3.47
Multi ultipl plee mode modess of shea shearr failu ailure re
In
rock
Les Les diff differ eren ents ts mode modess de ruptur rupture e par par cisai cisaille lleme ment nt dans dans les les roch roches es
Verschiede Verschiedene ne Arten des Felsscherbruch Felsscherbruches es
by F. D. PATTO PATTON, N,Ge Geolo ologis gistt
and Founda Foundatio tion n
Resear Research ch Associa Associate, te, Depart Departmen mentt Fellow, LNEC, Lisbon, Portugal) Portugal)
of Civil Civil Engi Engineer neering ing,,
Summary The mech mechan anis ism m of shear shear fail failur ure e in rock rock was was investi investiga gated ted by studyin studying g over over 300 300 rock rock slop slopes es in the the Rock ocky Mount ountai ains ns,, mak making ing labo labora rato tory ry slid slidin ing g fric fricti tion on test testss on rock rock sampl samples es and and direct direct shear shear tests tests on simu simulat lated ed rock rock surf surfac aces es,, and and rev review iewing ing the the shea shear r stren strengt gth h liter literatu ature re.. This This paper paper descri describes bes the Iabor Iabora a tory tory shea shearr test testss used used to prov provid ide e a theor theoreti etical cal fram framew ewor ork k for for interp interpre retin ting g the shea shearr stre streng ngth th of inta intact ct or disc discon onti tinu nuou ouss rock rock hav having ing an irre irreg gular ular fail failur ure e surf surfac ace. e. Spec Specim imen enss made made of plas plaste terr of Paris aris were ere cast cast with ith irre irreg gular ular surf surfac aces es and and test tested ed in a specia specially lly desig designe ned d shear shearing ing device device.. Test Test vari variabl ables es inclu included ded the incli inclina natio tion, n, numb number, er, and and stren strengt gth h of the speci specime men n teeth teeth,, and and the norm normal al loads loads appl applied ied.. The follo follow wing conconclusio clusions ns were were draw drawn: n: I) failu failure re enve envelo lopes pes for specimens specimens with with irregu irregular lar failure failure surface surfacess are are curv curved ed,, 2) chang changes es in the the slop slope e of a failure failure envelop envelope e reflect reflect changes changes in the mode mode of failur failure, e, and and 3) chan chang ges in the mode mode of fail failur ure e are are rela relate ted d to the the phy physica sicall prop proper er-ties ties of the the irre irreg gular ularit itie iess alon along g the the fail failur ure e Surfac Surface. e. An applicat application ion of these conclus conclusions ions was demon demonstr strate ated d by inter interpr preti eting ng a series series of labor laborato atory ry shear shear tests tests on rock. rock.
Engine Engineer er Univ Universi ersity ty
of Illin Illinois, ois, Urban Urbana, a, Illinoi Illinois, s, U. S. A., A., (pre (present sently ly
Resume
Zusammenfassung
On a etudie etudie Ie mecan mecanism isme e de ruptur rupture e des des roche rochess par par cisail cisaillem lemen ent, t, en obser observa vant nt plus plus de 300 300 pentes pentes rocheuse rocheusess dans dans les Montag Montagnes nes Roche ocheus uses es,, en faisan faisant, t, au labo labora rato toir ire, e, des des essais essais de frotte frotteme ment nt sur sur des epro eprouv uvett ettes es de roche rochess et des des essais essais de cisail cisaillem lemen entt direct directss sur sur des des mode modele less de surf surfac aces es roch rocheu euse ses, s, et en passa passant nt en revue revue la litera literatur ture e sur sur la resisresistanc tance e au cisa cisail ille lem ment, ent, Dans ans la pres presen ente te comm commun unic icat atio ion, n, on decr decrit it les les essa essais is de cisail cisaillem lemen entt execu executes tes au labor laborato atoir ire e qui qui ont ont servi II etablir etablir un cadre cadre theoriq theorique ue permett permettant ant l'int l'interp erpre retat tatio ion n de la resis resistan tance ce au cisaille cisaille-ment ment