A variational event-driven approach for the dynamic analysis of multi-block historical masonry structures under ground excitation

A variational event-driven approach is proposed to predict the dynamic response of historical masonry structures modeled as 2D systems of rigid blocks subjected to ground excitation. A unilateral contact, no-sliding behavior is assumed at the rigid interfaces between the blocks. Starting from a unitary impulse-theorem format of the equations of motion, involving suitable impulses for the contact reactions between the blocks, two distinct problems are derived for smooth-motion phases and impact instants. The variational structure of both problems is proven, resorting to quadratic programming formulations in the unknown velocities for computations. An event-driven scheme is thus set up, alternating smooth-motion phases with impacts. That conjugates the computational efficiency of the variational formulation with an accurate description of the impact behavior, generalizing the classical Housner impact model. Numerical results are presented to demonstrate the potentialities of the approach, consisting of applications to multi-block masonry arches and to a full-scale structural system formed by several tens of blocks. The dynamic response to a given ground excitation and the failure domain of those structures for a class of ground excitations are explored, showing that the seismic collapse capacity of multi-block masonry structures benefits from their distinctive energy-dissipating rocking motion.