The effects of stress and fluid pressure on the anisotropy of interconnected cracks

The cracks in a porous matrix that is subjected to a change in the applied stress or fluid pressure will undergo a distortion related to their orientation relative to the principal directions of the applied stress. Both the crack distribution and the fluid-flow properties of the aggregate will be altered as a consequence, of a change in either the applied stress or fluid pressure, resulting in a change in the effective elastic parameters of the material. An effective medium theory, based on the method of smoothing and incorporating a transfer of fluid between connected cracks via non-compliant pores, is used to derive an expression for the effective elastic parameters of the material, to first order in the crack density E. This expression involves a dependence on both the applied stress and the fluid pressure. and is used to determine the effects on the anisotropy of the effective medium of the applied stress and the fluid pressure. A number of azimuthally symmetric compressive stresses are applied to an isotropic crack distribution to determine the material properties of the resulting transversely isotropic effective medium, as a function of the excess in compressive stress over fluid pressure. As a result of competing processes, the theory predicts that, for a non-hydrostatic stress, there is a pressure at which the anisotropy reaches a maximum value before the properties of the effective medium decay, under increasing stress, to those of the uncracked matrix. The theory does not, however, account for the material failure that will occur at large compressive stresses, Finally, the theory predicts that S waves are more sensitive to changes in the applied stress or fluid pressure than P waves.