寒区隧道温度场Laplace变换解析计算  

Analytical Calculation on Temperature Field of Tunnels in Cold Region by Laplace Integral Transform

作　　者：冯强[1] 蒋斌松[1] 

机构地区：[1]中国矿业大学深部岩土力学与地下工程国家重点实验室,江苏徐州221008

出　　处：《采矿与安全工程学报》2012年第3期391-395,共5页Journal of Mining & Safety Engineering

基　　金：国家自然科学基金项目(50774082)

摘　　要：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 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 im-portant 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 calcula-tion,it is necessary to carry on numerical inversion for the solution in Laplace domain by stehfest inver-sion 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.

关 键 词：温度场 热传导 解析方法 Laplace积分变换 stehfest方法 

分 类 号：TD353[矿业工程—矿井建设]