Effective moduli of microcracked rocks: Theories and experiments

This paper compares and contrasts the predicted effective moduli by the self-consistent and noninteracting methods and examines the range of validity for both models; predictions by these two models are compared to experimental observations on natural rocks containing microcracks and artificial rocks containing inserted microcracks. Crack density (∈) in real rocks is obtained by counting cracks under microscope and those in replicated rocks is, of course, predetermined; these crack densities are then compared to the crack densities interpreted from the changes in ultrasonic wave speeds, using either self-consistent model or noninteracting crack model. For natural rocks, the noninteracting prediction seems to agree better with experiments than the self-consistent method for ∈ ≤ 0.2, but both theoretical predictions deviate from experimental observation for ∈ > 0.2. For replicated rocks, both theories give prediction comparable to experiments for ∈ ≤ 0.2, but underestimate the actual value for ∈ > 0.2. Therefore, a better damage model is needed for solids with crack density larger than 0.2.