Numerical upper bound limit analysis based on topology optimization considering soil-structure interaction

The discontinuity topology optimization (DTO) is an upper bound limit analysis technique for modeling the stability of geotechnical problems involving soil-structure interaction. The slip-lines or discontinuities used for DTO are typically generated by interconnecting a set of nodes located at regular grid points within a domain under consideration. A key feature of this implementation is that the soil reinforcement is simulated by the soil model such that allows the soil to flow past the reinforcement as might occur for soil nailing and propped wall. And also the procedure is extended to enable rotations at the boundaries of prescribed regions to be considered as well as translation failure mechanisms to be modelled. The resulting procedure is solved by the interior point method with linear programming formulation, which allows identification of a wide variety of failure modes, including translation and /or rigid body rotation, and rigid-plastic bending of the structure due to the formation of plastic hinge. The effectiveness of this procedure is demonstrated by analyzing the stability of masonry arch bridge, anchored sheet pile wall and propped wall. The DTO output is provided, which clearly illustrates the clarity and detail of the discontinuity collapse mechanism solutions.