Lower bound limit analysis of masonry bridges including arch–fill interaction

Collapse tests on full and model scale masonry bridges have shown the structural role of fill and spandrels, which has to be taken into account to obtain realistic evaluations of the load carrying capacity of existing bridges. A plane model of multi-span masonry bridge is proposed in which the vault–fill interaction effects are considered, whose lower bounds on collapse load are obtained by a finite element application of the lower bound theorem of limit analysis. Arches and piers are modelled as beams made up of no tension, ductile in compression material and the fill as a cohesive-frictional material with a tension cut-off. The fill domain is discretized by triangular elements connected by interface elements in order to increase the ratio of the unknowns to the conditions of static admissibility; arches and piers are discretized by two-node straight beam elements. By linearisation of the conditions of plastic admissibility, a Linear Programming problem is formulated and lower bounds on the collapse load are obtained. The procedure is successfully applied to two example bridge models, where a comparison with the results obtained from the kinematic approach is made. The first example is a simulation of a collapse test on a single span bridge; the second concerns a multi-span bridge and highlights the capability of the procedure to describe complex interactions between the arch–pier structural system and the fill at collapse.