ANALYSIS OF GEOSYNTHETICREINFORCED
SOIL WALLS WITH A TRUNCATED BASE
B .S.Arch.E., University of Colorado, 1991
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
by
Damon Brian Thomas
Master of Science
Civil Engineering
1997
I
i
This thesis for Master of Science
K
degree by
Damon Brian Thomas
has been approved
by
Dunja Peric
Thomas, Damon Brian (M.S., Civil Engineering)
Analysis of GeosyntheticReinforced Soil Walls with a Truncated Base
Thesis directed by Professor Jonathan T.H. Wu
ABSTRACT
This thesis focuses on the use of the finite element method to analyze
geosyntheticreinforced soil (GRS) retaining walls with a truncated base. The
objective of this study was to analyze a GRS wall with truncated base to evaluate
its performance for use in conditions where excavation for full length
reinforcement is impractical.
An initial analysis was performed on a GRS wall located in the DeBeque
Canyon. This wall was constructed with a truncated base and was outfitted with
strain gauges and deflection measurement posts. A base model was set up and
analyzed using the program GREWS. The results of the analysis indicate that the
base model correctly simulates the actual DeBeque Canyon wall.
Using the validated base model, a parametric analysis was conducted to
investigate the effects of tails, backfill types, foundation types, angle of
truncation, and combinations of backfill type, foundation type, surcharge loading
and geosynthetic properties.
The essential finding of the thesis is that the use of truncated
reinforcement at the base of a GRS wall is a viable alternative for use when
in
excavation for full embedment of the geosynthetic is not practical. However,
truncated base GRS walls will be prone to potential global sliding failure more
readily than full length GRS walls. Thus external stability should be thoroughly
checked.
The backfill and foundation soils have a significant influence on the
performance of GRS walls with a truncated base. The use of clay soils for either
foundation or backfill should be avoided when a truncated base configuration is
adopted.
The use of tails in the upper onehalf to onethird portion of the wall
does not significantly affect overall performance. An angle of truncation of less
than 45 degrees should be used where possible. However, steeper angles may be
used in some cases if densely compacted granular backfill is used. In cases of
large externally applied surcharge loads, GRS wall with truncated base should
only be used with a very densely compacted granular backfill.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed
IV
ACKNOWLEDGEMENTS
I would like to thank the University of Colorado at Denver for funding this
study and the Colorado Department of Transportation for providing configuration,
deformation and strain information on the walls constructed during the DeBeque
Canyon Rockfall project. Gratitude is also extended to CTL/Thompson, Inc. for
their financial assistance throughout my graduate studies and Dr. Jonathan Wu for
his guidance and assistance with this project. Finally, I would like to thank my
wife, family and friends for their love, support and understanding throughout this
entire process.
TABLE OF CONTENTS
Chapter
1. Introduction......................................................1
1.1 General.......................................................1
1.2 Advantages and Limitations of GRS Walls.......................1
1.3 Problem Statement.............................................4
1.4 Thesis Objectives.............................................5
1.5 Method of Research............................................5
1.6 Content of Thesis.............................................6
2. Background........................................................8
2.1 Theory of Reinforced Soil.....................................8
2.2 Geosynthetic Reinforcement...................................11
2.2.1 Properties of Geosynthetics..................................11
2.3 Soil Modeling................................................14
2.3.1 Linear Elastic Models........................................15
2.3.2 Nonlinear Elastic Models.....................................16
2.3.3 Other Models.................................................17
2.3.4 DuncanChang Model...........................................17
2.3.5 Modified Duncan Model........................................21
2.4 Finite Element Analysis of GRS Walls.........................22
VI
2.5 Design of GRS Walls.............................................24
3. DeBeque Canyon Rockfall Project.................................... 28
3.1 DeBeque Canyon Rockfall Project.................................28
4. Analytical Model.................................................. 33
4.1 GREWS...........................................................33
4.2 GREWS Input and Library Files...................................35
4.3 Model Configuration.............................................38
4.4 DeBeque Canyon Analysis.........................................43
5. Results and Discussion.............................................49
5.1 Use of GRS Walls with a Truncated Base..........................49
5.1.1 FullLength Configuration.......................................50
5.1.2 Lateral Soil Stresses...........................................51
5.1.3 Sliding Failure.................................................52
5.1.4 Evaluation of Bearing Capacity Failure..........................54
5.2 Parametric Analysis.............................................55
5.3 Results of Parametric Analysis..................................56
5.3.1 Effect of Tails.................................................57
5.3.2 Effect of Backfill Types........................................63
5.3.3 Effect of Angle of Truncation...................................66
5.3.4 Effect of Foundation Types......................................70
vii
5.3.5 Synergistic Effect of Multiple Factors
73
5.4 Global Failure Condition....................................80
5.5 Use of Cohesive Soils.......................................81
6. Summary and Conclusions........................................82
6.1 Summary.....................................................82
6.2 Conclusions.................................................83
6.3 Recommendations for Further Study...........................85
Appendix
A. Finite Element Analysis Data................................87
Bibliography......................................................192
viii
CHAPTER 1
INTRODUCTION
1.1 General
The development of Mechanically Stabilized Earth (MSE) walls has
represented a major advance in geotechnical engineering practices. The MSE wall
is a term describing a retaining wall that derives its strength from the inclusion of
steel strips, polymeric grids, geotextile sheets, steel nails or anchors. The
inclusions typically serve to reinforce the backfill in a manner that provides
tensile resistance to soil weight and loading. A geosyntheticreinforced soil (GRS)
wall, using either geogrid or geotextile sheets as inclusion, is a member of the
MSE wall family.
Figure 1.1 shows typical GRS walls and the available facing types. The
GRS wall comprised of five major components: backfill, geosynthetic
reinforcement, wall facing, foundation and retained soil.
1.2 Advantages and Limitations of GRS Walls
GRS walls have demonstrated numerous characteristics that are preferable
to conventional concrete retaining walls. These characteristics include:
l
krappedfaced wall
wrappedfaced wall
with shotcrete cover
GRS wall with
articulated concrete
facing
GRS wall with
fullheight concrete
facing
(twophase construction)
fullheight concrete
MSB wall
(CTI MSB Wall)
timberfaced wall
modular block wall
tirefaced wall
gabionfaced wall
Figure 1.1
Typical GRS Walls and Available Facing Types (Wu, 1994)
2
1. GRS walls are relatively flexible, therefore they are capable of
tolerating large foundation settlements or differential settlement.
2. GRS walls do not require embedment into the foundation soil to
achieve stability.
3. The tensile reinforcement in ISR walls will significantly reduce the
lateral earth pressure exerted on the wall facing provided that some
movement of the facing allows mobilization of the tensile strength of
the reinforcement.
4. GRS walls are comparatively low in cost. Studies have shown that in
general, GRS walls are verycosteffective when compared with
concrete walls, especially when the average wall height is greater than
15 feet, and/or when a deep foundation is required for conventional
concrete walls.
5. Construction requires neither heavy equipment or skilled labor.
6. Geosynthetic reinforcements are highly resistant to corrosion and
bacterial action, compared to metallic reinforcements.
In addition to the benefits, GRS walls also have several limitations. The
limitations of GRS walls include:
1. GRS walls are susceptible to damage during construction and
vandalism after construction.
2. The longterm durability of the GRS walls is uncertain.
3
3. There is lack of consistent design approaches that are based on sound
engineering research.
The first limitation can be reduced by proper construction and inclusion of
the proper wall facing. For the durability concern, comprehensive research studies
are being conducted on the durability of geosynthetic materials. The last
limitation, in portion, is the focus of this thesis.
1.3 Problem Statement
Many of the currently available design methods fail to sufficiently
accommodate the interaction of the soil, reinforcement and facing in a GRS wall.
Most of the methods are based on the limiting equilibrium approach and use
arbitrarily assigned safety factors. An inherent problem of the limiting
equilibrium approach is its inability to estimate the deformation under service
loads.
These design and construction practices are also limited when being
applied to nonideal field conditions. One such nonideal condition is in the case
where excavation for the full embedment length of the reinforcement is either not
possible or not practical. There has been little engineering analysis of GRS walls
which make use of a truncated or trapezoidal reinforcement configuration for use
in these situations.
4
1.4 Thesis Objectives
The main objectives of this study were twofold. The first objective was to
establish a reliable finite element model that is capable of analyzing the
performance of GRS walls constructed with a truncated base configuration. The
second objective was to investigate the effects of various factors on the
performance of GRS walls constructed with a truncated base. These factors
include: the effect of tails (shortened layers of geosynthetic used to increase the
facing stability), backfill types, foundation types, angle of truncation, and
combinations of backfill type, foundation type, surcharge loading and
geosynthetic properties.
1.5 Method of Research
To properly analyze GRS walls with a truncated base, a valid model must
first be established. The base model used in this study was setup to simulate the
GRS wall constructed in the DeBeque Canyon. A finite element analysis was
performed using the program GREWS. The strains and deformations obtained
from the finite element analysis were compared to those measured in the field at
the DeBeque Canyon wall.
5
The validated model was then employed to analyze the effects of various
factors on the performance of GRS walls with a truncated base. These factors
include the use of tails, angle of truncation, the effect of backfill and foundation
materials, the effect of surcharge loads and the effect of geosynthetic stiffness.
The results of the analysis were organized in tables and graphical forms to help
establish conclusions as to the use of GRS walls with a truncated base.
1.6 Content of this Thesis
Chapter 2 contains background information on the theory of reinforced
soil, geosynthetic reinforcement, a review of soil models including the Duncan
Chang model and the modified Duncan model, a summary of the finite element
method and its application to GRS walls and a brief summary of the current
design practices of GRS walls.
Chapter 3 provides a background of the DeBeque Canyon wall, which is
the subject of the base model. It contains photographs and descriptions of the
configuration and materials used in its construction.
Chapter 4 describes the analytical model. It provides a brief overview of
the finite element program GREWS. It also contains descriptions of the
configuration of the base model and results of our analysis of the DeBeque
Canyon wall.
