A mixed formulation of limit analysis based on the node-based smoothed finite element method for seismic slope stability

We shortly present a mixed formulation based on the node-based smoothed finite element method for estimating seismic slope stability. The final form of Hellinger-Reissner is cast as the min-max optimization problem with conic constraints. Solving the second-order cone programming directly determines both master fields, stress and displacement. It is shown from the numerical results that the stability numbers obtained are almost equal to the exact collapse loads given by Griffiths & Martin (2020) for the relatively flat slopes. Moreover, the effects of the dilation angle on the seismic stability number are studied by incorporating a simple iterative technique in the algorithm cast as max-min programming, arriving at the observation that both the static and the seismic stability numbers are susceptible to the dilation angle. Although the magnitude of the seismic stability number largely depends on the vertical seismic acceleration for a broad range of typical slope angles, the seismic stability number for the relatively flat slopes in cohesive-frictional soils is likely independent of the seismic acceleration in the vertical direction.