A comparison of slope stability analyses in two and three dimensions

Slope stability analyses have traditionally been undertaken in two dimensions assuming plane strain conditions. Although three-dimensional analysis techniques are widely available and used routinely for open pits, two-dimensional analyses are still more common due to the relative ease of model construction and the relatively rapid simulation times. Two-dimensional analyses will often produce different results to three-dimensional analyses for the same slope. It is generally thought that two-dimensional analyses will produce more conservative results. The main reason for the differences is the ability of three-dimensional analyses to account for the three-dimensional nature of the various model inputs, including the slope geometry, the distribution of soil and rock mass domains, the orientation of geological structures with respect to the excavation face, the orientation of the in situ stresses, and the distribution of pore pressure. In some cases, for a long, straight slope in basic geological conditions, two-dimensional analyses can provide a reasonable representation of the problem. However, in many cases, the inability of a two-dimensional analysis to represent the true three-dimensional nature of the problem will lead to unrealistic analysis results. This paper discusses the reasons, as detailed above, for the differences in two-dimensional and three-dimensional analysis results. Work by others is summarized, and additional numerical analyses are performed to provide an improved understanding of the effects of slope geometry, structural orientations, and in situ stresses on predicted stability. Case studies are presented for both stable and unstable slopes, and the behaviour of these slopes is related to the three-dimensional nature of the slope geometry and geology. The previous work, the new analyses performed here, and the case studies show that it is often important to provide a realistic representation of the slope in three dimensions in order to obtain reasonable stability analysis results. This is particularly true for hard rock environments where structurally controlled failure mechanisms are most likely. The paper also highlights the fact that back-analysed properties obtained from one analysis technique are not necessarily applicable to forward analyses using another technique.