Load carrying capacity of masonry arch bridges: numerical evaluation of the influence of fill and spandrels

The contribution of the arch-fill interaction to the load carrying capacity of masonry bridges can be large [1]. While a comprehensive description of the arch-fill-spandrels interaction requires a three-dimensional model, a simplified description of the fill contribution to the load carrying capacity of the bridge can be implemented in two-dimensional models. This is the way followed for instance in Hughes et al.[2] and by Bicanić et al. [3]. In Cavicchi and Gambarotta [4] the fill is described as a continuum in plane strain. This reduction of the fill to a plane model presents a critical aspect whose effects have to be evaluated: the dependence of the in-plane fill resistance on the containing capacity of the spandrels. This aspect is here considered in an approximated way by describing the fill as a continuum in a plane state where the out of plane normal stress is constrained in an admissible domain representing the limited containing action of the spandrels. A statically admissible two-dimensional model is defined and the Static Theorem of Limit Analysis is applied.