Global sensitivity analysis of reliability of structural bridge system

Abstract

The article deals with the analysis of the probability of failure of a load-bearing steel bridge member under bending. The focus is on fatigue failure caused by stress cycles from multiple repeated traffic loading on the bridge. Failure is defined by the occurrence of a fatigue crack of critical size. Crack propagation and the fatigue limit state are described using linear fracture mechanics. The failure probability is a function of the equivalent stress range, initial crack length, Paris exponent, number of load cycles (stress changes) increasing over time and other input random variables. The failure probability is evaluated in time steps and then studied using a new type of global sensitivity analysis subordinated to contrasts. The results of the sensitivity analysis show that the first (second) dominant variable is the equivalent stress range (initial crack length) at any given point in time of the bridge operation. Strong main effect of equivalent stress range is associated with higher values of failure probability at the end of the lifetime of the bridge. Small values of failure probability are strongly influenced by interactions among input variables, which cannot be expressed as the sum of main effects of the individual input variables. The main and higher-order indices of each input variable are supplemented by displaying its total index. The direct goal of probability and sensitivity analysis is structural reliability. Sensitivity analysis confirms and deepens the knowledge gained from the time-dependent probability analysis. The numerical example illustrates the rationality of probability-oriented sensitivity indices and the feasibility of their estimation using Latin Hypercube Sampling (LHS). In addition, structural reliability is studied using Bayesian probability, which identifies the times for planning bridge inspections.