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Cover of Bridge Assessment Beyond the AS 5100 Deterministic Methodology
Bridge Assessment Beyond the AS 5100 Deterministic Methodology
  • Publication no: AP-R617-20
  • ISBN: 978-1-925854-95-4
  • Published: 13 March 2020

Bridge assessments to AS 5100 express safety as a binary (yes/no) measure. The management of bridges deemed unsafe using this deterministic method is outside the scope of the standard. From international practice, the most holistic approach that provides quantifiable measures of safety is the probabilistic approach or structural reliability method.

This report investigates the use of probability-based bridge assessment (PBBA) as a viable option for bridge assessment beyond the AS 5100 deterministic methodology. First, the implied safety levels of a selected set of historical and contemporary bridges most prevalent in the Australian bridge inventory were obtained. Then, the current safety levels of these bridges under as-of-right (HML) road freight access were quantified. Ultimate bending and shear limit states for the superstructures were considered.

It was found that a reserve in safety exists compared to deterministic measures for some bridge designs. Further, rational asset management decisions can be based on the quantified safety metric. This demonstrates the benefit of using PBBA as the higher-tier bridge safety assessment framework. This framework provides more fit-for-purpose assessments, better utilising bridge assets, thereby facilitating an optimally productive road transport network.

  • Summary
  • Glossary
  • 1. Introduction
    • 1.1 Background
    • 1.2 Purpose
    • 1.3 Scope
    • 1.4 Outline
  • 2. Probability-Based Bridge Assessments
    • 2.1 Overview
      • 2.1.1 Comparison to Deterministic Approach
      • 2.1.2 Probability of Failure and Reliability Index β
      • 2.1.3 Comparison to Codes of Practice
      • 2.1.4 Acceptable Level of Safety
    • 2.2 International Adoption
      • 2.2.1 United Kingdom
      • 2.2.2 United States
      • 2.2.3 Europe
      • 2.2.4 Australia/New Zealand
  • 3. Framework for Bridge Assessment Beyond the Deterministic Method
    • 3.1 Overview
    • 3.2 Framework Demonstration
      • 3.2.1 Representative Bridges Subset
      • 3.2.2 Modes of Failure (Limit States)
      • 3.2.3 Traffic Considerations
  • 4. Framework Components
    • 4.1 Limit State Function
      • 4.1.1 Reference Period
    • 4.2 Capacity Uncertainty
      • 4.2.1 Function of Random Variables
      • 4.2.2 Monte Carlo Simulation
    • 4.3 Loading Uncertainty
      • 4.3.1 Uncertainty in Permanent Loads
      • 4.3.2 Uncertainty in Maximum Transient Loads
    • 4.4 Other Uncertainties
      • 4.4.1 Model Errors
      • 4.4.2 Dynamic Load Allowance
    • 4.5 Bridge Assessment and the Reliability Index
      • 4.5.1 Structural Reliability Index
      • 4.5.2 Structural Reliability Method
    • 4.6 Sensitivity Analysis
    • 4.7 Acceptability
  • 5. Example Application
    • 5.1 Capacity Uncertainty
    • 5.2 Loading Uncertainty
      • 5.2.1 Step 1: Code-Implied Safety
      • 5.2.2 Step 2: Current Safety
    • 5.3 Deterministic Approach: Rating Factor
    • 5.4 Beyond the Deterministic Approach: Structural Reliability Index
      • 5.4.1 Step 1: Code-Implied Safety
      • 5.4.2 Step 2: Current Safety
    • 5.5 Sensitivity Analysis (Importance Coefficients)
      • 5.5.1 Step 1: Code-Implied Safety
      • 5.5.2 Step 2: Current Safety
    • 5.6 Conclusions
  • 6. Results and Discussion
    • 6.1 Code-Implied Safety
      • 6.1.1 Annual Structural Reliability Indices
      • 6.1.2 Rating Factors vs. Reliability Index
      • 6.1.3 Sensitivity Analysis (Importance Coefficients)
      • 6.1.4 Discussion
    • 6.2 Current Safety
      • 6.2.1 Annual Structural Reliability Indices
      • 6.2.2 Rating Factors vs. Reliability Index
      • 6.2.3 Sensitivity Analysis (Importance Coefficients)
      • 6.2.4 Discussion
  • 7. Conclusions
    • 7.1 Main Findings
    • 7.2 Limitations
    • 7.3 Further Research
    • 7.4 Final Remarks
  • References
  • Appendix A Overview of Probability and Structural Reliability Analysis
    • A.1 Limit State Functions
    • A.2 Random Variables
      • A.2.1 Probability Distributions
      • A.2.2 Distribution Fitting
      • A.2.3 Correlations
      • A.2.4 Stochastic Variables
    • A.3 Structural Reliability Methods
    • A.4 Structural Reliability Index (β)
    • A.5 Sensitivity Analysis
      • A.5.1 Importance Coefficients
    • A.6 Time-dependent Reliability
    • A.7 Applications
      • A.7.1 Safety Factor Calibration
      • A.7.2 Higher-Tier Bridge Assessments
