A numerical study on the use of geofoam to increase the external stability of reinforced soil walls

Geosynthetics International, 2008, 15, No A numerical study on the use of geofoam to increase the external stability of reinforced soil walls K Hatami1 and A F Witthoeft2 Assistant Professor, School of Civil Engineering and Environmental Science, University of Oklahoma, 202 W Boyd St, Room 334, Norman, OK 73019, USA, Telephone: +1 405 325 2674; Telefax: +1 405 325 4217, E-mail: kianoosh@ou.edu Undergraduate Research Assistant, School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019, USA, Telephone: +1 765 494 6246; Telefax: +1 765 494 0395, E-mail: awitthoeft@purdue.edu Received January 2008, revised June 2008, accepted 17 June 2008 ABSTRACT: The potential benefit of placing a panel of compressible (i.e expanded polystyrene) geofoam behind the reinforced zone of mechanically stabilized earth (MSE) walls is investigated using a numerical modeling approach A panel of geofoam is placed immediately behind the reinforced zone during the construction phase of an idealized plane-strain reinforced soil segmental wall model The analysis procedure includes the modeling of soil compaction The magnitudes and distributions of earth pressure behind the reinforced zone in the wall models with and without the geofoam panel are compared to quantify the reductions in lateral earth pressure, resultant lateral force and overturning moment expected due to the placement of the geofoam material Predicted magnitudes of facing lateral deformation and reinforcement strains are also compared among cases studied in order to evaluate the effect of geofoam on wall serviceability It is shown that placing geofoam behind the reinforced zone can reduce the maximum lateral earth pressure behind this zone by as much as 50% depending on the geofoam thickness and stiffness values The magnitudes of total lateral earth force (i.e the resultant force of the lateral earth pressure distribution) behind the reinforced mass and overturning moment about the wall toe are shown to decrease by 31% and 26%, respectively These findings point to a significant potential for using geofoam to reduce the lateral earth pressure demand on MSE walls (i.e as opposed to rigid retaining walls examined previously) and thereby increase their serviceability and their factors of safety against external instability KEYWORDS: Geosynthetics, Geofoam, MSE retaining walls, Reinforced soil REFERENCE: Hatami, K & Witthoeft, A (2008) A numerical study on the use of geofoam to increase the external stability of reinforced soil walls Geosynthetics International, 15, No 6, 452–470 [doi: 10.1680/gein.2008.15.6.452] INTRODUCTION 1.1 Previous work regarding geofoam applications Expanded polystyrene (EPS) foam, commonly known as geofoam, has gained widespread popularity as a construction material in a variety of geotechnical and transportation engineering applications in recent years Example applications include construction of lightweight embankments and pavements (Duskov 2000; Jutkofsky et al 2000; Horvath 2004a, 2004b; Stark et al 2004), static and seismic earth pressure reduction behind rigid retaining walls (Horvath 1991a, 1991b; Inglis et al 1996; Aytekin 1997; Reeves and Filz 2000; Stark et al 2004; Zarnani et al 2005; Bathurst et al 2007a, 2007b; Zarnani and Bathurst 2007, 2008), and functions such as drainage, thermal insulation and attenuation of noise and vibration (Horvath 2005; Koerner 2005) The use of low-stiffness (i.e compressible) geoinclusions to allow controlled yielding of the backfill and hence reduce lateral earth pressures against rigid retaining walls has been reported in the literature as early as the mid-1980s (McGown et al 1987; Partos and Kazaniwsky 1987) McGown et al (1987, 1988) and Horvath (1991a, 1991b) examined the idea of using reinforcement layers in combination with a compressible layer (or geofoam) behind a rigid wall to achieve a greater reduction of earth pressure behind the wall compared with the case of using geofoam alone Horvath (1991a) investigated the influence of reinforcement tensile modulus and geofoam thickness on the reduction of lateral earth pressure behind an idealized mhigh rigid wall using a finite element approach His results indicated that a 0.05 m-thick geofoam panel compressed by 1072-6349 # 2008 Thomas Telford Ltd Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved 452 Use of geofoam to increase external stability of reinforced soil walls about 0.005 m could reduce the lateral earth pressure behind a rigid wall retaining an unreinforced backfill to the values corresponding to an active state Using a 0.6 m-thick geofoam panel would result in significantly lower lateral earth pressure magnitudes behind the rigid wall compared with the 0.05 m case Horvath (1991a) found that using very extensible reinforcement (i.e nonwoven geotextiles) would not result in any additional reduction in lateral earth pressure behind the wall compared with using geofoam alone On the contrary, using stiff reinforcement (i.e steel) combined with geofoam panels would reduce the lateral earth pressure behind the wall to negligible values Horvath (1991b) examined the extent of reduction in lateral earth pressure behind rigid walls for the case where the wall was subjected to surcharge loading on its backfill His analysis indicated that the structural demand on rigid walls subjected to backfill surcharge loading could be reduced significantly by using geofoam behind the wall, offering a cost-effective design approach in such loading situations The additional effect of backfill reinforcement on reducing lateral earth pressure behind a rigid wall has also been investigated in several other studies (e.g Tsukamoto et al 2002; Abu-Hejleh et al 2003; Horvath 2003; Hazarika and Okuzono 2004; Horvath 2004b, 2005) In all these studies the geofoam has been placed (or modeled in the analysis) between the backfill and a rigid retaining wall However, to the best of the present authors’ knowledge, no studies have addressed the potential use of geofoam behind the reinforced zone of mechanically stabilized earth (MSE) walls to reduce lateral earth pressures behind the reinforced mass Such an application is distinct from the configurations investigated in the previous studies The horizontal earth force and overturning moment resulting from the magnitude and distribution of lateral earth pressure behind the reinforced zone in MSE walls are important design parameters for their external stability analysis (e.g Elias et al 2001; AASHTO 2002; NCMA 2002) In this paper it is shown that the assumption of active state lateral earth pressure magnitudes behind the reinforced mass of MSE walls could be inaccurate and unsafe (see Section 1.2) This inaccuracy is attributed primarily to the compaction-induced increase in lateral earth pressures, which could approach (or even exceed) magnitudes corresponding to the at-rest conditions, as demonstrated in several past studies on rigid retaining walls (e.g Duncan et al 1991, Filz and Duncan 1996) Placement of geofoam panels behind the reinforced zone could help ensure that reduced lateral earth pressure magnitudes will develop behind the reinforced mass, as assumed in the current design guidelines 1.2 Lateral earth pressure magnitudes behind reinforced zone of MSE walls External stability analyses of MSE walls in the current limit-equilibrium design approaches are based on the assumption that an active state is developed over the entire wall height behind the reinforced zone (e.g Elias et al 2001; NCMA 2002) This assumption is made to reduce the conservatism in the design of MSE walls due to the overall satisfactory performance of these structures (e.g 453 Koerner 2005) This approach is based on the postulation that MSE walls are flexible structures and hence can undergo sufficient deformations during their construction that would result in fully active conditions in their backfills There is a wealth of experimental evidence that supports the notion of developing an active state within the reinforced zone behind the facing of MSE walls at the end of construction For instance, measured reinforcement strains in several instrumented MSE walls in the field and full-scale test walls in the laboratory reported by several past studies have indicated that maximum reinforcement strains at the end of construction are typically in the range 1–2% in MSE walls with select backfills, depending on the wall height and reinforcement properties (e.g Allen and Bathurst 2002) In addition, typical magnitudes reported for the frictional efficiency of the interface between high-quality backfill and geogrid reinforcement (e.g Holtz et al 1997; Koerner 2005), in addition to observations in recent full-scale prototype studies on MSE walls (Hatami and Bathurst 2005, 2006), have indicated that slippage of reinforcement within the backfill is unlikely, and therefore the strains in the geogrid reinforcement and in the backfill soil are compatible As a result, strains on the order of 1–2% are expected to develop in the backfill, which are sufficient to develop active states within the reinforced zone and especially behind the wall facing These strain magnitudes are also compatible with observations made by Allen et al (2003) and Miyata and Bathurst (2007) on the response of several instrumented MSE walls in the field, where satisfactory performance was observed in the walls with granular and cohesive (i.e c–
