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Fractal and Fractional in Cement-based Materials

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A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (31 January 2022) | Viewed by 59728

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Special Issue Editors

Dr. Shengwen Tang

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Guest Editor

School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China
Interests: civil engineering; cement-based materials; non-destructive measurement; transportation property; microstructure and durability; fractal analysis; electrical property; cement; concrete; construction materials; microstructure
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Giorgio Pia

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Guest Editor

Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Universita` degli Studi di Cagliari, via Marengo 2, 09123 Cagliari, Italy
Interests: nanostructured alloys; structural characterization; thermodynamic modelling
Special Issues, Collections and Topics in MDPI journals

Dr. E Chen

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Guest Editor

Architecture and Civil Engineering, Structural Engineering, Concrete Structures, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
Interests: chemo-mechanical coupled model for concrete durability; fractal dimensions of concrete pores; steel corrosion in fiber reinforced concrete; electrochemical measurement on steel corrosion; non-destructive measurement
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Cement-based materials are the most widely used materials in the world, apart from water and air. Cement-based materials have played a vital role in the development of the national economy. The microstructural investigation of cement-based materials has always been receiving the widespread attention of global scientists and engineers. In recent years, the application of fractal theory in the microstructure of cement-based materials has brought a new perspective to some properties (such as rheology, permeability, diffusivity and thermal transportation) of cement-based materials.

This Special Issue aims at demonstrating the state of the art in fractal-based approaches implemented in cement-based materials. We invite you to submit comprehensive review papers and original articles. This issue will cover topics of interest that include, but are not limited to, the following topics:

Fractal characterization of construction materials from the viewpoint of multi-scales;
Fractals combined with other theoretical, numerical and/or experimental methods, in the evaluation of mechanical performance/durability of cement-based materials;
Fractal approach to study the evolution of pore structure of hydrating cement-based materials;
Fractal approach to study the evolution of solid phase of hydrating cement-based materials;
Other fractal-based approaches in construction materials.

Authors are welcome to contact the Guest Editor (Dr. Shengwen Tang) to discuss ideas and suggest topics of interest relating to this Special Issue.

Dr. Shengwen Tang
Prof. Dr. Giorgio Pia
Dr. E Chen
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (13 papers)

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Editorial

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4 pages, 202 KiB

Open AccessEditorial

Editorial for Special Issue “Fractal and Fractional in Cement-Based Materials”

by Lei Wang, Shengwen Tang, Giorgio Pia and E Chen

Fractal Fract. 2022, 6(3), 144; https://doi.org/10.3390/fractalfract6030144 - 4 Mar 2022

Cited by 2 | Viewed by 1605

Abstract

Cement-based materials, including cement paste, mortar, and concrete, are the most widely used construction materials in the world [...] Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

Research

Jump to: Editorial, Review

17 pages, 2733 KiB

Open AccessArticle

Pore Structural and Fractal Analysis of the Effects of MgO Reactivity and Dosage on Permeability and F–T Resistance of Concrete

by Lei Wang, Xuefeng Song, Huamei Yang, Lei Wang, Shengwen Tang, Bo Wu and Wenting Mao

Fractal Fract. 2022, 6(2), 113; https://doi.org/10.3390/fractalfract6020113 - 15 Feb 2022

Cited by 50 | Viewed by 2497

Abstract

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. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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18 pages, 67591 KiB

Open AccessArticle

Segmentation of Concrete Cracks by Using Fractal Dimension and UHK-Net

by Qing An, Xijiang Chen, Haojun Wang, Huamei Yang, Yuanjun Yang, Wei Huang and Lei Wang

Fractal Fract. 2022, 6(2), 95; https://doi.org/10.3390/fractalfract6020095 - 9 Feb 2022

Cited by 40 | Viewed by 4026

Abstract

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%. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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20 pages, 4656 KiB

Open AccessArticle

Influence of MgO on the Hydration and Shrinkage Behavior of Low Heat Portland Cement-Based Materials via Pore Structural and Fractal Analysis

by Lei Wang, Xiao Lu, Lisheng Liu, Jie Xiao, Ge Zhang, Fanxing Guo and Li Li

Fractal Fract. 2022, 6(1), 40; https://doi.org/10.3390/fractalfract6010040 - 12 Jan 2022

