Predictive modelling and comparative evaluation of residual flexural strengths of steel fibre-reinforced concrete

Abstract Residual flexural tensile strengths ( $$f_{\textrm{R},i}$$ f R , i ) are key parameters for classifying performance and designing steel fibre-reinforced concrete (SFRC). Although many predictive formulations exist, their accuracy requires systematic validation against large experimental datasets. This study assembles a database of 1645 three-point bending tests on 365 SFRC mixes reinforced with single hooked-end steel fibres. Existing empirical and semi-empirical models are benchmarked against this dataset, after which a new predictive formulation for $$f_{\textrm{R},1}$$ f R , 1 and $$f_{\textrm{R},3}$$ f R , 3 is developed using Bayesian feature-importance analysis. The analysis identifies fibre volume fraction ( $$V_f$$ V f ) as the dominant variable governing post-cracking behaviour, followed by concrete compressive strength ( $$f_c$$ f c ) and fibre aspect ratio ( $$l_f/d_f$$ l f / d f ). Fibre tensile strength ( $$f_{fu}$$ f fu ) and fibre length ( $$l_f$$ l f ) become increasingly influential at larger crack openings. Guided by these findings, a nonlinear optimisation procedure is used to calibrate a model predicting flexural strengths at crack widths of 0.5 mm and 2.5 mm. Model performance is evaluated using multiple statistical indicators and compared with existing formulations. Results demonstrate that the proposed model achieves superior predictive accuracy, with an error distribution characterised by a mean close to unity and the lowest coefficient of variation. No systematic bias is observed with respect to $$V_f$$ V f , $$f_c$$ f c , $$l_f/d_f$$ l f / d f , or $$f_{fu}$$ f fu , indicating stable performance across the investigated parameter range. Finally, a reliability-based framework is applied to derive characteristic and design values of $$f_{\textrm{R},1}$$ f R ,