Post-cracking regimes in the flexural behaviour of fibre-reinforced concrete beams

The flexural behaviour of steel fibre-reinforced concrete beams is discussed in the framework of Fracture Mechanics. The Bridged Crack Model is updated by means of a cohesive softening constitutive law of the reinforcement layers, taking into account the fibre slippage within the cementitious matrix. In this way, the model is able to describe the global response of the composite, including the local instability phenomena characterizing the different post-cracking regimes. The structural response is found to be governed by two dimensionless numbers: the reinforcement brittleness number, NP, which defines the minimum reinforcement condition of the composite beam, and the pull-out brittleness number, Nw, which describes its plastic rotation capacity. The former, NP = (Vf σ¯s h1/2)/KIC, depends on the fibre volume fraction, Vf, on the fibre slippage strength, σ¯s, on the concrete fracture toughness, KIC, and on the beam depth, h. The latter, Nw = (wc E)/(KIC h1/2), depends on the fibre embedment length, wc, on the concrete Young's Modulus, E, on the concrete fracture toughness, KIC, and on the beam depth, h. These two parameters make it possible to identify a softening post-cracking response of the fibre-reinforced concrete element that is scale-dependent. Finally, the numerical analyses are compared to several experimental results reported in the scientific literature, proving the effectiveness of the described model.