Effective-medium theories for fluid-saturated materials with aligned cracks

There is general agreement between different theories giving expressions fo r the overall properties of materials with dry, aligned cracks if the numbe r density of cracks is small. There is also very fair agreement for fluid-f illed isolated cracks. However, there are considerable differences between two separate theories for fluid-filled cracks with equant porosity. Compari son with recently published experimental data on synthetic sandstones gives a good fit with theory for dry samples. However, although the crack number density in the laboratory sample is such that first-order theory is unlike ly to apply, expressions correct to second order (in the number density) pr ovide a worse fit. It also appears that the ratio of wavelength to crack si ze is not sufficiently great for any detailed comparison with effective-med ium theories, which are valid only when this ratio is large. The data show dispersion effects for dry cracks and scattering, neither of which will occ ur at sufficiently long wavelengths. Data from the water-saturated samples indicate that the effect of equant porosity is significant, although the tw o theories differ strongly as to just how significant. Once again, and in s pite of the reservations mentioned above, a reasonable fit between theory a nd observation can be shown.