Time-dependent reliability analysis for non-differentiable limit state functions due to discrete load processes

Abstract

In time-dependent structural reliability analysis it is not always the case that the limit state functions are continuous and differentiable. A commonly encountered case is the structures subjected to instantaneous loads with high intensity, such as seismic actions. This paper intends to propose an efficient method for time-dependent reliability analysis of structures with non-differentiable limit state functions. A new formulation is proposed for outcrossing rate based on the minimum value of limit state functions at the time of outcrossing. The developed method also considers the degradation of structural resistance. It is found in the paper that the instantaneous discrete load with high intensity can induce non-differentiable limit state functions and that the probabilistic information of such instantaneous loads significantly affects the time-dependent failure probabilities. The paper concludes that the proposed method can predict the time-dependent failure probability of structures for non-differentiable limit state functions accurately and efficiently. The proposed method contributes to the body of knowledge of time-dependent reliability with wider practical applications.