NUMERICAL SIMULATION OF CONCRETE GRAVITY

DAM UNDER SEISMIC LOADING

By

Mohamed Ashraf Mohamed Abdelazeez Elsayad

A Thesis Submitted to the Faculty of Engineering at Cairo University

in Partial Fulfillment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY

In Structural Engineering

FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT

2017

NUMERICAL SIMULATION OF CONCRETE GRAVITY

DAM UNDER SEISMIC LOADING

By

Mohamed Ashraf Mohamed Abdelazeez Elsayad

A Thesis Submitted to the Faculty of Engineering at Cairo University

in Partial Fulfillment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY In

Structural Engineering

Under the Supervision of

Prof. Dr. Walid A. Attia

…………………………………………..

Prof. Dr. Adel. M. Belal

…………………………………………..

Professor of Structural Analysis &

Mechanics Structures Structural Engineering Department

Department of Civil Engineering Faculty of Engineering, Cairo University

Professor of Structural Analysis

Construction and Building Engineering Department Faculty of Engineering, Arab

Academy for Science, Technology & Maritime Transport, Cairo branch

FACULTY OF ENGINEERING, CAIRO UNIVERSITY

GIZA, EGYPT

2017

NUMERICAL SIMULATION OF CONCRETE GRAVITY

DAM UNDER SEISMIC LOADING

By

Mohamed Ashraf Mohamed Abdelazeez Elsayad

A Thesis Submitted to the

Faculty of Engineering at Cairo University in Partial Fulfillment of the

Requirements for the Degree of DOCTOR OF PHILOSOPHY

In Structural Engineering

Approved by the Examining Committee

Prof. Dr. Walid Abdel Latif Attia, Thesis Main Advisor Professor, Structural Engineering Department, Faculty of Engineering, Cairo University

………………………………………………………………………………

Prof. Dr. Adel Mahmoud Belal, Advisor Professor, Construction and Building Engineering Department, Faculty of Engineering,

Arab Academy for Science, Technology& Maritime Transport

……………………………………………………………………………… Prof. Dr. Mohamed Mohsen El-Attar, Internal Examiner Professor, Structural Engineering Department, Faculty of Engineering, Cairo University

………………………………………………………………………………

Prof. Dr. Eehab Ahmed Badr El-Din Khalil External Examiner Professor, Construction Research Institute (CRI)

………………………………………………………………………………

FACULTY OF ENGINEERING, CAIRO UNIVERSITY

GIZA, EGYPT

2017

Engineer’s Name: Mohamed Ashraf Mohamed Abdelazeez Elsayad

Date of Birth: 6 / 6 / 1987

Nationality: Egyptian

E-mail: Mohamed_elsayaad@hotmail.com

Phone: +201001912278

Address: 20 Trablos St.-Abbas Elakkad- Nasr city

Registration Date: 1 / 10 / 2013

Awarding Date: / / 2017

Degree: Doctor of Philosophy

Department: Structural Engineering

Supervisors: Prof. Dr.Walid Abdel Latif Attia

Prof. Dr.Adel Mahmoud Belal Examiners: Prof. Dr.Walid Abdel Latif Attia (Thesis Main Advisor)

Prof. Dr.Adel Mahmoud Belal (Advisor)

Construction and Building, Arab Academy for Science,

Technology & Maritime Transport, Cairo branch Prof. Dr. Mohamed Mohsen El-Attar ( (Internal Examiner)

Porf. Dr. Ehab Ahmed Badr El-Din Khalil (External Examiner)

(Construction Research Institute (CRI))

Title of Thesis:

NUMERICAL SIMULATION OF CONCRETE GRAVITY DAM UNDER

SEISMIC LOADING

Key Words: Concrete gravity dams; Earthquake analysis; dam-water- foundation interaction; cracks propagation; Structural Optimization.

Summary:

Gravity dam is considered one of the most important massive concrete structures which depend on its own weight to resist the external loads. Partial or full failure of this

structure produces proper damages of the society and sometimes death for humans. Nowadays the construction of the concrete dams or rehabilitate work for existing dams

are required the creation for the development of modern tools and methods of the numerical analyses considering the dam-reservoir-foundation interaction. Moreover the transient simulation of the behavior for this structure is considered an important issue in

structural dynamics. In order to achieve the objectives of this thesis, many procedures are executed and explained as follow:

1. Comparisons between 2-D and 3-D F.E. models results are executed. 2. Studying the effect of dam-reservoir- foundation interaction through analyses. 3. Review the influence of the stiffness changes for the longitudinal direction of

the dams through the earthquakes. 4. Produce GUI for executing analyses and structural optimization for the concrete

dams’ cross-sections considering several types of loading.

i

Acknowledgments

First of all, I would like thank Allah (God) for giving me the patience, the knowledge and the strength to finish this work.

