Seismic overturning of rocking structures with external viscous dampers

Numerous structures exhibit rocking behavior during earthquakes and there is a continuing need to retrofit these structures to prevent collapse. The behavior of stand-alone rocking structures has been thoroughly investigated, but there are relatively few theoretical studies on the response of retrofitted rocking structures. In practice, despite the benefits of allowing rocking motion, rocking behavior is typically prevented instead of optimized. This study characterizes the fundamental behavior of damped rocking motion through analytical modeling. A single rocking block analytical model is utilized to determine the optimal viscous damping characteristics which exploit the beneficial aspects of rocking motion while dissipating energy and preventing overturning collapse. To clarify the benefits of damping, overturning envelopes for the damped rocking block are presented and compared with the pertinent envelopes of the free rocking block. Preliminary experimental work to verify analytical modeling is also presented. Finally, the same principles of controlling rocking behavior with damping are extended to a particular class of rocking problems, the dynamics of masonry arches. A pilot application of the proposed approach to masonry arches is presented