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Nonlinear analysis of MSE bridge abutment under seismic loads

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Title:
Nonlinear analysis of MSE bridge abutment under seismic loads
Creator:
Jalinsky, Michael J
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English
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xix, 225 leaves : ; 28 cm

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Subjects / Keywords:
Bridges -- Abutments ( lcsh )
Soil stabilization ( lcsh )
Earthquake resistant design ( lcsh )
Bridges -- Design and construction ( lcsh )
Bridges -- Abutments ( fast )
Bridges -- Design and construction ( fast )
Earthquake resistant design ( fast )
Soil stabilization ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Bibliography:
Includes bibliographical references (leaves 224-225).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Michael J. Jalinsky.

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Source Institution:
|University of Colorado Denver
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
63788074 ( OCLC )
ocm63788074
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LD1193.E53 2004m J34 ( lcc )

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Full Text
NONLINEAR ANALYSIS OF MSE BRIDGE ABUTMENT UNDER
SEISMIC LOADS
by
Michael J. Jalinsky
B.S., Southern Illinois University at Edwardsville, 1998
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

\T;:


This thesis for the Master of Science
degree by
Michael J Jalinsky
has been approved
by
Shing-Chun Trever Wang
ChengYu-Li
S'
ate


Michael Jess Jalinsky (M.S., Civil Engineering)
Nonlinear Analysis of MSE Bridge Abutment under Seismic Loads
Thesis directed by Professor Nien-Yin Chang
ABSTRACT
Bridge abutment is a structure located at the ends of a bridge which
provide the basic functions of: supporting the end of the superstructure at the
first and end span, supporting parts of the approaching roadway and retaining
the earth in front, underneath and adjacent to the approaching roadway.
There are several styles of abutment retaining structures used today and are
dependent on the geometry of the site, size of the structure and the
preferences of the owner. The more common types of abutments are:
concrete cantilever walls, gravity walls and reinforced soil structures
commonly referred to as MSE (Mechanically stabilized earth structures).
Currently the only published seismic design standard is contained in the
AASHTO Standard Specifications for Highway Bridges, which describes a
pseudo-static method of analysis based on the Mononobe-Okabe application
of conventional pressure theory. Also, the current seismic design codes do
not appear to fully incorporate the wall inherent flexibility. This is why more
studies and field observations on existing abutment structures are needed to
better understand the ductile response of MSE walls under the influence of
m


seismic loads and flexible composition of geosythetic reinforcement and
selected soil matrix.
The primary objective of this thesis study is to analyze the response of
MSE abutment retaining wall under seismic loading. Numerical analyses of
MSE retaining wall systems were performed using the finite element
computer program named NIKE3D. NIKE3D has the capability of time history
analysis, slide interfaces between different materials and nonlinear Ramberg-
Osgood material model. This study selected the accelerograms from the
Imperial Valley Earthquake El Centro dated October 15, 1979 and the
Northridge Earthquake dated January 17, 1994 in the dynamic finite element
analyses with difference ground motion acceleration combinations including
multidirectional shaking. From this study the insight to the behavior and
response of MSE walls under seismic load can be better understood.
This abstract accurately represents the content of the candidates
thesis. I recommend its publication.
Signed,
^/ftfien-Yin Chang
IV


ACKNOWLEDGEMENTS
This thesis was performed under the supervision of Dr. Nien-Yin
Chang and Dr.Shing-Chun TreverWang. I am grateful for their guidance and
encouragement throughout my journey and Dr. ChengYu-Li for his effort in
servicing on my examination committee is greatly appreciated. I would also
like to especially thank my wife (Patty) for her support and encouragement
over the years in completing my educational quest. Finally, I am also grateful
to the NIKE group members for their support and sharing of their knowledge
over the last couple of years.


CONTENTS
Figures..............................................................xi
Tables...............................................................xix
Chapter
1. Introduction.....................................................1
1.1 Problem Statement................................................1
1.2 Objectives.......................................................4
1.3 Significance of This Research....................................6
2. Literature Review................................................9
2.1 Introduction.....................................................9
2.2 AASHTO Current Design Guidelines.................................9
2.3 Mononobe-Okabe Method...........................................16
2.4 Evaluation of Seismic Performance in MSE Structures ............20
2.4.1 Northridge Earthquake...........................................21
2.4.2 Kobe Earthquake.................................................22
2.4.3 Izmit Earthquake................................................22
2.5 Conclusion......................................................23
3. Theroretical Background of NIKE3D Program.......................24
3.1 NIKE3D Finite Element Program...................................24
3.2 Microstation and Truegrid Mesh Generation Programs..............25
3.3 Material Model..................................................26
3.4 Ramberg-Osgood Elastopastic Model...............................27
3.5 Eigenvalue Analysis and Rayleigh Damping........................28
4. Ground Motion Used for this Study...............................32
4.1 Introduction....................................................32
vi


33
38
42
42
43
47
49
52
56
57
57
57
58
60
64
69
73
76
78
83
87
Ground Motion Time History and Input....................
Response Spectrum.....................................
Review of Study and Design Parameters.................
Introduction..........................................
Bridge Model Dimensions...............................
Boundary Conditions...................................
Slide Interfaces......................................
Material Model Parameters.............................
Summary...............................................
Northridge Earthquake Results.........................
Data Analysis.........................................
Study Items...........................................
Case 1: Static Loading Abutment 1...................
Inclusion Stresses Static Loading ..................
Case 2: Vertical, Transverse and Longitudinal Motion -
Abutment 1............................................
Inclusion Stresses Vertical, Transverse and Longitudinal
Motion Abutmentl....................................
Case 2: Vertical, Transverse Longitudinal
Motion Abutment 2...................................
Inclusion Stresses Vertical, Transverse and Longitudinal
Motion Abutment 2...................................
Case 3: Longitudinal and Transverse Motion Abutment 1
Inclusion Stresses Longitudinal and Transverse Motion -
Abutment 1............................................
Case 2: Longitudinal and Transverse Motion Abutment 2
Vll


..90
..92
..96
100
103
105
105
105
108
111
112
112
114
114
114
115
117
121
126
Inclusion Stresses Longitudinal and Transverse Motion -
Abutment 2.............................................
Case 4: Vertical and Longitudinal Motion Abutment 1 ....
Inclusion Stresses Vertical and Longitudinal Motion -
Abutment 1.............................................
Case 2: Vertical and Longitudinal Motion Abutment 2..
Inclusion Stresses Vertical and Longitudinal Motion -
Abutment 2.............................................
Interpretation of Analysis Results.....................
Analysis Results.......................................
Case 1: Static Loading.................................
Case 2: Vertical, Longitudinal and Transverse Motion...
Case 3: Longitudinal and Transverse Motion.............
Case 4: Vertical and Longitudinal Motion...............
Summary................................................
Imperial Earthquake Results............................
Data Analysis..........................................
Study Items............................................
Case 1: Static Loading Abutment 1....................
Inclusion Stresses Static Loading ...................
Case 2: Vertical, Transverse and Longitudinal
Motion Abutment 1....................................
Inclusion Stresses Vertical, Transverse and Longitudinal
Motion Abutment 1....................................
Case 2: Vertical, Transverse and Longitudinal
Vlll


130
133
135
140
144
147
149
153
157
161
163
163
163
166
169
170
170
172
172
172
Motion Abutment 2...................................
Inclusion Stresses Vertical, Transverse and Longitudinal
Motion Abutment 2...................................
Case 3: Longitudinal and Transverse Motion Abutment 1
Inclusion Stresses Transverse and Longitudinal
Motion Abutment 1...................................
Case 2: Longitudinal and Transverse
Motion Abutment 2...................................
Inclusion Stresses Longitudinal and Transverse
Motion Abutment 2...................................
Case 4: Vertical and Longitudinal Motion Abutment 1 ....
Inclusion Stresses Vertical and Longitudinal
Motion Abutment 1...................................
Case 2: Vertical and Longitudinal Motion Abutment 2.
Inclusion Stresses Vertical and Longitudinal
Motion Abutment 2...................................
Interpretation of Analysis Results....................
Analysis Results......................................
Case 1: Static Loading................................
Case 2: Vertical, Longitudinal and Transverse Motion..
Case 3: Longitudinal and Transverse Motion............
Case 4: Vertical and Longitudinal Motion..............
Summary...............................................
MSE Wall Design Examples..............................
Current Design Methods................................
AASHTO Design Method..................................
IX


8.3 Finite Element Design Method (NIKE3D).....................174
8.4 Comparison Between AASHTO and Finite
Element Method............................................175
9. Summary, Conclusions, Recommendations and Further
Studies...................................................176
9.1 Summary...................................................176
9.2 Conclusions...............................................177
9.3 Recommendations for Further Studies.....................177
Appendix
A. Truegrid Input File.......................................179
B. Ritz and Eigenvalues......................................221
References.....................................................224
x


FIGURES
Figure
1.1 Typical cantilever and spread footing abutments......................1
1.2 Typical MSE abutment.................................................2
1.3a Geosynthetics wrap...................................................3
1.3b Segment concrete block...............................................3
1.3c Full height panel....................................................3
1.4 Tensar geogrid geosythetic material..................................4
2.1 MSE wall element dimensions needed for design.......................11
2.2 ASSHTO seismic external stability of a MSE wall.....................13
2.3 Seismic internal stability of a MSE wall............................15
2.4a Forces acting on active wedge.......................................16
2.4b Forces acting on passive wedge......................................16
2.5 Total earth pressure distribution due to soil proposed
by Bathurst and Cari (1995).........................................19
3.1 NIKE3D bridge model.................................................26
4.1 Northridge vertical acceleration time history.......................35
4.2 Northridge horizontal @ 90 degree acceleration time history.........35
4.3 Northridge Horizontal @ 360 degree acceleration time history........36
4.4 Imperial Valley vertical acceleration time history..................36
4.5 Imperial Valley horizontal @ 360 degree acceleration time history..37
4.6 Imperial Valley horizontal @ 90 degree acceleration time history...37
4.7a Northridge 360 degree horizontal response spectrum..................39
4.7b Northridge 90 degree horizontal response spectrum...................39
4.8a Imperial Valley 360 degree horizontal response spectrum.............40
4.8b Northridge vertical response spectrum...............................40
4.9a Imperial Valley vertical response spectrum..........................41
XI


4.9b Imperial Valley 90 degree horizontal response spectrum..............41
5.1 Bridge plan view....................................................44
5.2 Bridge elevation and typical section................................45
5.3 Bridge elevation and boundary conditions............................48
5.4 Boundary conditions and material dimensions.........................49
5.5 Master and slave diagram............................................51
6.1 Static longitudinal MSE wall displacements..........................58
6.2 Static longitudinal earth pressures.................................58
6.3 Static longitudinal inclusion stresses..............................59
6.4 Maximum bearing compression contours at footing kpa...............59
6.5 1st Inclusion layer stress contours from top kpa..................60
6.6 2nd Inclusion layer stress contours from top kpa..................60
6.7 3rd Inclusion layer stress contours from top kpa..................61
6.8 4th Inclusion layer stress contours from top kpa..................61
6.9 5th Inclusion layer stress contours from top kpa..................62
6.10 6th Inclusion layer stress contours from top kpa..................62
6.11 7th Inclusion layer stress contours from top kpa..................63
6.12 Time history at top of wall.........................................64
6.13 Maximum MSE wall displacements......................................64
6.14 Maximum longitudinal earth pressures................................65
6.15 Maximum connection stresses.........................................65
6.16 Maximum bearing stress contours at footing kpa....................66
6.17 Backfill acceleration profile.......................................66
6.18 Maximum transverse MSE wall displacements...........................67
6.19 Maximum transverse earth pressures..................................67
6.20 Maximum MSE wing wall displacements.................................68
6.21 Bridge deck displacements...........................................68
6.22 1st Inclusion layer stress contours from top kpa..................69
xii


6.23 2nd Inclusion layer stress contours from top kpa..................69
6.24 3rd Inclusion layer stress contours from top kpa..................70
6.25 4th Inclusion layer stress contours from top kpa..................70
6.26 5th Inclusion layer stress contours from top kpa..................71
6.27 6th Inclusion layer stress contours from top kpa..................71
6.28 7th Inclusion layer stress contours from top kpa..................72
6.29 Maximum MSE wall displacements...................................73
6.30 Maximum longitudinal earth pressures.............................73
6.31 Maximum bearing compression contours at footing kpa............74
6.32 Maximum MSE wall transverse displacements........................74
6.33 Maximum MSE wall earth pressures.................................75
6.34 Maximum MSE wing wall displacements..............................75
6.35 1st Inclusion layer stress contours from top kpa..................76
6.36 2nd Inclusion layer stress contours from top kpa..................76
6.37 3rd Inclusion layer stress contours from top kpa..................77
6.38 Time history at bottom of wall.....................................78
6.39 Maximum MSE wall displacements...................................78
6.40 Maximum longitudinal earth pressures.............................79
6.41 Maximum bearing pressure contours at footing kpa...............79
6.42 Maximum transverse wall displacements............................80
6.43 Maximum transverse earth pressures...............................80
6.44 Maximum MSE wing wall displacements..............................81
6.45 Maximum transverse pressures at wing walls.......................81
6.46 Bridge deck vertical displacements.................................82
6.47 1st Inclusion layer stress contours from top kpa..................83
6.48 2nd Inclusion layer stress contours from top kpa..................83
6.49 3rd Inclusion layer stress contours from top kpa..................84
6.50 4th Inclusion layer stress contours from top kpa..................84
xiii


6.51 5th Inclusion layer stress contours from top - kpa...................85
6.52 6th Inclusion layer stress contours from top - kpa...................85
6.53 7th Inclusion layer stress contours from top - kpa...................86
6.54 Maximum MSE wall displacements....................................87
6.55 Maximum longitudinal earth pressures..............................87
6.56 Maximum bearing compression contours at footing kpa.............88
6.57 Maximum MSE wing wall displacements...............................88
6.58 Maximum MSE wall earth pressures..................................89
6.59 1st Inclusion layer stress contours from top kpa...................90
6.60 2nd Inclusion layer stress contours from top kpa...................90
6.61 3rd Inclusion layer stress contours from top kpa...................91
6.62 Time history at top of wall........................................92
6.63 Maximum MSE wall displacements....................................92
6.64 Maximum longitudinal earth pressures..............................93
6.65 Maximum bearing pressures contours at footing kpa..............93
6.66 Maximum transverse wall displacements................................94
6.67 Maximum transverse earth pressures...................................94
6.68 Maximum MSE wing wall displacements...............................95
6.69 Maximum transverse pressures at wing walls........................95
6.70 1st Inclusion layer stress contours from top kpa...................96
6.71 2nd Inclusion layer stress contours from top kpa...................96
6.72 3rd Inclusion layer stress contours from top kpa...................97
6.73 4th Inclusion layer stress contours from top kpa...................97
6.74 5th Inclusion layer stress contours from top kpa...................98
6.75 6th Inclusion layer stress contours from top kpa...................98
6.76 7th Inclusion layer stress contours from top kpa...................99
6.77 Maximum MSE wall displacements.....................................100
6.78 Maximum longitudinal earth pressures...............................100
XIV


6.79 Maximum bearing compression contours at footing kpa..............101
6.80 Maximum MSE wing wall displacements................................101
6.81 Maximum MSE wing wall earth pressures..............................102
6.82 1st Inclusion layer stress contours from top kpa.................103
6.83 2nd Inclusion layer stress contours from top kpa.................103
6.84 3rd Inclusion layer stress contours from top kpa.................104
7.1 Static longitudinal MSE wall displacements.........................115
7.2 Static longitudinal earth pressures................................115
7.3 Static longitudinal inclusion stresses.............................116
7.4 Maximum bearing pressure contours at footing - kpa.................116
7.5 1st Inclusion layer stress contours from top kpa.................117
7.6 2nd Inclusion layer stress contours from top kpa.................117
7.7 3rd Inclusion layer stress contours from top kpa.................118
7.8 4th Inclusion layer stress contours from top kpa.................118
7.9 5th Inclusion layer stress contours from top kpa.................119
7.10 6th Inclusion layer stress contours from top kpa.................119
7.11 7th Inclusion layer stress contours from top kpa.................120
7.12 Time history at top of wall........................................121
7.13 Maximum MSE wall displacements.....................................121
7.14 Maximum longitudinal earth pressures...............................122
7.15 Maximum connection stresses........................................122
7.16 Maximum bearing pressure contours at footing - kpa.................123
7.17 Soil acceleration profile..........................................123
7.18 Maximum transverse MSE wall displacements..........................124
7.19 Maximum transverse earth pressures.................................124
7.20 Maximum MSE wing wall displacements................................125
7.21 Bridge deck displacements..........................................125
7.22 1st Inclusion layer stress contours from top kpa.................126
xv


7.23 2nd Inclusion layer stress contours from top kpa.................126
7.24 3rd Inclusion layer stress contours from top kpa.................127
7.25 4th Inclusion layer stress contours from top kpa.................127
7.26 5th Inclusion layer stress contours from top kpa.................128
7.27 6th Inclusion layer stress contours from top kpa.................128
7.28 7th Inclusion layer stress contours from top kpa.................129
7.29 Maximum MSE wall displacements.....................................130
7.30 Maximum longitudinal earth pressures...............................130
7.31 Maximum bearing pressure contours at footing kpa.................131
7.32 Maximum MSE wall transverse displacements..........................131
7.33 Maximum MSE wall earth pressures...................................132
7.34 Maximum MSE wing wall displacements................................132
7.35 1st Inclusion layer stress contours from top kpa.................133
7.36 2nd Inclusion layer stress contours from top kpa.................133
7.37 3rd Inclusion layer stress contours from top kpa.................134
7.38 Time history at top of wall.......................................135
7.39 Maximum MSE wall displacements.....................................135
7.40 Maximum longitudinal earth pressures...............................136
7.41 Maximum bearing pressure contours at footing kpa.................136
7.42 Maximum transverse wall displacements..............................137
7.43 Maximum transverse earth pressures.................................137
7.44 Maximum MSE wing wall displacements................................138
7.45 Maximum transverse pressures at wing walls.........................138
7.46 Bridge deck vertical displacements................................139
7.47 1st Inclusion layer stress contours from top kpa.................140
7.48 2nd Inclusion layer stress contours from top kpa.................140
7.49 3rd Inclusion layer stress contours from top kpa.................141
7.50 4th Inclusion layer stress contours from top kpa.................141
xvi


7.51 5th Inclusion layer stress contours from top - kpa.................142
7.52 6th Inclusion layer stress contours from top - kpa.................142
7.53 7th Inclusion layer stress contours from top - kpa.................143
7.54 Maximum MSE wall displacements..................................144
7.55 Maximum longitudinal earth pressures............................144
7.56 Maximum bearing compression contours at footing kpa...........145
7.57 Maximum MSE wing wall displacements.............................145
7.58 Maximum MSE wall earth pressures................................146
7.59 1st Inclusion layer stress contours from top kpa.................147
7.60 2nd Inclusion layer stress contours from top kpa.................147
7.61 3rd Inclusion layer stress contours from top kpa.................148
7.62 Time history at top of wall.........................................149
7.63 Maximum MSE wall displacements......................................149
7.64 Maximum longitudinal earth pressures............................150
7.65 Maximum bearing pressures contours at footing kpa............150
7.66 Maximum transverse earth pressures.................................151
7.67 Maximum MSE wing wall displacements.............................151
7.68 Maximum transverse pressures at wing walls......................152
7.69 Maximum bridge deck displacements...............................152
7.70 1st Inclusion layer stress contours from top kpa.................153
7.71 2nd Inclusion layer stress contours from top kpa.................153
7.72 3rd Inclusion layer stress contours from top kpa.................154
7.73 4th Inclusion layer stress contours from top kpa.................154
7.74 5th Inclusion layer stress contours from top kpa.................155
7.75 6th Inclusion layer stress contours from top kpa.................155
7.76 7th Inclusion layer stress contours from top kpa.................156
7.77 Maximum MSE wall displacements....................................157
7.78 Maximum longitudinal earth pressures..............................157
xvii


7.79 Maximum bearing compression contours at footing kpa..............158
7.80 Maximum transverse earth pressures.................................158
7.81 Maximum transverse MSE wall displacements..........................159
7.82 Maximum MSE wing wall displacements................................159
7.83 Maximum MSE wing wall earth pressures..............................160
7.84 1st Inclusion layer stress contours from top kpa.................161
7.85 2nd Inclusion layer stress contours from top kpa.................161
7.86 3rd Inclusion layer stress contours from top kpa.................162
8.1 Stress distribution diagram........................................173
8.2 FE model stress distribution.......................................175
xviii


TABLES
Table
2.1 AASHTO factor of safety criteria................................10
2.2 Seismic Performance Category (SPC) with important
classification..................................................12
3.1 Mode shapes with frequencies and periods........................30
3.2 Displacement response spectrum values Northridge..............30
3.3 Acceleration response spectrum values Northridge..............30
3.4 Displacement response spectrum values Imperial Valley.........31
3.5 Acceleration response spectrum values Imperial Valley.........31
4.1 Earthquake ground motion information............................34
5.1a Bridge geometry.................................................46
5.1b Superstructure geometry.........................................46
5.1c Substructure geometry...........................................47
5.2 Interface properties............................................50
5.3 Material properties.............................................52
5.4 Physical and mechanical properties of commercially available
geogrid (after Korner, 1986)....................................54
5.5a Ramberg-Osgood material properties..............................55
5.5b Ramberg-Osgood material properties..............................55
6.1 Permanent displacement at top of wall..........................112
6.2 Summary of dynamic analysis results............................113
7.1 Permanent displacement at top of wall..........................170
7.2 Summary of dynamic analysis results............................171
8.1 Input parameters...............................................173
8.2 Finite element forces..........................................174
xix


1. Introduction
1.1 Problem Statement
The substructure of a highway bridge consists of components designed to
support the superstructure and highway overpass. Bridge abutments are
structures located at the ends of a bridge. Their main function is to retains the
earth underneath and adjacent to the approaching roadway, and support the
approaching roadway or approach slab. There are many types of bridge
abutments from gravity abutment, which resists horizontal earth pressure with
its own dead weight to cantilever abutment that is virtually identical to a
cantilever retaining wall. These are just a few of the many types of abutments
being constructed today. See figure 1.1 illustrating the gravity and cantilever
type bridge abutments.
TYPICAL CANTILEVER ABUTMENTS
TYPI CAL SPREAD FOOTING ABUTMENTS
Figure 1.1 Typical cantilever and spread footing abutments
1


One type that has been gaining popularity over the years is the
reinforced earth abutment commonly referred to as a mechanically stabilized
earth (MSE) structure. The soil behind this type of abutment is typically
reinforced with relatively light and flexible materials such as thin strips of
geosynthetics. These are extensible and have high tensile strengths
(Leshchinsky, 1995). Figure 1.2 illustrates the basic elevation of a MSE
bridge abutment.
TYPICAL MSE ABUTMENTS
Figure 1.2 Typical MSE abutment
The reinforced soil mass is typically supported by a facing panel that
prevents raveling of the soil immediately behind the facing. Depending on the
design and or aesthetic conditions the face may be geosynthetics wrapped
(type a), segment concrete block (type b), or full height precast panel (type c).
See figures 1.3 a,b or c on the next page for details
2


(a) (b) (c)
Figure 1.3a Geosynthetics wrap
Figure 1.3b Segment concrete block
Figure 1.3c Full height panel
The first design approach for reinforced earth structure was developed
in the 1960s by a French engineer named, Henry Vidal. Over the years MSE
type abutments have proved to be more economical than traditional solid
concrete abutments. Since MSE structures can be constructed relatively fast
and easily, large construction equipment is usually not needed to install the
reinforcement. The key requirements to proper installed MSE abutment wall
are quality control and trained construction personnel. Another major
consideration for MSE walls is that they are flexible and do not require deep
or rigid foundations; thus further reducing construction cost. Over the past
years there has been concern over the metal strip reinforcement being
susceptible to corrosion, creep, and deterioration to the wall. To
accommodate these concern additional safety factors for design loads are


required to account for potential degradation of the reinforcement over its
design life. Figure 1.4 illustrates Tensar geogrid geosythetic material
(manufactured by Tensar Earth Technologies, Inc) one of the commonly used
reinforced wall systems.
Eeoorixl Rib Sbim
Figure 1.4 Tensar geogrid geosythetic material
1.2 Objectives
The objective of this thesis is to research the behavior and response of a
simple span concrete bridge supported by MSE abutments under the
4


influence of a real ground motion time history or seismic acceleration record.
Will this bridge structure be functional and safe during and after a seismic
event? This research will be accomplished through the following tasks:
1. Develop a full scale 3 dimensional CADD graphic model of the bridge
structure including; MSE walls, abutments, with supporting soil using
the engineering graphic program Microstation-J, developed by Bently
Corporation. This model provided key nodal point coordinates in the
layout of the bridge geometry. These key nodal points were then
imported into True-grid developed by "XYZ Scientific Application, Inc.
True-Grid then generated the required output data that would later be
used as the input file for the finite element program.
2. A numerical analysis program will be used to solve this finite element
problem. The input file generated by True-Grid will be used for the
finite element computer program, NIKE3D, developed by Lawrence
Livermore National Laboratory.
3. Data output from NIKE3D was extracted and analyzed by the post
processor program, Griz, developed by "Lawrence Livermore
National Laboratory to interpret the response of the bridge and wall
systems. Griz also has the capability of graphically displaying selected
nodal points, displacements, accelerations and stresses. This feature
will aid in locating the maximum values with corresponding time event
5


4. Review reports submitted by reinforced wall companies reporting the
condition of existing MSE bridge abutments and walls after a seismic
ground motions event.
1.3 Significance of This Research
Mechanically stabilized earth (MSE) structures such as retaining walls for
bridge abutments, retaining walls with steep back slope are becoming more
popular in seismically active areas in the United States due to several factors.
a. Behavior of the structure.
b. Cost consideration
c. Ease of construction
d. Performance Base Seismic Engineering (PBSE)
a. Recent earthquake events have brought about renewed interest in the
response of MSE structures to seismic loading. With mechanically
stabilized earth structures, the current design code does not appear to
fully incorporate their inherent flexibility, which permits minor yielding
during a seismic event. Observation reports from local agencies on the
performance of MSE structures after a seismic event indicate no major
structural damage to many of their wall structures but minor concrete
spalling.
b. MSE structures have gained popularity over the past few years as a
method of constructing bridge abutments which are both functional and
6


aesthetically pleasing. In addition, mechanically stabilized earth
systems have proved to be more economical than traditional solid
reinforced concrete walls, since large rigid foundation systems are not
required, materials are fabricated at a plant providing for a more efficient
facing panel production and quality control.
c. Construction of MSE walls can usually be built relatively fast and easily
requiring less time on the project site and finishing the project on time or
ahead of schedule. Some factors that affect the construction of large or
small projects include equipment, material and workers. Since large
construction equipment is usually not required to install the
reinforcement materials or panels this will save construction time and
will be less complicated to install. Well-trained workers are extremely
important for proper installation of the MSE wall systems, in return will
save on construction time, less workers at the job site and completion of
the project more efficiently.
d. Performance base engineering (PBE), is not new. Many of our major
manufacturers use this approach to design and improve their prototype
through extensive testing prior to production. Until recently PBSE has
been more complicated, except for large-scale development of identical
buildings. Each structure designed by this process is virtually unique
and the experience obtained is not directly transferable to structures of
7


other types, sizes, and performance objectives. Now due to the recent
advancements in seismic hazard assessment, PBSE methodologies,
experimental facilities, and computer applications, PBSE has become
an increasingly more attractive option to engineers and developers in
seismic active areas. In order to utilize PBSE designs effectively, one
needs to be aware of the uncertainties involved in both the structural
performance and seismic hazard. Today the two available prominent
PBSE design guidelines are referred to as ATC-40 and FEMA-
273/274.
8


2. Literature Review
2.1 Introduction
In this literature review, several items will be discussed. First is the
current published seismic design standards and are contained in the
American Association of State Highways and Transportation Officials,
AASHTO, Standard Specifications for Highway Bridges 16th edition and the
Load Resistance Factor Design Bridge Design Specification, LRFD, and is
based on the Mononobe-Okabe theory. Secondly, a review of the pseudo-
static analysis method developed by Mononobe and Okabe to estimate the
lateral earth pressure acting on retaining structures during earthquake events.
Thirdly, the review of the performance of existing MSE structures after an
earthquake event.
2.2 AASHTO Current Design Guidelines
AASHTO, classifies retaining structures as gravity, semi-gravity, non-
gravity cantilever and anchor. Mechanically stabilized earth (MSE) walls fall
into the category of gravity walls since MSE walls derive their capacity to
resist lateral loads through a combination of dead weight and lateral
resistance. The type of construction for MSE walls can vary from modular
precast concrete panels, modular concrete blocks or geosynthetic
reinforcements with a cast in place concrete or shotcrete facing. MSE walls
9


are typically used where conventional gravity, or cantilever retaining
walls are considered, but are well suited where substantial differential
settlement is anticipated. The allowable settlement of MSE walls is limited by
the longitudinal deformability of the facing material and the performance
requirements of the structure.
ASSHTOs, Standard Specification for Highway Bridges 16th edition,
provides seismic design guidance regarding the lateral earth pressure
generated from a seismic event. This method a pseudo-static approach
developed by Monomobe and Okabe that estimates the equivalent static
forces from a seismic event. In addition when a wall supports a bridge
structure, the seismic design should include the forces transferred from the
bridge superstructure through the non-sliding bearings, such as "elastomeric
bearings into the abutment foundation. To ensure stability against possible
failure modes the MSE walls structural dimensions (figure 2.1) should
satisfying the following factor of safety (FS) criteria.
Sliding FS > 1.5
Overturning FS > 2.0 for footing on Soil
FS > 1.5 for footing on Rock
Bearing Capacity FS > 1.5 for footing on soil or rock -Seismic loading
Factor of safety against sliding and overturning failure under seismic may
be reduced to 75% of the factor of safety listed above
Table 2.1 AASHTO factor of safety criteria
10


FAILURE SURFACE FOR
Figure 2.1 MSE wall element dimensions needed for design
AASHTO assigns bridge structures to one of four Seismic Performance
Categories (SPC), A through D, based on the Acceleration Coefficient (A) and
the Importance Classification (IC). Minimum analysis and design
requirements are governed by these SPC values. See the following table 2.2
for Seismic Performance Category (SPC) with Important Classification (IC).
11


Acceleration Coefficient A Importance Classification I II
A < 0.09 A A
0.09 0.19 0.29 < A D C
Table 2.2 Seismic Performance Category (SPC) with important classification
For bridge structures in Category B with free standing abutments or
retaining walls which may displace horizontally without significant restraint,
the pseudo-static Mononobe-Okabe method of analysis is recommended for
computing the lateral active soil pressures during a seismic loading. A
seismic coefficient equal to one-half the acceleration coefficient is
recommended.
( Kh = 0.5A ) (2.1)
The effect of the vertical acceleration may be omitted. It should also be noted
that for AASHTO Category A structures there are no special seismic design
requirements for the foundations and abutments.
AASHTOs, LRFD bridge design specifications and seismic design
guidelines for MSE walls provide limited substantial information on MSE wall
design. AASHTO preesnrtly calculates the seismic earth pressure using the
Mononabe-Okabe method for external stability, Figure 2.2 provides additional
information to AASHTO internal and external stability requirements.
12


Mass for Inertial Force
Figure 2.2 ASSHTO seismic external stability of a MSE wall
The values for PAe and Pir for a horizontal back fill may be determined using
the following equations:
Am = (1.45 -A)A (2.2)
Pae = 0.375 Yeq Am Ys H2 (2.3)
Pir = 0.5 YEQ Am Ys H2 (2.4)
13


Where:
A = maximum earthquake acceleration coefficient
Yeq =Load factor for EQ loads
Am = Maximum wall acceleration coefficient at the centroid of the wall
mass
Ys = Soil unit weight (kef)
H = Height of wall (ft)
For most MSE abutment structures the backfill slope should be horizontal.
AASHTO does allow a reduced value for the Mononabe-Okabe
method for walls that can displace laterally. ASSHTO acknowledge that the
internal lateral deformation response of the MSE wall is more complex and
further research and testing is necessary. It is not clear at this time how much
the acceleration coefficient could be decreased due to the allowance of some
lateral deformation during a seismic loading internally in the MSE wall.
The internal stability including the soil reinforcement shall be designed
to withstand horizontal forces generated by the internal inertia force; Pj and
the static forces. Figure 2.3 illustrates the internal stability for inextensible
and extensible reinforced MSE walls.
14


Ff Internal Inertial force due to the weight of the
backfill within the active zone.
L ei The length of reinforcement in the resistant
zone of the i'th layer.
Tmax = The load per unit wall width applied to each reinforcement
due to static forces.
Tmd *= The load per unit wall width applied to each
reinforcement layer due to dynamic forces.
The total load per unit wall width applied to each layer, Ttotol = TmCD< + T,^
Figure 2.3 Seismic internal stability of a MSE wall
This internal force shall be distributed to the reinforcement
proportionally to their area on a load per width of wall basis as indicated
above. The maximum tension forces including static and dynamic component
applied to each layer is equal to:
Tmd = YP
m
Z(4,)
(2.5)
1 total
Tmax T
md.
(2.6)
15


2.3 Mononobe-Okabe Method
The current design method for reinforced walls experiencing dynamic
loading is an extension of the Coulomb sliding-wedge theory. The
Mononobe-Okabe analysis correctly includes the horizontal inertial forces for
the internal seismic resistance. This pseud-ostatic thrust that the backfill
imposes on the reinforced soil mass is also modeled in this analysis.
Therefore, the seismic design of reinforced walls is similar to the method used
for static stability, except and an additional horizontal force must be
accounted for in the analysis. Figure 2.4 illustrates the force equilibrium
diagram in Mononobe-Okabe analysis (Kramer 1996)
Figure 2.4b Forces acting on passive wedge
16


The pseudo-static acceleration components exerted on the wedge
mass, is ah (=khG) the horizontal component, and av (=kvG), the vertical
component, are based on the earthquake peak ground acceleration and G is
the gravitational acceleration. In an active earth pressure condition, the
active thrust with the effect of the earthquake, PAE, and from the force
equilibrium diagram shown in figure 2.4a, the following equation can be
determined:
The following parameters apply to the above equation: y is the unit weight of
the back fill; H is the total height of the wall; and KAE is the dynamic active
earth pressure coefficient and is given by the equation 2.8.
<|> p > y, and i|/ = tan"1[kh/ (1-kv)]; and soil-wall interface friction angle. aAE is the critical failure angle inclined from
the horizontal axis, cxAe in an earthquake event is smaller than one in a static
event. The critical failure surface angle is found by equation 2.9
Pae = 1/z Kae yH2 (1-Kv)
(2.7)
cos2^-#-1?)
(2.8)
17


