Passive Force on Bridged Abutments and Geofoam Inclusions
with Large-Scale Test
Eric Glenn Scott
A project submitted to the faculty of
Brigham Young University
In partial fulfillment of the requirements for the degree of
Master of Engineering
Kyle M. Rollins, Chair
Michael A. Scott
Paul W. Richards
Department of Civil Engineering
Brigham Young University
July 2015
Copyright © 2015 Eric Glenn Scott
All Rights Reserved
ABSTRACT
Passive Force on Bridge Abutments with Geofoam Inclusions
from Large-Scale Test
Eric G. Scott
Department of Civil and Environmental Engineering, BYU
Master of Engineering
A vertical zone of compressive material or an “inclusion” can be used as a barrier to decrease
lateral earth pressures placed on structures. Such load reduction can be of particular importance
when determining possible by either the structure or the soil backfill that is being separated. The
compressible material is typically expanded polystyrene (EPS), or geofoam. Geofoam inclusions
are often considered in reducing reduced active earth pressures felt by backfill structures.
However, in bridge abutments it is also necessary to understand the passive force versus
backwall deflection relationship when geofoam inclusions are in place. Neither current design
codes nor available field tests provide any understanding regarding the ability of a geofoam
inclusion to reduce passive lateral loads felt by a structure and the corresponding soil backfill
resistance. To explore this issue, large-scale field tests were conducted with a geofoam inclusion
acting as the barrier between the backfill soil and the simulated abutment backwall. By inducing
lateral forces to displace the backfill wall, it was possible to measure passive force-displacement
curves as well as geofoam and soil backfill compression behavior. These tests are the first of
their kind to investigate the behavior of geofoam inclusions on passive lateral soil resistance.
Keywords: passive force, EPS geofoam, bridge abutment, deflection curves
TABLE OF CONTENTS
1
2
Introduction ........................................................................................................................... 1
1.1
Objectives ......................................................................................................................... 2
1.2
Scope of Work.................................................................................................................. 2
1.3
Organization of Report ..................................................................................................... 3
Literature Review ................................................................................................................. 5
2.1
2.1.1
Horvath (1997) .......................................................................................................... 6
2.1.2
Ertugurl and Trandafir (2012) ................................................................................... 7
2.1.3
Ertugurl and Trandafir (2011) ................................................................................... 8
2.1.4
Bathurst, Zarnani, and Gaskin (2007) ....................................................................... 9
2.1.5
Bathurst and Zarnani (2013) ................................................................................... 10
2.2
Geofoam Properties ........................................................................................................ 11
2.3
Passive Force-Deflection Relationship for Sand ............................................................ 13
2.3.1
Duncan and Mokwa (2001) .................................................................................... 15
2.3.2
Cole and Rollins (2006) .......................................................................................... 16
2.4
3
Current Understanding of Geofoam Inclusions ............................................................... 5
Ultimate Passive Force Theories .................................................................................... 17
2.4.1
Rankine Earth Pressure Theory .............................................................................. 18
2.4.2
Coulomb Earth Pressure Theory ............................................................................. 18
2.4.3
Log-Spiral Theory................................................................................................... 19
Test Layout and Procedures .............................................................................................. 21
3.1
Test Layout ..................................................................................................................... 21
3.1.1
The Reaction Foundation ........................................................................................ 22
3.1.2
Loading Apparatus .................................................................................................. 23
3.1.3
Pile Cap ................................................................................................................... 25
3.1.4
Geofoam Inclusion .................................................................................................. 26
3.1.5
Soil Backfill Zone ................................................................................................... 27
3.2
Testing Instrumentation.................................................................................................. 28
3.2.1
String Potentiometers and Reference Frame........................................................... 28
3.2.2
Geofoam Compression............................................................................................ 30
3.2.3
Heave and Vector Displacement ............................................................................. 31
iii
3.2.4
3.3
4
Test Procedure ................................................................................................................ 33
3.3.1
Geofoam Placement ................................................................................................ 34
3.3.2
Backfill Placement and Test Preparation ................................................................ 34
3.3.3
Pile Cap Displacement ............................................................................................ 34
3.3.4
Final Measurements ................................................................................................ 35
Test Results .......................................................................................................................... 37
4.1
Passive Force-Deflection Curves ................................................................................... 37
4.2
Overall Failure Patterns .................................................................................................. 41
4.3
Backfill Heave and Surface Cracking ............................................................................ 45
4.4
Longitudinal Displacement and Strain of Geofoam and Backfill .................................. 48
4.4.1
5
6
Red Sand Columns and Internal Failure Surface .................................................... 32
Backfill Strain ......................................................................................................... 50
4.5
Backfill Soil Displacement Vectors ............................................................................... 52
4.6
Compression of Geofoam............................................................................................... 54
Analysis ................................................................................................................................ 57
5.1
Prediction of Passive Force ............................................................................................ 57
5.2
PYCAP Performance Prediction .................................................................................... 59
5.3
Observed Pile Cap Performance .................................................................................... 61
Conclusions .......................................................................................................................... 63
iv
v
LIST OF FIGURES
Figure 2-1: Geometry of the Log-Spiral Failure Plane (Marsh 2013) .......................................... 20
Figure 3-1: Plan View and Cross Section of Testing Layout ....................................................... 24
Figure 3-2: Plan View and Cross Section of Geofoam Inclusion ................................................. 25
Figure 3-3: Backfill Soil Gradation Curve.................................................................................... 28
Figure 3-4: String potentiometer locations on the pile cap (Marsh 2013) .................................... 29
Figure 3-5: Geofoam and Backfill Grid System ........................................................................... 32
Figure 3-6: Red Sand Columns to determine Failure Plane ......................................................... 33
Figure 4-1: Baseline for 0° Skew Test .......................................................................................... 38
Figure 4-2: Total Load, Baseline Load, Passive Force Comparison ............................................ 39
Figure 4-3: Passive Force versus Deflection ................................................................................ 39
Figure 4-4: Passive Force versus Displacement for 0° Skew Test and Geofoam Inclusion ......... 40
Figure 4-5: Internal Failure Plane ................................................................................................. 43
Figure 4-6: Failure Plane at Backfill Surface ............................................................................... 43
Figure 4-7: Geofoam Shear Cracking at the Corners of the Pile Cap ........................................... 44
Figure 4-8: Geofoam Inclusion Bending at the End of the Second Loading ................................ 44
Figure 4-9: Backfill Heave Contours and Cracks on a 2-ft grid for the Sand Backfill Test
(Marsh 2013) ................................................................................................................................. 46
Figure 4-10: Backfill Heave Contours and Cracks for the Geofoam Inclusion Test .................... 47
Figure 4-11: Total Backfill Displacement versus Distance from Backwall Face at Selected
Cap Displacements for 1st Loading of the Geofoam Inclusion Test. ........................................... 48
Figure 4-12: Total Backfill Displacement versus Distance from Backwall Face at Selected
Cap Displacements for 2nd Loading of the Geofoam Inclusion Test ........................................... 49
vi
Figure 4-13: Total backfill displacement versus distance from backwall face at selected cap
displacement intervals for the sand backfill test (Marsh 2013) .................................................... 49
Figure 4-14: Backfill Compressive Strain versus Original Distance from Pile Cap Face ............ 51
Figure 4-15: Backfill Compressive Strain versus Original Distance from Pile Cap Face for
Second Push .................................................................................................................................. 51
Figure 4-16: Backfill compressive strain versus original distance from backwall face at
selected displacement intervals for the sand backfill test (Marsh 2013) ...................................... 52
Figure 4-17: Soil Displacement for Geofoam Inclusion Testing .................................................. 54
Figure 4-18: Grid System on Geofoam ......................................................................................... 55
Figure 4-19: Geofoam Compression versus Distance from Pile Cap for Specified Passive
Forces ........................................................................................................................................... 55
Figure 5-1: Comparison of Low Bound and High Bound PYCAP Passive Force versus
Geofoam and Sand Backfill Deflection Curves ............................................................................ 59
Figure 5-2: Comparison of Low Bound and High Bound PYCAP Passive Force versus
Geofoam and 0° Skew Deflection Curves .................................................................................... 61
Figure 5-3: Rankine Failure Zone ................................................................................................. 62
vii
1
Introduction
A vertical zone of compressive material or an “inclusion” can be used as a barrier to
decrease lateral earth pressures placed on structures. Such load reduction can be of particular
importance when determining possible failure by either the structure or the soil backfill that is
being separated. The typical material of choice for the inclusion is expanded polystyrene (EPS),
or geofoam. Research indicates that EPS geofoam panels of low stiffness installed against rigid
retaining structures will readily compress under the lateral earth pressures exerted by the retained
soil mass since geofoam is intentionally the least stiff component (Ertugrul and Trandafir 2011).
Although the influence of geofoam inclusions has been investigated for the case of active
earth pressure(Ertugrul and Trandafir 2011; Ertugurl and Trandafir 2012; Horvath 1997), very
few tests have previously been conducted to examine the effect of geofoam inclusions on passive
earth pressure (Bathurst and Zarnani 2013; Horvath 1997). In some cases, it might be desirable
to isolate the bridge structure and abutment walls from the passive backfill force. For example, in
the event of liquefaction in an underlying sand layer, lateral spread displacements could cause
passive force to develop against the abutment as the overlying backfill soil slides towards the
bridge abutment. Alternatively, dynamic forces from inertial earthquake loading could cause
structure movement towards a soil backfill leading to large passive pressures on the backwall.
1
By performing large scale tests that use geofoam as a buffer between a bridge structure
and backfill soil we will be able to draw conclusions as to the effectiveness of including geofoam
as a compressible inclusion. Comparisons will be made with a previous test involving the same
backfill soil but without a geofoam inclusion. This report describes the properties of the backfill
and geofoam materials, describes the testing procedures employed, and provides results from the
tests. Test results include passive force-deflection curves, lateral and vertical deformation of the
geofoam and backfill soil, shear pane formation and surface cracking patterns, and backfill
strain.
