Time-Dependent Reliability Analysis of Deep Tunnel in the Viscoelastic Burger Rock with Sequential Installation of Liners

The behavior of deep tunnel is usually time dependent due to the sequential construction process as well as the rheological characteristic of the rock mass. Moreover, the uncertainty of different parameters such as the viscoelastic properties can play an essential role on the stability of tunnel and its supports. The reliability analysis based on the probabilistic approach, which has been largely applied in the last 2 decades to treat this kind of problems, presents an efficient tool but its application is usually limited in case of time-independent behavior of tunnel supported by a single liner. This study aims at assessment of time-dependent reliability of deep circular tunnel counting for rheological characteristic of rock mass and sequential construction of liners. Since the reliability analysis, using direct Monte Carlo Simulation and a FEM software could be very time-consuming, we establish firstly a closed form solution for the response of a deep tunnel excavated in the viscoelastic Burger rock accounting for the sequential installation of two liners. The validation of this analytical solution is performed by comparing the results of this solution with some previous existing analytical solutions as well as with numerical results obtained from the finite element simulation in some case studies. Once validated, this analytical solution is used as a fast tool for the time-dependent reliability analysis by direct Monte Carlo Simulation. The influence of different parameters on the probability of failure of a double liners tunnel in respect with its life service, by taking into account of the sequential construction, was discussed in the last part of the paper.