Analysis of Rock Slopes with Upper Bound Method and Discontinuity Topology Optimization Technique

Limit Analysis Theorems has revealed to be a powerful tool for the development of numerical models aiming the determination of the load bearing capacity of structures reached by plastic collapse. This work presents a numerical formulation for the computation of strict upper bounds of the collapse loads of rigid-perfectly plastic mechanical systems, derived within the kinematical theorem framework. A key advance of this present method is that the problem is described only in terms of nodes and discontinuities connecting those nodes rather than element or bodies. The alternative approximation procedure to the traditional finite element method might involve discretization of a given body using a suitably large number of nodes laid out on a grid, with the failure mechanism comprising the most critical subset of potential discontinuities interconnecting these nodes. Potential discontinuities which interlink nodes laid out across the problem domain are permitted to crossover one another, giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient interior point method solvers can be employed when certain popular failure criteria are specified (e.g. Mohr-Coulomb). By adopting this processing approach it is possible to solve very large problems which normally exceed the memory capacities of a single computer. The developed numerical tool reveals to be robust and versatile, able to solve a wide range of 2D problems. Velocity singularities are automatically identified and visual interpretation of the output is straightforward. Several numerical examples including rock slope are studied by the new method, and the results are very close to those calculated by using analytical method and FEM.