(2.9)
aAE = ~ys + tan
- tan(^ -y/ P) + C,E
'IE
CIE = ^jtanty-y/ f3)\\an((f) -y/ JJ)+cot($-y/ 8][\ + tanfA+^+^cot^-^--£?)]]
Where
C2E = 1 + {tan(£ + y/ + 0)[tan(^ y/ f3) + cot(^ -y/ 6)]}
The location of the resultant active thrust Pae from the soil retaining
wall in the Mononobe-Okabe method is the same as the static Coulomb
theory, and resultant force acting at a height of H/3 form the base of the wall.
The resultant active force Pae has two components, static and dynamic.
Pae = Pa + APae (2-10)
PA is the static component of the active force and APAe is the dynamic
component of the active force. As suggested by Seed and Whitman (1970)
the dynamic force component acts at a height approximately equal to 0.6H.
With this information the location of the resultant active force can be
determine by equation 2.6.
^f + AP,£(0-O (2.n)
18


Similar to the active earth pressure the passive earth pressure and dynamic
force components can be determine. For more detail information on passive
earth pressure derivations see appendix.
Since the development of the Mononobe-Okabe analysis,
improvements to this method were made by several individuals including
Seed and Withman (1970). Seed and Withman concluded that the vertical
acceleration could be ignored when the Mononobe-Okabe method is used to
estimate PAe for typical designs. Also the assumption is made that the backfill
is unsaturated, so that liquefaction problems will not arise. Bathurst and Cari
(1995) proposed the following active dynamic pressure distribution due to soil
self weight as shown in figure 2.5
0.8AKaeyH
0.8AKaeYH
1) static pressure 2) dynamic pressure
Figure 2.5 Total earth pressure distribution due
and Cari (1995)
mH
Pah
_________/
-K).2AKab^H
3)total pressure
to soil proposed by Bathurst
19


The dynamic active pressure coefficient KAe is the sum of the static
and dynamic earth pressure coefficient.
Kae = Ka + AKae (2-12)
The key parameter in the Mononobe-Okabe method is selecting the kh
(Horizontal peak ground acceleration coefficient). Currently, there is no
consensus on selecting this design value. AASHTO (1996) Standard
Specification for Highway Bridges uses the equation kh = 0.85 Am/G Am/G ,
where Am is the magnitude of the peak ground acceleration. AASHTO 2002
LFRD (Load Factor Resistance Design) specification recommends that kh =
Am = (1.45-A)*A where A is the maximum earthquake acceleration coefficient
from ASSHTO Division 1A contour map. Other sources like Whitman (1990)
recommend values for kh could range from 0.3 to 0.5 of Am.
2.4 Evaluation of Seismic Performance in MSE
Structures
In the last decade there have been major earthquake events in the
United States (Northridge, California, 1994, 6.7 Richter magnitude),
Japan (Great Hanshin, Kobe, 1995, 7.2 Richter magnitude), and Turkey
(North Anatolian, Izmit, 1999, 7.4 Richter magnitude). The Northridge
Earthquake was responsible for 57 deaths, 11,000 injuries and $20 billion in
damages, The Kobe Earthquake was a terrible tragedy that killed over 5,000
people, injured 27,000 more and destroyed over 150,000 structures. Izmit
20


Earthquake resulted in 16,000 deaths, 30,000 injuries and over $16 billion
dollar in damages.
In the three earthquakes cited, there were numerous MSE structures
constructed near the respective epicenter of the seismic event. The purpose
of this section is to briefly catalogue the conditions of the MSE structures
subjected to seismic events in the Northridge, Kobe and Izmit earthquakes.
2.4.1 Northridge Earthquake
A total of 23 MSE structures were located within the affected area of
the earthquake. Of these structures, more than 65% were higher than 5 m
and more than 25% were high than 10 m. The distance of the MSE structures
from the epicenter ranged from 13 to 83 km. The estimated ground
acceleration varied horizontally from 0.07 g to .91 g and varied vertically from
0.04 g to 0.62 g. A review of the MSE structures near the epicenter was
conducted by engineers from the MSE wall companies and the California
Department of Transportation, (CalTrans). The structures include 21 MSE
wall supporting the Los Angeles Metro Link, CalTrans mountain highways,
freeways off ramps, and two MSE bridge abutments in Corona. The only
major damage that appeared was some minor spalling of the concrete panels
in some of the walls. It was noted that, adjacent structures to the MSE walls,
such as buildings suffered much more severe damage and in some instances
were posted unsafe.
21


2.4.2 Kobe Earthquake
Of the 120 MSE structures inspected after the earthquake,
approximately 70% were over 5 m high and 15% were over 10 m high. The
actual ground acceleration was .27 g. Ground motion was evident above or
adjacent to several wall structures. Many walls showed minor cracking of the
isolated concrete panels and 3 walls exhibited significant lateral movement of
4 mm to 113 mm (displacement relative to bottom of panel at mid height and
top of walls). All of the walls remained functional after the earthquake.
2.4.3 Izmit Earthquake
A full evaluation of the MSE structures for this particular earthquake
has not yet been completed. However, one bridge and ramp structure was
surveyed at Arifiye, almost immediately adjacent to the epicenter. Although
the bridge itself collapsed, the MSE ramp wall sustained only nominal
damage and remained stable. Shear deformation from differential settlement
propagated upward through the panels, was separated by as much as 75
mm. These MSE walls were designed for a ground acceleration of .10 g. This
resulted in only a minor increase in the amount of reinforcement strips
compared to the static design. Yet the actual ground acceleration was
measured at 0.4 g. It is interesting to note that if the full effect of the ground
22


acceleration was considered in design under current practice, then at least
40% more reinforcement would have been added.
2.5 Conclusion
Recognizing that MSE walls can deflect and remain stable means that
establishing an inventory of wall deflections after seismic events and
corresponding wall heights will be an important step in seismic evaluation of
MSE structures. To be reliable, the location and the relationship of the base of
the wall with respect to the upper or top portion of the wall must be
established. Also, when significant seismic events occur in cities where base
line surveys have been completed, follow up measurements should be taken.
It is anticipated that actual deformation reading may be used to better tailor
design models and more realistic designs.
23


3. Theoretical Background of NIKE3D Program
3.1 NIKE3D Finite Element Program
As best described from the NIKE3D users manual, NIKE3D is a fully
implicit three-dimensional finite element code for analyzing the finite strain for
static and dynamic response of inelastic solid, shell, and beams. NIKE3D was
originally designed and developed by Dr. John O. Hallquist and has since
been used extensively by Lawrence Livermore National Laboratory on several
research projects. In addition, it has been used to study the static and
dynamic response of bridge structures undergoing finite deformations and
several other soil-structure interaction research projects at the Center for
Geotechnical Engineering Science, University of Colorado at Denver. The
uses of the 8-node solid elements, 4-node membranes and shell elements
and 2-node truss and beam elements, were provided to achieve this spatial
discretization. Over twenty constitute models are available for representing a
wide range of elastic, plastic, viscous and thermally dependent material
behavior. For this study the uses of the 8-node solid element were used to
built the bridge superstructure, abutments back wall and footing, MSE wall
facing, and soil backfill finite model. The 4-node shell element was
implemented in this finite element model primarily for the soil geosynthetic
reinforcing material. NIKE3D has a significant feature of interface formulation
24


capacity. In NIKE3D, surfaces between different material mesh and surfaces
could permit voids or frictional sliding during analysis. There are two main
algorithms that permit this interface capability:
Penalty formulation method
Augmented Lagrandian method
For the penalty method, penalty springs are generated between the
contract surfaces when an inter-material penetration is detected. This penalty
spring scale factor ranges from 0.1 to 0.001, so it may be used to ensure
convergence. The augmented Lagrangian method is iterative and an
additional penalty for enforcing contact constraints.
3.2 Microstation and Truegrid Mesh Generation
Programs
To develop a 3 dimensional finite element model mesh of the
mechanically stabilized earth walls (MSE), bridge superstructure, and
substructure, two programs were used to perform this task. These two
programs are, Bentley Systems Mircostation J and XYZ Scientific
Applications TrueGrid.
Microstation J is a 3 dimensional drawing software platform used to
develop the 3 dimensional scale model bridge structure based on a define
global coordinate system, (figure 3.1). From this 3D model, key coordinates
were extracted and imported into TrueGrid.
25


TrueGrid, is a finite element mesh generator program that provided the
final mesh configuration for the MSE wall and bridge structure. TrueGrid also
created the input file code for NIKE3D that will model the behavior of the
structure under the applied loads.
Wing Walls
Fnd Soil
MSE Wall-
Abutment 1
Abutment 2
Figure 3.1 NIKE3D bridge model
3.3 Material Model
NIKE3D includes twenty-two material models. These constitutive
models cover a wide range of elastic, plastic, viscous and thermally
dependent behavior. For this study four types of material were used.Three of
the four material (foundation soil, concrete for the MSE walls and bridge
structure, and inclusion) were simulated using the isotropic elastic model. The
fourth type of material, The MSE wall backfill, was simulated using the non-
linear Ramberg-Osgood model. The required input parameters for the
isotropic elastic material includs; the density, modulus of elasticity and
26


Poisson's Ratio. For the Ramberg-Osgood material input, the parameters are
discussed in the next section.
3.4 Ramberg-Osgood Elastoplastic Model
The Ramberg-Osgood elastoplastic model is used to treat the
nonlinear hysterestic elasto-plastic constitutive behavior of many materials.
This model allows a rate-independent representation of the hysterestic energy
dissipation observed in material subjected to cyclic shear deformation. The
model is intended as a material for shear behavior and it can be applied in
soil dynamics and seismic analysis of soil-structure.
In the Ramberg-Osgood model, five material parameters are required
Reference shear strain yy
Reference shear stress xy
Stress coefficient a
Stress exponent r
Bulk modulus K
The stress and strain relationship for monotonic loading in Ramberg-Osgood
model is give by the following equations.
Y_
yy
Z T
-----1-a
zy zy
ify >0
r_
yy
r
z z
h a
ify <0
zy zy
(3.1)
27


It should all be noted that there is a computer program named RAMBO that
was developed specifically for determiming these five material model
parameters.
3.5 Eigenvalue Analysis and Rayleigh Damping
NIKE3D has the capability of doing the eigenvalue analysis on the
proposed bridge model and the number of mode shapes can be specified in
the input file for NIKE3D. In this study a total of fifteen mode shapes were
used for this bridge model. After performing an analysis, NIKE3D will return a
natural frequency corresponding to each of the mode shape. Knowing the
natural frequency of the systems and natural frequency of the forcing motion,
amplification of the systems can be calculated. A systems natural frequency
associated with a mode shape can be used to determine the required
coefficient for the Rayleigh damping.
Rayleigh damping is a systems damping and is applied in chapter 6 of
this study. Rayleigh damping is considered as a damping matrix [C], and it is
a linear combination of the mass matrix [M] and the stiffness matrix [K]
according to the following equation.
[C] = a[M]+p[K] (3.2)
where a and p are the mass and stiffness proportional damping coefficient.
With A systems natural frequencies computed using eigenvalue analysis, a
and p coefficient for Rayleigh damping can be calculated. Natural
28


frequencies of the first fifteenth modes were selected in the computation. The
Rayleigh damping coefficient can be determined with the following equations;
a = 2co\ 2 2(a)2<*2 co&)
1 {g>\-cd])
(3.3)
p_ 2{(Q2t;2-CQ&)
(3.4)
where coi and 2 are respectively the first and fifteenth mode of a systems
natural frequency. The units for 1 and 2 are in radian/seconds. ^ and £2
are the fraction of critical damping corresponding to 1 and 2. Users have to
specify the fraction of critical damping. For structural engineering type
systems, 5% critical damping has been an acceptable value. In this studies £1
and £2, 5% of the critical damping was used. The calculated a and p value
were then specified in the material deck of NIKE3D input file. Since Rayleigh
damping is an overall system damping, the computed value for a and p
remained the same for all the material that comprised the bridge model.
The following table 3.1 provides the mode shape numbers along with
the frequencies and periods from the eigenvalue analysis.
29


Mode Shape No. Frequency (radian) Frequency (hertz) Period (sec)
1 16.65 2.61 .37
2 16.48 2.60 .36
3 17.91 2.94 .34
4 50.81 8.06 .12
5 50.90 8.07 .11
Table 3.1 Mode shapes with frequencies and periods.
Tables 3.2 through 3.5 are the response spectrum values for the first
five mode shapes interpolated from the response spectrum curves and using
the compute program NONIN.
NorthRidge Earthquake Displacements Response Spectrum Factors w/ Damping
Mode Shape Vertical Longitudinal Transverse
0% 5% 0% 5% 0% 5%
1 7.41 4.88 9.11 5.48 8.15 5.03
2 11.98 5.55 8.33 4.87 9.27 5.37
3 8.70 5.04 8.07 4.67 8.0 5.54
4 .92 .41 1.0 1.0 .51 .31
5 .58 .38 1.0 1.0 .41 .31
Table 3.2 Displacement response spectrum values Northridge
NorthRidge Earthquake Accelerations Response Spectrum Factors w/ Damping
Mode Shape Vertical Longitudinal Transverse
0% 5% 0% 5% 0% 5%
1 2.95 1.32 1.36 2.67 2.07 1.4
2 3.96 1.45 2.76 1.60 2.76 1.76
3 3.14 1.55 2.95 1.65 2.70 1.65
4 2.35 1.27 1.60 .95 1.50 1.08
5 2.0 1.05 1.25 .92 1.60 .90
Table 3.3 Acceleration response spectrum values Northridge
30


Imperial Earthquake Displacements Response Spectrum Factors w/ Damping
Mode Shape Vertical Longitudinal Transverse
0% 5% 0% 5% 0% 5%
1 1.74 1.43 3.80 3.85 2.10 1.61
2 2.33 1.53 3.80 3.85 2.02 1.51
3 2.48 1.33 2.78 2.80 2.30 1.60
4 .88 .33 1.0 1.0 1.0 1.0
5 .54 .31 1.0 1.0 1.0 1.0
Table 3.4 Displacement response spectrum values Imperial Valley
Imperial Earthquake Accelerations Response Spectrum Factors w/ Damping
Mode Shape Vertical Longitudinal Transverse
0% 5% 0% 5% 0% 5%
1 .55 .39 1.15 .78 .61 .40
2 .99 .42 .81 .76 .79 .52
3 .87 .42 .84 .71 .81 .44
4 .60 .84 .92 .59 .60 .41
5 .60 .92 .84 .52 .60 .40
Table 3.5 Acceleration response spectrum values Imperial Valley
Comparing the response spectrum tables for the Northridge and
imperial Valley earthquakes indicates that the Northridge earthquake has a
greater effect on the bridge and MSE wall structure. This could be caused by
by several factors. First, the structure in the Northridge analysis is closer to
the seismic epic-center. Secondly, the ground motion is stronger in the
Northridge earthquake as compared to the Imperial Valley earthquake. This
is also evident when comparing the response spectrum acceleration values.
31


4. Ground Motion Used for this Study
4.1 Introduction
Ground vibrations during an earthquake can severely damage
structures and equipment. The ground acceleration, velocity and
displacement are amplified when transmitted through a structure. This
amplified motion can produce forces and displacements which may exceed
the structure limits. Many factors influence ground motion and its
amplification, therefore the understanding of how these factors influence the
response of a structure is essential to design a safe and economical design.
Earthquake ground movement is measured by strong motion
instruments that record the acceleration of a structure or ground surface. The
recorded ground accelerograms is then corrected for instrument error and,
integrated to obtain the velocity and ground displacement time history. Three
orthogonal components of ground acceleration, two in the horizontal
directions and one in the vertical, are recorded by the field instrument.
Earthquake magnitude is a quantitative measurement of its size, and each
earthquakes motion exhibits its own unique motion parameters. Three
ground motion parameters of engineering significance are
32


amplitude, predominant frequency, and duration. So with the ground motion
parameters one could define the characteristics of an earthquake.
4.2 Ground Motion Time History and Input
For this study the ground motions or acceleration time histories
selected were all corrected records. The term corrected record stands for
filtered record. The corrected strong motion data had been corrected from the
raw data by filtering out high frequency or low frequency background noise,
correct the measurement errors and calibrating the instrument. The program
NONLIN Nonlinear Dynamic Time History Analysis of Single Degree of
Freedom Systems includes a CD-ROM collection of digitized earthquake
acceleograph records dating back to 1930. The two accelerograph records
selected for this study are;
Northridge, California Earthquake
Imperial Valley Earthquake
Table 4.1 list the dates, magnitude, intensity, depth, epicentral distance and
peak ground acceleration (PGA). Also note that the earthquake intensity is 9
Modified Mercalli (MM) intensity scale.
33


Category Magnitude 7 Magnitude 7
Record No. 1 2
Name Earthquake Northridge, California Imperial Valley
Date January 17,1994 October 15,1979
Magnitude 6.8 (ML) 6.6 (ML)
Intensity 9(MM) 9 (MM)
Depth 18 Km 0 Km
Site Geology Unknown Alluvium (>300m)
Epicentral Distance 19 Km 27 Km
PGA 0.54 G 0.45 G
(MM) = Modified Mercalli
Table 4.1 Earthquake ground motion information
The most commonly used amplitude parameter in characterizing a
particular ground motion is (PGA) peak ground acceleration. The PGA is
defined as the largest absolute value of acceleration from a given time
history. The acceleration time histories were plotted in figures 4.1 thru 4.6 for
both the vertical and horizontal components and were used as the input
ground motion in this study. Prior to starting the dynamic analysis, a static
analysis was performed in the first 10 seconds to allow for gravity dead load
to set within the structure.
34


NorthRidge Earthquake
Vertical Acceleration Time History January 17,1974
PGA =.54g at 15.38 sec.
0.6 ---s--....-----------------------------r--v7-
-0.6 J' .'--------------------------------------------J
0 5 10 15 20 25
Time (Seconds)
Figure 4.1 Northridge vertical acceleration time history
Northrldge Earthquake
Horizontal Acceleration -Time History 90 Degree January 17,1974
PGA= .57g at 15.34 sec.
Figure 4.2 Northridge horizontal @ 90 degree acceleration time history
35


NorthRldge Earthquake
Horizontal Acceleration Time History 360 Degree January 17,1974
PGA ,58g at 14.32 sec
Time (Seconds)
Figure 4.3 Northridge horizontal @ 360 degree acceleration time history
Imperial Valley EarthQuake EL Centro
Vertical Acceleration Time History Oct. 15,1979
PGA = .46g @ Time 12.8 sec
Figure 4.4 Imperial Valley vertical acceleration time history
36


Imperial Valley EarthQuake EL Centro
Horizontal Acceleration Time History S50W Oct. 15,1979
PGA = .45g @ Time 14.98 sec
j
Figure 4.5 Imperial Valley horizontal @ 360 degree acceleration time history
Imperial Valley EarthQuake EL Centro
Horizontal Acceleration Time History S40E Oct. 15, 1979
PGA = 0.34g @16.5 sec.
0.4
0 5 10 15 20 25
Time (Seconds)
Figure 4.6 Imperial Valley horizontal @ 90 degree acceleration time history
37


4.3 Response Spectrum
Response spectrum is an important tool in the seismic analysis and
design of structures. The response spectrum introduced by Biot and Housner
describes the maximum response of a damped single-degree-of-freedom
(SDOF) oscillator at different frequencies or periods. The computer program
NONLIM (Nonlinear Dynamic Time History Analysis of Single Degree of
Freedom Systems) and was developed by Finley A. Charney, PHD., P.E.
With Advance Structural Concepts, Inc.
The computed spectral values include absolute acceleration response,
relative velocity response, relative displacement response, and their
corresponding natural period. The Damping Ratio is defined as a fraction of
the critical damping for this study only the 0% and 5% damping ratio were
calculated. See Figures 4.7 thru 4.9 for response spectrum graphs.
38


Displacement, am
1000.00
100.00
10.00
1.00
0.01 0.10 1.00 10.00
Period, Seconds
0.01 0.10 1.00 10.00
Period, Seconds
0.01 0.10 1.00 10.00
Period, Seoonds
(a)
0.01 0.10 1.00 10.00
Period, Seconds
0.01 0.10 1.00 10.00
Period, Seconds
Pseudo Acceleration, (g)
Period, Seconds
(b)
Figure 4.7a Northridge 360 degree horizontal response spectrum
Figure 4.7b Northridge 90 degree horizontal response spectrum
.........Dash 5% Damping ---------Solid 0% Damping
39


Diaplaoaanant, can
Pariod, Saoonda
0.01 0.10 1.00 10.00
Pariod, Seoonda
0.01 0.10 1.00 10.00
Pariod, Saoonda
Paaudo Valocity, am/a
1000.00
100.00
10.00
1.00
0.01 0.10 1.00 10.00
Pariod, Saoonda
0.01 0.10 1.00 10.00
Pariod, Saoonda
Paaudo Aooalaration, (g)
10.00
1.00
0.10
0.01
0.01 0.10 1.00 10.00
Pariod, Saoonda
(a) (b)
Figure 4.8a Imperial Valley 360 degree horizontal response spectrum
Figure 4.8b Northridge vertical response spectrum
...........Dash 5% Damping -----------Solid 0% Damping
40


Displacement, cm
100.00
10.00
1.00
0.10
0.01 0.10 1.00 10.00
Period, Seconds
Displacement, on
Period, Seconds
Pseudo Velocity, cm/s
0.01 0.10 1.00 10.00
Period, Seconds
0.01 0.10 1.00 10.00
Period, Seconds
Pseudo Acceleration, (g)
Period, Seconds
Pseudo Acceleration, (g)
10.00
1.00
0.10
0.01
0.01 0.10 1.00 10.00
Perlod, Seconds
(a)
(b)
Figure 4.9a Imperial Valley vertical response spectrum
Figure 4.9b Imperial Valley 90 degree horizontal response spectrum
..........Dash 5% Damping ----------Solid 0% Damping
41


5. Review of Study and Design Parameters
5.1 Introduction
In order to determine the effect of earthquake ground motions on
bridge MSE abutment walls, two ground motions or acceleration time
histories, were selected for this study:
Northridge Earthquake California
Imperial Valley Earthquake EL Centro
These two ground motion records were selected due to similar frequencies
and durations but different acceleration amplitudes. For this study a static
analysis was performed prior to the three different dynamic analyses with
different directional ground motion acceleration combinations. The
directional ground motion combinations included;
Vertical, Transverse and Longitudinal
Longitudinal and Transverse
Vertical and Longitudinal
Chapter 6 and 7 will discuss the results from the finite element
analyses for the different directional ground motion combinations from the
Northridge and the Imperial Valley earthquakes. The finite element models
concerned two types of loading: static loading and dynamic loading. The
static loading or gravitational acceleration (G) 9.81 m/sec2 (32.2 ft/sec2) was
42


applied incrementally from 0 seconds to 10 seconds. This was done so that
the gravity effect on the structure would be set in the structure prior to
applying the dynamic loading. The ground motion time history started at 10
seconds and continued to 25 seconds for a total time of 15 seconds. The
time increment was broken down to 0.02 seconds with a total of 502 time
steps for each ground motions combination. The input ground motion
accelerations were applied at the fixed soil foundation base. The
acceleration time history plots for the above noted seismic earthquake
events are shown in chapter 4 figures 4.1 thru 4.6.
5.2 Bridge Model Dimensions
The same finite element model was used for both Northridge and
Imperial Valley ground motion analyses. A plan view of the bridge model is
shown in figure 5.1, (a simple span bridge with a total structure length of
48.8 meter 160-0). Figure 5.2 provides additional details on the
superstructure and substructure. The superstructure consists of a 203mm
(8) concrete deck and concrete barriers supported by BT84 Precast
Girders. The bridge abutments support the superstructure girders with a
standard back wall and beam seat founded on a concrete spread footing.
Wing walls are provided to retain the soil from the back wall and each side
of the approach roadway pavement.
43


Figure 5.1 Bridge plan view

160'-0
Ml. 76)


Figure 5.2 Bridge elevation and typical section
TYPICAL TRANSVERSE ABUTMENT PLAN
SECTION


The MSE walls are located in front of the abutment footing and wraps
around the abutment sides and parallel to the wing walls. See Figure 5.2
abutment plan for layout of MSE walls and Tables 5.1a thru 5.1c for
additional bridge model dimensions and clearances.
Span Length 160 ft 48.8 m
Bridge Deck Width 39 ft 11.9 m
Gutter line to Gutter Line 36 ft 11.0 m
MSE Wall Width 45 ft 13.7 m
MSE Wall Height 15.6 ft 4.8 m
Table 5.1a Bridge geomerty
Girder Type: BT84
Number of Girders: 6.0 ea
Girder Spacing: 4.8 ft 1.463 m
Girder Depth: 7.0 ft 2.134 m
Girder Area: 6.6 ft2 0.6 m2
Top Deck Thickness : 0.67 ft 0.2 m
Hanuch : 0.17 ft 0.1 m
Barrier Height: 2.8 ft 0.863 m
Barrier Width: 1.5 ft 0.457 m
Table 5.1b Superstructure geometry
46


Footing Width 9.0 ft 2.744 m
Footing Depth 2.0 ft 0.61 m
BackWall 3.0 ft 0.915 m
Diaphram 2.0 ft 0.61 m
Wing walls Thickness 1.0 ft 0.305 m
Wing Wall Depth 15.0 ft 4.573 m
Table 5.1c Substructure geometry
5.3 Boundary Conditions
Figure 5.3 shows the boundary conditions and spatial coordinate
systems adopted for this finite element model. Since NIKE3D is a three
dimensional finite element program, boundary conditions in the x, y and z
directions needs to be established to correctly model the structure. The
boundary conditions (Figure 5.3 and 5.4) indicate that the base soil
elements of this model are fixed with displacement constraints in the x y
and z directions. Roller conditions were applied along back face of the MSE
soil backfill. This rolled condition allow for displacement in the z and y
directions but constrain the displacement in the x direction. Figure 5.4 also
provides information on inclusion length and spacing, MSE wall height and
thickness, and bridge superstructure details.
47


Figure 5.3 Bridge elevation and boundary conditions


Figure 5.4 Boundary conditions and material dimensions
5.4 Slide Interfaces
Sliding interface is one of the major capabilities of NIKE3D. Sliding
interfaces simulate the resistance between the contact surface of two
different materials. For this bridge abutment study there were four different
sliding interfaces defined. See Table 5.4 for interface properties.
49


Interface (degree) 8 (degree) Fs Fk
Foundation Soil-Backfill 28 0.53 0.53
Concrete Foundation 28 19 0.34 0.34
Concrete BackFill 39 26 0.49 0.49
Inclusion-Backfill 14 0.25 0.25
<|) (degree) Internal friction Angle
8 (degree) Interface friction angle
(is Static friction coeifficient
|ik Kinetic friction coeifficient
Table 5.2 Interface properties
Sliding interface requires the input parameter of static friction and the
kinetic friction coefficient, for this study it was assumed that both the static
and kinetic would have the same value. In order to calculate the friction
coefficient, the internal friction angle () between the two materials needs to
be determined. In cases where interfaces lies between materials in contact
with concrete or inclusion, the interface friction angle (8) needs to be
determined before the friction coefficient can be computed. Using the shear
strength test, the soil internal friction angle can be calculated. Once the
internal friction angle is calculated the interface friction angle for concrete
surfaces and inclusion can be determined from Equation 5.1.

(5.11
50


From the interface friction angle (equation 5.2) the coefficient of friction (|i)
can be computed.
H = tan 5 (5.2)
It should be noted that for the sliding interface of foundation soil to backfill,
that equation 6.2 was used directly since 5=<(>. It was also assumed that the
foundation material supporting the bridge abutment was a overconsolidated
clay with a internal friction angle of 28. Whereas the MSE backfill material
was assumed to be a dense sand and gravel mixture with a internal friction
angle of 39. For the inclusion-backfill sliding interface, an interface friction
angle of 14 was selected based on direct shear test between
geomembrane and sandy gravel soil.
NIKE3D defines sliding interface between two contact materials as a
master surface and the other surface being the slave surface. See Figure
5.5 for
Figure 5.5 Master and slave diagram
51


master and slave surfaces orientation and configuration. The number of
sliding interfaces was based on past experiences and performance with
Nike3D which required defining different sliding interface definition at each
interface surface. Due to the number of different elements and inclusions
layers required a large number of slide interface definitions numbers.
5.5 Material Model Parameters
The model materials include foundation soil, concrete wall and
abutment materials. The foundation was assumed to be a rigid stiff hard clay
material, so bearing capacity and deformation on the foundation soil was not
a concern. It was assumed that the foundation soil would behave as an
elastic material when subject to both static and dynamic loading. Table 5.3
shows the elastic material properties of the foundation soil, concrete wall
and the geomembrane used in this study. Similarly the MSE concrete wall
has similar properties of standard 440 kpa or (4000 psi) concrete.
Material Name Density (psf) Modulas of Elasticity, E (psi) Poisson's Ratio, v
Foundation Soil (psf) (kg/mJ) (psi) (MN/m*) -
130 2083 16000 110 0.15
Concrete 145 2323 3472000 25000 0.15
Inclusion 65 1041 41000 288 0.40
Table 5.3 Material properties
52


A geosysthetic reinforced soil structure contains reinforcement are to
restrain longitudinal and lateral deformation of this composite material. The
reinforcement used in MSE structure is also called inclusion and is made
from polymer in the form of high density polyethylene (HDPE). For this
study a commercially available geosynthetic material called geogrid also
named Tensar SR2 was selected. The material properties were obtained
from geogrid specification published by Tensar Earth Technologies Inc., In
this study the inclusions were modeled to simulate elastic material
properties. See table 5.4 for physical and mechanical properties of
commercially available geogrid. To determine the appropriate Youngs
modulus, it was decided to take the strength at 5% strain, which is in units of
(Ibs/ft) and convert this to a force per unit area. To accomplish this the
strength at 5% strain was divided by the average thickness of the rib and
thickness at the rib junction. It was calculated that the average thickness
was approximately 0.003 m or (0.12 inch). So the calculated Youngs
modulus at 5% strain used in this study was 2900 MN/m2 or (3030 kip/ft2).
For this study a sliding penalty value of 1 was selected. It should be noted
that sliding interface formulation plays a major role in this type of study.
Selecting sliding surface penalties value greater than two can generate
unrealistic results. To model the inclusion in NIKE3D, the 4 node shell or
membrane element was used and assigned a thickness of .003 m. This 4
53


node shell element was selected because it has no torsional or bending
stiffness, thus the shell element nodes were to be constrained at the MSE
wall perimeter.
Tensar (uniaxial)
Properties Test Method units SR2
Tensile Strength at 2% Strain M TTM1.1 Ib/ft 1465
XM -
5% Strain M it 3030
XM -
Ultimate M m 5380
XM -
Initial Tangent Modulus M TTM1.1 kip/ft 136.2
XM -
Junction strength TTM1.2 % 80%
Weight Ib/yd2 1.55
Aperture size M in.
XM
Thickness rib in 0.05
junction 0.18
Polymer HDPE
Width ft 3.3
Length ft 98
Weight lb 61
Poisson ratio range v 0.37 -0.44
Table 5.4 Physical and mechanical properties of commercially available
geogrid (after Koerner, 1986)
The back-fill soil material was assumed to behave nonlinearly and
NIKE3D Ramberg-Osgood Elastoplastic nonlinear model was selected to
simulate this behavior. The computer program RAMBO developed by (Tzou-
shin Ueng and Jian-Chu Chen, 1992) was used to compute the required
54


input parameters. See Table 5.5a and Table 5.5b. for the Ramberg-Osgood
computed input values.
Material Name Density Reference Shear Strain, yy Reference Shear Stress, xy
BackFill Soil (psf) (kg/m3) (10-3) (psi) N/m2)
130 2083 0.105 10 72000
Table 5.5a Ramberg-Osgood material properties.
Stress Coefficient, a Stress Exponent, r Bulk Modulus, K
(psi) (MN/m2)
1.1 2.349 42000 302
Table 5.5b Ramberg-Osgood material properties.
The final parameter "K bulk modulus was calculated with the value
Gmax as computed from the program RAMBO, and Poissons ratio of 0.37
corresponding to dense cohesion less soil type. With Gmax and Poissons
ratio, (E), Young modulus can be calculated by the following Equation 5.3.
E=G(2)(1+v) (5.3)
With Youngs modulus and Poissons ratio known, the bulk modulus K can
be computed with the following Equation 5.4
K= E (5.4)
3(1 2u)
55


The bulk modulus K was computed to be 302 MN/m2 or (42000 psi).
5.6 Summary
This chapter outlined the design parameters and assumptions
required to analyze the MSE bridge structure under the effect of a seismic
earthquake event. The next two chapters 6 and 7 review the results from
the Northridge earthquake and the Imperial Valley earthquake. It should be
noted the same NIKE3D model parameter except for the ground motion
acceleration time histories were used for both earthquake events.
56


6. Northridge Earthquake Results
6.1 Data Analysis
A total of four NIKE3D cases were analyzed using the program
NIKE3D with different directional ground acceleration combination as listed
below. The numerical output of these four cases were extracted using the
post-processor GRIZ and then imported into spreadsheet program, Microsoft
Excel where the data was analyzed and graphed.
Static
Vertical, transverse and longitudinal
Longitudinal and Transverse
Vertical and longitudinal
6.2 Study Items
This chapter reviews the study items of interest for this research and
are listed as follows.
Static Loading
Lateral MSE wall displacements
Lateral earth pressure distribution on the MSE wall
Geosynthetics stress distribution
Bearing pressure on abutment footing
Dynamic Loading
Lateral MSE wall displacements
Lateral earth pressure distribution pressure
57


Connection strength
Inclusion tensile stress distribution
Bearing pressures on abutment footing
Soil Acceleration Profile
Wall Permanent forward displacement
Bridge structure vertical displacements
6.3 Case 1: Static Loading Abutment 1
NorthRidge Area Static Loading
Max. Longitudinal MSE Wall Displacement
Abutment 1 __________
: 4 Edge -R
i
NorthRidge Area Static Loading
Max. Longitudinal Soil Pressure
Abutment 1 -----------
Edge -R
Earth Pressures (kpa)
Figure 6.2 Static longitudinal earth pressures
58


o>
re
£
NorthRidge
Max. Longitudinal Inclusion Connection Stress
Static Loading
Figure 6.3 Static longitudinal inclusion stresses
Figure 6.4 Maximum bearing compression contours at footing kpa
59


6.3.1 Inclusion Stresses Static Loading
11.8m (39')
11.8m (39')
60


11.8m (39)
Figure 6.7 3rd Inclusion layer stress contours from top kpa
11.8m (39)
Figure 6.8 4th Inclusion layer stress contours from top kpa
61


11.8m (39)
11.8m (39)
62


11.8m (39')
63


6.4 Case 2: Vertical, Transverse and Longitudinal
Motion Abutment 1
NorthRidge Earthquake
Time History Displacement at Top of Wall
at center of wall
(Vertical,Transverse & Longitudinal Shaking)
Figure 6.12 Time history at top of wall
NorthRidge Earthquake
Max. Longitudinal MSE Wall Displacement
Abutment 1
Edge -R j j
1/4 point -R | i
i ACenter-R
* Center-L
1/4 point -L i i
; Edge-L
Figure 6.13 Maximum MSE wall displacements
64