) backfill soils when maximum local reinforcement strain was less than 3% and 4%, respectively (Huang et al 2007) In contrast to the availability of the experimental evidence on the response of soil within the reinforced mass, no measured data are available on the distributions of lateral earth pressure behind the reinforced zone of MSE walls Therefore, in this study, this information was extracted from a numerical model that was validated against measured data on several response parameters from a series of well-instrumented full-scale test walls simultaneously (Hatami and Bathurst 2005, 2006) The RMC walls have also been used to validate a numerical model by Guler et al (2007) The test walls were carefully constructed in a controlled laboratory environment at the Royal Military College of Canada (RMC) Figure shows an example numerical grid for the RMC test walls investigated in this study Each of these walls was constructed with a modular block facing, and was different from the other walls in its reinforcement design (i.e reinforcement tensile modulus and vertical spacing), as listed in Table Details of wall construction, instrumentation and monitoring program have been reported in several previous studies (e.g Bathurst et al 2000, 2001, 2006; Hatami and Bathurst 2005, 2006) The data used to calibrate and validate the numerical model for the MSE walls included wall facing deformations, axial strain distributions over the length of all reinforcement layers, reinforcement connection loads, independent horizontal Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved 454 Hatami and Witthoeft Interfaces Modular blocks Reinforcement 24 ⫻ 0.15 ⫽ 3.6 m 0.6 m 3.6 m Sand backfill 2.52 m Stiff facing toe 5.95 m Location where earth pressure distributions in Figure and horizontal displacements in Figure are reported Location of geofoam panel in proposed configuration Figure Typical numerical model for RMC test walls used to determine earth pressure distributions and horizontal displacements shown in Figures and Table Reinforcement properties and configurations in RMC test walls examined in this study (data from Hatami and Bathurst 2006) Wall Reinforcement Material type PP PP PP PET WWM PP Number of layers 6 6 11 Aperture dimensions (mm mm) 25 25 25 21 100 25 3 3 3 Tensile modulus properties (Equation 4) J0 (t ) (kN/m) (t ) Tf (kN/m) 115 56.5 115 57 3100 115 0.85 0.85 0.85 0 0.85 7.7 3.65 7.7 16 7.7 33 69 33 23 200 33 Note: Wall was constructed using a different facing and construction technique, and therefore it was not included in this study and vertical components of facing toe reactions, and vertical earth pressure distributions at the foundation level Horizontal earth pressures behind the reinforced mass were not measured in any of the test walls However, Figure shows the lateral earth pressure distributions for six of the RMC test walls as predicted using the validated numerical model Note that y and H (on the vertical axis) refer to the vertical distance from the bottom of the wall and the total wall height, respectively All earth pressure results (both vertical and lateral) are normalized with respect to the product of the soil bulk unit weight, ªs , and the total wall height, H These conventions are followed throughout the paper The results shown in Figure 2a depict predicted distributions for Walls 1–3, in which a lightweight vibrating plate compactor was used to compact the backfill during construction (Hatami and Bathurst 2005) Walls 5–7 (Figure 2b) were constructed using a jumping jack that exerted a greater compaction effort on Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved Use of geofoam to increase external stability of reinforced soil walls 1.0 1.0 Wall Wall Wall K0 Ka 0.8 Normalized elevation, y /H 455 1.0 Wall Wall Wall 0.8 0.6 Wall Wall Wall 0.8 0.6 0.6 0.4 0.4 0.2 0.2 K0 0.4 0.2 0 0.25 Normalized lateral K0 Ka Ka 0 0.50 Earth pressure, σh /γsH 0.5 1.0 Normalized vertical 0.25 Lateral earth pressure 0.50 Coefficient, K ⫽ σh /σv Earth pressure, σh /γsH (a) 1.0 0.8 Normalized elevation, y /H 1.0 1.0 Wall Wall Wall K0 Ka Wall Wall Wall 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 K0 0.2 Wall Wall Wall Ka K0 Ka 0 0 0.25 0.50 0.75 Normalized lateral Normalized vertical 0.50 1.00 Lateral earth pressure Earth pressure, σh /γsH Earth pressure, σh /γsH Coefficient, K ⫽ σh /σv 0.5 1.0 1.5 1.50 (b) Figure Earth pressure results behind reinforced zone of selected RMC test walls with modular facing as predicted using a validated numerical model: (a) walls compacted using lightweight vibrating plate; (b): walls compacted using higher-energy jumping jack the backfill (Hatami and Bathurst 2006) The undulatory characteristics observed in the results shown in Figure are attributed to the unloading–reloading model used for the soil subjected to a transitory uniform pressure applied at each soil lift during construction (Section 3.1.2) Nonetheless, the following observations can be made from the results shown in Figure 2 v : Vertical pressure distributions for all wall models show a satisfactory agreement with the theoretical prediction, ªs z, as assumed in the current design guidelines, where ªs and z are the soil bulk unit weight and depth in the backfill, respectively h : Predicted lateral earth pressure distributions in Walls 1–3, which were constructed using a lighter compaction effort, indicate an active state (Ka ) at the top of the wall and approach an at-rest condition (K0 ) toward the bottom of the backfill Predicted lateral earth pressure distributions for Walls 5–7, which were constructed using a jumping jack, indicate increased magnitudes comparable to (or exceeding) the at-rest conditions over the entire backfill depth This is attributed to greater locked-in stresses in the soil behind the reinforced mass when subjected to a more significant compaction effort compared with Walls 1–3 The predicted lateral earth pressure magnitudes in Walls 5–7 tend to exceed the at-rest value at the bottom of the backfill This tendency is common in all wall models in the vicinity of the rigid foundation, with the values for Walls 5–7 greater than those in Walls 1–3 K: The distributions of lateral earth pressure coefficient behind the reinforced mass verify the observations made on the distribution of h behind reinforced zone as described in item above An additional interesting observation is that significant Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved 456 Hatami and Witthoeft 1.0 1.0 0.8 0.8 Minimum displacement required for active state in the soil Normalized elevation, y /H Figure shows horizontal displacement of the backfill behind the reinforced zone for the same test walls as predicted using the validated numerical model The magnitudes of the predicted displacements are normalized with respect to the wall height The results shown in Figure indicate that predicted horizontal displacements behind the reinforced mass are slightly smaller in walls compacted with greater compaction effort than those compacted using a lighter compactor This observation is consistent with the expectation that a better-compacted soil will be stiffer and exhibit a reduced lateral deformation behavior At the same time, results shown in Figure indicate that the magnitudes of normalized lateral displacement of the backfill behind the reinforced zone in all walls examined are significantly smaller than those required for the soil to develop a fully active state For instance, magnitudes of lateral displacement needed for a dense cohesionless backfill material (e.g sand backfill used in RMC test walls) to fully develop an active state are about ˜/H ¼ 0.001–0.004, where ˜ is the horizontal displacement of the backfill and H is the height of the wall (e.g Bowles 1996; Das 2004) It should be noted that the range ˜/H ¼ 0.001–0.004 is approximate, and that other studies (e.g Sherif et al 1982) have reported the influence of factors such as the angle of internal friction of the backfill material on the amount of deformation required to reach an active state Displacement results for all RMC test walls shown in Figure are significantly less than ˜/H ¼ 0.001, and corroborate with the predicted magnitudes of lateral earth pressure behind their reinforced mass (Figure 2), which for the most part are greater than active lateral earth pressure magnitudes The results shown in Figures and indicate that reducing at-rest (i.e K0 ) lateral earth pressures to active (i.e Ka ) levels requires greater soil deformations than the magnitudes expected to occur behind the reinforced zone of typical segmental retaining walls in the field Placing a geofoam panel behind the reinforced mass is investigated in the present study as a possible method to achieve the 0.6 0.4 0.2 Minimum displacement required for active state in the soil K values could develop at the top of the walls subjected to significant compaction effort (e.g Walls 5–7 in Figure 2b) Also, the K values near the backfill surface are greater behind a stiffer reinforced zone (i.e when reinforcement tensile modulus is greater) The K values near the backfill surface decrease with depth, similar to those measured in the field walls that have been used as a basis for adopting approaches such as the coherent gravity method for the design of MSE walls (e.g Elias et al 2001) However, results shown in Figure 2b indicate that lateral earth pressure magnitudes behind the reinforced mass of well-compacted walls in the field could be significantly greater than the values suggested in the current design guidelines, based on the assumption of active state over the entire backfill depth As a result, the assumption of active (i.e Ka ) conditions over the entire wall height behind the reinforced zone may not be safe in the external stability analysis of MSE walls Development of compaction-induced, excess lateral earth pressures in MSE walls has been reported previously (e.g Ingold 1983) 0.6 0.4 0.2 Wall Wall Wall Wall Wall Wall 0 0.0005 0.0010 0.0005 0.0010 Normalized lateral displacement, ∆/H (a) (b) Figure Horizontal displacement of soil behind reinforced zone for selected RMC test walls with modular facing as predicted using a validated numerical model: (a) walls compacted using lightweight vibrating plate; (b) walls compacted using higherenergy jumping jack Note: minimum displacement required for active state in the soil is indicated Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved Use of geofoam to increase external stability of reinforced soil walls 457 reduced (i.e active state) lateral earth pressure magnitudes desired behind the reinforced zone was reported, based on the results of direct shear testing conducted on samples prepared to the same dry density 1.3 Present study 2.2 Numerical modeling of controlled yielding tests 2.2.1 Numerical model Physical tests at the University of Strathclyde were used to validate the numerical model developed in this study Selected results reported in the same study by McGown et al (1987) were also used to validate an FEM model by Karpurapu and Bathurst (1992) Figure illustrates the plane-strain numerical model simulating a representative physical test setup Dimensions of the numerical grid (1.00 m high 1.92 m long) are consistent with the dimensions of the retained soil as reported by McGown et al (1987, 1988) Except as mentioned below, an aspect ratio of 1H:1V was used for the zones throughout the numerical model A fixed boundary condition in the horizontal direction was applied at the numerical gridpoints on the backfill far-end boundary to simulate a smooth rigid vertical panel A fixed boundary condition in both horizontal and vertical directions was used at the bottom boundary to simulate a rigid foundation A thin (i.e aspect ratio of 5H:1V ) soil layer was used across the entire base of the retained soil mass to simulate an interface between the soil and the rigid foundation The authors and colleagues have successfully used such an approach to simulate the backfill/foundation interface in their previous studies to analyze the response of reinforced soil-retaining walls subjected to static and dynamic loading conditions (e.g Bathurst and Hatami 1998; Hatami and Bathurst 2000) MODEL DEVELOPMENT AND VALIDATION 2.1 Model tests used for validation of the numerical model A series of instrumented model-scale tests was conducted at the University of Strathclyde in order to investigate the reduction of lateral earth pressure in a soil mass due to lateral displacement (i.e controlled yielding) of a vertical boundary (McGown et al 1987, 1988) Soil was placed to a height of m inside a test tank 1.17 m high by 1.92 m long by 0.45 m wide The soil mass was constructed on a rigid foundation and was enclosed within three vertical faces using rigid glass wall panels The remaining vertical face of the soil mass was supported by a set of 20 plates, 0.05 m high by 0.45 m wide, which were able to move independent of each other The plates were coated with polytetrafluoroethylene (PTFE), and were restrained against vertical displacement Horizontal displacement of the plates in different tests was resisted by springs that had different stiffness magnitudes The soil used for the model tests was Leighton Buzzard sand The backfill material was placed to a dry density of 1730 kg/m3 using a sand-raining technique A friction angle value of 49.68 2.2.2 Soil The retained soil (including the thin soil simulating the backfill/foundation interface) was modeled as a homogeneous, isotropic, nonlinear elastic-plastic material with Mohr–Coulomb failure criterion and dilation angle (nonassociated flow rule) Nonlinear elastic behavior of the soil material was simulated using the hyperbolic Young’s modulus formulation proposed by Duncan et al (1980) and the hyperbolic bulk modulus formulation described by Boscardin et al (1990) The hyperbolic model has been B ⫽ 1.92 m Vertical boundary fixed in horizontal direction H ⫽ 1.00 m The primary objective of this paper is to examine the influence of placing a panel of geofoam between the reinforced and retained zones of a typical MSE wall on the magnitude and distribution of lateral earth pressure behind the reinforced zone at the end of construction It is postulated that controlled yielding of the retained soil against the compressible inclusion (i.e geofoam panel) behind the reinforced zone can help reduce the construction-induced stresses behind the reinforced mass over the entire height of the wall In this study, a numerical modeling approach is adopted to examine the influences of geofoam compressibility, geofoam panel thickness, and reinforcement tensile modulus on the amount of reduction in facing out-of-alignment and lateral earth pressure behind the reinforced zone The same numerical model that was validated against a series of RMC test wall results (Hatami and Bathurst 2005, 2006) was modified to include a geofoam panel behind the reinforced zone In addition, capabilities of the numerical model to simulate controlled yielding of a backfill against a moving/flexible boundary (e.g backfill/geofoam interface) were validated against measured data, as described in Section The program Fast Lagrangian Analysis of Continua (FLAC; Itasca 2005) was used to carry out the numerical simulations FLAC is suitable for modeling problems that involve large deformation and plastic behavior In addition, complex user-defined constitutive models for component materials can be programmed and included in the analysis, as needed Retained soil Spring–plate system Thin soil interface layer Fixed boundary Figure FLAC numerical grid used for validation of controlled yielding numerical model against test data reported by McGown et al (1987) Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved 458 Hatami and Witthoeft used in previous studies to simulate reinforced soil wall behavior with a satisfactory level of accuracy (e.g Ling 2003; Hatami and Bathurst 2005, 2006) and it has been shown to yield accuracy comparable to that of more complex models such as single-bounding models (Ling 2003) The model walls were constructed using the material properties listed in Table The soil properties used in this study were based on the values reported by Boscardin et al (1990) for a well-graded sand compacted to 95% standard Proctor density The friction angle and density values used in this study were the same as those reported by McGown et al (1987, 1988) and Karpurapu and Bathurst (1992) A nominal cohesion value (c ¼ kPa) was assumed to account for the apparent cohesion invariably present due to moisture (i.e suction) in the backfill soil The notion of apparent cohesion in soils due to a small amount of moisture has been reported in previous reinforced soil wall studies (Cazzuffi et al 1993; Rowe and Skinner 2001; Hatami and Bathurst 2005, 2006) The model was constructed in 0.05 m lifts, and was allowed to reach equilibrium after placement of each soil layer Table Soil properties for model verification Property Value Peak friction angle,
