Application of multifractal spectrum to characterize the evolution of multiple cracks in concrete beams
The quantitative characterization of concrete multiple cracks in fractal dimension is limited to the holistic macroscopic characterization of a particular damage state only, and fails to portray the local subtle variations of the cracks. Based on this, multifractal theory is introduced to quantitatively characterize the evolution process of concrete beam multiple cracks and to deeply analyze the relationship between the spectrum parameters and the typical mechanical parameters of concrete beams. Firstly, the simulation of the crack evolution process in concrete beams is executed precisely utilizing the nonlinear finite element software ATENA to enhance the dataset of multifractal analysis at each load step. Secondly, an enhanced C-J algorithm program for the multifractal spectrum is developed to determine the reasonable range of multifractal spectrum parameters and quantitatively characterize the multiple crack evolution of concrete beams at each loading step. Then the evolutionary characteristics and damage patterns of multiple cracks under varying reinforcement ratios and shear span ratios is elucidated. Additionally, the research probes into the relationships between the multifractal spectrum and the mechanical and damage parameters. The results demonstrate that higher reinforcement ratios in components lead to reduced crack extension and lower crack complexity, resulting in a generally decreasing trend for FD, as the reinforcement ratio increases by 0.957 %, the FD decreases by 0.76 %. Larger shear span ratios enhancing crack inhomogeneity and causing a gradual increase in both FD and Δa, as the shear span ratios decreases by 41.67 %, the FD decreases by 1.35 %. The drift of the multifractal spectrum and the variation of the multifractal spectrum parameters portray the evolution of the overall and local fine cracks in concrete beams. The multifractal spectrum can reflect the damage state of components in a more comprehensive and detailed way, which provides a new way for the damage warning and evaluation of concrete structures.
Fig. 1. Pixels of cracks at different box sizes.
Fig. 2. Finite element simulation cracks diagram under various levels of load in L1.
Fig. 3. Multifractal spectrum of cracks distribution in concrete beams under different loading steps of L1.
Fig. 4. Δ and FD and reinforcement ratio relationship diagram.
Fig. 5. Relationship between multifractal spectrum parameters and damage variables.