(A) novel reliability-based design optimization for PC and steel box girder bridges with emphasis on general and pitting corrosions

다국어 초록 (Multilingual Abstract)

Recently, many sudden collapses of post-tensioned concrete bridges due to the corrosion have been recorded in the world. The corrosion of tendons can seriously affect the reliability of the structure and can reduce its strength resistance, resulting in system failure. Structural damage can occur intermediately at any time, without any warning sign and it is difficult to prevent. Moreover, the cost for the corrosion detection and repairing of highway bridges is high, especially for steel bridges. It is reported that the annual corrosion costs of highway bridges reach to $10 billion each year in US, which is 37% of the total corrosion cost of the infrastructure system.
It can be classified that the corrosion of bridges into two types: uniform corrosion and local corrosion or pitting corrosion. However, the pitting corrosion particularly occurred in post-tensioned tendon and caused the sudden failure. The pitting corrosion not only causes the loss of sectional area of the tendon but also changes its mechanical property. The post-tensioned tendon becomes more brittle after the absorption of atomic hydrogen and possibly damages due to the stress corrosion cracking.
The modern reliability analysis methods have been really developed since the late 1960s. However, the development of reliability analysis theory is completed and available for application by the early 1980s. Recently, many modern design codes for bridges are developed basing on probabilistic models of loads and resistance such as AASHTO LRFD code, Eurocode and CHBDC. Over many centuries of development, the reliability analysis is now an advanced and efficient method when most of structural analysis, design, and optimization problems are nondeterministic.
This study develops the probabilistic models and approaches for analyzing the structural reliability for highway bridges with considering the environmental stressor. The time-variant probabilistic models that express the real failure of bridges in the world due to the corrosion phenomenon were applied for existing and new highway bridges. Effective approaches for solving highway bridges reliability analysis were derived in terms of first, second order approximation and Matlab optimization toolbox. For existing bridges, the time-variant probabilistic model is proposed and applied for a PC box girder bridge to analyze the failure due to the corrosion of shear reinforcements, tendons and the stress corrosion cracking. Three models including the ductile, ductile-brittle and brittle models are proposed to evaluate most dangerous failure mode as well as explain the sudden collapse of PC bridges with the lifetime of structure is over 30 years. Moreover, the stochastic data including the loss of tendon area due to the stress corrosion cracking of tendon are recommended for estimating existing PC bridges as well as the RBDO of new PC bridges. For new bridges, the RBDO analyses are performed for the PC box and steel box girder bridges. Probabilistic constraints are formulated according to AASHTO LRFD code. The range of target reliability index for ultimate limit state is proposed in terms the framework of RBDO. The range of target reliability index, which has been used in the modern bridge design specifications such as AASHTO, Euro, JCSS codes and other codes, will be investigated. These two ranges are compared to clarify the range of target reliability index that commonly uses in bridge engineering design by the RBDO concept. Furthermore, the range of target reliability index as well as the predefined reliability index is recommended for the practical design guideline of PC and steel box girder bridges. In general, the safety of PC and steel box girder bridges is analyzed, predicted and possibly account by advantages of RBDO approaches to reduce the sudden collapse of PC bridges as well as the great finance for repairing/replacing the damage of steel box girder bridges.

목차 (Table of Contents)

• Acknowledgements iv
• Abstract vi
• Table of contents x
• List of tables xv
• List of figures xviii
• Chapters
• 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
• 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 of post-tensioned tendon 40
• 2.4.1. Pitting corrosion mechanism 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
• 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 reinforcement 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 72
• 3.5 Analysis results and discussion 73
• 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 95
• 4 Efficiently approaches for reliability analysis and reliability-based design optimization of structures 96
• 4.1 Introduction 96
• 4.2 First order approximation for 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 with equality reliability constraints 114
• 4.4.1.2 Example 2 Design for minimizing the total cost (initial and failure cost) with equality reliability constraints 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
• 5 Time variant reliability-based design optimization of highway bridges 135
• 5.1 Introduction 135
• 5.2 RBDO of the 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 bridges 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
• 6 Effective target reliability index for bridges 175
• 6.1 Introduction 175
• 6.2 Background of the target reliability index for highway bridges 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 Summary and conclusions 186
• 7 Summary, conclusions and recommendations 187
• 7.1 Summary and conclusions 187
• 7.2 Recommendations for future research 195
• 8 Bibliography 197