2D coupled HM-XFEM modeling with cohesive zone model and applications to fluid-driven fracture network

• An XFEM coupled hydro-mechanical model with a non-regularized cohesive zone constitutive law is developed.
• A Lagrange multiplier formulation is considered to stabilize the fracture propagation and the fluid exchanges.
• The competition mechanisms between fluid-driven fractures are investigated.

The present work focuses on a new numerical model for the fully coupled hydro-mechanical analysis of groundwater flows through poroelastic saturated media. In particular, the presence and eventual propagation of fluid-driven fractures is accounted for within a non-regularized cohesive zone model. In this paper, the fracture propagation is considered as a reactivation process: the fracture already exists and evolves (i.e. opens or closes) on a pre-defined path initially constrained. The Talon-Curnier constitutive law is considered for the fracture interfaces and its expression has been adapted to the hydro-mechanical coupling related to the fracture evolution. The fluid pressure inside the fracture is governed by the lubrication equation. The momentum-stress balance equations involving fluid flow and deformation of the solid porous matrix are derived within the framework of the generalized Biot theory. The extended finite element method (XFEM) is preferred to a standard finite element spatial discretization in order to easily handle the presence and evolution of discontinuities in the porous medium. A set of four Lagrange multipliers is introduced to prevent spurious oscillations of the numerical solution at the interface. Comparisons between numerical results and theoretical solution assess the validity of the model presented in this paper. In addition, the hydro-mechanical interactions between neighboring fractures and the effects of the permeability of the porous medium are investigated. We also demonstrate the capability of our model to handle non-planar fracture paths.