Canadian Geotechnical Journal. Physical and Numerical Modelling of a Geogrid Reinforced Incremental Concrete Panel Retaining Wall

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1 Canadian Geotechnical Journal Physical and Numerical Modelling of a Geogrid Reinforced Incremental Concrete Panel Retaining Wall Journal: Canadian Geotechnical Journal Manuscript ID cgj r1 Manuscript Type: Article Date Submitted by the Author: 2-Jul-216 Complete List of Authors: Yu, Yan; Queen's University, Civil Engineering Bathurst, Richard; Queens University/Royal Military College, Allen, Tony; Washington State Department of Transportation Nelson, Renald; Department of National Defence, Wing Construction Engineering Keyword: Numerical modelling, Geosynthetics, Instrumented wall, Incremental panel facing, Geogrid reinforcement

2 Page 1 of 51 Canadian Geotechnical Journal Physical and Numerical Modelling of a Geogrid Reinforced Incremental Concrete Panel Retaining Wall Yan Yu 1, Richard J. Bathurst 2, Tony M. Allen 3 and Renald Nelson 4 1. Postdoctoral Fellow, GeoEngineering Centre at Queen s-rmc, Department of Civil Engineering, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada, yan.yu@queensu.ca 2. Professor and Research Director, GeoEngineering Centre at Queen s-rmc, Department of Civil Engineering, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada (corresponding author), tel: ext 6479; fax: ; bathurstr@rmc.ca 3. State Geotechnical Engineer, Washington State Department of Transportation, State Materials Laboratory, P.O. Box 47365, Olympia, WA , AllenT@wsdot.wa.gov 4. Former graduate student, now Major, Wing Construction Engineering, Department of National Defence, Astra, ON KK 3W, Canada, diren2@outlook.com Abstract: The paper presents the numerical modelling details using the finite difference method (FDM) to simulate the performance of a well-instrumented geogrid reinforced incremental concrete panel soil retaining wall. Two different constitutive models were investigated for the backfill soil (linear elastic-plastic model and nonlinear elastic-plastic model). Both constant stiffness and strain-dependent secant stiffness models were used for the reinforcement elements. The paper provides valuable lessons to modellers to simulate the performance of this type of earth retaining structure. For example, parametric investigation of the effect of a constant Young s modulus ranging from 4 to12 MPa for the linear-elastic Mohr-Coulomb model had only minor influence on the wall facing displacements and reinforcement loads. However, the choice of magnitude of transient compaction pressure near the facing can result in large differences in facing displacements. The paper also demonstrates that the method of construction including the location, sequence and stiffness of the temporary supports used to construct the wall plays an important role on measured and predicted wall performance. The physical measurements reported in this paper provide a benchmark for numerical modellers to verify other numerical models for walls of the type investigated here. Author keywords: Geosynthetics; Numerical modelling; Instrumented wall; Incremental panel facing; Geogrid reinforcement; FLAC. Page 1

3 Canadian Geotechnical Journal Page 2 of Introduction The internal stability design and analysis of geosynthetic reinforced soil walls in North America is based on a limit-equilibrium tie-back wedge method (e.g., AASHTO 214) that can be traced back to the early 197 s (Allen et al. 22). Reinforcement loads computed using tie-back wedge methods for geosynthetic reinforced soil walls under operational conditions have been shown to be excessively conservative. For example, Allen et al. (22) concluded that most walls built in the field could perform satisfactorily with only 5% of the reinforcement used in the original design. Statistical analyses of reinforcement loads recorded from instrumented fullscale geosynthetic reinforced soil walls constructed in the field and under operational (end of construction) conditions have shown that predicted reinforcement loads using tie-back wedge methods are much higher than measured values on average (e.g., Allen et al. 23; Bathurst et al. 25, 28; Miyata and Bathurst 27a, b; Allen and Bathurst 215). Improvements to current design and analysis methods or adoption of new methods require validation against measurements from instrumented walls in order to have confidence in their use. However, the number of instrumented field walls is limited and this number is even less when candidate walls are restricted to structures judged to have sufficient high-quality data for the component materials and comprehensive wall performance measurements. A complimentary strategy to gather sufficient data to assess the accuracy of current models or to calibrate new design methods is to use numerical models of reinforced soil walls that have been validated against the results of carefully constructed and comprehensively instrumented fullscale models. Validated numerical models can then be used to generate synthetic data that can be used to fill knowledge gaps in the available database of physical measurements. Another advantage of validated numerical models is that they can be used to estimate wall deformations which are necessary for performance-based design of these structures. However, predictions of wall deformations are not possible using current reinforcement strength-based (tie-back wedge) methods (e.g., AASHTO 214) and are tenuous using reinforcement stiffness-based methods (e.g., Allen and Bathurst 215). Page 2

4 Page 3 of 51 Canadian Geotechnical Journal Numerical approaches to simulate the performance of physical reinforced soil walls using extensible (geosynthetic) or inextensible (e.g., steel) reinforcement can be grouped into two main categories: (a) finite element method FEM (e.g., Cai and Bathurst 1995; Karpurapu and Bathurst 1995; Rowe and Ho 1997; Rowe and Skinner 21; Yoo et al. 211; Damians et al. 213, 215; Yu et al. 215a) and, (b) finite difference method FDM (e.g., Hatami and Bathurst 25, 26; Huang et al. 29, 21; Abdelouhab et al. 211; Damians et al. 214; Yu et al. 215a, 215b, 216). Both approaches have been demonstrated to give satisfactory predictions of important performance features of instrumented full-scale walls in the field and in the laboratory (Hatami and Bathurst 25, 26; Huang et al. 29, 21; Damians et al. 215; Yu et al. 215a, 216). The main objective of this paper was to develop a numerical model that can satisfactorily match measured performance features of a full-scale geogrid reinforced incremental concrete panel wall that was constructed at the Royal Military College of Canada (RMCC). The numerical model was implemented using the FDM program FLAC (Itasca 211). The motivation for the work was the need to develop a numerical model that can be used to generate complimentary synthetic data for the case of geosynthetic reinforced incremental panel walls. 2. Physical test wall model The full-scale geogrid reinforced incremental concrete panel retaining wall was the last in a series of eleven test walls constructed indoors in the Royal Military College of Canada (RMCC) Retaining Wall Test Facility (Kingston, Ontario). A number of the other walls in the same research program have been described in earlier papers (e.g., Bathurst et al. 2; Hatami and Bathurst 25, 26; Huang et al. 29). Each of the walls was constructed with the same sand backfill soil but varied with respect to wall facing type, facing batter, reinforcement type and properties, and reinforcement vertical spacing. The wall was built with six layers of a biaxial polypropylene (PP) geogrid reinforcement placed at a vertical spacing of.6 m (Figure 1). The geogrid layers were oriented with the weakest and least stiff (machine) direction in the direction of loading. The geogrid product used in the test was purposely chosen for its low stiffness in order to encourage detectable reinforcement strains and displacements during and after Page 3

5 Canadian Geotechnical Journal Page 4 of 51 construction (Bathurst et al. 2). The wall was 3.6 m high and 3.4 m wide at the face. The entire structure, including the wall face, reinforced soil zone and retained soil, extended 5.79 m beyond the toe of the wall. The concrete facing panels were 1.2 m in height and.14 m thick. The panels were arranged in three vertical columns supported by steel plates of the same width (i.e., 1 m wide in the centre and 1.2 m wide for each side column). A strip of 12-mm thick stiff rubber was placed at the horizontal joint between adjoining panels. The centre column of 1 m- wide panels and matching 1 m-wide reinforcement layers were instrumented. The facing panels and reinforcement layers on either side of the centre column of panels were 1.14 m wide. The discontinuous facing construction was selected to isolate the middle portion of the wall structure from the sides of the retaining wall test facility in order to approach a plane strain condition as far as practical. A similar strategy has been used for other large-scale walls constructed in laboratory environments at RMCC (e.g., Bathurst et al. 1988; Bathurst 199) and the Public Works Research Institute (PWRC) in Japan (e.g., Miyata et al. 215). It should be noted that in the field the concrete facing units are arranged in an interlocking pattern in both the vertical and horizontal directions. Hence, the physical wall in this study has a more flexible facing column than typical reinforced soil concrete panel walls constructed in the field. A composite arrangement of plywood, Plexiglas, and lubricated polyethylene sheets was placed over the inside wall surface of the test facility to minimize the friction between the side walls and backfill soil. The same technique was used for other walls in the same series of tests (Bathurst et al. 26, 29). The backfill used in this wall and the other 1 walls in the same suite of tests was a poorlygraded beach sand with mean particle diameter D 5 =.34 mm. The sand within the first.5 m distance from the back of the facing was hand-tamped using a rigid steel plate to a target of 95% of standard Proctor dry density. The rest of the sand was compacted with two passes of an electrically powered vibrating rammer. Bathurst et al. (29) reported that the measured bulk unit weight of the compacted sand using this compaction equipment was γ s = 17.2 ±.37 kn/m 3 where the range is ±1 standard deviation. Page 4

