## 3 Application and Illustration of the Proposed CRITIC-GRA Model
### Stability Index of Open Stoping
#### 3.2.2 Stability Results with FLAC3D Simulations
The properties of the cemented backfill were also tested with the cured samples by tailings and cement based on the designed backfill recipe in the illustrated iron mine. Figure 4: Numerical model constructed with FLAC3D for stability analysis of typical stopes in the illustrated iron mine: (**a**) overview; (**b**) mining sequence of primary and secondary stopes; (**c**) cross section along stope width; (**d**) cross section along stope length. As shown in Figure 4b, in the sequence of primary and secondary slopes in the single stage open stoping mining method illustrated in Figure 1a, the primary stope-1 between level \(-500\) m and level \(-440\) m was first excavated, and the stope void was then filled with the cemented backfill to provide the platform for the upper mining of the primary stope-2 between level \(-440\) m and level \(-380\) m. All stability indexes required for CRITIC-GRA model were collected around the excavated stope void which was \(60\) m in height. Moreover, for the simulations of mining procedure with double stage open stoping shown in Figure 1b, the primary stope-1\({}^{\prime}\) between level \(-500\) m and level \(-380\) m was excavated at one time, and the corresponding stability indexes of side walls and roof for different dimension schemes were then collected around the stope void which was \(120\) m in height. The practical cemented filling began after the excavation was fully completed for the two stages. Numerical simulations were performed in FLAC3D for the 20 preset schemes with different stope dimensions given in Table 1. The maximum displacement (m) of the roof and side walls (abbreviated as Roof Disp. and Wall Disp. ), the volume of the plastic zones in the roof and side walls (abbreviated as Roof Plastic Vol. and Wall Plastic Vol.) and the maximum principal stress (abbreviated as Max. stress, MPa) around the excavated stope voids are summarized in Table 1.  
Typical stability results for the No. 1 scheme in Table 1 are shown in Figure 5 with the double stage open stopes with a length of \(L\) = \(40\) m, a width of \(W\) = \(15\) m and a height of \(H\) = \(60\) m. Because of the limited space of the manuscript, the simulated results for the 20 schemes could not be fully presented here. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & **Density** & **Young’s** & **Poisson** & **Cohesion** & **Friction** & **Tensile** \\  & **(kg/m\({}^{3}\))** & **Modulus (GPa)** & **Ratio** & **(MPa)** & **Angle (\({}^{\circ}\))** & **Strength (MPa)** \\ \hline Rockmass & 2847 & 10.50 & 0.28 & 1.60 & 41.6 & 0.62 \\ Backfill & 1950 & 0.80 & 0.30 & 0.70 & 30.0 & 0.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Physical and mechanical parameters of the rockmass and backfill used in models. Figure 5: Numerical simulated results of typical stope dimension with width \(15\) m, length \(40\) m, height \(60\) m: (**a**) Maximum stress, Pa; (**b**) total displacement, m; (**c**) equivalent factor of safety; and (**d**) volume of plastic zones. Figure 5a shows the stress release from the initial stress state and redistribution around the slope void after the excavation of primary Stope-1. A significant concentration of the maximum principal stress was observed around the excavated void with a maximum value of 37 MPa at a distance about 15 m from the stope boundaries. From Figure 5b, the maximum total displacement of the rockmass occurred in the shallow parts of the stope roof at about 0.8 m. And the total displacement in the sidewalls was located in the part of middle height reaching about 0.7 m.  
Figure 5c illustrates the equivalent factor of safety which was higher than 1.0 in the roof and side walls around the excavated stope void. This indicated that after the excavation of Stope-1, the surrounding rockmass could still maintain a relatively stable state.