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依据传热学中的固体热传导理论,结合寒区隧道浅埋段传热特征,建立了考虑地表和洞内气温联合作用下的浅埋段隧道传热数学模型。为便于求解,根据空气温度周期变化的特点,运用热叠加原理把复杂温度边界条件下的隧道瞬态传热问题分解为温度周期变化下的瞬态传热问题和恒温边界作用下的稳态传热问题,综合运用分离变量法与Laplace变换法相结合,理论推导隧道浅埋段温度场的解析解,并将其与隧道温度场实测数据进行对比验证,理论解与实测值的误差为4.5%,理论解达到了工程精度要求。分析隧道埋深、洞内气温和保温层厚度对隧道温度场的影响规律,并建立了寒区隧道浅埋段保温层厚度的设计计算方法,可为工程人员提供指导。
Based on the theory of solid heat conduction in heat transfer and the heat transfer characteristics in the shallow section of tunnel in cold region, a mathematic model of heat transfer in shallow buried section considering the effect of surface temperature and temperature in the tunnel was established. In order to solve the problem easily, the transient heat transfer problem under complicated temperature boundary conditions is decomposed into the transient heat transfer problem under the temperature cycle and the steady state transfer under the constant temperature boundary condition In this paper, the analytical solution of the temperature field in the shallow section of the tunnel is deduced theoretically by combining the method of discrete variables with the Laplace transform method. The error between the theoretical solution and the measured value is 4.5% Theoretical solution has reached the requirements of engineering accuracy. The influence of tunnel depth, temperature in the tunnel and the thickness of thermal insulation on the temperature field of the tunnel is analyzed, and the design and calculation method of thermal insulation thickness in shallow section of tunnel in cold region is established, which can provide guidance to engineering staff.