de roch roches es inta intact ctes es ou disc discon onti tinu nues es ayan ayantt une une surf surfac ace e de rupt ruptur ure e irre irreg gulie uliere re.. Dans un dispo disposit sitif if proj projete ete expr express essern ernen entt II ce but, but, on a fait fait des des essa essais is de cisai cisaill llem emen entt sur sur des des echa echant ntil illo lons ns en plat platre re de Paris aris,, rnou rnoules les avec avec des surf surface acess irreg irregul ulier ieres es,, Les Les variabl variables es de J'essai J'essai compre comprenaie naient nt I'Incli I'Inclinainaison, son, Ie nom nombr bre, e, et la resista resistance nce des des reden redents ts de l'ec l'echa hant ntil illo lon n et les les char charg ges norm normal ales es app appliqu iquees, es, On en a conclu que: I) les cour courbe bess intri intrinse nsequ ques es de ruptur rupture e des echanechantill tillon onss ayan ayantt des des surf surfac aces es de rupt ruptur ure e irre irre-gulie uliere ress ne sont sont pas pas droi droite tes; s; 2) des des varia aria-tion tionss dans dans I'incl i nclin inai aiso son n de la cour courbe be inintrins trinseq eque ue tradu traduise isent nt des des varia variatio tions ns dans dans Ie mode mode de ruptu rupture; re; et 3) les les differe differents nts mode modess de ruptur rupture e refieten refietentt les carac caracteri teristiq stiques ues phyphysiq siques ues des des irre irreg gular ularit ites es de la surf surfac ace e de rupt ruptur ure. e. On a dern dernon ontr tre e les les conc conclu lusi sion onss ci-av ci-avant, ant, en les appliquan appliquantt II I'interpretation d'une d'une serie serie d'essai d'essaiss de cisaille cisaillemen mentt de roches roches execut executes es au laborato laboratoire. ire.
I. Introducti Introduction on
Previous work by NEWLANDand ALLELY (1957), RIPLEY and LEE(1961), LEE(1961), and WITHERS WITHERS(1964) (1964) indicated indicated that irregulari irregulari-ties ties along along fail failur uree surf surfac aces es shou should ld play play an impo import rtan antt role role in the the dete determ rmin inat atio ion n of shear shear stre streng ngth th char charac acte teri rist stic icss of rocks. rocks. With With this this in mind, mind, a field field and and labora laborator tory y invest investiga igatio tion n into into the the effe effect ct of surf surfac acee irre irregu gula lari riti ties es was was unde undert rtak aken en.. The The effe effect ctss of natu natura rall irre irregu gula lari riti ties es on the the stab stabil ilit ity y of rock rock slop slopes es were were stud studie ied d on over over 300 300 stable stable,, unst unstab able le,, and failed failed slopes slopes in the the Rocky Rocky Mount Mountain ainss (PATT (PATTON ON,196 ,1966). 6).
NATO Post-Doctora
Durch urch Unter ntersu such chun ung g von mehr mehr als als 300 Felsboschung Felsboschungen en in den «Rocky «Rocky Mountains» Mountains»,, Rutschreibu Rutschreibungsv ngsversuche ersuche von Gesteinspr Gesteinsproben oben und direkte direkte Scherversu Scherversuche che von vorge vorgetauschten tauschten Gestei Gesteinso nsober berflii fliichen chen im Labor, Labor, sowie sowie DurchDurchsich sichtt der der eins einsch chli liig igig igen en Lite Litera ratu tur, r, wurde urde der Mechan echanism ismus us des des Felss Felssche cherb rbru ruche chess ererfors forsch cht. t. Diese Diesess Refera eferatt besch beschrei reibt bt die La borversuche borversuche die durchgefiihrt durchgefiihrt wurden, wurden, urn ein theoreti theoretische schess Gedank Gedankeng engebii ebiiude ude zur zur ErkErklarun larung g der der Scher Scherfe festi stig gkeit keit ganzen anzen oder oder didiskon skontin tinuie uierli rlich chen en Felse Felsens ns entla entlang ng einer einer ununregelrn regelrnassi assigen gen Bruch Bruchflii fliiche che zu schaffen schaffen.. Es wurden urden Gipspr ipsprob oben en mit mit unreg unregelm elmiis iissig sigen en Oberfl berfliic iichen hen gefo geform rmt, t, und und in einer einer spez