SFPUC Contract No. CS-933
POLYSTYRENE AND SOIL COMPRESSION TESTING
EPS Packing Particles
One-Dimensional Test Procedure.
The one-dimensional stiffness of EPS packing particles was measured. The apparatus used was
a 6-in.-diameter CBR mold with a height of 7 in. Packing particles were placed loosely in the
mold and a 2.62-lb brass plunger placed on top. The plunger thickness was 0.25 in. The weight
of the plunger compressed the particles slightly and particles were added to bring the plunger
flush with the top of the CBR mold. The dry unit weight of the particles was d = 0.133 pcf.
Loads were applied and vertical displacements measured.
1-D Test Results
Figure 1 shows the stress-strain curve from one of the 1-D tests on the packing particles. The
best-fit equation for the data is:
v (psi)  0.0809  3.626 v  27.897 v2
(1)
Note that the 2nd order polynomial has a very small intercept at zero strain. This is a result of
curve fitting and can reasonably be ignored. Differentiating Eq. 1 results in the instantaneous
slope of the stress-strain curve, which also is the tangent constrained modulus, Dt. This equation
is:
dv
 Dt  psi   3.626  55.794 v
d
(2)
The tangent constrained modulus is shown in Figure 2. Figure 3 shows the secant constrained
modulus, Ds, of the packing particles. The data shown in Figure 3 were fitted to a linear
regression using the values for v > 0.5. This is because the early portion of the stress-strain
curve was “noisy” at very small stress levels. Also shown on Figure 3 is the secant constrained
modulus based on the regression in Eq. 1. Figure 4 compares the secant and tangent constrained
moduli. The secant modulus line in Figure 4 is that based on Eq. 1.
The relationship between constrained modulus and Young’s modulus, E, is given by:
E 1   1  2 

D
1   
(3)
in which  is Poisson’s ratio. Poisson’s ratio theoretically can range from -1 to 0.5. The
relationship given in Eq. 3 is shown in Figure 5. Rigid polystyrene foam has been reported to
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0
10
Vertical Strain, v (%)
20
30
40
50
0.4
0.5
10
Packing Particles
1-D Compression
v (psi) = 0.0809 + 3.626 v + 27.897 v2
r2 = 0.998
Vertival Stress, v (psi)
8
6
4
2
0
0
0.1
0.2
0.3
Vertical Strain, v
Figure 1. One-Dimensional Compressibility of Packing Particles
have Poisson’s ratio on the order of 1/3 (Rinde, 1970). Poisson’s ratio for the assemblage of
packing particles tested is not known.
Packing Particle Properties for Full-Scale Tests
Packing particles were placed in the 6-in.-wide 24-in.-deep space between the concrete segment
walls and the wooden secant piles. The particles were placed loosely. Following the loose
placement, the particles were compressed to a depth of 6 in., a polyethylene sheet placed on top,
and sand placed on top of the poly sheet. This was done to provide some level of confinement to
the packing particles. Assume that a vertical (volumetric) strain of 6”/24” = 0.25 was applied to
the particles. From the 1-D testing at a strain of v = 0.25 the tangent constrained modulus is
approximately Dt = 17 psi and the secant constrained modulus is approximately Ds =10 psi. If
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Vertical Strain, v (%)
20
0
10
0
0.1
30
40
0.3
0.4
Tangent Constrained Modulus, D t (psi)
25
20
15
10
5
0
0.2
Vertical Strain, v
Figure 2. Tangent Constrained Modulus, Dt, of Packing Particles
Poisson’s ratio of the particle assemblage is  = 1/3, then the secant Young’s modulus would be
approximately 6.7 psi and the tangent Young’s modulus would be approximately 11.5 psi.
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0
Vertical Strain, v (%)
20
30
10
40
50
20
Secant Constrained Modulus, D s (psi)
Packing Particles
1-D Compression
Ds (psi) = 4.62 + 25.6 v
r2 = 0.958
15
(Note: Fitted from v > 0.05)
10
5
Note: Dashed line is based on Eq. 1
(w/o intercept)
0
0
0.1
0.2
0.3
Vertical Strain, v
0.4
0.5
Figure 3. Secant Constrained Modulus, Ds, for Packing Particles
0
10
Vertical Strain, v (%)
20
30
40
50
25
Packing Particles
1-D Compression
Tangent, Dt
Constrained Moduli, D (psi)
20
17.2 psi
15
Secant, Ds
10
10.2 psi
5
0
0
0.1
0.2
0.3
Vertical Strain, v
0.4
0.5
Figure 4. Tangent and Secant Constrained Moduli for Packing Particles
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1
0.8
E/D
0.6
0.4
0.2
0
-0.8
Figure 5.
-0.4
0
Poisson's Ratio, 
0.4
Relationship between Constrained and Young’s Modulus as a Function of
Poisson’s Ratio
RCPS Testing
Cube Tests
Rigid cellular polystyrene (RCPS) geofoam was received from Thermal Foams/Syracuse, Inc.,
(6173 South Bay Road, Cicero, NY 13039 )in 8 ft x 2 ft x 5 7/16 in. panels and also in 5 in. x 10
in. x 2.75 in. “bricks.” The bricks were cut into 2 in. cubes and tested in axial compression
according to ASTM standards D6817-07 and D1621-04a (ASTM, 2009, 2009a). Tests 1 and 2
were performed with the manufacturer’s surface upward. This is referred to as the z plane. The
x and y planes correspond to a right-hand Cartesian system. In Tests 1 and 2 the axial stress, a,
was applied to the z plane. In Test 3 the axial stress was applied to the y plane to assess any
potential anisotropy. In Test 2, measurements were made if x and y (horizontal) strains.
Figure 6 shows the stress-strain results from the three tests. The test results are nearly
identical. Tests 1 and 2 are slightly offset from Test 3 because of small seating strains at the very
beginning of the test. Correcting for the small offset seating strains would bring the initial
portions of the test curves into nearly complete agreement. The initial portion of the stress-strain
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Axial Strain, a (%)
0
20
40
60
30
2 in. x 2 in. EPS cubes
Test 3
20
a ~ 16.5

