Integral Equations for a Planar Crack Subjected to Arbitrary Loadings in a Fluid-Filled, Poroelastic, Infinite Solid

Abstract

Integral equations are derived for a planar crack of arbitrary shape, subjected to both normal and shear tractions as well as fluid pressure, in an infinite, fluid-saturated, poroelastic, isotropic solid. The obtained equations relate the surface tractions and fluid pressure on crack surfaces to relative crack-surface displacements and leak-off flux into the porous medium. It is intended to implement the equations in a 3D simulator of hydraulic fracturing in oil reservoirs. Some discussions are given on reduction of the present solutions to the known ones as special cases and to pure shear mode solutions; it is found that the poroelastic effect does not disappear even for the pure shear mode.