## 4 Computational Results and Analysis
### Influence of the Bol Length on Mechanical Properties of Bolts Support  
Bolts with different lengths may also be used during anchorage design. To explore the influence of the bolt length on the mechanical properties of bolt supports, the bolt length was set to 80, 130, and 180 mm, and the corresponding computation schemes are shown as Schemes 1, 4, and 5 in Table 1. Therein, the condition with a bolt length of 130 mm has been computed in Section 4.1. The stress distributions of bolts that are 80 and 180 mm long are displayed in Figures 9a and 10a. Combining this with the stress distribution on the bolt with a length of 130 mm (Figure 5a), it is found that, as the rock mass is compressed, stresses on bolts of different  
Figure 8: Values of evaluation indices for support capacity of bolts with different diameters. Figure 7: Changes in the anchorage force of bolts with different diameters with the compressive displacement of rock mass. lengths all increase and then tend to decrease. When the bolt length is 80 mm, the peak stress on the bolt is not transferred to greater depth; this is because the bolt is relatively short, so it can only improve the bearing capacity in a small range of rock mass. Therefore, many fractures occur in the shallow part when the rock mass is compressed to a small displacement (3.0 mm)(Figure 9b), and shallow surrounding rocks fail. When increasing the bolt length to 130 mm and 180 mm, the locus of peak stress on the bolts shifts to greater depth. In addition, the longer the bolts are, the larger the maximum compressive displacement (separately 5.1 mm and 6.0 mm) and the higher the peak stress intensity thereon. This indicates that the bolt length only slightly affects the stress distribution law while greatly influencing the peak stress intensity in the bolts and the maximum compressive displacement of the rock mass. The fracture distributions at the failure of anchored rock mass are shown in Figures 9b and 10b. Combined with Figure 5b, fractures are found to be mainly distributed in the rock mass, while only a few are distributed in the grout, so the failure mode of anchored rock mass is still manifest as damage to the rock mass. Meanwhile, with the increase in bolt length, the range of the distribution of fractures in the rock mass gradually expands, and fractures are mainly distributed along the whole length of the bolts. This indicates  
Figure 10: Stress distribution on bolts with a length of 180 mm and fracture distribution in the anchored rock mass. (**a**) Stress distribution of bolts; (**b**) Fracture distribution at failure. Figure 9: Stress distribution on bolts with a length of 80 mm and fracture distribution in the anchored rock mass. (**a**) Stress distribution of bolts; (**b**) Fracture distribution at failure. that increasing the bolt length can mobilize a wider range of rock mass to give play to its self-supporting ability and also strengthen a wider range of rock mass. Changes in the anchorage force of bolts with different lengths with the compressive displacement of anchored rock mass are shown in Figure 11. The figure shows that with the compression of anchored rock mass, the anchorage force of all bolts gradually increases. Under the same compressive displacement of the rock mass, the longer the bolts are, the greater the anchorage force thereon. As the bolts are increased in length, the maximum anchorage forces are separately 51 kN, 156 kN, and 334 kN; this indicates that the bolt length significantly affects the anchorage force provided by such bolts. The values of evaluation indices for the support capacity of bolts with different lengths are displayed in Figure 12. It can be seen that the peak stress intensity of bolts, displacement of the bolt head, and number of fractures in anchored rock mass are positively correlated with the bolt length.