Experimental investigation of EPS geofoam seismic buffers using shaking table tests

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1 Geosynthetics International, 7,, No. Experimental investigation of EPS geofoam seismic buffers using shaking table tests S. Zarnani and R. J. Bathurst PhD candidate, GeoEngineering Centre at Queen s-rmc, Department of Civil Engineering, Queen s University, Kingston, Ontario, K7L N, Canada, Telephone: + (ext. 7), Telefax: +, saman@civil.queensu.ca Professor and Research Director, GeoEngineering Centre at Queen s-rmc, Department of Civil Engineering, General Crerar, Sawyer Building, Room, Royal Military College of Canada, Kingston, Ontario, K7K 7B, Canada, Telephone: + (ext. 79/7/9), Telefax: +, bathurst-r@rmc.ca Received November, revised March 7, accepted 9 March 7 ABSTRACT: The paper reports the results of six shaking table tests using reduced-scale model walls constructed with expanded polystyrene (EPS) panels to reduce dynamic earth loads due to base shaking. The results are compared with a nominal identical rigid (control) wall constructed without a seismic buffer. The test results show that dynamic load attenuation increased with decreasing geofoam stiffness. The test with the highest buffer stiffness resulted in a % reduction in dynamic load and the test with lowest stiffness resulted in a % reduction in dynamic load compared with the control wall. The results of these experiments provide proof of the concept that EPS panels placed against rigid walls can act as seismic buffers to attenuate dynamic loads due to ground shaking (e.g. earthquake). Additional quantitative data related to load deformation time response, back-calculated elastic modulus values for the EPS seismic buffer configurations, dynamic interface shear properties, acceleration amplification in the backfill soil and post-excitation stress relaxation-creep behaviour are also reported. KEYWORDS: Geosynthetics, Shaking table, Geofoam, Seismic, Buffer, Retaining wall, Expanded polystyrene (EPS) REFERENCE: Zarnani, S. & Bathurst, R. J. (7). Experimental investigation of EPS geofoam seismic buffers using shaking table tests. Geosynthetics International,, No., 77 [doi:./gein.7...]. INTRODUCTION Static earth pressures acting against rigid soil structures such as basement walls, integral bridge abutments and soil-retaining walls can be reduced to active or near-active earth conditions by placing a compressible inclusion between the rigid structure and the backfill soil. An early reported field application of this technique was described by Partos and Kazaniwsky (97). They used a prefabricated expanded polystyrene beaded drainage board mm thick that was placed between a m-high nonyielding basement wall and a granular backfill. The influence of the magnitude of wall compressibility (lateral stiffness) on the magnitude of wall deformations and lateral earth pressures was investigated by McGown and Andrawes (97) and McGown et al. (9) using m- high laboratory wall models constructed with horizontally compressible platens. Karpurapu and Bathurst (99) used these model tests to verify the results of a non-linear finite element model (FEM). The numerical code was then used 7-9 # 7 Thomas Telford Ltd to carry out a parametric analysis of controlled yielding of rigid walls using compressible inclusions with a range of thickness and elastic modulus. The results were presented as a series of design charts that can be used to select the thickness and elastic modulus of the compressible inclusion to minimise end-of-construction earth pressures against non-yielding retaining walls constructed to different heights and with a range of granular backfill materials compacted to different densities. Today the product of choice for the vertical compressible inclusion material is block-moulded low-density expanded polystyrene (EPS), which is classified as a geofoam material in modern geosynthetics terminology (Horvath 99, 997). The concept of EPS geofoam as a compressible inclusion for reduction of static earth pressures against rigid retaining structures can be extended to the case of attenuation of dynamic loads due to earthquake. Inglis et al. (99) reported the first use of EPS geofoam as a seismic buffer. Panels of EPS geofoam to mm

2 Zarnani and Bathurst thick were placed against rigid 9 m-high basement walls of a multi-storey underground parking structure at a site in Vancouver, British Columbia. Numerical analyses using the program FLAC (Itasca 99) predicted that lateral earth pressures against the walls during a seismic event could be reduced by about % using geofoam seismic buffers. The first experimental evidence to support the concept that geofoam compressible inclusions can reduce seismic earth pressures against rigid walls during earthquake loading was reported by Gaskin () based on the results of m-high model tests constructed on a shaking table. Hazarika et al. () also carried out shaking table tests. The wall models in this study were.7 m high by. m wide with EPS inclusions having a thickness of %, % and % of the wall height, and a control structure (i.e. rigid non-yielding wall model). The models were subjected to horizontal sinusoidal shaking at a frequency of. Hz for a period of min with peak acceleration amplitudes of.g,.g,.g and.g. The buffer was a sponge material with a density of kg/m and reported elastic modulus of about kpa. The granular backfill soil extended a distance of m from the front of the model, and was contained within a strong box mounted on the shaking table. The model facings were instrumented with earth pressure cells and accelerometers. The test data showed that the peak lateral loads acting on the compressible model walls were reduced to % to % of the value measured for the nominally identical structure but with no compressible inclusion. Zarnani et al. () and Bathurst et al. (7a) reported some preliminary results from the work by Gaskin (). This paper presents additional physical test results and further data analyses not previously reported. The results reported here demonstrate proof of concept by showing that compressible EPS geofoam panels (seismic buffers) placed against rigid soil-retaining structures can reduce dynamic earth pressures due to simulated earthquake by up to %.. EPS SEISMIC