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Shaking table testing of geofoam seismic buffers
ARTICLE IN PRESS
Soil Dynamics and Earthquake Engineering 27 (2007) 324–332 www.elsevier.com/locate/soildyn
Shaking table testing of geofoam seismic buffers Richard J. Bathursta,, Saman Zarnanib, Andrew Gaskinc 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, Department of Civil Engineering, Queen’s University, Kingston, Ont., Canada K7L 3N6 c Ontario Power Generation Inc., Bowmanville, Ont., Canada L1C 3Z8 Received 25 August 2006; accepted 31 August 2006
Abstract The paper describes the experimental design and results of tests used to investigate the use of compressible EPS (geofoam) seismic buffers to attenuate dynamic loads against rigid retaining wall structures. The tests were carried out using 1-m-high models mounted on a large shaking table. Three different geofoam buffer materials retaining a sand soil were tested under idealized dynamic loading conditions. The results of these tests are compared to a nominal identical structure without a seismic buffer. The test results demonstrate that the reduction in dynamic load increased with decreasing seismic buffer density. For the best case reported here, the maximum dynamic force reduction was 31% at a peak base acceleration of 0.7g. r 2006 Elsevier Ltd. All rights reserved. Keywords: Shaking table; Geofoam; Seismic; Buffer; Retaining wall; Expanded polystyrene (EPS)
1. Introduction The use of vertical compressible layers placed against rigid soil retaining wall structures to reduce lateral static earth pressures has been reported in the literature by different researchers [1–3]. The product of choice to perform this function is expanded polystyrene (EPS), which is called geofoam in modern geosynthetics nomenclature [4]. A logical extension of this application is to use vertical compressible inclusions of EPS geofoam as seismic buffers to attenuate earthquake-induced dynamic earth pressures against rigid walls [5]. Nevertheless, proof of concept through experimental testing is lacking. This paper describes the experimental design and results of tests used to investigate the use of compressible expanded polystyrene (geofoam) seismic buffers to attenuate dynamic loads against rigid retaining wall structures. The tests were carried out using 1-m high models mounted on a large shaking table. Three different geofoam buffer materials Corresponding author. Tel.: +1 613 541 6000x6479/6347/6391; fax: +1 613 545 8336. E-mail address: [email protected] (R.J. Bathurst).
0267-7261/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2006.08.003
retaining a sand soil were tested under idealized dynamic loading conditions. The results of these tests are compared to a nominal identical structure without a seismic buffer. The test results demonstrate that the reduction in dynamic load increased with decreasing seismic buffer density. For the best case reported here, the maximum force reduction was 31% at a peak base acceleration of 0.7g. Some preliminary results of this program have been reported by Zarnani et al. [6]. However, in the current paper, details of the experimental design and examples of test results not previously reported are described.
2. Shaking table The physical tests described in this paper were carried out on a 2.7 m 2.7 m shaking table located at the Royal Military College of Canada (RMC). The table has a 5tonne payload capacity and is driven by a 100-kN capacity MTS hydraulic actuator with ancillary controller and PC software. The table is driven in the horizontal direction only. However, the horizontal component of seismicinduced dynamic earth loading is typically the most
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Fig. 1. Cross-section view of general test arrangement and instrumentation.
important loading direction for the application under investigation. The table can excite the rated payload at frequencies up to 13 Hz and 72g. The maximum displacement of the actuator is 775 mm. The wall models were built in a stiff strong box (2.5 m long 1.4 m wide and 1.3 m high) bolted to the steel platform of the shaking table. A cross-section view of the general test arrangement is illustrated in Fig. 1. The backfill extended 2 m beyond the model wall at the front of the strong box. This dimension was selected to prevent intersection with a potential active failure mechanism computed using a Mononobe–Okabe wedge analysis. The sidewalls of the strong box are comprised of 13-mm-thick Plexiglas sheets that are laterally braced by steel frames. The inside surface of the Plexiglas is covered by two lubricated layers of clear 6-mil polyethylene film. The combination of friction-reducing membrane and rigid lateral bracing was adopted to ensure that the test models were subjected to plane strain boundary conditions. A plywood sheet was bolted to the top of the shaking table. A layer of sand was epoxied to the plywood surface to create a rough surface with a friction angle equal to that of the sand backfill. The back of the box was rigidly braced. This is an energy-reflecting boundary that was adopted for simplicity.
Fig. 2. Particle size distribution for sand backfill.
3. Materials 3.1. Backfill A dry synthetic olivine sand was used as the backfill in the test configurations. This material was selected because it is silica free and thus avoided the health danger of silica dust generation during material handling in an enclosed laboratory environment. The sand is composed of angular to sub-angular particles with a specific gravity of 2.88. The soil is uniformly graded with a maximum particle size of 2 mm, coefficient of curvature of 1.27, coefficient of uniformity of 2.5 and fines content less than 3% by weight. The particle size distribution is shown in Fig. 2. Conventional direct shear box tests [7] were carried out on
Fig. 3. Results of direct shear box tests on sand backfill.
10 cm 10 cm specimens of the sand at the same density as the sand in the shaking table models. The results of these tests are shown in Fig. 3. Sand properties are summarized in Table 1.
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Table 1 Soil properties
Table 2 Initial tangent elastic modulus for non-elasticized EPS based on correlations with density
Property
Value
Density Peak angle of friction Residual friction angle Cohesion Relative density Dilation angle
15.5 Mg/m3 511 461 0 86% 151
Note: Strength parameters from 10 cm 10cm in plan area direct shear tests.
