An immersed phase field fracture model for fluid-infiltrating porous media with evolving Beavers-Joseph-Saffman condition

TL;DR

This paper introduces a novel phase field model for brittle fracture in fluid-infiltrating porous media, integrating fluid flow and fracture evolution without explicit interface parametrization, suitable for complex geological applications.

Contribution

It develops a coupled phase field and flow model that handles fluid-solid interactions and evolving fractures in porous media without specialized meshing or interface tracking.

Findings

Successfully models fluid flow and fracture evolution in porous media.

Eliminates need for interface-specific meshing or enrichment functions.

Applicable to complex geological fracture problems.

Abstract

This study presents a phase field model for brittle fracture in fluid-infiltrating vuggy porous media. While the state-of-the-art in hydraulic phase field fracture considers Darcian fracture flow with enhanced permeability along the crack, in this study, the phase field not only acts as a damage variable that provides diffuse representation of cracks or cavities, but also acts as an indicator function that separates the domain into two regions where fluid flows are governed by Stokes and Darcy equations, respectively. Since the phase field and its gradient can be respectively regarded as smooth approximations of the Heaviside function and Dirac delta function, our new approach is capable of imposing interfacial transmissibility conditions without explicit interface parametrizations. In addition, the interaction between solid and fluid constituents is modeled by adopting the concept of mixture theory, where the fluid velocities in Stokes and Darcy regions are considered as relative measures compared to the solid motion. This model is particularly attractive for coupled flow analysis in geological materials with complex microstructures undergoing brittle fracture often encountered in energy geotechnics problems, since it completely eliminates the needs to generate specific enrichment function, integration scheme, or meshing algorithm tailored for complex geological features.