## 6 Conclusions  
Based on PFC3D simulation, this study analyzed the effects of different \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) and \(\overline{k}\) on the macro-properties of the model using PFC3D simulations. Ten different bond normal-to-shear stress ratios (\(\overline{\sigma}_{n}/\overline{\tau}_{n}=0.1\), 0.2, 0.4, 0.6, 0.8, 1, 2 3, 4, and 6) were considered with 10 different bond normal-to-shear stiffness ratios (\(\overline{k}=1.11\), 2, 3, 4, 5, 6, 7, 8, 9, and 10.11) set for each stress ratio. The effects of different KK on the macro-properties of the model were also considered. The simulation results were analyzed, and the following results were obtained:  
1. Changes in \(\overline{k}\)  altered the bond stress state within specimens and their overall stiffness, thereby affecting their strength and stress-strain characteristics. Changes in bond stress state with \(\overline{k}\)  altered the extent of influence that \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) exerted on sample strength. The change of \(\overline{k}\)  assignment mode also had a significant effect on the deformation ability of the model.
2. \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) altered the inter-particle bond strength. An increase in \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) improved the effect level of \(\overline{k}\)  on the sample strength. The sample strength increased with increasing \(\overline{\sigma}_{n}/\overline{\tau}_{n}\). However, when \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) exceeded a certain value N, the sample strength was restricted by \(\overline{\tau}_{n}\) and did not increase further. The N value was determined by a combination of \(\overline{\phi}\) and \(\overline{k}\).
3. An increase in KK resulted in a larger decrease in the overall stiffness of specimens after parallel-bond failure. The sample strength decreased as their deformability increased.
4. Considerable changes in the sample brittleness and ductility were observed under the combined effects of \(\overline{\sigma}_{n}/\overline{\tau}_{n}\) and \(\overline{k}\). When \(\overline{\sigma}_{n}/\overline{\tau}_{n}<1\), specimens changed from brittle to ductile with increasing \(\overline{k}\), and when \(\overline{\sigma}_{n}/\overline{\tau}_{n}>1\), they exhibited a reverse trend.  
Figure 19: Parallel-bond model.  
Figure 18: Changes in the N value with internal friction angle (\(\overline{\phi}\)) for different bond normal-to-shear stiffness ratios (\(\overline{k}\) ).  
According to the research results, the appropriate adjustment of the micro-parameters of PFC could make the mechanical properties of the simulation model more consistent with the actual mechanical properties of the rock material, improve the accuracy of the simulation results, and provide some help for the research of the rock mechanical behavior. Considering the variation range of micro-parameters in this paper, the results of this paper could only be used to simulate the mechanical properties of rock materials.  
Conceptualization, data curation, formal analysis, investigation, writing--original draft preparation, H.R.; funding acquisition, resources, G.L.; project administration, H.R. and G.L.; writing--review and editing, H.R. and G.L.; validation, D.L., C.S., Y.S., and S.Z. All authors have read and agreed to the published version of the manuscript.  
The work presented in this paper was supported by the projects of \"Supported by the Fundamental Research Funds for the Central Universities (2020 ZDPY0221)\", \"National Key Research and Development Program (2016 YFC0600901)\", \"National Natural Science Foundation of China (Grant No. 51574224)\", and a project funded by the \"Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)\".  
Additionally, the authors are grateful to the anonymous reviewers for their careful reading of the manuscript and their many helpful comments.  
The authors declare no conflicts of interest.