Method of defining rock damage variable on the basis of wave impedance

Abstract A method of determining rock damage variable from wave impedance, which is suitable for the study of dynamics, is presented. The determined variable provides a more reasonable quantitative description of the degree of rock damage. First, the Taylor model of mesoscopic damage mechanics is used to derive the relationship between the velocity of longitudinal waves and the density of rock materials. Based on the measured data of rock samples with different lithology and the same lithology, the relationship between the longitudinal wave velocity and density of rock materials is studied. It is demonstrated that using the wave impedance to define the rock damage variable has advantages over using the P‐wave velocity. Second, the relationship between the wave impedance and degree of damage to the rock material is studied using an electron microscope and ultrasonic testing technology, and the microstructure of rock samples with a wave impedance gradient and time–frequency‐domain characteristics of the ultrasonic signals are compared and analyzed. It is found that it is feasible to determine the damage degree of the rock from the wave impedance. Finally, a method of defining rock damage variable with the wave impedance is further proposed and its rationality verified. The research results show that there is a good positive correlation between the longitudinal wave velocity and density of rock materials, and there is a strong correlation between the degree of rock damage and its wave impedance. The damage variable defined by wave impedance can better reflect the damage state and damage evolution process of rock.