Sea to Sky Geotechnique 2006

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1 APPLICATION OF EPS GEOFOAM AS A SEISMIC BUFFER: NUMERICAL STUDY USING FLAC Saman Zarnani, Graduate student, GeoEngineering Centre at Queen s-rmc, Department of Civil Engineering, Queen s University, Kingston, Ontario, Canada Richard J. Bathurst, Professor, GeoEngineering Centre at Queen s-rmc, Department of Civil Engineering, Royal Military College of Canada, Kingston, Ontario, Canada ABSTRACT The paper describes the development and verification of a FLAC numerical code that was used to simulate the results of an experimental program of reduced-scale geofoam buffer tests. The tests were carried out on 1 m-high rigid wall structures mounted on a large shaking table at the Royal Military College of Canada. The tests showed that vertical inclusions of EPS (expanded polystyrene) geofoam placed against a rigid wall can be used to reduce seismic-induced dynamic earth forces. A numerical FLAC code was developed to simulate a number of physical tests with different stiffness of geofoam buffer materials and the control case with no geofoam inclusion. The paper shows that the numerical model was able to capture the trend in earth forces for different buffer configurations during simulated earthquake loading. In many cases, the quantitative measurements from physical and numerical models are in close agreement. The combined physical test results and numerical results demonstrate that the use of geofoam inclusions to reduce earthquake-induced dynamic earth forces against rigid wall structures is possible. Numerical results showed that for the configurations tested the reduction in dynamic earth forces could be as great as 36%. In addition, the numerical simulation results were in generally good agreement with experimental results that showed that as the geofoam modulus decreases, the seismic-induced earth pressure acting against the rigid wall decreases when all other factors are the same. RÉSUMÉ Cet article décrit le développement et la vérification d une simulation avec le logiciel FLAC, des résultats d un programme expérimental d essais à échelle réduite d amortisseurs de styromousse. Les essais ont été réalisés sur des murs de soutènement rigides construits sur une table vibrante au Collège militaire royal du Canada. Les essais ont montré que des inclusions verticales de styromousse mises en place contre un mur rigide peuvent réduire les efforts dynamiques des terres dues aux seismes. Un code numérique FLAC à été développé pour simuler un nombre d essais physiques avec des amortisseurs en styromousse de rigidités différentes et un cas témoin dépourvu d inclusions de styromousse. L artcle montre que le modèle numérique est capable de capter la tendance des forces des terres pour différentes configurations d amortisseur, durant l application simulée de charges sismiques. Dans plusieurs cas les mesures quantitatives des modèles physiques et numériques sont en accord étroit. Les résultats combinés d essais physiques et numériques démontrent que l utilisation d inclusions de styromousse pour la réduction des forces dynamiques sismiques des terres sur les murs rigides est possible. Les résultats numériques montrent que pour les configurations mises à l essai, la réduction des forces dynamiques peut atteindre 36%. De plus, les résultats de simulations numériques sont en accord général avec les résultats physiques qui montrent que, tous autres facteurs étant identiques, quand le module de rigidité du styromousse diminue les forces des terres sismiques agissant sur le mur rigide diminuent. 1. INTRODUCTION The magnitude of earth pressures acting on rigid earth retaining walls can be reduced by introducing a vertical compressible layer between the wall and the backfill soil. This technique to reduce static earth pressures has been demonstrated in earlier studies. Partos and Kazaniwsky (1987) reported one of the first field applications using a prefabricated expanded polystyrene beaded drainage board placed between a 1 m-high non-yielding basement wall and a granular backfill soil. McGown et al. (1988) carried out laboratory experiments on 1 m-high wall models constructed using horizontally compressible platens to measure the effect of wall material compressibility on the magnitude of earth pressures and wall deformations. A parametric analysis of controlled yielding of rigid walls using compressible inclusions was carried out by Karpurapu and Bathurst (1992) using a numerical finite element model (FEM). The numerical approach was first verified against the experimental results reported by McGown and Andrawes (1987) and McGown et al. (1988). Karpurapu and Bathurst then used the numerical code to develop a series of design charts to select the thickness and elastic modulus of the compressible inclusion to minimize 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. The product of choice for compressible vertical inclusions is block-molded low-density expanded polystyrene (EPS). 14