I would like to express my deep gratitude to my Ph.D advisor Professor Walid Abdel

Latif Attia for his guidance and mentorship with this dissertation and during my

doctoral studies. He has always been available, and he has provided valuable guidance

throughout my time. His technical guidance and continuous support and encouragement

proved to be invaluable.

I would like to express my deep gratitude to my advisor Professor Adel Mahmoud

Belal for the continuous support of my Ph.D study and research, for his patience, motivation, enthusiasm, and immense knowledge. His guidance helped me in all the time of research and writing of this thesis. He helped me find direction in my academic

career, and still provides advice whenever I need it.

I would like to thank my parents for their unfailing and unconditional love, for allowing

me to realize my own potential. All the support they have provided me over the years

was the greatest gift anyone has ever given me. I need to thank my father, who taught

me the value of hard work and an education. My sisters and little brother deserve my

wholehearted thanks as well. I also need to thank my mother because without her, I

may never have gotten to where I am today

I would like to thank my wonderful children for always making me smile and for

understanding on those weekend mornings when I was writing this book instead of

playing with them. I hope that one day they can read this book and understand why I

spent so much time in front of my computer.

Finally, and most importantly, I would like to thank my loving wife for her support

throughout the four years of my doctoral studies. I am indebted to her for her support,

understanding, and love throughout this endeavor. She has been my inspiration and

motivation for continuing to improve my knowledge and move my career forward.

ii

Dedication

To My Parents

To My Wife

To My children

iii

Table of Contents

ACKNOWLEDGMENTS ..............................................................................................I

DEDICATION ............................................................................................................... II

TABLE OF CONTENTS.............................................................................................III

LIST OF TABLES ....................................................................................................... VI

LIST OF FIGURES .................................................................................................. VIII

NOMENCLATURE ..................................................................................................... XI

ABSTRACT ............................................................................................................... XIV

CHAPTER 1 : INTRODUCTION ................................................................................ 1

1.1. BACKGROUND AND OVERVIEW ............................................................ 1

1.2. CONCRETE GRAVITY DAM...................................................................... 1

1.3. STATEMENT OF THE PROBLEMS FOR CONCRETE DAMS................. 2

1.4. STRUCTURAL FINITE ELEMENT METHOD………………………………..5

1.4.1. FINITE ELEMENT MODELING .............................................................. 5

1.4.2. FINITE ELEMENT CAPABILITIES ......................................................... 6

1.5. AIMS AND SCOPE OF THIS THESIS ......................................................... 6

1.6. THESIS OUTLINES...................................................................................... 6

CHAPTER 2 : LITERATURE REVIEW .................................................................... 8

2.1. INTRODUCTION ......................................................................................... 8

2.2. STRUCTURAL STUDIES .......................................................................... 10

2.3. THERMAL STUDIES ................................................................................. 13

2.4. FOUNDATION STUDIES .......................................................................... 16

2.5. SEISMIC STUDIES..................................................................................... 20

2.6. DAMS REHABILITATION STUDIES ...................................................... 24

CHAPTER 3 : FINITE ELEMENT ANALYSES ..................................................... 27

3.1. INTRODUCTION ....................................................................................... 27

3.2. DYNAMIC NUMERICAL METHODS ...................................................... 27

3.3. MODAL ANALYSIS .................................................................................. 28

3.4. HARMONIC RESPONSE ANALYSIS ...................................................... 29

3.5. TRANSIENT DYNAMIC ANALYSIS ....................................................... 30

3.6. DAMPING MECHANISM.......................................................................... 30

3.7. STRUCTURAL ELEMENTS...................................................................... 31

3.7.1. 2-D FINITE ELEMENT GEOMETRY......................................................31

3.7.2. 3-D FINITE ELEMENT GEOMETRY......................................................32

3.8. SOIL-STRUCTURE INTERACTION ........................................................ 34

3.9. FLUID-STRUCTURE INTERACTION ..................................................... 35

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3.9.1. 2-D FLUID FINITE ELEMENT TYPES ...................................................38

