Time-variant reliability analysis of underground structures against delayed failure based on the probability density evolution method

The unpredictable delayed failure of underground tunnels may occur after excavation due to the time-dependent behavior of surrounding rock mass, which brings a new consideration to the reliability evaluation of underground structures. In this study, a time-variant reliability analysis procedure via the probability density evolution method (PDEM) is proposed for underground tunnels against delayed failure. The creep-damage theory is introduced to model the time-dependent behavior of rock materials. A new energy-based stability criterion is developed to identify the structural delayed failure. By applying the PDEM with the absorbing boundary condition, the time-varying reliability of underground structures can be obtained. The proposed procedure is applied to a case study involving the deep tunnel with uncertain material parameters. Numerical results demonstrate that the inherent variability of rock properties could result in the large fluctuation of structural delayed responses, which has a significant influence on the time-varying reliability of the tunnels.