## 4 Computational Results and Analysis
### Influence of the Fracture Angle in Surrounding Rocks on the Mechanical Properties of the Bolts
As shown, secondary fractures are mainly distributed in the rock mass, so the failure modes of all anchorage bodies manifest as damage to the rock mass. When the fracture angle is \(90^{\circ}\), secondary fractures are distributed symmetrically on both sides of bolts and mainly occur at the ends of pre-existing fractures. There is a total of 9813 secondary fractures. When the fracture angles are \(60^{\circ}\), \(45^{\circ}\), and \(30^{\circ}\), secondary fractures no longer show a symmetric distribution; instead, they are mainly distributed at two positions: at the ends of pre-existing fractures and at the intersection of pre-existing fractures and bolts. Under these conditions, the total numbers of fractures in anchored rock mass are 8072, 6480, and 8384. This indicates that the angle of pre-existing fractures greatly affects the location and number of secondary fractures in the rock mass. This leads to differences in the failure zone and failure location at the failure of rock mass, thus affecting the stress distribution along the bolts. Changes in the anchorage force of bolts in anchored rock mass containing fractures with different angles with the compressive displacement of rock mass are displayed in Figure 22. It can be seen that as the anchored rock mass is compressed, the anchorage force of all bolts gradually grows. With the gradual reduction in the fracture angle, the maximum  
Figure 21: Stress distributions and fracture distribution on bolts under a fracture angle of \(30^{\circ}\). (**a**) Stress distribution of bolts; (**b**) Fracture distribution at failure. Figure 20: Stress distributions and fracture distribution on bolts under a fracture angle of \(45^{\circ}\). (**a**) Stress distribution of bolts; (**b**) Fracture distribution at failure. compressive displacement (separately 4.6 mm, 4.4 mm, 3.9 mm, and 4.1 mm) and anchorage force of bolts (separately 145 kN, 133 kN, 118 kN, and 137 kN) both decrease at first, then increase; the two indices are minimized when the fracture angle is 45\({}^{\circ}\). This suggests that when the angle between bolts and fractures is 45\({}^{\circ}\), it prevents the bolts from giving play to their anchoring capacity. Comparison with the maximum compressive displacement (5.1 mm) of the anchored rock mass and the maximum anchorage force (156 kN) of bolts in an intact rock mass reveals that the presence of fractures weakens the anchoring capacity of bolts and renders anchored rock mass more prone to failure. Under the most unfavorable condition (fracture angle of 45\({}^{\circ}\)), the maximum anchorage force of bolts in a fractured rock mass is only 75% of that in an intact rock mass. The values of evaluation indices for the support capacity of bolts in anchored rock mass containing fractures with different angles are illustrated in Figure 23. As the fracture angle decreases, all indices reduce at first and then increase. When the fracture angle is 45\({}^{\circ}\), all indices are minimum. This implies that although the peak stress intensity is minimum and bolts are not likely to be broken when the angle between bolts and fracture is 45\({}^{\circ}\), the anchoring effect is poorest, and anchored rock mass fails as long as the anchored rock mass suffers minor damage. Therefore, it needs to avoid an angle of 45\({}^{\circ}\) between bolts and pre-existing fractures during support. Figure 17.0 Values of evaluation indices for support capacity of bolts in anchored rock mass containing fractures with different angles. Figure 17.1 Changes in the anchorage force of bolts in anchored rock mass containing fractures with different angles with the compressive displacement of rock mass.