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.

Currently, the MgO expansion agent is widely used to reduce the cracking risk of concrete. The influence of MgO reactivity (50 s and 300 s) and dosage (0, 4 wt.% and 8 wt.%, by weight of binder) on the air void, pore structure, permeability and freezing–thawing (F–T) resistance of concrete were studied. The results indicate (1) the addition of 4–8 wt.% reactive MgO (with reactivity of 50 s and termed as M50 thereafter) and weak reactive MgO (with reactivity of 300 s and termed M300 thereafter) lowers the concrete’s compressive strength by 4.4–17.2%, 3.9–16.4% and 1.9–14.6% at 3, 28 and 180 days, respectively. The increase in MgO dosage and reactivity tends to further reduce the concrete strength at all hydration ages. (2) Permeability of the concrete is closely related to the pore structure. M50 can densify the pore structure and lower the fraction of large capillary pores at an early age, thus it is beneficial for the impermeability of concrete. In contrast, M300 can enhance the 180-day impermeability of concrete since it can densify the pore structure only at a late age. (3) The influence of MgO on F–T resistance is minor since MgO could not change the air void parameters. (5) MgO concretes exhibit obvious fractal characteristics. The fractal dimension of the pore surface (D_s) exhibits a close relationship with the permeability property of concrete. However, no correlation can be found between F–T resistance and D_s.

Concrete wall surfaces are prone to cracking for a long time, which affects the stability of concrete structures and may even lead to collapse accidents. In view of this, it is necessary to recognize and distinguish the concrete cracks. Then, the stability of concrete will be known. In this paper, we propose a novel approach by fusing fractal dimension and UHK-Net deep learning network to conduct the semantic recognition of concrete cracks. We first use the local fractal dimensions to study the concrete cracking and roughly determine the location of concrete crack. Then, we use the U-Net Haar-like (UHK-Net) network to construct the crack segmentation network. Ultimately, the different types of concrete crack images are used to verify the advantage of the proposed method by comparing with FCN, U-Net, YOLO v5 network. Results show that the proposed method can not only characterize the dark crack images, but also distinguish small and fine crack images. The pixel accuracy (PA), mean pixel accuracy (MPA), and mean intersection over union (MIoU) of crack segmentation determined by the proposed method are all greater than 90%.

In this study, coral powder with different contents and levels of fineness were incorporated into cement; then, the pore structure of a coral powder–cement slurry was measured using the MIP test at days 3 days and 28, respectively. Neimark’s model, Ji’s model, and Pfeifer and Avnir’s model were also used to analyze the fractal characteristics of the coral powder–cement slurry. The results show that the coral powder–cement slurry has multifractal characteristics when using Neimark’s model, and the entire pore size range of the cement slurry can be divided into three parts: Region I (1–200 μm), Region II (70 nm–4 μm), and Region III (5–500 nm). The pore surface fractal dimension of both Regions I and III is less than 3, while that of Region II is greater than 3. This indicates that Regions I and III have obvious fractal characteristics, which Region II does not. Meanwhile, the pore surface fractal dimension of Region I is positively correlated with hydration age, while the pore surface fractal dimension of Region III is less affected by hydration age and coral powder contents. Ji’s model reveals that coral powder–cement slurry also has multifractal characteristics, but the entire pore size range of the cement slurry can be divided into two parts: Region I (5.482 nm–500 m) and Region II (120 nm–370 μm). The pore volume fractal dimension of Region I is greater than 2 and less than 2.5, while that of Region II is greater than 2.9 and less than 3. Therefore, both Regions I and II have fractal characteristics. In addition, the coral powder admixture, fineness, and age have large effects on the pore volume fractal dimension and pore size range of Region II. Pfeifer and Avnir’s model reveals that the entire pore size range of cement slurry can also be divided into Region I (5.482–600 nm), Region II (120 nm–10 μm), and Region III (5–365 μm), and that the pore surface fractal dimension of both Regions I and III is less than 3, while that of Region II is greater than 3. This indicates that Regions I and III have fractal characteristics, while Region II does not have fractal characteristics.

It is difficult to entrain air into roller compacted concrete (RCC) using conventional air entraining agent (AEA) because of its low cement content. This paper examines whether modified absorbent polymer (MAP) can be used as an air entraining admixture to improve both freeze-thaw resistance and strength gain of roller compacted concrete with 40% fly ash content. Modified absorbent polymer is different from superabsorbent polymer because MAP particles are spherical, have low water-absorption capacity, do not entrain additional air by surfactant content, and can release the absorbed water during subsequent hydration. The influence of MAP and AEA on strength and freeze-thaw resistance of RCC is compared. The air void structure and pore structure are evaluated by microscopic imaging, mercury intrusion porosimetry, and nanoindentation. Compared with traditional AEA, the addition of MAP facilitates the formation of a more effective air void network, the improvement of capillary structure, and the enhancement of the strength of the matrix surrounding MAP voids, resulting in significant improvement of freeze-thaw resistance with great increase in strength.