6
Chapter 5 presents the results of the parametric analysis performed on the
validated base model. It contains tables and graphs to help determine trends and
effects of the various parameters on GRS walls with a truncated base. The
summary, conclusions and recommendations for further study are contained in
Chapter 6. Detailed finite element analysis data, which includes sample input
files, outputs of the nodal deformations for each case and the base materials
library are included in Appendix A.
7
CHAPTER 2
BACKGROUND
2.1 Theory of Reinforced Soil
GRS walls are designed based on the theory of reinforced soil. When a
soil mass is compressed in the vertical direction, tensile strain is developed within
the soil mass in the horizontal direction. A reinforced soil is a soil mass that is
strengthened by the inclusion of reinforcement, which restrains the development
of tensile strain in the direction of the reinforcement. Due to the relatively low
tensile strength of soil, restraint of the tensile strain is an effective way to increase
the load carrying capacity of a soil mass.
In a reinforced soil, the reinforcement is bonded with the confining soil
through friction and/or cohesion. This bonding allows the transfer of stresses
between the soil and the reinforcement. The soil is more effective in resisting
compressive and shear stresses, and the reinforcement effective in resisting tensile
stress.
The mechanism by which tensile reinforcement is responsible for the
increased shear strength of a reinforced soil has been explained in two ways. In
one explanation, the tensile strength of the reinforcement and the stress transfer
between the soil and reinforcement are said to give the reinforced soil mass an
8
apparent cohesion. Under the same confining pressure, c3c, the presence of the
apparent cohesion results in an increase in the major principal stress at failure,
Aoir, as shown in Figure 2.1.
Provided that failure is caused by rupture of the reinforcement, the
inclusion of tensile reinforcement results in an apparent cohesion, cr, while the
internal friction angle is not affected. For reinforcement having a tensile breaking
resistance Tf, and with a vertical spacing between horizontal layers of
reinforcements, sv, the apparent cohesion cR can be determined as:
Tf (b
Cr=tan (45 + ^) Equation 2.1
2 Sv 2
where is the internal friction angle of the soil.
9
The effect of the apparent cohesion provided by tensile reinforcement has
been demonstrated in numerous tests. In such a test, a pile of dry sand was placed
at its steepest angle, which is the angle of repose. In comparison, the same sand
was reinforced with strips of paper placed horizontally inside the soil. The strips
of paper provide the necessary apparent cohesion to the dry sand and allow the
slope to assume a vertical angle.
In the other explanation, the reinforcement is said to offer an anisotropic
restraint to soil deformation in the direction of the reinforcement. The restraint in
lateral deformation provides an increase in the effective confining pressure at
failure, Ao3R, as shown on Figure 2.2, which leads to a larger major principal
stress at failure, g!R.
a
Figure 2.2
Effect of Anisotropic Restraint (Wu, 1994)
It is to be noted that both explanations give the same resulting strength (i.e., the
same ct]R for a a3c) of a reinforced soil mass.
10
2.2 Geosynthetic Reinforcement
Geosynthetic is defined by the American Society for Testing and Materials
(ASTM) as a planar product manufactured from polymeric material used with
soil, rock, earth, or other geotechnical engineering related material as an integral
part of a manmade project, structure, or system. Several different types of
geosynthetics are available, including geotextiles, geomembranes, geocomposites,
geonets and geogrids. The two most commonly used geosynthetics in GRS walls
are geotextiles and geogrids.
2.2.1 Properties of Geosynthetics
Geosynthetics are widely tested and their mechanical properties readily
available for design purposes. Of the many properties, three are directly related to
the design of geosyntheticreinforced soil (GRS) walls. These include uniaxial
tensile strength, creep characteristics and soilgeosynthetic interface properties.
The most widely used testing procedures for determining the uniaxial
tensile strength are the grab tensile test (ASTM D 4632) and the widewidth test
(ASTM D 4595). Results of these tests typically are presented on a load versus
deformation curve which shows the tensile force per unit width of the specimen
against deformation (strain). Depending on the polymer type and manufacturing
11
process, the shape of the curve may vary and the loaddeformation relations are
often nonlinear. Therefore, it is common practice to use the loaddeformation
characteristics in the strain range in which the geotextile is expected to experience
in the field.
Creep refers to the timedependent deformation of a material subject to a
constant static stress. Since geosynthetics are generally considered creep
sensitive, it is an important property to evaluate in the design of GRS structures.
The most influential factors that affect the creep potential of geosynthetics
are stress level and polymer type. Since temperature is known to affect the rate of
creep of geosynthetics, creep tests should be conducted to cover a range of
temperatures in the anticipated field conditions.
It is important to understand that timedependent deformation of a GRS
structure is a result of soilgeosynthetic interaction. It can be misleading to
evaluate the longterm creep potential of a GRS structure based on the results of
creep tests performed by applying tensile forces to the geosynthetic reinforcement
alone.
Plane strain testing methods have been developed in which the soil and
geosynthetic are allowed to deform in an interactive manner. These methods can
be used to evaluate the longterm creep potential for a selected combination of
backfill and geosynthetic reinforcement to be used in the construction. Results
have shown that the measured creep strains obtained in the plane strain
12
performance tests were significantly smaller than those obtained from the element
creep tests.
Design of GRS structures also requires that the tensile reinforcement have
adequate interface bond strength with the confining soil. The interface bonding is
needed to effectively transfer the tensile stress induced in the soil to the
reinforcement and to prevent pullout failure of the GRS structure.
The interface bond strength between soil and reinforcement has commonly
been evaluated by two methods of test: the pullout test and the direct shear test.
These tests are different in terms of their configurations, loading paths and
boundary conditions. Published test results have shown that the interface shear
strength is often different for the two test procedures. It is generally recognized
that the direct shear test is more appropriate for evaluating slideout failure
between a reinforcement and the soil mass above it. The pullout test, on the other
hand, provides a better representation for pullout failure at the freeend of an
embedded reinforcement.
An interface pullout formula was derived from results of laboratory
pullout tests and finite element analysis. This formula is capable of describing the
relationship between forces and displacements along the length of an extensible
sheet reinforcement in a pullout test. The tensile force T induced at a point with
coordinate x in a pullout test specimen can be determined by:
13
Et
Equation 2.2
T = (F + Et)
where F = applied pullout force (per unit width) in the test, E = inherent confined
Youngs modulus of reinforcement, t = initial thickness of reinforcement, an =
overburden pressure and f = coefficient of friction at soilreinforcement interface.
2.3 Soil Modeling
Soils are multiphase materials that consist of variable amounts of solid
particles, water, gas and air. The soil mass is often found to be inhomogeneous
and anisotropic which renders the mechanical behavior dependent upon a number
of factors. Some of theses factors include mineralogical composition, void ratio,
stress level, stress path, stress history, temperature, time and degree of saturation.
If the results of an analysis are to be realistic, then it is important that the stress
strain characteristics of the soil be represented in a proper way.
It is very difficult to create a general stressstrain law which is valid for all
soils under all placement and loading conditions. By necessity, simplified models
have been created to represent soil behavior in analyzing stresses and
displacements of soil masses. It is convenient to classify the various simplified
models for defining timeindependent behavior of soils into several categories.
14
These categories include linear elastic models, nonlinear incrementally elastic
models, higher order elastic models and plastic models.
2.3.1 Linear Elastic Models
Linear elastic models are the simplest approach to model the stressstrain
behavior of soils. The stressstrain relationship, which is governed by the
generalized Hooks law of elastic deformations, may be expressed as follows for
conditions of plane strain:
Â£7 1 C 11 C 12 0 * Ex
< G ,  C 12 C 22 0 Â£>
T xy V. > 0 0 C 33 \ /
Equation 2.3
in which [ax, ay, Txy]T and [sx, sy, Yxy]1 are stress and strain vectors, respectively.
Subject to the further assumption of material isotropy, only two
independent elastic moduli are needed to completely define the coefficients Cn,
C12, C22 and C33. Any two of the following elastic moduli may be selected:
Youngs modulus (E), Poissons ratio (p), shear modulus (G), bulk modulus (B),
and the constrained modulus (M). Relationships have been determined which
correlate the coefficients to the moduli.
15
2.3.2 Nonlinear Elastic Models
Nonlinear elastic models are approximated by a set of stressstrain curves
determined from one or two loading conditions. In such cases, it is possible to
describe the soil behavior by modeling the set of test data. However, this
nonlinear elastic model is only valid for conditions where the stress paths are
similar to those of the test loading configuration.
Numerous simplified nonlinear elastic models have been proposed and
used in analyzing stressdeformation of soil masses. These models are found to
provide an expedient, and often acceptable means for solving many geotechnical
engineering problems. These models differ among themselves in the way a given
set of stressstrain curves are obtained and simulated. The schemes for
representing stressstrain relations of soil masses involve either a tabular form or a
functional relationship.
In tabular form, the points on a stressstrain curve are input in the
computer in the form of number pairs denoting stress and strain at those points.
The soil moduli required to relate stress and strain, as in Equation 2.3, are
computed from the data by interpolation. The main disadvantage of the tabular
form is that a large number of data points have to be input in the computer and the
procedure may become cumbersome.
16
In the function relationship method, a given set of stressstrain curves are
represented by using mathematical functions such as a hyperbolic function, power
function, parabolic function, Lagrangian (interpolation) formula and others.
Some of the commonly used functional relationships include: the Duncan
Chang model, the extended Hardin model, the modified Duncan model, the spline
function representation and the modified RambergOsgood model.
2.3.3 Other Models
Several higher order elasticity models as well as plastic models have been
developed as of late. These models can accommodate for such factors as
dilatancy, strain hardening, work softening and stress path dependence. However,
several problems exist, of which perhaps the key problem is that no competent
relation has been found between the response parameters and other common soil
properties, thus reducing the applicability of such models.
Due to the lack of practical information available on these higher order
models, much of the soil modeling done today makes use of the DuncanChang
and modified Duncan models.
2.3.4 DuncanChang Model
It is necessary to incorporate advanced soil modeling to study GRS walls
as realistically as possible. One of the most widely used functional relationships
17
(ai a3)
was developed by Duncan and Chang (1970). The model is based on Kondners
finding (1963) that stressstrain curves for a number of soils could be
approximated by hyperbolas as shown in Figure 2.3.
