Stability Analysis in Geomechanics by Linear Programming. II: Application
Publication: Journal of Geotechnical Engineering
Volume 118, Issue 11
Abstract
The limit analysis for stability problems in geomechanics can be formulated as a pair of primal‐dual linear programs. This formulation provides a solution that is both kinematically and statically admissible for a discretized soil mass; for the continuum, it gives an upper‐bound solution. This paper investigates the accuracy and the scope of applicability of this kinematic formulation. Several numerical examples of bearing capacity and slope stability problems are presented, including problems of a cohesive and frictional soil mass with inhomogeneous properties and varying pore‐water pressure. In bearing‐capacity analysis, the bearing pressure is considered to be “activating,” while the surcharge and self‐weight are considered to be “fixed.” In evaluating the safety factor for slope stability analysis, two different approaches are used: for frictional materials, the actual loading is considered to be “fixed,” and a fictitious horizontal loading is introduced as “activating”; for purely cohesive materials, the vertical loading is treated as “activating.” The computed results agree very well with analytical values and other numerical results. A comparison of this kinematic method with standard limit equilibrium methods is also presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bell, J. M. (1968). “General slope stability and analysis.” J. Soil Mech. and Found. Engrg. Div., ASCE, 94(6), 1253–1270.
2.
Bishop, A. W. (1955). “The use of the slip circle in the stability analysis of slopes.” Geotechnique, London, England, 5(1), 7–17.
3.
Brinch Hansen, J. (1966). “Comparison of methods for stability analysis.” Bulletin No. 21, The Danish Geotechnical Institute, Copenhagen, Denmark.
4.
Chuang, P. H. (1992). “Stability analysis in geomechanics by linear programming. I: Formulation.” J. Geotech. Engrg., ASCE118(11), 1696–1715.
5.
Drucker, D. C. (1953). “Limit analysis of two and three dimensional soil mechanics problems.” J. Mech. Physics of Solids, London, England, 1, 217–226.
6.
Fellenius, W. (1936). “Calculation of the stability of earth dams.” Trans. 2nd Cong. on Large Dams, Washington, D.C., 4, 445–459.
7.
Howells, D. A. (1977). “Discussions on Zienkiewicz et al. 1975.” Geotechnique, London, England, 27, 101–102.
8.
Lysmer, J. (1970). “Limit analysis of plane problems in soil mechanics.” J. Soil Mech. Found. Div., ASCE, 96(4), 1311–1334.
9.
Sarma, S. K. (1973). “Stability analysis of embankments and slopes.” Geotechnique, London, England, 23(3), 423–433.
10.
Sarma, S. K. (1979). “Stability analysis of embankments and slopes.” J. Geotech. Engrg. Div., ASCE, 105(12), 1511–1524.
11.
Whitman, R. V., and Bailey, W. A. (1967). “Use of computers for slope stability analysis.” J. Soil Mech. Found. Div., ASCE, 93(4), 475–498.
12.
Zienkiewicz, O. C., Humpheson, C., and Lewis, R. W. (1975). “Associated and non‐associated viscoplasticity and plasticity in soil mechanics.” Geotechnique, London, England, 25(4), 671–689.
13.
Zienkiewicz, O. C., Humpheson, C., and Lewis, R. W. (1977). “Discussion on Zienkiewicz et al. 1975.” Geotechnique, London, England, 27(1), 101–102.
Information & Authors
Information
Published In
Copyright
Copyright © 1992 ASCE.
History
Published online: Nov 1, 1992
Published in print: Nov 1992
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.