A comparative study of critical slip surface in 2D and 3D stability analysis of slopes

Various methods of optimization or random search have been developed for locating the critical slip surface of a slope and the related minimum safety factor. But all these methods are based on a two-dimensional (2D) method and no one had been adapted for a search of the three-dimensional (3D) critical slip surface. In this paper, a new Monte Carlo random simulating method has been proposed to identify the 3D critical slip surface, in which assuming the initial slip to be the lower part of an ellipsoid, the 3D critical slip surface in the 3D slope stability analysis is located by minimizing the 3D safety factor. Based on a column-based three-dimensional slope stability analysis model, a new Geographic Information Systems (GIS) grid-based 3D deterministic model is developed to calculate the 3D safety factor. Several practical examples, of obtained minimum safety factor and its critical slip surface by a 2D optimization or random technique, are extended to 3D slope problems to locate the 3D critical slip surface and to compare with the 2D results. The results shows that, comparing with the 2D results, the resulting 3D critical slip surface has no apparent difference only from a cross section, but the associated 3D safety factor is definitely higher.