Influence of toe restraint on reinforced soil segmental walls

885 Influence of toe restraint on reinforced soil segmental walls Bingquan Huang, Richard J. Bathurst, Kianoosh Hatami, and Tony M. Allen Abstract: A verified fast Lagrangian analysis of continua (FLAC) numerical model is used to investigate the influence of horizontal toe stiffness on the performance of reinforced soil segmental retaining walls under working stress (operational) conditions. Results of full-scale shear testing of the interface between the bottom of a typical modular block and concrete or crushed stone levelling pads are used to back-calculate toe stiffness values. The results of numerical simulations demonstrate that toe resistance at the base of a reinforced soil segmental retaining wall can generate a significant portion of the resistance to horizontal earth loads in these systems. This partially explains why reinforcement loads under working stress conditions are typically overestimated using current limit equilibrium-based design methods. Other parameters investigated are wall height, interface shear stiffness between blocks, wall facing batter, reinforcement stiffness, and reinforcement spacing. Computed reinforcement loads are compared with predicted loads using the empirical-based K-stiffness method. The K-stiffness method predictions are shown to better capture the qualitative trends in numerical results and be quantitatively more accurate compared with the AASHTO simplified method. Key words: reinforced soil, segmental walls, numerical modelling, toe restraint, K-stiffness method, simplified method. Résumé : Un modèle numérique vérifié FLAC est utilisé pour investiguer l’influence de la rigidité du pied horizontal sur la performance de murs de soutènement segmentés faits de sol renforcé en conditions de contraintes de travail (opérationnelles). Des essais en cisaillement à grande échelle à l’interface entre le bas d’un bloc modulaire typique et les plaques de nivellement de béton ou de pierre concassée ont été effectués. Les résultats de ces essais ont été utilisés pour déduire les valeurs de rigidité du pied. Les résultats des simulations numériques démontrent que la résistance du pied à la base d’un mur de soutènement segmenté en sol renforcé peut générer une portion importante de la résistance au chargement horizontal dans ces systèmes. Ceci explique en partie pourquoi les chargements de renforcement en conditions de contraintes de travail sont généralement surestimés à partir des méthodes courantes de conception basées sur les limites à l’équilibre. Les autres paramètres qui ont été évalués sont la hauteur du mur, la rigidité en cisaillement à l’interface entre les blocs, ainsi que l’espacement entre les renforcements. Les chargements de renforcement calculés sont comparés aux chargements prédits à l’aide de la méthode empirique basée sur la rigidité K. Les prédictions obtenues à partir de la méthode de la rigidité K permettent de mieux représenter les tendances qualitatives des résultats numériques et d’être plus précis quantitativement que la méthode AASHTO simplifiée. Mots-clés : sol renforcé, murs segmentés, modélisation numérique, restriction au pied, méthode de la rigidité K, méthode simplifiée. [Traduit par la Rédaction] Introduction Current design for the internal stability of geosynthetic reinforced soil walls is based on the ‘‘tie back wedge method’’ Received 11 October 2008. Accepted 11 December 2009. Published on the NRC Research Press Web site at cgj.nrc.ca on 21 July 2010. B. Huang. GeoEngineering Centre at Queen’s-RMC, Department of Civil Engineering, Queen’s University, Kingston, ON K7K 7B4, Canada. R.J. Bathurst.1 GeoEngineering Centre at Queen’s-RMC, Department of Civil Engineering, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada. K. Hatami. School of Civil Engineering and Environmental Science, University of Oklahoma, 202 W. Boyd Street, Room 334, Norman, OK 73019, USA. T.M. Allen. Washington State Department of Transportation, State Materials Laboratory, Olympia, WA 98504-7365, USA. 1Corresponding author (e-mail: [email protected]). Can. Geotech. J. 47: 885–904 (2010) or variants thereof (BSI 1995; AASHTO 2002; CFEM 2006; NCMA 2009). These approaches assign a load to each reinforcement layer based on the total load developed by a classical active failure wedge located directly behind the wall facing within the reinforced soil zone. The total active load (or pressure) is partitioned to each layer based on the tributary area of each reinforcement layer. For nonsurcharged or uniformly surcharged walls with reinforcement layers placed at uniform spacing, the tensile load in each layer increases linearly with depth below the top of the wall. Back-analysis of more than 30 full-scale instrumented field and laboratory geosynthetic reinforced soil walls has demonstrated that load predictions at the end of construction (working stress condition) using the AASHTO (2002) approach (the ‘‘simplified method’’) are very conservative for design (i.e., excessively safe). Specifically, predicted loads are (on average) three times greater than ‘‘measured’’ loads (Allen et al. 2003; Bathurst et al. 2005; Miyata and Bathurst 2007a, 2007b; Bathurst et al. 2008b). Typically, measured doi:10.1139/T10-002 Published by NRC Research Press 886 loads have been computed from best estimates of geosynthetic axial stiffness and strains recorded by strain gauges or extensometer points affixed to the reinforcement layers. The reasons for this discrepancy are as follows: (1) The underlying limit equilibrium-based deterministic model is not appropriate for walls under operational (working stress) conditions (i.e., an ultimate limit state is not present in walls with good performance at the end of construction). (2) Soil shear strength is typically underestimated. (3) The contribution of the structural facing in combination with a restrained toe to carry earth loads is ignored. A series of 11 instrumented full-scale reinforced soil walls have been constructed at the Royal Military College of Canada (RMC; Bathurst et al. 2000, 2006; Hatami and Bathurst 2005, 2006), some details of which appear later in this paper. Bathurst et al. (2006) quantified the contribution of a structural facing to carry earth loads by comparing the performance of two of these walls that were nominally the same with the exception of the facing. The sand backfill walls were 3.6 m high and reinforced with a polypropylene geogrid. One wall was constructed with a dry-stacked column of modular blocks and the companion wall was constructed with a very flexible wrapped face that provided little or no wall load capacity. They showed that the simplified method was able to make reasonably accurate estimates of the maximum load in the critical reinforcement layer of the wrap-faced wall if the peak plane strain friction angle was used in computations. However, the same method overpredicted the maximum reinforcement load by about a factor of 3 for the hard-faced wall, which is consistent with backanalyses of other full-scale walls in the database mentioned above. The paper by Bathurst et al. (2006) prompted a discussion (Leshchinsky 2007) and response (Bathurst et al. 2007) regarding the influence of the restrained toe boundary condition on the performance of the hard-faced wall. Leshchinsky (2007) opined that the toe in the RMC wall was an unusually severe constraint that resulted in undermobilization of reinforcement load capacity. Furthermore, the rigid foundation and low height of the RMC walls could be expected to further amplify the contribution of the toe to load capacity beyond what may be expected in actual field walls of greater height and with less rigid foundation support. Bathurst et al. (2007) responded that the toe constraint used in the RMC walls with a structural facing is reasonable because most field walls are embedded at the toe, mechanically attached to a footing, and (or) develop significant frictional resistance at the base of the wall facing. However, they acknowledged that the relative contribution of the toe to load capacity can be expected to decrease as wall height increases and all other parameters remain the same. Some evidence