## 3 Application and Illustration of the Proposed CRITIC-GRA Model
### Stability Index of Open Stoping
#### 3.2.3 Stope Stability Analysis with CRITIC-GRA Evaluation Model  
To investigate the stope stability of single stage and double stage open stoping, the stability probability of the roof and side walls was evaluated via the updated Mathew graph method. The simulated maximum displacement and the volume of plastic zones with FLAC3D were seamlessly brought into the CRITIC-GRA model together to carry out an integrated analysis on the stope stability under different dimensions which were initially performed parallel in the two methods with no interactions. Firstly, the prepared initial data shown in Table 1 were substituted into Equations (7)-(14) to calculate the weight values of all the considered influential factors on the stope stability, as shown in Table 5.  
Then, the weight values were substituted into Equations (15) and (16) to calculate the values of the grey correlation degree of each preset scheme with different stope dimensions, as shown in the column 'Only Safety Index' in Table 6, where the economic indexes for open stope mining have not been considered yet. In these three columns, the stability conditions only for the side wall, only for the roof, and for the overall stope void were considered to reveal their specific relationships with stope dimensions (length \(L\), width \(W\), height \(H\)), which were innovatively accomplished by the stability results combining the empirical graph method with the numerical simulation method. In addition, the corresponding grey correlation degree for the side walls, for the roof and for the overall stope void which varied with stope dimensions were further graphed in Figure 6 to illustrate their integrated stability conditions. Figure 6a shows the calculated values of grey correlation degree with the CRITIC-GRA model to illustrate the stability conditions of the side walls as a function of the stope length, width and height. A greater value of grey correlation degree means a better stability condition. It can be seen that the stability of the side walls in the single stage open stope was obviously greater than the double stage open stope. For the single stage open stope, when the length was less than 50 m, the stability of side wall with a width of 15 m and 20 m was almost the same. However, when the length was more than 50 m, the stability of the side wall with a width of 20 m showed a continuous decreasing trend that was much lower than that of the single stage open stope with a width of 15 m. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Factors**} & **Wall** & **Rood** & **Wall** & **Rood** & **Wall** & **Rood** \\  & **Prob.** & **Prob.** & **Disp.** & **Disp.** & **Plastic Vol.** & **Plastic Vol.** \\ \hline Weight values & 0.14 & 0.22 & 0.15 & 0.21 & 0.17 & 0.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Weight values for influential factors on stope stability with the CRITIC model. Figure 6: Grey correlation degree about stability conditions for preset schemes of different stope dimensions: (**a**) only for the side walls; (**b**) only for the roof; and (**c**) for the overall stope void predicted by the CRITIC-GRA model without considering economic indicators. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline  & & & & & \multicolumn{3}{c}{**Grey Correlation Degree**} \\ \cline{5-10}
**Preset** & **Length** & **Width** & **Height** & \multicolumn{1}{c}{**Only Safety Index**} & \multicolumn{3}{c}{**Integrated Safety and Economic Index**} \\ \cline{5-10}
**Scheme** & **\(L\)** & **W** & **H** & **Only** & **Only** & **Overall** & **Overall** & **Overall** & **Stability** & **Overall Stability** \\
**Wall** & **(m)** & **(m)** & **Wail** & **Roof** & **Stability  
In addition, from Figure 5(a), the stability of the side walls with a width of 15 m and 20 m for the double stage open stope reduced with the increase in stope length, and the stability of the side wall of the 15 m width stope was slightly higher than that of the 20 m width.