2 The generic name for this class of material is geofoam in modern geosynthetics terminology (Horvath 1995). The concept of static earth pressure reduction using a geofoam inclusion can be extended to the case of seismic-induced dynamic force attenuation. Specifically, a properly selected EPS geofoam material could be used to reduce the potentially larger earth forces that may develop during earthquakes. In this paper, we refer to the compressible material as a seismic buffer. Experimental evidence demonstrating the use of EPS geofoam inclusions to reduce seismic-induced lateral loading against non-yielding wall structures has been reported by Hazarika et al. (23). They conducted smallscale shaking table tests on.7 m-high by.295 m-wide models using an EPS geofoam inclusion with density 22 kg/m 3 and different thickness (2, 5 and 8% of the wall height). They reported that peak dynamic lateral forces acting on the walls could be reduced by 3 to 6% of the values for the walls without the EPS geofoam. The first documented field use of EPS geofoam as a seismic buffer in North America was reported by Inglis et al. (1996). EPS geofoam vertical layers were placed against the rigid walls of a multi-storey basement structure. Their design was based on the results of numerical simulations using the program FLAC (Itasca 25). They showed that a 1 m-thick EPS geofoam layer placed against a 1 m-high rigid basement wall would reduce earthquake-induced dynamic loads by up to 5% compared to the same wall without a seismic buffer. Other numerical modelling studies of the seismic geofoam buffer concept have been reported by Pelekis et al. (), Hazarika (21), Hazarika and Okuzono (22) and Armstrong and Alfaro (23). A shortcoming of the previous cited numerical modelling efforts is that numerical simulations were not verified against instrumented experimental results or field measurements. An initial effort in this regard using reduced-scale shaking table tests was reported by Zarnani and Bathurst (25). This paper first briefly describes an experimental test program that was carried out at Royal Military College of Canada to demonstrate proof of concept using the results of reduced-scale shaking table tests on rigid walls with and without EPS geofoam seismic buffers (Zarnani et al. 25). Next, a numerical FLAC model is described that was used to simulate the experimental shaking table tests carried out at RMC. The paper shows that the numerical model results were in generally good agreement with experimental measurements. Taken together, the numerical and physical tests demonstrate that an EPS geofoam seismic buffer constructed with typical commercially available materials can reduce dynamic earth forces simulating earthquake loadings. Numerical results showed that for the configurations tested the reduction in dynamic earth forces could be as great as 36%. 2. EXPERIMENTAL SHAKING TABLE TESTS AT RMC The RMC model walls were 1 m high, 1.4 m wide and 2 m long. They were constructed within a strong box rigidly attached to a large 2.7 m x 2.7 m shaking table driven by a computer-controlled hydraulic actuator. A stiffened aluminium bulkhead was used as the rigid wall and a synthetic granular soil as the backfill. Load cells were attached to the wall to record the total horizontal and vertical loads transmitted to the rigid wall at the end of construction and during subsequent horizontal shaking. Accelerometers and displacement potentiometers were also installed to monitor the performance of the walls during the tests. A vertical EPS geofoam layer with a thickness of 15 cm was placed against the rigid wall. Figure 1 illustrates the Figure1 Example shaking table test configuration and instrumentation 141