speziel ielll entworfenen entworfenen Schereinrichtu Schereinrichtung ng geprUft. geprUft. Unter Unter ander anderem em,, wurde urde die Abhiin Abhiingi gigk gkeit eit der ErErgebniss ebnisse e von von der Neigu Neigung ng,, Anza AnzahI hI und und Festig stigk keit eit der der Probe robeza zahn hne, e, sow sowie von der der Normallast Normallast untersucht. untersucht. Es wurden wurden folgende folgende Ergeb Ergebniss nisse e erhalten erhalten:: I) Die Die Mohrsch Mohrsche e UrnUrnhullungskur hullungskurve ve fur Proben mit unregelmiissig unregelmiissiger er Bruchf Bruchfliic liiche he ist krumm krummlini linig. g. 2) Steilhe Steilheitsa itsannderungen derungen der Mohrschen Mohrschen UmhUlI UmhUlIungs ungskurv kurve e zeige zeigen n Anderung Anderungen en der Bruchar Bruchartt an. 3) Anderung derungen en der Bruch Bruchart art hiingen hiingen von den physikalischen sikalischen Eigenschaft Eigenschaften en der Unregelmi Unregelmiissigissigkeite keiten n der Bruch ruchfli fliich iche e abo abo Die Die Erk Erkliiru liirung ng einer einer Reihe eihe von von Labo Labors rsch cherv erver ersu suche chen n mit mit Felse Felsen n zeig zeigtt eine eine erfo erfolg lgrei reiche che Anw Anwendun endung g dieser Schliisse. Schliisse.
By makin making g correc correcti tions ons for the geometry geometry of the rock disco disconntinu tinuit itie ies, s, the the angl anglee of fricti friction onal al slid slidin ing g resi resist stan ance ce alon along g a relati relativel vely y flat flat plane plane was determ determine ined d under under field field conditi conditions ons.. For For sand sandst ston ones es and and carb carbon onat atee rock rockss this this angle angle was was foun found d to comp compar aree favo favora rabl bly y with with the the angl anglee of resi residu dual al fric fricti tion onal al slid slidin ing g resi resist stan ance ce obta obtain ined ed from from labo labora rato tory ry test testss on wet, wet, rela relati tive vely ly flat flat,, roug roughh-sa sawn wn sand sandst ston onee and and carb carbon onat atee rock rock surfaces. The The field field and labora laborator tory y study study showed showed that that irregu irregular lariti ities es have have an apprecia appreciable ble influe influence nce upon upon the shearing shearing resist resistanc ancee of rock rock mass masses es.. Furt Furthe herm rmor ore, e, it seem seemed appa appare rent nt that that 509
B B B B
different modes of shear failure take place along irregular rock surfaces. For example, failures of rock masses have occurred by sliding along rock surfaces having various orientations, by shearing through intact rock, or both. A framework that would permit this multiple-mode failure mechanism to be better understood and allow an improved interpretation of the results of shear tests on rock was required. The laboratory tests described in this paper were devised to help provide such a framework.
"
B B
D. Test specimens The interpretation of the results of shear tests on real rocks is usual1y complicated by sample variability - even when several samples are taken from the same block of rock. To overcome this difficulty the laboratory specimens were made from an artificial material so that the shape, size, and internal strength of the irregularities or «teeth» on the surface of the test specimens could be evaluated separately. Plaster of Paris was selected as the testing material as it had rock-like properties, fil1ers could be added to vary its strength, and the shape of the teeth could be accurately reproduced using molds. Two different fillers - crushed quartz sand and kaolinite - were used to decrease the strength of the specimens. The properties and ingredients of the specimens are outlined in Table t.
•• Ill 01 1.5 5-
Fig. 1 -
Some
of the Different
Types of Plaster
Specimens
Cylindrical samples, which were cast and cured with each series of test specimens, were later tested for their point-load tensile strength and their unconfined compressive strength.
