Abstract Accurate evaluation of the frost heaving force and stress distribution plays an essential role in frost damage prevention design of cold region tunnels. To ensure the safe operation of tunnels in cold regions and develop new practical method for their design, an analytical solution of frost heaving force and stress distribution in cold region tunnels under non-axisymmetric stress and transversely isotropic frost heave of surrounding rock is established. The solution is of urgent demand because the tunnel sites with significant difference between horizontal and vertical initial ground stresses are frequently encountered. In analysis, the mechanical process is considered as two steps based on the linear superposition principle of elasticity theory. In step 1, the frozen zone freezes and expands without constraint first, and in step 2 the frost heaving displacement of the frozen zone is then inhibited by lining and unfrozen surrounding rock to reach a final balance state. The stress and displacement distributions of the above two steps are derived first, and then the solution of frost heaving force and stress is determined by boundary conditions. The analytical solution is verified with the existing solution under the axisymmetric stress condition. Furthermore, the stress distribution and the increment of stress in lining and surrounding rock induced by frost heave are analyzed. Finally, the influence of the related factors on stress distribution is analyzed. Results show that the increment of the stress in lining and surrounding rock significantly vary with the lateral pressure coefficient and the anisotropic frost heave coefficient, which demonstrates that the non-axisymmetric stress and the transversely isotropic frost heave of surrounding rock have considerable impact on the stress distribution and should be considered.

中文翻译：

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围岩非轴对称应力和横向各向同性冻胀作用下寒区隧道冻胀力及应力分布解析解

摘要 准确评估冻胀力和应力分布对寒区隧道防冻害设计具有重要意义。为保证寒冷地区隧道的安全运营，开发新的实用设计方法，建立了非轴对称应力和横向各向同性围岩冻胀条件下寒冷地区隧道冻胀力和应力分布的解析解。由于经常遇到水平和垂直初始地应力差异显着的隧道站点，因此迫切需要该解决方案。在分析中，基于弹性理论的线性叠加原理，机械过程被认为是两个步骤。在步骤1中，冻结区首先无约束地冻结和扩展，在步骤2中，通过衬砌和解冻围岩抑制冻结带的冻胀位移，达到最终平衡状态。先推导出上述两步的应力和位移分布，再由边界条件确定冻胀力和应力的解。解析解与轴对称应力条件下的现有解进行验证。进一步分析了冻胀引起的衬砌和围岩的应力分布和应力增量。最后分析了相关因素对应力分布的影响。结果表明，衬砌和围岩应力增量随侧压系数和各向异性冻胀系数变化显着，