## 3 Physical Simulation  
To further study and demonstrate the influence of the working face mining dimensions on the reduction effect of overburden subsidence, according to the rock structure of 8-15 borehole histogram in No.7 mining area of Wangzhuang coal mine [20], we used a plane stress model 2500 \(\times\) 200 \(\times\) 2000 mm (length \(\times\) width \(\times\) height) in size to make a physical similarity simulation, in order to simulate the process of pier-column backfilling after mining and monitor the overburden subsidence rules for pier-column backfilling. The similarity ratios of the physical model were referred to by [PERSON] et al., 2016 [20]. The simulation model was only paved to the position of the primary key stratum (PKS). There is a key stratum when it breaks all of the strata above will subside simultaneously, and then it will be defined as primary key stratum (PKS) [21]. The unpaved overlying strata above PKS was replaced by external hydraulic cylinder loading. The load required to apply can be calculated from Equation (1):  
\[\text{F}=\frac{\text{\textrho\  
F is the hydraulic cylinder pressure, KN;  
\(\rho\) is the density of rock strata, generally set as 2500 kg/m\({}^{3}\);  
H is the height of unpaved rock strata, m;  
L is the length of the model, m;  
W is the width of the model, m.  
After setting the model parameters (L = 2.5 m, W = 0.2 m, h = 188.63 m), the load required to apply hydraulic cylinder loading was calculated to be F = 30.23 KN. To ensure model stability during pressurization, two steel channels were mounted before and after the model for protection. Two physical experiment schemes with the same working face conditions (except mining height) were developed. In Figure 6a, the coal seam had a mining height of 2 cm as similar in-site size 1 m; in Figure 6b, it had a mining height of 4 cm as similar in-site size 2 m.  
The schematic diagram of pier-columns backfilling in the physical model is shown in Figure 7. A 21.5 cm coal pillar was reserved on both sides of the model to ensure the similarity of boundary conditions. The size of the backfilling pier-columns was 7.5 \(\times\) 7.5 cm (length \(\times\) width), different heights were 2 and 4 cm, respectively, and a row of backfilling pier-columns was arranged in the advancing direction. The row and column spaces were both set as 12 cm. See the mining and backfilling process in the physical simulation in Figure 8.  
To study the control effect of overburden subsidence in pier-column backfilling, it is necessary to observe strata movement. In this experiment, a DigiMetric 3D photogrammetric system (with a precision of less than 0.1 mm/4 m) was adopted to measure the strata movement in the model. Measuring points were horizontally laid out in the middle of four key strata (KS) (from the bottom up are KS1, KS2, KS3, and PKS) with a horizontal spacing of 5 cm, creating four measuring lines from down to up (namely L1 to L4, each line with 49 points). See the measuring points layout in Figure 9.  
Figure 6: Different mining height physical model: (**a**) 2 cm mining height model; (**b**) 4 cm mining height model. Figure 7: Schematic diagram of backfilling in the physical model. As can be seen from the overburden subsidence curves, in the excavation and backfilling of the coal seam, the subsidence of key strata gradually decreased from the bottom up, and the maximum subsidence point moved forward along with mining. The majority of subsidence was caused by the initial space between the backfilling body and the roof. To observe the overburden subsidence control effect after stabilization, strata movement was measured once on the day after the model was finished, and the subsidence curves are shown in Figures 10 and 11. It can be seen from Figure 10 that in the 2 cm mining height model, the curves of strata movement at the mining widths of 102 cm and 204 cm (the similar in-site size are 51 m and 102 m) were compared.