The mechanics of rocking structures subjected to ground motion

Abstract

This thesis describes an investigation into the dynamic response of structures that are permitted to rock or uplift when subjected to ground excitations. Previous studies have demonstrated that rocking motion can mitigate undesirable seismic actions on structures, and this has been further confirmed through extensive numerical time integration analyses in the present study. Despite the intuitive nature of rocking motion, it has been shown that the underlying process is in fact highly complex, sensitive to initial conditions, consequently history dependent and by no means well understood. The present work aims to contribute to the current understanding of the fundamental mechanics of rocking systems. With the aid of experimental data, the dynamic response of free rocking rigid blocks, controlled rocking systems and simple rocking structures was closely examined. It was found that Housner’s simple rocking model remains the most theoretically consistent and is the simplest model to implement. The result is also generally satisfactory for modelling rigid rocking blocks, apart from the model's inability to correctly predict energy dissipation at impacts. The migration of the rotation centre during rocking was identified as central to understand the dynamic characteristics of a controlled rocking system (an elastically restrained rocking system). A novel approach was proposed to describe the rotation centre’s migration behaviour. Then by considering the energy content of the system, the pseudo-static force-displacement behaviour of a controlled rocking wall was able to be accurately predicted. This was then successfully extended to predict the timehistory response of controlled rocking systems. Finally, new formulations were developed for predicting the time-history response of three idealised rocking structural systems from first principles. These were validated against published shake table tests results. Two of the highlights arising from these formulations were 1) a set of simplified, closed form formulae which precisely predicted the nonlinear static force-displacement relationship of a rigid rocking structure on flexible ground, and 2) the governing differential equations for a flexible structure rocking on rigid ground. This latter outcome provided users with a valuable quantitative tool for assessing the benefit of implementing a rocking isolation solution.