## 6 Conclusions  
In this study, numerical simulation was used to examine the shear coalescence mechanism, stress evolution, and crack type characteristics of the band-bedrock interface. Moreover, the effects of the sample and step geometry size on the shear mechanical properties of the band-bedrock interface were identified. The specific conclusions are as follows:  
1. The initiation and failure cracks in the first rock step are predominantly tensile. As the induced shear displacement increases, the influence of shear stress becomes more pronounced, leading to shear and mixed types of failure cracks in the subsequent rock slabs and steps.
2. The failure of the first rock step occurs before the peak, primarily due to tensile stress, resulting in a point-load stress state that induces splitting failure. The remaining steps transition into a complex compressive-tensile stress state, with their failure occurring progressively.
3. With the increase in the sample size, the post-peak plasticity of the stress curves with strain softening becomes the predominant characteristic when the sample size exceeds 200 mm. The variation in the shear parameters with sample size can be described by a negative exponential function. Once the sample size surpasses 350 mm, the shear parameter values approach consistency. The representative elementary volume of the shear parameters can be considered as a sample with a geometry size of 350 mm.
4. The rock step height significantly influences the failure mode and stress curve characteristics by affecting the stress concentration and shear dilation. The peak shear strength and shear elastic modulus increase with rock step height, with respective amplifications of 91.37% and 115.83%. The residual strength initially decreases and then gradually increases with step height, exhibiting amplitude reductions and amplifications of 23.73% and 116.94%.
5. A smaller step width results in a higher number of fractures during shearing, maintaining shear resistance through point contacts between rock slabs and step blocks. As the rock step width increases, the stress concentration is mitigated due to the reduced inclination of the broken rock slab, leading to the stabilisation of the shear parameter values.  
Conceptualization, H.W., X.G., X.L. and X.Z.; methodology, H.W., X.G. and X.Z.; software, H.W. and X.G.; validation, X.L., X.Z. and B.X.; formal analysis, H.W. and X.G.; investigation, H.W., X.G. and B.X.; resources, X.L. and B.X.; data curation, X.L., X.Z. and B.X.; writing--original draft preparation, H.W. and X.G.; writing--review and editing, X.G., X.L., X.Z. and B.X.; visualization, X.G. and X.Z.; supervision, X.L. and B.X.; project administration, X.L. and B.X.; funding acquisition, X.L. and B.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Chongqing Talents and Out-standing Scientists Project (cstc2024 cyjh-bgzxm0032), the National Natural Science Foundation of China (41972266), the China Postdoctoral Science Foundation (2023M730432) and the Special Funding for Chongqing Postdoctoral Research Project (2022 CQBSHTB1010). And The APC was funded by [PERSON], [PERSON] and [PERSON].  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Acknowledgments:** The authors are very grateful for the editor and the anonymous reviewers' valuable comments. The authors are also very grateful for the [PERSON]'s work on language proofreading which improves readability of this paper.  
**Conflicts of Interest:** The authors declare that they have no conflicts of interest which may affect paper publication.