3 acceleration (g) time (s) Figure 2 Stepped-amplitude sinusoidal base input excitation record general test arrangement and instrumentation. One control case (reference rigid wall) without an EPS geofoam inclusion was also investigated. The same stepped amplitude sinusoidal acceleration record with a frequency of 5 Hz was applied to the shaking table in the horizontal direction perpendicular to the wall in all tests (Figure 2). Based on the scaling laws proposed by Iai (1989), a 5 Hz frequency at 1/6 model scale corresponds to about 2 Hz at prototype scale. Frequencies of 2 to 3 Hz are the predominant frequency range of typical medium- to high-frequency earthquakes (Bathurst and Hatami 1998). The acceleration amplitude was increased in 5-second increments up to peak base acceleration amplitudes in excess of.8g and the test terminated. In this paper, we report the experimental and numerical simulation results of three tests constructed with different unmodified commercially available EPS geofoam materials and the control case without a seismic buffer. The density of the EPS geofoam materials was 16, 14 and 12 kg/m NUMERICAL SIMULATIONS Program FLAC 5 (Itasca 25) was used to carry out the numerical simulations reported in this paper. Figure 3 illustrates the numerical grid that was used in the FLAC program to simulate the plane strain experimental tests. 3.1 Material Properties Backfill soil An artificial sintered synthetic olivine material (JetMag 3-6) was used as the retained soil in the experimental shaking table tests. This granular soil was modelled as an elastic perfectly-plastic frictional material with the Mohr- Coulomb failure criterion. This model behaves elastically up to the yield (failure) point (defined by the friction angle) and with plastic flow during post-yield behaviour under Figure 3 FLAC numerical grid showing geofoam buffer, sand backfill and boundary conditions 142

4 Table 1 - Soil properties (from El-Emam and Bathurst 24) Property Value Bulk unit weight 15.7 kn/m 3 Peak angle of friction 58 Residual friction angle 46 Cohesion Dilation angle 15 Shear modulus 7 MPa Bulk modulus 6 MPa Table 2 - Elastic initial tangent Young s modulus for EPS based on correlations with density Reference constant stress. The backfill properties are summarized in Table EPS geofoam Elastic initial tangent Young s modulus (MPa) ρ = 16 kg/m 3 ρ = 12 kg/m 3 Hazarika (26) Missirlis et al. (24) Negussey and Anasthas (21) O Brien (21) Anasthas et al. (21) Duskov (1997a) Duskov (1997b) Negussey and Sun (1996) Horvath (1995) Eriksson and Trank (1991) Magnan and Serratrice (1989) Average Standard Deviation Density is a key material property to identify between EPS products. The elastic modulus and strength of these materials increases with increasing density. Typically, these materials behave linearly elastic up to 1% strain based on rapid cyclic compression loading (BASF 1997). Horvath (1995) reviewed five separate studies in which relationships were proposed to correlate the elastic initial tangent Young s modulus with EPS density. Based on all the data available he proposed the following expression: E =.45ρ 3 [1] where, E is the initial tangent Young s modulus in units of MPa and ρ is the density of EPS in kg/m 3. Many other Table 3 - EPS geofoam properties used in FLAC Property Young s modulus Poisson s ratio Yield strength researchers have also studied the linear elastic range of EPS compressive behaviour and proposed simple correlations. However, a complication that arises when selecting a particular correlation is that the elastic modulus values are sensitive to specimen size, shape and rate of loading. An example of the range of computed initial tangent modulus values from a large number of studies is shown in Table 2 for non-elasticized EPS products. The two densities in the table correspond to the density of two of the geofoam materials used in the current investigation. The third EPS geofoam material used in the current study was an elasticized type of geofoam with a density of 14 kg/m 3. This material is modified from EPS blocks by applying a cycle of compression load and unloading following manufacture. The result is that the linear elastic range is extended to higher strain values (~4%). However, the elastic Young s modulus is lower than the value for the unmodified geofoam with the same density (Horvath 1995). The correlations used in Table 2 are not applicable to elasticized EPS materials. In the FLAC simulations, the EPS geofoam material was modelled as a linear elastic-plastic material. Table 3 summarizes the properties for the three EPS geofoam materials used in the numerical simulations. The modulus values were estimated by back-calculation using measured buffer forces and deformations in the physical tests. This avoids possible errors introduced by using a particular modulus-density correlation from the studies cited in Table 2. Nevertheless, the values in Table 3 for the non-elasticized materials fall within the range of values reported in Table 2. Values for Poisson s ratio and yield strength were determined from correlations with EPS density reported by Horvath (1995). A more advanced non-linear strain-hardening model for the geofoam materials may be more attractive for simulation purposes. However, the strains recorded in the physical tests were less than 1% and hence in the elastic range. The numerical results presented later in the paper show that the linear elastic model was adequate to give reasonable agreement with physical test results. 