# The Bolt Anchorage Performance of Fractured Rock under a Freeze-Thaw Cycle Load
## 5 Conclusions  
This study conducted experimental research and a numerical simulation verification on specimens of rock-like materials under different crack conditions, and with or without anchor rods. The main conclusions drawn are as follows:  
1. The angle of pre-existing fractures significantly influences the strength of rocks, with their strength ranking consistently as follows: specimens with 45\({}^{\circ}\) fractures < specimens with 90\({}^{\circ}\) fractures < intact specimens. Stress concentration occurs around the bolt, which weakens the compressive performance of intact specimens but enhances the strength of specimens containing fractures. Additionally, the bolt induces plasticity at the specimen's peak, followed by post-peak ductility.
2. Freeze-thaw cycles notably degrade the compressive strength of specimens without cracks and with 90\({}^{\circ}\) pre-existing cracks, with a more pronounced weakening effect observed in specimens without anchor rods. The fitting line slopes of specimens without cracks and without anchor rods, specimens without cracks and with anchor rods, specimens with 90\({}^{\circ}\) pre-existing cracks and without anchor rods, and specimens with 90\({}^{\circ}\) pre-existing cracks and with anchor rods are \(-\)0.259, \(-\)0.134, \(-\)0.197, and \(-\)0.153, respectively. However, the effect of freeze-thaw cycles on specimens with 45\({}^{\circ}\) pre-existing cracks is less significant, indicating a weaker weakening effect on the strength of low-water-content pre-existing weak structural plane rocks.
3. The failure modes of specimens are influenced by the interaction between their pre-existing cracks and anchor rods. Both specimens with 45\({}^{\circ}\) pre-existing cracks and anchor rods and specimens without cracks and anchor rods exhibit sliding failure along the pre-existing crack plane, while specimens without cracks and with 90\({}^{\circ}\) pre-existing cracks, under no-anchor conditions, exhibit external spalling and internal large-angle shear failure. In terms of crack development, various types of specimens exhibit vertical or oblique wing cracks along the specimen surface, with specimens with 45\({}^{\circ}\) pre-existing cracks also exhibiting shear cracks generated by the extension of pre-existing cracks.
4. A coupled model combining the PFC3D discrete element method and FLAC3D finite difference method was employed to simulate the unfrozen experimental conditions. The specimen material was modelled using a parallel bonded constitutive model, the pre-existing structural plane was modelled using a smooth joint constitutive model, and the anchor rods were modelled using a linear elastic constitutive model. The simulation results are in good agreement with the experimental data.
5. Comparing the results of numerical simulations, specimens without bolts exhibit more pronounced localized spalling, whereas specimens with bolts show stress concentrations around the bolt, resulting in the formation of long and penetrating cracks. Internal microcracks within the specimens generally initiate from the bolt and pre-existing structural surfaces, with tension cracks being more prevalent than shear cracks.  
**Author Contributions:** Conceptualization, F.H. and Y.C.; Writing--original draft, F.H.; Writing--review & editing, Y.C.; Visualization, F.H.; Funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Acknowledgments:** [PERSON], [PERSON], [PERSON] and the Underground Space Engineering Group are acknowledged for the research.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.