## 6 Conclusions  
This study conducted cyclic loading and unloading tests on sandstone with a 45\({}^{\circ}\) pre-existing fracture, using acoustic emission (AE) and high-speed cameras to monitor the changes in the sandstone. The following conclusions were drawn from the mechanical parameters, energy, AE precursors of failure, AE fracture instability, and local deformation characteristics of the sandstone:  
1. As the cyclic load level increases, both the elastic modulus and deformation modulus exhibit a \"parabolic\" increase, with a rapid increase at the beginning and a slower rate of increase later on. The damping ratio shows an overall decreasing trend but increases near the peak load, fluctuating between 2.5% and 3.0%.
2. Based on the dissipation energy theory, it was found that the total energy, elastic energy, dissipation energy, damping energy, and damage energy all follow exponential function increases with the load level. Moreover, there are sudden increases in dissipation energy and damage energy during the final loading and unloading stage. Additionally, the proportion of elastic energy increases first and then decreases following a \"quadratic parabolic\" pattern with the cyclic load level, while the proportion of dissipation energy shows the opposite trend.
3. The number of AE hits and AE energy show sudden increases during the peak stage. By calculating the b-value, three early warning points were identified during the stable crack propagation stage, unstable crack propagation stage, and peak stage. The second warning point is the best predictor for rock instability and failure. When the FR \(>\) 1,  
Figure 16: Sandstone damage cross-section.  
the rock is relatively stable; when the FR \(<\) 1, the rock gradually moves toward an unstable state. The Felicity ratio can be used as a predictive tool for rock failure.
4. Shear cracks dominate during the compaction stage and peak stage, with a sudden increase in shear crack energy level at the peak point, while tensile cracks dominate during the crack propagation stage. Through calculations, it was found that tensile cracks account for 56%, which is higher than shear cracks, indicating tensile failure. Additionally, the CCD high-speed camera revealed that deformation first occurs at the tips of the pre-existing cracks and gradually spreads and deflects toward the ends of the sandstone.
5. Through cyclic loading and unloading tests, engineers can optimize design parameters, enhance the fatigue resistance of structures, reduce maintenance costs, and extend service life. This has a positive impact on the efficient use of resources and the reduction of waste production, aligning with the principles of sustainable development. Moreover, it aids in the development and evaluation of new materials and technologies, such as high-performance concrete and composite materials, which may offer better fatigue resistance and lower environmental impact, thereby promoting energy conservation and emission reduction.  
Conceptualization, K.S. and X.X.; methodology, K.S. and X.X.; software, K.S.; validation, K.S., X.X. and Y.S.; formal analysis, K.S.; investigation, K.S. and Y.S.; resources, K.S. and X.X.; writing--original draft preparation, K.S.; writing--review and editing, X.X.; supervision, X.X.; project administration, X.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Guangxi Key Research and Development Program No. AB18294004.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author. If any researcher is in need of the data and codes, Email: [EMAIL_ADDRESS].  
The authors declare no conflicts of interest.