Discretization-based kinematical analysis of three-dimensional seismic active earth pressures under nonlinear failure criterion

Abstract

The available theoretical models for evaluating seismic active earth pressures are limited to plane strain analyses and linear failure criterion. To fill this research gap, with a combination of the kinematical approach of limit analysis, the spatial discretization technique as well as the pseudo-static approach, this work develops a discretized three-dimensional failure mechanism of sloping backfills that is composed of an end cap and a central plane-strain insert to estimate the seismic active earth pressure coefficient under nonlinear failure criterion. Compared with the existing three-dimensional kinematically admissible failure mechanisms, the developed one has three significant merits: (1) the normality condition is strictly satisfied in the generation of the end cap; (2) the work rates can be computed by a summation of elementary work rates conveniently instead of tedious integral schemes; (3) the considerations of the nonlinear failure criterion and the sloping backfill. Comparisons with the existing upper bound solutions and experimental results in terms of active earth forces or active earth pressure coefficients are conducted to verify the proposed model. Parametric studies are performed to study the influences of model parameters, including the seismic coefficient, the sloping angle of backfills as well as the nonlinear parameters, on the active earth pressure coefficients.