BUFFER SHAKING TABLE TESTS.. General A total of six tests with an EPS seismic buffer and one control test without a compressible inclusion were carried out at the Royal Military College of Canada (Gaskin ). The experimental approach has been described in detail by Bathurst et al. (7a). Some of this information is briefly repeated here for completeness. Figure illustrates a cross-section of the reduced-scale shaking table tests with an EPS geofoam seismic buffer. The models were m high and. m wide, and extended m from the front of the rigid wall. The models were contained within a. m-high rigid strong box fixed to the steel platform of the shaking table. The back wall was an energyreflecting rigid boundary that was adopted for simplicity. At the front of the strong box, a rigid aluminium bulkhead (wall) was placed on an aluminium baseplate that was seated in turn on three friction-reducing linear bearings. The footing arrangement allowed the position of the front wall to be adjusted so that the volume of retained soil mass was the same for the tests with and without the geofoam inclusion. The linear bearings also allowed the measured vertical and horizontal loads at the base of the wall to be decoupled (Figure ). The EPS buffer was mm thick in all tests, and was placed against the back of the rigid wall and seated on the aluminium baseplate. The backfill material was placed and compacted in mm thick lifts while the rigid wall was braced. After backfilling, the external braces were removed from the front end so that the initial static earth loads were fully transmitted to the load cells located at the top and bottom of the rigid wall. Potentiometer-type displacement devices were located at four different elevations along the centreline of the rigid wall. The instrument cores were passed through the geofoam buffer and attached to metal plates affixed to the surface of the buffer in order to measure the horizontal deformation of the EPS buffer with respect to the rigid wall during subsequent shaking. An additional potentiometer was used to record the displacement of the shaking table platform with respect to the laboratory floor. Four accelerometers were placed in the backfill soil to record acceleration response at selected locations in the retained soil zone, and one accelerometer was attached directly to the table. A stepped amplitude sinusoidal base acceleration record was applied horizontally to the shaking table by a computer-controlled hydraulic actuator. The acceleration record had a frequency of Hz and a peak acceleration magnitude of about.g. Figure illustrates the measured table accelerogram filtered to Hz and with linear baseline correction. A Hz frequency (i.e.. s period) at /- model scale corresponds to Hz (i.e.. s period) at prototype scale according to the scaling laws proposed by Iai (99). Frequencies of to Hz are representative of typical predominant frequencies of medium- to highfrequency earthquakes (Bathurst and Hatami 99), and fall within the expected earthquake parameters for North American seismic design. The models were excited only in the horizontal cross-plane direction, to be consistent with the critical orientation typically assumed for seismic design of earth-retaining walls (AASHTO ). Based on the values predicted by closed-form solutions for linear elastic media reported in the literature (Hatami and Bathurst ; El-Emam and Bathurst ), the minimum natural frequency of the experiments was about Hz, which is well above the predominant frequency of the base input excitation record ( Hz). Hence system response due to possible resonance was not a concern in this experimental programme... Soil The backfill soil was an artificial sintered synthetic granular material with the commercial name of JETMAG -. This material is free of silica dust, which is desirable for work within an enclosed laboratory environment. The soil is composed of angular to sub-angular Geosynthetics International, 7,, No.

3 Experimental investigation of EPS geofoam seismic buffers using shaking table tests 7 Load cell Rigid wall. m. m. m Back of strong box Bracing Buffer potentiometer ACC Geofoam buffer ACC Sand backfill ACC ACC. m. m Backfill accelerometer Table potentiometer Plywood base Table accelerometer Linear bearings Shaking table platform Load cells Figure. Example shaking table test configuration and instrumentation Acceleration ( g ) Figure. Measured stepped-amplitude sinusoidal base excitation record, filtered to Hz and linear baseline corrected particles with a specific gravity of., coefficient of curvature of.7, coefficient of uniformity of., and fines content of less than % by weight. The soil is uniformly graded with a maximum particle size of mm. All tests in the current investigation were performed with the same volume and placement technique to ensure a consistent retained soil mass. Material properties of the backfill soil are summarised in Table. Table. Soil properties Property Value Density (kg/m ) Peak angle of friction (degrees) Residual friction angle (degrees) Cohesion Relative density (%) Peak dilation angle (degrees) Note: Strength parameters from cm by cm in plan area direct shear tests... EPS seismic buffer materials The wall configurations and properties of the EPS buffer materials in this study are summarised in Table. The density of the seismic buffer (based on total volume and mass) varied between kg/m and. kg/m. Two different types of non-elasticised EPS geofoam based on the ASTM C 7- standard classification system were used. The elasticised EPS is manufactured by applying a load unload cycle after manufacture. This makes the EPS exhibit linear elastic behaviour up to about % strain under compression and linear (proportional) behaviour up to about %, compared with about % strain for the unmodified material. However, the elasticised EPS geofoam has a lower elastic modulus than the non-elasticised material with the same density. The bulk density of the EPS panels for Walls, and 7 was modified by removing material from the original EPS panels. Thus it was possible to investigate the dynamic response of seismic buffers with densities and stiffness values that were much lower than those for intact EPS panels. It should be noted here that the sand backfill was Geosynthetics International, 7,, No.

