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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
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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Veröffentlichungsjahr: 2025
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Table of Contents
Cover
Table of Contents
Series Page
Title Page
Copyright Page
List of Figures
List of Tables
Preface
Acknowledgments
Notations
1 Introduction
1.1 An Overview of the Development of Structural Reliability Theory
1.2 Basic Concepts
1.3 Contents of this Book
References
2 Method of Uncertainty Analysis
2.1 Classification of Uncertainty
2.2 Probability Analysis Methods
2.3 Fuzzy Mathematical Analysis Method
2.4 Gray Theory Analysis Method
2.5 Relative Information Entropy Analysis Method
2.6 Artificial Intelligence Analysis Method
2.7 Example: Risk Evaluation of Construction with Temporary Structure Formwork Support
References
3 Reliability Analysis Method
3.1 First-Order Second-Moment Method
3.2 Second-Order Second-Moment Method
3.3 Reliability Analysis of Random Variables Disobeying Normal Distribution
3.4 Responding Surface Method
References
4 Numerical Simulation for Reliability
4.1 Monte-Carlo Method
4.2 Variance Reduction Techniques
4.3 Composite Important Sampling Method
4.4 Importance Sampling Method in V Space
4.5 SVM Importance Sampling Method
References
5 Reliability of Structural Systems
5.1 Failure Mode of Structural System
5.2 Calculation Methods for System Reliability
5.3 Example: Reliability of Offshore Fixed Platforms
5.4 Analysis on the Reliability of a Semi-Submersible Platform System
References
6 Time-Dependent Structural Reliability
6.1 Time Integral Method
6.2 Discrete Method
6.3 Calculation of Time-Dependent Reliability
6.4 Structural Dynamic Analysis
6.5 Fatigue Analysis
References
7 Load Combination on Reliability Theory
7.1 Load Combination
7.2 Load Combination Factor
7.3 Calculation of Partial Coefficient of Structural Design
7.4 Determination of Load Combination Coefficient and Design Expression
7.5 Example: Path Probability Model for the Durability of a Concrete Structure
References
8 Application of Reliability Theory in Specifications
8.1 Requirements of Structural Design Codes
8.2 Expression of Structural Reliability in Design Specifications
8.3 Example: Target Reliability and Calibration of Bridges
8.4 Reliability Analysis of Human Influence
References
Index
Also of Interest
End User License Agreement
List of Tables
Chapter 2
Table 2.1 Representation of membership function.
Table 2.2 Digital representation of gray scale.
Table 2.3 Indices and weights of a risk evaluation system for fastener-type st...
Table 2.4 Rating scale table.
Table 2.5 Weighting of individual differences.
Table 2.6 Expert ratings.
Table 2.7 Correlation matrix for each index in the D-layer; relative weight an...
Table 2.8 Relative weighting and correlation coefficient matrix of materials a...
Table 2.9 Relative weight and correlation matrix of index.
Chapter 3
Table 3.1 Relationship between reliability index and failure probability
P
f
.
Table 3.2 Comparison of results.
Table 3.3 Probabilistic characteristics of the random variables in Example 3.
Table 3.4 LS-SVM learning results.
Table 3.5 Probabilistic characteristics of random variables in Example 4.
Table 3.6 Effect of sample numbers on calculated results.
Chapter 4
Table 4.1 Simulation results of σ
1
versus σ when
G
(
X
)=3.0 -
x.
Table 4.2 Results of different sampling simulation methods.
Table 4.3 Relationship between area ratio of sampling ellipse δ
0
and k
0
.
Chapter 5
Table 5.1 Soil parameters.
Table 5.2 Uncertainty of soil parameters.
Table 5.3 Understanding the soil calculation model.
Table 5.4 Bearing capacity of a single pile.
Table 5.5 Bearing capacity under different supporting boundary conditions.
Table 5.6 Statistical results for shear capacity and simulation of the structu...
Table 5.7 Failure probability obtained by different reliability calculation me...
Table 5.8 Wave parameters for a 100-year-return period.
Table 5.9 Data on sectional force and bending moment of each working condition...
Table 5.10 Data for limit state parameters in each working condition.
Table 5.11 Calculated variable distribution types.
Table 5.12 Stochastic models of calculated variables.
Table 5.13 Reliability index and failure probability of a semi-submersible pla...
Table 5.14 Calculated values for sectional force of semi-submersible platform ...
Table 5.15 Resistance parameters for semi-submersible structural joints.
Table 5.16 Reliability data for local nodes.
Table 5.17 Overall reliability of target platform.
Chapter 6
Table 6.1 Statistical standard deviation of high frequency mooring force range...
Table 6.2 Statistical standard deviation of low frequency mooring force range.
Table 6.3 Mooring force discovery series under different effective wave height...
Table 6.4 Wave ocean state distribution.
Table 6.5 Low-frequency moving force cycles.
Table 6.6 False damage and false life of the main pipe joints.
Table 6.7 Design parameters of a submarine pipeline.
Table 6.8 Calculated case.
Table 6.9 Structural modal analysis results.
Table 6.10 Fatigue life and failure probability of a suspended pipeline in dif...
Table 6.11 Fatigue life and failure probability of a pipeline under different ...
Table 6.12 Fatigue life and failure probability of a pipeline at different wav...
Table 6.13 Fatigue life and failure probability of pipeline at different water...
Table 6.14 Fatigue life and failure probability of pipelines with different di...
Table 6.15 Fatigue life and failure probability of pipeline at different resid...
Table 6.16 Wave dispersion map of the South China Sea (ΣP=100).
Table 6.17 Fatigue reliability analysis parameters in the
S-N
curve method.
Table 6.18 Fatigue reliability analysis parameters for fracture mechanics.
Table 6.19 Fatigue reliability index and failure probability of key nodes base...
Table 6.20 Fatigue reliability index and failure probability of key nodes base...
Table 6.21
S-N
curves in different environments.
Table 6.22 Fatigue reliability index of key nodes at the No. 1 connection for ...
Chapter 7
Table 7.1 Different state combinations that cause crossing.
