Influence of Test Method on Direct Shear Behavior of Segmental Retaining Wall Units

Transcription

1 Geotechnical Testing Journal, Vol. 31, No. 2 Paper ID GTJ Available online at: Richard J. Bathurst, 1 Sebastian Althoff, 2 and Peter Linnenbaum 2 Influence of Test Method on Direct Shear Behavior of Segmental Retaining Wall Units ABSTRACT: This paper reports the results of interface shear testing carried out to investigate the influence of test methodology on sheardisplacement behavior of five different segmental (modular) masonry concrete block configurations. The tests were carried out in general conformance with existing ASTM and National Concrete Masonry Association test protocols. Three different normal load arrangements were investigated: (1) flexible airbag, (2) fixed vertical piston, and (3) an adjustable vertical piston. A video-extensometer camera device was used to record block deformations in the vertical plane during testing. The test results showed that the three load arrangements gave similar shear capacity failure envelopes for the frictional block system with flat concrete surfaces. For more typical block systems with concrete shear keys and trailing lips that exhibit dilatant interface shear behavior, or a system with shear pins, the most consistent test results were developed using the flexible airbag arrangement. The results of this paper can be used to guide the selection of the loading arrangement for conventional laboratory modular block shear testing. KEYWORDS: interface shear, masonry concrete, segmental block, video-extensometer Introduction Manuscript received November 13, 2006; accepted for publication July 31, 2007; published online September Professor and Research Director, GeoEngineering Centre at Queen s-rmc, Department of Civil Engineering, 13 General Crerar, Sawyer Building, Room 2085, Royal Military College of Canada, Kingston, Ontario, K7K 7B4 Canada, bathurst-r@rmc.ca. 2 Fachhochschule Muenster University of Applied Sciences, Department of Civil Engineering, Muenster, Germany. Segmental soil retaining walls constructed with stacked modular block units to form the facing column are now a well-established technology in North America and worldwide. The combination of stacked modular blocks in combination with geosynthetic reinforcement to stabilize the backfill soil first appeared in the mid- 1980s (Bathurst and Simac 1994). The vast majority of these structures are constructed with dry cast masonry concrete modular units to form the facing. The discrete nature of the dry-stacked column of modular concrete units has introduced unique analysis, design, and performance issues. The first comprehensive guidance document for design engineers was the National Concrete Masonry Association (NCMA) Segmental Retaining Wall Design Manual (Simac et al. 1993) and a second revised edition (NCMA 1997). Analysis and design principles that appear in these documents have been summarized by Bathurst and Simac (1993, 1994). The stability of the modular wall facing requires consideration of the connection, interface shear, and toppling stability of the facing column units. Design parameters for the connection between the modular block facing units and geosynthetic reinforcement layers require that specialized laboratory tests be carried out as first proposed by Bathurst and Simac (1993). Today, methods to quantify the connection performance of a specific combination of concrete block unit and geosynthetic soil reinforcement product are provided by the NCMA test method SRWU-1, Determination of Connection Strength Between Segmental Concrete Units, (NCMA 1997) and ASTM D 6683 (2001), Standard Test Method for Determining the Connection Strength Between Segmental Concrete Units and Geosynthetic Reinforcement. A test method to quantify the interface shear capacity between concrete modular blocks (with and without a geosynthetic layer inclusion) was first introduced by the National Concrete Masonry Association as NCMA test method SRWU-2, Determination of Shear Strength Between Segmental Concrete Units, (Simac et al. 1993) and currently in the second edition of the NCMA design manual (NCMA 1997). The equivalent ASTM standard is ASTM D (2003), Standard Test Method for Determining the Shear Strength Between Segmental Concrete Units (Modular Concrete Blocks). The methods of test introduced above are now used routinely to provide parameters for the design of reinforced soil retaining walls. Software packages are widely available to engineers to design segmental retaining wall structures. These packages require facing performance parameters that can only be determined