a ~0.35 = 35%

Axial Stress, a (psi)
E ~ 90 psi

Tests 1 & 2 - Axial stress on z faces
Test 3 - Axial stress on y face
Test 1
E ~ 25 psi
10

Initial "Yield"
a ~ 8 psi
a ~0.04 = 4%
E ~ 200 psi
0
0
0.2
Axial Strain, a
0.4
0.6
Figure 6. Stress-Strain Results from 2-in. Cube Tests
curve is nearly linear up to an initial yield point, as shown on the figure. The secant Young’s
modulus up to this initial yield is approximately Es = 200 psi (29 kPa).
ASTM D6817-07 tabulates typical physical properties of rigid cellular polystyrene
(RCPS) Geofoam for various foam classifications. Compressive Resistance (CR) at strains of 1,
5, and 10 % are given in the ASTM Standard for the RCPS designations. The CR is defined as
the axial stress on the 2-in. x 2-in. cubes at several axial strain levels. Table 1 lists the ASTM
D6817-07 compressive resistances, CR. of EPS12 and EPS 15 RCPS Geofoam. The cube tests
are uniaxial compression tests, and the secant Young’s modulus, Es, for the cubes can be
calculated by dividing the CR by the corresponding strain level. The secant Young’s moduli, Es,
for the 2-in. cubes for the ASTM D6817-07 standard are given in Table 2. Table 3 lists the
secant Young’s moduli for the 2-in. cubes tested in this study, at strains of 1, 5, and 10%.
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Table 1. Compressive Resistances, CR, of RCPS (ASTM D6817-07) for 2-in. Cubes
Property
CR @ 1% Strain (psi)
CR @ 5% Strain (psi)
CR @ 10% Strain (psi)
EPS12
2.2
5.1
5.8
EPS15
3.6
8.0
10.2
EPS19
5.8
13.1
16.0
Table 2. Secant Young’s Moduli, Es , of RCPS (after ASTM D6817-07) for 2-in. Cubes
Property
Es @ 1% Strain (psi)
Es @ 5% Strain (psi)
Es @ 10% Strain (psi)
EPS12
220
102
58
EPS15
360
160
102
EPS19
580
262
160
Table 3. Secant Young’s Moduli, Es, of RCPS 2-in. Cubes Tested in this Study
Property
Es @ 1% Strain (psi)
Es @ 5% Strain (psi)
Es @ 10% Strain (psi)
Test 1
310
164
106
Test 2
293
161
107
Test 3
306
175
111
Average
303
167
108
Std. Dev.
9
7
3
Comparison of the moduli from the ASTM Standard in Table 2 and the test data in Table 3
indicates that the tested RCPS cubes have an average modulus at a strain of 1% of Es = 303 psi.
This is roughly the average (290 psi) of the standard EPS12 and EPS15 RCPS modulus at this
strain level.
At 5 % strain the tested cubes have an average modulus of Es = 167 psi very close
to the EPS15 standard of Es =160 psi. At 10 % strain the tested cubes have an average modulus
of Es = 108 psi, again very close to the EPS15 standard of Es =102 psi. When the manufacturer
was contacted to supply the product, they reported that the particular mix they would deliver
would most likely have properties in between the EPS12 and EPS15 standard.
Cylinder Tests
The RCPS sheets were cut with a hot wire at a target diameter of 6 in. This is the internal
diameter of a rigid steel mold used for California Bearing Ratio (CBR) tests. Three tests were
performed. The first was with a trimmed cylinder in the mold. The trimming procedure for this
first test resulted in a cylindrical specimen that was moderately tight against the inside diameter
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Vertical Strain, v, (%)
0.1
0.2
0
0.3
16
RCPS Cylinders
Test 1 : In Steel Cylinder
Test 2 : Unconfined
Test 3 : In Steel Cylinder


