Recent Research on EPS Geofoam
Seismic Buffers
Richard J. Bathurst and Saman Zarnani
GeoEngineering Centre at Queen’s-RMC
Canada
What is a wall (SEISMIC) buffer?
•
•
•
•
•
•
A compressible inclusion placed between a rigid wall and the retained soil
Purpose: To reduce lateral earth pressure by allowing controlled yielding of
backfill (soil straining)
Can be used for both static and dynamic loading conditions
For static case, reduction of pressure to near “active” case (quasi-active)
For dynamic earth pressure case, the concept of earth pressure reduction
is the same except that the loads are higher
The product of choice is expanded polystyrene geofoam (EPS)
retained soil
rigid basement wall
buffer
Geofoam blocks
First example of EPS seismic buffer
• Inglis et al. 1996
Deep basement in Vancouver BC Canada
Numerical analysis (FLAC) showed that the EPS seismic buffer
(1 m thick) could reduce seismic forces on the rigid basement
walls by up to 50%
PROOF OF CONCEPT
Experimental study:
General arrangement of shaking table tests
One control wall without buffer and 6 walls with
different buffer densities were tested
(Bathurst, R.J., Zarnani, S. and Gaskin, A. 2007. Shaking table testing of geofoam seismic buffers.
Soil Dynamics and Earthquake Engineering, Vol. 27, No. 4, pp. 324-332.)
View of geofoam buffer during construction
1.4 m
Experimental study:
Properties of EPS geofoam buffer material
Wall #
EPS bulk density
(kg/m3)
EPS initial
tangent Young’s
modulus (MPa)
EPS
Thickness
(m)
EPS type
(ASTM C
578)
1
Control structure (rigid wall with no seismic buffer)
2
16
4.7
0.15
I
3
12
3.1
0.15
XI
4
14
0.6
0.15
Elasticized
5
6†
(50% removed by
cutting strips)
1.6
0.15
XI
6
6†
(57% removed by
coring)
1.3
0.15
XI
7
1.32†
(89% removed by
coring)
0.34
0.15
XI
Note:
†
Density of unmodified EPS geofoam = 12 kg/m3
Experimental study:
Properties of backfill soil
• artificial sintered synthetic olivine material
(JetMag 30-60)
• silica-free
Property
Value
Density
Peak angle of friction
Residual friction angle
Cohesion
Relative density
Dilation angle
1550 kg/m3
51
46
0 kPa
86%
15
Experimental study:
Table excitation
1.0
0.8
Acceleration (g)
0.6
0.4
stepped-amplitude
sinusoidal base input
excitation frequency = 5Hz
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
10
20
30
40
50
60
70
80
90
100
Acceleration (g)
Time (s)
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
3-second
window
39
40
41
Time (s)
42
Experimental study:
Buffer forces
horizontal wall force (kN)
Experimental study:
Total force versus (peak) acceleration
24
22
20
18
16
14
12
10
8
6
4
2
0
Ftotal
Wall 1
(no buffer)
Wall 2
3
buffer density =16 kg/m
Wall 7
3
buffer density =1.32 kg/m
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
acceleration (g)
(Zarnani, S. and Bathurst, R.J. 2007. Experimental Investigation of EPS geofoam seismic buffers
using shaking table tests, Geosynthetics International, Vol. 14, No. 3, pp. 165-177.)
Experimental study:
Buffer compressive strains and stresses
Experimental study:
Dynamic geofoam modulus
Experimental study:
Dynamic geofoam modulus
initial elastic Young's modulus, E i (MPa)
10
modified
EPS
maximum
1
range of values reported
range ofinmodulus
values
the literature
based on
correlations
(Bathurst et al. 2006a)
reported by Bathurst et al. (2006)
average
minimum
0.1
0
2
4
6
8
10
12
geofoam bulk density (kg/m3)
14
16
18
NUMERICAL MODEL VERIFICATION
Numerical studies:
Model in FLAC
A slip and separation interface
with friction angle of 15
Numerical study:
actual shaking
Constitutive models
• Soil modeled as a purely frictional, elastic-plastic
material with Mohr-Coulomb failure criterion
Perfectly plastic
Elastic
e
Soil M-C model
• Geofoam buffer material modeled as a linear elastic,
purely cohesive material
Elastic
1%
Geofoam
Numerical studies:
Numerical results - Forces
14000
12000
Wall 2, EPS
= 16 kg/m3
experimental
= 1.32 kg/m3
Wall 7, EPS
12000
10000
total wall force (N / m)
total wall force (N / m)
Ftotal
10000
8000
numerical
6000
4000
experimental
8000
6000
4000
numerical
2000
2000
0
0
0
10
20
30
40
50
60
70
80
time (s)
Wall 2, EPS =16 kg/m3
90
100
0
10
20
30
40
50
60
70
80
90
100
time (s)
Wall 7, EPS =1.3 kg/m3
(Zarnani, S. and Bathurst, R.J. 2008. Numerical modeling of EPS seismic buffer shaking table tests,
Geotextiles and Geomembranes. Vol. 26, No. 5, pp. 371-383.)
