A simple displacement model for response analysis of EPS geofoam seismic buffers

ARTICLE IN PRESS Soil Dynamics and Earthquake Engineering 27 (2007) 344–353 www.elsevier.com/locate/soildyn A simple displacement model for response analysis of EPS geofoam seismic buffers Richard J Bathursta,, Amin Keshavarzb,1, Saman Zarnanic, W Andy Takeb a GeoEngineering Centre at Queen’s-RMC, Department of Civil Engineering, 13 General Crerar, Sawyer Building, Room 2085, Royal Military College of Canada, Kingston, Ont., Canada K7K 7B4 b GeoEngineering Centre at Queen’s-RMC, Queen’s University, Kingston, Ont., Canada K7L 3N6 c GeoEngineering Centre at Queen’s-RMC, Department of Civil Engineering, Queen’s University, Kingston, Ont., Canada K7L 3N6 Received 28 July 2006; accepted 31 July 2006 Abstract A simple displacement-type block model is proposed to compute the compression–load–time response of an idealized seismic buffer placed against a rigid wall and used to attenuate earthquake-induced dynamic loads The seismic buffer is modelled as a linear elastic material and the soil wedge shear surface by a stress-dependent linear spring The model is shown to capture the trends observed in four physical reduced-scale model shaking table tests carried out with similar boundary conditions up to a base excitation level of about 0.7g In most cases, quantitative predictions are in reasonable agreement with physical test results The model is simple and provides a possible framework for the development of advanced models that can accommodate more complex constitutive laws for the component materials and a wider range of problem geometry r 2006 Elsevier Ltd All rights reserved Keywords: Geofoam; Expanded polystyrene; Earthquake; Seismic buffer; Displacement model; Shaking table; Numerical modelling; Physical testing Introduction The concept of reducing the magnitude of static earth pressures against rigid wall structures by placing a compressible vertical inclusion between the wall and the retained soil has been demonstrated in the laboratory [1,2] and in the field [3] A suitably selected compressible vertical inclusion will allow sufficient lateral expansion of soil (controlled yielding) such that the retained soil is at or close to active failure and hence the earth pressures against the rigid structure are (according to classical earth pressure theory) at a minimum value Today, the compressible vertical inclusion material of choice is block-moulded low-density expanded polystyrene (EPS), which is classified as a ‘‘geofoam’’ material in modern geosynthetics terminology [4] Corresponding author Tel.: +1 613 541 6000x6479/6347/6391; fax: +1 613 545 8336 E-mail address: bathurst-r@rmc.ca (R.J Bathurst) Permanent address: Civil Engineering Department, School of Engineering, Shiraz University, Iran 0267-7261/$ - see front matter r 2006 Elsevier Ltd All rights reserved doi:10.1016/j.soildyn.2006.07.004 Karpurapu and Bathurst [5] used a non-linear finite element code to numerically simulate the controlled yielding concept for static load conditions The accuracy of the code was verified using the results of the small-scale model test results reported by McGown and co-workers [1,2] The code was then used to carry out a numerical parametric study to develop a series of design charts for the proper selection of the modulus and thickness of the compressible layer for a given wall height and soil type The first reported field installation of a compressible inclusion to attenuate seismic-induced lateral earth forces against a rigid wall structure was described by Inglis et al [6] Panels of EPS from 450 to 610 mm thick were placed against rigid basement walls up to m in height at a site in Vancouver, BC Analyses using the program FLAC [7] showed that a 50% reduction in lateral loads could be expected during a seismic event compared to a rigid wall solution Hazarika et al [8], Zarnani et al [9] and Bathurst et al [10] performed physical shaking table tests on reducedscale models to examine the hypothesis that the concept of ARTICLE IN PRESS R.J Bathurst et al / Soil Dynamics and Earthquake Engineering 27 (2007) 344–353 Nomenclature xi A,B,C,D,E constant coefficients b width of the geofoam buffer d width of direct shear box Eb modulus of elasticity of buffer Es modulus of elasticity of soil Fi total force acting on soil wedge in the i direction g acceleration due to gravity H height of wall k spring stiffness kmax maximum spring