Table 7.2 Parameters of various random loads.
Table 7.3 Concentration of chloride ion on a concrete surface.
Table 7.4 Distribution of the standard value of compressive strength of a conc...
Table 7.5 Calculation parameters and distribution types.
Table 7.6 Calculation parameters and distribution types.
Chapter 8
Table 8.1 Target reliability index of current building structures in China.
Table 8.2 Factor for importance of structure
γ
0
.
Table 8.3 Load adjustment coefficient of service life for structural design
γL
...
Table 8.4 Signs of durability limit state of various structures
[8-16]
.
Table 8.5 Annual target reliability and failure probability of bearing capacit...
Table 8.6 Annual target reliability and failure probability of the serviceabil...
Table 8.7 Calibration operating condition.
Table 8.8 Function distribution and parameters *.
Table 8.9 Load ratio.
Table 8.10 Recommended cost for reliability calibration.
Table 8.11 Statistical data for geometric parameter uncertainty
K
A
.
Table 8.12 Geometric size distribution of components without the influence of ...
Table 8.13 Standard deviation of concrete strength.
Table 8.14 Estimation criterion for error coefficient EF.
Table 8.15 Human error rate and distribution parameters for degree of influenc...
Table 8.16 Influence of different human errors on the buckling strength of for...
Table 8.17 Occurrence of human error.
Table 8.18 Distribution of tightening torque on bolts in different parts.
Table 8.19 Average value of skid resistance for fasteners under different bolt...
Table 8.20 Comparison of failure probability.
List of Illustrations
Chapter 2
Figure 2.1 Three types of transfer function.
Figure 2.2 Diagram of two-layer BP neural netbook structures.
Figure 2.3 Diagram of support vectors.
Figure 2.4 Diagram of regression support vector machine.
Figure 2.5 Fuzzineation of score values.
Figure 2.6 Membership function of the evaluation grade.
Chapter 3
Figure 3.1 Diagram of structure failure probability.
Figure 3.2 Responding surface function.
Figure 3.3 Response surface method based on LS-SVM.
Figure 3.4 Number of FEM calculations.
Figure 3.5 Portal frame calculation diagram.
Figure 3.6 Calculation diagram for Example 4.
Chapter 4
Figure 4.1 Probability density function with truncated distribution.
Figure 4.2 Approximate parabolic surface of
V
space.
Figure 4.3 Important sampling area of
V
space.
Figure 4.4 Relationship between principal curvature k and sampling elliptic pa...
Figure 4.5 Influence of different confidence
a
on simulation results.
Chapter 5
Figure 5.1 Load-path relationship.
Figure 5.2 Different strength-deformation (R-A) relations.
Figure 5.3 Fault tree.
Figure 5.4 Event tree of structure.
Figure 5.5 Failure diagram of structure.
Figure 5.6 Series system.
Figure 5.7 Two-dimensional failure region for reliability problem of structura...
Figure 5.8 Two simple parallel systems.
Figure 5.9 Condition system.
Figure 5.10 The impact of correlation on system security indications.
Figure 5.11 Simple experimental design of two variables.
Figure 5.12 Systematic enumeration process.
Figure 5.13 t ∼ z curve.
Figure 5.14 Q ∼ Z curve.
Figure 5.15 P-y curve of soil.
Figure 5.16 p-y curve of sandy soil.
Figure 5.17 Calculation model of pile.
Figure 5.18 Load-bearing capacity under axial compression.
Figure 5.19 Load-bearing capacity under axial tension.
Figure 5.20 Lateral bearing capacity with different pile top constraints.
Figure 5.21 Deterministic analysis of computational structure model.
Figure 5.22 Shear and bending bearing capacity and structural placement diagra...
Figure 5.23 Statistical results and probability analysis of bearing capacity.
Figure 5.24 3D FEM model of a semi-submersible platform.
Figure 5.25 Analysis of structural reliability of a semi-submersible platform.
Figure 5.26 Reliability evaluation procedure for a semi-submersible platform.
Chapter 6
Figure 6.1 Sample function of random process of load effect.
Figure 6.2 Sample function and failure time of safety limit state process
Z
(
t
)...
Figure 6.3 Transcendence of random process vector
X(t).
Figure 6.4 Sample function of nonstationary load effect and resistance.
Figure 6.5 Sample function of load effect and resistance (when resistance is c...
Figure 6.6 Typical risk function.
Figure 6.7 Variation trend of risk function in different structural stage.
Figure 6.8 Sample functions of vector stochastic processes.
Figure 6.9 Sample function and spectral density of random process.
Figure 6.10 Probability density function of Rayleigh distribution.
Figure 6.11 Analysis on the relationship between input and output spectral den...
Figure 6.12 Coordinate system of a single point mooring offshore jacket platfo...
Figure 6.13 Structural model of a BZ28-1 SPM platform.
Figure 6.14 Prototype cross section of an oil pipeline.
Figure 6.15 Foree spectrum of pipeline nodes.
Figure 6.16 Power spectrum of pipeline midspan displacement response.
Figure 6.17 Linear and nonlinear calculation of maximum stress spectrum of mid...
Figure 6.18 Vibration displacement response spectrum of pipeline at different ...
Figure 6.19 Vibration stress response spectrum of pipeline at different water ...
Figure 6.20 Pipeline reliability index and peak stress spectrum at different w...
Figure 6.21 Vibration displacement response spectra of pipelines with differen...
Figure 6.22 Vibration stress response spectrum of pipelines with different dia...
Figure 6.23 Reliability index and peak stress spectrum of pipelines with diffe...
Figure 6.24 Vibration displacement response spectrum of pipeline at different ...
Figure 6.25 Vibration stress response spectrum of pipeline at different residu...
Figure 6.26 Pipeline reliability index and peak stress spectrum at different r...
Figure 6.27 Fatigue reliability analysis process for deep-water semi-submersib...
Figure 6.28 Fatigue reliability analysis for a deep-water semi-submersible pla...
Figure 6.29 Schematic diagram of the connection between the platform column an...
Figure 6.30 Comparison of calculated results for fatigue reliability index.