3.9.2. 3-D FLUID FINITE ELEMENT TYPES ...................................................38

3.10. CONTACT BETWEEN STRUCTURAL ELEMENTS .............................. 39

3.10.1. 2-D CONTACT ELEMENTS ...................................................................40

3.10.2. 3-D CONTACT ELEMENTS ...................................................................40

CHAPTER 4 : NUMERICAL MODEL VALIDATION.......................................... 41

4.1. INTRODUCTION ....................................................................................... 41

4.2. DESCRIPTION OF THE EXPERIMENTAL MODEL TESTS .................. 42

4.2.1. STATIC TESTS.......................................................................................42

4.2.2. DYNAMIC TESTS ..................................................................................44

4.2.3. IMPACT HAMMER TESTS ....................................................................44

4.3. THE VALIDATION OF THE FINITE ELEMENT MODEL...................... 45

4.3.1. TWO DIMENSIONAL FINITE ELEMENT MODEL ................................46

4.3.2. MODAL ANALYSIS...............................................................................46

4.3.3. STATIC TESTS.......................................................................................49

4.3.4. DYNAMIC ANALYSES..........................................................................51

4.3.5. TWO AND THREE DIMENSIONAL FINITE ELEMENT RESULTS

COMPARISON ......................................................................................................... 52

4.4. ANALYTICAL STUDY OF FULL SCALED CONCRETE DAM MODEL

……………………………………………………………………………54

4.4.1. THE FULL SCALED DAM MONOLITH NATURAL FREQUENCY

ANALYSIS .............................................................................................................. 55

4.4.2. THREE DIFFERENT FINITE ELEMENT SYSTEMS COMPARISON......55 4.4.2.1. STATIC ANALYSES............................................................................................................ 56 4.4.2.2. TRANSIENT ANALYSES.................................................................................................... 60

CHAPTER 5 : TRANSIENT BEHAVIOR OF DAM-RESERVOIR-

FOUNDATION SYSTEM ........................................................................................... 64

5.1. INTRODUCTION ....................................................................................... 64

5.2. THE CASE STUDY DESCRIPTION .......................................................... 65

5.2.1. MATERIAL PROPERTIES OF KOYNA DAM ........................................66

5.2.2. SEISMIC LOADING HISTORY ..............................................................67

5.3. FINITE ELEMENT MODELING IMPLEMENTATION ........................... 68

5.4. MODAL ANALYSIS .................................................................................. 70

5.5. TRANSIENT ANALYSIS ........................................................................... 73

5.6. EFFECT OF FOUNDATION FLEXIBILITY ON TRANSIENT DAM

ANALYSIS................................................................................................................. 86

CHAPTER 6 : CRACKS PROPAGATION DURING EARTHQUAKE

EXCITATION .............................................................................................................. 90

6.1. INTRODUCTION ....................................................................................... 90

6.2. NUMERICAL MODEL OF THE KOYNA DAM .................................................... 91

6.2.1. THE ANALYSES METHODS OF THE 3-D MODELS .............................94

6.2.2. MATERIAL PROPERTIES OF THE DAM...............................................94

6.2.3. THE SEISMIC LOADING .......................................................................94

6.2.4. SEISMIC ANALYSES RESULTS ............................................................95

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6.2.5. TENSILE DAMAGE OF THE DAM ........................................................98

