Slope Reliability Analysis Using Generalized Method of Slices
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 124, Issue 4
Abstract
Chen and Morgenstern extended Morgenstern and Price's method of slices by expressing force and moment equilibrium in two equations involving multiple integrals. In the present study a practical nested quadrature integration procedure is proposed and implemented in a spreadsheet, to obtain the factor of safety and side force inclinations that satisfy the Chen-Morgenstern equations. Since the deterministic factor-of-safety analysis does not explicitly reflect the uncertainties of the parameters that affect performance, the paper next considers the Hasofer-Lind second moment reliability index. It is shown that extending from the deterministic analysis—a demanding task in its own right, traditionally—to the hitherto equally complicated reliability index computation requires little extra effort. The spreadsheet approach is powerful and versatile, yet practical, and it affords the user an appreciation of what is being implemented.
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References
1.
Acquaah, C. G., and Gilbert, R. B. (1996). “Probabilistic analysis of tendon loads for a TLP in deep water.”ASCE Specialty Conf.—Advances in Prob. Mech. and Struct. Reliability, ASCE.
2.
Ang, H. S., and Tang, W. H. (1984). Probability concepts in engineering planning and design, Vol. II—Decision, risk, and reliability. John Wiley & Sons, Inc., New York, N.Y.
3.
Bishop, A. W., and Morgenstern, N. R.(1960). “Stability coefficients for earth slopes.”Géotechnique, London, U.K., 10(4), 129–150.
4.
Chen, Z., and Morgenstern, N. R.(1983). “Extensions to the generalized method of slices for stability analysis.”Can. Geotech. J., Ottawa, Canada, 20(1), 104–119.
5.
Chen, Z., and Shao, C.(1988). “Evaluation of minimum factor of safety in slope stability analysis.”Can. Geotech. J., Ottawa, Canada, 25(4), 735–748.
6.
Christian, J. T., Ladd, C. C., and Baecher, G. B.(1994). “Reliability applied to slope stability analysis.”J. Geotech. Engrg., ASCE, 120(12), 2180–2207.
7.
Ditlevsen, O. (1981). Uncertainty modeling: with applications to multidimensional civil engineering systems. McGraw-Hill Book Co., Inc., New York, N.Y.
8.
Duncan, J. M.(1996). “State of the art: limit equilibrium and finite-element analysis of slopes.”J. Geotech. Engrg., ASCE, 122(7), 577–596.
9.
Fredlund, D. G., and Krahn, J.(1977). “Comparison of slope stability methods of analysis.”Can. Geotech. J., Ottawa, Canada, 14(3), 429–439.
10.
Gerald, C. F., and Wheatley, P. O. (1994). Applied numerical analysis, 5th Ed., Addison-Wesley Publishing Co., Reading, Mass.
11.
Gilbert, R. B., Wright, S. G., and Liedtke, E. (1996). “Uncertainty in back analysis of slopes.”Proc., Uncertainty in Geologic Environment: from Theory to Practice, ASCE Geotech. Spec. Publ. No. 58, Vol. 1, ASCE, 494–517.
12.
Haldar, A., and Mahadevan, S. (1995). “First-order and second-order reliability methods.”Probabilistic structural mechanics handbook, C. (Raj) Sundararajan, ed., Chapman & Hall, Ltd., London, U.K.
13.
Hasofer, A. M., and Lind, N. C.(1974). “Exact and invariant second-moment code format.”J. Engrg. Mech., ASCE, 100(1), 111–121.
14.
Hornbeck, R. W. (1975). Numerical methods. Prentice-Hall, Inc., Englewood Cliffs, N.J.
15.
Janbu, N. (1973). “Slope stability computation.”Embankment-dam engineering, Casagrande Vol., R. C. Hirschfeld and S. J. Poulos, eds., Krieger Publishing Co., Melbourne, Fla., 47–86.
16.
Johnson, R. A., and Wichern, D. W. (1992). Applied multivariate statistical analysis, 3rd Ed., Prentice-Hall, Inc., Englewood Cliffs, N.J.
17.
Li, K. S., and Lumb, P.(1987). “Probabilistic design of slopes.”Can. Geotech. J., Ottawa, Canada, 24(4), 520–535.
