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Earth pressures on unyielding retaining walls of narrow backfill width W.A. Take and A.J. Valsangkar
Abstract: Abstract: Arching theory predicts a significant reduction in earth pressures behind retaining walls of narrow backfill width. An extensive series of centrifuge tests has been performed to evaluate the use of flexible subminiature pressure cells in the centrifuge environment and their subsequent use to measure lateral earth pressures behind retaining walls of narrow backfill width. Although the flexible earth pressure cells exhibit hysteresis and nonlinear calibration behaviour, the extensive calibration studies indicate that stiff diaphragm type earth pressure cells may be used with replicate models to measure earth pressures. Measurements of lateral pressures acting on the unyielding model retaining walls show good agreement with Janssen’s arching theory. Tests on backfills bounded by vertical planes of dissimilar frictional characteristics indicate arching theory with an average interface friction angle provides a reasonable estimate of lateral earth pressures. Key words: fascia retaining walls, silos, earth pressures, pressure cells, centrifuge modelling.
Résumé : La théorie d’arc-boutement prédit une réduction significative des pressions des terres à l’arrière des murs soutenant un remblai de faible largeur. Une série importante d’essais au centrifuge a été réalisée pour évaluer l’utilisation de cellules de pression miniatures flexibles dans l’environnement du centrifuge et leur utilisation subséquente pour mesurer les pressions latérales des terres à l’arrière de murs soutenant des remblais de faible largeur. Quoique les cellules flexibles de pression des terres montrent de l’hystérèse et un comportement non linéaire en calibrage, les études nombreuses de calibrage indiquent que les cellules de pression des terres avec diaphragme rigide peuvent être utilisées au moyen de reproductions de modèles pour mesurer les pressions des terres. Des mesures de pressions latérales agissant sur des modèles de murs de soutènement rigides concordent bien avec la théorie d’arcboutement de Janssen. Des essais sur des remblais avec des plans verticaux de caractéristiques de frottement non similaires aux frontières indiquent que la théorie d’arc-boutement avec un angle de frottement moyen à l’interface fournit une estimation raisonnable des pressions des terres. Mots clés : murs de soutènement en panneau, silos, pressions des terres, cellules de pression, modélisation par centrifuge.
[Traduit par la Rédaction]
Take and Valsangk sangkar ar
Introduction The width of backfill behind retaining walls can vary from being being effec effecti tivel vely y infini infinite te to very very narro narrow w where where site site constraints dominate the design. Fascia retaining walls represent one one such such case case of narr narrow ow backf backfil illl widt width h reta retain inin ing g wall wallss (Fig. (Fig. 1a). These These walls walls are construct constructed ed a short short distance distance in front of a rock face for a variety of reasons, including widenin ening g of urba urban n tran transp spor orta tati tion on corr corrid idor orss within within exis existi ting ng rights-of-way, reduction of rockfall risk, and aesthetics. With a narrow backfill width, the arching theory predicts that the lateral forces exerted on the retaining wall will be reduced due to the reduction of vertical stresses on both frictional boundaries of the backfill. Although this reduction can Received August 3, 2000. Accepted June 29, 2001. Published on the NRC Research Press Web site at http://cgj.nrc.ca on December 21, 2001. W.A. Take. Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, U.K. A.J. Valsangkar.1 Department of Civil Engineering, University of New Brunswick, P.O. Box 4400, Fredericton, NB E3B 5A3, Canada. 1
Corresponding author (e-mail:
[email protected]).
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have a major influence on lateral earth pressure values, the small small number number of high-qu high-quali ality ty earth earth pressu pressure re monito monitorin ring g studies typically results in a reluctance to fully rely on the arching effect in design. Unfortunately, the challenges associated with earth pressure measurement have the effect that what little little experi experimen mental tal data data are availa available ble exhibit exhibit a great great deal of scatter. This is an additional factor which leads to a reluctance to fully account for beneficial arching effects in the design of fascia retaining walls. This paper describes the results of a series of centrifuge tests conducted to develop a programme of repeatable model preparation, preparation, calibration of flexible flexible subminiature earth pressure cells, and the subsequent measurement of lateral earth pressures behind model fascia retaining walls.