Figure 2.3
Hyperbolic StressStrain Relationship (Wu, 1994)
The hyperbola in Figure 2.4 can be represented by an equation of the form:
a i a j
e
' n ( i
VE,J (cr i(73)01,
Equation 2.4
18
While other types of curves could also be used, a hyperbola has two
characteristics which make its use convenient:
(1) The parameters in Equation 2.4 have physical significance. Ej is the
initial tangent Youngs modulus and (ai a3)uit is the asymptotic
value of the stress difference which is related to the shear strength of
the soil.
(2) The values of Ej and (oi 03)uit for a given stressstrain curve can be
determined readily. The hyperbolic function can be transformed to a
linear relationship between s/(cti 03) and s as shown in Figure 2.4.
Figure 2.4
Transformation of Hyperbolic Function (Wu, 1994)
19
Using the relationship between Ej and <73, as proposed by Janbu (1963),
MohrCoulomb theory to obtain strength relationships, together with Equation
2.4, the expression for tangent Youngs modulus, Et, was given as:
Equation 2.5 involves five parameters: Rf is the failure ratio, which relates
compressive strength of the soil to (ai cj3)un; c and
strength parameters; and K and n are experimentally determined constants. Pa is
atmospheric pressure introduced into the equation to make the parameter n
independent of the chosen system of units. To account for variation of <() with
confining pressure, 03, the following equation was used:
Equation 2.5
4> = A
\P )
Equation 2.6
in which 0 is the value of ((> for 03 equal to Pa, and A((> is the reduction in 4> for a
10fold increase in 03.
20
An expression for the tangent Poissons ratio, p.t, was similarly obtained
as:
pt =
Equation 2.7
1
3 V R/(ai OsXl sin <())
Pa) 2c cos(() + 203 sin
In which parameters D, F and G are constants to be determined experimentally.
2.3.5 Modified Duncan Model
Duncan proposed a modified hyperbolic model which employed the bulk
modulus in place of Poissons ratio in the DuncanChang model. The model
assumed that bulk modulus, B, is independent of stress difference (oi 03), and
that it varies with confining pressure, 03, in the following form:
in which kb and m are dimensionless parameters to be determined experimentally,
and Pa is atmospheric pressure.
Equation 2.8
21
Duncan provided values of the bulk modulus parameters for a wide variety
of soils, which later were revised. Table 2.1 lists representative parameter values
taken from the latter report; they apply to soils tested under drained triaxial
conditions.
The values from Table 2.1 have been widely accepted for design of earth
structures where triaxial test data are not readily available. These values are
considered conservative in design. In addition, most finite element methods of
analysis include the use of the modified Duncan soil properties.
2.4 Finite Element Analysis of GRS Walls
The finite element method is a numerical procedure for obtaining solutions
to many of the problems encountered in engineering analysis. The method
combines several mathematical concepts to produce a system of liner or nonlinear
equations for analysis of statically indeterminate systems. The number of
equations formed during a finite element analysis is usually very large and
requires the computational power of a computer.
The advantages of the finite element method make it a well suited analysis
tool for GRS walls. These advantages include:
Any configuration of GRS wall, including truncated base, can be
analyzed.
The stressdeformation behavior of the soils can be simulated in a
realistic manner.
22
Table 2.1
Representative Parameter Values of the Modified
Duncan Model (from Duncan, et al., 1980)
Unified Soil Classification RC* Standard AASHTO Ym k/ft3 4*0 deg A(j> deg c psf K n Rr K m
105 0.150 42 9 50 600 0.40 0.7 175 0.2
GW, GP 100 0.145 39 7 50 450 0.40 0.7 125 0.2
SW, SP 95 0.140 36 5 50 300 0.40 0.7 75 0.2
90 0.135 33 3 50 200 0.40 0.7 50 0.2
100 0.135 36 8 50 600 0.25 0.7 450 0.0
SM 95 0.130 34 6 50 450 0.25 0.7 350 0.0
90 0.125 32 4 50 300 0.25 0.7 250 0.0
85 0.120 30 2 50 150 0.25 0.7 150 0.0
100 0.135 33 0 500 400 0.60 0.7 200 0.5
SMSC 95 0.130 33 0 400 200 0.60 0.7 100 0.5
90 0.125 33 0 300 150 0.60 0.7 75 0.5
85 0.120 33 0 200 100 0.60 0.7 50 0.5
100 0.135 30 0 400 150 0.45 0.7 140 0.2
CL 95 0.130 30 0 300 120 0.45 0.7 110 0.2
90 0.125 30 0 200 90 0.45 0.7 80 0.2
85 0.120 30 0 100 60 0.45 0.7 50 0.2
*RC = Relative compaction, in percent
The interactive behavior of the soil, the reinforcement and the facing
can be accounted for.
The construction sequence can be simulated.
For analysis of GRS walls, the strains and displacements before
construction are usually taken as zero. Increments of stress and displacement for
construction of each layer of geosynthetic and backfill are calculated and added to
the values for the previous construction step, thereby providing information on
stresses, strains, and movements for each stage of the analysis.
2.5 Design of GRS Walls
The design of GRS walls involves satisfying both external and internal
stability. External stability refers to the stability of the reinforced soil mass as a
whole in relation to the soil adjacent to it. Internal stability refers to stability
within the reinforced soil mass.
The external stability is generally evaluated by considering the reinforced
soil mass as a rigid gravity retaining wall with earth pressure acting behind the
wall. The wall is checked, using methods similar to those for conventional
stability analysis of rigid earth retaining structures, for stability against three
potential failure modes: sliding failure, foundation bearing failure and overall
slope failure (see Figure 2.5).
24
The internal stability of GRS walls requires that the wall be sufficiently
stable against failure within the reinforced soil mass. The wall is checked to
ensure that the reinforcement is not overstressed and its length is adequately
embedded. Internal failure modes include tensile rupture failure of reinforcement
and pullout failure of reinforcement (see Figure 2.6).
Many different design methods have been proposed for GRS walls. The
methods vary widely in approach and basis and can be divided into two general
categories. The safety factor methods consider limiting equilibrium state of stress
for evaluating the stability of GRS walls. The deformation limit methods consider
allowable lateral wall deformations of a GRS wall.
To generalize, while the many different methods vary in approach and
results, they all are based on a uniform length of reinforcement over the full
height of the wall. No design methods exist which take into consideration the use
of a truncated base configuration.
25
(a) Sliding Failure
(c) Slope Failure
External Failure Modes (Wu, 1994)
26
(a) Rupture Failure
(b) Pullout Failure
Figure 2.6
Internal Failure Modes (Wu, 1994)
27
CHAPTER 3
DeBEQUE CANYON ROCKFALL PROJECT
3.1 DeBeque Canyon Rockfall Project
The initial analysis of this study was performed on the GRS walls
constructed along the Interstate 70 corridor in the DeBeque Canyon in western
Colorado. The walls were constructed along a narrow rightofway with a steep
rock slope adjacent to the roadway. To reduce the potential of rock slides
affecting and potentially damaging vehicles travelling 170, the project was
undertaken to construct a geosyntheticreinforced soil retaining wall system along
the shoulder of the road.
The walls were built with varying backfill and geosynthetic
configurations. The presence of the steep, rock slope complicated the excavation
process, and thus, a decision was made to make use of a truncated base or
trapezoidal reinforcement configuration in portions of the wall.
In the area where the truncated reinforcement was used, the overall wall
height was 24 feet, which consisted of 36 courses of 8inch layers. The facing
used, was a 8inch high by 12inch deep segmental, Keystone type blocks. The
geosynthetic reinforcement consisted of Amoco 2044, a polypropylene woven
28
Load/Wldlh, Ib/ln.
fabric. The load versus deformation behavior of the Amoco 2044 is shown on
Figure 3.1.
Strain, %
Figure 3.1
LoadDeformation Behavior of Amoco 2044
(Courtesy of Amoco Fabrics and Fibers Company)
29
The Amoco 2044 has the following index properties in its fill direction:
Wide width strength (ASTM D 4595) of 400 lb/in,
Elongation at break (ASTM D 4595) of 18%,
Grab tensile strength (ASTM D 4632) of 600 lb,
Elongation at break (ASTM D 4632) of 20%
From Figure 3.1, an average Youngs modulus of 4,000 lb/in was calculated for
use in the analysis. The crosssectional configuration of the wall is shown on
Figure 3.2.
18 ft
24 ft
Backfill
Zone
Geosynthetic
<
4ft
Figure 3,2
CrossSection of DeBeque Canyon Wall
The geosynthetic was 4 feet in length at the base of the wall and an angle
of truncation of 45 degrees was used to increase the geosynthetic length for each
30
additional layer. The full embedment length of the geosynthetic was 18 feet.
Tails were installed in every other layer, starting between the 11th and 12th
course of blocks. The tails were 2 feet in length and were installed to increase
facing stability.
The backfill consisted of densely compacted gravelly sands, with a small
amount (10% to 20%) of fines. Three of the geosynthetic layers (between courses
3 and 4, 9 and 10, and 16 and 17) had strain gauges installed during construction
for long term monitoring of deformation within the reinforcement. In addition,
four vertical posts were installed away from the facing of the walls so that
deflection measurements could be obtained over the full height of the walls.
Figure 3.3 shows two photographs of the DeBeque Canyon wall taken during
construction.
This configuration, with the truncated base and the installed strain gauges
and deflection monitoring posts make the DeBeque Canyon wall an ideal case for
validating the analytical model in this study.
31
Figure 3.3
Photographs of the DeBeque Canyon Wall
32
CHAPTER 4
ANALYTICAL MODEL
4.1 GREWS
The finite element analysis performed in this study was conducted using
the program GREWS, developed by Wu, et. al. in 1994. GREWS is a
comprehensive design and analysis tool for use with geosyntheticreinforced
walls and slopes and is an acronym for GeosyntheticREinforced Walls and
Slopes. GREWS is coded in the Fortran programming language for use on several
computing platforms. This study made use of the DOS version on a standard
IBM compatible desktop computer.