Vertival Stress, v (psi)

Test 2
12
Test 1
Test 3
8
4
0
0
0.1
Strain, v
0.2
0.3
Figure 7. Stress-Strain Curves from Cylinder Tests on RCPS
of the mold.
The second test was conducted without the mold so it was an unconfined
compression test. The third specimen was trimmed to be a tight fit in the steel mold. The
specimens were loaded axially in compression.
Figure 7 presents the stress-strain curves for these three tests. The test results are quite similar,
with Test 1 having the highest initial stiffness. The Test 3 data are from a snug fit in the steel
mold. If the RCPS has a positive Poisson’s ratio, the curve would have a characteristic concave
upward shape, similar to the general shape of the packing particle 1-D test shown in Figure 1.
Test 1, which was a relatively loose fit of the cylinder in the mold would have been expected to
show the concave upward shape once the RCPS expanded outward and came in full contact with
the steel mold, if Poisson’s ratio were positive. Test 2, the unconfined test, has a stress-strain
curve with the same shape as Tests1 and 3. This indicates that Poisson’s ratio for these RCPS
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Table 4. Secant Young’s Moduli, Es, of RCPS 6-in.-Diameter Cylinders Tested in this Study
Property
Es @ 1% Strain (psi)
Es @ 5% Strain (psi)
Es @ 10% Strain (psi)
Test 1
566
198
116
Test 2
460
187
109
Test 3
458
183
113
Average
495
189
109
Std. Dev.
62
8
7
specimens was practically  = 0. Referencing back to Figure 5, for  = 0 the ratio of Young’s
Modulus, E, to constrained modulus, D, is one.
Table 4 presents the secant young’s moduli for the cylinder tests (using E/D = 0). The secant
modulus at the 1% strain level is substantially higher for the cylinder test compared to the cube
tests. This stiffness would correspond to an ASTM D6817-07 designation between an EPS15
(Es = 360 psi) and an EPS19 (Es = 580 psi) material at the 1% strain level. The cylinder tests at
a strain of 5% have stiffness roughly midway between the EPS15 and EPS19 materials. At the
10% strain level the cylinders tested in this study have a secant modulus corresponding to the
EPS15 standard.
The reasons for the differences in cube and cylinder stiffness are not clear at this time. However,
the cubes have from 2 to 3 “factory” molding edges from the supplier. With 2 factory edges and
4 cut edges, the ratio of “cut to factory” surface are for the cubes is 2. With and equal number of
factory and cut edges the cut to factory surface area ratio is 1. The cylinders had the top and
bottom as factory edges. The sides were all trimmed with the hot wire knife. The cut to factory
area ratio for the cylinders was approximately 3. The effect of specimen geometry may be
significant relative to the actual field prototype. Larger RCPS blocks may have higher stiff
nesses than the 2-in.x 2-in.-cube tests indicate.
Soil Testing
Cylinder Test
The soil used in the Cornell large-scale tests was compacted in the CBR mold and tested in 1-D
compression. The water content for the Test 1 soil was w = 5.4% and the dry unit weight was d
= 98.0 pcf (15.4 kN/m3). The water content for the Test 2 soil was w = d = 105.9 pcf (16.7
kN/m3). The water content for the full-scale tests typically was w = 3-4% with d = 100.6 –
103.8 pcf (15.8 – 16.3 kN/m3).
Figure 7 shows the stress-strain curve from one of the 1-D tests on the soil. The best-fit
equations for the data for are:
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Vertical Strain, v (%)
1
2
0
3
200
1-D Compression
Compacted Sand
Test 1
v (psi) = 0.39 + 1200.98 v + 30253.46 v2
r2 = 0.9999
Test 2
v (psi) = -3.47 + 1804.18 v + 169874.39 v2
r2 = 0.9993
120

