Impact of fractal dimension on recycled aggregate concrete performance: Relationship with damage variables and flexural capacity calculation of normal sections via fractal-based crack analysis

The construction industry generates massive amounts of concrete waste, making the development of sustainable alternatives imperative. Recycled aggregate concrete (RAC) offers an environmentally friendly option, yet its heterogeneous nature complicates the prediction of damage evolution under bending loads. To address this challenge, this study establishes a fractal-dimension-based damage constitutive model for RAC. Beams with varying replacement ratios of recycled coarse and fine aggregates were tested under flexural loading, while the box-counting method was applied to quantify the fractal characteristics of crack distributions. Results show that RAC exhibits earlier damage onset and faster crack propagation than natural aggregate concrete. Crack patterns display statistical self-similarity, and the fractal dimension correlates linearly with load level. More importantly, quadratic functions provide accurate fits between fractal dimension and flexural parameters such as crack width, mid-span deflection, and the damage variable, with high coefficients of determination (R 2 > 0.90). The proposed model thus enables accurate prediction of flexural capacity and crack development. This framework not only advances the theoretical understanding of RAC damage mechanisms but also provides a quantitative tool for optimizing RAC mix design, enhancing durability assessment, and supporting sustainable construction practices.