Earthquake destructiveness potential factor and slope stability

This note presents a mathematical analysis procedure to estimate earthquake-induced displacements of embankments and slopes. It approximates the effects of the main seismic factors governing the stability of slopes by introducing the earthquake destructiveness potential factor Pd, which the authors claim to provide the most information on ground motion for the purpose of predicting the cumulative displacement of a slope. Pd is defined as the ratio between the Arias intensity and the square of the number of zero crossings per second of the accelerogram. Empirical regression equations were formulated for Pd in terms of the displacement of Newmark's rigid block vibrating horizontally with completely asymmetrical resistance; they were derived by analysing 310 horizontal components of actual accelerograms. In addition, graphs were obtained for calculating the seismic coefficients kc, which are needed to define the sliding surface, and the correction terms for estimating the displacements. This was done for the most important practical cases: (1) homogeneous infinite slope; (2) local plane slope failure; and (3) local log-spiral slope failure. Illustrative examples are given.