Background Arching theory The arching theory attributed to Janssen (1895) describes the reduct reduction ion in verti vertical cal pressu pressures res within within a granul granular ar materi material al bounded by two vertical planes with specific reference to silo structures. For the case of fascia retaining walls, the cumulative effect of the transfer of vertical stress to the boundaries has the potential to reduce the lateral earth pressures. Defining a hori-
DOI: 10.1139/cgj-38-6-1220
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Fig. 1. (a) Fascia retaining wall of backfill width, B, and height, H . (b) Horizontal element of backfill material (after Spangler and Handy 1984).
zontal element bounded by two unyielding frictional boundaries (Fig. 1b), the vertical frictional boundary forces will reduce the vertical stress, which will in turn reduce the horizontal stresses acting on the wall. Spangler and Handy (1984) have applied Janssen’s theory to the design problem of fascia retaining walls. The vertical force equilibrium of the horizontal element of Fig. 1 b requires [1]
2K tan δ
V B
d z − γ Bd z
+ dV = 0
where γ is the unit weight of soil; B is the backfill width; z is the backfill depth; δ is the interface friction angle between the backfill and walls, K is the earth pressure coefficient; and V is the vertical force at depth z. From the solution of eq. [1], an equation for lateral earth pressure, σ h , can be postulated as [2]
− 2 K z tan δ B γ σh = 1 − e B 2 tan δ
The magnitude of the reduction in lateral earth pressures behind fascia retaining walls is predicted by eq. [2] to be a function of wall geometry, z / B, the frictional characteristics of the boundaries, δ, and the coefficient of lateral earth pressure, K . For the case of unyielding retaining walls (zero lateral strain condition), the coefficient of earth pressure “at-rest” attributed to Jaky (1948) is defined as [3]
K 0 = 1 – sin
φ′
where φ′ is the effective angle of internal friction. The effect of the mobilized interface friction angle at zero lateral strain conditions, δ 0 , on the earth pressure coefficient, K 0, has been theorized by Zhang et al. (1998) by extending Coulomb’s equations for different lateral strain conditions. The relationship proposed by Zhang et al. (1998) indicates that the maxi mum change in K 0 with estimated mobilized interface
friction angle would be negligible. Therefore K 0 is assumed to be independent of the mobilized interface friction angle in this paper. The only experimental study known to the authors which deals specifically with the measurement of lateral earth pressures behind fascia retaining walls was conducted by Frydman and Keissar (1987). In this work, two pressure cells were used to measure the transition from at-rest to active earth pressure conditions behind a centrifuge model of a fascia retaining wall. The results from their 11 determinations of at-rest earth pressures for various z / B ratios are shown in Fig. 2. The effect of the reduced vertical effective stress on the lateral earth pressure can be observed by expressing the observed lateral earth pressures in terms of σh′ / γ z . For an infinite backfill width, the ratio σh′ / γ z tends towards the coefficient of lateral earth pressure, K . With an increase in the ratio z / B there is a reduction in vertical effective stress due to friction on the side walls, with a corresponding reduction in the ratio σ h′ / γ z . Despite showing an overall agreement with Janssen’s arching theory, the earth pressure observations of Frydman and Keissar (1987) exhibit a considerable amount of scatter. The actual distribution of earth pressure is also indeterminate in the work of Frydman and Keissar, as only two pressure cells were used to measure the earth pressures in any given experiment. Experimental work related to arching has also been carried out with reference to the storage of granular materials within silo structures. These measured at-rest lateral pressures, although exhibiting considerable scatter, indicate a general agreement with the values predicted by the arching theory (e.g., Blight 1986; Jarrett et al. 1995).
Earth pressure cell calibration The degree of scatter witnessed in most earth pressure measurement studies is representative of the difficulty of obtaining repeatable measurements. In an effort to increase the quality of earth pressure observations, much work has been undertaken in the literature to define the factors which affect pressure cell calibration behaviour and field measurement usage (Clayton and Bica 1993; Garnier et al. 1999). © 2001 NRC Canada
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Fig. 2. Measured reduction in lateral at-rest earth pressure with the ratio z / B (Frydman and Keissar 1987).
Fig. 4. Orientation of earth pressure cells during ( a) calibration and (b) fascia wall experiments.
Fig. 3. Instrumented model retaining wall illustrating the locations of boundary earth pressure cells.