in support of this hypothesis was presented using preliminary numerical modelling work by the writers (Huang et al. 2007). However, the results of a systematic quantitative investigation of this important issue were not available at that time. This paper first presents measurements taken from fullscale reinforced soil walls that directly or indirectly show the influence of the toe boundary condition on wall performance. However, the bulk of the paper reports results from a Can. Geotech. J. Vol. 47, 2010 numerical investigation focused largely on the influence of toe restraint stiffness on the performance of segmental (modular block) geosynthetic reinforced soil walls. The numerical simulations were carried out using a previously verified numerical code for the RMC test walls (Hatami and Bathurst 2005, 2006; Bathurst et al. 2009a; Huang et al. 2009). Verification was carried out using model material properties deduced from independent laboratory testing of the wall components and quantitative comparison of wall performance predictions with measurements from several of the walls in the RMC test program. The current study includes equivalent toe stiffness values back-calculated from direct shear tests on concrete blocks placed over crushed stone and concrete levelling pads. This numerical study allows the effect of toe restraint on wall behaviour to be investigated more fully than is possible using the results from full-scale tests alone. Other parameters investigated are wall height, interface shear stiffness between blocks, wall facing batter, reinforcement stiffness, and reinforcement spacing. Results from full-scale wall testing A cross-sectional view of the control structure (wall 1) in the series of 11 structures built in the RMC retaining wall test facility is shown in Fig. 1. The solid segmental blocks used in these tests were 0.3 m wide (toe to heel). The base of the wall facing column was placed on steel plates and rollers and was supported by load cells. This arrangement allowed the measured horizontal and vertical toe loads to be decoupled. The horizontal toe was restrained laterally by a series of load rings and a steel reaction frame bolted to the laboratory structural floor. The horizontal stiffness of the reaction system was 4 (MN/m)/m computed from measured loads and horizontal displacements (Hatami and Bathurst 2005). Load rings were used to record the (connection) load transferred from each layer of reinforcement to the structural facing column. Details of the instrumentation deployed in this wall can be found in earlier related papers and are not repeated here (e.g., Bathurst et al. 2000, 2006). The wall was constructed from the bottom up at a target batter of u = 88 from the vertical. After each row of facing blocks was seated, a 150 mm thick lift of sand was placed and compacted. Following construction, uniform surcharge loading was applied in stages across the entire backfill surface using a system of airbags. Surcharge loading was continued until large facing deformations were recorded and an internal soil failure mechanism was detected in the reinforced soil zone. Following surcharge unloading, the horizontal structural support at the toe was removed. The evolution of horizontal toe load and sum of connection loads during construction and during staged uniform surcharge loading is shown in Fig. 2. The data show that horizontal toe and connection loads were mobilized progressively with height of wall during construction and during subsequent surcharging. There was a small local deviation from the general trends in the plots at low wall height that was likely the result of construction activities. The uneven toe load response at high surcharge load levels (i.e., greater than an equivalent height of 6 m) was likely the result of redistribution of earth loads to the reinforcement layers at locations back from the connections. At the end of construcPublished by NRC Research Press Huang et al. 887 Fig. 1. Cross-section view of wall 1. u, facing batter. Fig. 2. Evolution of horizontal toe load and sum of connection loads in RMC wall 1. h, height of wall above toe; q, post-construction uniform surcharge pressure; g, bulk unit weight of sand backfill. tion approximately 80% of the total horizontal load acting against the facing column was carried by the restrained toe. At the end of surcharging, about 60% of total load was carried by the reinforcement and the remainder by the toe. The initial greater load carried by the toe is attributed to larger toe stiffness compared with that of the reinforcement layers. However, as the wall moved outward the reinforcement layers strained axially, thus mobilizing tensile load capacity and reducing the amount of load that must be carried by the wall toe to maintain horizontal equilibrium. The distribution of load between the reinforcement layers and the toe can be expected to be influenced by the interface stiffness between facing column blocks. The influence of block interface shear stiffness is investigated numerically later in the paper. Published by NRC Research Press 888 Post-construction wall profiles up to the maximum surcharge load applied are shown in Fig. 3. At the end of the test, the horizontal toe support was removed. The resulting outward toe displacement was about 20 mm. Figure 4 shows connection loads and horizontal toe load at the end of surcharge unloading and at subsequent toe release. The plots show that a portion of the load taken by the toe was redistributed to the lowest layer, causing the load in this reinforcement layer to increase. Interestingly, the total load on the back of the facing column, computed as the sum of the connection loads plus the toe load, decreased. This is attributed to the further mobilization of soil shear strength consistent with the notion of a stress state in the soil that is closer to an active earth pressure condition. Clearly, a significant amount of horizontal load was carried by the toe during this test. This was true for all RMC walls constructed with a modular block facing in this test series, although there were some quantitative differences depending on wall batter angle, reinforcement type (stiffness), number of reinforcement layers, and type of compaction equipment used to prepare the sand backfill. However, it should be noted that toe release occurred after the maximum surcharge load had been applied to the structure and an internal soil failure mechanism was fully developed. Internal soil failure was detected based on local strain peaks measured in the reinforcement layers and large increases in wall deformation (Bathurst et al. 2009c). Had toe release been carried out at the end of construction, while the wall was under working stress conditions, it is reasonable to expect that the magnitude of toe movement would have been smaller. Evidence of the combined effect of toe fixity and facing type (stiffness) on load distribution to the wall toe (or foundation) and reinforcement layers can be seen in Fig. 5. All the walls in this figure were vertical-faced and were constructed with geosynthetic reinforcement and sand backfill. Furthermore, the walls had uniform spacing, but only selected layers were instrumented. The strains (3max) are the maximum strains recorded in the instrumented layers at the end of construction. These values do not include strain measurements that may have been influenced by proximity to the facing connections. Locally high strains may be anticipated at these locations due to soil settlement relative to the structural facing. The reader is directed to the papers by Allen et al. (2003), Bathurst et al. (2008b), and Miyata and Bathurst (2007a, 2007b) for detailed descriptions of the case studies identified in Fig. 5. Figure 5a presents data for instrumented field walls. Walls GW5, GW8, and GW10 show that the bottommost monitored layer (where the layer is within 10% of the height of the wall from the base) has the locally lowest strain value. Wall GW26C shows a reduction in the rate of strain accumulation with depth at the wall base. However, the strain in the lowermost layer may be less due to the higher stiffness of the reinforcement at this location compared with