NorthRidge Earthquake
Max. Longitudinal Earth Pressure
Abutment 1
E
JZ
U)
5
X
re
£
Edge -R
1/4 point -R
A Center-R
* Center-L
1/4 point -L
j Edge-L
0 200 400 600 800 1000
Earth Pressures (kpa)
(Vertical, Transverse & Longitudinal Shaking)
Figure 6.14 Maximum longitudinal earth pressures
NorthRidge Earthquake
Max. Longitudinal Inclusion Connection Stress
Abutment 1
Connection Stresses (kpa)
(Vertical, Transverse & Longitudial Shaking)
Edge -R
1/4 point -R l
Center-R j
Center-L !
1/4 point -L
Edge-L
Figure 6.15 Maximum connection stresses
65


1 1 fim
3
c
o
*3
re
L_
_QJ
O
O
<
North Ridge Earthquake
Positive X Backfill Acceleration Profile
Along center of Abutment No.1
Station Along Backfill
- 1 st Bottom
layer
2nd layer
3th layer
I -_-5f_4th layer
' * 5th Layer i
i
6th Layer |
i 7th Layer ,
|-----8th Layer |
i
----9th !
Figure 6.17 Backfill acceleration profile
66


NorthRidge Earthquake
Max. Transverse MSE Wall Displacement
Abutment 1
Edge -R
1/4 point -R
| A Center-R
I
Figure 6.18 Maximum transverse MSE wall displacements
NorthRidge Earthquake
Max. Transverse Earth Pressure
Abutment 1
Earth Pressures (kpa)
(Vertical, Transverse & Lonitudinal Shaking)
Edge-R i
1/4 point -R
ACenter-R
Figure 6.19 Maximum transverse earth pressures
67


NorthRidge Earthquake
Max. MSE WingWall Displacement
@ Center of WingWall
WingWall -L i
--WingWall-R
Figure 6.20 Maximum MSE wing wall displacements
l
NorthRidge Earthquake
Bridge Deck Displacement
w
a
(A
5
C.L.
Bridge
0.05 0.03 T nni . 1 - |
!
-0.03 T -0.05 1 i
0 10 20 30 40
: Length on Superstructure (m)
! (Vertical.Transverse & Longitudinal Shaking) '
Abutment #1 Abutment #2
Figure 6.21 Bridge deck displacements
68


6.4.1 Inclusion Stresses Vertical, Transverse
Longitudinal Motion Abutment 1
11.8m (39)
!-------------------------------------------------------------------------
Figure 6.22 1st Inclusion layer stress contours from top kpa
69


11.8m (39)
Figure 6.24 3rd Inclusion layer stress contours from top kpa
11.8m (39')
70


11.8m (39)
11.8m (39')
71


11.8m (39)
72


6.4.2 Case 2: Vertical, Transverse and Longitudinal
Motion Abutment 2
NorthRidge Earthquake
Max. Longtudinal MSE Wall Displacement
Abutment No.2
(Vertical, Transverse & Longitudinal Shaking)
Edge-R
A Center-R j
Figure 6.29 Maximum MSE wall displacements
NorthRidge Earthquake
Max. Longitudinal Earth Pressure
Abutment No.2
Edge -R
A Center-R j
Earth Pressures (kpa)
(Vertical, Transverse & Longitudinal Shaking)
Figure 6.30 Maximum longitudinal earth pressures
73


11.8m (39)
<
>
CL of Bridge
Figure 6.31 Maximum bearing compression contours at footing kpa
NorthRidge Earthquake
Max. Transverse MSE Wall Displacement
Abutment No.2
I
Displacements (m)
(Longitudinal, Vertical & Transverse Shaking)
Edge -R
*r- Center-R
Figure 6.32 Maximum MSE wall transverse displacements
74


Wall Height (m) p Wall Height (m)
NorthRidge Earthquake
Max. Transverse MSE Wall Earth pressure
Abutment No.2
Earth pressures (kpa)
(Vertical, Transverse & Longitudinal Shaking)
Edge -R J
a Center-R I
33 Maximum MSE wall earth pressures
NorthRidge Earthquake
Max. Displacement MSE WingWall
@ Center of WingWall Abutment 2
(Vertical, Transverse & Longitudinal Shaking)
WingWall -L
WingWall -R
Figure 6.34 Maximum MSE wing wall displacements
75


6.4.3 Inclusion Stresses Vertical, Transverse and
Longitudinal Motion Abutment 2
Figure 6.35 1st Inclusion layer stress contours from top kpa
76


11.8m (39)
77


6.5 Case 3: Longitudinal and Transverse
Motion Abutment 1
NorthRidge Earthquake
Time History Displacement at Top of Wall
Center of wall abtument 1
E
c
0)
E
0)
o
ra
a
a
Time (sec)
(Longitudinal & Transverse Shaking)
Figure 6.38 Time history at bottom of wall
North Ridge Earthquake
Max. Longitudinal MSE Wall Displacement
Abutment No.1
(Longitudinal & Transverse Shaking)
Edge-R
1/4 point -R
A Center-R
* Center-L
* 1/4 point -L
Edge-L
Figure 6.39 Maximum MSE wall displacements
78


NorthRidge Earthquake
Max. Longitudinal Earth Pressure
Abutment No.1
iEdge-R i
1/4 point-R J
| ACenter-R
Center-L
| *1/4 point-L j
Edge-L |
Earth Pressures (kpa)
(Longitudinal & Transverse Shaking)
Figure 6.40 Maximum longitudinal earth pressures
Figure 6.41 Maximum bearing pressure contours at footing kpa
79


NorthRidge Earthquake
Max. Transverse MSE Wall Displacement
Abutment No.1
r" 5.0
j= 4.0
.? 3.0
I 2.0
! I 1.0 -
= o.o -
$ -0.006 -0.004 -0.002 0 0.002 0.004
I Displacements (m)
(Longitudinal & Transverse Shaking)
Edge-R j
j 1/4 point -R |
A Center-R
Figure 6.42 Maximum transverse wall displacements
NorthRidge Earthquake
Max. Transverse Earth Pressure
Abutment No.1
Edge -R
1/4 point -R :
A Center-R
Figure 6.43 Maximum transverse earth pressures
80


Wall Height (m) p Wall Height (m)
NorthRidge Earthquake
Max. MSE WingWall Displacement
@ Center of WingWall Abutment No.1
(Longitudinal & Transverse Shaking)
j-*WingWall -L |
WingWall -R j
I
,44 Maximum MSE wing wall displacements
NorthRidge Earthquake
Max. Earth Pressure MSE WingWalls
Abutment No.1
Earth Pressures (kpa)
(Longitudinal & Transverse Shaking)
Figure 6.45 Maximum transverse pressures at wing walls
81


Full Text

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NONLINEAR ANALYSIS OF MSE BRIDGE ABUTMENT UNDER SEISMIC LOADS by Michael J. Jalinsky B.S., Southern Illinois University at Edwardsville, 1998 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

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This thesis for the Master of Science degree by Michael J Jalinsky has been approved by Shing-Chun Trever Wang ChengYu-Li

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Michael Jess Jalinsky (M.S., Civil Engineering) Nonlinear Analysis of MSE Bridge Abutment under Seismic Loads Thesis directed by Professor NienYin Chang ABSTRACT Bridge abutment is a structure located at the ends of a bridge which provide the basic functions of: supporting the end of the superstructure at the first and end span, supporting parts of the approaching roadway and retaining the earth in front, underneath and adjacent to the approaching roadway. There are several styles of abutment retaining structures used today and are dependent on the geometry of the site, size of the structure and the preferences of the owner. The more common types of abutments are: concrete cantilever walls, gravity walls and reinforced soil structures commonly referred to as MSE (Mechanically stabilized earth structures). Currently the only published seismic design standard is contained in the AASHTO Standard Specifications for Highway Bridges, which describes a pseudo-static method of analysis based on the Mononobe-Okabe application of conventional pressure theory. Also, the current seismic design codes do not appear to fully incorporate the wall inherent flexibility. This is why more studies and field observations on existing abutment structures are needed to better understand the ductile response of MSE walls under the influence of lll

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seismic loads and flexible composition of geosythetic reinforcement and selected soil matrix. The primary objective of this thesis study is to analyze the response of MSE abutment retaining wall under seismic loading. Numerical analyses of MSE retaining wall systems were performed using the finite element computer program named NIKE3D. NIKE3D has the capability of time history analysis, slide interfaces between different materials and nonlinear Ramberg Osgood material model. This study selected the accelerograms from the Imperial Valley EarthquakeEl Centro dated October 15, 1979 and the Northridge Earthquake dated January 17, 1994 in the dynamic finite element analyses with difference ground motion acceleration combinations including multidirectional shaking. From this study the insight to the behavior and response of MSE walls under seismic load can be better understood. This abstract accurately represents the content of the candidate's thesis. I recommend its publication. IV

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ACKNOWLEDGEMENTS This thesis was performed under the supervision of Dr. Nien-Yin Chang and Dr.Shing-Chun Trever Wang. I am grateful for their guidance and encouragement throughout my journey and Dr. ChengYu-Li for his effort in servicing on my examination committee is greatly appreciated. I would also like to especially thank my wife (Patty) for her support and encouragement over the years in completing my educational quest. Finally, I am also grateful to the NIKE group members for their support and sharing of their knowledge over the last couple of years.

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CONTENTS Figures ........................................................................................................... xi Tables ............................................................................................................ xix Chapter 1. Introduction ........................................................................................... 1 1.1 Problem Statement ............................................................................... 1 1.2 Objectives ............................................................................................. 4 1.3 Significance of This Research .............................................................. 6 2. Literature Review .................................................................................. 9 2.1 Introduction ........................................................................................... 9 2.2 AASHTO Current Design Guidelines .................................................... 9 2.3 Mononobe-Okabe Method .................................................................. 16 2.4 Evaluation of Seismic Performance in MSE Structures ..................... 20 2.4.1 Northridge Earthquake ........................................................................ 21 2.4.2 Kobe Earthquake ................................................................................ 22 2.4.3 lzmit Earthquake ................................................................................. 22 2.5 Conclusion .......................................................................................... 23 3. Theroretical Background of NIKE3D Program .................................... 24 3.1 NIKE3D Finite Element Program ........................................................ 24 3.2 Microstation and Truegrid Mesh Generation Programs ...................... 25 3.3 Material Model .................................................................................... 26 3.4 Ram berg-Osgood Elastopastic Model ................................................ 27 3.5 Eigenvalue Analysis and Rayleigh Damping ....................................... 28 4. Ground Motion Used for this Study ..................................................... 32 4.1 Introduction ......................................................................................... 32 Vl

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4.2 Ground Motion Time History and Input ............................................... 33 4.3 Response Spectrum ........................................................................... 38 5. Review of Study and Design Parameters ........................................... 42 5.1 Introduction ......................................................................................... 42 5.2 Bridge Model Dimensions .................................................................. .43 5.3 Boundary Conditions ........................................................................... 47 5.4 Slide Interfaces ................................................................................... 49 5.5 Material Model Parameters ................................................................. 52 5.6 Summary ............................................................................................ 56 6. Northridge Earthquake Results ........................................................... 57 6.1 Data Analysis ...................................................................................... 57 6.2 Study Items ......................................................................................... 57 6.3 Case 1: Static Loading-Abutment 1 ................................................. 58 6.3.1 Inclusion StressesStatic Loading ................................................... 60 6.4 Case 2: Vertical, Transverse and Longitudinal MotionAbutment 1 ......................................................................................... 64 6.4.1 Inclusion StressesVertical, Transverse and Longitudinal Motion Abutment1 ............................................................................ 69 6.4.2 Case 2: Vertical, Transverse Longitudinal Motion-Abutment 2 ........................................................................... 73 6.4.3 Inclusion StressesVertical, Transverse and Longitudinal Motion Abutment 2 ........................................................................... 76 6.5 Case 3: Longitudinal and Transverse Motion-Abutment 1 ............... 78 6.5.1 Inclusion StressesLongitudinal and Transverse Motion-Abutment 1 ......................................................................................... 83 6.5.2 Case 2: Longitudinal and Transverse Motion-Abutment 2 ............... 87 Vll

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6.5.3 Inclusion Stresses-Longitudinal and Transverse Motion Abutment 2 ......................................................................................... 90 6.6 Case 4: Vertical and Longitudinal Motion-Abutment 1 ................... 92 6.6.1 Inclusion Stresses-Vertical and Longitudinal Motion-Abutment 1 ......................................................................................... 96 6.6.2 Case 2: Vertical and Longitudinal Motion -Abutment 2 ................... 100 6.6.3 Inclusion Stresses-Vertical and Longitudinal Motion-Abutment 2 ....................................................................................... 1 03 6.7 Interpretation of Analysis Results ..................................................... 105 6. 7.1 Analysis Results ............................................................................... 1 05 6. 7.2 Case 1 : Static Loading ...................................................................... 1 05 6.7.3 Case 2: Vertical, Longitudinal and Transverse Motion ...................... 108 6.7.4 Case 3: Longitudinal and Transverse Motion .................................... 111 6. 7.5 Case 4: Vertical and Longitudinal Motion .......................................... 112 6.7.6 Summary .......................................................................................... 112 7. Imperial Earthquake Results ............................................................. 114 7.1 Data Analysis .................................................................................... 114 7.2 Study Items ....................................................................................... 114 7.3 Case 1: Static Loading-Abutment 1 ............................................... 115 7.3.1 Inclusion Stresses-Static Loading ................................................. 117 7.4 Case 2: Vertical, Transverse and Longitudinal Motion Abutment 1 ......................................................................... 121 7.4.1 Inclusion Stresses-Vertical, Transverse and Longitudinal Motion Abutment 1 ......................................................................... 126 7.4.2 Case 2: Vertical, Transverse and Longitudinal Vlll

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Motion Abutment 2 ......................................................................... 130 7.4.3 Inclusion StressesVertical, Transverse and Longitudinal Motion-Abutment 2 ......................................................................... 133 7.5 Case 3: Longitudinal and Transverse Motion -Abutment 1 ............. 135 7 .5.1 Inclusion StressesTransverse and Longitudinal Motion Abutment 1 ......................................................................... 140 7 .5.2 Case 2: Longitudinal and Transverse Motion Abutment 2 ......................................................................... 144 7.5.3 Inclusion Stresses-Longitudinal and Transverse Motion Abutment 2 ......................................................................... 14 7 7.6 Case 4: Vertical and Longitudinal Motion-Abutment 1 .................. 149 7 .6.1 Inclusion Stresses-Vertical and Longitudinal Motion Abutment 1 ......................................................................... 153 7.6.2 Case 2: Vertical and Longitudinal Motion-Abutment 2 ................... 157 7.6.3 Inclusion Stresses-Vertical and Longitudinal Motion-Abutment 2 ......................................................................... 161 7. 7 Interpretation of Analysis Results ..................................................... 163 7. 7.1 Analysis Results ............................................................................... 163 7. 7.2 Case 1 : Static Loading ...................................................................... 163 7.7.3 Case 2: Vertical, Longitudinal and Transverse Motion ...................... 166 7.7.4 Case 3: Longitudinal and Transverse Motion .................................... 169 7.7.5 Case 4: Vertical and Longitudinal Motion .......................................... 170 7.7.6 Summary .......................................................................................... 170 8. MSE Wall Design Examples ............................................................. 172 8.1 Current Design Methods ................................................................... 172 8.2 AASHTO Design Method .................................................................. 172 IX

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8.3 Finite Element Design Method (NIKE3D) .......................................... 174 8.4 Comparison Between AASHTO and Finite Element Method ................................................................................ 175 9. Summary, Conclusions, Recommendations and Further Studies .............................................................................................. 176 9.1 Summary .......................................................................................... 176 9.2 Conclusions ...................................................................................... 177 9.3 Recommendations for Further Studies ............................................. 177 Appendix A. Truegrid Input File ............................................................................. 179 B. Ritz and Eigenvalues ........................................................................ 221 References .................................................................................................. 224 X

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FIGURES Figure 1 .1 Typical cantilever and spread footing abutments .................................. 1 1.2 Typical MSE abutment.. ........................................................................ 2 1.3a Geosynthetics wrap .............................................................................. 3 1 .3b Segment concrete block ....................................................................... 3 1.3c Full height panel ................................................................................... 3 1.4 Tensar geogrid geosythetic material .................................................... .4 2.1 MSE wall element dimensions needed for design .............................. 11 2.2 ASSHTO seismic external stability of a MSE wall ............................... 13 2.3 Seismic internal stability of a MSE wall ............................................... 15 2.4a Forces acting on active wedge ........................................................... 16 2.4b Forces acting on passive wedge ......................................................... 16 2.5 Total earth pressure distribution due to soil proposed by Bathurst and Cari (1995) ................................................................ 19 3.1 NIKE3D bridge model ......................................................................... 26 4.1 Northridge vertical acceleration time history ....................................... 35 4.2 Northridge horizontal @ 90 degree acceleration time history ............. 35 4.3 Northridge Horizontal @ 360 degree acceleration time history ........... 36 4.4 Imperial Valley vertical acceleration time history ................................ 36 4.5 Imperial Valley horizontal @ 360 degree acceleration time history ..... 37 4.6 Imperial Valley horizontal@ 90 degree acceleration time history ....... 37 4. ?a Northridge 360 degree horizontal response spectrum ........................ 39 4. ?b Northridge 90 degree horizontal response spectrum .......................... 39 4.8a Imperial Valley 360 degree horizontal response spectrum ................ .40 4.8b Northridge vertical response spectrum .............................................. .40 4.9a Imperial Valley vertical response spectrum ......................................... 41 XI

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4.9b Imperial Valley 90 degree horizontal response spectrum .................. .41 5.1 Bridge plan view ................................................................................. 44 5.2 Bridge elevation and typical section ................................................... .45 5.3 Bridge elevation and boundary conditions ......................................... .48 5.4 Boundary conditions and material dimensions ................................... .49 5.5 Master and slave diagram ................................................................... 51 6.1 Static longitudinal MSE wall displacements ........................................ 58 6.2 Static longitudinal earth pressures ...................................................... 58 6.3 Static longitudinal inclusion stresses .................................................. 59 6.4 Maximum bearing compression contours at footing-kpa ................... 59 6.5 1st Inclusion layer stress contours from top-kpa ............................... 60 6.6 2nd Inclusion layer stress contours from top-kpa .............................. 60 6.7 3rd Inclusion layer stress contours from top-kpa ............................... 61 6.8 4th Inclusion layer stress contours from top-kpa ............................... 61 6.9 5th Inclusion layer stress contours from top-kpa ............................... 62 6.10 6th Inclusion layer stress contours from top-kpa ............................... 62 6.11 ]'h Inclusion layer stress contours from top-kpa ............................... 63 6.12 Time history at top of wall ................................................................... 64 6.13 Maximum MSE wall displacements .................................................... 64 6.14 Maximum longitudinal earth pressures ............................................... 65 6.15 Maximum connection stresses ............................................................ 65 6.16 Maximum bearing stress contours at footing -kpa ............................. 66 6.17 Backfill acceleration profile ................................................................. 66 6.18 Maximum transverse MSE wall displacements ................................... 67 6.19 Maximum transverse earth pressures ................................................. 67 6.20 Maximum MSE wing wall displacements ............................................ 68 6.21 Bridge deck displacements ................................................................. 68 6.22 15tlnclusion layer stress contours from top-kpa ................................ 69 Xll

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6.23 2"d Inclusion layer stress contours from top-kpa ............................... 69 6.24 3rd Inclusion layer stress contours from top kpa ................................ 70 6.25 4th Inclusion layer stress contours from top-kpa ................................ 70 6.26 5th Inclusion layer stress contours from top-kpa ................................ 71 6.27 6th Inclusion layer stress contours from top-kpa ................................ 71 6.28 th Inclusion layer stress contours from top-kpa ................................ 72 6.29 Maximum MSE wall displacements .................................................... 73 6.30 Maximum longitudinal earth pressures ............................................... 73 6.31 Maximum bearing compression contours at footing kpa .................. 7 4 6.32 Maximum MSE wall transverse displacements ................................... 74 6.33 Maximum MSE wall earth pressures .................................................. 75 6.34 Maximum MSE wing wall displacements ............................................ 75 6.35 1st Inclusion layer stress contours from top-kpa ................................ 76 6.36 2nd Inclusion layer stress contours from top kpa ............................... 76 6.37 3rd Inclusion layer stress contours from top-kpa ................................ 77 6.38 Time history at bottom of wall ............................................................. 78 6.39 Maximum MSE wall displacements .................................................... 78 6.40 Maximum longitudinal earth pressures ............................................... 79 6.41 Maximum bearing pressure contours at footing kpa ........................ 79 6.42 Maximum transverse wall displacements ............................................ 80 6.43 Maximum transverse earth pressures ................................................. 80 6.44 Maximum MSE wing wall displacements ............................................ 81 6.45 Maximum transverse pressures at wing walls ..................................... 81 6.46 Bridge deck vertical displacements ..................................................... 82 6.47 1st Inclusion layer stress contours from top-kpa ................................ 83 6.48 2nd Inclusion layer stress contours from top kpa ............................... 83 6.49 3rd Inclusion layer stress contours from top-kpa ................................ 84 6.50 4th Inclusion layer stress contours from top-kpa ................................ 84 Xlll

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6.51 5th Inclusion layer stress contours from top-kpa ................................ 85 6.52 6th Inclusion layer stress contours from top-kpa ................................ 85 6.53 7th Inclusion layer stress contours from top-kpa ................................ 86 6.54 Maximum MSE wall displacements .................................................... 87 6.55 Maximum longitudinal earth pressures ............................................... 87 6.56 Maximum bearing compression contours at footing-kpa .................. 88 6.57 Maximum MSE wing wall displacements ............................................ 88 6.58 Maximum MSE wall earth pressures .................................................. 89 6.59 15tlnclusion layer stress contours from top-kpa ................................ 90 6.60 2nd Inclusion layer stress contours from top-kpa ............................... 90 6.61 3rd Inclusion layer stress contours from top-kpa ................................ 91 6.62 Time history at top of wall ................................................................... 92 6.63 Maximum MSE wall displacements .................................................... 92 6.64 Maximum longitudinal earth pressures ............................................... 93 6.65 Maximum bearing pressures contours at footing-kpa ...................... 93 6.66 Maximum transverse wall displacements ............................................ 94 6.67 Maximum transverse earth pressures ................................................. 94 6.68 Maximum MSE wing wall displacements ............................................ 95 6.69 Maximum transverse pressures at wing walls ..................................... 95 6.70 15tlnclusion layer stress contours from top-kpa ................................ 96 6. 71 2nd Inclusion layer stress contours from top-kpa ............................... 96 6. 72 3rd Inclusion layer stress contours from top kpa ................................ 97 6.73 4th Inclusion layer stress contours from top-kpa ................................ 97 6.74 5th Inclusion layer stress contours from top-kpa ................................ 98 6.75 6th Inclusion layer stress contours from top-kpa ................................ 98 6.76 7th Inclusion layer stress contours from top-kpa ................................ 99 6.77 Maximum MSE wall displacements .................................................. 100 6.78 Maximum longitudinal earth pressures ............................................. 100 XIV

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6.79 Maximum bearing compression contours at footing-kpa ................. 101 6.80 Maximum MSE wing wall displacements .......................................... 1 01 6.81 Maximum MSE wing wall earth pressures ........................................ 102 6.82 1st Inclusion layer stress contours from top-kpa .............................. 103 6.83 2nd Inclusion layer stress contours from top kpa ............................. 103 6.84 3rd Inclusion layer stress contours from top-kpa .............................. 1 04 7.1 Static longitudinal MSE wall displacements ...................................... 115 7.2 Static longitudinal earth pressures .................................................... 115 7.3 Static longitudinal inclusion stresses ................................................ 116 7.4 Maximum bearing pressure contours at footing-kpa ....................... 116 7.5 1st Inclusion layer stress contours from top-kpa .............................. 117 7.6 2nd Inclusion layer stress contours from top-kpa ............................. 117 7.7 3rd Inclusion layer stress contours from top-kpa .............................. 118 7.8 4th Inclusion layer stress contours from top-kpa .............................. 118 7.9 5th Inclusion layer stress contours from top-kpa .............................. 119 7.10 6th Inclusion layer stress contours from top-kpa .............................. 119 7.11 ih Inclusion layer stress contours from top-kpa .............................. 120 7.12 Time history at top of wall ................................................................. 121 7.13 Maximum MSE wall displacements .................................................. 121 7.14 Maximum longitudinal earth pressures ............................................. 122 7.15 Maximum connection stresses .......................................................... 122 7.16 Maximum bearing pressure contours at footing kpa ....................... 123 7.17 Soil acceleration profile ..................................................................... 123 7.18 Maximum transverse MSE wall displacements ................................. 124 7.19 Maximum transverse earth pressures ............................................... 124 7.20 Maximum MSE wing wall displacements .......................................... 125 7.21 Bridge deck displacements ............................................................... 125 7.22 1st Inclusion layer stress contours from top-kpa .............................. 126 XV

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7.23 2nd Inclusion layer stress contours from top kpa ............................. 126 7.24 3rd Inclusion layer stress contours from top-kpa .............................. 127 7.25 4th Inclusion layer stress contours from top-kpa .............................. 127 7.26 5th Inclusion layer stress contours from top-kpa .............................. 128 7.27 6th Inclusion layer stress contours from top-kpa .............................. 128 7.28 ih Inclusion layer stress contours from top-kpa .............................. 129 7.29 Maximum MSE wall displacements .................................................. 130 7.30 Maximum longitudinal earth pressures ............................................. 130 7.31 Maximum bearing pressure contours at footing-kpa ...................... 131 7.32 Maximum MSE wall transverse displacements ................................. 131 7.33 Maximum MSE wall earth pressures ................................................ 132 7.34 Maximum MSE wing wall displacements .......................................... 132 7.35 1st Inclusion layer stress contours from top-kpa .............................. 133 7.36 2nd Inclusion layer stress contours from top kpa ............................. 133 7.37 3rd Inclusion layer stress contours from top-kpa .............................. 134 7.38 Time history at top of wall ................................................................. 135 7.39 Maximum MSE wall displacements .................................................. 135 7.40 Maximum longitudinal earth pressures ............................................. 136 7.41 Maximum bearing pressure contours at footing kpa ...................... 136 7.42 Maximum transverse wall displacements .......................................... 137 7.43 Maximum transverse earth pressures ............................................... 137 7.44 Maximum MSE wing wall displacements .......................................... 138 7.45 Maximum transverse pressures at wing walls ................................... 138 7.46 Bridge deck vertical displacements ................................................... 139 7.47 1st Inclusion layer stress contours from top-kpa .............................. 140 7.48 2nd Inclusion layer stress contours from top-kpa ............................. 140 7.49 3rd Inclusion layer stress contours from top-kpa .............................. 141 7.50 4th Inclusion layer stress contours from top-kpa .............................. 141 XVl

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7.51 5th Inclusion layer stress contours from top-kpa .............................. 142 7.52 6th Inclusion layer stress contours from top-kpa .............................. 142 7.53 7th Inclusion layer stress contours from top-kpa .............................. 143 7.54 Maximum MSE wall displacements .................................................. 144 7.55 Maximum longitudinal earth pressures ............................................. 144 7.56 Maximum bearing compression contours at footing-kpa ................ 145 7.57 Maximum MSE wing wall displacements .......................................... 145 7.58 Maximum MSE wall earth pressures ................................................ 146 7.59 1st Inclusion layer stress contours from top-kpa .............................. 147 7.60 2nd Inclusion layer stress contours from top-kpa ............................. 147 7.61 3rd Inclusion layer stress contours from top-kpa .............................. 148 7.62 Time history at top of wall ................................................................. 149 7.63 Maximum MSE wall displacements .................................................. 149 7.64 Maximum longitudinal earth pressures ............................................. 150 7.65 Maximum bearing pressures contours at footing kpa .................... 150 7.66 Maximum transverse earth pressures ............................................... 151 7.67 Maximum MSE wing wall displacements .......................................... 151 7.68 Maximum transverse pressures at wing walls ................................... 152 7.69 Maximum bridge deck displacements ............................................... 152 7.70 1st Inclusion layer stress contours from top-kpa .............................. 153 7.71 2nd Inclusion layer stress contours from top-kpa ............................. 153 7.72 3rd Inclusion layer stress contours from top-kpa .............................. 154 7.73 4th Inclusion layer stress contours from top-kpa .............................. 154 7.74 5th Inclusion layer stress contours from top-kpa .............................. 155 7.75 6th Inclusion layer stress contours from top-kpa .............................. 155 7.76 y!h Inclusion layer stress contours from top-kpa .............................. 156 7. 77 Maximum MSE wall displacements .................................................. 157 7. 78 Maximum longitudinal earth pressures ............................................. 157 XVll

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7.79 Maximum bearing compression contours at footing-kpa ................. 158 7.80 Maximum transverse earth pressures ............................................... 158 7.81 Maximum transverse MSE wall displacements ................................. 159 7.82 Maximum MSE wing wall displacements .......................................... 159 7.83 Maximum MSE wing wall earth pressures ........................................ 160 7.84 151 Inclusion layer stress contours from top-kpa .............................. 161 7.85 2"d Inclusion layer stress contours from top-kpa ............................. 161 7.86 3rd Inclusion layer stress contours from top-kpa .............................. 162 8.1 Stress distribution diagram ............................................................... 173 8.2 FE model stress distribution .............................................................. 175 XVIIl

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TABLES Table 2.1 AASHTO factor of safety criteria ......................................................... 10 2.2 Seismic Performance Category (SPC) with important classification ....................................................................................... 12 3.1 Mode shapes with frequencies and periods ........................................ 30 3.2 Displacement response spectrum valuesNorthridge ....................... 30 3.3 Acceleration response spectrum values Northridge ......................... 30 3.4 Displacement response spectrum valuesImperial Valley ................. 31 3.5 Acceleration response spectrum valuesImperial Valley ................... 31 4.1 Earthquake ground motion information ............................................... 34 5.1 a Bridge geometry ................................................................................. 46 5.1 b Superstructure geometry .................................................................... 46 5.1 c Substructure geometry ........................................................................ 47 5.2 Interface properties ............................................................................. 50 5.3 Material properties .............................................................................. 52 5.4 Physical and mechanical properties of commercially available geogrid (after Korner, 1986) ................................................................ 54 5.5a Ram berg-Osgood material properties ................................................. 55 5.5b Ram berg-Osgood material properties ................................................. 55 6.1 Permanent displacement at top of wall ............................................. 112 6.2 Summary of dynamic analysis results ............................................... 113 7.1 Permanent displacement at top of wall ............................................. 170 7.2 Summary of dynamic analysis results ............................................... 171 8.1 Input parameters ............................................................................... 173 8.2 Finite element forces ......................................................................... 174 XIX

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1. Introduction 1.1 Problem Statement The substructure of a highway bridge consists of components designed to support the superstructure and highway overpass. Bridge abutments are structures located at the ends of a bridge. Their main function is to retains the earth underneath and adjacent to the approaching roadway, and support the approaching roadway or approach slab. There are many types of bridge abutments from gravity abutment, which resists horizontal earth pressure with its own dead weight to cantilever abutment that is virtually identical to a cantilever retaining wall. These are just a few of the many types of abutments being constructed today. See figure 1.1 illustrating the gravity and cantilever type bridge abutments. ._,INGVALL I I L SLIPERSTAUCTURE OIAOERS CoQIII"T !LEVER AOOOWAY WIOT'"' OR WAl[A V.r::l'r TYPICAL CANTILEVER ABUTMENTS I PRECAST GIRDERS L SuPEASHlUCTUAE Q I ROE !ItS LRQAOWAY SLAB TYP I CA.L. SPREAD FOOT! NG ABUTMENTS Figure 1.1 Typical cantilever and spread footing abutments

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One type that has been gaining popularity over the years is the reinforced earth abutment commonly referred to as a mechanically stabilized earth (MSE) structure. The soil behind this type of abutment is typically reinforced with relatively light and flexible materials such as thin strips of geosynthetics. These are extensible and have high tensile strengths (Leshchinsky, 1995). Figure 1.2 illustrates the basic elevation of a MSE bridge abutment. I PRECAST G I ROERS R IOGE ADUTMENT L SuPERSTRUCTliAE GIRDERS BRIDGE A!JUlH[N 1'----' WALL ROADWAY WtCJTH OR WATER WilY MSE lRQAOIIIAY SLAB TYPICAL MSE ABUTMENTS Figure 1.2 Typical MSE abutment The reinforced soil mass is typically supported by a facing panel that prevents raveling of the soil immediately behind the facing. Depending on the design and or aesthetic conditions the face may be geosynthetics wrapped (type a), segment concrete block (type b), or full height precast panel (type c). See figures 1.3 a,b or c on the next page for details 2

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WARP AROUND ==r-FACE -------->--GEDTEXT!LE OR >---GROGR I D ------->----FINISH GRADE = o BRIDGE ---1 MODULAR CONCRETE ==r-BLOCKS (a) Figure 1 .3a Geosynthetics wrap Figure 1.3b Segment concrete block Figure 1.3c Full height panel (b) EVELING PAD (c) The first design approach for reinforced earth structure was developed in the 1960's by a French engineer named, Henry Vidal. Over the years MSE type abutments have proved to be more economical than traditional solid concrete abutments. Since MSE structures can be constructed relatively fast and easily, large construction equipment is usually not needed to install the reinforcement. The key requirements to proper installed MSE abutment wall are quality control and trained construction personnel. Another major consideration for MSE walls is that they are flexible and do not require deep or rigid foundations; thus further reducing construction cost. Over the past years there has been concern over the metal strip reinforcement being susceptible to corrosion, creep, and deterioration to the wall. To accommodate these concern additional safety factors for design loads are ,., .)

