Analytical bond model for general type of reinforcements of finite embedment length in cracked cement based materials

In this work, a computational model for simulating the relevant mechanisms governing the pull-out of a discrete reinforcement embedded into cement based materials is described. The model accounts for the material and geometric properties of the reinforcement, which can include an anchored end, the interface between reinforcement and surrounding medium, and the relative inclination of the reinforcement to the crack plane. The reinforcement is modelled as a Timoshenko beam resting on a cohesive-like foundation that allows all the failure modes seen in the experiments to be accounted for, namely: debonding at the interface between the reinforcement and the concrete, cracking and spalling of the concrete matrix, rupture of the reinforcement. A comprehensive comparison with the experimental data available in the literature highlights the good predicting capabilities of the proposed model in terms of both peak force and dissipated energy. Furthermore, since the model is capable of simulating a discrete reinforcement of any direction towards the crack plane, complex mechanisms like micro-spalling of the matrix at the exit point of the reinforcement can be captured conveniently. By carrying out parametric analysis is possible to optimize the geometry of the anchored ends for maximizing the peak force and/or the energy dissipation in the pull-out process. Therefore, the developed model constitutes a relevant numerical tool for the optimization of discrete and continuous reinforcements of concrete structures including Fibre Reinforced Polymer (FRP) systems and Steel Fibre Reinforced Concrete (SFRC).