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

In recent years, the construction of cold-region tunnels has increased in western China. However, the studies of the analytical elasto-plastic solution for the stress and deformation of surrounding rock in cold-region tunnels are limited. To solve this engineering problem and propose new theoretical insights for analysis and design, the elasto-plastic calculation model for surrounding rock in cold-region tunnels is established in this paper. In this model, the entire surrounding rock is divided into four zones, namely, the unfrozen elastic zone, the frozen elastic zone, the frozen plastic zone and the support zone. The frozen surrounding rock is assumed to conform to the ideal elasto-plastic model and the Mohr–Coulomb yield criterion. The stress and deformation fields in each zone are solved according to continuity conditions. A case is introduced to obtain the distribution of stress and strain in the surrounding rock of cold-region tunnels. The reason that the circumferential stress is less than the radial stress in the unfrozen zone is explained and the range of that is also addressed. Moreover, the location in which no displacement is generated is determined in the freezing circle. The produced high stress is mainly influenced by the linear frost strain. The results of stress field and strain field are verified by the existing elastic solution. At last, parameter analysis is performed to obtain the influence of the related parameters on plastic radius and the surrounding rock stresses at the inner and outer edges of the freezing circle. The results can guide for numerical simulations and field engineering practice.