# 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
#### 4.2.3 Effect of Dynamic Stress Amplitude  
Figure 13a,b illustrate the dynamic elastic modulus variations of the specimens under different confining pressures and frequencies. Figure 13a displays the variation of the dynamic elastic modulus with increasing dynamic stress amplitude at various confining pressures, represented by the black curves, with the data points corresponding to the black y-axis. Similarly, Figure 13b depicts the dynamic elastic modulus with increasing dynamic stress amplitude at different frequencies, using the black curves. The blue curves, obtained by normalizing the data separately, reveal the trends in the dynamic elastic modulus of the specimens, with the data points corresponding to the blue y-axis. In Figure 13a, the dynamic elastic modulus of the specimens increases as the dynamic stress amplitude rises. Nevertheless, under high confining pressure, the growth rate of the dynamic elastic modulus slows down with increasing dynamic stress amplitude. We postulate that the relationship between the dynamic elastic modulus and dynamic stress amplitude follows a power function. In Figure 13b, it can be observed that the dynamic elastic modulus of the specimens increases with the increment of dynamic stress amplitude. Notably, at high frequencies, the growth rate of the dynamic elastic modulus diminishes with increasing dynamic stress amplitude. We hypothesize a power-function correlation between the dynamic elastic modulus and dynamic stress amplitude. Furthermore, the increase in the dynamic elastic modulus of the specimen is more pronounced at a frequency of 10 Hz. This pattern is consistent in both Figure 13a,b During the loading of dynamic stress amplitude, the particles inside the specimen undergo compression, leading to a tighter inter-particle contact. Consequently, the rock stiffness increases, resulting in an elevated dynamic elastic modulus of the specimen.  
Figure 14a,b present the dynamic damping ratio variations of the specimens. In Figure 14a, the dynamic damping ratio of the specimens decreases with increasing dynamic stress amplitude, as indicated by the black curves, with the data points corresponding to the black y-axis. We postulate that the relationship between them follows a power function. Moreover, the blue curves, obtained by normalizing the data separately, reveal the trends in the dynamic elastic modulus of the specimens, with the data points corresponding to the blue y-axis. We can see that with the increment of confining pressure, the dynamic damping ratio of the specimens exhibits a slower rate of decrease with increasing dynamic stress amplitude. Figure 14b reveals that the dynamic damping ratio of the specimens decreases with increasing dynamic stress amplitude, displaying a potential power-function relationship between them. Furthermore, the dynamic damping  
Figure 12: Dynamic damping ratio of specimens with frequencies: (**a**) the dynamic damping ratio of the specimens; (**b**) the average dynamic damping ratio of the specimens.  
ratio of the specimens declines at a faster rate with the increase of frequency and dynamic stress amplitude. This phenomenon is attributed to the tightening of contact between mineral particles inside the specimen due to the increase in dynamic stress amplitude. Consequently, the energy consumption resulting from frictional and viscous resistance inside the specimen diminishes as a proportion of the total energy consumption at high dynamic stress amplitudes [52; 53], leading to a decrease in the dynamic damping ratio.