Stress wave attenuation in shock damaged rock

The attenuation of ultrasonic stress waves in samples of gabbroic rock subjected to shock loading in the 11 Gpa range were studied. We determined the damage deficits, D_p, and attenuation coefficients, α_p, for the samples with different damage deficits under dynamic strains of 2×10^(−7) and at frequencies around 2 MHz using ultrasonic pulse-echo method. A fit to the data yields the P-wave spatial attenuation coefficient versus damage deficit: α_p=40.9D_p−30.5D^2_p (db/cm). Basing on the O'Connell-Budiansky theory, the relation between attenuation coefficient and crack density is given. The predictions of α_p from Walsh's theory agrees well with the experiment results for the samples with different damage deficits.