Using variational method to evaluate the effects of slip surface shape on the safety factor of slope stability

Abstract

    This paper presents the results of the research on the effects of slip surface shape on the safety factor of homogeneous soil slopes. The investigation has been performed by comparison of three types of slip surfaces (i.e. circular, parabolic, and third-order polynomial slip surfaces) using the variational method, which basically based on solving Euler-Lagrange differential equation to find out the relationship between the slip surface equation and the equation describing the law of normal stress distribution along the surface. This method satisfies all the equilibrium equations of the soil mass as well as the boundary conditions at the two endpoints of the slip surface in terms of the stresses and the direction of the slip surface.