Finite-friction least-thickness self-standing domains of symmetric circular masonry arches

This paper concerns a general aspect, 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 an ideal continuous arch), in a limit least-thickness condition, under self-weight, namely the role that a finite inherent (Coulomb) friction, among the theoretical joints, may play in ruling 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 matter is first systematically investigated, by a full analytical treatment, then validated and illustrated 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 and relevant characteristic features. 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 fundamental aspects in the methodological description, and physical interpretation, of the mechanics of masonry arches, in terms of natural bearing capacity, as linked to structural form optimization and relying on basic underlying physical properties such as a finite amount of inherent friction, 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 a historical character and architectural value, to be currently preserved and renewed.