The collapse settlement displacement: a kinematic approach for symmetric semicircular masonry arches

In this paper, the behavior of circular masonry arches, with radial stereotomy, subjected to dead loads and to an increasing support displacement, occurring along any direction in space, is investigated with an innovative model based on the kinematic thrust theorem. Masonry is modeled as a material rigid in compression and not resistant to tension and the possibility of having a sliding failure is not considered. The initial state of the arch, characterized by a null value of the displacement of its supports and subjected to its self-weight only, is found with the well-established theorems of Limit Analysis, in the undeformed configuration. Subsequently, the arch is subjected to an increasing finite displacement of the supports, up to the collapse of the arch. In the framework of large displacement analysis, the arch and its kinematics evolve by passing through different states of kinematically admissible equilibrium, to accommodate the large displacement of the supports. The collapse state of the arch is evaluated by implementing four kinematically admissible collapse modes and considering the possibility of a change of the hinge position, with increasing displacement values. A numerical survey is carried out to investigate the influence of the main parameters, including the thickness to mean radius ratio, the direction of the support displacement and the blocks discretization. The obtained results clearly highlight the importance of including the possibility of movement of the supports, when assessing the structural response of arches or more complex systems, such as, for example, portals with semi-circular arches.