Upper bound limit analysis of multispan mansory bridges including arch-fill interaction

A numerical procedure for the limit analysis of multispan masonry bridges including the arch-fill interaction is developed based on the upper bound theorem. A twodimensional model is defined in which arches and piers are described as beams made up of no tensile resistant (NTR), ductile in compression material, and the fill as a Coulomb material modified by a tension cut off under plane strain conditions. The model is discretized by finite elements: triangular constant strain rate elements and interface elements discretize the fill domain; the interface elements, connecting adjacent triangular elements, allow velocity discontinuities to develop; straight two-noded beam elements discretize arch and pier domains. Once the limit domains in the generalised stress space have been approximated by linear externally tangent domains, a linear programming problem is formulated and upper bounds of the collapse loads are obtained. Two examples are discussed, concerning a real single span bridge, that was subjected to a collapse test, and a three-span bridge. The effects of the fill resistance on the collapse load and the corresponding mechanism and the dependence of the load carrying capacity on the mechanical properties of fill and masonry are shown.