Method for determining yield state and new solutions for stress and displacement fields of cold region tunnels under freeze-thaw cycles

The water-bearing surrounding rock in cold region tunnels is significantly affected by freeze-thaw (F-T) cycles generated by seasonal temperature changes, which can severely lead to tunnel lining failure due to increased loads. This study considers the non-uniform frost heave properties and the deterioration effects of F-T cycles on the surrounding rock. Six mechanical models for cold region tunnels are established based on the different yield states of frozen and unfrozen surrounding rock. Utilizing the unified strength theory, the solutions of stress and displacement fields for each model are derived, respectively, and a method for identifying the actual yield state of the tunnel is provided. The derived solutions are compared and verified, and the influence of various parameters on the solutions and yield states of cold region tunnels is explored. It is indicated herein that the proposed solutions have been validated by the results in the literature, demonstrating broad theoretical significance and practical engineering guidance value. When the F-T cycle counts increase from 0 to 75, the support pressure rises by 48.54%, and the plastic zone expands by 0.76 m. The deterioration effects of long-term F-T cycles on surrounding rocks should be quantified. As the intermediate principal stress effect increases, the support pressure decreases by 15.35%, and the development of the plastic zone is restricted. The unified strength theory should be used as the yield criterion. The greater the degree of non-uniform frost heave, the greater the load borne by the support structure. Insulation measures should be adopted to prevent excessive temperature gradients in the surrounding rock. In addition, failing to utilize the mechanical model corresponding to the actual yield state will result in significant calculation errors. The yield state determination method proposed in this study should be adopted. The results can offer theoretical references for designing cold region tunnels and safeguarding tunnel structures during service periods under F-T cycles.