MULTISCALE FLOW AND DEFORMATION IN HYDROPHILIC SWELLING POROUS-MEDIA

A three-scale theory of swelling porous media is developed. The colloi dal or polymeric sized fraction and vicinal water (water next to the c olloids) are considered on the microscale. Hybrid mixture theory is us ed to upscale the colloids with the vicinal water to form mesoscale sw elling 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 consis ting of swelling porous particles. Two Darcy type laws are developed o n the macroscale, each corresponding to a different bulk water connect ivity. in one, the bulk water is entrapped by the particles, forming a disconnected system, and in the other the bulk water is connected and hows between particles. In the latter case the homogenized equations give rise to a distributed model with microstructure in which the vici nal water is represented by sources/sinks at the macroscale. The theor y is used to construct a three-dimensional model for consolidation of swelling clay soils and new constitutive relations for the stress tens or of the swelling particles are developed. Several heuristic modifica tions to the classical Terzaghi effective stress principle for granula r (non-swelling) media which account for the hydration forces in swell ing clay soils recently appeared in the literature. A notable conseque nce of the theory developed herein is that it provides a rational basi s for these modified Terzaghi stresses.