寒区隧道围岩最大冻结深度计算的半解析方法

寒区隧道围岩的最大冻结深度是隧道抗冻胀结构设计、防排水与保温隔热层设计的重要基础参数。基于准稳态假定，采用积分法推导了能够考虑衬砌、保温层及冻结围岩中未冻水含量的寒区隧道围岩最大冻结深度的解析计算公式；利用围岩温度场数值模拟结果反演得出了解析计算公式中的参数影响半径与冻结半径比 的取值，从而得到了围岩最大冻结深度的半解析解。将所得解的计算结果与现场实测数据及数值模拟结果进行了对比，验证了所得解的合理性。利用得到的半解析解分析了工程冻土段围岩冻结深度的影响因素，结果表明：初始地温、年平均气温对冻结深度的影响最为明显，岩体骨架导热系数、岩体孔隙率的影响次之。

Semi-analytical method of maximum frozen depth calculation in cold region tunnel

The maximum frozen depth of surrounding rock is an important basic parameter in cold region tunnel design, such as frozen-preventing lining design, waterproof and drainage design, insulating layer design. To predict frozen depth of surrounding rock, various researches have been conducted, including field monitoring, numerical simulation, and derivation of practical estimation equations. In this study, a semi-analytical method is proposed to obtain the maximum frozen depth. First, the temperature acting on the lining surface is equivalent to a constant temperature according to the principle of equal annual accumulated temperature. Then, based on the quasi-steady state assumption, an analytical formula of the maximum frozen depth which considers the existing of lining, thermal insulation layer and the unfrozen water content in frozen rock is derived, using integration method. Next, the back analysis method is used to obtain the parameter which refers to the ratio of influence radius and frozen radius in the analytical formula, combined with the numerical simulation results of the temperature field. Finally, the semi-analytical solution of the maximum frozen depth is obtained. Through comparisons of the field monitoring data and the results of numerical simulation, the rationality of the proposed method is proved. Furthermore, the influence factors of the frozen depth are analyzed using the proposed semi-analytical solution, and the results show that the initial temperature and the annual average temperature have the most significant influence, and the rock conductivity coefficient and the porosity are less influential.