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 Model 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. (C) 2014 Elsevier Ltd. All rights reserved.