from the results of laboratory tests carried out in conformance with the protocols cited here. Discussion on the interpretation of connection tests and examples of test results can be found in the conference and journal literature. However, similar publications in the open literature on interface shear testing are sparse (Bathurst et al. 1993; Bathurst and Simac 1994, 1997). Bathurst and Simac (1997) showed that in general, a shear connector or shear key increased the interface shear capacity of modular block units. They also showed that the presence of a geogrid inclusion at the interface might increase or decrease the interface shear capacity of the system. They gave an example where the inclusion of a relatively thick stiff integral drawn-hdpe geogrid reduced the interface shear capacity of a block system with a concrete shear key while the inclusion of a relatively flexible woven polyester geogrid inclusion with the same block type increased interface shear capacity. The increase in shear capacity was ascribed to the cushion effect of the flexible geogrid to minimize local high stresses at points of contact between the interface shear key and adjoining block unit. The need to revisit interface shear testing methodology and to provide generic examples of test results has been sparked by the recent use of numerical models to extend the performance database Copyright 2008 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA

2 2 GEOTECHNICAL TESTING JOURNAL TABLE 1 Modular units of segmental retaining walls to include a wider range of soils, geometry, modular block types, geosynthetic reinforcement products, and loading conditions (e.g., Hatami and Bathurst 2005, 2006; Yoo and Song 2006; Huang and Wu 2006). Examples of interface shear behavior of typical modular block units including shear strength and deformation parameters are of great value to researchers pursing this line of investigation. In the current ASTM D test protocol, the use of a rigid vertical piston or actuator is recommended together with rubber mats (if necessary) to ensure a uniform vertical pressure distribution to the test specimen. A pressurized airbag system is offered as an alternative vertical loading arrangement in the event modular block units exhibit dilatant behavior during shear. It is left to the user to determine which loading arrangement is best. The use of an airbag is a more difficult and time-consuming test arrangement. Examples of modular block systems that can be tested with and without an airbag are of value to laboratories that carry out modular block interface shear testing. Objectives The experimental program described in this paper was carried out with the following objectives: 1. Quantify the performance difference between interface shear tests carried out in conformance with current interface shear testing protocols but with different vertical loading arrangements and make recommendations regarding the choice of loading arrangement. 2. Develop and demonstrate the use of a video-extensometer technique to record the displacement response of modular block units during shear. 3. Provide examples of shear strength and deformation performance of four different types of modular block units varying with respect to the interface shear transfer mechanism. 4. Compare the shear performance of one modular block type with and without a single layer of a typical polyester geogrid placed at the interface surface. Modular Block Units and Interface Shear Conditions Four different modular block systems were investigated. The dimensional details and interface shear transfer mechanisms are summarized in Table 1. All units were dry cast masonry units and are commercially available products. Type I were solid cap units that were selected to investigate the simplest possible interface shear system in which interface capacity is developed solely by friction between two flat concrete surfaces. The remaining units were selected to investigate the performance of blocks with different shear transfer devices that are used to enhance shear performance and (or) used to assist with block alignment during wall construction. It should be noted that for the Type II block system, the hollow portions of the blocks were not filled with a granular soil as would be typically recommended for a field installation. The voids were not filled in order to simplify the test arrangement and to minimize the number of parameters that could influence test results. The Type IV blocks have a trapezoidal shape in plan view and are formed with a concrete trailing lip that extends the full width of the back of the units. The lip