Plane strain analysis of a stationary hydraulic fracture in a poroelastic medium

This paper presents a plane strain analysis of a constant length hydraulic fracture embedded in an infinite poroelastic domain. The fracture is uniformly loaded by fluid pressurisation. For clarity of physical interpretation, this loading is decomposed into two modes, consisting respectively of a unit step for the normal stress and a unit step for the pore pressure along the fracture. For each loading mode, the transient fracture profile, the fracture volume, the leak-off volume, and the stress intensity factor are analyzed. First, short- and long-term asymptotic expressions are derived in closed form based on analytical arguments. The full transient behaviors are then formulated as a pair of coupled singular integral equations. The solutions are found via Laplace transform, and numerical discretization of the integral equations.