Analytical solution for a deep tunnel with arbitrary cross section in a transversely isotropic rock mass

摘要

Deep tunnels such as wells and highway tunnels are common geotechnical structures, and it is of interest to derive analytical solutions in studying the stability and safety of tunnels. But, it remains a hard challenge due to the theoretical and practical complexity. Analytical solution for a circular tunnel under different boundary conditions have been studied, respectively, by Poulos and Davis [1], Pender [2], Carter and Booker [3], and Verruijt [4]. Exadaktylos gave the analytical solution for the case of a semi-circular tunnel in an infinite elastic body [5]. Muskhelishvili and Cai derived the analytical solution for an elliptical tunnel subject to the different boundary conditions [6,7]. Lu and Zhang obtained the analytical solution for a tunnel with the arbitrary cross section under different ground stress conditions [8,9].