Chapter 7
Figure 7.1 The combination of random process.
Figure 7.2 Typical sample function of mixed rectangular update stochastic proc...
Figure 7.3 Borges process combination.
Figure 7.4 TR combination diagram of three load combinations.
Figure 7.5 Process combination of three rectangular wave.
Figure 7.6 Comparison of several combination rules.
Figure 7.7 Flow chart of specification method 1.
Figure 7.8 Flow chart of specification method 2.
Figure 7.9 Corrosion path model.
Figure 7.10 Corrosion multi-path model.
Figure 7.11 Carbonation diagram.
Figure 7.12 Curve of pH value and critical chloride concentration.
Figure 7.13 Simulated flow diagram.
Figure 7.14 Bridge structural status.
Figure 7.15 Number of cracks in piers.
Figure 7.16 PDF of main rebars.
Figure 7.17 CPDF of main rebars.
Figure 7.18 PDF of corrosion-induced crack width.
Figure 7.19 CPDF of corrosion-induced crack width.
Figure 7.20 Time-dependent CPDF of main rebar.
Figure 7.21 Time-dependent CPDF of corrosion-induced crack width.
Figure 7.22 Structural damage to the bridge.
Figure 7.23 PDF of chloride threshold value.
Figure 7.24 PDF of time to corrosion initiation of main rebars.
Figure 7.25 PDF of time to crack initiation of concrete.
Figure 7.26 PDF of corrosion ratio of main rebars.
Figure 7.27 CPDF of corrosion ratio of main rebars.
Figure 7.28 PDF of corrosion-induced crack width.
Figure 7.29 CPDF of corrosion-induced crack width.
Chapter 8
Figure 8.1 Limit state of structural design.
Figure 8.2 Wind speed span-time rate distribution curve of a bridge.
Figure 8.3 Calibration process.
Figure 8.4 Human error event tree.
Figure 8.5 Block diagram of human error simulation program for E3 and E7.
Figure 8.6 Block diagram of human error simulation programs for E1(a), E1(b) a...
Figure 8.7 Human error simulation program block diagram for E8 and E9.
Figure 8.8 Flow chart for structural system reliability calculation in constru...
Figure 8.9 Influence of human error.
Guide
Cover Page
Table of Contents
Series Page
Title Page
Copyright Page
List of Figures
List of Tables
Preface
Acknowledgments
Notations
Begin Reading
Index
Also of Interest
WILEY END USER LICENSE AGREEMENT
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Scrivener Publishing100 Cummings Center, Suite 541JBeverly, MA 01915-6106
Publishers at ScrivenerMartin Scrivener ([email protected])Phillip Carmical ([email protected])
Structural Reliability in Civil Engineering
Wei-Liang Jin
Qian Ye
and
Yong Bai
This edition first published 2025 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA© 2025 Scrivener Publishing LLCFor more information about Scrivener publications please visit www.scrivenerpublishing.com.
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Library of Congress Cataloging-in-Publication Data
ISBN 978-1-119-41815-3
Front cover images supplied by Adobe FireflyCover design by Russell Richardson
List of Figures
Figure 2.1 Three types of transfer function.
Figure 2.2 Diagram of two-layer BP neural netbook structures.
Figure 2.3 Diagram of support vectors.
Figure 2.4 Diagram of regression support vector machine.
Figure 2.5 Fuzzineation of score values.
Figure 2.6 Membership function of the evaluation grade.
Figure 3.1 Diagram of structure failure probability.
Figure 3.2 Responding surface function.
Figure 3.3 Response surface method based on LS-SVM.
Figure 3.4 Number of FEM calculations.
Figure 3.5 Portal frame calculation diagram.
Figure 3.6 Calculation diagram for Example 4.
Figure 4.1 Probability density function with truncated distribution.
Figure 4.2 Approximate parabolic surface of V space.
Figure 4.3 Important sampling area of V space.
Figure 4.4 Relationship between principal curvature k and sampling elliptic parameters
a
,
b
and
k
(
β
=3, Δ
β
=1.0, δ
0
=0.8).
Figure 4.5 Influence of different confidence
a
on simulation results.
Figure 5.1 Load-path relationship.
Figure 5.2 Different strength-deformation (R-A) relations.
Figure 5.3 Fault tree.
Figure 5.4 Event tree of structure.
Figure 5.5 Failure diagram of structure.
Figure 5.6 Series system.
Figure 5.7 Two-dimensional failure region for reliability problem of structural system.
Figure 5.8 Two simple parallel systems.
Figure 5.9 Condition system.
Figure 5.10 The impact of correlation on system security indications.
Figure 5.11 Simple experimental design of two variables.
Figure 5.12 Systematic enumeration process.
Figure 5.13 t ∼ z curve.
Figure 5.14 Q ∼ Z curve.
Figure 5.15 P-y curve of soil.
Figure 5.16 p-y curve of sandy soil.
Figure 5.17 Calculation model of pile.
Figure 5.18 Load-bearing capacity under axial compression.
Figure 5.19 Load-bearing capacity under axial tension.
Figure 5.20 Lateral bearing capacity with different pile top constraints.
Figure 5.21 Deterministic analysis of computational structure model.
Figure 5.22 Shear and bending bearing capacity and structural placement diagram.
Figure 5.23 Statistical results and probability analysis of bearing capacity.
Figure 5.24 3D FEM model of a semi-submersible platform.
Figure 5.25 Analysis of structural reliability of a semisubmersible platform.
Figure 5.26 Reliability evaluation procedure for a semisubmersible platform.
Figure 6.1 Sample function of random process of load effect.
Figure 6.2 Sample function and failure time of safety limit state process
Z
(
t
).
Figure 6.3 Transcendence of random process vector
X(t).
Figure 6.4 Sample function of nonstationary load effect and resistance.
Figure 6.5 Sample function of load effect and resistance (when resistance is constant).
Figure 6.6 Typical risk function.
Figure 6.7 Variation trend of risk function in different structural stage.
Figure 6.8 Sample functions of vector stochastic processes.
Figure 6.9 Sample function and spectral density of random process.
