# A Thorough Investigation of the Dynamic Properties of Granite under Cyclic Loading
## 6 Conclusions  
To construct a back-analysis model for a granite sample, we conducted a series of triaxial tests, controlling the confining pressure, loading amplitude, loading frequency, and number of cycles. The dynamic properties of the provided granite sample were meticulously studied, and a dynamic response model was developed using the test data. The following conclusions can be drawn:  
1. The dynamic response of granite was examined under various factors, including loading frequency (1-20 Hz), confining pressure (5-30 MPa), dynamic stress amplitude (5-27.5 MPa), and the number of cycles (0-50 times).
2. The dynamic elastic modulus of granite increased by approximately 6%, 13%, and 20% as the dynamic stress amplitude went from 5 MPa to 10 MPa, 20 MPa, and 30 MPa, respectively. This behavior can be attributed to the closure of microdefects and reduced energy consumption. On the contrary, the dynamic damping ratio exhibited a decline due to diminished energy consumption resulting from friction and viscous resistance.
3. Granite's dynamic elastic modulus and dynamic damping ratio displayed an upward trend with loading frequency. The dynamic elastic modulus increased by approximately 7% (from 1 Hz to 5 Hz), 28% (from 1 Hz to 10 Hz), and 80% (from 1 Hz to 20 Hz). Enhanced dynamic stress amplitude led to an increased dynamic elastic modulus and a decreased dynamic damping ratio. These outcomes are associated with microcrack closure, increased intergranular viscosity, and heightened energy consumption.
4. Increasing dynamic stress amplitude resulted in a higher dynamic elastic modulus and a lower dynamic damping ratio. This is attributed to particle compression, leading to tighter contacts and decreased energy consumption from friction and viscous resistance.
5. The dynamic elastic modulus and dynamic damping ratio of granite decreased before stabilizing with an increase in the number of cycles. The initial loading stage induced significant deformation and energy consumption, followed by gradual stabilization as equilibrium was reached.
6. The modified Duncan-Chang model established a dynamic stress-strain relationship for granite and demonstrated good alignment with experimental data. It is noteworthy that high frequency had a more significant impact on material behavior compared with confining pressure. These experimental data and the constructed model will be further integrated into Part II of our research, enabling a comprehensive investigation and a deeper understanding of the proposed study.  
Conceptualization, X.D. and M.Z.; Data curation, J.Z. and Y.D.; Funding acquisition, X.D. and M.Z.; Methodology, X.D. and M.Z.; Resources, X.D. and M.Z.; Supervision, X.D.; Writing--original draft, J.Z.; Writing--review & editing, X.D. and J.Z. All authors have read and agreed to the published version of the manuscript.  
This research was financially supported by the National Natural Science Foundation of China (Grant No. 41827807, 42276213) and Guangdong Provincial Key Laboratory of Modern Civil Engineering Technology (2021B1212040003). All the sources of support are gratefully acknowledged.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the back analysis experiment has not yet been completed.  
The authors declare no conflict of interest.