GREWS has four levels of sophistication, which make it a powerful
analysis tool that can be applied to almost any type of reinforced earth wall or
slope configuration. These four levels of sophistication are as follows:
Level 1 uses existing limit equilibrium design methods for design of GRS
walls.
Level 2 is capable of performing design and analysis of a variety of GRS
walls and slopes under certain prescribed conditions.
Level 3 allows the user to make modifications to the prescribed
configurations and properties of Level 2, thus providing more flexibility.
33
Level 4 allows analysis of GRS walls using user input configurations and
properties using the finite element method.
Much of the code for GREWS was derived from the finite element
program DACSAR (Deformation Analysis Considering Stress Anisotropy and
Reorientation), which was developed by Iizuka and Otha (1987) at Kyoto
University in Japan. Extensive work has been performed to verify DACSAR
through comparisons with various soil element tests, laboratory model tests, full
scale loading tests and field tests.
Depending on the chosen level of sophistication, GREWS allows the user
to perform analysis and/or design of reinforced walls and/or steep slopes. Level 1
is for design of reinforced walls only. Levels 2 and 3 can be used for either design
or analysis of reinforced walls or slopes. Level 4 is for analysis only.
In the analysis mode, the user inputs the geometry of the wall or slope,
reinforcement configuration and properties, soil properties and loading conditions.
GREWS will then calculate the response of the reinforced soil structure, including
the displacements, stresses, strains, reinforcement tensions and the apparent factor
of safety.
In the design mode, on the other hand, the user supplies the same
information as in the analysis mode, except that the maximum allowable lateral
movement is input in place of reinforcement configuration and properties.
34
GREWS then will determine the required reinforcement properties, its
configuration and the corresponding deformation and factor of safety.
The program makes use of truss elements within the soil mass to represent
the reinforcement and beam elements to simulate the facing. It also assumes plane
strain geometry (i.e., the wall or slope is far wider that it is high). Levels 2, 3 and
4 are cast in incremental form to simulate sequential construction operations.
These features, coupled with the ability to input custom finite element meshes,
makes GREWS a very powerful tool for design and analysis of GRS walls.
4.2 GREWS Input and Library files
There are six prescribed configurations where GREWS will generate the
meshes with simple input data. These configurations vary, based on backfill,
inclination of wall facing and foundation as shown on Figure 4.1.
These prescribed configurations are quite useful, when they can be applied
properly. To use one of these configurations, GREWS simply requires the overall
geometry of the model, the material properties of its components and the number
of construction increments (i.e., the number of layers). The geometry parameters
required (in inches) are the overall height of the retaining wall, the thickness of
the foundation, the width of the backfill, the width of the foundation and the
length of the geosynthetic reinforcement. The required material properties are the
35
Figure 4.1
GREWS Prescribed Configurations (Wu, et. al. 1994)
AL,
CASH n
CASE C
AL,
CASE D
CASE E
CASE F
backfill material, the geosynthetic material, the facing material and the foundation
material.
The program operates by inputting a data file (grews.dat) containing the
previously mentioned parameters. The material properties are input as a reference
to a soil type within a base library (library.dat). This base library is a text file
that can be modified to include an unlimited number of different soil, facing and
geosynthetic types.
For soil types, the library file includes all of the modified Duncan soil
parameters presented on Table 2.1. For wall facing, the library file contains the
elastic modulus (E), the crosssectional area (A) and the moment of inertia (I).
These properties allow GREWS to simulate beam type reactions for the facing.
The geosynthetic properties contained in the library file include the elastic
modulus (E) and the crosssectional area (A). GREWS uses these properties to
simulate truss type behavior for the geosynthetic.
Once GREWS reads in the geometry parameters from the input file, it
produces an automatically generated finite element mesh based on the particular
case (see Figure 4.1). This mesh is created by discretizing the input geometry into
a set number of elements. These elements and corresponding nodes are then
numbered, beginning from the lowerleft portion of the mesh. Once the generation
reaches the wall portion of the model, GREWS inserts additional elements,
between common nodes, for the geosynthetic reinforcement and the wall facing. It
37
continues to build the mesh upward until it reaches the number of construction
increments input.
Once the mesh is generated, GREWS assigns each element to a particular
material type, based on the input file and the material library. After the material
properties are assigned to the elements, GREWS analyzes the model
incrementally as each increment or lift is added until the wall is completed.
4.3 Model Configuration
The base model used in this study was created to match the configuration
of the DeBeque Canyon wall. If the model could be setup in such a manner that
the strains and deformations output from GREWS agreed well with those
measured in the field, then that would lend validity to the model. Some degree of
accuracy in the setup of the model was sacrificed to allow quicker modification
for parametric study purposes that would follow after verifying the model.
With this in mind, sophistication Level 3 was selected to model the
DeBeque Canyon wall. Level 3 provides the benefit of the use of one of the six
previously mentioned prescribed configurations.
Of the six prescribed cases shown on Figure 4.1, Case B was selected
because it allows for study of deformable foundation soils, which would be part
of the parametric study that would follow. Once the case was selected, the initial
geometry was setup.
38
To match the conditions of the DeBeque Canyon wall as closely as
possible, the dimensions shown in Table 4.1 were used for the model.
Table 4.1
DeBeque Canyon Dimensions
Geometry Dimeasien (to.)
Height of Retaining Wall 268
Length of Geosynthetic Reinforcement 216
Width of Backfill Zone 324
Thickness of Foundation 288
Width of Foundation 864
Since Case B was selected for use, the overall geosynthetic length is
divided into six equallength elements. In this case, that made each element of the
geosynthetic 36.0 inches. In order to properly model truncated reinforcement, the
geosynthetic elements had to be adjusted. Input Level 3 allows for modification of
material types for any element. To do so, it is required that the element number,
its corresponding nodes and new material property be included in the input file.
The input file was modified for 114 of the geosynthetic elements, setting their
material properties to have and elastic modulus of 0, thus providing no strength to
the GRS wall and effectively modeling a truncated configuration. Figure 4.2 is a
39
graphical representation of the initial model for the DeBeque Canyon wall. It
shows the nodal locations and the elements representing the geosynthetic
reinforcement. Note that the elements where the geosynthetic elasticity was set to
0 are not indicated in the mesh.
While the overall length of the geosynthetic reinforcement was the same
as used in the DeBeque Canyon walls, discrepancies came into play when the
reinforcement was truncated. The actual wall was constructed with a 48inch long
reinforcement layer at the bottom of the wall. Each subsequent lift, the
reinforcement was increased 8 inches until the full length of reinforcement (18
feet) was achieved as shown on Figure 4.3.
40
700
600
500
400
300
200
100
0
s *
Hr mrmi*, T  )
100 200 300
H
400
i i !
500 600
(in)
700
800
900
10
Figure 4.2 DeBeque Canyon Wall Configuration
K18 ft
>k
*
Backfill
Zone
X
Geosvnthetic
<
4ft
Figure 4.3
DeBeque Canyon Wall Configuration
As stated previously, the elements were 36 inches in length. Therefore, the model
was setup with uniform geosynthetic lengths for several consecutive layers,
before increasing the length by 36 inches as shown on Figure 4.4.
18ft
Backfill
Zone
Geosynthetic
Figure 4.4
Base Model Configuration
24 ft
42
The length of the tails in the model were 36 inches, whereas they were 24 inches
as constructed.
With this configuration, the analysis was started under the hope that the
deformations would be at least on the same order of magnitude as those obtained
from the field measurement. If the analysis were to vary too much, the simplified
model would have to be adjusted to have varied geosynthetic reinforcement
lengths for each layer. This would involve switching to analysis Level 4, with a
custom finite element mesh.
4.4 DeBeque Canyon Analysis
The initial trial of the previously described base model produced
horizontal deformations on the order of 0.6 inches approximately 1/3 of the way
up the face of the wall. This initial trial run was done using backfill type
corresponding to the modified Duncan soil Type 2. This particular soil type is
correlated to a relatively clean, gravelly sand (GW, GP, SW or SP) compacted to
100% of standard Proctor maximum dry density (AASHTO T99).
These values appeared reasonable as a starting point, as the backfill placed
was a gravelly sand. However, information from previous studies in the Colorado
Rocky Mountains revealed that the modified Duncan values were conservative.
Taking this into account, some values of the material parameters were modified.
43
The following strength soil parameters were selected for use: ym = 150
pcf, (J>0= 42, A(J> = 7, c = 50 psf, K = 1,500, n = 0.7, Rf = 0.85, kb = 250, and m =
0.2. The model was analyzed again using these parameter values and a maximum
horizontal deformation of 0.38 inches was obtained. This maximum deformation
occurred at approximately 1/3 of the way up the face of the wall.
In comparison, the measured deformation of the DeBeque Canyon wall
varied between 0.18 and 0.44 inches with an average of 0.30 inches. The
maximum measured lateral movement of the DeBeque Canyon wall occurred at
different locations along the wall face, depending on which segment of the wall
the measurements were taken from. However, the maximum deformation
generally occurred between the lower XA to 1/3 of the wall facing. Figure 4.5
shows the actual measured lateral displacements plotted against those obtained
from the model.
In addition to the deformations, GREWS outputs stresses and strains for
each element of the system. Since strain gauges were installed on select layers of
geosynthetic reinforcement during construction, the measured strains could also
be compared to the strains calculated in the analysis. Figure 4.6 is a comparison of
the measured strains of the DeBeque Canyon wall versus modeled strains in the
geosynthetic between blocks 3 and 4, blocks 9 and 10 and blocks 16 and 17.