4 Zarnani and Bathurst Table. EPS geofoam buffer properties Wall no. Buffer thickness (m) Type a Density, r (kg/m ) Geofoam Dynamic elastic modulus, (MPa) Literature Back-calculated Minimum Maximum Average Control wall without geofoam buffer I.7 e (..9) f. XI. e (..) f. Elasticised.7 e.9... XI b.... XI c XI. d..9. a ASTM C 7- classification system. Since the original experimental work was carried out, a modified classification system for geofoam has been published as ASTM D 7-. b % of material removed by cutting strips; density of intact EPS geofoam ¼ kg/m. c % of material removed by coring; density of intact EPS geofoam ¼ kg/m. d 9% of material removed by coring; density of intact EPS geofoam ¼ kg/m. e Manufacturer s literature. f Average modulus and standard deviation using published correlations with density (Bathurst et al. 7a). in direct contact with the EPS panels in all tests, with the exception of Wall. For this structure, the bulk density of the seismic buffer was reduced by cutting mm thick strips from the EPS panels. In order to form a continuous seismic buffer/soil interface, thin mm-thick plywood strips were placed in horizontal layers across the front of the buffer, and duct tape was used to seal the horizontal joints. The elastic Young s modulus of the geofoam material is a key parameter influencing model response. Its value is strongly dependent on density. However, the determination of its value is also influenced by specimen size, rate of loading and loading path. Many correlations between the elastic modulus of non-elasticised EPS and density can be found in the literature. Bathurst et al. (7a) showed that the average value of initial elastic modulus (from different correlations) ranged from. to. MPa with a standard deviation of.9 to. MPa, for EPS with densities from kg/m to kg/m, respectively. Elastic modulus values from the manufacturer s literature for the unmodified EPS material used in this investigation are given in Table. Also shown in the table are elastic modulus values from back-calculation using the slope of the dynamic load displacement loops measured during model shaking. These results are discussed later.. TEST RESULTS.. Horizontal wall forces The experimental result of most interest is the magnitude of maximum wall force with time (or increasing base acceleration) for each wall configuration. The average maximum measured compressive force acting against the wall and corresponding average maximum measured base acceleration in the direction of the buffer over successive short time increments (less than. s) were calculated from the load acceleration data plot for each test (e.g. Figure ). The horizontal wall force was computed from the sum of loads recorded by the four load cells used to brace the rigid aluminium bulkhead (Figure ). These results are summarised in Figure, and show that in general, as the base acceleration amplitude increases, the peak horizontal force acting against the rigid panel wall increases. However, it can be noted that, at the start of the tests corresponding to low base acceleration magnitudes (,.g), there is a trend towards decreasing horizontal forces. It is believed that this initial response is due to the initial soil state in the physical experiments. In the Horizontal wall force (kn) Geosynthetics International, 7,, No. Acceleration ( g) Wall no. * 7 Geofoam buffer (kg/m ) (MPa) rigid * Elasticised Figure. Horizontal total wall forces for all tests ρ

5 Experimental investigation of EPS geofoam seismic buffers using shaking table tests 9 physical tests, the soil was gently vibro-compacted in mm lifts using the shaking table, and this probably resulted in locked-in stresses. Once the base excitation applied during the physical experiments reached about.g, these locked-in stresses were released, and increasing horizontal force with base acceleration was observed thereafter. The results in Figure also show that, by introducing a compressible layer behind the rigid wall, the horizontal forces acting on the rigid wall are reduced compared with the control rigid wall case (Wall ). Also, as the density (or stiffness) of the ESP geofoam is reduced from kg/ m (Wall ) to. kg/m (Wall 7), more load attenuation is observed in the shaking table tests. In other words, as the density of the non-elasticised EPS geofoam is decreased, the horizontal wall forces acting against the rigid wall are also decreased. These results clearly demonstrate proof of concept that EPS geofoam can be used as a seismic buffer against rigid walls to attenuate seismic earth pressures. The magnitude of horizontal wall force reduction using EPS geofoam seismic buffers with respect to the control rigid wall case varies between % for the wall with highest buffer stiffness (Wall ) and about % for the wall with lowest buffer stiffness (Wall 7)... Peak buffer compression The compression time response