# A Dynamic Numerical Simulation on the Grouting Timing in Retained Rib of Pillarless Mining
## 4 Plastic Zone and Grouting Diffusing Range Development  
As shown in Figure 5, when the working face advances by 120 m, the plastic zone begins to develop in the coal seam. Outside the mining disturbed area, the depth of the plastic zone of the roadway was only about 1 m, mainly manifested as shear failure. Cracks were mostly developed from the original small cracks caused by the mining-induced stress during the roadway excavation and weathering of coal on the roadway surface. The original bolting support maintained the stability of the roadway in the driving stage. Outside the mining disturbance range, the depth of the plastic zone in the surrounding rock of the roadway was only about 1 m. The fragmented surrounding rock was mainly in the form of shear failure. The main cause of cracks was the development of original small cracks caused by the mining stress during the excavation of the roadway and the weathering of the coal on the roadway surface. During the excavation process, the bolt support maintained the stability of the roadway before mining. With the advancement of the working face, cracks gradually penetrated into the retained coal rib. As the coal rib displacement increased, some tensile failures were observed in the roadway surrounding rock. In the area of 10 m depth before the working face, the plastic zone began to expand under the influence of mining-induced stress. The mining-induced stress caused a large number of new cracks in the retained coal rib and caused the original cracks to expand further. Since the roadway adopted the active strong bolting support, and the main roof above the roadway was not fragmented or rotated and subsided, the range of the plastic zone in coal rib had not been greatly expanded at this time. During the advancing process of the working face, the cracks gradually penetrated into the retained coal rib. With the increase in the displacement of the coal rib, a tensile failure area appeared on the surface of the surrounding rock of the roadway. In the area 10 m ahead \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Thickness** & **Lithology** & **Density** & **Bulk Modulus** & **Shear Modulus** & **Friction** & **Cohesion** & **Tensile Strength** \\
**(m)** & **Lithology** & **(kg\(\cdot\)m\({}^{-3}\))** & **(GPa)** & **(GPa)** & **(c\({}^{*}\))** & **(MPa)** & **(MPa)** \\ \hline
20 & Fine sandstone & 2750 & 12.74 & 12.35 & 39 & 6.15 & 2.51 \\
20 & Coarse sandstone & 2750 & 10.21 & 10.25 & 38 & 5.58 & 2.31 \\
12 & Silstone & 2700 & 10.35 & 8.74 & 38 & 4.15 & 2.24 \\
4 & Silstone & 2600 & 8.35 & 5.74 & 36 & 3.15 & 2.01 \\
4 & Sandy mudstone & 2500 & 3.6 & 2.89 & 29 & 2.35 & 1.32 \\
4 & Mudstone & 2000 & 2.88 & 1.53 & 26 & 1.07 & 0.98 \\
4 & Mudstone & 1700 & 2.51 & 1.58 & 25 & 0.95 & 0.82 \\
2 & Coal & 1400 & 1.87 & 0.63 & 21 & 0.56 & 0.05 \\
2 & Mudstone & 2000 & 2.64 & 1.54 & 23 & 1.45 & 1.07 \\
2 & Mudstone & 2000 & 2.88 & 1.73 & 24 & 1.67 & 1.21 \\
6 & Silstone & 2400 & 3.88 & 3.53 & 26 & 2.17 & 1.54 \\
20 & Coarse sandstone & 2700 & 7.35 & 7.74 & 36 & 3.15 & 1.69 \\ - & Filling wall & 2500 & 1.72 & 0.86 & 25 & 0.81 & 2.35 \\ - & Caved zone [33] & 1700 & 13.89 & 0.15 & 30 & 0.001 & 0 \\ \hline \end{tabular}
\end{table} 
Table 1: Rock physical and mechanical parameters. Figure 5: Plastic zone development in coal rib. of the working face, the plastic zone began to expand under the action of mining stress. The mining stress caused a large number of new cracks to be generated in the retained coal rib, and at the same time caused the original cracks to further expand. Because the roadway was supported by active strong bolts, the main roof was not fragmented, rotated or subsided. During this process, the plastic zone of the coal rib did not expand significantly.