extends 10 mm below the bottom of the block and is 15-mm wide. However, because of the trapezoidal shape of the blocks, the concrete lip is not in continuous contact with the bottom layer of blocks when they are placed in a staggered configuration. Type V tests were carried out using Type I blocks but with a single layer inclusion of a woven PVC-coated polyester geogrid. The geogrid has a rupture tensile strength of 83 kn/m (based on the manufacturer s literature) and aperture sizes of 22 mm in the machine direction and 25 mm in the cross-machine direction. Test Methodology The modular block units were tested in a modified large-scale direct shear box apparatus (Fig. 1). A schematic of the general test ar-

3 BATHURST ET AL. ON DIRECT SHEAR BEHAVIOR OF SEGMENTAL RETAINING WALL UNITS 3 FIG. 1 Photograph of direct shear apparatus showing airbag loading arrangement, vertical load cell, and horizontal displacement transducers. FIG. 3 Photograph of method 2 and 3 loading arrangement (vertical piston) with block configuration Type V (geogrid inclusion at interface). rangement using an airbag loading system is illustrated in Fig. 2. The vertical load was applied using three difference methods: (1) a vertically restrained airbag, (2) a vertical piston without vertical load control, and (3) a vertical piston with vertical load control. A photograph of the method 2 and 3 loading arrangement (vertical piston) with block configuration Type V (geogrid inclusion at interface) is shown in Fig. 3. In Type V tests, the geogrid was oriented with the machine direction in the shear direction and was clamped at the back end to prevent slippage. The airbag is a commercially available product manufactured from a polyethylene bladder encapsulated in a paper shell and has a rated unconfined burst pressure of 70 kpa. The airbag was placed between two 12-mm thick plywood sheets. The top plywood sheet was reinforced with a steel plate that was placed in contact with the load cell at the base of the vertical loading piston. The pressure applied to the airbag was regulated so that the contact pressure was constant over the top unit. The airbag arrangement allowed the blocks to rotate and move vertically during shear. FIG. 2 Schematic cross-section view of direct shear apparatus showing airbag loading arrangement (dimensions in cm). Test configurations (2) and (3) used a vertical hydraulic piston with a capacity of 444 kn. A rigid steel plate was placed between the top block and the vertical load cell (Fig. 3). The piston load was maintained constant for configuration (3) by manually controlling a bleed valve between the piston and the hydraulic reservoir. Potential vertical movement of the blocks during shear was prevented by keeping the bleed valve closed during shear (configuration 2). The horizontal load was applied at a rate of 1 mm/min using a computer-controlled hydraulic actuator with a rated capacity of 222 kn. A pair of potentiometer-type displacement transducers was used to monitor the horizontal deformation of the top block unit that was seated over two rigidly restrained bottom units. The top unit was seated over the running joint between the two bottom units matching the staggered placement arrangement that would be used in the field. In order to record the deformation of the top block in the vertical plane of the test parallel to the direction of loading, a videoextensometer method was also employed. The equipment is comprised of a high-resolution digital charged coupled device (CCD) camera (video extensometer) and ancillary data acquisition system. Details of the equipment have been reported by Shinoda and Bathurst (2004) who used the same equipment to record strain response at multiple locations on geogrid specimens during inisolation wide-width strip tensile tests. The camera was mounted so that the focal plane of the device was parallel to the vertical side of the top block unit and at a distance of 0.8 m from the block. A total of four targets were painted on the side of the top block unit (Fig. 4) and two on the side of the bottom block closest to the camera. These points were tracked for the duration of each test. The targets and camera system allowed photographs of the shear tests to be captured at intervals and horizontal and vertical deformations to be recorded in real time at 1 Hz. The software was programmed to convert target displacements in pixels to physical deformations in engineering units (mm). The computed deformations were checked against the deformations recorded by the displacement transducers. The resolution of deformations recorded by the camera system was 8 m.

