NUMERICAL INVESTIGATION OF GEOFOAM SEISMIC BUFFERS USING FLAC
Saman Zarnani and Richard J. Bathurst
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 wall models with a
seismic geofoam buffer inclusion using a large shaking table. Two physical tests constructed
with EPS geofoam materials having different modulus values and a control case with no
geofoam inclusion were simulated. The paper shows that the numerical model was able to
capture the trend in earth forces with increasing base acceleration for all three models. The
numerical simulation results are also shown to be in quantitative agreement with the relative
reduction of the earthquake-induced dynamic earth forces generated against the rigid wall
structures with an EPS geofoam seismic buffer compared to the control case without seismic
protection.
INTRODUCTION
In a companion paper by Zarnani et al. (2005) the concept of reducing earth forces against
rigid wall structures by placing a compressible vertical inclusion between a rigid wall and the
backfill was reviewed for the cases of static and earthquake loading. The proof of concept has
been demonstrated for the static case from the results of small-scale laboratory tests (McGown
and Andrawes 1987, McGown et al. 1988) and a monitored field installation (Partos and
Kazaniwsky 1987). Physical shaking table tests demonstrating that the same approach can be
used to reduce the potentially much larger seismic-induced forces during earthquake have been
reported by Hazarika et al. (2003) and Zarnani et al. (2005). Both studies used a vertical
inclusion of expanded polystyrene (EPS) geofoam as the compressible layer. They demonstrated
that the peak lateral loads acting on the compressible model walls during simulated earthquake
loading were reduced to as much as 60% of the value measured for the nominally identical
structure but with no compressible inclusion. Inglis et al. (1996) reported the first documented
field installation of a rigid basement wall constructed with a compressible EPS geofoam layer for
the purpose of seismic-induced earth load reduction. The design of the structure was carried out
using the program FLAC. The results of numerical modeling predicted that a 1-m wide layer of
EPS geofoam placed between a 10 m-high wall and granular backfill could reduce lateral loads
during an earthquake event by 50% compared to the unprotected wall option.
Parametric studies using a FEM code to model rigid wall structures with a compressible
inclusion have been reported in the literature for the static loading case by Karpurapu and
Bathurst (1992). Their FEM program was first verified against the physical model tests reported
by McGown and Andrawes (1987) and McGown et al. (1988) and then used to generate design
charts. The design charts can be used to select the combination of geofoam buffer thickness and
modulus required for different combinations of wall height and granular backfill soils to
minimize static earth forces. In addition to the work of Inglis et al. (1996), other numerical
modeling studies of the seismic geofoam buffer concept have been reported by Pelekis et al.
(2000), Hazarika (2001), Hazarika and Okuzono (2002) and Armstrong and Alfaro (2003).
However, none of numerical models developed by these researchers have been verified against
instrumented physical test results. Hence, while qualitative trends in the numerical predictions
may appear reasonable, confidence in the magnitude of numerical results must be accepted with
caution.
In this study, a numerical model using the program FLAC is described that was used to
simulate the dynamic response of 1 m-high reduced-scale models of rigid walls with and without
a geofoam seismic buffer. The physical tests were carried out on a shaking table at the Royal
Military College of Canada. The physical test program and example test results are described in
the companion paper by Zarnani et al. (2005). These carefully conducted and instrumented
physical tests provide a useful dataset for verification of the numerical model.
RMC SHAKING TABLE TESTS
A brief description of the RMC shaking table tests is described here for completeness. One
meter-high by 1.4 m-wide by 2 m-long models were constructed in a strong box bolted to a large
steel shaking table. A rigid wall constructed from a stiffened aluminum bulkhead was attached to
the shaking table platform and used to retain a synthetic granular soil. The rigid wall was
attached to load cells to record total horizontal and vertical loads transmitted to the wall at end of
construction and during subsequent horizontal shaking. Accelerometers were also installed to
record accelerations recorded at the wall boundary and within the backfill. A geofoam buffer 150
mm thick was placed between the rigid wall and the backfill. A control test without the geofoam
seismic buffer was also carried out to quantify the performance benefit due to the presence of the
geofoam buffer to reduce dynamic loads on the rigid wall. Potentiometer-type displacement
devices were mounted on the front of the rigid wall to record the horizontal movements of small
metal plates attached to the geofoam-sand interface. A stepped-amplitude sinusoidal acceleration
record with a frequency of 5 Hz was applied to the base of the models in all tests. The
acceleration amplitude was increased at 5-second intervals (0.05g increments) up to peak base
acceleration amplitude in excess of 0.8g and the test terminated.
