Fast integration algorithms for time-dependent structural reliability analysis considering correlated random variables

During the service life of civil infrastructures, their performance, functionality, and serviceability are essentially time-dependent reliability problems as both structural resistance and load effect are related with time. With respect to the practical engineering, the performance function is usually complicated, multi-dimensional and implicit and involves both correlated and non-correlated random variables; thus the computational process of time-dependent reliability analysis is relatively challenging. To address this issue, the time-dependent failure probability of structures with complicated, multi-dimensional and implicit performance functions involving correlated random variables is mathematically formulated in this paper. A novel and efficient approach is then proposed to compute the time-dependent failure probability. In the proposed method, the integral of time-dependent failure probability with respect to time domain and random-variate space are estimated by Gauss-Legendre quadrature and point-estimate method based on bivariate dimension-reduction integration, respectively. Accordingly, the time-dependent probability of failure within a given period is decomposed into a series of probabilities of failure with time-dependent random variables at specified time points conditioned on the estimating points of the time-independent random variables, which can be evaluated from state-of-the-art techniques for reliability assessment. The efficiency and accuracy of the proposed method are demonstrated by three numerical examples with either explicit or implicit performance functions involving correlated random variables, in which Monte Carlo simulations are employed for comparison.