  • Appendix B Target Reliability Index Selection
    • B.1 Economic Optimisation Approach
      • B.1.1 Consequences of Failure
      • B.1.2 Relative Cost of Safety Measures
    • B.2 Life Quality Index
    • B.3 Additional Considerations
    • B.4 Summary
  • Appendix C Justification for Selected Bridge Families
    • C.1 Material Type
    • C.2 Structural Form
    • C.3 Number of Lanes
    • C.4 Span Length
    • C.5 Design Codes and Load Models
    • C.6 Case Studies
  • Appendix D Traffic Flows (Step 2)
  • Appendix E Step 1 Methodology
    • E.1 Overview
    • E.2 Capacity Methodology
      • E.2.1 Establishing Bridge Section Properties
      • E.2.2 Probability Distribution of Capacity using Correlated Monte Carlo Simulation
    • E.3 Loading Methodology
      • E.3.1 Design Loads
      • E.3.2 Finite Element Models
      • E.3.3 Probabilistic Distribution of Loading
    • E.4 Reliability Analysis
  • Appendix F Step 2 Methodology
    • F.1 Overview
    • F.2 Vehicle Fleet
    • F.3 Traffic Simulation
      • F.3.1 Methodology
    • F.4 Loading
      • F.4.1 Influence Lines
      • F.4.2 Probability Distribution of Traffic Loading
    • F.5 Reliability Analysis
  • Appendix G Bridge Capacity
    • G.1 Structural Models for Assessment of Capacity
      • G.1.1 Model for Ultimate Bending Capacity assessment
      • G.1.2 Model for Ultimate Shear Capacity Assessment
    • G.2 Characteristic Capacity and Probability Distributions
      • G.2.1 MS18 designed U-Slabs Bending Capacity Distribution
      • G.2.2 MS18 designed PSC Planks Bending Capacity Distribution
      • G.2.3 MS18 designed I-girders Bending Capacity Distribution
      • G.2.4 T44 designed I-girders Bending Capacity Distribution
      • G.2.5 T44 designed Precast Tee Slabs Bending Capacity Distribution
      • G.2.6 T44 designed Super-T girders Bending Capacity Distribution
      • G.2.7 SM1600 designed Super-T girders Bending Capacity Distribution
      • G.2.8 MS18 designed U-Slabs Shear Capacity Distribution
      • G.2.9 MS18 designed PSC Planks Shear Capacity Distribution
      • G.2.10 MS18 designed I-girders Shear Capacity Distribution
      • G.2.11 T44 designed I-girders Shear Capacity Distribution
      • G.2.12 T44 designed Precast Tee Slabs Shear Capacity Distribution
      • G.2.13 T44 designed Super-T girders Shear Capacity Distribution
      • G.2.14 SM1600 designed Super-T girders Bending Capacity Distribution
  • Appendix H Bridge Load Effects
    • H.1 Finite Element Models
      • H.1.1 Representative Bridges Decks Cross-Sections
    • H.2 Characteristic Load Effects
    • H.3 Influence Lines
      • H.3.1 MS18 designed U-Slabs
      • H.3.2 MS18 designed PSC Planks
      • H.3.3 S18 designed I-girders
      • H.3.4 T44 designed I-girder
      • H.3.5 T44 designed Precast Tee Slabs
      • H.3.6 T44 designed Super-T girder
      • H.3.7 SM1600 designed Super-T girder
    • H.4 Probability Distributions (Step 2)
      • H.4.1 MS18 designed U-Slabs Maximum Annual Bending Moment Distribution
      • H.4.2 MS18 designed PSC Planks Maximum Annual Bending Moment Distribution
      • H.4.3 MS18 designed I-girders Maximum Annual Bending Moment Distribution
      • H.4.4 T44 designed I-girders Maximum Annual Bending Moment Distribution
      • H.4.5 T44 designed Precast Tee Slabs Maximum Annual Bending Moment Distribution
      • H.4.6 T44 designed Super-T girders Maximum Annual Bending Moment Distribution
      • H.4.7 SM1600 designed Super-T girders Maximum Annual Bending Moment Distribution
      • H.4.8 MS18 designed U-Slabs Maximum Annual Shear Force Distribution
      • H.4.9 MS18 designed PSC Planks Maximum Annual Shear Force Distribution
      • H.4.10 MS18 designed I-girders Maximum Annual Shear Force Distribution
      • H.4.11 T44 designed I-girders Maximum Annual Shear Force Distribution
      • H.4.12 T44 designed Precast Tee Slabs Maximum Annual Shear Force Distribution
      • H.4.13 T44 designed Super-T girders Maximum Annual Shear Force Distribution
      • H.4.14 SM1600 designed Super-T girders Maximum Annual Shear Force Distribution
      • H.4.15 Summary Tables
  • Appendix I Model Errors
    • I.1 Bending Capacity Model Error
    • I.2 Shear Capacity Model Error
    • I.3 Loading Model Error
  • Appendix J Step 1 (Code-Implied Safety) Results
    • J.1 Ultimate Bending
      • J.1.1 Annual Structural Reliability Indices
      • J.1.2 Importance Coefficients
    • J.2 Ultimate Shear
      • J.2.1 Annual Structural Reliability Indices
      • J.2.2 Importance Coefficients
  • Appendix K Step 2 (Current Safety) Results
    • K.1 Ultimate Bending
      • K.1.1 Annual Structural
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