceeds the critical level, then block ABC will start rotating with relative acand an additional term will appear in celeration the equation of motion

e,

where G is the weight of the moving block, g is the gravity acceleration, and 1 is the distance from the center of gravity of the block to point 0 (both G and 1 are given in Appendix). Acceleration 4 necessary to maintain transient equilibrium now can be calculated by subtracting eq. ( 5 ) from eq. (7) Q = (k:

Figure I : Collapse of a slope: (a) rotational mechanism, and (b) displacements.

-

Y r,3 k,) E 12 ( f ;

-

f2"

-

f3")

(8)

9

Expressions similar to eq. (8) were developed earlier by Chang et al. (1984), for both the translational and rotational failures.

638

3.3

Toe displacement

where

was performed for a number of different acceleration records. An example of results for the Northridge (1994) record at Moorpark Station is shown in Fig. 4. The displacement is, of course, dependent on both the duration of the seismic event and the pattern of the acceleration record above the critical Seismic events are characterized here by level. their peak acceleration k,. To make the application of different earthquake records possible for a wide range of earthquake intensity, peak acceleration for different seismic records was scaled in such a way so that the integral in eq. (10) could be presented as a function of the difference between peak acceleration and the critical acceleration of the structure ( k , - k,) for different k,. Results for a variety of earthquake records will be shown elsewhere (You and Michalowski 1999).

Coefficient C depends on the slope inclination, internal friction angle of the soil, and the geometry of the displacement mechanism associated with 00 and 6 h such that this mechanism is the most adverse of all rotational patterns. There are four parameters needed for calculations of C: p, p, ;;"i? and k,. However, the number of independent parameters is reduced to three if C is determined from the mechanism for which k, is to be the minimum. An example of results is shown in Fig. 3 for slopes whose critical acceleration is equal to 0.2. According to eq. (10) the displacement of the

The traditional block sliding technique appears to be quite useful in calculations of displacement of slopes subjected to seismic loads. This technique, as presented here, allows one for estimating of displacements using precalculated charts and thus eliminating the necessity of elaborate integration of seismic records or optimization of collapse mechanisms for slopes. Reinforced soil slopes and walls seem to have performed well in recent earthquakes both in the U.S. and Japan. The extension of the technique for reinforced soil structures seems to be straightforward.

The acceleration in eq. (8), integrated twice over the shaking record for time intervals for which the velocity is positive, leads to the irreversible rotation of block ABC (Fig. 1). Maximum horizontal displacement occurs at the toe of the slope, and it can be written as

Consequently, the horizontal displacement at the toe of the slope can be written as U% =

Cllg(k

- k,)dtdt

(10)

ACKNOWLEDGMENT Results presented in this paper came from research supported by the National Science Foundation under grant No. CMS-9634193. This support is greatly appreciated.

Figure 3: Coefficient C for slopes with critical acceleration k, = 0.2. slope at its toe can be calculated as the product of coefficient C and the double time integral of an acceleration record above the critical threshold. To facilitate practical use of the technique, integration

of double time integral for a Figure 4: An specific seismic record. 639

center of rotation, both of which appear in eq. (7) and eq. (8), can be expressed as follows

REFERENCES Cai, Z. & Bathurst, R.J. 1996. Deterministic sliding block methods for estimating seismic displacements of earth structures. Soil Dynamics and Earthquake Engineering I996 15: 255-268. Chen, W.F., Giger, M.W. & Fang, H.Y. 1969. On the limit analysis of stability of slopes. Soils and Foundations 9(4): 23-32. Chang, C-J., Chen, W.F. & Yao, J.P. 1984. Seismic displacements in slopes by limit analysis. J. Geot. Engrg. 1lO(7): 860-874. Goodman, R. & Seed, H.B. 1966. Earthquakeinduced displacements in sand embankments. J. Soil Mech. Found. Div. 92(2): 125-146. Ling, H.I. & Leshchinsky, D. 1995. Seismic performance of simple slopes. Soils and Foundations 35(2): 85-94. Newmark, N.M. 1965. Effects of earthquakes on dams and embankments. GLotechnique15: 139160. You, L. & Michalowski, R.L. 1999. Displacement charts for slopes subjected to seismic loads. Cornputers and Geotechnics 24.

1 = -:7

APPENDIX Coefficients fi were first derived by Chen et al. (1969), and can be found also in Chen (1975). Coefficients f ,are given below

1B fi = -sin 280

3 To

where

H

__ -

s i n ~ ~ e ( ’ h - ’ ~ ) t ’* ~sinQ0

TO

The weight of block ABC (Fig. l(a)), and the distance from the gravity center of that block to the 640

J( f

1- f2

- f3)2

+ (ff - f2”

-

fa2

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999Balkema, Rotterdam, ISBN 90 5809 079 5

Permanent displacement analysis of circular sliding block during shaking H. R. Razaghi, E.Yanagisawa & M. Kazama Civil Engineering Department, Tohoku Universig, Sendai, Japan

ABSTRACT The model of a rigid block sliding on a circular surface is used to analyze the effect of inertia forces on the stability of a slope subjected to different input motions. The study is based on Newmark’s method, and the Mohr-Coulomb failure criterion is assumed. A soil mass with a circular sliding surface inside the earth slope is considered to be a rigid block that will move relative to the slope when the driving moment exceeds the resisting moment. Permanent displacement must be studied for a critical slip surface that is determined by pseudo-static slope stability analysis. Sinusoidal waves and random waves are used as input acceleration data, and then the effect of the maximum acceleration magnitude, the natural frequency of earth slopes, the frequency of input motion, the time history of acceleration, and the strength parameters of soils on the permanent displacement are evaluated. the circular rigid block. Consider a soil slope with a slope angle of a which has strength parameters of c and $ and which is subjected to horizontal acceleration, a(t), (Figure 1). The earth slope is connected to the ground by a spring and a damper and behaves in the manner of a mass spring system with one degree of freedom. The equation of motion is solved to determine the displacement. To determine the critical slip surface, pseudostatic analysis is used. Assuming that the input acceleration is constant, the safety factor is calculated based on a fraction of the gravitational acceleration, g, and the geometry of the circle. By changing the radius and the coordinates of the center of the slip circle at a certain acceleration, the minimum safety factor of the case is determined. The minimum acceleration that makes the minimum safety factor against rotation equal to 1 is defined as the yield acceleration in the pseudo- static method, and the corresponding circle is the critical slip surface.

1 INTRODUCTION

In the analysis and design of earth slopes and embankments under seismic loading conditions, permanent displacement is one of the significant parameters which shows the degree of deterioration in the stability of slopes. Displacement depends on the shear strength of the embankment materials and on the inertial force during shaking. A circular rigid block model, Newmark’s method and MohrCoulomb failure criterion are used for the calculation of the safety factor along a circular slip surface. The problem is analogous to the problem of a rigid block resting on an inclined plane. Herein, it is assumed that a soil mass resting on a circular sliding surface inside the slope is a rigid block that will not move relative to the slip surface as long as the driving moment, including moment due to inertial force, does not exceed the resisting moment due to frictional force and cohesion. When the acceleration exceeds, the circular block will rotate relative to slip surface. The movement continues until the inertial force drops below the frictional force long enough for reduction of the relative velocity of the circular block to zero.

3 ROTATION OF A CIRCULAR RIGID SLIDING BLOCK

2 THE EQUATION OF MOTION

3.1 General concept

The permanent rotation of a circular rigid sliding block is estimated by simultaneously solving the equation of motion for the earth slope body and

A sliding block resting on the critical circular slip surface is assumed to be rigid. This block is subjected to a sinusoidal acceleration wave of a(t)=aosincut. 641

Figure 1. Circular sliding block inside an earth slope: a) earth slope and circular rigid block, b) analytical model Newmark’s method and the equation of motion are used to determine the angular velocity and rotation of the rigid block during a certain time history. The moment due to gravitational force and inertial force acts as the driving moment and the moment corresponding to cohesion and frictional force on the sliding surface acts as the resisting moment:

M,

=

mg(x, - x,)

+ ma, sin c.t(y,

- y,)

(1)

where x,, and y,, are the coordinates of the gravitational center of the circular block, and xc and y , are the coordinates of the center of the circle.

X’

MR’

=

-tana - -(ye

total resisting moment increases. In this situation the resistance is so high that it is not usually overcome by the driving moment and the movement will stop in this direction. The equation of motion for the circular block is given by:

R:gm2$= M D- M R

(5)

where R,, is the distance between the gravitational center of the b&k, m2 is the mass of the block and 8 is the angular acceleration of the rigid block which causes rotation. As initial conditions for solving this equation, angular velocity and rotational displacement are given as zero at t=O. I[ the absolute value of the driving moment is less than that of the resisting moment, there is no relative movement:

+ x,tana) + xxcyc When l M ~ lbecomes greater than IMRI, sliding occurs. Rotation starts and continues until reversal of inertial force; furthermore the relative angular velocity between the block and the slope becomes zero. Figure shows the plot of the angular velocity, Re, and the rotational displacement, R e , versus time for a slope with values of a=25, +=30, c=4O KPa and an input acceleration of OSgsinot. This stepwise plot shows when the acceleration reverses, the velocity in the upward direction becomes zero and displacement remains constant. As time passes the displacement increases. In this case, effect of damping is not taken into account, although it plays an important role in the motion.

4

(4) where a is the soil slope, y is the unit weight of the soil and R is the radius of the circular block. PI and pz are the angles shown in Figure 1. While the inertial force acts in the downward direction of the slope, M R ~is negative and the total resisting moment decreases. When the direction of the inertial force changes to the upward, the

642

Figure 2. Angular velocity and displacement during sinusoidal shaking

Figure 3. Effect of damping on displacement during harmonic motion

3.2 Effect of damping

found in the previous section, there will be failure and considerable rotation in the slope under the resonance condition and also at some frequencies around the natural frequency. This means pseudo-static solutions do not yield acceptable results, at least when the frequency of input waves is sufficiently close to the natural frequency.

