基于多孔介质理论的冻土水热迁移耦合模型推导

在多孔介质理论的基础上，基于非线性达西定律并假设水分迁移过程为单向、可逆及水分迁移过程中无溶质迁移，推导得出了无相变以及考虑相变的水分迁移方程；引入土体传热方程和土骨架质量密度变化方程，过程中考虑了冻土中温度变化，扩散和对流，以及水分相变和温度、质量变化之间的相互影响。联立各方程得到了非饱和冻土水热分布控制方程，建立了非饱和冻土水热迁移耦合模型。文中亦对模型中具体参数的确定方法提出了建议。方程属于非线性偏微分方程，无法得出解析解，须采用数值解法。

Derivation of water and thermal migration coupled model based on theory of porous media in seasonal frozen soil

In this paper, unsaturated frozen soil moisture and heat transfer coupling model were estab- lished based on the theory of porous media. Assuming that the water migration process was one - way and reversible and without solute transport, water transport equation of without and with phase transi- tion were derived based on nonlinear Darcy＇s law. Then the heat transfer equation in soil and the change equation of quality of soil skeleton density were introduced into the model and in this process, the temperature variation during phase change of water in frozen soil and the interaction between tem- perature and quality changes were considered. At the same time, the effect of diffusion and convec- tion were taken into account too. Eventually the equation of water and thermal distribution of unsatu- rated frozen soil was got. And the method for determining the model parameters was given. Model e- quations are nonlinear partial differential equations, only numerical method but analytical solution can be obtained.