layers located higher in the wall. For walls GW5, GW8, and GW10, the maximum strains in the reinforcement increase with decreasing facing stiffness (i.e., in the order of GW5, GW8, and GW10). There is an exception to this trend for wall GW26C, but this may be because this wall was designed using the original K-stiffness method (Allen et al. Can. Geotech. J. Vol. 47, 2010 2003; Allen and Bathurst 2006) and hence, higher strains were anticipated compared with values using the more conservative simplified method (AASHTO 2002). Data for carefully instrumented field walls are limited compared with full-scale laboratory walls, and deviation from the trends noted here may be expected for walls with other foundation conditions, facing types, and qualities of construction. Figure 5b shows similar strain data for a series of walls built at the Public Works Research Institute (PWRI) in Japan. In these tests, the bottom of the wall was horizontally restrained with the exception of GW21. For these walls there is visually apparent local reduction in strain for layers located within the bottom 20% of the wall height for those structures with a restrained toe. There is a visually apparent reduction in rate of strain accumulation with depth below the wall crest for the wall with the least restrained toe condition (GW21). For the walls with the same toe fixity but varying facing type, there is a trend towards decreasing strains with increasing wall structural stiffness (wall structural stiffness increasing in the order of GW22 to GW25). Taken together, the data in Figs. 3–5 show that strain (or load) in reinforcement layers is often attenuated with increasing proximity to the wall toe (foundation) and that strain (or load) is further attenuated with increasing stiffness of the wall facing. An important implication to wall performance is that load that is not being resisted by the bottom layer(s) must be carried by the foundation (including the toe) to satisfy horizontal equilibrium. Horizontal toe load capacity is considered by the writers to be typical for a wall with a structural facing due to friction between the base of the facing column and a concrete or gravel levelling pad, embedment, and (or) structural attachment to a concrete footing. However, there is no data from physical full-scale testing that can be used to quantitatively isolate the contribution of horizontal toe stiffness to wall capacity. The only practical methodology is numerical modelling using computer codes previously verified against carefully instrumented and monitored physical tests. This is the strategy adopted in this paper. Numerical model General approach The writers have developed a series of numerical twodimensional finite difference fast Lagrangian analysis of continua (FLAC) codes (Itasca 2005) to predict performance features of several RMC test walls including the control wall described earlier (Hatami and Bathurst 2005, 2006; Bathurst et al. 2009a; Huang et al. 2009). The models have used strain- and time-dependent constitutive models to simulate the behaviour of the polymeric geogrid reinforcement materials used in the RMC walls and three different constitutive models for the sand backfill. In order of increasing complexity, the soil models were (i) linear elastic–plastic Mohr– Coulomb; (ii) modified Duncan–Chang hyperbolic; and (iii) Lade’s single hardening. Calculated results were compared against measured toe footing loads, foundation pressures, facing displacements, connection loads, and reinforcement strains. In general, all three approaches gave similar results for wall performance under operational (working stress) conditions prior to development of contiguPublished by NRC Research Press Huang et al. 889 Fig. 3. Post-construction wall deformation profiles for RMC wall 1. Fig. 4. Connection and toe loads at end of surcharge unloading and toe release for RMC wall 1. ous shear failure zones in the reinforced soil zone. Furthermore, the predictions were typically within measurement accuracy for the end-of-construction and surcharge load levels below pressures needed to generate soil failure. However, numerical results using the linear elastic–plastic Mohr–Coulomb model were sensitive to the choice of a single-valued elastic modulus, which is problematic when this value is deduced from conventional triaxial compression tests. The results of these investigations show that numerical models that incorporate the hyperbolic soil model are adequate to predict the performance of reinforced soil walls under typical operational conditions provided that the reinforcement, interfaces, construction sequence, soil, and soil compaction are modelled correctly. The writers concluded that further improvement of predictions using more sophisticated soil models is not guaranteed. A similar conclusion has been reached by Ling (2003), who compared results of numerical simulations using a hyperbolic soil model with measured results from an instrumented full-scale reinforced soil wall constructed in Japan. In the current investigation, a version of the numerical code described by Bathurst et al. (2009a) and Huang et al. (2009) was used. The construction process was modelled by sequential bottom-up placement of the blocks and matching soil layer placement and compaction. The thickness of each block–soil layer was taken as an individual block height (0.15 m). Compaction effects were simulated as a transient uniform surcharge pressure of 8 kPa applied to the top surface of each soil layer following the procedure described by Hatami and Bathurst (2005). Computations were carried out in large-strain mode to ensure sufficient accuracy in the event of large wall deformations or reinforcement strains. Published by NRC Research Press 890 Can. Geotech. J. Vol. 47, 2010 Fig. 5. Maximum reinforcement strains from instrumented full-scale vertical walls with granular backfill (data from Miyata and Bathurst 2007a; Bathurst et al. 2008b): (a) field walls; (b) Public Works Research Institute (PWRI) of Japan test walls. EPS, extruded polystyrene; H, wall height; z, the depth below crest of wall. The numerical mesh was updated to simulate the moving local datum as each row of facing units and each soil layer was placed during construction. The same reinforcement length to wall height ratio of 0.7 matching the original RMC test walls was used in the numerical models. This value is also recommended by AASHTO (2002). The ratio Published by NRC Research Press Huang et al. 891 Fig. 6. Example numerical FLAC grid. of wall height, H, to length of soil mass, B, was kept the same at 0.65 in the wall models of different height. Figure 6 shows a typical numerical FLAC grid. Material properties Soil The compacted backfill sand was assumed to be an isotropic, homogeneous, nonlinear elastic material using the Duncan–Chang hyperbolic model. The elastic tangent modulus, Et, is expressed as    n Rf ð1  sinfÞðs 1  s 3 Þ 2 s3 Ke pa ½1 Et ¼ 1  pa 2c cosf þ 2s 3 sinf where s1 is the major principal stress, s3 is the minor principal stress, pa is the atmospheric pressure, and other parameters are defined in Table 1. The original Duncan–Chang model was developed for axi-symmetric (triaxial) loading conditions and therefore the bulk modulus is a function only of s3; specifically  m s3 ½2 Bm ¼ Kb pa pa where Kb is the bulk modulus number and m is the bulk modulus exponent. However, under plane strain conditions, s2 > s3, where s2 is the intermediate principal stress, and the confining pressure is hence underestimated. Hatami and Bathurst (2005) showed that the Duncan–Chang parameters back-fitted from triaxial tests on the RMC sand underestimated the stiffness of the same soil when tested in a plane strain test apparatus. In the current study and in previous related modelling (Bathurst et al. 2009a; Huang et al. 2009), the bulk modulus formulation proposed by Boscardin et al. (1990) was used to Table 1. Material properties. Property Value Soil Elastic modulus number, Ke Unloading–reloading modulus number, Kur Elastic modulus exponent, n Failure ratio, Rf Tangent Poisson’s ratio, nt Peak plane strain friction angle, f (8) Cohesion, c (kPa) Initial bulk modulus number, Bmi/pa Asymptotic volumetric