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

There is general agreement between different theories giving expressions for the overall properties of materials with dry, aligned cracks if the number density of cracks is small. There is also very fair agreement for fluid-filled isolated cracks. However, there are considerable differences between two separate theories for fluid-filled cracks with equant porosity. Comparison 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 unlikely to apply, expressions correct to second order (in the number density) provide a worse fit. It also appears that the ratio of wavelength to crack size is not sufficiently great for any detailed comparison with effective-medium theories, which are valid only when this ratio is large. The data show dispersion effects for dry cracks and scattering, neither of which will occur at sufficiently long wavelengths. Data from the water-saturated samples indicate that the effect of equant porosity is significant, although the two theories differ strongly as to just how significant. Once again, and in spite of the reservations mentioned above, a reasonable fit between theory and observation can be shown.