## 5 Conclusions  
This study investigates the rock mass structure and geological characteristics of a slope in an open-pit mine using acoustic testing, ground-penetrating radar, mutation theory, and energy conservation principles. The Weibull distribution was employed to simulate parameter uncertainty, and a dissipative energy mutation model based on cusp catastrophe theory was utilized to assess the slope stability at the 1195-1240 m platform during excavation. The key findings are as follows:  
Acoustic Testing: Loose rock zones range from 2.50 to 3.75 m, with acoustic velocities between 2500 and 4000 m/s, indicating widespread jointing and a fragmented structure.  
Numerical Calculation: Dissipated energy and displacement increase during excavation, with a factor of safety (FOS) of 0.962 indicating instability before support, and 1.31 after the installation of the anchor frame beam, confirming stability.  
Energy Damage: Maximum damage (ds = 0.82) occurs in the weak chlorite interlayer before excavation, decreasing to ds = 0.48 after support.  
Field Monitoring: Displacement and anchor rod axial force data show stability improvements post-support.  
These findings demonstrate the effectiveness of support measures in enhancing slope stability.  
Furthermore, considering the complexity of engineering practice, future research should explore the environmental sustainability and economic feasibility of the support system, assessing material efficiency and ecological benefits. In addition, practical challenges in applying mutation theory during field monitoring warrant further case studies and technical optimization to improve monitoring accuracy and early warning capability. Lastly, the long-term durability of support measures and their ability to ensure slope stability under evolving climatic and geological conditions should be systematically evaluated to provide comprehensive theoretical support and technical guidance for slope engineering under complex conditions.  
Figure 15: Displacement monitoring curve. (**a**) Slope anchor cable axial force monitoring schematic diagram; (**b**) slope displacement monitoring schematic diagram.  
**Author Contributions:** Conceptualization, Methodology, Formal analysis, Writing--original draft, T.D.; Investigation, Data curation, X.P.; Supervision, Project administration, J.S.; Methodology, Software, Writing--review and editing, C.Z.; Validation, Investigation, D.W.; Investigation, S.Z.; Resource, Funding acquisition, X.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by National Natural Science Foundation of China, 52304131.  
**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], [PERSON], [PERSON] and [PERSON] were employed by the company Pangang Group Mining Co., Ltd. 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.