Abstract: The P-wave velocities of rock with axial pre-compression cannot be measured during cyclic impacts on coupled static and dynamic test equipment, and the characteristics of rock damage evolution in the process of cyclic impacts are not able to be studied with variation of wave velocities. A method for defining damage variable of rock based on its wave impedance is proposed. Firstly, the good positive correlation between density and P-wave velocity of jointed rock was verified; and it was obtained that the variation range of wave impedance is similar with that of wave velocity on the same damage process; the damage variable of rock can be defined both density and wave velocity by theoretical calculation and analysis; so it was concluded that wave impedance can be used for defining damage variable of rock, and the expression for defining damage variable is given. Then, a formula to express wave impedance from incident wave and reflected wave or transmitted wave is derived. The elastic wave may reflect and transmit time after time on the input bar/specimen and specimen/output bar interfaces when a test is conducted with split Hopkinson pressure bar (SHPB). According to one-dimensional theory, a method for calculating wave impedance of rock is determined from test data on the cyclic test. Finally, a cyclic impact experiment on rock without precompression stress is performed; and the P-wave velocity is measured after impacting every time; the damage variables defined by wave velocity and wave impedance was found to have the same trend approximately. Compared with the variable of acoustic wave velocity, density variation is very smaller, so there is a difference between two damage variable defined by wave velocity and wave impedance. The results show that the damage variable of rock can be defined by wave impedance when rock is subjected to cyclic impact loading with same incident energy.

Key words: rock mechanics, wave impedance, damage variable, cyclic impact, static-dynamic coupling loading