Considering the mass and spring system for connecting the earth slope to the ground, the effect of the natural frequency of the embankment and the frequency of the input wave are taken into consideration. By assuming certain values for the coefficient of damping in the equation of motion, the influence of damping on permanent displacement can also be calculated. In Figure 3, it is assumed that the natural frequency of the embankment is 2 Hz and the frequency of the input wave is 2.5 Hz. Then the value of permanent rotational displacement against the time history for the harmonic motion is plotted. Three cases with respective damping coefficient of 1%, 5% and 10% are comparcd with the case without damping. As shown in this figure, by considering a damping ratio of only 1%,the displacement after 10 seconds is reduced from 5.76 m without damping to 3.24 m for a damping ratio of 1%.

3.4 Effect of maximum amplitude Figure 5 shows the permanent displacement versus the maximum amplitude of sinusoidal wave acceleration after 10 seconds for various frequencies of input waves. It can be seen from this figure that the permanent displacement increases as the maximum acceleration increases. In the resonant state, however, the values of the displacement become far larger than those of the non-resonant states. It can be said that the ratio of frequency to natural frequency is more important than the magnitude of amplitude in terms of the permanent displacement.

3.3 Effect of frequency of input waves

To show the effect of frequency, it is again assumed that the natural frequency f, is 2 Hz and that the time history of dynamic loading is 10 seconds. Figure 4 shows a plot of circular block rotation after 10 sec versus different frequencies of input waves. It can be seen that the rotational displacement will increase when the input frequency is close to the natural frequency. Maximum displacement corresponds to f= fn (i.e. resonance condition). Even if the input acceleration is less than the yield acceleration of the critical circular slip surface which is

4 STRENGTH PARAMETERS O F SOILS One of the important parameters which affects the permanent displacement under dynamic loads is the strength parameters of soils. In this section, the influences of the strength parameters are examined. For determining quantitative values of dynamic sliding of a soil mass with different angles of internal friction and the different values of cohesion, other conditions ar assumed to be constant as follows: a=25, fn=2 Hz,

643

Figure 4. Effect of frequency on the displacement for differnt acceleration

Figure 6, Muence of internal friction angle of material (c=40 KPa)

Figure 5. Effect of acceleration on the displacement for differnt frequency

Figure 7. Maximum diplacement after 10 seconds against internal friction angle

a(t)= OSgsinot , f=2.5 Hz. In the first stage, it is assumed that the value of the cohesion is constant; c=40 KPa, and the internal friction is changed from 15 to 45 at 5 intervals. The results of permanent rotational displacement after 10 seconds for different internal frictions are shown in Figure 6. The coefficient of damping is considered to be 1% in all cases. As it is shown in Figure 7, the maximum permanent rotational displacement after 10 seconds is plotted against the internal angleof friction. It can be seen in this case, when the angle of friction is increased from 15 to 45, the permanent displacement is decreased from 7.21 m to 1.23 m.

In the next stage, keeping the friction angle constant at +=30, the cohesion changes from 0 to 50 KPa at intervals of 10 KPa. The effect of the cohesion o n the permanent displacement during shaking is shown in Figure 8. The coefficient of damping is the same as that previous cases (i.e., 1%). The maximum permanent deformation after 10 seconds against the cohesion is plotted in Figure 9. As shown in this figure, when the cohesion is increased from 0 to 50 KPa , the displacement decreases from 4.94 m to 2.89m. Comparison of these results indicates that the strength of the soils under seismic loading is more influential in the internal friction than the cohesion.

644

Figure 9. Maximum displacement after 10 seconds against cohesion of material

Figure 8. Influence of cohesion of material (+=30)

5 EARTHQUAKE ACCELERATION AS AN INPUT MOTION

5.1 Displacement during random shaking For engineering purposes, the responses of slopes to the real earthquakes must be studied. For this purpose, the random shaking based on earthquake motion records of acceleration is employed as input waves instead of sinusoidal waves. If the coefficient of damping is considered to be zero, the earth slope which is considered to be connected to the ground by a spring will continue its movement even after cessation of the input earthquake. Herein, the component N-S of the Kushiro earthquake record of acceleration is used to analyze the permanent displacement of the slope. Maximum amplitudes of this wave are 496 and +351 Gal with a time history of 100 seconds. Assuming the same condition for the earth slope as discussed in the previous section and a natural frequency of 2 Hz, the permanent displacement is calculated and plotted in Figure 10. The damping coefficient changes from 1% to 5%. As shown in this figure, the displacement diagram is stepwise. This means that the driving moment is below the resisting moment when the acceleration reverses to the upward direction of the slope. Consequently, the velocity becomes zero and the displacement remains constant. If the value of deformation is small, the coefficient of damping is usually considered to be less than 5% to 10%. Since the block movement is not continuous and stops at each step of the displacement plot, the displacement and shear strain are not so large at each step. However, when the deformation and shear strain are not

small enough to limit the damping coefficient to 1096, then the Hardin and Drnevich method should be utilized to calculate the coefficient of damping at each step. It can be seen that the ultimate displacement due to the Kushiro earthquake changes from 1.9 m for 1% damping to 11 cm for 5% damping.

5.2 Influence of natural frequency of slopes As seen in harmonic motion, the ratio of the frequency of input waves to the natural frequency of the slope has a considerable influence on the

Figure 10. Comparison between displacements for various coefficients of damping (Kushiro Eq.)

645

Figure 12. Predominant frequency of the Kushiro earthquake displacement. It is expected that the ratio of the pr e do mi n an t of ear t hq u ak e fr e q u e nc y acceleration to the natural frequency of slope affects the displacement. To observe this effect, the natural frequency of the slope is changed from 0 to 5 Hz. Then the permanent rotational displacement of each case is calculated. Figure 11 shows the ultimate permanent displacement against the natural frequency for two cases of damping: 1% and 3%). It can be seen that the maximum displacement occurs when the natural frequency becomes 0.65 Hz. The Fourier Transform is utilized to compute the predominant frequency of the earthquake acceleration. The result is shown in Figure 12 for the N-S component of the Kushiro earthquake. By comparing Figure 11 and 12, it can be seen that there is good agreement between the predominant frequency and the natural frequency for maximum displacement. 6 CONCLUSION Bascd on thc results of this study, the following conclusions can be made: 1) One of the important parametcrs affecting the failure of slopes is the relation between the frequency of seismic loading and the natural frequency of slopes. This appears while utilizing sinusoidal waves with various frequencies and when the predominant frequency of an

646

earthquake wave is near the natural frequency of earth slopes. This is usually ignored in pseudostatic analysis and determination of the dynamic safety factor, and may result in unrealistic findings. 2) Increasing the maximum amplitude of the input wave increases the permanent displacement. In the resonant state, however, the values of the displacement become far larger than those of the non-resonant states. 3) Improvement of the strength parameters of the soils results in a decrease in the permanent displacement of the sliding block under seismic loading. However, improvement in internal friction is more influential than improvement of cohesion. REFERENCES Cai 2. & Bathurst R.J. 1996. Deterministic sliding block methods for estimating seismic displacements of earth structures. Soil Dynam. Earthq. Engg. 15, Elsevier: 255-268 Kramer S.L. & Smith M.W. 1997. Modified Newmark model for seismic displacements of complaint slopes. J. Geotech. Engg, ASCE, 123(7): 635-644 San K. C. & Leshchinsky D. 1995. Seismic slope stability design by pseudo static variational method. Earthquake Geotechnical Eng., Balkema: 1123-1128

Slope Stability Engineering, Yagi, Yamagami& Jiang (( 1999 Balkema, Rotterdam, lSBN 90 5809 0795

Dynamic analyses of slopes based on a simple strain-softening model of soil A.Wakai & K.Ugai Gunma Universir), Kiryu, Japan

ABSTRACT: In this paper, the seismic response analyses of a simple homogeneous slope which consists of strain-softening soil are presented. The analyses are based on the elasto-plastic finite element method (FEM) in which a very simple strain-softening model of soil is used. In order to evaluate a strain concentration along the slip surface, the width of shear band is also considered in the analyses. It is shown that the dynamic FEM can evaluate the residual deformation of slopes induced by a large earthquake.

1 INTRODUCTION The total stability of a slope is usually estimated by the peak strength of soils in the ground. However, over-consolidated clayey soils and dense sandy soils show a strain-softening characteristics in their stressstrain relationships. In cases where such soils are included in the ground, the strain-softening effect often cause the degradation of the total stability of the slope. In this paper, the numerical analyses on a simple homogeneous slope are presented. These are based on the 2D elasto-plastic FEM in which a very simple strain-softening model of soil is used. In order to evaluate a strain concentration along the slip surface, the width of shear band is also considered in the analyses. With regard to the modeling of shear bands and strain softening, a very simple analytical method has been proposed by Tanaka (1996). In the analyses presented here, we have adopted this method. In this method, only the volume ratio of the strain-softening zone in each finite element is considered. This feature is completely different from other more strict approaches such as the smeared crack model (Pietruszczak & Mroz, 1981) in which the geometrical shape of shear band is strictly considered. The model proposed by Tanaka has been applied to various problems with strain softening, such as the lateral behavior of a short pile and the passive earth pressure of a retaining wall (Mori & Tanaka, 1995). There have been a few studies on the stability of slopes with strain softening. Lo & Lee (1973) have evaluated the total stability of a slope which consists of over-consolidated clayey soils, based on the

strain-softening model. They have indicated the possibility such that the total factor of safety was overestimated when the peak strength was used. Ugai & Ida (1994) have performed the analyses of a homogeneous vertical slope and reported about a comparison of analytical results based on the simple strain-softening model and the elasto-perfectly plastic model. They did not referred to shear bands. As a result, it was shown that the strain-softening effect of soil would cause the degradation of the total stability of slopes. In their report, the total factor of safety Fs was investigated by the shear strength reduction finite element method (SSRFEM), which had been originally proposed by Zienkiewicz et al. (1975). If the associated flow rule is adopted, the factor of safety obtained by this method, by definition, is the same as the one in limit equilibrium analysis. More detailed discussion about this topic has been presented by Ugai & Leshchinsky (1 995). In this paper, both the static and seismic response analyses of a simple homogeneous slope are presented. In the static analyses, the total factor of safety is calculated by SSRFEM. On the other hand, in the seismic response analyses, the residual displacement induced by earthquakes are evaluated by the dynamic elasto-plastic FEM (Ugai et al, 1996a, 1996b). The horizontal acceleration is applied to the base of the ground and the response of the system is analyzed numerically. The attention of this paper is focused on investigating the effect of strain-softening behavior on the seismic stability of slopes. It is shown that the results obtained by these analyses are useful for the seismic design of slopes, based on the allowable displacement for earthquake resistance.