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required to account for potential degradation of the reinforcement over its design life. Figure 1.4 illustrates Tensar geogrid geosythetic material (manufactured by Tensar Earth Technologies, Inc) one of the commonly used reinforced wall systems. ---------:7 Ten.sar Geognd Transverse Bar Figure 1.4 Tensar geogrid geosythetic material 1.2 Objectives The objective of this thesis is to research the behavior and response of a simple span concrete bridge supported by MSE abutments under the 4

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influence of a real ground motion time history or seismic acceleration record. Will this bridge structure be functional and safe during and after a seismic event? This research will be accomplished through the following tasks: 1. Develop a full scale 3 dimensional CADD graphic model of the bridge structure including; MSE walls, abutments, with supporting soil using the engineering graphic program Microstation-J, developed by "Bently Corporation". This model provided key nodal point coordinates in the layout of the bridge geometry. These key nodal points were then imported into True-grid developed by "XYZ Scientific Application, Inc." True-Grid then generated the required output data that would later be used as the input file for the finite element program. 2. A numerical analysis program will be used to solve this finite element problem. The input file generated by True-Grid will be used for the finite element computer program, NIKE3D, developed by "Lawrence Livermore National Laboratory". 3. Data output from NIKE3D was extracted and analyzed by the post processor program, "Griz", developed by "Lawrence Livermore National Laboratory" to interpret the response of the bridge and wall systems. Griz also has the capability of graphically displaying selected nodal points, displacements, accelerations and stresses. This feature will aid in locating the maximum values with corresponding time event 5

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4. Review reports submitted by reinforced wall companies reporting the condition of existing MSE bridge abutments and walls after a seismic ground motions event. 1.3 Significance of This Research Mechanically stabilized earth (MSE) structures such as retaining walls for bridge abutments, retaining walls with steep back slope are becoming more popular in seismically active areas in the United States due to several factors. a. Behavior of the structure. b. Cost consideration c. Ease of construction d. Performance Base Seismic Engineering (PBSE) a. Recent earthquake events have brought about renewed interest in the response of MSE structures to seismic loading. With mechanically stabilized earth structures, the current design code does not appear to fully incorporate their inherent flexibility, which permits minor yielding during a seismic event. Observation reports from local agencies on the performance of MSE structures after a seismic event indicate no major structural damage to many of their wall structures but minor concrete spalling. b. MSE structures have gained popularity over the past few years as a method of constructing bridge abutments which are both functional and 6

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aesthetically pleasing. In addition, mechanically stabilized earth systems have proved to be more economical than traditional solid reinforced concrete walls, since large rigid foundation systems are not required, materials are fabricated at a plant providing for a more efficient facing panel production and quality control. c. Construction of MSE walls can usually be built relatively fast and easily requiring less time on the project site and finishing the project on time or ahead of schedule. Some factors that affect the construction of large or small projects include equipment, material and workers. Since large construction equipment is usually not required to install the reinforcement materials or panels this will save construction time and will be less complicated to install. Well-trained workers are extremely important for proper installation of the MSE wall systems, in return will save on construction time, less workers at the job site and completion of the project more efficiently. d. Performance base engineering (PBE), is not new. Many of our major manufacturers use this approach to design and improve their prototype through extensive testing prior to production. Until recently PBSE has been more complicated, except for large-scale development of identical buildings. Each structure designed by this process is virtually unique and the experience obtained is not directly transferable to structures of 7

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other types, sizes, and performance objectives. Now due to the recent advancements in seismic hazard assessment, PBSE methodologies, experimental facilities, and computer applications, PBSE has become an increasingly more attractive option to engineers and developers in seismic active areas. In order to utilize PBSE designs effectively, one needs to be aware of the uncertainties involved in both the structural performance and seismic hazard. Today the two available prominent PBSE design guidelines are referred to as "ATC-40" and FEMA273/274. 8

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2. Literature Review 2.1 Introduction In this literature review, several items will be discussed. First is the current published seismic design standards and are contained in the "American Association of State Highways and Transportation Officials", AASHTO, Standard Specifications for Highway Bridges 16th edition and the "Load Resistance Factor Design" Bridge Design Specification, LRFD, and is based on the Mononobe-Okabe theory. Secondly, a review of the pseudo static analysis method developed by Mononobe and Okabe to estimate the lateral earth pressure acting on retaining structures during earthquake events. Thirdly, the review of the performance of existing MSE structures after an earthquake event. 2.2 AASHTO Current Design Guidelines AASHTO, classifies retaining structures as gravity, semi-gravity, non gravity cantilever and anchor. Mechanically stabilized earth (MSE) walls fall into the category of gravity walls since MSE walls derive their capacity to resist lateral loads through a combination of dead weight and lateral resistance. The type of construction for MSE walls can vary from modular precast concrete panels, modular concrete blocks or geosynthetic reinforcements with a cast in place concrete or shotcrete facing. MSE walls 9

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are typically used where conventional gravity, or cantilever retaining walls are considered, but are well suited where substantial differential settlement is anticipated. The allowable settlement of MSE walls is limited by the longitudinal deformability of the facing material and the performance requirements of the structure. ASSHTO's, Standard Specification for Highway Bridges 16th edition, provides seismic design guidance regarding the lateral earth pressure generated from a seismic event. This method a pseudo-static approach developed by Monomobe and Okabe that estimates the equivalent static forces from a seismic event. In addition when a wall supports a bridge structure, the seismic design should include the forces transferred from the bridge superstructure through the non-sliding bearings, such as "elastomeric bearings" into the abutment foundation. To ensure stability against possible failure modes the MSE walls structural dimensions (figure 2.1) should satisfying the following factor of safety (FS) criteria. Sliding FS > 1 .5 OverturningFS > 2.0 for footing on Soil FS > 1 .5 for footing on Rock Bearing CapacityFS > 1.5 for footing on soil or rock -Seismic loading Factor of safety against sliding and overturning failure under seismic may be reduced to 75% of the factor of safety listed above Table 2.1 AASHTO factor of safety criteria 10

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H TOP OF WALL FOR DESIGN FAILURE SURFACE FOR INTERNAL STABILITY WALL FACING PANEL OR UNIT REINFORCED SOIL MASS ,. Y,.. K,. ACTIVE ZONE I I RESISTANT ZONE BENCH I REINFORCEMENT LENGTH L WALL BASE WIDTH B WALL BACKFILL REINFORCUIENT I FAILURE SURFACE FOR I EXTERIOR STABilllY --..; I I I I RETAINED FILL ,. Yr K.,r Figure 2.1 MSE wall element dimensions needed for design AASHTO assigns bridge structures to one of four Seismic Performance Categories (SPC), A through D, based on the Acceleration Coefficient (A) and the Importance Classification (IC). Minimum analysis and design requirements are governed by these SPC values. See the following table 2.2 for Seismic Performance Category (SPC) with Important Classification (IC). 11

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Acceleration Coefficient Importance Classification A I II A< 0.09 A A 0.09
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Moss for Inertial Force H Moss for resasting forces (a) Level backfill condition Moss for Inertial Force Mass for resasting forces Figure 2.2 ASSHTO seismic external stability of a MSE wall 0.5 p"" The values for P AE and P1R for a horizontal back fill may be determined using the following equations: Am = (1.45 A)A PAE = 0.375 YEa Am Ys H2 P1R = 0.5 YEa Am Ys H2 13 (2.2) (2.3) (2.4)

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Where: A = maximum earthquake acceleration coefficient YEa =Load factor for EQ loads Am = Maximum wall acceleration coefficient at the centroid of the wall mass Ys =Soil unit weight (kef) H = Height of wall (ft) For most MSE abutment structures the backfill slope should be horizontal. AASHTO does allow a reduced value for the Mononabe-Okabe method for walls that can displace laterally. ASSHTO acknowledge that the internal lateral deformation response of the MSE wall is more complex and further research and testing is necessary. It is not clear at this time how much the acceleration coefficient could be decreased due to the allowance of some lateral deformation during a seismic loading internally in the MSE wall. The internal stability including the soil reinforcement shall be designed to withstand horizontal forces generated by the internal inertia force; Pi and the static forces. Figure 2.3 illustrates the internal stability for inextensible and extensible reinforced MSE walls. 14

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2 3 P, Pa I i -tth Loyer lnextenslble Reinforcements Extensible Reinforcements Trnax Internal Inertial force due to the weight of the backfill within the active zone. The length of reinforcement in the resistant zone of the i'th la)ler. The load per unit wall width applied to each reinforcement due to static forces. The load per unit wall width applied to each reinforcement Ioyer due to dynamic forces. 'The total load per unit wall width applied to each Ioyer, Ttotol = TmCD< + Tmc1 Figure 2.3 Seismic internal stability of a MSE wall This internal force shall be distributed to the reinforcement proportionally to their area on a load per width of wall basis as indicated above. The maximum tension forces including static and dynamic component applied to each layer is equal to: L,i Tmd=YP--'1 m 2)L.,) 1=1 Ttotal = T max + T md. (2.5) (2.6) 15

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2.3 Mononobe-Okabe Method The current design method for reinforced walls experiencing dynamic loading is an extension of the Coulomb sliding-wedge theory. The Mononobe-Okabe analysis correctly includes the horizontal inertial forces for the internal seismic resistance. This pseud-ostatic thrust that the backfill imposes on the reinforced soil mass is also modeled in this analysis. Therefore, the seismic design of reinforced walls is similar to the method used for static stability, except and an additional horizontal force must be accounted for in the analysis. Figure 2.4 illustrates the force equilibrium diagram in Mononobe-Okabe analysis (Kramer 1996) Figure 2.4a Forces acting on active wedge Figure 2.4b Forces acting on passive wedge 16

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The pseudo-static acceleration components exerted on the wedge mass, is ah (=khG) the horizontal component, and av (=kvG), the vertical component, are based on the earthquake peak ground acceleration and G is the gravitational acceleration. In an active earth pressure condition, the active thrust with the effect of the earthquake, PAE. and from the force equilibrium diagram shown in figure 2.4a, the following equation can be determined: (2.7) The following parameters apply to the above equation: y is the unit weight of the back fill; H is the total height of the wall; and KAE is the dynamic active earth pressure coefficient and is given by the equation 2.8. K = cos2(-B-\f') AE [ ]2 sino+ sin -COSJ'COs2Bcos(o+B+J") 1+ ( ) ( fJ /') cos(o + B + /') cos(flB) (2.8) p;::: \jf, and \Jf = tan-1[kh/ (1-kv)]; is the soil friction angle; and o is the soil-wall interface friction angle. aAE is the critical failure angle inclined from the horizontal axis, aAE in an earthquake event is smaller than one in a static event. The critical failure surface angle is found by equation 2.9 17

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a AE =-If/+ tan -I 'f' ., tt [ tan(""' '" /3) + C ] czE (2.9) C1 E -If/-fJ)[tan( -If/fJ) +cot( -If/-B] [1 + tan(b +If/+ B) cot( -If/-B)] Where c2E = 1 + {tan(b +If/+ B)[tan( -If/-/3) +cot( -If/-B)]} The location of the resultant active thrust Pae from the soil retaining wall in the Mononobe-Okabe method is the same as the static Coulomb theory, and resultant force acting at a height of H/3 form the base of the waiL The resultant active force PAE has two components, static and dynamic. (2.1 0) PAis the static component of the active force and is the dynamic component of the active force. As suggested by Seed and Whitman (1970) the dynamic force component acts at a height approximately equal to 0.6H. With this information the location of the resultant active force can be determine by equation 2.6. (2.11) 18

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Similar to the active earth pressure the passive earth pressure and dynamic force components can be determine. For more detail information on passive earth pressure derivations see appendix. Since the development of the Mononobe-Okabe analysis, improvements to this method were made by several individuals including Seed and Withman (1970). Seed and Withman concluded that the vertical acceleration could be ignored when the Mononobe-Okabe method is used to estimate P AE for typical designs. Also the assumption is made that the backfill is unsaturated, so that liquefaction problems will not arise. Bathurst and Cari (1995) proposed the following active dynamic pressure distribution due to soil self weight as shown in figure 2.5 + = 1 ) static pressure 2) dynamic pressure 3) total pressure Figure 2.5 Total earth pressure distribution due to soil proposed by Bathurst and Cari (1995) 19

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The dynamic active pressure coefficient KAE is the sum of the static and dynamic earth pressure coefficient. (2.12) The key parameter in the Mononobe-Okabe method is selecting the kh (Horizontal peak ground acceleration coefficient). Currently, there is no consensus on selecting this design value. AASHTO (1996) Standard Specification for Highway Bridges uses the equation kh = 0.85 Am/G Am/G where Am is the magnitude of the peak ground acceleration. AASHTO 2002 LFRD (Load Factor Resistance Design) specification recommends that kh = Am = (1.45-A)* A where A is the maximum earthquake acceleration coefficient from ASSHTO Division 1A contour map. Other sources like Whitman (1990) recommend values for kh could range from 0.3 to 0.5 of Am. 2.4 Evaluation of Seismic Performance in MSE Structures In the last decade there have been major earthquake events in the United States (Northridge, California, 1994, 6.7 Richter magnitude), Japan (Great Hanshin, Kobe, 1995, 7.2 Richter magnitude), and Turkey (North Anatolian, lzmit, 1999, 7.4 Richter magnitude). The Northridge Earthquake was responsible for 57 deaths, 11,000 injuries and $20 billion in damages, The Kobe Earthquake was a terrible tragedy that killed over 5,000 people, injured 27,000 more and destroyed over 150,000 structures. lzmit 20

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Earthquake resulted in 16,000 deaths, 30,000 injuries and over $16 billion dollar in damages. In the three earthquakes cited, there were numerous MSE structures constructed near the respective epicenter of the seismic event. The purpose of this section is to briefly catalogue the conditions of the MSE structures subjected to seismic events in the Northridge, Kobe and lzmit earthquakes. 2.4.1 Northridge Earthquake A total of 23 MSE structures were located within the affected area of the earthquake. Of these structures, more than 65% were higher than 5 m and more than 25% were high than 10 m. The distance of the MSE structures from the epicenter ranged from 13 to 83 km. The estimated ground acceleration varied horizontally from 0.07 g to .91 g and varied vertically from 0.04 g to 0.62 g. A review of the MSE structures near the epicenter was conducted by engineers from the MSE wall companies and the "California Department of Transportation", (CaiTrans). The structures include 21 MSE wall supporting the Los Angeles Metro Link, CaiTrans mountain highways, freeways off ramps, and two MSE bridge abutments in Corona. The only major damage that appeared was some minor spalling of the concrete panels in some of the walls. It was noted that, adjacent structures to the MSE walls, such as buildings suffered much more severe damage and in some instances were posted unsafe. 21

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2.4.2 Kobe Earthquake Of the 120 MSE structures inspected after the earthquake, approximately 70% were over 5 m high and 15% were over 10 m high. The actual ground acceleration was .27 g. Ground motion was evident above or adjacent to several wall structures. Many walls showed minor cracking of the isolated concrete panels and 3 walls exhibited significant lateral movement of 4 mm to 113 mm (displacement relative to bottom of panel at mid height and top of walls). All of the walls remained functional after the earthquake. 2.4.3 lzmit Earthquake A full evaluation of the MSE structures for this particular earthquake has not yet been completed. However, one bridge and ramp structure was surveyed at Arifiye, almost immediately adjacent to the epicenter. Although the bridge itself collapsed, the MSE ramp wall sustained only nominal damage and remained stable. Shear deformation from differential settlement propagated upward through the panels, was separated by as much as 75 mm. These MSE walls were designed for a ground acceleration of .1 0 g. This resulted in only a minor increase in the amount of reinforcement strips compared to the static design. Yet the actual ground acceleration was measured at 0.4 g. It is interesting to note that if the full effect of the ground 22

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acceleration was considered in design under current practice, then at least 40% more reinforcement would have been added. 2.5 Conclusion Recognizing that MSE walls can deflect and remain stable means that establishing an inventory of wall deflections after seismic events and corresponding wall heights will be an important step in seismic evaluation of MSE structures. To be reliable, the location and the relationship of the base of the wall with respect to the upper or top portion of the wall must be established. Also, when significant seismic events occur in cities where base line surveys have been completed, follow up measurements should be taken. It is anticipated that actual deformation reading may be used to better tailor design models and more realistic designs. 23

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3. Theoretical Background of NIKE3D Program 3.1 NIKE3D Finite Element Program As best described from the NIKE3D user's manual, NIKE3D is a fully implicit three-dimensional finite element code for analyzing the finite strain for static and dynamic response of inelastic solid, shell, and beams. NIKE3D was originally designed and developed by Dr. John 0. Hallquist and has since been used extensively by Lawrence Livermore National Laboratory on several research projects. In addition, it has been used to study the static and dynamic response of bridge structures undergoing finite deformations and several other soil-structure interaction research projects at the Center for Geotechnical Engineering Science", University of Colorado at Denver. The uses of the 8-node solid elements, 4-node membranes and shell elements and 2-node truss and beam elements, were provided to achieve this spatial discretization. Over twenty constitute models are available for representing a wide range of elastic, plastic, viscous and thermally dependent material behavior. For this study the uses of the 8-node solid element were used to built the bridge superstructure, abutments back wall and footing, MSE wall facing, and soil backfill finite model. The 4-node shell element was implemented in this finite element model primarily for the soil geosynthetic reinforcing material. NIKE3D has a significant feature of interface formulation 24

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capacity. In NIKE3D, surfaces between different material mesh and surfaces could permit voids or frictional sliding during analysis. There are two main algorithms that permit this interface capability: Penalty formulation method Augmented Lagrandian method For the penalty method, penalty springs are generated between the contract surfaces when an inter-material penetration is detected. This penalty spring scale factor ranges from 0.1 to 0.001, so it may be used to ensure convergence. The augmented Lagrangian method is iterative and an additional penalty for enforcing contact constraints. 3.2 Microstation and Truegrid Mesh Generation Programs To develop a 3 dimensional finite element model mesh of the mechanically stabilized earth walls (MSE), bridge superstructure, and substructure, two programs were used to perform this task. These two programs are, Bentley Systems' Mircostation J and XYZ Scientific Applications' TrueGrid. Microstation J is a 3 dimensional drawing software platform used to develop the 3 dimensional scale model bridge structure based on a define global coordinate system, (figure 3.1 ). From this 3D model, key coordinates were extracted and imported into TrueGrid. 25

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TrueGrid, is a finite element mesh generator program that provided the final mesh configuration for the MSE wall and bridge structure. TrueGrid also created the input file code for NIKE3D that will model the behavior of the structure under the applied loads. Wing Walls Fnd Soil Abutment 1 Figure 3.1 NIKE3D bridge model 3.3 Material Model BackFill Girder MSE Wall Abutment 2 NIKE3D includes twenty-two material models. These constitutive models cover a wide range of elastic, plastic, viscous and thermally dependent behavior. For this study four types of material were used. Three of the four material (foundation soil, concrete for the MSE walls and bridge structure, and inclusion) were simulated using the isotropic elastic model. The fourth type of material, The MSE wall backfill, was simulated using the non linear Ramberg-Osgood model. The required input parameters for the isotropic elastic material includs; the density, modulus of elasticity and 26

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Poisson's Ratio. For the Ramberg-Osgood material input, the parameters are discussed in the next section. 3.4 Ramberg-Osgood Elastoplastic Model The Ramberg-Osgood elastoplastic model is used to treat the nonlinear hysterestic elasto-plastic constitutive behavior of many materials. This model allows a rate-independent representation of the hysterestic energy dissipation observed in material subjected to cyclic shear deformation. The model is intended as a material for shear behavior and it can be applied in soil dynamics and seismic analysis of soil-structure. In the Ramberg-Osgood model, five material parameters are required Reference shear strain yy Reference shear stress r:y Stress coefficient a Stress exponent r Bulk modulus K The stress and strain relationship for monotonic loading in Ramberg-Osgood model is give by the following equations. r r r -=-+a-ifr > o JY 'Z}' 'Z}' r r r -=-+aify
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It should all be noted that there is a computer program named RAMBO that was developed specifically for determiming these five material model parameters. 3.5 Eigenvalue Analysis and Rayleigh Damping NIKE3D has the capability of doing the eigenvalue analysis on the proposed bridge model and the number of mode shapes can be specified in the input file for NIKE3D. In this study a total of fifteen mode shapes were used for this bridge model. After performing an analysis, NIKE3D will return a natural frequency corresponding to each of the mode shape. Knowing the natural frequency of the systems and natural frequency of the forcing motion, amplification of the systems can be calculated. A systems natural frequency associated with a mode shape can be used to determine the required coefficient for the Rayleigh damping. Rayleigh damping is a systems damping and is applied in chapter 6 of this study. Rayleigh damping is considered as a damping matrix [C], and it is a linear combination of the mass matrix [M] and the stiffness matrix [K] according to the following equation. [C] = (3.2) where a and are the mass and stiffness proportional damping coefficient. With A systems natural frequencies computed using eigenvalue analysis, a and for Rayleigh damping can be calculated. Natural 28

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frequencies of the first fifteenth modes were selected in the computation. The Rayleigh damping coefficient can be determined with the following equations; fJ = 2( m2c;2 ml c;J) ( wi ) (3.3) (3.4) where ro 1 and ro 2 are respectively the first and fifteenth mode of a systems' natural frequency. The units for ro1 and ro2 are in radian/seconds. and are the fraction of critical damping corresponding to ro1 and ro2. Users have to specify the fraction of critical damping. For structural engineering type systems, 5% critical damping has been an acceptable value. In this studies and 5% of the critical damping was used. The calculated a and p value were then specified in the material deck of NIKE3D input file. Since Rayleigh damping is an overall system damping, the computed value for a and p remained the same for all the material that comprised the bridge model. The following table 3.1 provides the mode shape numbers along with the frequencies and periods from the eigenvalue analysis. 29

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Mode Frequency Frequency Period Shape (radian) (hertz) (sec) No. 1 16.65 2.61 .37 2 16.48 2.60 .36 3 17.91 2.94 .34 4 50.81 8.06 .12 5 50.90 8.07 .11 Table 3.1 Mode shapes with frequencies and periods. Tables 3.2 through 3.5 are the response spectrum values for the first five mode shapes interpolated from the response spectrum curves and using the compute program NONIN. NorthRidge Earthquake Displacements Response Spectrum Factors w/ Damping Mode Vertical Longitudinal Transverse Shape 0% 5% 0% 5% 0% 5% 1 7.41 4.88 9.11 5.48 8.15 5.03 2 11.98 5.55 8.33 4.87 9.27 5.37 3 8.70 5.04 8.07 4.67 8.0 5.54 4 .92 .41 1.0 1.0 .51 .31 5 .58 .38 1.0 1.0 .41 .31 Table 3.2 Displacement response spectrum values-Northridge NorthRidge Earthquake Accelerations Response Spectrum Factors w/ Damping Mode Vertical Longitudinal Transverse Shape 0% 5% 0% 5% 0% 5% 1 2.95 1.32 1.36 2.67 2.07 1.4 2 3.96 1.45 2.76 1.60 2.76 1.76 3 3.14 1.55 2.95 1.65 2.70 1.65 4 2.35 1.27 1.60 .95 1.50 1.08 5 2.0 1.05 1.25 .92 1.60 .90 Table 3.3 Acceleration response spectrum values-Northridge 30

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I Imperial Earthquake Displacements Response Spectrum Factors w/ Dampjng_ Mode Vertical Longitudinal Transverse Shape 0% 5% 0% 5% 0% 5% 1 1.74 1.43 3.80 3.85 2.10 1.61 2 2.33 1.53 3.80 3.85 2.02 1.51 3 2.48 1.33 2.78 2.80 2.30 1.60 4 .88 .33 1.0 1.0 1.0 1.0 5 .54 .31 1.0 1.0 1.0 1.0 Table 3.4 Displacement response spectrum values -Imperial Valley Imperial Earthquake Accelerations Response Spectrum Factors w/ Damping Mode Vertical Longitudinal Transverse Shape 0% 5% 0% 5% 0% 5% 1 .55 .39 1.15 .78 .61 .40 2 .99 .42 .81 .76 .79 .52 3 .87 .42 .84 .71 .81 .44 4 .60 .84 .92 .59 .60 .41 5 .60 .92 .84 .52 .60 .40 Table 3.5 Acceleration response spectrum values-Imperial Valley Comparing the response spectrum tables for the Northridge and imperial Valley earthquakes indicates that the Northridge earthquake has a greater effect on the bridge and MSE wall structure. This could be caused by by several factors. First, the structure in the Northridge analysis is closer to the seismic epic-center. Secondly, the ground motion is stronger in the Northridge earthquake as compared to the Imperial Valley earthquake. This is also evident when comparing the response spectrum acceleration values. 31

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4. Ground Motion Used for this Study 4.1 Introduction Ground vibrations during an earthquake can severely damage structures and equipment. The ground acceleration, velocity and displacement are amplified when transmitted through a structure. This amplified motion can produce forces and displacements which may exceed the structure limits. Many factors influence ground motion and its amplification, therefore the understanding of how these factors influence the response of a structure is essential to design a safe and economical design. Earthquake ground movement is measured by strong motion instruments that record the acceleration of a structure or ground surface. The recorded ground accelerograms is then corrected for instrument error and, integrated to obtain the velocity and ground displacement time history. Three orthogonal components of ground acceleration, two in the horizontal directions and one in the vertical, are recorded by the field instrument. Earthquake magnitude is a quantitative measurement of it's size, and each earthquake's motion exhibits it's own unique motion parameters. Three ground motion parameters of engineering significance are 32

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amplitude, predominant frequency, and duration. So with the ground motion parameters one could define the characteristics of an earthquake. 4.2 Ground Motion Time History and Input For this study the ground motions or acceleration time histories selected were all corrected records. The term "corrected record" stands for filtered record. The corrected strong motion data had been corrected from the raw data by filtering out high frequency or low frequency background noise, correct the measurement errors and calibrating the instrument. The program NON LIN "Nonlinear Dynamic Time History Analysis of Single Degree of Freedom Systems" includes a CD-ROM collection of digitized earthquake acceleograph records dating back to 1930. The two accelerograph records selected for this study are; Northridge, California Earthquake Imperial Valley Earthquake Table 4.1 list the dates, magnitude, intensity, depth, epicentral distance and peak ground acceleration (PGA). Also note that the earthquake intensity is 9 Modified Mercalli (MM) intensity scale. 33

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Category Magnitude -7 Magnitude -7 Record No. 1 2 Name Earthquake Northridge, California Imperial Valley Date January 17, 1994 October 15,1979 Magnitude 6.8 (ML) 6.6 (ML) Intensity 9(MM) 9 (MM) Depth 18 Km 0 Km Site Geology Unknown Alluvium (>300m) Epicentral Distance 19 Km 27Km PGA 0.54 G 0.45 G (MM) = Modified Mercalli Table 4.1 Earthquake ground motion information The most commonly used amplitude parameter in characterizing a particular ground motion is (PGA) peak ground acceleration. The PGA is defined as the largest absolute value of acceleration from a given time history. The acceleration time histories were plotted in figures 4.1 thru 4.6 for both the vertical and horizontal components and were used as the input ground motion in this study. Prior to starting the dynamic analysis, a static analysis was performed in the first 1 0 seconds to allow for gravity dead load to set within the structure. 34

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0.6 0.4 1: 0.2 0 = Ill 0 Iii -0.2 .li! -0.4 NorthRidge Earthquake Vertical AccelerationTime HistoryJanuary 17,1974 PGA =.54g at 15.38 sec. -0.6 +--'"'-'-'"""--"""'-i'=="--".::.,:...:;= 0 5 10 15 20 25 Time (Seconds) Figure 4.1 Northridge vertical acceleration time history 0.6 0.4 : 0.2 1: 0 = 10 0 ... C1l Qj -0.2 u .li! -0.4 -0.6 0 Northridge Earthquake Horizontal Acceleration -Time History90 Degree January 17, 197 4 PGA= .57g at 15.34 sec. 5 10 15 20 25 Time (Seconds) Figure 4.2 Northridge horizontal @ 90 degree acceleration time history 35 l I

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0.6 0.4 : 1: 0.2 0 .. ftl 0 Iii a; -0.2 -0.4 -0.6 0 NorthRidge Earthquake Horizontal AccelerationTime History360 DegreeJanuary 17, 1974 PGA .58g at 14.32 sec 5 10 15 20 25 Time (Seconds) Figure 4.3 Northridge horizontal @ 360 degree acceleration time history 0.4 : 0.2 1: 0 0 = ftl ... Ill -0.2 iii (..) -0.4 -0.6 0 Imperial Valley EarthQuake -EL Centro Vertical Acceleration Time HistoryOct. 15, 1979 PGA = .46g@ Time 12.8 sec 5 10 15 20 Time (Seconds) Figure 4.4 Imperial Valley vertical acceleration time history 36 25

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0.5 ![ 0.3 c:: 0.1 0 = l'CI .... CD -0.1 Gi u -0.3 -0.5 0 Imperial Valley EarthQuake EL Centro Horizontal Acceleration Time History S50W Oct. 15, 1979 PGA = .45g@ Time 14.98 sec 5 10 15 20 25 Time (Seconds) Figure 4.5 Imperial Valley horizontal@ 360 degree acceleration time history IIJllerial Valley EarthQuake-EL Centro Horizontal Acceleration Time History S40E Oct. 15, 1979 PGA = 0.34g@ 16.5 sec. 0.4 ., . 2. 0.3 0.2 c: 0.1 0 7i: 0 .. -0.1 u .:l. -0.2 -0.3 -0.4 0 5 10 15 20 25 Time (Seconds) Figure 4.6 Imperial Valley horizontal @ 90 degree acceleration time history 37

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4.3 Response Spectrum Response spectrum is an important tool in the seismic analysis and design of structures. The response spectrum introduced by Biot and Hausner describes the maximum response of a damped single-degree-of-freedom (SDOF) oscillator at different frequencies or periods. The computer program NONLIM (Nonlinear Dynamic Time History Analysis of Single Degree of Freedom Systems) and was developed by Finley A. Charney, PHD., P.E. With "Advance Structural Concepts, Inc." The computed spectral values include absolute acceleration response, relative velocity response, relative displacement response, and their corresponding natural period. The Damping Ratio is defined as a fraction of the critical damping for this study only the 0% and 5% damping ratio were calculated. See Figures 4.7 thru 4.9 for response spectrum graphs. 38

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1000.00 100.00 10.00 1.00 0.01 I 0.10 1.00 10.00 Peri.od, Seconda Pseudo Vel.oci. ty, em/ a 1.000.00 100.00 10.00 f l..OO 0.01 LIH _\ 1111 ., IIIII 1111 IIIII 0.10 1. 00 10.00 Peri.od, Seconds Pseudo Aooel.erati.on, (g) 10.00 1.00 v 0.10 0.01 0.01 0.10 l..OO 10.00 Peri.od, Seconds (a) Diapl.aoemant, om 100.00 10.00 1.00 0.10 0.01 ), 0.10 1.00 10. DO Peri.od, Seconds Pseudo Vel.cci.ty, cm/s 1000.00 100.00 10.00 / 1.00 0.01 I .V\_ Jl' 0.10 1.00 10.00 Peri.od, Seconds Pseudo Aocel.erati.on, (g) 10.00 1.00 0.10 0.01 0.01 rf...< lA 0.10 1.00 10.00 Peri.od, Seconds (b) Figure 4.7a Northridge 360 degree horizontal response spectrum Figure 4.7b Northridge 90 degree horizontal response spectrum ------Dash 5% Damping --------------Solid 0% Damping 39

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1000.00 100.00 10.00 1.00 0.01 '"" } 0.10 1. 00 10.00 Period, S.aoncla Paauclo t:y, em/ 1000.00 100 .. 00 10.00 "' 1.00 0.01 v:;. ... 0.10 1.00 10.00 Period, Seoond.a P .. udo (g) 10.00 l...OO 0.01 0.01 I lA IIIII 0.10 1.00 10.00 Peri.od, Second (a) aa 100.00 10.00 1.00 0.10 0.01 1000.00 100.00 10.00 1.00 0.01 10.00 l..OO 0.10 0.01 0.01 II A ffv, 1 0.10 1.00 10.00 Period, Seaond f Ill! IIIII O.l.O 1. 00 10.00 Peri.od, Second ( .,.. .. 1\v: 1.111 l llH 1.00 10.00 Period, Seoond.a (b) Figure 4.8a Imperial Valley 360 degree horizontal response spectrum Figure 4.8b Northridge vertical response spectrum ------Dash 5% Damping --------------Solid 0% Damping 40

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om 1.00.00 F"' I 10.00 1// 1.00 1/ nr Ill 0.10 0.01 A'Ulll nnn 0.1.0 1.00 10.00 Per:iod., Seconds Pseudo Ve1ocity, am/a 1.000.00 100.00 10.00 l,b J..OO O.Ol. r .,r, 0.10 1.00 10.00 Period, Seconds Pseudo Aooal.aration, (g) 10.00 1..00 ii = 0.10 0.01 0.01 \ 0.1.0 1.00 10.00 Peri.od, Seconds (a) u1splaoement, em 1000.00 100.00 10.00 1 .00 0.01 I IIIII mm 0.10 1. 00 10.00 Period., Seconds Pseudo Vel.ocity, em/a 1.000.00 100.00 10.00 l..OO 0.01 r-.. I/ IIIII I nm IIIII I lUll 0.10 1. 00 10.00 Period., Seconds Pseudo Acoel.aration, (g) 1.0.00 1.00 0.10 0.01 0.01 nr I ill I IIIII Till II I IIIII I I IIIII 0.10 1..00 1.0.00 Per:iod, Seconds (b) Figure 4.9a Imperial Valley vertical response spectrum Figure 4.9b Imperial Valley 90 degree horizontal response spectrum ------Dash 5% Damping --------------Solid 0% Damping 41

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5. Review of Study and Design Parameters 5.1 Introduction In order to determine the effect of earthquake ground motions on bridge MSE abutment walls, two ground motions or acceleration time histories, were selected for this study: Northridge Earthquake California Imperial Valley Earthquake-EL Centro These two ground motion records were selected due to similar frequencies and durations but different acceleration amplitudes. For this study a static analysis was performed prior to the three different dynamic analyses with different directional ground motion acceleration combinations. The directional ground motion combinations included; Vertical, Transverse and Longitudinal Longitudinal and Transverse Vertical and Longitudinal Chapter 6 and 7 will discuss the results from the finite element analyses for the different directional ground motion combinations from the Northridge and the Imperial Valley earthquakes. The finite element models concerned two types of loading: static loading and dynamic loading. The static loading or gravitational acceleration (G) 9.81 m/sec2 (32.2 tusec2 ) was 42

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applied incrementally from 0 seconds to 10 seconds. This was done so that the gravity effect on the structure would be set in the structure prior to applying the dynamic loading. The ground motion time history started at 10 seconds and continued to 25 seconds for a total time of 15 seconds. The time increment was broken down to 0.02 seconds with a total of 502 time steps for each ground motions combination. The input ground motion accelerations were applied at the fixed soil foundation base. The acceleration time history plots for the above noted seismic earthquake events are shown in chapter 4 figures 4.1 thru 4.6. 5.2 Bridge Model Dimensions The same finite element model was used for both Northridge and Imperial Valley ground motion analyses. A plan view of the bridge model is shown in figure 5.1, (a simple span bridge with a total structure length of 48.8 meter 160'-0"). Figure 5.2 provides additional details on the superstructure and substructure. The superstructure consists of a 203mm (8") concrete deck and concrete barriers supported by BT84 Precast Girders. The bridge abutments support the superstructure girders with a standard back wall and beam seat founded on a concrete spread footing. Wing walls are provided to retain the soil from the back wall and each side of the approach roadway pavement. 43

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.J::.. .J::.. c6' c ro (}1 ...... ro ..., 0.: co CD "0 ru :::J < ro .., ... ;;; 10 ... ... 0 en .. ... : 160'-o" I w t) 0 "' Ill c 41.761 1 BRC. I l '"' "'" "' I ----------------. 1" -----.----t: ==:::::;::;, ,;tiniiVEOGE Of FOOTING -------------------------------MSE Woll BACK FACE llyp. 1_/ w MSE Woll BACK FACE llyp. I BR lOGE PLAN 21.0' 16.41 N ... ... ... b In ...

