Quantifying the Progressive Fracture Damage of Granite Rocks by Stress–Strain, Acoustic Emission, and Active Ultrasonic Methods

The accurate identification and quantification of rock damage are important for the reliable safety assessment of rock engineering. In this paper, stress-strain behavior, passive acoustic emission (AE), and active ultrasonic transmission were measured simultaneously under uniaxial compression to characterize the fracture damage of granites. The deformation and acoustic behaviors with respect to crack initiation and crack damage thresholds were analyzed. Meanwhile, irreversible damage was quantified using different methods. The results show that the marked increase in the AE rate and the average hit energy coincide with the crack initiation stress, ranging from $0.41{\sigma }_c\text{–}0.45{\sigma }_c$ (uniaxial compressive strength), which occurs earlier than the decrease of the $P$-wave velocity and onset of the rock dilation. The moment in which the average hit energy and ratio of low-frequency AEs start to increase rapidly corresponds to the crack damage stress of $0.71{\sigma }_c\text{–}0.74{\sigma }_c$. In addition, the fracture damage was quantified by the crack volumetric strain, dissipated energy, modulus loss, AE characteristics, $b$ value (defined as the log-linear slope of the frequency-magnitude distribution of AEs), and ultrasonic properties. It is revealed that the majority of rock damage accumulates after the crack damage stress, corresponding to the appearance of most high-magnitude hypocenters. Rock damage quantified by dissipated energy and AE energy with clear physical meaning is more reasonable and less subjective. Moreover, the precipitous reduction of the $b$ value, a sharp increase in AE energy, and the ratio of low-frequency AEs prior to peak failure is a perfect precursor of potentially brittle failure.