Notch sensitivity on post-cracking behaviour of ultra-high performance fibre-reinforced concrete

The present study focuses on investigating the influence of structural size effect and pre-notch on post-cracking behaviour through extensive numerical and analytical approaches for ultra-high performance fibre-reinforced concrete (UHPFRC). The ductility of UHPFRC is primarily governed by the fibre bridging action that leads to a wider nonlinear inelastic damage zone compared to conventional concrete. This nonlinear inelastic damage zone length is considered as a critical parameter in determining the nominal stress and characterizing the post-cracking tensile behaviour. It significantly governs the size effect behaviour in quasi-brittle materials. Therefore, the proposed study incorporates the effect of nonlinear inelastic damage zone length into the boundary effect model (BEM). The derived formulations consider both the peak load point ($P_{Peak}$) and the second local peak load point ($P_{MOR}$) in the post-peak region of UHPFRC. A mathematical model for nonlinear inelastic damage zone length has been derived considering three different beam specimens of 75 mm, 150 mm, and 300 mm, having span-to-depth ratio as 2.5. Notch-depth has been varied between 0.1 to 0.27. Within this range, normalized nonlinear inelastic damage zone length at peak load ($l_p$/$D$) has been observed to vary between 0.2–0.23, 0.25–0.29, and 0.33–0.4 for small, medium, and large specimens, respectively. The calibrated numerical results show a good correlation with experimental and analytical outcomes. Further, based on parameter sensitivity analysis on derived formulation, the specimen size and the length of the nonlinear inelastic damage zone length have been found to be significantly more influential than other parameters.