# Study on the Stability and Control of Gob-Side Entry Retaining in Paste Backfill Working Face
## 5 Results of Numerical Simulation  
### Deformation Law of Roadway Surrounding Rock with Different Backfill Ratios  
As shown in Figure 8, the roof, floor, and two ribs displacement curves of the roadway 100 m behind the working face are presented under backfill ratios of 65%, 75%, 85%, and 95%. From Figure 8a, it can be seen that under different backfill ratios, the roof subsidence of the roadway follows an asymmetric pattern. The subsidence near the solid coal side is smaller than that near the backfill side, with the subsidence increasing as the distance to the backfill side decreases. At a backfill ratio of 65%, the maximum subsidence of the roof is 1010 mm, and the displacement difference between the two sides of the roof is approximately 683 mm. At a backfill ratio of 75%, the maximum subsidence of the roof is 692 mm, and the displacement difference between the two sides of the roof is about 441 mm. At a backfill ratio of 85%, the maximum subsidence of the roof is 451 mm, and the displacement difference between the two sides of the roof is around 296 mm. At a \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Density** & **Bulk Modulus** & **Shear Modulus** & **Cohesion** & **Friction Angle** & **Dilatancy Angle** \\ /(kg/m\({}^{3}\)) & **/GPa** & **/GPa** & **/MPa** & **/(\(\times\))** & **/(\(\times\))** \\ \hline
1500 & 0.12 & 0.133 & 0.85 & 30 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical parameters of paste materials. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Strain** & **Cohesion/MPa** & **Friction Angle/(\({}^{\star}\))** \\ \hline
0.00 & 0.85 & 30 \\
0.05 & 0.80 & 28 \\
0.10 & 0.60 & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Strain softening parameters. Figure 7: Strain softening model calibration results. backfill ratio of 95%, the maximum subsidence of the roof is 157 mm, and the displacement difference between the two sides of the roof is about 70 mm. As the backfill ratio increases, the maximum subsidence of the roof decreases, and the displacement difference between the two sides of the roof reduces, indicating an improvement in roof deformation uniformity. From Figure 8b, it can be seen that the floor heave decreases as the backfill ratio of the gob increases. At backfill ratios of 65%, 75%, 85%, and 95%, the maximum floor deformation is approximately 204, 155, 94, and 52 mm, respectively. When backfill ratio reaches 95%, there is a significant reduction in the maximum floor deformation. This suggests that at higher backfill ratios, the backfill material provides good support, reducing the compression on the floor of the roadway. From Figure 8c, the deformation of the solid coal rib follows a similar trend, with the maximum deformation decreasing as the backfill ratio increases. At backfill ratios of 65%, 75%, 85%, and 95%, the maximum deformation of the solid coal rib is approximately 250, 228, 141, and 78 mm, respectively. This indicates that increasing the backfill ratio reduces the abutum stress on the solid coal side, improving the stability of surrounding rock. From Figure 8d, the deformation of the backfill rib also shows a similar trend, with the maximum deformation decreasing as the backfill ratio increases. At backfill ratios of 65%, 75%, 85%, and 95%, the maximum deformation of the backfill rib is approximately 173, 124, 83, and 62 mm, respectively. From the above data, it is clear that the backfill ratio significantly impacts the deformation and stability of roadway surrounding rock. At a backfill ratio of 65%, due to the weak supporting effect of the backfill material on the roof and the large rotation space for the roof in gob, the mining-induced stress is more intense, failing to effectively support the  
Figure 8: Deformation of roadway surrounding rock with different backfill ratios: (**a**) roof; (**b**) floor; (**c**) solid coal rib; (**d**) backfill rib. overlying rock layers.