A critical analysis of some variational methods in slope stability analysis

Abstract During the last ten years the Calculus of variations technique has been applied to solve the problem of stability of slopes. All published methods are essentially based on the attainment of a functional and the search for its absolute minimum or maximum by vanishing its first variation. Obviously this statement of the problem is valid only if such a minimum or maximum exists and can be obtained by making the first variation of the functional equal to zero. So, these implicit hypotheses must be checked. This work analyses from this point of view the validity of the methods proposed by ‘Baker and Garber’, ‘Chen’ and ‘Castillo and Revilla’, and demonstrates that the first two methods are incorrectly stated while the third one is correct at least in the case of a frictionless soil.