Kinematic FE limit analysis homogenization model for masonry walls reinforced with continuous GFRP grids

The utilization of GFRP continuous grids for strengthening masonry structures is becoming very popular as rehabilitation technology, due to the increasing reduction of the costs of the fibers. On the other hand, a continuous grid allows to avoid premature collapses of single portions of the structure in the unreinforced regions. Unfortunately, differently from the reinforcement with traditional FRP strips, no numerical models are available in the literature to predict to ultimate behavior of masonry reinforced with GFRP grids. In this paper, starting from the observation that a continuous grid preserves the periodicity of the internal masonry layer, rigid-plastic homogenization is applied directly on a multi-layer heterogeneous representative element of volume (REV) constituted by bricks, finite thickness mortar joints and external GFRP grids. In particular, 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 and FRP grid is applied on the external surfaces of the REV. 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 and bricks with six-noded wedge shaped elements and the FRP grid through rigid infinitely resistant truss elements connected node by node with bricks and mortar. A possible jump of velocities is assumed at the interfaces between contiguous wedge and truss elements, where plastic dissipation occurs. For mortar and bricks interfaces, a frictional behavior with possible limited tensile and compressive strength is assumed, whereas for 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 truss from the support.