A continuum framework for three-phase soils including microstructural effects

Nature as described by classical mechanics is governed by a set of physical laws in the balanced form of various physical entities, including mass, linear and angular momenta, energy, and entropy (entropy inequality). These laws must be obeyed in the development of any theory of applied mechanics. In soil mechanics, one deals with porous material composed of solids and fluids strongly interacting with each other. Within the framework of continuum mechanics, materials are assumed to be infinitesimally continuous, which renders an unavoidable hypothesis for soil. That is, each of the solid, liquid, and gaseous phases can be treated as a ‘smeared’ medium superimposed by and interacting with other constituents at the same infinitesimal point. Such treatment, however, requires the fundamental balance laws be recast into more elaborative forms involving microstructural effects (inter-phase actions). This paper introduces such a continuum framework based on existing theories of immiscible mixtures. To accommodate the pre-flow response, in the present work, the energy terms attributable to shear deformation and spin, allied with a coupling effect, are included. In the framework, a set of extended effective stresses is defined; indicating that the soil skeleton has an effective stiffness, which may still be positive-definite after failure. The framework is general and may pave a way for solving practical geotechnical problems covering both pre- and post-failure stages.