Citation
U-shaped mechanically stabilized earth wall supported abutment under static loadings for highway bridge

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Title:
U-shaped mechanically stabilized earth wall supported abutment under static loadings for highway bridge
Creator:
Yip, Man Cheung
Publication Date:
Language:
English
Physical Description:
xi, 264 leaves : illustrations ; 28 cm

Subjects

Subjects / Keywords:
Retaining walls -- Design and construction ( lcsh )
Geosynthetics ( lcsh )
Bridges -- Design and construction ( lcsh )
Bridges -- Abutments -- Design and construction ( lcsh )
Soil conditioners ( lcsh )
Soil stabilization ( lcsh )
Bridges -- Abutments -- Design and construction ( fast )
Bridges -- Design and construction ( fast )
Geosynthetics ( fast )
Retaining walls -- Design and construction ( fast )
Soil conditioners ( fast )
Soil stabilization ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 263-264).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Man Cheung Yip.

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Source Institution:
|University of Colorado Denver
Holding Location:
|Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
57543126 ( OCLC )
ocm57543126
Classification:
LD1190.E53 2004m Y56 ( lcc )

Full Text
U-SHAPED MECHANICALLY STABILIZED EARTH WALL SUPPORTED
ABUTMENT UNDER STATIC LOADINGS FOR HIGHWAY BRIDGE
by
Man Cheung Yip
B.S., University of Colorado at Denver, 1992
B.S., University of Colorado at Denver, 1996
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2004


This thesis for the Master of Science
degree by
Man Cheung Yip
has been approved
by
Date


Yip, Man C. (M.S., Civil Engineering)
U-shaped Mechanically Stabilized Earth Wall Supported Abutment under
Static Loadings for Highway Bridge
Thesis directed by Professor Nien-Yien Chang
ABSTRACT
Geosynthetic reinforced soil (GRS) technology has been widely used in the
construction of retaining walls, embankments, reinforced soil slopes, and shallow
foundations on poor soil. The applicability of GRS technology in the construction
of Mechanically Stabilized Earth Wall (MSEW) Supported abutments has been
investigated and prototypes constructed in a number of recent studies. The concept
of U-shaped MSE systems to support bridge abutments has been put in place under
the leadership of Dr. Nien-Yien Chang and Dr. Trever S.C. Wang at the Center of
Geotechnical Engineering Science at the University of Colorado at Denver. The
concept of this type of structural abutment support system, being similar to a
traditional MSE retaining wall, has attributes of reinforcement in the backfill soil.
However, a structural abutment support system requires adequate strength for the
additional loading of supporting bridge loadings. To have an efficient design of an
abutment support system, the response of the system subjected to various loading
needs to be analyzed and examined numerically beforehand. The primary theme of
this thesis study was to analyze and examine the response of abutment support
structures under static bridge loadings. Numerical analyses of MSEW abutment
support systems were performed with the finite element method, using the
NIKE3D computer program with time history analysis. In addition to selecting a
predefined span length, a reasonable type of superstructure and live load were
applied to the discretized models. As indicated by the analyses results, the response
of an MSEW abutment support system can be predicted. Recommendations for
making the use of MSEW systems to viably support bridge abutments were
included. This thesis study could consequently be extended to a series of analyses
on the abutment support systems.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed
m


ACKNOWLEDGEMENT
The concept of Mechanically Stabilized Earth Supported Abutments with
geosynthetic reinforced soil technology was initiated by Dr. Nien-Yien Chang. The
author would like to express his appreciation to Dr. Chang for providing the
concept and study plan for this thesis study, along with his supervision, guidance
and encouragement throughout the research. Moreover, Dr. Chang provided advice
and support throughout the entire process. Dr. Chang provided many suggestions
for improvements to creating the finite element models and this documentation. I
also wish to thank Dr. Trever S.C. Wang for providing the concept of bridge
design and MSE retaining walls during the NIKE/SSI Research Group
deliberation, and for his guidance and sharing of practical and technical knowledge
about bridge design concepts and MSE wall systems. Gratitude is also extended to
our research team members for sharing their knowledge and information.


CONTENTS
Figures................................................................ viii
Tables..................................................................... xi
Chapter
1. Introduction.........................................................1
1.1 Problem Statement.................................................. 1
1.2 Objective..................................................... 3
1.3 Scope of Study......................................................4
1.4 Engineering Significance.............................................6
2. Literature Revi ew...................................................7
2.1 Introduction....................................................... 7
2.2 Current Standard Method of Analysis .................................7
2.2.1 Limit Equilibrium Method.............................................9
2.3 Design of MSEW Supported Abutment in Accordance
with FHWA Design Guidelines ....;.............................. 18
2.3.1 Design of MSEW Supported Bridge Abutment............................18
2.4 Potential Failure Modes........................................... 25
2.4.1 Potential Failure Modes of MSE Wall............................... 25
2.4.2 Potential Failure Modes of Abutment on MSEW.........................26
2.5 Staged Construction Procedures..................................... 28
2.6 Study Case of Performance of MSEW Supported Abutment................29
3. Theoretical Background of the NIKE3D Program........................31
3.1 Implementation of the NIKE3D Program in the Study...................31
3.2 Solution Procedure..................................................34
3.3 Nonlinear Solution and Linear Solvers Algorithms....................36
3.4 Sliding Interfaces................................................ 36
3.5 Material Model......................................................38
3.5.1 Isotropic Elastic Model............................................ 38
3.5.2 Ramberg-Osgood Elastic-Plastic Model.............................. 39
4. Overview of Study...................................................42
4.1 Purpose......................................................... 42
4.2 Study Parameters....................................................46
4.2.1 NIKE3D Model Configurations...................'.....................46
4.2.2 Bridge Configuration with AASHTO LRFD Loadings......................51
4.3 Loading Configurations..............................................54
v


4.4 Material Model and Input Parameter................................59
4.4.1 Con crete Wal 1 F acing...........................................60
4.4.2 Foundation.................................................... 60
4.4.3 Inclusion..................................................... ...62
4.5 Sliding Interfaces and Boundary Conditions....................... 66
4.6 Study Items..................................................... 70
4.7 Data Analyses................................................... 71
4.7.1 Stresses and Resultant Stress Imparted on Concrete Wall Section...71
4.7.1.1 Earth Pressure Exerted on the Back Face of the MSEW Front Wall
and on Different Locations far from the Wall in the
Longitudinal Direction...........................................71
4.7.1.2 Tensile Inclusion Connection Stress.............................80
4.7.2 Bearing Pressure and Settlement................................ 81
4.7.3 Wall Deformation and Rotation....................................86
4.7.4 Inclusion Tensile Stress.........................................89
4.7.5 Potential Failure Surface..................................... 100
4.7.6 Comparison of NIKE3D Output and FHWA Design Guidelines..........100
4.8 Results.................................................. 109
4.8.1 Results of First Stage Analysis................................ 109
4.8.2 Results of Second Stage Analysis.................................109
4.9 Discussion.......................................................110
5. Summary, Conclusions, and Recommendations for Further Study......115
5.1 Summary........................................................ 115
5.2 Conclusions..................................................... 116
5.3 Recommendations for Future Study.................................118
Appendix
A. Longitudinal Inclusion Connection Stress....................... 120
B. Longitudinal Inclusion Stress, Vertical Inclusion Stress,
Rotation and Deflection of MSEW Front Wall ...................... 125
C. Contour Graphs for MSE Abutment..................................143
D. Contour Graphs for U-shaped MSEW with Widths
of Abutment Footings of 2.13m(7), 3.05m(10) and 3.96m(13) ...148
E. Contour Graphs of Inclusion Stress for U-shaped MSEW.............164
F. Locations of Output Data in MSE Abutment Model...................183
G. Locations of Output Data in MSEW Supported Abutment Model........189
H. Earth Pressure, Bearing Pressure and Inclusion Stress
in Accordance with FHWH Design Guidelines.......................195
vi


References
263
vii


FIGURES
Figure
2.1 External analyses: earth pressure and eccentricity.....................11
2.2 Variation of stress ratio with depth in a MSE wall.....................20
2.3 Location of potential failure surface for internal stability design
of MSE walls...................................................... 20
2.4a Distribution of stress for internal stability calculations.............21
2.4b Distribution of stress for external stability calculations.............21
2.5 Distribution of stress from concentrated vertical load for internal and
external stability calculations.......................................23
2.6 Location of external failure mechanisms for MSE wall...................24
2.7 Construction sequence for geosynthetic MSE walls
without reinforcement connection.................................... 27
4.1 a 3D visualization of MSE abutment................................. 43
4.1b 3D visualization of MSEW supported abutment.......................... 43
4.1 c 3D visualization of MSEW supported abutment (abutment wall and
inclusion)............................................................44
4.1 d 3D visualization of MSEW supported abutment without backfill...........44
4.2a Typical section of abutment.......................................... 47
4.2b Elevation MSE abutment with inclusion................................47
4.3 Elevation of abutment footings with different sizes....................49
4.4a Dimensions of MSEW in Elevation........................................50
4.4b Dimensions of MSEW in Plan.............................................50
4.5a Typical section of bridge.......................................... ...53
4.5b Elevation of abutment................................................ 53
4.6a Boundary condition of backfill in MSEW............................... 69
4.6b Boundary condition of MSEW in Elevation................................69
4.7 Summary of earth pressure behind back face of MSEW front wall
with bridge loadings versus wall height...............................73
4.8a Earth pressure at back face of MSEW front wall
versus bridge loadings............................................ 74
4.8b Earth pressure at section of middle of abutment footing
versus bridge loadings............................................ 74
4.8c Earth pressure at section of back face of abutment footing
versus bridge loadings............................................ 75
viii


4.8d Earth pressure at section of 6m from back face of MSEW front wall
versus bridge loadings...............................................75
4.9a Summary of longitudinal inclusion connection stress 2.13m(7)
abutment footing with bridge loadings versus wall height.............77
4.9b Summary of longitudinal inclusion connection stress 3.05m(10)
abutment footing with bridge loadings versus wall height.............78
4.9c Summary of longitudinal inclusion connection stress 3.96m(13)
abutment footing with bridge loadings versus wall height.............79
4.10 Inclusion connection stress of MSEW front wall
versus bridge loadings................................................79
4.11a Average settlement of backfill at bottom of MSEW
versus bridge loadings............................................ 82
4.11b Average settlement at top of backfill of MSEW
versus bridge loadings................................................83
4.11c Average settlement backfill at MSEW versus bridge loadings.............83
4.11 d Average settlement MSEW and abutment versus bridge loadings...........84
4.11 e Settlement of leveling pad MSEW versus bridge loadings............... 84
4.12a Bearing pressure underneath abutment footing versus bridge loadings.... 85
4.12b Bearing pressure at the bottom of MSEW versus bridge loadings..........85
4.12c Rotation of MSEW front wall versus bridge loadings.....................88
4.13 Summary of longitudinal deformation of MSEW front wall
versus bridge loadings.............................................. 88
4.14a Summary of vertical inclusion stress with 3.02m (7) footing
versus wall height....................................................91
4.14b Summaiy of vertical inclusion stress with 3.05m (10) footing
versus wall height....................................................91
4.14c Summary of vertical inclusion stress with 3.96m (13) footing
versus wall height.................................................. 92
4.14d Summary of longitudinal inclusion stress with 2.13m (7) footing
versus wall height....................................................92
4.14e Summary of longitudinal inclusion stress with 3.05m (10) footing
versus wall height................................................ ..93
4.14f Summary of longitudinal inclusion stress with 3.96m (13) footing
versus wall height................................................. 93
4.15a Selected locations for results for inclusions..........................94
4.15b Selected locations of inclusion layers for results in dimensions .....94
4.15c Location of potential failure surface for internal stability design with
width of abutment footing: 2.13m(7) and 100% bridge loadings........95
4.15d Location of potential failure surface for internal stability design with
width of abutment footing: 2.13m(7) and 150% bridge loadings........95
IX


4.15e Location of potential failure surface for internal stability design with
width of abutment footing: 2.13m(7) and 200% bridge loadings..........96
4.15f Location of potential failure surface for internal stability design with
width of abutment footing: 3.05m(10) and 100% bridge loadings...........96
4.15g Location of potential failure surface for internal stability design with
width of abutment footing: 3.05m(10) and 150% bridge loadings.........97
4.15h Location of potential failure surface for internal stability design with
width of abutment footing: 3.05m(10) and 200% bridge loadings.........97
4.15i Location of potential failure surface for internal stability design with
width of abutment footing: 3.96m(13) and 100% bridge loadings.........98
4.15j Location of potential failure surface for internal stability design with
width of abutment footing: 3.96m(13) and 150% bridge loadings.......... 98
4.15k Location of potential failure surface for internal stability design with
width of abutment footing: 3.96m(13) and 200% bridge loadings.........99
x


