Coupling of the Finite Element Limit Equilibrium Method with the Stochastic Search Algorithm and Its Application for an Embankment Dam

Slope stability analysis is a crucial task in the design of geotechnical structures. In many computational methods, such as those combining displacement-based finite element methods and strength reduction techniques, no assumptions are made a priori about the shape or position of the failure mechanism. This is usually considered to be a positive feature but there are situations where the ability to control the search domain for the critical slip surface might be of interest. These are the cases where the critical slip surface converges towards a local (unintended) one, or when it is necessary to determine the factor of safety for slopes with varying inclinations such as the upstream and downstream slopes of embankment dams. This article presents the Finite Element Limit Equilibrium Method (FELEM), which integrates stress states computed by the finite element method along a predefined trial slip surface to determine the factor of safety. This method is combined with a swarm-based metaheuristic optimization algorithm to identify the critical slip surface with the lowest factor of safety. The combined approach is tested on two numerical examples, addressing issues such as discretization error, optimization procedure settings, and non-associated plastic flow. Finally, the combination of FELEM and the optimization algorithm is applied to a boundary value problem of a newly designed embankment dam. Slope stability is evaluated independently for both the upstream and downstream slope, each with a different inclination. Computations are performed for the hydrostatic and steady-state seepage conditions.