Some remarks on non-standard plastic behaviour with Coulomb’s friction starting from an unconventional stone flat arch

The present article aims to explore the non-standard plastic behaviour that occurs in masonry structures when considering a finite Coulomb friction, by starting from the equilibrium analysis of an interesting case study inspired by an unconventional architectural element, i.e., the flat arch crowning the transept portal in the Prato Cathedral, characterized by a ‘wrong’ shape of certain voussoirs. Investigations using various methods are conducted to assess the equilibrium of such a non-traditional blocky structure. At first a novel non-standard approach which couples static and kinematic analyses is proposed. The static method exploits the so-called ‘stability area method’, theoretically framed in the context of the lower bound theorem of Limit Analysis, assuming a limited friction coefficient. This procedure is capable of considering also the effects of a limited compression strength for masonry. By combining such method with kinematic analyses based on the virtual work theorem, the limit friction coefficient compatible with the safety of the structure is found. Following that, the results of these preliminary analyses are compared to those derived by other approaches - that is, a plastic limit state lower approach, finite element analyses, and a Non-Smooth Contact Dynamics approach. Some reflections are provided on the difficulties related to the adoption of a lower bound approach to capture the actual mechanical behaviour of this flat arch, highlighting the need to integrate the equilibrium analyses with kinematic/dynamic investigations or Finite Element Analysis aimed at describing the behaviour of the structure near collapse. It is observed that the anomalous mechanical behaviour is due not only to the presence of a finite Coulomb friction but also to the atypical stereotomy of the voussoirs, which could be subject to mutual detachment. This research, starting from a specific, unconventional, case study demonstrates the need for a critical perspective in the analysis of the mechanical behaviour of masonry vaulted structures.