The relative dynamic resilience of masonry collapse mechanisms

Masonry structures have exhibited recurrent collapse mechanisms during past earthquakes, and building codes now require that the seismic capacities of typical mechanisms are assessed. In this paper, a new framework is proposed for predicting out-of-plane seismic collapse of masonry walls. The method remains relatively simple by utilizing linearized equations of motion, while improving upon previous methods by considering the dynamic rocking response. The equations of motion for the rocking response of masonry walls with three fundamental scenarios of loading are first presented. Both applied external forces and external inertial forces are considered, in addition to the possible formation of a two-body (three-hinge) mechanism if the wall is restrained at its top and bottom. After linearization, these fundamental loading scenarios are all described by a single equation of motion, allowing them to be combined to consider a much wider variety of loading scenarios. The proposed framework is then used to investigate the dynamic resilience of different collapse mechanisms by considering the response to pulse-type ground motions. For this purpose, an analytical solution which describes the collapse envelope for pulse-type ground motions and one-sided rocking is derived. The comparison between collapse envelopes makes it possible to describe the relative resilience of each mechanism compared to the others. Eventually, the proposed framework is used to investigate the relative resilience of the mechanisms observed in a church damaged in the 2009 L'Aquila earthquake.