Cited by 68 | Viewed by 4232

Abstract

Currently, low heat Portland (LHP) cement is widely used in mass concrete structures. The magnesia expansion agent (MgO) can be adopted to reduce the shrinkage of conventional Portland cement-based materials, but very few studies can be found that investigate the influence of MgO on the properties of LHP cement-based materials. In this study, the influences of two types of MgO on the hydration, as well as the shrinkage behavior of LHP cement-based materials, were studied via pore structural and fractal analysis. The results indicate: (1) The addition of reactive MgO (with a reactivity of 50 s and shortened as M50 thereafter) not only extends the induction stage of LHP cement by about 1–2 h, but also slightly increases the hydration heat. In contrast, the addition of weak reactive MgO (with a reactivity of 300 s and shortened as M300 thereafter) could not prolong the induction stage of LHP cement. (2) The addition of 4 wt.%–8 wt.% MgO (by weight of binder) lowers the mechanical property of LHP concrete. Higher dosages of MgO and stronger reactivity lead to a larger reduction in mechanical properties at all of the hydration times studied. M300 favors the strength improvement of LHP concrete at later ages. (3) M50 effectively compensates the shrinkage of LHP concrete at a much earlier time than M300, whereas M300 compensates the long-term shrinkage more effectively than M50. Thus, M300 with an optimal dosage of 8 wt.% is suggested to be applied in mass LHP concrete structures. (4) The addition of M50 obviously refines the pore structures of LHP concrete at 7 days, whereas M300 starts to refine the pore structure at around 60 days. At 360 days, the concretes containing M300 exhibits much finer pore structures than those containing M50. (5) Fractal dimension is closely correlated with the pore structure of LHP concrete. Both pore structure and fractal dimension exhibit weak (or no) correlations with shrinkage of LHP concrete. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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23 pages, 5917 KiB

Open AccessArticle

Effect of Chemical Composition of Fine Aggregate on the Frictional Behavior of Concrete–Soil Interface under Sulfuric Acid Environment

by Jie Xiao, Zhenming Xu, Yikang Murong, Lei Wang, Bin Lei, Lijing Chu, Haibo Jiang and Wenjun Qu

Fractal Fract. 2022, 6(1), 22; https://doi.org/10.3390/fractalfract6010022 - 31 Dec 2021

Cited by 25 | Viewed by 3296

Abstract

Through direct shear tests, this paper aimed to research the effect of fine marble aggregate on the shear strength and fractal dimension of the interface between soil and concrete corroded by sulfuric acid. More realistic concrete rough surfaces than the artificially roughened surfaces were formed by immersing four concrete plates in plastic buckets filled with sulfuric acid for different periods of time. The sand was adopted to imitate the soil. 3D laser scanner was employed to obtain the digital shapes of concrete plates subjected to sulfuric acid, and the rough surfaces were evaluated by fractal dimension. Large direct shear experiments were performed to obtain the curves of the interface shear stress and shear displacement between sand and corroded concrete plate. The method of data fitting was adopted to calculate the parameters of shear strength (i.e., friction angle and the cohesive) and the parameters of the Clough–Duncan hyperbolic model. The results indicated that as the corrosion days increased, the surface of the concrete plate became rougher, the surface fractal dimensions of the concrete corroded by sulfuric acid became bigger, and the interface friction angle became greater. The friction angle of the interface and the fractal dimensions of the surface of the concrete plate containing crushed gravel and marble sand were smaller than that of the concrete plate containing crushed gravel and river sand. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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18 pages, 5419 KiB

Open AccessArticle

Fractal Analysis on Pore Structure and Hydration of Magnesium Oxysulfate Cements by First Principle, Thermodynamic and Microstructure-Based Methods

by Jiasheng Huang, Wenwei Li, Desheng Huang, Lei Wang, E Chen, Chengyou Wu, Baoshan Wang, Hongyang Deng, Shengwen Tang, Yan Shi and Yang Li

