Debonding sawtooth analytical model and FE implementation with in-house experimental validation for SRG-strengthened joints subjected to direct shear

A novel and simple analytical debonding model for Steel Reinforce Grout (SRG)-strengthened specimens subjected to direct shear tests is proposed. All the nonlinearity is lumped at the interface between reinforcement chords and mortar, the substrate is assumed perfectly glued to mortar, infinitely stiff and resistant and the steel grid is considered linear elastic. The non-linear interface tangential stress-slip relationship is assumed discontinuous and multi-linear and constituted by four phases, three elastic with progressively reduced stiffness and the last perfectly plastic. The assumption of a non-vanishing residual tangential strength is paramount to reproduce the typical pseudo-linear hardening observed experimentally in the global force-displacement curves when the debonding frontier is triggered starting from the loaded edge. Under such hypotheses, the second order differential field equation describing the slippage of the reinforcement on the support admits closed form solutions, which are suitably derived. An implementation into a standard Finite Element (FE) commercial code is also proposed, which relies in a discretization of the reinforcement through three cutoff bars (one ductile and two brittle) disposed in-parallel, elastic elements for the steel grid and rigid beams used as transversal connections. The reliability of the sawtooth and the FE models is assessed by means of a thorough comparison with experimental data obtained by the authors for this purpose testing five replicates of a concrete specimen strengthen with a SRG and subjected to a standard shear test