stiffness kN i normal spring stiffness at boundary i kSi shear spring stiffness at boundary i ksoil soil–soil interface stiffness L length of soil shear surface m mass of soil wedge Ni normal force at boundary i Si shear force at boundary i t time W width of soil wedge and buffer in plane strain direction u€ g horizontal acceleration x_ i x€ i earth force reduction using a compressible inclusion placed against a rigid wall can be extended to the case of dynamic earth loading The test data from Hazarika et al [8] showed that the peak lateral loads acting on the compressible model walls were reduced from 30% to 60% of the value measured for the nominally identical structure but with no compressible inclusion The test results by Zarnani et al [9] show that the magnitude of dynamic lateral earth force attenuation increased with decreasing geofoam modulus For the best case, the total earth force acting against the rigid wall during seismic shaking was reduced to 60% of the value for the nominally identical structure without a geofoam buffer inclusion The results of numerical modelling reported in the current paper are compared to physical test results reported by Zarnani et al [9] and Bathurst et al [10] a Dd Dni Dsi Dt Dtc b d f rb sn t m w horizontal displacement of soil wedge in the i direction horizontal velocity of soil wedge in the i direction horizontal acceleration of soil wedge in the i direction inclination angle of soil shear surface horizontal shear displacement in direct shear box test incremental normal displacement in the direction of Ni incremental sliding displacement in the direction of Si time step critical time step mass damping factor interface friction angle between soil wedge and buffer soil friction angle density of EPS geofoam buffer normal stress shear stress interface friction coefficient soil stress factor backfill soil from the heel of the buffer at a to the horizontal The system of forces acting on the block is shown in Fig Here, m is the mass of the soil block and uăg and g are the corresponding accelerations in the horizontal and vertical directions, respectively Here we assume that only seismic-induced horizontal ground motions occur Hence, the model is excited using a forcing function uăg(t) representing a prescribed horizontal ground acceleration record The normal and shear forces acting at the block boundaries are denoted as Ni and Si, respectively Numerical model 2.1 Block wedge A simple one-block model is proposed for calculating the dynamic response analysis of seismic buffer retaining walls The soil wedge is modelled as a rigid block under plane strain conditions Fig shows the problem geometry representing an idealized seismic buffer placed between a rigid retaining wall and soil Parameters H and b are the height and width of the geofoam buffer, respectively A linear failure plane is assumed to propagate through the 345 Fig General arrangement for geofoam buffer wall ARTICLE IN PRESS 346 R.J Bathurst et al / Soil Dynamics and Earthquake Engineering 27 (2007) 344–353 Fig Forces acting on soil wedge Fig Block forces and deformations 2.2 Numerical approach The solution scheme used in this investigation is based on an explicit time-marching finite difference approach, which is commonly used for the solution of discrete element problems (e.g [11–13]) The approach has been modified in this study to consider the compressible geofoam-soil boundary condition and changes in geometry of the soil wedge (block) At each time step, the numerical scheme involves the solution of the equations of motion for the block followed by calculation of the forces Fig Springs used in the block model The forces at the boundaries are computed using linear spring models (Fig 3) described later in the paper The compression-only force developed at the boundary between the soil wedge and geofoam buffer is computed using a single linear compression-only spring (kN ) The linear normal spring acting at the soil–soil wedge boundary (kN ) permits tension and compression but was observed to develop only compressive forces during computation cycles The shear springs at block boundaries are modelled as stress-dependent linear-slip elements to permit plastic sliding The displacements and forces for the model are shown in Fig Forces Fi are the force components assumed to act at the centre of gravity of the soil wedge The displacement of the soil wedge can be defined by horizontal and vertical