On the Poroelastic Biot Coefficient for a Granitic Rock

Abstract

The Biot coefficient is a parameter that is encountered in the theory of classical poroelasticity, dealing with the mechanics of a fluid-saturated porous medium with elastic grains and an elastic skeletal structure. In particular, the coefficient plays an important role in the partitioning of externally applied stresses between the pore fluid and the porous skeleton. The conventional approach for estimating the Biot coefficient relies on the mechanical testing of the poroelastic solid, in both a completely dry and a fully saturated state. The former type of tests to determine the skeletal compressibility of the rock can be performed quite conveniently. The latter tests, which determine the compressibility of the solid material constituting the porous skeleton, involve the mechanical testing of the fully saturated rock. These tests are challenging when the rock has a low permeability, since any unsaturated regions of the rock can influence the interpretation of the compressibility of the solid phase composing the porous rock. An alternative approach to the estimation of the solid grain compressibility considers the application of the multi-phasic theories for the elasticity of composite materials, to estimate the solid grain compressibility. This approach requires the accurate determination of the mineralogical composition of the rock using XRD, and the estimation of the elasticity characteristics of the minerals by appealing to published literature. This procedure is used to estimate the Biot coefficient for the Lac du Bonnet granite obtained from the western region of the Canadian Shield.