# A Status Evaluation of Rock Instability in Metal Mines Based on the SPA-IAHP-PCN Model
## 4 Results and Discussion
### Risk Variation of Rock Instability  
Since the risk of rock instability in metal mines evolves continuously during mining operations, static risk assessment alone is inadequate. Building on the findings in Section 4.3, the method described in Section 2.3 is employed to predict the trend of rock instability risk in the metal mine. Specifically, the partial connection number is calculated using the approach outlined in Section 2.3. From the calculation results, the first-order PCN is determined using Equation (14), as shown in Figure 7a. Subsequently, the second-order and third-order PCNs are computed based on Equations (15) and (16), with their respective results illustrated in Figure 7b.c. Figure 7 lists the coefficients of each PCN order. Appropriate values are selected based on the actual conditions of the mine and substituted into the equations for each PCN order. If the result is greater than 0, it indicates a decreasing trend in rock instability risk for the subsequent phase. A result equal to 0 signifies a transitional state between ascending and descending trends, while a result less than 0 indicates an increasing trend in rock instability risk for the next phase.  
To ensure the scientific rigor and reliability of the results, the worst-case scenario was selected to calculate the PCN values for the mine, with parameters defined as \(i_{1}=i_{2}=0\) and \(i_{3}=-1\) (Section 2.3). The calculated PCN values for each order are shown in Figure 8. As observed, in the first-order PCN, all parameters, except for Cumulative Apparent Stress, which is in a transitional state between an ascending and descending trend, indicate an increasing trend in rock instability risk for the next phase of the lead-zinc mine. Among these, the first-order PCN for cumulative microseismic event energy is the smallest, suggesting that this parameter requires the most attention in monitoring and prevention efforts.  
Figure 6: The evaluation result of rock instability.  
The TCN for the first-order PCN is less than zero, indicating an overall increase in rock instability risk, with a likely progression of the mine's instability status from risk level II (good) to risk level III (medium). However, timely preventive measures based on collected microseismic data, including the cumulative number of events, cumulative microseismic event energy, and cumulative logarithmic seismic moment, could avert this outcome.  
The second-order PCN values are all negative, indicating that without corresponding preventive measures, the likelihood of rock instability will further increase. Moreover, in the third-order PCN results, the cumulative number of events, cumulative microseismic event energy, cumulative logarithmic seismic moment, and TCN are all negative. This suggests that, from a comprehensive perspective of these four parameters, the rock instability hazard remains on a declining trajectory. During this phase, it is particularly crucial to consider the trends reflected by the cumulative number of events, cumulative microseismic event energy, and cumulative logarithmic seismic moment in devising prevention strategies.  
In contrast, all results from the fourth-order PCN are positive, indicating that the parameters collectively reflect a stabilization trend in the mine's rock instability hazards over time.  
Figure 8: The “worst-case” of PCN value.  
Figure 7: The calculation results: (**a**) the calculation results of the first-order PCN; (**b**) the calculation results of the second-order PCN; (**c**) the calculation results of the third-order PCN.