Concrete is widely used in the building and construction industry. Typically, concretes are nonhomogeneous composites comprising cement, aggregates and other mixtures. And the stress-strain curves are still widely used as the basis for structural design and simulation of the mechanical properties of concretes. Over the past decades, the mechanical properties of concretes have been extensively researched for possible improvements to meet the different structural applications. In particular, the discrete nature of the mechanical properties of concrete in the non-elastic phase, as well as the random nature of their damaged cracks, have attracted significant research attention. Due to their detrimental practical implications on the mechanical properties and overall structural performance, it is important to understand the randomness of damage cracks and the discreteness of the stress-strain curves of concretes.
The aggregate distribution in concrete is widely associated with the random damage cracks and discretization of stress-strain curves. This can be attributed to the close relationship between the macroscopic mechanical properties, the heterogeneity of the internal composition, and the meso-structure of concrete. Numerous theoretical and experimental studies have been conducted to explore the discrete and random properties of concrete materials. Nevertheless, despite the good progress, the characterization of aggregate and damage crack distribution is still lacking. The irregularity of the aggregates and the crack propagation path under external loading make it even more difficult to understand and characterize the influence of aggregate distribution on concrete materials. Therefore, new reliable methods are highly desirable.
Fractal and multifractal theory has emerged as a promising method for solving irregular problems of quantifying irregular patterns. Its feasibility has been demonstrated in various research work. Equipped with this knowledge, Dr. Yajuan Yin, Professor Qingwen Ren and Dr. Lei Shen from Hohai University proposed a new mesoscopic concrete mechanic model based on fractal and multifractal theory to characterize the crack and aggregate distributions. The aim was to understand the influence of aggregate distribution on mechanical properties and damaged cracks of concrete. The work is currently published in the journal, Construction and Building Materials.
In their approach, the numerical model was established based on the assumption that the concrete is a three-phase composite material. The model was utilized to determine the macroscopic mechanical properties and damage crack distribution for 36 concrete specimen groups, with different aggregate behaviors, subjected to uniaxial tensile leading. The relationships amongst crack and aggregate distribution as well as concrete brittleness and peak stress, were extensively studied and discussed. Notably, the box dimension and multifractal spectrum were both used to characterize the crack and aggregate distributions.
Results showed that the box dimension method was suitable for quantifying the crack distribution, but it could not distinguish the aggregate distribution. However, the multifractal spectrum could quantify the aggregate distribution and obtain local detail features. The box dimension of the crack distribution and the multifractal spectrum width of the aggregate distribution negatively correlated with the brittleness and peak stress. On the other hand, the multifractal spectrum width of the aggregate distribution positively correlated with the box dimension of the crack distribution. Furthermore, low multifractal spectrum indicated uniform aggregate distribution, resulting in high peak stress, large brittleness, regular crack propagation, and low box dimension.
In summary, the study investigated the effect of aggregate distribution on the damaged cracks and mesoscopic mechanical properties of concrete. The correlations between the crack distribution, aggregate distribution, brittleness, and peak stress were established, and their influences on the damaged cracks and mechanical properties of the concrete were unraveled. The multifractal spectrum emerged as a new and robust method for the quantitative study of aggregate distribution. This research provides an effective method for better and more in-depth study of damage cracking and mechanical properties of concrete.
Yin, Y., Ren, Q., & Shen, L. (2020). Study on the effect of aggregate distribution on mechanical properties and damage cracks of concrete based on multifractal theory. Construction and Building Materials, 262, 120086.