of the EPS geofoam buffer was measured at the backfill interface using four displacement potentiometers installed at the centreline of the walls at,, and cm from the bottom of the wall. Figure shows the geofoam peak compression time histories measured for Walls to 7. The shaded area in each plot corresponds to the range of maximum and minimum values of peak compression measured by the potentiometers. The bold line is the average geofoam peak compression time history of all four potentiometers at each measurement time. The measurements show that there is a general trend of increasing buffer compression with time (or peak acceleration). Also, by comparing all the results it can be seen that, as the elastic modulus of the EPS geofoam decreases, average compression during shaking increases. This trend is consistent with the trend in earth force attenuation described earlier. The maximum average buffer compression varies between. mm and. mm for Wall ( ¼. MPa) and Wall 7 ( ¼. MPa), respectively. Figure presents buffer compression profiles for each of the walls at three different stages: end of construction (before dynamic loading); maximum buffer compression during dynamic loading; and final static loading (after dynamic loading). The measured initial static loading deformations were less than the resolution of the potentiometers, estimated to be about. mm. All data points in each profile are time coincident. Figures a, b and c correspond to the walls with unmodified EPS panels. The maximum buffer deformed shapes are similar. The maximum deformation of the buffer occurs at the top potentiometer, located at cm elevation, and the minimum deformation occurs at (or close to) the bottom potentiometer, located at cm elevation. However, as the stiffness of the EPS geofoam decreases, the amount of deformation increases, consistent with the data presented earlier. After dynamic loading, the unmodified EPS panels returned to their original shapes (within instrument resolution), consistent with linear elastic behaviour. Figures d, e and f correspond to the walls with modified EPS panels to investigate the dynamic response of seismic buffers with very much lower stiffness (or bulk density). The profiles corresponding to maximum deformation become greater and more sigmoidal-shaped with decreasing elastic modulus. The highest buffer compression occurs close to the bottom of the wall, and the least compression close to the top of the wall. This nonuniformity indicates that lateral earth pressure along the height of the geofoam buffers was not uniform. A possible explanation for this observation is that the deformation mode shapes of the sand geofoam buffer systems during excitation were influenced by the compressibility of the buffer materials (i.e. the retained soil mass did not move monolithically with time). The static deformation profiles after dynamic loading show that there were permanent non-uniform deformations at the end of the experiments, and these permanent deformations were greatest for the wall with lowest EPS stiffness (or bulk density). Table summarises the maximum buffer compression during dynamic load excitation and post-excitation for all tests. The results show that for Walls, and the maximum peak compressive strain during excitation is less than %, while the post-excitation compressive strains for these tests are not greater than.7% (based on the resolution of the displacement instruments). Hence, for practical purposes, the EPS geofoam materials in these tests are judged to have exhibited linear elastic compressive behaviour. However, for Walls, and 7 the peak compressive strain during excitation varies between.% and.%, which is higher than the linear elastic strain limit of %, indicating that the EPS buffer materials were compressed beyond their elastic limit. This conclusion is consistent with the plastic strains, which ranged from.% to.% at the end of the experiments... Dynamic elastic modulus The compressive stress strain properties of EPS materials have been demonstrated to be sensitive to method of test, rate of loading, and specimen size (Negussey ). The experimental technique used in this investigation provides a unique opportunity to back-calculate the dynamic modulus of the EPS panels during shaking. Example hysteretic dynamic stress strain plots computed from measured wall loads and displacements recorded at four different locations are shown in Figure. The dynamic elastic modulus values ( ) are estimated from the slope of the axis of the stress strain loops. For this wall (Wall ), varies from about to.9 MPa with an average value of. MPa. The variability is probably due to non-uniform pressure along the height of the EPS panel, which is not captured by taking the total wall force and dividing by the wall face area to compute contact stress. Back-calculated values of Geosynthetics International, 7,, No.

