Unified plastic solution for stress and displacement of tunnels in cold regions considering transversely isotropic frost heave

The unified strength theory is used as a yield criterion to determine the plastic state of frozen surrounding rock of tunnels in cold regions. Taking comprehensive influences of the intermediate principal stress effect and transversely isotropic frost heave on the strength of frozen surrounding rock into account, a unified analytical plastic solution for the stress and displacement of tunnels in cold regions is proposed. A method is then introduced to address the plastic state of frozen surrounding rock. Furthermore, discussions, verifications and parametric studies of the proposed solution are performed. It is found herein that the validity of the unified solution is demonstrated by comparing with the results from Mohr-Coulomb criterion and circumscribed Drucker-Prager criterion available in the reference, thus it is of extensive theoretical significance and good engineering application prospect. The intermediate principal stress has a significant impact on the displacement of frozen surrounding rock, and then more rock strength potentialities are achieved. The frost-heave force increases with the increase of the anisotropic frost-heave coefficient and the volumetric frost-heave strain. It results in that the stability of tunnels in cold regions decreases, and effective insulation measures are taken to reduce the frost-heave effect of the surrounding rock. The result of this study can provide some theoretical suggestions for the design of tunnels in cold regions.