Abstract
Previous researches on the mechanical model of toppling failure mainly concentrated on two-dimensional mechanical model (TwDM) analysis. The TwDM analysis assumes the width of the slab beam is unit width without considering the lateral constraint force. The assumed conditions are obviously different from the site conditions, thus there is a certain difference between the calculated results and the field work. A three-dimensional mechanical model (ThDM) of toppling failure was established, considering that the slab beam was mainly subject to self-weight, the frictional resistance of interlayer and lateral constraint force. Due to the progressive characteristics of toppling failure, the concept and the formula of the first fracture depth (FFD) of toppling was raised and constructed. The case study indicates that the ThDM is more effective and can be accurately used to calculate the toppling fracture depth of the slab beam. The FFD decreases proportionally with the increase of slab beam width. FFD grows fast when the slab beam width is less than 2.0 m and it tends to be stable when the slab beam width is above 2.0 m. The FFD decreases with the increase of the lateral constraint coefficient, indicating that the boundary condition of the free space is positively correlated with the stability and depth of toppling. This is a good explanation of the free space effect. This study provides a reference for the stability evaluation and prevention-control design of toppling slope in the future.
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Acknowledgments
We appreciate the linguistic assistance provided by AJE during the preparation of this manuscript. Special thanks go to the expertise comments from the reviewers and editors for improving the manuscript. The study is financially supported by the National Key R&D Program of China (2018YFC1504905), the Funds for Creative Research Groups of China (41521002), the Opening fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology, SKLGP2022K004) and the National Natural Science Foundation of China (41907250, 41772317, 52104082).
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Cai, Jc., Zheng, D., Ju, Np. et al. Boundary effect of toppling failure based on three-dimensional mechanical model. J. Mt. Sci. 19, 3314–3322 (2022). https://doi.org/10.1007/s11629-022-7337-2
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DOI: https://doi.org/10.1007/s11629-022-7337-2