Slope stability using discontinuity topology optimization technique

Many efforts have been focused on the stability problems of geotechnical structures with the limit analysis methods. A key advance of the proposed method is that the problem is described only in terms of nodes and discontinuities connecting those nodes rather than elements or bodies. The alternative approximation procedure might involve discretization of a given body under consideration 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. The discontinuity topology optimization (DTO) technique using the Mohr-Coulomb failure criterion to formulate the objective function is developed and the collapse load multiplier is determined from optimization. Incorporating the pore-water pressure and factor of safety is consistent with the formulation of nodal grid and inter-node connections, and the ability of the DTO procedure extended to handle the slope problems involving ground water pressures is demonstrated. The use of DTO can be an effective tool for establishing a critical failure mechanism and its corresponding safety factor without the constraints or assumptions regarding entrance/exit limits or points of the slip surface. The uses of various methods and DTO for several examples that focus on complex geotechnical scenarios are compared to illustrate the agreement and difference between the analyses. The developed techniques are shown to provide a viable alternative to analyze the stability of slopes with demanding material behavior, complex geometry and loading conditions.