displacements computed at the centre of gravity of the mass In reality the soil wedge is constrained to displace laterally The small volume of soil at toe of the wedge is neglected to simplify the model 2.2.1 Equations of motion If xi is the displacement of the soil wedge in the i direction and Fi is the force acting on the block, then Newton’s second law can be written as dx_ i F i ¼ , (1) dt m where x€ i , x_ i and m are the acceleration, velocity and mass of the wedge and t is time Using a central difference approximation with time step Dt x i ẳ dx_ i x_ i ịtỵDt=2  x_ i ịtDt=2 ẳ dt Dt Substituting Eq (2) into (1) (2) Fi Dt (3) m The updated displacements at the end of each time step can be calculated from x_ i ịtỵDt=2 ẳ x_ i ịtDt=2 ỵ xi ịtỵDt ẳ xi ịt ỵ Dtx_ i ịtỵDt (4) 2.2.2 Force equations The normal and shear forces at the block boundaries are calculated from the following force–displacement laws: ðN i ịtỵDt ẳ N i ịt  Dni kN i , (5) ARTICLE IN PRESS R.J Bathurst et al / Soil Dynamics and Earthquake Engineering 27 (2007) 344353 Si ịtỵDt ẳ ðS i Þt  Dsi kSi , (6a) ðSi Þ ¼ minðmN i ; jS i jÞsignðS i Þ, (6b) where Dni and Dsi are the incremental normal and shear displacements in the direction of Ni and Si, respectively; kN i and kSi are the normal and shear spring stiffness values with units of force/length For the soil–soil boundary, kS2 ¼ ksoil Eq (6b) describes the implementation of a limiting Coulomb strength for the shear surface at block boundaries The interface friction coefficient is computed as m ¼ tan f for the soil–soil interface where f is the soil friction angle, and m ¼ tan d for the geofoam–soil interface where d is the geofoam–soil interface friction angle The incremental normal and shear displacements Dni and Dsi are computed from horizontal and vertical components of incremental displacements from the previous time step (Eq (4)) For the compression-only forces described earlier, values of Ni that become positive are set to zero at each time step Updated horizontal and vertical total forces (Fig 4) acting on the soil wedge are calculated as follows:   F ¼ N  mu g  N sin a ỵ S2 cos a  b mu_ tỵDt , (7) 347 This stress factor parameter is used to vary shear stiffness of the soil in proportion to normal load (stress level) 2.4 Evolution of soil wedge geometry during excitation Pseudo-static analyses using closed-form solutions predict that the critical orientation of the sliding surface (a) will become shallower as the magnitude of horizontal acceleration (u€ g ) increases Angle a for a soil wedge with a single linear failure surface can be computed as follows [14]:     DA u€ g a ẳ f  tan1 , (12) ỵ tan1 E g where    u€ g A ¼ tan f  tan1 , g p D ẳ AA ỵ BịB  C ỵ 1ị, E ẳ ỵ C A ỵ Bị, B ẳ 1=A,    u g C ẳ tan d ỵ tan1 g Included in the formulation above is the provision for mass damping where u_ i is velocity and b is a mass damping factor Positive values of u€ g correspond to outward acceleration of the soil wedge and compression of the seismic buffer In this numerical approach, if the applied horizontal acceleration is less than the maximum previously computed value, the value of a remains unchanged (Fig 5) 2.3 Calculation of material parameters 2.5 Numerical implementation 2.3.1 Interface stiffness values The values of the normal spring constants at the soil wedge boundaries are calculated based on assumed values for the modulus of elasticity of the materials and the depth of the zone in the direction of normal force The stiffness of spring kN (soil–buffer interface) is calculated as A computer code written in Visual Basic was used to implement the calculations described above Numerical instability was prevented by selecting a time step Dt ¼ 0.1 Dtc where the critical time step Dtc is computed as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (13) Dtc ¼ m=kmax F ẳ S  mg ỵ N cos a ỵ S2 sin a  b mu_ ịtỵDt (8) HW , (9) b where W ¼ m is the unit width and Eb is the modulus of elasticity of the buffer The corresponding normal spring stiffness for the soil–soil interface is kN ¼ E b 2W , (10) cos a sin a where Es is the modulus of elasticity of the soil assumed as a constant The normal stiffness value varies non-linearly with orientation of the soil shear surface The minimum value of the normal spring constant occurs at a ¼ 451 The stress-dependent shear stiffness of the soil is computed here as kN ¼ E s sin a , (11) H where w is a dimensionless stress factor, sn is normal stress