1.1 Objectives
The research and presentation of the corresponding results will try to meet the following
objectives:
1. Identify the overall reduction in peak passive force as a result of a geofoam inclusion
2. Compare the changes in the passive force- deflection curves between tests with and
without a geofoam inclusion.
3. Identify the effect of geofoam inclusions on the backfill deformation, crack and internal
shear patterns, and the backfill strain.
1.2 Scope of Work
Large-scale lateral passive force tests for this study involved a 5.5 ft high pile cap used to
simulate a bridge abutment along with transverse wingwall. A compressible inclusion consisting
of geofoam blocks was constructed adjacent to the pile cap with that was 3 ft deep in the
direction of loading, 16 ft transverse to the loading and 6 ft tall. Clean sand was compacted to a
depth of 6 feet behind the geofoam inclusion. Load was applied incrementally until cumulative
deflection of the pile cap reached about 6 inches so that the influence of the inclusion could be
2
examined at large deflection levels. Because the testing of the geofoam block included using
dense, clean sand with a 0° skew angle similar to testing done by Marsh (2013), such test results
serve as a baseline comparison for the testing with the geofoam inclusion conducted in this
study. Therefore, comparisons between the results from this study will be made with previous
tests conducted by Marsh (2013) to highlight the influence of the geofoam inclusion on passive
force behavior.
1.3 Organization of Report
This report will begin with a literature review that addresses the current knowledge of
geofoam and how inclusions specifically change surrounding soil behavior. Attention will be
given to the passive force-deflection relationships for backfills involving soil only. Additionally,
a discussion will be presented with regards to the need for further research on geofoam
inclusions. Next, the testing layout, setup, and site features will be presented. The tests results
will then be compared against the current methods used for predicting the passive force. Lastly,
appropriate conclusions will be presented along with recommendations.
3
4
2
Literature Review
The concept of including a compressible inclusion for geotechnical uses is not new to
today’s society. Materials such as cardboard, glass-fiber insulation, or even bales of hay have
been used with the intent to reduce stress felt by surrounding soil (Horvath 1997). While the
fore-mentioned materials have provided solutions to stress problems for soils, they have their
short-comings; materials that have organic properties often display unpredictable stress-strain
relationships (Horvath 1997). Even though there is not a lot of information present from largescale testing on geofoam inclusions subject to dynamic loading, there is a basic understanding of
being able to reduce forces felt by both structures and surrounding soil through the use of a
compressible system.
2.1 Current Understanding of Geofoam Inclusions
Various applications of compressible inclusions in geotechnical settings are currently in
use. While proper design and use must be determined by an engineer who understands geofoam
properties, there are various categories in which geofoam inclusions have been implemented.
These include the use of geofoam behind earth-retaining structures, beneath foundation elements,
or above pipes, culverts, and tunnels (Horvath 1997). Additionally, Athanasopoulus et. al (1999)
suggest EPS geofoam blocks for use in scenarios involving thermal insulation, lightweight fills,
compressible inclusion, and vibration damping. The selection of a material to be used as the
inclusion requires a product that can be purposefully designed as the weakest link in a scenario.
5
Thus, the geofoam must readily compress before the failure of surrounding soil or an adjacent
structure. Additionally, as the compressible inclusion is in direct contact with soil, it must be able
to withstand the demands of biodegradation. Consequently, because geofoam readily compresses
under loading, and can endure the stresses of an organic material, it is widely selected as the
material of choice for earth-fill scenarios. Furthermore, geofoam proves to be advantageous
because of the ability to accurately measure and predict a stress-strain relationship for the
material whereas other inclusions have fallen short in this regard.
2.1.1 Horvath (1997)
Horvath (1997) described the early state of understanding regarding geofoam inclusions
and presented potential uses of geofoam inclusions. In particular, he hypothesizes the idea of a
‘Reduced Earth Pressure (REP) Wall’ concept along with a ‘Zero Earth Pressure (ZEP) Wall’
idea when referring specifically to retaining wall design. The major difference between the
ability to obtain a ZEP wall versus that of a REP wall is whether a designer decides to include
layers of tensile reinforcement in the soil backfill, such as a geogrid or geotextile product. Thus,
by implementing a correct combination of stiffness from geofoam and a horizontal reinforcement
in the soil backfill, designers can decrease the lateral earth pressures to zero. The author further
contends that the seismic stresses on soil backfills caused by shaking can be significantly
reduced through use of a compressible inclusion. He mentions that the concept of using a
compressible inclusion to reduce the seismic earth pressure can be beneficial for both new
construction and existing structures. Retrofitting existing structures with a geofoam inclusion can
help to satisfy the current code requirements for seismic resistance. Numerous finite element
models have been run to try and predict the behavior of a seismic loading scenario where
geofoam was used to attenuate the lateral forces. However, the author does mention that most of
6
the research and experimentation (both computer models and large-scale testing) have been done
with coarse-grained soils. Thus, more attention is necessary for fine-grained soils.
2.1.2 Ertugurl and Trandafir (2012)
Ertugurl and Trandafir conducted studies having to do with yielding flexible retaining
walls that have geofoam inclusions and the corresponding reduction in static lateral loads. In so
doing the authors worked with two different geofoam inclusions of varying thickness. The
authors used a stiff sand box and performed three tests to measure the lateral loads and the wall
stem (retaining wall) deflections. The first test (used as a baseline) did not include a geofoam
inclusion but rather had a dry clean sand in direct contact with the yielding wall. In the second
and third tests, EPS geofoam panels of 50mm and 100mm thick were used, respectively. The dry
sand backfill was placed in four lifts of approximately 180mm thick. After backfill placement
was completed, the lateral stresses were recorded at four different locations along the retaining
wall and the lateral wall displacement was measured at the top and mid-height of the wall.
Testing was done by releasing hydraulics jacks that restricted the lateral movement of the
yielding wall, thereby stimulating behavior expected of a flexible or yielding retaining wall. Data
acquisition occurred until the yielding wall saw no more lateral deflection. Thus, testing was able
to find correlation between the wall fixidity and wall deflection. Furthermore, by comparing the
results from the three tests, the authors were able to draw conclusions as to the effectiveness of a
geofoam inclusion at reducing wall deflections. They concluded that the presence of a geofoam
inclusion reduced the wall deflection depending on the wall flexibility and the inclusion
thickness. This reduction in wall deflection and lateral forces was attributed to the arching effect
in the backfill soil by the lateral compression of panels of geofoam inclusions.
7
2.1.3 Ertugurl and Trandafir (2011)
With the intent of understanding how geofoam inclusions can be used to reduce lateral
loads in a static setting, Ertugurl and Trandafir (2011) performed testing to stimulate using a
rigid, non-yielding retaining wall. Additionally, a finite-element model was developed to
estimate the lateral earth pressures against various retaining walls that both included and
disregarded a compressible inclusion. Small-scale testing was done by using a 0.7 meter high
wall. Four different model wall configurations were tested in the physical study. In the first
configuration, the lateral stresses on the wall were measured without a geofoam inclusion. This
served as the control test for the other three test set-ups that included geofoam panels of three
thicknesses characterized by a thickness to height ratio. Thickness to height ratios of 0.07, 0.14,
and 0.28 were tested by installing the appropriate geofoam inclusion behind the rigid retaining
wall. Four earth pressure cells were installed with a 200-mm spacing along the height of the wall
to measure the lateral earth pressures. These pressure cells were installed in small recesses in the
wall to ensure that the sensor was flush with the face of the wall that sat against the geofoam
inclusion.
Finite-element modeling was performed to be able to accurately predict the lateral earth
pressures that could be experienced by the rigid retaining wall. Boundary conditions for the
model included horizontal and vertical displacement restrictions on bottom horizontal boundary
along with a horizontal displacement boundary along vertical extension of the wall. Furthermore,
to produce reasonably accurate results, an elastoplastic model was used for the soil backfill
whereas a linear-elastic model was implemented for the geofoam. The results from the pressure
cells used in the physical model were compared against the finite-element model.
8
From the physical and finite-element models, the authors were able to draw conclusions
as to the effectiveness of a geofoam inclusion at reducing lateral earth pressures on a rigid, nonyielding retaining wall. The relative thickness and stiffness of the geofoam inclusion appeared to
be the biggest factor in determining a lateral earth pressure reduction. Both models indicated a
significant reduction in the earth thrust when the set-up included a compressible inclusion
installed behind the wall (Ertugrul and Trandafir 2011).
2.1.4 Bathurst, Zarnani, and Gaskin (2007)
Large-scale testing for geofoam inclusions subjected to dynamic forces was stimulated by
Bathurst, Zarnani, and Gaskin (Bathurst et al. 2007). Testing was done using a shake-table with
the intent to understand geofoam’s ability at reducing dynamic forces that would be present from
earthquake or other types of lateral loading. The test set-up included a test without a geofoam
inclusion (base-line) and three other tests with geofoam that had varying densities. By merely
changing the geofoam density between the different tests, authors were able to draw conclusions
to the effectiveness of a geofoam inclusion at attenuating dynamic forces felt by a rigid retaining
wall. The instrumentation for the test set-up included the use of pressure cells placed against the
boundary of the retaining wall and the geofoam inclusion. Also, displacement potentiometers
were placed at the boundary between the soil backfill and the geofoam to show the lateral
deformations in the geofoam during loading. Embedded in the soil backfill were four
accelerometers that allowed for the recording of the soil backfill movement. In order to stimulate
earth-quake loading, the models were excited by using an acceleration history that increased in
0.05g increments and held each amplitude for 5 seconds. The maximum base acceleration from
the shake tables was 0.8g. The model was excited only in the horizontal cross-plane direction in
order to be consistent with the critical orientation for the seismic design of retaining walls.
