Rocking instability of free-standing statues atop slender cantilevers under ground motion

This paper deals with the dynamic response of free-standing statues on the top surface of slender elastically supported cantilevers subjected to horizontal ground motion. Given that there is no link between the base of the statue and the top surface of the monolithic cantilever the statue is in equilibrium in the vertical direction under its own weight. Attention is focused on the determination of the minimum amplitude ground acceleration which leads to the rocking (overturning) instability of the statue whose mass and rotatory inertia are a priory known. It is assumed that the friction between the base of the statue and the top surface of the cantilever is sufficiently large to prevent sliding so that rocking prevails. After simulating the statue by a rigid block freely supported on the top surface of the elastically restrained monolithic cantilever, a theoretical dynamic analysis of the cantilever–rigid block system under horizontal ground motion is comprehensively presented. Two modes of overturning instability of the free standing rigid block are discussed: instability without or with impact. Criteria for overturning instability of the rigid block associated with the minimum amplitude ground acceleration which leads through the vanishing of the angular velocity to an escaped motion in the phase-plane portrait, are properly assessed.