Comparative analyses of slope reliability in 3D

• Two contrasting methodologies have been used to analyse slope reliability in 3D.
• The relative performances of the two approaches are evaluated.
• The influence of heterogeneity on slope reliability and failure is highlighted.
• Failure mechanisms are attracted to the path of least resistance.
• Advanced methods are used to gain insight into the performance of simpler methods.

An idealised 3D slope stability problem, incorporating spatial variability of undrained shear strength, has been analysed by Vanmarcke's (1977b) simplified method and the more advanced random finite element method (RFEM), and the two solutions compared. Both methods lead to predictions of reliability (or, alternatively, to probability of failure), as opposed to a single factor of safety. However, they may give significantly different results, depending on the scale of fluctuation (SOF) of undrained shear strength in the horizontal direction relative to the slope dimensions. It is shown that, in a heterogeneous soil, failure mechanisms seek out the weakest path. It is therefore the spatial average of material properties over this general failure surface that determines slope stability, rather than simple spatial averages over a pre-defined failure surface such as the cylindrical surface assumed in the simpler model. The results demonstrate that the RFEM response of the slope is weaker than the Vanmarcke solution in most cases and that the difference is greatest for small SOFs, due to differences in the predicted failure length and thereby to the exaggerated contribution to resistance then predicted by the cylinder ends in the Vanmarcke solution. In contrast, for large horizontal SOFs relative to the slope length, the two methods agree. This is because the failure surfaces in the RFEM analyses then tend to be cylindrical and propagate along the entire length of the slope, thereby matching Vanmarcke's solution for this limiting case. The investigation highlights the merits of advanced methods of analysis in assessing the performance of simpler methods used in design.