Semiempirical Predictive Models for Seismically Induced Slope Displacements Considering Ground Motion Directionality

Conventional semiempirical predictive models for seismically induced slope displacement ($D$) are generally developed based on as-recorded orthogonal ground motion components. Considering orthogonal records reveals that the predicted $D$ is associated with intensity measure (IM) of a specific ground motion time history. However, current practice generally utilizes average IM (e.g., median over all horizontal ground motion orientations) as input of displacement models, and this tends to underestimate $D$ when earthquake shaking along the downslope sliding direction is stronger than the average shaking level at a site. In this study, more than 190 million coupled sliding-block analyses were conducted using 3,092 ground motion records rotated over all orientations. Generic models were subsequently developed by integrating two machine learning algorithms for predictions of the maximum displacement ($D_{100}$) or median displacement ($D_{50}$) over all orientations. These models exhibit excellent generalization capability, yielding considerably lower bias and uncertainty than conventional polynomial forms. The results indicate that the predicted $D_{100}$ could be significantly larger than $D_{50}$ and the conventional displacement index for orthogonal records, and the $D_{100}$ direction is dependent on both ground motion characteristics and slope properties. The proposed models outperform the existing models regarding ground motion directionality representation and prediction uncertainty mitigation. The associated mathematical equations are presented, with executable files also included for engineering applications.