Stability Analysis of Prescribed Slip Surfaces Based on a Combination of the Equilibrium Equation and the Critical Unstable Condition
Publication: International Journal of Geomechanics
Volume 17, Issue 12
Abstract
Stability analysis of potential slip surfaces is one of the core steps of slope safety evaluation. In this study, a novel model was developed that considers the critical unstable condition that represents the limit equilibrium and displacement constraints along a prescribed slip surface. The stress distribution and the safety factor of the prescribed slip surface in the critical state can be obtained by directly solving the nonlinear equations formed by the model. By incorporating the finite-element stress analysis, the proposed model does not require interslice force assumptions as do the traditional limit-equilibrium methods and can consider the influence of stress perturbation from outside of the slip body on its stability. The numerical algorithm is also detailed in the article. In addition, an analysis of three examples is carried out to validate the effectiveness of the proposed model and to demonstrate its feature of fast convergence.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the Major Science and Technology Special Projects in the Three Five Plan of the Metallurgical Corp. of China, Ltd. (No. 0012012009). Many thanks to Dr. Li Chun-guang and Guan-hua Sun for technical discussions.
References
Ahmed, A., Ugai, K., and Yang, Q. Q. (2012). “Assessment of 3D slope stability analysis methods based on 3D simplified Janbu and Hovland methods.” Int. J. Geomech., 81–89.
Bai, B., Yuan, W., and Li, X.-C. (2014). “A new double reduction method for slope stability analysis.” J. Cent. South Univ., 21(3), 1158–1164.
Belytschko, T., and Black, T. (1999). “Elastic crack growth in finite elements with minimal remeshing.” Int. J. Numer. Methods Eng., 45(5), 601–620.
Bishop, A. W. (1955). “The use of the slip circle in the stability analysis of slopes.” Géotechnique, 5(1), 7–17.
Brown, C. B., and King, I. P. (1966). “Automatic embankment analysis: Equilibrium and instability conditions.” Géotechnique, 16(3), 209–219.
Burden, R. L., and Faires, J. D. (2011). Numerical analysis, 9th Ed., Brooks/Cole, Boston.
Chen, Z. (1998). “On Pan’s principles of soil and rock stability analysis.” J. Tsinghua Univ. Sci. Technol., 38(3), 1–4.
Chen, Z. (2003). Soil slope stability analyses—Theory, method and programs, Water Power Press, Beijing.
Cheng, Y. M., Lansivaara, T., and Wei, W. B. (2007). “Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods.” Comput. Geotech., 34(3), 137–150.
Cheng, Y. M., Zhao, Z. H., and Wang, J. A. (2008). “Realization of Pan Jiazheng’s extremum principle with optimization methods.” Chin. J. Rock Mech. Eng., 27(4), 782–788.
Dawson, E. M., Roth, W. H., and Drescher, A. (1999). “Slope stability analysis by strength reduction.” Géotechnique, 49(6), 835–840.
Donald, I. B., and Giam, P. (1992). “The ACADS slope stability programs review.” Proc., 6th Int. Symp. on Landslides, D. H. Bell, ed., A. A. Balkema, Rotterdam, Netherlands, 1665–1770.
Fredlund, D. G., Scoular, R. E. G., and Zakerzadeh, N. (1999). “Using a finite element stress analysis to compute the factor of safety.” Proc., 52nd Canadian Geotechnical Conf., Canadian Geotechnical Society, Richmond, BC, Canada, 73–80.
Ge, X.-R. (2010). “The vector sum method: A new approach to calculating the safety factor of stability against sliding for slope engineering and dam foundation problems.” Advances in environmental geotechnics, Springer, New York, 99–110.
Griffiths, D. V., and Lane, P. A. (1999). “Slope stability analysis by finite elements.” Géotechnique, 49(3), 387–403.
Hirmand, M., Vahab, M., and Khoei, A. R. (2015). “An augmented Lagrangian contact formulation for frictional discontinuities with the extended finite element method.” Finite Elem. Anal. Des., 107, 28–43.
Isakov, A., and Moryachkov, Y. (2014). “Estimation of slope stability using two-parameter criterion of stability.” Int. J. Geomech.,.
Janbu, N. (1975). “Slope stability computations.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 12(4), 67.
Kulhawy, F. H. (1969). “Finite element analysis of the behavior of embankments.” Ph.D. thesis, Univ. of California, Berkeley, CA.
Liu, S. Y., Shao, L. T., and Li, H. J. (2015). “Slope stability analysis using the limit equilibrium method and two finite element methods.” Comput. Geotech., 63, 291–298.
Liu, Y., Wang, C., and Yang, Q. (2012). “Stability analysis of soil slope based on deformation reinforcement theory.” Finite Elem. Anal. Des., 58, 10–19.
Matsui, T., and San, K.-C. (1992). “Finite element slope stability analysis by shear strength reduction technique.” Soils Found., 32(1), 59–70.
Morgenstern, N. R., and Price, V. E. (1965). “The analysis of the stability of general slip surfaces.” Géotechnique, 15(1), 79–93.
Naylor, D. J. (1982). “Finite elements and slope stability.” Numerical methods in geomechanics, J. B. Martins, ed., Springer, New York, 229–244.
Simo, J. C., and Laursen, T. A. (1992). “An augmented Lagrangian treatment of contact problems involving friction.” Comput. Struct., 42(1), 97–116.
SLIDE [Computer software]. Rocscience, Toronto.
Spencer, E. (1967). “A method of analysis of the stability of embankments assuming parallel inter-slice forces.” Géotechnique, 17(1), 11–26.
Wang, W., Yuan, W., Li, X.-C., and Bai, B. (2016). “Evaluation approach of the slope stability based on deformation analysis.” Int. J. Geomech.,.
Yuan, W., et al. (2016). “An approach to determining critical slip surface based on displacement field analysis.” Rock Soil Mech., 37(6), 1791–1798.
Zheng, H., Liu, D. F., and Li, C. G. (2005). “Slope stability analysis based on elasto-plastic finite element method.” Int. J. Numer. Meth. Eng., 64(14), 1871–1888.
Zheng, H., Sun, G., and Liu, D. (2009). “A practical procedure for searching critical slip surfaces of slopes based on the strength reduction technique.” Comput. Geotech., 36(1–2), 1–5.
Zienkiewicz, O. C., Humpheson, C., and Lewis, R. W. (1975). “Associated and non-associated visco-plasticity and plasticity in soil mechanics.” Géotechnique, 25(4), 671–689.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 17 • Issue 12 • December 2017
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Dec 7, 2016
Accepted: Jul 18, 2017
Published online: Sep 29, 2017
Published in print: Dec 1, 2017
Discussion open until: Mar 1, 2018
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.