(degrees) Cohesion, c (kPa) Dilation angle, ł (degrees) Density, rs (Mg/m3 ) Elastic modulus number, Ke Unloading–reloading modulus number, Kur Elastic modulus exponent, n Failure ratio, Rf Tangent Poisson’s ratio, t Initial bulk modulus number, Bi /pa Asymptotic volumetric strain value, u 49.6 11 1.73 950 1140 0.60 0.70 0–0.49 74.8 0.02 Note: The friction angle value at the soil/foundation interface was assumed to be the same as the soil internal friction angle value 2.2.3 Spring–plate system The system of springs and independently movable plates was modeled as a column (i.e stack) of independent linear elastic zones separated from each other through interfaces that were rigidly supported in the vertical direction (Figure 4) All gridpoints (one at each corner for a total of four) of these zones were fixed in the vertical direction to simulate the horizontal rails on which the plates were mounted (providing vertical support) In addition, the two gridpoints at the left of each zone were fixed in the horizontal direction (as shown in Figure 4) to simulate the mounting plate, which prevented global lateral (i.e rigid body) translation of the facing system All five different test cases reported by McGown et al (1987), including a rigid boundary case (i.e the vertical boundary was fixed in horizontal direction) and four cases with different spring stiffness values for the linear elastic spring–plate system, were simultaneously modeled in the present study Each of the 20 springs in the stack of springs used in the model tests (Section 2.1) was simulated using one elastic zone with material properties as listed in Table The qualifying terms used in Table to describe the stiffness of the springs are as reported by McGown et al (1987), who also reported nominal spring constants for the different springs they used in their model tests However, the actual spring constants, determined based on the measured lateral stresses and lateral displacements reported by McGown et al (1987), differed from the nominal values Therefore the Young’s modulus values for the elastic column used in the numerical model (Table 3) were calculated using the actual (i.e back-calculated) spring constants and accounting for the width of the column of linear elastic zones In order to simulate independent horizontal springs, the Poisson’s ratio values for all zones in the elastic column were assumed as  ¼ 0, and each zone in the elastic column was isolated from the neighboring zones using free-sliding interfaces so as to deform independently Rigid facing plates were simulated by attaching one structural node to each of the gridpoints of Table Elastic zone properties simulating the spring–plate system for model verification Very soft springs Soft springs Medium stiff springs Stiff springs 13.6 0.0 7.8 23.9 0.0 7.8 50.8 0.0 7.8 180 0.0 7.8 Spring–plate system Young’s modulus, E (kPa)a Poisson’s ratio,  Density, r (Mg/m3 ) Soil/plate interface Friction angle,  (degrees) Cohesion, c (kPa) Dilation angle, ł (degrees) Normal stiffness, kn ((kN/m)/m) Shear stiffness, ks ((kN/m)/m) 10 0 7000 7000 a These values correspond to a zone size of 0.05 m by 0.05 m and equivalent spring constants backcalculated from the soil pressure and boundary displacements reported by McGown et al (1987) Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved Use of geofoam to increase external stability of reinforced soil walls the elastic column (for a total of 40 structural nodes) and constraining the two structural nodes representing each plate to move together The interface strength and stiffness values reported in Table were determined by matching the lateral earth pressure distribution results obtained for the case of rigid vertical boundary with the measured values reported by McGown et al (1987) The same interface properties were subsequently (and consistently) used for all other cases that included spring–plate systems (i.e compliant boundary) as listed in Table Two of the compliant boundary systems, i.e the ‘soft’ and ‘stiff’ spring cases, were also simulated in a verification study reported by Karpurapu and Bathurst (1992) 2.3 Results Figures 5a and 5b show normalized measured and predicted distributions of horizontal stress h , evaluated at the spring–plate vertical boundary The predicated horizontal stresses are normalized with respect to ªs H, where H is the backfill height and ªs is the bulk unit weight of the soil Figure 5a shows the results for the soft spring and stiff spring cases, together with the corresponding simulated results reported by Karpurapu and Bathurst (1992) Figure 5b shows the results for the additional cases of rigid spring, very soft spring, and medium spring, which are plotted in a separate graph for clarity It can be observed that all predicted results show satisfactory agreement with the measured data with respect to both magnitudes and distributions of earth pressures for all five cases reported by McGown et al (1987) Figures 5c and 5d show values of measured and predicted lateral displacement of the model wall, ˜, normalized with respect to its height H, for all four flexible boundary cases reported by McGown et al (1987) The results shown in Figures 5c and 5d are also presented in two sections for clarity Figure 5c shows measured and predicted results for stiff and soft spring cases, together with the predicted distributions reported by Karpurapu and Bathurst (1992) for comparison Figure 5d shows results for the additional verification cases simulated in this study It can be observed that predicted values from the present study are in satisfactory agreement with the corresponding measured values for all the cases reported by McGown et al (1987) RESPONSE OF FIELD-SCALE SEGMENTAL WALLS WITH GEOFOAM PROTECTION BEHIND REINFORCED ZONE 3.1 Numerical model and material properties 3.1.1 Numerical model Following the verification of the numerical approach, as described in Section 2, a field-scale segmental retaining wall model was developed to carry out the primary analyses of this study Figure shows a typical planestrain numerical model of a m-high segmental wall used in this study The control case (i.e with zero geofoam thickness) model shown in Figure was developed using 459 FLAC models that were validated against extensive measured performance results from a series of well-instrumented 3.6 m-high prototype walls tested in a controlled laboratory environment (Hatami and Bathurst 2005, 2006; Hatami et al 2005; Bathurst and Hatami 2006) A backfill width-to-height ratio of to was adopted to represent a sufficiently wide backfill This was done to ensure that potential failure planes in the backfill would not be intercepted by the far-end boundary A fixed boundary condition in the horizontal direction was assumed at the numerical gridpoints on the backfill far-end boundary to allow for free settlement of soil along that boundary A rigid foundation beneath the backfill soil was simulated using linear elastic continuum zones fixed in the vertical and horizontal directions An interface was placed across the entire rigid foundation to allow for its interaction with the backfill soil and the bottom facing block (Hatami and Bathurst 2005, 2006) Description of the interface model is given in the FLAC manual (Itasca 2005), and the interface properties are given in Table The wall facing was modeled as a column of concrete blocks 0.15 m high 0.30 m wide, using linear elastic continuum zones with the batter angle equal to 38 The bulk and shear modulus values of the facing blocks were Kw ¼ 10 952 MPa and Gw ¼ 10 000 MPa, respectively