Since diaphragm pressure cells must deflect to record pressure, there exists potential for stress redistribution in the granular material above the pressure cell. The calibration between output voltage arising from applied fluid and soil pressure, therefore, can be vastly different due to stress redistribution in the latter case. This effect has been defined in the literature in terms of a cell action factor (CAF). The CAF is simply the ratio of the normal stress measured by the cell to that which would have existed in the absence of the cell (Clayton and Bica 1993). Physical and numerical studies have demonstrated that the magnitude of this phenomenon is a function of both the stiffness of the granular material and the pressure cell diaphragm (Trollope and Lee 1961; Clayton and Bica 1993). Clayton and Bica (1993) have defined this stiffness ratio as the flexibility factor F : [4]
F =
3 E soil R
Ecell t 3
where E soil is Young’s modulus of the soil;
E cell is Young’s modulus of the cell diaphragm material; R is the radius of the cell diaphragm; and t is the thickness of the cell diaphragm. The results reported in the literature indicate that as the relative flexibility of the diaphragm, F , increases, the cell action factor decreases, indicating additional stress redistribution. For values of CAF greater than 0.9, the flexibility factor has to be less than 0.7 (Clayton and Bica 1993). Although the direct use of eq. [4] is hampered by the lack of knowledge of the exact construction details and material properties of the commercial sensors, eq. [4] indicates that the stiffest pressure cells are desirable in measuring earth pressures.
Centrifuge modelling Centrifuge The principles and scaling laws associated with geotechnical centrifuge modelling have been reported in detail by Schofield (1980). Unlike full-scale modelling, the reduced scale of centrifuge models allows greater control of the magnitude and homogeneity of soil properties and a sufficiently quick turn-around time to create the capability of performing experimental parametric studies. © 2001 NRC Canada
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Table 1. Internal (φ) and interface ( δ) friction angles of model backfill material. Friction angle
φp′ backfill (°) φcv′ backfill (°) δ p backfill and aluminum (°) δcv backfill and aluminum (°) δ p backfill and 120A-grit sandpaper (°) δcv backfill and 120A-grit sandpaper (°)
Loose backfill (34% relative density)
Dense backfill (79% relative density)
30
36
28
29
23
25
22
23
32
36
29
29
Note: Subscripts p and cv denote peak and critical state, respectively.
Fig. 5. Particle-size distribution of model backfill material.
The geotechnical centrifuge at the University of New Brunswick was used to perform both the calibration of the earth pressure cells and the subsequent modelling of fascia retaining walls. Classified as a medium-size centrifuge, the 3.2 m diameter beam centrifuge is capable of a maximum inertial acceleration of 200 g at a payload of 100 kg. The centrifuge features an on-arm data-acquisition system controlled remotely through a serial connection through three slip-rings. In this manner, the potential for slip-ring-induced signal noise is eliminated, thereby allowing the use of small output devices without resorting to amplification.
Instrumented retaining wall The model instrumented retaining wall was designed to house six boundary pressure cells distributed evenly over the height of the model fascia retaining wall (Fig. 3). The earth pressure cells were mounted with epoxy into individually sized cavities in a 12.5 mm thick aluminum wall. The cavities were fabricated in such a manner as to ensure that the diaphragm of each pressure cell was flush with the wall surface. During the calibration of the pressure cells, the model retaining wall was bolted to the base of the centrifuge package (Fig. 4a). Once the calibration phase of the experimental programme was competed, the model retaining wall was bolted in a vertical position onto one end of the centrifuge package with a variable spacing to the model rock face (Fig. 4 b). To investigate the effect of providing vertical boundaries of dissimilar frictional characteristics, the aluminum model rock face was later bonded with a sheet of 120A-grit sandpaper. At an ac-
celeration of 35.7 g, the 140 mm model retaining wall is analogous to a 5 m high prototype wall.
