On the relationship between stress and elastic strain for porous and fractured rock

Modeling the mechanical deformations of porous and fractured rocks requires a stress–strain relationship. Experience with inherently heterogeneous earth materials suggests that different varieties of Hooke's law should be applied within regions of the rock having significantly different stress–strain behavior. We apply this idea by dividing a rock body conceptually into two distinct parts. The natural strain (volume change divided by rock volume at the current stress state), rather than the engineering strain (volume change divided by the unstressed rock volume), should be used in Hooke's law for accurate modeling of the elastic deformation of that part of the pore volume subject to a relatively large degree of relative deformation (i.e., cracks or fractures). This approach permits the derivation of constitutive relations between stress and a variety of mechanical and/or hydraulic rock properties. We show that the theoretical predictions of this method are generally consistent with empirical expressions (from field data) and also laboratory rock experimental data.