Three-dimensional slope stability analysis using an extended spencer method

A search procedure is presented to locate 3D critical slip surfaces by combining dynamic programming with a column method extended from the Spencer safety factor equation for 2D analysis. The procedure was applied to typical 3D problems (conical heaps) in order to make a meaningful comparison with variational approaches. Both minimum safety factors and their associated slip surfaces predicted using the two analyses agreed well for all cases investigated. As variational analysis is a rigorous limit equilibrium method without priori statical assumptions, this good agreement adds confidence to the simplifying assumptions of intercolumn forces for the 3D Spencer method. The comparative study presented in this paper strongly supports a recommendation of the use of a statically rigorous limit equilibrium approach satisfying both force and moment equilibrium for a realistic 3D analysis of the slope stability.