寒冷地区隧道防冻保温层等效厚度计算方法误差分析

Error analysis of equivalent thickness calculation method of tunnel thermal insulation layer in cold area

为分析寒冷地区隧道防冻保温层等效厚度计算方法的计算误差,考虑年周期下的隧道沿径向深度瞬态传热特性,提出了基于数值模拟计算的防冻保温层等效厚度法误差计算方法。同时采用控制变量法计算分析空气年平均温度、年温度振幅、围岩初始温度、围岩导热系数和导温系数5类因素对等效厚度法计算误差的影响。结果表明:在隧道衬砌表面铺设防冻保温层后,围岩温度影响深度减小,衬砌结构和围岩最大冻结深度出现时间较无防冻保温层铺设时,提前近20 d,说明防冻保温层铺设前后隧道结构内部传热状态存在差异,此外,衬砌结构和围岩内部为瞬态传热,因此效厚度法计算原理、假定条件与实际不符,计算结果存在误差;等效厚度法计算结果整体偏小,但在空气年温度振幅较小或围岩初始温度较大时,计算结果存在偏大的情况;空气年平均温度、围岩初始温度、围岩导热系数越低,空气年温度振幅、围岩导温系数越高,计算误差越大;围岩导热系数和围岩初始温度对计算误差影响较大,当围岩导热系数为2 W·(m·K)^(-1)、围岩初始温度为5℃时,计算误差分别可达1.6 cm和1.4 cm,其余参数变化所形成的计算误差均小于1 cm。

In order to analyze the calculation error of the equivalent thickness calculation method for thermal insulation layer in tunnel in cold areas,the transient heat transfer characteristics of tunnel along the radial depth under annual cycles was considered.A calculation method for the error of the equivalent thickness calculation method of thermal insulation layer based on numerical simulation was proposed.Meanwhile,the control variable method was adopted to calculate and analyze the influence of the five factors,including of annual average air temperature,annual air temperature amplitude,initial temperature,thermal conductivity and thermal diffusion coefficient of rock mass,on the calculation error of the equivalent thickness method.The results show that after the thermal insulation layer is laid on the tunnel lining surface,the influence depth of surrounding rock temperature is decreased,and the maximum freezing depth of lining and surrounding rock occurs nearly 20 d earlier compared to when there is no thermal insulation layer.It indicates that there are differences in the internal heat transfer state of tunnel lining and surrounding rock before and after the thermal insulation layer laid.Additionally,the transient heat transfer occurs within the tunnel lining and surrounding rock,Therefore,the calculation principle and assumed condition of the equivalent thickness calculation method do not conform to the actual situation,resulting in an error in the calculation results.The calculation results of the equivalent thickness method are generally smaller.However,there are cases where the calculation results are larger when the annual temperature amplitude is low or the initial temperature of the surrounding rock is high.The calculation error is larger when the annual average air temperature and the initial temperature and thermal conductivity of the surrounding rock are lower.Conversely,the calculation error is larger,when the annual air temperature amplitude and thermal diffusivity of the surrounding rock are higher.The thermal conductivity and the initial temperature of the surrounding rock have a significant impact on the calculation error.When the thermal conductivity of the surrounding rock is 2 W·(m·K)^(-1) and the initial temperature of the surrounding rock is 5℃,the calculation errors can reach 1.6 cm and 1.4 cm,respectively.The calculation errors resulting from variations in other parameters are all less than 1 cm.