4 4 GEOTECHNICAL TESTING JOURNAL The load-displacement curves for all test configurations show increasing shear resistance with increasing normal load level (Figs. 5(a) 5(c)). Each plot in these figures is identified by the normal load level that was recorded at the time the peak shear force was generated. Depending on the vertical load arrangement, this value may or may not be representative of the load level at other stages during a test. The configuration with a fixed vertical piston (Fig. 5(b)) shows increasing shear force with increasing shear displacement up to large shear displacements. The rate at which the shear force increases with displacement increases with normal load level. Figure 6 shows that the accumulation of shear resistance was accompanied by increasing normal load. In this vertical load arrangement, the vertical load piston rotated slightly out of vertical as the upper block was pushed forward. Hence, the piston locked against the top block leading to increasing normal load level. In these tests a unique peak shear load could not be detected prior to the end of the test for the three highest normal load levels. Nevertheless, the linear shear capacity envelopes deduced from the peak or maximum recorded shear load versus normal load data plot together very closely as illustrated in Fig. 7. The reason for this good correspondence is that this interface is essentially purely frictional so that the shear strength increases with normal load level whether or not the normal load is constant over the course of the test. In Figs. 5(a) 5(c), a serviceability deformation value corresponding to 2 % of the width of the block (toe to heel dimension) is identified. This displacement criterion is recommended in the original NCMA design guidance document (Simac et al. 1993) to ensure that interface shear capacity values selected for design do not correspond to excessive interface shear deformations which could in turn lead to unacceptable facing deformations and misalignment in the field. Shear capacity envelopes based on this displacement-based criterion also plot as linear curves with very little difference between curves and essentially no apparent cohesive strength component. Based on the data presented in Fig. 7 it can be argued that the interface shear strength values are independent of the method of vertical load application used in this investigation if the interface shear strength is purely frictional. However, the interpretation of individual shear force-displacement plots using the fixed piston arrangement for implementation within numerical models is problematic since the normal load for each curve varies in an uncontrolled manner with shear displacement. FIG. 4 Photograph of video-extensometer camera image at beginning of the test showing tracking targets and superimposed rotation of the top block that occurred at the end of the test (Type III block with shear key). Test Results General For brevity, only selected load-displacement results for the five test series are presented. The horizontal and vertical loads were calculated in units of force per unit running length of wall consistent with load units used for wall design. Type I (Solid Concrete Block with Flat Concrete-toconcrete Interface) Type II (Hollow Concrete Block with Two Fiberglass Shear Pins) Shear force-displacement curves for the hollow block system gave a similar presentation regardless of the loading arrangement. However, binding of the blocks occurred for the loading arrangement with the fixed vertical piston similar to that observed for the Type I block. Shear capacity envelopes are plotted in Fig. 8. It is clear from the data in this figure that the shear pins provide a normal-load independent shear strength component (apparent cohesion) to the system. Regardless of the loading arrangement there is some scatter of the data points about the regressed lines based on the 2 % displacement criterion. This is due to unavoidable small variations in the setup of the blocks and placement of the shear pins. Scatter is less for the data taken at peak shear capacity. However, the regressed line for the fixed vertical piston case has a noticeably shallower slope than for the data derived from tests in which the vertical load was kept constant. Type III (Solid Concrete Block with Concrete Shear Key) In these tests there was a tendency for the top block to slide up and over the lower blocks (see Fig. 4). This dilatant interface shear behavior resulted in very large normal loads being developed against the fixed piston as shear progressed. In fact, only three tests were carried out