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西部寒区低温环境对已开凿和正开凿的隧道危害很大,研究其隧道温度场的分布对开展防冻害工作起到重要作用。针对这一问题建立分析模型,采用Laplace变换,建立了隧道温度场的解析分析方法;将时间域上的问题转化为Laplace域上的问题,得到Laplace域上的解,再将Laplace域上的解反变换到时间域上。由于时间域上的解进行实际计算较困难,需将Laplace域上的解采用stehfest反演方法进行数值逆变换,得到时间域上的数值解答;通过对stehfest方法进行误差验算,得出当循环级数N=18时,误差达到10-5～10-7,从而说明此方法是可靠的。最后通过对风火山隧道实例验算,得到和实际工程相符的结果,从而为寒区工程设计提供理论依据和计算方法。
The low temperature environment in the western cold area is very harmful to the tunnels that have been drilled and being cut. Studying the distribution of the temperature field in the tunnels plays an important role in the prevention of frost damage. In order to solve the Laplace domain problem, an analytical model is established for this problem. Laplace transform is used to establish the analytic method for the temperature field in the tunnel. The Laplace domain solution is obtained by solving the problem in the Laplace domain. Transform to the time domain. Due to the difficulty of calculating the solution in the time domain, the inversion of the Laplace domain solution using the stehfest inversion method is required to obtain the numerical solution in the time domain. By checking the error of the stehfest method, The number of N = 18, the error of 10-5 ~ 10-7, indicating that this method is reliable. Finally, through the verification of the example of the Fenghuoshan Tunnel, the results consistent with the actual project are obtained, which will provide theoretical basis and calculation method for engineering design in the cold area.