Fundamental solutions for an instantaneous point force and an instantaneous fluid point source are derived for an infinite, fluid-saturated, poroelastic solid with zero permeability in one direction. Applying these solutions and Cleary’s reciprocal theorem to the three-dimensional problem of a pressurized plane crack yields two integral equations, which relate normal tractions and fluid pressure on the crack faces to crack opening and fluid injection rate per unit fracture area. An important application of these equations is the prediction of hydraulic fractures induced during water-flooding of reservoirs to enhance gas and oil recovery. Zero permeability in one direction may be a good approximation for the case in which the reservoir is sandwiched between two impermeable rock layers.

M. P.
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Fundamental Solutions for a Fluid-Saturated Porous Solid
International Journal of Solids and Structures
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