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 (e) 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 E c 0.2, but both theoretical predictions deviate from experimental observation for e > 0.2. For replicated rocks, both theories give prediction comparable to experiments for E c 0.2, but underestimate the actual value for e > 0.2. Therefore, a better damage model is needed for solids with crack density larger than 0.2.