Multimodal reliability analysis of 3D slopes with a genetic algorithm

  • Ye W. Tun
  • Marcelo A. Llano-Serna
  • Dorival M. Pedroso
  • Alexander Scheuermann
Research Paper


This paper presents a genetic algorithm (GA) to solve the multimodal optimisation problem resulting from 3D slopes prone to multiple regions of failure. A probabilistic approach is taken by using the first-order reliability method (FORM) to approximate the probability of failure. The 3D Bishop method is selected but can be replaced as appropriate. Since 3D analyses have higher computational costs than 2D simulations, we demonstrate that the FORM approach is very practical to large-scale geotechnical problems compared to alternatives such as Monte Carlo simulations (MCS). Furthermore, we show that the GA optimiser can obtain reliability indices and find critical failure regions that would not be found by the MCS easily. These characteristics are demonstrated by some simple test cases and the more complex topography of the Mount St. Helens in the USA.


3D Bishop method FORM Genetic algorithm Multimodal optimisation Probability of failure 



The support from the Australian Research Council under Grant DE120100163 is gratefully acknowledged. We also thank the developers of the free software Scoops3D and QGIS and the team behind the Google Earth software.


  1. 1.
    Adeli H, Cheng N (1993) Integrated genetic algorithm for optimization of space structures. J Aerosp Eng 6(4):315–328CrossRefGoogle Scholar
  2. 2.
    Arai K, Tagyo K (1985) Determination of noncircular slip surface giving the minimum factor fo safety in slopes stability analysis. Soils Found 25:43–51CrossRefGoogle Scholar
  3. 3.
    Bishop A (1955) The use of the slip circle in the stability analysis of earth slopes. Geotechnique 5(1):7–17CrossRefGoogle Scholar
  4. 4.
    Bistacchi A, Massironi M, Superchi L, Zorzi L, Francese R, Chistolini F, Genevois R (2013) A 3D geological model of the 1963 vajont landslide. Ital J Eng Geol Environ 6:531–539Google Scholar
  5. 5.
    Borja RI, White JA (2010) Continuum deformation and stability analyses of a steep hillside slope under rainfall infiltration. Acta Geotech 5:1–14CrossRefGoogle Scholar
  6. 6.
    Borja RI, White JA, Liu X, Wu W (2012) Factor of safety in a partially saturated slope inferred from hydro-mechanical continuum modeling. Int J Numer Anal Methods Geomech 36(2):236–248CrossRefGoogle Scholar
  7. 7.
    Carrion M, Vargas EA, Velloso RQ, Farfan AD (2017) Slope stability analysis in 3D using numerical limit analysis (NLA) and elasto-plastic analysis (EPA). Geomech Geoeng 12(4):250–265CrossRefGoogle Scholar
  8. 8.
    Cavazzi S, Corstanje R, Mayr T, Hennam J, Fealy R (2013) Are fine resolution digital elevation models always the best choice in digital soil mapping? Geoderma 195–196:111–121CrossRefGoogle Scholar
  9. 9.
    Chen Z (1992) Random trials used in determining global minimum factors of safety of slopes. Can Geotech J 29:225–233CrossRefGoogle Scholar
  10. 10.
    Chen Z, Mi H, Zhang F, Wang X (2003) A simplified method for 3D slope stability analysis. Can Geotech J 40:675–683CrossRefGoogle Scholar
  11. 11.
    Chen HX, Zhang S, Peng M, Zhang LM (2016) A physically-based multi-hazard risk assessment platform for regional rainfall-induced slope failures and debris flows. Eng Geol 203:15–29CrossRefGoogle Scholar
  12. 12.
    Coello CC, Lamont BG, van Veldhuizen AD (2007) Evolutionary algorithms for solving multi-objective problems. Springer, BerlinzbMATHGoogle Scholar
  13. 13.
    Cui L, Sheng D (2005) Genetic algorithms in probabilistic finite element analysis of geotechnical problems. Comput Geotech 32:555–563CrossRefGoogle Scholar
  14. 14.
    Deb K (2001) Multi-objective optimisation using evolutionary algorithms. Wiley, HobokenzbMATHGoogle Scholar
  15. 15.
    Donald I, Giam P (1995) The ACADS slope stability review. In: 6th international symposium on Lanslides, ChristchurchGoogle Scholar
  16. 16.
    Donnadieu F, Merle O, Besson J-C (2001) Volcanic edifice stability during cryptodome intrusion. Bull Volcanol 63:61–72CrossRefGoogle Scholar
  17. 17.
    Gao W (2005) Method for searching critical slip surface of soil slope base on ant colony algorithm. J Hydraul Eng 36(9):1100–1104 (in Chinese) Google Scholar
  18. 18.
    Gitirana G, Santos MA, Fredlund M (2008) Three-dimensional analysis of the Lodalen Landslide. In: GeoCongress, New Orleans, LA.
  19. 19.
    Goldberg D (1989) Genetic algorithms in search, optimisational and machine learning. Addison-Wesley, BostonGoogle Scholar
  20. 20.
    Greco V (1996) Efficient Monte Carlo technique for locating critical slip surface. J Geotechn Eng 122(7):517–525CrossRefGoogle Scholar
  21. 21.
    Hajela P (1990) Genetic search: an approach to the non-convex optimisation problem. AIAA J 28(7):1205–1210CrossRefGoogle Scholar
