## 4 Results and Analysis
### Influence of Roadway Height-Width Ratio
#### 4.1.3 Vertical Stress of Roadway Sidewall  
The vertical stress distribution of various roadway aspect ratios \(h/w\) is depicted in Figure 10. As the height-width ratio \(h/w\) of a roadway increases, the area affected by the excavation disturbance gradually expands. Consequently, both the stress release zone and areas with high stress values expand accordingly. The areas with high vertical stress values  
Figure 8: Scatter of the relationship between \(h/w\) and the depth of the tensile plastic zone and shear plastic zone of a roadway sidewall.  
Figure 9: Relationship between \(h/w\) and horizontal displacement of the roadway sidewall.  
in the sidewall rock mass moves to the deeper surrounding rock area, ultimately resulting in two extreme stress points forming within the deeper rock mass area of the roadway.  
The variation of vertical stresses inside a sidewall with increasing distance from the boundary of the roadway sidewall is illustrated in Figure 11. Initially, as the distance from the sidewall boundary increases, the vertical stress escalates swiftly until it reaches a peak. Subsequently, it undergoes a slight decline before gradually ascending to a second peak, followed by a gradual decrease and eventual stabilization. When \(h/w\) is small, for example, when \(h/w=0.25\), the vertical stress inside the sidewall has only one stress concentration point. With the increase of \(h/w\) to 0.75, two vertical stress concentration points appear inside the roadway sidewall. As \(h/w\) continues to increase from 0.75, the second stress peak gradually rises, eventually approaching the value of the first stress peak.  
The relationship between \(h/w\) and maximum vertical stress inside of a roadway sidewall is shown in Figure 12. When \(h/w\) increases from 0.25 to 0.50, the vertical stress value at the first stress concentration point is rapidly reduced from 41.5 MPa to 33.07 MPa. The vertical stress decreases slowly, and then increases slightly. When \(h/w=0.25\), the vertical stress changes to 31.35 MPa. In general, the stress value of the first stress concentration point inside a roadway sidewall first decreases and then increases as the height-width ratio \(h/w\) of the roadway rises, showing a secondary polynomial relationship. As the height-width ratio \(h/w\) of the roadway rises, the stress concentration point moves progressively deeper into the surrounding rock. When \(h/w\) was increased from 0.25 to 2.00, several notable changes occurred. First, the distance between the stress concentration position and the roadway sidewall increased from 0.5 m to 3.27 m. The distance between the maximum stress concentration point and boundary of the sidewall rock mass and the aspect ratio \(h/w\) of the roadway increase linearly. Additionally, the stress value at the second stress concentration point showed an increase with the rising roadway's \(h/w\), exhibiting a quadratic polynomial relationship. Furthermore, as the \(h/w\) ratio increased, the stress concentration position shifted gradually deeper into the rock mass. Specifically, when the \(h/w\) ratio was increased from 0.25 to 2.00, the distance between the vertical stress concentration position and the roadway sidewall extended from 0.75 m to 6.25 m. The  
Figure 10: Vertical stress of sidewall under various height-width ratio \(h/w\) (green is tensile and red is shear): (**a**) \(h/w=0.25\); (**b**) \(h/w=0.50\); (**c**) \(h/w=0.75\); (**d**) \(h/w=1.00\); (**e**) \(h/w=1.25\); (**f**) \(h/w=1.50\); (**g**) \(h/w=1.75\); (**h**) \(h/w=2.00\).  
stress concentration position has a linear growth relationship with the roadway sidewall distance and the roadway height-width ratio \(h/w\).