3.2. Geofoam Three commercially available EPS materials were selected in this investigation. The first product was a Type I material according to the ASTM classification system [8] with a density of 16 kg/m3. The second product was an elasticized material with a density of 14 kg/m3. This 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 behavior. The third material was a modified Type XI material according to the ASTM classification system [8]. The geofoam inclusions were constructed from three 50-mmthick sheets of EPS glued together. The Type XI material was modified by removing 57% of the EPS foam from two of the sheets by circular coring using a 80-mm-diameter hole saw. The coring was done on a hexagonal close–packing pattern. The third sheet was only partially cored from one side so that the surface of the seismic buffer was continuous at the soil–geofoam interface in the test configuration. Coring reduced the density of the geofoam from 12 to 6 kg/m3. This material was modified in order to investigate the influence on wall response of geofoam density and modulus values that are significantly lower than those of the two unmodified geofoam materials. The density of EPS is used as a characteristic property of different commercially available products [8]. However, the mechanical property of interest when these products are used as compressible inclusions to attenuate lateral earth pressures is the elastic modulus. A large number of correlations are reported in the literature to equate the initial elastic modulus of EPS to product density. The results of these correlations for the Type I and XI materials used in this investigation are summarized in Table 2. The range of values is due to different methods of testing, specimen size, shape and rate of loading. Nevertheless, non-elasticized EPS products are linear elastic up to 1% strain. Elasticized EPS materials have a linear elastic range up to 40% strain but have a lower elastic modulus [4]. Properties of the three materials used in this investigation are summarized in Table 3. The elastic moduli reported in this table are based on the manufacturers’ literature. The values for Poisson’s ratio and yield strength are based on correlations with density for non-elasticized EPS reported
Reference
Initial tangent elastic modulus, Ei (MPa) Type I
Type XI
r ¼ 16 kg/m3
r ¼ 12 kg/m3
Hazarika [9] Missirlis et al. [10] Negussey [11] Negussey and Anasthas [12] Obrien [13] Anasthas et al. [14] Duskov [15] Duskov [16] Negussey and Sun [17] Horvath [4] Eriksson and Trank [18] Magnan and Serratrice [19]
3.76 4.55 3.30 8.22 9.17 4.48 5.73 5.7 3.00 4.20 4.79 4.06
2.12 2.98 1.80 4.94 6.02 2.98 5.48 3.84 1.29 2.40 2.87 3.03
Average Standard deviation
5.08 1.89
3.31 1.48
Note: r ¼ density. Table 3 Unmodified EPS geofoam properties Property
Elastic modulus, Eia(MPa) Poissions ratioc Yield strength (kPa)c
EPS type and density Type I
Elasticized
Type XI
16 kg/m3
14 kg/m3
12 kg/m3
4.7 0.09 30.4
0.27 0.08 23.6
3.1 (1.6)b 0.07 16.8
Note: a from manufacturers’ literature. b With 50% of material removed. c Assumed using correlations for non-elasticized EPS by Horvath [4].
by Horvath [4]. These values were required during experimental design to ensure that the combination of elastic properties and thickness of the compressible inclusion for the geofoam configurations could be expected to reduce lateral earth pressures in the physical experiments. This experimental design stage was carried out using a numerical model based on a FLAC code [20]. Examples of FLAC numerical modeling of the tests described in the current paper have been reported by Zarnani and Bathurst [21]. The back-calculated values of elastic modulus for the three products in Table 4 are discussed later in the paper. 4. Test methodology 4.1. General arrangement A total of seven test configurations were investigated. Four tests that capture the range of response in this
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Table 4 Wall model configurations Wall
Geofoam Thickness (mm)
1 (control) 2 4 6
Type (ASTM-C578-06)
0 150 150 150
Density (kg/m3)
Initial tangent elastic modulus, Ei (MPa)a
N/A I Elasticized XI
16 14 6b (50% removed by coring)
4.8 1.3 0.6
Note: a Back-calculated values from stress-strain load cycles. b Original density of EPS geofoam was 12 kg/m3.
experimental program are summarized in Table 4. Wall 1 was the control test configuration with no geofoam seismic buffer. This wall was constructed using a 1-m-high by 1.4m-wide rigid aluminum bulkhead. The three walls with a geofoam seismic buffer were constructed with the configuration illustrated in Fig. 1. The geofoam seismic buffer was placed between the aluminum wall and the sand backfill. Each wall was 1 m in height and each seismic buffer was 150 mm thick. Hence, the only variable between the seismic buffer tests was the geofoam properties. The aluminum bulkhead was supported laterally by five load cells rigidly braced to the shaking table platform. The bulkhead (and seismic buffer) was seated on an instrumented footing supported by three frictionless linear bearings. The linear bearings were seated on five load cells. The footing arrangement allowed the vertical and horizontal load measurements at the wall boundaries to be fully decoupled.
Fig. 4. Placement of 1-m-high by 1.4-m-wide geofoam seismic buffer against rigid aluminum bulkhead.