9
In looking at the results, researchers used hysteric response curves developed from the
recorded forces of the pressure cells and strain values computed from the displacement as
measured by potentiometers. However, of greatest importance were the results found from
plotting the force felt by the pressure cells located at the retaining wall against the base
acceleration from the shake-table. The authors show that structures that included geofoam
against the retaining wall generated less horizontal load than the rigid wall without an inclusion
during dynamic shaking. Furthermore, a reduction was shown by using a geofoam inclusion with
an initial stiffness of 12 kg/m3, and then removing 50% of the foam via coring to produce a new
density of 6 kg/m3. Researchers were able to measure a 31% reduction in lateral forces when
comparing the above mentioned geofoam inclusion against the rigid retaining wall at a common
peak base acceleration of 0.7g. Such results prove geofoam’s ability to attenuate horizontal
forces when a system is subject to dynamic loading.
2.1.5 Bathurst and Zarnani (2013)
In order to justify their work on force attenuation of dynamic loads by geofoam inclusions,
Bathurst and Zarnani used several numerical models for comparison against large-scale testing
scenarios. The authors tried to produce computer models that closely displayed results measured
from their shake-table testing (Bathurst et al. 2007). The first of such models was a displacement
model that used springs to measure the forces acting on the various components of the test set up.
A linear failure plane was assumed to propagate through the backfill soil from the heel of the
buffer at an angle to the horizontal. Thus, spring components were used to determine the force
present in both the geofoam-soil backfill boundary and the boundary created by the failure plane.
Multiple springs were used at each boundary condition to model both the normal forces and the
interface shear forces. Using a dynamic loading pattern on the shake-table as described in section
10
2.1.4, the authors found that the numerical displacement model was a very accurate fit for
determining the peak force on the backfill wall. There were various discrepancies in the model
up the excitation acceleration of 0.7g. They estimated that at higher accelerations there are more
complex system responses that cannot be accurately captured by the simple displacement model
that was employed.
Authors additionally used the finite difference method computer program FLAC to
estimate the peak forces felt by the test set-up. The first of such models employed a linear-elastic
plastic geofoam material subjected to a Mohr-Coulomb failure criterion and Rayleigh damping.
A second model used the equivalent linear method to also estimate the peak force felt by the
backfill wall during dynamic loading. Models were found to show that there is reasonably good
agreement between measured and predicted results regardless of the model type.
Through the process of developing numerical models to estimate the peak backwall
forces that were reduced by geofoam inclusions, the authors aimed to provide useful design
information to the engineering community through preliminary design charts. Through the
numerical models that essentially confirmed the physical test models, design charts were created
to quantify the isolation efficiency of geofoam inclusions based on their values for Young’s
modulus, the type of geofoam used, and thickness of the inclusion.
2.1 Geofoam Properties
As shown by various studies on geofoam inclusions, the most important properties when
selecting an inclusion are the geofoam density and the thickness to be used in the set-up. Horvath
speculates that the minimum density of geofoam that can be manufactured is 10 kg/m3 or slightly
less (Horvath 1997). Manufacturing geofoam inclusions with density lower than 10 kg/m3 would
11
result in an insufficient fusion between the individual expanded polystyrene beads. Insufficient
bonding between these beads would lead to a material that would readily break apart. Thus,
selecting a material that has a specific density that allows for ready compressive but still
provides adequate strength becomes the challenge. “Experience indicates that the minimum EPS
density that strikes an economical balance between stiffness and durability is approximately 12
kg/m3” (Horvath 1997). Using a high density of geofoam can lead to strength benefits for system
as long as the geofoam inclusion is the weakest component of a set-up. By being weaker than the
other various components, one can assure that a geofoam inclusion will readily compress under
static or dynamic loads. Hesitation can arise from the inclusion of allowing something overly
soft in a system. Thus, mid-range density foams are often used because they are lower in density
yet still strong, or stiff, enough for operation purposes.
Selecting a thickness of geofoam requires the ability for soil to mobilize resistance.
Traditional approaches for designing a retaining structure would require that sufficient strength
be provided to resist at-rest earth pressure or the pressure from a dynamic loading scenario.
Using a geofoam inclusion in the system would allow for a structure to be designed with lower
requirements for forces yet still have an ability to withstand the stresses. Designing a geofoam
inclusion for thickness requires for arching to occur within the soil. Thus, it is desired for the
compression of a compressible inclusion to be sufficient as to allow soil to strain and mobilize its
strength. If a small thickness inclusion were used, it would compress easily but not allow for soil
arching to occur and would be useless to the system. While geofoam thickness is an interesting
parameter in design, internal strain of geofoam blocks is only partially dependent on thickness.
Internal strain is also a function of foam density and strain rate (loading rate) of geofoam
inclusions (Bret Lingwall, email correspondence, May 07, 2013).
12
A basic method for selecting the proper thickness, as described by Horvath, requires
matching the “displacement of the retained soil necessary to mobilize the active state with the
stress-displacement characteristics of the compressible inclusion” (Horvath 1997). Since the
stress-displacements of geofoam inclusions are a function of its stress-strain behavior and
thickness, designers can appropriately select the required thickness to be used in specific
applications. Other approximations for determining the thickness to be included are frequently
used throughout the industries that are based on intuition and experience.
Another important property of geofoam inclusions is Young’s modulus of elasticity.
According to Athanasopoulus et al (2009), in geofoam with “low compressive strains (up to
approximately 1%), the geofoam appears to behave linearly and an initial tangent Young’s
modulus of elasticity, Eti, can be defined. He suggests the following empirical equation for
estimating the modulus of elasticity as seen by equation 2-1
𝐸𝑡𝑖 = 0.45 ρ – 3
(2-1)
Where Eti is in units of MPa and ρ is the geofoam inclusion density in units of kg/m3
(Athanasopoulos et al. 1999). When the compressive strain placed on geofoam is greater than
1%, the material behaves nonlinearly and the tangent value for Young’s modulus will decrease
with increasing strain values. There are only a few instances of experimental data reported that
shows the varying effects of loading strain on geofoam response. However, authors agree that on
the nonlinear behavior of EPS geofoam for strain rates greater than 1%.
2.3 Passive Force-Deflection Relationship for Sand
Numerous factors affect how passive force pressures are developed. Among those include
structure movement, structure shape, soil strength parameters, and the soil-structure interaction
parameters (Duncan and Mokwa 2001). Most theories used for calculating the ultimate passive
13
force independently do so of movement from the structure. Thus, in order to determine the
relationship between structure movement and developed passive forces researchers have
performed tests and numerical analyses. Researchers agree that a passive force versus backwall
deflection relationship can be approximated with a hyperbola. However, the magnitude of such a
backwall deflection require to develop a peak passive for is still unclear. Numerous large-scale
tests were performed with the intent of showing that for dense sand the peak passive force
occurred at deflections between 3% and 5.2% of the backwall height (Cole and Rollins 2006).
The equation for determining the passive force with respect to wall displacement is
approximated by a spreadsheet program developed by Duncan and Mokwa (2001). PYCAP is
used to provide a quick and easy method for determining the passive force-displacement
relationship for a given backfill material. This sheet includes the Brinch-Hansen correct factor
for three-dimensional effects and is shown in Equation 2-2.
𝑃=
𝑦
1
𝑦
𝐾𝑚𝑎𝑥 + 𝑅𝑓 𝑃𝑢𝑙𝑡
(2-2)
where
𝑃 = passive resistance
𝑃𝑢𝑙𝑡 = ultimate passive resistance as calcualted by the log-spiral method
𝑦 = wall deflection
𝐾𝑚𝑎𝑥 = initial slope of the load-deflection curve
𝑅𝑓 =
𝑃𝑢𝑙𝑡
(dimensionless)
hyperbolic asymptote
14
Various researchers have prepared laboratory and field tests with the intent of showing a
relationship between the passive force and displacement for pile caps or bridge abutment
backwalls. The following sections will discuss such research.
2.3.1 Duncan and Mokwa (2001)
Authors of this paper discussed the resistance to structure movement as provided by the
passive soil pressure. In specifically gauging the resistance to pile cap movement the authors
used two test set ups where they tried to measure the passive soil pressure that was developed as
a pile cap was pushed into a soil backfill. In the first test set up a natural soil existing at the site
was used. This soil was classified as a desiccated hard sandy silt (ML) and sandy clay (CL). The
pile cap was loaded horizontally as to push it into the natural soil with incrementing loads
ranging from 12.5 to 15 kips until a peak load of 138 kips was applied. Load increments were
maintained for about 1 minute before applying the next load. Deflections were observed to about
1.6 inches. Cracks were then observed off of the corners of the pile cap extending parallel to the
direction of loading. At the same time, the passive resistance dropped off indicating that a failure
surface had developed in the soil. A similar procedure was done for the second soil testing set
up. However, prior to the second test, the existing soil was excavated and replaced with a gravel
backfill classified as a crusher run aggregate (GW-GM and SW-SM). Load increments ranged
from 10 to 15 kips until a maximum load of 91.7 kips was applied resulting in a deflection of 1.5
inches. During the second test, a bulge was observed in the backfill a distance of 7.5 feet from
the pile cap face. Cracks were observed extending from the pile cap out towards the bulge.
The authors and those conducting this experiment wanted to use their data to compare the
deflection of the pile cap and soil backfill against the applied load. Secondly, they were
interested in showing how the predominate passive soil pressure theories compare against their
15
measured values. The most correct values were found from using the log spiral method
combined with the Ovesen-Brinch Hansen correction factor for 3D effects (Duncan and Mokwa
2001).