3.2 Interface Properties EPS density 16 kg/m kg/m3 12 kg/m Elasticized 5.4 MPa 4 MPa 2.8 MPa kpa 16.8 kpa 23.6 kpa A no-slip boundary condition was applied to the bottom of the model to simulate the rough boundary between the 143

5 soil and a layer of sand epoxied to the bottom of the strong box in experimental tests. Between the EPS geofoam and the backfill soil a slip and separation boundary condition was defined in FLAC simulations. This interface allowed the soil and buffer to separate with no tensile stress. The friction angle of the rough interface between the backfill sand and the geofoam was set to 15 based on recommendations by Xenaki and Athanasopoulos (21) and Kramer (1996). Based on recommendations in the FLAC manual (Itasca 25), the normal and shear stiffness of the buffer-soil interface were set to 1 times the equivalent stiffness of the stiffest neighbouring material, which is the backfill soil in this example. For the FLAC slip and separation interface, the elastic properties of the interface have no physical meaning, however they must be selected carefully to ensure numerical stability (i.e. neither too large nor too small compared with the adjacent materials). 3.3 Numerical construction and dynamic excitation The 2D (plane strain) models were constructed in one step and gravity was turned on in one step as well. Then the models were brought to equilibrium. A gentle shaking with duration of 5 seconds, frequency of 9 Hz and amplitude of.1g was applied to the entire model by a constant amplitude sinusoidal acceleration record. This gentle shaking was an attempt to model the vibrocompaction that was applied to each lift of soil during the construction of the physical models. Next, the model was brought to equilibrium again. During simulated dynamic loading, the base and the two vertical boundaries of the model were excited with the same acceleration record that was applied to the experimental tests. The acceleration record is shown in Figure 2. The horizontal acceleration record was applied as a velocity record (integrated acceleration record) in the FLAC models with base line corrections to ensure zero displacement at the base at the end of shaking. Data was acquired at a rate of 5 Hz to avoid aliasing effects and to capture the peak values of dynamic wall response induced by base shaking. 4. NUMERICAL RESULTS The numerical results of interest are the peak magnitudes of horizontal force developed at end of construction and during base excitation. Wall force versus peak base acceleration histories for both physical tests and numerical simulations are presented in Figure 4. The horizontal axis in the plots corresponds to the peak base horizontal acceleration acting towards the wall during shaking. The vertical axis is the total horizontal earth force acting against the rigid wall per unit width of wall. The physical shaking table test data show that wall forces increase as peak base acceleration increases in all tests. The trend in data is captured in the corresponding FLAC simulations. The experimental test results also show that by applying a vertical compressible inclusion of EPS geofoam against the rigid wall, the forces acting on the wall were less than those recorded for the rigid wall case with no geofoam buffer with the exception at, in some cases, the beginning of the tests. The magnitude of force attenuation in the physical tests was generally greater as the elastic modulus of the geofoam buffer was decreased. A similar trend was observed in the numerical simulations at peak base acceleration values greater than about.1g. This trend is highlighted by plotting the results of the FLAC simulations together in Figure 5. There are differences in quantitative values between numerical and physical test results for wall forces at some acceleration values (Figure 4). For example, in the control case without a EPS geofoam buffer, the computed forces are lower at the end of construction and the numerical results have a steeper slope than the experimental result during base excitation. In fact, the FLAC force results are lower than the experimental values at small