Collapse displacements for a mechanism of spreading-induced supports in a masonry arch

Masonry arch systems and vaulted structures constitute a structural typology widely spread in the historical building heritage. Small displacements of the supports, due to different causes, among which subsidence of foundation systems or movements of underlying structures can lead the masonry arch to a condition of collapse because of gradual change in its geometry. This paper presents a tool, based on a kinematic approach, for the computation of the magnitude of the displacements that cause the collapse of circular arches subject to dead loads, and allows the evaluation of the related thrust value. A parametric study has been carried out in order to develop a deeper understanding of the influence of the involved parameters. In addition, analytic formulations of the maximum allowed displacement and the associated thrust are proposed. Finally, a case study related to the behavior of a masonry arch on spreading-induced abutments is undertaken and discussed.