2.3.2 Cole and Rollins (2006)
Testing was conducted in the Salt Lake City area to investigate the relationship between
pile cap deflection and lateral resistance (provided by passive forces). Tests were performed with
a pile cap supported by 12 steel piles oriented in a 4 x 3 pattern. Loads were applied by hydraulic
jacks with the application of load placed 0.36 meters above the bottom of the pile cap. String
potentiometers (SP) and linear variable differential transducers (LVDT) were used to measure
the displacement of the pile cap in both the horizontal and vertical direction. Loads were applied
to result in a targeted displacement and held for 5-10 minutes. Then the load was reapplied and
cycled for 10-15 times to the same approximate displacement. The final load cycle was then held
for 30-40 minutes while inclinometer and elevation readings were taken. For the next loading
sequence the process was repeated and set to a different displacement. Several tests were run
with no backfill soil in place behind the cap, four different tests using varying soil types for a
backfill, and a test using a 0.3 meter trench separating the backfill and pile cap. Tests that did not
include a backfill along with the trenched tests served as baseline tests for comparison against
testing that include soil backfills. The authors observed that the peak passive force occurred for
normalized deflections between 3.0 and 3.5% of the pile cap height for the clean sand, fine
gravel, and coarse gravel tests. The silty sand test required a wall movement of 5.2% of the wall
height to develop the full passive force resistance. The authors attributed this higher amount to a
higher fines content present than in the other soil backfills. Additionally, testing results showed
16
that the log spiral method can be used with accuracy to estimate the length of the failure surface
beyond the face of the pile cap (Cole and Rollins 2006).
2.4 Ultimate Passive Force Theories
Several theories are commonly used to estimate the ultimate passive for earth retaining
structures. Passive pressures arise when a wall that is used to retain soil masses are pushed into
the soil. With sufficient wall movement, a soil wedge will fail and thus the lateral pressure that
occurs from this condition is called the passive earth pressure. The varying methods are
commonly used for estimating passive forces are the Coulomb (1776), Rankine (1857), and LogSpiral (1943) theories. These theories each have their own set of assumptions and advantages
when compared against each other. The Coulomb and Rankine pressure theories are used more
commonly because of their ease to effectively use. Whereas, the Log-Spiral method is used less
frequently due to complex calculations. The three theories reduce to the general form shown in
Equation (2-3) for calculating the passive pressure, ’p.
σ′p =
1
K P γH 2 + 2√𝐾𝑃 𝑐′𝐻
2
KP =
σ`p
= passive earth pressure coefficient
σ`0
(2-3)
where
γ = moist unit weight of the soil
H = backfill height
𝑐 ′ = soil cohesion
17
The major difference between the three theories is the method of determining the passive earth
pressure coefficient. Methods of determining the passive earth pressure coefficient, Kp,
according to the Coulomb, Rankine, and Log-Spiral methods are explained below.
2.4.1 Rankine Earth Pressure Theory
The Rankine earth pressure theory assumes a linear failure surface place that begins at the
bottom of the wall. When working with passive soil pressures the Rankine method sees the
failure plane extending from the bottom of the wall through the soil backfill at an angle equal to
45° - ϕ /2, where ϕ is the angle of internal friction of the soil used for the backfill. Even though
the method assumes a linear failure plane, it will not produce accurate results where the wall
friction angle is greater than approximately 40% of the soil friction angle (Duncan and Mokwa
2001). Equation (2-4) shows the passive earth pressure coefficient as determined by Rankine.
𝐾𝑃 = tan2 (45 +
where
𝜙′
)
2
(2-4)
𝜙 ′ = effective soil friction angle
2.4.2 Coulomb Earth Pressure Theory
The Coulomb earth pressure theory takes into account the Mohr-Coulomb failure
criterion. Similar to the Rankine earth pressure theory, Coulomb’s theory assume a linear failure
plane that develops at the base of a backfill wall and extends into the soil. The angle of rise from
the backfill wall through the soil is determined iteratively either with the help of graphical
solutions or by computer computations. Equation (2-5) shows the passive earth pressure
coefficient as determined by the Coulomb theory.
18
𝐾𝑃 = sin
sin2 ( 𝛽 − 𝜙 ′ )
2
2
sin2 𝛽 sin(𝛽 + 𝛿 ′ ) [1 − √
sin(𝜙 ′
𝛿 ′ ) sin(𝜙 ′
+
+ 𝛼)
]
sin(𝛽 + 𝛿 ′ ) sin(𝛽 + 𝛼)
(2-5)
where
𝛽 = angle of backwall from horizontal
𝜙 ′ = effective soil friction angle
𝛿 ′ = wall friction angle
𝛼 = angle of the backfill from horizontal
In the same fashion as the Rankine earth pressure theory, the Coulomb method will not produce
accurate results where the wall friction angle is greater than approximately 40% of the soil
friction angle (Duncan and Mokwa 2001). Other researchers have modified the Coulomb
equation allowing it to take in mind both wall friction and non-horizontal backfills.
2.4.3 Log-Spiral Theory
The Log-Spiral method is widely considered to be the most accurate at solving for the
passive earth pressure coefficient, Kp, when realistic wall friction is considered. Unlike the
Rankine and Coulomb theories, the log-spiral approach does not assume a linear failure plane
extending from the backfill wall. Rather, the log-spiral method assumes a curved portion of a
failure zone that is most accurately modeled by a log-spiral. The curved portion of the graph is
found to be a part of the Prandtl zone, and connects to a linear failure surface named the Rankine
zone. A smooth connection is found between the two zones as shown by figure 2-1.
19
Figure 2-1: Geometry of the Log-Spiral Failure Plane (Marsh 2013)
There are various methods that allow for the calculation of the passive force using the Log-Spiral
method. The most robust method includes the use of a graphical solution which has been
implemented into an excel spreadsheet call PYCAP (Mokwa and Duncan, 2001). Although this
method for solving the Log-Spiral theory may become the most difficult to solve, it can account
for soil cohesion and complex backfill geometries.
20
3 Test Layout and Procedures
Large-scale lateral load tests with a geofoam inclusion were performed at a site located
near the control tower at the Salt Lake International Airport. A variety of in-situ and laboratory
tests have been done on the subsurface soil in the area to understand the specific interactions
between the piles and the soil (Christensen 2006). However, the information available with
respect to these subsurface soil properties will not be discussed here because they have little
relevance to the testing performed.
3.1 Test Layout
As indicated previously, in this study a large-scale lateral load test was performed to
define the passive force-deflection curve for a sand backfill with a geofoam block inclusion.
Previous tests conducted with the same test layout and backfill but without an inclusion had
previously been performed as reported by Marsh (2013). Tests performed by Marsh (2013) and
others included the use of angle wedges, concrete wingwalls, and varying backfill heights that
allowed an investigation into the results of skew angles and other variables on the passive soil
pressures developed by the backfill soil. With the geofoam testing, skew angles were not
investigated, thus results will be compared against the 0° skew testing done by Marsh. The
layout for the test consisted of several components: the geofoam block inclusion, the backfill
zone, loading apparatus, pile cap and the reaction foundation. Figure 1-1 shows plan and profile
21
views of the test set-up with the geofoam inclusion. Additionally, Figure 1-2 shows a schematic
of the geofoam inclusion used in the testing layout along with the joints between the geofoam
blocks. The test layout used by Marsh (2013) was identical; however, the inclusion was not
present.
3.1.1 The Reaction Foundation
The reaction foundation was used to create a sturdy structure against which the actuators
could push. This reaction foundation was created by installing two 4-foot diameter drilled shafts
spaced 12 feet apart center to center. The east and west shafts extend to depths of 70.5 feet and
55.2 feet, respectively. Each shaft was capped with a four-foot square by two-foot thick cap.
Reinforcement for the shafts was provided by 18 #11 vertical bars with a #5 bar spiral at a pitch
of 3 inches for the top 35 feet of the shaft. Below the 35 feet mark, vertical reinforcement
consisted of 9 #11 bars with a #5 bar spiral at a pitch of 12 inches. The concrete cover over the
reinforcement was approximately 4.75 inches throughout the length of the shaft. Concrete
throughout the length of the shaft had a compressive strength of 6,000 psi. Additionally, two
large I-beams were placed directly south of the drilled shafts and north of a sheet pile wall. The
I-beams had an approximate depth of 64 inches and were 16 inches high while spanning 28 feet
in the east-west direction. Both I-beams had their strong axis oriented in the north-south
direction. I-beams were used with the intention to provide lateral rigidity to the foundation
reaction system. Additional stiffeners were installed between the flanges to prevent the beam
from buckling during loading. Furthermore, a sheet-pile wall spanned the north side of the drilled
shafts. AZ-18 sheet piling was used for the sheet wall. This was made from ASTM A-572 Grade
50 steel. Also, a vibratory hammer was used to install the wall as close as possible to the drilled
22
shafts. The sheet piling wall extended to depths ranging from 33.6 feet to 35.6 feet below the
ground surface.
3.1.2 Loading Apparatus
The loading apparatus used for testing included two MTS hydraulic actuators capable of
pushing against the reaction foundation. Figure 3-1 shows the actuators placed north of the
reaction foundation. Also, as seen in Figure 3-1, the actuators had a capacity of providing 600
kips of force in extension and 450 kips of force in contraction. In order to tie the system together,
DYWIDAGs served as the connection between the actuators and the reaction foundation.
Similarly, eight DYWIDAGs were embedded into the pile cap to function as the connection
between the pile cap and the actuators. These actuators were centered 2.75 feet above the base of
the pile cap. In the loading scenario, the actuators were used to displace the pile cap to certain
pre-determined displacements and then the corresponding actuator load for the desired
displacement was recorded. Careful consideration was given to the possibility of rotating the pile
cap rather than directing it with a straight displacement into the soil backfill. Thus, by using the
string pots connected to the pile cap, loads were able to be increased in the actuators in order to
ensure a balance between the east-west sides of the pile cap and their respective displacement.
