Time-Variant Reliability of Brittle Structural Systems

This paper proposes a failure path approach for time-variant system reliability estimation of brittle structures. The significant failure sequences are identified by the branch-and-bound method, and the damage states in these sequences are grouped together into discrete damage levels ranging from intact structure to system collapse. The grouping is based on the number of degrees of redundancy in the structure as it accumulates different amounts of damage. The Markov chain assumption is used to model the cumulative damage under time-varying loads. The expressions for transition probabilities from one damage level to another are derived. The effect of load overlapping under multiple load processes is investigated. The method is applicable to large structures due to the systematic failure sequence identification strategy employed. The resultant probability transition matrix is found to be more compact and to represent the accumulation of damage better than existing methods. Two numerical examples are used to illustrate and examine the proposed method.