On A Saturated Poromechanical Framework and Its Relation to Abaqus Soil Mechanics and Biot Poroelasticity Frameworks

Abstract

We introduce a conservational and constitutive framework for a closed and isothermal two-phase material system consisting of a deformable porous solid matrix and a fully saturating, single-phase, and compressible pore fluid without inter-phase mass exchange. We re-derive a generalized fluid mass balance law using fundamental transport rules. We also summarize from the literature a fundamental force balance law for the fluid-solid mixture that does not require any effective stress law a priori. We show that the two conservation laws are coupled naturally to second-order without any constitutive prerequisites. This differs from Biot poroelasticity, which first postulates first-order fluid-solid coupling as two linearized constitutive relationships and then enforces them into simple Eulerian form of conservation laws. Next, we examine a limiting-case unsaturated soil mechanics framework implemented in Abaqus, by assuming isothermal conditions, full saturation, and no adsorption, and then relate it to our framework. We prove that (1) the two mass balance laws are always equivalent regardless of fluid constitutive behaviors, and (2) the two force balance laws are equivalent in their specific forms with a linearly elastic solid skeleton. Finally, taking advantage of a fundamental pore constitutive law, we show how our framework, and by extension the limiting-case Abaqus framework, naturally gives rise to the distinction between drained and undrained settings, and reduces to Biot poroelasticity under simplifying conditions. Notably, our framework indicates the presence of an additional solid-to-fluid coupling term when the solid particle velocity is non-orthogonal to the Darcy velocity.