A COMPARISON OF DESIGN METHODS FOR
GEOSYNTHETIC-REINFORCED EARTH WALLS
by
Alan F. Claybourn
B.S., University of Colorado, 1979
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Civil Engineering
1990
This thesis for the Master of Science degree by
Alan F. Claybourn
has been approved for the
Department of
Civil Engineering
by
Date
Claybourn, Alan F. (M.S., Civil Engineering)
A Comparison of Design Methods for Geosynthetic-
Reinforced Earth Walls
Thesis directed by Associate Professor Tzong H. Wu
The design of geosynthetic-reinforced earth walls
in engineering practice is currently conducted using a
number of diverse design methods. These design methods
are typically based on relatively simple analytical models
rather than on more realistic models that account for the
complex stress distributions which probably occur in such
structures. Since relatively little investigation of the
behavior of these structures has been conducted to date,
most of the analytical models used are based more on
assumptions than on supporting empiricism. The.outcome is
diverse results among the various methods.
The study consisted of a review and comparison of
six published design methods. The methods used are: the
Forest Service Method (Steward, Williamson, and Mohney,
1977, revised 1983); the Broms Method (Broms, 1978) ; the
Collin Method (Collin, 1986); the Bonaparte et al. Method
(Bonaparte, Holtz, Giroud, ASTM STP 952, 1987); the
Leshchinsky and Perry Method (Leshchinsky and Perry,
1987) ; and the Sehmertmann et al. (Tensar) Method
(Schmertmann, Chouery-Curtis, Johnson, and Bonaparte,
1987).
These six methods demonstrate the range of techniques
most commonly being used in current practice to analyze
iv
steep-faced geosynthetic-reinforced earth structures.
Comparisons were made of the results of designs for
various wall heights and geometries for each of the
methods by strictly following the design procedures. The
results of tests conducted on two geosynthetic-reinforced
test walls which were loaded to failure were then used to
evaluate each of the analytical models by using the design
methods without any safety margins. The design methods
and the concepts on which they are based are described and
their differences summarized. The results of the
comparisons are presented along with conclusions based on
the results.
To some extent, the differences in results
obtained by the various methods result from obvious
differences in the analytical models used. However, the
more prominent differences are due to significant
disparity in defining allowable reinforcement strength and
safety factors. For the most part, the demonstrated
success of these structures to date is probably more
attributable to the conservatism inherent in the design
methods than to the accuracy of the analytical models.
The form and content of this abstract are approved,
recommend its publication.
Signed
Tzong H. Wu
I
CONTENTS
Tables..............................................viii
Figures.............................................ix
CHAPTER
1 INTRODUCTION
1.1 General Background ....................... 1
1.2 General Description of Study ............. 4
1.3 Purpose and Scope of Study.................8
2 DESIGN METHODOLOGIES
2.1 General ..................................10
2.2 Design Input Parameters . ..............12
2.3 Factor of Safety..........................15
2.4 Description of Design Methods
Used for Study..........................17
2.4.1 Forest Service Method ............ 20
2.4.2 Broms Method ......................23
2.4.3 Collin Method......................25
2.4.4 Bonaparte et al. Method............29
2.4.5 Leshchinsky and Perry Method .32
2.4.6 Schmertmann et al. Method .... 36
3 DESIGN COMPARISONS
3.1 General ..................................39
3.2 Descriptions of Design Configurations 39
vi
3.3 Additional Assumptions Made ............. 41
3.3.1 Forest Service Method ............ 41
3.3.2 Broms Method ......................43
3.3.3 Collin Method.....................43
3.3.4 Bonaparte et al. Method...........45
3.3.5 Leshchinsky and Perry Method .45
3.3.6 Schmertmann et al. Method .... 46
3.4 Results of Comparisons...................46
3.4.1 Design Results ...................4 6
3.4.2 Reinforcement Quantity Comparisons 47
4 CASE HISTORY EVALUATIONS
4.1 General ..................................60
4.2 Description of Case Histories ............60
4.2.1 STS/FHWA Geotextile Test Wall . 60
4.2.2 RMC Geogrid Model Wall ............63
4.3 Summary and Results of Comparisons ... 66
4.3.1 Forest Service Method ............ 74
4.3.2 Broms Method ......................75
4.3.3 Collin Method.....................77
4.3.4 Bonaparte et al. Method...........79
4.3.5 Leshchinsky and Perry Method . .81
4.3.6 Schmertmann et al. Method . . . .83
5 SUMMARY AND CONCLUSIONS
5.1 General ..................................86
5.2 Analytical Models ...................... 89
5.3 Reinforcement Strength and
Soil/Reinforcement Interaction .......... 94
Vll
5.4 Factor of Safety..........................97
5.5 Concluding Comments ..................... 98
REFERENCES............................................101
APPENDIXES
A. Computer Printouts and Calculations for
Design Evaluations ......................... 104
B. Computer Printouts and Calculations for
Case History Evaluations ................... 139
TABLES
Table
3.1 Summary of Design Parameters ................. 48
3.2 Summary of Design-Forest Service Method ... 49
3.3 Summary of Design-Broms Method ............... 50
3.4 Summary of Design-Collin Methods ............. 51
3.5 Summary of Design-Bonaparte et al.
Method........................................52
3.6 Summary of Design- Leshchinsky and
Perry Method..................................53
3.7 Summary of Design- Schmertmann et al.
Method........................................54
3.8 Summary of Reinforcement Quantity
Comparisons- 12-foot High Wall................58
3.9 Summary of Reinforcement Quantity
Comparisons- 30-foot High Wall................59
5.1 Design Reinforcement Quantity Versus
Reinforcement Quantity for FS=1.0
(Fabric 2, 30-foot height, vertical face) 87
/
Figure
1.1
FIGURES
Schematic Representations of a Typical
Geosynthetic-Reinforced Soil Wall and
its Conceptually Equivalent Gravity
Retaining Structure ........................... 2
2.1 Geometry and Nomenclature Used for Forest
Service, Broms, Collin and Bonaparte et al.
Methods...................................... 19
2.2 Summary of Lateral Pressures and Input
Parameters and Equations for Forest
Service Method ............................... 21
2.3 Summary of Lateral Pressure and Input
Parameters and Equations for Broms Method .24
2.4 Summary of Lateral Pressure and Input
Parameters and Equations for Collin
Geotextile Method .................... 27
2.5 Summary of Lateral Pressure and Input
Parameters and Equations for Collin
Geogrid Method ............................... 28
2.6 Geometry, Nomenclature, Summary of
Lateral Pressure, and Input Parameters
and Equations for Bonaparte et al. Method .31
2.7 Geometry, Nomenclature, and Summary of Input
Parameters and Equations for Leshchinsky
and Perry Method...............................34
2.8 Geometry, Nomenclature, and Summary of Input
Parameters and Equations for Schmertmann
et al. Method..................................38
3.1 Example Design Comparisons, 12-foot High
Wall, Fabric 1.................................55
3.2 Example Design Comparisons, 30-foot High
Wall, Fabric 3 56
4.1 Summary of Test Wall Geometries................68
X
4.2 Reinforcement Tension Calculated for
STS/FHWA Test Wall............................70
4.3 Reinforcement Tension Calculated for
RMC Model Wall Geometry.......................71
4.4 Comparison of Methods for FS= 1.0
(20-foot High Wall, 1320 lb/ft
Reinforcement Strength) ................... 72
4.5 Comparison of Methods for FS=1.0
(9.8-foot High Wall, 500 Ib/ft
Reinforcement Strength, 1045 psf
Surcharge) ........................
73
CHAPTER 1
INTRODUCTION
1.1 General Background
The concepts of reinforced soil and gravity
retaining structures are both centuries old. The use of
modern geosynthetic reinforcement to construct a
reinforced soil mass which essentially constitutes a
gravity retaining structure is relatively new. Henry
Vidal of France introduced a new era of relatively
flexible retaining walls in the 1960's with the concept of
reinforced earth (Koerner, 1986). Metal strips were used
to anchor facing panels at the wall face and to reinforce
the backfill soil mass.
Geosynthetics have found some use in reinforced
soil walls in the past 10 to 15 years and are becoming
more common as their behavior becomes better understood.
Similar in concept to the patented "Reinforced Earth"
structures using metal strips, layers of geotextile or
geogrid are embedded in a backfill soil to construct a
free standing wall. Figure 1.1 shows a schematic
representation of such a wall and its conceptually
equivalent gravity retaining structure. These walls tend
to be quite flexible when compared with more conventional
structural retaining walls. They are also frequently less
2
SURCHARGE
(a) Section of Typical Geosynthetic-Reinforced
Soil Wall.
SURCHARGE
(b) Equivalent Gravity Retaining Structure
Figure 1.1- Schematic Representations of a
Typical Geosynthetic-Reinforced
Soil Wall and its Conceptually
Equivalent Gravity Retaining Structure.
3
costly than more conventional walls.
The design of any retaining structure must
consider both internal and external stability. External
stability typically considers the wall itself to be a
rigid structure and addresses its potential for sliding or
overturning, or bearing capacity or slope stability
failure beneath or behind it. Internal stability
addresses the structural integrity of the wall itself.
For a conventional wall constructed of a material such as
concrete or reinforced concrete, the internal stability is
addressed by the structural design. The internal
stability of geosynthetic-reinforced soil walls is the
subject of this study.
A number of approaches have been developed for the
design of geosynthetic-reinforced walls. These are
discussed in some detail in Chapter II. All of the
methods normally considered applicable to routine design
use limiting equilibrium analyses to determine factors of
safety against failure. Most of them use a conceptually
simple analysis of destabilizing horizontal forces
resulting from earth pressures and stabilizing horizontal
forces due to the reinforcement. These methods typically
do not include a stress-deformation analysis to evaluate
performance.
4
1.2 General Description of Study
This report presents the results of a study of six
design methods for evaluating the internal stability of
geosynthetic-reinforced earth walls. The study consisted
of reviewing the design methodologies, comparing design
concepts, comparing the results of designs for various
slope heights and geometries using each of the methods,
and comparing two case histories of test walls which were
loaded to failure with the results predicted by each of
the six design methods. This report describes each of the
design methods, summarizes the differences in concepts,
and presents the results of the comparisons made.
Conclusions are drawn based on the results of the study.
Six published design methods were selected for
this study. The selection was based primarily on the
writer's perception that they represent the range of
methods most frequently being used in practice. The
methods used are:
(1) "Guidelines For Use of Fabrics in Construction and
Maintenance of Low-Volume Roads," Chapter 5:
Earth Reinforcement, (Steward, Williamson and
Mohney, 1977, revised 1983), subsequently referred
to as the Forest Service method;
5
(2) "Design of Fabric Reinforced Retaining
Structures," (Broms, 1978), subsequently referred
to as the Broms method;
(3) "Earth Wall Design," (Collin, 1986), subsequently
referred to as the Collin geotextile and Collin
geogrid methods;
(4) "Soil Reinforcement Design Using Geotextiles and
Geogrids," (Bonaparte, Holtz and Giroud, 1987),
subsequently referred to as the Bonaparte et al.
method;
(5) "A Design Procedure for Geotextile-Reinforced
Walls," (Leshchinsky and Perry, 1987),
subsequently referred to as the Leshchinsky and
Perry method; and,
(6) "Design Charts for Geogrid-Reinforced Soil
Slopes," (Schmertmann, Chouery-Curtis, Johnson and
Bonaparte, 1987), subsequently referred to as the
Schmertmann et al. method.
Descriptions of the methods are presented in
Chapter 2. With the exception of the method presented by
Schmertmann et al., computer spread sheet programs were
6
written and used for applying the various design methods
to different slope geometries and reinforcement types
selected for analysis. Hand calculations were used for
the Schmertmann et al. method. Printouts and calculations
are presented in the appendices.
Designs were conducted using each of the methods
for combinations of two wall heights, two wall face
inclinations and three reinforcement material types.
Chapter 3 presents the results in terms of reinforcement
lengths and spacings for each of the cases and then
summarizes them in terms of the required reinforcement
quantity per unit length of wall.
The results of tests conducted on two
geosynthetic-reinforced test walls which were loaded to
failure were used to evaluate each of the design methods
used for .the study. The first case involved a full scale,
geotextile-reinforced test wall constructed as part of a
Federal Highway Administration (FHWA) study entitled,
"Behavior of Reinforced Soil," (Christopher, 1988-1989).
The principal investigator for the study, which is in
progress, is Mr. Barry Christopher of STS Consultants,
Ltd. This wall is subsequently referred to as the
STS/FHWA test wall in this report.
The other case was a large scale model geogrid-
reinforced wall constructed as part of a long term
research project at the Royal Military College of Canada
7
(RMC), the results of which were published in
"Geosynthetics for Soil Improvement," ASCE Geotechnical
Special Publication No. 18 (Bathurst, Benjamin and
Jarrett, 1988). That case is subsequently referred to as
the RMC model wall in this report. Comparisons were made
by utilizing each of the design methods for the test wall
geometries and loading conditions with all safety factors
set equal to one. The results of this aspect of the study
are presented in Chapter 4.
