Multifractal-spectrum shape parameters for characterizing distribution and evolution of multiple cracks in concrete structures

Abstract

The evolution of cracks in reinforced concrete (RC) structures may trigger critical failure modes of the entire structure. In order to adequately assess the damage in RC structures, it is essential to characterize the distribution and evolution of cracks. Compared with existing quantitative methods of describing concrete cracks, multifractal analysis (MUTFA) is an emerging and sophisticated tool for characterizing the complexity and irregularity of crack distributions in RC structures. Despite the fact that MUTFA embodies a greater capability than monofractal analysis (MONFA), the uncertainty of the mechanism of the multifractal spectrum for representing concrete cracks is a major limitation in using MUTFA to depict cracks. To address this drawback, this study illustrates the difference between the features of MUTFA and MONFA as well as proposes a multifractal-spectrum shape parameter to characterize the complexity and irregularity of fractal-like cracks. The advantages of MUTFA in portraying concrete cracks are demonstrated in two typical cracking scenarios of concrete structures, namely, crack distributions in shear-controlled concrete beams and crack patterns in thin and lightly-reinforced concrete walls. The results of the study show that the proposed multifractal-spectrum shape parameter offsets the deficiency of traditional multifractal parameters in revealing the heterogeneity of crack distributions. The results demonstrate that MUTFA is competent in distinguishing the subtle differences between two similar distributions of concrete cracks, and it provides a path to assess damage in concrete structures.