## 3 Results and Discussion
### The Influence of the Yielding Bolt Spacing on Its Support Effect  
To study the impact of the spacing of yielding bolts on support effectiveness, the optimal length of 5 m was selected. Utilizing the same plane strain model of the tunnel, as shown in Figure 7, excavation and support simulations were conducted. Along the circumferential direction of the tunnel, the spacing of the yielding bolt support was set at 0.75 m, 1 m, 1.25 m, and 1.5 m. After calculations, the deformation of the surrounding rock at the arch crown, sidewalls, and arch base, as well as the total displacement change at the location of maximum deformation in the tunnel under different spacing of bolt support, were obtained, as shown in Table 6. The variation pattern of the resultant displacement at the location of maximum deformation in the tunnel is illustrated in Figure 26.  
As the bolt spacing decreases, the deformation of the surrounding rock at the arch crown, left and right sidewalls, and the arch base followed a pattern of initially stabilizing,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Bolt Spacing**} & \multicolumn{4}{c}{**Deformation (cm)**} \\ \cline{2-5}  & **Arch Crown** & **Arch Base** & **Left Sidewall** & **Right Sidewall** \\ \hline
0.75 & 9.34 & 9.53 & 7.51 & 7.49 \\
1 & 9.39 & 9.57 & 7.39 & 7.33 \\
1.25 & 9.94 & 10.16 & 7.79 & 7.77 \\
1.5 & 9.92 & 10.13 & 7.77 & 7.74 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Key point deformation of the surrounding rock with different spacings of bolt support.  
Figure 26: The resultant displacement of the maximum and minimum deformation of the surrounding rock with different spacing support.  
then decreasing, and then finally stabilizing again. This pattern was similarly reflected in the resultant displacement at the location of the maximum deformation in the surrounding rock. When the bolt spacing decreased from 1.5 m to 1.25 m, the deformation of the surrounding rock did not decrease but slightly increased. As the bolt spacing decreased from 1.25 m to 1 m, there was a significant reduction in the deformation of the surrounding rock, with the resultant displacement at the location of the maximum deformation decreasing from 10.16 cm to 9.57 cm and the resultant displacement at the location of minimum deformation decreasing from 7.77 cm to 7.33 cm. Further decreasing the bolt spacing from 1 m to 0.75 m resulted in a minimal reduction in the deformation of the surrounding rock, with the resultant displacement at the location of maximum deformation decreasing from 9.57 cm to 9.54 cm. Therefore, bolt spacings of 0.75 m and 1 m demonstrated better support effects, and the difference in support effects between the two was extremely small. Under the same support area, a spacing of 1 m will save a great deal of yielding bolts compared to a spacing of 0.75 m. Considering utilization and cost, a preliminary determination suggests that 1 m is the optimal spacing for yielding bolts under these conditions.  
Comparing Tables 5 and 6 and focusing on the two groups of data with the greatest change in arch crown settlement, for yielding bolt lengths of 2 m and 5 m, the difference in deformation at the arch crown was 0.69 cm, and the difference in the arch base uplift was 0.65 cm. With support spacings of 1 m and 1.25 m, the difference in arch crown deformation was 0.55 cm, and the difference in the arch base uplift was 0.59 cm. This indicates that support spacing has a greater impact on the support effectiveness than bolt length.