Acta Geotechnica

, Volume 14, Issue 1, pp 207–223 | Cite as

Multimodal reliability analysis of 3D slopes with a genetic algorithm

  • Ye W. Tun
  • Marcelo A. Llano-Serna
  • Dorival M. PedrosoEmail author
  • 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.


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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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