Vertical Stress, v (psi)
160
Test 2
80

Test 1
40
0
0
0.01
0.02
Vertical Strain, v
0.03
Figure 7. One-Dimensional Compression Tests for Soil used for Full-Scale Testing
Test 1: v (psi)  0.39  1200.98 v  30253.46 v2
(3a)
Test 2: v (psi)  3.47  1804.18 v  169874.39 v2
(3b)
Again, note that the 2nd order polynomials have very small intercepts at zero strain. This is a
result of curve fitting and can reasonably be ignored. Differentiating Eqs. 3a and 3b results in
the instantaneous slope of the stress-strain curve, which also is the tangent constrained modulus,
Dt. The equations are:
dv
 Dt  psi   1201  60507  v
d
(4a)
dv
 Dt  psi   1804  339749  v
d
(4a)
The tangent and secant constrained moduli for the two tests are shown in Figure 8.
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Vertical Strain, v (%)
0
1
2
3
15000
Tangent, Dt
10000

Test 2

Secant, Ds

5000
Test 1
Tangent, Dt

Constrained Modulus, D, (psi)
Soil used For Full-Scale Tests

Secant, Ds

0
0
0.01
0.02
Vertical Strain, v
0.03
Figure 8. Tangent and Secant Constrained Moduli for Soil used for Full-Scale Testing
Stiffness Comparisons
The stiffnesses of the both the prototype soil and backfill are not defined at this point. For
comparison purposes, assume that the strains mobilized in the soil and backfill will be on the
order of 5 to 10%. Table 5 lists the stiffnesses of the tested materials at these strain levels. For
the packing particles, the model-scale lab tests the particles were compressed to roughly 25%
prior to testing. Thus, the tabulated data in Table 5 for the particles will be the incremental
stiffnesses from the 1-D tests at incremental strains of 5 and 10% relative to a 25% initial strain.
For the soil tests, the vertical strains did not exceed roughly 3% due to the high stiffness of the
soil. So, the moduli at 3% strain are tabulated. Also note that for a typical drained Poisson ratio
of soil of on the order of 1/3, the ratio of E/D is 2/3, so the tabulated constrained moduli, D, for
soil shown in Table 5 would be multiplied by 2/3 to obtain Young’s moduli, E.
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Table 5. Stiffnesses of Materials Tested at Various Strain Levels
Material
3%
Packing Particles
Packing Particles
2 in. x 2. in RCPS cubes
6-in.-Diameter RCPS Cylinders
Soil, Test 1
5%
10%
Dt ~ 20 psi
Ds ~ 12 psi
Dt ~ 22 psi
Ds ~ 13 psi
Es ~ 170 psi
Es ~ 190 psi
Es ~ 110psi
Es ~ 110 psi
Dt ~ 3000 psi
Ds ~ 2200 psi
Soil, Test 1
Et ~ 2000 psi
Es ~ 1470 psi
Soil, Test 1 ( = 1/3)
Soil, Test 1 ( = 1/3)
Soil, Test 2
Dt ~ 12000 psi
Ds ~ 6800 psi
Soil, Test 2
Et ~ 8000 psi
Es ~ 4530 psi
Soil, Test 2 ( = 1/3)
Soil, Test 2 ( = 1/3)
Stiffness Ratios
Field Soil Properties
The stiffness of the soil at the field site (prototype site) was evaluated using lateral plate load test
(PLT) data (WIP, 2004). A 15.5-in.-diameter plate was loaded at several locations. The field
data were used to estimate the soil stiffness. The PLT data were evaluated at a displacement of
0.01 D, where D is the plate diameter. The rationale for this is that if EPS is placed between the
concrete segments and native soil, most of the deformation during fault movement will occur in
the EPS. This would result in low levels of lateral deformation imposed on the native soils.
Thus, a deflection of h = 0.01 D = 0.01 (15.5 in.) = 0.0015 in. ~ 0.16 in. was used in the PLT
data reduction. For the field PLT data evaluated, the lateral force at h = 0.16 in. ranged from P
= 9000 – 15000 lb.
To back-calculate the field soil modulus, the relationship between initial settlement, geometric
parameters, applied load, and soil properties given below was used (Kulhawy, et al., 1983):

