A three-dimensional slope stability method based on finite element stress analysis and dynamic programming

The application of limit equilibrium finite element slope stability methods is examined. Two-dimensional studies are presented to provide a better understanding of the interaction between a stress-deformation analysis and the slope stability calculations. Special attention is directed towards the influence of the stress-strain characteristics of the soil, the influence of Poisson's ratio and stress history. Studies are presented to investigate concerns that an isotropic linear elastic soil model might not provide a reliable estimate of the factor of safety in slopes where there is potential for extensive yielding, because the shear stress is permitted to increase beyond the shear strength of the soil. The influence of Poisson's ratio and stress history is shown to be related to the rotation of the principal stress that is part of the collapse process. The accuracy of the factor of safety is shown to depend on the degree of compatibility between the orientation of the principal stress and the admissibility criteria used to control the shape of the slip surface. The fluctuations in the factor of safety can be eliminated using an elasto-plastic stress analysis and kinematic admissibility criteria can be used to control the shape of the slip surface.;The development of a stress-based three-dimensional slope stability method is also presented. The factor of safety is computed based on the results of an independent stress-deformation analysis. The resulting factor of safety equation is determinate, linear and satisfies all conditions of equilibrium. The search for the slip surface is completed using traditional trial and error techniques where the shape of the critical slip surface is pre-defined along with a more advanced non-linear searching procedure. The characteristics of the derived factor of safety equation support the design of a searching algorithm based on a combination of dynamic programming and a series of geometric and kinematic admissibility criteria. The admissibility criteria are used to refine the searching procedure and distinguish between reasonable and unreasonable slip surfaces. The shape of the slip surface becomes part of the slope stability evaluation and is integrated with the method used to compute the factor of safety.