  22. 22.
    Holland HJ (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT Press, CambridgezbMATHGoogle Scholar
  23. 23.
    Hungr O (1987) An extension of Bishop’s simplified method of slope stability analysis to three dimensions. Geotechnique 37(1):113–117CrossRefGoogle Scholar
  24. 24.
    Hungr O, Salgado F, Bryne P (1989) Evaluation of a three-dimensional method of slope stability analysis. Can Geotech J 26(4):679–686CrossRefGoogle Scholar
  25. 25.
    Jenkins W (1991) Towards structural optimisation via genetic algorithms. Comput Struct 40(5):1321–1327CrossRefzbMATHGoogle Scholar
  26. 26.
    Kahatadeniya K (2009) Determination of the critical failure surface for slope stability analysis using ant colony optimisation. Eng Geol 108:133–141CrossRefGoogle Scholar
  27. 27.
    Kaymaz I (2005) Application of kriging method to structural reliability problems. Struct Saf 2005:133–151CrossRefGoogle Scholar
  28. 28.
    Liang JJ, Qin AK (2006) Comprehensive learning particle swarm optimiser for global optimisation of multimodal functions. IEEE Trans Evol Comput 10(3):281–295CrossRefGoogle Scholar
  29. 29.
    Llano-Serna MA, Farias MM, Pedroso DM (2015) An assessment of the material point method for modelling large scale run-out processes in landslides. Landslides 13:1057–1066CrossRefGoogle Scholar
  30. 30.
    McCombie P, Wilkinson P (2002) The use of the simple genetic algorithm in finding the critical factor of safety in slope stability analysis. Comput Geotech 29:699–714CrossRefGoogle Scholar
  31. 31.
    Michalewicz Z (1996) Genetic algorithms data structures evolution programs. Springer, SpringerCrossRefzbMATHGoogle Scholar
  32. 32.
    Monde G (2016) Create contours and DEM using Google Earth and QGIS 2.10. Monde Geospatial. Accessed 5 March 2016
  33. 33.
    Nikolakopoulos KG, Kamaratakis EK, Chrysoulakis N (2006) SRTM vs ASTER elevation products. Comparison for two regions in Crete, Greece. Int J Remote Sens 27(21):4819–4838CrossRefGoogle Scholar
  34. 34.
    Pal S, Wathugala G, Kundu S (1996) Calibration of a constitutive model using genetic algorithms. Comput Geotech 19(4):325–348CrossRefGoogle Scholar
  35. 35.
    Pedroso DM, Williams DJ (2011) Automatic calibration of soil–water characteristic curves using genetic algorithms. Comput Geotech 38:330–340CrossRefGoogle Scholar
  36. 36.
    Pham H, Fredlund D (2003) The application of dynamic programming to slope stability analysis. Comput Geotech 40(4):830–847CrossRefGoogle Scholar
  37. 37.
    Reale C, Xue J, Pan Z, Gavin K (2015) Deterministic and probabilistic multip-modal analysis of slope stability. Comput Geotech 66:172–179CrossRefGoogle Scholar
  38. 38.
    Reid M, Christian S, Brien D (2000) Gravitational stability of three-dimensional stratovolcano edifices. J Geophys Res 105:6043–6056CrossRefGoogle Scholar
  39. 39.
    Reid ME, Christian SB, Brien DL, Henderson ST (2015) USGS science for a changing world. Accessed Nov 2015
  40. 40.
    Reid ME, Christian SB, Brien DL (2015) Scoops3D: software to analyze 3D slope stability throughout a digital landscape. USGS. Accessed 14 Nov 2015
  41. 41.
    Rezaeean A, Noorzad R, Dankoub AKM (2011) Ant colony optimisation for locating the critical failure surface in slope stability analysis. World Appl Sci J 13(7):1702–1711Google Scholar
  42. 42.
    Simpson A, Priest S (1993) The application of genetic algorithms to optimization problems in geotechnics. Comput Geotech. 15(1):1–19CrossRefGoogle Scholar
  43. 43.
    Sulebak JR (2000) Applications of digital elevation models. In: SINTEFGoogle Scholar
  44. 44.
    Tran C, Srokosz P (2010) The idea of PGA stream computations for soil slope stability evaluation. CR Mec 338:499–509CrossRefzbMATHGoogle Scholar
  45. 45.
    Tun YW, Pedroso DM, Scheuermann A, Williams DJ (2016) Probabilistic reliability analusis of multiple slopes with genetic algorithms. Comput Geotech 77:68–76CrossRefGoogle Scholar
  46. 46.
    Wang Y (2011) Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet. Can Geotech J 48:162–172CrossRefGoogle Scholar
  47. 47.
    Xie M, Esaki T, Cai M (2004) A GIS-based method for locating the critical 3D slip surface in a slope. Comput Geotech 31:267–277CrossRefGoogle Scholar
  48. 48.
    Zhang H, Dai H, Beer M, Wang W (2013) Structural reliability analysis on the basis of small samples: an interval quasi-Monte Carlo method. Mech Syst Signal Process 37:137–151CrossRefGoogle Scholar
  49. 49.
    Zolfaghari AR, Heath AC, McCombie PF (2005) Simple genetic algorithm search for critical non-circular failure surface in slope stability analysis. Comput Geotech 32:139–152CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Civil EngineeringThe University of QueenslandSt LuciaAustralia

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