23
24
Figure 3-1: Plan View and Cross Section of Testing Layout
24
Figure 3-2: Plan View and Cross Section of Geofoam Inclusion
3.1.3 Pile Cap
Concrete that had a compressive strength of 6,000 psi was used to construct the pile cap
and to fill the steel piles. The top of each pile was embedded a minimum of 6 inches into the
base of the pile cap. Furthermore, in order to provide a sufficient connection between the piles
and the pile cap, 18-foot long reinforcing bar cages were extended into the steel piles. These
cages consisted of 6 #8 vertical bars and a #4 bar that spiraled at a pitch of 6 inches. 4.8 feet of
the cages extended upwards into the pile cap and the remaining 13.2 feet was lowered into the
piles. The steel piles had an outside wall thickness of 12.75 inches with a wall thickness of 0.75
inches. ASTM A252 Grade 3 steel was used for the piles. The piles had an average yield strength
of 57 ksi and were driven approximately 43 feet below the ground surface. The piles were placed
in two rows of three piles oriented in the east-west direction. Additionally, reinforcement was
provided for the pile caps with upper and lower mats that had #5 bars placed in the longitudinal
and transverse direction at 8 inches on center. The pile cap dimensions were 15 feet long (north25
south direction), 11 feet wide (east-west direction) and 5.75 feet high. The south edge of the pile
cap was located 16.4 feet to the north of the reaction foundation.
3.1.4 Geofoam Inclusion
The geofoam barrier that was placed between the pile cap and the soil backfill consisted
of four blocks of EPS19 geofoam. EPS19 is a medium density geofoam that provides strength in
application situations but is also readily compressible when subjected to various loads. Four
geofoam blocks were placed on the existing soil. The bottom two blocks were 4 feet tall while
the upper blocks were 2 feet tall as seen in Figure 3-2. These dimensions allowed the geofoam
inclusion to extend beneath the pile cap while the top surface of the geofoam remained relatively
level to the top of the pile cap. All blocks were 3 feet thick in the direction of loading, and 8 feet
wide. Thus, the blocks spanned 16 feet on the face of the backfill zone. The selected geofoam
inclusion was an EPS19 type geofoam with a density of 1.15 lb/ft3 or about 1/90th of the dry unit
weight of the backfill sand. EPS19 type geofoam is a medium density geofoam. The “19”
describes that the geofoam has a density of 19 kg/m3. The minimum density EPS that can be
manufactured is 10 kg/m3, however experience shows that the minimum density of EPS that has
an economical balance between stiffness and durability is approximately 12 kg/m3 (Horvath
1997). Various densities of EPS geofoam is used depending on the application. Projects that
require higher strength geofoam inclusions can find EPS46 (46kg/m3) available. The elastic
modulus of the selected geofoam was 580 psi. These geofoam blocks offer 13.1 psi of
compressive resistance at 5% deformation or 16.0 psi of compressive resistance at 10%
deformation (EPS Geofoam 2012). Geofoam interestingly has a negative Poisson’s ratio, and
will therefore contract rather than expand when subject to a compressive load. Normal polymer
foams have a positive Poisson’s ratio, whereas re-entrant polymer foams (geofoam included)
26
have a negative Poisson’s ratio (Hazarika 2005). Although the Poisson’s ratio of EPS19 is not
supplied directly by the manufacturer, we do know it to be a negative value. The pieces of
geofoam were relatively light and lifted into place by a two man crew during the test set-up. The
blocks were simply stacked on top of each other and not connected using any mechanical or
geometric interlocking system. The upper blocks weighed approximately 55 lbs. while the lower
blocks weighed approximately 110 lbs.
3.1.5 Soil Backfill Zone
The backfill zone used for both the 0° skew test and the geofoam inclusion test was
approximately 24 feet wide and 24 feet long. The zone was placed directly north of the pile cap
and geofoam inclusions. With the intent of accommodating the predicted failure zone modeled
by the log-spiral method, the soil backfill extended 1 foot below the pile cap for the first 8 feet of
backfill. Such accommodations hoped to allow for the formation of Prandtl zone failure surface
as described in section 2.4.3. During placement of the backfill zone, two nuclear density gauge
measurements were taken for each lift of soil placed as to ensure compaction and to determine
the moisture content and unit weight of the soil used. Soil for all of the tests was imported to the
site. The backfill soil was poorly graded sand and classified as SP soil type according to the
Unified Soil Classification System. The maximum density of the soil according to the modified
Proctor compaction test (ASTM D1557) was 111.5 lbf/ft3 with an optimum moisture content of
7.1%. Figure 3.3 shows the soil gradation curve for the imported soil.
27
100
90
80
Percent Passing
70
60
50
40
30
Pre-Test
20
10
0
0.01
0.1
1
10
Particle Size [mm]
Figure 3-3: Backfill Soil Gradation Curve
3.2 Testing Instrumentation
The test set-up required a variety of monitoring systems for measurement of how the pile
cap, geofoam inclusion and backfill soil acted under loading. The following sections will
describe the instrumentation used to measure this response.
3.2.1 String Potentiometers and Reference Frame
String Potentiometers (string pots) were used to measure the displacement of the pile cap
and the reaction foundation. By attaching them to an independent reference frame we were able
to accurately determine the displacement of the pile cap and the reaction foundation during
testing. Two of these six string pots were attached to the reaction beam while four of the string
pots were attached to the corners of pile cap at 3 inches and 51 inches from the top of the pile
cap, and 3 inches and 129 inches from the west side of the pile cap. These locations are shown in
Figure 3-4. The other two string pots that were attached to the reference frame also attached to
the large I-beam found to the north of the drilled shafts. They were placed in line to be at the
28
same level as the line of action of the actuators and the approximate middle of the drilled shafts.
Thus, the two additional string pots were able to measure the north/south movement of the
foundation reaction during the loading process.
Furthermore, additional string pots were placed in the soil backfill and on the geofoam
inclusion. By including string pots on the backfill and the geofoam we were able to measure the
movement in these components during testing and compare them against the pile cap
displacement. Seven additional string pots were mounted to the top of the pile cap 10 inches
from north face of the cap. Stakes were driven into the soil backfill and the geofoam inclusion.
String pots were attached to the surface of the soil and geofoam at distances from the pile cap as
shown in Table 3-4. String pots were located at 0.5 ft longitudinal intervals in the geofoam and at
2 ft intervals in the backfill soil behind the geofoam. Ideally we would have been able to place
all of the string pots along the centerline of the pile cap and the soil backfill, but this was not
possible because of the width of the instruments used.
Figure 3-4: String potentiometer locations on the pile cap (Marsh 2013)
29
Table 3-1: String Potentiometers Distances from the Pile Cap Face Measured Parallel to
the Direction of Pile Cap Movement
Geofoam Inclusion Test
Dist. from Face
Dist. from Center
SP963
SP965
ft
0.50
1.00
ft
-0.33
-0.33
SP964
1.50
-0.33
SP969
2.00
-0.33
SP10
2.50
-0.33
SP970
5.00
-0.33
SP967
7.00
-0.33
SP962
9.00
-0.33
SP971
11.00
-0.33
SP968
13.00
-0.33
SP11
15.00
-0.33
SP2
17.00
-0.33
String Pot ID
NOTE: Negative distances from center of pile cap
indicates the string pot is located to west of backfill
centerline
The use of string potentiometers allowed us to measure the compressive strain,, in the
backfill soil. This strain was calculated using Equation (3-1).
𝜀 = Δ𝐿/𝐿
(3-1)
where
Δ𝐿 = change in distance between stringpots
𝐿 = original north − south distance between adjacent stakes
3.2.2 Geofoam Compression
In order to understand how the geofoam would act under compressive loading, a 2 inch
square grid pattern was drawn on top of the geofoam block. The 2 inch squares were measured at
30
several loading intervals in order to see how sections of the geofoam would compress under the
loads provided by the actuators. Measurements provided insight into what sections of the
inclusion experienced more compressive displacement than others and whether or not the
inclusion responded in a linear fashion or not. Figure 3-5 shows the grid pattern on the geofoam
inclusion.
3.2.3 Heave and Vector Displacement
In order to understand the heave and displacement of both the geofoam and the soil
backfill, a total station surveying system was used to measure the changes seen in the system. To
facilitate these measurements, a two ft square grid pattern was spray painted on the backfill soil
to complement the grid pattern on the geofoam. In some cases behind the geofoam a one foot
grid was employed to increase resolution. Between the load sets, the total station was used to
measure the horizontal displacement and vertical heave of both the geofoam inclusion and the
sand backfill. In measuring the heave, the total station was used to determine the relative
elevation change of each grid intersection point. In so doing we were able to produce contour
drawing showing heave behind the pile cap which facilitates understanding of the governing
failure mechanisms. Using the displacements from the total station at the end of the test, vectors
of horizontal displacement were subsequently computed at each grid point to understand how the
soil backfill had displaced. Figure 3-5 shows the grid system that was used to determine the
heave and vector displacement from both the soil backfill and the geofoam inclusion. The
corresponding images are shown in the heave and vector displacement results section. The
circular targets shown in the photo at each grid point were used in connection with a video
displacement measurement system which was not successful and will not be discussed further.
Lastly, surface cracks that developed throughout the load testing were mapped against the grid
31
pattern to provide an indication of the failure surface that developed in the backfill soil. These
cracks are shown on the heave contour plots.
Figure 3-5: Geofoam and Backfill Grid System
3.2.4 Red Sand Columns and Internal Failure Surface
In an attempt to locate the internal failure surface as characterized by the passive force
analysis methods, vertical sand columns were excavated and fill with red sand.. A 2-inch
diameter hand auger was used to core holes in the soil backfill. These cored holes were then
refilled and compacted with red-dyed soil. After the completion of testing a trench was
excavated next to these holes and the offsets in the sand columns produced by shearing on the
failure surface were used to identify the failure plane. Sand columns were located on the
longitudinal centerline at 2, 4, 6, and 8 feet from the backwall face. Figure 3-6 shows an example
32
of two of these sand columns. Their corresponding failure plane locations will be discussed in
the test results section. .
Figure 3-6: Red Sand Columns to determine Failure Plane
3.3 Test Procedure
A series of lateral passive force tests were performed in the summer of 2013 at the Salt
Lake City Airport. These tests included baseline tests that were run without soil backfill and
other backfilled tests that experimented with various design parameters. As described before,
only the 0° skew unconfined test reported by Marsh (2013) and the geofoam inclusion test are
described in the current report. Such test comparisons will allow us to draw conclusions as to the
effectiveness of including geofoam from compressible inclusions. The passive force on the wall
was obtained by subtracting the baseline resistance from the total force measured by the
actuators.
