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