18.
Low, B. K. (1996). “Practical probabilistic approach using spreadsheet.”Proc., Uncertainty in Geologic Environment: from Theory to Practice, ASCE Geotech. Spec. Publ. No. 58, Vol. 2, ASCE, 1284–1302.
19.
Low, B. K.(1997). “Reliability analysis of rock wedges.”J. Geotech. and Geoenvironmental Engrg., ASCE, 123(6), 498–505.
20.
Low, B. K., and Einstein, H. H. (1992). “Simplified reliability analysis for wedge mechanisms in rock slopes.”Proc., 6th Int. Symp. on Landslides, A. A. Balkema, Rotterdam, The Netherlands, 499–507.
21.
Low, B. K., and Tang, W. H.(1997a). “Efficient reliability evaluation using spreadsheet.”J. Engrg. Mech., ASCE, 123(7), 749–752.
22.
Low, B. K., and Tang, W. H.(1997b). “Reliability analysis of reinforced embankments on soft ground.”Can. Geotech. J., Ottawa, Canada, 34(5), 672–685.
23.
Madsen, H. O., Krenk, S., and Lind, N. C. (1986). Methods of structural safety. Prentice-Hall, Inc., Englewood Cliffs, N.J.
24.
Morgenstern, N. R., and Price, V. E.(1965). “The analysis of the stability of general slip surfaces.”Géotechnique, London, U.K., 15(1), 79–93.
25.
Morgenstern, N. R. (1995). “Managing risk in geotechnical engineering.”Proc., Pan Am. Conf., International Society of Soil Mechanics and Foundations Engineering.
26.
Shinozuka, M.(1983). “Basic analysis of structural safety.”J. Struct. Engrg., ASCE, 109(3), 721–740.
27.
Spencer, E.(1967). “A method of analysis of the stability of embankments assuming parallel inter-slice forces.”Géotechnique, London, U.K., 17(1), 11–26.
28.
Tang, W. H. (1993). “Recent developments in geotechnical reliability.”Probabilistic methods in geotechnical engineering, K. S. Li and S.-C. R. Lo, eds., A. A. Balkema, Rotterdam, The Netherlands, 3–28.
29.
Tang, W. H., Yucemen, M. S., and Ang, A. H.-S.(1976). “Probability-based short term design of soil slopes.”Can. Geotech. J., Ottawa, Canada, 13, 201–215.
30.
Vanmarcke, E. H.(1976). “Reliability of earth slopes.”J. Geotech. Engrg., ASCE, 103(11), 1247–1265.
31.
Veneziano, D. (1974). “Contributions to second moment reliability.”Res. Rep. No. R74-33, Dept. of Civ. Engrg., MIT, Cambridge, Mass.
32.
Whitman, R. V.(1984). “Evaluating calculated risk in geotechnical engineering.”J. Geotech. Engrg., ASCE, 110(2), 143–188.
33.
Whitman, R. V., and Bailey, W. A.(1967). “Use of computers for slope stability analysis.”J. Soil Mech. and Found Div., ASCE, 93(4), 475–498.
34.
Winterstein, S. R., Ude, T. C., Cornell, C. A., Bjerager, P., and Haver, S. (1993). “Environmental parameters for extreme response: inverse FORM with omission factors.” International Conference on Structural Safety and Reliability, Innsbruck, Australia.
35.
Wolff, T. F. (1996). “Probabilistic slope stability in theory and practice.”Uncertainty in the Geologic Environment: from Theory to Practice, ASCE Geotech. Spec. Publ. No. 58, ASCE.
36.
Wright, S. G., Kulhawy, F. G., and Duncan, J. M.(1973). “Accuracy of equilibrium slope stability analysis.”J. Soil Mech. and Found. Div., ASCE, 99(10), 783–791.
37.
Wu, T. H., and Kraft, L. M.(1970). “Safety analysis of slopes.”J. Soil. Mech. and Found. Div., ASCE, 96(2), 609–630.
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Copyright © 1998 American Society of Civil Engineers.
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Published online: Apr 1, 1998
Published in print: Apr 1998
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