Interfaces were used to allow for the interaction of backfill soil with the segmental facing, and for the interaction between the individual blocks Interface properties used in the wall models are listed in Table 3.1.2 Soil The soil constitutive model described in Section 2.2.2 was used to simulate the backfill material for the m wall cases with material properties as given in Table The soil model represented a good-quality granular soil (e.g wellgraded sand) with material properties as reported by Huang et al (2007) The wall models were constructed in 0.15 m backfill lifts The facing blocks, soil, reinforcement elements and geofoam panel (in models with geofoam) were constructed in layers, and the model was allowed to reach equilibrium following the placement of each layer After placement of each backfill lift, compaction was simulated by application of an kPa vertical load across the top of each soil lift It has been observed in previous studies (Hatami and Bathurst 2005) that an equivalent static vertical load may be used to approximate the effects of compaction on lateral earth pressure in the backfill and on wall facing deformation with reasonable accuracy 3.1.3 Geofoam An elasticized geofoam material model was used in this study Elasticized geofoam is produced by mechanical or thermal treatment of EPS, which results in the reduction of its Young’s modulus value but increases the range of strains for which the EPS maintains a linear response to compressive stresses (e.g Horvath 1995) Both elasticized and non-elasticized EPS have been shown to exhibit linear elastic response to compressive loading over the range of strains encountered in this study (e.g  , 5% for Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved Normalized elevation, y /H 460 Hatami and Witthoeft 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0.05 0.10 0.15 0.20 0.05 0.10 0.15 0.20 Normalized lateral earth pressure, σh /γsH McGown et al (1987), stiff McGown et al (1987), rigid McGown et al (1987), soft McGown et al (1987), medium Karpurapu and Bathurst (1992), stiff McGown et al (1987), very soft Karpurapu and Bathurst (1992), soft FLAC, medium FLAC, stiff FLAC, very soft FLAC, rigid FLAC, soft Normalized elevation, y /H (a) (b) 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Normalized lateral displacement, ∆/H (%) McGown et al (1987), stiff McGown et al (1987), medium McGown et al (1987), soft McGown et al (1987), very soft Karpurapu and Bathurst (1992), stiff FLAC, medium Karpurapu and Bathurst (1992), soft FLAC, very soft FLAC, stiff FLAC, soft (c) (d) Figure (a, b) Measured and predicted lateral stress distributions at end of construction; (c, d) wall lateral displacements at end of construction elasticized geofoam and  , 0.5% for stiff non-elasticized geofoam: Horvath 1995; Athanasopoulos et al 1999) Therefore all geofoam types were modeled as linear elastic materials The density of the geofoam was assumed to be 20 kg/m3 , which is within the range 11–50 kg/m3 reported in the literature (e.g Negussey and Jahanandish 1993; Horvath 1995; Koerner 2005) The geofoam control stiffness value was selected as Ef ¼ 250 kPa, based on a Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved Use of geofoam to increase external stability of reinforced soil walls 461 Vertical boundary fixed in horizontal direction L ⫽ 3.9 m Geofoam panel Retained zone Reinforced zone Reinforcement layers at 0.6 m spacing (layer number increases upward from layer at 0.3 m from foundation) H ⫽ 6.0 m Segmental facing with 3° batter Interfaces Rigid foundation B ⫽ 12.0 m Figure Typical FLAC numerical grid for m-high segmental wall simulations Table Interface properties for m-high segmental wall models Table Soil properties for m-high segmental wall models Property Property Peak friction angle,
(degrees) Cohesion, c (kPa) Dilation angle, ł (degrees) Density, rs (Mg/m3 ) Elastic modulus number, Ke Unloading–reloading modulus number, Kur Elastic modulus exponent, n Failure ratio, Rf Tangent Poisson’s ratio, t Initial bulk modulus number, Bi /pa Asymptotic volumetric strain value, u Block/block interface Friction angle,  (degrees) Cohesion, c (kPa) Dilation angle, ł (degrees) Normal stiffness, kn ((kN/m)/m) Shear stiffness, ks ((kN/m)/m) 57 45.7 11 106 1000 Soil/block interface Friction angle,  (degrees) Cohesion, c (kPa) Dilation angle, ł (degrees) Normal stiffness, kn ((kN/m)/m) Shear stiffness, ks ((kN/m)/m) 48 11 105 1000 Soil/foundation interface and block/foundation interface Friction angle,  (degrees) Cohesion, c (kPa) Dilation angle, ł (degrees) Normal stiffness, kn ((kN/m)/m) Shear stiffness, ks ((kN/m)/m) Value Value 48 0 106 106 mechanical response curve reported by Horvath (1995) A geofoam Poisson’s ratio value of f ¼ 0.1 was calculated according to the regression equation suggested by Horvath (1995), a 48 11 1.68 950 1140 0.60 0.70 0–0.49a 74.8 0.02 The range of permissible values f ẳ 0:0056rf ỵ 0:0024 (1) where f and rf are the geofoam Poisson’s ratio and density (in kg/m3 ), respectively However, Equation does not account for the dependence of geofoam Poisson’s ratio value on confining pressure as reported in earlier studies (e.g Negussey and Jahanandish 1993; Preber et al 1994; Horvath 1995) The effective Poisson’s ratio value for the range of confining pressure values applicable to model walls examined in this study is approximately zero (Preber et al 1994) Furthermore, it was observed that the variation of Poisson’s ratio value within the range f ¼ 0–0.1 did not result in significant variation in predicted geofoam performance Therefore results for the f ¼ case are reported throughout this paper The value f ¼ Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved 462 Hatami and Witthoeft is also consistent with the Poisson’s ratio value used in the verification study reported in Section 2.2.3 A geofoam stiffness value Ef ¼ 8000 kPa was also included to broaden the range of stiffness values investigated in the parametric study This value is greater than the typical values expected for elasticized geofoams, and was calculated using the following empirical relationship for nonelasticized geofoams, as reported by Athanasopoulos et al (1999): Ef ¼ 16:431
1:645rf ỵ 0:061r2f (2) The results presented by Athanasopoulos et al (1999) of monotonic compression tests on EPS with a density of 20 kg/m3 corroborate the estimated value of Ef ¼ 8000 kPa Another estimate for non-elasticized geofoam elastic modulus values using the relation Ef ¼ 0:45rf
(3) results in the value Ef ¼ 6000 kPa, which is within the range of Ef values examined in this study An intermediate stiffness value of Ef ¼ 1000 kPa was also included in the parametric study Five different (non-zero) geofoam thickness values were examined in the numerical models, as reported in Table During construction of the wall model the geofoam layer was placed behind the reinforced mass incrementally as the backfill lifts were constructed and the model was brought to equilibrium A similar procedure can be used to place the geofoam panels in the field, in which the height of each panel is chosen to be the same as each backfill lift 3.1.4 Reinforcement Reinforcement layers in the FLAC simulations were modeled using two-noded elastic-plastic cable elements with strain-dependent tangent tensile modulus J t (, t ) in the form J t , tị ẳ  1  tị J tị ỵ  J tÞ T f ð tÞ (4) 2 where J0 is the initial tensile modulus, Tf (t ) is the tensile failure (or rupture) strength, and (t ) is a scaling function The tensile modulus of each reinforcement element in the FLAC numerical code is continuously updated, based on the calculated axial strain during construction or surcharge Table Geofoam material properties Property Young’s modulus, Ef (kPa) Poisson’s ratio, f Thickness, tf (m) Density, rf (Mg/m3 ) Values 250a , 1000, 8000b 0.0 0, 0.0375, 0.075, 0.15, 0.30, 0.60c 0.02 a Based on load–displacement response of an elasticized geofoam reported by Horvath (1995) b Calculated using Equation c For Ef ¼ 1000 kPa and 8000 kPa only loading of the wall using Equation Hatami and Bathurst (2006) determined J t (, t ) using the isochronous data from creep tests carried out on commercially available polypropylene (PP) and polyester (PET) geogrid products for durations in the range h < t < 1000 h They used the 1000 h isochronous results to simulate the construction of a series of instrumented full-scale test walls The duration of 1000 h may also be considered as a representative construction time for MSE walls in the