3D FE limit analysis model for multi-layer masonry structures reinforced with FRP strips

A heterogeneous full 3D limit analysis model for the evaluation of collapse loads of FRP-reinforced multi-layer masonry structures loaded in- and out-of-plane is presented. Four-noded rigid infinitely resistant tetrahedrons are used to model bricks, stones and filler. Three-noded rigid infinitely resistant triangles are used to model FRP strips. Plastic dissipation is allowed only at the interfaces between adjoining elements, i.e. on mortar joints reduced to interfaces, on brick-brick interfaces and on filler. A possible dissipation at the interfaces between FRP triangles and masonry wedges is also considered in order to take into account, in an approximate but effective way, the possible delamination of the strips from the supports. Italian code CNR-DT200 formulas are used as a reference to evaluate peak interface tangential strength. While the delamination from the support can be modeled only in an approximate way within limit analysis, the aim of the paper is to accurately reproduce the change in the failure mechanism observed in experiments due to the introduction of strengthening elements.A 3D approach to model masonry is used in order to take into account both the real texture of the panels along the thickness (i.e. multi-layer regular and irregular texture, presence of internal filler, etc.) and the presence of FRP strips either at the extrados or at the intrados of the structural elements.Two numerical examples are critically analyzed, consisting of a two leaf thick masonry wall simply supported at three edges, reinforced at the extrados and subjected to uniform lateral pressure and a complex three-layer tuff masonry shear wall with cavities filled with mortar and reinforced with horizontal and diagonal FRP strips at both faces. For the first example analyzed, full sensitivity analyses varying both FRP-brick peak strength and filler mechanical properties have been conducted in order to evaluate the capabilities of the model proposed when varying constituent materials mechanical properties. An additional FE simulation conducted with a standard code is also discussed to validate the model. When dealing with the second example, full comparisons with experimental data available are reported. Comparisons with experimental evidence and alternative FE procedures confirm that the limit analysis approach proposed may represent a valuable tool for predicting failure mechanisms and collapse loads of complex 3D multi-layer masonry structures reinforced with FRP strips.