Multiscale flow and deformation in hydrophilic swelling porous media

Abstract

A three-scale theory of swelling porous media is developed. The colloidal or polymeric sized fraction and vicinal water (water next to the colloids) are considered on the macroscale. Hybrid mixture theory is used to upscale the colloids with the vicinal water to form mesoscale swelling particles. The mesoscale particles and bulk phase water (water next to the swelling particles) are then homogenized via an asymptotic expansion technique to form a swelling mixture on the macroscale. The solid phase on the macroscale can be viewed as a porous matrix consisting of swelling porous particles. Two Darcy type laws are developed on the macroscale, each corresponding to a different bulk water connectivity. In one, the bulk water is entrapped by the particles, forming a disconnected system, and in the other the bulk water is connected and flows between particles. In the latter case the homogenized equations give rise to a distributed model with microstructure in which the vicinal water is represented by sources/sinks at the macroscale. The theory is used to construct a three-dimensional model for consolidation of swelling clay soils and new constitutive relations for the stress tensor of the swelling particles are developed. Several heuristic modifications to the classical Terzaghi effective stress principle for granular (non-swelling) media which account for the hydration forces in swelling clay soils recently appeared in the literature. A notable consequence of the theory developed herein is that it provides a rational basis for these modified Terzaghi stresses.