44
Figure 4.5
Face Deformations of the DeBeque Canyon Wall
45
Strain Distribution in the Geosynthetic Reinforcement
Between Blocks #16 & #17
 Modeled
Measured
Strain Distribution in the Geosynthetic Reinforcement Between Blocks #9 & #10
1.75 1.50 E 125 5 1.00 c > 0.75 0.50 0.25
AModeled Measured
.0
m : A A
0 0 2 0 4 0 6.0 8.0 10.0 12.0 14 Distance from facing blocks (ft) .o ie .0 1fi
Strain Distribution in the Geosynthetic Reinforcement
Between Blocks #3 & #4
Distance from facing blocks (ft)
Modeled
Measured
Figure 4.6 Strain Distribution for the DeBeque Canyon Wall
46
In comparing the measured strains versus the modeled strains, it is seen
that they are generally in very good agreement and at least on the same order of
magnitude where different. Also of notice is that the geosynthetic elements that
were assigned zero strength in the model are showing nonzero strains. This is to
be expected, as the soil elements above and below this zero strength geosynthetic
have induced strains. Thus the strain shown for these zero strength elements is
actually the strains induced in the confining soil elements. To confirm this
conclusion, the stresses were plotted over the same geosynthetic layers as shown
on Figure 4.7.
Examining the plot of the stresses, it is seen that the zero strength elements
have zero stress. This is in support of the fact that the geosynthetic in the model is
not taking any of the load.
In summary, the measured displacements and the modeled displacements
were in very good agreement both in magnitude and in location along the wall
facing. In addition, the measured strains and modeled strains agreed quite well.
These correlations and that fact that the zero strength geosynthetic elements of the
model showed zero stress indicate that the model is valid for simulation of the
actual constructed wall in the DeBeque Canyon.
47
Stress Distribution in the Geosynthetic Reinforcement
Between Blocks #16 & #17
Modeled
Distance from facing blocks (ft)
Stress Distribution in the Geosynthetic Reinforcement
Between Blocks #3 & #4
Distance from facing blocks (ft)
Figure 4.7 Stress Distribution for the DeBeque Canyon Wall
48
CHAPTER 5
RESULTS AND DISCUSSION
5.1 Use of GRS Walls with a Truncated Base
Based on the analysis performed on the base model and the actual
observed performance of the DeBeque Canyon wall, the use of truncated
reinforcement at the base of a GRS wall appears to be a valid and cost effective
alternative to constructing GRS walls at sites where excavation for full
embedment of the reinforcement is not practical. The finite element analysis of
the DeBeque Canyon wall indicates that the internal stability is satisfied.
However, the external stability still needs to be evaluated. When evaluating the
external stability, there are several issues that need to be addressed, including the
effects of lateral soil stresses, sliding and the reaction of the base of the wall (i.e.
foundation bearing failure).
The following sections describe an analysis of a full reinforcement length
configuration (no truncation) and a discussion of the external stability of GRS
walls with a truncated base. Following the discussion of these issues, a parametric
analysis is described. A complete summary of the input files and results of the
DeBeque Canyon wall, the base model and parametric analysis are presented in
Appendix A.
49
5.1.1 FullLength Configuration
The base model of the DeBeque Canyon wall was modified to compare
the effect of truncation of the reinforcement. All layers of geosynthetic were set to
18 feet in length. The remaining material properties remained the same as the base
model. The analysis on the fulllength configuration produced an apparent factor
of safety and deformations that were nearly identical to those obtained from the
DeBeque Canyon wall. A comparison of the results of the fulllength and
truncated configurations is presented in Table 5.1.
Table 5.1
Effect of Truncated Reinforcement
Deformations
Case Apparent Factor of Safety Lateral (> Vertical (in.) Output Reference
DeBeque Canyon (truncated) 6.5 0.38 0 93 Figure A. 1
DeBeque Canyon (fulllength) 6.5 0.34 0.92 Figure A. 69
As evidenced by the analysis, the truncation of the reinforcement of the
lower layers did not significantly reduce the internal stability of the GRS wall.
However, the effects of truncation of the reinforcement should be evaluated with
respect to the external stability.
50
5.1.2 Lateral Soil Stresses
Chou and Wu (1993), studied the magnitude of the lateral earth pressure,
or more properly termed, lateral soil stresses of GRS walls. Their study indicates
that the magnitude of the lateral soil stresses in a reinforced soil mass may vary
significantly from the facing to the back of the wall. From a design standpoint,
there are three locations where the lateral soil stresses are of interest. These are
the stresses against the facing, against the reinforced soil mass and along the plane
of maximum tensile force in the reinforcement.
Unless a rigid facing is employed, the lateral soil pressure against the
facing is typically smaller than any other vertical section in the reinforced soil
mass due to lateral expansion of the soil and the fact that part of the lateral thrust
is being resisted by the friction induced between the reinforcement and the
backfill. The stresses (pressures) against the facing is useful for design of the
facing and the connection between the facing and reinforcement. In the finite
element analysis, the lateral soil stresses (pressures) against the facing are
generally not equal to the horizontal stress in the soil elements immediately
behind the facing. The lateral pressure can be obtained by the tensile forces
induced in the reinforcement attached to the facing.
51
The lateral soil stress against the reinforced soil mass is useful in
calculating the apparent factors of safety for external stability. In the finite
element analysis, the lateral soil stresses against the reinforced soil mass can be
obtained by the horizontal stress in the soil elements immediately behind the
reinforced zone.
The lateral soil stress along the plane of maximum tensile force in the
reinforcement is useful in evaluating the required anchorage length behind the
potential failure plane. In the finite element analysis, the lateral soil stresses can
be obtained by the horizontal stress in the soil elements along the plane of
maximum tensile force.
As shown in the Chou and Wu study, the lateral soil stresses in these three
locations were significantly different. The lateral soil stresses against the wall
facing were the smallest and the stresses against the reinforced soil mass the
largest. Therefore, in evaluation of the external stability, it is important to use the
lateral soil stresses acting on the reinforced soil mass, and not against the facing
of the wall. The use of the finite element method allows convenient evaluation of
these stresses for use in the external stability analysis.
5,1.3 Sliding Failure
As discussed in Chapter 2, sliding along the base is one of the potential
failure modes of GRS walls. In evaluating the apparent factor of safety against
52
sliding, the driving factor is the lateral soil stresses against the reinforced soil
mass. The resistance is provided along the base of the reinforced soil mass. The
apparent factor of safety against sliding can be expressed by:
^ (W)f + cD c . 1
Fs =  Equation 5.1
Ph
Where W is the total weight of the reinforced soil mass, f is the friction
coefficient between the reinforced soil mass and the foundation soil, c is the
cohesion and D is the length of the reinforced soil mass at its base. Ph is the total
lateral thrust acting against the reinforced soil mass. Using the output from the
analysis of the DeBeque Canyon wall, the calculated apparent factor of safety for
the DeBeque Canyon wall against sliding is 1.5. In comparison, the apparent
factor of safety for the full length configuration is 2.0. Factors of safety of 1.5 or
higher are considered acceptable. From this comparison, it is evident that the
truncation of the reinforcement increases the potential for global sliding failure.
Another indication of the safety margin against sliding failure is the lateral
movement of the facing at the wall base. In both the truncated and frill length
configurations, the lateral movement of the facing at the wall base was zero.
53
5.1.4 Evaluation of Bearing Capacity Failure
The effect of the base reaction of the wall must also be evaluated in
regards to bearing capacity failure. The bearing capacity of the foundation soil
supporting the GRS wall must be sufficient to avoid bearing failure. According to
the current design concept for GRS walls, the truncation of the reinforcement
reduces the area of the base of the wall. This reduced area still supports the entire
weight of the structure which produces a higher concentrated bearing load as
compared to a full length GRS wall. The apparent factor of safety against bearing
capacity failure can be expressed as:
Fs =
Ultimate Bearing Capacity of Foundation Soils
_
Equation 5.2
Where Pv is the total vertical stress, due to the weight of the soil mass, acting on
the foundation soils from the reinforced soil mass. Based on the output of the
DeBeque Canyon wall, and assuming an ultimate bearing capacity of 7,500 psf
for the rock foundation, the apparent factor of safety for the DeBeque Canyon
wall is calculated as 2.9. In comparison, the apparent factor of safety for the full
length configuration is 3.0. Factors of safety of 2.0 or higher for granular
foundation soils and of 3.0 or higher for cohesive foundation soils are considered
54
acceptable. From this comparison, it appears that the truncation of the
reinforcement does not significantly increase the potential for bearing capacity
failure, at least for configurations with rigid foundations.
5.2 Parametric Analysis
Now that the base model of the DeBeque Canyon wall has been validated,
and the analysis indicates the use of truncated reinforcement is a valid alternative,
a parametric analysis could be performed to further evaluate the effectiveness of
truncated base GRS walls under various conditions. This section describes the
different cases within the parametric analysis, and the results of each case.
The parametric analysis was set up to account for numerous possible types
of conditions under the same basic wall configuration. A total of 66 cases were
analyzed. The overall wall height remained 24 feet (288 inches) and the full
reinforcement length was 18 feet (216 inches), tapering to 3 feet (36 inches) at the
base.
The parametric analysis began with a look at the use of tails, backfill types
and angles of truncation, followed by an analysis taking into consideration the
modification of the various material properties including backfill types,
foundation types, geosynthetic types, the application of surcharges and
combinations of some of these factors. Tables summarizing the parameters varied
for each case are included in Appendix A.
55
5.3 Results of the Parametric Analysis
The first result that many in the engineering profession would look at is
the apparent factor of safety. The lowest apparent factor of safety in this study
is 2.3. Although the value is sufficiently high, it does not necessarily imply
satisfactory performance. Recall the discussion in Chapter 2, GRS walls typically
do not have a catastrophic failure, as governed by the apparent acceptable
factors of safety. GRS walls are designed to deform within an acceptable limit,
and not fail. Designs are generally governed by what the acceptable deformations
are, and not the apparent factor of safety.
The apparent factors of safety are not, however, of no significant value.
The apparent factor of safety calculated by GREWS is an average factor of safety
against shear failure of the soil mass and is obtained by first assuming a failure
wedge at an angle of 45 + <)/2 through the soil mass, starting at the base of the
wall. The shear stress state, as determined by GREWS, for each element of
reinforcement that is intersected by this assumed failure plane is compared to the
failure shear stress determined from the MohrCoulomb failure criterion. The
ratio of the failure shear stress to the maximum shear stress in an element is
indeed an elemental factor of safety. The overall apparent factor of safety is
56
simply the average of these elemental factors of safety along the assumed
failure plane.
