## 4 Sensitivity Analyses
### Deformation of Surrounding Rock Mass
#### 4.2.2 Displacements  
Figure 12 shows the relationship between the displacement of the surrounding rock at the cave wall and the length of the bolt under different in situ stress conditions. The displacement of the surrounding rock \(X\) is expressed in a dimensionless form by means of subdividing the diameter of the tunnel, \(D\):  
\[\psi=\frac{X}{D} \tag{38}\]  
It can be seen from the figure that as the in situ stress increases, the displacement of the surrounding rock of the tunnel wall gradually increases, and the maximum deformation of the tunnel wall and the high in situ stress show a strong nonlinearity. The large deformation mechanism of high in situ stress in soft rock tunnels results from the coupling effect of high in situ stress and the weak surrounding rock. When there is Class A large extrusion deformation, the displacement of the surrounding rock of the tunnel wall does not change significantly. The application of bolts at this time has no significant impact on the tunnel excavation. Other forms of support should be considered if the amount of deformation in the actual project is large. When there is Class B large extrusion deformation, the change in the surrounding rock of the tunnel wall is almost linear. In these conditions, bolt support can effectively restrain the deformation and displacement of the surrounding rock of the tunnel after excavation. When there is Class C or Class D large extrusion deformation, the change in the surrounding rock becomes nonlinear, and the increase in the surrounding  
Figure 11: Variation in the extent of plasticity with time under different in situ stresses conditions: (a) \(\xi\) = 0.3; (b) \(\xi\) = 0.9.  
rock displacement is larger when the short bolt is applied. The increase in the displacement of the surrounding rock is not significant when a long bolt is used.  
In addition, when the change in the surrounding rock of the cave wall reaches a specific value, it tends to be stable, indicating that after bolt support is applied, it can effectively control displacement in the applied area. It can also be seen from the deformation diagram that the rock mass anchored by the bolt forms a pressure zone, thereby improving the strength of the surrounding rock and significantly reducing the deformation and development of the plastic zone. As the rock bolt length increases, the plastic zone and the displacement of the surrounding rocks decrease. However, when the rock bolt length reaches a specific value, the plastic zone of the surrounding rock does not change much as the rock bolt length further increases, and the displacement also tends to stabilize. In summary, this optimized rock bolt length for this tunnel site is 9 m.  
In order to quantify the influence of the length of the bolts on the convergence of the tunnel, the relative difference of the dimensionless displacement of the surrounding rock at t = 1000 h was calculated for short bolts (\(\xi\) = 0.1) and long bolts (\(\xi\) = 0.9). For Classes A, B, C, and D, i.e., few, minor, severe, and very severe squeezing problems, differences were equal to 2%, 8%, 18%, and 4%. Therefore, we can conclude that the influence of bolt length on tunnel convergence is significant for minor and severe squeezing problems. In cases with few squeezing problems, the rock mass is strong enough to control the deformation. As for very severe squeezing problems, the primary support for the tunnel rests on a combination of shotcrte, steel arches, and bolts. Shotcrte and the steel arches were excluded from the model. Therefore, the influence of the bolts, if bolts alone are being used as the primary support, becomes insignificant in cases with few and severe squeezing problems.