## 4 Numerical Simulation and Engineering Verification
### Verification Against Field Data  
The mine was mined in strict accordance with the design discussed above. From steps 1 to 3, the difficulty of mining gradually increases but the ore recovery rate increases. To understand the wall stability and the roof collapse within the barrier pillar slopes after mining, the Cavity Monitoring System (CMS) developed by Optech Company (Troy, MI, USA), was used to scan the goaf [30]. The collected data were further processed using the Qvol software, and then a 3D model of the goaf was built using the DIMINE modeling software. Examples of the typical cross-sectional profiles of the G6 goal in the panel barrier pillar slope are shown in Figure 9.  
The scan results shown in Figure 9 indicate that the width of the retained walls is in good agreement with the design value without significant over-break or under-break. The scanning confirmed that both walls remain in good integrity with no significant peeling or cracking identified. No large quantities of backfill materials were found to have entered the stope during the mining process, and the walls performed well in isolating the backfill from the slopes. In addition, BGK-A3 multi-point displacement gauges were installed on the roof of the barrier pillar slopes to monitor the roof displacements. After 6 months of monitoring, the maximum displacements were 34 mm at the monitoring points in the G6 goal. It is worth explaining that the maximum displacement monitored by numerical simulation is 12 cm, which is 3.5 times that of the on-site monitoring result, and there is some error. The main reason for this phenomenon is that the on-site monitoring results only represent the maximum displacement near the monitoring point, and do not represent the maximum displacement of the whole roof, so the maximum displacement of the roof on-site will be greater than 34 mm. In addition, the simulation parameters are the average of the rock tests at several sampling points, which may have some differences with the rock at the location of the monitoring point. Also, the simulation process simplifies the strata, and other reasons can lead to these errors. Although there was some error in the modeling and monitoring results, these displacements were within the safe range, proving that the backfill in this case had provided sufficient additional support to the roof strata.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Name** & **Starting Point Coordinates (\(P_{1}\))** & **Ending Point Coordinates (\(P_{2}\))** & **Width** & **Average Horizontal Displacement** \\ \hline \(l_{h-1}^{l}\) & (12.5, 179.5) & (12.5, 182.75) & 3.25 & 4.92 \\ \(l_{h-2}^{l}\) & (12.5, 200) & (12.5, 196.75) & 3.25 & 7.28 \\ \(l_{h-1}^{l}\) & (12.5, 181) & (12.5, 183.5) & 2.50 & 5.96 \\ \(l_{h-2}^{l}\) & (12.5, 201.5) & (12.5, 197.5) & 4.00 & 5.72 \\ \hline \end{tabular}
\end{table}
Table 2: Parameters of selected segments in the middle of the thin wall.  
Figure 9: Typical profiles of the G6 goat in the panel barrier pillar slope.  
The results demonstrated that the backfill, in this case, worked well, the thin wall did not appear to have large deformations or damages, the theoretical and numerical simulation results agreed well, and the layout of non-equal-width walls had a great application value in this type of mining operation.