Limit analysis solutions for three dimensional undrained slopes

This paper uses numerical finite element upper and lower bound limit analysis to produce stability charts for three dimensional (3D) homogeneous and inhomogeneous undrained slopes. Although the conventional limit equilibrium method (LEM) is used more often in practice for evaluating slope stability, the accuracy of the method is often questioned due to the underlying assumptions that it makes. Using the limit theorems can not only provide a simple and useful way of analysing the stability of slopes, but also avoid the shortcomings and arbitrary assumptions under pinning the LEM. The rigorous limit analysis results in this paper were found to bracket the slope stability number to within ±9% or better and therefore can be used to benchmark for solutions from other methods. In addition, it was found that using a two dimensional (2D) analysis to analyse a 3D problem will lead to a significant difference in the factors of safety depending on the slope geometries. This is of particular relevance to any back analyses of slope failure as it will lead to an unsafe estimation of material strengths.