and N2 is the force acting normal to the soil shear surface kS2 ¼ wsn W ¼ wN Fig Evolution of soil failure angle with input horizontal accelerogram ARTICLE IN PRESS R.J Bathurst et al / Soil Dynamics and Earthquake Engineering 27 (2007) 344–353 348 Here, kmax is the maximum computed spring stiffness during a computation cycle Since, the normal and shear spring stiffness for the soil wedge will change during a simulation run as a decreases, the value of Dt will also change over the course of a simulation run Numerical examples 3.1 Physical tests A series of shaking table tests were carried out at the Royal Military College of Canada [9,10] The physical models were m high (H) and 1.4 m wide (W) as shown in Fig The models comprised of a very stiff aluminium bulkhead (wall) rigidly attached to the shaking table platform (2.7 m  2.7 m in plan area) A compressible EPS layer of thickness 0.15 m was attached to the wall The wall and retained soil mass were contained in a rigid strong box affixed to the table platform The soil extended m from the back of the seismic buffer The length of the soil volume behind the buffer was sufficient to prevent intersection of any soil failure mechanism with the back boundary of the rigid soil container The strong box was excited in the horizontal direction only An artificial sintered silica-free synthetic olivine sand was used as the retained soil The soil properties are summarized in Table The same material has been used in experimental work that investigated the response of reduced-scale models of geosynthetic reinforced soil walls under simulated earthquake loading [15,16] All tests in the current investigation were performed with the same soil volume and placement technique Four of the physical tests reported by Zarnani et al [9] are considered here The properties of the geofoam buffer materials were varied between tests and are summarized in Table The EPS panels for walls 2–4 were commercially available products Wall was constructed with a reduced gross density by removing 50% of the EPS material by coring The elasticized product is produced from solid EPS block that is subjected to a cycle of compression load–unloading in order to increase the linear elastic range of the material behaviour Non-elasticized EPS products are linear elastic up to about 1% strain Elasticized EPS materials have a linear elastic range up to 40% strain but have a lower elastic modulus [4] The soil was placed in thin lifts and compacted by lightly shaking each lift using the shaking table Thereafter, the same target stepped-amplitude sinusoidal record with a frequency of Hz was used as the horizontal base excitation history in all tests The model base excitation was increased at 5-second intervals to peak acceleration amplitude of 0.8 g, at which point the test was terminated [10] A Hz frequency (i.e 0.2 s period) at 16 model scale corresponds to Hz (i.e 0.5 s period) at prototype scale according to the scaling laws proposed by Iai [17] Frequencies of 2–3 Hz are representative of typical predominant frequencies of medium to high frequency earthquakes Nevertheless, this simple base excitation record is more aggressive than an equivalent true earthquake record with the same predominant frequency and amplitude The total horizontal force transmitted to the rigid wall was measured by load cells attached to supports used to Table Backfill soil properties Parameter Value Soil density Peak friction angle Residual friction angle Soil–buffer interface friction angle Cohesion Soil elastic modulus, Es Soil shear stiffness, ksoil Soil stress factor (dimensionless) 1600 kg/m3 511 461 151 15.2 MPa (varies) (Eq (11)) 500–2000 Note: Soil shear strength parameters and shear stiffness determined from 0.1  0.1 m direct shear box tests [15,20] Fig General arrangement of shaking table test configuration and instrumentation (after Bathurst et al [10]) ARTICLE IN PRESS R.J Bathurst et al / Soil Dynamics and Earthquake Engineering 27 (2007) 344–353 349 Table EPS geofoam buffer properties Geofoam Walla Typeb Density, rb (kg/m3) Dynamic elastic modulus, Eb (MN/m2) Literature I XI Elasticized XI 3.3 d 1.8 d 0.27 e — 16 12 14 6c Back-calculated Numerical Minimum Maximum 4.1 2.0 0.89 0.38 5.3 4.9 1.7 0.71 4.1 3.2 1.3 0.40 a Numbering scheme from [9]; Wall was a control wall with no seismic buffer (rigid wall case) ASTM classification system [22] c 50% of material removed by coring d From correlation with ESP