关键词: 非稳态热传导, 解析层元, 层状路面体系, 温度响应, 平面应变

Abstract: 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.

Key words: unsteady heat conduction, analytical layer-element, layered pavement system, thermal responses, plane strain