Reliability analysis of face stability for tunnel excavation in a dependent system

From a practical perspective, it is necessary to consider multivariate failure mechanisms in reliability analysis. The multivariate in a system may be dependent on each other, which should be considered in reliability analysis. To investigate the reliability of a structural system, this study develops a copula-based approach to construct dependence structures of different failure mechanisms. Herein, a novel two-step parameter estimation method based on a hybrid-evolution Markov chain Monte Carlo (MCMC) algorithm has been developed to estimate copula parameters with high accuracy and less bias. To verify the validity and robustness of proposed method, the face stability issue in shield tunneling has been used as an illustrative example. Results indicate that: (1) the novel two-step parameter estimation method yields reasonable parameter values; (2) the calculated values based on copula model are more accurate than Nataf model in practical engineering; (3) the failure probability pf calculated by copula model is obviously different (almost over 50% in both examples) from Independent scenario. The proposed reliability analysis using the copula model provides guidelines for face stability control under uncertainty and randomness, which can reduce the failure probability ahead of time and mitigate risk magnitudes to some degree after failure occurrence.