647

2 ELASTO-PLASTIC MODEL WITH STRAIN SOFTENING (2D FORMULATIONS) 2.1 Modeling of strain softening According to Tanaka (1996), the yield function J' is given by Eq.(l) which is similar to that of the elasto-perfectly plastic model based on MohrCoulomb failure criterion.

a, =sin4, af = sin 4r,

=2ccos@

(31

3 /, = 2cr cos br

(4)

p,

cr and #r indicate the values of and 4 in the residual stress state, respectively. A and B are constants. y p is a hardening Parameter which is related to the accumulated pla&i shear strain.

" p " added to each strain component indicates the plastic component. On the other hand, the plastic potential g is given by Eq. (7), which is also similar to MohrCoulomb equation.

g=

Jm 1 - %ox+ oY

(7)

Figure 1. Relationships between p and

yp

2.2 Modeling of shear band The stress-strain relationship for each element is generally given by Eq. (9)* (

i3u

f i3f

dEp =A-

ag

a0

7'

(10)

D e is the elasticity matrix. K is a hardening parameter which corresponds to the parameter y p in this model. Therefore, the next equation concerning with A is derived from Eqs. (5), (7) and (1 0).

A parameter s in Eq. (9) is assumed to be given C is a constant. U ,I is the dilatancy angle at the by Eq. (12) (Tanaka, 1996). peak stress. According to Eqs. (7) and (8), the plastic volumetric strain decreases, as the plastic shear strain increases. After the shear stress reaches to the residual state, the dilatation induced by shear becomes almost zero. d and 1 are the width of a shear band and of a A , B and C are related to the rapidity of strain finite element, respectively. This equation means the softening. Figure 1 shows the variation of the volume ratio of the strain-softening zone in each relationship between the accumulated plastic shear finite element. In this study, I is assumed to be strain y p and the strength parameter ,8 in Eq. (l), given by the average of the length of each side in where the constant B was varied. Other input each finite element. d is an input parameter. parameters are consistent with material constants used in the analyses of a simple slope as described in the following chapter. It can be seen that the strain- 3 ANALYSES OF A SIMPLE HOMOGENEOUS softening behavior occurs more rapidly as the value SLOPE of B decreases. 3.1 Analytical model Figure 2 shows an example slope with finite element 648

meshes for both the static and dynamic analyses. The height of the slope is 10m and its gradient ratio is 1 : 2. The soil is assumed to be homogeneous. The material constants, in cases where the strainsoftening model is adopted, are shown in Table 1. The width of shear band is assumed to be 1Ornm.

softening soils can be designed based on the allowable displacement for earthquake resistance.

Table 1. Material constants used in the analyses. Young’s modulus Poisson’s ratio Cohesion (peak) Friction angle (peak) Dilatancy- angle - (peak) .. Cohesion (residual) Friction angle (residual) Softening uarameter A Softening parameter B Softening uarameter c Unit weight Shear band width

3.2 Total factor of safety Fs Based on SSRFEM, the total factor of safety of the slope was calculated. The analytical results in both cases of the elasto-perfectly plastic model and the strain-softening model are shown in Table 2. It is found that the values of the total factor of safety obtained in both cases are close to each other. This is because the values of input parameters A , B and C were relatively large in these cases and the effect of strain softening was relatively small in such a static equilibrium analysis.

I

40000 kPa 0.4 10 kPa 15” 10” 6 kPa 9”

E V

c

4 Y cr

C A

B

I

1

c I Y d

0.3 0.3 0.3

I 16. kN/m3

1

IOmm

3.3 Effects of strain softening on seismic behavior In order to evaluate the seismic stability of the slope, the dynamic elasto-plastic analyses were performed. The constitutive model adopted here is the same as the one used in the static analyses. Rayleigh damping ( a = 0 , p = 0 . 0 2 ) was adopted in the analyses. The positive direction of horizontal acceleration and displacement in the following figures corresponds to the movement to the right in Figure 2. Similarly, the vertical component of them corresponds to the upward in Figure 2. The input horizontal acceleration is 10 sine waves whose amplitude is 200gal. The period of input sine waves is 0.75 sec. Figures 3 and 4 show the histories of acceleration and displacement at the “top” and “toe” of the slope, respectively. The strain-softening model described before was adopted here. As seen in Figure 3, the acceleration response is magnified at the top of the slope, while the one at the toe is relatively small. In addition, the responses to the negative direction of the axis of acceleration are very sharp and greatly magnified at the top. On the other hand, the responses to the positive direction are not sharp because the sliding of the slope occurs during the duration of those periods. This phenomenon is also suggested by the histories of displacement as shown in Figure 4. A large residual deformation after earthquake can be seen in the figure. Based on the dynamic elasto-plastic FEM presented here, actual slopes composed of strain-

Table 2. Total factor of safety Fs calculated by the static FEM. 1 2

With strain softening Elasto-perfectly plastic (no strain softening)

1.226 1.228

Figure 3. Histories of acceleration (with softening). Figure 2. Finite element meshes for a simple slope.

649

(b) Vertical displacement Figure 4. Histories of displacement (with Softening).

Figure 6. Histories of displacement (no softening)

Figure 5. Residual deformation after earthquake (with softening).

near the toe. It suggests that the strain softening during excitation occurred in the area around the toe. In order to investigate the effect of strain softening, a similar analysis based on the elastoperfectly plastic model was performed. In this case, the residual strength are consistent with the peak strength, that is, c = Cr = lOkPa and 4 = @ = 15" . Figure 6 shows the history of calculated relative displacement in this case. Compared them to the results based on the strain-softening model, it is found that the residual deformation based on the elasto-perfectly plastic model is smaller. As described before, the total factor of safety calculated by SSRFEM are almost the same in these cases. This indicates that the strain softening has a greater influence on the seismic stability, compared to the stability based on the static equilibrium.

Figure 5(a) shows the residual deformation after earthquake. The magnitude of relative deformation has been emphasized as 5 times the real scale. A large settlement and upheaving can be seen at the top and the toe, respectively. Figure 5(b) shows the calculated shear strain in the slope after earthquake. Residual shear strain is concentrated to the region 650

3.4 Parametric studies on the width of shear band d

The results calculated by changing the width of shear band are stated here. Figure 7 shows the time histories of horizontal displacement at the top of the slope. The following four cases were performed here; (i) the elasto-perfectly plastic model (indicated as 'no soft.'), (ii) the strain-softening model without

shear bands (as ‘d=non’), (iii) the strain-softening model with shear bands whose width is 50mm (as ‘d=50’) and (iv) the width of shear band is lOmm (as ‘d=10’). As seen in the figure, the decrease of the width of shear band slightly increases the residual deformation. This is a similar tendency to the analytical results reported by Tanaka (1996), such that the decrease of the width of shear band decreases the shear resistance after the peak stress. This is caused by the difference of the extent of a strain concentration along the slip surface.

composed of the first shock (maximum acceleration is 818gal) and the following three aftershocks (max. is 102gal). Figure 9 shows the history of horizontal displacement at the top of the slope, in a case where the material constants used are the same as Table 1. As seen in Figure 9, most part of the total displacement was induced by the first shock, while slight deformations were induced by each small aftershock. Figure 10 shows the horizontal displacement at the top induced by each aftershock. The following three cases were performed here; (i) the elastoperfectly plastic model (indicated as ‘no soft.’), (ii) the parameters are as Table 1 (as ‘A=B=C=0.3’) and (iii) the same as (ii) except for the values of A, B and C replaced by 0.2 (as ‘A=B=C=0.2’). As seen in Figure 10, the residual displacements based on the strain-softening model were much larger than the one based on the elasto-perfectly plastic model. In addition, the increase of the number of aftershock slightly increases the residual displacement during each aftershock, in cases where the strain softening is considered. It is shown that the strain-softening phenomena have a great influence on the residual displacement induced by small aftershocks as well as the first shock.

3.5 Analyses for aftershocks Several aftershocks often occur after a large earthquake. The amplitude of them is much smaller than the main earthquake. Therefore, the damage of slopes during aftershocks is usually very small. However, if the strain-softening soils are included in the slope, there is a possibility of the large deformation induced by aftershocks. In this section, in order to evaluate such phenomena caused by strain softening, a few cases of the seismic response analyses were performed. Figure 8 shows the input waves which is

3.6 Analysis for more sensitive soils Figure 11 shows the history of horizontal displacement at the top and toe of the slope, in a case where A , B and C are assumed to be 0.G1. Shear bands are not considered in this case. Input waves are 10 sine waves whose amplitude is 200gal. It is found that the residual displacement increases even after the earthquake has ended. This seems to be caused by the progressive failure of soil after the earthquake. This suggests that the analyses presented in this paper can simulate the behavior of more sensitive soils such as quick clay. Figure 7. Horizontal displacement in each case. (width of shear band is varied)

4. CONCLUSIONS The summary of this paper is as follows: (1) The seismic behavior of actual slopes composed

Figure 8. Input random waves composed of the first shock and three aftershocks. 651

ACKNOWLEDGEMENT The authors wish to thank Mr. Kei Takafuji, a graduate student of Gunma University, for his great help in FE calculations. REFERENCES Lo, K. Y. and Lee, C. F. (1973) : Stress analysis and slope stability in strain softening materials, Geotechnique, Vo1.23, No. 1, pp. 1- 11. Mori, H. and Tanaka, T. (1995) : Three-dimensional elasto-plastic finite element analysis of short pile and retaining wall and model test, Proc. Symp. on the Three-dimensional Evaluation of Ground Failure, Japanese Geotechnical Society, pp.267274 (in Japanese). Pietruszczak, S.T. and Mroz, Z. (1981) : Finite element analysis of deformation of strainsoftening materials, Int. J. Numer. Meth. Engng. , V01.17, pp.327-334. Tanaka, T. (I 996) : 3-2 Constitutive Relationships for Strain Softening and Dilatancy Properties, The Three-dimensional Elasto-plastic Finite Element Analysis of Ground (a joint work), Maruzen Press., Tokyo, pp.81-86 (in Japanese). Ugai, K. and Ida, H. (1994) : Calculations of total safety factor for slopes of strain-softening soils, Proc. 29Ih Meeting of Japanese Geotechnical Society, pp. 1825-1826 (in Japanese). Ugai, K. and Leshchinsky, D. (1995) : Threedimensional limit equilibrium and finite element analyses; a comparison of results, Soils and Foundations, Vo1.35, No.4, pp. 1-8. Ugai, K., Wakai, A. and IdayH. (1996a) : Static and dynamic analyses of slopes by the 3-D elastoplastic FEM, Proc. 7th Int. Symp. on Landslides, pp.1413-1416, Trondheim, Norway. Ugai, K., Ida, H. and Wakai, A. (1996b) : 3D effects on the stability of slopes during earthquakes, Proc. JSCE, No.554 / 111-37, pp.119-128 (in Japanese). Zienkiewicz, O.C. et al. (1975) : Associated and non-associated visco-plasticity in soil mechanics, Geotechnique, Vo1.25, No.4, pp.671-689.

