FRACTURE MECHANICS APPROACH TO FLEXURAL BEHAVIOR OF HYBRID REINFORCED CONCRETE (HRC) BEAMS

Hybrid Reinforced Concrete (HRC) can be defined as a cementitious material, in which the reinforcing secondary phase consists in a combination of continuous steel rebars and of short discontinuous fibres, randomly distributed within the concrete matrix. For these structural elements, experimental flexural tests highlight how the post-cracking response of the composite is strongly affected by the amount of steel bars together with reinforcing fibres. In the present work, it is shown that the action of these two contributions can be clearly interpreted in the framework of Fracture Mechanics through the updated Bridged Crack Model. The model assumes nonlinear constitutive laws to describe the toughening action of the reinforcing secondary phases, which are related to the yielding of steel rebars and to the pull-out of the short fibres. Under these assumptions, different post-cracking regimes depending on three scale-dependent dimensionless numbers can be predicted: the bar-reinforcement brittleness number, NP,b, which is directly related to the steel bar area percentage, ρ; the fibre-reinforcement brittleness number, NP,f, which is directly related to the fibre volume fraction, Vf; and the pull-out brittleness number, Nw, which depends on the critical embedment length of the fibre-reinforcement, wc. The critical values of the two reinforcement brittleness numbers define the minimum reinforcement condition of the HRC structural element ─i.e., the combination of ρmin and Vf,min required to guarantee a stable post-cracking response─ including its scale-dependence. A parametrical analysis is presented together with the modelling of an experimental campaign reported in the literature, in order to assess the effectiveness of the updated Bridged Crack Model.