Study on Damage Process and Damage Degree of Recycled Aggregate Concrete Using Improved Differential Box-Counting Method and BFEM Based on Complementary Energy Principle

The quantification of the damage process and damage degree in recycled aggregate concrete (RAC) holds significant importance due to the challenges associated with capturing the initiation and propagation of internal cracks in conventional macroscopic tests. The fractal dimension can quantitatively define the irregularity of meso-damage in RAC. Based on this, the study applied the base force element method (BFEM) and the improved differential box-counting (DBC) method to analyze the damage process and damage degree in RAC. This study developed two two-dimensional models of RAC using the BFEM, both with identical circular aggregate distribution patterns. Then, the two models were subjected to uniaxial compression simulation experiment to obtain damage images at different strain stages. To analyze these images, an improved DBC method was proposed to calculate fractal dimensions. The results indicated that when reaching the ultimate strain, the fractal dimension of the 100% replacement ratio is 0.0259 higher than that of the 0% replacement ratio. The variation in fractal dimensions can be attributed to the differing damage process modes inherent in RAC, with which the growth rate of the fractal dimension significantly decreases as strain increases. The main reason is that the propagation of mesocracks in RAC exhibits fractal characteristics. Moreover, a distinct univariate cubic function relationship emerges between strain and fractal dimension, which indicates that the fractal dimension can effectively characterize the variation in strain. Finally, the severity of injury ([Formula: see text] is proposed to more intuitively and quantitatively analyze the damage process and damage degree of RAC.