Nonlocal Variational Method in Stability Analysis

A mathematical technique is developed for analyzing the stability analysis in terms of effective stresses. The stability equations are obtained based on limiting equilibrium conditions. The factor of safety defining the stable state of equilibrium is derived with respect to shear strength and follows Coulomb-Mohr failure criterion. The analysis considers the influence of effective inter-slice forces, and makes no a priori assumption regarding the shape of the slip surface, internal stress distribution or on the point of application of horizontal effective thrust line. In this method the stability analysis is transcribed as a minimization problem in the calculus of variations. Using this the critical slip surface associated with the minimum factor of safety is obtained. The numerical solutions obtained by the variational technique showed that the technique can be more appropriately utilised for the rigorous stability analysis of slopes. The slip-surface obtained by variational technique resembles more closely to logarithmic spiral. The analysis satisfies all equilibrium, boundary necessary and sufficient conditions. For the existence of a minimal, the functional is verified for Legendre and Weierstress conditions of positive definiteness and global extremal.