Multifractal Analysis of Crack Propagation in Concrete Specimens Considering the Influence of the Aggregates’ Grading

Abstract

From a mechanical point of view, the phenomenon of damage in concrete members is represented by surface discontinuities in the form of cracks and crack networks, in progressive form, or volume discontinuities in the form of cavities. Crack width is commonly used as a damage indicator for concrete members, but more detailed information of the corresponding crack network such as its distribution and pattern is not considered in this indicator. To study the influence of aggregate’ grading on the multifractal behavior of the crack networks, fractal and multifractal analysis have been employed. These analyses reveal the fractal geometry and pattern of the crack network in both well-graded and gap-graded aggregate specimens. Box-counting fractal analysis is traditionally used to capture the concept of multifractality. While box-counting fractal dimension analysis is incapable of explaining the fractal nature of crack networks in gap-graded aggregate specimens, the applied multifractal measures can shed some light on their heterogeneity distribution. The monotone decreasing of the generalized dimension D q for increasing all real q values shows that crack networks follow multifractal patterns even in gap-graded aggregate specimens. Studying the symmetric shape of the singularity spectrum emphasizes that the degree of multifractality of the crack network depends on the heterogeneity degree of crack propagation on the damaged surfaces.