6 Page 5 of 51 Canadian Geotechnical Journal The base of the wall was seated on a rigid concrete foundation (Figure 1b). A double row of steel plates separated by a set of steel rollers were used to decouple the vertical and horizontal facing toe load components. The vertical toe loads at the base of the three discontinuous facing column sections were measured by two parallel rows of load cells supporting the bottom row of steel plates. Measurements of horizontal toe loads were taken from load rings placed between a reaction beam fixed to the laboratory strong floor and the top row of steel plates supporting the first row of facing panels. The first row of panels was placed vertically on the top row of the steel plates and braced using a row of timber props (Prop-1) near the upper end of the first row of facing panels. The backfill sand was then placed and compacted to the target density with a lift thickness of.15 m. After two lifts, the first layer of geogrid reinforcement was placed on the compacted sand surface and the geogrid front end attached to the back of the facing. The geogrid was clamped between the two pieces of slotted steel angle that were bolted to the facing. The mechanical details can be found in the paper by Bathurst (199). Thereafter, four more lifts of the backfill soil were placed followed by the second layer of reinforcement. Two more lifts were required to reach the top of the first row of panels and then the timber props (Prop-1) were removed. The same construction procedure was repeated for the remainder of the wall. The location of the props and the sequence of prop placement and removal for each layer (Prop-2, -3, -4 and -5) were reproduced in the numerical simulation of the wall construction. During construction, a horizontal layer of rubber bearing pads was placed between the concrete panels to avoid direct contact and to provide some articulation and compressibility at the horizontal joints as is the practice for concrete panel-faced walls in the field (Damians et al. 213, 215). 3. Numerical wall model 3.1 FDM numerical grid and interfaces Figure 2 shows the 2D FDM numerical grid with the simplified boundary conditions for the wall at the end of wall construction. The concrete foundation was simulated by one row of 47 zones with thickness of.15 m. The thickness of the concrete foundation modelled in this paper did not Page 5

7 Canadian Geotechnical Journal Page 6 of 51 affect the numerical results reported here. The bottom of the foundation was fixed in both x- and y-directions. The upper steel plates were modelled by one zone. The bottom of the upper steel plates was fixed in y-direction and free in x-direction because of the rollers between the upper and lower steel plates. It was not necessary to model the lower steel plates used at the wall toe. The facing was modelled using one column of 5 zones (48 zones for facing panels and 2 zones for each layer of rubber bearing pads). The backfill was discretized into 2256 zones. The right side of the backfill was fixed in x-direction and free in y-direction due to the rear bulkheads used to contain the soil at the back of the test facility. The interactions between dissimilar materials were modelled using interfaces (e.g., interfaces between the backfill and the concrete foundation, between the backfill and the facing, between the facing panel and the bearing pads, and between the first concrete panel and the supporting steel plates). The props used to support the facing during wall construction are not shown in Figure 2 because there was no support for the facing at the end of the construction. The six geogrid reinforcement layers were modelled using a total of 48 FLAC cable elements. The grout of the cable elements was used to model the interaction between the backfill and geogrid reinforcement layers. 3.2 Soil constitutive models and material parameter values To examine the influence of different soil constitutive models on the performance of the wall, two different constitutive models were considered for the backfill. The first was a linear elastic model with Mohr-Coulomb (MC) failure criterion from the FLAC constitutive model library. The second soil model was a nonlinear elastic model with Mohr-Coulomb failure criterion developed by Yu et al. (216) to model two instrumented geogrid reinforced modular block walls constructed to support the approach embankment for a highway bridge (Allen and Bathurst 214a, b). The second model was a modified version of the model originally coded by Huang et al. (29) based on the Duncan-Chang model (Duncan et al. 198) but modified by adopting the soil bulk modulus formulation proposed by Selig (1988) and Boscardin et al. (199). These modifications to the Duncan-Chang model were necessary in order to better capture the contribution of the intermediate confining pressure under the plane strain conditions assumed for the physical test wall in the current investigation. A brief description of the nonlinear elastic-plastic model is given below. Page 6

8 Page 7 of 51 Canadian Geotechnical Journal The soil nonlinear elastic tangent modulus (E t ) and the unloading-reloading soil elastic modulus (E ur ) are computed using the equations from the Duncan-Chang model (Duncan et al. 198) as: = 1 (1) = (2) where R f = failure ratio, ϕ = soil friction angle, σ 1 = major principle stress, σ 3 = minor principle stress, c = soil cohesion, K e = soil elastic modulus number, p a = atmospheric pressure, n = soil elastic modulus exponent, and K ur = unloading-reloading modulus number (K ur = 1.2K e ; Duncan et al. 198). The soil bulk modulus (B) based on a formulation from Selig (1988) and Boscardin et al. (199) and its range are given as: = 1+ ɛ,, (3) (4) where B i = initial tangent bulk modulus, ɛ u = asymptotic value of the volumetric strain at large stresses, and σ m = mean stress [i.e., σ m = (σ 1 + σ 2 + σ 3 )/3], B i and ɛ u = intercept and inverse of the slope from a plot of σ m /ɛ vol versus σ m, respectively, in an isotropic compression test (ɛ vol = volumetric strain), v t,min = minimum tangent Poisson s ratio (v t,min = in this investigation), and v t,max = maximum tangent Poisson s ratio (v t,max =.49 in this investigation). After the soil reaches peak shear strength, the modelling of the plastic part of the soil behaviour is based on the Mohr-Coulomb failure criterion. It should be noted that the plastic part of the model can be turned off at any stage during the modelling resulting in a nonlinear elastic model which is the same as that developed by Huang et al. (29). Page 7

9 Canadian Geotechnical Journal Page 8 of 51 For the linear elastic-plastic model and plane strain conditions, the soil was assigned Young s modulus E = 8 MPa, peak friction angle ϕ = 44, dilation angle ψ = 11, and Poisson s ratio v =.3. These values are the same as those reported by Huang et al. (29) for the same sand and method of compaction for a similar wall in the RMCC test series but constructed with a masonry concrete block facing. The sand cohesion was set to c = 1 kpa (Hatami and Bathurst 25). For the nonlinear elastic-plastic model, the peak friction angle, dilation angle, and cohesion were taken to be the same as those for the linear elastic-plastic model. Other parameter values for the nonlinear elastic part of the soil model were taken from Huang et al. (29). The challenge using the linear elastic-plastic model is the selection of a single stress-independent soil elastic modulus (e.g., Huang et al. 29; Yu et al. 216). Yu et al. (216) used both the linear and nonlinear elastic-plastic models to model two full-scale geogrid reinforced modular block facing walls. They demonstrated how the nonlinear model can be used to assist in the selection of a suitable stress-independent elastic modulus for the simpler model. Figure 3 shows the numerical predictions of stress-strain responses using both soil constitutive models. Also shown in Figure 3 are the laboratory results of triaxial (axisymmetric) compression and plane strain tests on the wall backfill soil. Details of the triaxial and plane strain tests can be found in the paper by Hatami and Bathurst (25). Table 1 provides a summary of soil properties for both constitutive models. The concrete foundation, concrete panels and bearing pads were modelled as linear-elastic materials. The weight of each panel was measured before wall construction. The concrete material in this investigation had a unit weight of 22.9 kn/m 3. Figure 4 shows the nonlinear stress-strain relationship for the gum rubber bearing pad material. The Young s modulus of the rubber bearing pad is about 3.1 MPa at strains less than 6.5% and increases to about 21.4 MPa when the strain is between 6.5% and 21%. At strains greater than 21% the Young s modulus is 3 MPa. To simplify numerical simulations a constant Young s modulus (i.e., 12 MPa) was selected. The influence of other constant Young s modulus values (i.e., 3.1 and 21.4 MPa) on wall displacements is examined later in the paper. Based on typical values found in the literature, the Young s modulus and Poisson s ratio of the concrete panels and foundation were taken to be Page 8

