A multifrequency ultrasonic approach to extracting static modulus and damage characteristics of rock

Understanding the mechanical behavior of rock is a fundamental requirement for many geological explorations. Based on the frequency dependence of primary and shear wave velocities (P- and S-wave velocities), this work proposed a new approach to obtaining the static modulus of rocks without using empirical correlations. Six group granite specimens are treated by different temperatures, then the P- and S-wave velocities of these specimens at various frequencies were tested. The static moduli of all the specimens were calculated by deriving the newly proposed critical P- and S-wave velocities with a classical formula. The results showed that the static moduli of all the specimens obtained from the ultrasonic approach complied with the initial modulus obtained from uniaxial compression tests, demonstrating the reasonability of the proposed ultrasonic approach. The reasonability of the proposed approach was further proven by using a distinct lattice spring model. Numerical results showed that the calculated modulus is consistent with the true value. In addition, the standard deviation of wave velocities at different frequencies was adopted to describe the damage characteristics in rock, which well explained the change in damage variable during the thermal process. The proposed approach provides a potential method to fast obtain the static modulus and damage characteristics of rock.