Planar crack assumption as an alternative to Navier's hypothesis in the modelling of fibre-reinforced concrete sections

The present article describes a model, based on concepts of Fracture Mechanics, to evaluate the behavior of fiber reinforced concrete (FRC) sections. It is developed by an analytical method that represents tension in concrete by means of the linear softening law (σ-w) included in the Model Code 2010. The method also uses a compatibility equation for the cracked zone based on the planar crack hypothesis, i.e. the assumption that the crack surfaces remain plane throughout the fracture process, in conjunction with the Navier’s hypothesis applied only to the non-cracked zone. The model reproduces the experimental size-effect on the rupture-modulus for concrete and FRC sections and points at Hillerborg’s brittleness number as a common characterization parameter for concrete and FRC sections behavior. The study concludes that planar crack assumption can be considered as an alternative to Navier’s hypothesis, since it gives a more physical approximation to the FRC fracture behavior.