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11 cB" c ..., <0 1\.) CD ..., 0.: (.Q <0 <0 <0 < OJ .... a ::l OJ ::l 0.. -< "0 c:; OJ Vl en <0 () .... o ::l I TYPICAL TRANSVERSE SECTION Girder (2.13) ... ... \!) a:: CD r-r= l-4 < ABUTMENT PLAN EDGE OF FOOTING ( Typ. l I tOG'-<>" < Bri to < e.-,. 148.76) r'"'' ''"'" Ro11 I / ISpeolol l t.ISE Wo II ( Typ. l :lEI() Grode "''"' ,..,,._..:% \1). CJ _lj tUJ n ITlP. I :r / zt.....L.I::t.J, l TYPICAL LONGITIDUAL SECTION WALL HEIGHT BASED ON a 1.201 INCREMENT NOTE DIMENSIONS IN IXXl ARE IN METERS. ROCK BASE IJg:H'll BASE SOIL1 7 1< H=

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The MSE walls are located in front of the abutment footing and wraps around the abutment sides and parallel to the wing walls. See Figure 5.2 abutment plan for layout of MSE walls and Tables 5.1 a thru 5.1 c for additional bridge model dimensions and clearances. Span Length 160 ft 48.8 m Bridge Deck Width 39 ft 11.9 m Gutter line to Gutter Line 36 ft 11.0 m MSE Wall Width 45 ft 13.7 m MSE Wall Height 15.6 ft 4.8 m Table 5.1 a Bridge geomerty Girder Type: BT84 Number of Girders: 6.0 ea Girder Spacing: 4.8 1.463 m Girder Depth: 7.0 ft 2.134 m Girder Area: 6.6 tf 0.6 ,2 m n-op Deck Thickness: 0.67 ft 0.2 m Hanuch: 0.17 ft 0.1 m Barrier Height: 2.8 ft 0.863 m Barrier Width: 1.5 ft 0.457 m Table 5.1 b Superstructure geometry 46

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Footing Width 9.0 ft 2.744 m Footing Depth 2.0 ft 0.61 m BackWall 3.0 0.915 m Diaphram 2.0 ft 0.61 m walls Thickness 1.0 ft 0.305 m Wall Depth 15.0 ft 4.573 m Table 5.1 c Substructure geometry 5.3 Boundary Conditions Figure 5.3 shows the boundary conditions and spatial coordinate systems adopted for this finite element model. Since NIKE3D is a three dimensional finite element program, boundary conditions in the x, y and z directions needs to be established to correctly model the structure. The boundary conditions (Figure 5.3 and 5.4) indicate that the base soil elements of this model are fixed with displacement constraints in the x y and z directions. Roller conditions were applied along back face of the MSE soil backfill. This rolled condition allow for displacement in the z and y directions but constrain the displacement in the x direction. Figure 5.4 also provides information on inclusion length and spacing, MSE wall height and thickness, and bridge superstructure details. 47

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! \Ill T,l I I' D .. Iii :! t1J i w = ;;2 I ;i .. 111 8 .... e ;; >-;; w t J ;D I t!jt!j '/ Ln -' i /),,, Figure 5.3 Bridge elevation and boundary conditions 48

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(6.0> l BTB4 CliROER 1 -e ACK-FILL SOIL n ------j";=. GEOTEXTILE OR I GROGR 1 0 f >) w.... r-s MS WALL CTYP> 8" () -------=--1+--8' -q. ") F IN I SH ClAAi 4 Qh ( 20 ( 2. 7 l "":> ( 1.21 -"'--INCLUSION LrLEVELING PAO lSI;::: (NOT INCLUDE N ro) IN HODEL --I : .-/ I I / j / I i / l l _.__ ____ /_ '////// ROCK BASE FOUNDATION SOIL NOTE: DIMENSIONS IN (XX) ARE IN METERS. 24' ( 7-5) Figure 5.4 Boundary conditions and material dimensions 5.4 Slide Interfaces 1, Sliding interface is one of the major capabilities of NIKE30. Sliding interfaces simulate the resistance between the contact surface of two different materials. For this bridge abutment study there were four different sliding interfaces defined. See Table 5.4 for interface properties. 49

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Interface Foundation Soil-Backfill 28 Concrete Foundation 28 Concrete BackFill 39 Inclusion-Backfill --(degree)Internal friction Angle & (degree)Interface friction angle 1-1s Static friction coeifficient Ilk Kinetic friction coeifficient Table 5.2 Interface properties & (degree) lls Ilk ---0.53 0.53 19 0.34 0.34 26 0.49 0.49 14 0.25 0.25 Sliding interface requires the input parameter of static friction and the kinetic friction coefficient, for this study it was assumed that both the static and kinetic would have the same value. In order to calculate the friction coefficient, the internal friction angle (cj>) between the two materials needs to be determined. In cases where interfaces lies between materials in contact with concrete or inclusion, the interface friction angle{&) needs to be determined before the friction coefficient can be computed. Using the shear strength test, the soil internal friction angle can be calculated. Once the internal friction angle is calculated the interface friction angle for concrete surfaces and inclusion can be determined from Equation 5.1. (5.1) 50

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From the interface friction angle (equation 5.2) the coefficient of friction (ll) can be computed. f..l. =tan o (5.2) It should be noted that for the sliding interface of foundation soil to backfill, that equation 6.2 was used directly since It was also assumed that the foundation material supporting the bridge abutment was a overconsolidated clay with a internal friction angle of 28. Whereas the MSE backfill material was assumed to be a dense sand and gravel mixture with a internal friction angle of 39. For the inclusion-backfill sliding interface, an interface friction angle of 14 was selected based on direct shear test between geomembrane and sandy gravel soil. NIKE3D defines sliding interface between two contact materials as a master surface and the other surface being the slave surface. See Figure 5.5 for Slave Surface geomembrane Back-Fill Figure 5.5 Master and slave diagram 51

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master and slave surfaces orientation and configuration. The number of sliding interfaces was based on past experiences and performance with Nike3D which required defining different sliding interface definition at each interface surface. Due to the number of different elements and inclusions layers required a large number of slide interface definitions numbers. 5.5 Material Model Parameters The model materials include foundation soil, concrete wall and abutment materials. The foundation was assumed to be a rigid stiff hard clay material, so bearing capacity and deformation on the foundation soil was not a concern. It was assumed that the foundation soil would behave as an elastic material when subject to both static and dynamic loading. Table 5.3 shows the elastic material properties of the foundation soil, concrete wall and the geomembrane used in this study. Similarly the MSE concrete wall has similar properties of standard 440 kpa or (4000 psi) concrete. Material Name Density (psf) Modulas of Poisson's Elasticitv, E (psi) Ratio, v (psf) (kg/mj) (psi) (MN/mL) -Foundation Soil 130 2083 16000 110 0.15 Concrete 145 2323 3472000 25000 0.15 Inclusion 65 1041 41000 288 0.40 Table 5.3 Material properties 52

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A geosysthetic reinforced soil structure contains reinforcement are to restrain longitudinal and lateral deformation of this composite material. The reinforcement used in MSE structure is also called inclusion and is made from polymer in the form of high density polyethylene (HOPE). For this study a commercially available geosynthetic material called geogrid also named Tensar SR2 was selected. The material properties were obtained from geogrid specification published by Tensar Earth Technologies Inc., In this study the inclusions were modeled to simulate elastic material properties. See table 5.4 for physical and mechanical properties of commercially available geogrid. To determine the appropriate Young's modulus, it was decided to take the strength at 5% strain, which is in units of (lbs/ft) and convert this to a force per unit area. To accomplish this the strength at 5% strain was divided by the average thickness of the rib and thickness at the rib junction. It was calculated that the average thickness was approximately 0.003 m or (0.12 inch). So the calculated Young's modulus at 5% strain used in this study was 2900 MN/m2 or (3030 kip/W). For this study a sliding penalty value of 1 was selected. It should be noted that sliding interface formulation plays a major role in this type of study. Selecting sliding surface penalties value greater than two can generate unrealistic results. To model the inclusion in NIKE3D, the 4 node shell or membrane element was used and assigned a thickness of .003 m. This 4 53

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node shell element was selected because it has no torsional or bending stiffness, thus the shell element nodes were to be constrained at the MSE wall perimeter. Tensar (uniaxial) Properties Test Method units SR2 Tensile Strength at 2% Strain M TTM1.1 lblft 1465 XM -5% Strain M 3030 XM -Ultimate M 5380 XM -Initial Tangent Modulus M TTM1.1 kip/ft 136.2 XM -lJunction strength TTM1.2 % 80% Weight lb/yd2 1.55 Aperture size M in. XM Thickness rib in 0.05 junction 0.18 Polymer HOPE Width ft 3.3 Len_gth ft 98 lb 61 Poisson ratio range v 0.37-0.44 Table 5.4 Physical and mechanical properties of commercially available geogrid (after Koerner, 1986) The back-fill soil material was assumed to behave nonlinearly and NIKE3D Ramberg-Osgood Elastoplastic nonlinear model was selected to simulate this behavior. The computer program RAMBO developed by (Tzoushin Ueng and Jian-Chu Chen, 1992) was used to compute the required 54

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input parameters. See Table 5.5a and Table 5.5b. for the Ramberg-Osgood computed input values. Material Name Density Reference Reference Shear Strain, yy Shear Stress, -ry BackFill Soil (psf' (kg/m3 ) (10-31 (psi) N/m2 ) 130 2083 0.105 10 72000 Table 5.5a Ramberg-Osgood material properties. Stress Stress Bulk Coefficient, a Exponent, r Modulus, K (psi) (MN/m2 ) 1.1 I 2.349 42000 302 Table 5.5b Ramberg-Osgood material properties. The final parameter "K" bulk modulus was calculated with the value Gmax as computed from the program RAMBO, and Poisson's ratio of 0.37 corresponding to dense cohesion less soil type. With Gmax and Poisson's ratio, (E), Young modulus can be calculated by the following Equation 5.3. E=G(2)(1 +v) (5.3) With Young's modulus and Poisson's ratio known, the bulk modulus K can be computed with the following Equation 5.4 K= E (5.4) 3(1-2v) 55

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The bulk modulus K was computed to be 302 MN/m2 or (42000 psi). 5.6 Summary This chapter outlined the design parameters and assumptions required to analyze the MSE bridge structure under the effect of a seismic earthquake event. The next two chapters 6 and 7 review the results from the Northridge earthquake and the Imperial Valley earthquake. It should be noted the same NIKE30 model parameter except for the ground motion acceleration time histories were used for both earthquake events. 56

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6. Northridge Earthquake Results 6.1 Data Analysis A total of four NIKE3D cases were analyzed using the program NIKE3D with different directional ground acceleration combination as listed below. The numerical output of these four cases were extracted using the post-processor GRIZ and then imported into spreadsheet program, Microsoft Excel where the data was analyzed and graphed. Static Vertical, transverse and longitudinal Longitudinal and Transverse Vertical and longitudinal 6.2 Study Items This chapter review's the study items of interest for this research and are listed as follows. Static Loading Lateral MSE wall displacements Lateral earth pressure distribution on the MSE wall Geosynthetics stress distribution Bearing pressure on abutment footing Dynamic Loading Lateral MSE wall displacements Lateral earth pressure distribution pressure 57

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Connection strength Inclusion tensile stress distribution Bearing pressures on abutment footing Soil Acceleration Profile Wall Permanent forward displacement Bridge structure vertical displacements 6.3 Case 1: Static Loading Abutment 1 -----------, J: lm a; :I: E i ,NorthRidge Area Static Loading Max. Longitudinal MSE Wall Displacement Abutment 1 0 0.001 0.002 0.003 Displacements (m) Figure 6.1 Static longitudinal MSE wall displacements -+-Edge -R 1-1/4 point -R 1 ----.-Center-R 1 ----*1/4 point -L I :-+-Edge-L 0.004 ------------J: 0') a; :I: E 0 NorthRidge Area Static Loading Max. Longitudinal Soil Pressure Abutment 1 200 400 600 800 Earth Pressures (kpa) 1000 -+-Edge-R 1/4 point -R -center-R 1/4 point -L --+-Edge-L -----------Figure 6.2 Static longitudinal earth pressures 58

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-.c C') a; :I: ;: NorthRidge Max. Longitudinal Inclusion Connection Stress Static Loading 0 200 400 600 600 1000 1200 Connection Stresses (kpa) 1-+Edge -R 1 1-1/4 point-R .....,._ Center-R -----1/4 point -L I Edge-L Figure 6.3 Static longitudinal inclusion stresses 2.74m (9.0') 50 11.8m (39') CL of Bridge I 100 MT Toe of Footing Figure 6.4 Maximum bearing compression contours at footing-kpa 59

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6.3.1 Inclusion Stresses Static Loading 6.4m (21.0') Ml 11.8m (39') CL of Bridge Figure 6.5 1st Inclusion layer stress contours from top-kpa 11.8m (39') 6.4m (21.0') Ml CL of Bridge Figure 6.6 2nd Inclusion layer stress contours from top-kpa 60 Front face MSE

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6.4m (21') Ml 11.8m (39') CL of Bridge Figure 6.7 3rd Inclusion layer stress contours from top-kpa 11.8m (39') 6.4m (9.0') I' Ml CL of Bridge I ---.........;.--900 Figure 6.8 41 h Inclusion layer stress contours from top-kpa 61 Front face MSE Front face MSE

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6.4m (9.0') Ml 11.8m (39') CL of Bridge Figure 6.9 5th Inclusion layer stress contours from top-kpa 6.4m (21.0') Ml 11.8m (39') CL of Bridge Figure 6.10 6th Inclusion layer stress contours from top-kpa 62

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6.4m (21.0') MI 11.Bm (39') CL of Bridge Front face MSE Figure 6.11 7th Inclusion layer stress contours from top kpa 63

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6.4 Case 2: Vertical, Transverse and Longitudinal Motion Abutment 1 NorthRidge Earthquake Time History-Displacement at Top of Wall at center of wall c 0. 060 I Q) o.o4o _0.020 u E 0. 000 1 -:o.o2o In -0.040 I c -0.060 -t-"--"-=---'---"-..,---"--"'"'---..,------..,----"--"----''---,_:;------'-----1 10 12 14 16 18 Time (sec) (Verticai,Transverse & Longitudinal Shaking) Figure 6.12 Time history at top of wall NorthRidge Earthquake 20 Max. Longitudinal MSE Wall Displacement Abutment 1 0.02 0.03 Displacements (m) (Vertical, Transverse & Longitudial Shaking) --------Figure 6.13 Maximum MSE wall displacements 64 0.04 --+-1/4 point -R i ......._. Center-R ----*-Center-L 1/4 point -L i l 1 ___.__ Edge-L -------------

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NorthRidge Earthquake Max. Longitudinal Earth Pressure Abutment 1 Earth Pressures (kpa) -+-Edge-R 1/4 point -R ---.Center-R ----*-Center-L -iiE1/4 point -L ......._Edge-L (Vertical, Transverse & Longitudinal Shaking) Ji --------------------------------------------Figure 6.14 Maximum longitudinal earth pressures ---------------------------------------------NorthRidge Earthquake Max. Longitudinal Inclusion Connection Stress Abutment 1 5.0 -E 4.0 -"6, 3.0 a; J: 2.0 1.0 0.0 0 100 200 300 400 500 Connection Stresses (kpa) (Vertical, Transverse & Longitudial Shaking) Figure 6.15 Maximum connection stresses 65 600 -+-Edge-R '-1/4 point -R: ---.Center-R ----*-Center-L -iiE1/4 point -L ......,_Edge-L

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2.74m (9.0') 100 11.8m (39') CL of Bridge I 50 "'Toe of Footing Figure 6.16 Maximum bearing stress contours at footing kpa C) -c 0 ]:;:I I ca 0.4 I Q) ,_ 0.2 Q) I (,) (,) 0.0 <( North Ridge Earthquake Positive X Backfill Acceleration Profile Along center of Abutment No.1 0 2 4 6 Station Along Backfill -+-1 st Bottom layer -2nd layer 3th layer -:<(-4th layer Layer --+-6th Layer --+-7th Layer i -8th Layer i I -9th 1 -----Figure 6.17 Backfill acceleration profile 66

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NorthRidge Earthquake Max. Transverse MSE Wall Displacement Abutment 1 .. 5.0 i t8j 2.0 :I: 1.0 + ...... ra 0.0 0 0.0005 0.001 0.0015 0.002 0.0025 Displacements (m) (Vertical, Transverse & Longitudinal Shaking) I L_ Figure 6.18 Maximum transverse MSE wall displacements -+-Edge-R I -1/4 point -R i I 1 ......._.. Center-R NorthRidge Earthquake Max. Transverse Earth Pressure Abutment 1 Earth Pressures (kpa) (Vertical, Transverse & Lonitudinal Shaking) Figure 6.19 Maximum transverse earth pressures 67 '-+-Edge-R -1/4 point -R' ......._Center-R I

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-NorthRidge Earthquake Max. MSE WingWall Displacement @ Center of WingWall ... 5.0 C'l 3.0 a; 2. 0 -!.....;.;_' __ --:-"--1 :I: 1 0 0.0 0 0.002 0.004 0.006 0.008 0.01 Displacements (m) (Vertical, Transverse & Longitudinal Shaking) Figure 6.20 Maximum MSE wing wall displacements -+-WingWaii-L I -WingWall -R i NorthRidge Earthquake Bridge Deck Displacement -----------------------! Length on Superstructure (m) (Verticai,Transverse & Longitudinal Shaking) Abutment #1 Figure 6.21 Bridge deck displacements 68 I Abutment If.!

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6.4.1 Inclusion Stresses -Vertical, Transverse Longitudinal Motion Abutment 1 6.4m (21.0') Ml 11.8m (39') CL of Bridge I 40 400::----.__ ___ I" Figure 6.22 1st Inclusion layer stress contours from top kpa 11.8m (39') 6.4m (21.0') 30 CL of Bridge > Front face MSE Ml Front face MSE Figure 6.23 2nd Inclusion layer stress contours from top-kpa 69 ]

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6.4m (21.0') Ml 11.8m (39') CL of Bridge Figure 6.24 3rd Inclusion layer stress contours from top kpa 11.8m (39') 6.4m (21.0') Ml CL of Bridge Figure 6.25 4th Inclusion layer stress contours from top-kpa 70 200 Front face MSE

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6.4m (21.0') Ml 11.8m (39') CL of Bridge 0 Front face MSE Figure 6.26 5th Inclusion layer stress contours from top-kpa 6.4m (21.0') Ml 11.Bm (39') CL of Bridge 500-r---. I 6oo 1 500 10n-r \J J_J_S 1 I _____./ 400 -500 300 ---\. 400 0 Front face MSE Figure 6.27 6th Inclusion layer stress contours from top-kpa 71

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6.4m (21.0') MI 11.8m (39') CL of Bridge .r-----+--ooo Figure 6.28 ih Inclusion layer stress contours from top-kpa 72

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6.4.2 Case 2: Vertical, Transverse and Longitudinal Motion Abutment 2 NorthRidge Earthquake Max. Longtudinal MSE Wall Displacement Abutment No.2 0.005 0.01 0.015 0.02 0.025 Displacements (m) (Vertical, Transverse & Longitudinal Shaking) -+-Edge-R ..........,._ Center-R! -----------' --------------Figure 6.29 Maximum MSE wall displacements NorthRidge Earthquake Max. Longitudinal Earth Pressure Abutment No.2 Earth Pressures (kpa) -----------+-Edge-R ..........,._ (Vertical, Transverse & Longitudinal Shaking) Figure 6.30 Maximum longitudinal earth pressures 73

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2.74m (9.0') .. Ml 11.8m (39') CL of Bridge I Figure 6.31 Maximum bearing compression contours at footing-kpa NorthRidge Earthquake Max. Transverse MSE Wall Displacement Abutment No.2 Displacements (m) (Longitudinal, Vertical & Transverse Shaking) Figure 6.32 Maximum MSE wall transverse displacements 74 I Ed R i I '-+ge. I : I Center-R :

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NorthRidge Earthquake Max. Transverse MSE Wall Earth pressure Abutment No.2 Earth pressures (kpa) (Vertical, Transverse & Longitudinal Shaking) Figure 6.33 Maximum MSE wall earth pressures NorthRidge Earthquake __,._ Edge -Ri : I .........,_Center-R i Max. Displacement MSE WingWall @Center of WingWallAbutment 2 E = 5. 0 .c 4 0 C) 3.0 a; 2. 0 :I: 1 0 0. 0 0 0.002 0.004 0.006 0.008 0.01 Displacements (m) (Vertical, Transverse & Longitudinal Shaking) Figure 6.34 Maximum MSE wing wall displacements 75 __,._ WingWall -L 1 -wingWaii-R ---------

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6.4.3 Inclusion Stresses -Vertical, Transverse and Longitudinal Motion Abutment 2 6.4m (21.0') Ml 11.Bm (39') Front face of MSE Figure 6.35 151 Inclusion layer stress contours from top kpa 11.Bm (39') .. .. I CL of Bridge 300 Ml Front face of MSE Figure 6.36 2"d Inclusion layer stress contours from top kpa 76

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6.4m (21.0') 11.8m (39') CL of Bridge I Ml Front face of MSE Figure 6.37 3rd Inclusion layer stress contours from top-kpa 77

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6.5 Case 3: Longitudinal and Transverse Motion Abutment 1 NorthRidge Earthquake Time HistoryDisplacement at Top of Wall Center of wall abtument 1 E -c Q) E Q) (.) 0.020 0.000 "' c. II) c -0.020 + -,.-, -.--.-T-..:.::,--.--,---,---,--,--r--.-'--r-.-.,--.,--,.:.:.:--r-r--i 0 1 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 16 17 18 19 20 Time (sec) (Longitudinal & Transverse Shaking) --------------Figure 6.38 Time history at bottom of wall ---------------------North Ridge Earthquake Max. Longitudinal MSE Wall Displacement Abutment No.1 .. 5. 0 tn 3. 0 1.0 0 0.01 0.02 0.03 0.04 Displacements (m) (Longitudinal & Transverse Shaking) ----------------------------Figure 6.39 Maximum MSE wall displacements 78 -+-Edge-R -1/4 point -R ___._ Center-R ___...__ 1 /4 point -L --+--Edge:L __

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-NorthRidge Earthquake Max. Longitudinal Earth Pressure Abutment No.1 E s.o -4.0 .s:::: C) 3.0 2.0 1.0 0.0 0 200 400 600 800 1000 1200 Earth Pressures (kpa) (Longitudinal & Transverse Shaking) Figure 6.40 Maximum longitudinal earth pressures 2.74m (9.0') Ml 11.8m (39') CL of Bridge I -+-Edge-R 1 -1/4 point -R I I --.Center-R """"'*""" Center-L ---1 /4 point -L I Toe of Footing Figure 6.41 Maximum bearing pressure contours at footing kpa 79

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I I L__ NorthRidge Earthquake Max. Transverse MSE Wall Displacement Abutment No.1 -E = 5.0 .c: 4.0 3. 0 :I: 1.o 0.0 += -0.006 -0.004 -0.002 0 0.002 Displacements (m) (Longitudinal & Transverse Shaking) 0.004 ------i -+-Edge -R 1 I [ -1/4 point -R! __........ Center-R I I -----i I -____ __j Figure 6.42 Maximum transverse wall displacements ----------0 NorthRidge Earthquake Max. Transverse Earth Pressure Abutment No.1 200 400 600 Earth Pressures (kpa) (Longitudinal & Transverse Shaking) 800 1-+-Edge -R -1/4 point -R __........ Center-R -. Figure 6.43 Maximum transverse earth pressures 80 1

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-E NorthRidge Earthquake Max. MSE WingWall Displacement @ Center of WingWall -Abutment No.1 :: 5.0 .=. 4.0 C') 3.0 a; 2. 0 ::I: 1.0 0. 0 0 0.002 0.004 0.006 0.008 Displacements (m) (Longitudinal & Transverse Shaking) 0.01 Figure 6.44 Maximum MSE wing wall displacements 0 NorthRidge Earthquake Max. Earth Pressure MSE WingWalls Abutment No.1 400 600 Earth Pressures (kpa) (Longitudinal & Transverse Shaking) 800 Figure 6.45 Maximum transverse pressures at wing walls 81 -+-WingWall -L : [-i __________ ] -------

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c Q) 0.05 E 0.03 Q) u E ca -0.03 c. -0.05 II) c 0 Abutment #1 NorthRidge Earthquake Bridge Deck Displacement 10 20 C.L. I 30 40 Length on Superstructure (m) (Longitudinal & Transverse Shaking) Figure 6.46 Bridge deck vertical displacements 82 I Abutmentll2

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6.5.1 Inclusion Stresses Longitudinal and Transverse Motion Abutment 1 6.4m (21.0') M .5 11.8m (39') Figure 6.47 1st Inclusion layer stress contours from top-kpa 11.8m (39') 6.4m (21.0') r M .S CL of Bridge I Front face MSE Figure 6.48 2"d Inclusion layer stress contours from top-kpa 83 .. I

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6.4m (21.0') M .5 11.8m (39') CL of Bridge 3rct Inclusion layer stress con ou Figure 6.49 t rs from top kpa 6.4m (21.0') M .5 11.8m (39') CL of Bridge 4th Inclusion layer stress con o Figure 6.50 t urs from top-kpa 84

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6.4m (21.0') Ml 11.8m (39') CL of Bridge Front face MSE Figure 6.51 5th Inclusion layer stress contours from top-kpa 6.4m (21.0') M .5 11.8m (39') CL of Bridge Figure 6.52 6th Inclusion layer stress contours from top-kpa 85

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6.4m (21.0') Ml 11.8m (39') CL of Bridge Front face MSE Figure 6.53 7th Inclusion layer stress contours from top-kpa 86

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6.5.2 Case 2: Longitudinal and Transverse Motion Abutment 2 NorthRidge Earthquake Max. Longtudinal MSE Wall Displacement Abutment No.2 0 0.005 0.01 0.015 0.02 Displacements (m) (Longitudinal & Transverse Shaking) 0.025 -+-Edge-R I --1/4 point -R ........,._Center-R '-----I I --Figure 6.54 Maximum MSE wall displacements ... -0 NorthRidge Earthquake Max. Longitudinal Earth Pressure Abutment No.2 200 400 600 800 Earth Pressures (kpa) (Longitudinal & Transverse Shaking) 1000 Figure 6.55 Maximum longitudinal earth pressures 87 ,-------:-+-Edge-R --1 /4 point -R I ........,._Center-R

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2.74m (9.0') 0 \ )\ \\\ I \ \ 50 \V / A, }00 / I I I 11.8m (39') CL of Bridge I of Footing Figure 6.56 Maximum bearing compression contours at footing kpa -E NorthRidge Earthquake Max. Displacement MSE WingWall @ Center of WingWallAbutment No.2 = 5.0 J: 4. 0 3.0 Q) 2.0 :I: 1.0 ..... -0.005 0 0.005 0.01 0.015 Displacements (m) (Longitudinal & Transverse! Shaking) 0.02 Figure 6.57 Maximum MSE wing wall displacements 88 1--+-WingWall -L WingWall -R I

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0 NorthRidge Earthquake Max. Earth Pressure MSE WingWalls Abutment No.2 200 400 600 800 Earth Pressures (kpa) (Longitudinal & Transvers Shaking) 1000 Figure 6.58 Maximum MSE wall earth pressures 89 :1 -+-WingWall -R Wingwall -L I _,

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6.5.3 Inclusion Stresses Longitudinal and Transverse Motion Abutment 2 6.4m (21.0') j 11.8m (39') Ml Figure 6.59 151 Inclusion layer stress contours from top-kpa 11.8m (39') 6.4m (21.0') Ml CL of Bridge Front of MSE Figure 6.60 2nd Inclusion layer stress contours from top-kpa 90 .I

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6.4m (21.0') Ml 11.8m (39') CL of Bridge Front of MSE Figure 6.61 3rd Inclusion layer stress contours from top-kpa 91

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6.6 Case 4: Vertical and Longitudinal Motion Abutment 1 NorthRidge Earthquake Time History-Longitudinal Displacement at Top of Wallat Center wall i';:' s:::::0.02 (I) I o.oo ...__. . CJ 1 -E:o.o2 U) C-o 0 04 10 11 12 13 14 15 16 17 18 19 20 Time (sec) (Vertical & Longitudinal Shaking) Figure 6.62 Time history at top of wall North Ridge Earthquake Max. Longitudinal MSE Wall Displacement Abutment No.1 I .. 5. 0 I -4 0 .s::::: 0 m 3.0 I 2. 0 1 0 0 0 0 0 0 0.01 0.02 0.03 Displacements (m) (Vertical & Longitudinal Shaking) Figure 6.63 Maximum MSE wall displacements 92 0.04 --+-Edge-R :-----1/4 point -R I I --+--Center-R Center-L 1 ---*1/4 point -L 1 _._ Edge-L

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NorthRidge Earthquake Max. Longitudinal Earth Pressure Abutment No.1 200 400 600 BOO 1000 1200 1400 Earth Pressures (kpa) (Vertical & Longitudinal Shaking) Figure 6.64 Maximum longitudinal earth pressures 11.Bm (39') CL of Bridge I I -+-Edge-R 1/4 point -R! _....,_ Center-R 1---*'1/4 point -L 1 j-Edge-L 2.74m (9.0') \_so Toe of Footing Figure 6.65 Maximum bearing pressure contours at footing kpa 93

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-NorthRidge Earthquake Max. Transverse MSE Wall Displacement Abutment No.1 ... 5. 0 4. 0 C) 3.0 2.0 1.0 -t o.o 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 Displacements (m) (Vertical & Longitudinal Shaking) I 1--.Center 1 I j-+-Edge-L. --------_______ _. __ ------------Figure 6.66 Maximum transverse wall displacements ---------------0 NorthRidgeEarthquake Maximum Transverse Earth Pressure Abutment No. 1 200 400 600 800 Earth Pressures (kpa) (Vertical & Longitudinal Shaking) 1000 --..-1/4-R !-+-Center ----.----------------------------------Figure 6.67 Maximum transverse earth pressures 94

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NorthRidge Earthquake Max. Transverse Displacement WingWalls Abutment No.1 Displacements (m) (Vertical & Longitudinal Shaking) Figure 6.68 Maximum MSE wing wall displacements -+-L WingWall i ......._ R Wingwall i --------------------; 1.0 NorthRidgeEarthquake Max. Earth Pressure MSE WingWalls Abutment No.1 0.0 0 200 400 600 800 Earth Pressures (kpa) (Vertical & Longitudinal Shaking) 1000 Figure 6.69 Maximum transverse pressures at wing walls 95 -----------+Wingwaii-L ......._ Wingwaii-R

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6.6.1 Inclusion Stresses -Vertical and Longitudinal Motion Abutment 1 6.4m (21.0') Ml 11.8m (39') CL of Bridge Front face MSE Figure 6.70 151 Inclusion layer stress contours from top-kpa 6.4m (21.0') j 96 11.8m (39') CL of Bridge

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6.4m (21.0') Ml 11.8m (39') CL of Bridge Front face MSE Figure 6.72 3rd Inclusion layer stress contours from top-kpa 6.4m (21.0') 11.8m (39') CL of Bridge I 400 I I : >OO 500 L_ c__3) 1 \ Ml Front face MSE Figure 6.73 4th Inclusion layer stress contours from top-kpa 97 .. I I

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6.4m (21.0') Ml 11.8m (39') CL of Bridge ----------
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6.4m (21.0') M .5 11.8m (39') CL of Bridge i 400 Figure 6.76 7th Inclusion layer stress contours from top-kpa 99

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6.6.2 Case 2: Vertical and Longitudinal Motion Abutment 2 NorthRidge Earthquake Max. Longtudinal MSE Wall Displacement Abutment No.2 Displacements (m) (Vertical & Longitudinal Shaking) !-+--Edge-R I i -..Center-R 1 '-----------------------------------------Figure 6.77 Maximum MSE wall displacements 0 NorthRidge Earthquake Max. Longitudinal Earth Pressure Abutment No.2 200 400 600 Earth Pressures (kpa) (Vertical & Longitudinal Shaking) ---------------------Figure 6.78 Maximum longitudinal earth pressures 100 -+-Edge-R I 1-..Center-R i 800

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I. 11.8m (39') CL of Bridge I \ 100 I .. 5 \ 100 2.74m \\ '" ) ( (9.0') \ I /'I ) I \I (\ /'00 I I I I \. 150 / /\ 100 \\ l5 1\ 15\ I I I I ; r 50 1op MT Toe of Footing Figure 6.79 Maximum bearing compression contours at footing-kpa NorthRidge Earthquake Max. Displacement MSE WingWall @ Center of WingWallAbutment No. 2 Displacements (m) (Vertical & Longitudinal Shaking) Figure 6.80 Maximum MSE wing wall displacements 101 --+-L I) -WingWaii-RJ I __ I

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I ] 1.0 NorthRidge Earthquake Max. Earth Pressure MSE WingWalls Abutment No.2 WingWall -R l 0 200 400 600 Earth Pressures (kpa) (Vertical & Longitudinal Shaking) 800 Figure 6.81 Maximum MSE wing wall earth pressures 102

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6.6.3 Inclusion Stresses Vertical and Longitudinal Motion Abutment 2 6.4m (21.0') l Ml 11.8m (39') CL of Bridge Figure 6.82 1st Inclusion layer stress contours from top-kpa 6.4m (21.0') 11.8m (39') Ml Front Face MSE Figure 6.83 2nd Inclusion layer stress contours from top-kpa 103

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6.4m (21.0') Ml 11.8m (39') Front Face MSE Figure 6.84 3rd Inclusion layer stress contours from top-kpa 104 I

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6.7 Interpretation of Analysis Results 6.7.1 Analysis Results This section will summarize the analyses results for the four NIKE3D load case presented earlier in this chapter. The deflections, pressures, and stress contours and graphs presented here are based on maximum values from this study. This is based on another important concept synchronization with peak ground acceleration with corresponding maximum values. Since massive amounts of data can be extracted from these finite element models, only major elements were selected for this study. The presentation of the results are grouped in their respective load case as follows: 6.7.2 Case 1: Static Loading Nodes were selected at key locations along the front face of the MSE wall as shown in the graph to determine the maximum and minimum wall movements. The maximum movement in the MSE wall occurs at the base located horizontally in the center of the wall. The minimum movement occurs at the MSE wall corners (Figure 6.1 ). The top of the wall had similar displacements in the range of 0.003 m to 0.013 m. Since the largest displacements occurred at the base of the wall, this was a result of modeling the connection between the MSE wall and the foundation soil as a friction connection and not as fixed connection at the base of the wall. The corner displacements are relativity small compared to the other locations. 105