110
Influence of constitutive model on numerical
results?
Simple M-C model
Equivalent Linear Method (ELM)
unload-reload cycles with
hysteresis behavior
modulus degradation and
damping ratio variation
Influence of material constitutive model, ELM
Shear modulus
variation
Damping ratio
variation
Resonant column testing of geofoam specimens
Cyclic load testing of geofoam specimens using PIV
EPS material properties for ELM hysteresis model
1.0
a)
EPS
type confinement
G / Gmax
0.8
Athanasopoulos et al.
(1999)
D24 - 0 kPa
D24 - 30 kPa
D24 - 60 kPa
Ossa & Romo
(2008)
D30 - 0 kPa
D30 - 30 kPa
D32 - 60 kPa
D15 - 0 kPa
D15 - 20 kPa
current study
D29 - 0 kPa
D29 - 20 kPa
Athanasopoulos et al.
used in this study
(2007)
0.6
0.4
0.2
0.0
0.00001
0.0001
0.001
0.01
0.1
1
10
100
cyclic shear strain (%)
30
b)
damping ratio (%)
25
20
Athanasopoulos
et al. (1999)
15
10
5
0
0.00001
0.0001
0.001
0.01
0.1
cyclic shear strain (%)
1
10
100
Influence of material constitutive model, ELM
1.0
a)
G / Gmax
0.8
0.6
fit with FLAC default function
0.4
0.2
range of shear modulus values for sand
(Seed and Idriss 1970)
Sand modulus
degradation &
damping curves
0.0
0.00001
0.0001
0.001
0.01
0.1
1
10
100
10
100
cyclic shear strain (%)
70
b)
damping ratio (%)
60
fit with FLAC default function
50
40
30
range of damping ratio values for sand
(Seed and Idriss 1970)
20
10
0
0.00001
0.0001
0.001
0.01
0.1
cyclic shear strain (%)
1
Numerical studies:
Influence of material constitutive model
Comparison of numerical results (RIGID wall)
20
experimental, Test 1, Rigid control wall
numerical (ELM, with hysteresis damping)
numerical (linear elastic-plastic,
with constant Rayleigh damping)
18
wall force (kN/m)
16
a)
rigid wall
geofoam
14
12
F
10
8
6
4
2
0
0
20
40
60
80
100
time (s)
(Zarnani, S. and Bathurst, R.J. 2009. Influence of constitutive model on numerical simulation of EPS
seismic buffer shaking table tests. Geotextiles and Geomembranes, Vol. 27, No. 4, pp. 308-312.)
Numerical studies:
Influence of material constitutive model
Comparison of numerical results (EPS wall)
20
experimental, Test 2, EPS density = 16 kg/m3
numerical (ELM, with hysteresis damping)
numerical (linear elastic-plastic,
with constant Rayleigh damping)
18
wall force (kN/m)
16
b)
14
12
10
8
6
4
2
0
0
20
40
60
80
100
time (s)
(Zarnani, S. and Bathurst, R.J. 2009. Influence of constitutive model on numerical simulation of EPS
seismic buffer shaking table tests. Geotextiles and Geomembranes, Vol. 27, No. 4, pp. 308-312.)
