## 4 Computational Results and Analysis
### Influence of the Bolt Diameter on Mechanical Properties of Bolts Support  
Bolts with different diameters need to be used according to the rock conditions during anchorage design. To study the influence of the bolt diameter on the mechanical properties of bolt supports, the bolt diameter was separately set to be 12 mm, 16 mm, and 20 mm, and the corresponding computation schemes are Conditions 1, 2, and 3 in Table 1.  
As the rock mass is constantly compressed, the stress distributions of bolts with different diameters are shown in Figures 4a, 5a and 6a. It can be seen that in the initial stage of loading (0.5 and 1.5 mm), the overall stresses on the bolts are small, and the stress begins to decline after reaching the peak at the front end of the bolts (0.01 m from the hole), showing the tendency to increase, then decrease. In the middle stage of loading (2.5 mm and 3.5 mm), the overall stresses on the bolts continue to increase with the compression of the rock mass, while the stress distribution and peak location do not change. When the compressive displacement of the rock mass reaches 4.5 mm, the peak stresses on bolts with diameters of 12 mm and 16 mm begin to shift to greater depths, and the peak stress intensity constantly increases. Meanwhile, stress in the shallow part of bolts reduces. It is worth noting that because of the different bolt diameters, the rock mass shows different compressive displacements (with maxima of 4.9 mm, 5.1 mm, and 5.3 mm) upon failure of the anchored rock mass. Upon failure of the anchored rock mass, the peak stress intensity of bolts with different diameters continues to increase and the peak stress on the bolt with a diameter of 20 mm also begins to shift to greater depth. The stress distributions of all bolts remain unchanged; this suggests that the bolt diameter only slightly affects the stress distribution law while greatly influencing the stress on such bolts and the compressive displacement of the rock mass during the shift in the locus of peak stress. That is to say, the larger the diameter, the lower the overall stress on the bolts; the peak stress on the bolts does not shift to greater depth until the rock mass is significantly deformed. The fracture distributions at the failure of anchored rock mass are shown in Figures 4b, 5b and 6b: fractures are mainly distributed in the rock mass, only a few are found in the grout, and no fractures are developed within the bolts. Therefore, the final failure mode of anchorage is shown as the damage to rock mass. A comparison shows that the anchored rock mass exhibits consistent fracture locations and failure modes when using bolts with different diameters, so the bolt diameter only slightly affects the fracture distribution and failure mode of the anchored rock mass. Figure 4: Stress distribution on bolts with a diameter of 12 mm and fracture distribution in the anchored rock mass. (**a**) Stress distribution of bolts; (**b**) Fracture distribution at failure. Figure 5: Stress distribution on bolts with a diameter of 16 mm and fracture distribution in the anchored rock mass. (**a**) Stress distribution of bolts; (**b**) Fracture distribution at failure. Figure 6: Stress distribution on bolts with a diameter of 20 mm and fracture distribution in the anchored rock mass. (**a**) Stress distribution of bolts; (**b**) Fracture distribution at failure. Changes in the anchorage force of bolts with different diameters with the compressive displacement of rock mass are illustrated in Figure 7. It can be seen that, throughout the loading process, the anchorage force of all bolts shows a gradually increasing trend, and the maximum anchorage force of bolts increases with the bolt diameter. The maximum anchorage forces are 140 kN, 156 kN, and 160 kN.