Fractal Fract. 2021, 5(4), 164; https://doi.org/10.3390/fractalfract5040164 - 11 Oct 2021

Cited by 124 | Viewed by 3782

Abstract

Magnesium oxysulfate (MOS) cement is a typical eco-friendly cementitious material, which presents excellent performances. In this work, a novel multiscale modeling strategy is proposed to simulate the hydration and pore structure of MOS cement system. This work collected and evaluated the Gibbs free energy of formation for main hydrates and equilibrium constant of main reactions in MOS cement system based on a first principle calculation using Material Studio. Followingly, the equilibrium phase compositions of MOS cement system were simulated through PHREEQC to investigate the molar ratio dependence of equilibrium phase compositions. Results showed that large M (MgO/MgSO₄) was beneficial for the formation of 5Mg(OH)₂·MgSO₄·7H₂O (Phase 517) and large H (H₂O/MgSO₄) tended to decompose MOS cement paste and cause leaching. The microstructure-based method visualized the hydration status of MOS cement systems at initial and ultimate stages via MATLAB and the results showed that large M was significant to reduce porosity, and similar results for the case of small H. Fractal analysis confirms that fractal dimension of pore structure (D_f) was significantly decreased after the hydration of MOS and was positively correlated to the porosity of the paste. In addition, it can be referred that large M and small H were beneficial for modifying the microstructure of MOS paste by decreasing the value of D_f. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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15 pages, 5548 KiB

Open AccessArticle

May the Piezoresistivity of GNP-Modified Cement Mortar Be Related to Its Fractal Structure?

by Nanxi Dang, Jin Tao, Qiang Zeng and Weijian Zhao

Fractal Fract. 2021, 5(4), 148; https://doi.org/10.3390/fractalfract5040148 - 30 Sep 2021

Cited by 9 | Viewed by 2126

Abstract

High piezoresistivity of cement-based composites tuned by conductible fillers provides a feasible way to develop self-sensing smart structures and buildings. However, the microstructural mechanisms remain to be properly understood. In the present work, the piezoresistivity of cement mortar with different dosages of graphene nanoplatelets (GNPs) was investigated, and the microstructure was assessed by electron scanning microscopy (SEM) and mercury intrusion porosimetry (MIP). Two surface fractal models were introduced to interpret the MIP data to explore the multi-scale fractal structure of the GNP-modified cement mortars. Results show that the incorporation of GNPs into cement mortar can roughen the fracture surfaces due to the GNPs’ agglomeration. Gauge factor (GF) rises and falls as GNP content increases from 0% to 1% with the optimal piezoresistivity observed at GNP = 0.1% and 0.05%. The GF values of the optimum mortar are over 50 times higher than those of the reference mortar. Fractal dimensions in macro and micro fractal regions change with GNP content. Analysis shows that the fractal dimensions in micro region decrease first and then increase with the increase of GF values. GNPs not only impact the fractal structure of cement mortar, but also alter the tunneling and contact effects that govern the piezoresistivity of composite materials. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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17 pages, 5167 KiB

Open AccessArticle

Study on the Influence of Three Factors on Mass Loss and Surface Fractal Dimension of Concrete in Sulfuric Acid Environments

by Jie Xiao, Xiang Long, Long Li, Haibo Jiang, Yaowen Zhang and Wenjun Qu

Fractal Fract. 2021, 5(4), 146; https://doi.org/10.3390/fractalfract5040146 - 30 Sep 2021