PARAMETRIC NUMERICAL STUDY
Parametric numerical studies:
Matrix of variables
Input excitation
Wall height (H) ×
backfill width (B)
Thickness of
geofoam (t / H)*
Type of EPS
geofoam #
1 (m) × 5 (m)
0
EPS19
0.3
3 (m) × 15 (m)
0.025
EPS22
0.5
6 (m) × 30 (m)
0.05
EPS29
0.85
Peak
acceleration
(f / f11)‡
0.7g
9 (m) × 45 (m)
0.1
1.2
0.2
1.4
0.4
t = seismic buffer thickness = 0 to 3.6 m
# based on ASTM D6817-06
‡ f = predominant frequency of the input excitation and
f11 = natural frequency of the wall-backfill system
Parametric numerical studies:
Model excitation
• Variable amplitude sinusoidal acceleration record:
e t t sin(2 ft)
u(t )
0.8
f = 1.25 Hz
0.6
f / f11 = 0.5 for 6 m high wall
acceleration (g)
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
2
4
6
8
10
time (s)
12
14
16
18
Parametric numerical studies:
Material properties of backfill soil
• loose to medium dense sand
• modeled as frictional material with elastic-perfectly plastic MohrCoulomb failure criterion
• small cohesion to ensure numerical stability at the unconfined
soil surface when models were excited at high frequencies
Property
Value
Unit weight
18.4 kN/m3
Friction angle
38°
Cohesion
3 kPa
Shear modulus
6.25 MPa
Bulk modulus
8.33 MPa
Parametric numerical studies:
Material properties of EPS geofoam
•
Modeled as purely cohesive material with elastic-perfectly
plastic Mohr-Coulomb failure criterion
Property
Type
EPS19 EPS22
EPS29
Density (kg/m3)
19
22
29
Yield (compressive)
strength (kPa)
81.4
102
150
Shear strength (kPa)
40.7
51
75
Young’s modulus (MPa)
5.69
6.9
9.75
Poisson’s ratio
0.1
0.12
0.16
Parametric numerical studies:
Example wall force-time response
• 3 m-high wall with EPS22 excited at 0.3 × f11
300
H=3m
EPS22
f = 0.3×f11
wall force (kN/m)
250
Control
Control
wall
Control
wall
wall
maximum
maximum
maximum
wall
wall
force
force
wall
with
with
force
geofoam
geofoam
with tgeofoam
=t 0.05×H
= 0.05×H
t = 0.05×H
maximum
maximum
wall force
wallwith
force
geofoam
with geofoam
t = 0.1×H
t = 0.1×H
maximum wall force with geofoam t = 0.2×H
200
maximum wall force-control case
150
100
50
0
0
2
4
6
8
10
time (s)
12
14
16
18
Parametric numerical studies:
New design and performance parameters
Buffer stiffness K (MN/m3 )
Isolation efficiency
E
t
Elastic modulus of geofoam
geofoam thickness
peak force (rigid wall) peak force (seismic buffer)
peak force (rigid wall)
(Zarnani, S. and Bathurst, R.J. 2009. Numerical parametric study of EPS geofoam seismic
buffers, Canadian Geotechnical Journal Vol. 46, No. 3, pp. 318-338.)
100%
Design charts
0.3×f11
a) H = 1 m
isolation efficiency (%)
60
50
70
1.4×f11
EPS19
EPS19
EPS22
EPS22
EPS29
EPS29
40
30
20
60
10
50
1.4×f11
EPS19
EPS19
EPS22
EPS22
EPS29
EPS29
40
30
20
10
0
0
0
50
100
150
200
0
50
3
0.3×f11
c) H = 6 m
60
50
150
K = E/t (MN/m )
70
1.4×f11
EPS19
EPS19
EPS22
EPS22
EPS29
EPS29
40
30
20
10
0.3×f11
d) H = 9 m
60
isolation efficiency (%)
70
100
3
K = E/t (MN/m )
isolation efficiency (%)
0.3×f11
b) H = 3 m
isolation efficiency (%)
70
50
1.4×f11
EPS19
EPS19
EPS22
EPS22
EPS29
EPS29
40
30
20
10
0
0
0
20
40
60
80
3
K = E/t (MN/m )
100
0
10
20
30
40
3
K = E/t (MN/m )
50
Influence of earthquake record
0.8
acceleration (g)
0.6
0.4
0.2
0.0
-0.2
17
-0.4
-0.6
-0.8
0
10
20
30
40
time (s)
Kobe earthquake (1995)
50
60
Conclusions
• Experimental shaking table test results and numerical simulations
demonstrated proof of concept for using EPS geofoam material as a seismic
buffer to attenuate dynamic earth pressures against rigid retaining walls.
• The magnitude of seismic load reduction in shaking table models was as high
as 40% for the softest geofoam.
• The numerical simulations of the experiments showed similar reductions in
seismic-induced lateral earth force observed in physical tests.
• A verified FLAC numerical model was used to carryout a parametric study to
investigate the influence of different parameters on buffer performance and
isolation efficiency:
• Significant load attenuation occurs by introducing a thin layer of geofoam
(> 0.05H) at the back of the wall and the attenuation increases as the
thickness of the buffer increases.
• The least stiff EPS geofoam in this study resulted in the largest load
attenuation.
Conclusions
• The practical quantity of interest to attenuate dynamic loads
using a seismic buffer is the buffer stiffness defined as:
K=E/t
• For the range of parameters investigated in this study,
K < 50 MN/m3
was observed to be the practical range for the design of these
systems to attenuate earthquake loads.
Recent example of EPS application as seismic buffer
Queen Elizabeth Water Reservoir - Vancouver - Sandwell Engineering
Protected with EPS geofoam from Beaver Plastics
Recent Research on EPS Geofoam
Seismic Buffers
Tusen Takk