寒区圆形截面隧道温度场的解析解  

Approximate Analytical Solution for the Temperature Fields of a Circular Tunnel in Cold Regions

作　　者：赖远明[1] 喻文兵[1] 吴紫汪[1] 何平[1] 张孟喜[2] 

机构地区：[1]中国科学院寒区旱区环境与工程研究所冻土工程国家重点实验室,甘肃兰州730000 [2]兰州铁道学院土木工程系,甘肃兰州730000

出　　处：《冰川冻土》2001年第2期126-130,共5页Journal of Glaciology and Geocryology

基　　金：中国科学院寒区旱区环境与工程研究所知识创新工程项目! (CACX2 10 0 13 )

摘　　要：根据冻土地区的实际情况对圆形隧道正冻区和未冻区的热传导方程进行简化 ,应用无量纲量和摄动技术对简化方程进行求解 ,给出了圆形隧道冻结过程的近似解析解 .通过和有限元数值解结果比较 ,发现该近似解析解具有较高的精度 ,能满足工程实际的精度要求 .该解既可用于工程估算也可用来检验数值计算的计算程序及结果 .According to the situation in permafrost regions, the governing differential equations of heat transfer in frozen zone and unfrozen zone are simplified. Then, using dimensionless and perturbative method, an approximate analytical solution for simplified heat transfer equation has been obtained. A research of freezing process of circular tunnel with initial temperature near 0 ℃has been made. As a numerical example, a circular tunnel incold region has been studied.Its inner radius is3.0 m. The thermal conductivity and the volumetric specific heat of its surrounding rock infrozen area are λ f=1.8247 W·m -1·K -1and C f=1.617×10 6 J·m -3·K -1, respectively. The thermal conductivity and the volumetric specific heat of its surrounding rocks in unfrozen area are λ u =1.4338 W·m -1·K -1 and C u=1.929×10 6J·m -3·K -1. Besides, its volumetric phase-change latent heat, ρL, is 46.44×10 6 J·m -3. The air temperature T a is -3 ℃. The precision of the approximate formulae in this paper has been examined under following two conditions: Condition 1The convective heat-transfer coefficient between air and rocks is 15.0(W·m -2·K -1) and T f, the frozen temperature of the rock-surrounding tunnel, is -0.1 ℃. The approximate analytical results for the initial temperature of the surrounding rock of 0 ℃can be obtained using the formulae of this paper. Again the numerical results worked out by a computation method, presented by Lai et al., are given in Table 1 for two initial temperatures of the surrounding rock. Table 1 shows that for the frost front radius of 7.837 m, the frozen time determined by the approximate analytical solutions of this paper is5.039 years. The time determined by the numerical solution is only 5 years for the same frost front radius. The errors between the approximate analytical results and the numerical results are 4.6%, 6.62%, 7.05%, 7.63% and 8.83% for the initial temperature of surrounding rocks of1.5 ℃. Forthe initial temperature of surroun

关 键 词：寒区 隧道 温度场 近似解析解 冻土地区 热传导方程 数学模型 

分 类 号：U452[建筑科学—桥梁与隧道工程]