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^-^--Â£?)]]

Where

C2E = 1 + {tan(Â£ + 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,Â£(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 Â£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 Â£1

and Â£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

Â£

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

Â£

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