CHAPTER 7 : GEOMETRIC OPTIMIZATION OF CONCRETE DAMS........ 107

7.1. INTRODUCTION ..................................................................................... 107

7.2. DESCRIPTION OF THE MODEL ............................................................ 107

7.2.1. DATA ENTRY STAGE ......................................................................... 109

7.2.2. GRAPHICAL USER INTERFACE......................................................... 110

7.2.3. COMPILING METHOD ........................................................................ 111

7.3. NUMERICAL APPLICATION IMPLEMENTATION ............................ 112

7.3.1. THE MODEL CHARACTERISTICS...................................................... 112

7.3.2. THE GRAVITY AND HYDROSTATIC SIMULATIONS ....................... 113

7.3.3. MODAL ANALYSIS............................................................................. 116

7.3.4. TRANSIENT ANALYSIS...................................................................... 117

7.4. OPTIMIZATION IMPLEMENTATION .................................................. 121

7.4.1. PROBLEM FORMULATION ................................................................ 122

7.4.2. OPTIMIZED GEOMETRY USING DECREASING PROCESS ............... 123

7.4.3. ANALYSES RESULTS OF DECREASING GEOMETRY PROCESS ..... 124

7.4.4. OPTIMIZED GEOMETRY USING INCREASING PROCESS ................ 128

7.4.5. ANALYSES RESULTS OF INCREASING GEOMETRY PROCESS ...... 128

CHAPTER 8 : CONCLUSIONS AND RECOMMENDATIONS ......................... 131

8.1. SUMMERY ............................................................................................... 131

8.2. CONCLUSION .......................................................................................... 131

8.2.1. TWO AND THREE DIMENSIONAL FINITE ELEMENT ANALYSES .. 131

8.2.2. DAM-RESERVOIR-FOUNDATION INTERACTION ............................ 132

8.2.3. CRACKS PROPAGATION.................................................................... 133

8.2.4. STRUCTURAL OPTIMIZATION .......................................................... 133

8.3. RECOMMENDATIONS FOR FUTURE WORK ..................................... 134

REFERENCES ........................................................................................................... 135

APPENDIX A: SAMPLE OF INPUT SCRIPT FILES FOR F.E. ANALYSES .. 141

APPENDIX B: EXCEL FILE & MATLAB SCRIPT SAMPLES......................... 151

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List of Tables

Table 4.1: Natural frequencies of the finite element model ........................................... 47 Table 4.2: The comparison between 2-D and 3-D gravity and hydrostatic analysis...... 53 Table 4.3: The full scale natural frequencies comparison .............................................. 55

Table 4.4 Y-Stress results for the gravity and hydrostatic F.E. analyses ....................... 56 Table 5.1: The material properties of the dam, water and foundation rock ................... 66

Table 5.2: Peaks displacement and acceleration values ................................................. 86 Table 6.1 Peak values of different models .................................................................... 97 Table 7.1: Validation of the analyses dam model ........................................................ 120

Table 7.1: Optimization analyses for Pine Flat dam cross section using different ground excitation ..................................................................................................................... 127

Table 7.2: Optimization analyses for Koyna dam cross section using different ground excitation ..................................................................................................................... 130

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List of Figures

Figure 1.1.a: Constructionstage of Austin dam ................................................................ 3 Figure 1.1.b: Sliding failure in 1911of Austin dam ......................................................... 3

Figure 1.2.a: St. Francis dam at downstream ................................................................... 3 Figure 1.2.b: St. Francis dam after the failure .................................................................. 3

Figure 1.3.a: Malpasset dam before failure ..................................................................... 4 Figure 1.3.b: Malpasset Left abutment after failure ......................................................... 4 Figure 1.4.a: Koyna dam downstream view ..................................................................... 4

Figure 1.4.b: Supported buttresses after damage of Koyna dam...................................... 4 Figure 2.1: Typical loads acting on Gravity dam ............................................................. 8

Figure 2.2.a: Sliding stability consideration of Gravity dam ........................................... 9 Figure 2.2.b: Overturning stability consideration of Gravity dam ................................... 9 Figure 2.2.c: Over Stressed stability consideration of Gravity dam ................................ 9

Figure 2.3: Nodal displacement of the dam for O.W.+ full reservoir level + silt pressure condition ......................................................................................................................... 13

Figure 2.4.a: Actual temperature contours for the dam .................................................. 14 Figure 2.4.b: Stresses results at center of dam base ....................................................... 15 Figure 2.5: Observed in-situ cracks for buttress dam in Sweden ................................... 15

Figure 2.6.a: Maximum principal tensile stresses due to summer temperature ............. 16 Figure 2.6.b: Cracks propagation for the fifth year due to summer temperature .......... 16

Figure 2.7: Variation of stresses at the dam base for empty reservoir ........................... 18 Figure 2.8: Variation of stresses at the dam base for full reservoir ................................ 18 Figure 2.9: Maximum principal stresses for Koyna dam due to earthquake in 1967..... 22

Fig.2.10.a: Frequency at point A of acceleration responses to upstream incident waves ........................................................................................................................................ 23

Fig.2.10.b: Frequency at point B of acceleration responses to upstream incident waves ........................................................................................................................................ 23 Figure 2.11: Fariman dam with the new part ................................................................. 26