At the inception of the study, it was to have
included evaluating the effects of varying the slope angle
from 40 to 90 (vertical). However, it became apparent
that most of the design methods which address relatively
flat slopes are not applicable to vertical walls.
Conversely, the design methods for reinforced earth walls
are typically intended exclusively for vertical or very
steep slopes.
The early stages of the study included a method
presented in "Design of Slopes Reinforced with Geotextiles
and Geogrids," (Schneider and Holtz, 1986). After some
effort was expended attempting to compare the results
based on this method with those obtained from the six
methods listed above, it became apparent that it does not
apply to slopes inclined steeper than the internal angle
of friction of the soil. It appeared to be intended to
address either relatively flat slopes comprised of
8
granular soils with pore pressures or cohesive soils with
low internal friction angles. Subsequently, the scope of
the study was restricted to address slope angles ranging
from approximately 68 (l horizontal to 2.5 vertical) to
908 (vertical). A number of other methods are available
to address relatively flat reinforced slopes (Bonaparte et
al., 1987; NCHRP Report 290, 1987). These typically
utilize conventional slope stability analysis techniques
modified to accept the inclusion of tensile reinforcement.
1.3 Purpose and Scope of Study
There were two primary objectives to this study.
The first was to compare the results of designs using the
different methods which would be obtained by a civil
design engineer with limited geotechnical and
geosynthetics engineering background by following the
procedures outlined by the methods as strictly as
possible. The intent was to show the differences in
results obtained using the various methods. The second
objective was to judge the suitability of the analytical
models on which the design methods are based utilizing the
results of test walls which were loaded to failure.
The various design methods, and consequently this
study, address internal stability. With the exception of
sliding of the reinforced mass, external stability is not
addressed. The evaluation of external stability is
9
essentially the same for all of the methods, and is based
on the same principles used for evaluating foundations and
other types of retaining structures. However, sliding is
accounted for by most of the methods since it may be
controlled by a preferential slip plane between the bottom
layer of reinforcement and the foundation soil, and
therefore depends on the interaction between the soil and
reinforcement specified by the design method.
This report describes the analytical concepts for
all of the design methods. It also presents general
descriptions of the design methods; however, it is not
intended to be a design guide and not all of the design
details are addressed. In particular, the study
concentrated on reinforcement length and spacings, and did
not address details such as wrap-around, overlap or the
effect of facing elements on earth pressures near the face
of a wall. The intent was to demonstrate the results
obtained by the various methods in terms of overall wall
geometry and to assess how well the analytical concepts
model observed behavior by comparison with test results.
CHAPTER 2
DESIGN METHODOLOGIES
2.1 General
Numerous and diverse methods have been developed
to evaluate the stability of reinforced earth slopes and
walls. Methods which address the stability of relatively
flat slopes (i.e., less than about 45) typically use
conventional analytical methods for unreinforced soil
slopes which have been modified to account for the
inclusion of tensile reinforcement. An evaluation of
these methods is beyond the scope of this study. Finite
element methods can be used to address essentially any
slope or wall configuration; however, at the present time,
these are not normally well suited for routine design due
to their complexity.
The majority of actual wall designs and four of
the six methods addressed by this study are based on
lateral earth pressure considerations. These methods tend
to be conceptually simple and probably do not model the
stresses in the soil nor, in many cases, the mechanisms by
which failure occurs. Limiting equilibrium analysis is
used to equate the horizontal forces due to lateral earth
pressures tending to cause instability to the stabilizing
11
tensile forces in the horizontal reinforcement. The only
stresses considered are vertical and lateral earth
pressures, the horizontal tensile stresses in the
reinforcement, and the horizontal resistance to pullout of
the reinforcement from behind a failure surface. The
pullout resistance is provided by horizontal shear
stresses resulting from soil/reinforcement interface
friction under the vertical confining stress. These
methods typically presume a failure surface through the
reinforced mass described by a Rankine active failure
condition. They do not directly address stresses on the
failure plane. As a result, they are frequently
collectively referred to as tied-back wedge analysis
methods. Although these methods have many similarities,
they all use different lateral earth pressure
distributions to describe the horizontal forces which need
to be resisted.
The remaining two methods used for this study
consider the stresses on a failure surface. Leshchinsky
and Perry used limiting equilibrium analyses of rotational
(log-spiral) and translational (planar) failure surfaces.
The method was based on Leshchinskys earlier work
(Leshchinsky, 1985), which used techniques similar to
those presented in "Variational Approach to Slope
Stability," (Baker and Garber, 1977). The Schmertmann et
al. method is based on limiting equilibrium analysis using
12
wedge failure models. Straight line and bi-linear wedges
are used for different aspects of the analysis. Extended
versions of Bishop's modified and Spencer's methods of
slope stability analysis were used to modify the results
of the wedge analyses to develop design charts.
2.2 Design Input Parameters
Nearly all of the methods available for designing
reinforced soil walls utilize the same basic input
parameters. First, the slope geometry must be defined in
terms of height and face inclination. Most of the methods
also allow for a surcharge behind the top of the wall
face. Second, the strength properties of the reinforced
soil mass must be described. The parameters used to do
this typically consist of soil unit weight and internal
angle of friction, reinforcement strength and a parameter
or parameters describing the frictional interaction
between the soil and the reinforcement.
In some cases, the properties of the underlying
foundation soil and backfill soil behind the reinforced
mass must also be described. Although these properties
are actually used to evaluate external stability, they
should probably be applied according to criteria
prescribed by the particular internal design method used.
For example, the sliding resistance at the interface of
the foundation and bottom reinforcement layer should
13
probably be based on the same soil/reinforcement
frictional interaction criteria used for the internal
stability evaluation.
Description of the wall geometry is typically
straightforward. Most of the methods require only a slope
height, slope face inclination and surcharge. The tied-
back wedge methods used for this study apply only to
vertical face inclinations. Nearly vertical walls can be
evaluated but the analyses assume them to be vertical.
Two other aspects which may be considered to describe wall
geometry are reinforcement length and reinforcement layer
spacing. For some of the methods, length and spacing can
be considered input parameters which are varied until the
desired safety factors are attained. For other methods,
the spacing and lengths are directly calculated.
All of the design methods require the input of an
allowable reinforcement tensile capacity. Diverse
guidelines are presented for selecting allowable
reinforcement strength. Some of these describe allowable
strengths as a fraction of the ultimate strength
determined by the wide width tensile test (ASTM D 4595).
Others specify only that an allowable value be used but do
not offer guidelines for selection. In general,
reductions are made in the ultimate strength to account
for construction damage, time dependent deterioration and
creep. For some of the methods, the reductions are a
14
function of fabric polymer type or manufacturing process
(e.g., woven or non-woven). The result is that, depending
on the method used, the allowable reinforcement strength
may vary from less than 10% to about 50% of the ultimate
wide width tensile strength.
The majority of design methods available for
reinforced soil walls are for granular backfill soils
only. Although there are methods available to design
reinforced slopes which account for cohesion and/or soil
pore pressures, all of those used for this study are for
drained granular soils only. Most of them also assume
that the backfill soil behind and foundation soil beneath
the reinforced mass have the same properties as the soil
of which the reinforced mass is constructed of. None of
the methods account for the effects of settlement of the
foundation soils, backfill soils behind the reinforced
mass, or of the reinforced soil mass itself. For all of
the methods evaluated for this study, the strength of the
soil component of the structure is described entirely in
terms of its internal friction angle and unit weight.
Once the soil and reinforcement strength
parameters are defined, a parameter (or parameters) which
describes the interaction between the soil and
reinforcement is required. For most of the methods, this
consists of a coefficient of friction between the
reinforcement and the soil. For geogrids, it may also
15
include passive soil resistance against the transverse
ribs of the grid. The soil/reinforcement friction
coefficient is typically considered to be a function of
the soil's internal friction angle. A frictional
"efficiency" can be defined as (Martin, Koerner and
Whitty, 1984)
E = tan ^j/tan
, (2.1)
where
E = frictional efficiency,
0a soil/reinforcement interface friction angle, and
= soil internal friction angle.
The interface frictional behavior between soil and
reinforcement can be evaluated by using either direct
shear tests or pullout tests. Ideally, the method used
should model the behavior which occurs in the structure.
However, the results obtained from a direct shear test can
be significantly different from those obtained from a
pullout test, particularly for geogrids.
Soil/reinforcement interaction is discussed in more detail
in Chapter 5.
2.3 Factor of Safety
Most design methods for reinforced soil walls use
limiting equilibrium analyses. However, there are
significant variations among methods in the definition of
16
the factor of safety. Two general approaches are
typically used for defining a factor of safety for a
limiting equilibrium analysis in geotechnical engineering
applications. The first is to define it as the ratio of
forces or moments resisting instability to the forces or
moments tending to cause instability. This method is
frequently used when the zone of soil (or other structure)
considered potentially unstable is treated as a rigid
block. Full mobilization of the soil's strength is
assumed to occur and stability is evaluated based on
static equilibrium. The second general method for
applying a factor of safety is to use it to reduce the
strength parameters. In this case, the mechanics of the
material (soil) are considered and full mobilization of
strength is not assumed. In the realm of limiting
equilibrium methods used for stability analysis in
geotechnical engineering applications, the first method is
typically used to evaluate bearing capacity and retaining
wall stability. The second method is generally used to
evaluate the stability of unreinforced soil slopes.
Both methods of defining factor of safety are used
among the six methods evaluated for this study. Some of
the methods use both, resulting in factors of safety
applied to parameters which have already been factored.
This tends to lead to conservative results. For the
purpose of this study, factors of safety prescribed by the
17
design methods were used when provided. However, some of
the design methods do not explicitly discuss safety
factors. In these cases, the writer selected to follow
the recommendations of Bonaparte et al. (1987). They
recommend that a working value for reinforcement tension
be defined considering creep, aging and potential
construction damage and that this strength not be further
reduced by additional factors. They also recommend that,
for evaluation of internal stability, the factor of safety
be applied to the soil shear strength, as follows:
tan / FS (2.2)
where
0 = internal angle of friction of soil;
FS = factor of safety.
They claim, and the writer agrees, that this
concept for applying a safety factor is consistent with
that most commonly used for unreinforced slopes.
2.4 Description of Design Methods Used for Study
A description of each of the design methods used
for this study is presented below. The descriptions focus
on the design concepts and include general descriptions of
the design procedures. The intent is to describe the
conceptual similarities and differences among the methods
18
and to explain the computer spread sheet programs
developed for this study.
Figures are presented to explain the geometry and
nomenclature used for each of the methods and to present
the input parameters and equations used in the computer
programs written for this study. The Forest Service,
Broms, Collin and Bonaparte et al. methods are all tied-
back wedge methods which are conceptually similar. The
geometry and nomenclature for these are described on
Figure 2.1. The following sections of the report
andsubsequent figures describe each of the methods and
their input parameters and equations in more detail. The
Leshchinsky and Perry method and Schmertmann et al. method
are conceptually somewhat different from the tied-back
wedge methods and are discussed separately.
The four tied-back wedge methods are based on
limiting equilibrium analysis of horizontal forces due to
lateral earth pressure and the resistance of those forces
by horizontal layers of reinforcement. All of these
methods assume a planar failure surface described by the
Rankine active condition.
The tied-back wedge methods all calculate a
horizontal force due to lateral earth pressure for each
layer of soil. Stability is then checked for two
different failure mechanisms. The reinforcement must have
sufficient strength that it does not rupture and it must
19
q* Uniform Surcharge
Le= Length of Reinforcement Embedment Beyond
Failure Plane
L= Total Reinforcement Length
SOIL PARAMETERS: y (GAMMA)= Soil Unit Weight (pcf)
(degrees)
REINFORCEMENT
PARAMETERS: T Allowable Reinforcement Tensile Resistance
(lbs/ft width)
3,
Friction Angle (degrees)
EFF Soil/Reinforcement Interface. Frictional
Efficiency (tan^/taniji )
n Number of Reinforcement Layers
Figure 2.1- Geometry and Nomenclature Used for
Forest Service, Broms, Collin and
Bonaparte et al. Methods.
20
have sufficient embedment behind the failure plane that it
does not pull out of the backfill soil. Although all four
methods use the same basic analytical model, they all
differ in their descriptions of lateral earth pressure,
factors of safety, allowable tensile resistance of the
reinforcement and, to some extent, the soil/reinforcement
interface friction providing pullout resistance.
2.4.1 Forest Service Method
The Forest Service method is based on a lateral
earth pressure distribution based on an at-rest condition.
Uniform surcharges are accounted for by factoring the
vertical surcharge pressure by the at-rest earth pressure
coefficient. Although live loads of limited areal extent
were not accounted for in this study, the method accounts
for such loads by assuming a lateral pressure component
defined by elastic theory using the Boussinesq solution.
The lateral pressure distributions used for the method are
described on Figure 2.2.