4.2. Construction The seismic buffer was held in place temporarily using duct tape (Fig. 4). The sand was placed in five 200-mmthick lifts and manually leveled. Each lift was vibrocompacted by gently shaking the table for 90 s at 9 Hz (peak base acceleration ¼ 0.1g). The final placement of the sand backfill is shown in the photograph in Fig. 5. The final density of the tests was 15.5 Mg/m3 as measured using a nuclear density meter. 4.3. Instrumentation The test models were instrumented with load cells to measure the boundary loads on the aluminum bulkhead as mentioned earlier. The load cells were button-type (Honeywell Sensotec, compression load cell model 53). Four displacement potentiometers (Data Instruments) were used to measure lateral deformations at the geofoam–soil interface. The potentiometers were mounted directly on the aluminum bulkhead and the cores passed through a 20mm-diameter opening through the bulkhead and the geofoam buffer to aluminum plates inserted flush with
Fig. 5. Final placement of sand backfill against geofoam seismic buffer.
the buffer surface (Fig. 4). An additional potentiometer was mounted against the shaking table to measure the displacement-time history of the model base. An accelerometer was also mounted directly on the shaking table to
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record the input base acceleration–time excitation history. Four other accelerometers (Schaevitz S05E Silicon model type) were embedded in the backfill soil at the locations shown in Fig. 1. The accelerometers were anchored within a 100-mm-diameter by 70-mm-deep section of PVC pipe to ensure that the devices remained level and moved in phase with the surrounding sand during shaking. The instruments were monitored by a separate highspeed data acquisition system (SERIES-7000 from Symmetric Instruments Inc. and using SYSTEM 200 software). Data from a total of 19 instruments were recorded at a speed of about 100 Hz in order to prevent aliasing and to capture peak response values.
As a check on the input base acceleration, frequency analysis of the entire measured accelerogram was carried out and this analysis is shown in Fig. 8. The measured predominant frequency of the unfiltered input accelerogram can be seen to be close to a target value of 5 Hz.
4.4. Model excitation Fig. 7. Two-second accelerogram window at amplitude step.
Following construction, the models were excited using a displacement–time history selected to match a target stepped-amplitude sinusoidal accelerogram with a frequency of 5 Hz (Fig. 6). A 2-s window of the target accelerogram is illustrated in Fig. 7. The acceleration record was stepped in 0.05g increments and each amplitude increment was held for 5 s. The maximum base acceleration was 0.8g. A 5 Hz frequency (i.e. 0.2 s period) at 1/6 model scale corresponds to 2 Hz (i.e. 0.5 s period) at prototype scale according to the scaling laws proposed by Iai [22]. Frequencies of 2–3 Hz are representative of typical predominant frequencies of medium-to high-frequency earthquakes [23] and fall within the expected earthquake parameters for North American seismic design [24,25]. This simple base excitation record is more aggressive than an equivalent true earthquake record with the same predominant frequency and amplitude [23,26]. However, it allowed all walls to be excited in the same controlled manner and this allowed valid quantitative comparisons to be made between different wall configurations. As noted earlier in the paper, the models were only excited in the horizontal cross-plane direction to be consistent with the critical orientation typically assumed for seismic design of earth retaining walls [25].
Fig. 8. Unfiltered measured base input accelerogram frequency distribution.
Fig. 6. Target base excitation accelerogram.
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5. Test results The dynamic compressive stress–strain responses of the three geofoam layers used in the models are shown in Fig. 9. The hysteretic response curves have been calculated using the forces recorded by the lateral load cells supporting the aluminum bulkhead and strains computed from the displacement potentiometers attached to the buffer surface. The measurements are taken with respect to end of static construction. The strain amplitude for Tests 2 and 4 is within the linear elastic range cited in the literature (1% strain). Test 6 with 50% material removed recorded a strain amplitude of about 2.2%. Hence, this material is likely to have exceeded the elastic limit of the material. The relative dynamic compressibility of the three geofoam materials can be compared by taking the slope of the lines passing through the origin of the plots and parallel to the long axis of the hysteresis loops. The initial compressibility of the three geofoam buffers in this investigation can be seen to vary through about one order of magnitude (e.g. Ei ¼ 4.8, 1.3 and 0.6 MPa). For an ideal linear elastic material, the load–unload response curves would fall on a line with slope equal to the linear elastic modulus of the medium. For Tests 2 and 4, the slope can be taken as an approximation to the linear initial tangent elastic modulus and the values for these lines taken from Fig. 9 are reported in Table 4. The backcalculated elastic modulus for Test 2 falls within the range of values reported in the literature (Table 2). For Test 6, the linear elastic modulus is taken from the axis slope of the loops for compressive strains over the range of 0–0.5% (Ei ¼ 0.6 MPa). The linear approximation to the hysteresis curves with larger amplitudes can be approximated by a reduced modulus value (e.g. E p ¼ 0:4 MPa). The discrepancies between manufacturers’ literature and back-calculated values for the initial elastic modulus of the EPS materials used in Tests 4 and 6 are likely due to the influence of specimen size and rate of loading noted earlier. Finally, there are more advanced models available to characterize hysteretic stress–strain loops for polymeric materials [27,28]. However, the simple descriptors used here are adequate to differentiate between the stiffness properties of the geofoam materials used in this investigation. Four accelerometers were placed in the backfill soil as described earlier. The frequency response from these devices is shown in Fig. 10 for Test 2. Comparison with Fig. 8 shows that the predominant frequency of the backfill was constant in this experiment but that there was acceleration amplification through the backfill. For example the maximum ratio of the Fast Fourier Transform (FFT) power values is 1.6. The experimental design included the measurement of vertical toe forces (Fig. 1). Fig. 11 shows the peak vertical force–time response of the four walls in this study. The horizontal line in the figure is the self-weight of the aluminum (rigid) panel wall. The vertical load for the
Fig. 9. Measured dynamic compressive stress–strain load cycles.
control test is greater than the wall self-weight during excitation which may be expected assuming some interface friction between the retained sand soil and the panel face. The difference in self-weight of the walls with and without a geofoam buffer is negligibly small due to the low density of the geofoam material. The data in Fig. 11 show that as the stiffness of the geofoam buffer material decreases, the
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Fig. 10. Acceleration frequency content and amplification in soil backfill during base excitation (Test 2).