Boundary earth pressure cells The reduced scale of centrifuge models requires that the scale of instrumentation must be correspondingly reduced to a size consistent with the model. The pressure cells used in the present study have a diameter of 6.35–7.37 mm. This diameter corresponds to approximately 16 times the average grain size, d 50 , of the model backfill material. This reduction in scale of instrumentation, however, must be balanced with the knowledge that the diaphragm stiffness is a key factor in determining the behavioural characteristics of boundary earth pressure cells. For a given cell geometry, increased diaphragm stiffness can only be achieved in standard commercial pressure cells (i.e., without resorting to a custom order) by selecting a device with an increased pressure range. Three pairs of commercial subminiature pressure cells of varying stiffness values were purchased to assess their usage in the measurement of earth pressures in centrifuge models. One limitation connected with this approach is that sensitivity and temperaturesusceptibility problems are often associated with operating solely within the lower range of any instrumentation device. Specifications supplied by manufacturers of pressure cells tend to describe thermal compensation in terms of a percentage of the full-scale output (FSO). This has important consequences for the large-range pressure cells. Although the quoted thermal zero shift is within 1% of FSO for all devices, it will play a significant role in the use of the stiffer pressure cells. The majority of the thermal shift was noted to occur during the first 20 min of pressure cell excitation. Stiff pressure cells (A 1 and A2) were noted to be more susceptible to thermal-compensation errors. Through a series of preliminary centrifuge calibration tests, the thermal-compensation problem was overcome to start the main experimental programme. The mitigating factors developed during this preliminary work consisted of embedding the cells into an aluminum retaining wall (heat sink), providing a 40 min “warm-up” period, and completely encapsulating the centrifuge package in high-density foam insulation to reduce thermal variations. Model preparation The potential sensitivity of earth pressure cells to variations in soil stiffness dictates a rigorous programme of model preparation. The factors associated with creating uniform sand models through air pluviation have been described by © 2001 NRC Canada
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Fig. 6. Calibration response of ( a) stiff and (b, c) flexible earth pressure cells with applied fluid and soil pressure.
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Fig. 7. Hysteresis between initial loading, unloading, and reloading stages of calibration for pressure cell B1 (dense sand).
over the centrifuge package. A plumb bob was attached to the portable hopper to ensure a constant height difference between the sand nozzle and the model surface at all times. Creating the soil model on the centrifuge had the additional benefit of eliminating the potential disturbance to the soil sample by impact loading during model installation. The mass rate of deposition was controlled by a small pointsource nozzle consisting of a piece of 4 mm flexible tubing. The nozzle diameter was sufficient to ensure an extremely slow deposition rate of 0.31 kg/min. Using these techniques, repeatable soil models were constructed at relative densities of 34 and 79%, corresponding to drop heights of 25 and 300 mm, respectively. The final stage of model preparation consisted of levelling the upper surface of the model backfill by transverse passes of a vacuum source.
Backfill soil properties The model backfill material is classified as a poorly graded sand with little or no fines. The backfill material has a uniformity coefficient of 2.2, a coefficient of curvature of 1.0, and a mean particle size of 0.4 mm (Fig. 5). The maximum and minimum dry densities were 1.62 and 1.34 g/cm 3, respectively. A series of direct shear tests was performed on the granular backfill material to determine the angle of internal friction and the interface friction angles with aluminum and 120A-grit sandpaper. The results of these tests performed at relative densities of 34 and 79% are presented in Table 1.
Calibration of load cells
Vaid and Negussey (1988) and Cresswell et al. (1999). These factors include drop height, particle-size gradation, mass rate of deposition, nozzle sweep rate, and container geometry. The model preparation procedure adopted consisted of raining the soil from an adjustable-height hopper suspended
A rigorous programme of calibration was undertaken to address the suitability of the three different types of subminiature pressure cells for the measurement of pressures in granular materials. This assessment was carried out by calibrating the devices against applied pressures by fluids and by soils of differing stiffness. The calibration programme included both 1 g and centrifuge fluid calibration and centrifuge calibration under the self-weight of loose and dense sand. © 2001 NRC Canada
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Fig. 8. Variation in soil placement conditions between ( a) calibration and ( b, c) retaining wall experiments.
Fluid calibration The initial fluid calibration of the pressure cells was performed at 1 g by applying a known air pressure to the cell diaphragm. The resulting relationship between the voltage output from all devices and the applied fluid pressure was both linear and repeatable. To ensure that the fluid calibration relationship remained unaltered following the mounting of the devices into the model retaining wall, the pressure cells were further calibrated under fluid pressure in the centrifuge. The calibration relationship between voltage and applied fluid pressure from a representative of each of the three types of pressure cells is presented in Fig. 6. Soil calibration The second stage of calibration consisted of subjecting the earth pressure cells to the self-weight of 50 mm of dense sand (79% relative density) in the centrifuge. The selfweight of the soil was increased through incremental steps
of 2g until the maximum acceleration level of 38 g was reached. The calibration process was repeated with five replicate centrifuge tests, with the best-fit calibration being shown in Fig. 6. Lastly, the calibration process was repeated for the calibration under the self-weight of 50 mm of loose sand (34% relative density). Using the concept of “modelling of models,” a further series of calibration tests was performed with a reduced sand height of 25 mm but twice the magnitude of centrifuge acceleration. These results were in close agreement with those from the first series.
