To study the evolution of the frost–heaving pressure and frost–heaving deformation of the lining for a tunnel in cold regions, a frost–heaving strain model of rocks with self–constraint that considers the porosity, water content, temperature, and elastic modulus of the rock is first derived through the mechanical balance equation and geometric equation of the rock mesostructure. The laboratory test results verify that the frost–heaving strain model of the rocks with self–constraint is reliable. After analyzing the boundary conditions of the freeze–thaw ring of the surrounding rock along the radial direction of the tunnel, a constant stiffness constraint model of the freeze–thaw ring is proposed. Then the frost–heaving process of the surrounding rock is divided into three stages, and the mechanical models for the calculation of the frost–heaving pressure and the frost–heaving deformation are derived based on the constant stiffness constraint model and the frost–heaving strain model of the rocks. Finally, the evolutions of the frost–heaving pressure and the frost–heaving deformation of the tunnel lining are investigated. The results show that the frost–heaving ratio of the surrounding rock of the tunnel increases nonlinearly as the frost–heaving factor increases. The frost–heaving factor has a linearly positive correlation with the porosity and the water content of the surrounding rock, and a negative correlation with the unfrozen water mass ratio and the rock elastic modulus. The rock resistance coefficient and the lining equivalent resistance coefficient affect the frost–heaving pressure and the frost–heaving deformation significantly. With the increase in the rock resistance coefficient or in the lining equivalent resistance coefficient, the frost–heaving deformation increases or decreases, respectively, while the frost–heaving pressure increases gradually as the rock resistance coefficient or the lining equivalent resistance coefficient increases.

为研究寒冷地区隧道衬砌的冻胀压力和冻胀变形演化，建立了考虑孔隙度、含水量、温度和弹性模量的自约束岩石冻胀应变模型首先通过岩石细观结构的力学平衡方程和几何方程推导出岩石的力学平衡方程。室内试验结果验证了自约束岩石冻胀应变模型的可靠性。在分析了沿隧道径向围岩冻融环边界条件的基础上，提出了冻融环恒刚度约束模型。那么围岩的冻胀过程分为三个阶段，基于岩石的常刚度约束模型和冻胀应变模型，推导了冻胀压力和冻胀变形计算的力学模型。最后，研究了隧道衬砌的冻胀压力和冻胀变形的演变规律。结果表明，随着冻胀系数的增加，隧道围岩的冻胀比呈非线性增加。冻胀系数与围岩孔隙度和含水量呈线性正相关，与未冻水质量比和岩石弹性模量呈负相关。岩石阻力系数和衬砌等效阻力系数对冻胀压力和冻胀变形有显着影响。随着岩石阻力系数或衬砌等效阻力系数的增大，冻胀变形分别增大或减小，而冻胀压力则随着岩石阻力系数或衬砌等效阻力系数的增大而逐渐增大。