Figure 6.10 Probability density function of Rayleigh distribution.
Figure 6.11 Analysis on the relationship between input and output spectral density function of offshore platform structure.
Figure 6.12 Coordinate system of a single point mooring offshore jacket platform.
Figure 6.13 Structural model of a BZ28-1 SPM platform.
Figure 6.14 Prototype cross section of an oil pipeline.
Figure 6.15 Foree spectrum of pipeline nodes.
Figure 6.16 Power spectrum of pipeline midspan displacement response.
Figure 6.17 Linear and nonlinear calculation of maximum stress spectrum of midspan section of suspended pipeline for various cases.
Figure 6.18 Vibration displacement response spectrum of pipeline at different water depths.
Figure 6.19 Vibration stress response spectrum of
Figure 6.20 Pipeline reliability index and peak stress spectrum at different water depths.
Figure 6.21 Vibration displacement response spectra of pipelines with different diameters.
Figure 6.22 Vibration stress response spectrum of pipelines with different diameters.
Figure 6.23 Reliability index and peak stress spectrum of pipelines with different outer diameters.
Figure 6.24 Vibration displacement response spectrum of pipeline at different residual stresses.
Figure 6.25 Vibration stress response spectrum of pipeline at different residual stresses.
Figure 6.26 Pipeline reliability index and peak stress spectrum at different residual stresses.
Figure 6.27 Fatigue reliability analysis process for deep-water semi-submersible platform structure.
Figure 6.28 Fatigue reliability analysis for a deep-water semisubmersible platform.
Figure 6.29 Schematic diagram of the connection between the platform column and the transverse brace.
Figure 6.30 Comparison of calculated results for fatigue reliability index.
Figure 7.1 The combination of random process.
Figure 7.2 Typical sample function of mixed rectangular update stochastic process with given probability density function.
Figure 7.3 Borges process combination.
Figure 7.4 TR combination diagram of three load combinations.
Figure 7.5 Process combination of three rectangular wave.
Figure 7.6 Comparison of several combination rules.
Figure 7.7 Flow chart of specification method 1.
Figure 7.8 Flow chart of specification method 2.
Figure 7.9 Corrosion path model.
Figure 7.10 Corrosion multi-path model.
Figure 7.11 Carbonation diagram.
Figure 7.12 Curve of pH value and critical chloride concentration.
Figure 7.13 Simulated flow diagram.
Figure 7.14 Bridge structural status.
Figure 7.15 Number of cracks in piers.
Figure 7.16 PDF of main rebars.
Figure 7.17 CPDF of main rebars.
Figure 7.18 PDF of corrosion-induced crack width.
Figure 7.19 CPDF of corrosion-induced crack width.
Figure 7.20 Time-dependent CPDF of main rebar.
Figure 7.21 Time-dependent CPDF of corrosion-induced crack width.
Figure 7.22 Structural damage to the bridge.
Figure 7.23 PDF of chloride threshold value.
Figure 7.24 PDF of time to corrosion initiation of main rebars.
Figure 7.25 PDF of time to crack initiation of concrete.
Figure 7.26 PDF of corrosion ratio of main rebars.
Figure 7.27 CPDF of corrosion ratio of main rebars.
Figure 7.28 PDF of corrosion-induced crack width.
Figure 7.29 CPDF of corrosion-induced crack width.
Figure 8.1 Limit state of structural design.
Figure 8.2 Wind speed span-time rate distribution curve of a bridge.
Figure 8.3 Calibration process.
Figure 8.4 Human error event tree.
Figure 8.5 Block diagram of human error simulation program for E3 and E7.
Figure 8.6 Block diagram of human error simulation programs for E1(a), E1(b) and E2.
Figure 8.7 Human error simulation program block diagram for E8 and E9.
Figure 8.8 Flow chart for structural system reliability calculation in construction period under the influence of human errors.
Figure 8.9 Influence of human error.
List of Tables
Table 2.1 Representation of membership function.
Table 2.2 Digital representation of gray scale.
Table 2.3 Indices and weights of a risk evaluation system for fastener-type steel pipe formwork support construction.
Table 2.3 Indices and weights of a risk evaluation system for fastener-type steel pipe formwork support construction.
Table 2.4 Rating scale table.
Table 2.5 Weighting of individual differences.
Table 2.6 Expert ratings.
Table 2.7 Correlation matrix for each index in the D-layer; relative weight and correlation coefficient matrix of fastener and pole index.
Table 2.8 Relative weighting and correlation coefficient matrix of materials and erection indices.
Table 2.9 Relative weight and correlation matrix of index.
Table 3.1 Relationship between reliability index and failure probability
P
f
.
Table 3.2 Comparison of results.
Table 3.3 Probabilistic characteristics of the random variables in Example 3.
Table 3.4 LS-SVM learning results.
Table 3.5 Probabilistic characteristics of random variables in Example 4.
Table 3.6 Effect of sample numbers on calculated results.
Table 4.1 Simulation results of σ
1
versus σ when
G
(
X
)=3.0 -
x.
Table 4.2 Results of different sampling simulation methods.
Table 4.3 Relationship between area ratio of sampling ellipse δ
0
and k
0
.
Table 5.1 Soil parameters.
Table 5.2 Uncertainty of soil parameters.
Table 5.3 Understanding the soil calculation model.
Table 5.4 Bearing capacity of a single pile.
Table 5.5 Bearing capacity under different supporting boundary conditions.
Table 5.6 Statistical results for shear capacity and simulation of the structure.
Table 5.7 Failure probability obtained by different reliability calculation methods.
Table 5.8 Wave parameters for a 100-year-return period.
Table 5.9 Data on sectional force and bending moment of each working condition.
Table 5.10 Data for limit state parameters in each working condition.
Table 5.11 Calculated variable distribution types.
Table 5.12 Stochastic models of calculated variables.
Table 5.13 Reliability index and failure probability of a semisubmersible platform.
Table 5.14 Calculated values for sectional force of semisubmersible platform node.
Table 5.15 Resistance parameters for semi-submersible structural joints.
