Journal of Central South University

, Volume 18, Issue 5, pp 1626–1637 | Cite as

Reliability analysis of earth slopes using hybrid chaotic particle swarm optimization

  • M. KhajehzadehEmail author
  • M. R. Taha
  • A. El-Shafie


A numerical procedure for reliability analysis of earth slope based on advanced first-order second-moment method is presented, while soil properties and pore water pressure may be considered as random variables. The factor of safety and performance function is formulated utilizing a new approach of the Morgenstern and Price method. To evaluate the minimum reliability index defined by Hasofer and Lind and corresponding critical probabilistic slip surface, a hybrid algorithm combining chaotic particle swarm optimization and harmony search algorithm called CPSOHS is presented. The comparison of the results of the presented method, standard particle swarm optimization, and selected other methods employed in previous studies demonstrates the superior successful functioning of the new method by evaluating lower values of reliability index and factor of safety. Moreover, the presented procedure is applied for sensitivity analysis and the obtained results show the influence of soil strength parameters and probability distribution types of random variables on the reliability index of slopes.


reliability analysis stability assessment earth slopes particle swarm optimization harmony search 


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  1. [1]
    ANG A H S, TANG W H. Probability concepts in engineering planning and design, Vol. 2-Decision, risk, and reliability [M]. New York: Wiley, 1984: 333–346.Google Scholar
  2. [2]
    CHRISTIAN J T, LADD C C, BAECHER G B. Reliability applied to slope stability analysis [J]. Journal of Geotechnical Enggineering, 1994, 120(12): 2180–2207.CrossRefGoogle Scholar
  3. [3]
    HASOFER A, LIND N. Exact and invariant second-moment code format [J]. Journal of Engineering Mechanics, 1974, 100(1): 111–121.Google Scholar
  4. [4]
    KENNEDY J, EBERHART R C. Particle swarm optimization [C]// Proceeding of the IEEE international conference on neural networks. Perth, Australia, 1995: 1942–1948.Google Scholar
  5. [5]
    GEEM Z W, KIM J H, LOGANATHAN G V. A new heuristic optimization algorithm: Harmony search [J]. Simulation, 2001, 76(2): 60–68.CrossRefGoogle Scholar
  6. [6]
    CHENG Y M, LI L, CHI S C, WEI W B. Particle swarm optimization algorithm for the location of the critical non-circular failure surface in two-dimensional slope stability analysis [J]. Computers and Geotechnics, 2007, 34(2): 92–103.CrossRefGoogle Scholar
  7. [7]
    CHENG Y M, LI L, CHI S C. Performance studies on six heuristic global optimization methods in the location of critical slip surface [J]. Computers and Geotechnics, 2007, 34(6): 462–484.CrossRefGoogle Scholar
  8. [8]
    CHENG Y M, LI L, LANSIVAARA T, CHI S C, SUN Y J. An improved harmony search minimization algorithm using different slip surface generation methods for slope stability analysis [J]. Engineering Optimization, 2008, 40(2): 95–115.CrossRefGoogle Scholar
  9. [9]
    LI L, YU G M, CHEN Z U, CHU X S. Discontinuous flying particle swarm optimization algorithm and its application to slope stability analysis [J]. Journal of Central South University of Technology, 2010, 17(4): 852–856.CrossRefGoogle Scholar
  10. [10]
    MORGENSTERN N R, PRICE V E. The analysis of the stability of general slip surfaces [J]. Geotechinque, 1965, 15(1): 79–93.CrossRefGoogle Scholar
  11. [11]
    ZHU D Y, LEE C F, QIAN Q H, CHEN G R. A concise algorithm for computing the factor of safety using the Morgenstern-Price method [J]. Canadian Geotechnical Journal, 2005, 42(1): 272–278.CrossRefGoogle Scholar
  12. [12]
    BISHOP A W. The use of the slip circle in the stability analysis of earth slopes [J]. Geotechinque, 1955, 5(1): 7–17.CrossRefGoogle Scholar
  13. [13]
    SPENCER E. A method of analysis of the stability of embankments assuming parallel inter-slice forces [J]. Geotechnique, 1967, 17(1): 11–26.CrossRefGoogle Scholar
  14. [14]
    JANBU N. Slope stability computations: Embankment dam engineering [M]. New York: John Wiley, 1973: 47–87.Google Scholar
  15. [15]
    FREDLUND D G, KRAHN J. Comparison of slope stability methods of analysis [J]. Canadian Geotechnical Journal, 1977, 14(3): 429–439.CrossRefGoogle Scholar
  16. [16]
    DITLEVSEN O. Uncertainty modeling with applications to multidimensional civil engineering systems [M]. New York: McGraw-Hill, 1981: 245–290.zbMATHGoogle Scholar
  17. [17]
    LOW B K, TANG W H. Reliability analysis of reinforced embankments on soft ground [J]. Canadian Geotechnical Journal, 1997, 34(5): 672–685.CrossRefGoogle Scholar
  18. [18]
    LOW B K, TANG W H. Reliability analysis using object-oriented constrained optimization [J]. Structural Safety, 2004, 26(1): 69–89.CrossRefGoogle Scholar
  19. [19]
    LIU P L, KIUREGHIAN A D. Optimization algorithms for structural reliability [J]. Structural Safety, 1991, 9(3): 161–177.CrossRefGoogle Scholar
  20. [20]
    SHI Y H, EBERHART R C. A modified particle swarm optimizer [C]// IEEE World Congress on Evolutionary Computation. Anchorage, Alaska, 1998: 69–73.Google Scholar
  21. [21]
    MAY R M. Simple mathematical models with very complicated dynamics [J]. Nature, 1976, 261: 459–467.CrossRefGoogle Scholar
  22. [22]
    CHOWDHURY R N, XU D W. Reliability index for slope stability assessment-two methods compared [J]. Reliability Engineering and System Safety, 1992, 37(2): 99–108.CrossRefGoogle Scholar
  23. [23]
    PHOON K K, KULHAWY F H. Characterization of geotechnical variability [J]. Canadian Geotechnical Journal, 1999, 36(4): 612–624.CrossRefGoogle Scholar
  24. [24]
    HASSAN A M, WOLFF T F. Search algorithm for minimum reliability index of earth slopes [J]. Journal of Geotechnical and Geoenvironmental Engineering, 1999, 125(4): 301–308.CrossRefGoogle Scholar
  25. [25]
    BHATTACHARYA G, JANA D, OJHA S, CHAKRABORTY S. Direct search for minimum reliability index of earth slopes [J]. Computers and Geotechnics, 2003, 30(6): 455–462.CrossRefGoogle Scholar
  26. [26]
    XU B, LOW B K. Probabilistic stability analyses of embankments based on finite-element method [J]. Journal of Geotechnical and Geoenvironmental Engineerin, 2006, 132(11): 1444–1454.CrossRefGoogle Scholar
  27. [27]
    CHOWDHURY R, RAO B N. Probabilistic stability assessment of slopes using high dimensional model representation [J]. Computers and Geotechnics, 2010, 37(7/8): 876–884.CrossRefGoogle Scholar

Copyright information

© Central South University Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Civil and Structural Engineering DepartmentUniversity Kebangsaan MalaysiaSelangorMalaysia

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