III. Test apparatus and procedure A direct shear device was constructed to permit electronic recording of the loads and the vertical and horizontal
Table 1
Summary
of Physical
Properties
Filler
Sand
Ratio Filler: Plaster by weight Weight Mixing Water Ibs/IOO Ibs Plaster Unit weight at testing lbs/cu ft ~, degrees (1)
3: I 148 88.9 34-36
of Plaster
of Paris
Sand
3:2 85 94.3 35-39
Specimens
Kaolinite
I: I 127 64.5 27-28
Kaolinite
I: 2 96 66.9 29-30
Tests on Cilinders
Av. unconfined comp, strength Av. point-load tensile strength Average E, x 108 psi (I)
(I) (2)
psi psi
248 53
.65
601 70 .22
98 8 90 . 45
Obtained from direct shear tests after large displacements E is the tangent modulus of elasticity at Soo/u ultimate stren&tb 1
Five to eight identical specimens of 12 geometrical configurations were made for each of the four mixes. Four types of inclined teeth with slopes of 25°, 35°, 45°, and 55° were formed. Two series of specimens - one with four teeth and the other with two - were cast for each type of inclined teeth. All the teeth had a height of 0.20 inches. Both halves of each specimen were cast simultaneously in a brass mold the surfaces of which were machined to within ±.005 inches. Similar specimens were cast within one or two days of each other. The kaolinite-plaster specimens were cured at 70°F and 5C% relative humidity until testing ccrrmenced 45 to 50 days after casting. When both halves of the specimen were placed tcgether after casting, each specimen was 2.95 inches long, 1.75 inches wide, and 2.0 inches high. Figure 1 shows some of the different types of specimens.
510
1240 120 1.15
displacements. This allowed the complete load-displacement curve to be obtained even with «brittle» materials. The shearing device consisted of 1) a shear box in which a horizontal shearing force was applied, 2) a motor, variablespeed transmission, and a worm gear-ram arrangement that developed and transmitted the shearing force, 3) a loading frame and weights for applying the normal force, 4) twin load cells to measure the shearing force in tension, and 5) three LVDT transducers to measure horizontal and vertical displacements. Shearing was at a constant rate of displacement of .0624 inches per minute. Most of the results were plotted directly upon a Moseley x-y recorder. After a series of tests on one type of specimen, the peak and residual shear strengths were taken from the load-horizontal displacement graph made by the x-y recorder and plotted on a shear strength diagram at the appro-
priate normal load. The results of several such tests were joined by lines which formed two failure envelopes, one representing maximum shear strength and the other residual shear strength.
IV. Definition of terms ~ is the angle of sliding or shearing resistance. It is used where a more specific term does not seem warranted. ~I.l is the angle of frictional sliding resistance. Its value changes with the surface characteristics of the rock. For most practical problems involving rocks, the appropriate value of ~I.l can apparently be obtained after large displacements have occurred along macroscopically smooth and flat but microscopically irregular (i. e., unpolished) wet surfaces. ~r is the angle of residual shearing resistance of materials which initially were partly or completely intact. It is obtained from the asymptotic minimum values of shear strength following large displacements. . i is the angle of inclination of the failure surfaces with respect to the direction of application of the shearing force. It is also used in a graphical sense as a particular angle on a shear strength diagram.
V. Resnlts The results presented here are from the tests on specimens of kaolinite-plaster. Similar results were obtained from tests on the sand-plaster specimens.
2)
Specimens with inclined teeth at low normal loads
Figure 3 shows two failure envelopes typical of those obtained from tests at low normal loads on specimens with inclined teeth. The maximum strengths recorded for a number of specimens were used to form the maximum strength envelope (line A). The residual strengths remaining in these same specimens after large displacements had occurred were the basis for the residual strength envelope (line B). The equation describing the maximum strength envelope + i) where S is the total shearing strength N tan (~I.l is S= and N is the total normal load. The inclination of the residual envelope is ~r and the envelope can be described by the N tan ~r' For the various plaster specimens, equation S= the angle ~r was always within 11° of ~I.l and the two were often identical. Line A of Figure 3 represents two different types of strengths. It represents the value of the external frictional resistance along the inclined planes, and it represents the internal strength of the teeth at the point of failure. When failure occurs these two strengths are equal. It may be noted from line A that although intact material was sheared there was no cohesion intercept indicated when the results were plotted. Yet the internal «cohesive» strength of the teeth still contributed to the total strength by making possible the development of increased frictional resistance along the surface of the teeth. The precise contribution of the internal «cohesive» strength of the teeth at any given normal load is the difference in strengths between the maximum and residual strength envelopes. A cohesion intercept would occur if the sum of ~I.l+i became equal to or greater than 900.
1) Specimens with fiat surfaces
3)
Figure 2 shows a typical failure envelop , from a series of ,direct shear tests on relatively flat, unpolished, surfa7es. FaIlure envelopes from these specimens were straight lines passing through the origin and inclined at an angle The angle ~I.l for the specimens of ~I.l from the horizontal. the stronger mix (kaolinite-plaster I :2) was 310. For the weaker mix ~I.l was 2710.
