Dynamic response of masonry arch with geometrical irregularities subjected to a pulse-type ground motion

Ancient masonry structures often rely on the masonry arch as a load bearing element. The understanding of its response under seismic actions is a first fundamental step towards the comprehension of the behaviour of more complex structures. It is well known that the stability of masonry arches is primarily related to the geometry. The safety assessment under seismic actions is usually carried out by considering known deterministic geometrical parameters, such as thickness, rise and span, and the voussoirs are assumed with equal dimensions. However, many factors, like defects or irregularities in the shape of the voussoirs and imprecise construction, produce variations of the geometry with respect to the nominal one and, as a consequence, may effect the ability of the arch to resist seismic actions. In this paper, the effect of geometrical irregularities on the dynamic response of circular masonry arches is considered. Irregular geometries are obtained through a random generation of the key geometrical parameters, and the effect of these irregularities is quantified by analysing the dynamic response to ground motion. The masonry arch is modelled as a four-link mechanism, i.e. a system made of three rigid blocks hinged at their ends. The position of the hinges at the instant of activation of the motion is determined through limit analysis. Lagrange’s equations of motion have been written for the generated irregular geometries and solved through numerical integration. The results are summarised by a fragility surface that quantify the extent to which geometrical uncertainties can alter the dynamic response of the masonry arch and increase its seismic vulnerability.