using this test configuration since there was a danger that the capacity of the vertical load cell would be exceeded and two of these tests were terminated early. The dilatant behavior of this block type can be appreciated from Fig. 9 for a test with an airbag loading arrangement. Maximum shear resistance occurred at the onset of block interface dilation. Vertical heave of the upper block in this particular test continued as the test progressed further. Ultimately the shear key failed and shear capacity was lost. The sudden drop in shear capacity due to partial shear key rupture was observed in all tests regardless of loading arrangement. Finally, the normal force curve in Fig. 9 shows that the airbag arrangement was effective in keeping the normal load on the test specimen constant despite the large vertical deformations and rotations that developed over the course of the test. The shear capacity envelopes deduced for this block type and the three different loading arrangements are plotted in Fig. 10. The data for the fixed vertical piston arrangement must be discarded for the reasons discussed. The scatter in the data points for the adjusted vertical piston tests is likely due to the difficulty in manually maintaining a constant vertical load over the course of the test by adjusting the hydraulic bleed valve attached to the piston. The data for the tests carried out with the airbag are the

5 BATHURST ET AL. ON DIRECT SHEAR BEHAVIOR OF SEGMENTAL RETAINING WALL UNITS 5 FIG. 5 Type I (solid concrete block with flat concrete-to-concrete interface). (a) Airbag, (b) fixed vertical piston load, (c) adjusted vertical piston load. most consistent. The approximations to the datasets for tests with an adjustable vertical loading arrangement have been plotted using a horizontal line. This is consistent with the normal-load independent shear capacity developed by passive bearing of the concrete shear key during shear. This is interpreted as a constant interface yield strength or apparent cohesion in a Mohr-Coulomb failure envelope plot. The scatter in the airbag tests that does appear in the plot is likely the result of small variations in block setup, block geometry, concrete surface asperities, and the pattern of contact points between upper and lower block layers in the vicinity of the shear key. Nevertheless, the variation in peak shear capacity values for the three repeat tests carried out at about 55 kn/m normal load is within 8 % of the mean value of the three tests and hence within ±10 % as recommended by Simac et al. (1993). Type IV (Solid Concrete with Trailing Concrete Lip) The shear force-displacement plots for the tests carried out on the block type with a trailing concrete lip show a distinctive saw-tooth pattern at shear displacements typically greater than the 2 % deformation criterion (Fig. 11). This phenomenon is due to progressive rupture of the trailing concrete key. Recall that the shear lip is not in continuous contact with the underlying row of blocks due to the trapezoidal shape of these units. Hence, the shear lip on the top block typically sheared at one side and then the other. This behavior also made it difficult to use the video-extensometer to monitor block displacements because the progressive rupture of the shear lip caused the blocks to rotate in the horizontal plane. Thus the target dots used to track block deformations tended to move out of focus. However, the two potentiometer-type displacement trans-

6 6 GEOTECHNICAL TESTING JOURNAL FIG. 6 Load-displacement response of Type I block with fixed vertical piston configuration (solid concrete block with flat concrete-to-concrete interface). FIG. 8 Shear capacity envelopes for Type II block (hollow concrete block with fiberglass shear pins) and different vertical loading arrangements. ducers mounted against the two corners of the top block could be used to record horizontal deformations. Similar to the other tests with a fixed piston, the normal load using this test arrangement varied during the test. The shear capacity envelopes for this block type and three different loading arrangements are summarized in Fig. 12. The data are scattered about the regressed lines fitted to each dataset and there is a large difference in the fitted lines particularly for the 2 % displacement criterion data. A portion of the scatter in FIG. 7 Shear capacity envelopes for Type I block (solid concrete block with flat concrete-to-concrete interface) and different vertical loading arrangements. FIG. 9 Load-displacement response of Type III block with flexible airbag (solid concrete block with shear key).

