Rigorous Limit-Equilibrium Solution for Three-Dimensional Slope Stability with an Asymmetric Slip Surface
Publication: International Journal of Geomechanics
Volume 24, Issue 2
Abstract
In practice, slope instability failure often occurs in the form of an asymmetric three-dimensional (3D) slip surface. The movement trend of the asymmetric sliding body is in the form of simultaneous translation and rotation around the vertical axis; thus, the route of the main sliding (RMS) exhibits non-linear characteristics. Therefore, the purpose of this study was to propose a rigorous 3D limit equilibrium method for slope stability with the asymmetric 3D slip surface. The function of normal stress over the slip surface was assumed, and all the equilibrium conditions of the entire sliding body (i.e., three forces and three moments) were considered. The mapping function relationship between curvilinear coordinates and Cartesian coordinates was established, and the expressions of basic physical quantities in the equilibrium equations were derived. Through optimizing the RMS, a rigorous solution of the factor of safety was obtained for an asymmetric slip surface. The research results indicated that the present method well reflected the influence of the RMS, which was applicable to analyzing 3D slope stability with an asymmetric slip surface. We found that if the RMS is ignored, the factor of safety will be overestimated. The more significant the asymmetry of the 3D slip surface, the greater the proportion of rotation for the sliding body, and the more significant the bending degree of the RMS. The study results suggested that a rotation hardly existed, and the RMS tended to be a linear route in a symmetrical sliding body. The research results can provide a theoretical reference for 3D slope stability evaluation.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Data are available upon request from the corresponding author.
Acknowledgments
The research was supported by the National Natural Science Foundation of China (Grant No. 52079121) and the Natural Science Foundation of Anhui Province (Grant No. 2208085ME149).
References
Bishop, A. W. 1955. “The use of the slip circle in the stability analysis of slopes.” Geotechnique 5 (1): 7–17. https://doi.org/10.1680/geot.1955.5.1.7.
Chen, C. F., and J. F. Zhu. 2010. “A three-dimensional slope stability analysis procedure based on Morgenstern-price method.” Chin. J. Rock Mech. Eng. 29 (7): 1473–1480.
Chen, Z. Y., H. L. Mi, and X. G. Wang. 2001. “A three-dimensional limit equilibrium method for slope stability analysis.” Chin. J. Geotech. Eng. 5: 525–529.
Deng, D. P., and L. Li. 2017. “Three-dimensional limit equilibrium method for slope stability based on the assumption of stress on slip surface.” Rock Soil Mech. 38 (1): 189–196.
Deng, J. H., Y. J. Gao, Z. H. Yu, and H. P. Xie. 2019. “Analysis on the formation mechanism and process of Baige landslides damming the upper reach of Jinsha River, China.” Adv. Eng. Sci. 51 (1): 9–16.
Fadaie, S., and M. Veiskarami. 2020. “Bearing capacity failure of supported cuts in the presence of seepage flow by coupled finite elements and stress characteristics method.” Int. J. Civil Eng. 18 (7): 817–825. https://doi.org/10.1007/s40999-020-00495-7.
Fellenius, W. 1936. “Calculation of the stability of earth dams.” In Vol. 4 of Proc., 2nd Int. Congress on Large Dams, 445–463. Washington, DC: ICLD.
He, Y., Y. Liu, Y. Zhang, and R. Yuan. 2019. “Stability assessment of three-dimensional slopes with cracks.” Eng. Geol. 252: 136–144. https://doi.org/10.1016/j.enggeo.2019.03.001.
Hovland, H. J. 1977. “Three-dimensional slope stability analysis method.” J. Geotech. Eng. Div. 103 (9): 971–986. https://doi.org/10.1061/AJGEB6.0000493.
Hungr, O. 1987. “An extension of Bishop’s simplified method of slope stability analysis to three dimensions.” Geotechnique 37 (1): 113–117. https://doi.org/10.1680/geot.1987.37.1.113.
Hungr, O., F. M. Salgado, and P. M. Byrne. 1989. “Evaluation of a three-dimensional method of slope stability analysis.” Can. Geotech. J. 26 (4): 679–686. https://doi.org/10.1139/t89-079.
Hwang, Y. W., and E. M. Rathje. 2023. “Insights into seismic slope deformation patterns using finite element analysis.” Soil Dyn. Earthquake Eng. 164: 107660. https://doi.org/10.1016/j.soildyn.2022.107660.
Jiang, Q. H., and C. B. Zhou. 2018. “A rigorous method for three-dimensional asymmetrical slope stability analysis.” Can. Geotech. J. 5 (4): 495–513. https://doi.org/10.1139/cgj-2017-0317.
Kalatehjari, R., A. S. A. Rashid, M. Hajihassani, M. Kholghifard, and N. Ali. 2014. “Determining the unique direction of sliding in three-dimensional slope stability analysis.” Eng. Geol. 182: 97–108. https://doi.org/10.1016/j.enggeo.2014.06.002.