TABLES
Tables
4.1 Unit weights of each component in accordance with AASHTO..............54
4.2 Loading of dead load for superstructure...............................55
4.3 Loading of live load for superstructure...............................57
4.4 Inputted material parameters for the detailed study...................59
4.5 Range of value for the modulus of elasticity E for selected soils
(after Bowles, 1996)........................................... ....61
4.6 Range of value for the Poissons ratio (after Bowles, 1996)...........61
4.7 Physical and mechanical properties of commercially available
geogrid (after Koemer, 1986).........................................63
4.8 Some values of Poisson's ratio for elastically isotropic solids
(after Ruoff, 1972)............................................. 63
4.9 Typical values of compressive wave velocity and shear wave velocity
(after Das, 1993)....................................................65
4.10 Values for the Poissons ratio v (after Bowles, 1996).................65
4.11 Summary the results of earth pressure and bearing pressure based on
FHWA design guidelines for MSEW supported abutment..................101
4.12 Summary the results of tensile inclusion stress with 2.13m
and 3 .05m footing based on FHWA design guidelines for
MSEW supported abutment.............................................102
4.13 Summary the results of tensile inclusion stress with 3.96m footing
based on FHWA design guidelines for MSEW supported abutment.........103
4.14 Summary the output results of earth pressure and bearing pressure
based on finite element model with NIKE3D program...................104
4.15 Summary the results of tensile inclusion stress with 2.13m and 3.05m
footing based on finite element model with NIKE3D program...........105
4.16 Summary the results of tensile inclusion stress with 3.96m footing
based on finite element model with NIKE3D program...................106
4.17 Summary the results of settlement of MSEW with MSE abutment..........107
4.18 Comparison the results based on FHWA design guidelines and
NIKE3D model for MSEW supported MSE abutment........................108
xi


1.
Introduction
1.1 Problem Statement
Mechanically Stabilized Earth Wall (MSEW) Supported Abutment Geosynthetic
Reinforced Soil (GRS) technology has been widely used in the construction of
MSEW, which can be found in many places, such as highways, and even in remote
locations like mountain areas, where they have performed excellently.
MSEW, classified as internally stabilized walls, have been used to retain soil for
the past several decades. An MSEW features geosynthetic reinforcement in the
backfill soil and wall facing. Due to the cost effectiveness, MSEW are superior in
competition with other alternatives, such as conventional reinforced concrete
retaining structures, at sites requiring wall heights in excess of 2m. The use of
MSEW results in savings on the order of twenty five to fifty percent in comparison
with traditional reinforced concrete retaining walls. Moreover, another advantage
of MSEW is the possibility of less soil mass excavation.
To increase the usage of MSEW, an MSE system has been used to support bridge
abutments, and this type of structural abutment support system has performed well,
without any observed bridge damage. The beneficial effects of this usage in
highway projects are: decreasing bridge spans to save construction time and
material, minimizing right-of-way for embankment, and increasing the valuable
1


space for traffic, as well as other environmental constraints. On the other hand,
abutment with spread footing on MSEW is evaluated as a cost-effective combined
system. Recently the Standard Specification of AASHTO, 16th Edition, and
AASHTO LRFD Standard Specifications for abutment on MSEW has been added
and applied on construction projects. However, no specific AASHTO guideline is
presently available for MSE abutment on U-shaped MSEW and we have little
experience with design and construction of this type of MSE structural system. At
this stage, many unknown details of using MSEW as bridge supporting structures
exist. Many highway engineers have wrongly believed that a heavily loaded spread
footing would cause large settlements in even the most densely compacted granular
soil masses, resulting in differential settlement, which could cause distress. The
Center for Geotechnical Engineering Science at the University of Colorado at
Denver has made its best effort to investigate the response of abutments on U-
shaped MSEW subject to different types of loading with numerical analysis. One
could hope that this research study will lead to the development of a complete and
reliable MSEW supported abutment system. This thesis study was aimed towards
the evaluation of the response of MSEW as abutment supporting structures by
applying the dead load of typical superstructure and AASHTO LRFD HL93
standard live load for bridge. It is also the interest of this study to examine the
effect of the size of abutment footings on the reinforcement of MSEW. With the
2


result obtained from this study, and future efforts, MSEW as abutment supporting
structures can be designed effectively, and be constructed safely and cost
efficiently.
1.2 Objective
The objective of this thesis study was to examine the applicability of U-shaped
Mechanically Stabilized Earth Wall Supported MSE Abutments under static
loadings for Highway Bridge. The study was to demonstrate the ability to construct
an U-shaped MSEW supporting a full size MSE bridge abutment over a rigid
foundation, as solid as bedrock. In addition, the performance of the MSE system
under various loading schemes, including superstructure loading with composite
and non-composite dead load and AASHTO HL 93 live loads, was investigated.
A numerical analysis involves utilization of a finite element computer program,
NIKE3D, to solve the proposed problem. Therefore, the inductive procedure was
adopted to determine an effective configuration of the bridge abutment on the
MSEW prototype model. Once the configuration of the wall was set, the model
was discretized into finite elements along with material properties such as rigid
wall facing, inclusion, foundation, and backfill with boundary conditions. Dead
load of the superstructure and Standard Highway live load, HL93, were imposed
into the prototype as a pressure load on an abutment seat. Data output by NIKE3D
was analyzed to interpret the response of the MSE abutment support system.
3


Conclusions regarding loading the MSE system were drawn from all limited cases
analyzed. The results of the MSE system were compared with earlier studies for
design guidelines for MSEW supported abutment in Publication of Federal
Highway Administration (FHWA), Mechanically Stabilized Earth Walls and
Reinforced Soil Slopes Design and Construction Guidelines. The available results
indicate that the MSE system has the potential to enhance the capacity of GRS.
1.3 Scope of Study
The scope of this thesis study is outlined below:
Determination of wall configuration, specifically the mechanically
stabilized earth wall height and abutment wall height, for the finite element
model in accordance with AASHTO LRFD Specifications.
Selection of road width, thickness of asphalt, dimensions of essential
components such as bridge rail, and specification of bridge span length for
loading.
Selection of superstructure type, such as girder type, and standard
AASHTO Highway Live Load, HL93, for loading on abutment seat.
Selection of material properties of components for stabilized earth walls
and abutment.
4


The inclusions with the 30 cm spacing, applied on the abutment, were
analyzed separately to determine the earth pressure on the back face of the
abutment wall and the self weight of backfill pressure on the U-shaped
MSEW in the second stage of the study.
Discretization of the three models: 2.13 m (7-0), 3.05 m (10-0) and
3.96 m (13-0) abutment footing seat, on the U-shaped MSEW with 4.6 m
wall height. The inclusions with the 40 cm spacing were attached to the
back face of the MSEW front wall and two parallel, rigid- sided walls
back-to-back.
To show wall responses such as earth pressure thrust and location of the
thrust imparted, bearing pressure on foundation, wall face displacement,
rotation, inclusion tensile stress, inclusion connection stress and settlement
from the output data of the Finite Element model.
Determination of earth pressure thrust, the location of thrust, bearing
pressure and inclusion tensile stress in accordance with FHWA Design
Guidelines.
Comparison between the results from NIKE3D finite element model and
results from traditional calculations in accordance with FHWA Design
Guidelines.
Recommendations for future studies
5


1.4 Engineering Significance
The engineering significance deduced from the conclusions of this thesis study is
included in the following:
Responses of U-shaped MSEW supported MSE abutment systems could be
evaluated via the NIKE3D program.
Optimized MSEW system could be a feasible alternative to conventional
systems used as abutment support structures.
One could use the dead load of the superstructure and HL 93 live load
along with the span length of the bridge being 48.8 m (160-0) as index to
predict wall performance with a specific size of abutment footing.
6


2.
Literature Review
2.1 Introduction
In the literature review, five items were discussed. First of all, the Limit
Equilibrium method for design and analysis of traditional MSE walls was reviewed
and discussed. The minimum standard requirements are for the stability of MSE
walls was stated.
The second item considered the design and analysis of MSEW supported
abutments in accordance with FHWA design guidelines. In addition, Potential
Failure Modes and construction sequence of full height rigid facing retaining walls
were included in the third and fourth items, respectively. The fifth item considered
a case study of the performance of an MSE abutment supported structure with full
height rigid facing in Colorado, which was instrumented in monitoring its
performance.
2.2 Current Standard Method of Analysis
In the last decade, a general agreement has been reached that a complete design
approach should consist of Working Stress Design, Limit Equilibrium analyses,
and Deformation Evaluations.
Current analysis of MSE retaining walls consists of determining the geometric and
reinforcement requirements to prevent internal and external failure using Limit
7


Equilibrium methods. It is limited to MSE walls having a near-vertical face, and
uniform length reinforcements.
A Limit Equilibrium analysis consists of a check of the overall stability of the
structure, including external and internal types of stability.
External stability involves the overall stability of the stabilized soil mass,
considered as a whole, and is evaluated using slip surfaces outside the stabilized
soil mass. External stability evaluations for MSE structures treat the reinforced
section as a composite homogeneous soil mass and evaluate the stability according
to conventional failure modes for classical gravity type wall systems.
Internal stability analysis consists of evaluating potential slip surfaces within the
reinforced soil mass. Internal stability is treated as a response of discrete elements
in a soil mass. For internal stability, evaluation determines the reinforcement
required, principally in the development of the internal lateral stress, to locate the
most critical failure surface. This suggests that deformations are controlled by the
reinforcements rather than total mass, which appear inconsistent given the much
greater volume of soil in such structures. Moreover, with respect to lateral wall
displacements, no method is presently available to definitely predict lateral
displacements, most of which occur during construction. Therefore, deformation
analyses and working stress analysis are generally not included in current practice.
8


2.2.1 Limit Equilibrium Method
The external stability and internal stability should meet the minimum requirements
of all the stability of MSE walls.
For external stability, the essential items such as vertical bearing pressure, earth
pressure for overturning, sliding stability and overall stability should be
determined. If following the steps as below, all the items should be acquired. The
current limit equilibrium analysis uses a coherent gravity structure approach to
determine external stability of the whole reinforced mass, similar to the analysis
for any conventional or traditional gravity structure. The state of stress for external
stability is assumed to be equivalent to a Coulomb state of stress with a wall
friction angle 0 equal to zero.
Stability computations for walls with a vertical face are made by assuming that the
MSE wall mass acts as a rigid body with earth pressures developed on a vertical
pressure plane arising at the back end of the reinforcements.
Equation 2.1 calculates the active coefficient of earth pressure for vertical walls
with a horizontal backslope.
Ka = tan2 (45 q>/2) (2.1)
Vertical stresses were computed at the base of the wall defined by the wall height.
It should be noted that the weight of any wall facing is typically neglected in the
9


calculations. Equation 2.2 gives calculation steps for the determination of vertical
bearing stress for step 1.
Calculate FT = a{

Calculate eccentricity of the resulting force on the base by summing the moments
of the mass of the reinforced soil section about the centerline of mass.
Noting that R in figure 2.1 must equal the sum of the vertical forces on the
reinforced fill, this condition is found by Equation 2.3 for step 2.
Ft (cos/?) % Ft(sinP) l/2 V2 (%)
e -
V] + V2 + FT sin P
(2.3)
In this study, only horizontal backslope is considered, so p = 0 should be applied
on all general formulas with a backslope condition.
Figure 2.1 illustrates external stability for regular MSE walls.
Calculate the equivalent uniform vertical stress on the base by using Equation 2.4
for the final step.
Vj + V2 + Ft sin P
cr =
L-2e
(2.4)
This approach, proposed originally by Meyerhof, assumes that eccentric loading
results in a uniform redistribution of pressure over a reduced area at the base of the
wall. This area is defined by a width equal to the wall width less twice the
eccentricity.
10


HolJtrto! Bodskpt With Iwffk Svrtftrgt
'jiriTunTui
Assuwtf for towing apoclty
cot1 onr oft igktooUslotHty
coops.
I pi -.-i Aisunxd tor wturolng itcunirtcfyi
* HllHl sliding l pjlkti rtslsiom
coops.
Figure 2.1 External analyses: earth pressure and eccentricity
11


