饱和多孔介质流固耦合渗流的数学模型

将基于多孔介质的有效应力原理引入流固耦合渗流中，并根据平衡条件得出了应力场方程；充分分析流固耦合渗流的物理特性，建立起孔隙度和渗透率动态模型；依据流体力学连续性方程，考虑流固耦合情形下多孔介质骨架变形特性和流体的可压缩性，得到了孔隙流体的连续性方程，即渗流场方程。在以上诸方程的基础上辅助以定解条件，建立起了完备的饱和多孔介质流固耦合渗流的数学模型。本文还对模型进行了简化分析，并与经典一维固结理论作定性对比，分析表明，经典的固结理论可认为是本文模型的一种简化。进一步的算例求解和验证工作正在进行中。

Mathematical modeling of flow in saturated porous media on account of fluid-structure coupling effect

Principle of effective stress in porous media is introduced into fluid-structure coupling theory, then according to the equilibrium condition, the stress equation is established. On account of physical properties of coupling, the dynamic models of porosity and permeability are acquired. Meanwhile, in consideration of the deformation of the skeleton and the compressibility of the fluid, the flow equation is obtained. Thus, self-contained governing equations for fluid structure coupling in porous media are constructed by combining the aforementioned equations and the constraint conditions. One dimensional consolidation equation is obtained by simplifying the model, and it is compared with the traditional consolidation equation by qualitative analysis. The results indicate that the traditional consolidation theory can be regarded as one particular case of our model. Numerical simulations and validations of some samples are the subject of ongoing research.