strain value, 3u Density, r (kg/m3) 950 1140 0.70 0.80 0–0.49 48 0.2 74.8 0.02 2250 Reinforcement Stiffness of polyester, JPET (kN/m)* Stiffness of steel, Jsteel (kN/m){ 285 30000 *Ultimate (index) strength: 80 kN/m. { Yield strain: 0.2%. replace the original formulation. The bulk modulus, Bt, is expressed as   sm 2 ½3 Bt ¼ Bmi 1 þ Bmi 3u where sm is the mean pressure, (s1+s2+s3)/3, and Bmi and 3u are material properties that are determined as the intercept and the inverse of slope from a plot of sm/3vol versus sm in an isotropic compression test, where 3vol is the volumetric strain. Table 1 summarizes the properties of the backfill soil. The Duncan–Chang parameters were taken from Boscardin et al. (1990) with some adjustments to represent a high quality sand material prepared to 95% standard Proctor Published by NRC Research Press 892 Can. Geotech. J. Vol. 47, 2010 dry density and designated poorly graded sand (SP) using the Unified Soil Classification System (ASTM 2006). Reinforcement Soil reinforcement layers were simulated using FLAC cable elements. Two reinforcement materials were used to represent polymeric geogrid and steel strip reinforcement products having very different stiffness properties (values). To simplify parametric analyses and focus the results on the influence of toe stiffness, both materials were assigned linear load–strain properties. The stiffness of polyester (PET) geogrid materials has been shown to be sensibly time- and strain-independent over the range of strains anticipated at the end of construction in typical reinforced soil walls (Walters et al. 2002; Bathurst et al. 2009c). Reinforcement stiffness values are given in Table 1. The stiffness value for the PET material is within the range of stiffness values for geosynthetic reinforcement materials. The steel material is approximately 100 times stiffer than the polymeric material, but only about 50% of the stiffness of typical steel strip reinforcement (Bathurst et al. 2009b). Nevertheless, the focus of this paper is on geosynthetic reinforced soil walls. A very stiff reinforcement material (steel strip) was used in numerical simulations to generate large detectable qualitative and quantitative differences between walls that can be ascribed to the influence of reinforcement stiffness. The (index) global reinforcement stiffness of the walls with PET and steel reinforcement materials falls within the range of values determined from instrumented field and full-scale laboratory walls (Allen et al. 2003, 2004). The (index) global reinforcement stiffness value, Sglobal, is calculated as ½4 Sglobal ¼ k X i¼1 H Ji ¼ Jave H=n where Ji is the tensile stiffness of an individual polymeric reinforcement layer at 2% strain as measured in a laboratory tensile test (e.g., ASTM 2001) and at the elastic limit for steel strip reinforcement; and Jave is the average tensile stiffness of all n reinforcement layers in a wall with height H. Using eq. [4], the (index) global reinforcement stiffness value for walls with spacing Sv = 0.6 m is 475 and 50 (MN/m)/m for the PET and steel reinforced walls, respectively. Interfaces and boundary conditions The interfaces between facing–backfill, block–block, foundation–backfill, and reinforcement–backfill were modelled as linear spring–slider systems with interface shear strength defined by the Mohr–Coulomb failure criterion. Details can be found in the FLAC manual (Itasca 2005). In this study, the facing column stiffness was assumed to be controlled by the interface shear stiffness between modular blocks. The value for the solid masonry blocks used in the original RMC test walls was back-calculated to be 40 (MN/m)/m from direct shear tests (Hatami and Bathurst 2005). All RMC test walls were built on a rigid concrete floor (Fig. 1). In the numerical models, a fixed boundary condition in both horizontal and vertical directions was assumed at the foundation level representing a similar rigid founda- tion condition. A fixed boundary condition in the horizontal direction was assumed at the backfill far-end boundary. The toe of the facing column was restrained horizontally by a spring element whose stiffness was varied in the current study to represent different toe restraint conditions. The control stiffness value was taken as 4 (MN/m)/m, matching measurements recorded at this boundary in the RMC physical tests. The bottom of the facing column was fixed in the vertical direction, but free to translate in the horizontal direction and to rotate. The interface between the bottom block and the foundation was unrestrained (as in the RMC physical tests) so that the axial force recorded in the spring element could be interpreted as the toe load. In some simulations, a perfectly rigid horizontal toe condition was applied by fixing the toe of the facing column in the horizontal direction. In this case, the horizontal toe force was computed from the horizontal reaction force at the corresponding numerical grid point. Direct interface shear testing was carried out using a large dry-cast masonry concrete block seated on three different base materials. The bottom of the block was flat. The bases were a poured-in-place unreinforced wet-cast concrete mat and two different crushed stone materials. Crushed stone 1 was well-graded with a mean particle size, D50, of 12 mm and crushed stone 2 was uniformly graded with D50 = 22 mm. The tests were carried out under a range of normal loads corresponding to wall heights up to about 12 m. The shear load per unit length (V) to generate 2 and 6 mm of shear displacement (D) was recorded and the interface shear stiffness computed as V/D. The results of these tests are plotted in Fig. 7. The value of 2 mm corresponds to the displacement estimated for the RMC walls at the end of construction. The value of 6 mm is a typical maximum displacement value predicted for the PET wall simulations presented later using H = 6 m and a toe stiffness value 4 (MN/m)/m. It is also a maximum value from the results of steel wall simulations of the same height. The shear test results show that the concrete mat provided the greatest shear stiffness using the same displacement criterion. For the same configuration, the computed stiffness values decreased with increasing displacement. The data show that the toe stiffness computed for the RMC walls falls within the range of values plotted in Fig. 7 and, hence, a value of 4 (MN/m)/m is considered reasonable for these structures. It is possible that greater interface shear stiffness values would result for a block with a rougher base or a shear key that projects below the base of the block into a granular base material. However, later in the paper, it is demonstrated that equivalent toe stiffness values orders of magnitude lower than those shown in Fig. 7 are required to generate qualitatively different wall response from walls with a reference toe stiffness of 4 (MN/m)/m. The reinforcement was bonded to the backfill using the FLAC built-in grout algorithm. A large bond strength value was assigned to the reinforcement–backfill interface to prevent slip. A perfect bond assumption has been adopted in other numerical studies to simplify modelling and the interpretation of results (Rowe and Ho 1997; Leshchinsky and Vulova 2001; Hatami and Bathurst 2005, 2006). Experience with the high quality sand used in RMC tests and measured reinforcement displacements suggest that this is a reasonable Published by NRC Research Press Huang et al. 893 Fig. 7. Toe interface shear stiffness values computed from block–foundation interface shear testing. W, width of block. Table 2. Interface properties. Property Value Backfill soil–block Friction angle, dsb (8) Dilation angle, jsb (8) Normal stiffness, Knsb ((MN/m)/m) Shear stiffness, Kssb ((MN/m)/m) 48 6 100 1 Block–block Friction angle, dbb (8) Cohesion, cbb (kPa) Normal stiffness, Knbb ((MN/m)/m) Shear stiffness, Ksbb ((MN/m)/m) 57 46 1000 40 Backfill–reinforcement Friction angle, fb (8) Adhesive strength, sb (kPa) Shear stiffness, Kb ((MN/m)/m) 48 1000 1 assumption to simulate the soil–geogrid shear transfer under working stress conditions. To keep the interpretation of results as simple as possible, the same no-slip interface was