Results from three series of tests, each made on specimens with different inclinations of teeth, are shown in Figure 4. The failure envelope for specimens with i =25 0 is a straight line -line 350 A. For specimens with i = and i = 45° the failure envelopes are curved but each envelope can be approximated by two straight lines as are envelopes Band C, respectively. Line D is drawn through the residual shear strengths of aU three series of specimens.
.•
Different inclinations of teeth
..
(/)
..c:.
.•..
•en. .
s:
C'I
C
c
•.. QI
•QI. .
.•..
• ..
(/)
(/)
en
01
c
C
•..
•..
e
t l
QI
QI
..c:.
s:
(/)
(/)
No rm al Fig. 2 -
L oad , N
Failure Envelope for Specimens with Flat Surfaces
No rm al
L oad " N
Fig. 3- Failure Envelopes for Specimens with Irregular Surfaces
511
o 6 .
~ MAll VALU[~ I t( SI QU Al r"PC5
~llOAO,H
..
'Oft
M Al l V Al U( ~' () II I
,
6
' Ol t
V AL Un
or
" '"
100 1'0011I"'''''
the number
of teeth
Figure 5 shows the effect of doubling the number of teeth from two to four and keeping the specimens identical in other respects. Each maximum strength failure envelope, although curved, is approximately described by two straight lines. The secondary portion of the failure envelope for specimens with four teeth '(line A) is about twice as far above the residual envelope' (line C) as the envelope for specimens with two teech (line B). The steeply sloping primary portions of the failure envelopes are approximately equal to ~11+ i , The inclinations of the secondary portions of the failure envelopes are approximately «i,. The change in slope again is related to a change in the mode of failure associated with the initial displacements. The effect of having additional teeth is to move the abrupt change in slope of the failure envelope to a higher normal load and to move the secondary portion of the failure envelope about twice as far above the residual envelope as the failure envelope for two teeth. This diagram illustrates the difficulties encountered in attaching any real meaning to the average shearing stresses computed for tests on real rocks. In rocks the number, size, and shape of the irregularities are unknown; hence the real shearing and normal stresses are also unknown. 512
200 lOAO.
PLAST[lt
,PLAST!1t ll21.,.4S"
I
"lASTEoII
"
1t[5'OUAL
VAlUeS
•
It[SIDUAL
VALUES II II SPECIMENS
1l.11,;'U" 11:21 SP[CIM[N5
11.1 1
300 N
1M.
Fig. 5 - Failure Envelopes for Specimens with Different Numbers of Teeth
The inclinations of the lower or primary portions of lines A , B , and C are equal to, or within one degree of, «i11+i . The inclinations of the upper or secondary portions of lines Band C are very close to the 'value «i,. The abrupt changes in the slopes of lines Band C are related to changes in the mode of failure. Below the changes in slope the maximum shearing strength is related to the frictional resistance along the inclined surfaces. Above the transition in slope the maximum strength is unrelated to the increased surface friction due to the inclination of the teeth. The cross-sectional area of the intact material at the base of the 350 teeth is greater than for the 450 teeth. This explains why the transition in the mode of failure for the two inclinations of teeth occurred at different normal loads. Line A is straight because the range of normal loads used was not high enough to reach the transition for the specimens with 250 teeth. Varying
1 I0 TH
~"[CIM[N~
KAOLINIT[ 1M.
Fig. 4 - Failure Envelopes for Specimens with Different Inclinations of Teeth
4)
o KAOllNlf[
TE(IH
2 fE tf H
Fig. 6 - Failure Envelopes for Specimens with Different Internal Strengths
From tests made on higher strength specimens it was found that specimens with four teeth often gave failure envelopes that were only slightly greater than the envelopes for specimens with two teeth. This was interpreted as evidence of progressive failure. 5)
Varying
the strength
of the teeth
Figure 6 shows the results of tests on two series of specimens with identical surface configurations but different internal strengths. Line A is the failure envelope for the stronger specimens and line B for the weaker specimens. Lines C and D are their respective residual strength envelopes. Slopes of the primary and secondary portions of the failure envelopes are slightly different for each series of tests. These differences reflect a change in ~11 and ~, for the two strengths of specimens. The change in mode of failure occurs at a higher normal stress for the stronger specimens than for the weaker ones. Thus, increasing the strength of the specimen teeth has an effect similar to that of increasing the number of teeth.