7 BATHURST ET AL. ON DIRECT SHEAR BEHAVIOR OF SEGMENTAL RETAINING WALL UNITS 7 FIG. 10 Shear capacity envelopes for Type III block (solid concrete block with shear key) and different vertical loading arrangements. FIG. 12 Shear capacity envelopes for Type IV block (solid concrete block with trailing lip shear key) and different vertical loading arrangements. strength values is ascribed to the discontinuous lip engagement at the back of the blocks, which leads to small variations in test setup and block-to-block contact. If the shear capacity envelopes for the tests carried out with a fixed vertical piston are discarded, then the remaining datasets can be approximated by linear envelopes with both frictional and cohesive strength components. The initial shear response is governed by concrete-to-concrete surface friction that is mobilized first followed by shear capacity mobilized due to passive bearing of the shear lip at the back of the blocks. FIG. 11 Type IV block (solid concrete block with trailing lip shear key) with airbag loading. Type V (Solid Concrete Block with Flat Concrete-toconcrete Interface and Polyester Geogrid Inclusion) These tests were carried out using the Type I block but with a polyester geogrid layer inclusion. The shear force-displacement curves for this series of tests had the same distinctive shape (Fig. 13) regardless of the vertical loading arrangement. The initial response is controlled by the geogrid inclusion up to about 2 to 4 mm of deformation. There is then a reduction in shear strength as the PVCcoated geogrid members are compressed. Finally there is shear strength recovery as a new interface is formed with the compressed geogrid. The presence of the geogrid inclusion does not prevent binding of the unadjusted piston load configuration that was noted for the nominally identical Type I tests described earlier. The shear capacity envelopes deduced for all three series of tests are plotted in Fig. 14. The envelopes for each group of peak and displacementbased shear capacity curves plot together very closely indicating that the shear capacity envelopes are essentially independent of method of vertical load application. It is interesting to note that the

8 8 GEOTECHNICAL TESTING JOURNAL friction angle deduced from the displacement-based criterion is 2 to 6 degrees higher when the geogrid is present (compare Fig. 14 with Fig. 7) but these envelopes have otherwise little or no cohesive shear strength component. However, the presence of the very flexible polyester geogrid inclusion increases the peak shear capacity by developing additional apparent cohesion of about 3 kn/ m. Otherwise, the frictional component of peak interface shear strength component based on peak friction angle remains the same within about 2 degrees. The increase in shear strength at the 2 % displacement value and at peak capacity for these test series compared to the otherwise identical configurations without the geogrid is due to the cushion effect of the flexible inclusion. This inclusion improves shear transfer across the block by minimizing point contacts at the concrete surfaces. Nevertheless, it should be noted that polymeric reinforcement materials and their coatings have properties that are both temperature and rate-of-loading dependent. Hence, there may be quantitative differences in shear force-displacement response curves and shear capacity for tests carried out at different temperatures and at different rates of deformation from those reported here. FIG. 13 Type V configuration (solid concrete block with flat concrete-toconcrete interface and single layer inclusion of polyester geogrid) with airbag loading. FIG. 14 Shear capacity envelopes for Type V configuration (solid concrete block with flat concrete-to-concrete interface and single layer inclusion of polyester geogrid). Conclusions This paper reports the results of interface shear testing carried out to investigate the influence of test methodology on sheardisplacement behavior of five different segmental (modular) masonry concrete block configurations. The tests were carried out in general conformance with existing ASTM and National Concrete Masonry Association test protocols. Three different normal load arrangements were investigated: (1) flexible airbag, (2) fixed vertical piston, and (3) an adjustable vertical piston. Based on the results reported here the following conclusions can be summarized: 1. A video-extensometer camera with ancillary hardware and software was used to record block deformations in real time. The automated photographic record of block behavior during shear was useful to understand interface shear mechanisms. This technique may be valuable to block designers when developing new segmental retaining wall systems and for routine interface shear testing to reduce testing times. 2. The type of vertical loading arrangement used in this study did not influence the magnitude of the parameters used to quantify linear shear capacity envelopes when the interface between concrete block surfaces was flat and purely frictional. 3. For block configurations with both a frictional strength component and (or) a apparent cohesive strength component there were differences in interface shear capacity envelopes depending on the type of loading arrangement. 4. The use of a fixed vertical piston arrangement led to binding of the piston as it moved out of vertical during shear. 5. The use of an adjustable vertical piston was problematic when blocks developed a saw-tooth-shape shear loaddeformation response because it was not possible to manually adjust the normal load rapidly enough to keep the vertical load constant over the entire duration of the test. 6. The best arrangement for interface shear testing was a flexible airbag arrangement which was observed to keep the normal load constant while allowing the block to rotate or move vertically as a result of the shear connection mechanism.