For checking Sliding Stability, the minimum safety factor of 1.5 must be met.
Horizontal resisting force is determined by Equation 2.5
rc, Z horizontalresistingforces Y,Pr
i 5 ^ 1.5 (21
s Z horizontaldrivingforces
Any soil passive resistance at the toe due to embedment is ignored due to the
potential for the soil to be removed by natural or manmade processes, such as
erosion or utility installation, during its service life. The shear strength of the
facing system is also conservatively neglected.
Additional surcharge loads may include live and dead load surcharges.
Calculate the driving force using Equation 2.6
Pd=FH=FT (2.6)
Calculate the resisting force per unit length of wall given using Equation 2.7
Pr = (V,+V2+Ft)*p (2.7)
where p= frictional properties
Overall stability is determined using rotational or wedge analyses, as appropriate,
which can be performed using a classical slope stability analysis method. The
reinforced soil wall as a rigid body is considered, and only failure surfaces
completely outside a reinforced mass are considered. For simple structures with
rectangular geometry, relatively uniform reinforcement spacing, and a near vertical
face, compound failures passing both through the unreinforced and reinforced
12


zones will not generally be critical. If the minimum safety factor is less than the
usually recommended minimum FS of 1.3, increase the reinforcement length or
improve the foundation soil. In general, the MSE wall designer never performs
overall stability. Evaluations of this type of analysis are the responsibility of
Geotechnical engineers.
For internal stability potential failure surface, stress on tensile inclusion and
pullout capacity are the primary concerns.
The potential failure surface in a simple reinforced soil wall is assumed to coincide
with the maximum tensile force line that is the locus of the maximum tensile force
in each reinforcement layer. The shape and location of this line is assumed to be
known for simple structures. This maximum tensile force surface has been
assumed to be approximately linear in the case of extensible reinforcements shown
in figure 2.3, and passes through the toe of the wall. Dividing the reinforced mass
in active and resistant zones is required, and then an equilibrium state should be
achieved for a successful design. When failure develops, the reinforcement may
elongate and be deformed at its intersection with the failure surface. As a result,
the tensile force in the reinforcement would increase and rotate. Consequently, the
component in the direction of the failure surface would increase and the normal
component may increase or decrease. Elongation and rotation of the
reinforcements may be significant with geosynthetics.
13


FHWA indicated that the maximum tensile force is primarily related to the type of
reinforcement in the soil mass, which is a function of the modulus, extensibility
and density of reinforcement. A relationship between the type of the reinforcement
and the overburden stress has been developed as shown in figure 2.2. The resulting
K/Ka for extensible reinforcement ratio is unity independent with wall height.
This graphical figure was prepared by back analysis of the lateral stress ratio K,
where stresses in the reinforcements have been measured and normalized as a
function of an active earth pressure coefficient, Ka. The ratios shown in figure 2.2
correspond to values representative of the specific reinforcement systems that are
known to give satisfactory results, assuming that the vertical stress is equal to the
weight of the overburden and any surcharge loads. The lateral earth pressure
coefficient K is determined by applying a multiplier to the active earth pressure
coefficient. The active earth pressure coefficient is determined using the Rankine
equation.
internal failure of an MSE wall can occur in two different ways. Firstly, the tensile
forces in the case of rigid inclusions become so large that the inclusions elongate
excessively or break, leading to large movements and possible collapse of the
structure. This mode of failure is called failure by elongation or breakage of the
reinforcements. Secondly, the tensile forces in the reinforcements become larger
than the pullout resistance, the force required to pull the reinforcement out of the
14


soil mass. This increases the shear stresses in the surrounding soil, leading to large
movements and possible collapse of the structure. This mode of failure is called
failure by pullout. The process of sizing and designing to preclude internal failure,
therefore, consists of determining the maximum developed tension forces, their
location along a locus of critical slip surfaces, and the resistance provided by the
reinforcements both in pullout capacity and tensile strength.
Stresses on tensile inclusion and pullout capacity of inclusion are the major items
in the checklist for internal stability.
Calculate, at each reinforcement level, the horizontal stresses cth along the
potential failure line from the weight of the retained fill yjZ plus, if present,
uniform surcharge loads q, and concentrated surcharge loads Actv and Aoh, as found
by Equation 2.8.
Acth = Kr Aav +Aah (2.8)
where av =7r*Z +02+q+Aov
where Z is the depth referenced below the top of wall, Aav is the increment of
vertical stress due to concentrated vertical loads using a 2V: 1H pyramidal
distribution.
Calculate the maximum tension in each reinforcement layer per unit width of wall
based on the vertical spacing S, from Equation 2.9
T max = tfH*Sv (2.9)
15


Calculate internal stability with respect to breakage of the reinforcement.
Stability with respect to breakage of the reinforcement is provided by Equation
2.10.
_ T max
T >
(2.10)
where Rc, is the coverage ratio b/Sh, with b the gross width of the reinforcing
element and Sh is the center-to-center horizontal spacing between reinforcements.
Ta is the allowable tension force per unit width of the reinforcement.
The connection of the reinforcements with the facing shall be designed for Tmax,
under all conditions.
Pullout Failure is one of the common problems for designing MSE walls.
The minimum required embedment length in the resistance zone beyond the
potential failure surface could be determined to satisfy stability with respect to
pullout of the reinforcements by Equation 2.11
Le>
\5T
C*F yZpRca
(2.11)
where:
FSp0= Safety factor against pullout > S.
Tmax = Maximum reinforcement tension.
C = 2 for strip, grid, and sheet type reinforcement,
a = Scale correction factor.
16


F = Pullout resistance factor.
Rc = Coverage ratio.
yZp = the overburden pressure, including distributed dead load surcharges,
neglecting traffic loads.
Le = the length of embedment in the resisting zone. Note that Equation 2.12 then
determines the total length of reinforcement, L, required for internal stability.
L=La+Le (2.12)
Figure 2.3 shows the location of potential failure surface for internal stability
design with extensible reinforcement. Calculate the length of inclusion in the
active zone from, Equation 2.13.
L.=(H-Z) tan(45-|) (2.13)
where Z is the depth to the reinforcement level.
Connection Strength is one of the major keys affecting the wall displacement. In
the model, geogrid reinforcements were assumed to be structurally connected to
the rigid wall face by casting a tab of the geogrid into the wall facing and
connecting to the full-length performance of geogrid with a botkin joint. However,
no assumption has been made not to cast connections into concrete, due to
potential chemical degradation.
Settlement Estimate is the major concern of the design of MSE walls. Differential
settlement can cause wall collapse. Normally, conventional settlement analyses
17


should be carried out to ensure that immediate, consolidation, and secondary
settlement of the wall are less than the performance requirements of the project.
2.3 Design of MSEW Supported Abutment
in Accordance with FHWA Design Guidelines
Current design methodologies use Limit Equilibrium methods as the simplified
design guidelines for design and analysis of MSEW supported abutments. The
major difference between MSEW supported abutments and MSE retaining walls is
that the former not only requires adequate capacity for the regular retaining wall
loadings, but also supports the bridge loads transferred from the abutment seat.
2.3.1 Design of MSEW Supported Bridge Abutment
MSEW bridge abutments are designed as rectangular MSE walls fully supporting
the bridge load at the top. The design procedures for MSE walls taking account of
surcharge loads for external and internal stability analysis have been outlined in
section 2.2. The same type of procedure is used for MSEW supported bridge
abutment structures in accordance with FHWA design guidelines.
The distribution of concentrated horizontal dead loads within and behind the
reinforced soil mass is determined by the vertical component of stress
corresponding to depth. The bridge dead loads and live loads shall be incorporated
into the internal and external stability design by using a simplified uniform vertical
distribution of 2 vertical to 1 horizontal within the reinforced soil mass. Calculate
the horizontal stress ah at each level by the following Equation 2.14.
18


Qh = K(y*Z+Aav) +Acih
(2.14)
where Aav is the increment of vertical stress due to the concentrated vertical
surcharge Pv, assuming a 2V:1H pyramidal distribution. Aoh is the increment of
horizontal stress due to the horizontal loads Ph as calculated. y*Z is the vertical
stress at the base of the wall or layer in question due to the overburden pressure.
Concentrated horizontal loads at the top of the wall shall also be distributed within
as illustrated in figures 2.4a and figure 2.4b. Determination of the vertical
component of stress with depth within the reinforced soil mass is illustrated in
figure 2.5.
If concentrated dead loads are located behind the reinforced soil mass, they shall
be distributed in the same way as would be done within the reinforced soil mass.
The vertical stress distributed behind the reinforced zone in this way shall be
multiplied by ka to determine the effect this surcharge load has on external
stability. The concentrated horizontal stress distributed behind the wall can be
taken into account directly. The combination of loads with using the supeiposition
principle should be applied to evaluate external and internal wall stability.
Depending on the size and location of the concentrated dead load, the location of
the boundary between active and resistance zones may be adjusted as shown in
figure 2.3. In the study, the MSE supported abutment is assumed to be located on
19


c
Docs not include polymer strip reinforcement
Figure 2.2 Variation of stress ratio with depth in a MSE wall
Zon* f*axt*ru*rR iVtss
for iih c fc bettor }0 or nor* fron th vtrtieeU
, -tonw- V^U>nl-g Xn>r'<4- Bi coU- i - ton ts *M8 I test <+ > -*jgn
t* ,T_* I tan t* ->! t* W-JIJ+ co*<*+ *-S8iJ
atK %* $
Etensibl Remforcementa
Figure 2.3 Location of potential failure surface for internal stability design of
MSE walls
20


$
If*?. ? <>
F. : laurel fere* due to
1 *Ofln
FjJ ItUftl force due to
traffic surcharge
Pjjj! lelarpl force due ta
superstructure or ether
teegntreud lateral loads
es eccentricity of feed on footing
e. DuvitoUsn pf Supsi for Internet Stability Calculations.

Figures 2.4a and 2.4 b Distribution of stress for internal and external stability
calculations
21


a firm foundation with adequate bearing capacity. This eliminates one of the
common problems of excessive settlement of retaining walls. The strength of the
MSEW supported abutment is required to increase by the inclusion of horizontal
tensile reinforcement within the MSE backfill due to applied high loadings. The
reinforced backfill was chosen as homogeneous saturated and cohesionless
material. The material exhibits improved shear and compressive strengths. The
inclusions, as horizontal elements, are placed between successive layers of
compacted soil to provide tensile reinforcement to restrain soil deformation in the
direction of reinforcement. The behavior of the interaction of inclusions and
backfill was similar to that of the relationship between concrete and steel
reinforcement in the reinforced concrete. The backfill soil was assumed incapable
of carrying any tensile stress and only carried compression. All the tensile stress
was carried by the inclusions. The advantages of each material seemed to
compensate for the weaknesses of the other. The great shortcoming of backfill soil
is its lack of tensile strength, but the tensile strength is one of the great advantages
of the inclusions. Backfill and inclusions work together in MSE supported systems,
and act as a unit to resist force. In the design guidelines, the wall facing is assumed
not to be structural element even though it connects with the inclusions and makes
the MSEW structure system as a complete unit for bridge abutment. Moreover, the
other function of wall facing
22


vnrni P, tMrt|y snom coo**
b, victh of oppllto loop, fee footings tnleh ioos< It.f., fcrl<>9 WutMDt lootings)* |*t I;ivltn4 ( by riduclrtg It ty }'( Vrttr *" It IHB
ocsmr Wrlty e iM resting toes (}.. fc, -2s*I.
L Ungtn f ftnlnt
r. Loop p*r I lover mi or P, loop on isoiotoo rcctonguior tooting or point loop
li* eoptn *n*r* oftoettvo *l*ih inivrsvcts bock of *0)1 toeo it* |>
(um Thy inenent y*r*ieol strm on to 1h igrchorg* lost hoi no
Inflvvnci on jirtiics wet to ivolutt* Intornsl llsblllty If tno
lurchsrf* loop li Jocbtit bohlnt Iht rilntoTtit toll *tt< tor out of no I
nstlllijr. Q)iw>i iht sprowgi hn no Inflwtnet 'lf It Is Jeoelsc
cviilM 1h actios ism gshlM tin wll>
Figure 2.5 Distribution of stress from concentrated vertical load for internal
and external stability calculations
23


