Copula-based system reliability analysis of shallow-buried rectangular tunnels considering groundwater and multiple failure modes

Shallow-buried rectangular tunnels are widely used in urban underpasses because of their favorable structural performance and limited disturbance to existing infrastructure. During construction, however, multiple failure modes may be triggered by uncertainties in geotechnical properties, pore water pressure, and ground load. Existing studies often neglect the explicit role of pore water pressure and rarely account for uncertainty in both the probability distributions and cross-correlation of key geotechnical parameters. This study develops a copula-based system reliability framework for shallow-buried rectangular tunnels by integrating upper-bound limit analysis with probabilistic modeling. Analytical upper-bound solutions for the support pressures associated with vault, sidewall, and invert failures are first derived with pore water pressure and ground load explicitly incorporated. The optimal marginal distributions and copula function for the geotechnical parameters are then identified using model-selection and goodness-of-fit criteria (AIC, BIC, and RMSE), and the resulting joint model is evaluated via copula-based Monte Carlo simulation to quantify component and system failure probabilities. The framework is applied to the Guansheng-Dahe tunnel and complemented by a comprehensive sensitivity analysis. The results show that pore water pressure, marginal distribution choice, and c - φ dependence markedly affect failure probability; among the candidate models, the Weibull marginal combined with the Gaussian Copula provides the most accurate estimates. Importantly, neglecting dependence among component failure modes can underestimate the system failure probability by up to 11.5%, whereas the proposed framework yields a more consistent and realistic assessment for support design in water-bearing soft ground.