Figure 9. Horizontal displacement in a case where the random waves including aftershocks are input.

Figure 10. Horizontal displacement by aftershocks.

Figure 11. Typical result for the progressive failure. of strain-softening soils can be simulated by FEM. The effect of strain softening has a great influence on the residual displacement induced by small aftershocks as well as the first shock. (2) The decrease of the width of shear band assumed in the analyses slightly increases the residual deformation of slopes after earthquake.

652

Slope Stability Engineering, Yagi, Yamagami & Jiang cc) 1999 Balkema, Rotterdam, ISBN 905809 0795

Slope instability due to rainfall and earthquake KShimada, H. Fujii, S. Nishimura & T. Nislyama Faculty of EnLGronmentul Science and Technology, Okayuma Universig,Japan

T. Morii Fmulty of Agriculture, Niigata Universitv,Jupun

ABSTRACT : This paper discusses the coincident effects of rainfall and earthquake on the slope stability.Anumerical program for the analysis of the slope instability due to rainfall has been already developed.The program unites a finite element program for the infiltration analysis and a Rigid-Body-Spring-Model(RBSM) program for the slope stability analysis. The numerical results for a model slope show that the reduction of the shear strength of the slope surface soil due to rain infiltration causes the reduction of the safety factor of the slope. When the slope suffers from both rainfall and earthquake, its safety factor will decrease more and it must become more unstable. The effect of seismicity is taken into account by applying the additional horizontal seismic force in RBSM as the pseudo-staticlimit equilibrium procedure of the slope stability analysis. The calculation results show that the slope suffering from the rain infiltration becomes more unstable when the additional seismic force acts. The greater magnitude of the seismic intensity strongly reduces the safety factor of the model slope.

showing the relationship between the horizontal displacements and the shear stresses. The shear test was carried out with the stress-controlled method under the drained condition. Figure 1(b) shows a test result of the same soil with soaking. The shear stress was increased with the same procedure as that of Figure 1 (a) up to the stress level of 80 % of the shear strength. Water for soaking was supplied to the specimen through the lower porous stone while the stress level was kept constant. When the specimen was soaked, the horizontal displacement started to increase gradually, and then the specimen finally failed. Figure 1 shows that the specimen compacted even with the optimum water content has failed by soaking at the 80 % stress level of the shear strength. However, the change of the matric suction was not measured in the soaking test. We therefore only recognize the reduction of the shear strength due to soaking, but we cannot obtain the shear strength of the soil for an arbitrary matric suction. Figure 2 (Shimada et al. 1998) shows results of the suction-controlled direct shear box tests for an unsaturated decomposed granite soil, showing the relationship between the horizontal displacements and the shear stresses with the different matric suctions (S,). The shear strengths decrease with the decrease of the matric suction under the same normal stress (0).The shear tests were carried out with the controlled matric suction method. We can therefore obtain the shear strength for an arbitrary rnatric suction.

1 INTRODUCTION Rainfall and earthquake are essential factors in slope stability. When rain water penetrates into unsaturated slope soils, the matric suction in the soils will decrease. This change will cause the reduction of the shear strength of the slope soils and will then cause the instability of the slopes. The major cause of the slope failures due to rainfall can be the rise of a ground water table and the reduction of the effective stress in the slope soil. Then, the reduction of the shear strength due to rain infiltration cannot be a major one. However, the slope becomes unstable even though it does not fail. If an earthquake strikes the slope during rainfall, its safety factor will decrease more and the slope must become more unstable. This paper discusses the coincident effects of rainfall and earthquake on the slope stability through the numerical analysis.

2 REDUCTION OF SHEAR STRENGTH OF UNSATUFUTED SOILS DUE TO WE?TING 2.1 Experimental results Shimada (1986) has shown the reduction of the shear strength of a compacted soil due to soaking. Figure 1(a) presents a result of the direct shear box test for a clayey soil compacted with the optimum water content,

653

2.2 Introducing strength change due to wetting into numerical analysis We have two approaches for introducing the change of shear strength with the matric suction into the numerical analyses. Elastoplastic deformation analyses coupled with the analysis of infiltration (Alonso et al. 1990, Kohgo et al. 1993) are rational, but are somewhat complicated. An uncoupled analysis is the other one, which is simple and is easily applicable to the slope stability analysis. When we confine discussion in the slope stability analysis, we can ignore the effect of the displacements prior to failure. We can then apply the uncoupled analysis for the stability analysis of unsaturated slopes considering the change of the matric suction within the slopes due to rain infiltration. Since we employ the total stress in the uncoupled analysis, we do not consider the change of the effective stress in describing failure, but consider the changes of the shear strength parameters, c and $, with the matric suction in the next Coulomb equation;

where c is cohesion, cp angle of shear resistance. Both parameters are associated with the total normal stress. They are not constant, but they vary with the matric suction. It is not difficult to introduce the change of the parameters into numerical analyses. Figure 3 (Shimada et al. 1998) summarizes the result of the direct shear box tests shown in Figure 2. The figure indicates that both the shear strength parameters,c and $, appear to vary with the matric suction. The variation of c and 4 can be directly introduced into the numerical analysis, and no functional relations of c and $ with the matric suction are employed in this paper. The magnitudes of c and $ for an arbitrary matric suction are linearly interpolated from the experimental data shown in Figure 3.

Figure 1 Reduction of shear strength due to soaking

Figure 2 Change of shear strength with matric suction

3 NUMERICAL ANALYSIS

3.1 Uncoupledprogram A FORTRAN program used herein has united 1) a finite element program for the infiltration analysis and 2) a Rigid-Body-Spring-Model program for the slope stability analysis. The finite element program for infiltration had been coded according to the paper by Neuman (1973), who had firstly presented the finite element treatment for saturated-unsaturated seepage. The Rigid-Body-Spring-Model (RBSM) had been originally proposed by Kawai et al. (1977). The model employs the Coulomb’s failure criterion and the associated flow rule for the plastic constitutive relations of the springs, which connect with rigid triangular elements. In the slope stability analysis, RBSM 654

Figure 3 Variation of cohesion and angle of shear resistance ofMasa96 with matric suction

multiplies the unit weight of a slope soil to yield the springs one by one. R m i n is the multiplying factor at which the slope becomes unstable. The program can predict the change of the safety factor, R m i n , of unsaturated slopes considering the reduction of shear strengths of the slope soils due to rain infiltration (Shimada et al. 1995). When the ground water table has developed in the slope, we can evaluate the stability of the slope in terms of effectivestress with introducing the seepage force and the buoyancy into the analysis for the domain of the positive pore water pressure (Morii et al., 1995). Figure 4 Mesh of model slope

3.2 Analysis for-earthquakes The effect of earthquake on slopes is analyzed with the pseudo-static limit equilibrium procedure, which applies the horizontal seismic force to each element in RBSM. The seismic force is assumed to be equal to the weight of a slope soil multiplied by the horizontal seismic coefficient, Kh. The effects of the rise of the pore water pressure and loss of the shear strength during dynamic loading imposed by an earthquake are ignored in this paper. Figure 4 shows the mesh descretization for the model slope used in the analyses. A soil spreads uniformly on a stiff rock foundation. The right boundary is located 50 m away from the origin of the coordinates for avoiding effects of constrains at the boundary, but is not shown in the figure. The calculation results are shown in Figure 5 , comparing with the result by the Bishop's simplified method considering seismicity. Presented with the line segments in the figure is the displacement vectors calculated from RBSM with soil constants indicated in the figure. The slip circle, which is calculated from the Bishop's method with the same soil constants, is also drawn in the figure. The magnitude of R m i n is almost equal to the safety factor (Fs)from the Bishop's method. The location of the slip circle is also fairly identical to the slip line presumed from the displacement vectors calculated from RBSM. When a slope suffers from raining, the safety factor of the slope decreases with time. If an earthquake strikes the slope suffering from rainfall, it must become more unstable and the safety factor drops suddenly. The situation is schematically shown in Figure 6.

4 COINCIDENT EFFECTS OF RAINFALL AND EARTHQUAKE ON SLOPE STABILITY Calculations are carried out for the model slope shown in Figure 4. Since the surface of the model slope is assumed to be bare, the effects of vegetation on the slope stability, i.e., the root reinforcement and the change of the infiltration rate etc, are ignored. Carrying out the uncoupled analysis, we need information of the changes of the shear strength

Figure 5 Results of slope stability analyses considering seismicity

Figure 6 Drop of safety factor due to earthquake

parameters with the matric suction, and that of the unsaturated properties of soils, i.e., the soil-water characteristic curve and the coefficient of unsaturated permeability. The following conditions are employed in the calculations: 1) The variation of the shear strength parameters, c and $, with the matric suction is that of the decomposed granite soil shown in Figure 3. 2) The unsaturated properties of the slope soil is that 655

of a decomposed granite soil, obtained by Aoyama (1987), shown in Figure 7. The maximum matric suction is modified according to that in the data set of the shear strength parameters. 3) The initial matric suction, S, = 50 kPa, spreads uniformly in the soil. 4) The rain intensities ( I ) on the slope surface are 20 and 30 mm/h, and are kept constant throughout the analyses. 5) Young's modulus = 9.81 x 104kPa, and Poisson's ratio = 0.3 for the soil in the slope. 6) The variation of the unit weight of the soil with the matric suction is also introduced. (Shimada et al. 1998) Figure 8 shows the result for the case of the horizontal seismic coefficient, Kh = 0 to 0.2, with the rain intensity, I = 20 m m h . The safety factor of the model slope drops fast for the greater magnitude of Kh. The simulation result for I = 30 mm/h is shown in Figure 9. The figure gives the same tendency as that in Figure 8, however safety factors of the slope decrease faster than that for I = 20 m m k .