The Forest Service design procedures indicate it
is intended for use with polyester and polypropylene,
needled or bonded non-woven and woven geotextiles and is
applicable for granular soils only. The lateral earth
pressure coefficient for the at-rest condition, K0, is
defined as 1-sin . The method determines reinforcement
length beyond the assumed failure surface to resist
21
LATERAL PRESSURE DISTRIBUTION-FOREST SERVICE METHOD
Surcharge
(Note: Live Load Surcharge Not
Pressure Distribution
Used for this Study)
INPUT PARAMETERS AND EQUATIONS
Kq = 1-sin
(PHIa)- (2/3) $
1.5 K H
Lmin (m*-niinum length)* ---------- (Base sliding, FS* 1.5)
n 2 tan d>
Ta
Zbot^= z^= Depth to ith Layer of Reinforcement
Zmid= zm^ z- (z- z1)/2
FHi= Kq y zmi(z1- z^)
Le.= L- (tan (45-
Pj 2 Y Le z tan$a
Pullout FSi= Pi/ FH1
Rupture FS T / FH^
i a i
Figure 2.2- Summary of Lateral Pressures and
Input Parameters and Equations
for Forest Service Method
22
pullout and reinforcement strength required to prevent
rupture based on the lateral earth pressure thrust. The
lengths of all of the reinforcement layers are the same
and depend on an evaluation of external stability
(sliding) and required embedment length beyond the assumed
failure surface.
Two methods are presented for determining the
allowable reinforcement strength. The first consists of
reducing the wide width tensile test results by a factor
depending on the fabric polymer type and manufacturing
process. The second is based on the lesser of 90% of the
1-inch cut strip strength (ASTMD 751) or 33% of the grab
tensile strength (ASTM D 4632, formerly ASTM D
1682) reduced by a factor depending on the polymer type and
manufacturing process.
Two factors of safety are determined for each
layer of reinforcement. The factor of safety for pullout
is defined as the ratio of pullout resistance to
horizontal driving force for that layer. The factor of
safety for rupture is described as the ratio of allowable
tensile resistance to horizontal driving force. Safety
factors ranging from 1.2 to 1.75 are recommended for
different aspects of the design. The soil/reinforcement
interface friction angle is defined as two-thirds of the
internal friction angle of the soil.
23
2.4.2 Broms Method
t
The Broms method was apparently developed for
walls with structural facing elements; however, it has
also been used for walls without facing elements. The
method is based on the results of model tests conducted at
the Royal Institute of Technology in Stockholm (Holtz and
Broms, 1977).
The lateral earth pressure distribution used by
Broms is a uniform rectangular distribution recommended by
Terzaghi and Peck for anchored sheet pile walls.
Figure 2.3 summarizes the lateral earth pressure
distribution and input parameters and eguations used for
this study. Consideration of internal stability requires
only that the reinforcement extend beyond the presumed
failure plane by the required embedment length. The other
tied-back wedge methods used for this study assume uniform
reinforcement summarizes the lateral earth pressurelength
which is controlled either by required embedment of the
upper layers or by sliding at the bottom layer. The
reinforcement lengths determined by the Broms method are
controlled by consideration of external stability. For
each successive layer upward, the failure surface is
assumed to project up into the slope from the end of the
layer beneath it, which has already been extended by its
required embedment length, resulting in a "stepped"
24
LATERAL PRESSURE DISTRIBUTION-BROMS METHOD
~T
O, (SIGMAh)* 0.65 K (1.5q+ y H)
n a
INPUT PARAMETERS AND EQUATIONS
-1
4> (PHIa)= tan ((EFF) (tan 4> ))
a
Ka= tan2(45- /2)
D = T / a,
max a h
D= H/n, where n= integer value of H/D for D > D
max max
Ln* Length of bottom layer*
FH= a. D
n
Zbot.= z .= D n
l l
1.5 a
Y tan _
FH
Le = Minimum embedment length* --------------
min 2 y z tan (})
i a
Ln^= Embedment length (external stability)
L (bottom layer)* Ln
1.3 T
Y z. tan 4>
i a
(layers above bottom)* L1+1+ D tan(45-4>/2) + Ln^
Figure 2.3- Summary of Lateral Pressure and
Input Parameters and Equations
for Broms Method
25
surface. This results in relatively long reinforcement
lengths for the upper layers.
The Broms method uses an allowable long-term
reinforcement strength equal to one-third of the ultimate
strength. The only factor of safety specified by the
design is a factor of 1.3 applied to the embedment length
of each layer. However, to stay consistent with the other
methods evaluated for this study, a safety factor of 1.5
was used for calculating the required length of the bottom
layer to resist sliding. The factor of 1.3 is described
by NCHRP Report No. 290 and Collin as being intended to
account for the variation of the tensile stresses in the
reinforcement behind the failure plane.
According to NCHRP Report No. 290, Broms suggests
that the soil/reinforcement interface friction angle
should be reduced to a value less than the soil friction
angle if the silt or clay content of the soil is greater
than 10%. For this study, interface frictional
efficiencies were assumed, as discussed in more detail in
Chapter III.
2.4.3 Collin Method
Collin presents two design methods applicable to
this study in his doctoral dissertation entitled, "Earth
Wall Design," (Collin, 1986) Of the two methods used for
this study, one is for geotextiles and the other is for
26
geogrids. As with the other methods evaluated for this
study, both apply only for granular soils.
Collin's study included a somewhat more
comprehensive review of existing design methodologies than
was conducted for this study. His study also addressed
reinforcement types besides geosythetics, such as steel
strips and steel bar mats. He used finite element
analyses which utilized data obtained from three field
instrumented walls to develop recommended lateral earth
pressure distributions. Therefore, the lateral earth
pressure distributions account for the interaction between
soil and reinforcement at the working stresses within the
reinforced mass. With the exception of the lateral earth
pressure distribution, Collin's method for geotextile
reinforced walls is very similar to the Forest Service and
Bonaparte et al. methods. This procedure is summarized on
Figure 2.4. The lateral earth pressure distribution is a
result of the finite element analyses.
Collin's recommended lateral earth pressure
distribution and design method is somewhat different for
geogrid reinforced walls. This method, summarized on
Figure 2.5, accounts for the fraction of the grid surface
area which is solid and for passive earth pressure
resistance on the transverse grid members. For both the
geogrid and geotextile cases, a Rankine active failure
surface is assumed up from the base of the wall.
LATERAL PRESSURE DISTRIBUTION
COLLIN GEOTEXTILE METHOD
27
H(ft]
*
CTh(SIGMAh)= 15 H (psf)
INPUT PARAMETERS AND EQUATIONS
(PHIa)*= (2/3) $
1.5 a, H
n
L = ------------ (Base sliding, FS*1.5)
min y H tan t
T a
D = T / a.
max a h
D*= H/n, where n* integer value of H/D for D t D
max max
Zbot^= D n
Zmidj,* zm^= Zj-(Zj-
FH= CL D
h
Le^ L-(tan(A5*- <^/2)) (H z^)
P.= 2 Le. z. V tand>
x i i Ta
Pullout FS^ P /FT^
Figure 2.4- Summary of Lateral Pressure and
Input Parameters and Equations
for Collin Geotextile Method
28
LATERAL PRESSURE DISTRIBUTION
COLLIN GEOGRID METHOD
INPUT PARAMETERS AND EQUATIONS
<|> (PHIa) (2/3) (}>
n/ft= Number of transverse ribs per foot
(ALPHAs)* Fraction of grid surface area which is solid
2
A^= Transverse bearing area per rib per foot width (ft /ft)
y (mu) = tan a
N = Passive resistance anchorage factor
^ (given in tabular form as function of
Zbot.= z.
l i
D.=Distance from midheight of ith layer of soil to i+lth
layer of soil (not z^- z. ^ as in other methods).
Program accounts for entire soil layer at top and bottom
Le^ L- (tan(45-*/2))(H- z)
As.= Reinforcement surface area" 2a Le,
l si
n- (Le^)(n/ft)
P= Y z (y As+ n Np Ajj) Pullout FSj- Pi/FHjL
Figure 2.5- Summary of Lateral Pressure and
Input Parameters and Equations
for Collin Geogrid Method
29
Collin does not explicitly recommend factor of
safety and reinforcement strength selection criteria.
However, his report presents examples demonstrating his
selection of these criteria. He used a factor of safety
for pullout as the ratio of pullout resistance to
horizontal force for each layer. He also used a
coefficient of interface friction for geogrids and
geotextiles equal to tan (2/3)
sliding at the base is controlled by soil friction only
and that a preferential slip plane does not develop at the
bottom reinforcement layer. For consistency with the
other methods, this study assumes sliding is controlled by
the same coefficient of friction at the bottom layer as is
used for pullout of the other layers.
2.4.4 Bonaparte et al. Method
The referenced paper (Bonaparte et al., 1987)
discusses other aspects of soil reinforcement besides the
design of walls. In most ways, the method is similar to
the other three tied-back wedge methods used for this
study. The main difference is in the definition of
lateral earth pressure.
The earth pressure distribution used by Bonaparte
et al. is somewhat more complex than those used for most
of the other methods. It accounts for different soil
properties between the retained fill behind the wall and
30
the fill within the reinforced mass. The earth pressures
within the reinforced soil mass include a vertical
component of the earth pressure thrust from the retained
fill. The lateral earth pressures, along with geometry
and other parameters, are summarized on Figure 2.6.
The vertical stresses induced by the thrust of the
retained fill are calculated using Meyerhof's
recommendations for eccentrically loaded footings.
Bonaparte et al. point out that other assumptions
regarding vertical stress distributions are possible. The
result of their description of earth pressure is that,
unlike the other methods, the horizontal forces, and
consequently reinforcement strength and embedment
requirements, are a function of total reinforcement
length. In addition, the horizontal force for each layer
increases at an increasing rate with depth. The safety
factors for rupture can be increased by increasing total
reinforcement length. This is the only method evaluated
which uses a non-linear relationship between reinforcement
strength requirements and depth.
Bonaparte et al. present a discussion of allowable
reinforcement strength for use in design. They suggest
that a wide width tensile test should be used to determine
ultimate strength and that the allowable strength should
consider limiting allowable deformations of the structure,
as well as the effects of soil/reinforcement interaction,
31
GEOMETRY AND LATERAL PRESSURE DISTRIBUTION
BONAPARTE ET AL METHOD
Retained fill
e Eccentricity for Meyerhoff
evaluation of eccentrically
loaded footing
FH = K O (z.- z, .)
i a z i i-1
Note: Vertical stresses within reinforced mass include vertical
component of stresses induced by thrust of retained fill
calculated using Meyerhoff's recommendations for eccen-
trically loaded footings (accounted for in equation
for FH^ below).
INPUT PARAMETERS AND EQUATIONS
$a(PHIa) tan_1((EFF) (tan
K = tan2(45 /2), K tan2(45-<}> /2)
S' IT IT
1.5 K Y H2 /2
r r
Lmin(minimum length) -----------------
(yH+q) (EFF) (tan(|))
(Base sliding
FS=1.5)
Zbot z^= depth to ith layer of reinforcement
Zmid= ziik
zi"(zr zi-i)/2
^i [zr zi-i]
Ka(y zi + q)
_ \ 3(Yr z.+ q) / ^
Le^* L- (tan(45-
P= 2 Le zi Y tan
Figure 2.6- Geometry, Nomenclature, Summary
of Lateral Pressure, and Input
Parameters and Equations for
Bonaparte et al. Method
32
time (including creep and age related deterioration),
temperature and construction damage. They suggest that
the allowable tensile resistance be limited to 20% to 40%
of the peak wide width tensile strength. They state that
the actual percentage to use in design should be
established on a product and project specific basis. For
the purpose of this study, an allowable reinforcement
strength equal to one-third of the ultimate strength was
used.
Bonaparte et al. recommend that factors of safety
for external stability analysis be defined as the ratio of
stabilizing forces or moments to the forces or moments
tending to cause instability. However, for internal
stability, they recommend that a factor of safety be
applied to the soil shear strength. They recommend using
allowable reinforcement tensile properties and a factored
soil strength and that additional safety factors should
not be used.
2.4.5 Leshchinskv and Perry Method
Except for the lateral earth pressure
distributions developed by Collin, the theoretical basis
of this method is somewhat more complex than for the
methods previously discussed. Unlike the tied-back wedge
methods, the Leshchinsky and Perry method considers
stresses on a failure surface. Leshchinsky developed
33
charts based on limiting equilibrium analysis of
rotational (log spiral) and translational (planar) failure
surfaces (Leshchinsky, 1985). The analysis utilized the
variational approach to slope stability (Baker and Garber,
1977), which corresponds to the upperbound theory of
plasticity.
Design charts were developed for slope angles
varying from about 68 (1:2.5) to vertical. The charts
account for a smooth transition from a translational
failure surface for near vertical slopes to a rotational
failure surface for somewhat flatter slopes. A detailed
description of the variational approach to slope stability
used in the method is beyond the scope of this study. The
geometry, nomenclature and a summary of input parameters
and equations used in the computer program written for
this study are presented on Figure 2.7.
