Observations on Limit Equilibrium–Based Slope Reliability Problems with Inclined Weak Seams
Publication: Journal of Engineering Mechanics
Volume 136, Issue 10
Abstract
This study addresses the complexity of slope reliability problems based on limit equilibrium methods (LEMs). The main focus is on the existence of multiple failure modes that poses difficulty to many LEM-based slope reliability methods. In particular, when weak seams are present, the failure modes associated with those seams may be difficult to detect. A systematic way of searching the failure modes is proposed, and its robustness over slopes with or without weak seams is demonstrated. It is found that in the presence of weak seams, assuming circular slip surfaces may cause underestimation of slope failure probability. The conclusion of the study promotes the use of finite elements as the stability method for reliability evaluation because it is not necessary to search for failure surfaces in finite-element stability analysis.
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References
Alonso, E. E. (1976). “Risk analysis of slopes and its application to slopes in sensitive Canadian clays.” Geotechnique, 26(3), 453–472.
Ang, A. H. S., and Tang, W. H. (1984). Probability concepts in engineering planning and design. Volume II: Decision, risk, and reliability, Wiley, New York.
Au, S. K., and Beck, J. L. (2003). “Importance sampling in high dimensions.” Struct. Safety, 25(2), 139–163.
Bhattacharya, G., Jana, D., Ojha, S., and Chakraborty, S. (2003). “Direct search for minimum reliability index of earth slopes.” Comput. Geotech., 30, 455–462.
Bishop, A. W. (1955). “The use of the slip circle in the stability analysis of slopes.” Geotechnique, 5, 7–17.
Ching, J., Phoon, K. -K., and Hu, Y. -G. (2009). “Efficient evaluation of reliability for slopes with circular slip surfaces using importance sampling.” J. Geotech. Engrg., 135(6), 768–777.
Chowdhury, R. N., and Xu, D. W. (1993). “Rational polynomial technique in slope-reliability analysis.” J. Geotech. Eng., 119(12), 1910–1928.
Chowdhury, R. N., and Xu, D. W. (1995). “Geotechnical system reliability of slopes.” Reliab. Eng. Syst. Saf., 47, 141–151.
Christian, J. T., Ladd, C. C., and Baecher, G. B. (1994). “Reliability applied to slope stability analysis.” J. Geotech. Eng., 120(12), 2180–2207.
Cornell, C. A. (1971). “First-order uncertainty analysis of soils deformation and stability.” Proc., 1st Int. Conf. on Application of Statistics and Probability to Soil and Structural Engineering, Hong Kong University Press, Hong Kong.
Duncan, J. M., Navin, M., and Wolff, T. F. (2003). “Discussion of ‘Probabilistic slope stability analysis for practice’.” Can. Geotech. J., 40, 848–850.
Fellenius, W. (1936). “Calculation of the stability of earth dams.” Proc., Trans. 2nd Congress on Large Dams, Washington, D.C., Vol. 4, U.S. Government Printing Office, Washington, D.C., 445–462.
Greco, V. R. (1996). “Efficient Monte Carlo technique for locating critical slip surface.” J. Geotech. Eng., 122(7), 517–525.
Griffiths, D. V., and Fenton, G. A. (2004). “Probabilistic slope stability analysis by finite elements.” J. Geotech. Geoenviron. Eng., 130(5), 507–518.
Griffiths, D. V., Fenton, G. A., and Denavit, M. D. (2007). “Traditional and advanced probabilistic slope stability analysis.” Proc., GSP 170 Probabilistic Applications in Geotechnical Engineering, GeoDenver 2007: New Peaks in Geotechnics, ASCE, Reston, Va.
Griffiths, D. V., and Lane, P. A. (1999). “Slope stability analysis by finite elements.” Geotechnique, 49(3), 387–403.
Grivas, D. A., and Chowdhury, R. N. (1983). “Probabilistic stability analysis in strain softening-soil.” Struct. Safety, 1, 199–210.
Hayashi, H., and Tang, W. H. (1994). “Probabilistic evaluation on progressive failure in cut slopes.” Struct. Safety, 14, 31–46.
Ishii, K., and Suzuki, M. (1986). “Stochastic finite element method for slope stability analysis.” Struct. Safety, 4, 111–129.
Low, B. K., Gilbert, R. B., and Wright, S. G. (1998). “Slope reliability analysis using generalized method of slices.” J. Geotech. Geoenviron. Eng., 124(4), 350–362.
Low, B. K., and Tang, W. H. (1997). “Probabilistic slope analysis using Janbu’s generalized method of slices.” Comput. Geotech., 21(2), 121–142.
Malkawi, A. I. H., Hassan, W. F., and Abdulla, F. A. (2000). “Uncertainty and reliability analysis applied to slope stability.” Struct. Safety, 22, 161–187.
Melchers, R. E. (1989). “Importance sampling in structural systems.” Struct. Safety, 6, 3–10.
Oka, Y., and Wu, T. H. (1990). “System reliability of slope stability.” J. Geotech. Eng., 116(8), 1185–1189.
Rosenblatt, M. (1952). “Remarks on a multivariate transformation.” Ann. Math. Stat., 23, 470–472.
Rubinstein, R. Y. (1981). Simulation and the Monte-Carlo method, Wiley, New York.
Shinozuka, M. (1983). “Basic analysis of structural safety.” J. Struct. Eng., 109, 721–740.
Silva, F., Lambe, W. T., and Marr, A. W. (2008). “Probability and risk of slope failure.” J. Geotech. Geoenviron. Eng., 134(12), 1691–1699.
Spencer, E. (1967). “A method of analysis of the stability of embankments assuming parallel interslice forces.” Geotechnique, 17(1), 11–26.
Vanmarcke, E. H. (1976). “Reliability of earth slopes.” J. Geotech. Eng., 96(2), 609–630.
Xue, J. F., and Gavin, K. (2007). “Simultaneous determination of critical slip surface and reliability index for slopes.” J. Geotech. Eng., 133(7), 878–886.
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© 2010 ASCE.
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Received: Feb 2, 2009
Accepted: Mar 9, 2010
Published online: Mar 12, 2010
Published in print: Oct 2010
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