It is to be noted that deformations are typically the determining factor in
whether a design is considered acceptable or not. Many factors influence the
decision on what the maximum allowable deformation should be. Perhaps the
biggest factor is the location of the wall. For instance, walls which are located
along less traveled roadways or in landscaped areas may be allowed to deform
more than a wall located along a major interstate highway. Thus, the acceptable
deformation comes down to appearance and what public perception will be. This
explains why there is no set standard of practice for what deformations are
allowable. A common rule of thumb, however, is that deformations should be less
than 1 inch for every 12 to 15 feet of wall height.
This rule of thumb was used to interpret the results of the parametric
analysis included herein. With the height of the studied wall of 24 feet, any
deformations exceeding 2 inches in either the lateral or vertical direction were
considered unsatisfactory.
5.3.1 Effect of Tails
The use of tails in design and construction of geosyntheticreinforced
retaining wall systems is becoming more popular. Tails are shortened segments of
the geosynthetic whose primary function is to connect the facing blocks to the
57
reinforced soil mass. Tails also serve a secondary function to reinforces the soil
mass. The advantages to using tails are relatively obvious in that their use
reduces the amount of geosynthetic required as well as speeding up the
construction process by allowing larger lifts of backfill to be placed. However,
little study has been performed on the effect of tails relating to overall wall
performance.
In the case of the DeBeque Canyon wall, 2ft long tails were used, starting
between the 11th and 12th block. From there, the tails were installed in every other
layer. A comparison model was setup identical to the base model without the use
of the tails. Instead of cutting every other layer of geosynthetic at the tail length,
the reinforcement was extended to either its full length or its truncated length,
depending on the layer as shown of Figure 5.1. This configuration is referred to as
the notails configuration. The material properties remained the same as the
DeBeque Canyon wall.
The analysis on the notails configuration produced an apparent factor of
safety and deformations that were nearly identical to those obtained from the
DeBeque Canyon wall. A comparison of the two cases is presented in Table 5.2.
58
700
600
500
400
300
200
100
0
X
100 200
300 400 500 600
(in)
"H
700
800 900
10
Figure 5.1 Configuration without Tails (Base Model)
Table 5.2
Effect of Tails
Deformations
Case Apparent Factor of Safety Lateral (in.) Vertical (in.) Output Reference
DeBeque Canyon Wall 6.5 0.38 0.93 Figure A.l
 NoTails Configuration 6.5 0.35 0.93 Figure A. 2
The strain and stress distribution between blocks 16 & 17, blocks 9 & 10
and blocks 3 & 4 were plotted against the distance from the facing blocks (Figures
5.2 and 5.3) for the notails configuration. Comparing these plots to the plots from
the case with tails (Figures 4.6 and 4.7) indicates that the strains and stresses in
the reinforcement for the case without tails are nearly identical to the case with
tails.
As evidenced by the analysis, the inclusion of the remaining layers of
geosynthetic did not significantly increase the stability of the truncated base GRS
wall when compared to the case with the tails. This can be explained by the fact
that the lateral soil stresses are largest at the base of the wall. The exclusion of the
reinforcement over the upper portion of the wall does not significantly impact the
performance of walls constructed similar to the DeBeque canyon wall.
60
Strain Distribution in the Geosynthetic Reinforcement
Between Blocks #16 & #17
'
Modeled
Measured
Strain Distribution in the Geosynthetic Reinforcement
Between Blocks #9 & #10
2.00 r
1.75 
1.50 
* 1.25 
c 1.00 
2
(O 0.75 
0.50 
0.25 
0.00 
1 A At A
Modeled
Measured
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
Distance from facing blocks (ft)
16.0
Strain Distribution in the Geosynthetic Reinforcement
Between Blocks #3 & #4
2.00
1.75
1.50
 1.25
Â£ 1.00
0.75
0.50
0.25
0.00
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
Distance from facing blocks (ft)
Figure 5.2 Strain Distribution for the No Tails Configuration (Base Model)
61
Stress Distribution in the Geosynthetic Reinforcement
Between Blocks #3 & #4
Figure 5.3 Stress Distribution for the No Tails Configuration (Base Model)
62
5.3.2 Effect of Backfill Types
This portion of the parametric analysis focused on the effect of backfill
types. The base configuration for this portion was the DeBeque Canyon wall,
without tails as shown on Figure 5.1. The analysis was performed by varying only
the backfill material properties using the modified Duncan soil types (refer to
Table 2.1 for the modified Duncan soil parameters).
Output from each case was imported into a spreadsheet and the magnified
nodal deformation were potted. Table 5.3 summarizes the cases investigated,
apparent factors of safety, maximum lateral and vertical deformations and the
output reference located in Appendix A. The maximum lateral deformations for
each of the sixteen cases are also plotted on Figure 5.4.
As is the case with full length GRS walls, the analysis of truncated base
GRS walls indicate that the backfill types have a significant effect on the wall
performance. One difference, however, is accentuated with the use of the
truncated base. Full length GRS walls allow the use of clay backfill as an
alternative in semiarid locations or where grading of the wall reduces the
likelihood of surface runoff infiltrating the backfill. However, as the deformation
plots on Figure 5.4 indicate, the cases with clay backfill exhibited excessive
deformations. As evidenced by the deformation plots for these excessive cases
63
Table 5.3
Effect of Backfill Types
Deformations
Case Apparent Factor of Safety Lateral (in.) Vertical (in.) Output Location
Base Model 6.5 0.35 0.93 Figure A.2
GP Soil Type, 100% Compaction 4.8 0.58 1.49 Figure A. 3
GP Soil Type, 95% Compaction 3.1 1.08 2.15 Figure A.4
GP Soil Type, 90% Compaction 2.3 2.04 3.19 Figure A. 5
SM Soil Type, 100% Compaction 4.8 0.53 1.03 Figure A. 6
SM Soil Type, 95% Compaction 3.2 0.77 1.00 Figure A.7
SM Soil Type, 90% Compaction 2.5 1.18 1.19 Figure A. 8
SM Soil Type, 85% Compaction 2.4 2.18 1.69 Figure A. 9
SC Soil Type, 100% Compaction 6.0 0.98 1.59 Figure A. 10
SC Soil Type, 95% Compaction 5.4 1.66 2.51 Figure A. 11
SC Soil Type, 90% Compaction 4.6 2.20 3.19 Figure A. 12
SC Soil Type, 85% Compaction 3.7 3.32 4.61 Figure A. 13
CL Soil Type, 100% Compaction 5.6 2.18 1.94 Figure A. 14
CL Soil Type, 95% Compaction 4.8 2.66 2.27 Figure A. 15
CL Soil Type, 90% Compaction 4.0 3.52 2.93 Figure A. 16
CL Soil Type, 85% Compaction 3.2 5.38 4.41 Figure A. 17
64
110
105
100
95
90
85
80
75
70
Figure 5.4 Comparison of Lateral Deformations for cases with varied Backfill Types
(Figures A. 12A. 17), the potential failure mode is a global sliding of the
reinforced soil mass.
5.3.3 Effect of Angle of Truncation
In their limited use to date, truncated base GRS walls typically use an
angle of truncation of 45 degrees. The angle of truncation is measured, from
horizontal, at the end of the first layer of geosynthetic. It is of importance to study
the effect of the angle of truncation to determine if higher angles may be used.
The use of higher angles of truncation would provide even greater cost savings
over full length GRS walls, especially if the field condition mandates a higher
truncation angle.
The analysis to study the effect of angle of truncation on the performance
of GRS walls included the base configuration and two additional wall
configurations. Due to the individual geosynthetic element length of 3 feet in the
setup of the finite element mesh, some approximations for the angle of truncation
had to be made. The angle of truncation for the base case can be approximated to
45 degrees. The two other cases can be approximated at 50 and 55 degrees. The
length of the first layer of reinforcement in all three cases was 3 feet.
66
In addition to the modification of the angle of truncation, the backfill
properties were varied. A total of twelve different cases were studied in this
portion of the analysis, including three cases from the previous analysis. Table 5 .4
summarizes the cases investigated, apparent factors of safety, maximum
deformations and the output reference located in Appendix A. The maximum
lateral deformations for each of the twelve cases are also plotted on Figure 5.5.
As evidenced from Figure 5.5, the deformations of the cases using the GP
and SM backfill showed very little difference for each of the three angles of
truncation. However, from the previous analysis on the effect of backfill types, as
the strength of the backfill materials dropped, the deformations increased. This is
to be expected as well with these cases. The cases with cohesive backfill as shown
on Figures A.22A.24 exhibit a potential sliding failure.
Based on the analysis, a steeper angle of truncation may be used for
densely compacted granular backfill. However, in cohesive backfill and in lower
strength granular backfill, the increase in angle of truncation will increase the
lateral deformations by an appropriate amount.
67
Table 5.4
Effect of Angle of Truncation
Deformations
Case Apparent Factor of Safety Lateral (in.) Vertical (in.) Output Location
Base Model, 45degree angle 6.8 0.35 0.93 Figure A. 2
GP Backfill, 50degree angle 6.7 0.36 0.93 Figure A. 18
GP Backfill, 55degree angle 6.7 0.37 0.93 Figure A. 19
SM Backfill, 45degree angle 3.2 0.77 1.00 Figure A. 7
SM Backfill, 50degree angle 3.2 0.80 1.01 Figure A.20
SM Backfill, 55degree angle 3.2 0.81 1.02 Figure A.21
SC Backfill, 45degree angle 5.4 1.66 2.51 Figure A. 11
SC Backfill, 50degree angle 5.4 1.90 2.72 Figure A.22
SC Backfill, 55degree angle 5.4 2.01 2.79 Figure A.23
CL Backfill, 45degree angle 4.8 2.66 2.27 Figure A. 15
CL Backfill, 50degree angle 4.8 3.04 2.53 Figure A.24
CL Backfill, 55degree angle 4.8 3.20 2.61 Figure A. 25
68
70
65 ............:.............\..............j.............I............i..............i
60 ............I........................................I............ ..............I
a
<
40 
35  i..........i.........{....................].........i..........