The method evaluates the internal stability based
on two different approaches; (1) the composite structure
stability and, (2) the required geotextile tensile
resistance. The required reinforcement strength is
checked for both cases. A factor of safety of 2.0 is
recommended for geotextile resistance and a value of 1.5
is recommended for the composite structure. The required
strength determined is greatest for the bottom layer, and
the required strength for each successive layer above the
34
GEOMETRY FOR LESHCHINSKY AND PERRY METHOD
INPUT PARAMETERS AND EQUATIONS
Fs= Factor of safety for composite structure
Fg= Factor of safety for reinforcement tensile resistance
(PHIm)= tan ^(tan <{>/ Fs)
m
(PHIa)= (2/3)
a
^(PHIf)= Internal friction angle of foundation soil
Tml is obtained from graph based on for composite
structure and based on (Fsl) for m
reinforcement resistance
tl=Tml Fs Y H2/n, t= tl((Y *+ q)/(Y H+ q) ]
XT
L is obtained from graph based on A_, and m
T<|>
le = tl/2 y H tan (J) , le.= tl/Y H(tan <{> + tan )
3 J. 3' IS
Use Jle* greater of Ã‚Â£e and Jle^
H-LH
Figure 2.7- Geometry, Nomenclature, and
Summary of Input Parameters
and Equations for Leshchinsky &
Perry Method
35
bottom is reduced in proportion to the depth of the layer.
The resulting reinforcement strength distribution is
triangular for an unsurcharged wall and trapezoidal for a
surcharged wall.
The procedure includes guidelines for selecting
allowable tensile resistance. The allowable reinforcement
strength is obtained by first reducing the wide width
tensile test results by 50% to account for potential aging
and construction damage, and then using 25% to 50% of that
value, depending on reinforcement material type, to limit
creep deformations. For some materials, this results in
using an allowable tensile resistance of as little as
12.5% of the ultimate strength. As discussed above, a
safety factor for geotextile resistance of 2.0 is then
used.
The method suggests soil/reinforcement interaction
governed by a coefficient of friction of tan (2/3)
is pointed out that more realistic (i.e., less
conservative) values may be determined using direct shear
tests. The method also allows for a soil/reinforcement
interaction at the bottom of the bottom layer based on
different soil properties than used in the backfill. This
can result in a bottom layer length different from the
lengths of the other layers above it, which are the same.
36
2.4.6 Schmertmann et al. Method
The method presented by Schmertmann et al. (1987),
is applicable for slope angles varying from 30 to 80.
The method was developed for Tensar, a major geogrid
manufacturer, and is the method recommended by Tensar.
The description of the method states that it was developed
for geogrids only; however, it was assumed to apply to
other types of geosynthetic reinforcement for this study.
The method presents design charts which are based
on limiting equilibrium analysis using wedge failure
models. A straight-line wedge is used for top
reinforcement length and a bi-linear wedge (with
interwedge friction) is used for bottom reinforcement
length and total reinforcement force. Extended versions
of Bishop's modified method (TENSLOl) and Spencer's method
for unreinforced slope stability were used to modify the
results of the wedge analyses to develop design charts.
As with the Leshchinsky and Perry method, the method is
based on consideration of stresses on a failure surface
rather than modelling the problem entirely in terms of
resisting lateral earth pressures.
The presentation of the design method concentrates
on limiting the required length of reinforcement and
provides for a variable reinforcement length as a function
37
of depth. The claim is made that the resulting
reinforcement lengths are significantly less than for most
other published design methods. A computer was not
utilized to apply the method for this study due to its
ease of application.
The geometry, nomenclature, parameters and
equations used are summarized in Figure 2.8. As with the
Bonaparte et al. method, the method uses an allowable
reinforcement strength and applies a factor of safety to
the tangent of the internal soil friction angle. The
safety factors recommended are on the order of those
typically used for unreinforced slope stability analysis
methods.
The design charts were developed based on a
soil/reinforcement interface frictional efficiency of 90%.
Although they claim the method is valid only for geogrids
with this frictional efficiency, they point out that
reducing the frictional efficiency from 90% to 80%
increases the predicted reinforcement length at the bottom
by 10% or less. For this study, this information was used
to increase the lengths of reinforcement layers by 10% for
the woven geotextile case, as discussed further in
Chapter 3.
38
GEOMETRY FOR SCHMERTMANN ET AL METHOD
T = Total lateral resistance required by all
reinforcement layers
Y H2 K
= 2
where K= value obtained from graph (function of 6 andf)
Ã‚Â£= tan *(tan /FS)
T^= Allowable tensile resistance of one layer of
reinforcement
n= Number of layers of reinforcement T / T
t a
(must be integer with T nST )
a t
Lg/H' and L^,/H' are obtained from graph
(also function of 8 and ^)
D is varied in inverse
T
^ 9
imax
K Y Z,
proportion to z according to:
Figure 2.8- Geometry, Nomenclature, and
Summary of Input Parameters
and Equations for Schmertmann
et al. Method
CHAPTER 3
DESIGN COMPARISONS
3.1 General
The results of designs using each of the design
methods described in Chapter 2 were compared. Several
different wall configurations were evaluated, as described
below. The purpose of the comparisons was to demonstrate
the differences in the results using the various methods
by following each of the methods as strictly as possible.
The intent was to approach the methods as a civil design
engineer with limited geotechnical and geosynthetics
engineering background would. Some of methods are
complete enough that few, if any, assumptions need to be
made. Others require assumptions regarding reinforcement
strength selection, soil/reinforcement interaction and
factors of safety. When assumptions were made, an attempt
was made to maintain consistency between the methods.
3.2 Descriptions of Design Configurations
Designs were conducted for two different wall
heights, three different reinforcement types and, for the
two methods which address it, two different wall face
inclinations. Slope heights of 12 feet and 30 feet were
40
used. The 12-foot height was selected based on the
writer's experience that numerous relatively low retaining
structures up to about that height are regularly
constructed with very limited geotechnical design input.
The 30-foot height was arbitrarily selected to represent
a relatively high retaining structure.
Three different reinforcement materials and
strengths were selected. Fabric 1 is a non-woven
polypropylene geotextile with a wide width tensile
strength of 1,800 pounds per foot width (lb/ft). Reported
frictional efficiencies (Martin, Koerner and Whitty, 1984;
Eigenbrod and Locker, 1987) typically vary from about 90%
to 100% for non-woven geotextiles and granular soils. A
frictional efficiency of 90% was selected for Fabric 1
unless the particular design method specified a different
value.
Fabric 2 is a woven polypropylene geotextile with
a wide width tensile strength of 3,600 lb/ft. Frictional
efficiencies for woven fabrics are typically somewhat less
than for non-woven fabrics and a value of 80% was selected
unless otherwise specified.
Fabric 3 is a high density polyethylene (HDPE)
geogrid. Reinforcement properties for Tensar SR3 (UX1300)
were selected. This material possesses a tensile
resistance of 2,000 lb/ft at 2% strain, 4,100 lb/ft at 5%
strain and an ultimate resistance of 7,500 lb/ft at 17%
41
strain. Tensar recommends an allowable reinforcement
tension of 3,000 lb/ft for this material for use with
their design method. They also use a frictional
efficiency of 90%, which was used for Fabric 3 for all
methods unless otherwise specified. Reinforcement
strength selection criteria are discussed in more detail
below.
As discussed in Chapter II, the tied-back wedge
methods are applicable for vertical face inclinations.
The Leshchinsky and Perry method allows for a face
inclination as flat as 68 (1:2.5) and the Schmertmann et
al., method accounts for slope angles varying from 30 to
80. Vertical or nearly vertical face inclinations were
evaluated for all six methods. Face inclinations of 68
were evaluated for the Leshchinsky and Perry and
Schmertmann et al. methods.
3.3 Additional Assumptions Made
3.3.1 Forest Service Method
The Forest Service method presents fairly detailed
guidelines for reinforcement strength selection and factor
of safety. However, the recommendations for factor of
safety are somewhat confusing. The method states,
"calculations for the fabric dimensions for overlap,
embedment length and vertical spacing should include a
safety factor of 1.2 to 1.5, depending on the confidence
42
level in the strength parameters." In the same
presentation of the design method, a safety factor of 1.5
to 1.75 is recommended for embedment length. For the
purpose of this study, a safety factor of 1.5 was selected
for sliding and a safety factor of 1.2 was used for
rupture. The safety factors for pullout were all well
above 2.0 based on the controlling lengths required by
sliding resistance.
The Forest Service design procedure presents
alternative criteria for selecting allowable reinforcement
strength. The preferred method is to use the wide width
tensile test results multiplied by a factor to account for
long-term creep. These factors are 55% for needled
polypropylene and 25% for woven polypropylene. Guidelines
are not offered for polyethylene or for geogrids in
general. These criteria result in an allowable
reinforcement strength of 990 lb/ft for Fabric 1 and of
900 lb/ft for Fabric 2. Since no guidelines were given
for Fabric 3, an allowable strength equal to one-third of
the ultimate strength was somewhat arbitrarily selected.
This is a higher proportion of the ultimate strength than
for Fabrics 1 and 2 but is generally consistent with the
assumptions made for the other methods when guidelines
were not given. This results in a value of 2,500 lb/ft
for Fabric 3.
43
3.3.2 Broms Method
The term which describes the embedment length
beyond the failure surface of the layer beneath it for
external stability, Ln,, includes a factor of safety of
1.3. This is intended to be a safety margin to account
for the possible variations in fabric stresses behind the
assumed potential failure plane. In addition, a factor of
safety of 1.5 was selected to determine the length of the
bottom layer required to resist sliding.
Broms suggests that the soil/reinforcement
interaction frictional efficiency may be 100% if the silt
or clay content of the soil is less than 10%. However, for
consistency with the other methods evaluated, frictional
efficiencies of 90% for Fabrics 1 and 3 and 80% for Fabric
2 were assumed.
The method suggests that the allowable long-term
reinforcement strength be equal to one-third of the
ultimate strength to account for creep and degradation
losses. This is consistent with the assumptions used for
the other methods when guidelines were not provided. This
results in reinforcement strengths of 600, 1,200 and
2,500 lb/ft for Fabrics 1, 2 and 3, respectively.
3.3.3 Collin Method
As discussed previously, Collin suggests a factor
of safety of 1.5 for sliding and of 2.0 for overturning
44
and bearing capacity. For internal stability, the design
\
method does not specify factor of safety values or
explicitly define factors of safety. However, the
examples presented in his dissertation imply the factor of
safety for pullout is the same as was used for the Forest
Service method, or P/FH. A factor of safety of 1.5 was
used for pullout for this study.
The design examples also imply that the
soil/reinforcement interface friction should be based on
two-thirds of the soil internal friction angle. In
addition, it is implied that sliding at the base is
controlled by the soil properties only, i.e., there is no
preferential slip plane at the soil/reinforcement
interface of the bottom layer. However,
soil/reinforcement interface friction the same as used for
pullout of the upper layers was used for sliding at the
base to maintain consistency with the other methods. One-
third of the ultimate reinforcement strength was used for
allowable reinforcement strength since no other guidelines
were offered.
Collin's proposed design method for geotextiles
was used for Fabrics 1 and 2. His proposed design method
for geogrids was used for Fabric 3. The other input
parameters required for the geogrid method were obtained
from published Tensar data.
45
3.3.4 Bonaparte et al. Method
The guidelines presented by Bonaparte et al.
(1987), were used. A safety factor of 1.5 was used to
factor the soil strength. An allowable reinforcement
strength equal to one-third of the ultimate wide width
tensile strength was selected for each of the
reinforcement materials. Soil/reinforcement interface
frictional efficiencies of 90% for Fabrics 1 and 3 and 80%
for Fabric 2 were assumed. A factor of safety of 1.5 was
used to determine the minimum bottom reinforcement length
required to prevent sliding.
3.3.5 Leshchinskv and Perrv Method
Additional assumptions were not required due to
the completeness of the fabric strength and interface
friction' selection criteria and recommended safety
factors. These result in allowable fabric strengths equal
to 12.5% of the ultimate strengths for polypropylene and
polyethylene geotextiles. Although the method does not
address geogrids, it was assumed that the same criteria
apply. The resulting allowable fabric strengths are 225,
450 and 940 lb/ft for Fabrics 1, 2 and 3, respectively.
A soil/reinforcement interface friction angle equal to
two-thirds of the soil friction angle and safety factors
of 1.5 for the composite structure and 2.0 for geotextile
tensile resistance were used. These values are all
46
consistent with those prescribed or recommended by the
method.
3.3.6 Schmertmann et al. Method
The Schmertmann et al. method was developed for
use with geogrids for Tensar, a major geogrid
manufacturer. Therefore, for Fabric 3, an allowable
tensile resistance of 3,000 lb/ft was used, as recommended
by Tensar. It was assumed that the method is also
applicable to geotextiles. To stay consistent with the
other methods, allowable reinforcement strengths for the
geotextiles equal to one-third of the ultimate strengths
were selected.
The method accounts for a soil/reinforcement
frictional efficiency of 90%. Schmertmann et al. state
that reducing the interface frictional efficiency from 90%
to 80% increases predicted bottom length values by as much
as 10%. For this study, the reinforcement lengths for all
layers of Fabric 2 were increased by 10%. A factor of
safety of 1.5 was applied to the soil strength.