VI. Conclusions Three general conclusions can be drawn from the results of the tests on plaster specimens: 1) failure envelopes for specimens with irregular failure surfaces are curved, 2) changes in the slope of the failure envelope reflect changes in the mode of failure, and 3) changes in the mode of failure are related to the physical properties of the irregularities along the failure surface. These conclusions, together with the fact that ~ does not vary throughout a wide range of normal loads (although ~+i does vary), have many practical applications. In particular, they facilitate the interpretation of curved failure envelopes.
VII. Interpretation of tests on real rocks From the results of shear tests on real rocks one would expect to obtain a superposition of the effects of the separate variables investigated for the plaster specimens. For example, in the same sample of rock the irregularities along the failure surface would have different sizes, inclinations, internal
SUMMARY
SUMMARY ill: 29~41° 300
ill~-4lr:33°
APPARENT
COHESION
300
INTERCEPT : 10- 50 psi
COHESION INTERCEPT:
0
VI
Q .
III III W It: 200
•..
200
III
100
00
100 AVERAGE
NORMAL
a) STRAIGHT· LI NE
Fig. 7 -
200 STRESS,
FAILURE
Two Interpretations
300
100 AVERAGE
psi
ENVELOPES
of Direct Shear
strengths, and coefficients of friction. Thus, failure envelopes for rocks would not reflect a simple change in the mode of failure but changes in the «intensities» of different modes of failure occurring simultaneously. . Figure 7 illustrates two interpretations that can be given to four series of tests (A , B , C , and D) on different surfaces of the same rock. Figure 70 shows the shear test results interpreted as forming straight-line failure envelopes. This is equivalent to saying that only one mode of failure o~urred during the tests at different stress levels. From F!gure 70 it would also appear that the value of ~ was dIfferent for each series of tests and was not a relatively c~nstant property of the material. In addition, the straightline envelopes could lead some designers to conclude that an appreciable amount of cohesive strength exists at zero nor mal load. These errors are avoided in Figure 7b in which the same data is used to form curved failure envelopes. The curved failure envelopes in Figure 7b also provide more information on the geometry and effectiveness of the surface irregularities than is offered in' Figure 70. For example, at a given normal stress the vertical distance between a point on any maximum strength failure envelope and the residual envelope (line E) gives the internal strength contributed by the irregularities. This strength is the strength that is lost when significant displacements occur along the failure plane. . From Figure 7b the rocks of the test series outlined by ~me A can be interpreted as having small relatively steep Irregularities which were effective between a normal stress of 0 to 40 psi. Above 40 psi these small irregularities failed before displacements could occur along them. Between a
200 NORMAL STRESS.
300 psi
b) CURVED FAILURE ENVELOPES REFLECTING MULTIPLE MODES OF fAILURE Tests on Ruck
Samples
with Irregular Surfaces
normal load of 120 and 270 psi some larger irregularities which had inclinations of 10° (43° minus 33°) became effective. Above 270 psi these larger irregularities began to fail before displacements could occur. For some engineering design purposes straight-line failure envelopes are adequate. But to facilitate an understanding of the failure mechanisms curved failure envelopes reflecting the multiple modes of shear failure appear to be a necessity.
VIII. Acknowledgments
This paper is based upon a thesis submitted in partial fulfillment of the requirements for a Ph. D. in Geology at the University of Illinois. The thesis was completed under the direction of Dr. D. U. Deere, professor of civil engineering and geology, who made many valuable contributions to the study.
References P.· L., and B. H. ALLELY- 1957, Volume changes in drained triaxial tests on granular materials, Geotechnique, Vol. VD, pp. 17-34. PATTON, F. D. - 1966, Multiple Modes of Shear Failure in Rock and Related Materials, Ph. D. Thesis, Univ. of Illinois, 282 pp. RIPLEY, C. F., and K. L. LEE - 1961, Sliding friction tests on sedimentary rock specimens, Communication 8, 7th Congress of Large Dams, Vol. IV, pp. 657-671. WITHERS, J. H. - 1964, Sliding Resistance Along Discontinuities In Rock Massi'S. Ph. D. Thesis. Univ. of Illinois. 124 pp.
NEWLAND.
5.13
