Abstract: 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.

Key words: cold region tunnel, frozen depth, semi-analytical method, influence factors