Spatial and temporal constraints of the cohesive modeling: A unified criterion for fluid-driven fracture

We present a unified criterion for cohesive modeling of fluid-driven fracture based on the dimensional analysis to simultaneously provide the constraint for cohesive element and time step sizes. Complicated by the nonlinear interaction between solid deformation and fluid flow, the underlying correlation between discretization and physical parameters of fluid-driven fracture is still unclear. This work studies this correlation through the dimensionless process of the governing equations that associate the cohesive element and time step sizes in a discrete regime. Three characteristic parameters (i.e., related to crack opening, fluid pressure, and fracture length) are introduced in the derivation, and two dimensionless parameters are proposed to construct the unified criterion. The criterion is validated by numerical tests of toughness-dominated fracture with various conditions including the modulus of solid, injection rate of fluid, fracture energy, and in-situ stress. The proposed criterion determines the spatial and temporal constraints of the cohesive zone model for modeling fluid-driven fracture, which is often treated empirically in previous practices.