assumed in all simulations in this numerical study. The influence of reinforcement–sand interface stiffness and strength was not investigated in this study. Leshchinsky and Vulova (2001) carried out similar numerical modelling and reported that reducing the interface friction angle did not significantly change simulation results. Interface properties used in the current study are summarized in Table 2. Variables in the parametric study A total of 42 wall cases were simulated in this study although not all results are presented. The model parameters that were investigated are summarized in Table 3. The simulation matrix was carried out with the objective of investigating the influence of parameter values in the first four rows of Table 3 in combination with the range of toe horizontal stiffness values shown in the bottom row. It should be recalled that the focus of this paper is on wall behaviour under operational conditions (i.e., working stress conditions). Allen et al. (2003) reviewed a large number of monitored geosynthetic reinforced soil walls with granular backfills and concluded that contiguous failure zones from the heel of the wall facing to the backfill surface and other obvious signs of poor wall performance did not occur if polymeric reinforcement strain levels were kept to less than about 3%. Using this value as an indicator of working stress conditions, it was found that all numerical results for PET wall models satisfied this constraint. The yield strain limit of steel reinforcement was assumed to be equal to 0.2% (Hatami and Bathurst 2006). Numerical results from the current study confirmed that strains in the steel reinforcement layers were less than this limit. Published by NRC Research Press 894 Can. Geotech. J. Vol. 47, 2010 Table 3. Values used in the parametric study. Parameter Wall height (m) Facing column interface shear stiffness ((MN/m)/m){ Facing batter from vertical (8) Spacing (m) Toe stiffness ((MN/m)/m) Values* (3.6), 6, 9, 12 0.4, 4, 20, (40), 80 0, 4, (8), 13 0.3, (0.6), 0.9 0.04, 0.4, (4), 40, fixed Normal load dependent (Fig. 7) *Values in parentheses match RMC control test (wall 1). { Block-to-block interface shear stiffness, Ksbb. Fig. 8. Influence of toe stiffness and reinforcement stiffness on facing displacements (H = 6 m, Sv = 0.6 m, u = 88 from vertical): (a) PET reinforcement; (b) steel reinforcement. Published by NRC Research Press Huang et al. Numerical results Facing displacements Normalized relative facing displacement profiles for a 6 m high wall with PET and steel reinforcement layers at spacing Sv = 0.6 m are plotted in Fig. 8. The target facing batter was u = 88 from the vertical. The displacements were computed with respect to the time that the layer was placed. Hence, the displacement profiles represent a moving datum and should not be confused with wall profiles at the end of construction. The normalized facing displacements in Figs. 8a(ii) and 8b(ii) are taken with respect to values for the case using the toe stiffness value of the RMC control wall (4 (MN/m)/m). Facing displacements at each elevation decrease nonlinearly with increasing toe stiffness (Figs. 8a(i), 8b(i)). The difference in deformations between walls with a fixed toe and a toe with stiffness of 40 (MN/m)/m is negligible. Not unexpectedly, displacements are larger for walls with lower reinforcement stiffness. The ratio of maximum wall displacements ranges from about 2 to 3 between the PET and steel reinforcement cases, respectively. The influence of relative toe stiffness value with respect to the control case can be seen to diminish with height above the toe and with increasing reinforcement stiffness. For toe stiffness values greater than 4 (MN/m)/m, the influence of the magnitude of toe stiffness on wall deformations can be argued to be limited to about 0.25H above the base of the wall (Figs. 8a(ii), 8b(ii)). The data plotted in Fig. 8 demonstrate that it is the combination of toe stiffness and global reinforcement stiffness that influences end-of-construction wall deformations. Figure 9a shows the influence of toe release on wall displacements for the same wall as in Fig. 8. The toe of the wall can be seen to move almost 20 mm and additional outward movements are largely restricted to the bottom half of the wall. These observations are similar to those for wall 1 in the RMC physical test program (Fig. 3) even though the RMC wall was shorter, less stiff reinforcement material was used, and the wall was surcharge-loaded well beyond working stress levels. The redistribution of the load from the toe to the two bottom-most reinforcement layers computed at the connections can be seen in Fig. 9b. Qualitative features are similar to those shown in Fig. 4. For example, the total load on the back of the wall decreases after toe release. However, individual connection loads do not become less than the end-of-construction values as shown in Fig. 4. This is because the numerical wall was not heavily surcharged at the end of construction and possibly because reinforcement stress relaxation was not simulated in the numerical model. Toe and connection loads The contribution of the toe to wall lateral load capacity can be quantified by considering the wall facing column as a free body. In this simple approach the sum of connection loads and toe loads must be equal to the horizontal component of total earth force acting against the back of the facing to satisfy horizontal equilibrium. Figure 10 shows plots of toe load, total load, and relative contribution of toe and connection loads to resist the total horizontal load acting against the wall facing. The load carried by the toe increases roughly log-linearly with increasing toe stiffness over much 895 of the range of stiffness values investigated (Figs. 10a(i), 10b(i)). Furthermore, there is a log-linear trend when the fractions of the total horizontal earth load carried by the toe and connections are plotted against toe stiffness (Figs. 10a(ii), 10b(ii)). However, the magnitude of loads and fractions of the total load carried by the toe and connections are sensitive to the magnitude of the reinforcement stiffness. As reinforcement stiffness increases the contribution of the toe decreases. This can be understood if the free-body analogue for the wall facing is further developed by considering the wall facing as a continuously supported beam with the toe and connections acting as spring reactions and the earth pressure as the distributed load (Bathurst et al. 2007). This analogue then leads to the expectation that as the toe stiffness increases, more load is carried by the stiffest spring (toe). For the reinforcement layers to carry the total earth load acting against the back of a wall with a structural facing, the toe must be unrestrained, which is, in the opinion of the writers, an unlikely boundary condition. Finally, the data show that the reference toe stiffness value (4 (MN/m)/m) used earlier gives results that fall roughly in the middle of the range of dependent values on the vertical axes in these plots. This gives some support to the argument that the RMC walls have a horizontal toe stiffness that falls in the middle of the range for walls with idealized unrestrained and fixed horizontal toe conditions. Reinforcement strains The magnitude and distribution of reinforcement strains at the end of construction for the 6 m high wall used in the parametric study are plotted in Fig. 11 for selected layers. The results for the fixed toe case are not visually distinguishable from the case with toe stiffness of 40 (MN/m)/m and, hence, are not presented here. In general, the strains increase with decreasing toe stiffness consistent with observations for connection loads discussed in the previous section. However, with the exception of layer 3 in the wall with the least stiff toe, the strains at the connections are the largest along the reinforcement length. This is attributed to the effect of relative soil settlement behind the facing column: as the soil is compacted, it compresses under self-weight and the wall facing rotates outward during construction. The observation that the highest strains in a reinforcement layer occur close to the