10 Page 9 of 51 Canadian Geotechnical Journal 32 GPa and.15, respectively. The gum rubber bearing pads were modelled assuming a unit weight of.1 kn/m 3 and Poisson s ratio of.45. For the steel plates, unit weight of 8 kn/m 3, Young s modulus of 21 GPa, and Poisson s ratio of.3 were used in this paper. 3.3 Geogrid constitutive model and parameter values The biaxial PP geogrid product used in the wall has rate-dependent properties (Shinoda and Bathurst 24) (i.e., tensile load varies nonlinearly with time and strain). Using the hyperbolic load-strain-time model proposed by Allen and Bathurst (214a, b), the PP geogrid secant stiffness, J(ɛ,t), and tangent stiffness, J t (ɛ,t), can be expressed as:, =, = (6) (5) where J (t) = initial tangent stiffness, χ(t) = empirical fitting parameter, t = time, and ɛ = strain. The values of initial tangent stiffness and empirical fitting parameter in the hyperbolic loadstrain-time model for the PP geogrid (machine direction) were calculated from the results of a set of constant load creep tests taken to rupture or 1 hours, whichever occurred first (Hatami and Bathurst 26). The tensile load in the geogrid reinforcement can be calculated from the geogrid secant stiffness multiplied by the geogrid strain (Walters et al. 22). However, program FLAC uses an incremental computation framework; hence, the tangent stiffness formulation (Equation 6) was implemented in the code. Figure 5 shows secant stiffness values for the PP geogrid plotted as a function of time and strain. The initial tangent stiffness at t = 1227 hours was J = 116 kn/m and the empirical fitting parameter was χ =.125 m/kn. These reinforcement parameter values correspond to the actual time to end of construction (i.e., t = 1227 hours) and were used later in the paper to compute reinforcement loads. The value of these parameters are reasonably constant Page 9

11 Canadian Geotechnical Journal Page 1 of 51 for t > 5 h so numerical outcomes in the current study were sensibly independent of time for time frames matching the duration of the wall construction (i.e., 1277 hours). Secant stiffness values corresponding to t = 1 h have been recommended for stiffness-based design (Allen et al. 23; Allen and Bathurst 215). The ultimate strength of this PP geogrid product was set to T y = 14 kn/m based on the peak strength measured during a 1% strain/min constant-rate-ofstrain test (Huang et al. 29). The tensile strength of the reinforcement used in this study decreases with decreasing rate of loading (Shinoda and Bathurst 24). However, the analyses in the current study were terminated at end of construction corresponding to predicted and measured tensile loads that were well below tensile strength values corresponding to very low strain rates (Ezzein et al. 215). Hence, the choice of tensile strength based on strain rate was not a concern. The influence of using a constant geogrid stiffness on facing displacements and geogrid strains is examined later in the paper by setting χ = and t = 1227 h. During the simulation of wall construction, the elastic modulus (E r ) of each cable element in FLAC was adjusted according to E r = J t /A r each time the tangent stiffness was updated with the current geogrid strain. Here, A r = cross-sectional area of the cable element. Table 2 summarizes the cable element properties in this investigation. 3.4 Interface parameter values and prop stiffness values The interfaces between the soil and concrete panel and foundation surfaces have a friction angle of ϕ sc = 44 and an apparent cohesion of c sc = 1 kpa by assuming a strength reduction factor of R i = 1. applied to the shear strength of the backfill soil (i.e., no strength reduction due to concrete surface roughness). The normal and shear stiffness values of these interfaces were taken to be k n,sc = 1 MPa/m and k s,sc = 1 MPa/m, respectively based on numerical analysis of a concrete panel wall reported by Yu et al. (215a). The friction angle at the interfaces between the facing panels (i.e., concrete material) and rubber bearing pads was set to ϕ cr = 45 (e.g., Serway and Jewett 214) and the apparent cohesion was taken to be c cr =. The friction angle for the concrete-steel interface between the first facing panel (i.e., concrete material) and the steel plate (i.e., steel material) was ϕ cs = 24 (e.g., Liu et al. 215) and the apparent cohesion was c cs =. The concrete-rubber interfaces and concrete-steel interface were assigned normal Page 1

12 Page 11 of 51 Canadian Geotechnical Journal stiffness of k n,sc = 1 MPa/m (same value used by Huang et al. (29) for the concreteconcrete interface) and shear stiffness k s,sc = 1 MPa/m. The simulation of the soil-reinforcement interaction was done using the grout shear strength and stiffness of the FLAC cable elements as noted earlier. The grout of the cable elements had a friction angle of ϕ sr = 44 (Huang et al. 29) and a cohesive strength component of C sr = 2 kn/m (i.e., C sr = c P r, where c = backfill cohesion and P r = perimeter of the cable element). The shear stiffness of the grout was taken to be K s,sr = 1 MN/m/m based on the same backfill and PP geogrid used in the numerical simulations by Hatami and Bathurst (25) and Huang et al. (29). In FLAC, the grout cohesive strength (force/length; e.g., kn/m) and shear stiffness (force/length/displacement; e.g., MN/m/m) are calculated from the interface cohesive strength component (stress; e.g., kpa) and shear stiffness (stress/displacement; e.g., MPa/m) multiplied by the perimeter of the cable element (Itasca 211). Table 3 shows the interface parameter values described in this section. As mentioned earlier, the horizontal movement of the top steel plates was restrained by the row of load rings used to measure the horizontal load at the toe. The load rings and their attachment to the wall toe were modelled by one beam element with left end fixed in both x- and y-directions and the right end defined using the grid number of the top-left corner of the steel plate zone. The axial stiffness of this toe beam representing the toe spring in Figure 2 was taken as K Toe = 4 MN/m based on measured loads and displacements (Hatami and Bathurst 25; Huang et al. 29). During the construction of the wall, rows of timber props were used to keep the facing panels vertical. The bracing system was not perfectly rigid and some visually detectable deformation during fill placement and compaction occurred. However, axial load and prop column compression measurements were not taken nor were deformation measurements taken of the external column supports against which the props were braced. Thus the selection of equivalent prop axial stiffness values in this investigation was based on trial-and-error to best match measured panel movements that occurred when each row of props was removed. The resulting axial prop stiffness values were K Prop-1 = 1 kn/m, K Prop-2 = 8 kn/m, K Prop-3 = 2 kn/m, K Prop-4 = Page 11

13 Canadian Geotechnical Journal Page 12 of 51 8 kn/m, and K Prop-5 = 2 kn/m. The influence of magnitude of other prop axial stiffness values on wall displacements is examined later in the paper. Each row of props was modelled by one beam element with the left-end node fixed in both x- and y-directions and the right-end node defined using the corresponding grid number at the facing panel where the row of props was located. The elastic modulus of each beam element in FLAC was calculated based on the beam stiffness (e.g., the elastic modulus of the FLAC beam element representing the toe spring is E Toe = K Toe L Toe /A Toe, where L Toe and A Toe are the length and cross-sectional area of the beam element at the wall toe, respectively). 3.5 Wall construction modelling The wall construction was modelled by sequentially activating the wall concrete panels, bearing pads, geogrid reinforcement layers and backfill layers in the FLAC model. The compaction of the backfill soil was simulated by applying a temporary surface surcharge on the new backfill layer and removing it before activating the next backfill layer (e.g., Gotteland et al. 1997; Hatami and Bathurst 25, 26; Huang et al. 29, 21; Yu et al. 216). In this investigation, the compaction of the backfill within.5 m distance from the back of the facing was modelled by applying a transient uniform surcharge of q 1 = 8 kpa (where the sand was handtamped using a rigid steel plate) and the rest of the backfill using q 2 = 16 kpa (where the sand was compacted by an electrically powered vibrating rammer; Hatami and Bathurst 25; Huang et al. 29). The influence of the magnitude of transient surcharge pressure used to simulate the effect of compaction near the facing on facing displacements is presented later. The same compaction modelling technique was also used to model the performance of two wellinstrumented field walls (Allen and Bathurst 214a, b) and resulted in encouraging agreement between measured and predicted wall performance (Yu et al. 216). Initially, the zones for the concrete foundation and the steel plate were activated and the toe spring (modelled by FLAC beam element) was added to the model. The numerical simulation of the wall construction began by activating the first concrete panel (with the interface between the first panel and the steel plate) and by adding the first row of props (i.e., beam element) (Figure 6a). After the first.15-m thick backfill layer was activated (with one interface between the first Page 12