U) Sliding
| Figure 2.6 Location of externa) failure mechanisms for MSE wall
24


of retaining the soil in place is ignored. Reinforced soil mass is assumed capable of
standing by itself without wall facing.
2.4 Potential Failure Modes
2.4.1 Potential Failure Modes of MSE Wall
Common potential failure modes of MSE retaining walls are shown in figure 2.6.
There are three general categories of failure modes as follows: External failure
modes, Internal failure modes and Facing failure modes. For external failure
modes facing unit, geosynthetic reinforcement and reinforced soil backfill is
considered as a whole. Bearing capacity failure, base sliding, overturning about the
toe, settlement, and deep-seated stability are common external failure modes.
Internal failure modes always relate to modes of pullout, tensile over stress, and
internal sliding that occur on the inclusions within the reinforced soil mass. For the
third failure mode facing failures modes include connection failure, column shear
failure, and toppling failure. The shear capacity of the facing can be developed
through interface friction, shear key, or mechanical connectors between concrete
block facing or inclusions and facing. The induced interface shear force subjected
to static loading is to be compared with available shear capacity in determination
of wall stability. Likewise, the flexibility of MSE walls should make the potential
for overturning failure very low. However, overturning criteria aid in controlling
lateral deformation by limiting tilting and, as such, should always be satisfied.
25


The foundation soil is primary key of bearing capacity of failure. Two modes of
bearing capacity failure exist; general shear failure and local shear failure. General
Shear To prevent bearing capacity failure, it is required that the vertical stress at
the base calculated with the Meyerhof distribution does not exceed the allowable
bearing capacity of the foundation soil determined. Local Shear -- Local shear is
characterized by a squeezing of the foundation soil when soft or loose soils exist
below the wall. A rigid foundation system is assumed throughout the study.
Therefore, the local shear failure does not need to be considered.
2.4.2 Potential Failure Modes of Abutment on MSEW
Preventing collapse is the main concern of any structure design. However, failure
of abutment footings can also develop gradually from excessive, long-term
settlement. The degree of settlement, such as differential settlement, can cause
varying degrees of damage, such as bumps, cracks in the superstructure, abutment
and wing wall, misalignments, utility line damage and damaged joints. Excessive
settlement can severely crack the abutment, or it can overstress superstructure
elements such as girders and deck slabs. Since bridges are highly visible, cracking
may cause public reaction. In this study, settlement of abutment footings is one of
the major considerations because excess settlement could cause the bridge failure.
Besides settlement issue, all potential failure modes of MSE wall in section 2.4.1
26


"FOR TEMPORARY FORM SYSTEM. SEE DETAIL MS SHEET.
I SET FORM OH COMPLETES) LIFT.
TAX
GEOTEXJJie
CEOSYHTHETK-

BACXFfU
UNROLL GEOSYNTBETK ANO POSTION fl
SO THAT A r- THE FORM IF A GEOGRID IS USED FOR THE
GEOS YNTHETK REINFORCEMENT. POS1DOH
GEOTEXTRE TO PREVENT BACFFI1
FROM SPRUNG THROUGH GEOGRID OPENMGS
. PLACE THE BACKERt IMTK THE
BATXFRL tS OP TOHAtf OF THE
PC CURED VERTKAi GEOS YN WE DC
LAYER SPAONG
V. PLACE A WINDROW TO SUGHTlY
GREATER THANFVUirrHEIGHT
against the form
& PLACE THE GEOSYHTUETK'TAR'OVER
THE WINDROW AND LOCK INTO PLACE
WITH BACKFRL
& COMPLETE BACXERlHGUm
THE COMPACTED BACRFTU LAYER
THKXNESS IS EQUAL ID WE REOUStED
VERTICAL GEOSYMMEHCLAYERSPACW&
7. RESET THE FORM AND REPEA T
THE SEQUENCE
GEOSYNTHETIC WALL
CONSTRUCTION SEQUENCE
< FORMING TWO LAYERS AT A TIME MU. HELP MAM Taw WE WALL FACE BATTER
Z CONSTRUCTION JUSTS M WE CONC FASCIA BASE SHAU BE SPACED AT UDOO FT. MAR
X FOR DETARS OF EXPANSION JOINTS M CONC FASCIA SEE STAND. PUD! 0-Jfc
Figure 2.7 Construction sequence for geosynthetic MSE walls without
reinforcement connection
27


should be included and considered for this bridge support application.
2.5 Staged Construction Procedures
By the staged construction method, potential damage caused by differential
settlement between facing and inclusions and between cohesionless soil and facing
can be minimized. In the staged construction procedure, good compaction of the
backfill is essential, and important for allowing relatively large outward lateral
displacement to occur at the wall. Sufficiently large tensile strain can be developed
in the inclusion. The cast-in-place rigid facing should be constructed after primary
deformation of backfill and settlement of the foundation. Laboratory tests have
been performed which confirmed that MSE walls with rigid facing can support
large vertical and lateral loads acting at the crest of the wall without unacceptable
deformation. For construction ease, a final uniform length is commonly chosen,
based on the maximum length required. The following construction sequence for
Geosynthetic walls with Cast-In-Place concrete facing is suggested in accordance
with FHWA design guidelines.
1. Preparation of subgrade.
2. Placement of a leveling pad for concrete facing.
3. Pouring concrete facing with connection elements on the prepared leveling
pad.
28


4. Placement and compaction of backfill on the subgrade to the level of the first
layer of reinforcement.
5. Placement of the first layer of reinforcing elements on the backfill.
6. Placement of the backfill over the reinforcing elements to the level of the next
reinforcement layer and compaction of the backfill. The previously outlined
steps are repeated for each successive layer.
7. Construction of traffic barriers and copings in the final construction sequence.
Standard drawing from WSDOT of the construction sequence for geosynthetic
MSE walls without reinforcement connection is illustrated in Figure 2.7.
2.6 Study Case of Performance of MSEW Supported
Abutment
Two GRS bridge abutments were constructed to support the Bobtail Road Bridge,
a 36- m span steel arched bridge, in Black Hawk, Colorado in 1997. The abutment
with full height rigid facing constructed by Yenter Companies were situated along
a hill slope on the east and west sides of the creek. Each GRS abutment consisted
of a two-tier rock-faced geosynthetic-reinforced soil mass, with two square
footings on the lower tier, and a strip footing on the upper tier. The abutments were
constructed with the on-site soil and reinforced with layers of a woven geotextile at
a vertical spacing of 0.3 m. The front edge of each reinforcement sheet was placed
between vertically aligned rocks at the wall face to form a frictional connection
between the reinforcement layers and the facing rocks. The base of the reinforced
29


soil mass was located at different depths in the excavated stiff soil. The lower part
of the GRS abutment was embedded in the ground, and the upper part was above
ground. Only the portion above ground was constructed with rock facing. The front
edge of the square footings was 1.5 m behind the rock-faced wall. The square
footings were constructed in two stages. The bottom 0.6 m thickness of the
footings was first constructed to serve as a reaction pad for pre-loading. The top
1.05 m thickness was poured and leveled after pre-loading was completed. In
October 1997, the GRS bridge abutments were pre-loaded. The main purpose of
the preloading was to limit the post-construction settlement of the GRS abutments
under service conditions. The abutment not only was instrumented to monitor
performance during preloading and subsequent reloading operation, but also to
monitor the settlement of the footings, the lateral deformation of the rock-faced
wall, and the strains in the geotextile reinforcement. For this bridge support
application, the additional cost of placing the reinforcement between each layer of
fill did not add significantly to the cost of construction. This closer spacing,
combined with high strength reinforcement, and well-compacted road base, forms
a strong composite mass more suitable for bridge support.
30


3. Theoretical Background of the NIKE3D Program
3.1 Implementation of the NIKE3D Program
in the Study
NIKE3D, a finite element computer program, is the primary numerical tool of
analysis used to perform static response of the U-shaped MSEW as the bridge
supporting structure in this study. The benefit of finite element analysis is its
ability to analyze the structure under bridge loading without wasting a lot of time
and money. For example, it saves using a number of instruments such as strain
gages for vertical settlement and inclusion tensile stress. In addition, full scale
testing takes a long time to produce data to be analyzed.
To create these detailed finite element models using about 2,000 elements for each
model required three different computer programs: pre-processor TRUEGRID,
finite element program NIKE3D, and post-processor Griz. NIKE3D has been
used extensively to conduct research at the Center for Geotechnical Engineering
Science, University of Colorado at Denver. A preprocessor, TRUEGRID and a
post-processor, GRIZ, were used with NIKE3D to perform the NIKE3D analysis
efficiently. Moreover, NIKE3D has been used at the Lawrence Livermore National
Laboratory for the past twenty years to study static and dynamic response of
structures undergoing finite deformations. NIKE3D is a nonlinear, implicit, three-
31


dimensional finite element code for solid and structural mechanics, computer
program. The major task of the program is to analyze the finite strain, static and
dynamic response of structures comprising inelastic 8-node solids, 4-node shell
and 2-node beams. In addition, the other powerful function of this program is that
contact-impact algorithms permit gaps, frictional sliding and mesh discontinuities
along material interfaces. The resulting system of simultaneous linear equations
uses element-by-element methods for which case bandwidth minimization is
optional. In this analysis, solid elements and shell elements have been chosen in
the model.
The model is implemented with four different kinds of solid elements: abutment
wall, backfill, rigid MSE wall face, foundation soil, and one kind of shell element:
the inclusions. The NIKE3D models are built by 8-node solid elements for the first
four structural elements and 4-node shell element for inclusions. The sliding
interface algorithm has also been extended to shell elements and modified to
increase its reliability and accuracy.
NIKE3D utilizes implicit time integration, making it most efficient for static and
low rate dynamic problems. Using many efficient elements, the analyst may
describe the complex geometries typical of large finite element models accurately.
NIKE3D enhances the models overall coherence, simplicity and detail.
Nonlinearities may be introduced to an analysis in different ways. Geometric
32


nonlinearities involve large deformations and rotations. Contact between two
bodies introduces a nonlinear process when a separation is allowed and contact
areas change. NIKE3D allows the analyst to consider plasticity, creep and thermal
distortion, introduce nonlinearities, and nonlinear phenomenon.
Analyses with NIKE3D typically involve loadings applied in several increments,
or steps to accurately resolve geometric or material nonlinearities. Within each
step, a nonlinear solver drives the iterative process used to satisfy equilibrium.
Within each equilibrium iteration, a system of linear equation must be solved.
Several nonlinear and linear solvers are available.
A preprocessor, TRUEGRID, developed by XYZ Scientific Applications Inc., is a
three-dimensional, multi-block, structured mesh generator for finite element
simulation codes that started with the INGEN mesh generator. INGRID mesh 1
generator came next in the line developed at Lawrence Livermore National
Laboratory. TRUEGRID incorporates almost all of INGRIDs features with
improved and new features that go far beyond INGRIDs scope. One of the most
important features that distinguish TRUEGRID from the old mesh generator,
INGRID, is interactivity. Besides mesh generation, TRUEGRID can also specify
loading, element type, boundary condition and sliding faces for NIKE3D analysis.
The output file from TRUEGRID becomes the input file for NIKE3D. TRUEGRID
33


is a non-unit program, so the units should be consistent throughout the whole
analysis. SI units were chosen in this study.
A Processor, GRIZ, is an interactive application for visualizing finite element
analysis results on three-dimensional unstructured grids to help to extract results
from large models. Lawrence Livermore National Laboratory also developed
GRIZ. The output file from NIKE3D becomes the input file for GRIZ. Result can
be directly visualized on the terminal with GRIZ after the analysis. One important
feature is that the chosen material could be displayed with chosen results such as:
displacement, stress, strain, etc. in GRIZ to minimize the graphic display. Another
useful function is to create ASCII format files that contain the selected results from
GRIZ for further analyses.
3.2 Solution Procedure
In NIKE3D, spatial discretization is accomplished with solid, beam and shell
elements. Eight node solid elements are integrated with a 2x2x2 point Gauss
Quadrature rule. Four node shell elements use 2x2 point Gauss integration in the
plane, one of many available schemes for integration through the thickness that
provides finite strain and thinning behavior. The majority of the material models in
NIKE3D are based on incremental formulations. In the solid elements, these
materials use the Green-Naghdi stress rate to integrate stress objectively.
34


