It is unfortunate that valuable information concerning fallacies in soil mechanics can get lost in the course of time. This has happened with the use of variational calculus in slope stability problems.
The variational method, for determining the critical slip surface as the surface that minimizes the load at rupture, was presented in soil mechanics by Kopácsy (1957, 1961). He published in the 1957 London conference a three-dimensional version of it. The shape of the surface is suitably established in the 1957 paper by vector analysis and described by equation (16) of that paper which, with ϖ defined by equation (20), can be expressed in words as follows.
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de Jong, G.D.J. (2006). A variational fallacy. In: Schotting, R.J., van Duijn, H.C.J., Verruijt, A. (eds) Soil Mechanics and Transport in Porous Media. Theory and Applications of Transport in Porous Media, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3629-3_9
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