Fig. 11. Peak vertical wall force versus time.
vertical toe forces generally increase. This may be due to greater penetration of the sand particles into the less stiff polystyrene materials. Fig. 12 shows the dynamic compression–time response of the three walls with a geofoam seismic buffer. The data have been plotted to show the average, minimum and maximum horizontal deformations taken at the same time. The data in the figures shows that as the modulus of the geofoam decreases, the magnitude of average horizontal compression increases. The lower bound on the shaded response curves for Walls 2 and 4 corresponds to measurements recorded by the lowest elevation displacement potentiometer, and the upper bound to the highest elevation displacement potentiometer. Hence, the lateral deformations over the height of the wall were in phase during dynamic excitation. For Wall 6, however, the reverse was true. Hence the deformations
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Fig. 13. Peak horizontal wall force versus peak base acceleration.
tion value during base shaking. The structures with a geofoam inclusion generated less horizontal load than the rigid structure during base shaking. The greatest reduction occurred for Test 6, which was constructed with the lowest density geofoam inclusion and the lowest stiffness. The reduction in lateral earth forces from the rigid wall case at a common peak base acceleration of 0.7g was 16, 20 and 31% for Tests 2, 4 and 6, respectively. 6. Conclusions This paper describes the details of an experimental program that was undertaken to examine quantitatively the concept of geofoam compressible inclusions to reduce the magnitude of earthquake-induced dynamic forces against rigid earth retaining wall structures. The experimental design and test methodology using a shaking table shows that large detectable differences in dynamic force reduction were observed between rigid walls with and without a geofoam seismic buffer. The results presented here demonstrate proof of concept and are a valuable set of results that can be used to verify numerical codes [21,29]. Numerical codes can then be used to investigate a wider range of problem geometry, soil conditions and geofoam thickness and stiffness with a view to optimizing these systems for site-specific earthquake design.
Fig. 12. Dynamic compression–time response of seismic buffer models.
were not in phase due to the reduced stiffness of the geofoam. A primary objective of this study was to demonstrate proof of concept by quantifying the reduction of dynamic earth forces against a rigid wall due to the inclusion of a geofoam seismic buffer. Fig. 13 shows the peak horizontal force recorded at the end of construction and during dynamic loading versus the measured peak base accelera-
Acknowledgements The authors 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). The many discussions with our colleagues K. Hatami and M. El-Emam during the preparation of this paper are also gratefully acknowledged. Finally, the authors thank D. Van Wagoner of Geotech Systems Corporation for supplying the EPS material and associated technical data.
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References [1] 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. [2] Horvath JS. Compressible inclusion function of EPS geofoam. Geotextiles and Geomembranes 1997;15(1–3):77–120. [3] Karpurapu R, Bathurst RJ. Numerical investigation of controlled yielding of soil-retaining wall structures. Geotextiles and Geomembranes 1992;11:115–31. [4] Horvath JS. Geofoam Geosynthetic. Scarsdale: Horvath Engineering, P.C.; 1995. [5] 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. Vancouver, BC, Canada, 1996, 18pp. [6] Zarnani S, Bathurst RJ, Gaskin A. Experimental investigation of geofoam seismic buffer using a shaking table. In: Proceedings of the North American geosynthetics society (NAGS)/GRI19 conference, Las Vegas, NV, USA, 2005, 11pp. [7] ASTM D 3080-04. Standard Test Method for Direct Shear Test of Soils Under Consolidated Drained Conditions. American Society for Testing and Materials, Philadelphia, Pennsylvania, USA, 2004. [8] ASTM C 578-06. Standard Specification for Rigid Cellular Polystyrene Thermal Insulation. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA, 2006. [9] Hazarika H. Stress-strain modeling of EPS geofoam for large-strain applications. Geotextiles and Geomembranes 2006;24(2):79–90. [10] Missirlis EG, Atmatzidis DK, Chrysikos DA. Compressive creep behavior of EPS geofoam. In: Proceedings of the 3rd European Geosynthetics Conference. Munich, Germany, 2004, vol. 2, pp. 749–54. [11] Negussey D. Design Parameters for EPS Geofoam. (Keynote paper). In: Proceedings of the international workshop on lightweight Geomaterials, Tokyo, Japan, 2002, 19pp. [12] Negussey D, Anasthas N. Young’s modulus of EPS geofoam by simple bending test. In: Proceedings of the 3rd international conference of EPS Geofoam, Salt Lake City, Utah, USA, 2001, 14pp. [13] O’Brien AS. EPS behavior during static and cyclic loading from 0.05% strain to failure. In: Proceedings of the 3rd international conference of EPS Geofoam, Salt Lake City, Utah, USA, 2001, 11pp. [14] Anasthas N, Negussey D, Srirajan, S. Effect of confining stress on compressive strength of EPS geofoam. In: Proceedings of the 3rd international conference of EPS Geofoam, Salt Lake City, Utah, USA, 2001. 14pp.