NIKE3D is based on an updated Lagrangian formulation. During each load step,
NIKE3D computes the nodal displacement increments, which produces a geometry
that satisfies equilibrium at the end of the step. This involves, the solution of a set
of nonlinear equations. Several nonlinear solvers based on the Newton methods are
available. The nonlinear solution process in each is iterative. Equilibrium is
obtained when one or more user defined convergence tolerances are met.
During each equilibrium iteration of the nonlinear solver, NIKE3D recomputes
internal and external forces and the global stiffness matrix using the current
estimate of geometry. These forces are combined to form the right hand side or
residual vector. The system of linear equations [K] {Au} = {R} formed by the
stiffness matrix {K} and the right hand side vector {R} is then solved to produce a
new displacement increment {Au}. Solution of this linear system consumes the
majority of the computational effort in a large NIKE3D analysis. Both direct and
iterative linear solvers are available.
After obtaining updated displacement increments, the displacement, energy and
residual norms are computed and equilibrium convergence is tested using the user
defined tolerances. These norms are optionally printed to the terminal so that the
user can monitor the progress of the equilibrium iteration process. Once
convergence is obtained, displacement and stresses are updated, output is
optionally generated and NIKE3D proceeds with the next load step. If convergence
35


is not achieved within the user-specified iteration limits, the optional automatic
time step controller will adjust the step size and repeat the step.
3.3 Nonlinear Solution
and Linear Solvers Algorithms
The nonlinear solver is responsible for finding a set of nodal displacements, which
satisfy equilibrium at each load step. Several iterative nonlinear solvers are
implemented in NIKE3D. The full Newton method recomputes and refactors the
global stiffness matrix at each iteration. The modified Newton method reforms the
global stiffness matrix after a user specified number of iterations.
Within the iteration loop of the nonlinear solution algorithm, a linearized system of
simultaneous equations of the form [K] {Au} = {R} must be solved for linear
solvers. Two linear solution schemes are now available, a direct method and an
iterative method.
3.4 Sliding Interfaces
In this study, the model was created with interface behavior dominant. Over 90
interface definitions were created based on different kinds of material to assign
their coefficients of sliding and kinetic interface. The defined sliding surfaces were
all planar in.the model. The frictional sliding with gap interface was chosen among
over 10 available interface types in NIKE3D. The coefficient of penalty was also
applied in the model.
36


NIKE3D's multi-body contact algorithms are based on a master slave approach.
Typically, one side of a potential interface is identified as the "master" side, the
other side the "slave". Each side is identified in the input deck as an arbitrarily
ordered list of facets. These facets are typically element faces.
Internal logic identifies a master facet for each slave node and a slave facet for
each master node. This information is updated each time step as the slave and
master nodes slide along their respective surfaces. NIKE3D computes a total
reaction force across each interface. During initialization, NIKE3D checks for
interpenetration between master and slave surfaces in the initial geometry, and
adjusts nodal coordinates if necessary to return nodes to their opposing surfaces.
NIKE3D's contact algorithms are based on the penalty method, where penalty
springs are automatically generated between contact surfaces when
interpenetration is detected. These springs produce contact forces that are
proportional to interpenetration depth. To achieve this, NIKE3D employs a
complex algorithm to compute the default penalty stiffness, which depends on
material, and mesh properties. A penalty stiffness scale factor is available to adjust
the default stiffness of the contact interface. A penalty stiffness factor between
0.01 and 0.9 could be used to accelerate convergence and more interpenetration.
For analyses, a penalty stiffness scale was chosen as 0.8 and 2,0 for stage one and
stage two respectively. The augmented Lagrangian contact formulation has proven
37


to be very effective for many contact dominated problems. The method is iterative,
and is applied after convergence is obtained with the standard penalty method.
After each augmentation, the time step is repeated and a new equilibrium
configuration is determined. Convergence of the augmentation procedure assures
the accuracy of the contact constraint to within the range of the users specified
tolerance and independence of penalty stiffness value.
3.5 Material Model
Twenty-three constitutive models are available in NIKE3D. These models include
elastic, plastic, oriented brittle damage, transversely isotropic visco-hyperelasticity,
and viscous thermally dependent material behavior. In this study, the isotropic
elastic model and the Ramberg-Osgood model were adopted. The isotropic elastic
model for concrete material such as the abutment wall and MSEW, as well as
inclusions and foundation soil was used. The reinforced backfill was chosen for the
Ramberg-Osgood model because dissipation of energy is allowed.
3.5.1 Isotropic Elastic Model
The essential required input parameters are density, p, Young's modulus, E and
Poisson's ratio, v.
Linear material behavior is produced, where the rate of Cauchy stress a evolves
as a function of the rate of deformation e in the unrotated configuration according
to:
38


cr = X (tr£ )I + 2\is
where X and p are the Lame parameters:
#1.. Ev
(1 + v)(l + v)
E
u: ---------
2(1 + v)
For small strain linear analysis, other pertinent parameters are:
£
Shear Modulus: G =----------
2(1 +v)
Bulk Modulus: K = --------
3(1 -2v)
In this case the stress may be written directly as a function of strain e:
a = X (tr e) I + 2p e
3.5.2 Ramberg-Osgood Elastic-Plastic Model
The Ramberg-Osgood Elastic-Plastic model used for backfill in the NIKE3D
model requires reference density (p), shear strain (yy), reference shear stress (xy),
stress coefficient (a), stress exponent(r) and Bulk modulus (K).
The Ramberg-Osgood equation is an empirical constitutive relation that represents
the one-dimensional elastic-plastic behavior of many materials. This model allows
a simple rate-independent representation of the hysteretic energy dissipation
39


observed in materials subjected to cyclic shear deformation. The model is
primarily intended as a simple model for shear behavior.
For monotonic loading, the stress-strain relationship is given by
y t
= + a
ry t,
if
T
y >0
r_
ry
Y T
=-----a-
if
y<0
where y is the strain and x is the shear stress. The model approaches perfect
plasticity as the stress exponent r > oo.
After the first reversal, the stress-strain relationship is modified to:
r-Yo
2ry
if y>0
2 r
+ a
T~T
2
2 ry 2ty
if y<0
where y and x represent the values of strain and stress are the point of load reversal.
Subsequent load reversals are detected by
40


(r-r0)r The Ramberg-Osgood relations are multi-dimensional and are assumed to apply to
shear components. A projection is used to map the result back into deviatoric stress
space if required. The volumetric behavior is elastic and therefore the pressure p is
given by p = -Ksv, where ev is the volumetric strain.
41


4.
Overview of Study
4.1 Purpose
Regarding the use of Mechanically Stabilized Earth (MSE) Wall to support a
bridge abutment, additional research should be performed even though standard
specifications have been provided in the AASHTO Standard Specifications for
Highway Bridges, 16th Edition and AASHTO LRFD Bridge Design Specifications.
The technology is still in the developing stage, and there are many sources of
uncertainty involved in the design. However, no specific AASHTO guideline is
presently available for U-shaped Mechanically Stabilized Earth Wall. Note that the
term MSEW stands for U-shaped Mechanically Stabilized Earth Wall in the
NIKE3D model. Research on the MSEW used as bridge supporting structure has
been performed at the Center for Geotechnical Engineering Science, University of
Colorado at Denver. Unlike the regular MSE wall, the wall not only needs to have
adequate strength to support dead load of bridge superstructure and vehicular live
load but also have additional capacity to support the dead load of the abutment
wall and backfill. The focus of this research was to advance the state of practice of
reinforced soil technology by demonstrating what was known about the technology
based on finite element analysis before performing full size experimental testing.
42


Figure 4.1a 3D visualization of MSE abutment
43


Figure 4.1c 3D visualization of MSEW supported abutment (abutment wall
and inclusion)
Figure 4.Id 3D visualization of MSEW supported abutment without backfill
44


The major issue of the study was to concentrate on the understanding of MSEW
performance under bridge loadings, considering static behavior with specific a
span length. The essential components of an MSEW consist of rigid wall facing,
inclusions, backfill, and leveling pad. Figures 4.1a and 4.1b thru 4.1 d illustrate the
principal elements of the MSEW supported MSE abutment for stage one and stage
two analysis respectively. In the future, one could construct a bridge supporting
structure easily and economically. This study was developed in two stages. Both
stages involved and required NIKE3D. In the first stage, the analysis of the MSE
abutment itself was performed with Ramberg Osgood material as backfill. The
earth pressure at the back face of the abutment wall and self-weight pressure of the
reinforced soil mass was achieved. In the second stage analysis, the MSEW
consisting of two parallel, back-to-back sidewalls and a front wall was considered.
The MSE abutment was located on the MSEW. During the second stage, an
MSEW supported abutment system with configurations of three different widths of
abutment footings was analyzed. Each size of abutment footing with the same
configuration of the model was subjected to the same coefficients of friction
between the same kinds of materials. The width of the three abutment footings was
combined with the three bridge loadings cases from 100% to 200% of total dead
load of superstructure and live load with increments of 50%. Thus there were a
total of 9 numerical analytic cases to be performed with the NIKE3D program.
45


After finishing all the analytic cases, stress on inclusion reinforcement, earth
pressure, wall deformation, settlement, and bearing pressure on the bottom of the
reinforced soil mass at the MSEW were discussed and summarized. Moreover, in
order for the MSEW to be competitive for bridge supporting structure, the results
based on the finite element model were compared and summarized with FHWA
design guidelines for MSEW supported abutment with the analytic cases.
4.2 Study Parameters
4.2.1 NIKE3D Model Configurations
The same friction coefficients were applied between the same kinds of materials in
both analyses. They were 1.0 between inclusion and backfill interface within the
MSEW; 0.5 between concrete and backfill interface within the MSEW; 0.55
between foundation and backfill interface within the MSEW; 0.35 between
foundation and concrete interface within the MSEW.
In the first stage of the finite element model analysis, a full size MSE abutment
with equal length of inclusion using Ramberg Osgood material as reinforced soil
mass was analyzed. The Typical Section and Elevation of the MSE abutment are
shown in figures 4.2a and 4.2b. For the abutment, the wall height was 3.3 m from
the top of the footing to the top of the wall. The same wall stem thickness was 0.26
m from the abutment seat to the top of the wall. The back face of the abutment was
attached with 0.3 m spacing inclusions, without wing walls, as shown in the
46


3rp,
ft5*
*1

£{:,'?(ermine B&arinp Pa "*\ .f\V V- .'t'.V-l
v :*-iv4
i i_ '^esl
,*ti$
>i.:
:M
: +. 1* \* i,
.j'J .ji'.-
. r* -?
*5^
\ -r^ fatei;- fo&frwMw
i?
l3 .^G'V/TG^;
K^s l>':
W-r
- exp. j£>?ni moi'L ^
sTfastoess vonss \
UMti&r g?rd&r) ^
&
TYPICAL SECTION
Figure 4.2a Typical section of abutment
Figure 4.2b Elevation MSE abutment with inclusion
47


model. The inclusion selected was geosynthetic reinforcement, specifically geogrid
reinforcement. The inclusion length was long enough to minimize the effect on the
result of earth pressure by the boundary condition at the end of the reinforced soil
mass, since the result would be applied in the second stage. The footing, with a
thickness of 0.6m, was assumed to be sliding free on the rigid foundation. In the
second stage, the length of the abutment and its footing in the transverse direction
measured from edge of deck to edge of deck, limited by the width of the bridge,
was 11.9 m. The whole MSEW model was situated on a rigid solid foundation
except that no restraint was applied at the top of the foundation. The front and side
edges of the bridge abutment footing were next to the back face of the MSEW, and
adjacent to the back face of the MSEW side walls, respectively. So there was no
horizontal clearance between the front face of the abutment footing and the back
face of the MSEW. The foundation soil was almost the same height as the MSEW
to provide realistic results.
As for the second stage, the dimension of the MSEW was determined by the width
of the superstructure and length of the inclusion reinforcement. MSEW
configurations were the same with the width of the three abutment footings in the
cases analyzed. The widths of abutment footings were 2.13 m (7), 3.05 m (10),
3.96 m (13).
48


4^
o
e,13n <7'-D*>
Width of atoutneirt footing'
3.05 n CIO-O')
Figure 4.3 Elevation of abutment footings with different sizes.