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This indicating that the corners are much stiffer than the center of the wall allowing for redistributions of movements. For lateral wall displacement criteria, ASSHTO provides empirical curves to estimate the anticipated lateral displacement during construction. This establish an appropriate wall batter to obtain a near vertical wall or to determine minimum clearances requirements to adjacent structures. Figure 6.2 displays the earth pressures at various locations behind the MSE wall. From this graph the maximum pressure is located horizontal in the center of the wall with the minimum pressure at the wall corners. The earth pressures along the height of the wall are fairly uniform until the 1 m elevation where they decrease approximately 150 kpa to the base of the wall. The normal earth pressure distribution for static loads without surcharge would have an earth pressure of zero at the surface and increasing with depth. Since this model has a surface surcharge from the abutment and superstructure loading, the earth pressure effect would cause a more uniform pressure until a depth of approximate 3 m or the width of the abutment footing. From this point the surcharge loading has little effect on the normal earth pressure. The pressure diagram also decreases at a normal rate to the bottom of the wall. The wall corner earth pressure diagram also indicates high pressures at the top of the wall, which is caused by the higher stiffness of the corners. 106

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Similar to the earth pressure's graph, Figure 6.3 displays the connection stresses at the back face of MSE wall and geogrid material. The maximum stress occurs at the center of the wall and decreases as you move towards MSE wall corners. The stresses range from a minimum of 200 kpa at the corner to a maximum of 1 050 kpa at the center of the wall. Based on AASHTO, the connection strength is the lesser value of the pullout capacity of the connection, the long term rupture strength, or connection strength is determined from laboratory tests. Figure 6.5 through 6.11 illustrates the stress contour plots for the different inclusion layers. Reviewing the stress contour plots indicates that the maximum stress occurs at the center of the wall and decreases toward the MSE corners. Similarly the stress also decreases from 1 050 kpa at the front face to 700 kpa at the end of the reinforced backfill. The inclusions used in this analysis have properties of geogrid called SR2, manufactured by Tensar Earth Technologies, Inc. The ultimate tensile strength for SR2 is 5,380 lb/ft (=78511 N/M) (Table 5.4 ). With an average thickness of 3 mm, the ultimate capacity is 26,170,428 N/M2 For a static loading condition a factor of safety against rupture of 1.5 is recommended per AASHTO (1998) interim specification. This ultimate capacity of 26,170,428 N/M2for SR2 and a maximum applied tension load of 1,900,000 N/M2 provides a factor of safety of 13. Another observation based on the stress contour plots is that the tensile stresses are fairly uniform and 107

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consistent from the top layer through to the bottom layer. This correlates with the earth pressure contour plots and the uniform pressure from the top of the wall to the base. Figure 6.4 illustrates the maximum bearing pressure contours at the bottom of abutment 1 footing. The maximum stress occurs at the outside edges of the abutment footing. The bearing pressure in the center of the abutment footing is approximately 1 00 to 150 kpa, and a maximum pressure of 350 kpa at the edge of the footing. Hand calculations were performed to estimate the static uniform bearing pressure to verify the model results. The hand calculations indicate a bearing pressure of 225 kpa. This discrepancy in bearing pressures may be caused by the wing walls being cantilever off the abutment back wall without any support at the end of the walls or an numerical round-off due to the finite element mesh size and spacing. For allowable bearing pressures on typical projects 225 to 250 kpa is an acceptable bearing pressure for most local county or state agencies. Values above these would need to be evaluated on a case by case basis. 6.7.3 Case 2: Vertical, Longitudinal and Transverse Motion The time history diagram for the top of wall displacements is illustrated in Figure 6.12. From this diagram the time period of maximum displacement can be determine and based on synchronization with peak ground 108

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acceleration should correspond to the maximum displacement value. There are some other factors that could affect this maximum displacement value including; structure damping, period of the structure and the response spectrum, (figures 4.7 thru 4.9). The maximum displacement at the base of the MSE wall is approximately 0.034 m and the top displacement of 0.02 m occurring at the center of MSE wall. The minimum displacement occurs at the MSE wall corners with virtually little to no movement. Currently the only design guideline for acceptable wall displacements is left to the project design criteria and on a project to project basis. As mentioned earlier in the static load case section, the same friction boundary condition at the base was used here and in all other load cases. Figure 6.14 and 6.15 illustrates the earth pressures and connection stresses at the back face of the MSE wall. The earth pressures were the greatest near the center of the wall and decrease as you moved to the corners. The earth pressure also varied from the top of the wall to the bottom with the maximum pressure located approximate 1m from the bottom. The connection stress graph varied from the top and increased as you move towards the bottom, with the maximum near the bottom of the wall. This also corresponds to the earth pressure graph. The footing bearing pressure is shown in Figure 6.16. These bearing pressure varies from edge of footing to edge of footing from 200 to 300 kpa. These differences may be caused by the combination of different ground accelerations. One important 109

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graph that correlates the structure response with different ground motion and its acceleration amplification is shown in Figure 6.17. The Backfill acceleration profile graph illustrates the change in horizontal acceleration with increasing height of backfill. For this structure there is an increase in horizontal acceleration in the backfill, approximately half way up from the base and then it starts to decrease until it reaches the top of the abutment. This decease in horizontal acceleration is the result of the rigid superstructure restraining the top of the back-fill. The lateral displacements at the bottom and top of the wall and earth pressures at the back face of the MSE wall are relatively small (Figure 6.18) and (Figure 6.19). This is also true for the wing wall displacements shown in (Figure 6.20). Node points located on the top of the bridge deck, along both abutments and at each girder, and at center of span, were selected to evaluate the bridge displacements in the vertical direction. Figure 6.21 gives the results with both the minimum and maximum displacements shown. These displacements indicate that the bridge is moving as a rigid mass with no relative difference from one abutment to the other. This is an indication that abutment 1 and abutment 2 are synchronized with the ground motion. The inclusion stress (Figure 6.22 through Figure 6.28) decease from the front face at the MSE wall to the back side of the backfill or inclusion. Also, the tension stress is fairly uniform from the top inclusion layer to the 110

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bottom layer. The stress range from the static condition to dynamic loading indicates a reduction of approximately 50%. This reduction in tension stress is cause by the dynamic effect of the ground motion particularly by the vertical ground motion which relaxes the friction interface between geogrid and soil. Currently AASHTO does not take the vertical acceleration component into consideration in their seismic design guideline. Abutment 2 (Figures 6.29) show a reduction in MSE wall displacements. This reduction in MSE wall displacement reflects the wall compression against the earth backfill. This computation was used to compare the two displacements movement, away from the soil and against the soil. The horizontal earth pressure at abutment 2 is comparable to the other load cases, the sign convention was changed here so the true compression on back of the MSE wall was reported. 6.7.4 Case 3: Longitudinal and Transverse Motion Many of the same analyses conditions and results have all ready been discussed in the static load case 1 or the dynamic load case 2 and don't need to be repeated in this section. Finding and discussion will main pertain to this section. The wall displacements and earth and bearing pressures are consistent with the previous section. It should be noted that for this load case there is no vertical acceleration component and the tension stresses in the inclusion have are in the range of 11 00 to 600 kpa. But, these values are in the magnitude of double to the load case with vertical acceleration Ill

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6. 7.5 Case 4: Vertical and Longitudinal Motion The results here for displacements, pressures, tension stress at abutment 1 or 2 abutment are very similar to the other load cases previously mentioned. 6.7.6 Summary The previous sections summarize the results from the figures and graphs for chapter 6. Table 6.1 provides a summary of the permanent horizontal MSE wall displacements for the load cases in this study. NorthRidge Area Permanent MSE Wall Displacement at Top of wall At Center of Abutment 1 Direction Load Case Load Case Load Case Load Case 4 #1 #2 #3 Vertical & Static Vertical, Longitudinal & Transverse Transverse & Transverse Longitudinal Horizontal .002 m (1/8") .02 m (3/4") .03 m (1 1/8") .02 m (3/4") Transverse .015 (1/2") .002 (1/8") .015m (1/2") Table 6.1 Permanent displacement at top of wall With different directional ground acceleration combinations it is sometime difficult to visualized the effect this motion has on the bridge or wall structure behavior. However, comparing the graphs and contour plots for all the load cases, indicates a similarity in behavior between the structures, displacements, pressures, stresses, and forces. With this analyses output and information it may verify that the method used in this study was model 112

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correctly. The following Table 6.2 summarizes the dynamic analyses results for the front MSE wall studied in this research and their maximum corresponding value. NorthRidge Area Summary of Maximum Dynamic Results Abutment 1-Front Face of MSE Wall Item Load Case #2 Load Case #3 Load Case 4 Vertical, Longitudinal & Vertical & Transverse & Transverse Transverse Longitudinal Earth Pressure max. (kpa) 775 1050 975 Earth Thrust (N/M) 166.7 158.1 146.5 Thrust Location from base (m) 2.3 3.11 2.67 Connection Stress max (kpa) 500 1300 600 Connection Stress min (kpa) 375 500 400 Inclusion Stress -max (kpa) 600 1800 700 Inclusion Stress -min (kpa) 300 500 300 Bearing Pressure max(kpa) 300 180 250 Soli Acceleration Profile max. (g) .62 -Soli Acceleration Profile min. (g) .22 -Bridge Vertical Max. (m) .48 0 0 Bridge Vertical Min. (m) -.015 -.015 -.015 Table 6.2 Summary of dynamic analysis results At the end of Section 7.7.6, comments and compares for the results of these two tables 6.2 and 7.2 are discuss. 113

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7. Imperial Earthquake Results 7.1 Data Analysis A total of four NIKE3D cases were analyzed using the NIKE3D program with different directional ground acceleration combination as listed below. The numerical output of these four cases were extracted using the post-processor GRIZ and then imported into spreadsheet program, Microsoft Excel where the data was analyzed and graphed. Static Vertical, transverse and longitudinal Longitudinal and transverse Vertical and longitudinal 7.2 Study Items This chapter review's the study items of interest for this research and are listed as follows. Static Loading Lateral earth pressure distribution on the MSE wall Lateral MSE wall displacements Geosynthetics stress distribution Bearing pressure on abutment footing Soil acceleration profile Dynamic Loading Lateral earth pressure distribution 114

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Lateral MSE wall displacement Connection strength Inclusion tensile stress distribution Bearing pressures on abutment footing Bridge structure vertical displacements 7.3 Case 1: Static Loading Abutment 1 ,--------------------: Imperial Valley Area Static Loading Max. Longitudinal MSE Wall Displacement Abutment 1 ..c 5.0 4. 0 Q) 3.0 :I: ... 2. 0 ;: 0. 0 0 0.001 0.002 0.003 0.004 Displacement ( m) -+-Edge-R ---1/4 point -R --.Center-R I I Center-L I 1/4 point -L i _--+-_Edge-_L______; I -------------------------Figure 7.1 Static longitudinal MSE wall displacements -----------------Imperial Valley Area Static Loading Max. Longitudinal Earth Pressure Abutment 1 200 400 600 800 1000 1200 Earth Pressures (kpa) -+-Edge-R I -1/4 point -R' __..,_ Center-R ---*"""Center-L _....._ 1/4 point -L --------------------------Figure 7.2 Static longitudinal earth pressures 115

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5.0 .. 4.0 ", 3.0 a; 2.0 J: 1.0 0.0 Imperial Valley Static Load Case Max. Longitudinal Inclusion Connection Stress Abutment 1 0 200 400 600 BOO 1000 Connection Stress (kpa) 1200 1--+Edge -R I :-1/4 point -R I ............_Center-R I """'"*""" Center-L I 'I """'"*"'"" 1 /4 point -L ......_Edge-L Figure 7.3 Static longitudinal inclusion stresses 2.74m (9.0') MT lOO 11.8m (39') CL of Bridge I I ;=p lOO 150 100 Figure 7.4 Maximum bearing pressure contours at footing-kpa 116

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7 .3.1 Inclusion Stresses Static Loading 6.4m (21.0') Ml 11.8m (39') CL of Bridge Figure 7.5 151 Inclusion layer stress contours from top-kpa 11.8m (39') CL of Bridge Ml Front face MSE Figure 7.6 2nd Inclusion layer stress contours from top-kpa 117

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6.4m (21.0') Ml 11.8m (39') CL of Bridge I I 100 Figure 7.7 3rd Inclusion layer stress contours from top-kpa 11.8m (39') 6.4m (21.0') Figure 7.8 4th Inclusion layer stress contours from top-kpa 118

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6.74m 21.0') Ml 11.8m (39') Front face MSE Figure 7.9 5th Inclusion layer stress contours from top-kpa 6.4m (21.0') Ml 11.8m (39') CL of Bridge I Figure 7.10 6th Inclusion layer stress contours from top-kpa 119

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6.4m (21.0') Ml 11.8m (39') CL of Bridge Front face MSE Figure 7.11 71 h Inclusion layer stress contours from top-kpa 120

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7.4 Case 2: Vertical, Transverse and Longitudinal Motion Abutment 1 Imperial Valley Earthquake Time HistoryDisplacement at Top of Wall at center of wall -E o.o6o -0.040 ai 0.020 0. 000 -0.020 c.. -0.040 en c -0.060 10 12 14 16 18 Time (sec) (Verticai,Transverse & Longitudinal Shaking) Figure 7.12 Time history at top of wall ,----------------Imperial Valley Earthquake 20 Max. Longitudinal MSE Wall Displacement Abutment 1 -E s. o -J: C) 3.0 2. 0 1 0 0.0 0 0.01 0.02 0.03 0.04 Displacements (m) (Vertical, transverse & Longitudinal Shaking) Figure 7.13 Maximum MSE wall displacements 121 ---------+-Edge-R -1/4 point -R I .......-center-R i --*1 /4 point -L 1 I ---. Edge-L -----------

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0 Imperial Valley Earthquake Max. Longitudinal Earth Pressure Abutment 1 200 400 600 800 1 000 1200 Earth Pressures (kpa) (Vertical, Longitudinal & Transverse Shaking) -+-Edge-R --1/4 point -R .........-center-R -----1 /4 point -L -+-Edge-L I I I _j Figure 7.14 Maximum longitudinal earth pressures -5.0 E -4.0 .c C) 3.0 a; 2.0 :I: 0.0 Imperial Valley Earthquake Max. Longitudinal Inclusion Connection Stress Abutment 1 0 200 400 600 BOO 1000 1200 1400 Connection Stresses (kpa) (Vertical, transverse & Longitudinal Shaking) -+-Edge-R --1/4 point -R .........-center-R -----1/4 point -L -+-Edge-L Figure 7.15 Maximum connection stresses 122

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2.74m (9.0') uo 11.Bm (39') CL of Bridge I \-----50 Figure 7.16 Maximum bearing pressure contours at footing-kpa c:: 0 ca I..-Q) en -Q) 0 0 <( Imperial Valley Earthquake Positive Acceleration in X Direction Backfill Along center of Abutment No.1 0.6 0.4 0.2 0.0 0 2 4 6 Station along Backfill Figure 7.17 Soil acceleration profile 123 -+-1st Bottom :I layer -2nd layer I 3th layer ... :-4th layer Layer ___.__ 6th Layer -+--7th Layer -8th Layer I --9th __j

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Imperial Valley Earthquake Max. Transverse MSE Wall Displacement Abutment 1 I-+Edge -R 1 ___...,_ Center-R I 1 _..._Edge-'=--__ 0.001 0.002 0.003 0.004 0.005 Displacements (m) (Vertical, Transverse & Longituinal Shaking) Figure 7.18 Maximum transverse MSE wall displacements Imperial Valley Earthquake Max. Transverse Earth Pressure Abutment 1 E 5. o __,.., -4.0 J: tn 3.0 2.0 1.0 0 200 400 600 800 1 000 Earth Pressures (kpa) (Vertical, Transverse & Longitudinal Shaking) Figure 7.19 Maximum transverse earth pressures 124 -+-Edge-R ___...,_ Center-R 1 ___.,_ 1/4 point -L

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-E 5.0 --4.0 .c 0) 3.0 a; 2.0 :I: 1.0 0.0 0 Imperial Earthquake Max. MSE WingWall Displacement @ Center of WingWall 0.002 0.004 0.006 0.008 Displacements (m) (Vertical, Transverse & Longitudinal Shaking) Figure 7.20 Maximum MSE wing wall displacements 0 10 I Imperial Valley Earthquake Bridge Deck Displacement 20 C.L. I 30 40 --+-WingWall -L ----WingWall -R J Length (m) Abutmen1112 (Vertical, Longitudinal & Transverse Shaking) ----Figure 7.21 Bridge deck displacements 125

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7 .4.1 Inclusion Stresses -Vertical, Transverse and Longitudinal Motion Abutment 1 6.4m (21.0') Ml 11.8m (39') CL of Bridge 600 Front face MSE Figure 7.22 1st Inclusion layer stress contours from top-kpa 11.8m (39') 6.4m (21.0') Ml CL of Bridge Figure 7.23 2nd Inclusion layer stress contours from top-kpa 126

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6.4m (21.0') Ml 11.Bm (39') CL of Bridge I Front face MSE Figure 7.24 3rd Inclusion layer stress contours from top-kpa 6.4m (21.0') Ml 11.Bm (39') CL of Bridge Front face MSE Figure 7.25 4th Inclusion layer stress contours from top-kpa 127 ..

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6.4m (21.0') Ml 11.Bm (39') CL of Bridge Front face MSE Figure 7.26 5th Inclusion layer stress contours from top-kpa 6.4m (21.0') Ml 11.8m (39') CL of Bridge Figure 7.27 6th Inclusion layer stress contours from top-kpa 128

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6.4m (21.0') Ml 11.8m (39') Front face MSE Figure 7.28 ih Inclusion layer stress contours from top-kpa 129

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7.4.2 Case 2: Vertical, Transverse and Longitudinal Motion Abutment 2 Imperial Valley Earthquake I I Max. Longitudinal MSE Wall Displacement Abutment No.2 .c 5.0 4.o e 3.o 2.0 = 1.0 -0.03 -0.02 -0.01 0 0.01 Displacements (m) (Vertical transverse & longitudinal Shaking) .-+-Edge-R I 1 __..._ Center -R I I I J L__ ----------------------------------Figure 7.29 Maximum MSE wall displacements --------------------------Imperial Valley Earthquake Max. Longitudinal Earth Pressure Abutment No.2 E :E 4.1 C) a; 2.7 :X: 1.4 0.0 + 0 200 400 600 Earth Pressures (kpa) (Vertical, transverse & Longitudinal Shaking) 800 -=-;_Edge -R 1 I -center 1 ---------------------------------------------------_i Figure 7.30 Maximum longitudinal earth pressures 130

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2.74m (9.0') MT 11.8m (39') CL of Bridge I Figure 7.31 Maximum bearing pressure contours at footing-kpa -E = 5.0 .c 4.0 C) 3.0 a; 2.0 ::I: 1.0 ca 0.0 I 0 Imperial Earthquake Max. Transverse MSE Wall Displacement Abutment No.2 0.001 0.002 0.003 0.004 0.005 0.006 Displacements (m) (Vertical, Transverse & Longitudinal Shaking) -1/4 point -L I' ......-center-R ----------Figure 7.32 Maximum MSE wall transverse displacements 131

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Imperial Earthquake Max. Transverse MSE Wall Earth pressure Abutment No.2 -E = 5.0 .c 4.0 --r: 3.0 (I) 2.0 ............ J: 1.0 0. 0 -!-'--'----".;.;..;.....;.---r-'--"-'..F---'----r--'---"---'----'-r--'---'--"'-i 0 200 400 600 Earth pressures (kpa) (Vertical, Transverse & Longitudinal Shaking) BOO Figure 7.33 Maximum MSE wall earth pressures 'E 5.o Imperial Earthquake Max. Displacement MSE WingWall @Center of WingWallAbutment 2 = 4.0 .c C) 3.0 2.0 -1 0 +"-':-:-:-:::f;;'=:----"'-::'o:---' > 0. 0 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 Displacements (m) dVertical, Transverse & Longitudinal Shaking) -+-Edge-R ......,_ Center-R --+-WingWall -L i -------------------Figure 7.34 Maximum MSE wing wall displacements 132

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7.4.3 Inclusion StressesVertical, Transverse and Longitudinal Motion Abutment 2 6.4m (21.0') Ml 11.8m (39') CL of Bridge Front Face MSE Figure 7.35 151 Inclusion layer stress contours from top-Kpa 6.4m (21.0') 11.8m (39') CL of Bridge "I Ml Front Face MSE Figure 7.36 2nd Inclusion layer stress contours from top Kpa 133

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6.4m (21.0') MI 11.8m (39') CL of Bridge Front Face MSE Figure 7.37 3rd Inclusion layer stress contours from top-kpa 134

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7.5 Case 3: Longitudinal and Transverse Motion Abutment 1 Imperial Valley Earthquake Time History Displacement at Top of Wall -E o.o4o -; 0.030 i 0.020 (J ..! 0.010 Q. .!! 0. 000 + :;;;..' .......:_:.:.:;....:..:=.;_--r-'_...;.-=:;___,.:..;--.:::.:..:.:...-:::.__-,--;;:...:;;.:..;'-"--.,...-=='-'=--''--'"! c 10 12 14 16 Time (sec) (Longitudinal & Transverse Shaking) Figure 7.38 Time history at top of wall 18 20 ---------------Imperial Valley Earthquake Max. Longitudinal MSE Wall Displacement Abutment No.1 .. 5.0 C) 3. 0 1 0 s: 0.0 0 0.01 0.02 0.03 Displacement (m) (Longitudinal & Transverse Shaking) Figure 7.39 Maximum MSE wall displacements 135 0.04 -+-Edge-R I -1/4 point -R I --.-Center-R I : --*-Center-L 1/4 point -L __._ Edge-L ------------

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0 Imperial Valley Earthquake Max. Longitudinal Earth Pressure Abutment No.1 200 400 600 BOO 1 000 1200 1400 Earth Pressures (kpa) (Longitudinal & Transverse Shaking) I-+Edge I 1-+1/4 pornt -R r 1 ___...,_ Center-R I I --*'Center-L ] 1/4 point -L I I -+-Edge-L : Figure 7.40 Maximum longitudinal earth pressures 2.74m (9.0') 130 1110 11.8m (39') CL of Bridge Toe of Footing Figure 7.41 Maximum bearing pressure contours at footing-kpa 136

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Imperial Valley Earthquake Max. Transverse MSE Wall Displacement Abutment No.1 .. 5.0 :E 4.0 C') 3.0 2. 0 0.0 -0.01 -0.005 0 0.005 0.01 0.015 0.02 Displacements (m) (Longitudinal & Transverse Shaking) Figure 7.42 Maximum transverse wall displacements ------------0 Imperial Valley Earthquake Max. Transverse Earth Pressure Abutment No.1 200 400 600 800 1 000 1200 Earth Pressures (kpa) (Longitudinal & Transverse Shaking) i--+Edge -R __.,_ Center-R ___.__ Edge-L --+-Edge -R 1 __._Center-R : ___.__ ------------------------Figure 7.43 Maximum transverse earth pressures 137

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Imperial Earthquake Max. MSE WingWall Displacement @ Center of WingWallAbutment No.1 e 5.o ::4.0 J: C) 3.0 a; :I: 2. 0 -1 0 +"-..,.::.;:.:::;;.=..:=,.......=:;'-'-"""' > 0. 0 0 0.005 0.01 0.015 0.02 Displacements (m) (Longitudinal & Transverse Shaking) Figure 7.44 Maximum MSE wing wall displacements 0.025 !-+-WingWaii-L --WingWaii-R, I ----------------------Imperial Valley Earthquake Max. Earth Pressure MSE WingWalls Abutment No.1 -+-WingWallR! Wingwall 200 400 600 BOO Earth Pressures (kpa) (Longitudinal & Transverse Shaking) -------------------1000 Figure 7.45 Maximum transverse pressures at wing walls 138 _______ j

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Imperial Valley Earthquake Bridge Deck Displacement C.L. Bridge I I 0.01 0.01 _o.oo -Q Abutment#1 10 20 30 40 Superstructure Length (m) (Longitudinal & Transverse Shaking) Abulmen 1112 -------------Figure 7.46 Bridge deck vertical displacements 139

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7.5.1 Inclusion Stresses-Transverse and Longitudinal Motion Abutment 1 6.4m (21.0') 11.8m (39') CL of Bridge I Figure 7.47 1st Inclusion layer stress contours from top-kpa 11.8m (39') Ml CL of Bridge I Figure 7.48 2nd Inclusion layer stress contours from top-kpa 140

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6.4m (21.0') 11.8m (39') CL of Bridge Ml Front face MSE Figure 7.49 3rd Inclusion layer stress contours from top-kpa 11.8m (39') 6.4m (21.0') so Ml CL of Bridge I 250-----Figure 7.50 4th Inclusion layer stress contours from top-kpa 141 uo

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6.4m (21.0') Ml 11.8m (39') CL of Bridge _r----:--lOO Figure 7.51 5th Inclusion layer stress contours from top-kpa 6.4m (21.0') Ml 11.8m (39') CL of Bridge I I \ \ lOO 500 4v400 I 30\ ____ J Front face MSE Figure 7.52 61 h Inclusion layer stress contours from top-kpa 142 I 10

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6.74m (21.0') I. Ml 11.8m (39') CL of Bridge I 1.50 I Figure 7.53 71 h Inclusion layer stress contours from top kpa 143 100

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7 .5.2 Case 2: Longitudinal and Transverse Motion Abutment 2 Imperial Valley Earthquake Max. Longitudinal MSE Wall Displacement Abutment No.2 .c: 5.0 4. 0 'E 3. o 2.0 1.0 -0.03 -0.02 -0.01 0 Displacements (m) (Longitudinal & Transverse Shaking) Figure 7.54 Maximum MSE wall displacements ---------------------Imperial Valley Earthquake Max. Longitudinal Earth Pressure Abutment No.2 E 5.4 4.1 C) a; 2.7 J: 1.4 0.0 +--+-'-'....:.....:..:,----o;:::=-------'--r-----l 0 200 400 600 800 Earth Pressures (kpa) (Longitudinal & Transverse Shaking) 1000 0.01 1 I __._. Center-R ----Center -----------Figure 7.55 Maximum longitudinal earth pressures 144

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2.74m (9.0') 11.8m (39') CL of Bridge I 150\ .,._ __ 150__-/ 300 lSO _lOO 'I u "'Toe of Footing Figure 7.56 Maximum bearing pressure contours at footing kpa Imperial Earthquake Max. Displacement MSE WingWall @ Center of WingWall -Abutment No.2 5. 0 :[ 4.0 3. 0 Gi 2.0 1 0 0. 0 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 Displacements (m) (longitudinal & Transverse shaking) Figure 7.57 Maximum MSE wing wall displacements 145 -+-WingWall -L I __ I

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Imperial Valley Earthquake Max. Earth Pressure MSE WingWalls Abutment No.2 200 400 600 800 Earth Pressures (kpa) (Longitudinal & Transverse Shaking) Figure 7.58 Maximum MSE wall earth pressures 146 -+-WingWallR' I 1000

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7.5.3 Inclusion StressesLongitudinal and Transverse Motion Abutment 2 6.4m (21.0') 11.8m (39') CL of Bridge I I 6oo I Figure 7.59 151 Inclusion layer stress contours from top-kpa 6.4m (21.0') Ml 11.8m (39') CL of Bridge I Figure 7.60 2nd Inclusion layer stress contours from top kpa 147 .I

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6.4m 21.0') Ml 11.Bm (39') CL of Bridge Front face MSE Figure 7.61 3rd Inclusion layer stress contours from top-kpa 148 .I

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7.6 Case 4: Vertical and Longitudinal Motion Abutment 1 Imperial Valley Earthquake Time HistoryDisplacement at Top of Wall at center of wall Time (sec) (Vertical & Longitudinal Shaking) ----------------------Figure 7.62 Time history at top of wall -------------------Imperial Valley Earthquake Max. Longitudinal MSE Wall Displacement Abutment No.1 ... 5. 0 C'l 3. 0 2.0 1 0 0 0.01 0.02 0.03 0.04 Displacements (m) (Vertical & Longitudinal Shaking) -+Edge -R : I -1/4 point -R i---.-.-Center-R : Center-L I ____..._ 1/4 point -L ; I -------------------------------Figure 7.63 Maximum MSE wall displacements 149

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Imperial Valley Earthquake Max. Longitudinal Earth Pressure Abutment No.1 0 200 400 600 BOO 1000 1200 Earth Pressures (kpa) (Veritical & Longitudinal Shaking) Figure 7.64 Maximum longitudinal earth pressures 2.74m (9.0') llO llO 100 11.8m (39') CL of Bridge I --+--Edge -R I -1/4 point -R I .........._ Center-R I I""""*Center-L 1 __._ 1 /4 point -L [__._Edge-L j Toe of Footing Figure 7.65 Maximum bearing pressure contours at footing kpa 150

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Imperial Valley Earthquake Max. Transverse Earth Pressure Abutment No.1 E 5.4 i-+-Edge -R :c 4.1 C) a:; 2. 7 ::I: 1.4 ..........,_Center-R 1/.0::_point -L 0 0 0 0 200 400 600 800 1000 Earth Pressures (kpa) (Vertical & Longitudinal Shaking) ------------------------Figure 7.66 Maximum transverse earth pressures 'E 5.o ::-4.0 .c C) 3.0 a; 2.0 ::I: 1.0 0.0 0 Imperial Earthquake Max. MSE Wing Wall displacement @ Center of Wing Wall -Abutment No.1 0.005 0.01 0.015 0.02 Displacements (m) (Vertical & Longitudinal Shaking) ----------0.025 Figure 7.67 Maximum MSE wing wall displacements 151 -+-WingWaii-L l !_-WingWaii-R j

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-E 5.0 Imperial Valley Earthquake Max. Earth Pressure MSE WingWalls Abutment No.1 =-4.0 .s::::: --+-WingWall -R I C) 3.0 2.0 1.0 iWingwall -L _j 0.0 0 200 400 600 800 Earth Pressure (kpa) (Vertical & Longitudinal Shaking) 1000 Figure 7.68 Maximum transverse pressures at wing walls Imperial Valley Earthquake Bridge Deck Displacement C.L. Bndge I 0. 01 0.01 _o.oo Abutment111 10 20 30 40 Superstructure Length (m) (Vertical & Longitudinal Shaking) Figure 7.69 Maximum bridge deck displacements 152 Abutment#2

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7 .6.1 Inclusion Stresses Vertical and Longitudinal Motion Abutment 1 6.4m (21.0') Ml 11.8m (39') CL of Bridge 150 Figure 7.70 1st Inclusion layer stress contours from top-kpa 6.4m (21.0') I. 11.8m (39') CL of Bridge I lOo-..._;..---, lOO lOO 100 .I 100 \' ) 100 Ml Front of MSE Figure 7.71 2nd Inclusion layer stress contours from top-kpa 153

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6.4m (21.0') Ml 11.8m (39') CL of Bridge JOO I :150 I J5o -----Joo--Figure 7.72 3rd Inclusion layer stress contours from top-kpa 11.8m (39') 6.4m (21.0') Ml CL of Bridge I Figure 7.73 4th Inclusion layer stress contours from top-kpa 154 'I :

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6.4m (21.0') Ml 11.8m (39') CL of Bridge Figure 7.74 5th Inclusion layer stress contours from top-kpa 6.4m (21.0') 11.8m (39') CL of Bridge I ,.. '"V.. ,l Ml Front face MSE Figure 7.75 6th Inclusion layer stress contours from top-kpa 155 '

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6.4m (21.0') Ml 11.8m (39') CL of Bridge Figure 7.76 ih Inclusion layer stress contours from top-kpa 156 .. 100

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7 .6.2 Case 2: Vertical and Longitudinal Motion Abutment 2 Imperial Valley Earthquake Max. Longitudinal MSE Wall Displacement Abutment No.2 .. 5.0 .1; 4.0 -+-Edge-R I i I I I I C) 3. 0 ......... 2.0 1 ---.Center -R 1 I 1.0 ;: 0.0 + 0 0.002 0.004 0.006 0.008 0.01 0.012 Displacements (m) (Vertical & Longitudinal Shaking) --------------------------------Figure 7.77 Maximum MSE wall displacements ----------------------Imperial Valley Earthquake Max. Longitudinal Earth Pressure Abutment No.2 E 5.4 0 200 400 600 800 Earth Pressures (kpa) (Vertical & Longitudinal Shaking) Figure 7.78 Maximum longitudinal earth pressures 157 1000 -+-Edge-R! -center

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11.8m (39') CL of Bridge I 2.74m (9.0') I uo--;--__..-.----uo ------+----:wo Toe of Footing Figure 7.79 Maximum bearing compression contours at footing-kpa Imperial Valley Earthquake Max. Transverse Earth Pressure Abutment No.2 E 5.4 4.1 C) a; 2.7 :I: 1 .4 I 0.0 0 200 400 600 800 Earth Pressures (kpa) (Vertical & Longitudinal Shaking) Figure 7.80 Maximum transverse earth pressures 158 1000 !-+-Edge-R I :-Center

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Imperial Valley Earthquake Max. Transverse MSE Wall Displacement Abutment No.2 .. 5.0 C) 3.0 2.0 1.0 0.0 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 Displacements (m) (Vertical & Longitudinal Shaking) -------------Figure 7.81 Maximum transverse MSE wall displacements Imperial Earthquake -+-Edge-R __._.._ Center-R Max. Displacement MSE WingWall @Center of WingWallAbutment No.2 e 5.o :: 4.0 .c: C) 3. 0 a; :I: 2. 0 1 0 > 0.0 0 0.002 0.004 0.006 0.008 Displacements (m) Nertical, longitudinal Shaking) 0.01 -----------c -+WingWall -L 1 __ I --------Figure 7.82 Maximum MSE wing wall displacements 159

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Imperial Valley Earthquake Max. Earth Pressure MSE WingWalls Abutment No.2 Earth Pressures (kpa) (Vertical & Longitudinal Shaking) Figure 7.83 Maximum MSE wing wall earth pressures 160

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7.6.3 Inclusion StressesVertical and Longitudinal Motion Abutment 2 6.74m (21.0') j 400 Ml 11.8m (39') CL of Bridge Front face MSE Figure 7.84 151 Inclusion layer stress contours from top-kpa 11.8m (39') CL of Bridge Figure 7.85 161

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6.4m (21.0') Ml 11.8m (39') CL of Bridge I Figure 7.86 3rd Inclusion layer stress contours from top-kpa 162

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7.7 Interpretation of Analysis Results 7.7.1 Analysis Results This section will summarize the analyses results for the four NIKE3D load case presented earlier in this chapter. The deflections, pressures, and stress contours and graphs presented here are based on maximum values from this study. This is based on another important concept synchronization with peak ground acceleration with corresponding maximum values. Since massive amounts of data can be extracted from these finite element models, only major elements were selected for this study. The presentation of the results are grouped in their respective load case as follows: 7.7.2 Case 1: Static Loading Nodes were selected at key locations along the front face of the MSE wall as shown in the graph to determine the maximum and minimum wall movements. The maximum movement in the MSE wall occurs at the base located horizontally in the center of the wall. The minimum movement occurs at the MSE wall corners (Figure 7.1 ). The top of the wall had similar displacements in the range of 0.0035 m to 0.013 m. Since the largest displacements occurred at the base of the wall, this was a result of modeling the connection between the MSE wall and the foundation soil as a friction connection and not as fixed connection at the base of the wall. The corner displacements are relativity small compared to the other locations. 163