[15] Duskov M. Materials research on EPS20 and EPS15 under representative conditions in pavement structures. Geotextiles and Geomembranes 1997;15(1–3):147–81. [16] Duskov M. EPS as a light weight sub-base material in pavement structures. PhD. thesis, Delft University of Technology, Delft, the Netherlands, 1997. [17] Negussey D, Sun MC. Reducing lateral pressure by geofoam (EPS) substitution. In: Proceedings of the international symposium on EPS construction method (EPS). Tokyo, Japan, 1996, pp. 202–11. [18] Eriksson L, Trank R. Properties of expanded polystyrene—laboratory experiments, expended polystyrene as light fill material; technical visit around Stockholm June 19, 1991, Swedish Geotechnical Institute, Linkoping, Sweden, 1991. [19] Magnan JP, Serratrice JF. Proprie´te´s me´caniques du polystyre`ne expanse´ pour ses applications en remblai routier, Bulletin Liaison Laboratoire Ponts et Chausse´es, LCPC, No. 164, 1989, pp. 25–31. [20] Itasca Consulting Group. FLAC: Fast Lagrangian Analysis of Continua, version 5. Itasca Consulting Group, Inc., Minneapolis, Minnesota, USA, 2005. [21] Zarnani S, Bathurst RJ. Numerical investigation of geofoam seismic buffers using FLAC. In: Proceedings of the North American geosynthetics society (NAGS)/GRI19 conference, Las Vegas, NV, USA, 2005, 8pp. [22] Iai S. Similitude for shaking table tests on soil-structure-fluid model in 1 g gravitational field. Soils and Foundations 1989;29:105–18. [23] Bathurst RJ, Hatami K. Seismic response analysis of a geosynthetic reinforced soil retaining wall. Geosynthetics Int 1998;5(1&2):127–66. [24] NBCC. National Building Code of Canada, National Research Council of Canada, Ottawa, Ontario, Canada, 1990. [25] AASHTO. Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials, Seventeenth Edition, Washington, DC, USA, 2002 [26] Matsuo O, Tsutsumi T, Yokoyama K, Saito Y. Shaking table tests and analysis of geosynthetic-reinforced soil retaining walls. Geosynthetics Int 1998;5(1&2):97–126. [27] Bathurst RJ, Hatami K, Alfaro MC. Geosynthetics and Their Applications, Geosynthetic-reinforced soil walls and slopes—seismic aspects, Chapter 14. Thomas Telford, 2002. [28] Yogendrakumar M, Bathurst RJ. Numerical simulation of reinforced soil structures during blast loadings. Transport Res Rec 1992;1336:1–8. [29] Bathurst RJ, Keshavarz A, Zarnani S, Take A. A simple displacement model for response analysis of EPS geofoam seismic buffers. Soil Dy Earthq Eng, in press.
Soil Dynamics and Earthquake Engineering 27 (2007) 324–332 www.elsevier.com/locate/soildyn
Shaking table testing of geofoam seismic buffers Richard J. Bathursta,, Saman Zarnanib, Andrew Gaskinc 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, Department of Civil Engineering, Queen’s University, Kingston, Ont., Canada K7L 3N6 c Ontario Power Generation Inc., Bowmanville, Ont., Canada L1C 3Z8 Received 25 August 2006; accepted 31 August 2006
Abstract The paper describes the experimental design and results of tests used to investigate the use of compressible EPS (geofoam) seismic buffers to attenuate dynamic loads against rigid retaining wall structures. The tests were carried out using 1-m-high models mounted on a large shaking table. Three different geofoam buffer materials retaining a sand soil were tested under idealized dynamic loading conditions. The results of these tests are compared to a nominal identical structure without a seismic buffer. The test results demonstrate that the reduction in dynamic load increased with decreasing seismic buffer density. For the best case reported here, the maximum dynamic force reduction was 31% at a peak base acceleration of 0.7g. r 2006 Elsevier Ltd. All rights reserved. Keywords: Shaking table; Geofoam; Seismic; Buffer; Retaining wall; Expanded polystyrene (EPS)
1. Introduction The use of vertical compressible layers placed against rigid soil retaining wall structures to reduce lateral static earth pressures has been reported in the literature by different researchers [1–3]. The product of choice to perform this function is expanded polystyrene (EPS), which is called geofoam in modern geosynthetics nomenclature [4]. A logical extension of this application is to use vertical compressible inclusions of EPS geofoam as seismic buffers to attenuate earthquake-induced dynamic earth pressures against rigid walls [5]. Nevertheless, proof of concept through experimental testing is lacking. This paper describes the experimental design and results of tests used to investigate the use of compressible expanded polystyrene (geofoam) seismic buffers to attenuate dynamic loads against rigid retaining wall structures. The tests were carried out using 1-m high models mounted on a large shaking table. Three different geofoam buffer materials Corresponding author. Tel.: +1 613 541 6000x6479/6347/6391; fax: +1 613 545 8336. E-mail address: [email protected] (R.J. Bathurst).
0267-7261/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2006.08.003
retaining a sand soil were tested under idealized dynamic loading conditions. The results of these tests are compared to a nominal identical structure without a seismic buffer. The test results demonstrate that the reduction in dynamic load increased with decreasing seismic buffer density. For the best case reported here, the maximum force reduction was 31% at a peak base acceleration of 0.7g. Some preliminary results of this program have been reported by Zarnani et al. [6]. However, in the current paper, details of the experimental design and examples of test results not previously reported are described.