P 1  2

i   
h E A
z
where:
(5)
i = h = Initial settlement,
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P = Total load,
 = Poisson’s ratio ( ~ 0.3 – 0.5 for the native field soil)
E = Young’s modulus
A = Loaded area, and
z = shape and rigidity factor (z = 1.13 for stiff, circular plate)
Using the above equation, h = 0.16 in., and P = 9000 – 15000 lb, the back-calculated Young’s
modulus of the field soil was estimated to be E = 3260 – 5430 psi. This value is taken as the
secant Young’s modulus, Es, in the following discussions.
Stiffness Ratio: Prototype
The secant modulus range for EPS12 and EPS15 Geofoams at 10% strain ranges from roughly
(Es)EPS = 100 to 160 psi. The secant modulus for the native prototype soil ranges from (Es)NS
= 3260 – 5430 psi. These values would result in a prototype stiffness ratio of:
  Es 

NS 

 40  10
  Es 

EPS Protoype

(6)
Should say Prototype in subscript
Stiffness Ratio: Model
The secant Young’s modulus for the EPS packing particles (i.e., peanuts) at 10% strain is on the
order of (Es)EPSP = 13 to 22 psi with and average of roughly 17.5 (assuming at  = 0 as with
the EPS cubes and cylinders.) The stiffness at 10% strain was used with the concept that a
significant amount of deformation will occur in the soft EPS particles. The stiffness of the test
soil in the large-scale test basin is approximately (Es)TS = 1000 psi. These values would result
in a prototype stiffness ratio of:
  Es 

TS 

 60  10
  Es 

EPSP Model

(7)
Stiffness Ratio Conclusions
The evaluations given above indicate that the prototype stiffness ratio for EPS Geofoam adjacent
to native soil would be on the order of 40 ± 10. The stiffness ratio of the lab model tests is on the
order of 60 ± 10. Thus, the is reasonable stiffness similitude between the model tests using EPS
packing particles (peanuts) and the field prototype with EPS Geofoam and the stiff native soil.
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References
Rinde, JA “Poisson's Ratio for Rigid Plastic Foams,” J. Applied Polymer Science, 14, 19131926, 1970.
ASTM D6817-07, “Standard Specification for Rigid Cellular Polystyrene Geofoam,” ASTM
International, West Conshohocken, PA, 2009.
ASTM D1621-04a, “Standard Test Method for Compressive Properties of Rigid Cellular
Plastics,” ASTM International, West Conshohocken, PA, 2009a.
Kulhawy, FH, CH Trautmann, JF Beech, TD O’Rourke, W McGuire, “Transmission Line
Structure Foundations for Uplift-Compression Loading,” EL-2870, Electric Power Research
Institute, Palo Alto, CA, 1983.
WIP, “Geotechnical Investigation, Seismic Upgrade of BDL Nos. 3 and 4 at the Hayward Fault
Crossing,” WIP Task Order No. 67-2, Waterfront Infrastructure Partners, Inc., 2004
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