A generalized complex variable method for multiple tunnels at great depth considering the interaction between linings and surrounding rock

The mechanical analysis of multiple tunnels at great depth is an extremely common problem in practical engineering. Previous studies usually used the Schwarz alternating method to solve the multiple-tunnel problem with an iterative scheme, which resulted in low efficiency and precision. To this end, this paper presents a non iterative analytical method to calculate the mechanical field of multiple lined tunnels. In this method, the analytic function is expanded by Laurent series on each tunnel boundary so that the stress and displacement fields in the whole multiply-connected domain can be expressed accurately. The conformal mappings of different tunnels are independent of each other, which makes it convenient to deal with multiple arbitrary-shaped boundaries. The basic equations for solving the mechanical fields are obtained according to the contact conditions and stress boundary conditions. In the solving process, the Fourier transform method is used to transform the boundary conditions into the frequency equations. Compared with the Schwarz alternating method, our method can directly obtain the high-quality result without any iteration. Finally, several examples are given to verify the accuracy and effectiveness of the proposed method.