Permanent displacement of slopes under multi-point earthquake ground motions considering site effects

The nonlinear dynamic response of slope soils caused by seismic motion may lead to inconsistent time histories of seismic acceleration at different positions of a slope. This will affect the limit equilibrium state and the cumulative seismic permanent displacement of the slope. In order to investigate the influences of site effects on the permanent displacement of slopes during earthquakes, a method for considering the multi-point earthquake ground motions is presented. The proposed method is derived based on the limit equilibrium slice method by considering different time histories of horizontal and vertical seismic motions for slices and can be used for circular and arbitrary-shaped slip surfaces. The method is capable to reasonably consider the site effects through a comparison with numerical results obtained by the FLAC. The effects of different distributions of multi-point ground motions and vertical ground motions on the permanent displacement of slopes are investigated. The results indicate that the amplification of horizontal ground motions and the different distributions of multi-point ground motions induced by the site effects have a significant impact on seismic slope displacement, while the influence of vertical ground motions are small. The method is then applied to a case study of post-earthquake deformation of the Lexington Dam. The calculated seismic permanent displacement agrees well with the observed post-earthquake values. This confirms the importance of considering the site effects and the rationality of the proposed method in this study.