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对路面结构瞬态温度场进行了求解,并提出了一种空间上解析而时间上有限差分离散的半解析法。首先,根据路面结构层状特征、传热特点和传热学原理,建立了路面结构瞬态热传导问题的数学模型,该模型综合考虑了大气温度、日辐射和地面反射等环境因素变化的影响。其次,基于时间有限差分离散,推导了以层间状态变量(温度和热流密度)表示的状态方程。最后,根据矩阵分析理论,给出了路面结构瞬时温度场的逐时递进公式和基于MATLAB5.2平台编制了相应的计算软件。对某一典型路面结构夏冬季瞬态温度场进行了计算,获得了其时空分布规律,并与ANSYS10.0计算结果进行比较。路面结构上部温度随时间和深度均有显著变化,当太阳辐射最强时,温度变化更突出;随着深度的增加,温度变化越来越弱。不论何时,路面结构内存在着沿深度方向的不均匀分布温度场,所产生的温度应力会诱发裂缝,路面结构设计时应注意。
The transient temperature field of pavement structure is solved, and a semi-analytical method of spatial discretization and finite difference discretization in time is proposed. First, according to the layered structure, the heat transfer characteristics and the heat transfer theory, the mathematical model of the transient heat conduction problem of pavement structure is established. The model considers the influence of atmospheric factors such as atmospheric temperature, solar radiation and ground reflection. Secondly, based on the finite difference time dispersion, the state equation expressed by the inter-layer state variables (temperature and heat flux density) is deduced. Finally, according to the matrix analysis theory, the gradual progress formula of instantaneous temperature field of pavement structure is given and the corresponding calculation software is compiled based on MATLAB5.2 platform. The transient temperature field of a typical pavement structure was calculated in summer and winter, and its temporal and spatial distribution was obtained. The results were compared with those of ANSYS10.0. The temperature of the pavement structure changes significantly with time and depth. When the solar radiation is the strongest, the temperature changes more prominent. As the depth increases, the temperature changes become weaker and weaker. Whenever there is uneven temperature distribution in the pavement structure along the depth direction, the temperature stress generated will induce cracks. Pay attention to pavement structure design.