field Hatami and Bathurst (2006) found that the long-term tensile response of PET reinforcement was practically linear (i.e (t )  0) In the present study, a PET reinforcement with J ¼ 500 kN/m and (t ) ¼ was used for MSE wall models with geosynthetic reinforcement In addition, the values J ¼ 69 000 kN/m and (t ) ¼ were used to model walls with metallic reinforcement (Bathurst and Hatami 1998) Both reinforcement types were assumed to have no compressive strength The reinforcement rupture strength values for geosynthetic and metallic reinforcement materials were assumed as Tr ¼ 50 kN/m and 150 kN/m, respectively Relatively high tensile strength values were assumed for the reinforcement materials to ensure that reinforcement rupture was not encountered as a failure mechanism in the simulations The results of previous experimental and numerical studies (Hatami and Bathurst 2005, 2006) have indicated that reinforcement rupture (or even reinforcement slippage within the backfill) is highly unlikely at the end of wall construction No indication of reinforcement rupture or slippage was observed in a series of well-instrumented full-scale (i.e 3.6 m high) test walls that were purposely designed with minimum factors of safety against internal instability Therefore the reinforcement nodes were rigidly attached to the backfill grid points to simulate a perfect bond between the soil and reinforcement layers This significantly reduced the computation time of the simulations 3.2 Results 3.2.1 Lateral earth pressures in the backfill Figure shows predicted distributions of lateral earth pressure acting on the reinforced zone at the end of wall construction Figures 7a and 7b show results for Ef ¼ 250 kPa with J ¼ 500 kN/m and J ¼ 69 000 kN/m, respectively Figures 7c and 7d show corresponding results for the case with Ef ¼ 1000 kPa, and Figures 7e and 7f likewise show results for the case with Ef ¼ 8000 kPa Lateral earth pressure distributions for the at-rest state (using Jaky’s equation) and active state as predicted by both Rankine theory and Coulomb theory (for no-geofoam cases) are also plotted in Figure for comparison The results predicated using Coulomb theory are based on the assumption that the interface friction angle (i.e backfill soil friction angle) is fully mobilized Note that only the horizontal component of Coulomb earth pressure is shown, for consistency Owing to the structural flexibility inherent in the reinforced zone, the mobilized friction angle at the interface between the reinforced and retained zones is likely to be negligible, and Coulomb lateral earth pressure theory is reduced to Rankine theory at this boundary This is confirmed by the results shown in Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved Use of geofoam to increase external stability of reinforced soil walls 1.0 1.0 No geofoam 3.75 cm 7.5 cm 15 cm 30 cm 60 cm Jaky at-rest Rankine active Coulomb active 0.8 0.6 0.4 463 No geofoam 3.75 cm 7.5 cm 15 cm 30 cm 60 cm Jaky at-rest Rankine active Coulomb active 0.8 0.6 0.4 0.2 0.2 0 0.1 0.2 0.3 0.1 (a) 1.0 Normalized elevation, y /H 0.2 0.3 (b) 1.0 No geofoam 3.75 cm 7.5 cm 15 cm 30 cm 60 cm Jaky at-rest Rankine active Coulomb active 0.8 0.6 0.4 No geofoam 3.75 cm 7.5 cm 15 cm 30 cm 60 cm Jaky at-rest Rankine active Coulomb active 0.8 0.6 0.4 0.2 0.2 0 0.1 0.2 0.3 0.1 (c) 0.2 0.3 (d) 1.0 1.0 No geofoam 3.75 cm 7.5 cm 15 cm 30 cm 60 cm Jaky at-rest Rankine active 0.8 0.6 0.4 No geofoam 3.75 cm 7.5 cm 15 cm 30 cm 60 cm Jaky at-rest Rankine active Coulomb active 0.8 0.6 0.4 0.2 0.2 0 0.1 0.2 0.3 (e) 0.1 0.2 0.3 (f) Normalized lateral earth pressure, σh /γsH Figure Lateral earth pressure distributions at end of construction for models with (i.e different tf values) and without geofoam behind reinforced zone: (a) J 500 kN/m, Ef 250 kPa; (b) J 69 000 kN/m, Ef 250 kPa; (c) J 500 kN/m, Ef MPa; (d) J 69 000 kN/m, Ef MPa; (e) J 500 kN/m, Ef MPa; (f) J 69 000 kN/m, Ef MPa Figure 7, which indicate that active pressures developed as a result of using adequate geofoam thickness at this location approach the magnitudes predicted using Rankine theory, as opposed to the values corresponding to the horizontal component of Coulomb theory The results shown in Figure also indicate that lateral earth pressure distributions predicted using FLAC for both the geofoam and no-geofoam cases generally fall between the analytical values for the at-rest and active conditions However, lateral earth pressure values for the no-geofoam cases tend to approach the at-rest conditions over the lower half of the wall The results shown for geosyntheticreinforced soil wall models (i.e Figures 7a, 7c and 7e) indicate that lateral earth pressure values near the top of the retained zone are comparable to the Rankine’s active values, regardless of the geofoam thickness (including tf ¼ 0) This is due to the greater lateral deformation of the reinforced mass at the top However, Figures 7b, 7d and 7f indicate that greater local lateral earth pressure values approaching, or even exceeding, the at-rest conditions could be expected for the metallic reinforced cases This is explained by the fact that reinforced zones with a stiffer reinforcement (i.e metallic reinforcement with J ¼ 69 000 kN/m) undergo smaller lateral deformations, and hence can generate greater local, compaction-induced lateral earth pressure magnitudes, as compared with reinforced zones with relatively extensible reinforcement (i.e geosynthetic reinforcement with J ¼ 500 kN/m) The influence of backfill compaction to increase lateral earth pressure values was verified in this study by comparing the lateral earth pressure distributions shown in Figure with the results obtained for otherwise identical cases where backfill compaction was not simulated in the models However, the latter results are not shown here, for brevity Increased (i.e locked-in) lateral earth stresses on rigid and MSE walls as a result of backfill compaction have been discussed in previous studies (e.g Ingold, 1979, 1983; Duncan et al 1991; Filz and Duncan 1996) Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved 464 Hatami and Witthoeft 70 60 Optimal thickness, (t f )opt The results shown in Figure clearly show that placement of geofoam behind the reinforced zone could alleviate compaction-induced stresses behind the reinforced mass The magnitude of reduction in lateral earth pressure is overall a function of geofoam stiffness and thickness, and could be significant (e.g as great as 50%) over the lower half of the wall height, where the nogeofoam earth pressure values are generally the greatest Reduced lateral earth pressure magnitudes observed in Figure as a result of placing geofoam behind the reinforced zone are in general agreement with similar reductions behind rigid retaining walls reported in earlier studies (e.g Horvath 1991a; Koerner 2005) As illustrated in Figure 7, the amount of reduction in lateral earth pressure behind the reinforced zone increases with panel thickness for the relatively stiff geofoam materials (i.e cases with Ef ¼ 1000 kPa and 8000 kPa) In contrast, for a significantly compressible geofoam (e.g Ef ¼ 250 kPa), only a relatively thin panel (i.e tf ¼ 3.75 cm or slightly thicker) would be required to reduce the magnitudes of lateral earth pressure behind the reinforced mass to those corresponding to an active state for both extensible (i.e geosynthetic) and relatively inextensible (i.e metallic) reinforcement cases (Figures 7a and 7b) Assuming the geofoam panel as a stack of horizontal 1-D structural elements with Young’s modulus Ef and length tf (i.e panel thickness), the axial (i.e horizontal) stiffness of these elements (and therefore the lateral stiffness of the geofoam panel) is proportional to the ratio Ef /tf Therefore increasing the panel thickness while holding the Young’s modulus constant results in lower panel lateral stiffness without any upper limit However, in the context of interaction with the backfill soil, there is an expected upper-bound geofoam thickness value beyond which no further reduction in the lateral earth pressure could be achieved (i.e reduction below the active state value) This phenomenon can be observed in the trend of lateral earth pressure magnitudes plotted in Figure 7, which were used to determine the variation of resultant lateral earth force behind the reinforced zone, FE, with tf The variations of FE with tf plotted for geosynthetic and metallic reinforced soil wall models indicated optimum geofoam thickness values, (tf )opt , needed