9 BATHURST ET AL. ON DIRECT SHEAR BEHAVIOR OF SEGMENTAL RETAINING WALL UNITS 9 7. The airbag arrangement facilitates interpretation of shear load-displacement curves since it removes the complication of a variable normal load during the shear test. This is important if shear-deformation curves of the type reported here are to be used in constitutive models implemented within numerical models of reinforced soil segmental retaining walls. 8. The use of a flexible woven geogrid was demonstrated to improve the interface shear performance of the frictional interface block used in this investigation by reducing stress concentrations at the interface between concrete surfaces. However, the potential benefit of any geosynthetic inclusion with other block systems can only be established by carrying out physical tests of the type described in this paper. Acknowledgments The second and third authors are grateful for the support provided by Deutscher Akademischer Austauschdienst to visit the GeoEngineering Centre at Queen s-rmc at RMC where the work described in this paper was carried out. The authors wish to thank Mr. Peter Clarabut and Mr. Mike Domingo at BCGT Inc. in Kingston, Canada, who provided the equipment and technical support to carry out the experimental work. Additional support was provided by a grant from the Natural Sciences and Engineering Research Council awarded to the first author. References ASTM Standard D 6683, 2001, Standard Test Method for Determining the Connection Strength Between Segmental Concrete Units and Geosynthetic Reinforcement, Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA. ASTM Standard D , 2003, Standard Test Method for Determining the Shear Strength Between Segmental Concrete Units (Modular Concrete Blocks), Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA. Bathurst, R. J. and Simac, M. R., 1993, Laboratory Testing of Modular Unit-Geogrid Facing Connections, Geosynthetic Soil Reinforcement Testing Procedures, ASTM STP 1190, S.C.J. Cheng, Ed., ASTM International, West Conshohocken, PA, pp Bathurst, R. J. and Simac, M. R., 1994, Geosynthetic Reinforced Segmental Retaining Wall Structures in North America, Invited keynote paper, 5th International Conference on Geotextiles, Geomembranes and Related Products, 6 9 September 1994, Singapore, Vol. 4, pp Bathurst, R. J. and Simac, M. R., 1997, Design and Performance of the Facing Column for Geosynthetic Reinforced Segmental Retaining Walls, International Symposium on Mechanically Stabilized Backfill, Denver, Colorado, 6 8 February 1997, Balkema, J. Wu, Ed., pp Bathurst, R. J., Simac, M. R., and Berg, R. R., 1993, Review of the NCMA Segmental Retaining Wall Design Manual for Geosynthetic-Reinforced Structures, Transp. Res. Rec., No. 1414, pp Hatami, K. and Bathurst, R. J., 2005, Development and Verification of a Numerical Model for the Analysis of Geosynthetic Reinforced Soil Segmental Walls Under Working Stress Conditions, Can. Geotech. J., Vol. 42, No. 4, pp Hatami, K. and Bathurst, R. J., 2006, A Numerical Model for Reinforced Soil Segmental Walls Under Surcharge Loading, J. Geotech. Geoenviron. Eng., Vol. 132, No. 6, pp Huang, C.-C. and Wu, S.-H., 2006, Simplified Approach for Assessing Seismic Displacements of Soil-Retaining Walls. Part I: Geosynthetic-Reinforced Modular Block Walls, Geosynthet. Int., Vol. 12, No. 6, pp National Concrete Masonry Association Segmental Retaining Wall Design Manual, nd ed., National Concrete Masonry Association, Herndon, VA, J. Collin, Ed. 289 pp. Shinoda, M. and Bathurst, R. J., 2004, Strain Measurement of Geogrids Using a Video-Extensometer Technique, Geotech. Test. J., Vol. 27, No. 5, 8 pp. Simac, M. R., Bathurst, R. J., Berg, R. R., and Lothspeich, S. E., 1993, National Concrete Masonry Association Segmental Retaining Wall Design Manual, 1st ed., National Concrete Masonry Association, Herndon, VA, 250 pp. Yoo, S. and Song, A. R., 2006, Effect of Foundation Yielding on Performance of Two-tier Geosynthetic-reinforced Segmental Retaining Walls: A Numerical Investigation, Geosynthet. Int., Vol. 13, No. 5, pp