Abstract
Cement-based materials, including cement and concrete, are the most widely used construction materials in the world. In recent years, the investigation and application of fractal theory in cement-based materials have attracted a large amount of attention worldwide. The microstructures of cement-based materials, such as the pore structures, the mesostructures, such as air voids, and the morphological features of powders, as well as the fracture surfaces and cracks, commonly present extremely complex and irregular characteristics that are difficult to describe in terms of geometry but that can be studied by fractal theory. This paper summarizes the latest progress in the investigation and application of fractal theory in cement-based materials. Firstly, this paper summarizes the principles and classification of the seven fractal dimensions commonly used in cement-based materials. These fractal dimensions have different physical meanings since they are obtained from various testing techniques and fractal models. Then, the testing techniques and fractal models for testing and calculating these fractal dimensions are introduced and analyzed individually, such as the mercury intrusion porosimeter (MIP), nitrogen adsorption/desorption (NAD), and Zhang’s model, Neimark’s model, etc. Finally, the applications of these fractal dimensions in investigating the macroproperties of cement-based materials are summarized and discussed. These properties mainly include the mechanical properties, volumetric stability, durability (e.g., permeability, frost and corrosion resistance), fracture mechanics, as well as the evaluation of the pozzolanic reactivity of the mineral materials and the dispersion state of the powders.
Highlights
The review includes the following parts: (1) A summary of the principles and classification of the commonly used fractal dimensions applied in the research field of cement-based materials; (2) A summary and analysis of the testing techniques and fractal models determining and calculating these fractal dimensions; (3) An introduction and discussion on the application of fractal theory for studying the macroproperties of cement-based materials, including the mechanical properties, volumetric stability, durability, the fracture mechanism and fracture mechanics, the flexural performance and fracture energy, as well as the pozzolanic reactivity of the mineral materials and the dispersion state of the powders
As for the fractal analysis of the irregularity of cracks, Shang et al [26] used the CT technique and fractal geometry to quantitatively characterize the mesocracks and the mesocrack propagation of recycled aggregate concrete. Their results reveal that the fractal dimensions in the 2D images and the 3D mesocracks of cracks decrease with an increasing recycled aggregate replacement rate
Fractal theory is a new tool for revealing the complex nature of cement-based materials at the micro, meso, and macrolevels
Summary
[1,2,3,4,5,6,7] Cement-based materials always show highly heterogeneous compositions and complex spatial distributions, from the nano- to the macroscales [8,9,10]. 2021, 5, 247 structure at the micro- and mesoscales [11,12,13,14,15,16,17,18], and resolving their structure–property relationships is essential to the novel design and usage of cement-based materials in practice [9,19,20,21,22,23]. Fractal theory has been rapidly applied in many research fields, such as civil engineering, materials science, information science, and computer science [26,27].
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