On plane-strain fluid-driven shear fracture propagation in elastic solids

Abstract

SUMMARY We present a numerical model for the nucleation and propagation of a plane-strain fluid-driven fracture on a plane of weakness, subjected to remote shear and compressive stresses. Shearinduced dilatation, which is the normal opening of fracture surfaces associated with shear slippage, plays an important role in providing fluid conductivity. An incompressible Newtonian fluid with low viscosity is injected into the shear fracture in an impermeable elastic medium. On the basis of the plane-strain elasticity, the resulting slip, crack length and net shear stress which is defined as the difference between applied shear stress and frictional stress based on the Coulomb law, are interconnected. A slip-weakening friction law is implemented to account for surface roughness and shear-induced dilatation. On the plane of weakness, there is no stress singularity at the shear crack tip. The governing equations are derived for equilibrium cracks and a scaling is proposed to simplify those equations. Numerical results based on a Chebyshev polynomial expansion show that the size of slipping region can grow under negative net shear stresses as a result of the slip-weakening mechanism, which helps explain the success of hydraulic fracturing in promoting shear fracturing along planes of weakness. A critical length for hydraulic shear fracture initiation exists as a result of use of a slip-weakening friction law and removal of stress singularity. It is found that the nucleation length corresponds to the second eigenvalue of an eigenvalue problem. Similar to dislocation cores, expenditure of energy is required for crack nucleation from this critical size. The crack can grow stably after nucleation if the fluid pressure decreases accordingly. For stable shear crack growth, the net shear stress should follow a critical curve obtained numerically for the quasi-static equilibrium cracks. If the net shear stress is larger than its critical value indicating the onset of a dynamic instability, the shear crack will propagate unstably, or it will be arrested as lack of driving forces. Since the net shear stress is bounded, there is therefore another critical length for the onset of unstable crack growth.