3.4 Results of Comparisons
3.4.1 Design Results
Computer printouts showing the results of the
designs for each of the cases evaluated are presented in
Appendix A for all methods except the Schmertmann et al.
47
method, for which hand calculations are presented. As
discussed in Section 2.4, Figures 2.1 through 2.7 describe
the contents of the printouts. Typically, reinforcement
lengths, depths, forces and safety factors are indicated.
However, they are presented somewhat differently for each
of the methods.
Table 3.1 presents a summary of design parameters,
indicating which were assumed, for each of the methods as
discussed in Section 3.3. The design results which are
presented in Appendix A are summarized in Tables 3.2
through 3.7. These tables summarize the geometry of each
case evaluated in terms of reinforcement layer spacings
and lengths, describe factors of safety, and include
comments concerning which of the design alternatives
appear practical. To visually demonstrate the
comparisons, graphical summaries of the design results for
two example cases (12-foot high wall with Fabric 1 and 30-
foot high wall with Fabric 3) are presented on Figures 3.1
and 3.2.
3.4.2 Reinforcement Quantity Comparisons
A somewhat qualitative yet practical comparison
was made of the six design methods based on the quantity
of fabric required per unit length of wall. This is
probably the type of comparison a design engineer would
typically be interested in.
TABLE 3.1
Summary of Design Parameters
****************************************************************************************************************************************
DESIGN ALLOWABLE SOIL/REIN FORCEMENT FACTOR OR SAFETY
METHOD REINFORCEMENT INTERFACE FRICTION
STRENGTH
************** ************************** ****************************** *************************************************************
Fabric 1, 55% ultimate =(2/3) Rupture- 1.2 (Method suggests 1.2 to 1.5)
FOREST Fabric 2, 25% ultimate Sliding- 1.5 *
SERVICE Fabric 3, 1/3 ultimate * a Pullout- (Method's recommendations are not clear, see text.
All were above 2.0 by using FS= 1.5 for sliding.)
1/3 ultimate strength Frictional efficiency of 90% 1.3 for embedment length beyond failure surface of
BROMS for all reinforcement types. for non-woven geotextile and geogrid and of 80% for underlying layer.
woven geotextile. * Sliding at bottom of bottom layer- 1.5. *
1/3 ultimate strength =(2/3) <)> * Rupture- 1.0 (Allowable strength is working value)
COLLIN for all reinforcement
types. * (fmplied by examples) Pullout- 1.5 *
1/3 ultimate strength Frictional efficiency of 90% Method recommends safety factor be applied to soil
BONAPARTE for all reinforcement for non-woven geotextile strength and that working value be used for
ET AL. types. * and geogrid and of 80% for reinforcement strength.
(20% to 40% suggested) woven geotextile. * FS= 1.5 (Used to factor soil strength and to
evaluate sliding.)
LESHCHINSKY Fabric 1, 12.5% ultimate Composite structure- 1.5
& PERRY Fabric 2, 12.5% ultimate d> =(2/3) d> Reinforcement tensile resistance- 2.0
Fabric 3, 12.5% ultimate* Ta T
SCHMERTMANN Fabric 1, 1/3 ultimate * Method has frictional
ET AL. Fabric 2, 1/3 ultimate * efficiency of 90% built in
Fabric 3, 3000 Ib/ft (assumed appropriate for 1.5 (Applied to soil strength)
(recommended by Tensar) Fabrics 1 and 3). 80% efficiency used for Fabric 2. (see text)
***************1 **************************4 ******************************* **************************************************************
*- Asterisks indicate assumed parameters.
TABLE 3.2
Summary of Design- Forest Service Method
SLOPE
HEIGHT
(ft)
******
SLOPE
INCLINATION
*******
ALLOWABLE
TENSILE
RESISTANCE
(Ib/ft)
**********
NUMBER OF
REINFORCEMENT
LAYERS
REINFORCEMENT
LAYER SPACING
(ft)
REINFORCEMENT
LENGTH
(ft)
FACTOR OF SAFETY
***************
*************
*********************
COMMENTS
******************************************
12
Vertical
or nearly
vertical
30
990
(Fabric 1)
6
1 a 5.5
1 3 2.0
2 a 1.5
2 a 0.75
8.9
(Based on base
sliding with
FS=1.5)
Pullout:4.1 a top
25 a bottom
Rupturervaries from
1.3 to 2.2
900
(Fabric 2)
6
1 a 5.5
1 a 2.0
2 a 1.5
2 a 0.75
8.9
Pullout:4.1 a top
25 a bottom
Rupturervaries from
1.2 to 2.2
2500
Fabric 3)
2
1 a 9
i a 3
8.9
Pullout:3.3 a 91
6.9 a 12'
Rupture:1.2 a 9'
1.6 a 12'
Retention-near slope face requires
additional layers at shallow depths.
The most practical design will probably
consist of 9 layers of Fabric 1 at
I. 5, 3.0, 4.5, 6.0, 7.5, 9.0, 10.5,
II. 25, and 12.0 feet.
990
(Fabric 1)
37
900 38
(Fabric 2)
2500 13
(Fabric 3)
1 a 5.5
1 a 2.0
2 3 1.5
6 a i.o
27 a 0.5
1 a 5.5
1 a 2.0
2 a 1.5
5 a i.o
29 a 0.5
1 a 9.0
2 a 3.0
1 a 2.5
2 a 2.0
3 a 1.5
4 a i.o
22.2
(Based on base
sliding with
FS=1.5)
22.2
22.2
Pullout:7.0 a top
91 a bottom
Rupture:varies from
1.2 to 2.3
Pul lout:7.0 a top
91 a bottom
Rupturervaries from
1.2 to 2.2
Pullout:5.1 a top
46 a bottom
Rupturervaries from
1.2 to 1.8
Design not practical using only one
material type (too many layers for
Fabric 1 and spacing too wide for
Fabric 3).
The most practical design will probably
consist of Fabric 3 at the spacings
indicated with shallow and intermediate
layers of Fabric 1 at maximum 1.5-foot
spacings for retention near the slope
face.
There appears to be no advantage to
using Fabric 2 since a much greater
reduction is required for creep
when determining Ta for the
woven fabric than for the non-woven
Fabric 1.
*************************************************************************************************************************************************
.C*
VO
TABLE 3.3
Summary of Design- Broms Method
SLOPE SLOPE ALLOWABLE NUMBER OF REINFORCEMENT REINFORCEMENT
HEIGHT INCLINATION TENSILE REINFORCEMENT LAYER SPACING LENGTH
(ft) RESISTANCE LAYERS (ft) (ft)
(Ib/ft)
****** ************** ********** *************** ************* ***************
12 Vertical 600 6 2 22.0 a 2'
or nearly (Fabric 1) 5.0 a 12'
vertical
1200 3 4 18.5 a 4'
(Fabric 2) 5.7 a 12'
2500 2 6 15.3 a 6*
(Fabric 3) 5.0 a 12'
30 600 32 0.9 72.0 a top
(Fabric 1) - 12.6 a bottom
1200 16 1.9 69.9 3 top
(Fabric 2) 14.2 a bottom
2500 8 3.8 56.0 a top
(Fabric 3) 12.6 a bottom
******1 **************1 **********1 '***************1 *************1 ***************1
FACTOR OF SAFETY
*********************
For fabric rupture,
the design method
uses an allowable
long-term tension
equal to 1/3 of the
ultimate fabric
strength (assumed to
be the wide-width
tensile strength)
to account for creep
and degradation
losses. For pullout,
the method includes
a factor of 1.3
applied to the
embedment length,
which is intended to
be a factor of safe-
ty against the
possible variations
in fabric stresses
behind the failure
plane. Safety fac-
tors are not calcu-
lated as part of the
design procedure.
COMMENTS
******************************************
Design method allows for a reduction
in reinforcement length for upper
layers provided overall combined pullout
resistance is sufficient.This effectively
means the lateral pressure distribution
is reduced near the top and increased
near the bottom.
The most practical design will consist
of six layers of Fabric 1 at 2-foot
spacings. The lengths of the upper
layers may be reduced to between 10
and 15 feet.
Any of the three alternatives appear
feasible. In the case of Fabric 3, and
possibly for Fabric 2, intermediate
layers would be required for retention
near the slope face. In all cases,
the fabric lengths could probably be
reduced to approximately 20 feet in the
upper portions of the wall.
TABLE 3.4
Summary of Design- Collin Methods
SLOPE
HEIGHT
(ft)
******
SLOPE
INCLINATION
**************
ALLOWABLE
TENSILE
RESISTANCE
(Ib/ft)
**********
NUMBER OF
REINFORCEMENT
LAYERS
REINFORCEMENT
LAYER SPACING
(ft)
REINFORCEMENT
LENGTH
(ft)
*************
***************
FACTOR OF SAFETY
COMMENTS
12
Vertical
or nearly
vertical
600
(Fabric 1)
Geotextile 1200
reinforcement (Fabric 2)
4
2
3
6
30
600
(Fabric 1)
23
1.3
1200
(Fabric 2)
12
2.5
7.3
5.7
21.5
21.0
Pullout:1.5 a top
16.8 a bottom
Ta/FH=1.1
Pullout:1.5 a 6*
6.6 a 12'
Ta/FH=1.1
Pullout:1.5 a top
114 a bottom
Ta/FH=1.0
Pul lout:1.5 a top
58 a bottom
Ta/FH=1.1
As discussed in the text, a factor
of safety for fabric rupture is assumed
to be accounted for in the allowable
fabric strength, Ta. The safety factor
for pullout is taken as the ratio of
pullout resistance to lateral thrust
for each layer.
The most practical design for a 12-foot
high wall is probably four layers of
Fabric 1 or more layers of an even weaker
fabric. All three cases appear feasible
for a 30-foot high wall; however, the
cases using Fabrics 2 and 3 would require
intermediate layers of weaker material
for retention near the slope face.
12
Vertical
or nearly
vertical
2500
(Fabric 3)
12
2.5
Pullout:1.6
Ta/FH=1.0
30
Geogrid
reinforcement
2500
(Fabric 3)
7
Layers at
depths 6',
8.5',13.5',
16.5',21.5',
23.5 & 30'.
17.5
Pullout: 1.5 a top
34.4 a bottom
Ta/FH=1.0-1.3
1 ****************************************************************************************************4*******************************************
TABLE 3.5
Summary of Design- Bonaparte et al. Method
*************************************************************************************************************************************************
SLOPE SLOPE ALLOWABLE NUMBER OF REINFORCEMENT REINFORCEMENT FACTOR OF SAFETY COMMENTS
HEIGHT INCLINATION TENSILE REINFORCEMENT LAYER SPACING LENGTH
(ft) RESISTANCE LAYERS (ft) (ft)
(Ib/ft)
****** ************** ********** *************** ************* *************** ********************* ******************************************
12 Vertical 600 7 1 a A.o 7.2 The paper in uhich Either of the designs for Fabrics 1 or
or nearly (Fabric 1) 1 a 2.5 the design method 2 appear feasible. Both will require
vertical 2 a 1.5 is presented rec- some intermediate layers of reinforce-
1 a i.o comnends lab test- ment for retention near the slope
2 a 0.75 ing to determine face.
II 11 II II II II II II II II II II II II II II II II II II II II II II II II II II tl II II II It II li II II It allowable rein-
1200 4 i a 5.5 6.4 forcement tension
(Fabric 2) i a 3.o and soil/fabric
1 a 2.25 interface friction.
i a 1.25 However, it suggests
II II II II II It II II II 11 II II II II II II II II II II II II 11 u II =2==S==S===2= II II 11 11 11 II II II II II II II II II II that allowable ten-
2500 2 1 a 8 5.7 si on not exceed 20X
Fabric 3) 1 a 4 to 40X of the wide width tensile strength and that
design be based on this working value
30 600 39 1 a 4.0 14.5 The design for Fabric 3 is probably
(Fabric 1) 1 a 2.5 with no further red- the most practical with the provision
1 a 2.0 uctions. A working of intermediate layers where required.
1 a 1.5 value of 33X of the Construction using only Fabric 1 or
7 a 1.0 ultimate strength Fabric 2 would be labor intensive
6 a 0.67 was used for this considering the large nurber of layers
10 a 0.5 study. required.
12 a 0.33 For internal stab-
ssssssssss II II II II II It 11 II II II II II II II II II II II II 11 II II II II II II II 11 II II It II II II II II II II II II II II ility, the soil/fab-
1200 20 i a 6.0 15.5 ric interface fric-
(Fabric 2) 2 a 3.0 tion is based on
2 a 2.0 presumed frictional
2 a 1.5 efficiencies of 90X
8 a 1.0 for nonwoven geo-
3 a 0.67 textiles and geo-
2 a 0.5 grids and 80% for
11 11 II II II II II II II II II II II II II II II II II II II II 11 II II II II II II II II It II II II II II II II II 11 II II II It II II II II II II II II woven geotextiles.
