Interlocking jack arches with step joints: A frictionless equilibrium stereotomy

This study examines the bearing capacity of stone jack arches with step joints, subjected to self-weight and the weight of a superimposed wall. Jack arches characterized by stone blocks with stepped joints are a feature that is difficult to address using classical limit analysis. The challenge of this work is to develop simple approaches based on the static theorem of Limit Analysis, which are able to capture the collapse behaviour of such structures under increasing loads. To clearly understand the role of the stepped joints, the investigation focuses on the frictionless equilibrium of such type of structures. Jack arches are modelled as sets of adjacent stone blocks with stepped joints. Two jack arches with the same intrados span are considered, but with a different step width (and, consequently, a different number of voussoirs). The analyses are conducted using two different limit analysis methods: a newly developed version of the stability area method and a mathematical programming method. Additionally, advanced finite element analyses have been developed to critically comment the results. This paper represents a preliminary study aimed at understanding the role of step joints on the collapse response of stepped jack arches, starting from simplified assumptions on the masonry material, namely a finite compressive strength, a zero tensile strength and zero friction at the interfaces, and highlighting possible further developments to capture the role of both geometry and more realistic mechanical parameters.