## 3 Results
### Characteristics of Infrasonic Energy Rate  
Energy rate, as an important characteristic parameter of signal processing, provides a better representation of the energy and strength of the signal. Infrasonic energy rate is the energy of infrasonic waves passing through a unit area per unit time, and the energy rate is not affected by the threshold value. The energy corresponding to a certain event is the square of the amplitude; the rock specimens change under the action of the load, the infrasonic amplitude is changing constantly, and the infrasonic waves energy rate is changed accordingly. Figure 10 shows the infrasonic energy rate characteristics of the rock specimens under uniaxial compression, and there is a significant change in the infrasonic energy rate before peak strength. The axial stress at point A is 81.02 MPa (about 85% of the peak strength), and the infrasonic energy rate is 0.0027 V\({}^{2}\). After point A, the infrasonic energy rate starts to increase significantly, with infrasonic energy rates of 0.005 V\({}^{2}\) and 0.0068 V\({}^{2}\) at points B and C, respectively, where the infrasonic energy rate reaches a maximum at point C. When peak strength is reached, the infrasonic energy rate is also more significant at 0.005 V\({}^{2}\). Prior to reaching peak strength, the rock specimen undergoes rapid fracture propagation and coalescence, accompanied by significant infrasonic signal variation. As shown in Figure 11, rock specimen A-4 exhibits relatively low and stable infrasonic energy rates during the low-stress phase, which can be attributed to its compaction stage with the minimal generation of new fractures. As stress increases, the infrasonic energy rate begins to show more obvious changes, and at the point A of the upper stress of the third cycle, the infrasonic energy rate is 0.00879 V\({}^{2}\), which is obviously increased, indicating that the internal fracture of the rock changes significantly with the increase in the stress. The variation in infrasonic energy rate is most obvious in the high-stress stage, such as at point B of the fifth cyclic loading stage, where the infrasonic energy rate is 0.0245 V\({}^{2}\)  
Figure 9: Infrasonic time-domain characteristics of rock specimens under the cyclic loading and unloading of rock specimen A-4. which reaches the maximum value. The infrasonic energy rates at point C and D of the fifth cycle are 0.0165 V\({}^{2}\) and 0.0108 V\({}^{2}\), respectively, which are also relatively high, but gradually show a decreasing trend. In the high-stress phase, the internal fracture and microfracture structures of the rock propagation and coalescence dramatically, releasing a large amount of energy, and the infrasonic energy rate varies significantly. The infrasonic energy rate values are lower after the D point and before peak strength. As shown in Figure 12, the infrasonic energy rate of rock specimen A-6 is relatively low during the low-stress stage, which is determined by the characteristics of the compaction phase. With the increase in stress, the infrasonic energy rate appears to increase significantly in the fourth cycle, such as the infrasonic energy rate of 0.0064 V\({}^{2}\) and 0.0107 V\({}^{2}\) at points A and B, respectively, where the infrasonic energy rate reaches the maximum value at point B, which indicates that there is a large change in the internal fracture of the rock. In the high-stress phase, the infrasonic energy rate also undergoes a very pronounced change. For example, the infrasonic energy rate at point C of the upper stress in the fifth cyclic phase is 0.0085 V\({}^{2}\), and the higher infrasonic energy rate occurs most intensively. The infrasonic energy rates of 0.00282 V\({}^{2}\) and 0.00582 V\({}^{2}\) at points D and E, respectively, in the sixth cyclic loading stage are also relatively high, indicating that the structures such as cracks and fractures inside the rock propagation and coalescence dramatically in the high-stress stage. The infrasonic energy rate values are similarly low after the E point and before peak strength.