## 4 Discussion  
### Effect of Fissure Penetration on Sidewall Failure  
#### 4.1.1 Sidewall Failure Process  
In underground engineering, under three-dimensional stress conditions, tunnel sidewall failure processes can vary due to changing geological conditions. Using acoustic emission probes and video monitoring equipment, signals from the surrounding rock were observed for sandstone specimens with different fissure penetrations. Taking specimen \"S-0-0\" as an example, the sidewall failure of the surrounding rock occurred in four stages, as illustrated in Figure 14.  
Calm Stage: In this initial phase, no visible changes occurred in the tunnel's surrounding rock. As vertical stress rose, energy built up in the rock, causing microscopic cracks not visible to the naked eye. This occurred because the shallow tensile strain of the sidewall exceeded the deep tensile strain (Figure 15a).  
Fine Particle Spalling Stage: In this stage, fine rock particles in the upper-left shoulder began to buckle and spall from the surrounding rock, either due to gravity or projectile ejection when stress exceeded a threshold. Microscopically, this phase was marked by the branching and unstable expansion of micro-fissures in the surrounding rock (Figure 15b).  
Crack Generation and Propagation Stage: As vertical stress rose, spalling in the upper-left shoulder intensified, resulting in the development of macroscopic axial fissures. Internally, stress in the surrounding rock adjusted, and cracks extended along the axial direction. Simultaneously, longitudinal cracks formed, microscopically penetrating the surface and deeper layers of the sidewall, damaging the rock structure (Figure 15c).  
Figure 14: Damage characteristic points and AE signals of “S-0-0”.  
Rock Slab Spalling and Failure Stage: In the final stage, longitudinal and axial cracks intersected, causing rock slabs to deform and fail under radial compression and gravity. This resulted in the toppling of rock slabs in a layered fashion, progressing from shallow to deeper layers. The rock slabs gradually narrowed, creating a distinct V-shaped notch (Figure 15d), which aligns with the findings in ref. [46]. At the conclusion of this stage, stress concentrations shifted to the right sidewall. Following these four stages, both sidewalls of the surrounding rock underwent axial penetration, indicating large-scale failure in the sandstone specimen.  
When prefabricated fissures were introduced, they compromised the structural integrity of the right sidewall, increasing its susceptibility to damage. Consequently, during the first stage, the compaction and development of micro-fissures were primarily concentrated on the right sidewall (Figure 16a). In the second stage, initial buckling deformation moved from the upper-left to the lower-right shoulder, with rock particle ejection noticeably reduced relative to the non-fissure specimen \"S-0-0\" (Figure 16b). During the third stage, the prefabricated fissure tip quickly propagated towards the upper ends of the spalling rock slab on the right side of the rectangular hole, leading to slab fissure failure on the right sidewall (Figure 16c). This resulted in a larger failure area during the fourth stage, forming a more pronounced V-shaped notch (Figure 16d). Throughout the entire failure process, the addition of fissures reduced the overall strength of the sandstone specimen compared to non-fissure specimens. As a result, the failure of the left sidewall began earlier, at the end of the third stage (whereas in the non-fissure specimen \"S-0-0\", this occurred at the end of the fourth stage). This shift in failure timing became more pronounced as the degree of fissure penetration increased.  
Figure 15: Sidewall failure evolution of non-fissure sandstone specimen. (**a**) Calm Stage (**b**) Fine Particle Spalling Stage (**c**) Crack Generation and Propagation Stage (**d**) Rock Slab Spalling and Failure Stage.