Dynamic response of rocking masonry circular arches

The behaviour of masonry constructions against seismic actions, very far from the one characterizing ductile structures, is based on the activation of a rocking motion rather than a dissipating mechanism. A strength resource of masonry structures consists in exhibiting rocking behaviour, until a failure condition is attained. The paper deals with the topic of the seismic assessment of masonry circular arches, one of the typical resistant systems of unreinforced masonry structures, whose vulnerability has been highlighted by damages and collapses occurred with recent seismic events. The paper aims to investigate the dynamic behaviour of masonry circular arches, according to the studies performed by Housner and Oppenheim. A single-degree-of freedom analytical model is proposed to study their dynamic behaviour, representing the structure as an assembly of rigid bodies, connected through hinges with each other and subjected to a horizontal ground acceleration. Starting from the evaluation of the incipient rocking acceleration of the system, the free and forced motions of the arch are examined. An ad hoc energy dissipation model is specifically implemented for the studied case, according to the classical Housner's approach. Finally, a numerical application, considering a simple constant horizontal acceleration impulse of given duration has been carried out.