## 6 Conclusions  
1. Under the conditions of graded cyclic loading-unloading, the compressive strength of the rock is 98.8 MPa. The rock exhibits through-going fractures from bottom to top during failure. On the other hand, under the conditions of variable lower limit cyclic loading-unloading, the compressive strength of the rock is 99.87 MPa. Numerous fractures are observed during rock failure, indicating the poor integrity of the rock. This suggests that the variable lower limit cyclic loading-unloading path has a significant influence on the instability and failure of the rock.
2. Under the graded cyclic loading-unloading path, the energy storage ratio of the rock ranges from 81% to 85%. This indicates that the internal damage accumulation in the rock is relatively small. The rock produces less sound during failure, and through-going cracks are observed on the macroscopic surface. On the other hand, under the variable lower limit cyclic loading-unloading path, the energy storage ratio gradually decreases, leading to an increasing energy dissipation ratio. Ultimately, both ratios approach 50%. The damage accumulation in the rock steadily increases, and the rock exhibits significant sound during loading and large cracks on the macroscopic surface. This represents a typical brittle failure.
3. The elastic strain energy, dissipative energy, total energy, and plastic deformation energy of the rock exhibit similar trends and are positively correlated with the number of cycles under both graded and variable lower limit cyclic loading-unloading paths. By studying the damage accumulation in the rock using the energy dissipation method, it is found that the damage values for the graded and variable lower limit cyclic loading-unloading paths are 0.48 and 0.85, respectively. This indicates that the internal damage accumulation in the rock is more severe under the variable lower limit cyclic loading-unloading path.
4. Under both types of cyclic loading-unloading paths, the early stages of acoustic emission characteristics exhibit the Kaiser effect, and the Felicity ratio is negatively correlated with the number of cycles. Under the graded cyclic loading-unloading path, when the applied stress exceeds 60% of the peak stress, the Felicity ratio is less than one, indicating the failure of the Kaiser effect. Similarly, under the variable lower limit cyclic loading-unloading path, when the applied stress exceeds 50% of the peak stress, a Felicity ratio less than one is observed, indicating the failure of the Kaiser effect. This phenomenon becomes more pronounced with an increasing number of cycles, indicating the gradual accumulation of internal damage in the rock.  
Figure 15: Depicts the juxtaposition of Felicity and the curve of iteration-count.  
Studying the evolutionary patterns of rock energy during cyclic loading and unloading, as well as the characteristics of acoustic emissions, holds significant scientific and engineering value in deepening our understanding of rock behavior, predicting rock damage and failure, and optimizing engineering designs.  
Conceptualization, Z.W. and Y.Y.; methodology, Z.W.; validation, Y.X., P.L. and N.G.; formal analysis, Z.W.; data curation, C.X.; writing--original draft preparation, N.G.; writing--review and editing, Z.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.