Global Search Method for Locating General Slip Surface Using Monte Carlo Techniques
This article has a reply.
VIEW THE REPLYPublication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 127, Issue 8
Abstract
Searching for the critical slip surface and the lowest factor of safety in slope stability analysis can be achieved by means of optimization techniques. A new search procedure in generating kinematically admissible slip surfaces has been introduced in this paper. Such a procedure is based, mainly, on the Monte Carlo methods, where both the critical global slip surface as well as its associated factor of safety is determined. Several practical examples, of known minimum factor of safety and its associated slip surface, have been used to demonstrate the efficiency and capability of the proposed method. The method is intended to be robust and effective to solve problems that involve extremely complicated slope geometry. It is as powerful as any other powerful optimization methods.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Arai, K., and Tagyo, K. ( 1985). “Determination of non-circular slip surface giving the minimum factor of safety in slope stability analysis.” Soils and Found., Tokyo, 25(1), 43–51.
2.
Baker, R. ( 1980). “Determination of the critical slip surface in slope stability computations.” Int. J. Numer. and Analytical Methods in Geomech., 4, 333–359.
3.
Baker, R., and Gaber, M. ( 1977). “Variational approach to slope stability.” Proc., 9th Int. Conf. on Soil Mech. and Found. Engrg., Vol. 2, Japan Society for Soil Mechanics and Foundation Engineering, Tokyo, 9–12.
4.
Baker, R., and Gaber, M. ( 1978). “Theoretical analysis of the stability of slopes.” Géotechnique, London, 28(4), 395–411.
5.
Bhattacharya, G., and Basudhar, P. K. ( 1997). “Convergence of slope stability computations using GPS.” Indian Geotech. J., 27(4).
6.
Bishop, A. W. ( 1955). “The use of slip circle in the stability analysis of slopes.” Géotechnique, London, 5, 7–17.
7.
Bromhead, E. N. ( 1992). The stability of slopes, 2nd Ed., Chapman & Hall, London.
8.
Broyden, C. G. ( 1970). “The convergence of a class of double-rank minimization algorithms.” J. Inst. Math. Applications, 6, 76–90, 222–231.
9.
Castillo, E., and Luceno, A. ( 1982). “A critical analysis of some variational methods in slope stability analysis.” Int. J. Numer. and Analytical Methods in Geomech., 6, 195–209.
10.
Celestino, T. B., and Duncan, J. M. ( 1981). “Simplified search for non-circular slip surface.” Proc., 10th Int. Conf. SMFE, 391–394.
11.
Chen, Z.-Y. ( 1992). “Random trials used in determining global minimum factors of safety of slopes.” Can. Geotech. J., Ottawa, 29, 225–233.
12.
Chen, Z.-Y., and Shao, C.-M. ( 1988). “Evaluation of minimum factor of safety in slope stability analysis.” Can. Geotech. J., Ottawa, 25, 735–748.
13.
Cherubini, C., and Greco, V. R. ( 1987). “A probabilistic method for locating the critical slip surface in slope stability analysis.” Proc., 5th ICSAP, Vol. 2, 1182–1187.
14.
Ching, R. K. H., and Fredlund, D. G. ( 1983). “Some difficulties associated with the limit equilibrium method of slices.” Can. Geotech. J., Ottawa, 20, 661–672.
15.
Chowdhury, R. N., and Zhang, S. ( 1990). “Convergence aspect of limit equilibrium methods for slopes.” Can. Geotech. J., Ottawa, 27, 145–151.
16.
Davidon, W. C. ( 1959). “Variable metric method of minimization.” Rep. ANL-5990, Argonne National Laboratory, Argonne, Ill.
17.
De Josselin De Jong, G. ( 1980). “Application of the calculus of variation to the vertical cut off in cohesive frictionless soil.” Géotechnique, London, 30(1), 1–16.
18.
De Natale, J. S. (1991). “Rapid identification of critical slip surface: Structure.”J. Geotech. Engrg., ASCE, 117(10), 1568–1589.
19.
Donald, I. B., and Chen, Z.-Y. ( 1997). “Slope stability analysis by the upper bound approach: Fundamentals and methods.” Can. Geotech. J., Ottawa, 34, 853–862.
20.
Duncan, J. M. (1996). “State of the art: Limit equilibrium and finite element analysis of slopes.”J. Geotech. Engrg., ASCE, 122(7), 577–596.
21.
Fellenius, W. ( 1936). “Calculation of the stability of earth dams.” Trans. 2nd Congr. on Large Dams, Vol. 4, 445–459.
22.
Fletcher, R. ( 1970). “A new approach to variable metric algorithms.” Comp. J., 13, 317–322.
23.
Fletcher, R., and Powell, M. J. D. ( 1963). “A rapidly convergent descent method for minimization.” Comp. J., 6(2), 163–168.
24.
