Modeling fracture propagation in a rock‐water‐air system with the assumed enhanced strain method

Abstract This article presents a fully coupled finite element method for the single cohesive fracture propagation in a deformable porous medium (rock) interacting with two immiscible pore fluids, that is, water and air. The cohesive fracture is represented with the assumed enhanced strain method which can be cast into a classical plasticity framework. The governing equations for the solid skeleton deformation, pore water flow, and pore air flow are derived based on the mixture theory. The coupled nonlinear global system is then solved by the standard Galerkin finite element method. The numerical implementation is verified against the numerical and analytical solutions previously reported in the literature. The proposed model is capable of capturing fluid transfer between the fracture and the host rock due to the pressure difference. The numerical examples demonstrate that the behavior of fracture propagation can be significantly influenced by the capillary pressure inside fracture and vice versa. Since the fracture is represented at the level of Gauss points, the proposed numerical model can be easily implemented on any standard finite element code base.