Scale effects in the post-cracking behaviour of fibre-reinforced concrete beams

The scale effects on the global structural response of fibre-reinforced concrete (FRC) beams subjected to bending are discussed in the framework of Fracture Mechanics by means of the Updated Bridged Crack Model (UBCM). This model predicts different post-cracking regimes depending on two dimensionless numbers: the reinforcement brittleness number, NP, which is related to the fibre volume fraction, Vf; and the pull-out brittleness number, Nw, which is related to the fibre embedment length, wc. Both these dimensionless numbers depend on the beam depth, h, which, keeping the other variables to be constant, drives a ductile-to-brittle transition in the post-cracking regime of the composite. The critical value of the reinforcement brittleness number, NPC, allows for prediction of the minimum (critical) specimen size, hmin, which, analogously to the minimum fibre volume fraction, Vf,min, is required to achieve a stable post-cracking response. Numerical simulations are compared to experimental results reported in the scientific literature, in which FRC specimens, characterized by the same fibre volume fraction but different sizes, are tested in bending.