6 7 Zarnani and Bathurst..7.. Displacement (mm)... Displacement (mm)..... Measured range Average.... Displacement (mm).... Displacement (mm) (c) (d) 7 Displacement (mm) Displacement (mm) (e) (f) Figure. Peak buffer compression with time for all walls: Wall, r kg/m,. MPa; Wall, r kg/m,. MPa; (c) Wall, r kg/m elasticised,. MPa; (d) Wall, r kg/m,. MPa; (e) Wall, r kg/m,. MPa; (f) Wall 7, r. kg/m,. MPa dynamic elastic modulus for all walls in this test series are summarised in Table. For the unmodified non-elasticised geofoam materials used in Walls and, the modulus values reported by the manufacturer fall within the range of back-calculated values determined in this investigation. However, for the elasticised geofoam case (Wall ), the back-calculated elastic modulus values are higher than the value reported by the manufacturer. The modified geofoam buffer materials in Walls and, which had the same bulk density, gave similar dynamic elastic modulus values. The modified geofoam buffer material in Wall 7 with the lowest bulk density gave the lowest average back-calculated dynamic elastic modulus for all test configurations. The trend in dynamic elastic modulus with bulk density for the non-elasticised EPS materials used in this study is plotted in Figure 7... Dynamic interface friction angle at sand backfill and EPS geofoam interface Estimates of interface friction angle between EPS seismic buffers and retained granular backfill soils are required if wall loads are to be estimated using conventional pseudostatic earth pressure theory or displacement-based methods Geosynthetics International, 7,, No.

7 Experimental investigation of EPS geofoam seismic buffers using shaking table tests 7 Elevation (m) Elevation (m) Elevation (m) Elevation (m) Elevation (m) Elevation (m) initial static loading maximum value during excitation final static loading potentiometer plate geofoam (c) (d) (e) backfill Buffer deformation (mm) (f) rigid wall Figure. Time-coincident deformation profiles for geofoam buffer walls: Wall, EPS r ¼ kg/m, ¼. MPa; Wall, EPS r ¼ kg/m, ¼. MPa; (c) Wall, elasticised EPS r ¼ kg/m elaaticised, ¼. MPa; (d) Wall, EPS r ¼ kg/m, ¼. MPa; (e) Wall, EPS r ¼ kg/m, ¼. MPa; (f) Wall 7, EPS r ¼. kg/m,. MPa 7 (Bathurst et al. 7b). Dynamic interface friction angles can be back-calculated using the measured horizontal loads at the back of the aluminium bulkhead and vertical forces measured at the wall toe. The vertical loads were measured by five load cells mounted on three linear bearings that supported the base of the aluminium bulkhead and EPS buffer. The horizontal loads were recorded by the load cells used to brace the wall laterally, as mentioned earlier. If possible interface adhesion is ignored, then the interface friction angle can be calculated as the arctangent of the ratio of vertical toe force in excess of the wall self-weight to horizontal wall force (i.e. a secant friction angle). Figure shows examples of the variation of maximum interface friction angle at the backfill/eps geofoam interface with time for unmodified and modified EPS seismic buffer tests. For Wall, with the relatively dense unmodified EPS geofoam material, the maximum interface friction angle initially increases and stays reasonably constant with increasing time (or increasing peak acceleration) at about. However, for the test with less dense modified EPS geofoam buffer material (Wall 7), the maximum interface friction angle occurs at the beginning of the test () and decreases to a minimum value of about as dynamic loading progresses. Similar qualitative trends for modified and unmodified EPS buffer tests were observed for the other tests in this investigation. Alternatively, back-calculated peak interface shear resistance can be plotted using conventional c ö Mohr Coulomb (M-C) strength envelopes. This is done in Figure 9 for the same two tests discussed here. The data in Figure 9b for the most compressible seismic buffer case are reasonably well represented by the two-parameter M-C failure envelope fitted to the data using linear regression. The higher shear resistance for Wall 7 at low normal contact pressures is probably due to the higher initial compressibility of the EPS geofoam, which allows greater penetration of the granular backfill particles into the EPS surface during construction. Xenaki and Athanasopoulos () carried out geofoam/sand interface shear tests using a direct shear box. They also found that, under low normal stresses (e.g., kpa in their tests), the interface shear resistance increased with decreasing EPS density. Their experimental results also showed that at low normal stresses the interface shear resistance of low-density EPS ( kg/m ) had a detectable cohesive (or adhesive) component, while relatively high-density EPS ( kg/m ) exhib- Table. Compression of geofoam buffers Wall no. Buffer bulk density (kg/m ) Compression (mm) Compressive strain (%) Peak Post-excitation Peak Post-excitation Geosynthetics International, 7,, No.

8 7 Zarnani and Bathurst Dynamic compressive stress (kpa) Compression Dynamic compressive stress (kpa) Compression Dynamic compressive strain (%) Dynamic compressive strain (%) Dynamic compressive stress (kpa) Compression Dynamic compressive stress (kpa) Compression Dynamic compressive strain (%) (c) Dynamic compressive strain (%) (d) Rigid wall EPS geofoam.. Dynamic compressive stress (kpa) Compression Dynamic compressive strain (%) (e) Potentiometer Elev. cm Elev. cm Elev. cm Elev. cm Backfill Table acceleration Figure. Dynamic compressive stress strain cycles of EPS geofoam for Wall : elevation cm,. MPa; elevation cm,.9 MPa; (c) elevation cm,. MPa; (d) elevation cm, MPa; (e) average,. MPa ited essentially frictional interface shear strength. The relative trend in their data is consistent with the relative shear strength behaviour of the materials in the current study (e.g. Figure 9). To investigate the relationship between shear resistance and EPS compressibility further, the maximum and minimum secant interface friction angles calculated from all tests are plotted against initial elastic modulus in Figure. For unmodified EPS geofoam tests (Walls, and ) the maximum secant interface friction angle occurred during shaking. For the modified EPS geofoam tests (Walls and 7) the maximum value occurred at the beginning of the tests (initial static loading). The minimum secant interface friction angles for the unmodified Geosynthetics International, 7,, No.