(cc.9 n>
75'-[i -
(7.6 r,>
-a5'-[r-
£'-0<
(Cl.6 n>
15-4* <4.6 m)
-6' <0.15 r-i'1
<7.6 pi> c5"-C|*
dimension of model in Elevotion
Figure 4.4a Dimensions of MSEW in Elevation
26'3' l'-0"-+>
n) (0,3 n)
(typ.)
7
MSE Vail
abut nent
footing
-47'-0'-
(14.3 m)
plan
Figure 4.4b Dimensions of MSEW in Plan
L
-0'-^
<0.3 m>
50


The same wall height, 4.6 m, with 0.3 m stem width, was applied on all analytic
eases of the MSEW measuring from the top of the leveling pad to the bottom of
the footing because there should be a minimum of 5.03m(16-6) vertical clearance
from the lowest point of the bottom of the girder to the roadway underneath the
structure to meet the minimum requirements of AASHTO. The dimensions of the
abutment footings are shown in figure 4.3. The MSEW sidewalls were 8.0 m in
length from the back face of the MSEW front wall. The length of the inclusion was
set to match the length of the MSEW sidewalls. The dimensions of the MSEW in
Elevation and in Plan are shown in figure 4.4a and figure 4.4b, respectively. The
total width of the front face of MSEW was 14.3 m. The reinforced soil was
composed of layers of inclusion reinforcement with a constant vertical spacing of
0.4 m, which differed from that in the MSE abutment in the first stage. The front
edge of each layer of the inclusion reinforcement sheet was placed attached to the
back face of MSEW to form a rigid connection between the inclusions and the
rigid facings. The leveling pad thickness was 0.15 m extending continuously along
all the walls from the wall face to the edge of the leveling pad. As demonstrated in
the model, the rigid concrete MSEW was provided with a vertical face.
4.2.2 Bridge Configuration with AASHTO LRFD
Loadings
A single span bridge with six prestressed concrete BT84 girders was assumed to be
designed to carry two lanes with the potential of adding additional lanes. Type 7
51


bridge rail was assumed at each side of the deck. The abutment was on a spread
footing located in the center of the MSEW in the transverse direction. The equal
spacing of each girder is 2m(6-6) to minimize the loading of dead load on the
abutment. The span length, 48.8m(160-0), was measured from the center of the
abutment seat to the center of the abutment seat. The roadway width, curb to curb,
was 11.9m(39-0) and the high point on the roadway was located on the centerline
of the road. Since the bridge was assumed to be a typical grade separation structure
over a major highway, the minimum requirement for a vertical clearance for a
highway, 5.03 m (16-6), should be met. The Typical Section of the
superstructure and the Elevation of the abutment are illustrated in figure 4.5a and
figure 4.5b respectively. The abutment was assumed to have adequate capacity to
carry superstructure dead load with composite dead load and standard AASHTO
HL93 highway live load. The BT84 girders and their spacing were selected after
performing preliminary prestress girder design with the specific span length and
100% loading. The composite dead load in this case included 50 mm (2) HBP
plus an additional 50 mm (2) HBP for future repaving and Type 7 bridge rail on
both sides. According to section 3.5 in the LRFD Bridge Design Specifications
2000 AASHTO, the unit weights of the components were used in the analysis. The
unit weights of the components are specified in table 4.1.
52


H.CL
Figure 4.5a Typical section of bridge
HCL
£~7
/A T! ON OF ABUTMENT
Figure 4.5b Elevation of abutment
53


Table 4.1 Unit weights of each component in accordance with AASHTO
Component unit weight, pcf
For Abutment
Girder 150
Wearing surface 144
Diaphragm 150
Abutment wall 150
Footing 150
Mechanically stabilized earth wall
Rigid wall facing 150
Inclusion negligible
Backfill 120
Leveling pad 150
4.3 Loading Configurations
The first stage was conducted on the self-weight of the MSE abutment and the
reinforced soil mass. The second stage was conducted not only with the self-
weight of the entire structure and the earth pressure behind the abutment wall, but
also with bridge loadings on the abutment seat. The entire loading curve for the
abutment, except for bridge loadings, was applied at the same time as that of the
gravity load for the MSEW.
The bridge loadings of the dead load of the superstructure and HL 93 live load
were applied at the abutment seat. The dead load of the superstructure consisted of
the weight of all components of the bridge including non-composite and composite
dead load with appurtenances. According to section 3.5 in LRFD AASHTO, the
composite dead load should include the weight of the girder, the wearing surface,
54


Table 4.2 Loading of dead load for superstructure
To compute dead load reaction for each girder for superstructure loadings
Span length (cl of brg cl of brg), ft 160
out-to-out span width, ft: 39
curb-to-curb span width, ft: 36
Girder type: BT 84
Section area, in2: 948
Number of girder: 6
girder spacing cl-cl,ft 6.5
width of top flange, inch 43
Thickness of deck, inch 8
Overhang (slope 1:3)
width, ft 1.46
height, ft 0.49
Thickness of haunch, inch 8
Hot Bituminous Pavement, inch: 4
Intermediate diaphragm 1 kips for interior girder
Intermediate diaphragm 0.5 kips for exterior girder
Unit load of barrier Type 7 500 lb/ft
The following items of dead load in kip are per entire bridge:
DC DW
Girder 953 Type 7 Rails 160
Haunch (8") 346 HBP (4") 278
Deck (8") 659
End Diaphragms. 130
Intermediate Diaphragms. 14
Overhangs 17
Total dead load per entire bridge, kips
Total dead load per each abutment, kips
Dead load reaction per each abutment per each girder, kips:
Notes:
DC: calculated dead load from structural components
DW: wearing surfaces
2556
1278
213
55


diaphragms, and rails. The detailed calculations are illustrated in table 4.2.
Standard vehicular highway live load for bridge, designated HL-93, consists of a
combination of design truck or design tandem and design lane load conforming to
section 3.6 in AASHTO. The design truck loadings consist of a tractor truck with a
semi-trailer. The front axle load is 35,000 N gross, and second and third axle loads
are 145,000 N each. The spacing between the second and third axle loads is
variable from 4,300 mm to 9,000 mm to provide more critical loadings. The design
tandem consists of a pair of 110,000 N axles spaced 1,200 mm apart. The
transverse spacing of the wheels is 1,800 mm. The design lane load is a load of 9.3
N/mm, uniformly distributed in the longitudinal direction. Transversely* the design
load is assumed to be uniformly distributed over a 3,000 mm width. Each design
lane under consideration is occupied with either the design truck or tandem,
coincident with the lane load, when applicable. The critical loading condition of
live load would be applied in the design. Loading of triangular live load was
applied on one side of the footing more than the other side because a certain
number of lane loads occupied one side only with no live load assumed on the
other side at the same time. The detailed calculations are illustrated in table 4.3.
The bridge loadings finally would be transformed from concentrated loads into
pressure loads that were applied on the abutment seat.
56


Table 4.3 Loading of live load for superstructure
To compute Live load reaction (transverse) of each girder for superstructure
loadings
Span length: 160'
Impact: 1.33
Number of Lane 1 2 3
1.2 1.0 0.85
Maximum reaction at support per each live load (10' width)
Truck load 32k-32k-8k 67800 LB
Lane load 0.64k/ft 51200 LB
Total Live load per lane (10' width) 119000 LB
7 bearing pad assumed spacing of each beanng:5.57'
Section modulus:543 ft4
# oflane 1
Axial load: 169649 LB
Max. moment: 2205434 LB-ft
Max. Axial load, LB @1 lane
92095
# of lane 2 governs
spread footing method
Section modulus: 8107
Eccentricity
-16.7 -11.1 Min. -5.6 0.00 5.6
1 2 3 4 5
-243 1312 2866 4421 5975
-1.2E4 6.3E4 1.4E5 2.1E5 2.9E5
Area of abutment seat:
pile method Bearing Min.
1 2 3 4 5
-2.9E4 -6.0E3 1.7E4 4.0E4 6.4E4
-457 -94 269 632 994
# of lane 2 # of lane 3
282748 LB 360504 LB
2261984 LB-ft 1081511 LB-ft
@2 lane @3 lanes
109992 84778
11.1 16.7
Max.
6 7
7530 9084 psf
3.6E5 4.3E5 Pa
1.64'X39'
Max.
6 7
8.7E4 1.1 E5 LB
1357 1720 psf
57


All NIKE3D analytic models were performed through all cases of time history
analysis. The NIKE3D program provides implicit real time analysis. The role of
loading time history affects the results. Small loading time steps stimulated by the
program could induce loading onto the modeled system. As impact accumulates,
the model could be unstable and even terminate running. In this study, a time step
size of 1 second was adopted to avoid potential impact loading and make it
practical. In the load curve for the MSE abutment analysis, gravitational
acceleration, G, of 9.81 m/s imposed y-direction body force to all components
corresponding to the vertical direction within the model, linearly, in the span of 5
seconds from the beginning of the time history analysis, and then increased
constantly from 5 seconds to 10 seconds. For the MSEW supported MSE abutment
model, there were two loading curves. The first curve was about self-weight. The
gravitational acceleration would be 0 G at the time of 0 second and 1 G at the time
of 5 seconds on all the components of the model with loading of earth pressure and
self-weight of backfill behind the back face of the abutment above the MSEW.
There were a total of 5 time steps in the gravitational acceleration with a time
increment of 1 second. The static gravitational acceleration was maintained at 1 G
throughout the whole analysis process of time history analysis. For the second load
curve, no bridge loading was applied from 0 second until 5 seconds. Then the input
applied loading of superstructure dead load and highway live load as bridge
58


loadings were applied to the abutment seat from 5 seconds to 10 seconds
constantly. The bridge loadings imposed y-direction pressure load. The time
increment of every time step in the pressure load was 1 second. Appendices F and
G illustrate the elements and nodes selected for the data in the modes of MSE
abutment and the MSEW supported MSE abutment respectively.
4.4 Material Model and Input Parameter
Table 4.4 provides the summary of all the material properties as below.
Table 4.4 Inputted material parameters for the detailed study
Elastic Material Model
Modulus of Poisson's
Material Density Elasticity, E Ratio,v
[kg/m3] [MN/m2]
Foundation 2100 25,000 0.15
Concrete 2300 25,000 0.15
Inclusion 1030 290 0.4
Ramberg-Osgood Material Model
Reference Bulk
Material Density Shear Stress,-c. f Modulus, K
[kg/m3] [N/m2] [MN/m2]
Backfill 2000 11003 314
Material Stress Stress Reference
Coefficient,a Exponent, r Shear Strain,yy
Backfill 1.1 2.349 1.05E-04
Sliding Interface
Interface * 8 E
[degree] [degree]
Foundation-backfill 28 0.55
Concrete-foundation 28 19 0.35
Concrete-backfill 39 26 0.50
Inclusion-backfill 45 1.00
59


The inclusions, backfill soil, MSEW facing, abutment wall, foundation soil and
dirt are basic essential components of the MSEW.
4.4.1 Concrete Wall Facing
The concrete material was designated as MSEW facing and abutment wall with
elastic behaviors. The mass density, Poissons ratio, and modulus of elasticity of
the concrete materia] were 2300 kg/m 0.15, and 2.5E10 N/m respectively. The
Portland cement concrete material was assumed to have a compressive strength of
30 MPa after 28 days.
4.4.2 Foundation
Another elastic material model used in the analyses was foundation soih
Foundation soil had amass density of 2100 kg/m Poissons ratio of 0.15, and
modulus of elasticity of 2.5E10 N/m Based on the information of the Poissons
ratio and modulus of elasticity, it was indicated that the type of foundation was
rigid and was as hard as bedrock. Tables 4.5 and 4.6 provide the summary of
modulus of elasticity and Poissons ratio of the material properties for various
components respectively. Analyses emphasized the results of earth pressure, stress
on inclusions, bearing pressure and settlement. The foundation soil type was
provided as rigid. Then the bearing capacity of the MSEW was not a studied item
anymore. The other kind of foundation soil should be included in a further study.
60


Table 4.5 Range of value for the modulus of elasticity E for selected soils
(after Bowles, 1996)
Soil E, MPa
Clay
Very Soft 2-15
Soft 5-25
Medium 15-50
Hard 50-100
Sandy 25-250
Glacial till
Loose 10-150
Dense 150-720
Very dense 500-1440
Loess 15-60
Sand
Silty 5-20
Loose 10-25
Dense 50-81
Sand and gravel
Loose 50-150
Dense 100-200
Shale 150-5000
Silt 2-20
Table 4.6 Range of value for the Poisson's ratio (after Bowles, 1996)
Type of soil
Clay, saturated
Clay, unsaturated
Sandy clay
Silt
Sand, gravelly sand
Commonly used
Rock
Loess
Ice
Concrete
Steel
Poisson's ratio n
0.4-0.5
0.1-0.3
0.2-0.3
0.3-0.35
0.1-1.0
0.3-0.4
0.1 -0.4(depends on type of rock)
0.1-0.3
0.36
0.15
0.33
61


