Wave velocity and stress/strain in rock brittle failure

This paper reports the relationship between wave velocity and stress/strain during rock brittle failure under compression. It is assumed that the rock is a strain-softening medium whose strength can be described by Weibull's distribution. Based on renormalization group theory, it is found that the stress ratio lambda (c) (the ratio of the stress at the critical point to the peak stress) depends mainly on the homogeneity index or shape parameter m in the Weibull's distribution for the rock. Measured stress-strain curves and corresponding wave velocity-strain curves in four case studies suggest that the changes caused by internal cracking are correlated to variations of rock wave velocity, and the stress at the critical point on the stress-strain curve is considered to correspond to the rapid decreasing point on the wave velocity-strain curve. For uniaxial compression, the critical stress ratio lambda (c) is derived to be about 75.4 %, which is very close to the measured value.