A Multiscale Theory of Swelling Porous Media: II. Dual Porosity Models for Consolidation of Clays Incorporating Physicochemical Effects

A three-scale theory of swelling clay soils is developed which incorporates physico-chemical effects and delayed adsorbed water flow during secondary consolidation. Following earlier work, at the microscale the clay platelets and adsorbed water (water between the platelets) are considered as distinct nonoverlaying continua. At the intermediate (meso) scale the clay platelets and the adsorbed water are homogenized in the spirit of hybrid mixture theory, so that, at the mesoscale they may be thought of as two overlaying continua, each having a well defined mass density. Within this framework the swelling pressure is defined thermodynamically and it is shown to govern the effect of physico-chemical forces in a modified Terzaghi's effective stress principle. A homogenization procedure is used to upscale the mesoscale mixture of clay particles and bulk water (water next to the swelling mesoscale particles) to the macroscale. The resultant model is of dual porosity type where the clay particles act as sources/sinks of water to the macroscale bulk phase flow. The dual porosity model can be reduced to a single porosity model with long term memory by using Green's functions. The resultant theory provides a rational basis for some viscoelastic models of secondary consolidation.     

Micromechanical computational modeling of expansive porous media

A modified Terzaghi principle is proposed to describe the influence of locally coupled electro-chemo-mechanical processes in highly compacted swelling clays upon the form of the macroscopic modified effective stress principle. The two-scale model is derived using the homogenization procedure to upscale the microscopic behavior of a two-phase system composed of clay particles saturated by a completely dissociated electrolyte aqueous solution. Numerical experiments are performed to illustrate the results in a particular cell geometry. To cite this article: M.A. Murad, C. Moyne, C. R. Mecanique 330 (2002) 865–870.     

A Two-Scale Model for Coupled Electro-Chemo-Mechanical Phenomena and Onsager’s Reciprocity Relations in Expansive Clays: I Homogenization Analysis

The macroscopic model governing coupled electro-chemo-mechanical phenomena in expansive clays is revisited within a rigorous homogenization procedure applied to the microscopic governing equations which describe the local interaction between charged clay particles and a binary monovalent aqueous electrolyte solution. The up-scaling of the microscopic electro-hydro-dynamics leads to a two-scale approach wherein the macroscopic model appears governed by a fully coupled form of Onsager’s reciprocity relations, mass conservation equations and a modified Terzaghi’s effective stress principle. In addition, the two-scale approach provides microscopic representations for the effective coefficients which are exploited herein to obtain further insight in the constitutive behavior of the electrochemical parameters and the swelling pressure. Among other effects, we show that these microscopic closure relations are mainly dictated by the spatial variability of a microscale electric potential which satisfies a local version of the Poisson–Boltzmann problem in a periodic unit cell, The proposed framework allows to address various relevant still open issues regarding the constitutive behavior of swelling systems, Among them we give particular emphasis on the analysis of the influence of the fluctuation and distortion of the electrical double layer upon the magnitude of the electrochemical coefficients and the precise local conditions for the validity of the symmetry of Onsager’s relations.