density reported by Negussey [21] e Manufacturer’s literature b rigidly restrain the wall in the horizontal direction The wall footing support was comprised of frictionless linear bearings to decouple horizontal and vertical wall forces Four potentiometer-type displacement transducers located at different elevations above the base of the wall were connected to metal plates embedded in the surface of the geofoam layer to record lateral displacements (compression) of the geofoam Details of the experimental design, test configurations and interpretation of results can be found in the paper by Bathurst et al [10] 3.2 Selection of model input parameters The general model explained earlier was implemented with d ¼ 151 to compute a in Eq (12) This value was assumed based on recommendations by Xenaki and Athanasopoulos [18] and Kramer [19] However, interface friction was set to zero at the soil–wall boundary (i.e shear force S1 ¼ in Fig 2) This assumption is reasonable since interface friction could not be mobilized due to cyclic normal force load–unloading at this interface during base shaking The friction angle of the soil (f) in the numerical model was taken as the peak friction angle value The stiffness factor w used to adjust the shear stiffness of the soil (Eq (11)) was back-calculated from the results of conventional direct shear tests on specimens 0.1  0.1 m in plan area [15] under a range of normal stress sn (Fig 7) The calculation was carried out as follows: w¼ t=sn , Dd=d (14) where stress ratio t=sn was computed over the initial linear portion of the plots in Fig (0.05–0.2% strain) Values of w from 500 to 2000 were used in the numerical simulations The lower value was used in tests and that were constructed with the most compressible buffer materials It is believed that this more compressible boundary condition Fig Approximation to stress-dependent shear stiffness and peak strength behaviour of direct shear box tests on shaking table sand (physical tests from El-Emam and Bathurst [15]) during model construction may have led to a less stiff soil placement The elastic modulus of the sand (Es) was taken from a value reported by El-Emam et al [20] to reproduce the direct shear box test data using a numerical FLAC code Values for the dynamic elastic modulus of the geofoam buffer materials were calculated by plotting the measured dynamic compressive stress–strain response at each of the four displacement transducers arranged along the height of the wall models The stress was calculated as the dynamic horizontal force recorded by the horizontal load cells divided by the surface area of the geofoam inclusion The dynamic strain was calculated by dividing the dynamic displacement readings by the geofoam thickness (0.15 m) An example of dynamic stress–strain response is shown in Fig The datum for stress and strain values is the end of construction The ranges of values using maximum and minimum measured dynamic deflections are summarized in ARTICLE IN PRESS 350 R.J Bathurst et al / Soil Dynamics and Earthquake Engineering 27 (2007) 344–353 damping also occurs when the shear strength of the soil is reached (Eq (6b)) 3.3 Comparison of physical and numerical results Fig Measured average post-construction dynamic compressive stress– strain response of EPS geofoam buffer (test 4) Table Comparison of these values with values from other sources is problematic since there are a large number of correlations between elastic modulus and EPS density in the literature Furthermore, the stiffness of these materials is sensitive to specimen size and rate of loading For example, Bathurst et al [10] showed that published correlations for 16 kg/m3 (Type I) and 12 kg/m3 (Type XI) density materials gave a range (mean71 standard deviation) of 5.171.9 and 3.371.5 MPa, respectively The ranges quoted here capture the range of values used later in the numerical simulations Nevertheless, Negussey [21] showed that a 10-fold increase in specimen cube size resulted in a doubling of the specimen elastic modulus The values used in numerical simulations are also larger than the values for the two unmodified EPS materials using a linear correlation between elastic modulus and EPS density reported by Negussey [21] Consistent with the trend for non-elasticized EPS, is the observation that the elastic modulus for the elasticized material reported by the manufacturer is also less than the range of values backcalculated from the