14 Page 13 of 51 Canadian Geotechnical Journal backfill layer and the concrete foundation and the other between the first backfill layer and the concrete panel), the model was then solved to reach equilibrium under both self-weight and compaction pressures on the backfill surface (i.e., q 1 and q 2 ). The compaction pressures were removed after equilibrium was reached. Thereafter, the second.15-m backfill layer was turned on (with the interface between the current backfill layer and the concrete panel) and the same modelling procedure was applied for the remaining backfill soil layers. When the backfill height reached the elevation of each reinforcement layer, the first cable node of each reinforcement layer was defined using the grid number at the back of the facing panel matching the elevation of the reinforcement layer (i.e., the first cable node is attached to and moves with the grid with the same x- and y-displacements). The remaining cable nodes for each reinforcement layer were similarly defined using their corresponding x- and y-coordinates. The first row of props (beam element) was removed after the backfill height reached the height of the first facing panel. The modelling of the wall construction was continued by turning on the zones for the bearing pad and the second facing panel (with interfaces between the pad and facing panels), and by adding the second and third beam elements representing the props (Figure 6b). These two beam elements were removed once the backfill height reached the top elevation of the second panel, which was followed by activating the zones for the bearing pad and the third facing panel and by adding the fourth and fifth beam elements (props) (Figure 6c). At the end of the wall construction, the fourth and fifth beam elements were removed resulting in the final numerical grid shown in Figure 2. The modelling in this investigation was executed using the large-strain mode in FLAC. 4. Results 4.1 Facing displacements The facing displacements at the end of construction of each panel are shown in Figure 7. Measured data are compared with calculated values using the two different backfill constitutive models and strain-dependent geogrid tangent stiffness. The measured data show that the panels moved outward as rigid units due to their high bending stiffness but displaced laterally and Page 13

15 Canadian Geotechnical Journal Page 14 of 51 rotated at the toe of the wall and at the panel joints. The displacements occurred after the temporary props were removed in the sequence described earlier. At the end of wall construction (Figure 7c), the calculated facing displacements at the base and top of the first, second, and third panel were about 2, 26, 24, 36, 17 and 15 mm, respectively using the linear elastic-plastic model and about 2, 31, 27, 38, 17 and 16 mm, respectively using the nonlinear elastic-plastic model. The maximum difference between the calculated and measured values was at the elevation of 1.35 m for both models. The overestimated displacement was about 8 mm using the linear elastic-plastic model and about 11 mm using the nonlinear elastic-plastic model at the end of wall construction. These differences are judged to be small given the complexity of the wall models and not significant from a practical point of view. Both soil models appear to give encouraging agreement with the measured data using the stiffness values assigned to the temporary props. Figure 8 shows the calculated displacement vectors for the numerical grid at the end of wall construction using the linear elastic-plastic soil model. The vector field shows a wedge shape of relatively high displacements which is consistent with the development of a zone of soil that could evolve into a failure wedge according to conventional notions of active earth pressure theory if the wall had been constructed to greater height. Figure 9 shows the influence of magnitude and distribution of prop axial stiffness values on the facing displacements using the linear elastic-plastic soil model and strain-dependent geogrid tangent stiffness. The uniform prop stiffness case corresponds to K Prop-1 = K Prop-2 = K Prop-3 = K Prop- 4 = K Prop-5 = 1 MN/m (a factor of 125 times the stiffest prop in the control case). The numerical results show that the assumption of uniform (and greater) prop stiffness resulted in less predicted facing displacements except at the top of the third panel at the end of construction (Figure 9c). However, the final predicted displacement profile for the wall using both sets of stiffness values can be judged to be acceptable when compared to measured values. The influence of constant and strain-dependent geogrid tangent stiffness values on facing displacements is shown in Figure 1. The constant geogrid tangent stiffness assumption gave Page 14

16 Page 15 of 51 Canadian Geotechnical Journal lower predicted facing displacements than numerical simulations with strain-dependent tangent stiffness when all other conditions were the same. However, from a practical point of view, the differences are judged to be negligible. As mentioned in the previous section, a transient compaction pressure of q 1 = 8 kpa was chosen for the backfill lifts within.5 m distance from the back of the facing. A larger value of q 2 = 16 kpa was used for the rest of the backfill corresponding to the areas over which a heavier compactor was used during construction. Figure 11 shows the influence of three different compaction pressures near the facing (i.e., q 1 =, 8 and 16 kpa) on the calculated facing displacements using the linear elastic-plastic soil model. In general, increasing the magnitude of the compaction load near the facing increased the facing displacements. For example, the maximum facing displacement at the end of wall construction was about 33 mm when q 1 =, and increased to about 37 and 49 mm for q 1 = 8 and 16 kpa, respectively. The results show that the overall predictions of facing displacements from Figures 11a, 11b, and 11c using q 1 = 8 kpa are better than those using q 1 = and 16 kpa when comparing with measured data and all other conditions are equal. Figure 12 shows the influence of the Young s modulus of the backfill on the calculated facing displacements using the linear elastic-plastic soil model with Young s moduli E = 4, 8 and 12 MPa. The numerical results show that this range of Young s modulus assigned to the backfill soil had negligible influence on the calculated facing displacements when all other conditions were the same. The lateral deformation of the retaining wall is caused primarily by the local yielding of the soil after the placement of each transient surcharge used to simulate soil compaction. These yielded soil zones then unload back into the elastic region after the transient pressure is removed. The influence of the Young s modulus of the bearing pads placed between the concrete panels on facing displacements is shown in Figure 13. The numerical results show that Young s moduli E rb = 12 and 21.4 MPa give similar results that are both in reasonable agreement with the measured data. However, poorer agreement between measured and calculated facing displacements was observed when Young s modulus of the bearing pads was reduced to E rb = 3.1 Page 15

17 Canadian Geotechnical Journal Page 16 of 51 MPa. The maximum compression strain in the bearing pads at the end of wall construction was about 9%. The use of elastic modulus E rb = 12 MPa is a simple approach to approximate the initial bi-linear compression behaviour of the bearing pads at low strains. 4.2 Vertical and horizontal toe loads The measured and calculated horizontal and vertical toe loads at the base of the first panel are shown in Figure 14. The calculated vertical toe load for the linear elastic-plastic model was about 7.3 kn/m at the end of construction of the first panel, and increased to about 2 and 35 kn/m at the end of construction of the second and third panel, respectively (Figure 14a). The differences between the calculations from the two models were minor (e.g., the maximum difference was about.8 kn/m). The predicted vertical toe loads using both soil models were judged to be in good agreement with measured values. Also presented in Figure 14a is the selfweight of the facing during the construction of the wall. Based on the measured data, the vertical toe loads were about 2., 2.6 and 3.1 times the facing self-weight at the end of construction of the first, second and third panel, respectively. The corresponding vertical load factors (i.e., the vertical toe load divided by the facing self-weight) for this wall are within the range of vertical load factors for five instrumented field walls reported by Damians et al. (213). The facing vertical toe load is greater than the facing self-weight because of the vertical down-drag loads acting at the back of the facing panels and connections due to settlement of the soil backfill as the soil is placed and compacted, and the panels move outward. The calculated horizontal toe loads using the linear elastic-plastic model (Figure 14b) were 1.9, 4.5 and 6.7 kn/m at the end of construction of the first, second and third panel, respectively. The calculations using the nonlinear elastic-plastic model were generally similar to those from the linear elastic-plastic model with a maximum difference of about.7 kn/m. The calculated horizontal toe loads from both models generally agreed well with the measured data before the end of construction of the second panel. During the construction of the third panel, the predicted horizontal toe loads were up to 4% greater than the measured value regardless of soil model. The horizontal toe loads at the toe beam were generated only by the friction between the first panel base and the supporting steel plate. This represents the field case when the bottom-most Page 16