Figure 7 Unsaturated properties of Masuda Masa (Aoyama 1987, partly modified)

5 CONCLUSIONS When a slope suffers from both rainfall and earthquake, its safety factor will decrease and it must become more unstable. This paper presents the coincident effects of rainfall and earthquake on the slope stability through the numerical analysis. Simulation results for a model slope show that the slope suffering from the rain infiltration becomes more unstable when the additional seismic force acts. The greater magnitude of the seismic intensity strongly reduces the safety factor of the model slope.

Figure 8 Reduction of safety factor of slope of Masuda Masa, I = 20 mm/h

REFERENCES Alonso, E.E., A.Gens & A.Josa 1990. A constitutive model for partially saturated soils. Gkotechnique, 40(3) : 405430. Aoyama C. 1987. Physical and engineering properties of decomposed granite soils. Doctoral dissertation :Kansai Universip. (in Japanese) Kawai T. & Toi Y. 1977.Anew element in discrete analysis of plane strain problem. Journal of Seisan Kenkyu' Institute of Industrial Science, University of Tokyo 29(4) : 204-207. Kohgo Y., Nakano M. & Miyazaki T. 1993. Theoretical aspects of constitutive modelling for unsaturated soils. Soils and Foundations, 33(4) : 49-63. Morii T., Hattori K., Hasegawa T. & Shimada K. 1995. Stability of earth dams subjected to storms with changing external water levels, Tram of JSIDRE, 180 : 85-92. Neuman, S.P. 1973. Saturated-unsaturatedseepage by finite elements. Proc. of ASCE 99(HY12) : 2233-2250. Shimada K. 1986. Changes in shear characteristics of compacted soils due to soaking, Bulletin of Ishikawa Prefecture College ofAgriculture, 16 : 29-37. 656

Figure 9 Reduction of safety factor of slope of Masuda Masa, I = 30 mm/h Shimada K., Fujii H., Nishimura S. & Morii T. 1995. Stability analysis of unsaturated slopes considering changes of matric suction. Proc. of 1st. Int. Conf on Unsaturated Soils, 1:293-299.Rotterdam : Balkema. Shimada K., Fujii H., Nishimura S., Nishiyama T. & Morii T. 1998. Hysteresis effect of decomposed granite soil on slope instability due to rainfall. Proc. of 8th. Int. Cong. International Association for Engineering Geology and the Environment : 1981-1986.Rotterdam : Balkema.

Slope Stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Shaking table tests of concrete block retaining walls S. Mori Department of Civil and Environmental Engineering, Ehime Universig, Japan

T. Matsuyama Nihon Kogyo Incorporated, Japan

T.Ushiro Dai-lchi Consultants Incorporated, Japan

ABSTRACT: Authors conducted 1G shaking table tests with models of concrete block retaining walls for the development of their seismic safety evaluation method. The objectives of this paper are to investigate the failure mechanism of the block retaining walls, to understand the influential factors on their failure, and to clarify the effect of the reinforcement on the walls. The test results clarified the failure process, and enabled us to define the yield of the walls. It is concluded that the weight of the block composing the walls, the apparent cohesion of the backfills behind the walls, and the presence of the reinforcement increase the acceleration amplitude required to make the walls yield; also that the reinforcement makes their ductility increase effectively. light block, and the other the same filled up with concrete as a heavy block.

1 INTRODUCTION Precast concrete block retaining walls are being widely used in Japan in recent days, because of the performance and the economy in construction (Research Committee for Aseismic Large Concrete Block Retaining Walls 1998). However, the methodology to evaluate their seismic safety has not yet been established. For this reason, authors conducted a series of 1G shaking table tests with instrumented models of block retaining walls for the seismic safety evaluation. The objectives of this paper are to explain the failure mechanism of the block retaining walls, to understand the influential factors on their failure, and to clarify the effect of the reinforcement on the walls.

2 EXPERIMENT 2.1 Experimental uppuratus and models Model wall and backfill prepared for the test in a container were excited in horizontal direction on a shaking table by’ using a mechanical vibrator. Figure 1 shows the experimental apparatus and the model. The container 90 cm wide, 60 cm high, and 30 cm deep was made of a steel frame with three pieces of transparent acrylic plate fixed on it. The model wall consisting of 10-step blocks was 50 cm high with a slope of 1: 0.5. Two blocks different in weight were prepared: one composed of some pieces of chloro-vinyl plate, 5 cm in height, 5 cm in thickness, and attached with a shear key, as a

Figure 1-Experimental apparatus and model

657

2.3 Shaking condition and measurements The models were shaken by sinusoidal waves of 5 to 5.5 Hz in predominant frequency with 50 cycles. The shaking amplitude was adapted to adequate level for each specimen based on the results of preliminary tests. The horizontal acceleration of container, top block and bottom block of the wall were measured by strain-gauge type transducers (AS-2GB), and recorded in 0.006 second’s interval. Moreover, deformation images of the wall and the backfill were taken by a CCD digital video camera at a rate of 30 frames per second.

Figure 2. Configuration of model blocks

3 RESULTS AND DISCUSSIONS After a series of tests, all the unreinforced walls collapsed but most of the reinforced walls did not. Therefore in this reason, in this section, the failure mechanism and the vibration characteristics of unreinforced walls, and the deformation process and the deformation resistance of both reinforced and unreinforced walls are discussed.

Figure 3. Grain size distribution of test soil Figure 2 shows the configuration of the blocks. The bottom of the wall was horizontally restrained, but free to rotate. Backfill with 1.5 g/cm3 dry density was prepared behind the wall by tamping dry or wet decomposed granite soils. Figure 3 shows the grain size distribution of the test soil. Colored sand as index was put horizontally into the backfill at an interval of 10 cm so as to be observed the deformation of the backfill and slip lines in it.

3.1 ~~~l~~~~ illec.zani,srlz of block retainiizg wall The digital video images made it easy to understand the failure mechanism of the block retaining wall. The illustration of the failure process of the unreinfoced wall is shown in Figure 4. In the cases of the unreinforced walls, when the backfill began to move backward just after the return, the wall remained moving forward due to the inertial force. This resulted in the phase delay in the motion of wall, in the separation of the backfill and the wall. Subsequently the separation led to a slide in the backfill. The slide was then promoted by the oscillation inducing new slides in further interior region, which led to the expansion of the sliding area, and to the accumulation of the whole deformation of backfill. The progress in sliding caused deformation in the wall, which was folded out at the mid-height. After this, the upper portion of the wall leaned backward and the lower portion forward, pushing the middle portion outward resulting to the wall collapse. This is the process of the accumulation of the residual deformation and the subsequent collapse of the wall. On the other hand, in the cases of the textilereinforced walls, no sliding occurred in the backfill and the residual deformation of the wall was very small.

2.2 Experimental paranieters The main experimental parameters were the weight of the blocks, the strength of the backfill soil and the reinforcement. The apparent densities of the light and the heavy blocks were 0.61 and 1.55 g/cm3 respectively. The strength of the backfill was controlled by its water content, w. According to preparatory direct shear tests, values of apparent cohesion of the soils with 0, 5 , and 10 96 in water content were 0.98, 10.8, and 19.6 kPa respectively; and value of internal friction angle of all the three cases was the same, 42 degree. For the reinforcement, two types of model wall were prepared; one was unreinforced, and the other reinforced with some pieces of cotton textile as geotextile. A piece of cotton textile, 1 cm wide and 20 cm long was used as a model of geotextile. Three pieces were horizontally set up on every stage at 5, 15, 25, 35, and 45 cm in height from the bottom of the container, and one end of every piece was fixed on the top of the corresponding block.

3.2 Mbration charucteristics of block retaining wall The acceleration time histories of the container and the top of the wall in the case of unreinforced heavy 658

Figure 4. Schematic diagram for failure process of unreinforced wall

Figure 5. Acceleration time histories of container and top of wall in a case of unreinforced heavy block wall with no water content backfill block wall with no water content backfill are shown in Figure 5, as an example of the cases of the unreinforced walls. The accelerogram of the container seemed to be approximately steady sinusoidal oscillation, whereas two distinctive features are recognized in that of top of the wall: one is the subsequence of gradual amplification and sudden attenuation, and the other the appearance of pointed sharp wave-peaks during the amplification process. The amplification may be attributed to the deformation of the wall, the sudden attenuation to the fall-down of the top block, and the pointed sharp peaks to the re-contact of the blocks during their rocking (Fig.5). In the cases of reinforced walls, the response of the wall was almost steady. Based on the analysis of the acceleration records described above, Fourier spectra of the wall and container, and their transfer function are shown in Figures 6a and 6b respectively. Figure 6a indicates

that the predominant frequencies of the container and the wall coincide at about 5 Hz. Both figures show the amplification of the wall at 10 Hz, which may be due to rocking of blocks. According to the observation of video images, the response displacement in the wall amplified consistently with the height of block, and when the wall moved backward, the joints of blocks opened at the front side and the whole wall bent visibly. In the cases of reinforced walls, residual deformation of the wall and amplification of its displacement was relatively very small.