2. Shaking table The physical tests described in this paper were carried out on a 2.7 m 2.7 m shaking table located at the Royal Military College of Canada (RMC). The table has a 5tonne payload capacity and is driven by a 100-kN capacity MTS hydraulic actuator with ancillary controller and PC software. The table is driven in the horizontal direction only. However, the horizontal component of seismicinduced dynamic earth loading is typically the most
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Fig. 1. Cross-section view of general test arrangement and instrumentation.
important loading direction for the application under investigation. The table can excite the rated payload at frequencies up to 13 Hz and 72g. The maximum displacement of the actuator is 775 mm. The wall models were built in a stiff strong box (2.5 m long 1.4 m wide and 1.3 m high) bolted to the steel platform of the shaking table. A cross-section view of the general test arrangement is illustrated in Fig. 1. The backfill extended 2 m beyond the model wall at the front of the strong box. This dimension was selected to prevent intersection with a potential active failure mechanism computed using a Mononobe–Okabe wedge analysis. The sidewalls of the strong box are comprised of 13-mm-thick Plexiglas sheets that are laterally braced by steel frames. The inside surface of the Plexiglas is covered by two lubricated layers of clear 6-mil polyethylene film. The combination of friction-reducing membrane and rigid lateral bracing was adopted to ensure that the test models were subjected to plane strain boundary conditions. A plywood sheet was bolted to the top of the shaking table. A layer of sand was epoxied to the plywood surface to create a rough surface with a friction angle equal to that of the sand backfill. The back of the box was rigidly braced. This is an energy-reflecting boundary that was adopted for simplicity.
Fig. 2. Particle size distribution for sand backfill.
3. Materials 3.1. Backfill A dry synthetic olivine sand was used as the backfill in the test configurations. This material was selected because it is silica free and thus avoided the health danger of silica dust generation during material handling in an enclosed laboratory environment. The sand is composed of angular to sub-angular particles with a specific gravity of 2.88. The soil is uniformly graded with a maximum particle size of 2 mm, coefficient of curvature of 1.27, coefficient of uniformity of 2.5 and fines content less than 3% by weight. The particle size distribution is shown in Fig. 2. Conventional direct shear box tests [7] were carried out on
Fig. 3. Results of direct shear box tests on sand backfill.
10 cm 10 cm specimens of the sand at the same density as the sand in the shaking table models. The results of these tests are shown in Fig. 3. Sand properties are summarized in Table 1.
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Table 1 Soil properties
Table 2 Initial tangent elastic modulus for non-elasticized EPS based on correlations with density
Property
Value
Density Peak angle of friction Residual friction angle Cohesion Relative density Dilation angle
15.5 Mg/m3 511 461 0 86% 151
Note: Strength parameters from 10 cm 10cm in plan area direct shear tests.
3.2. Geofoam Three commercially available EPS materials were selected in this investigation. The first product was a Type I material according to the ASTM classification system [8] with a density of 16 kg/m3. The second product was an elasticized material with a density of 14 kg/m3. This 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 behavior. The third material was a modified Type XI material according to the ASTM classification system [8]. The geofoam inclusions were constructed from three 50-mmthick sheets of EPS glued together. The Type XI material was modified by removing 57% of the EPS foam from two of the sheets by circular coring using a 80-mm-diameter hole saw. The coring was done on a hexagonal close–packing pattern. The third sheet was only partially cored from one side so that the surface of the seismic buffer was continuous at the soil–geofoam interface in the test configuration. Coring reduced the density of the geofoam from 12 to 6 kg/m3. This material was modified in order to investigate the influence on wall response of geofoam density and modulus values that are significantly lower than those of the two unmodified geofoam materials. The density of EPS is used as a characteristic property of different commercially available products [8]. However, the mechanical property of interest when these products are used as compressible inclusions to attenuate lateral earth pressures is the elastic modulus. A large number of correlations are reported in the literature to equate the initial elastic modulus of EPS to product density. The results of these correlations for the Type I and XI materials used in this investigation are summarized in Table 2. The range of values is due to different methods of testing, specimen size, shape and rate of loading. Nevertheless, non-elasticized EPS products are linear elastic up to 1% strain. Elasticized EPS materials have a linear elastic range up to 40% strain but have a lower elastic modulus [4]. Properties of the three materials used in this investigation are summarized in Table 3. The elastic moduli reported in this table are based on the manufacturers’ literature. The values for Poisson’s ratio and yield strength are based on correlations with density for non-elasticized EPS reported
Reference
Initial tangent elastic modulus, Ei (MPa) Type I
Type XI
r ¼ 16 kg/m3
r ¼ 12 kg/m3
Hazarika [9] Missirlis et al. [10] Negussey [11] Negussey and Anasthas [12] Obrien [13] Anasthas et al. [14] Duskov [15] Duskov [16] Negussey and Sun [17] Horvath [4] Eriksson and Trank [18] Magnan and Serratrice [19]
3.76 4.55 3.30 8.22 9.17 4.48 5.73 5.7 3.00 4.20 4.79 4.06
2.12 2.98 1.80 4.94 6.02 2.98 5.48 3.84 1.29 2.40 2.87 3.03
Average Standard deviation
5.08 1.89
3.31 1.48
Note: r ¼ density. Table 3 Unmodified EPS geofoam properties Property
Elastic modulus, Eia(MPa) Poissions ratioc Yield strength (kPa)c
EPS type and density Type I
Elasticized
Type XI
16 kg/m3
14 kg/m3
12 kg/m3
4.7 0.09 30.4
0.27 0.08 23.6
3.1 (1.6)b 0.07 16.8
Note: a from manufacturers’ literature. b With 50% of material removed. c Assumed using correlations for non-elasticized EPS by Horvath [4].
