半无限空间饱和土一维热固结精确积分解

Exact integral solutions for one-dimensional thermal consolidation of semi-infinite saturated soils

基于Coussy提出的饱和多孔介质热-水-力耦合理论,给出考虑热渗效应和等温热流效应的饱和土热固结耦合控制方程,然后通过正弦和余弦变换方法,结合Hamilton-Cayley定理,给出了两类任意非齐次边界条件下,半无限空间饱和土一维热固结精确积分解的求解方法,避免了Laplace变换处理复杂边界问题时的数值反演。最后,通过算例验证了本文解析解的正确性,并分析了半无限空间表面透水或不透水时,饱和土体在季节性温度荷载作用下的温度、超静孔压和位移响应特性。结果表明:温度、超静孔压和位移受季节性温度荷载影响而呈现周期性波动,表面不透水情形的土体超静孔压和位移响应明显高于相应的表面透水情形的土体响应。

Based on the thermo-hydro-mechanical coupled theory for saturated porous media proposed by Coussy,two coupled governing equations for thermal consolidation of saturated soils are presented,taking thermo-osmosis and thermo-filtration into account.The sine and cosine transforms as well as the Hamilton-Cayley law are used to obtain exact integral solutions for one-dimensional thermal consolidation of semi-infinite saturated soils with two types of arbitrary nonhomogeneous boundary conditions.It helps avoid the errors of numerical inverse Laplace transform when dealing with complex boundary conditions.Finally,case studies are provided to validate the proposed analytical solutions and to investigate the thermal responses of saturated soils with seasonal thermal loads on the permeable or impermeable surface.The results show that temperature change,excess pore water pressure and displacement all fluctuate periodically due to seasonal thermal loads.The responses of the excess pore water pressure and displacement of the saturated soils with an impermeable surface are much higher than those with a permeable surface.