Finite-Friction Effects in Self-standing Symmetric Circular Masonry Arches

This note concerns a general issue, in the mechanics of masonry arches, with reference to symmetric circular geometries, with variable opening, and possible stereotomy with radial joints (to be potentially formed, at failure, within the ideal continuous arch), in a least-thickness condition, under self-weight, namely the role that a finite inherent friction, among the theoretical joints, may play in ruling out the self-standing conditions and the mechanical features at incipient collapse, setting a change from purely-rotational modes to mechanisms that may include sliding. The issue is systematically investigated, by a full analytical derivation, and validated through an original Complementarity Problem/Mathematical Programming formulation, and numerical implementation, reconstructing the complete underlying map of thickness-to-radius ratio versus friction coefficient of all arch states, and corresponding collapse mechanisms. This investigation shall clear the issue, of the theoretical influence of finite friction, in the above-stated setting, and contribute to provide a full understanding of basic aspects in the methodological description, and physical interpretation, of the mechanics of masonry arches, with implications that may come up to appear also in practical terms, once dealing with this traditional and remarkable structures, in real cases, possibly endowed of historical character and architectural value, to be preserved and renewed.