to reduce the lateral earth pressure behind the reinforced zone to a level comparable to Rankine active state values The results shown in Figure show the dependence of (tf )opt on the geofoam Young’s modulus for the parametric values used in this study For instance, the required geofoam thickness in order to achieve an active state increases with geofoam stiffness from 7.5 cm for Ef ¼ 250 kPa to at least 60 cm for Ef ¼ 8000 kPa It can also be observed that the value of (tf )opt is essentially the same for both geosynthetic and metallic reinforced walls for the case of more flexible geofoams The existence of an optimum geofoam thickness in reducing lateral earth pressure behind retaining walls has also been noted in previous studies (e.g Hazarika et al 2002) Figures and 10 show the influences of geofoam stiffness and thickness, and that of the reinforcement 50 40 30 20 10 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Geofoam stiffness, Ef Figure Influence of geofoam stiffness on optimal geofoam thickness to achieve active state behind reinforced zone tensile modulus on the predicted lateral earth force FE behind the reinforced zone, its line of action yR, and the resulting overturning moment M, in normalized form The results shown in Figures and 10 also indicate that the amount of reduction in lateral earth pressure behind the reinforced zone is a function of both geofoam stiffness and thickness These results show that for the 6m-high wall models and range of material properties investigated, total lateral earth force behind the reinforced zone and overturning moment about the wall toe could be reduced significantly (i.e by as much as 31% and 26%, respectively) with a sufficiently compressible and thick geofoam panel (e.g Figures 9c and 10c with Ef ¼ 250 kPa and tf ¼ 0.60 m) These results also indicate that slightly greater reduction in the magnitudes of lateral earth force and overturning moment would be expected in reinforced zones with more extensible (i.e geosynthetic) reinforcement In all cases shown in Figures and 10, as the geofoam stiffness value increases, the magnitudes of lateral earth force and overturning moment approach those of the control (i.e no-geofoam) case Within the same range of parametric values examined, the elevation (i.e line of action) of the lateral earth force behind the reinforced zone increases by only a slight amount (i.e by a maximum of about 9%) with geofoam compressibility and, conversely, approaches the level for the control case value (i.e yR /H ¼ 0.33) from the top as the Ef value increases 3.2.2 Facing out-of-alignment Figure 11 shows facing out-of-alignment results at the end of wall construction Out-of-alignment as presented herein is defined as the difference between the actual final position of the facing column at the end of construction and the position based on a target batter angle of 38 from the vertical Figures 11a and 11b show predicted out-ofalignments for geofoam stiffness Ef ¼ 250 kPa with J ¼ 500 kN/m and J ¼ 69 000 kN/m, respectively Figures 11c and 11d and Figures 11e and 11f show corresponding results for Ef ¼ 1000 kPa and Ef ¼ 8000 kPa, respectively, for all geofoam thickness values examined in this study Comparison of no-geofoam cases for the two reinforce- Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved Use of geofoam to increase external stability of reinforced soil walls 1.0 1.5 0.8 1.0 Normalized lateral earth force, FE /0.5K0γs H 0.6 0.8 1.0 0.6 0.4 0.5 0.4 0.5 0.2 100 1000 (a) 1.5 10 000 1.0 0.2 100 1000 (b) 1.0 1.5 0.8 1.0 0.6 0.8 1.0 0.6 0.4 0.5 0.4 0.5 0.2 100 10 000 Normalized elevation of resultant, yR /H 1.0 1.5 465 1000 (c) 10 000 0.2 100 1000 (d) 10 000 Geofoam Young’s modulus, Ef (kPa) Geofoam, lateral force No geofoam, lateral force Geofoam, line of action No geofoam, line of action Figure Variation of predicted lateral earth force behind reinforced zone and its line of action with geofoam stiffness value: (a) J 500 kN/m, tf 0.0375 m; (b) J 69 000 kN/m, tf 0.0375 m; (c) J 500 kN/m, tf 0.60 m; (d) J 69 000 kN/m, tf 0.60 m ment types shown in Figures 11a and 11b indicates that magnitudes of the predicted facing out-of-alignment at end of construction are smaller (by as much as 60%) in a wall with metallic reinforcement than in an otherwise identical wall with more extensible (i.e geosynthetic) reinforcement for the reinforcement tensile modulus values examined in this study The results shown in Figure 11 indicate that placement of geofoam behind the reinforced zone does reduce the magnitude of predicted facing out-of-alignment at the end of construction The maximum reduction values obtained in the results shown in Figure 11 (i.e compared with the corresponding no-geofoam cases) are 35% for the geosynthetic reinforcement (Figure 11a) and 60% for the metallic reinforcement cases (Figure 11b), respectively These reduction magnitudes are predicted for the case of a sufficiently compressible (i.e Ef ¼ 250 kPa) and thick (i.e tf ¼ 0.60 m) geofoam It can be observed in Figure 11 that the effectiveness of the geofoam panel in reducing the facing out-of-alignment increases with its thickness and compressibility The influence of panel thickness in reducing wall facing deformation is substantially reduced for stiffer geofoams, and becomes negligible for Ef ¼ 8000 kPa 3.2.3 Reinforcement strains Figure 12 shows typical plots of reinforcement strains at the end of construction as obtained in this study Separate panes within Figures 12a and 12b correspond to individual reinforcement layers vertically spaced as shown in Figure Figure 12a compares the results for two extreme cases of a no-geofoam wall model and a model with Ef ¼ 250 kPa and tf ¼ 0.60 m, both with reinforcement tensile modulus value J ¼ 500 kN/m Figure 12b shows corresponding results for J ¼ 69 000 kN/m Comparison of the no-geofoam cases between Figures 12a and 12b shows that magnitudes of reinforcement strains are significantly smaller in metallic reinforcement than in the more extensible geosynthetic reinforcement However, the maximum reinforcement load in the metallic reinforced wall model (not shown) was determined to be about three times as great as that in the geosynthetic-reinforced wall This observation (i.e development of greater axial loads in stiffer reinforcement layers) is consistent with both measured and predicted results reported in previous studies (Bathurst and Hatami 1998, 2006; Hatami and Bathurst 2006) It is also observed from Figure 12 that the overall locations of maximum reinforcement strains depend on the reinforcement tensile modulus In more extensible (i.e geosynthetic) reinforcement layers maximum strains develop at the connection with the facing, whereas in very stiff (i.e metallic) reinforcement, maximum strains develop within the backfill away from the facing The reason for this difference is that a wall with more extensible reinforcement undergoes greater lateral displacement, and backfill settles more behind the hard facing The resulting Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved Normalized overturning moment, M/[0.5KaγsH ⫻ (H/3)] 466 Hatami and Witthoeft 1.5 1.5 1.0 1.0 0.5 0.5 0 100 1000 10 000 100 1000 (b) 10 000 100 1000 10 000 (a) 1.5 1.5 1.0 1.0 0.5 0.5 0 100 1000 10 000 (d) (c) Geofoam Young’s modulus, Ef (kPa) Geofoam No geofoam Figure 10 Variation of predicted overturning moment about wall toe with geofoam stiffness value: (a) J 500 kN/m, tf 0.0375 m; (b) J 69 000 kN/m, tf 0.0375 m; (c) J 500 kN/m, tf 0.60 m; (d) J 69 000 kN/m, tf 0.60 m downdrag forces in the reinforcement layers (i.e the connection loads) are therefore comparatively greater in geosynthetic-reinforced walls than in walls with metallic reinforcement The concept of downdrag forces behind hard facing of reinforced soil walls has been discussed in several previous studies (e.g Bathurst et al 2001; Elias et al 2001; NCMA 2002; Hatami and Bathurst 2005, 2006; Koerner 2005) Comparison of the geofoam cases with the corresponding no-geofoam cases in Figure 12 shows that, for the most part, the distribution and magnitude of strains in all reinforcement layers remain unaffected by the presence of geofoam However, reinforcement strains toward the tail end of each layer are slightly greater in the cases that include a geofoam panel behind the reinforced zone This mobilization of reinforcement strains is a result of local soil deformation toward the geofoam panel However, in none of the geofoam models were the magnitudes of increased reinforcement strains