# A Status Evaluation of Rock Instability in Metal Mines Based on the SPA-IAHP-PCN Model
## 4 Results and Discussion
### Construction Five-Element Connection Number Evaluation Model  
This study selected all microseismic events, six hours after concentrated blasting, at a lead-zinc metal mine in Shaanxi Province from 16 September to 25 September 2022. Based on the parameters of the collected microseismic events, the cumulative values for each day were computed for the cumulative number of events, the cumulative microseismic event energy, the cumulative apparent stress, and the cumulative logarithmic seismic moment. The processed data are shown in Figure 5.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Index** & **Weight** \\ \hline Cumulative Number of Events (\(A_{1}\)) & 0.1918 \\ \hline Cumulative Microseismic Event Energy (\(A_{2}\)) & 0.2028 \\ \hline Cumulative Apparent Stress (\(A_{3}\)) & 0.2467 \\ \hline Cumulative Logarithmic Seismic Moment (\(A_{4}\)) & 0.3587 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Calculated values of index weights.  
Due to the differences in magnitude between the processed data, normalization of each parameter was performed to facilitate a better comparison of the indicators. Subsequently, the normalized parameters were classified into different levels according to Table 2. The results of this classification are shown in Table 6.  
According to the data in Table 6, matrix R was further processed. Taking the cumulative number of events as an example, among the ten days of statistical values, two days have a level classification of I; five days have a classification of II; one day has a classification of III; one day has a classification of IV; and one day has a classification of V. Thus, \(\mu_{1}=(2/10,\,5/10,\,1/10,\,1/10,\,1/10)\) is defined. Similarly, the results for indices \(A_{2}\), \(A_{3}\), and \(A_{4}\) are obtained using the same method. Ultimately, matrix R is derived.  
\[R=\begin{pmatrix}\frac{2}{10}&\frac{5}{10}&\frac{1}{10}&\frac{1}{10}&\frac{1}{1 0}\\ \frac{1}{10}&\frac{3}{10}&\frac{2}{10}&\frac{2}{10}&\frac{2}{10}\\ \frac{1}{10}&\frac{1}{10}&\frac{1}{10}&\frac{2}{10}&\frac{2}{10}\\ \frac{3}{10}&\frac{5}{10}&\frac{1}{10}&\frac{1}{10}\end{pmatrix}\]  
Taking the weight (0.1918, 0.2028, 0.2467, 0.3587) into consideration, the connection number of the index can be calculated according to Equation (13) as follows:  
\[\mu_{CN}=0.19+0.36i_{1}+0.16i_{2}+0.14i_{3}+0.14j\]  
Based on the above calculations, the static risk level of rock instability for the metal mine can be determined. According to the method described in Section 2.3, the evaluation levels for rock instability based on individual parameters are as follows: cumulative number  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{8}{c}{**Date**} \\ \cline{2-10}  & **16** & **17** & **18** & **19** & **20** & **21** & **22** & **23** & **24** & **25** \\ \hline Cumulative Number of Events & II & I & II & II & III & II & V & IV & I & II \\ \hline Cumulative Microseismic Event Energy & II & III & IV & V & V & II & IV & II & I & III \\ \hline Cumulative Apparent Stress & IV & V & V & V & IV & IV & I & II & V & V \\ \hline Cumulative Logarithmic Seismic Moment & III & V & IV & III & V & IV & III & III & I & II \\ \hline \hline \end{tabular}
\end{table}
Table 6: The results of grading.  
Figure 5: The value of each parameter per day.  
of events indicates a risk level of II (the status is good); cumulative microseismic event energy also indicates a risk level of II (the status is good); cumulative apparent stress indicates a risk level of III (the status is medium); and cumulative logarithmic seismic moment indicates a risk level of II (the status is good). However, the reference value of individual parameters for assessing rock instability risk is limited. Therefore, the combined evaluation of all parameters provides a more meaningful assessment. Using the proposed method in this study, the combined risk level for rock instability at the metal mine is assessed as level II (the status is good). This is illustrated in Figure 6.