空心圆柱饱和多孔介质热固结问题的解析解

Analytical solutions of thermal consolidation for a hollow cylinder saturated porous medium

基于考虑热渗效应和等温热流效应的热-水-力耦合的线性热弹性固结控制方程,建立无限长空心圆柱饱和多孔介质热固结问题的一种理论求解方法。该方法先给出Laplace变换域上的解,然后,利用Stehfest法求其数值逆变换。该理论解考虑了空心圆柱体内、外透水界面随时间变化的外力和温度荷载耦合作用过程。最后,通过一算例分析了饱和多孔介质的热固结特征,给出其温度、孔压、位移和应力的演化规律。

An analytical method is derived for the thermal consolidation of a hollow cylinder saturated porous medium with infinite length.In the coupled governing equations of linear isotropic porous thermoelastic medium,the influences of thermo-osmosis effect and thermal filtration effect are introduced.The solutions in Laplace transform space are first obtained and then numerically inverted by Stehfest method.These solutions consider the variable thermal loading and variable mechanical loading applied on the inner and outer pervious surface of the hollow cylinder with time.Finally,the evolutions of temperature,pore water pressure and displacement along radial direction with time are analyzed by a typical numerical example.