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在多年冻土地区修建隧道,会影响到多年冻土的热稳定性,目前一般采用在隧道衬砌中设置隔热层的方法来防止冻土围岩融化.根据隧道现场实测的气温资料,考虑正弦曲线规律变化的对流换热边界条件,建立了一次衬砌、隔热层、二次衬砌及围岩4层结构的圆形隧道热传导方程.运用微分方程求解方法和贝塞尔特征函数的正交和展开定理,对4个热传导方程进行了求解,得到隧道一次衬砌、隔热层、二次衬砌及围岩4层结构温度场的解析解,将计算结果与现场实测结果进行比较,吻合良好.计算结果还表明,在衬砌中铺设厚5 cm、导热系数为0.03 W.m-1.℃-1的隔热层可以保证风火山隧道围岩不发生季节性融化.该解析解可用于验证其它数值方法的计算结果,也便于工程设计人员和施工人员对同类寒区隧道进行温度场的计算,因而具有一定的工程应用价值.
The construction of tunnels in permafrost regions will affect the thermal stability of permafrost. At present, the method of insulating layers in tunnel linings is generally adopted to prevent the surrounding rock from melting. According to the measured temperature data in tunnels, The heat conduction equation of a circular tunnel with 4-layer structure of lining, thermal insulation layer, secondary lining and surrounding rock is established. By using the method of differential equation and the orthogonal sum of Bessel’s eigenfunction The theorems of heat conduction are solved and the analytical solutions of the temperature field in the four-layer structure of tunnel lining, thermal insulation layer, secondary lining and surrounding rock are obtained. The calculated results are in good agreement with the field measurements. The results also show that the thermal insulation layer with a thickness of 5 cm and a thermal conductivity of 0.03 Wm-1. ℃ -1 can be used to ensure that the surrounding rocks of the Fenghuoshan tunnel will not melt seasonally. The analytical solution can be used to verify the validity of other numerical methods The calculation results also facilitate the engineering designers and constructors to calculate the temperature field of tunnels with the same kind of cold region, so it has certain engineering application value.