4.4.3 Inclusion
The inclusion is a geosyntheic reinforcing material, which was an extensible
reinforcing element within the backfill. It may elongate sufficiently under the
applied design loads to allow soil deformations to develop the active state along
the potential failure surface within the reinforced soil mass. Geogrid was used as
the inclusion in the study for the analyses. One of the commercial products of
Tensar Earth Technologies Inc., Tensar SR2, was selected as the inclusion in the
analysis. Table 4.7 shows the mechanical properties of Tensar SR2 geogrid. The
Youngs modulus was selected to be secant modulus at 5% strain. The information
was provided in English units. In order to determine the Youngs modulus, the
strength at 5% strain was divided by the average thickness to obtain the units of
force per unit area. The average rib thickness and junction thickness was 0.003m,
which was the thickness of the inclusion in the model. The Youngs Modulus at 5%
strain was 1450 MN/m2(3030 kips/ft2). The ultimate tensile strength,
78.5 kN/m(5.38 kips/ft), did not include any reduction factor such as creep,
durability and installation damage but the term of long-term tensile strength did.
Table 4.8 shows the range of Poissons ratio values for selected material. The
geogrid was made from polymer in the form of high-density polyethylene.
Poissons ratio for polyethylene ranges from 0.347 to 0.44. Selecting 0.4 as the
Poisson ratio was reasonable. As for the density, an inclusion was assumed to be
62


Table 4.7 Physical and mechanical properties of commercially available
geogrid (after Koerner, 1986)
Tensar (uniaxial) Test Method Units
Properties TTM 1.1 Ib/ft SR2
Tensile Strength at 2% Strain M 1465
XM -
5% Strain M 3030
XM -
Ultimate M 5380
XM -
Initial Tangent Modulus M TTM 1.1 kips/ft 136.2
XM -
Junction strength TTM 1.2 % 80
Weight Ib/yd2 1.55
Aperture Size M inch 3.9
Tensile Strength at 2% Strain XM 0.6
Thickness rib inch 0.05
junction 0.18
Polymer HDPE
Width ft 3.3
Length ft 98
Weight lb 61
Table 4.8 Some values of Poisson's ratio for elastically isotropic solids
(after Ruoff, 1972)
Material Poisson's ratio n
Beryllium 0.05
Glass 0.20-0.25
Rock 0-Jan
Steel 0.28
Copper 0.33
Nylon 0.48
Rubber ~0.5
Polyethylene 0.37-0.44
63


<5
1030 kg/m In the finite element model, the inclusion was a membrane that was
modeled as a 4 node element; all the other materials were modeled as 8 node solid
elements. Since the membrane elements had no torsional or bending stiffness,
rotational degree freedom at the membrane element nodes had to be constrained.
Each layer of reinforcing inclusions was attached to the stem of the front and the
MSEW sidewalls. Since the connection between the inclusion and the concrete
stem was firm, the inclusion shared the same node numbers at the connection.
The thickness of the inclusion was limited to 0.003 m. The unusual inclusion
thickness was to avoid divergence to the numerical solution. If the thickness of the
inclusion was too small, it could result in a problem with the convergence of the
numerical solution. In addition, the length of inclusion was selected to be the same
as the length of the MSEW sidewalls to capture enough information of interaction
between backfill and inclusion along the entire structure. Moreover, the purpose of
setting the vertical spacing of the inclusion, 0.4 m, and the length of the structure
was to reduce the analytic time and perform the analyses efficiently. Extremely
high bridge loadings could require closer spacing to resist the tension.
Besides the Ramberg Osgood Elastoplastic Model as backfill soil material, the
elastic material model was selected. The mass density of the Ramberg-Osgood
Elastic-Plastic material was 2000 kg/m3. The essential 6 input parameters other
than mass density were a shear strain (yy>0.3 052E-3), reference shear stress
64


Table 4.9 Typical values of compressive wave velocity and shear wave
velocity (after Das, 1993)
Soil type
Fine sand
Dense sand
Gravel
Moist clay
Granite
Sandstone
Table 4.10 Values for Poissons ratio v (after Bowles, 1996)
Type of soil Poisson's ratio n
Clay, saturated 0.4-0.5
Clay, unsaturated 0.1-0.3
Sandy clay 0.2-0.3
Silt 0.3-0.35
Sand, gravelly sand 0.1-1.0
Commonly used 0.3-0.4
Rock 0.1-0.4 (depends somewhat on type of rock)
Loess 0.1-0.3
Ice 0.36
Concrete 0.15
Steel 0.33
Compressive
Wave velocity
[ft's]
1,000
1.500
2.500
4.000- 4,500
13.000- 18,000
4,500-14,000
Shear
wave velocity
[ft's]
300-500
750
600-750
500
7.000- 11,000
2.000- 7,000
65


(xy> 11003 N/m2), stress coefficient (a>1.1), stress exponent (r>2.349), and
Bulk modulus (K>314000000 N/m ). All of these parameters were generated
using the RAMBO computer program and were finished in the earlier study. The
information was provided by Dr. Chang. The backfill was assumed as dense sand
with a density of 2000 kg/m3(125 Ib-f/ft3), shear wave velocity of 750 ft/s and
Poisson ratio of 0.3. After performing the detailed analyses, the parameters
generated with the RAMBO program and all the studies in this research were used
with the same backfill material for performing all analyses. Tables 4.9 and 4.10
were used to determine the material properties of the backfill. The backfill soil
behind the abutment and inside the MSEW were also specified with the same
essential input parameters of the Ramberg-Osgood Elastic-Plastic material in both
analysis stages.
4.5 Sliding Interfaces and Boundary Conditions
Since the models throughout the entire study were created with interface behavior
dominant, the contact condition between two materials had to be chosen wisely.
One of NIKE3Ds most powerful capacities is the sliding interface that will be
introduced at the contacting surfaces between two elements with a sliding penalty.
The sliding interface requires the input parameters of static friction coefficient and
kinetic friction coefficient. Throughout the models, there were several different
kinds of sliding interface such as foundation soil/concrete leveling pad, foundation
66


soil/dirt, backfill soil/back face of MSEW, abutment footing/back face of MSEW,
backfill/abutment footing, backfill/inclusion as well as dirt/MSEW front face. All
sliding interfaces had their own coefficient of friction. In order to compute the
friction coefficient, the internal friction angle () should be determined. Generally,
the internal friction angle of the soil was obtained from shear strength experiments.
The friction coefficient (p) should be computed with the internal friction angle
with known common material. For a sliding interface between two different soils
with internal friction angle ( The foundation soil was assumed to be as hard as bedrock with internal friction
angle of 28. Thus the friction coefficient for sliding interface between foundation
and backfill was close to 0.55.
To determine the interface friction angle between concrete and inclusion/backfill,
the equation of 5=(2/3)*0 should be applied and then p=tan (8) used to acquire the
friction coefficient. The backfill material was assumed to be the dense sand and
gravel mixture and the friction angle was 39. The corresponding interface friction
angle was 26. The friction coefficient for the sliding interfaces of concrete and
backfill is calculated as 0.5. The same procedure was used for the sliding interface
of concrete and foundation that gave the corresponding interface friction angle as
19. For the interface between inclusion and backfill with the assumed interface
friction angle of 45, the corresponding coefficient of friction was computed as 1.0.
67