Cited by 13 | Viewed by 2203

Abstract

When exposed to sulfuric acid environments, the service life of concrete structures would be reduced due to the high alkalinity of concrete. The influence of three factors including water/cement ratio, the pH value of the solution, and the chemical composition of the aggregate on the resistance of concrete subjected to sulfuric acid has been widely investigated by previous researchers. This paper aims to investigate the influence of these three factors on the durability evaluation indicators including mass loss and surface fractal dimension through orthogonal experiments, which has been reported rarely in previous research. Four combinations of coarse and fine aggregate including gravel and river sand, gravel and crushed marble sand, crushed marble stone and river sand, and crushed marble stone and marble sand were adopted, and three water/cement ratios including 0.35, 0.45, and 0.55 were selected, and the sulfuric acid solution pH values 0.95, 2, and 4 were chosen in this paper. The results showed that the larger the water/cement ratio, the smaller the mass loss and the surface fractal dimension of the specimens, and with the decrease of the pH value of the sulfuric acid solution, the mass loss and the surface fractal dimension of the specimens would be increased. The concrete specimen containing gravel and river sand had the greatest surface fractal dimension and greatest mass loss, while the concrete specimen containing crushed marble sand had a smaller surface fractal dimension and a smaller mass loss. The dominant and secondary order of three factors on mass loss and surface fractal dimension of concrete subjected to sulfuric acid was the pH value of the solution > the chemical composition of the aggregate > the water/cement ratio. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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23 pages, 7961 KiB

Open AccessArticle

Surface Cracking and Fractal Characteristics of Bending Fractured Polypropylene Fiber-Reinforced Geopolymer Mortar

by Li Li, Hai-Xin Sun, Yang Zhang and Bo Yu

Fractal Fract. 2021, 5(4), 142; https://doi.org/10.3390/fractalfract5040142 - 28 Sep 2021

Cited by 45 | Viewed by 2694

Abstract

Fiber is effective in restricting cracks and improving the toughness of geopolymer composites, but few studies have focused on the surface crack characteristics of fiber-reinforced geopolymer composites. In this paper, after flexural tests of polypropylene fiber-reinforced geopolymer mortar, the surface cracking image was collected by a digital camera and cracking information was extract by deep learning. Finally, the cracking and fractal characteristics were specifically discussed. The semantic segmentation network can accurately extract surface cracks for calculating various parameters. The results showed that the mean intersection over union (mIoU) and mean pixel accuracy (mPA) of the cracks are 0.8451 and 0.9213, respectively. Generally, the crack length, width, area, and fractal dimension of the specimen are all increased with the increase in the fiber volume fraction. These crack parameters grow rapidly when the fiber content is small, and the growth of the crack parameters gradually slows down as the fiber volume fraction increases to approximately 1.5%. The highest crack parameter values were found in the geopolymer mortar, with a 0.48 water–binder ratio and 12 mm fiber length. The variation of the bottom crack length and the side crack fractal dimension can be used to represent the overall crack variation patterns. Meanwhile, the crack parameters increase with the increased fiber factor in a quadratic function. Based on these crack parameters, the critical fiber factor and dense fiber factor of polypropylene fiber-reinforced geopolymer mortar were 200 and 550, respectively. They are greater than those of fiber-reinforced Portland cementitious composites. The influence of various crack parameters on the flexural strength is in the order of the crack area, width, length, and fractal dimension. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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26 pages, 10307 KiB

Open AccessArticle

Influence of Different Alkali Sulfates on the Shrinkage, Hydration, Pore Structure, Fractal Dimension and Microstructure of Low-Heat Portland Cement, Medium-Heat Portland Cement and Ordinary Portland Cement

by Yang Li, Hui Zhang, Minghui Huang, Haibo Yin, Ke Jiang, Kaitao Xiao and Shengwen Tang

Fractal Fract. 2021, 5(3), 79; https://doi.org/10.3390/fractalfract5030079 - 27 Jul 2021

Cited by 72 | Viewed by 3244

Abstract

In cement-based materials, alkalis mainly exist in the form of different alkali sulfates. In this study, the impacts of different alkali sulfates on the shrinkage, hydration, pore structure, fractal dimension and microstructure of low-heat Portland cement (LHPC), medium-heat Portland cement (MHPC) and ordinary Portland cement (OPC) are investigated. The results indicate that alkali sulfates magnify the autogenous shrinkage and drying shrinkage of cement-based materials with different mineral compositions, which are mainly related to different pore structures and hydration processes. LHPC has the lowest shrinkage. Otherwise, the effect of alkali sulfates on the autogenous shrinkage is more profound than that of drying shrinkage. Compared with the pore size distribution, the fractal dimension can better characterize the shrinkage properties of cement-based materials. It is noted that the contribution of K₂SO₄ (K alkali) to the promotion effect of shrinkage on cement-based materials is more significant than that of Na₂SO₄ (Na alkali), which cannot be ignored. The microstructure investigation of different cement-based materials by means of nuclear magnetic resonance (NMR), mercury intrusion porosimetry (MIP) and scanning electron microscope (SEM) shows that this effect may be related to the different pore structures, crystal forms and morphologies of hydration products of cement-based materials. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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19 pages, 10861 KiB

