## 5 Application Case
### Process of Numerical Modeling
#### 5.3.1 Modeling of the Excavation of the First to Fourth Layers  
In the numerical simulation, it is more convenient to simulate the filling layer during excavation. During the first excavation, the filling layer (the first layer) was removed, and the mechanical parameters of the second layer were changed to those of the filling layer, indicating that the filling layer moved down to the position of the second layer after the ore body of the second layer was excavated. In Figure 11, the ore body and the filling layer make up twenty layers in total; however, according to the mining plan, we only simulated the excavation of the first twelve layers.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name** & **C (MPa)** & \(\varphi\) (\({}^{\circ}\)) & **E (GPa)** & \(\mu\) & \(\rho\) **(kg/m\({}^{3}\))** \\ \hline Iron Mine & 0.95 & 41 & 40 & 0.2 & 3100 \\ Migmatite & 0.45 & 39 & 18 & 0.23 & 2670 \\ Phyllite & 0.365 & 36.5 & 15 & 0.25 & 2740 \\ Quaternary & 0.2 & 25 & 0.05 & 0.3 & 1980 \\ Filling Layer & 0 & 24 & 0.06 & 0.32 & 1550 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mechanical parameters of rock masses and soil in Yanqianshan Iron Mine (where \(C\) is the cohesion, \(\varphi\) is the internal friction angle, \(E\) is the young’s modulus, \(\mu\) is the Poisson’s ratio, \(\rho\) is the density).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Slicing Mining** & **1 st** & **2 nd** & **3 rd** & **4 st** & **5 st** & **6 st** & **7 st** & **8 st** & **9 st** & **10 th** & **11 th** & **12 th** \\  & **Layer** & **Layer** & **Layer** & **Layer** & **Layer** & **Layer** & **Layer** & **Layer** & **Layer** & **Layer** \\ \hline Thickness (m) & 17.5 & 19.7 & 18.9 & 17.0 & 16.5 & 15.2 & 20.8 & 15.5 & 17.9 & 18.6 & 16.6 & 16.9 \\ Width (m) & 158.1 & 158.2 & 159.7 & 163.1 & 163.9 & 163.7 & 163.3 & 164.3 & 167.2 & 212.9 & 213.8 & 213.7 \\ Length (m) & 300 & 300 & 300 & 300 & 300 & 300 & 300 & 300 & 300 & 300 & 300 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dimensions of each excavation.  
In the initial stage of ore body excavation, for example, during the excavation of the third layers, the displacement of the free surface of the slope is less, and most of the displacement is concentrated in the filling layer. Because the original filled ore body was excavated, the unloading effect and the surrounding rock stress caused the uplift of the ore body; thus, the displacement of this part is larger (Figure 11(a)).  
The stress release due to the excavation of the third layer is less, the stress concentration of the slope foot is not high, the plastic zone of the slope is small (Figure 11(b)), the degree of shear deformation is not high, and the shear strain increment zone is concentrated mainly in the filling layer (Figure 11(c)). The stability of the slope is high, and the convergence of the numerical calculation is faster.  
With the increase in the excavation depth, the lateral unloading increases, and the displacement of the slope increases. The displacement of the slope foot, shown in Figure 12(a),  
Figure 12: Numerical results after mining the third layer.  
reaches 2.6 m. The internal stress of the slope changes, particularly in the direction of the maximum principal stress, thus increasing the maximum principal stress near the foot of the slope, decreasing the minimum principal stress, and leading to stress concentration near the foot of the slope due to the stress difference. The penetration of the maximum shear strain increment belt appears at the foot of the slope, resulting in shear failure at the foot of the slope. The tension zone exists at the shoulder of the slope, leading to tensile failure of the meshes in this part of the model, as shown in Figures 12(b) and 13(a).