Fletcher, R., and Reeves, C. M. ( 1964). “Function minimization by conjugate gradient.” Comp. J., 7, 149–154.
25.
Goldfarb, D. ( 1970). “A family of variable metric methods derived by variational means.” Math. Computation, 24, 23–26.
26.
Greco, V. R. (1996). “Efficient Monte Carlo technique for locating critical slip surface.”J. Geotech. Engrg., ASCE, 122(7), 517–525.
27.
Husein Malkawi, A. I., and Hassan, W. F. ( 2001). “Stability analysis of slope using Monte Carlo Technique.” SAS-MCT software, User's manual, version 3.0. for Windows 95 and NT, Geotech. Group, Civ. Engrg. Dept., Jordan University of Science and Technology, Irbid, Jordan.
28.
Husein Malkawi, A. I., Hassan, W. F., and Sarma, S. K. ( 2001). “An efficient search method for finding critical circular slip surface using Monte Carlo techniques.” Can. Geotech. J., Ottawa.
29.
Janbu, N. ( 1954). “Application of composite slip surface for stability analysis.” Proc., Eur. Conf. on Stability of Earth Slopes, 43–49.
30.
Janbu, N. ( 1973). “Slope stability computations.” Embankment dam engineering, Casagrande memorial volume, E. Hirschfield and S. Poulos, eds., Wiley, New York, 47–86.
31.
Li, K. S., and White, W. ( 1987). “Rapid evaluation of the critical slip surface in slope stability problems.” Int. J. Numer. and Analytical Methods in Geomech., 11, 449–473.
32.
Luceno, A., and Castillo, E. ( 1980). “Evaluation of variational methods in slope analysis.” Proc., 1st Int. Symp. on Landslides, Meerut: Sarita Prakashan, Vol. 1, 255–258.
33.
Morgenstern, N. R., and Price, V. E. ( 1965). “The analysis of stability of general slip surface.” Géotechnique, London, 15, 79–93.
34.
Morrison, I. M. ( 1988). “Discussion of `A note on the stability analysis of slopes,' by S. K. Sarma.” Géotechnique, London, 38, 157–159.
35.
Nelder, J. A., and Mead, R. ( 1965). “A simplex method for function minimization.” Comp. J., 7, 308–313.
36.
Nguyen, V. U. (1985). “Determination of critical slope failure surfaces.”J. Geotech. Engrg., ASCE, 111(2), 238–250.
37.
Sarma, S. K. ( 1973). “Stability analysis of embankments and slopes.” Géotechnique, London, 23(3), 423–433.
38.
Sarma, S. K. (1979). “Stability analysis of embankments and slopes.”J. Geotech. Engrg. Div., ASCE, 105(12), 1511–1524.
39.
Sarma, S. K. ( 1987). “A note on the stability analysis of slopes.” Géotechnique, London, 37, 107–111.
40.
Shanker, K., and Mohan, C. ( 1987). “A random technique for the global minima of constrained nonlinear optimization problems.” Proc., Int. Conf. on Optimization Techniques and Their Applications, 905.
41.
Shanno, D. F. ( 1970). “Conditioning of quasi-Newton methods for function minimization.” Math. Computation, 24, 647–657.
42.
Sharma, S., and Moudud, A. ( 1992). “Interactive slope analysis using Spencer's method.” Stability and performance of slopes and embankments—II A 25-Years Perspective, Vol. 1, Geotech. Spec. Publ. No. 31, ASCE, New York.
43.
Siegel, R. A., Kovacs, W. D., and Lovell, C. W. (1981). “Random surface generation in stability analysis.”J. Geotech. Engrg. Div., ASCE, 107(7), 996–1002.
44.
Spencer, E. E. ( 1967). “A method of the analysis of the stability of embankments assuming parallel inter-slice forces.” Géotechnique, London, 17, 11–26.
45.
Spencer, E. E. ( 1973). “The thrust line criterion in embankment stability analysis.” Géotechnique, London, 23, 85–100.
46.
Sridevi, B., and Deep, K. ( 1991). “Application of global optimization technique to slope stability analysis.” Proc., 6th Int. Symp. on Landslides, 573–578.
47.
Ting, J. M. (1983). “Geometric concerns in slope stability analysis.”J. Geotech. Engrg., ASCE, 109(11), 1487–1491.
48.
Whitman, R. V., and Bailey, W. A. (1967). “Use of computers for slope stability analysis.”J. Soil Mech. and Found. Engrg. Div., ASCE, 93(4), 475–498.
49.
Yamagami, T., and Ueta, Y. ( 1988). “Search for noncircular slip surfaces by the Morgenstern-Price method.” Proc., 6th Int. Conf. Numer. Methods in Geomechanics, 1219–1223.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 127 • Issue 8 • August 2001
Pages: 688 - 698
History
Received: Jan 21, 2000
Published online: Aug 1, 2001
Published in print: Aug 2001
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.