## 2 Numerical Simulation  
According to the field working face conditions [20], the coal seam in the mining area of the Wangzhuang coal mine had a very small dip angle of less than 5 degrees; hence, the coal seam, as well as the overburden, were set as horizontal in the numerical model. In this  
Figure 1: Schematic diagram of longwall pier-column backfilling. Figure 2: Pier-column backfilling in the goat: (**a**) before backfilling solidification; (**b**) after backfilling solidification. FLAC3D model, the plane of the pier-column was a square with a side length of 6 m. The interval of the pier-columns was equal in row and column directions, both of which were 4 m.  
Parameter settings of the numerical simulation: geometric similarity ratio: 1:1; model length: 800 m; model width: 440 m; model height: 263 m; coal seam floor elevation: z = 0 (Figure 3). The model was composed of about 915,560 block elements and 1,083,742 grid nodes. This model was primarily used to study the reduction effect of overburden subsidence in longwall pier-column backfilling, simplify the overlying strata and floor where necessary, and assigning rock mechanics parameters according to corresponding strata. Table 1 shows the mechanical parameters of the numerical model. The control variable method was used to qualitatively investigate the influence of mining height and width on the control effect of overburden subsidence. We performed simulations using 25 condition combinations (five different mining heights (1 m, 1.5 m, 2 m, 2.5 m, and 3 m) \(\times\) five different mining widths (80 m, 120 m, 160 m, 200 m, and 240 m)). See the numerical simulation schemes in Table 2.  
According to the numerical simulation of strata movement, we explored the qualitative relationships of overburden subsidence with different mining heights and widths in longwall pier-column backfilling. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lithology** & **Layer No. ** & **Density** & **Volume** & **Shear** & **Cohesive** & **Frictional** & **Tensile** \\  & **(kg/m\({}^{3}\))** & **Modulus** & **(Pa)** & **Force (Pa)** & **Angle (\({}^{\circ}\))** & **Strength (Pa)** \\ \hline Topsoil & 11 & 1800 & 2.0 \(\times\) 10\({}^{7}\) & 1.4 \(\times\) 10\({}^{7}\) & 5 \(\times\) 10\({}^{4}\) & 18 & 2 \(\times\) 10\({}^{4}\) \\ Primary key stratum & 10 & 2500 & 4.0 \(\times\)  
In Figure 4, the first number in the legend denotes the mining width of the working face, and the second number in the legend denotes its mining height. Taking a mining width of 80 m as an example, when mining height changed from 1 m to 1.5 m, the maximum overburden subsidence increased by a factor of 1.9 times from 65.61 mm to 121.63 mm; when mining height changed from 1.5 m to 2 m, the maximum overburden subsidence increased by a factor of 1.1 times to 130.38 mm; when mining height changed from 2 m to 2.5 m, the maximum overburden subsidence increased by a factor of 1.02 times to 133.07 mm; when mining height changed from 2.5 m to 3 m, the maximum overburden subsidence increased by a factor of 1.02 times to 135.28 mm. As can be observed from the above discussion, given the mining width of the working face, a mining height less than 1.5 m had a significant influence on the overburden subsidence. Each time the mining height increased, the overburden subsidence increased markedly. When the mining height exceeded 1.5 m, the overburden subsidence increased only slightly with increasing mining height. This suggests that, at a mining height of above 1.5 m, the influence of mining height on overburden subsidence tends to be stable. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Model Number**} & **Pier-Column** & **Pier-Column** & **Mining Width** & **Mining Height** \\  & **Space (m)** & **Width (m)** & **(m)** & **(m)** \\ \hline  
\\ \hline \end{tabular}
\end{table} 
Table 2: Numerical simulation schemes. In Figure 5, the first number in the legend denotes the mining width of the working face, and the second number in the legend denotes its mining height.