Different methods to model the post-cracking behaviour of hooked-end steel fibre reinforced concrete

When designing an element made of steel fibre reinforced concrete (SFRC) subjected to bending, the post-cracking residual stress capacity is taken into consideration. Characterization of this residual flexural capacity is generally performed by means of standardized three-point bending tests on notched specimens (NBN EN 14651) and is further used in the constitutive model for the Mode I crack opening of SFRC, needed for design calculations. Alternative to the constitutive models proposed by Model Code 2010, a new model for the Mode I behaviour of SFRC is proposed, which allows to also consider pseudo-hardening behaviour of SFRC. This model is available in two variants: (1) a tri-linear constitutive model derived by means of inverse analysis and (2) an analytical model based on the fibre pull-out of a single fibre. A thorough discussion on the derivation and the evaluation of the models is presented. Furthermore, this work is extended into a new method to implement the fibre pull-out behaviour into 3D finite element modelling of SFRC prisms subjected to bending, taking into consideration the variability in material parameters, spatial distribution and orientation of fibres.