at their tail end greater than the maximum values in the same layers Therefore placement of geofoam behind the reinforced mass of segmental retaining walls is not believed to adversely affect the internal stability of the reinforced zone CONCLUSIONS As a result of increased lateral stresses due to compaction, the assumption of a fully developed active state (e.g Rankine Ka value) behind the reinforced zone of MSE structures in current design approaches may not be realistic In this study, lateral earth pressure magnitudes behind the reinforced mass of six 3.6 m-high test walls were predicted using a validated numerical model It was shown that, except for a small area near the top of the wall, lateral earth pressure magnitudes behind the reinforced mass are likely to be greater than the active state values Since additional stresses due to compaction are not included in the current external stability analysis procedures for MSE walls, actual factors of safety against both lateral sliding and overturning could be considerably smaller than those calculated using active state earth pressures In this study, the possibility of using geofoam to reduce lateral earth pressure behind the reinforced zone in MSE walls was investigated using a numerical simulation approach It was postulated that controlled yielding behind the reinforced zone would help reduce these pressures to the levels approaching the active state and hence increase the external stability of the reinforced mass The study included different geofoam stiffness and thickness configurations The backfill type examined represented a wellcompacted select soil (i.e a drainable soil with a high friction angle value), as recommended by current design guidelines and specifications The reinforcement types examined included stiffness values representative of both geosynthetic and metallic materials The constitutive model for the retained soil was validated in this study using measured results for lateral earth Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved Use of geofoam to increase external stability of reinforced soil walls 1.0 1.0 0.8 0.8 0.6 467 0.6 No geofoam No geofoam 3.75 cm 3.75 cm 0.4 0.4 7.5 cm 7.5 cm 15 cm 0.2 15 cm 30 cm 0.2 30 cm 60 cm 60 cm 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.1 Normalized elevation, y /H (a) 0.2 0.3 (b) 1.0 1.0 0.8 0.8 No geofoam 0.6 0.6 No geofoam 3.75 cm 0.4 3.75 cm 0.4 7.5 cm 7.5 cm 15 cm 0.2 15 cm 0.2 30 cm 30 cm 60 cm 60 cm 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.1 (c) 0.2 0.3 (d) 1.0 1.0 0.8 0.8 0.6 0.6 No geofoam No geofoam 3.75 cm 3.75 cm 0.4 0.4 7.5 cm 7.5 cm 15 cm 15 cm 0.2 0.2 30 cm 30 cm 60 cm 60 cm 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (e) 0.1 0.2 0.3 (f) Normalized out-of-alignment, ∆OOA/H (%) Figure 11 Facing out-of-alignment at the end of construction for models with (i.e different tf values) and without geofoam behind reinforced zone: (a) J 500 kN/m, Ef 250 kPa; (b) J 69 000 kN/m, Ef 250 kPa; (c) J 500 kN/m, Ef MPa; (d) J 69 000 kN/m, Ef MPa; (e) J 500 kN/m, Ef MPa; (f) J 69 000 kN/m, Ef MPa pressure behind a movable boundary and its deformation from a series of reduced-scale controlled yielding tests reported in the literature Predicted and measured results were shown to be in satisfactory agreement for all five different boundary stiffness conditions tested The numerical model used in this study to investigate the influence of a geofoam panel behind the reinforced zone on the response of segmental retaining walls had been validated against test data from several carefully constructed and well-instrumented full-scale test walls The results of this study indicate that placement of a geofoam panel behind the reinforced zone of segmental reinforced soil walls could significantly reduce the magnitudes of lateral earth pressure behind the reinforced mass and facing deformation, depending on the geofoam stiffness and panel thickness The findings of this study could have important implications for both the external stability and the serviceability of MSE walls In addition to the abatement of compaction-induced lateral stresses in the backfill, the placement of geofoam behind the reinforced mass might lead to cost savings such as the cost of reinforcement and select fill material Alternatively, the use of geofoam behind the reinforced zone could be beneficial in situations where limited space is available to construct the reinforced mass, such as in the construction of shored MSE walls (e.g Morrison et al 2006) It is concluded that installing a panel of geofoam with sufficient thickness and compressibility could reduce the lateral earth force behind the reinforced zone and overturning moment by as much as 31% and 26%, respectively The abating effect of an extremely compressible geofoam panel (e.g Ef ¼ 250 kPa) was found to be independent of its thickness On the other hand, the influence of geofoam panel thickness on the size of reduction in facing deformation was found to be significant for extremely compressible geofoam The influence of geofoam on internal stability (represented by maximum reinforcement strain) was found to be relatively insignificant It is important to note that the numerical results Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved 468 Hatami and Witthoeft 1.0 0.02 Layer 10 0.5 0 1.0 0.02 Layer 0.5 Layer 0.01 0 Strain (%) Layer 10 0.01 1.0 0.02 Layer 0.5 Layer 0.01 0 4 0.02 1.0 Layer Layer 0.01 0.5 0 1.0 0.02 Layer Layer 0.5 0.01 0 (a) (b) Distance from back of the facing (m) Geofoam No geofoam Figure 12 Reinforcement load distributions at the end of construction (Ef 250 kPa): (a) J Note: for brevity, only the results for alternate reinforcement layers are shown reported in this study are subject to several assumptions with respect to the material models, wall height and geometry, foundation condition and wall type Nevertheless, the broad conclusions reported in this paper are believed to remain valid ACKNOWLEDGEMENTS The financial support of the Office of the Vice President for Research at the University of Oklahoma during the course of this study through the Junior Faculty Research Program Award is acknowledged NOTATIONS FE Gw H J, J t (, t ) J0 (t ) kn ks K Ka Ke K0 Kur Basic SI units are given in parentheses B Bi c E Ef backfill width (m) soil initial bulk modulus number (dimensionless) backfill cohesion (Pa) Young’s modulus (Pa) geofoam Young’s modulus (Pa) Kw L M n pa Rf 69 000 kN/m resultant lateral earth force behind reinforced zone (N/m) shear modulus of wall facing blocks (Pa) wall height (m) reinforcement tensile modulus (N/m) reinforcement initial tensile modulus (N/m) interface normal stiffness ((N/m)/m) interface shear stiffness ((N/m)/m) lateral earth pressure coefficient (dimensionless) active lateral earth pressure coefficient (dimensionless) soil elastic modulus number (dimensionless) at-rest lateral earth pressure coefficient (dimensionless) soil unloading–reloading modulus number (dimensionless) bulk modulus of wall facing blocks (Pa) reinforcement length (m) overturning moment about wall toe (N.m/m) soil elastic modulus exponent (dimensionless) atmospheric pressure (Pa) failure ratio (dimensionless) Geosynthetics International, 2008, 15, No Downloaded by [ UC San Diego Libraries] on [14/09/16] Copyright © ICE Publishing, all rights reserved 500 kN/m; (b) J Use of geofoam to increase external stability of reinforced soil walls t tf (tf )opt Tf (t ) Tr y yR z ªs ˜ ˜OOA   u (t )  f t rf rs h v
ł reinforcement creep time (s) geofoam thickness (m) optimal (i.e required to achieve active state) geofoam thickness (m) reinforcement failure stress in Equation (N/m) reinforcement rupture strength used in numerical models (N/m) elevation along wall height (m) line of action of resultant lateral earth force behind reinforced zone (m) depth in backfill (m) backfill soil unit weight (N/m3 ) lateral displacement in the backfill (or, of wall facing) (m) out of alignment of wall facing (m) interface friction angle (degrees) axial strain (dimensionless) soil asymptotic volumetric strain (dimensionless) scaling function (dimensionless) Poisson’s ratio of elastic column (dimensionless) geofoam Poisson’s ratio (dimensionless) soil tangent Poisson’s ratio (dimensionless) geofoam density (kg/m3 ) soil density (kg/m3 ) horizontal (lateral) stress in backfill (Pa) vertical stress in backfill (Pa) backfill angle of internal friction (degrees) backfill dilation angle (degrees) REFERENCES AASHTO 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