Nonlinearity Each of the three types of subminiature pressure cell had differing responses to an applied soil pressure. The calibration relationship of pressure cells of type “A” experienced only minor variations with loading type or soil stiffness. In contrast, the calibration relationship of pressure cells of types “B” and “C” exhibited large deviations from that of © 2001 NRC Canada
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Fig. 9. Variation in observed earth pressure with adopted calibration relationship ( B = 184 mm).
the fluid, with the degree of nonlinearity being a function of soil stiffness. These observations are consistent with those presented by Clayton and Bica (1993). As predicted in the literature, each of the three pairs of pressure cells behaved according to their stiffness. Pressure cells of type A have been observed to be sufficiently stiff that the variation in soil stiffness with density is small with respect to that of the cell diaphragm. The variation of CAF with soil stiffness observed in pressure cell types B and C is consistent with cells of relatively low diaphragm stiffness, as changes in soil stiffness can appreciably alter the flexibility factor. Although exhibiting nonlinear characteristics, the potential use of flexible pressure cells such as those of types B and C to measure lateral earth pressures was investigated by incorporating the nonlinearity associated with a given soil stiffness into the calibration relationship. The nonlinearity of the calibration of voltage output, ∆V , with applied soil pressures, ∆ P, was captured using two calibration constants, m1 and m2, in an equation of the form [5]
∆V =
m 1 ∆ P + m 2 ( ∆P ) 2
The quadratic form of eq. [5] was chosen to facilitate the comparison of the degree of observed nonlinearity of the pressure cell calibration relationship with the soil stiffness. The value of m2, therefore, indicates the degree of nonlinearity of the relationship between applied pressure and the observed voltage output.
Hysteresis Significant hysteresis was observed during calibration of the pressure cells with soil (Fig. 7), with the magnitude of the hysteresis being inversely related to the stiffness of the device relative to that of the soil. Similar hysteresis behaviour was also reported by Frydman and Keissar (1987) in their centrifuge modelling of fascia walls. The possible influence of this hysteretic behaviour on the retaining wall experiments was eliminated by measuring the lateral earth pressures during the initial acceleration of the soil model to the required g level and by mechanically regulating the
speed of the centrifuge. An unloading cycle accompanying the “overshooting” of the required acceleration level, and the subsequent operator correction has the potential to greatly influence the observed pressure reading. Protection against this eventuality was accomplished by controlling the speed of the centrifuge by a fractional RPM timing motor operating in one direction only.
Effect of vertical measurement boundary As the nonlinear calibration of the pressure cells incorporates a correction for boundary soil stiffness, it is appropriate to consider the differences in the localized stiffness boundary condition between the calibration (horizontal) and measurement (vertical) positions of the instrumented retaining wall. During soil placement for calibration, grains of sand fall through the air until their kinetic energy is translated into compaction effort at impact (Vaid and Negussey 1988). In the horizontal (calibration) orientation of the retaining wall, compaction occurs directly on plane incorporating the pressure cell diaphragm (Fig. 8 a). It has been reported in the literature that the side boundaries of a container can influence the density of an airpluviated sample (Kolbuszewski 1948; Vaid and Negussey 1988). It is unrealistic to assume that, through the process of air pluviation, the falling grains of sand can align themselves perfectly along the vertical boundary of the model retaining wall with a lack of direct compaction effort. In addition, the vertical boundary ensures an unavoidable boundary layer of less dense sand as a result of the sand stream either striking the boundary (Fig. 8b) or missing the region entirely (Fig. 8c). In both of these situations, the full kinetic energy of the falling soil cannot be transferred into compaction effort for the case of a vertical measurement boundary. To assess the validity of the calibration relationship obtained for dense soil for a retaining model backfilled with dense soil, five replicate centrifuge tests were performed for the widest backfill width allowable in the model configuration ( B = 184 mm). As shown in Fig. 9, the mean pressures recorded by types B and C cells (open symbols) using the dense soil calibration relationship exceed at-rest earth pressure conditions. However, the pressures observed by the two type A (solid symbols) pressure cells exhibit a reasonable agreement with the predicted at-rest earth pressures. The differences in behaviour between the pressure cells of type A and the more flexible pressure cells are indicative of a zone of lower soil stiffness on the vertical measurement boundary. As a better estimate for the nonlinearity of the calibration associated with a less stiff material, the loose soil calibration has been applied to the observed voltages observed in the retaining wall. As shown in Fig. 9, the resulting pressures agree very well with the at-rest conditions. The ratio of pressure obtained from a dense soil calibration to that from a loose soil calibration is greater than 0.9 for both type A pressure cells over the pressure range encountered. This ratio was 0.87 or more for load cell B 1 and 0.7 or more for load cell B 2 over the pressure range encountered. As such, the calibration for type A cells and cell B 1 is largely independent of the soil stiffness and is not greatly affected by the zone of looser material at the boundary. © 2001 NRC Canada
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Fig. 10. Mean (±1 standard deviation) measured earth pressures on model retaining wall backfilled with dense sand to widths of (a) 184, (b) 75, ( c) 38, and ( d ) 15 mm (δwall = δ rock ).
