## 6 Conclusions  
Based on the findings derived from cyclic loading and unloading tests conducted on sandstone samples, the relationship between rock dissipated energy and plastic strain was explored. The following conclusions were drawn:  
1. Prior to reaching the stress peak, dissipated energy and plastic strain demonstrate a linear increase with input energy and axial strain. The conversion ratio of input energy to dissipated energy aligns closely with the transformation ratio of axial strain to plastic strain. In the residual stress stage, the growth trends of plastic strain under different confining pressures exhibit similarities, with comparable growth rates.
2. By introducing the elastic energy correction parameter, a method for estimating the input energy, elastic energy, and dissipated energy during the rock damage process was proposed, and it was validated using experimental results. A plastic strain estimation method based on the evolution mechanism of dissipated energy was also proposed, which enables the calculation of plastic deformation at any given time during the rock damage evolution process.
3. An improved rock damage model was proposed based on the correlation characteristics of energy dissipation and plastic growth in this work. The model can reflect the rock damage evolution process under different confining pressures, and the model error mainly exists in the instability process of rock near the peak stress.
4. Based on the damage model, a numerical calculation program using the finite volume method (FVM) was developed. The surrounding rock damage and vertical stress evolution process in the Yimaqianqiu Coal Mine was simulated, and the results showed that the proposed program can provide a basis for risk analysis of rockburst.
5. In this work, due to only exploring the correlation between energy dissipation and plastic growth of sandstone specimens, the broader applicability of the proposed model has not been validated. Energy dissipation and plastic growth are common accompanying phenomena in the damage and failure process of rock materials. The difference between different rocks lies in the possible evolution relationship between energy dissipation and plastic growth, which is reflected in the selection of material parameters.  
Data curation: Y.C. and X.Z.; Formal analysis and investigation: L.W.; Writing--original draft preparation: T.Z.; Writing--review and editing: Y.C. and Q.L.; Software: T.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This study was supported by the National Natural Science Foundation of China (No. 52204220, No. 52304088), the National Key Research and Development Program of China (No. 2023 YFC3009002), the Science and Technology Innovation and Entrepreneurship project of TDTEC (No. 2024-TD-ZD011-02).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** Authors [PERSON] and [PERSON] are employed by the China Coal Research Institute. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.