On constitutive equations and effective stress principles for deformable, double-porosity media

Tuncay and Corapcioglu [1995] used volume averaging methods to derive an effective stress principle for the bulk volumetric strain in a deformable double-porosity medium. The coefficients of the matrix pore pressure and fracture pore pressure in their equation for the effective stress are shown to be identical to those which can be obtained from the constitutive equation approach of Berryman and Wang [1995]. Representative values for a fractured Berea sandstone show that a change in pore pressure within matrix blocks produces about 10% of the volume change resulting from an equal but opposite change in confining pressure, whereas the same change in pore pressure within fractures is about 90% as effective. A similar result is true for Westerly granite.