## 4 Numerical Simulation and Engineering Verification
### Analysis of Simulation Results  
The simulation was conducted according to the three-step mining processes. Figure 6 shows the contour plot of the vertical displacement in cross-section I-I (Figure 5) after the mining of the barrier pillar slopes is completed. The maximum displacement is found to be about 12 cm at the roof of the panel barrier pillar slope. The backfill materials of room stopes and pillar stopes play a partial bearing role and restrict the roof displacement, so the displacement at these locations is about 3 cm. The contour map of the vertical displacements shows a dome structure, which is in general agreement with the assumptions of a caved natural arch formed at the top of the excavation.  
In this study, simulations were run for both equal-width and non-equal-width thin walls. For the first case, the room stopes and pillar stopes were set to the same size, and the width of the thin walls was set at 3.25 m, as shown in Figure 7a. As different backfill materials were used in the room stopes and pillar stopes, the horizontal displacement of the thin wall near the pillar stop is greater than that near the room stope, which is expected. For the case when the width of the thin walls is different, at 2.5 m and 4 m, respectively, the results are shown in Figure 7b. Compared with Figure 7a, the horizontal displacement of the thin wall close to the room stopes becomes much larger, while the horizontal displacement of the wall close to the pillar  
Figure 5: Numerical model: (**a**) meshing, (**b**) the location of the ore body, and (**c**) the layout of stopes.  
Figure 6: Contour plot of the vertical displacement on the I-I cross-section.  
To have a better understanding of the horizontal displacement of the thin wall, the horizontal displacement in the middle of the thin walls from different slopes was extracted and is plotted in Figure 8. \(l_{\text{a}-1}\), \(l_{\text{a}-2}\), \(l_{\text{b}-1}\), and \(l_{\text{b}-2}\) are the four segments, as shown in Figure 7, and their corresponding simulation results are listed in Table 2. When the width of the thin wall is 3.25 m, the average horizontal displacement of the wall close to the room stope is 4.92 cm, while the average horizontal displacement of the wall close to the pillar slope is 7.28 cm. The horizontal displacement of the wall close to the room stope is only 67.6% of that close to the pillar slopes. In other words, the wall close to the pillar slopes may be damaged first, leading to stress concentration in the walls close to the room stopes which may be subsequently damaged. If the width of the wall was reduced to 2.5 m near the room stopes and increased to 4 m near the pillar slopes, it could be found that the average horizontal displacement of the wall increased to 5.96 cm for the 2.5 m wall and decreased to 5.72 cm for the 4 m wall. In this case, the horizontal displacements of both walls are approximately equal. In other words, the deformations of both walls were relatively more coordinated, and the risk of partial failure and overall collapse was reduced.  
Figure 8: Horizontal displacement in the middle of the thin wall.  
Figure 7: Horizontal displacement of the thin walls: (**a**) equal-width walls and (**b**) non-equal-width walls.