connections has been made for the RMC walls and other instrumented field and full-scale laboratory walls where strain monitoring was carried out in close proximity to the back of structural facings. As toe stiffness decreases, there is a detectable increase in local strain at locations well beyond the back of the facing. This is attributed to the onset of internal soil shear failure mechanisms in the reinforced soil zone. The development of soil shear zones can be seen in Fig. 12. The contours are shown with two intervals (<2% and 2%–5%). For the two least stiff toe cases, there are local high strain levels at the heel of the wall that were developed during initial bottom-up construction. However, these zones are not contiguous through the height of the backfill and reinforcement strains are less than 3% (Fig. 11). Hence, these walls are assumed to be under working stress conditions according to criteria introduced earlier in the paper. Published by NRC Research Press 896 Can. Geotech. J. Vol. 47, 2010 Fig. 9. Influence of toe release following end of construction (EOC) for wall with PET reinforcement (H = 6 m, Sv = 0.6 m, u = 88 from vertical): (a) wall displacements; (b) connection and toe loads. Fig. 10. Influence of toe stiffness and reinforcement stiffness on magnitude and distribution of toe and connection loads (H = 6 m, Sv = 0.6 m, u = 88 from vertical): (a) PET reinforcement; (b) steel reinforcement. Influence of wall height The influence of wall height on toe and connection loads is shown in Fig. 13. The reference toe stiffness value of 4 (MN/m)/m and a fixed toe condition were used in these simulations. The magnitude of toe load can be seen to increase with wall height for both reinforcement stiffness Published by NRC Research Press Huang et al. Fig. 11. Influence of toe stiffness on reinforcement strains for wall with PET reinforcement layers (H = 6 m, Sv = 0.6 m, u = 88 from vertical). 897 wall batter (Fig. 14a). However, in these simulations, the magnitude of toe load remained reasonably constant for the same toe boundary condition while the fraction of total load carried by the toe increased with increasing wall batter (Fig. 14b). Influence of reinforcement spacing It can be expected that, as the reinforcement spacing increases, the magnitude of reinforcement (or connection), loads and toe load will increase when all other parameters remain the same. To remove the influence of reinforcement stiffness as a variable when investigating the effect of spacing, simulations were carried out with different reinforcement spacing, but with the same global reinforcement stiffness value (Sglobal = 475 ((kN/m)/m) computed using eq. [4]). Using a common global stiffness value, the plots in Fig. 15 show that the magnitude of loads and the distribution of total load to the connections and toe are sensibly independent of spacing for the same toe boundary condition. This observation is consistent with load predictions using the working stress method (K-stiffness method) originally proposed by Allen et al. (2003). This method was calibrated by fitting to loads deduced from instrumented full-scale field and laboratory walls. The influence of reinforcement stiffness is not accounted for in current limit equilibrium-based (tie-back wedge methods) such as the AASHTO (2002) simplified method. For example, for a set of nominally identical walls varying only with respect to stiffness of the polymeric reinforcement, the loads in the reinforcement layers are always the same. cases (Fig. 13a). For the same height and reinforcement type, the magnitude of toe load is less for the compliant toe case. However, for the same wall height and toe condition, the load is generally higher for the PET reinforcement case, which is attributed to the relatively higher toe reaction stiffness with respect to the reinforcement layers as discussed earlier in the context of the continuously supported beam analogue. The relative contributions of the toe reaction and reinforcement layers are plotted in Fig. 13b. For both reinforcement stiffness cases, the relative contribution of the toe to carry horizontal earth loads decreases with wall height, but at a diminishing rate. However, the contribution of the toe for the PET reinforcement model is greater than for the steel reinforcement case for walls of the same height and toe boundary condition. For the highest wall considered (12 m) and a toe stiffness value of 4 (MN/m)/m, 70% of the load is carried by the PET reinforcement layers; whereas for the matching steel reinforcement case, the reinforcement layers carry about 90% of the total load. A practical implication of this observation is that, for tall steel reinforced soil walls, the assumption in current AASHTO (2002) design practice to assign all earth loads to the reinforcement layers may be reasonable. For walls with more extensible reinforcement materials (i.e., geosynthetics), this assumption leads to very conservative (i.e., excessively safe) internal stability design. Influence of block–block interface stiffness Segmental retaining wall units transmit shear through interface friction, shear keys, pins, and various types of connectors (NCMA 2009). The shear capacity and magnitude of interface stiffness may vary widely between different facing systems (Bathurst et al. 2008a). It may be expected that the interface shear stiffness will influence wall deformations and the distribution of total load to the toe and connections. Figure 16 shows the influence of block–block interface stiffness on wall facing loads. The total load and the load carried by the toe increase as interface shear stiffness increases, but at a diminishing rate (Fig. 16b). The distribution of the load to the toe and reinforcement layers (connections) becomes sensibly constant beyond (say) Ksbb = 20 (MN/m)/m, which is five times the reference toe stiffness value of 4 (MN/m)/m that is judged to be a reasonable value for these systems when seated on a rigid foundation. Influence of wall batter The influence of wall batter on toe and connection loads for PET reinforced soil walls is shown in Fig. 14. A facing batter angle of u = 08 corresponds to a vertical face. Most reinforced segmental retaining walls are constructed with 18 < u < 158 (NCMA 2009). As expected, the total load acting on the back of the wall facing decreases with increasing Maximum reinforcement loads computed in numerical simulations can be compared with predicted loads using the AASHTO (2002) simplified method (tie-back wedge method) and the most recent version of the K-stiffness method (Bathurst et al. 2008b). According to the AASHTO approach, the maximum reinforcement load, Tmax, for nonsurcharged walls can be calculated as Comparison of reinforcement loads with predicted values using current design methods Published by NRC Research Press 898 Can. Geotech. J. Vol. 47, 2010 Fig. 12. End-of-construction soil shear strain contours for walls with PET reinforcement and different toe stiffness (H = 6 m, Sv = 0.6 m, u = 88 from vertical): (a) 40 (MN/m)/m; (b) 4 (MN/m)/m; (c) 0.4 (MN/m)/m; (d) 0.04 (MN/m)/m. ½5 Tmax ¼ K g z Sv where z is the depth of the reinforcement layer below the crest of the wall; g is bulk unit weight of soil; and K is calculated as ½6 K¼ cos2 ðf þ uÞ   sinf 2 cos2 u 1þ cos u All other parameters have been defined previously. The maximum reinforcement load using the K-stiffness method and nonsurcharged walls is ½7 1 Tmax ¼ KgHSv Dtmax Fg Flocal Ffs Ffb Fc 2 where Dtmax is the load distribution factor that modifies the reinforcement load based on layer location. The remaining terms, Fg, Flocal, Ffs, Ffb, and Fc are influence factors that account for the effects of global and local reinforcement stiffness, facing stiffness, face batter, and soil cohesion, respectively. The coefficient of lateral earth pressure is calculated as K = 1 – sinf, where f is the secant peak plane strain friction angle of the soil. It is important to note that parameter K is used as an index value and does not imply that at-rest soil conditions exist in the reinforced soil back- fill according to classical earth pressure theory. In the current parametric study with PET reinforcement, spacing Sv = 0.6 m and