Structural Reliability in Civil Engineering
Description
Structural Reliability in Civil Engineering gives essential insights into the complexities of uncertainty in engineered structures, along with practical examples and advanced methods, making it an invaluable resource for both theory and real-world application in your civil engineering projects.
Uncertainties are associated with the design, evaluation, and dynamic analysis of engineered structures. Structural Reliability in Civil Engineering introduces a developmental overview and basic concepts of reliability theory, uncertainty analysis methods, reliability calculation methods, numerical simulation methods of reliability, system reliability analysis methods, time-varying structural reliability, load and load combination methods, the application of reliability in specifications, and the application of reliability theory in practical engineering. This book not only discusses reliability theory in civil structural engineering but also presents valuable examples to illustrate the application of reliability theory to practical questions and comprehensively elaborates on some theories related to reliability from a brand-new perspective.
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Persons
Wei-Liang Jin, PhD, is a professor in the College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China. For a number of years, he has been engaged in research on full life analysis of engineering structures, basic performance of concrete structures, theory of masonry structures, and their applications. He has successfully undertaken over 100 research projects for several organizations and has published over 500 papers, ten academic monographs, and three textbooks in domestic and foreign academic journals.
Qian Ye, PhD, is a Lecturer at the School of Civil Engineering and Architecture of Taizhou University, located in Taizhou City, Zhejiang Province. He received his doctoral degree in Structural Engineering from Zhejiang University (Zhejiang Province) in 2013. Since then, he has published nearly 20 academic papers and has led three department-level research projects. His research areas focus on steel structures and offshore floating structures.
Yong Bai, PhD, is a professor and doctoral supervisor in the Institute of Structural Engineering, School of Construction and Engineering, Zhejiang University. He is a member of Zhejiang Province's Hundred Talents Plan and the American Society of Shipbuilding and Marine Engineers. In 2000, he won the Best Paper Award at the International Conference on Ocean Mechanics and Polar Engineering.
Content
List of Figures xiii
List of Tables xix
Preface xxiii
Acknowledgments xxv
Notations xxvii
1 Introduction 1
1.1 An Overview of the Development of Structural Reliability Theory 3
1.1.1 Method of the Degree of Reliability Calculated 3
1.1.2 Reliability Method of Structural Systems 10
1.1.3 Load and Load Combination Method 10
1.1.4 Engineering Applications 15
1.2 Basic Concepts 16
1.2.1 Reliability and Degree of Reliability 16
1.2.2 Uncertainty 17
1.2.3 Random Variables, Random Functions and Random Processes 18
1.2.4 Functional Function and Limit State Equation 18
1.2.5 Reliability Index and Failure Probability 19
1.2.6 Member Reliability and System Reliability 20
1.2.7 Time-Dependent Reliability and Time-Independent Reliability 20
1.3 Contents of this Book 21
References 21
2 Method of Uncertainty Analysis 33
2.1 Classification of Uncertainty 34
2.1.1 Classification on Uncertainty Type 34
2.1.2 Classification on Uncertainty Characteristics 35
2.1.3 Classification on Form of Manifestation 35
2.1.4 Classification on Uncertainty Attributes 36
2.2 Probability Analysis Methods 36
2.2.1 Classical Probability Analysis Method 36
2.2.2 Bayes Probability Method 37
2.3 Fuzzy Mathematical Analysis Method 37
2.3.1 Definition 37
2.3.2 Mode of Expression 39
2.4 Gray Theory Analysis Method 40
2.4.1 Basic Concept 40
2.4.2 Case Study 41
2.5 Relative Information Entropy Analysis Method 43
2.6 Artificial Intelligence Analysis Method 45
2.6.1 Neural Networks 45
2.6.2 Support Vector Machine 47
