Numerical Particle-Scale Study of Swelling Pressure in Clays

Given a montmorillonite clay at high porosity and saturated by monovalent counterions, the particle level responses of the clay to different external loadings are investigated. As analytical solutions are not possible for complex arrangements of particles, computational micromechanical models are employed (based on 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. Then the disjoining pressures are calculated 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 porefluid 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 estimates the swelling pressure in various periodic structured clay particle arrangements. This work may lead towards theoretical predictions of the macroscopic load deformation response of montmorillonitic soils based on micromechanical modelling of particles.