## 3 Numerical Model
### Model and Calculation Process  
The stability analysis model of the Beiyi quarry consists of overburden rock, ore body, softening zone rock, plastic zone rock, and peripheral geological rock. The overall length is 4536 m, the width is 3528 m, and the elevation of the model base is \(-\)720 m. The numbers of grids and nodes in this model are 814,812 and 900,478, respectively, and the specific model and ore body are shown in Figures 4 and 5. Table 2 shows the assignment of mechanical parameters.  
Figure 4: The 3D numerical calculation model.  
Figure 3: The variation in the elastic modulus of collapsed body and original rock with porosity.  
The ore body model is \"stacked\" according to the distribution of the mining approach. From the distribution of the ore body and surface topography, the main iron ore body in the north extends in a southeasterly direction, with an overall orientation of 315-135\({}^{\circ}\) and an assigned elevation of 0\(--\)602 m. The preliminary design mining range is 0\(\sim\)\(-\)360 m. The morphology is generally stratified-like-stratified, and it is continuously distributed along the strike direction. As can be seen from Figure 6, the overall distribution of the ore body mining range is bounded by E9, with the west ore body west of E9 located below the bottom of the open pit, and the east ore body east of E9 located below the east gang of the open pit and its eastern hills. The simulated mining area is divided into six stages: +30-0 m, 0-60 m, 60-120 m, 120-180 m, 180-240 m, and 240-360 m.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Lithology** & **Modulus of Elasticity** & **Poisson’s Ratio** & **Internal Friction Angle** & **Compressive Strength** & **Cohesion** \\ \hline Hematite & 65.12 MPa & 0.33 & 57.91\({}^{\circ}\) & 106.44 MPa & 3.25 kPa \\ Surrounding rock & 36.97 MPa & 0.26 & 42.55\({}^{\circ}\) & 68.09 MPa & 1.62 kPa \\ \hline \end{tabular}
\end{table}
Table 2: Model mechanical parameters.  
Figure 5: Beiyi ore body (red indicates west of E9 and green indicates east of E9).  
Figure 6: Distribution characteristics of stress field around goat at different levels after mining in Beiyi mining area (maximum principal stress, unit Pa). (**a**) is the 0 m level and (**b**) is the \(-\)120 m level.  
After completing the above model, the calculation process is briefly described as follows: assigning parameters to the model and imposing boundary conditions, imposing constraint boundary conditions on the sides of the whole model, and setting fixed boundary conditions at the bottom; making the model reach static equilibrium under the action of gravity, and then applying ground stress (see the next section for the specific content and effect of ground stress application), calculating the initial equilibrium calculation after equilibrium, zeroing the obtained displacement, and simulating the basic state of the ore rock before mining; opening the caved calculation mode, setting the calculation parameters related to the caved simulation; taking each stage as a step for mining calculation; calculating the changes in the surrounding rock stress field and the corresponding surrounding rock deformation after the end of segment mining until the calculation process stabilizes; and repeating the above mining steps until the end of mining of the ore body in the whole mining area.