Masonry arches are typical components of historic buildings throughout the world, and their damage or collapse is very often caused by earthquakes. The first-order seismic assessment of masonry structures can be represented by the equivalent static analysis method, which does not capture all of the dynamics, but provides a measure of the lateral loading that the structure can withstand before collapse. This study aims to understand the stability of unreinforced masonry arches and portals (i.e. buttressed arches) subjected to constant horizontal ground accelerations, combined with the vertical acceleration due to gravity. An analytical model based on limit analysis is developed to describe the relative stability of pointed and basket-handle arches and portals with respect to circular ones, for varying geometry parameters. The equivalent static analysis determines the value of the constant lateral acceleration needed to cause collapse of the structure, which coincides with the minimum peak ground acceleration needed to transform the vaulted system into a mechanism. Predictions of the analytical model are compared with results of numerical modelling by the Discrete Element Method (DEM). This numerical model considers masonry as an assemblage of rigid blocks with no-tension frictional joints, and is based on a time stepping integration of the equations of motion of the individual blocks. The satisfactory agreement between predictions of the two approaches validates the analytical model and verifies the potentials of the discrete element framework as a method of evaluating the quasi-static behavior of unreinforced masonry structures.
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