Probabilistic model for cracking localization in reinforced fibrous concrete beams

• Published in: Journal of engineering mathematics 2024-02, Vol.144 (1), Article 23
• Main Authors: Karinski, Yuri S., Dancygier, Avraham N., Gebreyesus, Yosef Y.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Cracks; Localization; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Probabilistic models; Reinforcement; Reinforcing steels; Statistical analysis; Steel fibers; Theoretical and Applied Mechanics
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-023-10330-2

This paper proposes a probabilistic model that explains the phenomenon of cracking localization (CL) in RC beams with addition of steel fibers. Quantification of the CL is defined as the ratio between the total number of cracks and the number of significantly wide cracks. The model considers both the fibers and conventional reinforcement ratios, as well as the steel stress hardening and the location of the rebars in the cross-section. The fiber distribution in the concrete mix is considered random while the conventional reinforcement—as deterministic. A cumulative function of the total steel distribution, and a binomial probability function are proposed for a newly defined variable that represents the distribution of the fibers effectiveness along the beam. The model was validated with available data from flexural experiments showing good agreement of the model’s prediction with the reported results. The model shows that the cracking localization level in beams is more pronounced in beams with low reinforcement ratios and relatively large fibers content and enables its quantification.