physical tests The compressive strains computed for the tests with unmodified EPS buffer materials were less than 1%, which is within the elastic limit of the materials Only at the end of the excitation record for test 6, did the maximum compressive strain approach 2% Each of the numerical models was excited by the horizontal accelerogram recorded by the accelerometer mounted on the shaking table platform (Fig 6) The accelerograms were adjusted using a conventional linear baseline correction During model initialization, mass damping (parameter b in Eqs (7) and (8)) was set to a large number to bring the model to static equilibrium within a reasonable number of computation cycles During dynamic loading b was set to 0.05 However, the solutions were not very sensitive to values of b in the range of 0–0.05 compared to the influence of the magnitude of other input values Additional system For clarity only the peak values from the input acceleration–time records for each numerical simulation are plotted in Figs 9a, 10a, 11a and 12a These data are taken from accelerations recorded at the shaking table platform in each corresponding physical test Computed compression–time and load–time responses of the four test cases are presented in the other plots in these figures The datum for the plots is the end of construction Hence, these values are the result of dynamic loading only The measured compressions are plotted as the average of peak values recorded from the four displacement transducers arranged along the height of the wall and the maximum Fig Comparison of physical and numerical results (test 2): (a) input accelerogram; (b) peak buffer compression; (c) peak buffer compressive force ARTICLE IN PRESS R.J Bathurst et al / Soil Dynamics and Earthquake Engineering 27 (2007) 344–353 351 Fig 10 Comparison of physical and numerical results (test 3): (a) input accelerogram; (b) peak buffer compression; (c) peak buffer compressive force Fig 11 Comparison of physical and numerical results (test 4): (a) input accelerogram; (b) peak buffer compression; (c) peak buffer compressive force and minimum values The peak dynamic horizontal forces from the physical tests were computed from the sum of readings from the horizontal load cells mounted against the back of the walls As may be expected, the compression–time response from the physical tests is generally greater with deceasing buffer elastic modulus Comparison of the Figs 9c and 12c shows that the measured peak horizontal force acting on the wall was less for the most compressible buffer (Eb ¼ 0.4 MN/m2) compared to the stiffest material (Eb ¼ 4.1 MN/m2) This is consistent with the hypothesis that peak dynamic loads can be attenuated by the use of a vertical compressible inclusion (seismic buffer) There is generally good agreement between the physical and numerical models for all configurations up to peak base input acceleration of about 0.7g At higher accelerations there are likely more complex system responses that cannot be captured by the simple displacement model employed For example, there are likely higher wall deformation modes at higher levels of base excitation The poor predictions at peak base excitation levels likely led to the overestimation of buffer compression and loads at the end of the tests when the walls were returned to the static condition Nevertheless, the trends in the measured data for the four walls with respect to buffer force and compression are generally captured by the numerical model up to about 0.7g, and in many instances there is good quantitative agreement Conclusions This paper describes a simple displacement-type block model that can be used to predict the compression and dynamic force response of an idealized system comprised of ARTICLE IN PRESS 352 R.J Bathurst et al / Soil Dynamics and Earthquake Engineering 27 (2007) 344–353 Acknowledgements The second author would like to acknowledge the financial support provided by the Iranian Ministry of Science, Research and Technology, for a Ph.D Visiting Fellowship held at the GeoEngineering Centre at Queen’sRMC The work reported in this paper was also supported by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) awarded to the first and fourth authors References Fig 12 Comparison of physical and numerical results (test 6): (a) input accelerogram; (b) peak buffer compression; (c) peak buffer compressive force a linear-elastic seismic buffer placed against a rigid wall Input