# Study on Asymmetric Support of Anchor Cable with C-Shaped Tube in Inclined Coal Seam Roadway
## 3 Roadway Deformation Law in Inclined Coal Seam
### Asymmetric Deformation Law of the Initial Support System  
Figure 10 displays the simulation results of roadway deformation under the initial support scheme. It can be seen from Figure 10 that the maximum settlement of the roof is 9.23 cm, and that the majority of the settlement occurs in the middle of the roof. The maximum displacement on the right side is 7.93 cm, and that on the left side is 6.77 cm. It can be seen that the right side has undergone significantly more deformation than the left. In addition, by observing the nephogram of the plastic zone, it can be found that shear and tensile failure occur around the roadway, with mostly shear failure. The plastic zone is large where it shows a tendency to develop along the coal seam, the right and left of which are asymmetrically distributed. Table 5 displays the horizontal displacement of the monitoring points for roadway displacement under the initial support scheme. Table 3 shows that the horizontal displacement of the monitoring point was gradually decreasing from surface to depth. When compared to the left, the right side has a displacement that is noticeably greater, indicating that the influence caused by roadway excavation gradually waned with increasing separation from the roadway surface, and the two sides of the roadway also clearly exhibited asymmetric deformation. In order to conduct a quantitative study on the asymmetric deformation properties of roadways, the two-side asymmetry degree \(t\) is defined in this paper. Considering the displacement direction of the two sides of the roadway, the calculation method is as follows:  
\[t=\frac{|A+B|}{|A|+|B|} \tag{10}\] \begin{table}
\begin{tabular}{c c c} \hline
**Type** & **Anchor Cable** & **Bolt** \\ \hline Diameter (mm) & 21.8 & 22 \\ Xcaera (mm\({}^{2}\)) & 373 & 380 \\ Emod (GPa) & 200 & 200 \\ Breaking load (kN) & 550 & 216 \\ Gr-per (mm) & 100 & 100 \\ Gr-k (MN/m/m) & 17.5 & 17.5 \\ Gr\_coh (MN/m) & 0.44 & 0.44 \\ \hline \end{tabular}
\end{table} 
Table 4: Support member parameters. Figure 10: Outcomes of the initial support scheme’s simulation: (**a**) vertical displacement; (**b**) horizontal displacement; (**c**) plastic zone. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Emod** & **Xcaera** & **Per (mm)** & **Cs\_sk** & **Cs\_soch** & **Cs\_nk** & **Cs\_ncoh** & **Cs\_sfric** & **Nu** \\
**(GPa)** & **(mm\({}^{2}\))** & **Per (mm)** & **(MPa)** & **(MN/m)** & **(MPa)** & **(MN/m)** & **(MPa)** & **Nu** \\ \hline pile & 200 & 4.02 & 100 & 13 & 13 & 13 & 0 & 25 & 0.3 \\ \hline \end{tabular}
\end{table} 
Table 3: Pile unit-related parameters. where the horizontal displacements of the right side are represented by \(A\) and the left side by \(B\). Underneath the initial support scheme, the variation law of the asymmetry of the displacement monitoring points on either side with respect to the distance from the road surface is shown in Figure 11. Figure 11 illustrates that the degree of asymmetry initially rises and then falls with increasing separation from the roadway surface and that the asymmetry characteristics become quite visible at a specific depth of roadway. In addition, Table 3 and Figure 11 demonstrate that serious deformation and large asymmetry occur at the shallow coal seam on the high side of the roadway, where it should be the key point of support. Figure 12 shows that the vertical stress increases as one moves away from the roadway surface. The stress distribution on both sides of the shallow seam is uneven, with characteristics of asymmetric stress distribution, specifically manifested as the vertical stress of the right side being greater than that of the left side. Figure 11: Asymmetry degree on both sides of displacement monitoring points under the initial support scheme.