Computer Methods and Recent Advances in Geomechanics – Oka, Murakami, Uzuoka & Kimoto (Eds.) © 2015Taylor & Francis Group, London, ISBN 978-1-138-00148-0 Multiple-slopes stability assessment by limit equilibrium and genetic algorithms Y.W. Tun, D.M. Pedroso, A. Scheuermann & D.J. Williams School of Civil Engineering, The University of Queensland, Brisbane, Australia ABSTRACT: Soil slope stability analysis is a key process in geotechnical engineering that aims to find the so-called factor of safety. The engineering practice usually employs the limit equilibrium method to this end. However this method possesses a number of limitations such as postulating a failure surface. Despite the limita- tions of the method, it became a standard in the industry and the results obtained from it are shown by academics to be not considerably different from results obtained with better methods such as the limit analysis method or the finite element method. The key for such accuracy is a well designed optimisation algorithm since the process reduces to a challenging optimisation problem. This paper investigates a robust algorithm based on a “genetic algorithm” that is able to provide accurate results, including for the case of multiple slopes cut in a large area such as in mining operations. Numerical simulations are presented and comparisons with conventional software are made illustrating the great capabilities of the proposed method. 1 INTRODUCTION In general, the limit equilibrium method (LEM) is the most commonly used method in geotechnical engi- neering because it is simple and somewhat classical. Its simplicity is a consequence from postulating a fail- ure mechanism allowing a direct computation of the so-called factor of safety (FOS) (see e.g. Duncan & Wright, 2005). Moreover, the results can be easily checked in an electronic spreadsheet or even with hand calculations for simple cases. One disadvantage comes from the fact that it gives upper bound solutions hence providing higher values than the ‘true’ collapse load (Zolfaghari et al., 2005); therefore reduced factors have to be empirically adopted. Another drawback of LEM is that potential failure surface needs to be postulated first. As an essential step for the successful application of the limit equilibrium method, a number of trials have to be examined in order to find the worst case and hence the critical factor of safety. Therefore, the proce- dure reduces to an optimization problem. In this paper, we propose to use a robust technique to find solve this optimization problem. The technique is based on genetic algorithms (GA) and is improved to the case of multiple-slopes stability situation as in large land cuts such as in mining operations. We then pro- vide a complete study of the GA code with regards to its robustness, accuracy and efficiency. The code is also compared against results obtained with popu- lar software in geotechnical engineering such as the SV-soilvision program (SVS).Two methods in SVS, namely the grid and the tangent algorithms for search- ing the failure surface are considered in this study. In this work, we consider homogeneous soil layers and therefore the study limits to circular failure surfaces. We note however that although most of the homogeneous soil layers have circular failure surface, multi-soil layers slope have non-circular failure shape (see e.g. Zolfaghari et al., 2005). In addition, slope failure mechanisms such as translation and rotational slide have circular failure surface and they can over predict the factor of safety for multiple layers slope (Budhu, 2011). A number of publications are available for the application of GA to slope stability analyses (Goh, 2000; McCombie & Wilkinson, 2002; Das 2005; and Zolfaghari et al., 2005). Nonetheless, GA has not being fully tested for multiple slopes to the authors’ knowl- edge. We note that for a single slope, there is one most critical failure surface region which is relatively easy to be found whereas the case of multiple slopes required finding many failing circles and ultimately the critical one. An advantage of optimising with GA is that the global optimum is also found; thus solving the problem. GA will search the worst critical failure surface regardless the existence of multiple slopes. Currently, there are other alternative optimisations techniques including dynamic programming (Pham & Fredlund, 2003), Monte-Carlo analysis (Greco, 1996), Ant Colony (Kahatadeniya et al., 2009), Grid and Tangent (SVSoilvision, 2014), and a somewhat “brute- force” algorithm that compares almost all combina- tions of centres and radii of failure circles. Because the majority of the commonly used com- mercial software employs either the grid-and-tangent or brute-force methods, this paper focus on compar- ing the proposed GA-based method against these two. 1427