Fig. 11. Observed reduction in lateral earth pressure with ratio z / B (dense backfill, δ wall = δ rock ).
Retaining wall experiments A series of retaining wall experiments was performed to investigate the applicability of Janssen’s arching theory to the design of unyielding fascia retaining walls. As predicted by eq. [2], the factors governing arching with the granular backfill in the narrow backfill width are the retaining wall geometry, z / B, the interface friction angle, δ, and the coefficient of lateral earth pressure, K . These factors will be investigated by modelling retaining walls of varying backfill width, density, and frictional characteristics. All centrifuge retaining wall experiments were performed at an acceleration of 35.7 g to simulate a 5 m high prototype wall.
Dense backfill, smooth rock face ( δwall = δrock ) Janssen’s arching theory, as expressed in eq. [2], assumes the case of equal interface friction angles on the boundaries, that is δwall = δrock . The first series of retaining wall experiments will therefore address this case. Five replicate centrifuge tests were performed at each of the 184, 75, 38, and 15 mm backfill widths. The mean (±1 standard deviation) ob© 2001 NRC Canada
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Fig. 12. Mean (±1 standard deviation) measured earth pressures on model retaining wall backfilled with dense sand to widths of (a) 184, (b) 75, ( c) 38, and ( d ) 15 mm (δwall < δ rock ).
Fig. 13. Observed reduction in lateral earth pressures with ratio z / B (dense backfill, δ wall < δ rock ).
served lateral earth pressures for each of these backfill widths are presented in Figs. 10 a–10d , respectively. The degree of variation observed even with the stiffest pressure cells (solid symbols) indicates the necessity to use replicate models to increase the quality of earth pressure measurements. With a reduction in backfill width, arching was observed to truncate lateral earth pressure from its triangular at-rest distribution. As predicted by arching theory, the z / B ratio has a dominant effect on the magnitude of the reduction of earth pressures within the narrow backfill. In each of the four backfill widths, the average measured earth pressure corresponds quite closely to that predicted by Janssen’s arching theory using Jaky’s K 0 and the measured interface friction angle, δ. Lastly, the results of the 20 centrifuge tests are summarized in Fig. 11. In general, Janssen’s arching theory using peak friction angles provides a good prediction of the reduction in earth pressures on unyielding walls for the case of identical interface friction angles. The data from earth pressure cells C1 and C2 were not included in Fig. 11 because of the sensitivity of the ratio σh′ / γ z to small changes in measured pressure at such low vertical effective stress levels (Take 1998). © 2001 NRC Canada
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Fig. 14. Mean (±1 standard deviation) measured earth pressures on model retaining wall backfilled with loose sand to widths of (a) 38 and ( b) 15 mm ( δwall < δ rock ).
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Fig. 15. Observed reduction in lateral earth pressures with ratio z / B (loose backfill, δ wall < δ rock ).
Frydman and Keissar (1987) to use the average interface friction angle in the analysis appears to provide a reasonable estimate of lateral earth pressure.