Figure 3.1: PLANE42 geometry and stress directions ................................................... 32 Figure 3.2: SOLID45 geometry...................................................................................... 32

Figure 3.3: 3-D failure surface for concrete ................................................................... 33 Figure 3.4: Substructure technique scheme .................................................................... 34 Figure 3.5: Distribution of the hydrodynamic pressure on finite element mesh ............ 35

Figure 3.6: CONTA172 geometry.................................................................................. 40 Figure 4.1: Schematic diagram of the experimental dam model .................................... 43

Figure 4.2: Experimental setup of static test .................................................................. 43 Figure 4.3: Impact hammer test ...................................................................................... 44 Figure 4.4: Finite element model dimensions ................................................................ 45

Figure 4.5: The mesh of the 2-D finite element model ................................................. 46 Figure 4.6: First mode shape .......................................................................................... 47

Figure 4.7: Second mode shape ...................................................................................... 48 Figure 4.8: Third mode shape ........................................................................................ 48 Figure 4.9: Y-component of displacement of 2-D model applied to gravity load (m) .. 49

Figure 4.10: Y-component of stress for 2-D model applied to gravity load (Pa) .......... 49 Figure 4.11: Y-component of displ. for 2-D model applied to hydrostatic load (m) ..... 50

Figure 4.12 Y-component of stress for 2-D model applied to hydrostatic load (Pa) .... 50

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Figure 4.13: The time history of the shaking table acceleration .................................... 51 Figure 4.14: Model acceleration response through harmonic motion at frequency of

17.5 Hz .......................................................................................................................... 52 Figure 4.15: Y-component of stress for 2-D model applied to harmonic load (Pa) ....... 52

Figure 4.16: The mesh of the 3-D finite element model ............................................... 53 Figure 4.17: Experimental, 2-D, and 3-D F.E. modeling response at frequency of 17.5 Hz ................................................................................................................................... 54

Figure 4.18.a: Dam monolith dimensions of the full scaled model................................ 54 Figure 4.18.b: The F.E. model components of the full scaled model ............................ 54

Figure 4.19.a: First mode of full scaled model............................................................... 55 Figure 4.19.b: Second mode of full scaled model ......................................................... 55 Figure 4.19.c: Third mode of full scaled model ............................................................ 55

Figure 4.20.a: Model II for three dimensional modeling ............................................... 56 Figure 4.20.b: Model III for three dimensional modeling .............................................. 56

Figure 4.21: X-component of displacement for model I applied to gravity load (m) .... 57 Figure 4.22: Y-component of stress for model I applied to gravity load (Pa)................ 57 Figure 4.23: X-component of displacement for model II applied to gravity load (m) ... 58

Figure 4.24: Y-component of stress for model II applied to gravity load (Pa) .............. 58 Figure 4.25: X-component of displacement for model III applied to grav. load (m) ..... 59

Figure 4.26: Y-component of stress for model III applied to gravity load (Pa) ............ 59 Figure 4.27.a: Nahanni ground acceleration................................................................... 60 Figure 4.27.b: Nahanni ground velocity ........................................................................ 60

Figure 4.27.c: Nahanni ground displacement ................................................................ 60 Figure 4.28: Spectral acceleration for 5% damping ....................................................... 61

Figure 4.29.a: The horizontal crest acceleration for model I ( ) ........................ 62 Figure 4.29.b: The horizontal crest acceleration for model II ( ) ....................... 62

Figure 4.29.c: The horizontal crest acceleration for model III ( ) ...................... 62

Figure 4.30: Time histories of the base sliding for the three models ............................. 63

Figure 5.1.a: Foundation’s surface topography (in meters) ........................................... 65 Figure 5.1.b: Plan view of the Koyna dam ..................................................................... 65

Figure 5.2.a: Geometry of Koyna dam non-overflow section ........................................ 66 Figure 5.2.b: Geometry of Koyna dam over-flow section.............................................. 66 Figure 5.3.a: Horizontal acceleration component of 1967earthquake............................ 67

Figure 5.3.b: Vertical acceleration component of 1967earthquake................................ 67 Figure 5.4: Reservoir-Dam-Foundation dimensions of Koyna dam model ................... 68