acceleration values for most tests. However, for the geofoam buffer simulations there is generally better agreement between force-acceleration histories than the control case for peak acceleration values greater than about.1g. The under prediction at the beginning of the tests is in the range of 12 to 41%. This discrepancy is believed to be due to the simple soil model adopted and the single-layer simulation of the compaction technique used in the physical tests. During the construction of the physical experiments, each 2 mm lift of backfill soil was vibro-compacted which likely resulted in locked-in soil stresses against the wall boundary. However, at higher base acceleration values there is better agreement between FLAC simulations and experimental test results once the level of initial compaction peak acceleration value is exceeded. Table 4 summarizes the results of physical and numerical experiments with respect to wall forces at peak base acceleration values corresponding to the end of the excitation stage. The data shows that at a common base acceleration value of about.7g, the reduction in total earth forces with respect to the control case ranged from 15 to 2% in the physical tests. The corresponding range for the numerical simulations is 28 to 36%. The discrepancy in the range of relative force reduction values is largely due to the over-prediction of wall force in the numerical simulation for the control case (Figure 4a). Nevertheless, the difference between the predicted wall forces and experimental test results for the same configuration at the common base acceleration value is reasonably small. The difference is in range of +15% (numerical over-prediction) and -8% (numerical underprediction). 5. CONCLUSIONS The paper describes a series of reduced-scale physical shaking table tests and numerical modelling that was carried out to investigate dynamic earth force reduction using a vertical EPS geofoam layer (seismic buffer) placed against a rigid wall. The numerical simulations were carried out using the program FLAC. The physical and numerical model results showed that as the elastic modulus of the geofoam decreased, the reduction in dynamic earth forces due to simulated seismic loading 144

6 18 1 a) No EPS geofoam buffer 18 1 b) EPS ρ =16 kg/m 3, E = 5.4 MPa 14 FLAC Shaking Table FLAC Shaking Table c) EPS ρ = 12 kg/m 3, E = 4 MPa 18 1 d) EPS ρ =14 kg/m 3, E = 2.8 MPa (elasticized) Shaking Table FLAC Shaking Table FLAC Figure 4 - Wall force - base acceleration histories from physical tests and numerical simulations Table 4 - Comparison of walls forces from numerical and physical experiments at peak base acceleration of.7g EPS density (kg/m 3 ) Control (no buffer) Elastic initial tangent Young s modulus (MPa) Force (kn/m) Physical test Force reduction (%) Numerical model Force (kn/m) Force reduction (%) Difference in force values between numerical and physical experiments (%) increased. The trend in the load-acceleration response of 145

7 1 without EPS with EPS ρ (kg/m 3 ) E (MPa) (elasticized) Figure 5 - Wall force - base acceleration histories from FLAC simulations increased. The trend in the load-acceleration response of the physical test results was captured reasonably well by numerical model. The numerical code generally underpredicted wall forces at the end of construction (initial static loading). However, at large peak base acceleration values in the range of.7g, the numerical results were within 15% of the physical test results. Taken together, the physical and numerical results demonstrate that seismic-induced dynamic earth forces against a rigid wall could be reduced by using an EPS geofoam inclusion. Numerical results showed that for the configurations tested the reduction in dynamic earth forces could be as great as 36% compared to the control case without a seismic buffer. References Anasthas, N., Negussey, D. and Srirajan, S. (21) Effect of Confining Stress on Compressive Strength of EPS Geofoam, 3 rd International Conference of EPS Geofoam, Salt Lake City, Utah, USA, 14 p. Armstrong, R. and Alfaro, M. (23) Reduction of Seismic-Induced Pressures on Rigid Retaining Structures using Compressible Inclusions: A Numerical Study, 56 th Canadian Geotechnical Conference, Winnipeg, Manitoba, 6 p. BASF. (1997) Styropor Technical Information CD-ROM, Ludwigshafen, Germany. Bathurst, R. J. and Hatami, K. (1998) Seismic Response Analysis of a Geosynthetic Reinforced Soil Retaining Wall, Geosynthetics International, Vol. 5, No. 1&2, pp Duskov, M. (1997a) Materials Research on EPS2 and EPS15 Under Representative Conditions in Pavement Structures, Geotextiles and Geomembranes, Vol. 15, Nos.1-3, pp Duskov, M. (1997b) EPS as a Light Weight Sub-Base Material in Pavement Structures, Ph.D. thesis, Delft University of Technology, Delft, the Netherlands. El-Emam, M. and Bathurst, R. J. (24) Experimental Design, Instrumentation and Interpretation of Reinforced Soil Wall Response Using a Shaking Table, International Journal of Physical Modeling in Geotechnics, Vol. 4, No. 4, pp

