Two-dimensional finite element upper bound limit analysis of masonry bridges

A two-dimensional model for the evaluation of the load carrying capacity of masonry bridges is proposed that takes into account the strengthening effects due to arch–fill interaction observed in experimental tests. Upper bounds on the collapse load and the corresponding mechanism are obtained by means of a finite element application of the Kinematic Theorem of Limit Analysis. Arches and piers are modelled as beams made up of non-tensile resistant (NTR) and ductile in compression masonry, while the fill is represented as a cohesive-frictional material with tension cut-off. Kinematically admissible mechanisms are obtained by discretizing the fill domain with triangular elements and including velocity discontinuities in order to increase the degrees of freedom of the model and thus reduce locking; arches and piers are discretized by two-node straight beam elements. A piecewise linearization of the limit domains allows the upper bound on the collapse load and the corresponding mechanism to be obtained as a solution of a Linear Programming problem. The capabilities and the validity limits of the proposed numerical model are shown in two examples. The collapse test on a real single span bridge is simulated and discussed in the first example; a multi-span bridge is analysed in the second, where complex interactions between arches, piers and fill are obtained.