18 Page 17 of 51 Canadian Geotechnical Journal concrete panel is seated on a concrete strip footing supported in turn by a very stiff competent foundation. 4.3 Foundation pressures and vertical stresses in backfill Interface shear stresses between the facing and the backfill and down-drag loads on the connections increased the facing vertical toe loads as discussed in the previous section. The numerical results in Figure 15 show that transfer of soil load to the facing results in a reduction of vertical foundation stress immediately behind the facing. In this figure the foundation pressures are normalized with respect to the product of the height of the wall and the unit weight of the panels or soil as applicable. Both soil models gave essentially the same results. This is expected since numerical simulations must satisfy force equilibrium. Predicted foundation pressures are judged to be in reasonable agreement with measured values. Figure 16 shows vertical stress contours through the backfill using the linear elastic-plastic soil model. There is a zone of high contact pressure (6 kpa) located at 1.2 to 3. m from the front of the wall which is consistent with an arching mechanism between the rough foundation floor and the back of the facing panels. This observation is in qualitative agreement with measured pressures plotted in Figure 15 from earth pressure cells mounted on the concrete floor of the test facility (Figure 1b). At distances at and beyond the back of the reinforced soil zone, vertical earth pressures at the base of the wall and throughout the height of the wall are uniform at each elevation and equal to the total earth pressure based on depth of soil at that elevation. 4.4 Reinforcement strains Figure 17 presents calculated and measured reinforcement strains for reinforcement layers at the end of wall construction using the linear and non-linear elastic-plastic models for the soil and the strain-dependent tangent stiffness model for the geogrid. The measured strains in Figure 17 are global strains. One set of strain values are from strain gauges bonded directly to the geogrid ribs. These have been corrected for under-registration effects due to bonding of the high-elongation foil-type strain gauges to the surface of biaxial geogrids at the midpoint of each longitudinal Page 17

19 Canadian Geotechnical Journal Page 18 of 51 member between transverse members (Walters et al. 22; Bathurst et al. 23). Hence, these are global strains representing average strains between transverse members. These strain values are in reasonable agreement with strains deduced directly from displacements recorded by pairs of extensometer points; hence, these measurements corroborate the accuracy of the technique used to correct the strain gauge strains. The numerical results show that both soil models predicted similar reinforcement strains for each layer. Both sets of calculated strains are judged to be in satisfactory agreement with measured values. Figure 18 shows the calculated and measured reinforcement strains at the end of wall construction using the linear elastic-plastic soil model with both constant and strain-dependent geogrid tangent stiffness. The results show that using constant geogrid tangent stiffness resulted in visually detectable smaller reinforcement strains near the facing. However the differences in reinforcement strain predictions between the constant and strain-dependent geogrid tangent stiffness model cases may be of little practical concern since the difference in strain values is less than the spread in measured strain values particularly close to the facing where maximum strains were about 3%. The maximum reinforcement strains in Figure 17 and Figure 18 can be seen to be located at or near the connections between the reinforcement layers and the facing units based on both the measured and calculated data. The high strain readings at the connections are consistent with down-drag loads developed at the back of the facing units at the connections described earlier and the resulting attenuation of vertical foundation pressures located immediately behind the facing column. 4.5 Reinforcement connection loads and maximum loads in backfill Figure 19 shows the calculated and measured reinforcement loads at the end of wall construction using reinforcement strain gauge readings converted to load. The calculated connection loads using the linear elastic-plastic model were similar to those using the nonlinear elastic-plastic Page 18

20 Page 19 of 51 Canadian Geotechnical Journal model. The maximum difference for the calculated connection load between the two models was about.15 kn/m (i.e., at reinforcement layer 5). The connection load at reinforcement layer 6 was overestimated and those at the reinforcement layers 2 and 4 were underestimated using both soil models when compared to the measured values as shown in Figure 19. However, the overall agreement between the calculated and measured data is encouraging especially when the measured values are shown with range bars representing estimates of ± 1 standard deviation on estimates of variability in strain (or load) values reported by Walters et al. (22). Figure 2 shows the calculated and measured maximum reinforcement loads within the backfill (.5 m distance from the back of the facing panel) at the end of wall construction. Both simulations with different soil models predicted similar maximum reinforcement loads within the backfill. The maximum difference was about.12 kn/m at reinforcement layer 2. The maximum reinforcement loads within the backfill for reinforcement layers 3 and 6 were overestimated using both soil models. Nevertheless, in general, the calculated values are in encouraging agreement with the measured data as shown in Figure Comparison of maximum reinforcement loads in the backfill with analytical solutions The maximum reinforcement loads at locations beyond the connections (i.e.,.5 m) estimated using the Simplified Stiffness Method (Allen and Bathurst 215) and AASHTO Simplified Method (AASHTO 214) are also plotted in Figure 2 using the peak friction angle from conventional compression triaxial tests on the backfill soil (i.e., 4 reported by Hatami and Bathurst 25). Only one half of the lateral earth pressure acting between the bottom reinforcement layer and the base of the wall was assigned to the bottom layer of reinforcement in both methods. In practice, the foundation (including the wall toe) are conservatively assumed to not carry lateral earth pressure which results in design outcomes that are slightly safer for design. Regardless, the results demonstrate that the measured reinforcement loads were underestimated by the Simplified Stiffness Method and overestimated by the AASHTO Simplified Method for the physical wall reported in this paper. The excessive conservatism of predicted reinforcement loads at end of construction using the AASHTO Simplified Method is well documented in the literature (e.g., Allen et al. 22; Allen et al. 215). However, it should be noted that the Page 19

21 Canadian Geotechnical Journal Page 2 of 51 stiffness of the panel facing in the physical test was very much more flexible than the incremental panels that are used in the field. In the field, the concrete panels have large shear resistance between units and the panels are placed in a staggered and horizontally interlocking pattern (see Damians et al. 213, 216). This was not the case for the panels in the physical test which were constructed with rubber pads at the horizontal joints and fully decoupled from the panels in the adjacent wall sections that were not instrumented. The AASHTO Simplified Method does not consider the influence of the wall facing on reinforcement loads but the Simplified Stiffness Method does. Furthermore, the Simplified Stiffness Method is an empirically calibrated model based largely on reinforcement load measurements recorded by full-scale instrumented field walls. The incremental panel field walls in this database are much less flexible than the panel wall in the physical test as noted above. Hence, the assumption that the physical test wall in the current study falls within the database of wall performance of actual incremental panel walls used to calibrate the Simplified Stiffness Method is not valid and the wall face behaves as a more flexible structure. This means that reinforcement loads using the Simplified Stiffness Method will be higher since the facing is less effective to carry soil loads. The actual facing stiffness likely falls between the case of a flexible (e.g., wrapped face wall) and a typical incremental concrete panel wall. If the facing is considered to very flexible matching a wrapped face wall type, then the predicted maximum reinforcement loads using the Simplified Stiffness Method are in close agreement with both the numerical predicted values in the current study and the physical test results. 5. Conclusions A full-scale geogrid reinforced incremental concrete panel retaining wall was constructed in the RMCC Retaining Wall Test Facility as part of a larger research project involving a total of eleven walls. The wall was well instrumented and the data collected during and after wall construction included wall facing displacements, vertical and horizontal loads at the toe of the facing, reinforcement strains, and foundation pressures. This paper presents the first attempt to compare measured performance data at the end of wall construction to results of numerical simulation of the same structure. The numerical modelling Page 2