33
3.3.1 Geofoam Placement
The geofoam inclusions were hand lifted into place by two men crews. Section 3.1.4 lists
the weights of the various geofoam inclusions. They were simply stacked on each other and did
not include any sort of connections between the blocks. Typical geofoam applications may
include mechanical or geometric interlocking devices, but such connections were not used in this
test as discussed in section 3.1.4.
3.3.2 Backfill Placement and Test Preparation
Backfill soil was placed in soil lifts approximately 6 to 8 inches thick. Each lift was
compacted with a drum roller and a walk-behind vibratory plate compactor, as described in
section 3.1.2. Backfill soil was compacted to a density greater than or equal to 95% of the
modified proctor maximum value, which was 111.5 pcf for the soil backfill used. Water was
added to the soil in order to help it reach the desired compaction while the target optimum
moisture content of 7.1% for the soil was used. After backfill placement, a 2 foot grid was
painted on the backfill surface and the relative elevations of each grid point were measured using
a surface level. As previously mentioned in section 3.2.4, a 2-inch diameter hand auger was used
to install the red-dyed sand columns.
3.3.3 Pile Cap Displacement
Following the backfill placement and test preparation, actuators were used to displace the
pile cap into the backfill zone. The actuators pushed the pile cap to target displacement intervals
of approximately 0.25 inches. Furthermore, they were used to displace the pile cap at a velocity
of 0.25 inches per minute. At the end of each displacement increment, the actuators were held in
place for approximately 2 minutes before additional load was applied so that manual readings of
34
the load and displacements could be obtained. This load-displacement sequence was repeated
various times until the pile cap had displaced about 3.5 inches into the geofoam-soil backfill.
Further pile cap displacements could not be used in order to prevent failure of the driven
piles used to support the pile cap. However, the passive force-deflection behavior of the
geofoam-soil backfill at higher displacement levels was important to the study. Therefore, at the
end of this loading sequence the actuators were used to bring the pile cap back to its original
starting position and plywood sheets were inserted into the resulting gap between the pile cap
and the geofoam inclusion. With these plywood shims in place, the actuators could push the pile
cap an additional 2.25 inches and extend the passive force-deflection curve for the geofoambackfill soil system. This procedure allowed for a further displacement into the soil backfill and
the geofoam without jeopardizing the integrity of the piles supporting the pile cap.
Load values used to displace the pile cap were recorded in order to understand the
passive force resisting movement and the corresponding displacement of the pile cap. Results are
presented in the section discussing the passive force-displacement relationship for the geofoam
inclusion test in comparison with sand backfill only.
3.3.4 Final Measurements
Following the final displacement of the pile cap into the soil backfill zone the final
measurements were taken on the geofoam grid pattern, the cracks in the backfill surface were
mapped with paint and then recorded, and the total station measurements were on each grid point
while the actuator load was still applied. After the actuator load was released, the soil adjacent to
the red-dye sand columns was excavated and photographs and measurements were taken in order
to identify the position of the failure plane.
35
36
4
Test Results
This section will describe the observed backfill failure mechanisms by considering
backfill lateral movement, lateral compressive strain, and internal and external failure
configurations. With the end goal of understanding the prevailing failure mechanisms the test
data will be presented as followed: 1) Overall failure patterns, 2) passive force-deflection curves,
3) backfill and geofoam heave, 4) Longitudinal displacement and strain of geofoam and backfill
and 5) compression of geofoam.
4.1 Passive Force-Deflection Curves
A baseline test was performed to define the ability of the pile cap to resist lateral
movement without the help of backfill materials. The baseline test was conducted in the summer
of 2013. In this test the actuators were used to displace the pile cap in absence of a soil backfill.
Using the actuators and the string pots, we were able to measure the deflection seen by the pile
cap and the corresponding loads required to displace the cap so that a baseline force-deflection
curve could be developed as plotted in Figure 4-1. The load in this figure was obtained from
actuator and the displacement was the average of the four string pots on the back side of the pile
cap.
Next, the displacement test involving the geofoam inclusion was conducted in June of
2013. This test included both the geofoam inclusion against the pile cap and backfill soil directly
north of the inclusion. Similarly to the baseline test, loads from the actuators were measured in
37
order to understand the required forces to displace the pile cap into the backfill a given
displacement.
In order to determine the passive force supplied by the soil backfill, we recognize that the
difference between the forces required to achieve displacement in the baseline and traditional test
is what must be supplied by the soil backfill. Figure 4-2 then shows the total load, the baseline
load, and the baseline resistance. Figure 4-3 shows the deflection versus passive force
comparison. Lastly, Figure 4-4 compares the passive force from the two tests.
600
Longitudinal Force [kips]
500
400
300
200
100
0
0.00
0.50
1.00
1.50
2.00
2.50
Pile Cap Deflection [in]
Figure 4-1: Baseline for 0° Skew Test
38
3.00
3.50
4.00
800
Lateral Backfill
Resistance
Longitudinal Force [kips]
700
600
Total Load
500
Baseline Load
Passive Force
400
300
200
100
0
0.00
0.50
1.00
1.50
2.00
2.50
Pile Cap Deflection [in]
3.00
3.50
4.00
Figure 4-2: Total Load, Baseline Load, Passive Force Comparison
200
180
Passive Force [kip]
160
140
120
100
80
60
40
20
0
0.00
1.00
2.00
3.00
4.00
Backwall Displacement [in]
5.00
Figure 4-3: Passive Force versus Deflection
39
6.00
7.00
600
0° Skew Test
Passive Force [kips]
500
Geofoam
400
300
200
100
0
0
1
2
3
4
5
6
7
Backwall Displacement [in]
Figure 4-4: Passive Force versus Displacement for 0° Skew Test and Geofoam Inclusion
As can be seen in Figure 4-3, the peak passive force of 162.2 kips occurs at the point of
maximum displacement of 3.78 inches for the first push. Both pushes are represented in Figure
4-3 with the second push including the 2.25 inches of plywood sheathing inserted between the
pile cap and the geofoam inclusion. Additionally, Figure 4-3 uses the baseline testing
information from two baseline tests. The first baseline test occurred when the pile cap had not
been displaced in some time, thus the area next to the piles had filled with soil. Whereas the
second baseline test was run immediately after the first, thus the surrounding soil had not had the
chance to fill into the areas around the piles. This is similar to the testing done on the geofoam
inclusion where the 1st push moved the pile cap while soil was around the piles. The 2nd push
occurred immediately after the 1st, and thus gave little time for the soil to settle around the piles.
Therefore, corresponding baseline test results were used to generate Figure 4-3 depending on
whether the data presented was from the 1st or 2nd push. Figure 4-4 shows the comparison of the
40
development of the passive force resistance in the geofoam testing against the 0° skew angle
testing involving a clean sand backfill.
As seen in Figure 4-4, the peak passive is 481 kips at 2.97 inches of deflection for the 0°
skew test. Whereas the geofoam testing has a peak passive for of 187 kips at 3.76 inches (Figure
4-8). A more reasonable comparison could be made by seeing that the geofoam test had a passive
force of 148 kips at 2.99 inches of deflection from the pile cap. Based on these contrasts we can
stipulate that the geofoam inclusion was very effective at reducing the passive forces due to
lateral backwall movement. As seen in Figure 4-4, the peak force from the geofoam inclusion
test is only about 30% of the peak passive force the sand passive force. This 70% reduction is
fairly uniform across the board when comparing the two tests. Additionally, Figure 4-4 shows
the initial stiffness in the geofoam inclusion as compared to the backfill sand, as measured by the
passive force. Obviously the sand test provides stiffer results. However, Figure 4-4 shows that
the geofoam stiffness behaves non-linearly until the backwall has displaced around 0.75 inches,
where the geofoam then begins to lose its stiffness. After 1.0 inches of backwall displacement,
the geofoam begins to translate in a linear fashion with the soil backfill.
4.2 Overall Failure Patterns
Failure in the soil backfill occurs when the soil is no longer able to sustain displacement
and loads from the pile cap. Consequently, the soil backfill exhibits the formation of a failure
surface as characterized by the ultimate passive force theories (Rankine, Coulomb, Log-Spiral).
As mentioned in the test layout and procedures section, core holes were drilled and filled with
red sand in order to help locate the failure plane. The inability to sustain loads past the full
development of the failure plane is characteristic of an overall failure pattern. Figure 4-5 shows
the failure plane as exhibited by the red-dyed soil. The failure plane initiates from the
41
intersection of the two blocks of geofoam and extends upward towards the surface. As seen in
Figure 4-6, the failure plane extends just beyond 4 feet in the direction of loading from the face
of the geofoam and soil backfill, or just beyond 6 feet from the face of the pile cap.
The angle of inclination of the failure plane, , is given by the equation
 = 45º - /2
where  is the internal friction angle of the sand. Assuming the failure surface daylights between
4.1 and 4.5 feet behind the wall leads to a friction angle between 38º and 42º. The failure surface
as seen by Figure 4-5 and Figure 4-6 showed a linear failure geometry. In contrast, the failure
zone observed by Marsh (2013) with the sand only scenario showed more of a log-spiral shape
with the Prandtl zone extending blow the base of the pile cap. The failure zone of the geofoam
inclusion test was relatively shallow when compared against the other tests that were run.
While the soil backfill showed signs of failure, distress was also seen in the geofoam
inclusion during testing. As seen in Figure 4-7, portions of the geofoam inclusion started to
exhibit shear cracks at the edges of the pile cap. Figure 4-7 shows the interface between the pile
cap and the geofoam inclusion. At the stage of testing shown in the figure, loading had
compressed the geofoam inclusion in the center portions where there was direct contact with the
pile cap face. The crack shown comes from the corner of contact with the pile cap. Figure 4-8
shows the bowing of the geofoam inclusion when subjected to loading.
