Analytical Solution for Stresses and Displacements of Deep Tunnels With Rockbolts Support Subjected to P and SV Waves

Abstract

Rockbolt support is one of the most commonly used reinforcement measures for rock tunnels. It is important to explore the effect of rockbolts on seismic design of tunnel structures, and therefore, a design method is required for the evaluation of such effect, which was, however, still vacant in current studies. In this paper, a novel analytical solution for the seismic response of deep tunnels with rockbolts support subjected to P and SV waves is presented. The rockbolts support region is assumed to be cylindrical and anisotropic based on the equivalent material method, and the ground and liner are considered homogenous, isotropic, and linear elastic. The general solutions for the response of a cylindrical anisotropic layer subjected to arbitrary dynamic loading are derived using generalized power series. The convergence and the linear independence of the solutions are proved. Then, the solutions for displacements and stresses of the tunnel liner are obtained by utilizing these proposed general solutions. The validity of the proposed solution is demonstrated by comparing its results and those from FEM. Parametric analysis is presented with the solution where the influences of the rockbolts length and modulus of the equivalent layer reinforced by the rockbolts support on seismic responses of deep tunnels are investigated.