Quantitative Fractal Analysis of Fracture Mechanics and Damage Evolution in Recycled Aggregate Concrete Beams: Investigation of Dosage-Dependent Mechanical Response Under Incremental Load

Abstract

This study investigated the fracture behavior of concrete beams with recycled coarse aggregate (RCA) and recycled fine aggregate (RFA) using the box-counting method to measure crack fractal dimensions under load. Beams with RCA showed higher fractal dimensions due to RCA’s lower elastic moduli and compressive strengths, resulting in reduced deformation resistance, ductility, and more late-stage crack propagation. A direct proportional relationship existed between RCA/RFA replacement ratios and crack fractal dimensions. Second-order and third-order polynomial trend surface-fitting techniques were applied to examine the complex relationships among RFA/RCA dosage, applied load, and crack fractal dimension. The results indicated that the RFA dosage had a negative quadratic influence, while load had a positive linear effect, with dosage impact increasing with load. A second-order functional relationship was found between mid-span deflection and crack fractal dimension, reflecting nonlinear behavior consistent with concrete mechanics. This study enhances the understanding of recycled aggregate concrete beam fracture behavior, with the crack fractal dimension serving as a valuable quantitative indicator for damage state and crack complexity assessment. These findings are crucial for engineering design and application, enabling better evaluation of structural performance under various conditions.