8 Eriksson, L. and Trank, R. (1991) Properties of Expanded Polystyrene - Laboratory Experiments, Expanded Polystyrene as Light Fill Material; technical visit around Stockholm June 19, 1991, Swedish Geotechnical Institute, Linkoping, Sweden. Hazarika, H. (26) Stress-Strain Modeling of EPS Geofoam for Large-Strain Applications, Geotextiles and Geomembranes, Vol. 24, No. 2, pp Hazarika, H., Okuzono, S. and Matsuo, Y. (23) Seismic Stability Enhancement of Rigid Non-Yielding Structures, 13 th International Offshore and Polar Engineering Conference, 25-3 May 23, Honolulu, HI, USA, pp Hazarika, H. and Okuzono, S. (22) An Analysis Model for a Hybrid Interactive System Involving Compressible Buffer Material, 12 th International Offshore and Polar Engineering Conference, May 22, Kitakyushu, Japan, pp Hazarika, H. (21) Mitigation of Seismic Hazard on Retaining Structures A Numerical Experiment, 11 th International Offshore and Polar Engineering Conference, June 21, Stavanger, Norway, pp Horvath, J. S. (1995) Geofoam Geosynthetic, Horvath Engineering, P.C., Scarsdale, NY, 217 p. Iai, S. (1989) Similitude for Shaking Table Tests on Soil- Structure-Fluid Model in 1g Gravitational Field, Soils and Foundations, Vol. 29, pp Inglis, D., Macleod, G., Naesgaard, E. and Zergoun, M. (1996) Basement Wall with Seismic Earth Pressures and Novel Expanded Polystyrene Foam Buffer Layer, 1 th Annual Symposium of the Vancouver Geotechnical Society, Vancouver, BC, Canada, 18 p. Itasca Consulting Group, (25) FLAC: Fast Lagrangian Analysis of Continua, version 5. Itasca Consulting Group, Inc., Minneapolis, Minnesota, USA. Karpurapu, R. and Bathurst, R. J. (1992) Numerical Investigation of Controlled Yielding of Soil-Retaining Wall Structures, Geotextiles and Geomembranes, Vol. 11, pp Kramer, S. L. (1996) Geotechnical Earthquake Engineering, Prentice Hall, New Jersey, USA, 653 p. Magnan, J. P. and Serratrice, J. F. (1989) Propriétés Mécaniques du Polystyrène Expansé pour ses Applications en Remblai Routier, Bulletin Liaison Laboratoire Ponts et Chaussées, LCPC, No.164, pp McGown, A. and Andrawes, K. J. (1987) Influence of Wall Yielding on Lateral Stresses in Unreinforced and Reinforced Fills, Research Report 113, Transportation and Road Research Laboratory, Crowthrone, Berkshire, UK. McGown, A., Andrawes, K. Z. and Murray, R.T. (1988) Controlled Yielding of the Lateral Boundaries of Soil Retaining Structures, ASCE Symposium on Geosynthetics for Soil Improvement, ed. R. D. Holtz, Nashville, TN, USA, pp Missirlis, E. G., Atmatzidis, D. K. and Chrysikos, D. A. (24) Compressive Creep Behavior of EPS Geofoam, 3 rd European Geosynthetics Conference, Munich, Germany, March 24, Vol. 2, pp Negussey, D. and Anasthas, N. (21) Young s Modulus of EPS Geofoam by Simple Bending Test, 3 rd International Conference of EPS Geofoam, Salt Lake City, Utah, USA, 14 p. Negussey, D. and Sun, M. C. (1996) Reducing Lateral Pressure by Geofoam (EPS) Substitution, International Symposium on EPS Construction Method (EPS Tokyo 96), Tokyo, Japan, pp O Brien, A. S. (21) EPS Behavior during Static and Cyclic Loading from.5% Strain to Failure, 3 rd International Conference of EPS Geofoam, Salt Lake City, Utah, USA, 11 p. Partos, A. M. and Kazaniwsky, P. M. (1987) Geoboard Reduces Lateral Earth Pressures, Geosynthetics 87, IFAI, New Orleans, LA, USA, pp Pelekis, P. C., Xenaki, V. C. and Athanasopoulos, G. A. () Use of EPS Geofoam for Seismic Isolation of Earth Retaining Structures: Results of a FEM Study, 2 nd European Geosynthetics Conference, Bologna, Italy, pp Xenaki, V. C. and Athanasopoulos, G. A. (21) Experimental Investigation of the Interaction Mechanism at the EPS Geofoam-Sand Interface by Direct Shear Testing, Geosynthetics International, Vol. 8, No. 6, pp Zarnani, S. and Bathurst, R. J. (25) Numerical Investigation of Geofoam Seismic Buffers Using FLAC, North American Geosynthetics Society (NAGS)/GRI19 Conference, 25, Las Vegas, NV, USA, 8 p. Zarnani, S., Bathurst, R. J. and Gaskin, A. (25) Experimental Investigation of Geofoam Seismic Buffers Using a Shaking Table, North American Geosynthetics Society (NAGS)/GRI19 Conference, 25, Las Vegas, NV, USA, 11 p. 147