Li, B., H. Tang, W. Gong, Z. Cheng, T. Li, and L. Wang. 2022. “Numerical study of the runout behavior of the Kamenziwan landslide in the Three Gorges Reservoir region, China.” Landslides 19 (4): 963–976. https://doi.org/10.1007/s10346-021-01804-4.
Liu, S. J., M. W. Guo, and C. G. Li. 2018. “Determination of main sliding direction for three-dimensional slope.” Rock Soil Mech. 39 (S2): 37–44.
Liu, Z. P., J. Liu, K. Bian, and F. Ai. 2019. “Three-dimensional limit equilibrium method based on a TIN sliding surface.” Eng. Geol. 262: 105325. https://doi.org/10.1016/j.enggeo.2019.105325.
Lu, K. L., L. F. Wang, Y. Yang, and G. G. Zhou. 2022. “Three-dimensional method for slope stability with the curvilinear route of the main sliding.” Bull. Eng. Geol. Environ. 81 (1): 1–16. https://doi.org/10.1007/s10064-021-02521-x.
Lu, K. L., and D. Y. Zhu. 2016. “A three-dimensional rigorous method for stability analysis and its application.” Bull. Eng. Geol. Environ. 75 (4): 1445–1457. https://doi.org/10.1007/s10064-015-0783-0.
Morgenstern, N. R., and V. E. Price. 1965. “The analysis of the stability of general slip surfaces.” Geotechnique 15 (1): 79–93. https://doi.org/10.1680/geot.1965.15.1.79.
Qi, S., D. Ling, Q. Yao, G. Lu, X. Yang, and J. W. Zhou. 2021. “Evaluating slope stability with 3D limit equilibrium technique and its application to landfill in China.” Eng. Geol. 280: 105939. https://doi.org/10.1016/j.enggeo.2020.105939.
Rajabian, A., and S. K. Shukla. 2023. “Stability analysis of anchor-reinforced soil slopes with Taylor’s stability chart.” Int. J. Geomech. 23 (2): 04022278. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002619.
Smith, J. D., and S. R. Mclean. 1984. “A model for flow in meandering streams.” Water Resour. Res. 20 (9): 1301–1315. https://doi.org/10.1029/WR020i009p01301.
Spencer, E. 1967. “A method of analysis of the stability of embankments assuming parallel inter-slice forces.” Geotechnique 17 (1): 1l–26. https://doi.org/10.1680/geot.1967.17.1.11.
Wan, Y. K., Y. F. Gao, and F. Zhang. 2016. “A simplified approach to determine the unique direction of sliding in 3D slopes.” Eng. Geol. 211: 179–183. https://doi.org/10.1016/j.enggeo.2016.07.001.
Yao, Y., and Z. Wang. 2023. “Study on upper bound limit analysis of horizontal layers slope stability based on optimization method.” Sci. Rep. 13 (1): 6106. https://doi.org/10.1038/s41598-023-33373-y.
Zhang, X. 1988. “Three-dimensional stability analysis of concave slopes in plan view.” J. Geotech. Geoenviron. Eng. 114 (6): 658–671. https://doi.org/10.1061/(ASCE)0733-9410(1988)114:6(658).
Zheng, H. 2007. “A rigorous three-dimensional limit equilibrium method.” Chin. J. Rock Mech. Eng. 8: 1529–1537.
Zheng, Y. R., W. M. Shi, and M. C. Yang. 2004. “Discussion on imbalanced thrust force method and Sarma’s method.” Chin. J. Rock Mech. Eng. 17: 3030–3036.
Zhou, X. P., and H. Chen. 2013. “Analysis of stability of three-dimensional slopes using the rigorous limit equilibrium method.” Eng. Geol. 160: 21–33. https://doi.org/10.1016/j.enggeo.2013.03.027.
Zhu, D. Y., X. L. Ding, and Q. H. Qian. 2007. “Three-dimensional limit equilibrium solution to general-shaped slope stability.” Chin. J. Geotech. Eng. 10: 1460–1464.
Zhu, D. Y., and Q. H. Qian. 2007. “Rigorous and quasi-rigorous limit equilibrium solution of 3D slope stability and application to engineering.” Chin. J. Rock Mech. Eng. 8: 1513–1528.
Zhu, D. Y., L. H. Wang, and K. L. Lu. 2023. “Simplified method for three-dimensional slope stability analysis based on rigorous limit equilibrium.” Int. J. Numer. Anal. Methods Geomech. 47 (4): 648–663. https://doi.org/10.1002/nag.3486.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 2 • February 2024
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Feb 19, 2023
Accepted: Jul 29, 2023
Published online: Nov 27, 2023
Published in print: Feb 1, 2024
Discussion open until: Apr 27, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.