22 Page 21 of 51 Canadian Geotechnical Journal was performed using the finite difference method (FDM) program FLAC with the large-strain mode option (Itasca 211). Two different soil constitutive models were considered for the backfill: (a) linear elastic model with Mohr-Coulomb (MC) failure criterion, and (b) nonlinear elastic model (modified from Duncan-Chang model) with Mohr-Coulomb failure criterion. The interactions between any two dissimilar materials (excluding the geogrid) were simulated using zero-thickness interfaces. The geogrid reinforcement layers were modelled using the cable elements in FLAC. The layer-by-layer construction of the wall in the RMCC Retaining Wall Test Facility was simulated by sequentially activating the zones for the concrete panels, rubber bearing pads, backfill layers and cable elements used for the geogrid reinforcement layers in the FLAC model. The major conclusions from this numerical modelling study can be summarized as follows: Numerical results showed that the two soil constitutive models with soil parameter values taken from independent element tests predicted similar wall performance with minor influence on the calculated facing displacements and reinforcement strains. The calculated data from both models agreed well with the measured values. The modelling demonstrated that a simple linear-elastic MC model may be adequate to capture the strong interactions among the different components for these types of reinforced soil walls under working stress (operational) conditions. The parametric study performed in this paper showed that the choice of constant geogrid tangent stiffness or strain-dependent stiffness had minor influence on the magnitude of facing displacements and reinforcement strains. However, in both cases the choice of stiffness values was based on interpretation of the results of independent laboratory creep load testing of the same geogrid material used in the physical retaining wall model. Using axially stiff temporary supports during model simulation resulted in acceptable predictions of facing displacements at the end of construction of the retaining wall. Young s modulus values between 4 and 12 MPa for the linear elastic-plastic soil model had minor effect on predicted wall facing displacements. However the choice of magnitude of the transient compaction pressure on backfill lifts within.5 m distance from the facing resulted in large differences in predicted facing displacements. Page 21

23 Canadian Geotechnical Journal Page 22 of 51 The paper demonstrates that the method of construction including the location, sequence and stiffness of the temporary supports used to construct the wall plays an important role in predicting wall performance. It is reasonable to assume that such construction details will influence the magnitude of wall displacements for similar walls in the field. Indeed, there are examples in the literature that have shown that the method of construction by the contractor can have a large influence on wall displacements and reinforcement loads in field walls (Allen and Bathurst 214b; Damians et al. 215). The full-scale wall in the current investigation provides an example of the high-quality material properties, wall construction details and measurements which are required to calibrate a matching numerical model using program FLAC or other commercially available finite element method software programs. Calibrated numerical models of the type demonstrated in this paper can be used to optimize the design of reinforced soil retaining wall structures at the design stage, to verify predicted loads using analytical solutions (as demonstrated in this study), and to conduct parametric studies. Synthetic data generated from parametric studies can also be collected to fill in the knowledge gaps for wall structures that are not represented in databases of instrumented field walls (e.g., Allen et al. 24; Miyata et al. 27a, b; Bathurst et al. 28; Allen and Bathurst 215). Acknowledgements The work reported in this paper was supported by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC), 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. Page 22

24 Page 23 of 51 Canadian Geotechnical Journal References Abdelouhab, A., Dias, D., and Freitag N Numerical analysis of the behaviour of mechanically stabilized earth walls reinforced with different types of strips. Geotextiles and Geomembranes, 29: Allen, T.M., and Bathurst, R.J. 214a. Performance of an 11 m high block-faced geogrid wall designed using the K-stiffness method. Canadian Geotechnical Journal, 51(1): Allen, T.M., and Bathurst, R.J. 214b. Design and performance of 6.3 m high block-faced geogrid wall designed using the K-stiffness method. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 142(2), Allen, T.M., and Bathurst, R.J An improved simplified method for prediction of loads in reinforced soil walls. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 1.161/(ASCE)GT , Allen, T.M., Bathurst, R.J., and Berg, R.R. 22. Global level of safety and performance of geosynthetic walls: a historical perspective. Geosynthetics International, 9(5-6): Allen, T.M., Bathurst, R.J., Walters, D.L., Holtz, R.D., and Lee, W.F. 23. A new working stress method for prediction of reinforcement loads in geosynthetic walls. Canadian Geotechnical Journal, 4(5): American Association of State Highway and Transportation Officials (AASHTO) LRFD bridge design specifications, 7th Ed., Washington, DC. Bathurst, R.J Instrumentation of geogrid-reinforced soil walls. Transportation Research Record, 1277: Bathurst, R.J., Allen, T.M., and Walters, D.L. 25. Reinforcement loads in geosynthetic walls and the case for a new working stress design method. Geotextiles and Geomembranes, 23(4): Bathurst, R.J., Benjamin, D.J. and Jarrett, P.M Laboratory study of geogrid reinforced soils walls. ASCE Special Publication No. 18, Geosynthetics for Soil Improvement, pp Bathurst, R.J., Blatz, J.A. and Burger, M.H. 23. Performance of full-scale reinforced embankments loaded to failure. Canadian Geotechnical Journal, 4(6): Page 23

25 Canadian Geotechnical Journal Page 24 of 51 Bathurst, R.J., Miyata, Y., Nernheim, A., and Allen, T.M. 28. Refinement of K-stiffness method for geosynthetic reinforced soil walls. Geosynthetics International, 15(4): Bathurst, R.J., Vlachopoulos, N., Walters, D.L., Burgess, P.G., and Allen, T.M. 26. The influence of facing rigidity on the performance of two geosynthetic reinforced soil retaining walls. Canadian Geotechnical Journal, 43(12): Bathurst, R.J., Nernheim, A., Walters, D.L., Allen, T.M., Burgess, P., and Saunders, D.D. 29. Influence of reinforcement stiffness and compaction on the performance of four geosynthetic reinforced soil walls. Geosynthetics International, 16(1): Bathurst, R.J., Walters, D., Vlachopoulos, N., Burgess, P., and Allen, T.M. 2. Full scale testing of geosynthetic reinforced walls. Invited keynote paper, ASCE Special Publication No. 13, Advances in Transportation and Geoenvironmental Systems using Geosynthetics, Proceedings of Geo-Denver 2, Denver, Colorado, pp Boscardin, M.D., Selig, E.T., Lin, R.S., and Yang, G.R Hyperbolic parameters for compacted soils. Journal of Geotechnical Engineering, 116(1): Cai, Z., and Bathurst, R.J Seismic response analysis of geosynthetic reinforced soil segmental retaining walls by finite element method. Computers and Geotechnics, 17(4): Damians, I.P., Bathurst, R.J., Josa, A., Lloret, A., and Albuquerque, P.J.R Vertical facing loads in steel reinforced soil walls. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 139(9): Damians, I.P., Bathurst, R.J., Josa, A., and Lloret, A Numerical study of the influence of foundation compressibility and reinforcement stiffness on the behavior of reinforced soil walls. International Journal of Geotechnical Engineering, 8(3): Damians, I.P., Bathurst, R.J., Josa, A., and Lloret, A Numerical analysis of an instrumented steel reinforced soil wall. ASCE International Journal of Geomechanics, 15(1), Damians, I.P., Bathurst, R.J., Josa, A. and Lloret, A Vertical facing panel-joint gap analysis for steel-reinforced soil walls. ASCE International Journal of Geomechanics (online) ( Page 24

26 Page 25 of 51 Canadian Geotechnical Journal Duncan, J.M., Byrne, P.M., Wong, K.S., and Mabry, P Strength, stress-strain and bulk modulus parameters for finite element analyses of stresses and movements in soil masses. Rep. No. UCB/GT/8-1, Dept. of Civil Engineering, Univ. of California, Berkeley, Calif. Ezzein, F., Bathurst, R.J., and Kongkitkul, W Non-linear load-strain modelling of polypropylene geogrids during constant rate-of-strain loading. Polymer Engineering and Science, 55(7): Gotteland, Ph., Gourc, J.P., and Villard, P Geosynthetics reinforced structures as bridge abutments: full scale experimentation and comparison with modelisations. In International Symposium on Mechanically Stabilized Backfill, Denver, Colorado, 6 8 February 1997, (J.T.H. Wu editor). Balkema, Rotterdam, The Netherlands. pp Hatami, K., and Bathurst, R.J. 25. Development and verification of a numerical model for the analysis of geosynthetic reinforced soil segmental walls under working stress conditions. Canadian Geotechnical Journal, 42(4): Hatami, K., and Bathurst, R.J. 26. Numerical model for reinforced soil segmental walls under surcharge loading. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 132(6): Huang, B., Bathurst, R.J., and Hatami, K. 29. Numerical study of reinforced soil segmental walls using three different constitutive soil models. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 135(1): Huang, B., Bathurst, R.J., Hatami, K., and Allen, T.M. 21. Influence of toe restraint on reinforced soil segmental walls. Canadian Geotechnical Journal, 47(8): Itasca FLAC: Fast Lagrangian Analysis of Continua. Version 7. [computer program]. Itasca Consulting Group, Inc., Minneapolis, Minn. Karpurapu, R.G., and Bathurst, R.J Behaviour of geosynthetic reinforced soil retaining walls using the finite element method. Computers and Geotechnics, 17(3): Liu, X., Bradford, M., and Lee, M Behavior of high-strength friction-grip bolted shear connectors in sustainable composite beams. ASCE Journal of Structural Engineering, 141(6), Miyata, Y., and Bathurst, R.J. 27a. Evaluation of K-Stiffness method for vertical geosynthetic reinforced granular soil walls in Japan. Soils and Foundations, 47(2): Page 25

27 Canadian Geotechnical Journal Page 26 of 51 Miyata, Y., and Bathurst, R.J. 27b. Development of K-stiffness method for geosynthetic reinforced soil walls constructed with c-ϕ soils. Canadian Geotechnical Journal, 44(12): Miyata, Y., Bathurst, R.J., and Miyatake, H Performance of three geogrid reinforced soil walls before and after foundation failure. Geosynthetics International, 22(4): Rowe, R.K., and Ho, S.K Continuous panel reinforced soil walls on rigid foundations. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 123(1): Rowe, R.K. and Skinner, G.D. 21. Numerical analysis of geosynthetic reinforced retaining wall constructed on a layered soil foundation. Geotextiles and Geomembranes, 19(7): Selig, E.T Soil parameters for design of buried pipelines. In Proceedings of the Conference of Pipeline Infrastructure, B.A. Bennet, Ed., ASCE, New York, NY, Serway, R.A., and Jewett, J.W Physics for Scientists and Engineers with Modern Physics. 9th Ed., Brooks/Cole Cengage Learning, New York. Shinoda, M., and Bathurst, R.J. 24. Lateral and axial deformation of PP, HDPE and PET geogrids under tensile load. Geotextiles and Geomembranes, 22(4): Walters, D.L., Allen, T.M., and Bathurst, R.J. 22. Conversion of geosynthetic strain to load using reinforcement stiffness. Geosynthetics International, 9(5-6): Yoo, C., Jang, Y.S. and Park, I.J Internal stability of geosynthetic-reinforced soil walls in tiered configuration. Geosynthetics International, 18(2): Yu, Y., Bathurst, R.J., and Miyata, Y. 215a. Numerical analysis of a mechanically stabilized earth wall reinforced with steel strips. Soils and Foundations, 55(3): Yu, Y., Damians, I.P., and Bathurst, R.J. 215b. Influence of choice of FLAC and PLAXIS interface models on reinforced soil-structure interactions. Computers and Geotechnics, 65: Yu, Y., Bathurst, R.J., and Allen, T.M Numerical modelling of the SR-18 geogrid reinforced modular block retaining walls. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 142(5), Page 26

28 Page 27 of 51 Canadian Geotechnical Journal FIGURE CAPTIONS Figure 1. Geogrid reinforced incremental concrete panel retaining wall constructed in the RMCC Retaining Wall Test Facility: (a) photograph of wall face at end of testing and bracing used to support instrumentation, and (b) cross-section view. Figure 2. Numerical grid and model components at the end of wall construction. Figure 3. Measured and calculated stress-strain response of RMCC sand: (a) triaxial tests and (b) plane strain tests (measured data from Hatami and Bathurst 25). Figure 4. Nonlinear compressive stress-strain behaviour of gum rubber bearing pad material. Figure 5. Secant stiffness for PP geogrid loaded in machine direction (measured data from Hatami and Bathurst 26). Figure 6. Boundary conditions during construction of (a) the first concrete panel, (b) the second concrete panel, and (c) the third concrete panel. Figure 7. Calculated and measured facing horizontal displacements at the end of (a) first, (b) second, and (c) third panel construction. Note: horizontal displacements of the facing are outward and taken with respect to the toe of the wall at start of construction and after all temporary props have been removed. Figure 8. Calculated displacement vectors at the end of wall construction using the linear elasticplastic soil model. Figure 9. Influence of prop stiffness on predicted facing horizontal displacements at the end of (a) first, (b) second, and (c) third panel row construction. Note: using linear elastic-plastic soil model. Figure 1. Influence of constant and strain-dependent geogrid tangent stiffness on predicted facing horizontal displacements at the end of (a) first, (b) second, and (c) third panel row construction. Note: using linear elastic-plastic soil model. Page 27

29 Canadian Geotechnical Journal Page 28 of 51 Figure 11. Influence of compaction pressure near facing on predicted facing horizontal displacements using the linear elastic-plastic soil model at the end of (a) first, (b) second, and (c) third panel row construction. Figure 12. Influence of soil Young s modulus on predicted facing horizontal displacements using the linear elastic-plastic soil model at the end of (a) first, (b) second, and (c) third panel row construction. Figure 13. Influence of Young s modulus (E rb ) for bearing pads on the facing horizontal displacements using the linear elastic-plastic soil model at the end of (a) first, (b) second, and (c) third panel row construction. Figure 14. Measured and calculated horizontal and vertical toe loads at the steel plate footing supporting the wall panels: (a) toe vertical load, and (b) toe horizontal load. Figure 15. Measured and calculated foundation pressures at the end of wall construction. Figure 16. Calculated vertical stress distribution (σ yy ) within the backfill at the end of wall construction using the linear elastic-plastic soil model. Figure 17. Calculated and measured reinforcement strains at the end of wall construction using two different soil constitutive models and strain-dependent geogrid tangent stiffness model. Note: range bars represent ±1 standard deviation on measured strain values. Figure 18. Calculated and measured reinforcement strains at the end of wall construction using strain-dependent and constant geogrid tangent stiffness model and linear elastic-plastic soil model. Note: range bars represent ±1 standard deviation on measured strain values. Figure 19. Calculated and measured reinforcement connection loads at the end of wall construction from strain gauges located closest to the connections. Note: range bars represent ±1 standard deviation on measured load values. Figure 2. Calculated and measured maximum reinforcement loads within the backfill (.5 m distance from the back of the facing panel) at the end of wall construction. Note: range bars represent ±1 standard deviation on measured load values. Page 28

30 Page 29 of 51 Canadian Geotechnical Journal cgj r1 July 216 (a) Wall height above base (m) Connection load rings Rubber bearing pad Steel plate (1) (2) (3) Concrete panel ( m).14 m Reinforced soil 2.52 m Sand backfill Reinforcement layer 5.65 m Retained soil.6 m Concrete foundation Earth pressure cell Note: (1) Horizontal toe load rings; (2) Reaction beam; (3) Vertical toe load cells (b) Figure 1. Geogrid reinforced incremental concrete panel retaining wall constructed in the RMCC Retaining Wall Test Facility: (a) photograph of wall face at end of testing and bracing used to support instrumentation, and (b) cross-section view. Page 1

31 Canadian Geotechnical Journal Page 3 of 51 cgj r1 July 216 Concrete panel ( m) Sand backfill Rubber bearing pad Reinforcement layer 3.6 m Steel plate Toe spring Concrete foundation.15 m.14 m 5.65 m Figure 2. Numerical grid and model components at the end of wall construction. Page 2

32 Page 31 of 51 Canadian Geotechnical Journal cgj r1 July 216 Deviatoric stress, - (kpa) E = 8 MPa 1 E 3 = 5 kpa Measured (triaxial tests) Calculated (linear elastic + MC criterion) Calculated (nonlinear elastic + MC criterion) 3 = 1 kpa 3 = 25 kpa (a) Axial strain, 1 (%) Deviatoric stress, - (kpa) E = 8 MPa 1 E 3 = 3 kpa Measured (plane strain tests) Calculated (linear elastic + MC criterion) Calculated (nonlinear elastic + MC criterion) 3 = 8 kpa 3 = 2 kpa (b) Axial strain, 1 (%) Figure 3. Measured and calculated stress-strain response of RMCC sand: (a) triaxial tests and (b) plane strain tests (measured data from Hatami and Bathurst 25). Page 3

