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

• The seismic response of free-standing statues atop multidrum columns is studied.
• Columns are modelled as monolithic viscoelastic cantilevers with structural damping.
• Damping is associated with energy dissipated due to impacting and sliding of the drums.
• The level of structural damping can be assessed experimentally.
• The proposed procedure is the best approximate solution for this complex problem.

The highly complex rocking response of free-standing statues atop multi-drum columns underground excitation resulting in insuperable difficulties for obtaining reliable solution is reexamined analytically. This is achieved after simulating the columns by monolithic viscoelastic cantilevers having structural damping, based on experiments, equivalent to the energy dissipation due to impact and sliding of multi-drum columns. Subsequently, the conditions of rocking (overturning) instability of free-standing rigid blocks (representing the statues) after their uplift from the top surface of the laterally vibrating cantilevers, are established, including overturning with or without impact. Attention focuses on the minimum amplitude ground acceleration which leads to an escaped motion through the vanishing of the angular velocity and acceleration. Maximization of such a minimum amplitude (implying stabilization) of the rigid block is obtained by seeking the optimum combination of values of the slenderness ratio of the column and its height. Analytically derived results based on linearised analyses are in excellent agreement with those obtained via nonlinear numerical analyses.