Three-dimensional displacement analysis of slopes subjected to seismic loads

Seismic excitation is among the many possible factors contributing to slope failures. Typical design of slopes and analyses of existing slopes are carried out assuming plane strain mechanisms of deformation, and replacing the seismic loading with a uniformly distributed static force. A three-dimensional (3D) analysis of slopes is described in this paper, based on the kinematic theorem of limit analysis. Critical acceleration is calculated for 3D slope failures, and an analysis of a rotating block is executed to develop a solution for displacements of slopes subjected to seismic shaking. The emphasis is more on applying the displacement analysis to a 3D collapse pattern, and less on the choice of ground motion records suitable for the 3D failure analysis of slopes. The analysis is applicable to slopes for which the geometry of the failure pattern is physically confined, as for instance, in the case of excavations. A 3D failure pattern is then expected, and the results of calculations are given for a reasonable range of the width-to-slope-height ratios. The method is illustrated with practical examples.