Homogenized upper bound FE limit analysis model for FRP-reinforced masonry vaults

A homogenized full 3D limit analysis model for the evaluation of collapse loads of FRP-reinforced masonry vaults is presented. A two steps approach is adopted in the paper; in step I, a simplified kinematic procedure is proposed at a cell level to obtain macroscopic masonry behavior in the case of unreinforced masonry curved structures, whereas in step II strips are applied at a structural level on the already homogeneous material. Six-noded rigid infinitely resistant wedges are used to model masonry. Three-noded rigid infinitely resistant triangles are used to model FRP strips. Plastic dissipation is allowed only at the interfaces between adjoining elements. Masonry ultimate strength is evaluated through an admissible rigid-plastic homogenization model, where joints are reduced to interfaces with frictional behavior and bricks are assumed obeying a Mohr-Coulomb failure criterion and are modeled by means of six noded infinitely resistant wedge shaped limit analysis elements with possible dissipation at the interfaces. The curved representative element of volume (REV) is constituted by a central brick interconnected with its six neighbors. A recently presented compatible identification procedure is finally adopted on the REV, a priori assuming a sub-class of macroscopic deformation modes on the REV and equating power dissipated in the heterogeneous model to power dissipated in a continuous homogeneous plate. A fast and reliable FE estimation of masonry homogenized failure surfaces when loaded in- and out-of-plane is thus obtained. At a structural level, a possible dissipation at the interfaces between FRP triangles and masonry wedges is considered in order to take into account, in an approximate but effective way, the possible delamination of the strips from the support. Italian code formulas are used to evaluate peak interface tangential strength. A numerical example is analyzed in order to evaluate the capabilities of the model proposed, relying on a hemispherical masonry structure reinforced with hooping FRP strips. For the example presented, both the unreinforced and FRP reinforced case are discussed in order to have a deep insight into the efficiency of the strengthening intervention proposed. Additional non-linear FE analyses are performed, modeling masonry through an equivalent macroscopic material with orthotropic behavior at failure and possible softening, in order to assess limit analysis results. Comparisons with experimental evidences, where available, are finally reported. Reliable predictions of collapse loads and failure mechanisms are obtained with the model proposed, meaning that the approach proposed may be used by practitioners for a fast and reliable evaluation of the effectiveness of a strengthening intervention.