# Impact of the Mining Dimensions on the Stability of Backfilled Pier-Columns
## 3 Numerical Simulation  
Based on the lithology histogram and key stratum identification results as above, a three-dimensional numerical model was established using FLAC3D. In this model, the pier-column has a square-shaped plane, and a side length of 6 m. The height of the coal seam was equal to the height of the pier-column. The spacing between the pier-columns, in the goat in the strike and dip directions, was also equal and set to 4 m.  
The simulation's model size was 800 m \(\times\) 400 m \(\times\) 240 m (length \(\times\) width \(\times\) height) (as shown in Figure 2). This model was mainly used to study the plastic zone distribution and stress variation of the pier-column. A numerical model was established by making necessary simplifications to the overlying strata and floor; the mechanical parameters are shown in Table 2.  
In the simulation schemes, the mining widths were set to 80, 160, and 240 m, and five mining thicknesses of 1, 1.5, 2, 2.5, and 3 m were selected for each mining width. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layer Number** & **Thickness (m)** & **Buried Depth (m)** & **Lithology** & **Key Stratum** \\ \hline
11 & 2.97 & 211.99 & Mudstone & \\
10 & 8.06 & 220.05 & Fine sandstone & \\
9 & 6.8 & 226.85 & Silstone & Key stratum 3 (KS3) \\
8 & 1.56 & 228.41 & Mudstone & \\
7 & 0.7 & 229.11 & Silstone & \\
6 & 3.98 & 233.09 & Fine sandstone & Key stratum 2 (KS2) \\
5 & 1.3 & 234.39 & Mudstone & \\
4 & 1.27 & 235.66 & Silstone & \\
3 & 3.1 & 238.76 & Mudstone & \\
2 & 1.36 & 240.12 & Fine sandstone & Key stratum 1 (KS1) \\
1 & 0.83 & 240.95 & Coal seam & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(Cont.\) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lithology** & **Density (kg/m\({}^{3}\))** & **Tensile Strength** & **Bulk Modulus (GPa)** & **Shear Modulus (GPa)** & **Cohesive Force** (MPa)** & **Angle of Friction (\({}^{\circ}\))** \\ \hline Top soil & 1800 & 0.02 & 0.02 & 0.014 & 0.05 & 18 \\ Key stratum & 2500 & 4.50 & 4.00 & 2.40 & 5.00 & 40 \\ Soft rock & 2000 & 2.20 & 2.50 & 1.30 & 3.00 & 28 \\ Pier-columns & 2500 & 3.00 & 3.00 & 2.10 & 4.00 & 30 \\ Coal seam & 1400 & 2.00 & 2.00 & 2.40 & 2.00 & 25 \\ Floor & 2500 & 4.50 & 4.00 & 2.40 & 5.00 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical parameters. Figure 2: Numerical model. We aimed to investigate the impact of the change in the mining thickness and width on the stability of the backfilled pier-column, from the initial stage of backfilling to the stage of a stable overburden movement. The changes in the stress and plastic zone of the pier-column during the experiment were recorded. A monitoring point for the stress was arranged in a pier-column to measure the changes in the stress and plastic zone of the pier-column as the working face advanced. It can be observed in the numerical simulation results that the measured stress profile of the pier-column had a constant mining width and a variable mining thickness, as shown in Figure 3.  
Figure 3 shows that when the distance between the monitoring point and the working surface was within 40 m, the stress of the pier-column increased sharply. After 40 m, the stress still increased, but the stress increased slowly until the maximum was reached, where it became stabilized. In Figure 4, given the condition that the mining width of the working face was 80 m and when the mining thickness was 1 m, the maximum stress of the pier-column was 8.2 MPa. When the mining thickness was 1.5 m, the maximum stress of the pier-column  
Figure 3: Stress profile of the backfilled pier-column with a constant mining width and variable mining thickness: (**a**) 80 m width; (**b**) 160 m width; (**c**) 240 m width.