Analysis on permanent displacement of slopes under the multi-point earthquake ground motions considering site effects

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