The effect of cracks in rocks on Poisson's ratio

An expression for the lateral strain under uniaxial compressive stress in a body containing cracks and voids of any size and shape is derived in terms of the elastic properties of the solid matrix and displacements at the boundaries of the cracks and voids. The effect of cracks is evaluated by using the plane stress solution for a low concentration of narrow elliptical cracks. At low stress when cracks are open, Poisson's ratio is found to be less than the intrinsic value. Cracks close under compressive stress, but possible sliding of one crack face relative to another is found to increase Poisson's ratio above the intrinsic value. It is shown that the hysteresis observed in plots of axial and lateral strain versus uniaxial compressive stress should not occur when plotted as volumetric strain versus stress. The predicted behavior compares favorably with that of Westerly granite in compression and with the observed behavior of crystalline rocks in general.