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This indicating that the corners are much stiffer than the center of the wall allowing for redistributions of movements. For lateral wall displacement criteria, ASSHTO provides empirical curves to estimate the anticipated lateral displacement during construction. This establish an appropriate wall batter to obtain a near vertical wall or to determine minimum clearances requirements to adjacent structures. Figure 7.2 displays the earth pressures at various locations behind the MSE wall. From this graph the maximum pressure is located horizontal in the center of the wall with the minimum pressure at the wall corners. The earth pressures along the height of the wall are fairly uniform until the 1 m elevation where they decrease approximately 150 kpa to the base of the wall. The normal earth pressure distribution for static loads without surcharge would have an earth pressure of zero at the surface and increasing with depth. Since this model has a surface surcharge from the abutment and superstructure loading, the earth pressure effect would cause a more uniform pressure until a depth of approximate 3 m or the width of the abutment footing. From this point the surcharge loading has little effect on the normal earth pressure. The pressure diagram also decreases at a normal rate to the bottom of the wall. The wall corner earth pressure diagram also indicates high pressures at the top of the wall, which is caused by the higher stiffness of the corners. 164

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Similar to the earth pressure's graph, Figure 7.3 displays the connection stresses at the back face of MSE wall and geogrid material. The maximum stress occurs at the center of the wall and decreases as you move towards MSE wall corners. The stresses range from a minimum of 210 kpa at the corner to a maximum of 1 050 kpa at the center of the wall. Based on AASHTO, the connection strength is the lesser value of the pullout capacity of the connection, the long term rupture strength, or connection strength is determined from laboratory tests. Figure 7.5 through 7.11 illustrates the stress contour plots for the different inclusion layers. Reviewing the stress contour plots indicates that the maximum stress occurs at the center of the wall and decreases toward the MSE corners. Similarly the stress also decreases from 1050 kpa at the front face to 700 kpa at the end of the reinforced backfill. The inclusions used in this analysis have properties of geogrid called SR2, manufactured by Tensar Earth Technologies, Inc. The ultimate tensile strength for SR2 is 5,380 lb/ft (=78511 N/M) (Table 5.4 ). With an average thickness of 3 mm, the ultimate capacity is 26,170,428 N/M2 For a static loading condition a factor of safety against rupture of 1.5 is recommended per AASHTO (1998) interim specification. This ultimate capacity of 26,170,428 N/M4'or SR2 and a maximum applied tension load of 1,900,000 N/M2 provides a factor of safety of 13. Another observation based on the stress contour plots is that the tensile stresses are fairly uniform and 165

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consistent from the top layer through to the bottom layer. This correlates with the earth pressure contour plots and the uniform pressure from the top of the wall to the base. Figure 7.4 illustrates the maximum bearing pressure contours at the bottom of abutment 1 footing. The maximum stress occurs at the outside edges of the abutment footing. The bearing pressure in the center of the abutment footing is approximately 100 to 150 kpa, and a maximum pressure of 350 kpa at the edge of the footing. Hand calculations were performed to estimate the static uniform bearing pressure to verify the model results. The hand calculations indicate a bearing pressure of 225 kpa. This discrepancy in bearing pressures may be caused by the wing walls being cantilever off the abutment back wall without any support at the end of the walls or a numerical round-off due to the finite element mesh size and spacing. For allowable bearing pressures on typical projects 225 to 250 kpa is an acceptable bearing pressure for most local county or state agencies. Values above these would need to be evaluated on a case by case basis. 7.7.3 Case 2: Vertical, Longitudinal and Transverse Motion The time history diagram for the top of wall displacements is illustrated in Figure 6.12. From this diagram the time period of maximum displacement can be determine and based on synchronization with peak ground acceleration should correspond to the maximum displacement value. There 166

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are some other factors that could affect this maximum displacement value including; structure damping, period of the structure and the response spectrum, (figures 4.7 thru 4.9). The maximum displacement at the base of the MSE wall is approximately 0.035 m and the top displacement of 0.018 m occurring at the center of MSE wall. The minimum displacement occurs at the MSE wall corners with virtually little to no movement. Currently the only design guideline for acceptable wall displacements is lett to the project design criteria and on a project to project basis. As mentioned earlier in the static load case section, the same friction boundary condition at the base was used here and in all other load cases. Figure 7.14 and 7.15 illustrates the earth pressures and connection stresses at the back face of the MSE wall. The earth pressures was the greatest near the center of the wall and decrease as you moved to the corners. The earth pressure also varied from the top of the wall to the bottom with the maximum pressure located approximate 1m from the bottom. The connection stress graph varied from the top and increased as you move towards the bottom, with the maximum near the bottom of the wall. This also corresponds to the earth pressure graph. The footing bearing pressure is shown in Figure 7.16. These bearing pressure varies from edge of footing to edge of footing from 150 to 250 kpa. These differences may be caused by the combination of different ground accelerations. One important graph that correlates the structure response with different ground motion and 167

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its acceleration amplification is shown in Figure 7.17. The Backfill acceleration profile graph illustrates the change in horizontal acceleration with increasing height of backfill. For this structure there is an increase in horizontal acceleration in the backfill, approximately half way up from the base and then it starts to decrease until it reaches the top of the abutment. This decease in horizontal acceleration is the result of the rigid superstructure restraining the top of the back-fill. The lateral displacements at the bottom and top of the wall and earth pressures at the back face of the MSE wall are relatively small (Figure 7.18) and (Figure 7.19). This is also true for the wing wall displacements shown in (Figure 7 .20). Node points located on the top of the bridge deck, along both abutments and at each girder, and at center of span, were selected to evaluate the bridge displacements in the vertical direction. Figure 7.21 gives the results with both the minimum and maximum displacements shown. These displacements indicate that the bridge is moving as a rigid mass with no relative difference from one abutment to the other. This is an indication that abutment 1 and abutment 2 are synchronized with the ground motion. The inclusion stress contours are (Figure 7.22 through Figure 7.28) decease from the front face at the MSE wall to the back side of the backfill or inclusion. Also, the tension stress is fairly uniform from the top inclusion layer to the bottom layer. The stress range from the static condition to dynamic 168

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loading indicates a reduction of approximately 50%. This reduction in tension stress is cause by the dynamic effect of the ground motion particularly by the vertical ground motion which relaxes the friction interface between geogrid and soil. Currently AASHTO does not take the vertical acceleration component into consideration in their seismic design guideline. Abutment 2 (Figures 7 .29) show a reduction in MSE wall displacements. This reduction in MSE wall displacement reflects the wall compression against the earth backfill. This computation was used to compare the two displacements movement, away from the soil and against the soil. The horizontal earth pressure at abutment 2 is comparable to the other load cases, the sign convention was changed here so the true compression on back of the MSE wall was reported. 7.7.4 Case 3: Longitudinal and Transverse Motion Many of the same analyses conditions and results have all ready been discussed in the static load case 1 or the dynamic load case 2 and don't need to be repeated in this section. Finding and discussion will main pertain to this section. The wall displacements and earth and bearing pressures are consistent with the previous section. It should be noted that for this load case there is no vertical acceleration component and the tension stresses in the inclusion have are in the range of 11 00 to 600 kpa. But, these values are in the magnitude of double to the load case with vertical acceleration 169

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7. 7.5 Case 4: Vertical and Longitudinal Motion The results here for displacements, pressures, tension stress at abutment 1 or 2 abutment are very similar to the other load cases previously mentioned. 7.7.6 Summary The previous sections summarize the results from the figures and graphs for chapter 6. Table 7.1 provides a summary of the permanent horizontal MSE wall displacements for the load cases in this study. Imperial Valley Area Permanent MSE Wall Displacement at Top of wall At Center of Abutment 1 Direction Load Case Load Case Load Case Load Case 4 #1 #2 #3 Vertical & Static Vertical, Longitudinal & Transverse Transverse & Transverse Longitudinal Horizontal .002 m (1/8") .01 m (3/8") .02 m (3/4") .002 m (1/8") Transverse .01 (3/8") .002 (1/8") .01m (3/8") Table 7.1 Permanent displacement at top of wall With different directional ground acceleration combinations it is sometime difficult to visualized the effect this motion has on the bridge or wall structure behavior. However, comparing the graphs and contour plots for all the load cases, indicates a similarity in behavior between the structures, displacements, pressures, stresses, and forces. With this analyses output and information it may verify that the method used in this study was model 170

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correctly. The following Table 7.2 summarizes the dynamic analyses results for the front MSE wall studied in this research and their maximum corresponding value. Imperial Valley Area Summary of Maximum Dynamic Results Abutment 1-Front of MSE Wall Item Load Case#2 Load Case#3 Load Case Vertical, Longitudinal & 4 Transverse & Transverse Vertical & Longitudinal Transverse Earth Pressure max. (kpa) 1000 1100 1000 Earth Thrust (N/M) 143.5 157.1 144.5 Thrust Location from base (m) 2.2 2.41 2.3 Connection Stress max (kpa) 1000 1300 1000 Connection Stress min (kpa) 200 500 300 Inclusion Stress-max (kpa) 600 1900 300 Inclusion Stress-min (kpa) 300 500 200 Bearing Pressure max(kpa) 250 250 250 Soli Acceleration Profile max. (g) .45 -Soli Acceleration Profile min. (g) .36 --Bridge Vertical Max. (m) .13 0 0 Bridge Vertical Min. (m) -.015 -.015 -.015 Table 7.2 Summary of dynamic analysis results The two tables 6.2 and 7.2 summarized the major items for the two earthquakes in this study. Comparing the values in the tables shows that the two structures are behaving similarly since the values are within 15% of each other. The connection and inclusion stresses as earlier mention are well within the capacity of the geogrid. The soil acceleration values are reasonable based on the time history graphs from chapter 4. The bridge maximum vertical movement is the result of the different vertical ground motion and, the minimum values is the simple span superstructure dead load delfecion. 171

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8. MSE Wall Design Examples 8.1 Current Design Methods This chapter will compare the finite element method used in this study with the current AASHTO design guidelines for designing MSE structures in seismic active areas. The current AASHTO design guideline estimate the dynamic horizontal thrust based on the modified pseudo-static Mononobe Okabe design method. With these conventional design guidelines they do not take into account the benefits of reinforced earth backfill and the additional stability and ductility inherent of MSE structures. The following section calculates the horizontal forces and overturning moments from the Northridge earthquake based on the AASHTO design method. 8.2 AASHTO Design Method Table 8.1 illustrates the design parameters used in this design comparison. For additional information on the AASHTO design method see Chapter 11.1 0, LRFD Bridge Design Specifications (2002) and Standard Specifications for Highway Bridges (1996) 172

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Am 0.47 A 0.5 Yea 1 Ys 130 H= 15.2 B= 10.5 Ka 0.30 IP 30 De= Max 1.00 De= Min 0.90 Table 8.1 Input parameters Mess for Inertial Force H ) Mess for forces pcf ft ft degree Figure 8.1 Stress distribution diagram Am=( 1 .45 )*A PAE=0.365*YeqAmY GH2 AASHTO (11.10.7.1-1) AASHTO (11.10.7.1-2) 173 (8.1) (8.2)

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Pir=0.05YeqAmY5H2 Psch= 4 ksf Fsur= 2.34 kip FT= 4.4 kip Fthrust =18.9 kip Mot=99.3 ft-kip Dot= 5.3 ft 84.0 KN 135.1 KN-m 1.6 m AASHTO (11.10.7.1-3) (8.3) H/2 =8ft H/3 = 5 ft 8.3 Finite Element Design Method (NIKE3D) The following design information was extracted from the finite element model Northridge Case 1: vertical, longitudinal and transverse motion, to compute the required forces. Forces Dist Moments F8= 0.71 kip/ft 14.4ft 1 0.29ft-kip F7= 1.39kip/ft 12.48ft 17.30ft-kip F6= 1.57kip/ft 1 0.56ft 16.60ft-kip F5= 1.68kip/ft 8.64ft 14.55ft-kip F4= 1.71 kip/ft 6.72ft 11.51ft-kip F3= 1.79kip/ft 4.8ft 8.61ft-kip F2= 1.66kip/ft 2.88ft 4.77ft-kip F1= 0.92kip/ft 0.96ft 0.88ft-kip Fsum.= 11.44kip Mot= 84.51ft-kip Dot= ?.39ft Table 8.2 Finite element forces 174

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Height Top of (m) 4.67 11.52 3.50 9.6 2.92 7.68 2.33 5.76 1.75 3.84 1.17 F5= 1.92 0.58 0 0.00 F4= F3= 1.t___ (typ Top of Leveling Figure 8.2 FE model stress distribution 8.4 Comparison Between AASHTO and Finite Element Method Results from the AASHTO Method Fthrust =18.9 kip Mot=99.3 ft-kip Dot= 5.3 ft 84.0 KN 135.1 KN-m 1.6 m 75.791 psf sf 750.39 psf 206.44 psf Results from the Finite Element Method Fthrust =11.4 kip Mot=84.5 ft-kip Dot= 7.3 ft 48.9 KN 114.2 KN-m 2.2 m 175 Resultant= 11.44 kip 50.88 KN 7.39 ft

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9. Summary, Conclusions, Recommendations and Further Studies 9.1 Summary The primary purpose and objective of this study was to examine the performance and behavior of MSE "Mechanically Stability Earth Structures" under the effect of a seismic event. To recapture the main theme of this thesis, Chapter 1 introduced the functions of bridge abutments and the different types of abutments currently being built today. Also, there are many choices of material types, from cast-in-place concrete, modular concrete blocks to precast panels. The choice depends on many factors such as: cost of the project or the best performing material under the imposed loading conditions. Also with recent advancements in seismic hazard assessments, computer application and experimental facilities have made PBSE (Performance Base Structural Engineering), a more attractive design option for developers and engineers for structures in seismic active areas. In Chapter 2 a literature review was performed on current design practices of MSE structures for stability and Mononbeo-Okabe analysis method. Chapter 3 reviewed the theoretical background of NIKE3D program and its application in this study. Microstation, Truegrid and Griz were also reviewed in this study and their applications in creating the three dimensional model. The ground accelerations time history records were provided in Chapter 4 for the vertical, 176

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transverse and longitudinal directions. Chapter 5, reviewed the design parameters, boundary conditions, earthquake motion combinations, material properties, master and slave surfaces, sliding interface values, and inclusion penalty values. Chapter 6 and 7 provided the results from NIKE3D analyses for Northridge and Imperial Valley earthquakes. 9.2 Conclusions The findings and conclusions of this study are summarized in the following. NIKE3D was a valuable tool in the nonlinear analyst of MSE bridge structures Results from finite element model and design criteria might not be conservative The stress in the inclusions is less than what's provided in the design criteria With 3 dimension analysis and ground motion from three direction simultaneously if can be difficult to visualize the results, where additional analyses would increase our understanding of the behavior of MSE structures. The two earthquakes provided in this study had different vertical and horizontal ground acceleration that affected the results of this analysis. Of the three ground motions the vertical acceleration appeared to have the greatest impact on the structures. The dynamic effect from the vertical acceleration and the relaxation of the friction interface between soil and the geogrid is key design element. 177

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With different earthquakes size, magnitude and location from the epic center will all have an affect the response spectrum and the design of the wall system. 9.3 Recommendations for Future Studies The Recommendations for future studies are as follows: Perform additional analyses on different bridge configurations, multi span bridge, skewed structure, and different superstructure types and distance boundaries Modify soil parameters, modulus of elasticity, Poisson's ratio, soil friction angle slide interface friction coefficients Study the effect of other ground motion acceleration records Develop performance base curves for MSE wall design. Calibrate results from FE models against shake table testing Perform similar analysis on linear stick models and compare results. This would be less time consuming that the nonlinear method. 178

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Appendix A. TrueGrid Input File 179

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title type 7 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c thesis_mike_5.0 c Geometry parameters c Bridge Deck and Abutments c cccccccccccccccccccccccccccccccccccccccccccccccccccccc para cc_st 0.5 cc_dyn 0.5 abutsoil_st 10.0 abutsoil_dyn 10.0 blockso_st .50 c blockso_dyn .50 memso_st 0.5 memso_dyn 0.5 founco_st 1.0 founco_dyn 1.0 founso_st 5.0 founso_dyn 5.0 pnlt 1.0 deckso_dyn 0.5; ccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Define load curves c ccccccccccccccccccccccccccccccccccccccccccccccccccccc include lc1.dat include lc2.dat include lc3.dat cccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Analysis parameters c cccccccccccccccccccccccccccccccccccccccccccccccccccccc nike3d nikeopts nsteps 10 delt 1 ngrav 0.0 2 0.0 3 32.2 1 mnss 1.00e-1 mxss 1 accflg 1 igapfg 1 anal stat bfor 0 iplt 1 iprt 99999 nsmd bfgs; cccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Define material properties 180

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c cccccccccccccccccccccccccccccccccccccccccccccccccccccc c c 1 jersey barrier c nikemats 1 1 e 518.40E+06 pr 1.500E-01 rho 5.39; c c 2 abutment c nikemats 2 1 e 518.4E+06 pr 1.500E-01 rho 5.39; c c 3 block facing c nikemats 3 1 e 518.40E+06 pr 1.500E-01 rho 5.39; c c 4 inclusion c nikemats 4 1 shell e 6.04E+06 pr 4.000E-01 rho 1.99 shth 0.02; c c 5 footing c nikemats 51 e 518.4E+06 pr 1.500E-01 rho 5.39; c c 6 foundation soil c nikemats 6 1 e 2.16E+06 pr 3.500E-01 rho 4.09; c 181

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c 7 backfill c nikemats 7 12 gammay .0001 05 tauy 220 r 2.349 k 6280000 ; c nikemats 8 12 gam may .0001 05 tauy 220 r 2.349 k 6280000; c c nikemats 9 12 gammay 0001 05 tauy 220 r 2 349 k 6280000; c nikemats 10 12 gam may 000105 tauy 220 r 2 349 k 6280000; c c MSE block c nikemats 11 1 e 518.40E+06 pr 1.500E-01 rho 5.39; nikemats 12 1 e 518.40E+06 pr 1.500E-01 rho 5.39; c nikemats 13 1 e 518.40E+06 pr 1.500E-01 rho 5.39; c nikemats 14 1 e 518 40E+06 pr 1 500E-01 182

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rho 5.39; c nikemats 15 1 e 518.4DE+06 pr 1.5DOE-01 rho 5.39; c nikemats 16 1 e 518.40E+06 pr 1.500E-01 rho 5.39; c nikemats 17 1 e 518.40E+06 pr 1.500E-01 rho 5.39; c c 18 superstructures c nikemats 18 1 e 518.4E+06 pr 1.500E-01 rho 5.39; c c 19 Backwall c nikemats 19 1 e 518.4E+06 pr 1.500E-01 rho 5 39; c c addtional backfill c nikemats 20 12 gam may 000105 tauy 220 r 2.349 k 6280000; c c addtional backfill c nikemats 21 12 gammay .000105 tauy 220 r 2.349 k 6280000 ; 183

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c c addtional backfill c nikemats 22 12 gammay 0001 05 tauy 220 r 2.349 k 6280000 ; c c addtional backfill c nikemats 23 12 gammay .000105 tauy 220 r 2.349 k 6280000; c c c Abutment 1 backfill c nikemats 24 1 e 2.16E+06 pr 3.500E-01 rho 4.09 ; c c Abutment 2 Backfill c nikemats 25 1 e 2.16E+06 pr 3 500E-01 rho 4.09; c c addtional backfill c nikemats 26 12 gam may .000105 tauy 220 r 2.349 k 6280000; c c addtional backfill c nikemats 27 12 gam may 000105 tauy 220 r 2.349 184

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k 6280000; c c addtional backfill c nikemats 28 12 gam may .0001 05 tauy 220 r 2.349 k 6280000; c c addtional backfill c nikemats 29 12 gam may .000105 tauy 220 r 2.349 k 6280000; c c cccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Define interface types c cccccccccccccccccccccccccccccccccccccccccccccccccccccc c c concrete to concrete c sid 1 sv pnlt %pnlt fric %cc_st kfric %cc_dyn; sid 2 sv pnlt %pnlt fric %cc_st kfric %cc_dyn; sid 3 sv pnlt %pnlt fric %cc_st kfric %cc_dyn; sid 4 sv pnlt %pnlt fric %cc_st kfric %cc_dyn; c c c batt of abut to backfill c sid 5 sv pnlt %pnlt fric %abutsoil_st kfric %abutsoil_dyn; sid 6 sv pnlt %pnlt fric %abutsoil_st kfric %abutsoil_dyn; sid 7 sv pnlt %pnlt fric %abutsoil_st kfric %abutsoil_dyn; sid 8 sv pnlt %pnlt fric %abutsoil_st kfric %abutsoil_dyn; sid 9 sv pnlt %pnlt fric %abutsoil_st kfric %abutsoil_dyn; sid 10 sv pnlt %pnlt fric %abutsoil_st kfric %abutsoil_dyn; c c c sid 11 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 12 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; 185

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sid 13 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 14 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 15 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 16 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 17 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 18 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 19 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 20 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 21 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 22 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 23 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 24 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 25 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 26 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 27 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 28 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 29 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 30 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 31 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 32 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 33 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 34 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 35 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 36 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 120 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 121 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 122 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 123 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 124 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 125 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 126 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 127 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 128 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 129 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 130 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 131 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 132 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 133 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 134 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 135 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 136 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 137 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; C Abutment 2 sid 200 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 201 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 202 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; 186

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sid 203 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 204 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 205 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 206 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 207 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 208 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 209 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 210 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 211 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 220 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 221 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 222 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 223 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 224 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 225 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 226 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 227 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 228 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 229 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 230 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 231 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 232 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 233 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 234 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 235 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 236 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; sid 237 sv pnlt %pnlt fric %blockso_st kfric %deckso_dyn; c c c mebrane to soil c c sid 41 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 42 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 43 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 44 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 45 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 46 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 47 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 48 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 49 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 50 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 51 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 52 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 53 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 54 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; 187

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sid 55 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 56 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 57 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 58 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 59 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 60 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 61 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 62 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 63 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 64 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 65 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 66 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 67 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 68 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; sid 69 sv pnlt %pnlt fric %memso_st kfric %memso_dyn; c c foundation soil to backfill c sid 70 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 71 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 72 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 73 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 74 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 75 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 76 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 77 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 78 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 79 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; sid 80 sv pnlt %pnlt fric %founso_st kfric %founso_dyn; c c c foundation soil to concrete block c sid 92 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 81 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 82 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 83 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 84 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 85 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 86 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 87 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 88 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 89 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 90 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 91 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; sid 180 sv pnlt %pnlt fric %founco_st kfric %founco_dyn; 188

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sid 181 sv pnlt %pnlt fric o/ofounco_st kfric o/ofounco_dyn; sid 182 sv pnlt o/opnlt fric o/ofounco_st kfric o/ofounco_dyn; sid 183 sv pnlt %pnlt fric %founco_st kfric o/ofounco_dyn; sid 184 sv pnlt %pnlt fric o/ofounco_st kfric o/ofounco_dyn; sid 185 sv pnlt %pnlt fric o/ofounco_st kfric o/ofounco_dyn; c c ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Girder 1 thru 6 c ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Girder Bott. Fig Block 1 2 3; 1 2 3 4; 1 2; -3.25 80.0 155.20; -17.35-16.54-15.95 -15.13; 4.5 5.29; mate 18 Block 1 2 3; 1 2 3 4; 1 2; -3.25 80.0 155.20; -10.88 -10.04-9.45 -8.63; 4.5 5.29; mate 18 Block 1 2 3; 1 2 3 4; 1 2; -3.25 80.0 155.20; -4.38 -3.55 -2.95 -2.13; 4.5 5.29; mate 18 Block 1 2 3; 1 2 3 4; 1 2; -3.25 80.0 155.20; 2.13 2.95 3.55 4.38; 4.5 5.29; mate 18 Block 1 2 3; 1 2 3 4; 1 2; -3.25 80.0 155.20; 8.38 9.45 10.04 10.88; 4.5 5.29; mate 18 Block 1 2 3; 1 2 3 4; 1 2; -3.25 80.0 155.20; 189

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15.13 15.95 16 54 17 38; 4.5 5.29; mate 18 c Girder web block 1 2 3; 1 2; 1 2; -3.25 80.0 155 20; -16.54 -15 95; 5.29 10.04; mate 18 block 1 2 3; 1 2; 1 2; -3 25 80.0 155.20; -10.04 -9.45 ; 5.29 10.04; mate 18 block 1 2 3; 1 2; 1 2; -3.25 80.0 155.20; -3.55 2.95; 5.29 10.04 ; mate 18 block 1 2 3; 1 2; 1 2; -3. 25 80.0 155 20 ; 2 95 3 55; 5.29 10.04; mate 18 block 1 2 3 ; 1 2; 1 2 ; -3.25 80.0 155 20; 9.45 10.04; 5.29 10 04; mate 18 block 1 2 3; 1 2; 1 2; -3.25 80.0 155 20; 15.95 16 54 ; 5.29 10 04 ; mate 18 c Girder Top Fig. w/ Haunch block 1 2 3; 1 2 3 4; 1 2 ; -3.25 80.0 155.20; -18.04-16.54-15. 95 -14.45; 10 04 11. 0 ; mate 18 block 1 2 3; 1 2 3 4; 1 2; -3 25 80.0 155 20; -11. 54 -10 .04-9.45 -7 97 ; 10.0411.0; mate 18 block 1 2 3 ; 1 2 3 4; 1 2; 190

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-3.25 80.0 155.20; -5.04 -3.55 -2.95 -1.45; 10.0411 .0; mate 18 block 1 2 3; 1 2 3 4; 1 2; -3.25 80.0 155.2; 1.45 2.95 3.55 5.05; 10 04 11.0; mate 18 block 1 2 3; 1 2 3 4; 1 2; -3.25 80.0 155.20; 7.95 9.4510.0411.54; 10.04 11.0; mate 18 block 1 2 3 ; 1 2 3 4; 1 2; -3.25 80.0 155.20; 14.45 15 95 16.54 18.04; 10. 04 11.0 ; mate 18 c Girder Deck block 1 2 3; 1 2 3 4 5 6; 1 2; -3.25 80.0 155.20; -19.5-18.04-16.54-15.95-14.45 -13.0; 11.0 11. 67; mate 18 block 1 2 3; 1 2 3 4 5 6; 1 2; -3.25 80.0 155.20; -13.0-11.54-10.04-9.45-7.97 -6.5 ; 10.04 11.67; mate 18 block 1 2 3 ; 1 2 3 4 5 6; 1 2; -3.25 80 0 155.20; -6.5 -5 04 -3.55 -2.95 -1.45 0.0; 11. 0 11.67; mate 18 block 1 2 3; 1 2 3 4 5 6; 1 2; -3.25 80.0 155.2; 0.0 1.45 2.95 3.55 5 05 6.5; 11.0 11.67; mate 18 block 1 2 3 ; 1 2 3 4 5 6; 1 2; -3.25 80.0 155.20; 6.5 7.95 9.4510.0411 5413.0; 11.0 11. 67 ; mate 18 block 1 2 3 ; 1 2 3 4 5 6; 1 2; 191

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-3.25 80.0 155.20; 13.0 14.45 15.95 16.54 18.04 19.5; 11.0 11.67; mate 18 ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Foundation Footing Abut 1 c ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Abut Footing Block 1 3 4 6; 1 2 3 4 56 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21; 1 2; 0 -3.25 -5.75 -9.0; -19.50-18.5-17.38-15.13-13.0-10.88-6.5-8.63-4.38-2.13 0.0 2.13 4.38 6.5 8.63 10.88 13.0 15.1317.38 18.5 19.50; 0.0 2.0; si 1 1 1 4 16 1 5 s; si 4214202135m; si 3213202135m; si 3 2 2 4 20 2 134 m; mate2 c Backwall Seat Block 1 2; 1 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45; 1 2; -3.25 -5.75; -19.5-18.50-18.04-17.35-16.54-15.95-14.45-15.13-13.0 -11.54 -10.88 -10.08 -9.45 -8.63 -7.95 -6.5 -5.04 -4.38 -3.55 -2.96 -2.12 -1.45 0.0 1.45 2.13 2.96 3.55 4.38 5.04 6.5 7.96 8.63 9.4510.0510.87511.5413.014.4615.12515.9516.5417.3818.04 18.5 19.50; 2.0 4.5; si 2212442135m; mate 19 c Backwall Block 1 2; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45; 1 2 56 7 8; -3.25 -5. 75; -19.5-18.50-18.04-17.35-16.54-15.95-14.45-15.13-13.0 -11.54 -10.88 -10.08 -9.45 -8.63 -7.95 -6.5 -5.04 -4.38 -3.55 -2.96 -2.12 -1.45 0.0 1.45 2.13 2.96 3.55 4.38 5.04 6.5 7.96 8.63 9.4510.0510.87511.5413.014.4615.12515.9516.5417.38 18.04 18.5 19.50; 4.5 5.29 10.04 10.66 11.00 11.67; 192

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si 2 2 1 2 44 6 135 m; mate 19 ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Abutment backfill 1 c ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc Block 1 5;1 8; 1 2; -9.0 -29; -18.5 18.5 0.0 2.0; si 1 1 1 2 2 1 79 s; si 1 1 1 1 2 2 135 s; si 1 1 1 2 1 2 136 s; si 1 2 1 2 2 2 136 s; b 2 1 1 2 2 2 dx 1 dy 1 dz 0; c C Abutment 1 backfil mate 24 block 1 5;1 8; 1 2 3 6 7 8 9; -9.0 -29.0; -18.5 1 8.5; 2.0 4.5 5.29 10.04 10.66 11.00 11.67; si 1 1 1 2 1 7 136 s; si 1 2 1 2 2 7 136 s; b 2 1 1 2 2 7 dx 1 dy 1 dz 0; mate 24 Block 1 3; 1 8; 1 2 3 6 7 8 9; -5.75 -9.0; -18.5 1 8.5; 2.0 4.5 5.29 10.04 10.66 11.00 11.67; si 1 1 1 1 2 7 135 s; si 1 1 1 2 2 1 134 s; si 1 1 1 2 1 7 136 s; si 1 2 1 2 2 7 136 s; c mate 24 ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Foundation Footing Abut 2 c ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Abut Footing Block 1 3 4 6; 1 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 16 17 18 19 20 21 ; 1 2; 151.95155.2157.70 160.95; -19.5-18.5-17.38-15.13-13.0-10.88-8.63-6.5-4.38-2.13 0.0 193

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2.13 4.38 6.5 8.63 10.88 13.0 15.13 17.38 18.5 19.50 0.0 2.0; si 1 1 1 4 16 1 6 s; si 4 2 1 4 20 2 235 m; si 3 2 2 4 20 2 234 m; mate 2 c Backwall Seat Block 1 2; 1 2 3 4 56 7 8 910111213141516171819 20 21 22 2324252627282930313233343536373839404142 43 44 45; 1 2; 155.20 157. 70; -19.5-18.50-18.04-17.35-16.54-15.95-14.45-15.13-13.0 -11.54-10.88 -10.08 -9.45 -8.63 -7.95-6.5-5.04-4.38-3.55 -2.96-2.12-1.45 0.0 1.45 2.13 2.96 3.55 4.38 5.04 6.5 7.96 8.63 9.4510.0510.87511.5413.014.4615.12515.9516.5417.3818.04 18.5 19.50; 2.0 4.5; si 2 2 1 2 44 2 235m; mate 19 c Backwall Block 1 2; 1 2 3 4 56 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2324252627282930313233343536373839404142 43 44 45; 1 2 56 7 8; 155.20 157.70; -19.5-18.50-18.04-17.35-16.54-15.95-14.45-15.13-13.0 -11.54 -10.88 -10.08 -9.45 -8.63 -7.95 -6.5 -5.04 -4.38 -3.55 -2.96 -2.12 -1.45 0.0 1.45 2.13 2.96 3.55 4.38 5.04 6.5 7.96 8.63 9.4510.0510.87511.5413.014.4615.12515.9516.5417.3818.04 18.5 19.50; 4.5 5.29 10.04 10.66 11.00 11.67; si 2 2 1 2 44 6 235 m; mate 19 ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Abutment backfill 2 c ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc Block 1 5;1 8; 1 2; 160.95 180.95; -18.5 18.5 0.0 2.0; si 1 1 1 2 2 1 92 s; si 1 1 1 1 2 2 235 s; si 1 1 1 2 1 2 236 s; 194

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si 1 2 1 2 2 2 236 s; b 2 1 1 2 2 2 dx 1 dy 1 dz 0; c C Abutment 1 backfil mate 25 block 1 5;1 8; 1 2 3 6 7 8 9; 160.95 180.95; -18.5 18.5; 2.0 4.5 5.29 10.04 10.66 11.00 11.67; si 1 1 1 2 1 7 236 s; si 1 2 1 2 2 7 236 s; b 2 1 1 2 2 7 dx 1 dy 1 dz 0; mate 25 Block 1 3; 1 8; 1 2 3 6 7 8 9; 157.70 160.95; -18.5 18.5; 2.0 4.5 5.29 10.04 10.66 11.00 11.67; si 1 1 1 1 2 7 235 s; si 1 1 1 2 2 1 234 s; si 1 1 1 2 1 7 236 s; si 1 2 1 2 2 7 236 s; c mate 25 cccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Wingwall Abutments 1 & 2 cccccccccccccccccccccccccccccccccccccccccccccccccccccccc C Abutment 1 left wing wall block 1 3 7;1 2; 1 2 3 6 7 8 9; -5.75-9.0 -29.0; -18.5 -19.5; 2.0 4.5 5.29 10.04 10.66 11.00 11.67; si 1 1 1 3 1 7 136m; b 3 1 1 3 2 7 dx 1 dy 1 ; mate 2 Block 1 5; 1 2; 1 2; -9.0 -29.0; -18.5 -19.5; 0 2; si 1 1 1 2 2 1 7 s; si 1 1 1 2 1 2 136 m; b 2 1 1 2 2 2 dx 1 dy 1 ; mate 2 c Abutment 1 Right wing wall block 1 3 7; 1 2; 1 2 3 6 7 8 9; -5.75-9.0 -29.0; 18.5 19.5; 2.0 4.5 5.29 10.04 10.66 11.0 11.67; si 1 1 1 3 1 7 136 m; 195