33 Canadian Geotechnical Journal Page 32 of 51 cgj r1 July Sample size:.15 m x.15 m Sample thickness:.12 m Measured Fitted 8 7 E rb = 3.1 MPa E rb = 21.4 MPa E rb = 3. MPa Stress (MPa) Strain (%) Figure 4. Nonlinear compressive stress-strain behaviour of gum rubber bearing pad material. Page 4

34 Page 33 of 51 Canadian Geotechnical Journal cgj r1 July 216 Secant stiffness, J( t) (kn/m) EOC = 1227 hours Calcuated (t = 5 hours) Calcuated (t = 1 hours) Calcuated (t = 1227 hours) Measured (t = 5 hours) Measured (t = 1 hours) 1 Secant stiffness: J ( ε, t) 1 χ( t) ε J ( t) Time t unit: hour PP geogrid: J (t) = 258t kn/m, (t) =.658t.83 m/kn Strain, (%) Figure 5. Secant stiffness for PP geogrid loaded in machine direction (measured data from Hatami and Bathurst 26). Page 5

35 Canadian Geotechnical Journal Page 34 of 51 cgj r1 July 216 Prop 1 spring Concrete panel ( m) Steel plate Toe spring 1.2 m (a).14 m Concrete foundation 5.65 m.15 m Prop 3 spring Concrete panel ( m) Prop 2 spring Sand backfill 1.2 m Steel plate Toe spring Reinforcement layer 1.2 m (b).14 m Concrete foundation 5.65 m.15 m Concrete panel ( m) Prop 5 spring Prop 4 spring Sand backfill 1.2 m Reinforcement layer 2.4 m Steel plate Toe spring (c).14 m Concrete foundation 5.65 m.15 m Figure 6. Boundary conditions during construction of (a) the first concrete panel, (b) the second concrete panel, and (c) the third concrete panel. Page 6

36 Page 35 of 51 Canadian Geotechnical Journal cgj r1 July (a) End of construction of the first panel Calculated (linear elastic + MC criterion) Calculated (nonlinear elastic + MC criterion) Measured (b) End of construction of the second panel (c) End of construction of the third panel Wall D Elevation (m) 3 2 E = 8 MPa E rb = 12 MPa q 1 = 8 kpa q 2 = 16 kpa Strain-dependent geogrid tangent stiffness Elastic non-uniform prop stiffness Facing horizontal displacement (mm) Figure 7. Calculated and measured facing horizontal displacements at the end of (a) first, (b) second, and (c) third panel construction. Note: horizontal displacements of the facing are outward and taken with respect to the toe of the wall at start of construction and after all temporary props have been removed. Page 7

37 Canadian Geotechnical Journal Page 36 of 51 cgj r1 July 216 Concrete panel ( m) Sand backfill 3.6 m Steel plate Toe spring Concrete foundation.15 m.14 m 5.65 m Figure 8. Calculated displacement vectors at the end of wall construction using the linear elasticplastic soil model. Page 8

38 Page 37 of 51 Canadian Geotechnical Journal cgj r1 July (a) End of construction of the first panel Calculated (non-uniform prop stiffness) Calculated (uniform prop stiffness) Measured (b) End of construction of the second panel (c) End of construction of the third panel Wall D Elevation (m) 3 2 Linear elastic model with Mohr-Coulomb criterion E = 8 MPa E rb = 12 MPa q 1 = 8 kpa q 2 = 16 kpa Strain-dependent geogrid tangent stiffness Facing horizontal displacement (mm) Figure 9. Influence of prop stiffness on predicted facing horizontal displacements at the end of (a) first, (b) second, and (c) third panel row construction. Note: using linear elastic-plastic soil model. Page 9

39 Canadian Geotechnical Journal Page 38 of 51 cgj r1 July (a) End of construction of the first panel Calculated (strain-dependent geogrid tangent stiffness) Calculated (constant geogrid tangent stiffness = 116 kn/m) Measured (b) End of construction of the second panel (c) End of construction of the third panel Wall D Elevation (m) 3 2 Linear elastic model with Mohr-Coulomb criterion E = 8 MPa E rb = 12 MPa q 1 = 8 kpa q 2 = 16 kpa Elastic non-uniform prop stiffness Facing horizontal displacement (mm) Figure 1. Influence of constant and strain-dependent geogrid tangent stiffness on predicted facing horizontal displacements at the end of (a) first, (b) second, and (c) third panel row construction. Note: using linear elastic-plastic soil model. Page 1

40 Page 39 of 51 Canadian Geotechnical Journal cgj r1 July Calculated (q 1 = 8 kpa) Calculated (q 1 = ) (a) End of construction of the first panel (b) End of construction of the second panel Calculated (q 1 = 16 kpa) Measured (c) End of construction of the third panel Wall D Elevation (m) 3 2 Linear elastic model with Mohr-Coulomb criterion E = 8 MPa E rb = 12 MPa q 2 = 16 kpa Strain-dependent geogrid tangent stiffness Elastic non-uniform prop stiffness Facing horizontal displacement (mm) Figure 11. Influence of compaction pressure near facing on predicted facing horizontal displacements using the linear elastic-plastic soil model at the end of (a) first, (b) second, and (c) third panel row construction. Page 11

41 Canadian Geotechnical Journal Page 4 of 51 cgj r1 July Calculated (E = 8 MPa) Calculated (E = 4 MPa) (a) End of construction of the first panel (b) End of construction of the second panel Calculated (E = 12 MPa) Measured (c) End of construction of the third panel Wall D Elevation (m) 3 2 Linear elastic model with Mohr-Coulomb criterion E rb = 12 MPa q 1 = 8 kpa q 2 = 16 kpa Strain-dependent geogrid tangent stiffness Elastic non-uniform prop stiffness Facing horizontal displacement (mm) Figure 12. Influence of soil Young s modulus on predicted facing horizontal displacements using the linear elastic-plastic soil model at the end of (a) first, (b) second, and (c) third panel row construction. Page 12

42 Page 41 of 51 Canadian Geotechnical Journal cgj r1 July Calculated (E rb = 12 MPa) Calculated (E rb = 21.4 MPa) (a) End of construction of the first panel (b) End of construction of the second panel Calculated (E rb = 3.1 MPa) Measured (c) End of construction of the third panel Wall D Elevation (m) 3 2 Linear elastic model with Mohr-Coulomb criterion E = 8 MPa q 1 = 8 kpa q 2 = 16 kpa Strain-dependent geogrid tangent stiffness Elastic non-uniform prop stiffness Facing horizontal displacement (mm) Figure 13. Influence of Young s modulus (E rb ) for bearing pads on the facing horizontal displacements using the linear elastic-plastic soil model at the end of (a) first, (b) second, and (c) third panel row construction. Page 13

43 Canadian Geotechnical Journal Page 42 of 51 cgj r1 July 216 Toe veritical load (kn/m) (a) Calculated (linear elastic + MC criterion) Calculated (nonlinear elastic + MC criterion) Measured Elevation (m) Facing self-weight Toe horizontal load (kn/m) (b) 1 5 Calculated (linear elastic + MC criterion) Calculated (nonlinear elastic + MC criterion) Measured Elevation (m) Figure 14. Measured and calculated horizontal and vertical toe loads at the steel plate footing supporting the wall panels: (a) toe vertical load, and (b) toe horizontal load. Page 14

44 Page 43 of 51 Canadian Geotechnical Journal cgj r1 July 216 Normalized pressure (-) Back of facing Calculated (linear elastic + MC criterion) Calculated (nonlinear elastic + MC criterion) Measured End of reinforcement Distance from front of facing (m) 5.8 Figure 15. Measured and calculated foundation pressures at the end of wall construction. Page 15

45 Canadian Geotechnical Journal Page 44 of 51 cgj r1 July 216 Figure 16. Calculated vertical stress distribution (σ yy ) within the backfill at the end of wall construction using the linear elastic-plastic soil model. Page 16