关键词:  , 温度场；热传导；解析方法；Laplace积分变换；stehfest方法

Abstract: The low temperature in cold region is quite harmful for the tunnels which are excavating or have been excavated. Therefore, the study on temperature field distribution of tunnel can play an important role in frost damage prevention. In view of this problem, an analytical model was established, and Laplace transform method was adopted to develop the analytical method of temperature field on tunnel. By means of transformation, the problem was transformed from time domain to Laplace domain; and the solution in Laplace domain was obtained, then the solution in Laplace domain was inverse transformed to that in time domain. Because the solution in time domain is difficult for actual calculation, it is necessary to carry on numerical inversion for the solution in Laplace domain by stehfest inversion method, to obtain the numerical solution in time domain. By error checking of stehfest method, it is obtained that when the cycle series N = 18, the error is about 10-5～10-7, suggesting that the method is reliable. Finally, based on the example checking of Fenghuo Mountain tunnel, the result obtained is identical with actual design, thus providing theory basis and calculation method for engineering design in cold region.

Key words: temperature field, thermal conduction, analytical method, Laplace integral transform, stehfest method