NUMERICAL MODELS
The numerical simulations were carried out using the program FLAC (Itasca 2005). The
FLAC numerical grid for the simulation of the geofoam buffer tests is shown in Figure 1. The
height of each model and the backfill width were kept at 1 m and 2 m, respectively in all tests.
The thickness of the geofoam was taken as 150 mm to match the physical tests. In this
investigation, the results of two numerical simulations with two different geofoam densities are
reported together with a control test without the geofoam buffer. The results of simulation runs
are compared to the results from the corresponding tests in the physical test program.
The backfill soil was modeled as a purely frictional, elastic-plastic material with MohrCoulomb failure criterion. This model allows elastic behavior up to yield (Mohr-Coulomb yield
point defined by the friction angle), and plastic flow at post-yield under constant stress. The soil
Figure 1 – FLAC numerical grid showing geofoam buffer, sand backfill and boundary
conditions
model is described by constant values of shear and bulk elastic modulus for pre-yield behavior.
The results of direct shear box tests on specimens of the same sand material have been reported
by El-Emam and Bathurst (2004, 2005) and are summarized in Table 1. They also carried out
numerical simulations of the direct shear tests using a FLAC code to back-calculate the peak
plane strain friction angle of the soil and modulus values. The peak plane strain angle from the
shear box simulations was φps = 58°, which is consistent with the value predicted using the
equation by Bolton (1986) to convert the peak friction angle from conventional direct shear box
tests to plane strain conditions. The soil properties for the backfill sand used in the numerical
analyses are also summarized in Table 1.
The geofoam buffer material was modeled as a linear elastic, purely cohesive material. The
elastic properties of EPS geofoam have been shown to vary linearly with EPS density. A
relationship proposed by Horvath (1995) was used to calculate the elastic modulus of the two
EPS materials (and hence the bulk and shear modulus values). While a more advanced non-linear
strain hardening model could have been implemented in the FLAC code, the simple constitutive
model adopted here was judged to be sufficient since the measured compressive strains in the
physical models were less than the elastic strain limit of 1% determined from rapid uniaxial
compression tests reported by the manufacturer (BASF 1997). The elastic properties assumed for
the geofoam materials in this investigation are shown in Table 2.
A no-slip boundary at the bottom of the sand backfill was assumed to simulate the rough
boundary in the physical tests (i.e. a layer of sand was epoxied to the bottom of the strong box
container). A slip and separation interface between the buffer and the soil was specified. This
Table 1 - Soil properties (from El-Emam and Bathurst 2004, 2005)
Property
Bulk unit weight
From direct
shear box tests*
Peak angle of friction
51°
Residual friction angle
46°
Cohesion
0
Dilation angle
15°
Shear modulus
Bulk modulus
* specimens 10 cm by 10 cm in plan area
Value
15.7 kN/m3
Back-calculated from plane strain direct
shear box test simulations using FLAC
58°
46°
0
15°
7 MPa
6 MPa
Table 2 - EPS geofoam properties (from Horvath 1995)
EPS density
Property
12 kg/m3
16 kg/m3
Value
Bulk modulus
Shear modulus
Cohesion
0.286 MPa
12 MPa
16.8 kPa
0.5 MPa
21 MPa
30.5 kPa
interface allowed the soil and buffer to separate with no tensile stress. An interface friction angle
of 15° was assumed for the rough geofoam-sand interface based on recommendations by Xenaki
and Athanasopoulos (2001) and Kramer (1996). The normal and shear stiffness values of the
interface were set to ten times the equivalent stiffness of the soil, as recommended in the FLAC
manual (Itasca 2005). 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).
The plane strain models were constructed in one step. Next, gravity was turned on in one
step and the model was allowed to come to equilibrium. A constant amplitude sinusoidal base
excitation record of 0.1g and a frequency of 9 Hz was then applied for 5 seconds to simulate the
gentle shaking (vibro-compaction) that was used in the physical tests to compact the sand
backfill. Following compaction, the system was brought to equilibrium once again. The base and
the two vertical boundaries of the models were then excited using the same base input
acceleration record used in the physical tests (see Zarnani et al. 2005) but terminated at 0.7g. The
horizontal input acceleration was actually applied using an equivalent velocity record (i.e.
integrated acceleration record) with base line correction to ensure zero displacement at the base
at the end of shaking. Simulation runs took about 10 hours on a personal computer with a P43.6GHz CPU and 1GB of RAM memory. Data was acquired at a rate of 500 Hz to avoid aliasing
effects and to capture the peak values of dynamic wall response induced by base shaking.