2500 10 1 a 8.0 14.5 The tangent of the
(Fabric 3) 1 a 5.0 factored interface
1 a 4.o friction angle is
1 a 3.0 then divided by a
3 a 2.0 factor of safety,
2 a 1.5 which was selected
1 a i.o as 1.5 for this study.
******4 **************J *********** r***************J *************4 ***************< r*********************< k*******************************************
cn
to
TABLE 3.6
Summary of Design- Leshchinsky and Perry Method
SLOPE HEIGHT (ft) ****** 12 SLOPE INCLINATION ************** Vertical ALLOWABLE TENSILE RESISTANCE (Ib/ft) ********** 225 NUMBER OF REINFORCEMENT LAYERS *************** 40 REINFORCEMENT LAYER SPACING (ft) ************* 0.3 REINFORCEMENT LENGTH (ft) *************** 10.8
450 20 0.6 11.0
940 10 1.2 11.3
30 225 250 0.12 25.0
450 125 0.24 25.0
940 60 0.5 25.0
12 1:2.5 (68 degrees) 225 27 0.444 8.4 3 top 12.5 3 bottom
450 5 2.4 8.6 3 top 12.7 3 bottom
940 2 6 8.9 3 6' 13.0 3 12'
30 225 60 0.5 17.6 3 top 26.6 3 bottom
450 30 1 17.7 3 top 26.7 3 bottom
940 12 2.5 17.8 3 top 26.8 3 bottom
FACTOR OF SAFETY
*********************
Design recommends
FS=1.5 for
composite soil/
geotextile structure
and FS=2.0 for
geotextile tension.
The required tensile
resistance is near
the design value at
the bottom layer and
is typically only a
small proportion of
the design value at
shallow depths.
COMMENTS
******************************************
This method yields results which appear
extremely conservative when compared with
the results of other design methods as
presented in this paper. This is a
result of the fabric strength selection
criteria and the application of safety
factors to strength and friction values
which have already been reduced. As
indicated by the comparisons in the
case history portion of this paper, the
method yields results similar to other
methods when evaluated for safety
factors equal to one.
TABLE 3.7
Summary of Design- Schmertmann et al. Method
*************************************************************************************************************************************************
SLOPE HEIGHT (ft) ****** 12 SLOPE INCLINATION ************** 80 degrees (1:5.7) ALLOWABLE TENSILE RESISTANCE (Ib/ft) ********** **600 . NUMBER OF REINFORCEMENT LAYERS *************** 6 MAXIMUM REINFORCEMENT LAYER SPACING (ft) ************* 1.2 8 bottom 2.0 a top REINFORCEMENT LENGTH (ft) *************** 8.2
1200 3 2.4 9.0
3000 1 7.2 8.2
30 600 35 0.5 a bottom 3.4 a top 20.4
**1200 17 1.0 3 bottom 7.1 a top 22.4
3000 7 2.6 3 bottom 4.3 a top 20.4
12 68 degrees **600 5 1.4 8.6
V1 1200 3 2.4 9.5
3000 1 7.2 8.6
30 **600 28 0.61 a bottom 4.3 a top 21.6
**1200 14 1.3 a bottom 6.4 a top 23.7
3000 6 3.0 a bottom 5.0 a top 21.6
FACTOR OF SAFETY
*********************
For pullout and
overall stability
of the slope, the
tangent of the
internal angle of
friction of the soil
is reduced by a
safety factor of
1.5. The method
accounts for a soil/
fabric frictional
efficiency of 90%.
For rupture, a
factor of safety is
accounted for in the
allowable tensile
resistance. For
Tensar geogrids, the
recommended design
values are typically
35% to 45% of the
ultimate strength.
However, these can
vary depending on
tolerable strains.
The values used in
this study are the
values recommended
by Tensar for use
with this design
method.
COMMENTS
******************************************
Several assumptions were made to apply
the method to slopes reinforced with
geotextiles since it was developed
for geogrids. The writer believes the
assumptions made are reasonable, as
discussed in the text.
*-The number of reinforcement layers
given are the minimum based on total
tensile resistance required and
allowable tensile resistance per
layer. Layer spacing requirements
may dictate that more than the
minimum nunber of layers be used.
**-Double asterisks indicate most
practical design alternatives.
For layer spacings greater than
about 2 to 3 feet, structural
facing units or intermediate
weaker geogrid or geotextile
layers are required for retention
near the slope face.
*************************************************************** A*********************************************************************************
55
56
57
Tables 3.8 and 3.9 present reinforcement
quantities in square feet per foot length of wall (sq
ft/ft). For each reinforcement type and design case, the
length and reinforcement quantity calculated by the design
method are presented. For some cases, wide reinforcement
spacings are calculated. Therefore, reinforcement
quantities were also calculated for a more practical
design for each case by assuming that the spacing between
primary reinforcement layers should not exceed
approximately 4 feet and that intermediate relatively weak
reinforcement is required at spacings of no more than 1.5
feet for retention near the slope face.
The intermediate reinforcement quantities were
calculated assuming they extend back into the wall a
distance equal to one-half of the length of the primary
reinforcement layers. All of the fabric quantities are
based on reinforcement length only and do not account for
wrap-around at the wall face. Therefore, for cases where
wrap-around and overlap result in a significant proportion
of the total quantity, the comparisons made for this study
may not accurately represent the differences between
methods. The comparisons are intended to provide an
indication of the reinforcing requirements and the
associated relative costs.
TABLE 3.8
Summary of Reinforcement Quantity Comparisons- 12-foot High Wall
FABRIC 1 (Tult=1800 Ib/ft) FABRIC 2 (Tult=3600 Ib/ft) FABRIC 3 (Tult=7500 Ib/ft)
DESIGN METHOO LENGTH (ft) CALCULATED QUANTITY (sq ft/ft) PR ACT IC/ DESIGN FABRIC QUANTITY (sq ft/ft) IL DESIGN INTERMEDIATE FABRIC QUANTITY (sq ft/ft) LENGTH (ft) CALCULATED QUANTITY (sq ft/ft) PRACTIC/ DESIGN FABRIC QUANTITY (sq ft/ft) IL DESIGN INTERMEDIATE FABRIC QUANTITY (sq ft/ft) LENGTH (ft) CALCULATED QUANTITY (sq ft/ft) PRACTIC/ DESIGN FABRIC QUANTITY (sq ft/ft) IL DESIGN INTERMEDIATE FABRIC QUANTITY (sq ft/ft)
VERTICAL OR NEARLY VERTICAL
FOREST SERVICE 8.9 53 80 . 8.9 53 80 - 8.9 18 36 18
BROMS 22/5 72 58 29 19/6 35 28 30 15/5 20 17 32
COLLIN 7.3 29 29 15 5.7 11 23 11 2.5 3 NA NA
LESHCHINSKY S PERRY 10.B 431 431 - 11.0 219 219 11.3 113 113 -
BONAPARTE ET AL 7.2 50 58 7 6.4 26 32 10 5.7 11 23 11
SCHMERTMANN ET AL 8.2 49 57 17 9.0 27 45 23 8.2 8 25 25
SLOPE ANGLE=68 DEGREES (1:2.5)
LESHCHINSKY & PERRY 8.4/12.5 274 274 . 8.6/12.7 145 145 - 8.9/13.0 76 76 -
SCHMERTMANN ET AL 8.6 43 52 13 9.5 29 48 24 8.6 9 26 26
NOTES: (1) The fabric lengths indicated are those calculated and do not account for
overlap or wrap-around at the slope face.
(2) For cases which do not have uniform lengths for all layers, the reported
lengths are top layer/bottom layer.
(3) Intermediate fabric quantities were determined by assuning that retention
is required at the slope face by using a relatively weak fabric of
length equal to 1/2 the required reinforcement length at vertical spacings
no greater than 1.5 feet. Ln
oo
TABLE 3.9
Summary of Reinforcement Quantity Comparisons- 30-foot High Wall
**************************************************************************************************************************************^***************
DESIGN METHOD LENGTH (ft) FABRIC 1 ( CALCULATED QUANTITY (sq ft/ft) rult=1800 l PRACTIC/ DESIGN FABRIC QUANTITY (sq ft/ft) 3/ft) \L DESIGN INTERMEDIATE FABRIC QUANTITY (sq ft/ft) LENGTH (ft) FABRIC 2 ( CALCULATED QUANTITY (sq ft/ft) rult=3600 l PRACTIC/ DESIGN FABRIC QUANTITY (sq ft/ft) 5/ft) \L DESIGN INTERMEDIATE FABRIC QUANTITY (sq ft/ft) LENGTH (ft) FABRIC 3 (1 CALCULATED QUANTITY (sq ft/ft) rult=7500 11 PRACTIC/ DESIGN FABRIC QUANTITY (sq ft/ft) 3/ft) IL DESIGN INTERMEDIATE FABRIC QUANTITY (sq ft/ft)
FOREST SERVICE VERTICAL OR NEARLY VERTICAL
22 821 848 22 821 848 - 22 289 355 89
BROMS 72/14 986 789 70/14 529 408 208 56/13 236 192 201
COLLIN 22 495 495 21 252 252 126 17.5 123 123 114
LESHCHINSKY & PERRY 25 6270 NOT PRACTICAL 25 3140 HOT PRACTICAL - 25 1520 1520 -
BONAPARTE ET.AL. 14.5 566 580 22 15.5 310 326 47 14.5 145 160 87
SCHMERTMANN ET.AL. 20.4 714 714 20 22.4 381 381 78 20.4 143 184 143
SLOPE ANGLE=68 DEGREES (1:2.5)
LESHCHINSKY & PERRY 17.6/27 3890 2" SPACING - 17.7/27 1870 4.5" SPACING - 17.8/27 950 9" SPACING -
SCHMERTMANN ET.AL. 21.6 605 605 43 23-7 ******** 332 ********** 356 **********< 119 ************1 21.6 ********1 130 ********** 173 **********4 HO ************1
NOTES: (1) The fabric lengths indicated are those calculated and do not account for
overlap or wrap-around at the slope face.
(2) For cases which do not have uniform lengths for all layers, the reported
lengths are top layer/bottom layer.
(3) Intermediate fabric quantities were determined by assuming that retention
is required at the slope face by using a relatively weak fabric of
length equal to 1/2 the required reinforcement length at vertical spacings
no greater than 1.5 feet.
vo
CHAPTER 4
CASE HISTORY EVALUATIONS
4.1 General
Two cases of geosynthetic-reinforced soil test
walls which were tested to failure under controlled
conditions were used to evaluate each of the design
methods used for this study. The purpose was to evaluate
the analytical models used in the design methods without
the influence of any of the empirical, and perhaps
somewhat subjective, criteria for defining factor of
safety and selecting allowable reinforcement strength.
Actual reinforcement strengths were used and all safety
factors were set equal to one.
4.2 Description of Case Histories
4.2.1 STS/FHWA Geotextile Test Wall
The first of the two case histories used for the
evaluations was a full scale test wall which was designed
to fail as part of a Federal Highway Administration (FHWA)
research project on the behavior of reinforced soil. The
results of that study had not been fully compiled nor
published at the time of this study. The description of
the wall's configuration, construction and conditions at
61
failure are based on verbal communication with Mr. Barry
R. Christopher of STS Consultants, the principal
investigator in charge of the study (Christopher, 1988-
1989).
According to Mr. Christopher, the wall was
constructed with a buttressing surcharge provided by a
water reservoir at the toe of the wall. After the wall
was constructed beyond the height at which failure was
anticipated, the reservoir was drained to a level at which
failure occurred.
The wall was constructed using a uniform
reinforcement layer spacing of 2.5 feet. The
reinforcement lengths were 14 feet. Deformation data had
not been compiled at the time of this study. However,
based on his observations and past experience, Mr.
Christopher believes a length of approximately 10 feet
would have yielded the same results and a length shorter
than 10 feet would have altered the results. Although the
test was not designed to evaluate the required
reinforcement length, an effective reinforcement length of
10 feet was used for this study based on Mr. Christopher's
judgement. This results in an effective reinforcement
quantity requirement of 80 sq ft/ft.
A relatively extensible needled, non-woven
polyester geotextile with a wide width tensile strength of
1,320 pounds per foot (lb/ft) at 80% strain was used. The
62
elastic modulus of the fabric was 14,400 lb/ft at 5%
strain, resulting in a tensile stress in the reinforcement
of 720 lb/ft mobilized at 5% strain. The foundation soil
and backfill consisted of a fairly well graded sand and
gravel with a peak internal friction angle of
approximately 39 at the density used for construction of
the wall. The unit weight was approximately 129 pounds
per cubic foot (pcf) at approximately 70% relative
density, or 95% standard Proctor density. A
soil/reinforcement interface frictional efficiency of 100%
was reported for these conditions.
As a result of the relatively wide reinforcement
spacings using conventional geotextile wall construction
methods (i.e., a wood form used for support at the face
during fill placement at each layer), fairly large lateral
deformations of the wall face, on the order of 1 to 1.5
feet, occurred during construction. These deformations
were relatively uniform over the wall's height.
