A coupled variational phase-field and multiphase flow model for hydraulic fracturing in quasi-brittle materials

Abstract This study presents a novel coupled variational phase-field and multiphase flow model for simulating quasi-brittle hydraulic fracturing in unsaturated porous media. The multiphase flow is governed by mass and momentum conservation, incorporating a modified Darcy–Poiseuille law to consistently describe wetting and non-wetting fluid transport in both porous matrix and fracture domains. Capillary effects are captured via the van Genuchten retention model. The fluid pressure field is coupled with a phase-field regularized cohesive zone model to simulate fluid-driven crack initiation and propagation. The coupled system is discretised using the finite element method and solved with a staggered Newton–Raphson scheme. Model verification is conducted against analytical benchmarks, followed by application to investigate the influence of non-wetting pressure on fracture interaction. Simulated results show that high non-wetting pressure promotes propagation of natural fractures upon intersection with hydraulic fractures, through the combined effects of pre-opening of natural fractures and the sustained high effective pressure within the connected fracture network. This observed phenomenon differs from single-phase simulation results in saturated-media, providing a novel perspective on hydraulic fracturing mechanisms. The capacity of the proposed model to simulate complex unsaturated hydraulic fracturing is well validated.