Phase field modeling of partially saturated deformable porous media

TL;DR

This paper introduces a phase field-based poromechanical model for partially saturated deformable porous media, enhancing surface tension description and capillary pressure relations, incorporating micro-scale effects and strain gradient theory.

Contribution

It presents a novel phase field approach with improved surface tension modeling and a generalized capillary pressure relation, integrating micro-scale effects into poromechanical modeling.

Findings

Enhanced surface tension description via phase field regularization.

Generalized Darcy's law with chemical potential gradient.

Inclusion of micro-scale effects and strain gradient effects.

Abstract

A poromechanical model of partially saturated deformable porous media is proposed based on a phase field approach at modeling the behavior of the mixture of liquid water and wet air, which saturates the pore space, the phase field being the saturation (ratio). While the standard retention curve is expected still to provide the intrinsic retention properties of the porous skeleton, depending on the porous texture, an enhanced description of surface tension between the wetting (liquid water) and the non-wetting (wet air) fluid, occupying the pore space, is stated considering a regularization of the phase field model based on an additional contribution to the overall free energy depending on the saturation gradient. The aim is to provide a more refined description of surface tension interactions. An enhanced constitutive relation for the capillary pressure is established together with a suitable generalization of Darcy's law, in which the gradient of the capillary pressure is replaced by the gradient of the so-called generalized chemical potential, which also accounts for the \lq\lq force\rq\rq\, associated to the local free energy of the phase field model. A micro-scale heuristic interpretation of the novel constitutive law of capillary pressure is proposed, in order to compare the envisaged model with that one endowed with the concept of average interfacial area. The considered poromechanical model is formulated within the framework of strain gradient theory in order to account for possible effects, at laboratory scale, of the micro-scale hydro-mechanical couplings between highly-localized flows (fingering) and localized deformations of the skeleton (fracturing).