FE homogenized limit analysis model for masonry strengthened by near surface bed joint FRP bars

A homogenized limit analysis model for the prediction of collapse loads and failure mechanisms of masonry walls reinforced with near surface bed joint GFRP bars is presented. Reinforced masonry homogenized failure surfaces are obtained by means of a compatible identification procedure, where each brick is supposed interacting with its six neighbors by means of finite thickness mortar joints, filler epoxy resin and FRP rods. 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 eight-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 meaningful examples are critically analyzed. The first relies on a reinforced masonry beam in four-point bending, whereas the second is a full scale wall constrained at three edges and loaded until failure with a distributed out-of-plane pressure. While the first example is useful to test the model at a cell level, since only horizontal ultimate bending moment is involved in the failure mechanism, the second provides a full assessment of the procedure proposed at a structural level. In both cases, very good agreement is found with literature data, meaning that the model proposed may provide useful information for all practitioners interested in the design of masonry walls reinforced with bed joint FRP bars.