by Horvath [4]. These values were required during experimental design to ensure that the combination of elastic properties and thickness of the compressible inclusion for the geofoam configurations could be expected to reduce lateral earth pressures in the physical experiments. This experimental design stage was carried out using a numerical model based on a FLAC code [20]. Examples of FLAC numerical modeling of the tests described in the current paper have been reported by Zarnani and Bathurst [21]. The back-calculated values of elastic modulus for the three products in Table 4 are discussed later in the paper. 4. Test methodology 4.1. General arrangement A total of seven test configurations were investigated. Four tests that capture the range of response in this
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Table 4 Wall model configurations Wall
Geofoam Thickness (mm)
1 (control) 2 4 6
Type (ASTM-C578-06)
0 150 150 150
Density (kg/m3)
Initial tangent elastic modulus, Ei (MPa)a
N/A I Elasticized XI
16 14 6b (50% removed by coring)
4.8 1.3 0.6
Note: a Back-calculated values from stress-strain load cycles. b Original density of EPS geofoam was 12 kg/m3.
experimental program are summarized in Table 4. Wall 1 was the control test configuration with no geofoam seismic buffer. This wall was constructed using a 1-m-high by 1.4m-wide rigid aluminum bulkhead. The three walls with a geofoam seismic buffer were constructed with the configuration illustrated in Fig. 1. The geofoam seismic buffer was placed between the aluminum wall and the sand backfill. Each wall was 1 m in height and each seismic buffer was 150 mm thick. Hence, the only variable between the seismic buffer tests was the geofoam properties. The aluminum bulkhead was supported laterally by five load cells rigidly braced to the shaking table platform. The bulkhead (and seismic buffer) was seated on an instrumented footing supported by three frictionless linear bearings. The linear bearings were seated on five load cells. The footing arrangement allowed the vertical and horizontal load measurements at the wall boundaries to be fully decoupled.
Fig. 4. Placement of 1-m-high by 1.4-m-wide geofoam seismic buffer against rigid aluminum bulkhead.
4.2. Construction The seismic buffer was held in place temporarily using duct tape (Fig. 4). The sand was placed in five 200-mmthick lifts and manually leveled. Each lift was vibrocompacted by gently shaking the table for 90 s at 9 Hz (peak base acceleration ¼ 0.1g). The final placement of the sand backfill is shown in the photograph in Fig. 5. The final density of the tests was 15.5 Mg/m3 as measured using a nuclear density meter. 4.3. Instrumentation The test models were instrumented with load cells to measure the boundary loads on the aluminum bulkhead as mentioned earlier. The load cells were button-type (Honeywell Sensotec, compression load cell model 53). Four displacement potentiometers (Data Instruments) were used to measure lateral deformations at the geofoam–soil interface. The potentiometers were mounted directly on the aluminum bulkhead and the cores passed through a 20mm-diameter opening through the bulkhead and the geofoam buffer to aluminum plates inserted flush with
Fig. 5. Final placement of sand backfill against geofoam seismic buffer.
the buffer surface (Fig. 4). An additional potentiometer was mounted against the shaking table to measure the displacement-time history of the model base. An accelerometer was also mounted directly on the shaking table to
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record the input base acceleration–time excitation history. Four other accelerometers (Schaevitz S05E Silicon model type) were embedded in the backfill soil at the locations shown in Fig. 1. The accelerometers were anchored within a 100-mm-diameter by 70-mm-deep section of PVC pipe to ensure that the devices remained level and moved in phase with the surrounding sand during shaking. The instruments were monitored by a separate highspeed data acquisition system (SERIES-7000 from Symmetric Instruments Inc. and using SYSTEM 200 software). Data from a total of 19 instruments were recorded at a speed of about 100 Hz in order to prevent aliasing and to capture peak response values.
As a check on the input base acceleration, frequency analysis of the entire measured accelerogram was carried out and this analysis is shown in Fig. 8. The measured predominant frequency of the unfiltered input accelerogram can be seen to be close to a target value of 5 Hz.
4.4. Model excitation Fig. 7. Two-second accelerogram window at amplitude step.
Following construction, the models were excited using a displacement–time history selected to match a target stepped-amplitude sinusoidal accelerogram with a frequency of 5 Hz (Fig. 6). A 2-s window of the target accelerogram is illustrated in Fig. 7. The acceleration record was stepped in 0.05g increments and each amplitude increment was held for 5 s. The maximum base acceleration was 0.8g. A 5 Hz frequency (i.e. 0.2 s period) at 1/6 model scale corresponds to 2 Hz (i.e. 0.5 s period) at prototype scale according to the scaling laws proposed by Iai [22]. Frequencies of 2–3 Hz are representative of typical predominant frequencies of medium-to high-frequency earthquakes [23] and fall within the expected earthquake parameters for North American seismic design [24,25]. This simple base excitation record is more aggressive than an equivalent true earthquake record with the same predominant frequency and amplitude [23,26]. However, it allowed all walls to be excited in the same controlled manner and this allowed valid quantitative comparisons to be made between different wall configurations. As noted earlier in the paper, the models were only excited in the horizontal cross-plane direction to be consistent with the critical orientation typically assumed for seismic design of earth retaining walls [25].
Fig. 8. Unfiltered measured base input accelerogram frequency distribution.
Fig. 6. Target base excitation accelerogram.
