Issues about the dynamic behaviour of rigid free-standing blocks under earthquake ground motion

The rocking response of rigid free-standing blocks under the action of ground motion is quite different from the typical response associated with a structural system, either elastic or ductile. Thus, the validated theories on the seismic behaviour of general structural systems cannot be applied directly to the safety of rigid systems subjected to overturning. In this paper, aimed at overcoming these difficulties, possible simplifications of the equation governing rocking behaviour are firstly summarised. However, taking the self-balanced effect of the earthquake as a reference point, elementary schemes characterised by zero final velocity and displacement, are introduced to represent the seismic input as a combination of them. The dynamic response of a rigid free-standing block is then analysed, focusing attention on the possible risks of divergence and on the maximum angular displacement involved. Appropriate diagrams show the influence of such parameters as the size and slenderness of the block, the coefficient of restitution and the features of the acceleration pulses representing earthquakes.