Effects of the vertical component of ground shaking on earthquake-induced landslide displacements using generalized Newmark analysis

The popular Newmark method calculates the cumulative permanent displacement of a landslide having a known critical acceleration as it is subjected to the effects of an earthquake acceleration time-history. For an infinite slope, this method considers ground acceleration as parallel to the slope and downslope which results in two important limitations: (1) vertical downslope acceleration only is considered; (2) the ratio of vertical to horizontal acceleration only depends on the inclination of the slope surface. In the model developed herein, the ground acceleration is not parallel to the slope; the ratio of vertical to horizontal acceleration, called the vertical accelerometric parameter, depends on the seismic situation of the slope (magnitude, earthquake source distance, style of faulting), and the vertical acceleration acts alternately upslope and downslope. Application of the principles of classical mechanics leads to the pseudo-static factor of safety and hence to the seismic horizontal critical acceleration of a potential landslide, which depends not only on its static factor of safety (geometry, geotechnical properties, and hydrogeologic conditions) but also on its seismic situation. It is shown that Newmark's model is in fact a particular case of the general model and, in most cases, the seismic horizontal critical acceleration results from vertical upslope acceleration and is lower than Newmark's critical acceleration. As a consequence, the displacements D resulting from the model developed herein will be greater than the displacements DN calculated from Newmark's approach. For some potential landslides, the difference (D − DN) is considerable and results in significant consequences in the seismic stability analysis of the affected slopes, which justifies the importance of the effects of vertical ground shaking.