Numerical Particle-Scale Study of Swelling Pressure in Clays

The particle level responses to different external loadings of a montmorillonitic clay soil are investigated numerically. The soil is saturated by a solution of monovalent counterions, of varying concentrations. We use finite element micromechanical models (based on the Poisson-Nernst-Planck equations) to estimate counterion and electrical potential distributions around individual clay particles at various distances from one another, since analytical solutions are not possible for these complex arrangements of particles. Disjoining pressures are then estimated 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 between 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 so-called “disjoining” or “osmotic” pressure. Because of this disjoining pressure, it is clear that particles need not 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 micro-electro-chemo-mechanical modelling of particles.