Table 5.16 Reliability data for local nodes.
Table 5.17 Overall reliability of target platform.
Table 6.1 Statistical standard deviation of high frequency mooring force range.
Table 6.2 Statistical standard deviation of low frequency mooring force range.
Table 6.3 Mooring force discovery series under different effective wave heights.
Table 6.3 Mooring force discovery series under different effective wave heights.
Table 6.4 Wave ocean state distribution.
Table 6.5 Low-frequency moving force cycles.
Table 6.6 False damage and false life of the main pipe joints.
Table 6.7 Design parameters of a submarine pipeline.
Table 6.8 Calculated case.
Table 6.9 Structural modal analysis results.
Table 6.10 Fatigue life and failure probability of a suspended pipeline in different cases.
Table 6.11 Fatigue life and failure probability of a pipeline under different span lengths.
Table 6.12 Fatigue life and failure probability of a pipeline at different wave heights.
Table 6.13 Fatigue life and failure probability of pipeline at different water depths.
Table 6.14 Fatigue life and failure probability of pipelines with different diameters.
Table 6.15 Fatigue life and failure probability of pipeline at different residual stresses.
Table 6.16 Wave dispersion map of the South China Sea (ΣP=100).
Table 6.17 Fatigue reliability analysis parameters in the
S-N
curve method.
Table 6.18 Fatigue reliability analysis parameters for fracture mechanics.
Table 6.19 Fatigue reliability index and failure probability of key nodes based on the
S-N
curve method.
Table 6.20 Fatigue reliability index and failure probability of key nodes based on fracture mechanics.
Table 6.21
S-N
curves in different environments.
Table 6.22 Fatigue reliability index of key nodes at the No. 1 connection for different
S-N
curves.
Table 7.1 Different state combinations that cause crossing.
Table 7.2 Parameters of various random loads.
Table 7.3 Concentration of chloride ion on a concrete surface.
Table 7.4 Distribution of the standard value of compressive strength of a concrete cube.
Table 7.5 Calculation parameters and distribution types.
Table 7.6 Calculation parameters and distribution types.
Table 8.1 Target reliability index of current building structures in China.
Table 8.2 Factor for importance of structure
γ
0
.
Table 8.3 Load adjustment coefficient of service life for structural design
γ
L
.
Table 8.4 Signs of durability limit state of various structures.
Table 8.5 Annual target reliability and failure probability of bearing capacity limit state.
Table 8.6 Annual target reliability and failure probability of the serviceability limit state.
Table 8.7 Calibration operating condition.
Table 8.8 Function distribution and parameters *.
Table 8.9 Load ratio.
Table 8.10 Recommended cost for reliability calibration.
Table 8.11 Statistical data for geometric parameter uncertainty
K
A
.
Table 8.12 Geometric size distribution of components without the influence of human factors.
Table 8.13 Standard deviation of concrete strength.
Table 8.14 Estimation criterion for error coefficient EF.
Table 8.15 Human error rate and distribution parameters for degree of influence.
Table 8.16 Influence of different human errors on the buckling strength of formwork support systems.
Table 8.17 Occurrence of human error.
Table 8.18 Distribution of tightening torque on bolts in different parts.
Table 8.19 Occurrence of human error.
Table 8.20 Distribution of tightening torque on bolts in different parts.
Table 8.21 Average value of skid resistance for fasteners under different bolt tightening torques.
Table 8.22 Comparison of failure probability.
Preface
Engineering structural reliability refers to the ability of a structure to complete predetermined functions within a specified time and under specified conditions, while the degree of structural reliability is a mathematical measure of reliability. According to the definition, the reliability of engineering structures should include three aspects: the first is the part of the structure itself, including structural resistance, structural type, and structural reuse; the second is the external effects that the structure is subjected to, including direct, indirect, and combined effects on the structure; the third involves the basic methods of structural reliability, including the calculation method of reliability, analysis of system reliability, and calculation of dynamic reliability. Therefore, the reliability of engineering structures mainly involves the basic methods of reliability, which is also the main content of this book.
The theoretical research on structural reliability flourished in the 1970s with the transition of structural design codes from the allowable stress design method to the probability-based limit state design method, while the domestic research work was relatively synchronized with the foreign research. However, in terms of basic theoretical research on structural reliability, there is a significant gap between the domestic research and the foreign research, which is basically modified according to the foreign regulatory systems, which means it is in a “running” stage compared to similar international research. With the continuous deepening of understanding and research on structural reliability theory in the domestic academic and engineering communities, especially the great discussion on structural reliability in the 1990s, it is necessary to consider both the theoretical system of structural specifications based on reliability and the practical functional requirements of structures in the application of engineering structures. This is mainly reflected in the formulation of unified standards for structural design reliability in the early 20th century. Changing “the structural reliability” to “the degree of structural reliability” is the biggest highlight of the unified standard formulation, which means it is in the “parallel” stage with similar international research. With the continuous progress of research on structural reliability theory by Chinese scientific and technological workers, and the deepening understanding of engineering structural reliability issues by engineering technicians, the establishment of China’s regulatory system and the application of engineering structural reliability will be more perfect, and it is fully possible to achieve a “leading” stage compared to similar international research. This is also the purpose of writing this book.
This book consists of eight chapters, mainly introducing the development overview and basic concepts of the basic theory of reliability, uncertainty analysis methods, reliability calculation methods, simulation methods of reliability, system reliability analysis, 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 can be used as a textbook and teaching reference for graduate and senior undergraduate students majoring in civil engineering, water conservancy, highway, railway, port, ship and ocean engineering in higher education institutions. It can also be a professional reference book for engineering technicians and scholars engaged in research and design in the fields of civil and industrial architecture, municipal facilities, bridges, roads (highways and railways), port and ocean engineering.
Acknowledgments
I would like to express my gratitude to Professor Guofan ZHAO of Dalian University of Technology in China for introducing me to the research field of structural reliability theory and application. In the future, he will continue to provide strong support and assistance in researching the reliability of marine structures, the durability of concrete structures, and other engineering structures, which I will never forget.