Failure was described as being due to creep. At
failure, rapid vertical deformation of about 1 inch
occurred at the top followed by progressive rotational
movements of the mass in front of the "failure surface."
Mr. Christopher perceived the mode of failure to be creep
within a zone between a Rankine active failure surface and
a log spiral surface contained within the Rankine wedge.
He believes failure in a wall reinforced with an
63
extensible material probably initiates as creep at a log
spiral surface relatively close to the wall face which
then progresses to the Rankine active surface, at which
point rupture occurs. He did not believe the
reinforcements had ruptured or pulled out in the subject
wall.
4.2.2 RMC Geoarid Model Wall
The second case history used for this study
consisted of a large scale model geogrid-reinforced wall.
The wall was constructed and tested as part of a long-term
research project at the Royal Military College of Canada
(RMC). The results of the test used for this study are
presented in a paper included in the ASCE Geotechnical
Special Publication No. 18, "Geosynthetics for Soil
Improvement" (Bathurst, Benjamin and Jarrett, 1988).
The major component of the model test facility
consisted of a reinforced concrete structure in which a
geosynthetic-reinforced wall could be constructed
approximately 12 feet high, approximately 8 feet wide and
nearly 20 feet in depth. A vertical surcharge was applied
at the top of the wall by pressurizing pneumatic bags. An
equivalent surcharge of up to approximately 20 feet of
fill could be provided. The walls of the structure
confining the model were lined with a composite of
64
plywood, plexiglass and polyethylene sheeting to reduce
the effects of friction.
The results of several tests using the facility
were presented in the referenced paper. The paper
concentrated on one of the tests, which is the one
selected for this study. That test involved the
construction of a wall approximately 9.8 feet high with
four layers of geogrid reinforcement, each approximately
9.8 feet long, at depths 1.6, 4.1, 6.6 and 9.0 feet. The
backfill soil consisted of an angular, uniformly graded
washed sand with some gravel with a unit weight of
approximately 112 pcf and a reported peak internal angle
of friction of 53. The wall was constructed by slightly
pre-tensioning the reinforcements and then carefully
compacting the granular backfill inside the concrete
forms. Timber facing elements backed with foam rubber to
reduce stress concentrations at the facing elements were
provided. Reinforcement strain measurements were obtained
at six points on each layer.
The reinforcement used consisted of Tensar SSI
geogrid oriented in its longitudinal (weak) direction.
Under these conditions, this material possesses an
ultimate wide width tensile strength of 840 lb/ft at 14%
strain. The model was surcharged in increments to
approximately 250, 625, 1,045, 1,250, 1,465 and 2,090
pounds per square foot (psf). The 1,045-psf surcharge was
65
sustained for 162 hours, during which time failure
occurred.
They described failure as significant movement
upon loading and fairly high creep for 70 hours, then
rapid deformation. At that time, the model wall
apparently became hung up in the test apparatus. Further
surcharging produced only small additional movements.
The strains that occurred during this test were
significantly less than for the STS/FHWA test. In the RMC
test, a stiff reinforcement which was pre-tensioned during
construction was used with a high strength soil. Lateral
deformations which occurred at failure were less than 1
inch.
A failure scarp which developed in the backfill
indicated that the failure surface resembled a log-spiral
geometry and can be approximated by a Rankine active
failure wedge for a soil friction angle of 53'. They
concluded that little to no strain occurred beyond a
reinforcement length of approximately 3.9 feet and that
all of the soil/reinforcement load transfer occurred
within this length. Therefore, an effective length of 3.9
feet was selected for this study. This results in an
effective reinforcement quantity requirement of 15.6 sq
ft/ft.
The peak reinforcement strains that occurred were
approximately 4.5% to 5.5% in the upper 3 layers and
66
approximately 1.5% in the bottom layer. The lower stress
mobilized in the bottom layer was attributed to the model
boundary effects at the bottom of the rigid box. Based on
the stresses mobilized in the reinforcement, an effective
reinforcement strength of 500 lb/ft was selected for this
study. This corresponds to approximately 4% strain in the
reinforcement. Although the average strain was closer to
5% in the upper 3 layers, the effective strength selected
was based on 4% strain to allow for some contribution from
the lower layer.
As with the STS/FHWA test wall, failure as defined
by the design methods was not attained in that the
reinforcement neither ruptured nor pulled out. Large
creep deformations were reported at the failure load
before the test became "hung up." Had the creep
deformations been allowed to progress to the point at
which "collapse" of the wall occurred, it is likely
rupture would have been the failure mode.
4.3 Summary and Results of Comparisons
The six design methods used for this study were
evaluated utilizing the two case histories described above
by modifying the design calculations to eliminate all
considerations for margins or factors of safety. The
ultimate reinforcement strength was used for the effective
strength for the STS/FHWA wall. The other effective length
67
and strength values used are described above. The test
wall geometries are summarized on Figure 4.1.
Even though neither rupture nor pullout occurred
in either of the test walls, they were both assumed to
represent limiting equilibrium conditions for both rupture
and pullout. This assumption is probably valid for
rupture since, in the case of the STS/FHWA test wall, the
stress ratio in the reinforcement can be assumed to be
high for the high creep which occurred and, for the RMC
model wall, the effective strength was based on measured
strains.
The assumption of limiting equilibrium may be less
valid for pullout. Even though the effective lengths are
those lengths below which the capacity of the structure is
reduced, the safety factor for pullout is not known to be
1.0. However, the design methods generally consider
rupture to be dependent only on reinforcement strength and
pullout to be dependent only on embedment length, and the
two failure modes to be independent of each other.
Therefore, these methods appear to assume that the aspect
of the analysis which addresses reinforcement length
(i.e., pullout resistance) is at a limiting value at the
length below which the performance of the structure is
affected. For an extensible reinforcement, the length of
reinforcement over which the soil/reinforcement interface
68
>0 ' 1 1
1 1
!
_
J
!
1 1 1 |
1 1
10 Effective!
14' Actual ^
3d-2-
5
8 Layers of
Nonwoven
Geotextile
1320 lb/ft
Ultimate Strength
STS/FHWA TEST WALL
H=9.81
q= 1045 psf Surcharge at Failure
i 1 < i ~T
3.9
Effective
I
i i.
4 Layers. Geogrid | i
500 lb/ft |
Effective Strength f
\D
vO
00
CT\
9.8 Actual
RMC GEOGRID MODEL WALL
Figure 4.1- Summary of Test Wall Geometries
69
shearing resistance is only partially mobilized within the
effective length is probably relatively short, and this
assumption may not be entirely unreasonable. However, for
a stiff reinforcement, the shearing resistance may be only
partially mobilized ever a significant length within the
effective length resulting in a safety factor
significantly greater than 1.0 for the effective length.
The evaluations were approached two ways. First,
the reinforcement tensions predicted by each method were
calculated for the test wall geometries. Figures 4.2 and
4.3 summarize the results of this method of comparison in
terms of calculated tension in each reinforcement layer
for the test wall reinforcement layer spacings. The
second approach was to determine the reinforcement
spacings and lengths determined by each method using the
test wall heights and reinforcement strengths with all
safety factors set as near 1.0 as practical. Figures 4.4
and 4.5 show the results of these comparisons. The
calculated embedment lengths represent the lower bound
values when compared with the actual embedment lengths
shown in Figure 4.1. The computer printouts and other
calculations used for the evaluations are presented in
Appendix B. Each case is discussed in more detail below.
It should be pointed out that most of the design
methods tacitly assume that the layer spacing and fabric
70
H
CM
W
O
" CALCULATED REINFORCEMENT TENSION
(lb/ft)
Figure 4.2- Reinforcement Tension Calculated
for STS/FHWA Test Wall Geometry.
71
q= 1045 psf
CALCULATED REINFORCEMENT TENSION
(lb/ft)
Figure 4.3- Reinforcement Tension Calculated
for RMC Geogrid Model Wall
Geometry.
72
7'
8 Layers
FOREST SERVICE METHOD
20.3'
14.9'
11.4'
8.5'
6.0'
3.7
6 Layers
BROMS METHOD
9.1'-
5 Layers
COLLIN METHOD
9.1'
7 Layers
BONAPARTE ET AL. METHOD
11.1
8 Layers
(Layers
above
bottom
reduced in
strength)
LESHCHINSKY & PERRY METHOD
SCHMERTMANN ET AL. METHOD
Figure 4.4- Comparison of Methods for FS= 1.0
(20-foot High Wall, 1320 lb/ft
Reinforcement Strength).
73
1 1 1 1 6.2' 4.0'
1 I 7 Layers i 2_5 4 Layers
1 1.2'
FOREST SERVICE METHOD BROMS METHOD
n 1 1 1 1 *-4.5' -H 1
1 1 1
' 6 Layers 1 1 1 1 5 Layers 1 1
1 1
COLLIN METHOD BONAPARTE ET AL. METHOD
1 *-3.8'-^ 1 6 1' j 1
' n 1 i 1 1 1
| 4 Layers 1 (Layers above | bottom reHncpd 1 4 Layers 1
! in strength) 1 1 1 1 1 1
LESHCHINSKY & PERRY METHOD SCHMERTMANN ET AL. METHOD
Figure 4.5- Comparison of Methods for FS= 1.0
(9.8-foot High Wall, 500 lb/ft
Reinforcement Strength ,
1045 psf Surcharge).
74
strength control the factor of safety against rupture and
that the embedment length and soil/fabric friction
determine the factor of safety against pullout; i.e.,
there is no interaction between the two modes of failure.
This assumption was followed in the evaluation of the case
histories.
4.3.1 Forest Service Method
4.3.1.1. STS/FHWA Test Wall
Evaluation for the test wall geometry results in
very high safety factors at all depths for pullout (5.8 to
18.6). The safety factors for rupture range from 8.8 for
the upper layer to 0.6 to 1.0 for the lower four layers.
Evaluation for safety factors of 1.0 results in
the same number of layers (8) as the test wall with
spacings ranging from 7 feet (top layer) to 1 foot (bottom
layer). The required reinforcement length is 7.0 feet,
resulting in a reinforcement quantity requirement of 56 sq
ft/ft, which is 70% of that required for the test wall,
based on the effective length of 10 feet.
The analytical model used for the Forest Service
method appears conservative for rupture of the lower
layers. The reinforcement lengths calculated are shorter
than the effective length selected for this study. The
triangular stress distribution based on an at-rest earth
75
pressure condition appears to overestimate reinforcing
requirements for the lower layers.
4.3.1.2 RMC Model Wall
Evaluation for the model wall geometry results in
safety factors ranging from 1.5 at the top layer to 10.3
at the bottom for pullout. The safety factors for rupture
range from 1.3 at the top to 0.5 at the bottom.
Evaluation for a safety factor near 1 results in
seven layers with lengths of 3.4 feet. The layer spacings
vary from 2 feet at the top to 1.1 feet at the bottom.
The reinforcement quantity required is 24 sq ft/ft, which
is 1.5 times the effective material quantity for the model
wall.
The analytical model yields conservative results
in that it overestimates the amount of reinforcement
required in the lower portion of the wall. As with the
STS/FHWA test wall, the calculated reinforcement length is
shorter than the effective length.
4.3.2 Broms Method
4.3.2.1 STS/FHWA Test Wall
The computer spread sheet program written for this
study automatically varies the reinforcement lengths and
spacings according to strength. A direct comparison with
the test wall was not practical because the reinforcement
76
length varies with depth. Because of this length
variation, a single factor of safety for the test wall
could not be determined. For the test wall height and
reinforcement strength, the reinforcement spacing is
3.3 feet assuming FS=1 for both pullout and rupture. For
the test wall height and reinforcement spacing, the
required reinforcement strength is 1,000 lb/ft. For both
cases, the reinforcement lengths vary from 3.7 feet at the
bottom to 20.3 and 21.9 feet at the top. The
reinforcement quantity requirements are 65 sq ft/ft for
the 1,320 lb/ft-strength material at 3.3-foot spacings and
89 sq ft/ft for the 1,000 lb/ft-strength material at
2.5-foot spacings.
The analytical model used appears unconservative
for total required reinforcement strength when compared
with the test wall.
4.3.2.2 KMC Model Wall
As discussed above, a direct evaluation was not
practical due to the variable reinforcement lengths
determined by the Broms method. In addition, for the
model wall, the upper layer is at a depth equal to two-
thirds of the spacing of the other three layers.
Consequently, since the Broms method uses uniform layer
spacings, the wall height was increased by one-third of
the spacing of the lower layers and the surcharge was
77
reduced by the same amount, resulting in a wall height of
9.8 feet with a surcharge of 950 psf. The bottom of the
wall is therefore considered to be at the bottom
reinforcement layer. For four equally spaced layers with
the effective ultimate strength of 500 lb/ft, the safety
factor for rupture calculated is 1.1. The reinforcement
lengths range from 1.2 feet at the bottom to 6.2 feet at
the top, which results in a reinforcement quantity
requirement of 88% of the effective quantity for the model
wall.
