Stress wave attenuation in shock-damaged rock

The velocity and attenuation of ultrasonic stress waves in gabbroic rock samples (San Marcos, California) subjected to shock loading in the 2 GPa range were studied. From P wave velocity measurements we determined the damage parameter D-p and crack density epsilon of the samples and related these to the attenuation coefficient (quality factor) under dynamic strains of 2 x 10(-7) and at a frequency of 2 MHz using the ultrasonic pulse-echo method. A fit to the data yields the P wave spatial attenuation coefficient at a frequency of 2 MHz, alpha(p)(D-p) = 1.1 + 28.2D(p) (decibels per centimeter). From the relation between the attenuation coefficient and quality factor, the quality factor Q is given by Q(-1) = 0.011(1 + 25.6D(p))(1 - D-p)(1/2). Using O'Connell-Budiansky theory relating crack density to velocity, the parameter in Walsh's theory was determined based on experimental data. An approximate method is also proposed to estimate the average half-length of cracks based on the attenuation measurements.