3.3 Deformation process of block retaining wall The displacement time histories of the container and the top blocks were calculated by double integral of their acceleration records with the linear acceleration method. Their displacement time histories and some phenomena like block separation, subsidence of backfill, etc. are shown in Figure 7. The separa659

Figure 6. Fourier spectra of container and wall’s top, and their transfer function

Figure 7. Time histories of integrated displacement of container and wall top, and some phenomena in a case of unreinforced heavy block wall with no water content backfill

Figure 8. Progress of residual shear deformation of the wall with number of cycles of excitation in all cases of unreinforced heavy block wall tion and the phase delay in the motion of wall observed through the video images, are supported by integrated displacement wave forms. These integration analyses clarify that the phase delay increased from 90 to 180 degree with increasing number of cycles, and the separation began when 660

relative forward displacement increased. However, the error in the double integration is not negligible, so that the residual displacement of the wall can not be evaluated quantitatively. Thereupon, shear deformation of the backfill was calculated based on the rotation of the lower portion of the wall measured on the video images. The number of cycles of excitation and the residual shear deformation of the wall in all the cases of the heavy block walls are shown in Figures 8 and 9; Figure 8 shows those for unreinforced wall and Figure 9 for reinforced. In the unreinforced cases, the shear deformation increases radically after it reaches 5 to 10 %. The number of cycles at the start of the radical shear deformation increases with the increase in cohesion of the backfill. According to analysis of the video images, the time of start of the radical increase corresponds to the time of occurrence of an initial evident slide in the backfill. Consequently, 5 % shear deformation, which is the start point of its radical increase due to the initial evident slide occurrence can be defined as the yield of the block wall. On the other hand, in case of the reinforced wall with dry backfill, shear deformation increases gradually after it reaches 5 to 10 %, whereas with the 5 % and 10% water content back-

Figure 12. Relation between yielding input acceleration, Ayield and cohesion of backfill, c (number of 5 5% shear deformation, N5=10)

Figure 9. Progress of residual shear deformation of the wall with number of cycles of excitation in all cases of heavy reinforced block wall

fills, it increases not so distinctly even after it reaches 2 to 5%. Consequently, this result reveals the effect of reinforcement that increases the ductility of the wall.

3.4 Deformation resistance of block retaining wall The deformation resistance of block retaining wall is discussed on the point of the yield of wall mentioned in the previous section. Based on the relation between the number of cycles of excitation and the residual shear deformation of wall as shown in Figures 8 and 9, the number of cycles at 5 % shear deformation, N5 can be obtained. Then, the amplitude of input acceleration, Airrpict is calculated as mean of the three peak values except the maximum and the minimum values from second to sixth pulses in the acceleration time history of container. The dynamic deformation resistance of wall is defined by the with N.5 which is a resistance relationship of Ai,~p~l curve as shown in Figures 10 and 11. These figures with various resistance curves lead us to understand that the input acceleration required to make the wall yield increases with the increase in water content or cohesion of backfill, the increase in weight of block, the existence of reinforcement, and the decrease in the number of cycles. So from the Figures 10 and 11, the yielding input acceleration, AyieId as a simple index of the strength of wall may be defined as the input acceleration required to make the wall yield at 10 cycles. The relationship between the yielding input acceleration and the cohesion of backfill is shown in Figure 12. This figure clearly summarizes the whole results of this research, as mentioned in the last paragraph. The results of the present study seem to provide some useful information for the development of seismic safety evaluation method, and for the development of seismic retrofit technique.

Figure 10. Relation between input acceleration and number of cycles at 5 % shear deformation in case of heavy block wall

Figure 11. Relation between input acceleration and number of cycles at 5 % shear deformation in case of light block wall

661

4 CONCLUSION The failure mechanism, the vibration characteristics, the deformation process and the deformation resistance of block retaining walls were studied by carrying out a series of shaking table tests with various models. Based on the results of the tests, following conclusions are drawn as follows: (1) The failure process of unreinforced wall was clearly understood after the tests. At first, there occurs a phase delay in the motion of wall that causes a separation of backfill and wall leading to a slide in the backfill. Then, the sliding gets promoted and expands due to the oscillation of the container. After that, the wall is folded out at the mid-height and the residual deformation of wall is accumulated, which finally causes the collapse of the wall. (2) In the case of reinforced wall, the shear deformation of wall increases gradually and reaches the maximum value of 2 to 5 %, which is not sufficient to cause the collapse of the wall. So none of the reinforced wall models collapsed during the tests. (3) The shear deformation of unreinforced wall increases radically after it reaches 5 to 10 %. So the 5 % shear deformation, which is the start point of its radical increase due to the initial evident slide occurrence, can be termed as the yield of block wall. (4) The input acceleration required to make the wall yield increases with the increase in water content or cohesion of the backfill, increase in weight of the block, and the existence of reinforcement. Consequently, it can be said that the reinforcement by geotextile is highly effective in increasing the ductility of block retaining walls.

ACKNOWLEDGEMENT Authors would like to express their sincere gratitude to Prof. N.Yagi and Prof. R.Yatabe of Ehime University for their advice. Authors would like to thank O.Futagami, technical official and K.Morino, undergraduate student of Ehime University for their assistance during the experiments. REFERENCE Research Committee on Aseismic Large Concrete Block Retaining Walls 1998: Manual of design and construction of large-block retaining walls. Takamatsu, Japan: Shikoku Blanch of Japan Society of Civil Engineers (in Japanese)

662

slope stability Engineering, Yagi, Yamagami & Jiang 0 1999 Balkema, Rotterdam, ISBN 90 5809 079 5

Shakedown analysis of soil foundations under varied loads Maotian Luan & Yongzhe Cao Department of Civil Engineering and State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, People’s Republic of China

Keizo Ugai Department of Civil Engineering, Gunma University, Kiryu, Japan

ABSTRACT: In this paper, the importance of fundamental concept and analysis method of plastic shakedown in geotmechanics is emphasized. The temperature parametric procedure developed by Qian & Wang (1989) in which nodal temperature is taken as adjustable variable of finite element analysis is introduced for constructing self-equilibrium stress field. Then the mathematical formulation and numerical algorithm for limit analysis and shakedown analysis are established on the basis of the lower-bound theorems. Numerical computations and analyses are made for strip footing on soil foundation subjected to varied loads and the effect of the cyclic and variable property of externally-applied loading on bearing capacity of foundation is discussed. A comprehensive method based on the envelope diagram of the shakedown load is proposed for evaluating stability of foundations under complex variable loading. 1 INTRODUCTION Ultimate bearing capacity of soil structures and foundations under simple loading programs can be predicted directly and effectively by applying limit analysis theorems of plasticity. In fact, loading mode or pattern exerted on structures and foundations are usually rather complex, e.g., for a gravity-type offshore platform foundation, seismically- or waveinduced loads are always alternating in both direction and acting position. However, the magnitude bounds of load variations can be defined. For these structures and foundations, only pseudostatic evaluation of bearing capacity under monotonic loads and purely elastic analysis of transient responses under cyclic loading do not mean that whole structures can offer sufficient strength to actual varied loads, also permanent deformation can be constrained. In fact, for the structure with the elastic-plastic deformation nature, unconstrained irrecoverable deformation will be either accumulated progressively or two-directional alternating plastic deformation will continue without ceasing under transient or cycle loading programs. If the increasing plastic deformation or hysteretic-energy dissipation can attain a stable state, the soil mass will be said to shakedown to corresponding deformation and residual stress field. If a stable plastic deformation state is attained after a finite number of cycles or within a limited time of instantaneous loading, the structures or foundations will behave purely

elastically upon subsequent cycles of loading as long as the applied loading varies arbitrarily within the given range. Otherwise, soil mass will be in either incremental collapse caused by one-way progressive plastic deformation, or alternating plasticity collapse caused by fatigue failure while different directional alternating plastic deformation will unceasingly continue. Soils in the shakedown state will deform continually until the deformation reaches a finite ultimate value and stabilizes after several cycles. In the case of incremental collapse or alternating plasticity, soils will deform limitlessly with loading time. Therefore, for the structures and foundations subjected to complex loading sequence, shakedown analysis is of practical significance. For the offshore platform foundations, shakedown under repeated varying loads or even dynamic loads should be ensured so that the structures are both safe under static loads and shakedown under varied loads. Shakedown analysis is the extension of limit analysis. In the engineering design, shakedown analysis is aimed to estimate shakedown loads of structures or foundations subjected to varied loads. In order to ascertain the actual meaning of shakedown analysis in geotechnical engineering, an effort is made to develop the computational method on the basis of existing elasto-plastic shakedown analysis theorem. In consideration of the state-ofthe-art and the importance and necessity of shakedown analysis (e.g., Aboustit & Reddy 1980, Pande et a1 1982), advanced numerical analysis

663

can be taken as independent variables and the corresponding thermo-stress field can be taken as self-equilibrium residual stress field. The procedure for constructing self-equilibrium stresses on the basis of the above-mentioned technique is called temperature-parametric method. By adjusting nodal temperature variables, the corresponding selfequilibrium thermo-stress fields will be changed. Additionally such self-equilibrium stress fields are constrained not to violent the yield condition in order to achieve statically admissible stress fields. The thermo-stress which can make the load multiplier acquire its maximum is the optimum residual stress field, and the corresponding load multiplier is shakedown load multiplier. The product of shakedown load multiplier and basic load factor is the shakedown load, which is one of the maximum lower bound of the real shakedown load. All the components of the shakedown load will constitute an outward convex envelope in the load space. The boundary-value problem to be evaluated can be induced to a mathematical extreme-value issue and can be solved by mathematical programming techniques. Since the widely-used Mohr-Coulomb yield criterion is the non-linear function of the stress components, therefore the resulting mathematical programming problem is usually of non-linear type. To simplify the problem, linearization of the MohrCoulomb yield criterion is conducted iii order to solve the final problem by using usual linear programming procedures. Limit analysis can be stated as the special case of shakedown analysis while the range of load is set to be zero. Numerical analysis approach based on finite element method is used. An unified computational formulation for both limit analysis and shakedown analysis is established on the basis of temperature parametric method. The resulting extreme-value problem is solved using linear programming techniques. The effective approaches to reduce the constraint number are proposed. A strip footing on soil foundation upon varied loads is analyzed as an illustrative example for application of shakedown analysis in geotechnicai engineering. Comparisons among the computed results and existing theoretical or numerical solutions are made for verifying the reasonability and effectiveness of the proposed technique.