Thank you to Professor Eberhard LUZ from Stuttgart University in Germany for providing me with a relaxed and enjoyable working environment during my Humboldt research work from the autumn of 1991 to 1993, which enabled me to conduct research on uncertainty and numerical simulation of reliability in structural reliability.
Thank you to Professor Torgeir MOAN from Norwegian University of Science and Technology during my Norwegian Research Council’s research work from 1994 to 1995. His extensive knowledge and working environment in marine engineering structures have enabled me to find new breakthroughs in the theory and application of structural reliability.
Thank you to colleagues from China National Offshore Oil Corporation (CNOOC) and the Engineering Reliability Committee of the Chinese Civil Engineering Society (CCES) for achieving reasonable application of structural reliability in structural design specifications, effectively promoting the development of structural reliability theory and application.
Since 1996, when I officially joined Zhejiang University, I have opened a research direction in structural reliability, established a new course called “Structural Reliability”, and trained many doctoral and master’s students. They all play important roles in their respective positions. This book also reflects their research achievements in the field of structural reliability. Here, I would like to express my heartfelt gratitude to them through this book.
I would like to express my special gratitude to Dr. Qian YE and Professor Yong BAI for their joint efforts and writing, which ultimately led to the formation of this manuscript.
The work of this book has received strong support from projects such as the National Natural Science Foundation of China (NSFC) and the Ministry of Science and Technology (MOST) of China; thank you to the teachers and graduate students of the research team on structural reliability at Zhejiang University, as well as to friends from all walks of life for their strong support and assistance in the publication of this book.
Dr. Wei-Liang JIN
Qiushi Distinguished ProfessorZhejiang University, P.R. China
Notations
a
Current crack length in Fracture mechanics model
A
Deflection of structural systems; Experience adjustment coefficient
a
a
The limit on crack length under certain functions after bearing secondary cyclic loads within its designed service life
A
eff
Effective sample area
A
limit
Maximum deflection of structural system
a
0
Initial crack length
A
q
Gross area of pile tip
A
s
Surface area of pile body
A
whole
Sampling area
B
Proposition supported by new experimental results
b(X)
Stress at any position in the structural system
B
Q
Deviation coefficient of Q
B
SC
Deviation coefficient of SC
C
Test constants in FractureEffect coefficient for converting load into effectThe specified limits for the structure or component body to meet the requirements for normal use
C
kX
Kurtosis coefficient
C
L
Lift coefficient of wave force
C
sX
Skewness coefficient
d
Truncated values in truncated distribution functions
D
Fatigue damageOuter diameter of pileEffects caused by dead load
Effects caused by the average value of dead load
D
f
Structural damage area
d
ij
Fatigue damage due to wave, low or high frequency combination stress S
i
under the sea case i and the wave direction j
D
S
Safety region of stochastic process in the whole life of structure
d
e
The displacement vector of all nodes in the element
E
Standard value effect of seismic loads
EF
Error factor
E
i
Subjective uncertainty
e
jk
Error term due to spatial averaging
E
k
Plastic failure of the first failure mode
f
Surface friction force per unit area
f
(
X
)
Joint density function of variables
X
(=(x
1
, x
2
, …, x
n
))
f
Gray
(
z
)
The built-in function of gray variable
f
Hi
Zero crossing rate of high-frequency mooring force
f
i
Average zero crossing rate
F
i
i
th
failure mode
f
k
Standard values of material properties
f
Li
Zero crossing rate of low-frequency mooring force
f
wi
Wave zero crossing rate
f
t
Concrete tensile strength
F
ij
i
th
failed component in the
j
th
failure mode
F
max X
Cumulative distribution function of
X
at maximum value
F
Mi
(
x
)
Cumulative distribution function for maximum load effects of various combinations
F
N
(
n
)
Cumulative distribution function in time integration method
f
R
()
Probability density function for the whole structure
f
R
(
t
)
Instantaneous probability density function of structural time-varying resistance
f
Ri
()
Probability density function of the strength of the
i
-th
link
f
rsf
(
x
)
Response surface function
F
s
Structural failure function
f
S
(
t
)
Instantaneous probability density function of time-varying load effects
f
X
(
x
,
t
)
Probability density function with time-varying state
Probability density function of
X
i
at
x
i
point
Conditional probability density function under given condition X
2
|X
1
g(
•
)
Functional function space composed of single limit state function
G(
•
)
Functional function space composed of multiple limit state functions
G
i
The importance of subjective uncertainty
G
max
Maximum allowable stress of structural system
H
(
ω
)
Frequency response function
h
(
x
)
Importance sampling probability density function for the variable
x
H
(
x
)
Shannon entropy
H
k
Characteristic wave height
h
T
(
t
)
Risk function
h
N
(
n
)
Risk function in time integration method
h
V
()
Importance sampling probability density function for the variable
v
i
Radius of gyration
I
Total error of commonly used
J
Jacobian matrix
K
Structural stiffnessTraditional model describing the fatigue life of components or structures under constant stress amplitudeLateral earth pressure coefficient
k
Initial modulus of soil
K
A
The ratio of actual and standard values of geometric features of structural components
K
a
Rankine active earth pressure coefficient
K
limit
Ultimate structural stiffness
K
0
Coefficient of static earth pressure
l
Number of support vectors in SVM
L
Effects caused by live load Unit length
L
i
Persistent live load
l
ij
Number of
i
th
effective mode under
j
th
condition
L
N
(
n
)
Reliability function in time integration method
Effect caused by the average distribution of live load at any time point
L
r