42
Figure 4-5: Internal Failure Plane
Figure 4-6: Failure Plane at Backfill Surface
43
Figure 4-7: Geofoam Shear Cracking at the Corners of the Pile Cap
Figure 4-8: Geofoam Inclusion Bending at the End of the Second Loading
44
4.3 Backfill Heave and Surface Cracking
Figure 4-9 and Figure 4-10 show the backfill heave contours and cracking patterns for the
sand backfill test and the geofoam inclusion test, respectively. For the sand test, heaving
occurred in relatively symmetric semi-circular shapes extending from the ends of the pile cap.
The maximum heave (>1.8 inch) occurred in half-elliptical strips stretching parallel to the
direction of loading. Heaving was seen to have affected the backfill material as far as 20 feet
from the face of the pile cap. The shear crack patterns radiated out from the corners of the pile
cap and extended to a distance of about 4.5 to 5 ft beyond the edge of the pile cap increasing the
effective width of the cap to about 20 ft. Based on other tests at the site where a complete failure
surface developed at the ground surface, the failure surface generally manifested itself at
locations where the heave was between 0.5 and 0.75 inch. Based on this criterion, the failure
surface would likely have day-lighted at about 17 ft behind the face of the pile cap.
Similarly, heave contours for the geofoam test also produced elliptical strips. However,
these elliptical strips stretch extending from the geofoam inclusion perpendicular to the direction
of loading. In comparing the two tests, it is seen that the geofoam mitigated the backfill heave to
12 feet north of the pile cap in contrast to 20 ft for the sand backfill test. Less heave was
measured in the sand backfill test than that seen in the geofoam inclusion test. However, heave
from the geofoam testing is more localized near the abutment than heave from the sand test.
Assuming that the ultimate failure surface would be located where heave was around 0.5 inches,
the failure surface may have ultimately developed at a distance of 8 to 10 ft from the back of the
geofoam block wall. Shear cracks initiated from the corners of geofoam block wall and extended
outward about 1 ft increasing the effective width of the shear zone to 18 ft. Shear zones clearly
daylighted at about 4 ft behind the geofoam wall; however, as indicated previously, this failure
45
wedge appears to be associated with the upper 2 ft block. The heave contours behind the shear
cracks at 4 ft suggests that a failure surface associated with the full block height might have
developed with greater displacement.
Figure 4-9: Backfill Heave Contours and Cracks on a 2-ft grid for the Sand Backfill Test
(Marsh 2013)
46
3 ft
Figure 4-10: Backfill Heave Contours and Cracks for the Geofoam Inclusion Test
Both tests show a maximum heave near the edge of the soil-structure boundary (counting
the geofoam as the structure). This would be consistent with the assumption that the peak passive
forces would occur at the edge of a wall face.
47
4.4 Longitudinal Displacement and Strain of Geofoam and Backfill
Obviously the loading scenarios caused displacement in the geofoam and the soil
backfill. As described in section 3.2.1, string pots were mounted to the top of the pile cap and
were located at various distances in soil backfill and the geofoam. The data from the string pots
allowed for measurement of the backfill movement and strain. Figure 4-11 and Figure 4-12 show
the deflection of the geofoam inclusion and the soil backfill during the first and second pushes as
measured by various string pots. Figure 4-13 shows the deflection from the soil backfill during
the sand backfill test as performed by Marsh (2013).
4.0
Backfill Displacement [in]
3.5
3.0
2.5
0.60 in
2.0
1.01 in
1.99 in
1.5
2.99 in
1.0
3.78 in
0.5
0.0
0
5
10
15
20
Initial Distance from Backwall Face [ft]
Figure 4-11: Total Backfill Displacement versus Distance from Backwall Face at Selected
Cap Displacements for 1st Loading of the Geofoam Inclusion Test.
48
4.0
Backfill Displacement (in)
3.5
3.0
0.54 in
2.5
1.01 in
2.0
1.99 in
1.5
2.98 in
3.76 in
1.0
0.5
0.0
0
5
10
Distance from Pile Cap (ft)
15
20
Figure 4-12: Total Backfill Displacement versus Distance from Backwall Face at Selected
Cap Displacements for 2nd Loading of the Geofoam Inclusion Test
0.0
Initial Distance from Backwall Face [m]
2.0
3.0
4.0
5.0
1.0
6.0
7.0
Backfill Displacement [in]
3.00
0.47 in
8.0
1.12 in
7.0
2.50
1.99 in
6.0
2.00
2.97 in
5.0
3.21 in
1.50
4.0
Surface Crack (Est.)
3.0
1.00
2.0
0.50
Backfill Displacement [cm]
3.50
1.0
0.00
0.0
0
5
10
15
Initial Distance from Backwall Face [ft]
20
25
Figure 4-13: Total backfill displacement versus distance from backwall face at selected cap
displacement intervals for the sand backfill test (Marsh 2013)
49
Figures 4-11 and 4-12 show that the majority of the movement occurred within the first 7
feet behind the pile cap. Beyond this zone the backfill displacement decreased roughly linearly
with respect to the original distance from the face of the backwall. Figure 4-12 also shows the
inability of the geofoam to compress during the second loading cycle. This points to some
obvious plastic deformation from the geofoam inclusion.
4.4.1 Backfill Strain
The backfill displacement information presented previous allows us to calculate the
backfill strain using Equation (3-3). Figure 4-14 shows the backfill strain of the soil with respect
to the distance from the backwall face for the geofoam inclusion test. This figure illustrates the
strain curves as shown at selected pile cap displacement intervals. Very low strain values were
seen in the range of 2 feet through 4 feet in the soil backfill. Figure 4-15 is showing the
compressive soil strain values in the soil backfill for the second loading push. The negative
compressive strain values seen are characteristic of tension effects in the soil. This corresponds
with the heave values of the geofoam inclusion and the soil backfill as discussed in section 4.3.
The larger strain values in the range from 4 to 8 feet in the soil backfill are consistent with the
observed shear zone failure as described in section 4.1. Figure 4-15 shows the second push data
after the plywood inclusions were stuck between the pile cap face and the geofoam inclusion.
The values shown in this figure are similar to those seen in Figure 4-14 with the exception of the
higher strain values seen 4 feet past the geofoam inclusion, or 6 feet north of the pile cap face.
These larger strain values illustrate the formation of a failure plane and are consistent with the
heave and cracking data shown in section 4.3 along with the overall failure data from section 4.1.
Figure 4-16 then shows the compressive soil strain data for the sand backfill skew test with pure
sand.
50
Compressive Soil Strain (%)
22.0
21.0
20.0
19.0
18.0
17.0
16.0
15.0
14.0
13.0
12.0
11.0
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
-1.0
0.60 in
1.01 in
1.99 in
2.99 in
3.78 in
0.0
5.0
10.0
15.0
Initial Distance from Pile Cap Face (ft)
20.0
Compressive Soil Strain (%)
Figure 4-14: Backfill Compressive Strain versus Original Distance from Pile Cap Face
15.0
14.0
13.0
12.0
11.0
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
-1.0
0.54 in
1.01 in
1.99 in
2.98 in
3.76 in
0.0
5.0
10.0
15.0
Initial Distance from Pile Cap Face (ft)
20.0
Figure 4-15: Backfill Compressive Strain versus Original Distance from Pile Cap Face for
Second Push
51
7.0
Compressive Soil Strain [%]
6.0
0.47 in
5.0
1.12 in
4.0
1.99 in
2.97 in
3.0
3.21 in
Surface Crack (Est.)
2.0
1.0
0.0
0
5
10
15
Initial Distance from Backwall Face [ft]
20
25
Figure 4-16: Backfill compressive strain versus original distance from backwall face at
selected displacement intervals for the sand backfill test (Marsh 2013)
As seen in Figure 4-16, an estimate was made as to where the surface crack should have
appeared. However, due to the limitations of the system set-up, such a failure plane did not fully
develop and was not visible at the conclusion of testing. Such is commonly the case as the peak
passive pressure forms and mobilization of the soil occurs, however additional displacement is
required for the full formation of the failure plane.
4.5 Backfill Soil Displacement Vectors
Figure 4-17 shows the displacement vector plot for the geofoam inclusion and the soil
backfill as recorded by the total station measurements at the end of testing. As seen in the figure,
the length of the arrows represents the amount of geofoam or backfill displacement. In addition,
the arrows are color-coded. Red arrows indicate a movement of more than two inches, green
arrows show movement between one to two inches, and the blue arrows show displacement that
is less than one inch. Thus, as seen in Figure 4-17, most of the major backfill movement occurred
52
in the geofoam and the soil backfill that is in the 8 feet directly north of the pile cap. Figure 4-17
also shows that the geofoam inclusion compressed in the east-west direction when subjected to
north-south compressive loads. This can be attributed to the negative Poisson’s ratio
characteristic of geofoam inclusions as discussed in section 3.3.2. Displacement vectors were not
obtained for the companion test with the sand backfill reported by Marsh (2013). However,
vector plots for other similar tests generally indicated a more gradual reduction in backfill
displacement with the distance from the pile cap due to the soil sliding up the failure plane. In
contrast for the geofoam inclusion test the majority of the movement occurred in the geofoam
inclusion and the backfill area directly next to the geofoam. This goes to show the effectiveness
of geofoam inclusions at attenuating the loads placed on the backfill wall.
53
Geofoam
Inclusion
Figure 4-17: Soil Displacement for Geofoam Inclusion Testing
4.6 Compression of Geofoam
To understand how the geofoam inclusion performed under compressive loads, a 2 inch
square grid was drawn onto the top of the geofoam inclusion as discussed in section 3.2.2.
Monitoring this grid allowed us to measure the compression strain to the passive force on the
geofoam block wall. Figure 4-18 shows the geofoam inclusion with the grid system drawn on the
top face. Figure 4-19 shows curves that depict the compressive strain of the geofoam squares as a
function of the passive force.
