## 4 Application: A Real Case
### Computational Results  
In the DEM calculation, the open-pit slope was excavated layer by layer to analyze the deformations and failures, and the SD/mean was calculated for each iteration interval for the excavation of every layer. Therefore, the relationship between the number of iterations corresponding to the excavation of every layer and the SD/mean values could be plotted. The Z-direction displacement after the excavation of the roof is shown in Figure 11, and the relationship between the number of iterations and the SD/mean values is shown in Figure 12a. The relationship between the difference of each adjacent two steps and the number of iterations is shown in Figure 12b. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subarea** & **South** & **Middle** & **North** \\ \hline \(E\) (GPa) & 15 & 40 & 18 \\ \(\mu\) & 0.25 & 0.2 & 0.23 \\ \(\rho\) (kg/m\({}^{3}\) ) & 2740 & 3100 & 2670 \\ \(c\) (MPa) & 0.365 & 0.95 & 0.45 \\ \(\varphi\) (\({}^{\circ}\)) & 36.5 & 41 & 39 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The physical and mechanical parameters of the study area (referred from [41]). Figure 10: Computational models divided by region and block. (**a**) Model divided by region; (**b**) Model divided by block. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Subarea** & & **South** & & **Middle** & & **North** \\ \hline
**Spacing** & **10 m** & **30 m** & **40 m** & **10 m** & **10 m** & **30 m** & **40 m** \\ \hline JKN (GPa) & 0.678 & 0.877 & 0.881 & 2.100 & 0.525 & 0.679 & 0.681 \\ JKS (GPa) & 0.674 & 0.509 & 0.493 & 0.891 & 0.211 & 0.158 & 0.151 \\ \(c\) (MPa) & 1.203 & 0.975 & 0.960 & 1.750 & 1.094 & 0.886 & 0.872 \\ \(\varphi\) (\({}^{\circ}\)) & 33.665 & 28.803 & 28.443 & 50.209 & 31.390 & 26.886 & 26.343 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The mechanical parameters of joints (referred from [27]). The excavation of the roof results in the rocks in the north slope moving along the joints to the middle. When the excavation of the roof is completed, from Figure 11, it is thought that the rock blocks on the north slope begin to slide, but no rock blocks fall on the surface of the first minelayer, and the rock blocks in the south slope are stable. Moreover, the excavation of the roof did not cause horizontal plane cracking or sliding. Figure 12 shows that when the number of iterations approaches the 8000 th step, the curve in Figure 12a tends to converge, and the SD/mean of the 9000 th step is approximately equal to the SD/mean of the 8000 th step. Therefore, it is thought that when the calculation reaches the 8000 th step, the iterative calculation would be terminated. To make the calculation convenient and accurate, the 10,000 th step is chosen to calculate. Figure 11: The Z-direction displacements after the excavation of the roof. Figure 12: The statistical results after the excavation of the roof. (**a**) The relationship between SD/mean and the number of iterations after the excavation of the roof; (**b**) The relationship between inter-step difference and the number of iterations after the excavation of the roof. When the excavation of the roof is completed and the iteration is terminated, the excavation of the first minelayer of the ore body is carried out. The Z-direction displacement after excavation of the first minelayer is shown in Figure 13, and the relationship between the number of iterations and the SD/mean values is shown in Figure 14a. The relationship between the difference of each adjacent two steps and the number of iterations is shown in Figure 14b. When the excavation of the first minelayer is completed, Figure 13 shows that the sliding of the north slope is relatively more sliding than that of the south slope, the blocks slide along the joints, and a small number of blocks fall on the iron ore bed. Additionally, a small part of the south slope begins to slide, also along the joint planes.