procedure is combined with mathematical programming techniques to develop practical mathematical formulations and effective numerical algorithm of shakedown analysis. Numerical computations are performed for a strip footing on soil foundation and comparisons between the limit loads and shakedown loads are made. Shakedown load envelope diagram in the load space is proposed for evaluating dynamic stability of soil foundations under complex loading condition. Some preliminary findings are given for improving design of foundation under varied load. 2

LIMIT ANALYSIS ANALYSIS

AND

SHAKEDOWN

In limit analysis and shakedown analysis of solid mechanics, two bound theorems are usually used to directly solve for the upper-bound or lower-bound ultimate loads of structures. Upper-bound theorem is based on kinematically allowable velocity fields while lower-bound theorem is on the basis of the statically admissible stress field. However, it is difficult to search the best kinematically allowable velocity field of structures by using finite element method. Therefore, in the most cases, to search for the optimum statically allowable stress field is the main objective in order to get the lower bound of limit load or shakedown load. Lower theorem of shakedown analysis, i.e., so-called Melan’s theorem, can be stated that if such a time-independent residual stress filed can be found that the combination of these residual stresses with elastic stresses 01“ induced by arbitrary load within a given range stifl does not violate the yield condition, i.e., f ( a g +oT)5 0 (1) then the structure will shakedown, where f(o,) I 0 is the yield function. Therefore in solving for lower-bound shakedown load based on statictype shakedown theorem, the key issue is to find or construct a time-independent residual stress field which is in self-equilibrium. The shakedown load corresponding to such a stress field will be a lower bound of the real shakedown load. Among all the statically allowable stress fields, the best or optimal one is the stress field that can allow the variation range of externally-applied loads to attain its maximum value. Two main aspects are contained in implementation of the lower-bound shakedown analysis, i.e., (1) constructing of self-equilibrium residual stress fields which meet all mechanical equilibrium conditions within the soil mass and boundaries and don’t violate the yield condition, (2) searching of the optimum self-equilibrium residual stress field. Noticing the fact that thermo-elastic stress field caused by temperature variation is a selfequilibrium stress filed, nodal unknown temperatures

3

SHAKEDOWN ANALYSIS BASED ON TEMPERATURE PARAMETRIC METHOD

In order to reduce the shakedown analysis issue to a linear programming problem, the linearization of the Mohr-Coulomb yield criterion is made. The yield criterion f(o,.) I 0 can be expressed in the form of linear inequalify as follows

664

in which N' is the assemblage of outward normal unit vector of the i-th element, NI is the unit outward normal vector of the j-th plane, ,K, represents the distance of the j-th linearized yield plane from the origin, r represents the number of elements, 1 is the number of linearized planes. Equation 2 indicates that the projection of stresses on the outward normal of each yield plane should not exceed the distance of the yield plane from the origin. The Mohr-Coulomb criterion in the plane condition can be expressed as follows

[ K ) = [ 2 c 2c 2c 2c 2c 2 c r

(5)

where c and p are cohesion and internal friction angle of soil respectively, e = sin p . For the j-th linearized plane, the yield condition can be written as 4; = Ni,QL + NfQ; - Ki, I 0 (6) where QE is elastic stress and QR is residual stress. This equation can be stated in the vector form as (7)

Furthermore (QE] can be resolved into two parts, i.e., purely-elastic stress {Qd,-} which is in equil'brium with basic loads, and elastic stress (Qs,-) which is corresponding to the fixed static loads. As a result, the lower-bound theorem of shakedown analysis can be stated that for a known elastic stress field (Q, ] which fulfills equilibrium conditions, a residual stress field {QR} which can make load multiplier A of basic load to attain its maximum value is to be found. This statement can be mathematically formulated max A s.t*

a[N](~d,}+[N]{~sE]+[N]{~~]-

'

(K}

(8)

220

Figure 1 Linearized Mohr-Coulomb criterion

The maximum of the projection of elastic stresses QiE(t) on the outward normal vector Ni, of the yield plane is assumed as M J

MJ = max{NJQ;, (t)) where

(9)

In shakedown analysis, it is assumed that the externally-applied load varies in the following pattern

<(,' ') = (')pk (t> {WI = PIT W I

(1 1)


or

Figure 2 Linearized Mohr-Coulomb criterion The yield surface is an elliptic awl in the stress space (ox,o Y zxJ,). , Six planes used to linearize the surface are shown in Figure 1 and Figure 2. The elements of the matrix N and vector K are given as follows (Luan 1989 after Anderhaggen)

(12)

where T k ( x ) represents the basic loading pattern, p k ( t ) is the combination coefficient of various loads . In the most cases, the variation range of each load coefficient is known or can be assumed in advance, e.g., p- 5 p ( t ) . < p + , the history of variation p ( t ) with the time is usually unknown, pi

pk (')' p i ,

'

{p-}' (p(')> (p')

(I3)

Elastic stress under the k-th basic load pattern T k ( x ) is stated as a,dE,the total elastic stress

665

under all load patterns can be written as odE

- C.OiEPk

tf)

(14) While ,u-=,u+,i.e., there is no variation of external load, the computation will be of limit analysis. While p- + p+ , all or parts of loading components are varied, each basic load component can vary independently in the given range. According to the temperature parametric method developed by Qian & Wang (1989), the temperatures of finite element nodes are taken as independent variable, the elastic stress field caused by the variation of temperatures is taken as self-equilibrium residual stress field. This self-equilibrium stress field will be adjusted by varying each nodal temperature and then will be statically allowable by fulfilling the no-yield condition. The optimum staticallyadmissible stress field can be constituted. The maximum of the load multiplier corresponding to such a stress distribution is the limit multiplier or shakedown multiplier. Triangle-type finite elements are used in the following as example. In constructing residual stress field QR,the temperature change of three nodes of triangle element in the plane problem is designated as T, , T, and T,n respectively and the temperature within element is assumed to distribute linearly, the interpolation function is taken as the same as the displacement function,

i

T(x,Y) = NJk

(15)

Equivalent nodal loads caused by this temperature field can be written as

[Q' ] = I [Bf'[DIQdy

= [G.

IT'}

'3

11 1 11 1

'H ' - 3 o - P )

0 0 0

Assembling leads to

b}= [DIIBl{4- [ M E 0 1= [SIKI-' {QI- [HIfO = [Sl[Kl-' [CllrrI- [Hl(r) (23)

Shakedown theorem can be stated as max A s.t. A { M }+ [N]([SIK]-'[G]{T}- [H]{7.}) i { K '} (24) 220

in which {K'} = ( K }- [NI' {osE } . Introducing nonnegative constraints and setting ( T }= (T'}- {T"}, the mathematical programming can be rewritten as max A s.t.

A ( M )+ [Ax{T')- {T"})i ( K }

a 2 O , T ~2 O,T" 2 o

(251

where

"1

QI

[AI = [Kl-"Gl- (HI) (26) Equation 25 is a standard linear programming problem. The constraint number is equal to rnl, i.e., product of the number r of elements, the number n of nodes and the number 1 of linearized yield planes, and the number of the variables is 2ri-1. Since the number of variable is less than the number of constraints, it will be more efficient to solve the dual form of the programming as stated as follows

(16)

where t is the thickness of structure. Substituting boundary conditio s and constitutive law as well as initial strain {EJ= aT[l 1 01' into the above equation leads to [Qe]

(o.)= [DekzO}= [ H e ] { T e } where

(17)

in which

{ ~ e ) =[T~ T, T J (19) Then the characteristic sub-matrices Q e , G', T' of each element are assembled to lead the global characteristic matrices Q , G, T of the structure. The varying temperature-caused stress of the element can be given

s.t.

(27)

The fact that [A]' {y}2 0 and -[A]' {y}5 0 leads to [A]' {y}= 0 . Therefore the problem can be finally stated as

Introducing artificial variables in the above formulation, a standard linear programming is obtained and can be solved by existing algorithms.

4 EXAMPLE STUDIES Shakedown analyses of the strip foundation under different circumstances are made by the above formulations and proposed method.

666

vertical component, horizontal component and moment (or eccentricity) will constitute an outward convex envelope in the load space. Typical illustrative presentations are shown in Figure 4 and Figure 5 . Such an interaction diagram is called here the ultimate load envelope for limit analysis or shakedown load envelope for shakedown analysis. When the actual load is located within the envelope, the structure or foundation will be statically safe under monotonic loading or will be shakedown under varied loading. Otherwise, limit equilibrium state or plastic non-shakedown (i.e., alternating plasticity or progressive failure) state will occur. Based on the ultimate load diagram and shakedown load diagram, a comprehensive method is proposed for evaluating static or dynamic stability Figure 3 Loading pattern and the finite of structures and foundations under complex loading element model of the strip footing. conditions. In three-dimensional space consisting of three loading components, various combinations of The loading mode and finite element model are shakedown loads or limit loads constitute a threeshown in Figure 3 in which B is the width of the strip dimensional outward convex surface. For a given footing and A is the area of the foundation with unit value of one component, the inter-relation graph length. p , = ‘yA represents the uniformlybetween other two components is called shakedown distributed vertical load, and p,, = ‘yA defines the load or limit load curve, which is an outward convex uniform horizontal load intensity while A4 is the curve and dependent on the third component value. gross moment acted on the footing. A number of For example, when the load eccentric distance e is cases are computed and main typical computational fixed, the horizontal component and vertical results are shown in Figure 4 and Figure 5 . Based on component of load in the shakedown state or the numerical results, comparative studies of limit limit-equilibrium state will establish the p,,-py analysis and shakedown analysis are performed. The diagram, as shown in Figure 4. The shape and main findings are presented as below, magnitude depend on the eccentric distance of the (1) For the strip footing founded on purely load and the soil strength property. Obviously the cohesive soil foundation subjected to the vertical shakedown load envelope must be situated in the loading, the vertical bearing capacity of 5 . 2 0 ~is inside of the limit load envelope. The difference estimated by the present method. The numerical between two envelopes indicates that variable nature solutions using elasto-plastic finite element method of cyclic or transient externally-applied loading has given by Hoeg, Chen, Valliappan, Aboustit and a significant effect on bearing capacity of Reddy are respectively 5.14c, 5.26c, 5 . 2 0 ~and 4 . 8 6 ~ foundation. (referring to Aboustit & Reddy 1980) while the Based on computational results, comparative theoretical solution given by Prandtl (192 1) is 5 . 1 2 ~ . studies show that the shakedown load is obviously It can be concluded that the present result agrees well lower than the limit load due to alternating or cyclic with the existing numerical or analytical solutions. nature of load. Therefore, in the design of structures However, the shakedown vertical load computed by and foundations subjected to varied loads, e.g., the present procedure is 4 . 3 0 ~which ~ is reduced by cyclic or transient load induced by earthquake 16% compared with the corresponding limit load. shaking or ocean wave, shakedown analysis is (2) For the strip footing founded on cohesivenecessary in addition to evaluation of bearing frictional soil under the inclined (the inclined angle capacity under monotonous loading. Furthermore, with vertical is +45’) and eccentric (the eccentricity both ultimate bearing capacity and shakedown load distance e varies between -B/12 and B/12) loads, the increase remarkably with the increase of soil numerical results show that shakedown load cohesion and internal friction angle. The influence increases linearly with the increase of the soil of the friction angle is more significant. Since uniaxial compressive strength f,,, where offshore foundations are usually subjected to fcL, = 2c cos @/(1 - sin 4). Therefore shakedown load horizontal loads, vertical loads and moments increases remarkably with increaseing of soil internal simultaneously, shakedown analysis is more friction angle. important compared with limit analysis and the (3) For the strip footing on cohesionless or proposed envelope can be used for rationally cohesive-frictional soil foundation subjected to evaluating stability under complex loading modes. simultaneous exerting of horizontal load and vertical load as well as moment, the inter-relationship among 667