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b 3 1 1 3 2 7 dx 1 dy 1 ; mate2 Block 1 5; 1 2; 1 2; -9.0 -29.0; 18.5 19.5; 0 2; si 1 1 1 2 2 1 8 s; si 1 1 1 2 1 2 136 m; b 2 1 1 2 2 2 dx 1 dy 1 ; mate 2 c Abutment 2 left wing wall block 1 3 7;1 2; 1 2 3 6 7 8 9; 157.70 160.95 180.95; -18.5 -19.5; 2.0 4.5 5.29 10.04 10.66 11.00 11.67; si 1 1 1 3 1 7 236 m; b 3 1 1 3 2 7 dx 1 dy 1 ; mate 2 block 1 5; 1 2; 1 2; 160.95 180.95; -18.5 -19.5; 0 2; si 1 1 1 2 2 1 9 s; si 1 1 1 2 1 2 236 m; b 2 1 1 2 2 2 dx 1 dy 1; mate 2 c Abutment 2 Right wing wall block 1 3 7; 1 2; 1 2 3 6 7 8 9; 157.70 160.95180.95; 18.5 19.5; 2.0 4.5 5.29 10.04 10.66 11.0 11.67; si 1 1 1 3 1 7 236 m; b 3 1 1 3 2 7 dx 1 dy 1; mate 2 block 1 5; 1 2; 1 2; 160.95 180.95; 18.5 19.5; 0 2; si 1 1 1 2 2 1 1 0 s; si 1 1 1 2 2 1 1 0 s; b 2 1 1 2 2 2 dx 1 dy 1; mate 2 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c Block Facing MSE Wall Abut 1 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c c starting from Bottom c layer 1 c Block 1 2;1 2 3 4 11 12 13 14;1 2; 1.0 2.0; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; 196

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-15.33 -13.42; si 1 1 1 2 8 1 80 s; si 1 2 1 1 7 2 20 s; c top side of block c si 1 1 2 2 8 2 1 m; mate 3 c c layer 2 c Block 1 2;1 2 3411121314;1 2; 1.0 2.0; 22.5 21.519.5 18.5-18.5-19.5-21.5 -22.5; -13.42 -11.50; c si 1 1 1 2 8 1 1 s; si 1 2 1 1 7 2 120 s; Mate 11 c c c layer 3 Block 12;1 23411121314;12; 1.0 2.0; 22.5 21.519.518.5-18.5-19.5-21.5 -22.5; -11.50 -9.58; c si 1 1 2 2 8 2 2 m; si 1 2 1 1 7 2 21 s; mate 12 c c c layer 4 Block 1 2;1 2 3 4 11 12 13 14;1 2; 1.0 2.0; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -9.58 -7.66; c si 1 1 1 2 8 1 2 s; si 1 2 1 1 7 2 121 s; mate 13 c layer 5 Block 1 2;1 2 3 4 11 12 13 14;1 2; 1.0 2.0; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -7.66 -5.75; c si 1 1 2 2 8 2 3 m; si 1 2 1 1 7 2 22 s; mate 14 c layer 6 Block 1 2;1 2 3 411121314;1 2; 197

PAGE 217

1.0 2.0; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -5.75 -3.83; c si 1 1 1 2 8 1 3 s; si 1 2 1 1 7 2 122 s; mate 15 c layer 7 Block 12;1 23411121314;12; 1.0 2.0; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -3.83 -1.92; c si 1 1 2 2 8 2 4 m; si 1 2 1 1 7 2 23 s; mate 16 c layer 8 Block 1 2;1 2 3 411121314;1 2; 1.0 2.0; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -1.92 -0.0; c si 1 1 1 2 8 1 4 s; si 1 2 1 1 7 2 123 s; mate 17 c c cccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Abut 2 MSE Wall cccccccccccccccccccccccccccccccccccccccccccccccccccccccc c starting from Bottom c layer 1 c Block 1 2;1 2 3 4 11 12 13 14;1 2; 149.95 150.95; 22.5 21.5 19.5 18.5-18.5 -19.5-21.5 -22.5; -15.33 -13.42; si 1 1 1 2 8 1 81 s; si 2 2 1 2 7 2 200 s; c c top side of block c si 1 1 2 2 8 2 1 m; mate 3 c c layer 2 c Block 1 2;1 2 3 4 11 12 13 14;1 2; 149.95 150.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; 198

PAGE 218

-13.42-11.50; c si 1 1 1 2 8 1 1 s; si 2 2 1 2 7 2 220 s; Mate 11 c c c layer 3 Block 1 2;1 2 3 4111213 14;1 2; 149.95 150.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -11.50 -9.58; c si 1 1 2 2 8 2 2 m; si 2 2 1 2 7 2 201 s; mate 12 c c c layer 4 Block 1 2;1 2 3 411121314;1 2; 149.95 150.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -9.58 -7.66; c si 1 1 1 2 8 1 2 s; si 2 2 1 2 7 2 221 s; mate 13 c layer 5 Block 1 2;1 2 3 4 11 12 13 14;1 2; 149.95 150.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -7.66 -5.75; c si 1 1 2 2 8 2 3 m; si 2 2 1 2 7 2 202 s; mate 14 c layer 6 Block 1 2;1 2 3 411121314;1 2; 149.95 150.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -5.75 -3.83; c si 1 1 1 2 8 1 3 s; si 2 2 1 2 7 2 222 s; mate 15 c layer 7 Block 1 2;1 2 3 4 11 12 13 14;1 2; 149.95 150.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -3.83 -1.92; c si 1 1 2 2 8 2 4 m; 199

PAGE 219

si 2 2 1 2 7 2 203 s; mate 16 c layer 8 Block 1 2;1 2 3 411121314;1 2; 149.95 150.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -1.92 -0.0; c si 1 1 1 2 8 1 4 s; si 2 2 1 2 7 2 223 s; mate 17 ccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Right side MSE wall 30' long Abut 1 ccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c layer 1 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; 21.5 22.5; -15.33 -13.42; c Bottom of block to foundation si 1 1 1 6 2 1 82 m; c si 1 1 2 6 2 2 1 m c inter side of MSE wall si 1 1 1 6 1 2 24 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1; mate 3 c c c layer 2 Block 1 2 3 4 5 9; 1 2; 1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; 21.5 22.5; -13.42 -11.50; c si 1 1 1 6 2 1 1 s; c inter side of MSE wall si 1 1 1 6 1 2 124 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 11 c c c layer 3 Block123459;12;12; 1.0 0 -3.25 -5.75 -9.0 -29.0; 21.5 22.5; -11.50 -9.58; c top of block c si 1 1 2 6 2 2 2 m; 200

PAGE 220

c inter side of MSE wall si 1 1 1 6 1 2 25 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 12 c c c layer 4 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; 21.5 22.5; -9.58 -7.66; c top of block c si 1 1 1 6 2 1 2 s; c inter side of MSE wall si 1 1 1 6 1 2 125 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 13 c c c layer 5 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; 21.5 22.5; -7.66 -5.75; c top of block c si 1 1 2 6 2 2 3 m; c inter side of MSE wall si 1 1 1 6 1 2 26 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 14 c c c layer 6 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; 21.5 22.5; -5.75 -3.83; c top of block c si 1 1 1 6 2 1 3 s; c inter side of MSE wall si 1 1 1 6 1 2 126 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1; mate 15 c c 201

PAGE 221

c layer 7 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; 21.5 22.5; -3.83 -1.92; c top of block c si 1 1 2 6 2 2 4 m; c inter side of MSE wall si 1 1 1 6 1 2 27 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 16 c c c layer 8 Block 1 2 3 4 5 9; 1 2; 1 2; 1.0 0 -3.25-5.75 -9.0 -29.0; 21.5 22.5; -1.92 0; c top of block c si 1 1 1 6 2 1 4 s; c inter side of MSE wall si 1 1 1 6 1 2 127 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 17 c ccccccccccccccccccccccccccccccccccccccccccccccccccccccc c left side MSE wall 30' long Abut 1 ccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c layer 1 Block 1 2 3 4 5 9; 1 2; 1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; -21.5 -22.5; -15.33 -13.42; c Bottom of block to foundation si 1 1 1 6 2 1 83 m; c si 1 1 2 6 2 2 1 m c inter side of MSE wall si 1 1 1 6 1 2 30 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1; mate 3 c c c layer 2 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; -21.5 -22.5; 202

PAGE 222

-13.42 -11.50; c si 1 1 1 6 2 1 1 s; c inter side of MSE wall si 1 1 1 6 1 2 130 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 11 c c c layer 3 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; -21.5 -22.5; -11.5 -9.58; c top of block c si 1 1 2 6 2 2 2 m; c inter side of MSE wall si 1 1 1 6 1 2 31 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 12 c c c layer 4 Block 123459;12;12; 1.0 0 -3.25 -5.75 -9.0 -29.0; -21.5 -22.5; -9.58 -7.66; c top of block c si 1 1 1 6 2 1 2 s; c inter side of MSE wall si 1 1 1 6 1 2 131 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 13 c c c layer 5 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; -21.5 -22.5; -7.66 -5.75; c top of block c si 1 1 2 6 2 2 3 m; c inter side of MSE wall si 1 1 1 6 1 2 32 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 14 203

PAGE 223

c c c layer 6 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; -21.5 -22.5; -5.75 -3.83; c top of block c si 1 1 1 6 2 1 3 s; c inter side of MSE wall si 1 1 1 6 1 2 132 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 15 c c c layer 7 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; -21.5 -22.5; -3.83 -1.92; c top of block c si 1 1 2 6 2 2 4 m; c inter side of MSE wall si 1 1 1 6 1 2 33 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 16 c c c layer 8 Block 1 2 3 4 5 9;1 2;1 2; 1.0 0 -3.25 -5.75 -9.0 -29.0; -21.5 -22.5; -1.92 0; c top of block c si 1 1 1 6 2 1 4 s; c inter side of MSE wall si 1 1 1 6 1 2 133 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 17 c ccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Left side MSE wall 30' long Abut 2 ccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c layer 1 Block123459;12;12; 204

PAGE 224

150.95 151.95 155.2 157.70 160.95180.95; 21.5 22.5; -15.33 -13.42; c Bottom of block to foundation si 1 1 1 6 2 1 84 m; c si 1 1 2 6 2 2 1 m c inter side of MSE wall si 1 1 1 6 1 2 208 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 3 c c c layer 2 Block 1 2 3 4 5 9;1 2;1 2; 150.95151.95 155.2 157.70 160.95180.95; 21.5 22.5; -13.42 -11.50; c si 1 1 1 6 2 1 1 s; c inter side of MSE wall si 1 1 1 6 1 2 228 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 11 c c c layer 3 Block 1 2 3 4 5 9; 1 2; 1 2; 150.95151.95155.2157.70 160.95180.95; 21.5 22.5; -11.50 -9.58; c top of block c si 1 1 2 6 2 2 2 m; c inter side of MSE wall si 1 1 1 6 1 2 209 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1; mate 12 c c c layer 4 Block 123459;12;12; 150.95151.95155.2157.70 160.95180.95; 21.5 22.5; -9.58 -7.66; c top of block c si 1 1 1 6 2 1 2 s; c inter side of MSE wall si 1 1 1 6 1 2 229 s; c End of MSE wall 205

PAGE 225

b 6 1 1 6 2 2 dx 1 dy 1; mate 13 c c c layer 5 Block 1 2 3 4 5 9;1 2;1 2; 150.95 151.95155.2157.70 160.95180.95; 21.5 22.5; -7.66 -5.75; c top of block c si 1 1 2 6 2 2 3 m; c inter side of MSE wall si 1 1 1 6 1 2 210 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 14 c c c layer 6 Block 1 2 3 4 5 9;1 2;1 2; 150.95 151.95 155.2 157.70 160.95180.95; 21.5 22.5; -5.75 -3.83; c top of block c si 1 1 1 6 2 1 3 s; c inter side of MSE wall si 1 1 1 6 1 2 230 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 15 c c c layer 7 Block 123459;12;12; 150.95 151.95155.2 157.70 160.95180.95; 21.5 22.5; -3.83 -1.92; c top of block c si 1 1 2 6 2 2 4 m; c inter side of MSE wall si 1 1 1 6 1 2 211 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 16 c c c layer 8 Block 1 2 3 4 5 9;1 2;1 2; 150.95 151.95 155.2 157.70 160.95 180.95; 21.5 22.5; 206

PAGE 226

-1.92 0; c top of block c si 1 1 1 6 2 1 4 s; c inter side of MSE wall si 1 1 1 6 1 2 231 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 17 c ccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Right side MSE wall 30' long Abut 2 ccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c layer 1 Block 1 2 3 4 5 9;1 2;1 2; 150.95 151.95 155.2157.70 160.95180.95; -21.5 -22.5; -15.33 -13.42; c Bottom of block to foundation si 1 1 1 6 2 1 85 m; c si 1 1 2 6 2 2 1 m c inter side of MSE wall si 1 1 1 6 1 2 204 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 3 c c c layer 2 Block 1 2 3 4 5 9;1 2;1 2; 150.95151.95155.2157.70 160.95180.95; -21.5 -22.5; -13.42 -11.50; c si 1 1 1 6 2 1 1 s; c inter side of MSE wall si 1 1 1 6 1 2 224 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 11 c c c layer 3 Block 123459;12;12; 150.95151.95155.2157.70 160.95180.95; -21.5 -22.5; -11.50 -9.58; c top of block c si 1 1 2 6 2 2 2 m; c inter side of MSE wall 207

PAGE 227

si 1 1 1 6 1 2 205 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 12 c c c layer 4 Block 123459;12;12; 150 95 151.95 155.2 157.70 160 95 180 95; -21.5 -22 .5; -9 58 -7 66 ; c top of block c si 1 1 1 6 2 1 2 s; c inter side of MSE wall si 1 1 1 6 1 2 225 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1; mate 13 c c c layer 5 Block 1 2 3 4 5 9;1 2;1 2; 150.95151 .95155.2157. 70 160 .95180. 95; -21. 5 -22 .5; -7.66 -5.75; c top of block c si 1 1 2 6 2 2 3 m; c inter side of MSE wall si 1 1 1 6 1 2 206 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 14 c c c layer 6 Block 1 2 3 4 5 9;1 2;1 2; 150.95151 .95155.2157.70 160 .95180. 95 ; -21.5 -22.5; -5.75 -3.83; c top of block c si 1 1 1 6 2 1 3 s; c inter side of MSE wall si 1 1 1 6 1 2 226 s ; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 15 c c c layer 7 208

PAGE 228

Block 1 2 3 4 5 9;1 2;1 2; 150.95 151.95155.2 157.70 160.95180.95; -21. 5 -22.5; -3.83 -1.92; c top of block c si 1 1 2 6 2 2 4 m; c inter side of MSE wall si 1 1 1 6 1 2 207 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 16 c c c layer 8 Block 1 2 3 4 5 9;1 2;1 2; 150.95151 .95155.2157.70160.95 180 95; -21. 5 -22.5; -1.92 0; c top of block c si 1 1 1 6 2 1 4 s; c inter side of MSE wall si 1 1 1 6 1 2 227 s; c End of MSE wall b 6 1 1 6 2 2 dx 1 dy 1 ; mate 17 c ccccccccccccccccccccccccccccccccccccccccccccccccccccc c Tensile Inclusions Abutment 1 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c c c 1 inclusions block 1 2 3 4 56 10;1 2 3 4 11 12 13 14; -1; 2.0 1.0 0 -3.25 -5.75 -9. 0 -29; 22 5 21. 5 19. 5 18.5 -18.5 -19.5 -21.5 -22 .5; -13.42; orpt-0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 53 s ; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 54 s ; mate 4 c c 1 a inclusions c block 1 2 3 4 56 10;1 2 3 411 1213 14; -1; 2.0 1.0 0 -3.25 -5. 75 -9.0 -29; 209

PAGE 229

22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -11.5; orpt-0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 60s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 61 s; mate4 c 2 inclusions block 1 2 3 4 5 610;1 2 3 411121314; -1; 2.0 1.0 0 -3.25 -5.75 -9.0 -29; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -9.58; orpt-0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 49 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 50s; mate 4 c c 2a inclusions block 1 2 3 4 56 10;1 2 3 4 11 12 13 14; -1; 2.0 1.0 0 -3.25 -5.75 -9.0 -29; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -7.66; orpt-0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 62 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 63 s; mate 4 c 3 inclusions block 1 2 3 4 5 6 1 0; 1 2 3 4 11 12 13 14; -1 ; 2.0 1.0 0 -3.25 -5.75 -9.0 -29; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -3.83; orpt-0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 64 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 65 s; mate 4 210

PAGE 230

c 3a inclusions block 1 2 3 4 56 1 0;1 2 3 4 11 12 13 14; -1; 2.0 1.0 0 -3.25 -5.75 -9.0 -29; 22.5 21.519.518.5-18.5-19.5-21.5 -22.5; -5.75; orpt0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 41 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 42 s; mate4 c 3b inclusions block 1 2 3 4 5 6 1 0; 1 2 3 4 11 12 13 14; -1; 2.0 1.0 0 -3.25 -5.75 -9.0 -29; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -1.92; orpt0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 43 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 44 s; mate4 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c Tensile Inclusions Abutment 2 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c c c 1 inclusions block12345610;123411121314;-1; 149.95150.95151.95155.2157.70 160.95180.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -13.42; orpt0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 55 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 56 s; mate 4 c c c 1 a inclusions block12345610;123411121314;-1; 149.95150.95151.95155.2157.70 160.95180.95; 211

PAGE 231

22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -11.5; orpt0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 66 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 67 s; mate 4 c c 2 inclusions block 1 2 3 4 5 6 1 0; 1 2 3 4 11 12 13 14; -1 ; 149.95150.95151.95155.2157.70 160.95180.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -9.58; orpt0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 51 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 52 s; mate 4 c c 2a inclusions block 1 2 3 4 56 1 0;1 2 3 4 11 12 13 14; -1; 149.95150.95151.95155.2 157.70 160.95 180.95; 22.5 21.5 19.5 18.5-18.5 -19.5-21.5 -22.5; -7.66; orpt0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 68 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 69 s; mate4 c 3 inclusions block12345610;123411121314;-1; 149.95150.95151.95155.2157.70 160.95180.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -3.83; orpt0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 58 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 59 s; 212

PAGE 232

mate4 c 3a inclusions block12345610;123411121314;-1; 149.95150.95151.95155.2157.70 160.95180.95; 22.5 21.519.5 18.5-18.5-19.5-21.5 -22.5; -5.75; orpt0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 45 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 46 s; mate4 c c 3b inclusions block12345610;123411121314;-1; 149.95150.95151.95155.2157.70 160.95180.95; 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5; -1.92; orpt0 0 1 c bottom side of inclusion membrane to soil sii 2 7;2 7;-1; 47 s; orpt + 0 0 1 c top side of inclusion membrane to soil sii 2 7;2 7;-1; 48 s; mate 4 c ccccccccccccccccccccccccccccccccccccccccccccccccccccc c BackFill Abutment 1 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c c layer 1 block 123459;12310 1112; 12; 1.0 0 -3.25 -5.75 -9.0 -29; 21.519.518.5-18.5 -19.5-21.5; -15.33-13.42; c bottom side back fill to support soil si 1 1 1 6 6 1 70 m; c Top of back bott side of inclusion membrane to soil si 1 1 2 6 6 2 53 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 220m; si 1 1 1 6 1 2 24 m; si 1 6 1 6 6 2 30 m; mate 20 213

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c clayer1a c block 123459;12310 1112; 12; 1.0 0 -3.25 -5.75 -9.0 -29; 21.519.518.5-18.5-19.5-21.5; -13.42 -11.5; c top of backfill top side of inclusion membrane to soil si 1 1 2 6 6 260m; si 1 1 1 6 6 1 54 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 120m; si 1 1 1 6 1 2 124m; si 1 6 1 6 6 2 130 m; mate 7 c c Layer 2 block 1 2 3 4 5 9; 1 2 3 10 11 12; 1 2; 1.0 0 -3.25-5.75 -9.0 -29; c 21.5 19.5 18.5 -18.5 -19.5 -21.5; -11.5 -9.58; c top side of inclusion membrane to soil si 1 1 1 6 6 1 61 m; si 1 1 2 6 6 249m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 21 m; si 1 1 1 6 1 225m; si 1 6 1 6 6 2 31 m; mate 22 c Layer 2a block 123459;12310 1112; 12; 1.0 0 -3.25 -5.75 -9.0 -29; 21.519.518.5-18.5-19.5-21.5; -9.58 -7.66; c c top side of inclusion membrane to soil si 1 1 1 6 6 1 50 m; si 1 1 2 6 6 2 62 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 121m; si 1 1 1 6 1 2 125m; si 1 6 1 6 6 2 131 m; 214

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mate 8 c c Layer 3 block 1 2 3 4 5 9;1 2 3 10 11 12; 1 2; 1.0 0 -3.25 -5.75 -9.0 -29; 21.519.518.5-18.5-19.5 -21.5; -7.66 -5.75; c top side of inclusion membrane to soil si 1 1 1 6 6 1 63 m; si11266241m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 22 m; si 1 1 1 6 1 2 26 m; si 1 6 1 6 6 2 32 m; mate 9 c Layer 3a block 123459;12310 1112; 12; 1.0 0 -3.25-5.75 -9.0 -29; 21.519.518.5-18.5-19.5 -21.5; -5.75 -3.83; c top side of inclusion membrane to soil si 1 1 1 6 6 1 42 m; si 1 1 2 6 6 2 64 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 2 1 6 2 122m; si 1 1 2 6 1 2 126m; si 1 6 2 6 6 2 132 m; mate 26 c c Layer 4 block 1 2 3 4 5 9; 1 2 3 10 11 12; 1 2; 1.0 0-3.25 -5.75 -9.0 -29; 21.5 19.5 18.5-18.5-19.5 -21.5; -3.83 -1.92; c top side of inclusion membrane to soil si 1 1 1 6 6 1 65 m; si 1 1 2 6 6 2 43 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 23 m; si 1 1 1 6 1 2 27 m; si 1 6 1 6 6 2 33 m; mate 10 c Layer 4a 215

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block 1 2 3 4 5 9;1 2 3 10 11 12; 1 2; 1.0 0 -3.25 -5.75 -9.0 -29; 21.5 19.5 18.5 -18.5 -19.5 -21.5; -1.92 -0.0; c top side of inclusion membrane to soil si 1 1 1 6 6 1 44 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 2 1 6 2 123m; si 1 1 2 6 1 2 127 m; si 1 6 2 6 6 2 133m; c Backfill to under side of wing walls si 5 2 2 6 3 2 8 m; si 54 2 6 5 2 7 m; si 5 3 2 6 4 2 79 m; c bottom of abut fnd top back fill si 2 2 2 5 5 2 5 m; mate 27 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c BackFill Abutment 2 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c c layer 1 block123459;123101112;12; 150.95 151.95 155.2 157.70 160.95 180.95; 21.519.518.5-18.5-19.5-21.5; -15.33 -13.42; c bottom side back fill to support soil si 1 1 1 6 6 1 71 m; c batt side of inclusion membrane to soil si 1 1 2 6 6 2 55 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 200 m; si 1 6 1 6 6 2 204 m; si 1 1 1 6 1 2 208 m; mate 21 c c layer 1 a c block 1 2 3 4 5 9; 1 2 3 10 11 12; 1 2; 150.95151.95155.2157.70 160.95180.95; 21.5 19.5 18.5 -18.5 -19.5 -21.5; -13.42 -11.5; c batt side of inclusion membrane to soil si 1 1 1 6 6 1 56 m; 216

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si 1 1 2 6 6 2 66 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 220m; si 1 6 1 6 6 2 224m; si 1 1 1 6 1 2 228 m; mate 7 c c Layer 2 block123459;123101112;12; 150.95151.95155.2157.70 160.95180.95; 21.519.518.5-18.5-19.5 -21.5; -11.5 -9.58; c c top side of inclusion membrane to soil si 1 1 1 6 6 1 67 m; si 1 1 2 6 6 2 51 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 201 m; si 1 6 1 6 6 2 205 m; si 1 1 1 6 1 2 209 m; mate 23 c c Layer 2a block123459;123101112;12; 150.95 151.95 155.2 157.70 160.95 180.95; 21.519.518.5-18.5-19.5 -21.5; -9.58 -7.66; c c top side of inclusion membrane to soil si 1 1 1 6 6 1 52 m; si 1 1 2 6 6 2 68 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 221 m; si 1 6 1 6 6 2 225 m; si 1 1 1 6 1 2 229 m; mate 8 c Layer 3 block 1 2 3 4 5 9;1 2 3 10 11 12; 1 2; 150.95151.95155.2157.70 160.95180.95; 21.519.518.5-18.5-19.5 -21.5; -7.66 -5.75; c top side of inclusion membrane to soil si 1 1 1 6 6 1 45 m; 217

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si 1 1 2 6 6 2 69 m; b 6 1 1 6 6 1 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 202 m; si 1 6 1 6 6 2 206 m; si 1 1 1 6 1 2 210m; mate 9 c c Layer 3a block 123459;12310 1112; 12; 150.95151.95155.2157.70 160.95180.95; 21.5 19.5 18.5 -18.5 -19.5 -21.5; -5.75 -3.83; c top side of inclusion membrane to soil si 1 1 1 6 6 1 46 m; si 1 1 2 6 6 2 58 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 2 1 6 2 222 m; si 1 6 2 6 6 2 226 m; si 1 1 2 6 1 2 230 m; mate 28 c Layer 4 block 1 2 3 4 5 9;1 2 3 10 11 12; 1 2; 150.95151.95155.2157.70 160.95180.95; 21.5 19.5 18.5-18.5-19.5 -21.5; -3.83 -1.92; c top side of inclusion membrane to soil si 1 1 2 6 6 2 47 m; si 1 1 1 6 6 1 59 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 1 1 6 2 203 m; si 1 6 1 6 6 2 207 m; si 1 1 1 6 1 2 211 m; mate 10 c Layer 4a block 1 2 3 4 5 9;1 2 3 10 11 12; 1 2; 150.95 151.95 155.2 157.70 160.95 180.95; 21.519.518.5-18.5-19.5 -21.5; -1.92 -0.0; c top side of inclusion membrane to soil si 1 1 1 6 6 1 48 m; b 6 1 1 6 6 2 dx 1 dy 1 dz 0; c Front face of soil to MSE si 1 1 2 1 6 2 223 m; 218

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si 1 6 2 6 6 2 227 m; si 1 1 2 6 1 2 231 m; c Backfill to under side of wing walls si 5 2 2 6 3 2 1 0 m; si 54 2 6 5 2 9 m; si 5 3 2 6 4 2 92 m; c bottom of abut fnd top back fill si 2 2 2 5 5 2 6 m; mate 29 c c ccccccccccccccccccccccccccccccccccccccccccccccccccccc c Supporting Soil Abut 1 ccccccccccccccccccccccccccccccccccccccccccccccccccccc block 1 2 3 4 5 6 7 11 12; 1 2 3 4 5 12 13 14 15 16; 1 2; 4.0 2.0 1.0 0 -3.25 -5.75 -9.0 -29 -34; 26.5 22.5 21.5 19.5 18.5-18.5-19.5-21.5 -22.5 -26.5; -15.33 -20.22; c Supporting Soil surface under Mse wall si 2 2 1 3 9 1 80 m; c Supporting soil under backfill si 3 3 1 8 8 1 70 s; c Supporting soil under mse wall si 3 2 1 8 3 1 82 s; si 3 8 1 8 9 1 83 s; b 1 1 1 1 10 1 dx 1 dy 1 dz 1; b 9 1 1 9 10 1 dx 1 dy 1 dz 1; b 2 1 1 8 1 1 dx 1 dy 1 dz 1; b 2 1 0 1 8 1 0 1 dx 1 dy 1 dz 1; b 1 1 2 9 1 0 2 dx 1 dy 1 dz 1 rx 1 ry 1 rz 1; mate 6 ccccccccccccccccccccccccccccccccccccccccccccccccccccc c Supporting Soil Abut 2 ccccccccccccccccccccccccccccccccccccccccccccccccccccc block 1 2 3 4 56 7 11 12;1 2 3 4 5 12 13 14 15 16; 1 2; 147.95149.95150.95151.95155.2157.70160.95180.95 185.95; 26.5 22.5 21.5 19.5 18.5 -18.5 -19.5 -21.5 -22.5 -26.5; -15.33 -20.22; c Supporting Soil surface under Mse wall si 2 2 1 3 9 1 81 m; c Supporting soil under backfill si 3 3 1 8 9 1 71 s; c Supporting soil under mse wall si 3 2 1 8 3 1 84 s; si 3 8 1 8 9 1 85 s; b 1 1 1 1 1 0 1 dx 1 dy 1 dz 1; 219

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b 9 1 1 9 10 1 dx 1 dy 1 dz 1; b 2 1 1 8 1 1 dx 1 dy 1 dz 1 ; b 2 1 0 1 8 1 0 1 dx 1 dy 1 dz 1 ; b 1 1 2 9 1 0 2 dx 1 dy 1 dz 1 rx 1 ry 1 rz 1 ; mate 6 dap merge stol 0.1 write 220

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Appendix B. Ritz and Eigenvalves 221

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********************************************************************** ** ****** ** ********* ********* ******* ** ** ****** ** ** ********* ******** ******** *** ** ** ** ** ** ** ** *** **** ** ** ** ** ** *** ** ** ** ** ** ** **** ******* ***** ** ** ** ** ** ** ***** ******* *** ** ** ** **** ** ** ** ** ** ** ** ** *** ** ** ** ** *** *** ** *** ** ** ****** ** ** ********* ******* ******** ** ****** ** ** ********* ***** ******* NIKE3D VERSION 3.3.7 COMPILED 3/05/01 ********************************************************************** CONSTITUTIVE history data ============================================================ type solid shell #elements 4186 1638 size (bytes) 3407232 2479104 tot a I mass= 0.41905E+06 LINEAR EQUATION SOLVER data blocks 3 2 ====================================================================== ========== number of equations = number of equations (symmetric ) = number of equations (unsymmetric) = number of nonzero coefficients in global stiffness matrix = number of slide surface coefficients added to global stiffness matrix list = Ritz values, Relative residuals, Absolute residuals Col 1 Col 2 Col 3 29190 29190 0 974724 138686 Row 1: 1.64631 0+01 5.505870-09 9.064390-08 Row 2: 1.646310+01 4.375170-09 7.202910-08 Row 3: 1 .791480+01 4.538390-09 8.130430-08 Row 4: 5.086780+01 1.770960-09 9.00851 D-08 Row 5: 5.086790+01 1.586980-09 8.072640-08 Row 6: 7.152830+01 1.154560-09 8.258350-08 Row 7: 7.152840+01 7.855860-10 5.619170-08 Row 8: 4.680120+02 2.635680-09 1.233530-06 Row 9: 7.432920+02 1.888380-09 1.403620-06 222

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Row 10: 8.463320+02 1.656330-09 1.401800-06 Row 11: 8.779160+02 1.675020-09 1.470530-06 Row 12: 1.071730+03 1.814800-09 1.944970-06 Row 13: 1.342550+03 7.374410-10 9.900480-07 Row 14: 1 .857180+03 5.336870-09 9.911550-06 Row 15: 2.15071 0+03 1.939030-06 4.170300-03 Size of the matrix is The number of Ritz values requested is 29190 15 30 The number of Arnoldi vectors generated (NCV) is What portion of the spectrum: LM The number of converged Ritz values is 15 2 39 1.0000000000000001 E-09 The number of Implicit Arnoldi update iterations taken is The number of OP'*x is The convergence criterion is finished eigensolve factorization time = backsolves time = M'*x time= Lanczos alg time = Ritz vectors time = error norms time = eigensolver time = requency shift (hertz ) = frequency shift (radians/time)= 4.943349E+02 1.8387 40E+02 count = 39 1.921997E+OO count= 128 5.648810E+01 count= 152 1.099988E+01 1.591705E+01 7.716862E+02 3.947842E+01 1.000000E+OO nonlinear iteration information number of time steps completed ......... total number of equilibrium iterations ..... average number of equilibrium iterations .... total number of stiffness formations ...... total time charged for run (w/ overhead) = total wallclock time for run = normal termination 223 0 0 0.00 0 1049.452 1071.080

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REFERENCES American Association of State Highway and Transportation Officials. 2002. Load Resistance Factor Design, Second Edition. Washington, D.C.: Author. American Association of State Highway and Transportation Officials. 1996. Standard Specifications of Highway Bridges, Sixteenth Edition. Washington, D.C.: Author. Bowles, Joseph E. 1996. Foundation Analysis and Design, Fifth Edition. New York: McGraw Hill. Chopra, Anil K. 2001. Dynamics of Structures, Theory and Applications to Earthquake Engineering, Second Edition. Upper Saddle River, NJ: Prentice Hall. Elias, V. and Christopher, B.R. 2001. Mechanically Stabilized Earth Walls and Reinforced Soil Slope Design and Construction Guidelines. FHWA Report No. FHWA-NHI-00-043. Washington, D.C.: Federal Highway Administration. Farzad, Naeim. 2001. The Seismic Design Handbook, Second Edition. New York: Van Nostrand Reinhold. Frankenberger, Paul C., Bloomfield, R. A., and Anderson, P. L. 2000. Reinforced Earth Walls withstanding Northridge Earthquake. Irvine, CA: The Reinforcement Earth Company. Maker, Bradley, N. 1995. NIKE3D: A Nonlinear, Implicit, Three Dimensional Finite Element Code for Solid and Structural Mechanics User's Manual. Livermore, CA: Lawrence Livermore National Laboratory. McCallen, David B., and Ramstad, K.M. 1993. Dynamic Analysis of Short Span, Box Girder Overpass. Livermore, CA: Lawrence Livermore National Laboratory and Davis, CA: University of California, Davis. 224

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Nien-Yin-Chang, Wang, Trever, and Suidimanan, Otgontulga. 2004. Synchronization of HTW Peak Responses with Peak Ground Acceleration. Submitted to Journal of Highway Engineering. Nien-Yin-Chang, Lee, Zeh-Zon, and Wang, Trever. 2004. Hybrid Tee Wall under Seismic Loads. Submitted to Journal of Highway Engineering. Rainsberger, R. and Eggleston, T. 1999. TRUEGRID: A Multi-block Structural Mesh Generator for Finite Element Simulation Codes User's Manual. Livermore, CA: XYZ Scientific Applications, Inc. Sankey, J.E,. and Segrestin, P. 2000. Evaluation of Seismic Performance in Mechanically Stabilized Earth Structures. Vienna, VA: The Reinforcement Earth Company. Seed, H. B., and Withman, R.V. 1970. Design of Earth Retaining Structures for Dynamic Loads. ASCE Specialty Conference on Lateral Stress in the Ground and Design of Earth Retaining Structures. Speck, D.E., and Dovey, D. J. 1996. GRIZ: Finite Element Analysis Results Visualization for Unstructured Grids User's Manual. Livermore, CA: Lawrence Livermore National Laboratory. Tzou-Shin, Ueng, and Chen, Jian-Chu. 1992. RAMBO: Computational Procedures for Determining Parameters in Ramberg-Osgood Elastoplastic Model Based on Modulus and Damping Versus Strain User's Manual. Livermore, CA: Livermore National Laboratory. 225