Standard value effect of roof live loadTemporary 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 amplitudeTest constants in fracture mechanics model
m
E
Influence degree of human error
M
i
The magnitude of subjective uncertainty
M
j
Plastic resistance moment in the
j
th
segment
n
Number of components in the ith failure mode in the failure mode methodnumber 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
N
c
Dimensionless bearing capacity coefficient of cohesive soil
n
i
Actual number of cycles under stress amplitude
S
i
N
i
Number of stress cycles at constant stress amplitude
n
L
Number of basic time periods
n
Li
Low frequency cycles
N
0
Number of cycles that the structure must be able to withstand to meet design requirements
N
q
Dimensionless bearing capacity coefficient of sandy soil
n
Wi
Number of cycles of waves
P
*
Design verification points corresponding to the maximum possible failure probability of the structure
P
(
A
)
Subjective level of belief in proposition
A
Degree of subjective negation of proposition
A
by humans
P
(
A
i
)
Prior probability
P
(
A
i
B
)
Revised posterior probability
p
(
x
i
)
Distribution probability of the
i
th
discrete point of a variable
P
(
error
)
Probability of truncated failure modes
P
f
Structural failure probability
p
f
(
t
)
Instantaneous failure probability at a certain moment
p
f
(
t
L
|
r
)
Conditional failure probability under given structural resistance
p
k
(
t
)
Probability of an event occurring within a time interval
P
0
Effective overburden pressure of soil at calculation point
P
p
(
s
)
Probability distribution of random stress
Pr
(
F
90
)
Probability distribution value with 90% error rate
Pr
(
F
10
)
Probability distribution value with 10% error rate
p
s
Peak factor for variable s in SRSS
P
S
Probability reliability of structures
p
X
Peak factor for variable X in SRSS
q
Unit pile end bearing capacity
Q
Dynamic pile end bearing capacityExternal effects borne by the structure
Q
1
Single parameter load system
Q
f
Friction force of pile body
Given load
Q
i
External load
Q
p
Support force at pile end
R
Structural resistanceStandard value effect of rain load
R
*
Coordinates of design verification points for resistance of structural components
R
(
t
)
Structural time-varying resistance
R
(·)
Resistance function of structural components
R
fL
(
τ
)
Autocorrelation of transverse wave force
r
i
The number of repetitions of variable loads during the design reference periodTotal number of time periods for each load
S
i
(t)
during the design reference period
r
k
Load increment
R
K
Standard value of resistance of structural components
ratio of the
i
th
structural component to the
j
th
load effect
R
XX
(
τ
)
Autocorrelation of stationary stochastic process
R
u
(
τ
)
Autocorrelation of water particle velocity
S
Effect of actionStandard value effect of snow load
SC
Resistance of offshore platform structural systems (ultimate bearing capacity)
S
(
t
)
Time-varying load effectStochastic process of comprehensive effect of n
th
kinds of loads
S
(
ω
)
Stress power spectrum
Extreme distribution of load effects within one year
Maximum load effect in the event
Corresponding load effect of the structure under a given load
S
fL
(
ω
)
Spectral density of transverse wave force
Coordinates of design verification points for dead load
S
GK
Dead load standard value
S
Hi
Hot spot stress amplitude of high-frequency tube nodes under working conditions
S
i
Constant stress amplitude
S
i
(
t
)
i
th
combined load with time-variance
S
i
(
t
)
Stochastic process of the kind of ith load effect Effective mode of the ith structure
S
i
(
t
0
)
Random variable at any time point for the type of ith load effect
Structural failure in the
i
th
effective mode
Large value distribution of load effect during the duration of the
i
th
load effect
S
Li
Low frequency hot spot stress amplitude under working conditions
S
M
Maximum value of load combination
S
M
Maximum comprehensive load
Maximum value of the jth load during the design reference period
S
max
(
t
L
)
The maximum value of load effect within the service life of the structure
Coordinates of design verification points for live loads
S
QK
Live load standard value
S
s
Structural effective
The effect caused by the average distribution of the maximum service life of snow load
Hotspot stress amplitude of working condition waves
S
X
(
ω
)
(mean square) Spectral density
S
u
Shear strength of cohesive soil
S
η
(
ω
)
Spectral density function of ocean waves
T
Return period
T
f
Fatigue life
Return period
t
L
Structural service life
|
T
u
(
ω
)|
Transfer function of horizontal velocity of wave water quality points
u
*
Maximum likelihood points on failure surface in
U
-space.
u
Displacement vector of any point within the element
u
(
t
)
Horizontal velocity of wave water quality points at the depth of the pipeline axis
u
p
Observation points for the overall state of the established
v
Average rate of event occurrence
Crossing rate of vector stochastic process leaving security region
v
i
Occurrence rate
v
i
(
u
)
Crossing rate of stochastic process
X
i
(t)
v
mi
Average arrival rate of mixed stochastic process pulse
Positive crossing zero frequency of stress processes
v
p
Maximum value frequency
w
Parameters related to the strength of all loads acting on the structure in plastic theory
W
Wind load/Effects caused by wind load, creep, shrinkage, or temperature changes
Effect caused by the average distribution of the maximum service life of wind load
x*
Maximum likelihood points on failure surface in
X
-space.
X
Random function
X
=
X
(x
1
, x
2
, …, x
n
)
Support vector in SVM
X
(
t
)
Stationary stochastic process
X
(
t
)
Stochastic process vector
x(t)
Value of
X
(
t
)
Maximum value during the time period
τ
2
X
a
The actual strength or performance of the structural
X
D
The best estimation point for design points
x
E
Parameter value when no one is wrong
X
G
Internal force generated by the standard value of dead load
Internal force caused by live load standard value (i.e. load effect standard value)
X
i
Samples generated by the importance sampling function in SVM
x
m
Parameter value in case of human error
X
m
Mean point
New average point
x
t
Random variable
X
r
Performance that the structure needs to achieve within its designed service life
y*
Maximum likelihood points on failure surface in
Y
-space.
