Three-Dimensional Asymmetrical Slope Stability Analysis Extension of Bishop’s, Janbu’s, and Morgenstern–Price’s Techniques
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 133, Issue 12
Abstract
Most existing three-dimensional (3D) slope stability analysis methods are based on simple extensions of corresponding two-dimensional (2D) methods of analysis and a plane of symmetry or direction of slide is implicitly assumed. In this paper, 3D asymmetric slope stability models based on extensions of Bishop’s simplified, Janbu’s simplified, and Morgenstern–Price’s methods are developed. Under these new formulations, the direction of slide is unique and is determined from 3D force/moment equilibrium. Results from the new formulations are similar to the classical methods in normal cases but are numerically stable under transverse load. Further, the writers demonstrate that the present formulation is actually equivalent to the axes rotation formulation by Jiang and Yamagami but is much more convenient to be used for general problems. The writers have also discovered some inherent limitations of 3D limit equilibrium analysis which are absent in the corresponding 2D analysis.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abramson, L. W., Lee, T. S., Sharma, S., and Boyce, G. M. (2002). Slope stability and stabilization methods, 2nd Ed., Wiley, New York.
Baker, R., and Garber, M. (1978). “Theoretical analysis of the stability of slopes.” Geotechnique, 28(4), 395–411.
Baker, R., and Leshchinsky, D. (1987). “Stability analysis of conical heaps.” Soils Found., 27(4), 99–110.
Baligh, M. M., and Azzouz, A. S. (1975). “End effects on the stability of cohesive soils.” J. Geotech. Engrg. Div., 101(11), 1105–1117.
Brent, R. P. (1973). Algorithms for minimization without derivatives, Prentice-Hall, Englewood Cliffs, N.J.
Cavounidis, S. (1987). “On the ratio of factors of safety in slope stability analyses.” Geotechnique, 37(2), 207–210.
Chen, R. H., and Chameau, J. L. (1982). “Three-dimensional limit equilibrium analysis of slopes.” Geotechnique, 32(1), 31–40.
Cheng, Y. M., and Liu, H. T., and Au, S. K. (2005). “Location of critical three-dimensional nonspherical failure surface by NURBS functions and ellipsoid with applications to highway slopes.” Comput. Geotech., 32, 387–399.
Hovland, H. J. (1977). “Three-dimensional slope stability analysis method.” J. Geotech. Engrg. Div., 103(9), 971–986.
Huang, C. C., and Tsai, C. C. (2000). “New method for 3D and asymmetrical slope stability analysis.” J. Geotech. Geoenviron. Eng., 126(10), 917–927.
Huang, C. C., Tsai, C. C., and Chen, Y. H. (2002). “Generalized method for three-dimensional slope stability analysis.” J. Geotech. Geoenviron. Eng., 128(10), 836–848.
Hungr, O. (1987). “An extension of Bishop’s simplified method of slope stability analysis to three dimensions.” Geotechnique, 37, 113–117.
Hungr, O. (1994). “A general limit equilibrium model for three-dimensional slope stability analysis: Discussion.” Can. Geotech. J., 31, 793–795.
Hungr, O. (1997). “Slope stability analysis.” Keynote Paper, Proc., 2nd Panamerican Symp. on Landsides, Rio de Janeiro, Brazil, Vol. 3, Int. Society for Soil Mechanics and Geotechnical Engineering, 123–136.
Hungr, O., Salgado, F. M., and Byrne, P. M. (1989). “Evaluation of a three-dimensional method of slope stability analysis.” Can. Geotech. J., 26, 679–686.
Jiang, J. C., and Yamagami, T. (1999). “Determination of the sliding direction in three-dimensional slope stability analysis.” Proc., 44th Symp. on Geotechnical Engineering, 193–200.
Lam, L., and Fredlund, D. G. (1993). “A general limit equilibrium model for three-dimensional slope stability analysis.” Can. Geotech. J., 30, 905–919.
Lam, L., and Fredlund, D. G. (1994). “A general limit equilibrium model for three-dimensional slope stability analysis: Reply.” Can. Geotech. J., 31, 795–796.
Leshchinsky, D., and Baker, R. (1986). “Three-dimensional analysis for slope stability analysis.” Int. J. Numer. Analyt. Meth. Geomech., 9, 199–223.
Leshchinsky, D., Baker, R., and Silver, M. L. (1985). “Three dimensional analysis of slope stability.” Int. J. Numer. Analyt. Meth. Geomech., 9, 199–223.
Leshchinsky, D., and Huang, C. C. (1992). “Generalized three-dimensional slope stability analysis.” J. Geotech. Engrg., 118(11), 1748–1764.
Stark, T. D., and Eid, H. T. (1998). “Performance of three-dimensional slope stability methods in Practice.” J. Geotech. Geoenviron. Eng., 124(11), 1049–1060.
Ugai, K. (1988). “3-D slope stability analysis by slice methods.” Proc., 6th Int. Conf. on Numerical Methods in Geomechanics, Innsbruck, Austria, 1369–1374.
Yamagami, T., and Jiang, J. C. (1996). “Determination of the sliding direction in three-dimensional slope stability analysis.” Proc., 2nd Int. Conf. on Soft Soil Engineering, Vol. 1, 567–572, Nanjing, China.
Yamagami, T., and Jiang, J. C. (1997). “A search for the critical slip surface in three-dimensional slope stability analysis.” Soils Found., 37(3), 1–16.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 133 • Issue 12 • December 2007
Pages: 1544 - 1555
Copyright
© 2007 ASCE.
History
Received: Sep 1, 2005
Accepted: Jun 19, 2007
Published online: Dec 1, 2007
Published in print: Dec 2007
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.