2.7 Example: Risk Evaluation of Construction with Temporary Structure Formwork Support 53
2.7.1 Basic Information of the Formwork Support Structure 53
2.7.2 Establishment of Construction Risk Evaluation System 54
2.7.3 Index Weighting 57
2.7.4 Expert Scoring Results and Risk Evaluation Grades 59
2.7.5 Evaluation of a Fastener-Type Steel Pipe Scaffold 61
2.7.6 Discussion and Summary Analysis 65
References 65
3 Reliability Analysis Method 67
3.1 First-Order Second-Moment Method 71
3.1.1 Central Point Method 71
3.1.2 Checking Point Method 74
3.1.3 Evaluation 78
3.2 Second-Order Second-Moment Method 79
3.2.1 Breitung Method 79
3.2.2 Laplace Asymptotic Method 82
3.2.3 Maximum Entropy Method 85
3.2.4 Optimal Quadratic Approximation Method 90
3.3 Reliability Analysis of Random Variables Disobeying Normal Distribution 92
3.3.1 R-F Method 93
3.3.2 Rosenblatt Transformation 94
3.3.3 P-H Method 97
3.4 Responding Surface Method 99
3.4.1 Response Surface Methodology for Least Squares Support Vector Machines (LS-SVM) 101
3.4.2 Examples 105
References 113
4 Numerical Simulation for Reliability 115
4.1 Monte-Carlo Method 116
4.1.1 Generation of Random Numbers 118
4.1.2 Test of Random Number Sequences 120
4.1.3 Generation of Non-Uniform Random Numbers 120
4.2 Variance Reduction Techniques 121
4.2.1 Dual Sampling Technique 122
4.2.2 Conditional Expectation Sampling Technique 123
4.2.3 Importance Sampling Technique 123
4.2.4 Stratified Sampling Method 126
4.2.5 Control Variates Method 127
4.2.6 Correlated Sampling Method 128
4.3 Composite Important Sampling Method 129
4.3.1 Basic Method 129
4.3.2 Composite Important Sampling 132
4.3.3 Calculation Steps 135
4.4 Importance Sampling Method in V Space 136
4.4.1 V Space 136
4.4.2 Importance Sampling Area 138
4.4.3 Importance Sampling Function 141
4.4.4 Simulation Procedure 143
4.4.5 Evaluation 143
4.5 SVM Importance Sampling Method 144
References 145
5 Reliability of Structural Systems 147
5.1 Failure Mode of Structural System 148
5.1.1 Structural System Model 148
5.1.2 Solution 152
5.1.3 Idealization of Structural System Failure 155
5.1.4 Practical Analysis of Structural System Failure 160
5.2 Calculation Methods for System Reliability 161
5.2.1 System Reliability Boundary 161
5.2.2 Implicit Limit State-Response Surface 169
5.2.3 Complex Structural System 173
5.2.4 Physically-Based Synthesis Method 180
5.3 Example: Reliability of Offshore Fixed Platforms 181
5.3.1 Overview 181
5.3.2 Calculation Model and Single Pile Bearing Capacity 182
5.3.3 Probability Analysis for the Bearing Capacity of a Single Pile 187
5.3.4 Bearing Capacity and Reliability of Offshore Platform Structural Systems 191
5.4 Analysis on the Reliability of a Semi-Submersible Platform System 197
5.4.1 Overview 197
5.4.2 Uncertainty Analysis 199
5.4.3 Evaluation of System Reliability 200
5.4.3.1 Analytical Process and Evaluation 200
5.4.3.2 Reliability Calculation of Main Components 202
5.4.3.3 Reliability Calculation for Local Nodes 204
5.4.3.4 Calculation of Overall Platform Reliability 206
References 207
6 Time-Dependent Structural Reliability 211
6.1 Time Integral Method 214
6.1.1 Basic Concept 214
6.1.2 Time-Dependent Reliability Transformation Method 217
6.2 Discrete Method 218
6.2.1 Known Number of Discrete Events 219
6.2.2 Unknown Number of Discrete Events 221
6.2.3 Return Period 222
6.2.4 Risk Function 223
6.3 Calculation of Time-Dependent Reliability 225
6.3.1 Introduction 225
6.3.2 Sampling Methods for Unconditional Failure Probability 227
6.3.3 First-Order Second-Moment Method 229
6.4 Structural Dynamic Analysis 230
6.4.1 Randomness of Structural Dynamics 230
6.4.2 Some Problems Involving Stationary Random Processes 231
6.4.3 Random Response Spectrum 233
6.5 Fatigue Analysis 234
6.5.1 General Formulas 234
6.5.2 S-N Model 235
6.5.3 Fracture Mechanics Model 237
6.5.4 Example: Fatigue Reliability of an Offshore Jacket Platform 238
6.5.5 Example: Fatigue Reliability of a Submarine Pipeline and Analysis of its Parameters 249
6.5.5.1 Introduction 249
6.5.5.2 Analytical Process 249
6.5.5.3 Finite Element Model 250
6.5.5.4 Random Lift Model 250
6.5.5.5 Structural Modal Analysis 253
6.5.5.6 Random Vibration Response of Suspended Pipelines 254
