A methodology to account for interface flexibility and crushing effects in multi-block masonry collapse mechanisms

Collapse of masonry structures under the influence of seismic action typically takes place via specific failure mechanisms, which have been well-documented. Assuming these mechanisms can be modelled as a kinematic chain, equations of motion can be derived and solved to predict dynamic rocking response. Previous derivations typically assume that the kinematic chain is comprised of rigid bodies with rigid interfaces, which are assumptions that can be both unrealistic and un-conservative. In this paper, rocking equations of motion are re-derived considering the presence of flexible interfaces and crushing effects. Specifically, new derivations are presented for single, two and multiple block mechanisms, while two different formulations for modelling non-rigid interfaces are also proposed. These formulations are compared, and the importance of interface flexibility is evaluated through comparison of the new models with previous formulations that assume purely rigid interfaces. The new equations of motion are also practically evaluated through comparison with advanced numerical modelling simulations.