Probabilistic model of the crack localization in axially loaded fibrous reinforced concrete bars

• We propose a model for cracking localization in reinforced fibrous concrete.
• It is a probabilistic model.
• The model takes into account both the fibers and conventional reinforcement ratios.
• The model shows very good agreement with available experimental results.

This paper proposes a model that explains a phenomenon of only few cracks that significantly widen more than other cracks in tensile reinforced fibrous concrete (RFC) bars. It is a probabilistic model that takes into account both the fibers and conventional reinforcement ratios, where the fiber distribution in the concrete mix is considered random while the conventional reinforcement – deterministic. The model allows the derivation of a binomial probability function, whose maximum value denotes the most expected number of cracks that widen more than the others. It shows a good agreement with available experimental results. A case study demonstrates that for low reinforcement ratios it is most probable that only one or two cracks will significantly widen, and as the conventional reinforcement increases the widths of the cracks become more uniform. This result qualitatively conforms to a similar phenomenon that has been observed in bending experiments.