6.5.5.7 Random Fatigue Life and Fatigue Reliability Analysis of a Suspended Pipeline 257
6.5.5.8 Sensitivity Analysis of Random Vibration Influencing Factors of a Suspended Pipeline 260
6.5.6 Example: Fatigue Reliability of Deep-Water Semi-Submersible Platform Structures 267
6.5.6.1 Analytical Process for Fatigue Reliability 267
6.5.6.2 Fatigue Reliability Analysis of Key Platform Joints 267
6.5.6.3 Sensitivity Analysis of Fatigue Parameters 276
References 281
7 Load Combination on Reliability Theory 285
7.1 Load Combination 286
7.1.1 General Form 286
7.1.2 Discrete Random Process 289
7.1.3 Simplified Method 292
7.2 Load Combination Factor 296
7.2.1 Peak Superposition Method 297
7.2.2 Crossing Analysis Method 298
7.2.3 Combination Theory with Poisson Process as a Simplified Model 300
7.2.4 Square Root of the Sum of the Squares (SRSS) 302
7.2.5 Use of a Combination of Local Extrema to Form a Maximum Value 302
7.3 Calculation of Partial Coefficient of Structural Design 308
7.3.1 Expression of Design Partial Coefficient 309
7.3.2 Determination of Partial Coefficient in Structural Design 310
7.3.3 Determination of Load/Resistance Partial Coefficient 311
7.4 Determination of Load Combination Coefficient and Design Expression 314
7.4.1 Design Expression Using Combined Value Coefficients 315
7.4.2 No Reduction Factor in the Design Expression 317
7.4.3 Method for Determining Load Combination Coefficient in Ocean Engineering 320
7.5 Example: Path Probability Model for the Durability of a Concrete Structure 323
7.5.1 Basic Concept 323
7.5.2 Multipath Probability Model 325
7.5.3 Probability Prediction Model Featuring Chloride Erosion 327
7.5.4 Probability Prediction Model for Concrete Carbonation 328
7.5.5 Probability Prediction Model under the Combined Action of Carbonation and Chloride Ions 331
7.5.6 Corrosion Propagation in a Steel Bar 332
7.5.7 Cracking of the Protective Layer and Determination of Crack Width 334
7.5.8 Bearing Capacity of Corroded Concrete Components 335
7.5.9 Engineering Example 337
7.5.9.1 Corrosion of Steel Bars in a Chloride Environment 337
7.5.9.2 Corrosion of Steel Bar Under the Combined Action of Carbonation and Chloride Corrosion 342
References 348
8 Application of Reliability Theory in Specifications 353
8.1 Requirements of Structural Design Codes 356
8.1.1 Requirements of Structural Design 356
8.1.2 Classification of Actions 357
8.1.3 Target Reliability 358
8.1.4 Limit State of Structural Design 361
8.2 Expression of Structural Reliability in Design Specifications 363
8.2.1 Design Expression of Partial Coefficients 363
8.2.2 Design Expression of Ultimate Limit State 365
8.2.3 Design Expression of Serviceability Limit State 367
8.2.4 Design Expression of Durability Limit State 368
8.3 Example: Target Reliability and Calibration of Bridges 371
8.3.1 Basic Issues 371
8.3.2 Parameter Analysis 372
8.3.3 Calibration Target Reliability 374
8.3.4 Operating Conditions and Parameters 375
8.3.5 Load Effect Ratio 375
8.3.6 Reliability Calibration Process 378
8.3.7 Results of Reliability Calibration Calculation 379
8.4 Reliability Analysis of Human Influence 381
8.4.1 Parameters of Human Influence 381
8.4.2 Influence of Human Error on Construction 383
8.4.3 Human Error Rate, and Degree and Distribution of Human Error Influence 384
8.4.4 Simulation of Human Error in Construction 387
8.4.5 Example: Support System for a Ten-Storey Beamless Floor Structure 394
8.4.6 Discussion 398
References 398
Index 403
Notations
a Current crack length in Fracture mechanics model A Deflection of structural systems; Experience adjustment coefficient aa The limit on crack length under certain functions after bearing secondary cyclic loads within its designed service life Aeff Effective sample area Alimit Maximum deflection of structural system a0 Initial crack length Aq Gross area of pile tip As Surface area of pile body Awhole Sampling area B Proposition supported by new experimental results b(X) Stress at any position in the structural system BQ Deviation coefficient of Q BSC Deviation coefficient of SC C Test constants in Fracture
Effect coefficient for converting load into effect
