Kinematic FE homogenized limit analysis model for masonry curved structures strengthened by near surface mounted FRP bars

Masonry curved structures, as for instance arches, domes and vaults, are very diffused in historical and existing structures and usually require seismic upgrading and/or rehabilitation. Where FRP external strips cannot be applied for some reasons, the utilization of FRP bars embedded near the external surface becomes a very interesting and effective alternative. In this paper, a kinematic Finite Element limit analysis model to predict collapse loads and failure mechanisms of masonry curved structures reinforced with near surface mounted FRP bars regularly distributed is presented. Reinforced masonry homogenized failure surfaces are obtained by means of a compatible identification procedure, where a central brick is supposed interacting with its neighbors by means of finite thickness mortar joints, filler epoxy resin and FRP rods. In the model, it is required only that the curved structure results from a periodic disposition of bricks, mortar and FRP bars. Therefore, any pattern (multi-leaf, multi-head and single leaf) may be potentially investigated with the procedure proposed. In the framework of the kinematic theorem of limit analysis, a simple constrained minimization problem is obtained on the unit cell, suitable to estimate – with a very limited computational effort – reinforced masonry homogenized failure surfaces. A FE strategy is adopted to solve the homogenization problem at a cell level, modeling joints, bricks, filler and FRP rods by means of 8-noded infinitely resistant parallelepiped elements. A possible jump of velocities is assumed at the interfaces between contiguous elements, where plastic dissipation occurs. For mortar and bricks interfaces, a frictional behavior with possible limited tensile and compressive strength is assumed, whereas for epoxy resin and FRP bars some formulas available in the literature are adopted in order to take into account in an approximate but effective way, the delamination of the bar from the epoxy and the failure of the filler at the interface with the joint. In order to validate the model proposed, two numerical examples are analyzed, consisting of a circular masonry arch and a hemispherical dome. For both the examples presented, comparisons with experimental evidences, where available, and alternative non-linear FE procedures are reported. Reliable predictions of collapse loads and failure mechanisms are obtained with the model proposed for all the cases analyzed, meaning that the approach may be used by practitioners for a fast and reliable evaluation of the effectiveness of a strengthening intervention.