# A Status Evaluation of Rock Instability in Metal Mines Based on the SPA-IAHP-PCN Model
## 2 Methodology
### Spa-Iahp-Pcn Model  
This paper extends a dynamic risk assessment method for rock mass instability in metal mines. Due to the continuously changing risk of rock mass instability during mining operations, effectively predicting the trend of risk development is crucial for determining the next steps in mining operations. Thus, a novel risk assessment method called the SPA-IAHP-PCN model is proposed. Given that a single parameter cannot directly reflect the changes in rock mass within the mine, four parameters were selected to predict the risk variation of rock instability in metal mines. These four parameters are the cumulative number of events, cumulative microseismic energy, cumulative apparent stress, and cumulative logarithmic seismic moment. The framework of the proposed method is illustrated in Figure 1, and the main steps of the SPA-IAHP-PCN model are outlined below.  
Step 1: Construction of index evaluation system. Based on the actual conditions of the mine and the collected data, relevant parameters were selected to establish a risk assessment system for rock mass instability in metal mines. The selected parameters must effectively reflect the changes in the rock strata during the mining process.  
Step 2: Calculation of index weight value. Based on the established risk assessment system for rock instability in mines, experts in the field were consulted to apply the SPA-IAHP method proposed in this paper. They scored each parameter according to its ability to reflect rock instability, thereby determining the weight of each parameter. The SPA-IAHP method effectively reduces the subjective influence of the experts.  
Step 3: Establishment of five-element identical-discrepancy-contrary model. Based on the evaluation system established in this paper, the corresponding data were selected according to the parameters chosen in the evaluation system. The selected data were then normalized, and the normalized results were used to determine the grade values of each parameter for each time period according to Table 2. Once the grade values were determined, the \(R\) matrix was obtained using the method described in Section 2.2. Finally, using the approach detailed in Section 2.2, the weight values of each parameter obtained in step 2 were combined with the \(R\) matrix and the Coefficient matrix \(E\). The five-element identical-discrepancy-contrary model is then constructed.  
Step 4: Based on the results obtained in step 3, the static risk level of the metal mine can be determined. However, the risk level during the mining process is constantly changing, making a simple static assessment of rock instability risks in metal mines of very limited value. Therefore, this paper introduces the PCN method. Using the five-element identical-discrepancy-contrary model derived in step 3 and the approach outlined in Section 2.3, the risk variation of rock instability during the mining process is further analyzed. This allows for the prediction of changes in the risk level during mining operations, providing valuable insights for mining activities and future planning. The flowchart of the proposed method is shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{5}{c}{**Normalized Result**} \\ \cline{2-6}  & **0–0.2** & **0.2–0.4** & **0.4–0.6** & **0.6–0.8** & **0.8–1** \\ \hline Cumulative Number of Events & I & II & III & IV & V \\ \hline Cumulative Microseismic Event Energy & I & II & III & IV & V \\ \hline Cumulative Apparent Stress & I & II & III & IV & V \\ \hline Cumulative Logarithmic Seismic Moment & I & II & III & IV & V \\ \hline \hline \end{tabular}
\end{table}
Table 2: Classification of normalized result grade values.