## 2 Current Status of Support Instability in the Working Face of SDCS
### Establishment of Numerical Model
#### 3.2.1 Determination of the Filling Range in the Goaf  
During fully mechanized top-coal cavity with SDCS, which occurs along the dip of the longwall face, the roof above the middle will fall or slip to the lower part of the working face when it collapses. Along the inclined direction, the goat will display zonal characteristics. From bottom to top, these zones are, respectively, the filling compaction area, the complete filling area, and the partial filling area [1]. The denser the filling degree of the goat, the stronger the supporting capacity for the overlying strata. Therefore, the range of the compaction area can be indirectly determined by the stress characteristics of the goat floor.  
The physical similarity simulation experiment employed an adjustable-angle testing rig measuring 2150 mm (length) \(\times\) 200 mm (width) \(\times\) 1800 mm (height). The material system comprised river sand (serving as the primary aggregate), a gypsum-line powder composite binder, mica schist laminations (1 mm thickness), and water. During the experimental setup phase, an array of wireless stress sensors was strategically embedded within the coal seam floor stratum. This instrumentation configuration enables real-time monitoring of load distribution characteristics. The wireless stress monitoring system is shown in Figure 6. According to the research objectives, the geometric similarity ratio is set  
Figure 5: Three-dimensional numerical model.  
as 1:100. Based on similarity theory, the similarity parameters for density, stress, load, and time are determined to be 1.6, 160, 1.6 \(\times\) 10\({}^{6}\), and 10, respectively.  
The distribution law of the floor load along the inclined direction of the working face exhibits a trend of decreasing first and then increasing, as shown in Figure 7. Along the dip direction of the working face, the internal stress decreases from 0.9 MPa to 0.5 MPa within the range of 0-70 m and then increases from 0.5 MPa to 0.7 MPa within the range of 70-100 m. Based on the comparison in Figure 8, because the lower part of the working face has a high filling density, the overlying strata are supported by the gangue. As the filling degree of the goaf weakens from the bottom to the top along the inclined direction of the working face, the load on the floor decreases.  
Figure 8: Distribution law of the floor load in goaf.  
Figure 6: Wireless stress sensor.  
Figure 7: Filling characteristics after overlying strata collapse.  
The weight of caving gangue in the upper part of the working face is much greater than that in the rest of the working face. Based on the maximum load of the upper floor of the working face, the middle and lower parts of the working face with the same load on the floor are found. This position is located 40 m from the working face, and it is under the action of two kinds of forces transmitted by the deadweight of gangue and overlying strata. This situation indirectly validates the extent of the filling compaction area. It is thus determined that the filling compaction area in the numerical simulation experiment of the goaf is 40 m. Additionally, a double yield model is adopted for goaf filling, and the filling range is shown in Figure 9.