Seismically-induced permanent displacements of slopes using 3D Nested Newmark method

Abstract

The Newmark method is a classic method for evaluating the permanent displacements of a slope under seismic loads. This study aims at proposing a three-dimensional nested Newmark method (3D-NNM) in the framework of the kinematic theorem of limit analysis. The classical three-dimensional rotational failure mechanism is discretized into a series of nested rotating wedges, each of which is subjected to a corresponding yield acceleration determined by employing the work rate balance, and each of which produces relative displacements under seismic excitations when it exceeds the yield acceleration. The total permanent displacement profile is further obtained by integration of the relative displacements from the slope toe to the slope crest. The obtained results show that the proposed 3D-NNM can effectively evaluate the permanent displacement profile of slopes under earthquakes, and the proposed 3D-NNM improves the Leshchinsky’s 2D nested Newmark method by 30.7%; the obtained total horizontal displacement at the slope middle height reduces with the number of nested blocks, but increases with the increasing of the slope-width-to-height ratios. Besides, the traditional Newmark method with a single sliding block tends to overestimate the permanent displacements of slope under seismic shakings.