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5. Test results The dynamic compressive stress–strain responses of the three geofoam layers used in the models are shown in Fig. 9. The hysteretic response curves have been calculated using the forces recorded by the lateral load cells supporting the aluminum bulkhead and strains computed from the displacement potentiometers attached to the buffer surface. The measurements are taken with respect to end of static construction. The strain amplitude for Tests 2 and 4 is within the linear elastic range cited in the literature (1% strain). Test 6 with 50% material removed recorded a strain amplitude of about 2.2%. Hence, this material is likely to have exceeded the elastic limit of the material. The relative dynamic compressibility of the three geofoam materials can be compared by taking the slope of the lines passing through the origin of the plots and parallel to the long axis of the hysteresis loops. The initial compressibility of the three geofoam buffers in this investigation can be seen to vary through about one order of magnitude (e.g. Ei ¼ 4.8, 1.3 and 0.6 MPa). For an ideal linear elastic material, the load–unload response curves would fall on a line with slope equal to the linear elastic modulus of the medium. For Tests 2 and 4, the slope can be taken as an approximation to the linear initial tangent elastic modulus and the values for these lines taken from Fig. 9 are reported in Table 4. The backcalculated elastic modulus for Test 2 falls within the range of values reported in the literature (Table 2). For Test 6, the linear elastic modulus is taken from the axis slope of the loops for compressive strains over the range of 0–0.5% (Ei ¼ 0.6 MPa). The linear approximation to the hysteresis curves with larger amplitudes can be approximated by a reduced modulus value (e.g. E p ¼ 0:4 MPa). The discrepancies between manufacturers’ literature and back-calculated values for the initial elastic modulus of the EPS materials used in Tests 4 and 6 are likely due to the influence of specimen size and rate of loading noted earlier. Finally, there are more advanced models available to characterize hysteretic stress–strain loops for polymeric materials [27,28]. However, the simple descriptors used here are adequate to differentiate between the stiffness properties of the geofoam materials used in this investigation. Four accelerometers were placed in the backfill soil as described earlier. The frequency response from these devices is shown in Fig. 10 for Test 2. Comparison with Fig. 8 shows that the predominant frequency of the backfill was constant in this experiment but that there was acceleration amplification through the backfill. For example the maximum ratio of the Fast Fourier Transform (FFT) power values is 1.6. The experimental design included the measurement of vertical toe forces (Fig. 1). Fig. 11 shows the peak vertical force–time response of the four walls in this study. The horizontal line in the figure is the self-weight of the aluminum (rigid) panel wall. The vertical load for the
Fig. 9. Measured dynamic compressive stress–strain load cycles.
control test is greater than the wall self-weight during excitation which may be expected assuming some interface friction between the retained sand soil and the panel face. The difference in self-weight of the walls with and without a geofoam buffer is negligibly small due to the low density of the geofoam material. The data in Fig. 11 show that as the stiffness of the geofoam buffer material decreases, the
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Fig. 10. Acceleration frequency content and amplification in soil backfill during base excitation (Test 2).
Fig. 11. Peak vertical wall force versus time.
vertical toe forces generally increase. This may be due to greater penetration of the sand particles into the less stiff polystyrene materials. Fig. 12 shows the dynamic compression–time response of the three walls with a geofoam seismic buffer. The data have been plotted to show the average, minimum and maximum horizontal deformations taken at the same time. The data in the figures shows that as the modulus of the geofoam decreases, the magnitude of average horizontal compression increases. The lower bound on the shaded response curves for Walls 2 and 4 corresponds to measurements recorded by the lowest elevation displacement potentiometer, and the upper bound to the highest elevation displacement potentiometer. Hence, the lateral deformations over the height of the wall were in phase during dynamic excitation. For Wall 6, however, the reverse was true. Hence the deformations
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Fig. 13. Peak horizontal wall force versus peak base acceleration.
tion value during base shaking. The structures with a geofoam inclusion generated less horizontal load than the rigid structure during base shaking. The greatest reduction occurred for Test 6, which was constructed with the lowest density geofoam inclusion and the lowest stiffness. The reduction in lateral earth forces from the rigid wall case at a common peak base acceleration of 0.7g was 16, 20 and 31% for Tests 2, 4 and 6, respectively. 6. Conclusions This paper describes the details of an experimental program that was undertaken to examine quantitatively the concept of geofoam compressible inclusions to reduce the magnitude of earthquake-induced dynamic forces against rigid earth retaining wall structures. The experimental design and test methodology using a shaking table shows that large detectable differences in dynamic force reduction were observed between rigid walls with and without a geofoam seismic buffer. The results presented here demonstrate proof of concept and are a valuable set of results that can be used to verify numerical codes [21,29]. Numerical codes can then be used to investigate a wider range of problem geometry, soil conditions and geofoam thickness and stiffness with a view to optimizing these systems for site-specific earthquake design.
Fig. 12. Dynamic compression–time response of seismic buffer models.
were not in phase due to the reduced stiffness of the geofoam. A primary objective of this study was to demonstrate proof of concept by quantifying the reduction of dynamic earth forces against a rigid wall due to the inclusion of a geofoam seismic buffer. Fig. 13 shows the peak horizontal force recorded at the end of construction and during dynamic loading versus the measured peak base accelera-
Acknowledgements The authors 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). The many discussions with our colleagues K. Hatami and M. El-Emam during the preparation of this paper are also gratefully acknowledged. Finally, the authors thank D. Van Wagoner of Geotech Systems Corporation for supplying the EPS material and associated technical data.
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