非稳态热传导时层状路面体系的温度响应

利用解析层元法推导温度荷载作用下非稳态热传导时层状路面体系的温度响应解答。从热弹性理论平面应变问题的控制方程出发，借助于Laplace-Fourier积分变换，推导出单层介质及下卧半平面的精确刚度矩阵即解析层元，结合有限层法原理及边界条件，组装并求解总刚度矩阵，得到其在变换域内的解答，最后通过相应的积分逆变换得到物理域内的真实解。由于该法刚度矩阵元素中不含正指数项，计算时不会出现溢出或病态矩阵的现象。编译了相应的计算程序，所得结果与有限元模拟结果吻合较好。在此基础上，对有限深度和半平面两种假定条件下的解答进行对比分析，并分析层状路面体系中位移和温度随时间的变化趋势及沿深度的分布规律。分析表明：温度场具有一定的影响深度，超过此深度，有限深度与半平面理论解答基本一致；温度荷载的影响深度与其强度有关，强度越大，其影响深度越深。

Thermal responses of layered pavement system with unsteady heat conduction

The analytical solutions of layered pavement system subjected to temperature loading are derived with the use of analytical layer-element method under unsteady heat conduction. Starting with the basic equations of plane strain problems of thermo-elasticity, the analytical layer-elements of a single layer and the underlying half-plane are obtained with the aid of Laplace-Fourier transform. Following the principle of the finite layer method and considering the boundary conditions, the total stiffness matrix is assembled and solved in the transformed domain, and the actual solutions in the physical domain are acquired by adopting the numerical inversion of Laplace-Fourier transform. Because positive exponential function is not included in the analytical layer-element, the computation overflow and ill-conditioned matrices can be avoided. Numerical results are obtained by corresponding computer procedures and are compared with those obtained by the finite element method, which shows a good agreement. The solutions under the assumption of a finite depth and a half-plane are derived and compared. Finally, the variation of vertical displacement and temperature increment along time factor and the distribution of vertical displacement along z direction are analyzed. The results reveal that the temperature change has a certain effect depth, and the results based on the finite depth assumption are consistent with those based on the half-plane assumption when the depth-of-interest is beyond the effect depth. The effect depth is related to the degree of temperature change, the greater the temperature intensity, the deeper the effect depth.