The specified limits for the structure or component body to meet the requirements for normal use CkX Kurtosis coefficient CL Lift coefficient of wave force CsX Skewness coefficient d Truncated values in truncated distribution functions D Fatigue damage
Outer diameter of pile
Effects caused by dead load Effects caused by the average value of dead load Df Structural damage area dij Fatigue damage due to wave, low or high frequency combination stress Si under the sea case i and the wave direction j DS Safety region of stochastic process in the whole life of structure de The displacement vector of all nodes in the element E Standard value effect of seismic loads EF Error factor Ei Subjective uncertainty ejk Error term due to spatial averaging Ek Plastic failure of the first failure mode f Surface friction force per unit area f(X) Joint density function of variables X(=(x1, x2, ., xn)) fGray(z) The built-in function of gray variable fHi Zero crossing rate of high-frequency mooring force fi Average zero crossing rate Fi ith failure mode fk Standard values of material properties fLi Zero crossing rate of low-frequency mooring force fwi Wave zero crossing rate ft Concrete tensile strength Fij ith failed component in the jth failure mode Fmax X Cumulative distribution function of X at maximum value FMi(x) Cumulative distribution function for maximum load effects of various combinations FN(n) Cumulative distribution function in time integration method fR() Probability density function for the whole structure fR(t) Instantaneous probability density function of structural time-varying resistance fRi() Probability density function of the strength of the i-th link frsf (x) Response surface function Fs Structural failure function fS(t) Instantaneous probability density function of time-varying load effects fX(x, t) Probability density function with time-varying state Probability density function of Xi at xi point Conditional probability density function under given condition X2|X1 g() Functional function space composed of single limit state function G() Functional function space composed of multiple limit state functions Gi The importance of subjective uncertainty Gmax Maximum allowable stress of structural system H(?) Frequency response function h(x) Importance sampling probability density function for the variable x H(x) Shannon entropy Hk Characteristic wave height hT(t) Risk function hN(n) Risk function in time integration method hV() Importance sampling probability density function for the variable v i Radius of gyration I Total error of commonly used J Jacobian matrix K Structural stiffness
Traditional model describing the fatigue life of components or structures under constant stress amplitude
Lateral earth pressure coefficient k Initial modulus of soil KA The ratio of actual and standard values of geometric features of structural components Ka Rankine active earth pressure coefficient Klimit Ultimate structural stiffness K0 Coefficient of static earth pressure l Number of support vectors in SVM L Effects caused by live load Unit length Li Persistent live load lij Number of ith effective mode under jth condition LN(n) Reliability function in time integration method Effect caused by the average distribution of live load at any time point Lr Standard value effect of roof live load
Temporary live load The effect caused by the average distribution of the maximum service life of live load m Random variables in Traditional model describing the fatigue life of components or structures under constant stress amplitude
Test constants in fracture mechanics model mE Influence degree of human error Mi The magnitude of subjective uncertainty Mj Plastic resistance moment in the jth segment n Number of components in the ith failure mode in the failure mode method
number of times a given load is applied in a time integration method N Total number of structural failures/sampling simulations N(s) Relationship between material fatigue parameters Nc Dimensionless bearing capacity coefficient of cohesive soil ni Actual number of cycles under stress amplitude Si Ni Number of stress cycles at constant stress amplitude nL Number of...
