It is rather important for designing and protecting the cold-region tunnel from freeze–thaw damage that the frost situation of rock surrounding tunnel is analyzed and predicted after the tunnel is excavated, which had been paid much attention by the researchers (He, 1999). However, the air temperature distribution in the tunnel is a basis of analyzing and forecasting the freeze–thaw situation of rock surrounding tunnel, and generally, it is obtained by both in situ observation and calculating analysis of heat convection between the air and the rock surrounding the tunnel. Some literatures ever reported the distribution of the air temperature in the cold-region tunnels. Shamsundar (1982) investigated the frost properties of soil surrounding the round cooling pipes, and got the change law of fluidal temperature inside the pipes. Using the conclusion given by Shamsundar, 1982 and Lunardin, 1991 discussed the temperature characteristics of rock surrounding the tunnels. In China, by the means of in-situ observation Nie (1988) studied the relationship between the air temperatures inside and outside the tunnels of Luoqi No. 2 and Ducao in Heilongjiang, and Kuixian in Xinjiang, respectively. By analyzing the in-situ observed data, Lai et al. (2003) researched the air temperature changes inside the Daban Mountain tunnel in Qinghai under the conditions with and without thermal insulation doors, respectively; and on the other hand, with antisnow shelters and without ones, respectively. He, 1998 and He, 1999 presented the numerical model of coupled problem of heat conduction of solid and convective exchange between the air and the surrounding rock inside the cold regions tunnel when the air is in the laminar or turbulent status, but in the model the tunnel was assumed axial symmetry. In fact, very few tunnels are in this situation. Han and Chen, 1997 Han, P., Chen, X., 1997.

 

 Discussion on the total solution for the coupled problem of convection and conduction. In: Proceedings of the Seventh National Conference on Numerical Heat Transfer, Beijing, 32–37.Han Peng et al. (1997) presented the concept of dummy density and conducted the total solution of coupled problem between convection and conduction. Based on the concept of the dummy density, Jiang et al. (1999) solved the coupled problem of instable heat convection and radiation exchange using PHOENICS software. Heng et al. (2002) investigated the thermal properties of coupled convection in the rotary winding pipe. However, until now there is no reports on three-dimensional model of coupled problem of the heat transfer of rock surrounding the tunnel and the heat convection between the air and the surrounding rock in cold regions tunnels. In order to solve the practical problem and provide a theoretical basis for the design of cold regions tunnels, this study presents three-dimensional calculating model of the coupled problem of the heat transfer in rock surrounding the tunnel and heat convection between the air in the tunnel and the surrounding rock according to the basic theories of heat transfer, geocryology and fluid mechanics. The finite-element formulae are derived by using the Galerkin method, and the finite-element calculating program is compiled. By the computer program, three-dimensional non-linear analysis for the coupled problem of the heat transfer of surrounding rock and the heat convection between the air and surrounding rock in Fenhuo Mountain tunnel on the Qinghai–Tibet railway is made.

 

According to the basic theories of heat transfer, geocryology and fluid mechanics, taking the coupled problem of the heat transfer of the rock surrounding the tunnel and the heat convective between the air in the tunnel and the rock surrounding the tunnel into account, three-dimensional calculating model of the coupled problem are presented. The finite element formulae of this problem are obtained by Galerkin’s method, and the computer program of the finite element is compiled. Using the program, three-dimensional nonlinear analyses for the coupled problem of the heat transfer of the rock surrounding the tunnel and the heat convective between the air in the tunnel and the rock surrounding Fenghuo mountain tunnel on the Qinghai–Tibet Railway are made. The agreement between the calculated results and the in-situ observed data is seen to be very good. The calculated results illustrate that the freezing–thawing situation of the rock surrounding the tunnel can correctly be predicted even if the air temperature distribution along the tunnel is unknown. In thus way, the large cost of in-situ observation for the air temperature in the tunnel can be saved.