9 Experimental investigation of EPS geofoam seismic buffers using shaking table tests 7 Initial elastic Young s modulus, (MPa) Maximum Average Minimum Modified EPS Range of values reported in the literature (Bathurst et al. 7a). Geofoam bulk density (kg/m ) Figure 7. Variation of initial elastic Young s modulus with bulk geofoam buffer density (non-elasticised EPS) geofoam tests have been taken at initial static loading (corresponding to end of construction) and minimum values for the modified geofoam tests just prior to the end of dynamic loading. The data show that the maximum and minimum interface friction angles increase linearly with decreasing log value of initial elastic modulus... Acceleration amplification The acceleration of the backfill soil was measured with four accelerometers placed at different locations in the soil, as shown in Figure. The acceleration time history of the shaking table was also measured with an accelerometer attached to the shaking table (Figure ). Typical fast Fourier transformations (FFTs) of the measured acceleration time histories for the tests in this paper have been reported by Bathurst et al. (7a). They showed that the FFT magnitudes typically increased towards the top of the backfill soil, indicating acceleration amplification (ratio of FFT magnitudes with respect to the base acceleration FFT magnitude) in the backfill soil. However, a shortcoming of the use of FFT for this purpose is that they are computed from the entire accelerogram record and therefore obscure the influence of time-varying base acceleration input on soil-structure response. In the current paper we plot the ratio of time-coincident measured accelerations for the soil and table at peak base input acceleration values during the course of each test. Figure illustrates the variation of acceleration amplification with measured base acceleration for Wall (control) and Wall (EPS seismic buffer) at all accelerometer locations. The results show that for the same test the accelerometers at the same elevation give a similar acceleration amplification history. However, acceleration amplification increases with height above the table, which is expected. The data points for acceleration amplification values for the wall with an unmodified non-elasticised seismic buffer (Wall ) are typically higher than for the rigid control wall (e.g. peak amplification factors equal to. and. for Walls and, respectively). This is not unexpected, based on the relative stiffness of the two systems. Figure shows the acceleration amplification time Secant interface friction angle (degrees) Secant interface friction angle (degrees) Geosynthetics International, 7,, No. Figure. Variation of back-calculated secant interface friction angles with time for seismic buffers with unmodified (high density) and modified (low density) EPS panels: Wall, r kg/m,. MPa; Wall 7, r. kg/m,. MPa response at two accelerometer locations (ACC and ACC) inside the backfill for three tests: Wall (control wall), Wall (stiffest EPS buffer case) and Wall 7 (least stiff EPS buffer case). The general trend in the data is that the magnitude of acceleration amplitude increases with decreasing buffer stiffness. This result is not unexpected, based on D elastic theory, which predicts that, as the average elastic stiffness decreases, the acceleration response ratio (i.e. amplification factor) increases for frequencies less than the natural frequency of the D elastic system (Paz 99)... Stress relaxation and creep In one test (Wall 7), buffer horizontal forces and deformations were recorded for 7 h after the end of shaking. This

10 7 Zarnani and Bathurst Interface shear stress (kpa) Interface shear stress (kpa) φ Interface normal stress (kpa) φ º experiment can be expected to persist for a significant time beyond the end of the simulated seismic event. Also shown on this figure are predicted values of total static horizontal earth force against the wall using classical Coulomb active earth pressure theory (horizontal shaded band). The range of predicted force values is the result of using secant friction angles for the soil in the range of and (Table ) and wall/soil interface friction angles in the range of and (Figure b). The range of predicted force is less than the observed value at both the end of construction and following base shaking. Recall that a vibro-compaction technique was used to initially densify the soil, and this probably created locked-in horizontal stresses at the end of construction. Similarly, a range of horizontal stresses acting against the seismic buffers at the end of base shaking is possible, depending on the magnitude of outward or inward accelerations that existed at the instant the test was terminated. A similar underprediction of wall forces at the beginning and end of dynamic loading using classical Coulomb active earth pressure theory was observed for all tests in this study. The average displacement (compression) time response of the EPS seismic buffer in the Wall 7 experiment is plotted in Figure. The range of measurements shown in the figure corresponds to readings taken by the four displacement potentiometers. Over a period of 7 h the average compression of the EPS geofoam layer increased from. to about. mm (.% to.