Empirical predictive relationship for seismic lateral displacement of slopes

The objective of this study is to develop an empirical predictive relationship for permanent lateral displacements for use in assessing the seismic stability of slopes, earthen dams and/or embankments subject to stable continental earthquake motions. The empirical relationship is developed from 620 horizontal motions for stable continental regions, consisting of 28 recorded motions and 592 scaled motions. For each motion, the permanent relative displacements are computed using the Newmark sliding block procedure for a suite of yield accelerations. The proposed predictive relationship is derived by performing separate regression analyses for each yield acceleration. This allows the relationship to be simply formulated in terms of ground motion characteristic parameters, independent of yield acceleration, and results in lower standard deviations than those for relations developed by regressing all the data in a single analysis. The non-linear mixed-effects technique is used to regress the data as functions of maximum ground accelerations and velocities. To account for the zero displacement data, logistic regression was conducted to model the probability of zero-displacement occurrences. Then, the probability models were applied as weighting functions to the non-linear mixed-effects regression results. Also, a similar relationship for active shallow crustal motions is developed and compared with the stable continental region relationship. Lastly, the predicted displacements from the proposed model are shown to be in good agreement with those computed using motions recorded during the Mineral, Virginia earthquake of 23 August 2011.