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Title Page
Abstract
Contents
Chapter 1. Introduction 24
1.1. Background 24
1.1.1. Historical review of structural reliability 24
1.1.2. Current context of bridges deterioration 26
1.2. Research objectives 28
1.3. Thesis organization 29
Chapter 2. Corrosion mechanisms for deteriorated bridges 33
2.1. Introduction 33
2.2. Corrosion mechanism of a steel box girder bridge 37
2.3. Corrosion mechanism of shear reinforcement of a PC box girder bridge 38
2.4. Pitting corrosion in post-tensioned tendon 40
2.4.1. Pitting corrosion mechanisms 41
2.4.2. Sources of Chloride 42
2.4.2.1. Grouting process 42
2.4.2.2. Material properties of grout 43
2.4.2.3. Corrosion of anchorage 43
2.4.2.4. Duct problems 44
2.5. Corrosion scenario 45
2.6. Corrosion initiation 46
2.7. Corrosion propagation-the stress corrosion cracking 49
2.8. Conclusions 50
Chapter 3. Failures analysis of PC box girder bridges under corrosion attack 51
3.1. Introduction 51
3.2. Structural configuration 53
3.2.1. Geometrical properties 53
3.2.2. Load models 56
3.3. Shear strength degradation modeling 59
3.3.1. Corrosion of shear reinforcements 59
3.3.2. Limit state function 60
3.4. Flexural strength degradation modeling 61
3.4.1. Ductile model 61
3.4.2. Ductile-brittle model 65
3.4.3. Brittle model 68
3.4.3.1. Corrosion initiation 68
3.4.3.2. Corrosion propagation 68
3.4.3.3. Computational procedure 73
3.5. Analysis results and discussions 74
3.5.1. Shear failure 74
3.5.2. Moment failure: ductile model 74
3.5.3. Moment failure: ductile-brittle model 77
3.5.4. Moment failure: brittle model 79
3.6. Stochastic data for RBDO analysis 86
3.7. Equivalence between ductile and brittle model 91
3.8. Conclusions 94
Chapter 4. Efficient approaches for reliability analysis and reliability-based design optimization of structures 96
4.1. Introduction 96
4.2. First order approximation for the reliability analysis 99
4.2.1. Background of reliability-based design theory 99
4.2.2. First and second order approximation for limit state functions 100
4.3. Probabilistic optimal approaches 103
4.3.1. Problem definitions 103
4.3.2. Probabilistic optimal approaches for RBDO problems 104
4.4. Numerical examples 111
4.4.1. RC girder design 111
4.4.1.1. Example 1: Design for minimizing the initial cost (initial and failure costs) with equality reliability constraints 114
4.4.1.2. Example 2: design for minimizing the total cost (initial and failure costs) 117
4.4.1.3. Example 3: Design for minimizing the total cost (initial and failure costs) with time-variant probabilistic inequality constraints 119
4.4.1.4. Results of the second order approximation 120
4.4.2. Example 4: PC girder design 125
4.5. Conclusions 133
Chapter 5. Time variant reliability-based design optimization of highway bridges 135
5.1. Introduction 135
5.2. RBDO of PC box girder bridges under corrosion attack 138
5.2.1. Problem definition 138
5.2.2. Load models 139
5.2.3. RBDO formulation of a PC box girder bridge 141
5.2.3.1. Sectional configurations 142
5.2.3.2. Objective function 144
5.2.3.3. Probabilistic constraints 145
5.2.3.4. Deterministic constraints 153
5.2.3.5. Analysis results and discussion 154
5.3. RBDO of the steel box girder bridge under corrosion attack 163
5.3.1. Problem definition 163
5.3.2. RBDO formulation of steel box girder bridge 163
5.3.3. Analysis results and discussion 167
5.4. Conclusions 173
Chapter 6. Effective target reliability indices for highway bridges 175
6.1. Introduction 175
6.2. Background of the target reliability index for highway bridges in bridge design specification codes 176
6.2.1. Target reliability index using in AASHTO and OHBDC codes 177
6.2.2. Target reliability index using in Euro code 180
6.2.3. Target reliability index using in JCSS and other codes 182
6.3. Effective target reliability index for highway bridges 183
6.4. Application of the predefined reliability index for the practical design 185
6.5. Conclusions 186
Chapter 7. Summary, conclusions and recommendations 187
7.1. Summary and conclusions 187
7.2. Recommendation for future research 195
Bibliography 197
Figure 2-1. The collapse of the Ynys-y-Gwas Bridge in UK in 1985 34
Figure 2-2. The collapse of the Silver Bridge in USA in 1967 35
Figure 2-3. The collapse of the Mianus River Bridge USA in 1983 35
Figure 2-4. Mechanism of thin oxide formation 38
Figure 2-5. Corrosion of shear reinforcements under environmental agents 40
Figure 2-6. Electrochemical process of tendon corrosion 42
Figure 2-7. Incomplete grouting process leading the corrosion 44
Figure 2-8. Corrosion of anchorages 45
Figure 2-9. The duct corrosion and bleed water void 45
Figure 2-10. Typical grout void inside the duct 46
Figure 2-11. Hydrogen generation inside the pit 49
Figure 3-1. Elevation of Back-Jun Bridge in Korea 56
Figure 3-2. Critical section at midspan 56
Figure 3-3. Critical section at support (diaphragm) 57
Figure 3-4. Moment diagram due to dead load 58
Figure 3-5. Moment diagram due to live load 58
Figure 3-6. Shear diagram due to live load 59
Figure 3-7. Tendon detail for maximum positive moment section at the external mid-span 63