NUMERICAL RESULTS
Due to page constraints, buffer deformation and soil acceleration predictions are not
reported here. However, the most important measurement to quantify wall performance with and
without a geofoam buffer inclusion are the histories of wall force at peak acceleration events
during dynamic loading. Figures 2a through 2d provide a summary of wall force versus peak
base acceleration for both physical and numerical experiments. The horizontal axes in the figures
refer to the peak horizontal base acceleration acting towards the wall during the test. The vertical
axis is the total horizontal earth force on a per-meter running length of wall basis.
The data for the physical tests show that there was an overall trend of increasing wall force
with base acceleration in each test and this trend was captured by the numerical results. The
experimental and numerical results also show that there is a significant reduction in wall force
during base shaking for the two walls constructed with an EPS geofoam inclusion compared to
the reference control wall without a compressible layer. Furthermore, there are small but
detectable lower forces recorded for the wall constructed with the lowest EPS density compared
to the wall with higher density geofoam. A summary of the numerical responses is presented in
Figure 2d to highlight the performance differences between the three test configurations.
There are differences in quantitative values between numerical and physical test results at
some acceleration values. For example, the force-base acceleration slope for the control wall was
steeper than that for the physical experiment. However, for the geofoam buffer simulations there
was good agreement over a wide range of base acceleration values. A persistent discrepancy
between physical and numerical results can be noted at the end of construction following vibrocompaction. Numerical results are consistently lower at the start of the tests and during the
initial application of the base excitation record. The under-prediction is in the range of 15 to
43%. This discrepancy is believed to be due to the inadequacy of the simple soil model and
numerical compaction procedure adopted to generate the initial soil state in the physical
experiments. In the physical tests, the soil was vibro-compacted in 200 mm lifts and this likely
resulted in locked in stresses that were not generated in the numerical simulations. However,
once the base excitation record applied during the physical experiments reached about 0.1g (the
peak acceleration amplitude used during vibro-compaction) these locked in stresses were
released. The improvement in numerical predictions can be seen to occur once this threshold
peak acceleration level is exceeded.
The results of physical experiments and numerical simulations at peak base acceleration
values applied at the end of numerical simulations are summarized in Table 3. The data shows
that at a common base acceleration value, the reduction in total earth forces ranged from 15 to
16% in the physical tests and this range was reasonably close to the predicted range of 18 to 21%
from the numerical simulations.
CONCLUSIONS
A series of numerical simulations are reported using a FLAC model to predict the dynamic
load response of reduced-scale rigid walls constructed with a geofoam seismic buffer and excited
using a large shaking table. The constitutive models used for the component materials in the
18000
18000
16000
14000
physical
test
12000
10000
8000
6000
wall force (N/m)
wall force (N/m)
14000
16000
FLAC
6000
2000
2000
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
peak base acceleration (g)
peak base acceleration (g)
b) geofoam density = 12 kg/m3
18000
18000
16000
16000
14000
FLAC
12000
physical
test
10000
8000
6000
wall force (N/m)
14000
physical
test
8000
4000
a) no geofoam inclusion (control wall)
wall force (N/m)
10000
4000
0
FLAC
12000
12000
10000
8000
6000
4000
4000
2000
2000
no geofoam
3
geofoam bulk density=16 kg/m3
geofoam bulk density=12 kg/m
0
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
peak base acceleration (g)
peak base acceleration (g)
c) geofoam density = 16 kg/m3
d) comparison of numerical results
Figure 2 – Wall force versus peak base acceleration from physical and numerical experiments
simulations (i.e. soil and EPS geofoam) were kept purposely simple as a first attempt to simulate
the physical test results. While the earth forces at the end of construction (after vibrocompaction) were under-predicted, the predicted earth force response of the models to
subsequent base shaking are judged to be reasonably accurate. The relative improvement of the
geofoam models with respect to the (control) rigid wall without seismic protection was very
close between physical and numerical results.
The FLAC model described here holds promise as a tool to investigate the prototype-scale
response of geofoam seismic buffers using a wider range of geofoam products, compressible
layer thickness, wall heights, seismic records and different soil backfills. The ultimate objective
Table 3 – Comparison of numerical and physical wall forces at maximum base acceleration
EPS density
(kg/m3)
Control
(no buffer)
16
12
∗ from FLAC model
Maximum
base
acceleration∗
(g)
Physical test
FLAC model
Force
(kN/m)
Force
reduction
(%)
Force
(kN/m)
Force
reduction
(%)
Difference
in force
values
(%)
0.7
12.8
-
14.8
-
15
0.7
0.7
10.9
10.8
15
16
12.2
11.7
18
21
12
8
of parametric analyses using this FLAC code (or improvements) is the development of design
charts that can be used by engineers to optimize the selection of geofoam type and thickness with
respect to project-specific conditions.
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). The many discussions with our colleagues K. Hatami
and M. El-Emam during the preparation of this paper are also gratefully acknowledged.
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