Growth of a radial hydraulic fracture accounting for the viscous fluid flow in a rough cohesive zone

We investigate the growth of an axisymmetric hydraulic fracture in an impermeable quasi-brittle material accounting for the presence of a fluid lag. The process zone is simulated using a linear softening cohesive zone model and is characterized by an increased resistance to the fluid flow due to fracture roughness. In the context of a partially-filled cohesive zone, the fracture roughness decreases the tip permeability and further localizes the pressure drop inside the cohesive zone. As a result, a wider fracture opening and higher net pressure are obtained, indicating an increase of the apparent fracture energy. Similar to the linear elastic case, the fracture growth is closely related to a dimensionless parameter ψ which describes the transition nature from the lag-viscosity-toughness regimes. The propagation also depends on the ratio between the in-situ minimum confining stress and the maximum cohesive traction σo/σT and the type of fluid flow deviation in small rough apertures.