Seismic instability of free-standing statues atop multispondyle columns: A heuristic very stable system of ancient technology

The very complex rocking-sliding response of a free-standing heavy statue atop multi-rigid block assemblies under ground excitation, is extended and supplemented, to the case of multispondyle columns of circular cross-section. After the analytical derivation of the system of highly nonlinear differential equations governing the rocking - sliding response of a N-spondyle cantilever column, attention is focused on seeking the most reliable approximate solution due to the insuperable difficulties for evaluating the loss of energy between successive spondyles which affects decisively the final solution. This is achieved simulating the structural system of a "N-spondyle column - heavy statue" by an "equivalent" system of a "monolithic viscoelastic column - heavy statue" with viscosity coefficient experimentally obtained so that it matches the total loss of energy along the column height due to small slidings and impacts between successive spondyles. In this respect it was found that the accuracy of solution of the aforementioned structural system does not depend solely on the knowledge of the very complex response of a multispondyle column which can be avoided and thus simplifying the entire analysis. Moreover, some qualitatively obtained findings regarding the stability between monolithic and multispondyle columns as well as between geometrically similar columns where confirmed through simple experiments. Finally, it was determined a reduced total number of geometrical configuration patterns which may lead to overturning, and among these the critical one which provokes the first rocking initiation.