An elastic-plastic solution for frost heaving force of cold region tunnels considering transversely isotropic frost heave and displacement release

The elastic solution and the unified plastic solution for the frost heaving force of tunnels in cold region as well as the implicit equation of plastic zone radius were proposed in this study based on the overall freeze-thaw circle frost heave model. The proposed solution can comprehensively account for the influences of the intermediate principal stress, the transverse isotropic frost heave and the displacement release of surrounding rock. Meanwhile, an approach was provided to determine the elastic-plastic state of frozen surrounding rock. Furthermore, comparability analysis and verification of the proposed solution were performed. The effects of various factors on the frost heaving force and plastic zone radius were investigated. Finally, the distance description of the surrounding rock displacement release was quantified through the supporting time. It was found that the proposed solution has good comparability and was verified by model tests in reference. As the yield criterion of frozen surrounding rock, the unified strength theory can fully make use of its bearing potentiality, the frost heaving force and plastic zone radius are decreased obviously. The frost heaving force and plastic zone radius are significantly affected by the anisotropic frost heave coefficient and the volume frost heave ratio. Therefore, it is necessary to consider the transverse isotropic frost heave of surrounding rock and take effective measures of tunnel waterproofing and drainage as well as insulation and frost resistance. The frost heaving force is large when the displacement release coefficient is small, while the plastic zone radius reaches its peak value when the displacement release coefficient reaches one. Therefore, a proper supporting time is beneficial to the safety of construction and operation for tunnels in cold region. The obtained results can provide some theoretical guidance for the design of tunnels in cold region.