Loose backfill To investigate the effect of soil density on the reduction in lateral earth pressures in a narrow backfill, the case of dissimilar boundary frictional characteristics was performed with a loose soil sample for backfill widths of 38 and 15 mm. The results of these tests are shown in Figs. 14 a and 14b, respectively. It should be noted that in this series of experiments the bulk stiffness of the backfill is the same as that of the loose boundary layer close to the wall. Thus, the loose sand calibration is used in analysing the data. Similar to the results of the dense backfill, the observed earth pressures are bounded by the arching-theory predictions based on K 0 conditions and the interface friction angles of the backfill (Fig. 15). Dense backfill, rough rock face ( δwall < δrock ) As expressed in eq. [3], Janssen’s arching theory does not account for boundary planes of dissimilar frictional characteristics. To investigate the effect of these boundary conditions on the observed lateral earth pressures, a series of five replicate models at each of the four backfill widths was performed with a rough rock face (sandpaper-coated wall). The results of this series are presented in Figs. 12 a–12d . Presenting the results of this second series of 20 centrifuge tests in a nondimensional form (Fig. 13), and comparing with Fig. 11, it can be seen that the presence of a rougher boundary has further reduced the lateral earth pressures acting on the model retaining wall. The predictions for the reduction in lateral earth pressure using arching theory based on the peak interface friction angles, δwall and δrock , are shown to provide a reasonable bound of the observed data in Fig. 13. The results from pressure cells type A and B together indicate that an average interface friction angle may provide a reasonable estimation of earth pressures with boundaries of dissimilar frictional characteristics. Thus the suggestion of
Discussion Although Janssen’s equation describing the beneficial effect of arching on lateral soil pressures is not complex for the case of unyielding retaining walls, the choice of the parameter K and the mobilized boundary friction angle δmob during the translation from at-rest to active conditions requires considerable engineering judgement. Neither the mobilized friction angle nor the lateral earth pressure coefficient will be constant with depth for some modes of lateral wall movement for a soil in an intermediate state between at-rest and active conditions (Zhang et al. 1998). The reduction in lateral earth pressure behind fascia retaining walls is dependent on the mobilization of friction on the wall–soil boundary. It is clearly inappropriate, therefore, to design retaining structures such as articulated bulkheads using the arching theory, as the magnitude of the mobilized friction angle may be negligible. Lastly, one of the few reported cases of the failure of fascia retaining walls underlies the importance of maintaining an aspect of “constructibility” if the beneficial effect of arching is to be used in design. Thompson and Martin (1984) de© 2001 NRC Canada
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scribe the failure of a tied-back fascia retaining wall in part due to overexcavation from the design backfill width arising from the difficulty in the placement of drains in the narrow backfill.
Conclusions The results from a series of centrifuge tests have been presented identifying the factors affecting the calibration of subminiature boundary pressure cells and investigating the reduction in lateral earth pressure within the narrow backfill width of an unyielding fascia retaining wall. The results of the calibration centrifuge tests on the three stiffness ranges of subminiature pressure cells confirms that stiff subminiature pressure cells can be successfully used in measuring earth pressures. In addition, this research also indicates that, where flexible boundary pressure cells are used, the calibration might need to be undertaken at a stiffness representative of the boundary zone next to the pressure cells rather than at the bulk stiffness of the entire model. To the authors’ knowledge, only one previous experimental programme dealing specifically with fascia retaining walls has been reported in the literature. The present study, therefore, provides a useful addition to the database of experimental earth pressure studies. The results indicate that the design of fascia retaining walls to the full at-rest earth pressure distribution for narrow backfill widths may be very conservative. Further, Janssen’s arching theory has proven to be a very simple and effective tool for describing the reduction in lateral earth pressure for the case of vertical boundaries of similar frictional characteristics. For the case of fascia walls bounded by planes of dissimilar frictional characteristics, the experimental evidence indicates that the arching theory prediction based on the average interface friction angle provides a reasonable estimate of the earth pressure distribution. More work with different soil types and laterally yielding walls is needed to confirm the current practices of fascia wall design.
Acknowledgements The first author would like to acknowledge the funding received during the scope of this project from the Natural Sciences and Engineering Research Council of Canada (NSERC). The research funds from NSERC to the second author in the area of soil–structure interactions were used to support this research. The authors would like to thank Pro-
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fessor Malcolm Bolton of Cambridge University for his ini tial review and more recent discussions on arching theory.
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