A Fully Coupled XFEM Model for Flow and Deformation in Fractured Porous Media with Explicit Fracture Flow

A hydro-mechanical model with explicit fracture flow is presented for the fully coupled analysis of flow and deformation in fractured porous media. Extended finite element method (XFEM) is utilised to model the fracture discontinuity in the two-dimensional plane-strain mechanical model. Two flow models, a one-dimensional laminar flow within the fracture and a two-dimensional Darcy flow through porous media, are considered. The flow domains are coupled through a mass exchange term (leak-off) accounting for discontinuous Darcy flow velocity across the fracture. Particular attention is given to the coupling of the flow domains with the mechanical model. Spatial and temporal discretisation is achieved using the standard Galerkin method and the finite difference technique, respectively. Unlike the successive coupled models where the results of the mechanical model is used to update the fracture flow model and vice versa, the fully coupled hydro-mechanical formulation is solved simultaneously. The model is verified against several closed form solutions from the literature. The impact of formation flow and leak-off flow on the fracture opening due to injected fluid pressure is discussed.