Seismic Slope Stability: A Comparison Study of Empirical Predictive Methods with the Finite Element Method

Abstract

This study evaluates the seismically induced displacements of a slope using the Finite Element Method (FEM) in comparison to the results of twelve empirical predictive approaches. First, the existing methods to analyze the stability of slopes subjected to seismic loads are presented and their capabilities to predict the onset of failure and post-failure behavior are discussed. These methods include the pseudostatic method, the Newmark method, and stress-deformation numerical methods. Whereas the pseudostatic method defines a seismic coefficient for the analysis and provides a safety factor, the Newmark method incorporates a yield coefficient and the actual acceleration time history to estimate permanent displacements. Numerical methods incorporate advanced constitutive models to simulate the coupled stress-strain soil behavior, making the process computationally more costly. In this study, a model slope previously studied at laboratory scale is selected and scaled up to prototype dimensions. Then, the slope is subjected to 88 different input motions, and the seismic displacements obtained from the numerical and empirical approaches are compared statistically. From correlation analyses between seven ground motion parameters and the numerical results, new empirical predictive equations are developed for slope displacements. The results show that overall the FEM displacements are generally in agreement with the numerically developed methods by Fotopoulou and Pitilakis (2015) labelled "Method 2" and "Method 3", and the Newmark-type Makdisi and Seed (1978) and Bray and Travasarou (2007) methods for rigid slopes. Finally, functional forms for seismic slope displacement are proposed as a function of peak ground acceleration (PGA), Arias intensity (Ia), and yield acceleration ratio (Ay/PGA). These functions are expected to be valid for granular slopes such as earth dams, embankments, or landfills built on a rigid base and with low fundamental periods (Ts<0.2).