parameters used to simulate the physical tests were estimated from independent laboratory direct shear box testing of the sand backfill and reasonable estimates of the dynamic modulus of the EPS materials used to construct the seismic buffers The model is shown to capture the trends observed in reduced-scale model shaking table tests carried out with similar boundary conditions up to peak acceleration levels of 0.7g The model is simple and provides a possible framework for the development of advanced models that can accommodate more complex constitutive laws for the component materials, other modes of deformation, and a wider range of problem geometry For example, possible non-uniform contact stress distributions and rotation of the soil–geofoam interface surface may have to be introduced into the model if the general approach is to be applied to field-scale structures [1] McGown A, Andrawes KZ Influence of wall yielding on lateral stresses in unreinforced and reinforced fills Research Report 113, Transportation and Road Research Laboratory, Crowthrone, Berkshire, UK, 1987 [2] McGown A, Andrawes KZ, Murray RT Controlled yielding of the lateral boundaries of soil retaining structures In: Holtz RD, editor Proceedings of the ASCE symposium on geosynthetics for soil improvement; 1988 p 193–211 [3] Partos AM, Kazaniwsky PM Geoboard reduces lateral earth pressures In: Proceedings of geosynthetics’87, Industrial Fabrics Association International, New Orleans, LA, USA, 1987 p 628–39 [4] Horvath JS Geofoam geosynthetic Scarsdale: Horvath Engineering, P.C; 1995 [5] Karpurapu R, Bathurst RJ Numerical investigation of controlled yielding of soil-retaining wall structures Geotextiles Geomembranes 1992;11:115–31 [6] Inglis D, Macleod G, Naesgaard E, Zergoun M Basement wall with seismic earth pressures and novel expanded polystyrene foam buffer layer In: Proceedings of the 10th annual symposium of the Vancouver Geotechnical Society; 1996 18pp [7] Itasca Consulting Group FLAC: Fast Lagrangian Analysis of Continua, version 3.3 Itasca Consulting Group, Inc Minneapolis, MN, USA, 1996 [8] Hazarika H, Okuzono S, Matsuo Y Seismic stability 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Cundall Associates, Report PCAR-1-80; European Research Office, U.S Army, Contract DAJA37-79-C0548, 1980 [14] Bathurst RJ, Hatami K, Alfaro MC Geosynthetic-reinforced soil walls and slopes—seismic aspects In: Shukla SK, editor, Geosynthetics and their applications, Thomas Telford, 2002 [chapter 14] [15] El-Emam M, Bathurst RJ Experimental design, instrumentation and interpretation of reinforced soil wall response using a shaking table Int J Phys Model Geotech 2004;4(4):13–32 ARTICLE IN PRESS R.J Bathurst et al / Soil Dynamics and Earthquake Engineering 27 (2007) 344–353 [16] El-Emam M, Bathurst RJ Facing contribution to seismic response of reduced scale reinforced soil walls Geosynth Int 2005;12(5): 215–38 [17] Iai S Similitude for shaking table tests on soil–structure–fluid model in 1g gravitational field Soils Foundations 1989;29:105–18 [18] Xenaki VC, Athanasopoulos GA Experimental investigation of the interaction mechanism at the EPS geofoam–sand interface by direct shear testing Geosynth Int 2001;8(6):471–99 [19] Kramer SL Geotechnical earthquake engineering New Jersey: Prentice-Hall; 1996 353 [20] El-Emam M, Bathurst RJ, Hatami K Numerical modeling of reinforced soil retaining walls subjected to base acceleration In: Proceedings of the 13th world conference on earthquake engineering, Vancouver, BC, 2004 15pp [21] Negussey D Design parameters for EPS geofoam (Keynote paper) In: Proceedings of the international workshop on lightweight geomaterials, Tokyo, Japan, 2002 19pp [22] ASTM C 578-06 Standard specification for rigid cellular polystyrene thermal insulation American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA, 2006  ... placed against a rigid wall can be extended to the case of dynamic earth loading The test data from Hazarika et al [8] showed that the peak lateral loads acting on the compressible model walls... Zarnani et al [9] are considered here The properties of the geofoam buffer materials were varied between tests and are summarized in Table The EPS panels for walls 2–4 were commercially available... load–unloading in order to increase the linear elastic range of the material behaviour Non-elasticized EPS products are linear elastic up to about 1% strain Elasticized EPS materials have a linear