Analytical elasto-plastic solution for stress and plastic zone of surrounding rock in cold region tunnels

To solve the engineering problem and put forward new practical theoretical insights to analysis and design, in this paper, an analytical solution for the frost heaving force in cold-region tunnel has been derived firstly using the continuity equation. Thereafter, a semi-analytical method to calculate the stress in the plastic zone of rock surrounding in cold-region tunnels is proposed by assuming that the frost rock was initially in the elastic state before the plastic zone was developed. Additionally, based on the approximate method for determining the plastic zone proposed by Kastner, the method for calculating the plastic zone in cold region tunnel is presented. Finally, the main results and conclusions are presented from a case study. The results show that frost heaving force results in a remarkable expansion of the plastic zone in the surrounding rock, and the rock in the plastic zone experiences hardening after the yield criterion is reached. Hardening effect can be taken into account in the proposed method for studying cold-region tunnels.