cyclic loading will result in obvious reduction of bearing capacity of soils. These results and conclusions have important indications on improving the design of offshore platform foundations. ACKNOWLEDGEMENTS The financial supports from the National Natural Science Foundation of China through the grant No. 597790 17 and from the Trans-Century Training Programme Foundation for the Talents offered by the Ministry of Education of China are gratefully acknowledged. The authors would like to express thanks to the Heiwa Nakajima Foundation which makes their cooperation possible.

Figure 4 pI,-pv interaction diagram

REFERENCES Aboustit, B.L. & D.V. Reddy 1980. Finite element linear programming approach to foundation shakedown. Proceedings of International Symposium on Soils under Cyclic and Transient Loading, Swansea, 7-1 1 January 1980: 727-738. Luan, M.T. 1989. Dynamic stability analyses of nonhomogeneous soil structures and foundations. Dissertation submitted in partial fulfil1 of the requirements for the degree of Doctor of Philosophy in Engineering, Dalian University of Technology, Dalian. Qian, L.X. & Z.B. Wang 1989. Limit analysis and shakedown analysis of engineering structures. Computational Structural Mechanics and Application, 6(1):113-121. Pande, G.N., W.S. Abdullah & E.H. Davis 1982. Shakedown of elasto-plastic continua with special reference to soil-rock structures. Proceedings of International Symposium on Soils under Cyclic and Transient Loading, Swansea, 7- 11 January 1980: 738-746.

Figure 5 p,-A4 interaction diagram

5 CONCLUSIONS In this paper, the lower-bound theorem of shakedown analysis is extended to the pressuredependent frictionally-behaving soil material. The approach for constituting self-equilibrium residual stress field by integrating the finite element method and temperature parametric procedure is developed for implementing the lower-bound theorem of the shakedown analysis and mathematical formulation and numerical algorithm are provided. For the strip footing on cohesive or sandy soil foundations, the shakedown loads are computed. For the soil structures and foundations subjected to complex loading, the comprehensive methodology for stability evaluation using the proposed limit load diagram and shakedown load diagram is presented. It is found that the variable nature of transient or 668

Abe, H. 141,483 Adachi, T. 333 Ali, EH. 375,393,399 Allersma, H.G. B. 447 Aoki, M. 121 Araki, S. 423 Baker, R. 253 Bianchi, E 233 Bijoy, A.C. 249 Bromhead, E. N.41 1 Cai, E 551 Cao, Y. 663 Chen, S.S. 329 Chen, Z. 15 Chen, Z.Y. 325 Chigira, M. 163 Cola, S. 239 Dangol, V. 193 Dembicki, E. 181 Dissanayake, A. K. 495 Dixon, N.151 Elleboudy, A. M. 103 Elsoufiev, S.A. 213 Enoki, M. 429 Fang, X.S. 329 Feng, T.Q. 31 1,317 Fredlund, D.G. 3 1 Fujii, A. 459 Fujii, H. 219, 653 Fujii, T. 607 Fujita, T. 169 Fujiwara, T. 147 Fukui, H. 333 Fukuoka, H. 577,589 Furuta, M. 459

Gardner, J.V. 127 Gottardi. G. 233 Han, D. 509 Hanagata, S. 245 Harris, A. J. 41 1 Hasegawa, S. 157 Hayamizu, H. 265 Hayashi, K. 489 Hayashi, S. 271 Hazarika, H. 265 He, S.X. 277 Hill, R. 151 Hiraiwa, Y. 417 Hori, T. 219 Hoshikawa, T. 225 Hu, Y. 349 Huang, R. 533 Huat, L.T. 393,399 Hughes Clarke, J. E. 127 Hyodo, M. 607

Kim, K. 509 Kitagawa, R. 109 Kitamura, H. 121 Kitamura, R. 141,483 Kobayashi, T. 539 Kobayashi, Y. 565,625 Kojima, J. 245 Kokubu, A.A. 429 Komatsu, M. 465 Kondo, K. 271,613 Koseki, J. 6 13 Kousteni, A. 151 Kudella, I? 619 Kumazaki, 1.417 Kusakabe, S. 607 Kuwano, J. 595 Kuwano, R. 595

Jiang, J.-C. 293,299,305,3 I 1, 3 17,545 Jomoto, K. 141

Lacerda, W.A. 199 Law, K.T. 281 Lee, C. E 28 1 Lee, H. 127 Leong, E.C. 387 Leshchinsky, D. 49 Liang, R. 355 Liu, Z.D. 277 Locat, J. 127 Low, B. K. 387 Luan, M. 281 , 663

Kamai, T. 565 Kammerer, E. 127 Karube, D. 381 Kato, K. 52 1,527 Kavanagh, J. 15I Kawai, K. 381 Kawamura, K. 361 Kazama, M. 641 Kempfert, H.-G. 349 Khan, Y.A. 299

Maharaj, R.J. I15 Marchi, G. 233 Mariappan, S. 393,399 Matsuka, S. 135 Matsumoto, N.5 15 Matsuo, 0. 613 Matsuyama, T. 657 Mayer, L. 127 Michalowski, R. L. 637 Mikasa, M. 259

Iryo, T. 141,483 Ishibashi, A. 147 Ishihara, K. 3,595

669

Miki, H. 459 Mizunaga, T. 539 Mochizuki, A. 259 Mokudai, K. 163 Monma, K. 147 Mori, S. 657 Morii, T. 653 Murata, S. 489 Nakai, T. 225 Nakamura, Y. 245 Nakata, Y. 607 Nakayama, S. 3 Nakayama, T. 339 Nara, T. 47 1 Narita, K. 245 Nawari, N.O. 355 Ng, F? B. 405 Nian, T. 28 1 Nishi, Y. 225 Nishida, K. 423,545 Nishigaki, M. 465 Nishihara, S. 6 13 Nishlkawa, T. 121 Nishimura, S. 219,653 Nishioka, M. 361 Nishiyama, T. 653 Nishizawa, N.417 Ohne, Y. 245 Oka, E 333 Okada, Y. 577 Okamoto, T. 63 1 Okimura, T. 571 Onitsuka, K. 441 Orihara, K. 405 Osaki, H. 333 Paudel, T. R. 193 Pender, M.J. 367 Poh, K. K. 40.5 Popescu, M. 67 Po~rlos,H.G. 83 Qin Siqing 207

Rahardjo, H. 387 Rasula, G. 501 Rasula, M. 501 Razaghi, H. R. 641 Sakajo, S. 521,527 Sakurai, S. 339 Sasaki, S. 423 Sasaki, Y. 495 Sassa, K. 577,585,589,601 Sato, T. 417 Sawada, T. 157 Scoular, R. E.G. 3 1 Seguchi, H. 38 1 Sehara, Y. 5 15 Seneviratne, N. H. 495 Shibuya, H. 489 Shimada, K. 219,653 Shimizu, M. 453 Shioi, Y. 559 Shuzui, H. 565 Simonini, I? 239 Sivakumar Babu, G. L. 249 Soon, €? K. 393 Subotowicz, W. 181 Subramaniam, R. 37.5 Sugii, T. 477 Sugiyama, T. 47 1 Sutoh, S. 559 Suzuki, M. 121,515 Taki, M. 293 Tamura, E. 135 Tanaka, Y. 253 Terachi, T. 14 I Terado, Y. 265 Togari-Ohta, A. 471 Tohari, A. 465 Tonni, L. 233 Torii, N. 57 1 Tsukamoto, Y. 3 Ueno, S. 175 Ueta, Y. 305 Ugai, K. 28 1,551,647,663

670

Umezaki, T. 121 Uno, T. 477 Ushiro, T. 657 Vallejo, L. E. 287 Vankov, D.A. 601 Wakai, A. 647 Wakamatsu, M. 417 Wang, C.-H. 435 Wang, EW. 589 Wang, G. 585 Wang, J. 325 Wang, X.G. 325 Wang, Y. J. 325 Watson, €? D. J. 41 1 Xiong, J. 259 x u , z . 533 Yabuki, K.607 Yagi, N. 187 Yakabe, H. 483 Yamabe, S. 293 Yamada, K. 477 Yamagami, T. 293,299,305,3 11, 317,545 Yamamoto, K. 141, 483 Yamamoto, T. 121, 5 15 Yamazaki, S. 471 Yamazaki, T. 265 Yanagisawa, E. 641 Yang, Q. 281 Yang, X.Q. 277 Yasuda, S. 539 Yatabe, R. 187 Yin, K. 345 Yokota, K. 187 Yoshida, N.571 Yoshida, Y. 539 Yoshimine, M. 595 Yoshitake, S. 441 You. L. 637 Zhang, E 333 Zhang, Y. 345