Figure 5.5.a: Case 1 of the Koyna finite element implementation ................................. 69 Figure 5.5.b: Case 2 of the Koyna finite element implementation................................. 69 Figure 5.5.c: Case 3 of the Koyna finite element implementation ................................. 70

Figure 5.5.d: Case 4 of the Koyna finite element implementation................................. 70 Figure 5.6: The first five modes shapes comparison for the dam cases ......................... 71

Figure 5.7.a: Mode 1 of Case 1 ...................................................................................... 71 Figure 5.7.b: Mode 1 of Case 2 ...................................................................................... 72 Figure 5.7.c: Mode 1 of Case 3 ...................................................................................... 72

Figure 5.7.d: Mode 1 of Case 4 ...................................................................................... 72 Figure 5.8.a: Horizontal displacement of Case 1 ........................................................... 73

Figure 5.8.b: Horizontal displacement of Case 2 ........................................................... 74 Figure 5.8.c: Horizontal displacement of Case 3 ........................................................... 74 Figure 5.8.d: Horizontal displacement of Case 4 ........................................................... 74

Figure 5.9.a: Horizontal acceleration of Case 1 ............................................................. 75 Figure 5.9.b: Horizontal acceleration of Case 2 ............................................................. 75

ix

Figure 5.9.c: Horizontal acceleration of Case 3 ............................................................. 76 Figure 5.9.d: Horizontal acceleration of Case 4 ............................................................. 76

Figure 5.10.a: Upstream variation of stresses in Y-direction for four cases (the dam movement in the upstream direction) ............................................................................. 77

Figure 5.10.b: Downstream variation of stresses in Y-direction for four cases (the dam movement in the upstream direction) ............................................................................. 77 Figure 5.11.a: Upstream variation of stresses in Y-direction for the four cases (the dam

movement in the downstream direction) ........................................................................ 78 Figure 5.11.b: Downstream variation of stresses in Y-direction for the four cases (the

dam movement in the downstream direction) ................................................................ 78 Figure 5.12.a: Upstream variation of stresses in X-direction for the four cases (the dam movement in the upstream direction) ............................................................................. 79

Figure 5.12.b: Downstream variation of stresses in X-direction for the four cases (the dam movement in the upstream direction) ..................................................................... 79

Figure 5.13.a: Upstream variation of stresses in X-direction four cases (the dam movement in the downstream direction) ........................................................................ 80 Figure 5.13.b: Downstream variation of stresses in X-direction four cases (the dam

movement in the downstream direction) ........................................................................ 80 Figure 5.14.a: Upstream variation of stresses in XY-direction for the four cases (the

dam movement in the upstream direction) ..................................................................... 80 Figure 5.14.b: Downstream variation of stresses in XY-direction for the four cases (the dam movement in the upstream direction) ..................................................................... 81

Figure 5.15.a: Upstream variation of stresses in XY-direction for the four cases (the dam movement in the downstream direction) ................................................................ 81

Figure 5.15.b: Downstream variation of stresses in XY-direction for the four cases (the dam movement in the downstream direction) ................................................................ 81 Figure 5.16: Peak dam horizontal displacement for case 1 (m) ..................................... 82

Figure 5.17: Peak Von-Misses stresses contours for case 1 (Pa) ................................... 82 Figure 5.18: Peak dam horizontal displacement for case 2 (m) ..................................... 83

Figure 5.19: Peak Von-Misses stresses contours for case 2 (Pa) ................................... 83 Figure 5.20: Peak dam horizontal displacement for case 3 (m) ..................................... 84 Figure 5.21: Peak Von-Misses stresses contours for case 3 (Pa) ................................... 84

Figure 5.22: Peak dam horizontal displacement for case 4 (m) ..................................... 85 Figure 5.23: Peak Von-Misses stresses contours for case 4 (Pa) ................................... 85

Figure 5.24.a: The peak Y-stresses distribution along the dam base when the peak displacement in downstream direction ........................................................................... 87 Figure 5.24.b: The peak Y-stresses distribution along the dam base when the peak

displacement in upstream direction ................................................................................ 87 Figure 5.25.a: The peak X-stresses distribution along the dam base when the peak

displacement in downstream direction ........................................................................... 88 Figure 5.25.b: The peak X-stresses distribution along the dam base when the peak displacement in upstream direction ................................................................................ 88

Figure 5.26.a: The peak XY-stresses distribution along the dam base when the peak displacement in downstream direction ........................................................................... 88

