# A Thorough Investigation of the Dynamic Properties of Granite under Cyclic Loading
## 4 Results and Discussion
### Dynamic Elastic Modulus and Dynamic Damping Ratio of Specimens  
#### 4.2.1 Effect of Confining Pressure  
Figure 9 presents the variations in the dynamic elastic modulus of the specimens. Figure 9a illustrates the influence of different confining pressures, dynamic stress amplitudes, and number of cycles on the dynamic elastic modulus of the specimens. It is evident that the dynamic elastic modulus of the specimens decreases with an increasing number of  
Figure 8: Hysteresis loop diagram: (**a**) Y1-20; (**b**) Y5-20; (**c**) Y10-20; (**d**) Y20-20.  
cycles, while it increases with increasing confining pressure and dynamic stress amplitude. Under the same stress amplitude, the dynamic elastic modulus of the specimens exhibits a maximum increase of approximately 6% from 5 MPa to 10 MPa, about 13% from 5 MPa to 20 MPa, and approximately 20% from 5 MPa to 30 MPa.  
To depict more accurately the trend of the dynamic elastic modulus with varying confining pressure, the average dynamic elastic modulus of the specimens with increasing confining pressure at different dynamic stress amplitudes is shown with black curves in Figure 9b, with the data points corresponding to the black y-axis. The average dynamic elastic modulus of the specimens demonstrates an increasing trend with the rise of the confining pressure, with a nearly linear relationship. The inclinations for different stress amplitudes are almost identical. The blue curve, obtained by normalizing the data (normalized with the starting modulus at each line), effectively represents the trend of the average dynamic elastic modulus of the specimens, with the data points corresponding to the blue y-axis. The variation of the fitted curves for dynamic stress amplitude from 5 to 25 MPa shows a consistent pattern. However, the dynamic stress amplitude of 27.5 MPa is close to the maximum dynamic stress amplitude required for the specimen to reach damage, causing a change in the curve's slope.  
The observed increase in the dynamic elastic modulus of the specimens with the rise in the confining pressure is in line with the findings reported by [PERSON] [49] and [PERSON] [50]. As the confining pressure increases, the closure of microdefects within the specimen occurs [50,51], resulting in a more compact and damage-resistant state. Consequently, this phenomenon contributes to the enhancement of the dynamic elastic modulus.  
Figure 10 illustrates the dynamic damping ratio of the specimens under investigation. Figure 10a presents the impact of the confining pressure, dynamic stress amplitude, and number of cycles on the dynamic damping ratio. It reveals that the dynamic damping ratio of the specimens declined with the increasing number of cycles, confining pressure, and dynamic stress amplitude. To better elucidate the relationship between the dynamic damping ratio and confining pressure, the average dynamic damping ratio of the specimen is plotted against increasing confining pressure at various dynamic stress amplitudes (represented by black curves) in Figure 10b, with the data  
(normalized with the starting damping ratio at each line), effectively represents the trend of the average dynamic damping ratio of the specimens, with the data points corresponding to the blue y-axis on the right. Furthermore, it is evident that the rate of decrease in the dynamic damping ratio of the specimens diminishes as the confining pressure increases at higher dynamic stress amplitudes.  
With the increase in confining pressure, closure of microdefects within the specimens was observed, leading to a gradual reduction in energy consumption [50; 51]. Additionally, the energy dissipation resulting from friction and viscous resistance between the particles and the fluid inside the specimens decreased under cyclic loading conditions [52; 53]. The observed decline in the dynamic damping ratio of the specimens can be attributed to the combined effect of these two factors.