3D stability analysis of convex slopes in plan view using lower bound linear finite element

Presented is a method of three-dimensional stability analysis of convex slopes in plan view based on the Lower-bound theorem of the limit analysis approach. The method’s aim is to determine the factor of safety of such slopes using numerical linear finite element and lower bound limit analysis method to produce some stability charts for three dimensional (3D) homogeneous convex slopes. Although the conventional two and three dimension 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. The rigorous limit analysis results in this paper together with results of other researchers were found to bracket the slope stability number to within ±10% or better and therefore can be used to benchmark for solutions from other methods. It was found that using a two dimensional (2D) analysis to analyze a 3D problem will leads to a significant difference in the factors of safety depending on the slope geometries. Numerical 3D results of proposed algorithm are presented in the form of some dimensionless graphs which can be a convenient tool to be used by practicing engineers to estimate the initial stability for excavated or man-made slopes.