A study about the influence of height on slope stability using limit equilibrium methods and evolutionary computation

Abstract

An optimization methodology to evaluate simultaneously optimum designs of multiple slope height values with their corresponding factors of safety is proposed in this paper when considering the problem of slope stability. Limit equilibrium methods and evolutionary computation are used as analysis and optimization tools, respectively. The slip surface with lower factor of safety determines the critical failure surface of a slope. When varying the slope height -maintaining the rest of parameters that influence its performance constant- the critical surface also varies, and its associated factor of safety diminish. When the slope height increases, it is associated with a greater terrain mass and that implies a greater chance to slip when the rest of factors do not vary. Therefore, the slope height and the associated factor of safety corresponding to its critical slip surface are objectives in conflict. A multiobjective optimization is proper then to obtain the non-dominated solutions that correspond either to: a) the minimum factor of safety for each slope height -finding the critical surface that corresponds to-, or b) the minimum slope height associated with each factor of safety. Evolutionary multiobjective algorithms have been a successful stochastic tool for engineering global optimum design since the final nineties. In a context of conflicting objectives where improving one of them implies the worsening of others, evolutionary multiobjective algorithms allow to obtain in one single run a set of non-dominated solutions in the sense of Pareto criterion. A set of equally optimum designs is offered where the values of the factor of safety corresponding to each critical slip surface for a wide range of different slope heights are shown. Results are validated comparing the simultaneous multiobjective approach with various single-objective optimization problems where the height of the slope is fixed and manifest the capability of this methodology to achieve final fronts constituted by nondominated designs which offer the best compromise among the factor of safety and the slope height.