# Flexural Buckling Failure of Rock Slopes: A Review of Influencing Factors and Analysis Methods
## 5 Concluding Remarks and Future Prospects  
To fully understand the behavior of buckling failure of dip rock slopes, a bibliometric analysis was conducted to synthesize relevant literature and systematically review research hotspots and development trends in this field. Although significant advancements have been made in studying the deformation process, influencing factors and analysis methods related to the flexural buckling failure of dip slopes, challenges remain in both theoretical research and engineering practice. Existing theoretical studies on instability mechanisms and stability evaluation of flexural buckling in dip rock slopes have primarily focused on exploring the influence of either intrinsic or triggering factors through numerical and analytical modelling, while rarely considering the coupled effects of multiple factors. The application of physical model tests, particularly centrifugal modeling which can reproduce prototype stress states while accounting for time-dependent effects, remains at an early stage. In future research, refined numerical methods should be combined with novel physical modelling techniquesto systematically investigate the influence mechanisms of multi-factor coupling on buckling failures of dip slopes. Based on case reviews, flexural buckling failures predominantly develop in soft-hard interbedded dip rock slopes with layer inclination of 20-50\({}^{\circ}\) and thin-to-medium thickness characteristics. For rapid assessment of dip slope buckling, analytical approaches and corresponding assessment indicators must be carefully selected. Regarding stiff and fragile rock layers, force-equilibrium or energy-based analytical methods at precise limit states are preferable. The assessment index of the elastic critical load is particularly useful here, as rock mass strength drops sharply once this threshold is reached, leading to destructive landslides. For soft rock layers, critical-displacement-based methods are more appropriate, although their application across different scenarios remains challenging. Civil engineering applications require strict displacement limits to protect structures and maintain serviceability. In contrast, mining engineering often permits larger displacements and operates with marginal safety conditions when short-term bench stability is prioritized. Conceptualization and methodology, Y.Z., N.F. and J.S. ; investigation, Y.Z., N.F., J.S., L.P., J.T. and R.Y. ; resources, Y.Z., N.F. and J.T. ; writing--original draft preparation, Y.Z., N.F. and J.S. ; writing--review and editing, Y.Z., N.F., J.S. and L.L. ; visualization, Y.Z., N.F., J.S. and L.P.; funding acquisition, Y.Z., N.F., R.Y. and L.L. All authors have read and agreed to the published version of the manuscript. This study was supported by the Hubei Provincial Natural Science Foundation of China (no. 2021 CFB280); the Follow-up of the Geological Disaster Prevention and Control Project in the Three Gorges area (no. 000121 2024C C60 002); the National Natural Science Foundation of China (nos. 52108337, 47102383); the \"Qianlong Plan\" Youth Talent Project of Wuhan Center, China Geological Survey (no. QL2022-10); and the Project of China Geological Survey (no. DD20221740). All data, models, and code generated or used during this study appear in the submitted article. The authors thank all the scholars responsible for the referenced work and professional websites for providing figures. All the authors of this manuscript have approved the submission of this article for publication, and there are no conflicts of interest to declare. This paper has not been published elsewhere and is not under consideration by another journal. The following symbols are used in this manuscript: