Davis and Knopoff [1995] presented a model based upon a boundary element method to compute the elastic properties of cracked solids. Then, they compared their results with the predictions of the noninteracting method, the self- consistent method and the differential self-consistent method. They showed that the noninteracting method "gives a more satisfactory approximation to the calculation of elastic moduli" than do the other studied methods. We modified the conclusions of Davis and Knopoff [1995]. The predictions derived from the noninteracting method are appropriate only when crack density is much smaller than 1 (<0.1). In addition, as the cracked solids are assumed to be isotropic, averages similar to the Voigt's and Reuss' averages must be performed to account for all crack orientations. Therefore, the previous statistical approaches lead to an upper and a lower bound for effective elastic moduli, instead of a single value. We pointed out that the noninteracting curve in the bulk modulus-crack density plane considered by Davis and Knopoff is midway between the bounds predicted by the differential self-consistent model. This result is valid at low crack densities, but also at high crack densities, where the noninteracting method is no more appropriate. Actually, the test provided by Davis and Knopoff [1995] is an additional one to show that the differential self-consistent method predictions are very good and fit well the numerical data obtained by these authors.
AGU Index Terms: 5100 Physical Rock Properties; 5102 Acoustic properties; 5104 Fracture and flow
Keywords/Free Terms: Effective medium, Elastic properties, Cracks.
JGR-Solid Earth 96JB02461
Vol. 101
, No. B11
, p. 25,373