A mixed smoothed finite element limit analysis formulation for static and seismic collapse loads

Abstract This paper introduces a novel stress-based upper bound limit analysis formulation based on nodal integrations for calculating static and seismic collapse loads in geotechnical engineering. Unlike the classical upper bound limit analysis, our newly proposed formulation is expressed in terms of the stress fields rather than displacement fields. Additionally, the determination of kinematically admissible displacement fields is achieved through duality theory. We demonstrate the robustness and accuracy of our numerical scheme through benchmark examples involving static and seismic collapse loads, such as bearing capacity and tunnel stability. Furthermore, we incorporate a simple non-associated plasticity scheme into the analyses to assess dilation-dependent collapse loads. The newly proposed numerical scheme is then utilised for assessing the influence of the dilation on the static and seismic collapse loads and its failure mechanism, giving some new valuable insights into the dilation-dependent collapse loads under seismic conditions.