Slope instability issues could cause severe damage and endanger the population, especially when dams are concerned. Over the past years, more and more refined numerical approaches have been proposed to evaluate the slope stability. However, a criterion based on the lack of numerical convergence is generally considered to compute the safety factor with this kind of approaches, which may result in a dramatic increase in the overall computation time for the probabilistic assessment of the safety factor (e.g., using Monte Carlo simulations that require the automation of a large number of simulations). This paper proposes an original approach coupling the shear strength reduction technique with the second-order work criterion. This approach is implemented in the open finite element software Cast3M, version 22.0. The relevance and efficiency of the developed approach is illustrated with two case studies: a heuristic slope and an existing earth dam. Safety factors similar to those calculated by classical approaches are obtained, but without pushing the calculation to the point of non-convergence. Among other advantages described in the paper, the proposed approach makes it possible to compute safety factors using a rational and physically based criterion, while facilitating probabilistic calculations.