3D stability analysis of concave slopes in plan view using linear finite element and lower bound method



It is well known that the plan curvature of curved slopes has an influence on the stability of the slopes.This paper aims to present a method of three-dimensional stability analysis of concave 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 concave 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 were found to be closely conservative results to exact solutions 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 lead to a significant difference in the factors of safety depending on the slope geometries. Numerical 3D results of the proposed algorithm are presented in the form of some dimensionless graphs, which can be a convenient tool for use by practicing engineers to esti­mate the initial stability for excavated or man-made slopes. The results obtained using this 3D method show that the stability of concave slopes in plan view increases as the relative curvature R/H and the relative width of slope decrease.