54
Figure 4-18: Grid System on Geofoam
12
162.2 kips
156.4 kips
131.8 kips
10
112.6 kips
Compressive Strain [%]
57.3 kips
8
6
4
2
0
0
5
10
15
20
25
30
35
40
Distance from Pile Cap [in]
Figure 4-19: Geofoam Compression versus Distance from Pile Cap for Specified Passive
Forces
55
Figure 4-19 shows the compressive strain as a function of distance from the pile cap. As
seen in Figure 4-19, the largest strain occurred near the face of the pile cap and near the
geofoam-soil boundary. This result is generally consistent with the data from the string
potentiometers show previously in Figures 4-14 and 4-15; however, the strain is apparently
greater near the center of the geofoam wall than at 5.5 ft from the center. A possible explanation
for this would be that the section of the geofoam next to the pile cap felt the most strain from
direct contact. Figure 4-19 also shows an increase in the overall strain near the geofoam-soil
boundary. This would possibly have resulted from the passive forces that developed in the soil
pushing against the geofoam inclusion. Though values for the second push are not presented,
their results are similar to those shown for the first push.
56
5
Analysis
This section will review the ultimate passive force as determined by the various theories.
Next the method currently available for approximating the complete passive force versus
backwall deflection curve (Duncan and Mokwa 2001) will be presented and compared. Lastly,
the method for predicting the observed performance of the pile cap and geofoam inclusion as
shown.
5.1 Prediction of Passive Force
As previously discussed in section 2.4, there are various theories for predicting the
passive forces that occur behind a backfill wall. Table 5-1 shows the predicted and measured
passive force values from the sand test. Table 5-2 shows the predicted and measured passive
force value for the geofoam inclusion test. In computing these values, the moist unit weight was
taken as 117 lbs/ft3,  was assumed to be 38.5º,  was assumed to be 0.70 for the log-spiral and
Coulomb methods, and 0º for the Rankine method. The width of the failure wedge transverse to
the direction of loading was 18.5 ft for the sand backfill using a 3D width correction factor
proposed by Brinch-Hansen (1966). For the geofoam inclusion test, the effective width of the
shear zone was also assumed to be 18 ft based on the observed shear crack patterns and wall
height was taken as 6 ft to match to match the height of the geofoam block wall. All other
parameters were the same as for the sand backfill test.
57
Table 5-1: Calculated and Measured Passive Forces for Sand Test
Method
Log Spiral
Coulomb
Rankine
Sand Test
Passive Force
Per width
Total Passive
Force
Total Passive
Force
kip/ft
24.1
35.9
9.73
24.4
kips
474
706
191
481
Percent Error
-1.50%
47%
-60%
N/A
Table 5-2: Calculated and Measured Passive Forces for Geofoam Inclusion Test
Method
Log Spiral
Coulomb
Rankine
Geofoam Inclusion Test
Passive Force
Per width
Total Passive
Force
Total Passive Force
kip/ft
24.1
35.9
9.73
9.5
kips
474
706
191
187
Percent Error
154%
278%
2.4%
N/A
As mentioned before, the Log Spiral method is commonly considered to be the most
accurate at predicting the passive force. However, the Coulomb method significantly
overestimated resistance while the Rankine theory significantly underestimated the passive force
that actually developed in the clean, sand backfill test. In contrast, the Rankine theory was the
most successful at explaining the results obtained from the geofoam test while the Log-spiral and
Coulomb methods greatly over predicted passive resistance. Table 5-2 shows the error that
occurred from trying to predict the passive force of the geofoam inclusion test using the various
passive force theories. A potential explanation for the success of the Rankine theory in predicting
the geofoam inclusion test results is the reduction in interface friction between the geofoam and
the backfill wall or the soil backfill and the geofoam. Somewhere the test set up has a friction
58
angle that is essentially reduced to zero, therefore the Rankine earth pressure theory is the most
accurate at predicting the failure zone to occur from the geofoam inclusion test.
5.2 PYCAP Performance Prediction
The PYCAP spreadsheet was created by Duncan and Mokwa (2001) with the intention of
helping to develop curves that show the lateral load versus deflection relationship. The soil
strength parameters used to develop the curves have a large effect on the passive forces that
develop. Figure 5-1 shows the actual test results from the sand backfill skew angle test, the
geofoam inclusion test, and the corresponding values from the PYCAP spreadsheet method.
700
0° Skew Test
600
Geofoam
Passive Force [kips]
500
400
300
200
100
0
0
1
2
3
4
5
6
7
Backwall Displacement [in]
Figure 5-1: Comparison of Low Bound and High Bound PYCAP Passive Force versus
Geofoam and Sand Backfill Deflection Curves
59
This figure shows the great difference that even a one degree change of the friction angle,
 along with possible changes to the cohesion, c, can have on the results. Table 5-2 shows the
soil strength parameters that were used to produce the low range and high range curves from the
PYCAP program. The bounds shown in Figure 5-1 are shown by the numerical values presented
in Table 5-2.
Table 5-3: PYCAP Soil Strength Parameters for Log-Spiral Solution
Low
Range
High
Range
Units
Friction Angle, 
38.5
40.8
Degrees
Cohesion, c
70.0
120.0
lbf/ft2
Interface Friction Ratio, 
0.7
0.7
–
Initial Tangent Modulus, E
415
415
kip/ft2
Poisson’s Ratio, 
0.33
0.33
–
Soil Parameter
As seen in the table, changing the friction angle by small amounts will produce a large
variation in the expected passive force. The best fit curve to match the sand backfill test used a
friction angle, , of 38.5º and a cohesion, c, value of 85.0 lb/ft2. Changes from 15 psf to 25 psf
also have a significant effect on the predicted amount of passive force supplied by the backfill
soil. As can be seen in Figure 5-1, the geofoam test measured values much lower than that found
with the PYCAP prediction. This goes to show that the geofoam inclusion was very effective at
reducing the passive forces seen by the soil backfill, as previously shown by other test
conclusions. Figure 5-2 and Table 5-4 show the PYCAP predictions for the geofoam inclusion
testing. As seen in Figure 5-2, PYCAP over predicts the measured values for the geofoam
inclusion test during early loading but is more accurate at higher deflection values.
60
600
Geofoam
Longitudional Force [kips]
500
Sand Backfill
400
300
 (deg.) = 46.0
200
 (deg.) = 38.0
100
0
0
1
2
3
4
5
6
7
Pile Cap Deflection [in]
Figure 5-2: Comparison of Low Bound and High Bound PYCAP Passive Force versus
Geofoam and 0° Skew Deflection Curves
Table 5-1: PYCAP Soil Strength Parameters for Rankine Solution
Low
Range
High
Range
Units
Friction Angle, 
38
46
Degrees
Cohesion, c
80
160
lbf/ft2
Interface Friction Ratio, 
0.7
0.7
–
Initial Tangent Modulus, E
375
375
kip/ft2
Poisson’s Ratio, 
0.33
0.33
–
Soil Parameter
5.3 Observed Pile Cap Performance
As explained in sections 4.1, the overall failure pattern was characterized by a linear
shear plane in the backfill soil. The location of the shear plane was shown by the red sand
61
columns in the soil backfill along with the surface cracking observed in the section of soil that
was between 4 and 5 feet north of the pile cap. Figure 5-2 shows a schematic of the pile cap,
geofoam inclusions, and the Rankine failure zone that was observed in the test. Furthermore,
using the Rankine theory, the passive pressure developed on the block would be 6.73 kips/ft.
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
0.0
Distance [ft]
1.0
2.0
Distance [ft]
3.0
4.0
5.0
6.0
7.0
Rankine Failure
Zone
Pile Cap
Figure 5-3: Rankine Failure Zone
As seen in the figure, the shear failure zone seems to propagate from the boundary area
between the upper and lower geofoam blocks. It appears that reasoning for this could include a
stress concentration under loading circumstances in the area that allows for an initiation of the
failure zone.
62
6
Conclusions
This report presented the results from a large-scale test of a pile cap and a geofoam
inclusion subjected to lateral loads. The intent of the test was to determine the effect that a
geofoam inclusion has on the ultimate passive force delivered by an unconfined soil backfill.
Additionally, the test was designed to determine the effect a geofoam inclusion had on the
passive force versus backwall deflection relationship. To evaluate these issues, comparisons
were made with a previous lateral load test in which the backfill consisted only of sand. Finally,
analyses were performed to investigate the most appropriate. Based on the test and results
described, the following conclusions and recommendations are presented.
1. Geofoam inclusions are very effective at reducing the peak passive force which
develops in sand backfills. In this case, the geofoam inclusion reduced the
passive force by 70% relative to the backfill composed only of sand.
2. The deflection required to mobilize the peak passive force was greater than
what has been reported in literature. The peak passive force occurred at 186.6
kips with a deflection of 3.76 inches. The normalized deflection necessary to
obtain the peak passive force is 5.7% of the backwall height, which is beyond
the 3% to 5% range reported in literature.
3. While the failure mechanism for a sand backfill typically involves a log-spiral
failure surface, the governing failure mechanism for a sand backfill with a
63
4. geofoam inclusion appears to be a linear shear failure as described by the
Rankine earth pressure theory.
4. The log-spiral method was able to predict the peak passive resistance for the
sand backfill with an error of less than 10% assuming a wall friction equal to
70% of the sand friction angle (38.5º), while the Rankine method significantly
underestimated resistance. In contrast, the Rankine method predicted the peak
passive resistance for the backfill with the geofoam inclusion within 10%,
assuming a wall friction of zero, while the log-spiral method significantly
overestimated resistance. Therefore, in computing the peak passive force for a
sand backfill with a geofoam inclusion, the wall friction should be assumed to
be zero and the Rankine method should be used. Placement of the geofoam
blocks between the pile cap and the sand backfill had the effect of reducing the
effective wall friction to zero.
5. Additional large scale tests should be run on geofoam inclusions with varying
geometries and densities to verify these conclusions and evaluate the influence
of these parameters on performance.
6. For future testing, solid or continuous geofoam blocks should be used rather
than adjoining geofoam pieces, if possible. If sections are to be used, the largest
sections should be placed on the top in order to produce a failure zone deeper in
the soil.
64
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