% compressive strain). Superimposed on the figure is the displacement time response based on a power function of the form å t ¼ å i þ a t n () c. kpa Interface normal stress (kpa) Figure 9. Back-calculated c ö interface shear strength envelopes for seismic buffers with unmodified (high density) and modified (low density) EPS panels: Wall, r kg/m,. MPa; Wall 7, r. kg/m,. MPa where å t is compressive strain, å i is the initial strain, t is elapsed time (in hours), and a and n are constant coefficients. This expression must be used with time in hours, and its general form has been proposed by Horvath (99) to predict the compression of unmodified geofoam materials under constant load (i.e. density in the range to kg/m ). As shown in Figure, the load is not constant, but nevertheless the form of the equation is reasonably accurate if coefficients a and n are assumed as. and., respectively, using regression analysis. In summary, the results of this test show that stress relaxation and compressive creep can occur in these EPS soil systems following dynamic loading. allowed stress relaxation and creep to be investigated, as shown in Figures and, respectively. The total horizontal force recorded against the rigid aluminium bulkhead can be seen to decrease linearly with the logarithm of elapsed time in Figure (i.e. from. to.9 kn in 7 h a % reduction). Assuming that this trend would persist over the long term, then the time to reach the initial static load condition (. kn) would be about years. Stress relaxation in this model is likely to be a complex phenomenon that is influenced by the creep properties of both the EPS geofoam and the soil, and hence the extrapolation carried out here is simplistic. However, the limited data do suggest that the reduction in lateral earth forces due to the EPS seismic buffer in this. CONCLUSIONS Geosynthetics International, 7,, No. A set of physical shaking table tests on reduced-scale ( m-high) rigid walls with EPS geofoam seismic buffers was carried out. The walls included EPS panels with a range of bulk density and stiffness values, and a rigid (control) case without a seismic buffer. The test results show that dynamic load attenuation increased with decreasing geofoam stiffness. The test with the highest stiffness resulted in a % reduction in dynamic load and the test with lowest stiffness resulted in a % reduction in dynamic load compared with the nominal identical wall without a geofoam seismic buffer. The results of these experiments provide proof of the

11 Experimental investigation of EPS geofoam seismic buffers using shaking table tests 7 Wall 7 Modified EPS Range of Ei values reported in the literature (Bathurst et al. 7a) Secant interface friction angle (degrees) General range Wall Wall (elasticised) ρ ρ kg/m kg/m kg/m Maximum values Wall Minimum values kg/m. Initial elastic modulus, (MPa) Figure. Summary of back-calculated EPS sand secant interface friction angles against EPS elastic modulus ρ ρ Wall Amplification factor..... ACC ACC ACC ACC Amplification factor ρ ρ Wall 7 (. kg/m ) Wall ( kg/m ) Wall (control) ACC Measured base acceleration ( g)...9. Amplification factor.... Amplification factor..... ACC Measured base acceleration ( g) Measured base acceleration ( g) Figure. Backfill acceleration amplification for Walls and : Wall (control); Wall (EPS seismic buffer, r kg/m ) Figure. Acceleration amplification at top and middle of backfill for Walls, and 7 Geosynthetics International, 7,, No.

12 7 Zarnani and Bathurst Dynamic loading Static loading Total horizontal force (kn) Range of active state total horizontal force Total horizontal force (kn) 7 9 Linear scale Log scale Time (hours) Figure. Stress relaxation of seismic buffer after dynamic loading (Wall 7) Deformation (mm)..... Average deformation. εt εi a t n Range of measurements... Time (hours) Figure. Creep deformation of seismic buffer after dynamic loading (Wall 7) : concept that EPS panels placed against rigid walls can act as seismic buffers to attenuate dynamic loads due to ground shaking (e.g. earthquake). The results of this test programme also have important implications for the design of EPS seismic buffers. The largest dynamic force attenuations in this test programme occurred using EPS materials that were compressed past their elastic limit. The stiffness of non-elasticised EPS buffer materials decreased with decreasing bulk density. The back-calculated initial dynamic elastic modulus of unmodified non-elasticised EPS geofoam material was in the range of reported values by the manufacturers based on laboratory compression testing. The back-calculated elastic-modulus for the elasticised EPS material was a factor of five times greater (on average) than the value reported by the manufacturer. Back-analysis using measured vertical and horizontal wall forces showed that, as EPS density and stiffness decreases, the cohesive (or adhesive) interface shear strength component for EPS/sand contact increases. Backfill acceleration ratios (amplification factors) increased with decreasing geofoam stiffness. EPS soil backfill systems can be expected to stressrelax and creep following dynamic loading. ACKNOWLEDGEMENTS The writers are grateful for funding provided by the Natural Sciences and Engineering Research Council of Canada, the Academic Research Program at RMC, and grants from the Department of National Defence (Canada). Finally, the authors thank D. Van Wagoner of Geotech Systems Corporation for supplying the EPS material and associated technical data. REFERENCES Geosynthetics International, 7,, No. AASHTO () Standard Specifications for Highway Bridges, 7th edn. American Association of State Highway and Transportation Officials, Washington, DC, USA. ASTM C 7-. Standard Specification for Rigid Cellular Polystyrene Thermal Insulation. ASTM International, West Conshohocken, PA, USA. ASTM 7-. Standard Specification for Rigid Cellular Polystyrene Geofoam. ASTM International, West Conshohocken, PA, USA. Bathurst, R. J. & Hatami, K. (99). Seismic response analysis of a geosynthetic reinforced soil retaining wall. Geosynthetics International,, No. /), 7.

