Shake table statistical validation of Finite Element models of rocking structures

Abstract

This paper presents a three-dimensional finite element (FE) modeling approach for predicting the response of rocking columns. The model is validated against experimental results, which involved testing three different cylindrical columns with different slenderness ratios under a set of 100 bidirectional ground motions. Each column was free-standing and allowed to slide and rock in all directions. Since the developed stresses in the columns were low, all columns were modeled as rigid.The contact surface was simulated using Coulomb friction for the tangential behavior and stiff contact for the normal direction. Two energy dissipation mechanisms were modeled; friction and radiation damping. Inherent numerical damping, as well as Rayleigh damping, were set to zero, with this approach complying to the physical problem.Rocking is characterized as a chaotic and unpredictable problem, with tests being non-repeatable. Therefore, this study employs a statistical approach to validate the numerical results, using the cumulative distribution function (CDF) for the main response quantity (i.e., maximum top displacement of the column). It was proved that the model performs poorly in the deterministic validation but demonstrates satisfying agreement with the experimental results when validated statistically.The influence of the main modeling parameters, meaning the friction coefficient and the radiation damping properties, was assessed through an extensive sensitivity analysis using non-linear time-history analyses. A small change of the value of these parameters leads to a different individual rocking oscillation but only smoothly influences the statistical response.