地埋点热源作用下层状半空间的热-力耦合响应

采用解析层元法对存在地下点热源的岩土工程问题进行解答。首先从热弹性力学三维问题的基本控制方程出发，利用拉普拉斯-傅里叶积分变换推导出其在变换域内单层介质及下卧半空间的解析层元；然后结合有限单元法原理组装得到总刚度矩阵，结合边界条件，得到其在变换域内的解答，最后应用拉普拉斯-傅里叶积分逆变换技术，得到物理域内的解。编制了相应的计算程序，算例分析表明：该结果与已有文献吻合较好，该方法求解层状半空间的热-力耦合响应问题具有较好的适用性和较高的精度；层状岩土介质体系中，热扩散系数对温度及地表隆起的变化过程影响显著，但对其初始值和最终稳定值影响不明显；分层特性对岩土介质温度分布及地表位移变化过程均有显著影响。

Thermo-mechanical coupling response of layered half-space with a buried point heat source

Analytical layer-element method is presented to study the thermo-mechanical coupling behavior of rock and soil medium with a buried point heat source in geotechnical engineering. Starting from the governing equations of three dimensional thermo-elasticity, analytical layer-elements of a single layer and the underlying half-space are derived in the transformed domain by Laplace-Fourier transform. A global stiffness matrix of layered media is assembled, which is further solved by considering the boundary conditions. The numerical inversion of Laplace-Fourier transform is adopted to obtain the actual solution. Numerical examples reveal that the calculated results acquired by the corresponding procedure show a good agreement with the results in existing literature, and the presented approach shows good applicability and high precision in studying the thermo-mechanical coupling response of layered half-space; in multilayered rock and soil system, the thermal diffusivity have a remarkable effects on the variation of temperature increment and the surface heave, while it shows negligible effects on the initial and steady state values of the temperature and surface heave; the influence of the stratification on the process of heat conduction and displacement variation is significant.