Figure 3-8. Calculation of residual area of a pitted bar 63
Figure 3-9. The discretization of girder into elements 69
Figure 3-10. The stress redistribution between wires in the tendon 71
Figure 3-11. Computational procedure for failure analysis of pitting corrosion 72
Figure 3-12. Distribution of shear reinforcement area 75
Figure 3-13. Deterioration of reliability index for shear capacity 75
Figure 3-14. Distribution of tendon area 76
Figure 3-15. Deterioration of reliability index for moment capacity 76
Figure 3-16. Deterioration of reliability index for fracture resistance 78
Figure 3-17. Reliability index for tendon fracture with values of diameter 78
Figure 3-18. Reliability index for tendon fracture with different values of pitting factor 80
Figure 3-19. Deterioration of reliability index after tendons failure 80
Figure 3-20. Failure process of PC girder with 1000 samples 82
Figure 3-21. Failure process of PC girder with 5000 samples 83
Figure 3-22. Failure process of PC girder with 10000 samples 83
Figure 3-23. Histogram of the time to failure of the critical element from the program started until the time of failure 84
Figure 3-24. Histogram of the reliability index of the critical element during the failure process 84
Figure 3-25. Histogram of tendon area loss of critical element from the program started until the time of failure 85
Figure 3-26. Distribution of reliability index of each element over the length of girder (horizontal axis: element number, vertical axis: reliability index) 86
Figure 3-27. Failure process of the PC box girder with β＝4 88
Figure 3-28. Failure process of the PC box girder with β＝4.5 88
Figure 3-29. Failure process of the PC box girder with β＝5 89
Figure 3-30. Histogram of tendon area loss with the reliability index level β＝4 89
Figure 3-31. Histogram of tendon area loss with the reliability index level β＝4.5 90
Figure 3-32. Histogram of tendon area loss with the reliability index level β＝5 90
Figure 3-33. The loss of tendon area with 30% corroded tendon in 45 year according to ductile model (wire diameter D＝12.7 mm) 93
Figure 3-34. Failure process of girder according to the brittle and ductile model 93
Figure 4-1. Transverse cross-section of the bridge 112
Figure 4-2. Geometry of the cross-section of the RC girder 112
Figure 4-3. Shear reinforcement at intervals of the RC girder 113
Figure 4-4. Optimal design variables: X₂ - X5 vs. target reliability indices(이미지참조) 117
Figure 4-5. Optimal design variables: X₁ and X₂ vs. target reliability indices 118
Figure 4-6. Example 1: comparison of the two results with respect to design variables 119
Figure 4-7. Example 2: comparison of the two results with respect to design variables 120
Figure 4-8. Example 3: comparison of the two results with respect to design variables 122
Figure 4-9. Comparison of results (example 1) 123
Figure 4-10. Comparison of results (example 2) 124
Figure 4-11. Comparison of results (example 3) 125
Figure 4-12. Loading condition and tendon profile for the simply-supported PC I-beam 126
Figure 4-13. Geometry of the cross-section and notation for the design variables 126
Figure 4-14. Design variables vs. span length 133
Figure 5-1. The torsion moment due to truck load 140
Figure 5-2. Geometry design variables 143
Figure 5-3. The tendon envelope 144
Figure 5-4. Calculation of residual area of a pitted bar 152
Figure 5-5. The tendon area versus target reliability indices 155
Figure 5-6. Shear and torsion reinforcements versus target reliability indices 156
Figure 5-7. Actual reliability indices versus target reliability indices 158
Figure 5-8. Optimal total costs versus target reliability indices 160
Figure 5-9. Total Costs versus span lengths with different levels of target reliability indices 160
Figure 5-10. Total Costs versus span lengths and target reliability indices 161
Figure 5-11. Actual reliability indices versus span lengths 161
Figure 5-12a. Typical cross section and design variables of steel box girder bridge 164
Figure 5-12b. Corrosion of steel box girder bridge 164
Figure 5-13. Graph of design variables vs. span length 170
Figure 5-14. Graph of total coats versus span length and target reliability indices 171
Figure 5-15. Graph of optimal cost with different level of target reliability indices 172
Figure 5-16. Combination effects of span length and target reliability indices 173
Figure 6-1. Load effect, resistance and safety margin probability distribution functions 177
Figure 6-2. Target reliability index for moment for non-LRFD and calibrated LRFD AASHTO code 178
Figure 6-3. Target reliability index for shear for non-LRFD and calibrated LRFD AASHTO code 178
Figure 6-4. Target reliability index for moment for non-LRFD and calibrated LRFD OHBDC code 179
Figure 6-5. Target reliability index for moment for non-LRFD and calibrated LRFD OHBDC code 179
Figure 6-6. Target reliability index using in Euro, Spain and AASHTO LRDF codes 180
Figure 6-7. Combination effects of span lengths and target reliability indices for PC bridges 184
Figure 6-8. Combination effects of span length and target reliability indices for steel bridges 185
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