Rocking Motion: Chaos and Seismic Design

Abstract

Predictability is a design requirement. Oftentimes, researchers argue that rocking motion is chaotic, in the sense that the motion of a rocking block is very sensitive to initial and boundary conditions. Such argument is supported by the inability to deterministically predict the response of a structure that uplifts and rocks to a given earthquake ground motion excitation. This has prevented engineers from using this seismic response modification technique in practice. A statistical comparison of the experimental and the numerical responses of a rigid rocking block not to a specific ground motion, but to ensembles of ground motions that have the same statistical properties is presented. It is shown that the simple analytical model proposed by Housner in 1963 is capable of predicting the statistics of seismic response of a rigid rocking block, and, therefore, can serve as the tool for design of rocking structures.