饱和多孔介质热-水-力控制方程耦合项的意义及耦合影响分析

Effects of coupling schemes of thermo hydro-mechanical governing equations for saturated porous medium

基于饱和多孔介质完全耦合条件下热-水-力控制方程的一般形式,对各耦合项的物理意义进行了分析。以等温条件下水-力耦合的Biot渗透固结理论和等压条件下热-力耦合的热弹性理论两种退化形式为基础,给出耦合系数的物理意义及其函数表达式。研究表明,其中一些耦合系数实际上有相同的物理意义和数学形式,因而可使控制方程得到简化。针对不同的介质特性以及热、水、力条件,给出几种特定情形下控制方程的简化形式。以无限大多孔介质中球域热源的热力学响应分析为例,对一些耦合项的影响程度进行了比较研究。

The governing equations of coupled thermo-hydro-mechanical consolidation for a homogeneous isotropic saturated porous medium are given firstly. The physical meanings of every coupling term are analyzed. Based on both Biot＇s consolidation theory under isothermal conditions and thermo-mechanical theory under isobaric conditions, the physical meanings of coupling coefficients and their expression equations are given. The studies show that some coupling coefficients are same in their function formations completely; and the governing equations can be simplified greatly. For this, some simplified governing equations for some typical condition in engineering are given. As an example, thermo-hydro-mechanical characteristics are discussed for the problem of infinite saturated porous medium subjected to a global heat source of variable strength with time. The effects of some coupling terms are analyzed comparatively.