## 4 Discussion
### Effect of Fissure Penetration on Sidewall Failure
#### 4.1.2 Influence of Fissure Penetration on Tunnel Stability  
Discontinuities such as fissures and joints significantly impact tunnel stability. Under specific in situ stress conditions, varying fissure penetrations cause significant differences in stress distribution, affecting the deformation and failure mechanisms of the tunnel walls. Table 4 presents the initial vertical failure stress (\(\sigma_{\text{zi}}\)) and peak vertical failure stress (\(\sigma_{\text{zp}}\)) for the sidewall of the rectangular tunnel at varying fissure penetration levels. The initial failure vertical stress (\(\sigma_{\text{zi}}\)) increased and then decreased with fissure penetration, reaching its peak at 50%. The reasons for this behavior are outlined below. First, in the early stages of sidewall failure, while the presence of non-penetrating fissures reduced the overall strength of the specimen, the sandstone specimen with fissures (S-0-25, S-0-50) provided a new release path for elastic strain energy. This path was created by the non-penetrating fissures on one side of the rectangular hole. Consequently, when fissure penetration was low (0-50%), the vertical stress \(\sigma_{\text{zi}}\) increased as fissure penetration grew. The presence of non-penetrating fissures contributes to improving the initial failure point of rectangular tunnels, which helps suppress initial failure in rock mass engineering. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Specimen** & **Initial Failure Stress/MPa** & **Peak Stress/MPa** \\ \hline S-0-0 & 47.50 & 72.00 \\ S-0-25 & 49.86 & 61.66 \\ S-0-50 & 54.00 & 64.00 \\ S-0-100 & 36.77 & 50.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Initial and peak failure stresses at varying fissure penetrations. Figure 16: Sidewall failure evolution of sandstone specimen with fissure. (**a**) Calm Stage (**b**) Fine Particle Spalling Stage (**c**) Crack Generation and Propagation Stage (**d**) Rock Slab Spalling and Failure Stage. Second, the peak failure vertical stress (\(\sigma_{\text{zp}}\)) generally decreased as fissure penetration increased. Specim \"S-0-100\" showed a significant drop in peak strength, indicating that when the fissure fully penetrated one side of the rectangular hole, the sandstone's structural integrity was compromised. This resulted in a large reduction in the load-bearing capacity, significantly lowering the initial failure stress (\(\sigma_{\text{zi}}\)). The trends in initial and peak failure vertical stress as a function of fissure penetration are shown in Figure 17. Detailed analysis reveals that the variation amplitude of both initial and peak failure vertical stress increased with fissure penetration. This indicates that the sensitivity of these stresses to fissure penetration grew progressively, which aligns with the findings of [PERSON] et al. (2016) and [PERSON] et al. (2019) regarding the relationship between crack length and failure degree. A similar conclusion can be drawn by comparing the failure times of sandstone specimens \"S-0-25\" and \"S-0-50\". Figure 18 compares the sidewall failure of all specimens at \(\sigma_{\text{z}}\) = 50 MPa, the highest stress level observed in specimen \"S-0-100\", to analyze the effect of fissure penetration on tunnel stability. Figure 18d shows that at a vertical stress of 50 MPa, both the left and right sidewalls of specimen \"S-0-100\" underwent complete axial failure. The left wall developed three distinct layers of rock slab, which spalled off sequentially from outer to inner layers. In contrast, the right sidewall formed only a single rock slab, which had not yet toppled following the failure. By comparison, the failures in the other specimens were less significant. Specim \"S-0-0\" exhibited minor rock spalling in the lower-left shoulder (Figure 18a), while specimen \"S-0-25\" showed localized fine particle spalling in the lower-right shoulder (Figure 18b). Notably, specimen \"S-0-50\" showed no visible signs of failure at 50 MPa (Figure 16c). Figure 17: Influence of fissure penetration on hole failure.