Reliability analysis on permanent displacement of earth slopes using the simplified bishop method

Assessing the seismic stability of earth slopes has long been a challenging task in geotechnical engineering mainly because of two reasons: (1) the mechanism of slope movement triggered by an earthquake is not fully understood, and (2) the criteria of seismic performance or failure state are hard to specify. As an attempt to address these concerns, this paper examines the seismic slope failure mechanism of rotational sliding mass. Permanent displacement is analyzed based on Newmark's sliding block theory, with extension to compute the rotational displacement in the presence of horizontal ground acceleration history. A simplified relationship between the rotational and horizontal motions of a circular failure mass is also obtained. By comparing case studies, the possible reasons whether and how the seismic slip surface differs from the static one are explained. In addition, we discuss the allowable displacement when a quantitative judgment of the slope performance is required. In this regard, the underlying uncertainties of the soil properties are introduced to probabilistically relate this threshold value to the reliability index, a substitute for the probability of failure or risk acceptance level. The results from the parametric studies indicate the reliability-based design of the allowable displacement is a promising approach for seismic slope analysis.