Probabilistic Seismic Hazard Analysis for the Sliding Displacement of Slopes: Scalar and Vector Approaches

Sliding block displacements often are used to evaluate the potential for ground failure due to slope instability. The procedures used to assess sliding block displacement typically use deterministic or pseudoprobabilistic approaches, in which the uncertainties in the expected ground motion and resulting displacement are either ignored or not treated in a rigorous manner. Thus, there is no concept of the actual hazard associated with the computed displacement. This paper presents a fully probabilistic framework for assessing sliding block displacements. The product of this analysis is a displacement hazard curve, which provides the annual rate of exceedance, λ, for a range of displacement levels. The framework considers two procedures that will yield a displacement hazard curve: (1) a scalar hazard approach that utilizes a single ground motion parameter and its associated hazard curve to compute permanent displacements; and (2) a vector hazard approach that predicts displacements based on two (or more) ground motion parameters and the correlation between these parameters. The vector approach reduces the displacement hazard significantly, as compared with the scalar approach, because of the reduction in the variability in the displacement prediction. Comparison of the fully probabilistic approach with an approach using probabilistically derived ground motions reveals that using a ground motion for a given hazard level does not produce a displacement level with the same hazard.