In this paper, an analytical solution is deduced for estimating the soil-lining interaction in a deep tunnel subjected to freezing action. The complete solution is found by the superposition of a frost heaving model and an excavation model considering the lining delayed installation. By treating the tunnel lining as a thick-walled shell, the internal force is discussed considering the convergence–confinement method. Then, specific consideration is given to the influence of the freezing process (increasing freezing depth). Generally, the results show that normal soil pressure around the lining increases significantly with increasing freezing depth. The frost heaving pressure and the lining's delayed installation contribute to reducing the nonuniformity of the axial force. Furthermore, to identify the key influencing factors, an orthogonal experiment is designed and conducted by the analytical solution mentioned. An increasing lining thickness could improve the axial force at the sidewall and weaken the axial force at the crown. The freezing depth is not statistically significant to the bending moment around the lining of the cold region tunnel. Overall, this study offers novel insights into the soil-lining interaction in deep tunnels built in cold regions and helps avoid frost damage at tunnel linings.

在本文中，推导出了一个解析解，用于估计受到冻结作用的深部隧道中土-衬砌的相互作用。考虑到衬砌延迟安装，通过冻胀模型和开挖模型的叠加找到完整的解决方案。通过将隧道衬砌视为厚壁壳，考虑收敛-约束法讨论内力。然后，具体考虑冷冻过程（增加冷冻深度）的影响。总的来说，结果表明，随着冻结深度的增加，衬砌周围的正常土压力显着增加。冻胀压力和衬砌的延迟安装有助于减少轴向力的不均匀性。此外，为了确定关键的影响因素，利用上述解析解设计并进行了正交试验。增加衬里厚度可以提高胎侧的轴向力，减弱胎冠的轴向力。冻结深度对寒冷地区隧道衬砌周围的弯矩无统计学意义。总体而言，这项研究为寒冷地区建造的深隧道土壤-衬砌相互作用提供了新的见解，并有助于避免隧道衬砌的冻害。