Probabilistic investigation of the seismic displacement of earth slopes under stochastic ground motion: a rotational sliding block analysis

Earthquakes frequently induce landslides and other natural disasters that would have a huge impact on human life and properties. In geotechnical engineering, evaluation of the seismic stability of earth slopes has been attracting a substantial amount of research interest. In this regard, the Newmark permanent displacement provides a simple yet effective index of slope co-seismic performance. The traditional Newmark method involves many assumptions and the displacement results thereby calculated are subject to various degrees of uncertainty. In this paper, a modified rotational sliding block model considering depth-dependent shear strength and dynamic yield acceleration is established. The seismic critical slip surface is analysed through a pseudo-static approach, where the failure volume is larger than that in the static condition. The dynamic yield acceleration is updated by considering the instantaneous movement of the sliding mass in each time-step. The parametric sensitivity of soil shear strength, slope geometry, and Arias intensity to the seismic displacement is also analysed. Results show that the internal friction angle and the cohesion have equal effects on the permanent displacement. On a logarithmic scale, the displacement approximately linearly correlates with Arias intensity. Furthermore, the underlying uncertainty of the ground motion is introduced to obtain the probabilistic distribution of the seismic slope displacement. The uncertainty of earthquake time history details has considerable influence on the permanent displacement results. Under the specific allowable displacement, the probability of failure increases exponentially with seismic intensity.