## 3 Application and Illustration of the Proposed CRITIC-GRA Model
### Optimization of Stope Dimensions with CRITIC-GRA Model Considering Stability and Economic Indexes  
To pick out the optimal scheme among the preset 20 schemes with different stope dimensions (length, width and height), the stope stability and corresponding economic indexes were jointly brought into the CRITIC-GRA model for integrative analysis. The stope stability indexes consist of the stability probability using the updated Mathews graph method, and the typical safety indexes simulated with FLAC3D for each scheme of stope sizes. Furthermore, the economic indexes include the mining cost and production capacity for the typical open stope in different schemes. Firstly, all 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 stope stability and economic indexes, as displayed in Table 9.  
According to data in Table 9, the weight values of the economic indexes were greater than those of safety indexes, which meant that the economic indexes of open stope in the preset schemes weighed more on the integrated analysis and optimal scheme selection. The calculated weight values in the CRITIC model gave an objective and quantitative evaluation of the importance of each considered index on the optimization of stope dimension. Then, the calculated weight values in Table 9 were substituted into Equations (15) and (16) to calculate the values of grey correlation degree of each preset scheme, which are listed in the columns of 'Integrated Safety and Economic Index' in Table 6 after considering the economic indexes for open stope mining. In addition, the integrated analysis about the 'overall stability + cost', 'overall stability + capacity' and the 'overall stability + cost + capacity' were separately given in detail for different considerations such as mining cost, mining capacity and their combination with the overall stability for the sake of stope dimension optimization. To deepen the exploration, Figure 7 plots the grey correlation degree of the integrated model that combines stability and economic indexes across all the preset schemes to illustrate the stope dimension optimization from multiple perspectives. Combining the information in Table 6 and Figure 7, the preset scheme No. 10 with the length of \(L=50\) m, width of \(W=15\) m and height of \(H=120\) m was the objectively selected optimal stope dimension using the proposed CRITIC-GRA model after comprehensively considering the open stoping stability, mining capacity and costs. With the optimized stopes dimension, the iron mine adjusted the stope design and carried out the practical mining operations which proved that the double stage open stoping for primary stopes with the above dimensions could obviously increase the mining production efficiency with a safe open stoping stability. The illustrated CRITIC-GRA model is a reliable reference tool for selecting the optimal stope dimension based on the designed schemes, rockmass quality, and the technical and economic indexes of mining process in different mines. \begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{2}{c}{**Updated Mathews Graph**} & \multicolumn{2}{c}{**Simulated Safety Indexes with FLAC3D**} & \multicolumn{2}{c}{**Economic Indexes**} \\ \cline{2-9}  & **Wall Prob.** & **Roof Prob.** & **Wall Disp.** & **Roof Disp.** & **Stope Overall Plastic Vol.** & **Max. Stress (MPa)** & **Capacity (t/d)** & **Cost (CNY/0)** \\ \hline Weight values & 0.111 & 0.111 & 0.108 & 0.106 & 0.110 & 0.110 & 0.181 & 0.163 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Weight values for influential factors on stope stability, mining capacity and costs. For double stage open slopes with widths of 15 m and 20 m, the grey correlation degree of comprehensive evaluation shows little variation with increasing stop length.