Fractal-Based Non-Linear Assessment of Crack Propagation in Recycled Aggregate Concrete Using 3D Response Surface Methodology

This study investigates the fracture behavior of recycled aggregate concrete by integrating fractal theory and empirical modeling to quantify how recycled coarse aggregates (RCAs) and recycled fine aggregates (RFAs) influence crack complexity and maximum crack width under varying content and loads. The results reveal distinct scale-dependent behaviors between RCA and RFA. For RCA, moderate dosages enhance fractal complexity (a measure of surface roughness) by promoting micro-crack proliferation, while excessive RCA reduces complexity due to matrix homogenization. In contrast, RFA significantly increases both fractal complexity and crack width under equivalent loads, reflecting its susceptibility to micro-scale interfacial transition zone (ITZ) degradation. Non-linear thresholds are identified: RCA’s fractal complexity plateaus at high loads as cracks coalesce into fewer dominant paths, while RFA’s crack width growth decelerates at extreme dosages due to balancing effects like particle packing. Empirical models link aggregate dosage and load to fractal dimension and crack width with high predictive accuracy (R2 > 0.85), capturing interaction effects such as RCA’s load-induced complexity reduction and RFA’s load-driven crack width amplification. Secondary analyses further demonstrate that fractal dimension correlates with crack width through non-linear relationships, emphasizing the coupled nature of micro- and macro-scale damage. These findings challenge conventional design assumptions by differentiating the impacts of RCA (macro-crack coalescence) and RFA (micro-crack proliferation), providing actionable thresholds for optimizing mix designs. The study also advances sustainable material design by offering a scientific basis for updating standards to accommodate higher recycled aggregate percentages, supporting circular economy goals through reduced carbon emissions and waste diversion, and laying the groundwork for resilient, low-carbon infrastructure.