Simple non-linear numerical modelling of masonry arches reinforced with SRG using elasto-fragile and elasto-ductile truss finite elements

A general and simple numerical strategy that can be used in common practice even by unexperienced users is proposed to analyze masonry arches reinforced with Steel Reinforced Grout (SRG). The reinforcement pack is modeled with elastic steel elements interacting with the substrate by means of non-linear interfaces. Bricks are meshed with elastic quadrilateral elements, whereas mortar joints and interface between substrate and rein-forcement steel are modeled with trusses assumed either elastic perfectly brittle or elastic perfectly ductile (cutoff bars). The aim is to reproduce the non-linear behavior of mortar under both a mode 1 and mode 2 deformation and the possible debonding of SRG. The dependance of the ultimate tangential resistance of the joints upon the acting compressive stress is accounted for simply updating the strength value of the shear cutoff bars at the end of each iteration step, considering the normal stresses calculated in post processing at the previous iteration and using a Mohr Coulomb cohesive frictional relationship. For the interface between steel and substrate, three different non-linear models are considered, the first relying in a fragile cutoff bar interposed between rein-forcement and substrate, the second constituted by two in parallel fragile cutoff bars and the third characterized by the presence of three in parallel cutoff bars (two fragile and one ductile). The procedure is benchmarked on a masonry arch reinforced with SRG and tested in place, for which experimental data and a variety of previously presented results obtained through numerical models characterized by different levels of complexity are avail-able. From the thorough analysis carried out on the global force displacement curves so obtained and a detailed observation of the non-linearity developing in the structural model, the reliability and simplicity of the approach proposed are assessed.