Open AccessArticle

Utilizing Fractals for Modeling and 3D Printing of Porous Structures

by AMM Sharif Ullah, Doriana Marilena D’Addona, Yusuke Seto, Shota Yonehara and Akihiko Kubo

Fractal Fract. 2021, 5(2), 40; https://doi.org/10.3390/fractalfract5020040 - 30 Apr 2021

Cited by 19 | Viewed by 13006

Abstract

Porous structures exhibiting randomly sized and distributed pores are required in biomedical applications (producing implants), materials science (developing cermet-based materials with desired properties), engineering applications (objects having controlled mass and energy transfer properties), and smart agriculture (devices for soilless cultivation). In most cases, a scaffold-based method is used to design porous structures. This approach fails to produce randomly sized and distributed pores, which is a pressing need as far as the aforementioned application areas are concerned. Thus, more effective porous structure design methods are required. This article presents how to utilize fractal geometry to model porous structures and then print them using 3D printing technology. A mathematical procedure was developed to create stochastic point clouds using the affine maps of a predefined Iterative Function Systems (IFS)-based fractal. In addition, a method is developed to modify a given IFS fractal-generated point cloud. The modification process controls the self-similarity levels of the fractal and ultimately results in a model of porous structure exhibiting randomly sized and distributed pores. The model can be transformed into a 3D Computer-Aided Design (CAD) model using voxel-based modeling or other means for digitization and 3D printing. The efficacy of the proposed method is demonstrated by transforming the Sierpinski Carpet (an IFS-based fractal) into 3D-printed porous structures with randomly sized and distributed pores. Other IFS-based fractals than the Sierpinski Carpet can be used to model and fabricate porous structures effectively. This issue remains open for further research. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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Review

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41 pages, 3869 KiB

Open AccessReview

Investigation and Application of Fractal Theory in Cement-Based Materials: A Review

by Lei Wang, Xiaoman Zeng, Huamei Yang, Xingdong Lv, Fanxing Guo, Yan Shi and Asad Hanif

Fractal Fract. 2021, 5(4), 247; https://doi.org/10.3390/fractalfract5040247 - 1 Dec 2021

Cited by 95 | Viewed by 5930

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. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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34 pages, 3351 KiB

Open AccessReview

Structure, Fractality, Mechanics and Durability of Calcium Silicate Hydrates

by Shengwen Tang, Yang Wang, Zhicheng Geng, Xiaofei Xu, Wenzhi Yu, Hubao A and Jingtao Chen

Fractal Fract. 2021, 5(2), 47; https://doi.org/10.3390/fractalfract5020047 - 17 May 2021

Cited by 109 | Viewed by 8736

Abstract

Cement-based materials are widely utilized in infrastructure. The main product of hydrated products of cement-based materials is calcium silicate hydrate (C-S-H) gels that are considered as the binding phase of cement paste. C-S-H gels in Portland cement paste account for 60–70% of hydrated products by volume, which has profound influence on the mechanical properties and durability of cement-based materials. The preparation method of C-S-H gels has been well documented, but the quality of the prepared C-S-H affects experimental results; therefore, this review studies the preparation method of C-S-H under different conditions and materials. The progress related to C-S-H microstructure is explored from the theoretical and computational point of view. The fractality of C-S-H is discussed. An evaluation of the mechanical properties of C-S-H has also been included in this review. Finally, there is a discussion of the durability of C-S-H, with special reference to the carbonization and chloride/sulfate attacks. Full article

(This article belongs to the Special Issue Fractal and Fractional in Cement-based Materials)

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