Estimating vertical and lateral pressures in periodically structured montmorillonite clay particles

Abstract

Given a montmorillonitic clay soil at high porosity and saturated by monovalent counterions, we investigate the particle level responses of the clay to different external loadings. As analytical solutions are not possible for complex arrangements of particles, we employ computational micromechanical models (based on the solution of the Poisson-Nernst-Planck equations) using the finite element method, to estimate counterion and electrical potential distributions for particles at various angles and distances from one another. We then calculate the disjoining pressures using the Van't Hoff relation and Maxwell stress tensor. As the distance between the clay particles decreases and double-layers overlap, the concentration of counterions in the micropores among clay particles increases. This increase lowers the chemical potential of the pore fluid and creates a chemical potential gradient in the solvent that generates the socalled 'disjoining' or 'osmotic' pressure. Because of this disjoining pressure, particles do not need to contact one another in order to carry an 'effective stress'. This work may lead towards theoretical predictions of the macroscopic load deformation response of montmorillonitic soils based on micromechanical modelling of particles.

Swelling and shrinking of porous materials: from colloid science to poromechanics

“…Some of the papers published in Physical Sciences concentrate their efforts on the mesoscale computational modeling of expansive porous media, such as clays and gels (see e.g. Narsilio et al 2010). The application in Medical Sciences focuses on biological tissues, such as intervertebral disc and osteo-articular porous materials at coarser scale where the fluid in the nano-pores and the solid matrix have been homogenized to give rise to a mesoscopic description (Lemaire et al 2010).…”