30 I>'i1 i 1i11'i11i111i1111ij11 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Maximum Lateral Deformation (in)
Figure 5.5 Comparison of Lateral Deformations for cases with varied Angles of Truncation
5.3.4 Effect of Foundation Types
This portion of the analysis focused on the effect of the foundation types.
The base model was the DeBeque Canyon wall, without tails as shown on Figure
5.1. The analysis was performed by varying only the foundation material
properties using the modified Duncan soil types (refer to Table 2.1 for the
modified Duncan soil parameters).
The output from each case was imported into a spreadsheet and the
magnified nodal deformation were potted. Table 5.5 summarizes the cases
investigated, the determined factors of safety, the maximum horizontal and
vertical deformations and the output reference in Appendix A. The maximum
lateral deformations for each of the cases are also plotted on Figure 5.6
As expected, the cases with the more rigid foundations exhibit the least
wall movement, and the wall tends to rotate about the toe of the wall. As shown
on Figures A.32, A.35 and A.36, the walls with the softer foundations tend to
rotate about the top of the wall, due to the significant movement of the
foundation. This rotation about the top of the wall was further evidenced in the
cases involving clay foundations (Figures A.37A.40).
70
Table 5.5
Effect of Foundation Types
Deformations
Case Apparent Factor of Safety Lateral (in.) Vertical (*> Output Location
Base Model 6.8 0.35 0.93 Figure A. 2
GP Soil Type, 100% Compaction 6.8 0.32 1.94 Figure A.26
GP Soil Type, 95% Compaction 6.8 0.42 3.14 Figure A. 27
GP Soil Type, 90% Compaction 6.9 0.79 4.86 Figure A.28
SM Soil Type, 100% Compaction 6.7 0.40 0.83 Figure A.29
SM Soil Type, 95% Compaction 6.7 0.45 1.06 Figure A.30
SM Soil Type, 90% Compaction 6.7 0.62 1.53 Figure A.31
SM Soil Type, 85% Compaction 6.8 1.38 2.88 Figure A.32
SC Soil Type, 100% Compaction 6.7 0.49 2.05 Figure A.33
SC Soil Type, 95% Compaction 6.8 0.99 4.20 Figure A.34
SC Soil Type, 90% Compaction 6.8 1.38 5.79 Figure A. 3 5
SC Soil Type, 85% Compaction 6.9 2.21 9.01 Figure A.36
CL Soil Type, 100% Compaction 6.7 1.43 3.26 Figure A. 3 7
CL Soil Type, 95% Compaction 6.8 1.85 4.20 Figure A. 3 8
CL Soil Type, 90% Compaction 6.8 2.59 5.84 Figure A. 3 9
CL Soil Type, 85% Compaction 6.9 4.12 9.40 Figure A.40
71
Relative Compaction (%)
Figure 5.6 Comparison of Lateral Deformations for cases with varied Foundation Types
GP
*SM
BSC
ICL
The large disparity in wall deformations of the cases indicates the
importance of including foundation soil in the analysis, especially when a soft
foundations is present. As discussed previously, the truncation of the
reinforcement tends to concentrate the weight of the wall on the foundation soils
more than conventional, full length GRS walls.
5.3.5 Synergistic Effect of Multiple Factors
This section presents the synergistic behavior or the base wall under the
influence of multiple factor variations. It is impractical to perform a finite element
analysis for all possible cases of multiple factor variations. Therefore, a simplified
method to account for multiple factor variations was implemented.
The base model was the DeBeque Canyon wall without the use of tails
(Figure 5.1). Instead of running an analysis on every soil type shown in Table 2.1,
a representative soil type was selected from each of the four main types of soil
(GP, SM, SC and CL). The selected representative soil types as referenced in
Table 2.1 are:
GP GW, GP, SW or SP placed at approximately 100% relative
compaction,
SM SM placed at approximately 95% relative compaction,
SC SC placed at approximately 95% relative compaction, and
CL CL placed at approximately 95% relative compaction.
73
While not providing a complete analysis of the various possible
conditions, an analysis performed on the four soil types listed above will at least
provide some insight into the effect of multiple variations. The types of multiple
variations analyzed include the synergistic effects of different foundation and
backfill types, the effects of varied surcharges and backfill types, and the effects
of different geosynthetic strengths and backfill types.
The first multiple factor cases involved variation of both the backfill and
foundation types. A total of twelve additional cases were analyzed using each of
the previously described material types. Table 5.6 summarizes the cases, the
determined factors of safety, the maximum horizontal and vertical deformations
and the output reference in Appendix A.
As shown in Table 5.6, the analysis confirms that both the backfill and
foundation materials have a significant effect on the performance of GRS walls
with a truncated base. The results also indicate that the cases with granular
backfill and foundations had acceptable deformations, while those with cohesive
materials had excessive deformations.
74
Table 5.6
Effect of Backfill and Foundation Types
Deformations
Case Apparent Factor of Safety Lateral (in.) Vertical Output Location
SM Foundation, GP Backfill 4.8 0.72 1.63 Figure A.41
SM Foundation, SM Backfill 3.2 0.88 1.11 Figure A.42
SM Foundation, SC Backfill 5.4 1.79 2.63 Figure A.43
SM Foundation, CL Backfill 4.8 2.80 2.38 Figure A. 44
SC Foundation, GP Backfill 4.9 1.24 5.02 Figure A.45
SC Foundation, SM Backfill 3.2 1.30 4.55 Figure A.46
SC Foundation, SC Backfill 5.4 2.20 4.79 Figure A.47
SC Foundation, CL Backfill 4.8 3.37 4.67 Figure A. 48
CL Foundation, GP Backfill 4.9 2.30 5.07 Figure A.49
CL Foundation, SM Backfill 3.2 2.18 4.55 Figure A.50
CL Foundation, SC Backfill 5.4 2.79 5.05 Figure A. 51
CL Foundation, CL Backfill 4.7 3.91 4.81 Figure A.52
The next multiple factor cases focus on the effect of surcharges with
different backfill types. The base model was analyzed with a 5psi and lOpsi
vertical surcharge at the surface of the backfill. Each of the four main types of
backfill were included in the analysis for each of the surcharge loads. Table 5.7
summarizes the cases, the determined factor of safety, the maximum horizontal
and vertical deformations and the output reference in Appendix A. Figure 5.7
75
shows the lateral deformations versus the surcharge load for each of the backfill
types for this case.
Table 5.7
Effect of Surcharge Loads and Backfill Types
Deformations
Case Apparent Factor of iiiiiii! Lateral (*) Vertical (> Output Location
5 psi Surcharge, GP Backfill 4.8 0.90 2.06 Figure A. 5 3
5 psi Surcharge, SM Backfill 3.2 1.16 1.43 Figure A.54
5 psi Surcharge, SC Backfill 5.4 2.46 3.70 Figure A. 5 5
5 psi Surcharge, CL Backfill 4.8 3.87 3.50 Figure A.56
10 psi Surcharge, GP Backfill 4.8 1.22 2.75 Figure A. 5 7
10 psi Surcharge, SM Backfill 3.2 1.58 1.94 Figure A.58
10 psi Surcharge, SC Backfill 5.4 3.30 5.63 Figure A.59
10 psi Surcharge, CL Backfill 4.8 5.12 5.35 Figure A.60
Figure 5.7 indicates that surcharge loading impacts the wall performance
for both the granular and cohesive soil types in a linear relationship. The impact is
more pronounced for the cases with cohesive backfill. As shown on Figures A.55
A.60, the surcharge loading tends to accelerate the potential for global sliding
failure. As is the case with conventional, fulllength GRS walls, the settlement at
the surface of the reinforced soil mass is also a factor to be evaluated.
76
J
J
+
GP
SM
SC
CL
Figure 5.7 Lateral Deformations for cases with varied Surcharge Loads and Backfill Types
The last multiple factor cases focus on the effect of reinforcement stiffness
and backfill types. The base model was used to analyze cases with varied
geosynthetic stiffness with each of the four backfill types. The base model used a
Youngs Modulus of 4,000 lb/in for the geosynthetic. The additional cases
analyzed during this phase used Youngs Moduli of 1,500 lb/in and 450 lb/in.
Table 5.8 summarizes the cases, the determined factors of safety, the maximum
horizontal and vertical deformations and the output reference in Appendix A.
Figure 5.8 shows the lateral deformations versus the surcharge load for each of
the backfill types for this case.
Table 5.8
Effect of Geosynthetic Stiffness and Backfill Types
Deformations
Case Apparent Fdttoirof Safety Lateral (in.) Vertical (in.) Output Location
Et = 1500 lb/in, GP Backfill 4.6 0.71 1.53 Figure A. 61
Et = 1500 lb/in, SM Backfill 2.9 0.90 1.07 Figure A.62
Et= 1500 lb/in, SC Backfill 4.9 2.02 2.88 Figure A. 63
Et= 1500 lb/in, CL Backfill 4.1 3.20 2.53 Figure A. 64
Et 450 lb/in, GP Backfill 4.4 0.85 1.61 Figure A.65
Et = 450 lb/in, SM Backfill 2.7 1.03 1.13 Figure A. 66
Et = 450 lb/in, SC Backfill 4.5 3.02 3.65 Figure A.67
Et = 450 lb/in, CL Backfill 3.5 4.49 3.39 Figure A.68
78
Young's Modulus of Reinforcement (lb/in)
GP
*SM
&SC
ICL
Figure 5.8 Lateral Deformations for cases with varied Geosynthetic and Backfill Types
As shown in Table 5.8 and Figure 5.8, for truncated base walls with
granular backfill, a decrease in reinforcement stiffness does not significantly
affect the deformations of the wall. For walls with cohesive backfill, however, the
reduction in stiffness of the geosynthetic significantly affects the wall
performance.
5.4 Global Failure Condition
Examining the nodal deformation plots contained in Appendix A, a trend
regarding potential failure modes can be determined. The deformation plots are
magnified 20 times the actual deformations. The cases that had excessive lateral
deformations take on the shape of a wall failing by a global, sliding failure along
the end of the truncated geosynthetic.
