Rocks as poroelastic composites

In Biot's theory of poroelasticity, elastic materials contain connected voids or pores and these pores may be filled with fluids under pressure. The fluid pressure then couples to the mechanical effects of stress or strain applied externally to the solid matrix. Eshelby's formula for the response of a single ellipsoidal elastic inclusion in an elastic whole space to a strain imposed at infinity is a very well-known and important result in elasticity. Having a rigorous generalization of Eshelby's results valid for poroelasticity means that the hard part of Eshelby' work (in computing the elliptic integrals needed to evaluate the fourth-rank tensors for inclusions shaped like spheres, oblate and prolate spheroids, needles and disks) can be carried over from elasticity to poroelasticity - and also thermoelasticity - with only trivial modifications. Effective medium theories for poroelastic composites such as rocks can then be formulated easily by analogy to well-established methods used for elastic composites. An identity analogous to Eshelby's classic result has been derived [Physical Review Letters 79:1142-1145 (1997)] for use in these more complex and more realistic problems in rock mechanics analysis. Descriptions of the application of this result as the starting point for new methods of estimation are presented.