水-气-颗粒固体三相混合系统的流体动力学

Hydrodynamic theory of grains, water and air

按照经典物理中处理混合物的一般热力学方法,将近年来报道的颗粒固体流体动力学进一步推广到孔隙被水和气填充的情形,建立了其自由能的初步模型.水-气-颗粒三相体系是与岩土工程和地质灾害密切相关的材料,但其经典宏观物理基础却一直未能全面澄清.目前用于分析这类混合物力学行为的基本工程理论含Darcy渗流定律、Terzaghi有效应力及其运动方程(即本构方程)等内容.通过与经典物理对比,本文澄清了渗流对应于不同相之间的质量扩散,有效应力与这类材料特有的体积填充形式自由能有关,这两部分内容工程与物理是一致的.目前的分歧具体体现在材料建模对象上,前者认为是本构方程,而后者是自由能和迁移系数.该分歧的解决将是建立这类材料的连续介质物理基础、突破本构方法面临的困境的一个关键.

Starting from the thermodynamic framework of a mixture, granular solid hydrodynamics （GSH）, which has been developed in recent years, is generalized to the cases in which water and/or gas are present in the interstitials of a granular solid. A preliminary model for the free energy of the mixture is proposed. The three-phase system of grains, water and air is a material relevant to soil mechanics and rock engineering, especially geological catastrophies, for which the macroscopic physics has not been clarified as yet. The engineering theory used currently for analyzing this mixture contains the Darcy’s law of intersticial flow, the effective stress by Terzaghi, including its equation of motion （i.e., the constitutive relation）. Comparing it with the theory of GSH, we clarify that Darcy’s equation represents mass diffusion, and the effective stress can be explained by the specific model of free energy that is volumetric fill-ing.The usual engineering approach and GSH, a theory based on physics, are consistent, but we do find some discrepancies, especially on how to parameterize the model：the engineering appraoch employs varying constitutive relation, but the physical approach considers the free energy and the transport coefficients. Clarifying this, we believe, is important for eventually obtaining a unified continuous mechanical theory of soils,especially nonsaturated ones, which is complete and satisfying from physics’s point of view.