## 2 Numerical Simulation of Anchored Structural Surface
### Analysis of Local Damage to Anchoring Agent  
When the structural surface of a rock mass is dislocated, the surrounding rock mass and anchoring agent near the structural surface will be damaged. When the bolt in the anchored structural surface yielded, FLAC\({}^{\text{3D}}\) was used to show the plastic zones on the surrounding rock and the anchoring agent, as shown in Figures 6 and 7, respectively. The yellow part is the plastic zone generated by the rock mass, and the red part is the plastic zone generated by the anchoring agent. It can be seen that the plastic zone was mainly distributed near the intersection of the bolt and the structural surface. The distribution range of the plastic zone was related to the lithology of the structural surface. When the bolt yielded, the lithology of the structural surface was weaker, and the range of the plastic zone on the surrounding rock and anchoring agent was larger.  
With the dislocation of the structural surface, local damage and destruction of the anchoring agent on the bolt near the structural surface occurred, so the bolt in this range was no longer restrained by the anchoring agent and was approximately free. At the same time, a large local deformation was generated. In order to obtain the damage range of the anchoring agent, FISH language was used to calculate the volume of the plastic element generated by the anchoring agent with the structural surface dislocation. The area of the cross-section of the anchoring agent was 1.0048 \(\times\) 10\({}^{-3}\) m\({}^{2}\). Since the plastic zone of the anchoring agent was concentrated near the structural surface, the damage range of the anchoring agent could be obtained by dividing the volume of the plastic zone by the cross-sectional area of the anchoring agent, and the curve is shown in Figure 8.  
Figure 6: Distribution of plastic zones on the surrounding rock.  
Figure 7: Distribution of plastic zones on anchoring agent.  
An exponential fit to the structural surface shear displacement-anchoring agent damage length curve was performed with the following fitting functions:  
Coal: \(a=12.637-11.444\cdot 0.541^{l}\)  
Sandstone: \(a=12.346-11.108\cdot 0.526^{l}\)  
Granite: \(a=11.803-10.563\cdot 0.502^{l}\)  
where \(a\) is the length of the anchoring agent damage range in cm and \(l\) is the shear displacement of the structural surface in mm.  
The shear displacements of the structural surface when the bolt yielded in the coal, sandstone, and granite structural surfaces were 5.363 mm, 5.030 mm, and 4.624 mm, respectively, and the corresponding damage ranges of the anchoring agent were 12.2132 cm, 11.9077 cm, and 11.3664 cm. It can be seen that the variation laws of the damage range curves of the anchoring agents of different rock mass structural surfaces were roughly the same. With the dislocation of the structural surface, the damage range of the anchoring agent first increased rapidly and then tended to level off. Under the same shear displacements of the structural surfaces, the lithologies of the structural surface rocks were stronger, and the extent of the anchoring agent damage was smaller.