热局部非平衡下饱和多孔弹性柱体的拟静态分析

Quasi-static analysis of incompressible saturated poroelastic column on local thermal non-equilibrium

基于多孔介质理论所建立的不可压饱和多孔介质热-流-固耦合模型,对于一端固定、绝热和不可渗透,另一端受机械和温度载荷联合作用且可自由排水的多孔弹性柱体,利用分离变量法和拉普拉斯变换推导给出了热局部非平衡下多孔弹性柱体拟静态问题的一般解析表达式.最后,针对阶梯机械和温度载荷联合作用的情况,数值研究了不同参数下温度载荷对固相变形和有效应力、流体速度和孔隙压力的影响.结果表明:在流固两相热扩散系数的比值较大和两相间热交换系数比较小的情况下,热局部平衡和非平衡下有关结果之间的差异在初始阶段是非常明显的.

Based on the theory of porous media, the governing equations of coupled mathematical model for incompressible saturated poroelastic column on local thermal non-equilibrium were presented for the first time. The quasi-static responses of a poroelastic column with a kind of boundary conditions subjected to mechanical and thermal loads were investigated. Using the separation of variables and Laplace transform method, a general analytic solution was achieved under the local thermal non-equilibrium condition. Finally, for the step mechanical and thermal loads, the evolutions of solid and fluid temperatures, solid displacement and effective stress, and fluid velocity and pore pressure with time factor were studied. The difference in results between the local thermal non-equilibrium and the local thermal equilibrium conditions was discussed, which was not negligible at the initial stage when the ratio of solid and fluid thermal diffusion coefficients was bigger and the heat exchange coefficient between solid and fluid was smaller.