The value of sliding penalty was used as 0.8 and 2.0 in first and second stage
analyses respectively. Sliding interface formulations played a major role in the
study. Penalty formulation, the scale factor for the sliding surface penalties of 2.0,
could be used. Sliding surface penalties of more than 2.0 should not be used in the
analysis as they make the sliding performed be far from reality. The boundary
conditions should also be selected reasonably. Using different boundary conditions
on the same model would result in great differences. No rotation restraint was
applied in any direction in the first and second stages of analysis. The boundary
conditions in Plan and Elevation are shown in figures 4.6a and 4.6b respectively.
The global x, y and z axes of the model were relatives to the transverse, vertical
and longitudinal direction of the structure respectively. The longitudinal and the
transverse direction were used to describe the axis of a bridge, which proceeds
from abutment to abutment and, which lies perpendicular to the centerline of the
structure respectively. In both stages, the interfaces on all sides of the foundation
soil had roller conditions in the y-axis, except that no restraint was applied on the
top face and the base was fixed. In the first stage, two sides of the abutment wall
had z-axis displacement restraint only and the two other directions were free to
move. At the front face of the abutment wall, roller condition in the y-axis was
applied. For the backfill behind the abutment wall, there were z-direction
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Boundary condiirion of node!
Rest ra i n t
Figure 4.6a Boundary condition of backfill in'MSEW
Boundary concJition of model in Elevation
R£li*Oirt
Figure 4.6b Boundary condition of MSEW in Elevation
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displacement restraints on both end sides and freedom to move at the other
displacement and rotation. At the end of the backfill, y-direction displacement and
rotations in all directions were free but x and z displacement directions were set to
be restrained.
For boundary conditions in the second stage, displacement restraint on the x-axis
was applied on the end of the MSEW sidewalls. The backfill at the end of the
MSEW had an x-axis and z-axis restraint the backfill and was to be free in the y-
axis displacement and all rotations. For the abutment wall, z-displacement restraint
was applied on both end sides from the top of the abutment seat to the top of the
abutment wall. The front of the abutment wall was set with x-and z-displacement
restrained. The foundation in the first stage was applied in the second stage.
4.6 Study Items
Static lateral pressure distribution and static thrust exerted on wall section
Location of static earth pressure thrust
Connection strength (connection-stress/connect-strength)
Inclusion tensile stress
Bearing Pressure
Settlement
Rotation
Font wall displacement
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4.7 Data Analyses
A total of nine cases were analyzed with the NIKE3D program: three different
widths of abutment footing subjected to up to 200% of bridge loadings. The
numerical outputs of all nine cases were extracted with the post-processor, GRIZ.
All of the outputs of the study items were stored in an ASCII format with respect
to each time step. The maximum data value of the study items was selected and
was sorted out in different configurations to fit a spreadsheet such as Excel, to plot
the processed output data. In addition, some other input data were prepared for a
Surface Modeling subprogram in the Eagle Point program to create Contours
graphs, and some of them were imported into the drawing of the MSEW with
AutoCAD to aid visualization.
4.7.1 Stresses and Resultant Stress Imparted
on Concrete Wall Section
Stress is exerted on the wall not by backfill only but also by inclusions. When
combining the lateral earth pressure and inclusion tensile resultant imparted on the
back face of the MSEW front wall, the resultant stress ran along the front face of
the backfill.
4.7.1.1 Earth Pressure Exerted on the Back Face of the
MSEW Front Wall and on Different Locations
far from the Wall in the Longitudinal Direction
Lateral earth Pressure was exerted on the back face of the MSEW front wall by the
reinforced soil mass and was acquired with the x-direction stress in longitudinal
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direction from the output of the NIKE3D analysis. The original unit of lateral earth
pressure was N/m The earth pressure contours were created by connecting the
nodal point x-stress along the front face of the reinforced soil mass with the Eagle
Point program from the top of the leveling pad to the bottom of the abutment
footing. In the model, all x-stress in all backfill elements behind the wall
represented lateral earth pressure that was exerted on it statically. The value of
negative stress in the reinforced soil mass in the x-direction indicated stress
exerted on the section and the value of positive stress indicated stress away from
the section in accordance with the designated coordinate convention. The absolute
value of the data was modified before importing into Eagle Point to pick out the
maximum value on the Contour graphs. In each graph, it was easy to point out the
maximum stress and the corresponding location. The contour graphs of the earth
pressure on the back face of the front wall and other locations from the back face
of front wall are shown in Appendix D. In addition, the earth pressure distribution
envelope on each section was plotted on the chart with processed output data.
Figure 4.7 shows the lateral earth pressure exerted by the backfill soil element on
the wall versus wall height. Figures 4.8a, b, c and d illustrate the lateral earth
pressure at a certain distance far from the back face of the MSEW front wall versus
bridge loadings. The locations of the sections were behind the back face of the
MSEW front wall, underneath a section of the middle of the abutment footing, the
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Combining maximum earth pressure behind back
face of MSEW front wall with different abut, footing
Earth Pressure in kPa
2.13171(7') 3.05m(10') 3.96m(13')
Figure 4.7 Summary of earth pressure behind back face of MSEW front wall
with bridge loadings versus wall height
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Maximum earth pressure at back face of MSEW front
wail for different abutment footing size
Bridge (DL+LL) in kN
-2.13m(7') 3.05m(10') -*r-3.96m(13)
Figure 4.8a Earth pressure at back face of MSEW front wall versus bridge
loadings
Maximum earth pressure at section of middle of
6950 10425 13900
Bridge (DL+LL) in kN
2.13m(7') 3.051X1(10') -*3r-3.96m(13')
Figure 4.8b Earth pressure at section of middle of abutment footing versus
bridge loadings
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Maximum earth pressure at section of back face of
Bridge (DL+LL) in kN
2.13m(7') --3.05m(10') -^-3.96m(13')
Figure 4.8c Earth pressure at section of back face of abutment footing versus
bridge loadings
Maximum earth pressure at section of 6m from back
face of MSEW front wall
Bridge (DL+LL) in kN
*-2.13m(7') 3.05171(10') -*-3.9601(13')
Figure 4.8d Earth pressure at section of 6m from back face of MSEW front
wall versus bridge loadings
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back face of the abutment footing, and a section 6m from the back face of the
MSEW front wall. The most interesting location was at the back face of the
MSEW front wall, and the summary of resultant earth pressure thrust with
corresponding locations was created in Table 4.14. By integration of the area under
the lateral earth pressure curve along the wall depth, the resultant force and its
location on the wall was determined. By multiplying each individual thrust and its
moment arm perpendicular to the c.g. of each individual thrust wall, the resultant
moment was determined. Location of the resultant thrust was calculated by
dividing the resultant moment by the resultant thrust. The resultant thrust would
act through the c.g. from the base of the wall. The earth pressure thrusts with
corresponding locations for three abutment footing sizes were determined as
shown in Appendix H. The general centroid equation, as shown in Equation 4.1,
was used to fmd the location of the total earth pressure thrust.
y =
Zpi*yi
Hpi
(4.1)
where pi*yi is the moment of individual resultant about the bottom of the wall and
pi is the individual resultant, y was the location of the total resultant applied from
the bottom of the wall calculated by dividing the summation of moments by the
summation of resultants. The output results of earth pressure thrust are
summarized in table 4.14.
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Maximum longitudinal inclusion connection stress -
2.13m (7*) width abutment footing with different
bridge loadings
longitudinal inclusion Stress in kPa
6950 kN -m-10425 kN -er-13900 kN
Figure 4.9a Summary of longitudinal inclusion connection stress 2.13m (7)
abutment footing with bridge loadings versus wall height
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Maximum longitudinal inclusion connection stress -
3.05m(1 O') width abutment footing with different
bridge loadings
0.00E+00 3.00E+02 6.00E+02 9.00E+02 1.20E+03 1.50E+03
longitudinal inclusion Stress in kPa
6950 kN *10425 kN -^-13900 kN
Figure 4.9b Summary of longitudinal inclusion connection stress 3.05m (10)
abutment footing with bridge loadings versus wall height
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Maximum longitudinal inclusion connection stress -
3.96m (13') width abut, ftg with different bridge
longitudinal inclusion Stress in kPa
6950 kN 10425 kN -*-13900 kN
Figure 4.9c Summary of longitudinal inclusion connection stress 3.96m (13)
abutment footing Avith bridge loadings versus wall height
Maximum connection stress between MSEW and
6950 10425 13900
Bridge (DL+LL) in kN
| 2.13m(7') 3.05m(10') -T&-3.96m(13')
Figure 4.10 Inclusion connection stress of MSEW front wall versus bridge
loadings
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4.7.1.2 Tensile Inclusion Connection Stress
One of the topics debated was the connection strength between the rigid facing and
the reinforced soil mass because the major function of the inclusion was to hold
the wall in place during applied earth pressure, surcharge and bridge loadings. As
for the inclusion, the nodal point x-stress at the inclusion-wall connection was
chosen for the inclusion pressure. Figures 4.9 and 4.10 illustrate the connection
inclusion stress distribution against the back face of the MSE front wall versus the
wall height and the stress versus the bridge loadings respectively. The thickness of
the inclusion element was much smaller than that of backfill element, but the
provided tensile strength of the inclusion should be high enough to overcome the
earth pressure generated by the backfill. As for the inclusion, each resultant tensile
inclusion was determined by multiplying the nodal point x-stress by the inclusion
thickness of 0.003 m. The design load at the connection should be equal to the
maximum load on the reinforcement. Normally, larger inclusion stress in the same
layer should occur at the connection in the upper part of the wall, particularly at the
first four layers of inclusion underneath the abutment footing. The maximum stress
should be in the first two layers of the inclusion depending on the size of the
footing and the amount of applied loadings. At the bottom part of the wall, the
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connection stress trends to decline greatly and about one third of the maximum
stress is left at the elevation of the leveling pad.
4.7.2 Bearing Pressure and Settlement
Settlement was relative to the amount of bearing pressure. Higher bearing pressure
caused more settlement. The nodes at the bottom of the backfill underneath the
reinforced soil mass were selected to determine the response of the bearing
pressure under applied loadings. Y-stress in the backfill element at the bottom of
MSEW that was extracted from the output analysis represented the bearing
pressure on the foundation. The maximum y-stress could control the size of the
structure system and the vertical deformation. Appendices C, D and E contain the
plots of contour graphs of bearing pressure and settlement with 200% applied
bridge loadings among all cases of abutment footing widths. Figures 4.1 la, b, c
and d indicate the settlement of the MSEW and the total settlement combining the
MSEW and the abutment. The total settlement combines the MSEW and the
abutment (in m) along with the footing size of 2.13m (7), 3.05m (10) and 3.96m
(13 ) was 2.13E-02 (0.83), 1.46E-02(0.57) and 1.44E-02 (0.57) with 200%
bridge loadings respectively. The maximum settlement in all cases was 21.3mm
(0.83), which was much less than the FHWA 245mm (9.6 inch) limit with 0.005
times the span length of 48.8m (160-0) for simple spans. Figures 4.12a and 4.12b
show the maximum bearing pressure underneath the abutment footing versus
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loadings and the maximum bearing pressure at the bottom of the MSEW versus
loadings. From the results, the maximum bearing pressure in kPa located about 4m
from the back face of the MSEW front wall in all cases was 241, 249 and 249 with
200% bridge loadings respectively. The size of the footing did not play an
important role in affecting the bearing pressure of the reinforced soil mass in the
MSEW. Appendix D contains the contour plots of bearing pressure for all 200%
applied bridge loadings in all cases.
Average settlement of backfill
at the bottom (MSEW)
Bridge (DL+LL) in kN
2.13171(7') 3.05171(10') 3.96m(13)
Figure 4.11a Average settlement of backfill at bottom of MSEW versus bridge
loadings
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Average settlement @ top of backfill
(MSEW)
Bridge (DL+LL) in kN
I*2.13m(7') 3.05m(10) -*-3.96m(13')
Figure 4.11b Average settlement at top of backfill of MSEW versus bridge
loadings
Average settlement of MSEW
Bridge (DL+LL) in kN
< 2.13m(7') 3.05m(10') -*-3.96m(13')
Figure 4.11c Average settlement backfill at MSEW versus bridge loadings
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Average settlement of MSEW
with MSE abutment
Bridge (DL+LL) in kN
2.13m(7) 3.05m(10') -*-3.96m(13')
Figure 4.1 Id Average settlement MSEW and abutment versus bridge loadings
Maximum settlement at the bottom
Bridge (DL+LL) in kN
2.13m(7') 3.05m(10') -^-3.96m(13')
Figure 4.11e Settlement of leveling pad MSEW versus bridge loadings
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Average bearing pressure
Bridge (DL+LL) in kN
[ 2.13m(7') -*-3.05171(10') -,*-3.96171(13')
Figure 4.12a Bearing pressure underneath abutment footing versus bridge
loadings
Average bearing pressure of backfill at the bottom of
MSEW
Bridge (DL+LL) in kN
2.13m(7') 3.05m(10') -*r-3.96m(13')
Figure 4.12b Bearing pressure at the bottom of MSEW versus bridge
loadings
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From the contour graphs of bearing pressure, the maximum absolute value of stress
and its corresponding location were apparent. The maximum absolute stress value
should be used to determine the minimum required bearing capacity of the
foundation soil with a factor of safety. The bearing capacity of the foundation soil
was calculated in accordance with Section 4.2 in the FHWA design guidelines.
quit=Cf*Nc+0.5*(L)yf*NY (4.2)
where Cf is the cohesion, yt the unit weight and Nc and Ny are dimensionless
bearing capacity coefficients.
In accordance with the assumed foundation information of § being 28 and c being
30,000 N/m the qui, should be straightforward according to the above equation.
Since a rigid foundation was assumed, the bearing capacity should not be an issue
and was not within the scope of this study.
4.7.3 Wall Deformation and Rotation
According to the regular MSE wall, the primary function of the rigid facing was to
act as a form for each lift of fill and provide an attractive facade. The facing was
not considered to contribute structural confinement; its contribution to soil
retainment was minor compared to the effect of the closely spaced reinforced soil.
The rigid facing had the function of limiting long-term creep deformation of the
reinforced soil mass.
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Wall deformation was a close relative to the stability of the wall system. In
addition, wall deformation not only affected the aesthetics, but also the internal
stability. Wall facing deformation was caused by the earth pressure and tensile
inclusion. The wall moved outward to relieve the burden of lateral earth pressure
and the inclusions held the wall in place. The nodal points along the back face of
the MSEW front wall were selected to extract wall deformation along the
longitudinal direction. The maximum wall deformation layouts were generated
after applying the critical loading condition. Figure 4.13 shows the static wall
deformation in all cases of abutment footings with applied bridge loadings. The
wall deformation and rotation layout was plotted in each analytic case versus the
wall height from the top of the leveling pad to the bottom of the abutment footing.
Appendix D provides the contour graphs of the front wall in the longitudinal
direction with 200% bridge loadings. The result indicated that the maximum
forward deformation of the wall in the longitudinal direction was 6.6mm(0.26),
which occurred 2.2m(7-2) from the bottom of the abutment footing in all cases
with 200% bridge loadings. For the regular MSEW, the facing system was
designed to move and retain its shape. The wall was battered to offset any lateral
deformations that were expected to occur. However, it was not necessary for the
MSEW to be battered because the wall had enough capacity to immunize the wall
deformation. Additionally, the rigid stiff wall facing system of
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Maximum rotation of MSEW front wall
Bridge (DL+LL) in kN
2.13m(7') 3.05m(10') -fi-3.96m(13)
Figure 4.12c Rotation of MSEW front wall versus bridge loadings
Maximum deformation of MSEW front wall
(Longitudinal) with different of abutment footing
9.00E-03
8.50E-03
l 8.00E-03
C 7.50E-03
1 7.00E-03
| 6.50E-03
6.00E-03
5.50E-03
5.00E-03
6950 10425 13900
DL+LL in kN
I 2..13m(7') 3.05m(10') a 3.96m(13')
Figure 4.13 Summary of longitudinal deformation of MSEW front wall versus
bridge loadings
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MSEW not only increase global rigidity and limit long-term creep deformation of
the reinforced soil mass, but also provide the function of structural element. The
rotations of the wall were calculated based on the processed output data of wall
deformation and the charts are shown in figure 4.12c.
The equation of the wall tilt is:
Ax: the horizontal distance between the top and bottom of the wall after
deformation.
H: the wall height.
0: the wall tilt from vertical.
Wall tilt was calculated using the arctangent of the top and bottom deformation
difference of the wall corresponding to the wall height. The maximum forward
rotation of the wall in the longitudinal direction was 0.0275 rad, 0.0277 rad and
0.0252 located at the top of the leveling pad in the cases of 2.13m (7), 3.05m (10)
and 3.96m (13) with 200% bridge loadings respectively.
4.7.4 Inclusion Tensile Stress
Typically, geosynthetics are used for extensible reinforcement. The primary
function of reinforcement is to restrain soil deformation. Inclusions within the
backfill are considered reinforcement because the backfill has no capacity for
tension. Inclusion stress performance was the major role in evaluating the wall
6 = arctan
89