Slope stability analysis by the upper bound approach: fundamentals and methods

A new method for stability analysis in soils and rocks is presented, based on the upper bound theorem of classical plasticity. The sliding mass is divided into a small number of discrete blocks, with linear interfaces between blocks and either linear or curved bases to individual blocks. By equating the work done by external loads and body forces to the energy dissipated in shearing, either a safety factor or a disturbance factor may be calculated. The rigorous theoretical background is established, from which it may be demonstrated that for several well-defined classical slope problems the equations for the multi-block solution reduce to the published closed-form solutions. Powerful optimization routines are provided in the computer program EMU to search for the critical failure mechanism giving the lowest factor of safety. Several examples are given to demonstrate that, for problems where the exact answers are known, the new method produces accurate values of safety factor and predictions of failure mechanism. Applications to practical problems have shown that the new method is as simple as the conventional limit equilibrium methods for practitioners.