## 6 Conclusions  
In this paper, granite anchorage test samples were prepared and a numerical model of anchored fractured granite samples was constructed. A series of indoor experiments and numerical simulation studies were undertaken, exploring from the perspectives of macroscopic mechanical properties, deformation, and fracture patterns, and the evolution of the force chain network information. The ultimate goal was to reveal the differences in the mechanical behavior under uniaxial compression between unanchored and anchored fractured granite samples with varying \(\alpha_{\rm s}\), as well as to elucidate the influence of rock bolts on the anchoring and crack-stopping effects in these samples with different \(\alpha_{\rm s}\). The main conclusions of this paper are as follows:  
1. It was found that there is a strong consistency in the trend of load-displacement results between experimental and simulation results. The macroscopic fracture patterns of unanchored samples all show obvious shear failure, with debris fields concentrated at the fracture tips and distributed along the diagonal of the samples, while the distribution of debris in anchored samples is more uniform. This, in turn, validates the effectiveness of the numerical model parameter calibration.  
Figure 17: Variation in force chain values required for single crack initiation in samples with different \(\alpha_{\rm s}\).  
2. The number of force chains, the average force chain value, and the total force chain count within the anchored samples all exceed those of the unanchored samples. This suggests that there are fewer cementation fractures within the anchored samples, which implies fewer cracks. Furthermore, as the \(\alpha_{\rm s}\) increase, the increase in force chain characteristics of the anchored samples compared to the unanchored samples decreases.
3. The results show that the volume of the three-dimensional rose diagrams of the anchored samples with fractures at various dips is greater than that of the unanchored samples. As the \(\alpha_{\rm s}\) increase, the above phenomenon becomes less apparent, which means that the anchored samples have a higher load-bearing capacity. In addition, as \(\alpha_{\rm s}\) increase, the anchoring reinforcement effect of the rock bolts becomes less obvious.
4. A quantitative exploration was conducted on the anchoring and crack-stopping effect of rock bolts on granite samples with different dip angles of fractures. The results show that at \(\alpha_{\rm s}=30^{\circ}\), the rock bolts have the best crack-stopping effect on the samples. As \(\alpha_{\rm s}\) increases, the crack-stopping effect gradually weakens and becomes less apparent. This suggests that in practical engineering, when dealing with fractured rock masses under different working conditions, targeted anchoring and support measures can be applied. This approach can help reduce costs to a certain extent.  
Conceptualization, J.G.; methodology, D.F.; validation, L.Y., T.Z. and B.H.; formal analysis, H.S.; investigation, M.S.; writing--original draft preparation, M.S.; writing--review and editing, B.H., D.F. and M.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (52274100, 42307238, 52409148), the Excellent Postdoctoral Program of Jiangsu Province (Grant No. 2023 ZB602) and the China Postdoctoral Science Foundation (Grant No. 2023M/337/3).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Author [PERSON] was employed by the company Shanxi Huaning Coking Coal Co., Ltd., China Coal Group Huajin Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.