13 Experimental investigation of EPS geofoam seismic buffers using shaking table tests 77 Bathurst, R. J., Zarnani, S. & Gaskin, A. (7a). Shaking table testing of geofoam seismic buffers. Soil Dynamics and Earthquake Engineering, 7, No.,. Bathurst, R. J., Keshavarz, A., Zarnani, S. & Take, A. (7b). A simple displacement model for response analysis of EPS geofoam seismic buffers. Soil Dynamics and Earthquake Engineering, 7, No.,. El-Emam, M. & Bathurst, R. J. (). Experimental design, instrumentation and interpretation of reinforced soil wall response using a shaking table. International Journal of Physical Modelling in Geotechnics,, No.,. Gaskin, P. A. (). Geofoam Buffers for Rigid Walls: An Investigation into the Use of Expanded Polystyrene for Seismic Buffers. MSc thesis, Civil Engineering Department, Queen s University, Kingston, Ontario, pp. Hatami, K. & Bathurst, R. J. (). Effect of structural design on fundamental frequency of reinforced-soil retaining walls. Soil Dynamics and Earthquake Engineering, 9, No., 7 7. Hazarika, H., Okuzono, S. & Matsuo, Y. (). Seismic stability enhancement of rigid nonyielding structures. Proceedings of the th () International Offshore and Polar Engineering Conference, May, Honolulu, HI, USA, pp. 9. Horvath, J. S. (99). Geofoam Geosynthetic. Horvath Engineering, Scarsdale, NY, 7 pp. Horvath, J. S. (997). Compressible inclusion function of EPS geofoam. Geotextiles and Geomembranes,, No., 77. Iai, S. (99). Similitude for shaking table tests on soil-structure-fluid model in g gravitational field. Soils and Foundations, 9, No.,. Inglis, D., Macleod, G., Naesgaard, E. & Zergoun, M. (99). Basement wall with seismic earth pressures and novel expanded polystyrene foam buffer layer. Tenth Annual Symposium of the Vancouver Geotechnical Society, Vancouver, BC, Canada, pp. Itasca (99). FLAC: Fast Lagrangian Analysis of Continua, version.. Itasca Consulting Group, Minneapolis, MN, USA. Karpurapu, R. & Bathurst, R. J. (99). Numerical investigation of controlled yielding of soil-retaining wall structures. Geotextiles and Geomembranes,, No.,. McGown, A. & Andrawes, K. J. (97). Influence of Wall Yielding on Lateral Stresses in Unreinforced and Reinforced Fills. Research Report, Transportation and Road Research Laboratory, Crowthorne, Berkshire, UK. McGown, A., Andrawes, K. Z. & Murray, R. T. (9). Controlled yielding of the lateral boundaries of soil retaining structures. Proceedings of the ASCE Symposium on Geosynthetics for Soil Improvement, ed. R. D. Holtz, Nashville, TN, USA, pp. 9. Negussey, D. (). Design parameters for EPS geofoam (Keynote paper). Proceedings of the International Workshop on Lightweight Geo-Materials, Tokyo, Japan, pp. 9. Partos, A. M. & Kazaniwsky, P. M. (97). Geoboard reduces lateral earth pressures. Proceedings of Geosynthetics 7, Industrial Fabrics Association International, New Orleans, LA, USA, pp. 9. Paz, M. (99). Structural Dynamics: Theory and Computation. Chapman and Hall, New York, pp. Xenaki, V. C. & Athanasopoulos, G. A. (). Experimental investigation of the interaction mechanism at the EPS geofoam-sand interface by direct shear testing. Geosynthetics International,, No., Zarnani, S., Bathurst, R. J. & Gaskin, A. (). Experimental investigation of geofoam seismic buffers using a shaking table. Proceedings of the North American Geosynthetics Society (NAGS)/ Geosynthetics Research Institute (GRI) 9 Conference, Las Vegas, NV, USA, pp (on CD-ROM). The Editors welcome discussion on all papers published in Geosynthetics International. Please your contribution to discussion@geosynthetics-international.com by December 7. Geosynthetics International, 7,, No.