facing batter u = 88, the influence factors are Fg = 0.37; Flocal = 1; Ffs = 0.51, 0.63, 0.76, and 0.86 for 3.6, 6, 9, and 12 m high walls, respectively; Ffb = 0.84; and Fc = 1. Details to calculate these values for the wall used as an example here can be found in Bathurst et al. (2008b). To remove the choice of friction angle as a variable between calculation methods, the same value of peak friction angle is used in all calculations (i.e., f = secant peak plane strain friction angle of the soil = 488; see Table 1). The reinforcement loads (Tmax) plotted in Fig. 17 are the maximum load in each reinforcement layer at the end of construction excluding connection loads (which are higher in some cases as illustrated by the strain plots in Fig. 11). The plots show that, as toe stiffness decreases, the magnitude of reinforcement load at each elevation increases and the load distributions become more triangular in shape. Nevertheless, the AASHTO (2002) simplified method overpredicts Tmax values regardless of toe stiffness magnitude and the overprediction increases with increasing toe stiffness. In practice, this overprediction would be greater because lower friction angle values from direct shear and triaxial compression tests are used in computations rather than larger values from plane strain tests. For the fixed toe and toe stiffness case with 40 (MN/m)/m, the K-stiffness Published by NRC Research Press Huang et al. 899 Fig. 13. Influence of wall height, reinforcement stiffness and toe stiffness on loads carried by the toe and connections (Sv = 0.6 m, u = 88 from vertical): (a) toe load; (b) relative contribution of total load carried by toe and connections. method is conservative. However, for the reference case corresponding to simulations matching the toe stiffness of the RMC walls, the K-stiffness method is very close, but slightly conservative for design. For less stiff toe cases (£0.4 (MN/m)/m), the K-stiffness method is nonconservative for design and simulation results can be seen to fall between predictions using the two methods. However, the database of wall case studies used to develop the K-stiffness method shows that the distribution of reinforcement loads deduced from measured strain values is typically trapezoidal with depth (Allen and Bathurst 2002; Allen et al. 2003; Bathurst et al. 2005, 2007, 2008b) lending support to the argument that the distribution of Tmax for numerical results with toe stiffness ‡4 (MN/m)/m represents typical field walls. Furthermore, the results of direct shear testing presented earlier in the paper (Fig. 7) show that this value is reasonable for modular block units seated on a concrete or granular levelling pad. As a further check on the influence of toe stiffness on reinforcement loads, an additional set of simulations were carried out using normal load (height) dependent toe stiffness values (see Fig. 7) and a range of wall heights. The stiffness values correspond closely to shear stiffness values computed for a concrete levelling pad and 6 mm displacement crite- rion. The numerical results in Fig. 18 show that the influence of toe restraint on the distribution of reinforcement loads with height becomes trapezoidal in shape as wall height increases. Predicted loads using the K-stiffness method are compared with numerical results in the same figure. The trapezoidal shape, which is a distinguishing feature of the K-stiffness method, is judged to capture the trend in numerical results particularly for the higher walls, while being conservatively safe (for design). This independent check of the accuracy of the K-stiffness method shows that this empirical-based design method is a promising approach for the internal stability design of these systems for working stress conditions. Conclusions and implications to design and construction Geosynthetic reinforced soil segmental retaining walls are mechanically complex systems. The magnitude of reinforcement loads under working stress conditions (i.e., operational conditions) is influenced by wall geometry, properties of the material components, boundary conditions, and construction method. The number of carefully instrumented and monitored walls (other than the 11 walls in the recent RMC test Published by NRC Research Press 900 Can. Geotech. J. Vol. 47, 2010 Fig. 14. Influence of facing batter (u) and toe stiffness on loads carried by the toe and connections for walls with PET reinforcement (H = 6 m, Sv = 0.6 m): (a) toe and connection loads; (b) relative contribution of total load carried by toe and connections. program) is limited. For example, there are 13 case studies for walls with granular backfills and another 18 case studies for walls constructed with c–f soils (Bathurst et al. 2008b). Nevertheless, there is strong evidence that the current AASHTO (2002) simplified method (or variants) is very conservative for walls (i.e., excessively safe) when predicting maximum reinforcement loads under typical operational conditions in internal stability design. Furthermore, the distribution of reinforcement loads using the simplified method does not match loads deduced from measured strains. The K-stiffness method, which is an empirical-based working stress method calibrated against measured reinforcement loads, has been demonstrated to give better predictions of reinforcement loads (e.g., Bathurst et al. 2008b). However, because the database of physical measurements used to develop the K-stiffness method is limited, numerical modeling is required to systematically investigate the sensitivity of material properties and boundary conditions on wall performance. The parametric study reported here is a small subset of a much wider range of parameters that could be investigated. An important advantage of the numerical model adopted in this investigation is that the accuracy of the model has been previously verified against a wide range of measured performance responses from a series of care- fully constructed, instrumented, and monitored RMC physical test walls (Hatami and Bathurst 2005, 2006; Bathurst et al. 2009a; Huang et al. 2009). The major conclusions from the current investigation are (1) A toe stiffness of 4 (MN/m)/m is a reasonable value to simulate the interface shear stiffness between the bottom of a 0.3 m wide concrete block and a concrete or crushed stone base. (2) For numerical simulations with toe stiffness greater than 4 (MN/m)/m, the influence of the magnitude of toe stiffness on wall facing displacements was limited to about 25% of the height of the wall above the base. (3) The magnitude of toe stiffness has a potentially significant effect on the magnitude and distribution of reinforcement loads. In general, for walls with uniform reinforcement spacing and type, as the toe stiffness decreases, reinforcement loads increase and their distribution with depth becomes more triangular. However, to generate a triangular load distribution for the reinforced soil walls with extensible geosynthetic reinforcement in this study, it was necessary to reduce the magnitude of toe stiffness to values that are orders of magnitude lower than those deduced from full-scale interface shear tests. Published by NRC Research Press Huang et al. 901 Fig. 15. Influence of reinforcement spacing and toe stiffness on loads carried by the toe and connections for walls with PET reinforcement. (Sglobal = 475 kN/m2, H = 6 m, u = 88): (a) toe and connection loads; (b) relative contribution of total load carried by toe and connections. (4) The influence of toe stiffness on reinforcement loads diminishes with height of the reinforcement layer above the toe. For a 6 m high wall and the range of toe stiffness values investigated, the toe effect was limited to the bottom half of the wall. (5) The fraction of total load carried by the toe increases with increasing horizontal toe stiffness, while the fraction of total load carried by the reinforcement layers decreases. (6) The magnitudes of load carried by the toe and reinforcement layers are influenced by the stiffness of the reinforcement layers. As reinforcement stiffness increases, reinforcement loads increase and the fraction of total earth load carried by the reinforcement layers increases. (7) The