A novel impact model for the rocking motion of masonry arches

The in-plane rocking motion of a masonry arch subjected to ground acceleration is investigated, focusing on the impacts at stereotomy sections, which may occur during the motion. It is assumed that the arch arrives at the impact moving along a prescribed four-hinge mechanism and that, after the impact, it continues its motion along a new four-hinge mechanism to be determined. The novel concept of impulse line, which is analogous to the thrust line computed during the smooth motion, is introduced to describe the impulsive stress state arising within the arch at the impact. That is the basis for extending the Housner impact model, initially proposed for the rocking motion of a free-standing column, to the more complicated case of a masonry arch behaving as a single-degree-of-freedom system. The mechanism after the impact is determined by minimizing the kinetic energy loss of the arch at impact, i.e. by maximizing its restitution coefficient, over the set of compatible mechanisms that fulfill a suitable formulation of the virtual work principle. The descending impulse line is proven to be equilibrated, kinematically admissible (i.e., not resisting the opening of the hinges after the impact), and statically admissible (i.e., corresponding to a compressive impulsive stress state). Numerical results are presented, discussing the restitution coefficient of discrete and continuous circular arches with parameterized geometry, for which the four-hinge mechanism before the impact is assumed to follow from an equivalent static analysis.