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The temperature of the surrounding rock in cold-region tunnels is crucial for antifreeze design, and the water-ice phase transition is essential to addressing the temperature field. This paper proposes a refined method that equates the latent heat of the ice-water phase transition to heat capacity and establishes a one-dimensional radial heat transfer model considering phase change. By defining an average thermal diffusivity coefficient through the concept of equal accumulated temperature, this method overcomes the limitations of classical heat transfer theory in directly solving the temperature field of three zone (unfrozen zone, freezing zone and frozen zone). Additionally, by employing the variable separation method and Fourier integral transformation method, the analytical formula for the transient temperature field considering phase change is derived. Then, the analytical solution was verified based on the field data. The results calculated using this method exhibit greater consistency with field temperature data and outperform the modified Stephan formula in determining the maximum frozen depth of the surrounding rock. Finally, the simplified form of the established analytical solution was further discussed. The research results can provide a theoretical basis for the analysis of the temperature field of the surrounding rock of the tunnel in cold regions and its antifreeze design.

In order to solve frost damage problems in cold-region tunnels, a new sustainable energy based freeze proof method for tunnel drainage system is proposed. The method is applied to Tianshan Shengli Tunnel, China as a case study to show the concept and details of tunnel drainage system ground heat exchangers (GHEs) including calculation of active heating length and maximum heating load, design of heat extraction in cross tunnel, the segmented design method. Long-term performance of tunnel drainage system GHEs is also fully discussed. Multi-field simulations are performed to achieve corresponding thermal responses of the tunnel drainage system GHEs. Results show that anti-freezing measures provide an initial heating length 900 m of the drainage system at the entrance of Tianshan Shengli Tunnel during full life cycle. When the tunnel drainage system GHEs are employed, the heating length can be reduced to 600 m. Maximum total heating load of the tunnel drainage system in heating period is 84.40 kW. The calculation method of segmented heating load is suggested for precise prevention and control of frost damage in cold-region tunnels, owing to varying tunnel air temperature with the distance from the tunnel entrance. The use of boiler heating in winter will enhance the compensation between operation and recovery period and provides good long-term performance. This study provides a potential reference for antifreeze design of cold-region tunnels utilizing geothermal energy.