Closed-form solution and reliability analysis of deep lined tunnel behavior in anisotropic viscoelastic rock

In this work, a combination effect of anisotropy and uncertainty on the behavior of deep tunnels excavated in the rheological rocks was studied. For this aim, a closed-form solution of deep tunnels in the anisotropic viscoelastic rock was developed in the first stage. Following that, using the well-known complex potential, the analytic solutions of stress and displacement solutions of both the liner and the anisotropic elastic surrounding rock were presented. Then based on the corresponding principle, the closed-form solution of the tunnel excavated in the anisotropic rheological rock characterized by the fractional Maxwell model was deduced. It was shown that the corresponding principle can be accurately applied using the Laplace transform or directly in time domain. The good agreement with finite element solution allows validating the developed solution. In the second stage, the Monte Carlo Simulation was performed, and probabilistic analysis highlighted the uncertainty effect of anisotropic viscoelastic rock parameters and initial stress state on the evolution in time of stress state in the liner. These numerical applications confirmed the essential role of anisotropy and uncertainty on the behavior of tunnel that must be considered on the liner design.