y
50
Displacement value corresponding to strain value
ε
50
z
Local displacement of piles
Z
Structural functional function
[
Z
]
Failure limits in physical synthesis method
Z
(
t
)
Safety limit state process
Maximum value during the time period
τ
1
α
Confidence coefficient of sampling function
α
1
Characteristic parameters of stress spectrum
α
2
Characteristic parameters of stress spectrum
α
c
1
Average axial compressive strength of the concrete
Gamma Function of the concrete
α
i
Sensitivity coefficient
α
k
Standard value of geometric dimensions
β
Reliable indicators
β
ij
Reliability indicator of the
j
th
component under the limit state design expression at the time of the
i
-th
component
β
T
Target reliability indicators
Target reliability index of
i
th
component
γ
D
Partial coefficient of effects caused by dead load
γ
G
Partial coefficient of permanent load
γ
L
Partial coefficient of effects caused by live load
γ
m
Model uncertainty parameters
γ
Q
Partial coefficient of live load
Partial coefficients for variable loads
γ
0
Structural importance coefficient
γ
R
Partial coefficient of resistance for structural components
γ
T
Partial coefficient of effects caused by uneven settlement, creep, shrinkage, or temperature changes
γ
W
Partial coefficient of effects caused by wind load
γ
u
Uncertainty parameters for ultimate strength calculation
δ
Dirac function
δ
0
Effective sampling area ratio (the ratio of effective sampling area to the entire sampling area)
δ
t
Any little time increment
Internal friction angle of sandy soil
Δ
Damage parameters in the linear damage accumulation rule
Δ
i
Relative deflection with Q
i
ΔK
Variation amplitude of stress intensity factor in fracture mechanics model
ΔK
th
Threshold value of change amplitude of stress intensity factor
ΔS
Applied stress amplitude
Δβ
Effective sampling area of sampling function
ε
relative error
ε
50
Strain at 50% maximum stress in undisturbed soil undrained test
η
(
t
)
Wave height function
θ
j
Plastic turning angle of section at the
j
th
point
κ
i
Principal curvature of the failed surface in
i
th
axil
λ
j
Slenderness ratio
λ
BE
Average estimate of the impact of human error
λ
m
The
m
th
order moment of stress spectrum
λ
UB
Maximum estimate of the impact of human error
μ
A
(
x
)
Membership function of A, simply called as
μ
A
(
x
)
Average duration of the
i
th
action
Reduction coefficient of concrete considering brittleness
Average compressive strength of concrete cubes
μ
si
The average value of the distribution of individual load effect sectionsMoment of the maximum value distribution during the design reference period
μ
SM
Average of the distribution of maximum combined effects
μ
st
The mean of the maximum value distribution during the design reference period
μ
i
Average duration of stochastic process
X
i
(t)
μ
Z
Mean value of functional function variable Z
ξ
Gamma function
ρ
Ratio of live load to standard value of dead load
σ
st
The second moment of the maximum value distribution during the design reference period
σ
Z
Mean square deviation of functional function variable Z
τ
i
Pulse duration
υ
X
(
r
)
Wearing rate (average passing rate per unit time)
υ
i
Average occurrence rate of the ith effect
φ
Stability coefficient
φ
[·]
Probability density function of standard Normal distribution
Φ[.]
Cumulation distribution function of standard Normal distribution
ψ
Load combination value coefficient
ψ
C
Combination value coefficient of secondary variable
ψ
ci
Combination value coefficient of the
i
th
variable load
Γ
Stress spectrum width parameter
⊗(
z
)
Grey variables formed by changes in basic variables within a fixed interval
π
(
x
i
/
R
)
Subjectivity of parameter uncertainty
x
i
/R
1Introduction
Civil engineering is the general term for all sciences and technologies involved in the construction of various land engineering facilities. It is a technical discipline that studies engineering facility structures, as well as rock, soil and the environment, and their interaction with engineering facilities. Civil engineering is the cornerstone of national economic development, the bearing structure of all industrial and civil buildings, bridges and aqueducts built across rivers and lakes, breakwaters built in oceans, as well as sea-crossing bridges and offshore platforms. These constructions are primarily made of steel, wood, masonry, concrete and reinforced concrete, and are collectively referred to as engineering structures. They are designed to carry loads consisting of equipment, people and vehicles, and to withstand wind, rain, snow, sunshine, waves, currents, earth pressure and earthquakes. Whether the engineering structure is safe or not has a direct bearing on people’s property, lives, safety and health, as well as on the progress of national modernization. Therefore, an engineering structure should be able to perform a variety of designed functions during its service life, without the need for excessive maintenance, while ensuring the safety, serviceability and durability of the structure. These are the basic concepts of engineering structural reliability [1-1][1-2][1-3].
There are some uncertainties in terms of structural design and use, which will inevitably affect structural resistance and load effect to a certain extent. In the early stages of structural design, people sometimes evaluate the influence of uncertainty on an engineering structure by means of a safety factor. This is also used as an evaluation index for civil engineering, without taking the randomness of these uncertainties into account. In fact, the relationship between safety factor and structural reliability is not all that clear, since structures with the same safety factor may have different levels of reliability. This demonstrates that the safety factor alone cannot accurately reflect the reliability of engineering structures.
Structural reliability is a subject concerning uncertainty research, and is designed to ascertain the effects of uncertainties arising from the entire life cycle of an engineering structure (including design, construction, application and maintenance) on its safety, serviceability and durability. With the development of computational science, engineering structures are required to be increasingly precise and intelligent, but in practice, the design and construction of engineering structures remains an iterative process in the conventional sense, far from being able to meet the needs of social development. If the uncertainty of design parameters is not taken into account, the benefits of accurate structural analysis will be overwhelmed by the use of safety indices determined roughly from experience. Therefore, it is of great significance to take parameter randomness into reasonable consideration during engineering design. Structural engineering should not only meet the pre-defined functional requirements, but also help to save costs as far as possible. This requires paying attention to the uncertainties existing in practical engineering, so that the structure can be designed scientifically using a more rational and realistic method, that is to say, a design method based on structural reliability [1-4][1-5][1-6][1-7][1-8][1-9][1-10][1-11][1-12][1-13].
Moreover, the reliability of in-service structures cannot be ignored either. This is because there are also many uncertainties arising from the construction and use of an engineering structure. These include load uncertainty, environmental uncertainty, resistance uncertainty, and effect uncertainty. Such uncertainties may bring about potential safety hazards, which may in turn lead to structural failure, resulting in a disastrous accident, causing great economic losses and endangering people’s lives and safety [1-14][1-15][1-16][1-17][1-18][1-19][1-20][1-21][1-22]. Therefore, it is imperative to analyze and evaluate the reliability of all engineering structures