distribution and magnitude of load (strain) in each reinforcement layer is influenced by the magnitude of toe stiffness. Maximum strains in numerical simulations typically occurred at the connections. In the example 6 m high wall, the reinforcement strains at the connections increased with decreasing toe stiffness over the bottom half of the wall. (8) The fraction of load carried by the reinforcement layers increased with wall height. For the same wall (9) (10) (11) (12) height, the fraction of load carried by the reinforcement layers increased with increasing reinforcement stiffness. However, for walls with H £ 12 m, a typical geosynthetic reinforcement stiffness, and a toe stiffness value of 4 (MN/m)/m, the fraction of load carried by the reinforcement layers did not exceed about 70%. As facing batter increased from 48 to 138 in this study, the magnitude of toe load remained reasonably constant, but the fraction of total earth load carried by the toe increased. For the walls in this numerical investigation with the same global reinforcement stiffness value, there was no practical influence of reinforcement spacing on reinforcement and toe loads. There was a diminishing influence of increasing magnitude of block–block interface stiffness on magnitude of toe and reinforcement loads for the range of block– block stiffness values investigated. For all toe stiffness cases investigated, the current AASHTO (2002) simplified method overpredicted the reinforcement loads. The K-stiffness method (Bathurst et al. 2008b) provided a very accurate estimate of endof-construction reinforcement loads when a singlevalue toe stiffness of 4 (MN/m)/m was used in compuPublished by NRC Research Press 902 Can. Geotech. J. Vol. 47, 2010 Fig. 16. Influence of block–block interface stiffness and toe stiffness on loads carried by the toe and connections for walls with PET reinforcement (H = 6 m, Sv = 0.6 m, u = 88): (a) toe and connection loads; (b) relative contribution of total load carried by toe and connections. tations for a 6 m high segmental wall seated on a rigid foundation and reinforced with a typical PET reinforcement material. The K-stiffness method was shown to capture the trend towards a trapezoidal distribution of reinforcement loads with increasing wall height, while being slightly conservative (i.e., safer for design). An important implication of the results of this numerical investigation to wall performance and design is that the horizontal toe of a reinforced soil segmental retaining wall can significantly contribute to the resistance against horizontal earth loads developed behind a structural facing under operational conditions (i.e., working stress conditions). The required toe resistance is available from interface shear capacity developed between the base of the modular block facing and a concrete or crushed stone levelling pad. This contribution is ignored in current design methods (e.g., AASHTO 2002) and partially explains the overestimation of reinforcement loads and the more uniform distribution of load observed in instrumented walls. This constraint can also be considered to be available at collapse of the structure if sufficient surcharge loading can be applied. However, the tests at RMC and the numerical modelling described herein demonstrate that an ultimate limit state defined by a contig- uous failure zone through the reinforced soil will occur well before these walls collapse due to reinforcement pullout or rupture. This internal ultimate (failure) limit state has been introduced in the K-stiffness method (e.g., Allen et al. 2003; Bathurst et al. 2008b). The focus of this investigation has been on walls under working stress conditions. This emphasis has been prompted in part because loads due to working stress (operational) conditions are assumed in current reliability-based design (load and resistance factor design (LRFD)) in North America (e.g., Canadian Geotechnical Society (CSA) 2006; AASHTO 2009). Hence, analytical methods and numerical models that can accurately predict reinforcement loads under operational conditions are of great interest to develop data for rigorous LRFD calibration. The empirical-based K-stiffness method was developed by fitting to measured reinforcement loads in instrumented fullscale walls and is demonstrated to better capture the qualitative trends in the numerical results and the magnitude of predicted loads. It should be noted that the database of fullscale walls used to calibrate the K-stiffness method did not include any of the RMC walls that were used to verify the numerical model in this investigation. Hence, this study is an independent verification of the K-stiffness method. Published by NRC Research Press Huang et al. Fig. 17. Influence of (constant) toe stiffness on maximum reinforcement loads and comparison with predictions using AASHTO (2002) simplified method and K-stiffness method (Bathurst et al. 2008b) for wall with PET reinforcement (H = 6 m, Sv = 0.6 m, u = 88). Fig. 18. Influence of normal load-dependent toe stiffness and wall height on maximum reinforcement loads and comparison with predictions using K-stiffness method (Bathurst et al. 2008b) for wall with PET reinforcement (Sv = 0.6 m, u = 88, toe stiffness values from Fig. 7). 903 An important implication of this investigation to good construction practice is that the wall toe should be embedded (this is typical design practice), good contact be developed at the base of the wall facing column and the concrete or granular levelling pad or a mechanical shear key be located between the bottom block and a concrete footing. Direct interface shear testing has shown that adequate shear resistance is available to develop significant toe resistance provided the levelling pad or footing is seated on a rigid or very stiff foundation. In practice, the bottom of retaining walls is typically embedded and can provide passive earth resistance according to classical notions of earth pressure theory. This potential additional toe capacity under working stress conditions has not been investigated in this study, particularly if the mobilized passive resistance is removed by excavation over the life of the structure. However, our work shows that significant toe restraint can be generated by friction alone between the bottom of the concrete wall and the concrete toe or levelling pad. The presence of passive fill in front of the wall may not be an issue because the lateral deformations required to fully mobilize passive resistance in front of the embedded toe are likely larger than the deformation required to fully mobilize base shear resistance. In our physical direct shear tests, the deformation required to fully mobilize base shear resistance was only 2 mm. Nevertheless, this issue requires further investigation. It is possible that, if poorer quality aggregate is used for the levelling pad and (or) more compliant foundation conditions are present, the effective horizontal toe stiffness available at the base of the wall may be less than that determined from the laboratory shear tests reported in this paper. The influence of foundation compressibility on wall performance is currently under investigation by the authors. Acknowledgements The work reported in this paper was supported by grants to the second author from the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Ministry of Transportation of Ontario, the Department of National Defence (Canada), and the following state departments of transportation in the USA: Alaska, Arizona, California, Colorado, Idaho, Minnesota, New York, North Dakota, Oregon, Utah, Washington, and Wyoming. References AASHTO. 2002. Standard specifications for highway bridges. 17th ed. American Association of State Highway and Transportation Officials (AASHTO), Washington, D.C. AASHTO. 2009. Interim LRFD bridge design specifications. 4th ed. American Association of State Highway and Transportation Officials (AASHTO), Washington, D.C. Allen, T.M., and Bathurst, R.J. 2002. Soil reinforcement loads in geosynthetic walls at working stress conditions. Geosynthetics International, 9(5–6): 525–566. Allen, T.M., and Bathurst, R.J. 2006. 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