With the assumption of FS=1.0, the analytical
model used yields results very close to those obtained
from the model wall test, except that the lengths
determined by the Broms method vary with depth. The
method indicates slightly unconservative reinforcement
strength requirements.
4.3.3 Collin Method
4.3.3.1 STS/FHWA Test Wall
As with the Broms method, the computer spread
sheet program written for this study automatically varies
a uniform reinforcement spacing according to its strength.
For a strength of 1,320 lb/ft, the resulting spacing is
4 feet with a required length of 9.1 feet. For the same
geometry as the test wall, the calculated reinforcement
strength required is 750 lb/ft, or 57% of that used for
78
the test wall, correlating to a factor of safety for
rupture of 1.8. The factor of safety calculated for
pullout varies from 1.2 at the top layer to 56 at the
bottom layer. The reinforcement quantity required for the
1,320-lb/ft material is 58% of the effective quantity
reported for the test wall. This is based on five layers
9.1 feet in length.
The analytical model appears unconservative for
required reinforcement strength when compared with the
test wall. Slightly shorter lengths and either lower
strengths or larger spacings are indicated for a safety
factor of 1.0.
4.3.3.2 KMC Model Wall
The RMC model wall was used to evaluate the Collin
geogrid method. Evaluation for the test wall geometry
results in safety factors for pullout ranging from 2.3 for
the top layer to 39.1 for the bottom layer. The safety
factors for rupture are 0.8 for the top and bottom layers
and 0.7 for middle two layers.
Evaluation for a rupture safety factor of 1.0
requires either four layers of a 750-lb/ft reinforcement
3.3 feet in length for the model wall spacings or six
evenly spaced layers of a 500-lb/ft reinforcement 3.2 feet
in length. These result in quantities of 81% and 119% of
79
the effective quantity required for the model wall for the
750-lb/ft and 500-lb/ft materials, respectively.
The analytical model appears conservative for
reinforcement strength in that it overestimates the
required reinforcement strength by about 50%. The
reinforcement lengths calculated are approximately 15%
less than the effective length selected for the study.
4.3.4 Bonaparte et al. Method
4.3.4.1 STS/FHWA Test Wall
Evaluation for the test wall geometry yields
results very similar to those obtained for the Forest
Service method. Safety factors for pullout are relatively
high (4.7 to 11.9). Those for rupture range from 7.2 at
the top layer to 0.6 to 1.0 for the lower three layers.
Evaluation for a rupture factor of safety of 1.0
results in seven layers 9.1 feet in length with spacings
from 6.5 feet (top layer) to 1.5 feet (bottom layer). The
resulting reinforcement quantity is 64 sq ft/ft, which is
80% of that for the test wall. Since the lateral pressure
is a function of reinforcement length, shortening the
lengths enough to result in a safety factor for pullout of
1.0 for the upper layer results in an apparently
unrealistically high number of layers required near the
bottom.
80
For the test wall geometry, the results are very
close to those obtained using the Forest Service method.
However, for the Forest Service method, the horizontal
forces (and consequently the strength and embedment
requirements) are independent of total reinforcement
length. For this method, the horizontal force is a
function of the reinforcement length and increases at an
increasing rate with depth. Safety factors for rupture
can therefore be increased by increasing the reinforcement
length. The safety factor for rupture of the bottom layer
is increased from 0.6 to 0.8 by increasing the
reinforcement length from 10 to 14 feet.
4.3.4.2 RMC Model Wall
As with the STS/FHWA test wall, the Bonaparte et
al. method yields similar results to those obtained using
the Forest Service method. Safety factors for pullout
range from 2.5 at the top to 5.5 at the bottom. Those for
rupture are from 2.2 at the top to 0.5 at the bottom. As
discussed above, the lateral pressure is a function of
reinforcement length for this method. Therefore, two
cases were evaluated for safety factors near 1.0. Five
layers 4.5 feet in length and seven layers 3.2 feet in
length both yield safety factors for rupture near 1.0 (1.0
to 1.3). Both yield essentially the same reinforcement
quantity requirement of approximately 140% of the
81
effective quantity for the model wall. The case with
longer reinforcement lengths results in higher safety
factors for pullout. For both cases, the layer spacings
are 3 feet for the first layer and decrease with depth.
The results are very similar to those obtained
using the Forest Service method, both in terms of safety
factors determined for the test wall geometry and the
geometry determined for a safety factor of 1.0. This
method is somewhat less conservative than the Forest
Service method for shallow depths but is very similar for
the bottom layers.
4.3.5 Leshchinskv and Perry Method
4.3.5.1 STS/FHWA Test Wall
With the assumption of FS=1.0 for both rupture and
pullout, evaluation for the test wall geometry results in
reinforcement layer spacing and bottom layer strength
nearly the same as those used for the test wall. The
reinforcement length is 12.1 feet, which includes the
somewhat arbitrary addition Of 1 foot in length for
"tolerance," which is presumably intended for production
walls and is probably not applicable to this evaluation.
The calculated length is 11.1 feet, which results in a
material quantity 111% of the effective quantity for the
test wall. The method results in required reinforcement
82
strengths for layers above the bottom layer reduced in
direct proportion to depth.
Evaluation for safety factors of 1.0 results in a
wall geometry and maximum reinforcement strength very
close to those used for the test wall. The length is
approximately 1 foot longer than the reported effective
length and approximately 3 feet shorter than the actual
length used for the test wall.
for both rupture and
geometry results in
4.3.5.2 KMC Model Wall
With the assumption of FS=1.0
pullout, evaluation for the test wall
a required fabric strength of 542 lb/ft, which is
approximately 8% greater than the strsss mobilized in the
reinforcement during the test. Fjor a reinforcement
j
strength of 434 lb/ft, five layers {are required. The
i
calculated reinforcement length is 3|.8 feet without the
I
i
additional 1 foot for "tolerance."
As with the Broms method,
a wall height of
9.8 feet was used with the wall bottomj coincident with the
I
i
bottom reinforcement layer. The design method uses charts
I
applicable up to soil friction angles of 45 for
increments of surcharge of 0.1, 0.2
times the wall height. Extrapolation beyond the 45
friction angle and interpolation
differing surcharge magnitudes were r
0.4, 0.7 and 1.0
between charts of
equired.
83
The analytical model yields results very close to
those obtained from the model wall test for effective
length and bottom reinforcement layer strength. The
predicted reinforcement strength for the bottom layer is
within 10% of the effective mobilized stress selected to
represent the test and the reinforcement length is within
2 inches of the effective length reported for the model
test. However, the method may be somewhat unconservative
for the upper layer strengths in that the required
reinforcement strength in all layers above the bottom is
decreased at shallower depths. For a surcharged wall, the
calculated reinforcement strength distribution is
trapezoidal. The test results indicated reinforcement
stresses were nearly the same in the upper 3 layers.
4.3.6 Schmertmann et al. Method
4.3.6.1 STS/FHWA Test Wall
Evaluation for the test wall geometry results in
a safety factor of 1.0 for a soil with an internal
friction angle of 23 for reinforcement strength and of
34 for reinforcement length. For the test wall geometry
with a 39 soil friction angle, the method indicates
safety factors of 1.9 for rupture and 1.2 for pullout.
For a soil friction angle of 39 and a safety factor of
1.0, the reinforcing required is four layers of the 1,320-
lb/ft material with lengths of 8.6 feet. This results in
84
a material quantity of 43% of the effective quantity for
the test wall.
The analytical model used appears unconservative.
It significantly underestimates the amount of
reinforcement required. Limiting equilibrium is indicated
to occur at a reinforcement stress level only 44% of that
for which the test wall provided for.
4.3.6.2 RMC Model Wall
Evaluation for the model wall geometry results in
a safety factor of 1.0 for a soil with an internal angle
of friction of 51 for reinforcement strength and of 67
for reinforcement length. Evaluation for a safety factor
of 1.0 results in four layers of a 500-lb/ft reinforcement
6.1 feet in length. The method results in larger
reinforcement spacings at shallow depth and smaller
spacings at greater depth, varied in direct proportion to
depth.
The analytical model very closely predicts the
required reinforcement strength but predicts a required
length over 1.5 times the effective length. However, the
validity of the comparison is in question since the method
models a surcharge by increasing the effective height,
which is reported to be applicable for effective slope
heights up to 20% greater than the actual height. For the
model test, the effective height was approximately two
85
times the actual height. In addition, extrapolation was
required to use the design charts for the relatively high
soil friction angle of 53.
CHAPTER 5
SUMMARY AND CONCLUSIONS
5.1 General
A review of Chapters 3 and 4 shows the various
methods yield widely varying results. To some extent, the
differences in results are a result of obvious differences
in the analytical models the methods are based on.
However, the more prominent differences in the design
results are due to significant disparity in defining
allowable reinforcement strength and safety factors.
One way to evaluate the combined (overall) safety
margin of the design methods is to compare their safety
ratios. The safety ratio is defined herein as the ratio
of reinforcement quantity determined using all of the
prescribed safety factors to that determined by following
the methods with all safety factors set equal to 1.0 and
using ultimate strength parameters. Table 5.1 shows the
safety ratios calculated using the design fabric
quantities presented in Table 3.9 for Fabric 2 (30-foot
high wall, vertical face, all safety margins included) and
the results for the same wall height and inclination with
all safety factors set equal to 1.0 and using the ultimate
reinforcement strength of 3,600 lb/ft. Table 5.1 shows
87
TABLE 5.1
Safety Ratios, the Design Reinforcement Quantity
versus the Quantity for FS = 1.0 for a Vertical
30-foot High Wall Reinforced with Fabric 2
*************************************************
Design Design Quantity Ratio of
Method Quantity for Design
(see Table FS=1.0 Quantity
3.9) (sq to
(sq ft/ft) ft/ft) Quantity for FS=1.0
************************************* ***********
Forest Service 821 81 10.1
Broms 529 127 4.2
Collin 252 58 4.3
Bonaparte et al. 310 100 3.1
Leshchinsky and Perry 3,140 136 23.1
Schmertmann 381 54 7.1
et al.
*************************************************
88
that the largest design reinforcement quantity is
approximately 12.5 times the smallest design quantity;
however, the ratio of largest to smallest reinforcement
quantity without considering safety factors is
approximately 2.5.
Comparison of safety ratios does not demonstrate
where the differences between methods in recommended
safety margins lie because the effects of strength
requirements are not separated from the effects of length
requirements. However, Table 5.1 demonstrates that,
although there are significant differences among the
methods for limiting equilibrium conditions
FS=1.0) (see for example, Figures 4.4 and 4.5) these
differences are relatively small compared with those
resulting from the application of the recommended safety
margins (see for example, Figures 3.1 and 3.2).
As discussed in subsection 4.3, neither of the
test walls used to evaluate the six design methods failed
in either pullout or rupture. However, the methods imply
limiting equilibrium for both of these failure modes for
the effective reinforcement lengths and strengths.
Although this assumption can be better supported for
rupture than for pullout, the methods imply it also
applies to pullout. As discussed in subsection 4.3, this
assumption may not be entirely unreasonable for an
89
extensible reinforcement and it is probably invalid for a
stiff reinforcement.
With a potentially unrealistic assumption of
FS=1.0 for pullout, the Leshchinsky and Perry method
yielded results closest to those determined for the test
walls discussed in Chapter 4 for reinforcement length and
bottom reinforcement layer strength. This is demonstrated
by comparing Figure 4.1 with Figures 4.4 and 4.5. This
method also yielded the most conservative results by far
after applying the recommended margins of safety. This
may be partly attributable to the fact that the design
method was developed for the U.S. Army Corps of Engineers
as a step by step procedure which may be used in
potentially sensitive situations by engineers with limited
geotechnical engineering background. For the case
presented in Table 5.1, 23 times as much reinforcement is
required if the guidelines for safety margins are followed
as for the case where no margins of safety are used. This
ratio varies from approximately 3 to 10 for the other
methods.
5.2 Analytical Models
In general, the design methods evaluated are
somewhat limited in that they do not directly address the
interaction between the soil and reinforcement in terms of
the actual stresses mobilized by the strains that occur.
90
The Collin and Broms methods indirectly address these
interactions to some degree. Collin's recommended lateral
pressure distributions are based on finite element models
that used actual wall performance data. The Broms method
was developed considering the results of model tests. The
Bonaparte et al. method considers strain compatibility and
deflections of the wall facing.
The stress distributions assumed in the analyses
are typically oversimplified, particularly in the case of
the tied-back wedge analyses. It is apparent that these
methods do not model the actual stresses occurring in the
reinforced mass. For example, Rankine earth pressure
theory assumes the major and minor principal stresses in
a homogeneous and isotropic mass are in the vertical and
horizontal directions, respectively. A reinforced soil
mass is not homogeneous and isotropic, and there is a
significant horizontal shear component due to the
reinforcement. The writer does not necessarily conclude
that these simplified methods are not suitable for design.
However, regardless of the analytical model used for
design, the relationship between lateral earth pressure
and reinforcement extensibility should be accounted for.
Consideration must be given to the influence of backfill
type and construction procedures.
Finite element analysis can be used to more
realistically model the stresses occurring in such a