Figure 5.26.b: The peak XY-stresses distribution along the dam base when the peak displacement in upstream direction ................................................................................ 89 Fig.6.1.a: The meshed element of model I for seismic analysis..................................... 92

Fig.6.1.b: The meshed finite elements of model II for seismic analysis ........................ 93 Fig.6.1.c: The meshed finite elements of model III for seismic analysis ....................... 93

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Figure 6.2: The time history of horizontal crest displacement for model I analysis compared by Chopra displacement during Koyna earthquake ....................................... 95

Figure 6.3: The time history of horizontal crest displacement for model I analysis compared by model II linear analysis during Koyna earthquake ................................... 96

Figure 6.4: The time history of horizontal crest displacement for model I analysis compared by model II non- linear analysis during Koyna earthquake............................ 96 Figure 6.5: The time history of horizontal crest displacement for model I compared by

model III during Koyna earthquake ............................................................................... 97 Figure 6.6: Formation failure criteria damage for model I........................................... 101

Figure 6.7: Red cross section that was used for the results extraction for model II..... 102 Figure 6.8: Frist crack propagation for model II at peaks times during Koyna earthquake..................................................................................................................... 103

Figure 6.9: Red cross section that was used for the results extraction for model III ... 104 Figure 6.10: Frist crack propagation for model III at peaks times during Koyna

earthquake..................................................................................................................... 105 Figure 7.1: General flowchart that describing the F.E. implementation model ........... 108 Fig.7.2.a: One part dam type that available in the developed program ........................ 109

Fig.7.2.b: Two parts dam type that available in the developed program ..................... 109 Figure 7.3: The designed GUI using MATLAB .......................................................... 110

Figure 7.4: The geometry of the selected model (m) ................................................... 112 Figure 7.5: The meshed finite element model .............................................................. 113 Figure7.6: X-displacement through gravity simulation................................................ 114

Figure7.7: Y-Stress through gravity simulation ........................................................... 114 Figure 7.8: X-displacement through hydrostatic simulation ........................................ 115

Figure 7.9: Y-Stress through hydrostatic simulation.................................................... 115 Fig.7.10.a: Mode shape number 1 of the F.E. model ................................................... 116 Fig.7.10.b: Mode shape number 2 of the F.E. model ................................................... 117

Fig.7.10.c: Mode shape number 3 of the F.E. model ................................................... 117 Fig.7.11.a: Horizontal acceleration records of Taft ground motion ............................. 118

Fig.7.11.b: Vertical acceleration records of Taft ground motion ................................. 118 Figure 7.12: Displacement time history of the model crest.......................................... 119 Figure 7.13: Displacement contours of the model at peak value time ........................ 119

Fig.7.14.a: Principal stresses of the model (Pa) ........................................................... 120 Fig.7.14.b: Principal stresses of Løkkeꞌs model (Pa) ................................................... 121

Figure 7.15: Geometrical model of the concrete dam .................................................. 122 Figure 7.16: Dimensions of the tallest monolith of Pine Flat dam............................... 124 Figure 7.17: The optimization trails of Pine Flat dam.................................................. 125

Figure 7.18: The horizontal displacement of the optimized section at peak time ........ 126 Figure 7.19: The vertical stresses of the optimized section at peak time ..................... 126

Figure 7.20: El-Centro horizontal acceleration records ............................................... 127 Figure 7.21: The optimization trails of Koyna dam ..................................................... 128 Figure 7.22: The horizontal displacement of the optimized section at peak time ........ 129

Figure 7.23: The vertical stresses of the optimized section at peak time .................... 129

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Nomenclature

Symbols

: Hydrostatic force

: Hydrodynamic force

: Silt load

: Own weight of the dam

: Vertical water force

U: Uplift force

: Horizontal earthquake component

: Vertical earthquake component

: Sliding factor of safety

: Overturning factor of safety

: Overstressing factor of safety

[M]: Structural mass matrix

[C]: Structural damping matrix

[K]: Structural stiffness matrix

: Nodal acceleration vector

: Nodal velocity vector

: Nodal displacement vector

: Applied load vector

{ (t)}: Internal load vector.

: The magnitude of the load

Ω: The model circular frequency measured in radians/time

Ψ: Stands for the load phase shift

α: Mass matrix multiplier

β: Stiffness matrix multiplier

: Variable stiffness matrix multiplier