Numerical analysis of size-effect in UHPFRC beams in pure bending with focus on transition from single to multiple cracking

Ultra-high performance fibre reinforced concrete (UHPFRC) emerged in the last two decades as a technologically sound building material.It is well known that, in direct tension, softening takes place for an UHPFRC as long as its fibre content is relatively small.However, strong hardening may still be obtained for such a material in bending with, possibly, concurrent stable, multiple cracking.Yet, the ability to harden under bending is not a material property, but a mixed material-structural property, and thus subjected, very particularly, to size-effect, where the expression size-effect is used in this context in its widest sense of the influence of size on all the aspects characterizing the mechanical response, such as the full load-displacement curve and the whole evolution of the crack pattern.In this paper, some basic results of a wider numerical study of size-and material-effect are reported for softening UHPFRCs characterized by a steep initial softening due to matrix cracking followed by a long, slow softening due to fibre-bridging.The simulations were devised to investigate the coupled influence of the initial softening slope and of the fibre bridging stresses on the response of similar beams in pure bending, and cracking was simulated using finite elements with embedded cohesive cracks (in Hillerborg's sense).The results show that the nominal stress at visible crack initiation depends essentially on the sharp initial softening and specimen size, while the intensity of post-crack hardening and mean crack spacing (as well as mean crack opening) depend on the fibre bridging strength and the specimen size.Dimensionless plots are provided that allow utilization of the results for other combinations of data in the domain of the simulations.