## 1 Introduction
However, all the above studies were focused on the characteristics of airflow temperature fields in tunnels, without considering temperature changes in tunnel linings and surrounding rocks. As tunnel ventilation is crucial to tunnel operation safety, ventilation systems should satisfy the design requirements for tunnels with different types and different functions. Tunnel ventilation systems are more important for long tunnels, where mechanical ventilation systems are usually required to be applied. [PERSON] et al. [16] proposed a numerical method to predict the thermal conductivity between trains and tunnel lining surfaces. [PERSON] et al. [17] also investigated the influences of the air temperature field inside tunnels on the temperature field of surrounding rocks, in which the air temperature was assumed to change following the sine function. [PERSON] et al. [18] performed a study on the temperature fields of the Fenghuo mountain tunnel based on two airflow models (a laminar model and a turbulence model), before verifying numerical results with experimental results. [PERSON] et al. [19] carried out a numerical study on the heat transfer between surrounding rocks and airflows under the effect of the piston action of trains based on the finite difference method. From the practical point of view, cold air from outside is usually carried by mechanical ventilation systems into tunnels in cold regions, which usually takes away the heat from surrounding rocks and tunnel linings. When an airflow moves from outside to the middle of a tunnel, the airflow temperature increases by absorbing the heat from the surrounding rock and the lining of the tunnel. Particularly, the air temperatures outside tunnels in cold regions are usually very low, which may easily cause damages from frost in tunnel linings near tunnel ends for long tunnels. Therefore, the characteristics of heat transfer between airflows outside tunnels and surrounding rocks should be carefully examined. This research is based on a real cold region tunnel (the Dege tunnel in Sichuan province), where one-year field test was carried out to investigate the temperature fields of the tunnel lining and the surrounding rock. In the test, temperatures of different measuring points in ten test sections in the tunnel were recorded. In the numerical analysis, a three-dimensional (3D) model was proposed based on the temperature field coupling theory (airflow-lining/heat-insulating layer-surrounding rock). By using the field test data from the Dege tunnel, the accuracy of the proposed numerical model is validated and calibrated. The present study has following highlights: (1) the research involves multi-physical domains, including a solid domain (the tunnel lining and the surrounding rock) and a fluid domain (the airflow); (2) the coupling characteristics of heat transfer between the fluid domain (airflow) and the solid domain (tunnel lining and surrounding rock) are considered carefully in the research; (3) the influences of different mechanical ventilation velocities and different heat-insulating materials on the design parameters for different heat-insulating layers are carefully examined and compared.