Finite element limit analysis of arch-fill interaction in arch bridges

Realistic evaluations of collapse load of masonry bridges can not be obtained avoiding the interaction phenomena between all their components [1]. In this work the attention is focused on the arch-fill interaction, analysed through a two-dimensional finite element model where arches and piers are described as beams made of no tensile resistant ductile in compression material, while the fill is idealized as a plane no tensile resistant frictional-cohesive continuum. In Cavicchi & Gambarotta [2-4] two finite element procedures are defined able to furnish the collapse configurations of this model both in terms of generalized stress field and collapse mechanisms by applying the limit analysis theorems. As known, limit analysis is a powerful tool that, implemented in a finite element framework, can furnish a direct evaluation of the collapse behaviour only resorting to the resistance properties of the materials and then avoiding elastic properties that represents a source of uncertainties. Moreover, upper and lower bounds on the true collapse load are obtained. In this work a deep investigation on the advantages and limits of finite element limit analysis approach in modeling arch bridges taking into account the arch-fill interaction is carried out by simulating experimental collapse tests and analysing the results in terms of ability to furnish realistic descriptions with limited computing times. Moreover, a comparison is carried out with the results obtained with a more classical incremental analysis, highlighting the analogies and differences in terms of computing times and accuracy of results. Finally, the effects of the out-of-plane boundary conditions defining the plane state of the fill are analysed by introducing a limitation on the out-of-plane normal stress component; this possibility allows for taking into account in a simplified way the limited capacity of the spandrels to contain the fill and discussing the limits of the two-dimensional modeling with respect to the possibilities offered by a much more complex three-dimensional approach.