This is also supported by the fact that the external factor of safety against
sliding was significantly lower for the truncated configuration as compared to the
fulllength configuration. From these results, it is apparent that global sliding is a
primary potential failure mode of truncated base GRS walls and should be
carefully evaluated when a truncated base configuration is used.
80
5.5 Use of Cohesive Soils
The analysis done in this study on the cohesive soils does not account for
the dissipation of pore pressures that occur over a period of time. The
deformations determined by the finite element method analysis conducted in this
study are of an immediate response. The actual strains and deformations can be
expected to be larger than those reported in this study, as the dissipation of pore
pressure may result in additional soil movement.
Another factor in the use of cohesive soils is the effect of moisture.
Moisture is the single most detrimental factor in the use of cohesive soils in any
geotechnical engineering project. The effect of partial saturation, complete
saturation and surface runoff are all conditions which were not addressed in this
study.
81
CHAPTER 6
SUMMARY AND CONCLUSIONS
6.1 Summary
A study was undertaken to investigate the effect of truncation of the lower
layers of the geosynthetic in GRS walls. The objective of this study was to
analyze GRS walls with a truncated base to evaluate their performance for use in
situations where full excavation is impractical. The analysis was conducted using
the finite element program GREWS. The analysis included an evaluation of the
effects of backfill soils, foundation soils, angle of truncation, use of tails,
surcharges and geosynthetic properties.
An initial analysis was performed on the GRS wall located in the DeBeque
Canyon. This wall was constructed with a truncated base and was outfitted with
strain gauges and deflection measurement posts. A base model was setup to
simulate the actual DeBeque Canyon wall. Analysis, which compared the actual
deformations and strains to the modeled deformations and strains, showed that the
behavior of the DeBeque Canyon wall could be properly simulated by the base
model.
Using the validated base model, a single factor parametric analysis was
conducted to investigate the effects of tails, backfill types, foundation types and
82
angle of truncation of GRS walls with a truncated base. A multiple factor
parametric study was then conducted to investigate the synergistic effects of
various factors on the performance of GRS walls with a truncated base. These
factors include combinations of backfill type, foundation type, surcharge loading
and geosynthetic properties.
6.2 Conclusions
1. Truncated reinforcement at the base of a GRS wall is a viable and
practical alternative for use when excavation for full embedment of the
geosynthetic is not practical.
2. When designing GRS walls with a truncated base, external stability should
be thoroughly checked. Truncated base GRS walls appear to have a
stronger tendency to fail in a global, sliding failure more readily than they
will from a rupture or pullout type failure.
3. The use of tails, generally 2 to 3 feet in length, in the upper 1/2 to 1/3 of
the wall section does not significantly impact the performance of GRS
walls with a truncated base.
4. The type and compaction of the backfill material plays a significant role in
the performance of GRS walls with a truncated base. The use of cohesive
backfill should be avoided when a truncated base is used.
83
5. An angle of truncation greater than 45 degrees may be used with densely
compacted granular backfill. Angles of truncation greater than 45 degrees
should be avoided if cohesive backfill soils are used, or in lower strength
granular backfill soils.
6. The strength of the foundation soil has a significant influence on the
performance of GRS walls with a truncated base. Due to the additional
concentrated loading of a truncated base, the walls on soft or cohesive
foundations may tend to rotate about the top of the wall due to excessive
foundation settlement.
7. The use of clay soils for either foundation or backfill should be avoided
when a truncated base configuration is desired. As evidenced by the
parametric analysis, nearly all cases that involve clay soils as either the
foundation or backfill exhibited larger than acceptable deformations.
8. If surcharge loading is anticipated on a GRS wall with truncated base, a
very densely compacted granular backfill should be used. The additional
loading due to the surcharge will tend to accelerate the global sliding
failure due to the truncation of the geosynthetic, especially with lower
strength backfill types.
9. For a GRS wall with truncated base and granular backfill, decreasing the
reinforcement stiffness from 4,000 lb/in to 450 lb/in does not significantly
affect the deformations of the wall. For walls with cohesive backfill,
84
however, the reduction in geosynthetic stiffness significantly affects the
wall performance.
6.3 Recommendations for Further Study
1. More controlled and instrumented fullscale tests should be performed to
gain a better understanding of GRS walls constructed with a truncated
base under different conditions to further validate the analysis contained in
this study.
2. Further studies are recommended for different reinforcement spacings and
angles of truncation. In addition, the effects of differential settlement in
the crosssection and alignment directions should be studied.
3. Long term effects such as creep of the geosynthetic, construction damage
and chemical degradation should be investigated as related to use with
truncated base GRS walls..
4. Further studies are recommended with other backfill types, such as silt,
swelling clay, recycled asphalt or concrete and waste products such as
shredded rubber and landfill.
5. Additional investigation into the difference in lateral soil stresses at
different locations within a truncated base GRS structure. These locations
should include the stresses against the wall facing, the stresses against the
85
reinforced soil mass, and the stresses along the plane of maximum tensile
force in the reinforcement.
6. Further study should be done to compare the effect of truncated base and
fulllength GRS walls on bearing capacity. The study should include both
configurations in cases with deformable foundations.
86
APPENDIX A
FINITE ELEMENT ANALYSIS DATA
Included herein are tables which summarize the cases of this thesis,
including apparent factors of safety, maximum lateral and vertical
deformations, and locations within the Appendix of output files.
Following each table are "typical" input files for each type of parametric
study, and plots of the nodal deformations for each case. The materials
library file is included at the back of this Appendix.
Table A.l DeBeque Canyon Wall & Effect of Tails
Deformations
Case Apparent Factor of Safety Lateral iiii Vertical Output Location
DeBeque Canyon wall 6.5 0.38 0.93 Figure A. 1
DeBeque Canyon wall (no tails) 6.5 0.35 0.93 Figure A. 2
Note: Following is the input files for the DeBeque Canyon wall
and the case with no tails. The case without tails also serves as
the base model for the remainder of the analysis.
87
Input File : DeBeque Canyon Wall
3
0
38
288
36
0.0694
4000
0
114
106
107
108
109
110
122
123
124
125
126
138
139
140
141
142
154
155
156
157
170
171
172
173
186
187
188
2 0 0
99 99 39 24 38
288 324 864 216
4000
114 115 0 0 26
115 116 0 0 26
116 117 0 0 26
117 118 0 0 26
118 119 0 0 26
136 137 0 0 26
137 138 0 0 26
138 139 0 0 26
139 140 0 0 26
140 141 0 0 26
146 147 0 0 26
147 148 0 0 26
148 149 0 0 26
149 150 0 0 26
150 151 0 0 26
156 157 0 0 26
157 158 0 0 26
158 159 0 0 26
159 160 0 0 26
166 167 0 0 26
167 168 0 0 26
168 169 0 0 26
169 170 0 0 26
176 177 0 0 26
177 178 0 0 26
178 179 0 0 26
88
189 179 180 0 0 26
202 186 187 0 0 26
203 187 188 0 0 26
204 188 189 0 0 26
205 189 190 0 0 26
218 196 197 0 0 26
219 197 198 0 0 26
220 198 199 0 0 26
234 206 207 0 0 26
235 207 208 0 0 26
236 208 209 0 0 26
250 216 217 0 0 26
251 217 218 0 0 26
252 218 219 0 0 26
266 226 227 0 0 26
267 227 228 0 0 26
268 228 229 0 0 26
282 236 237 0 0 26
283 237 238 0 0 26
284 238 239 0 0 26
285 239 240 0 0 26
286 240 241 0 0 26
298 246 247 0 0 26
299 247 248 0 0 26
314 256 257 0 0 26
315 257 258 0 0 26
316 258 259 0 0 26
317 259 260 0 0 26
318 260 261 0 0 26
330 266 267 0 0 26
331 267 268 0 0 26
346 276 277 0 0 26
347 277 278 0 0 26
348 278 279 0 0 26
349 279 280 0 0 26
350 280 281 0 0 26
362 286 287 0 0 26
89
378 296 297 0 0 26
379 297 298 0 0 26
380 298 299 0 0 26
381 299 300 0 0 26
382 300 301 0 0 26
394 306 307 0 0 26
410 316 317 0 0 26
411 317 318 0 0 26
412 318 319 0 0 26
413 319 320 0 0 26
414 320 321 0 0 26
442 336 337 0 0 26
443 337 338 0 0 26
444 338 339 0 0 26
445 339 340 0 0 26
446 340 341 0 0 26
474 356 357 0 0 26
475 357 358 0 0 26
476 358 359 0 0 26
477 359 360 0 0 26
478 360 361 0 0 26
506 376 377 0 0 26
507 377 378 0 0 26
508 378 379 0 0 26
509 379 380 0 0 26
510 380 381 0 0 26
538 396 397 0 0 26
539 397 398 0 0 26
540 398 399 0 0 26
541 399 400 0 0 26
542 400 401 0 0 26
570 416 417 0 0 26
571 417 418 0 0 26
572 418 419 0 0 26
573 419 420 0 0 26
574 420 421 0 0 26
602 436 437 0 0 26
90
603
604
605
606
634
635
636
637
638
666
667
668
669
670
437 438 0 0 26
438 439 0 0 26
439 440 0 0 26
440 441 0 0 26
456 457 0 0 26
457 458 0 0 26
458 459 0 0 26
459 460 0 0 26
460 461 0 0 26
476 477 0 0 26
477 478 0 0 26
478 479 0 0 26
479 480 0 0 26
480 481 0 0 26
91
Input File : DeBeque Canyon Wall without tails (Base Model)
3
0 2 0 0.00
38 99 99 39 24 38
288 288 324 864 216
36
0.0694
4000 4000
0
114
106 114 115 0 0 26
107 115 116 0 0 26
108 116 117 0 0 26
109 117 118 0 0 26
110 118 119 0 0 26
122 136 137 0 0 26
123 137 138 0 0 26
124 138 139 0 0 26
125 139 140 0 0 26
126 140 141 0 0 26
138 146 147 0 0 26
139 147 148 0 0 26
140 148 149 0 0 26
141 149 150 0 0 26
142 150 151 0 0 26
154 156 157 0 0 26
155 157 158 0 0 26
156 158 159 0 0 26
157 159 160 0 0 26
92
