Slope Stability Analysis: Generalized Approach
Publication: Journal of Geotechnical Engineering
Volume 116, Issue 5
Abstract
Limit equilibrium analysis of slope stability is comprised of two coupled problems: kinematical (i.e., find the critical slip surface) and statical (i.e., assure the existence of global equilibrium at the defined limit state). Determination of the general‐shaped critical slip surface can be attained by available optimization techniques where the minimal factor of safety is sought. However, since the problem is statically indeterminate, assumptions are necessary. The available general methods suggests the wide variety of possible statical assumptions. Consequently, there might be a question whether the critical results are indeed critical. The presented method, which is a generalization of Baker and Garber's approach, attempts to avoid statical assumptions by using a variational technique to minimize the safety factor. The variational analysis results in an ordinary differential equation that describes the normal stress distribution over a slip surface. Solving this equation numerically, and substituting the resulting stress into the global limiting equilibrium equations for the sliding body, one can determine the factor of safety corresponding to the user's specified slip surface. The general‐shaped slip surface is left to be varied, as done in other rigorous limit equilibrium methods, until a feasible surface that renders the absolute minimum factor of safety is located. To enable the application of the presented generalized method, a numerical scheme is proposed. The solutions to three example problems, involving complex slopes, soil profiles, and total and effective stress analyses, are presented in detail. These examples provide insight as to the method's performance.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Baker, R. (1980). “Determination of the critical slip surface in slope stability computations.” International J. for Numerical and Analytical Methods in Geomechanics, 4, 333–359.
2.
Baker, R. (1981). “Tensile strength, tension cracks, and stability of slopes.” Soils and Foundations, J. of the Japanese Soc. of Soil Mech. and Foundation Engrg., 21(2), 1–17.
3.
Baker, R., and Garber, M. (1977). “Variational approach to slope stability,” Proc. of the 9th International Conference on Soil Mech. and Foundation Engrg., Tokyo, 2, 9–12.
4.
Baker, R., and Garber, M. (1978). “Theoretical analysis of the stability of slopes.” Geotechnique, 28(4), London, England, 395–411.
5.
Castillo, R., and Luceno, A. (1983). “Variational methods and upper bound theorem.” J. of Engrg. Mech., ASCE, 109(5), 1157–1174.
6.
Celestino, T. B., and Duncan, J. M. (1981). “Simplified search for noncircular slip surfaces.” Proc. of the 10th Intl. Conf. on Soil Mech. and Foundation Engrg., Stockholm, 3, 391–394.
7.
DeJong De Josselin, G. (1980). “Application of the calculs of variations to the vertical cut‐off in cohesive frictionless soil.” Geotechnique, 30(1), London, England, 1–16.
8.
DeJong De Josselin, G. (1981). “Variational fallacy.” Geotechnique, 31(4), London, England, 289–290.
9.
Edris, E. V., and Wright, S. G. (1987). “User's guide: UTEXAS2 slope‐stability package.” Instruction Report GL‐87‐1, U.S. Army Corps of Engrs., Waterways Experiment Station, Vicksburg, Miss.
10.
Janbu, N. (1973). “Slope stability computations.” Embankment‐dam engineering, Casagrande Volume, R. C. Hirschfeld and S. S. Poulos, eds., John Wiley and Sons, New York, N.Y., 47–86.
11.
Leshchinsky, D., Baker, R., and Silver, M. L. (1985). “Three‐dimensional analysis of slope stability.” International J. for Numerical and Analytical Methods in Geomechanics, 9, 199–223.
12.
Luceno, A., and Castillo, E. (1981). Discussion of “Extreme‐value problems of limiting‐equilibrium,” by M. Garber and R. Baker, J. of the Geotech. Engrg. Div., ASCE, 107(1), 118–121.
13.
Morgenstern, N., and Price, V. E. (1965). “The analysis of the stability of general slip surfaces.” Geotechnique, 15(1), London, England, 79–93.
14.
Spencer, E. (1967). “A method of analysis of the stability of embankments assuming parallel inter‐slice forces.” Geotechnique, 17(1), London, England, 11–26.
15.
Taylor, D. (1948). Fundamentals of Soil Mechanics, John Wiley and Sons, New York, N.Y.
Information & Authors
Information
Published In
Copyright
Copyright © 1990 ASCE.
History
Published online: May 1, 1990
Published in print: May 1990
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.