Editorial

4 pages, 195 KiB

Open AccessEditorial

Investigation and Application of Fractals in Civil Engineering Materials

by Lei Wang and Shengwen Tang

Fractal Fract. 2023, 7(5), 369; https://doi.org/10.3390/fractalfract7050369 - 29 Apr 2023

Viewed by 1011

Fractals is a new branch of nonlinear science that was established in the 1970s, focusing on irregularities, haphazard phenomena and self-similarities in nature [...] Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

Research

Jump to: Editorial

15 pages, 8254 KiB

Open AccessArticle

Mechanical Behaviors and Acoustic Emission Fractal Characteristics of Bump-Prone Coal under Different Loading Rates

by Bin Liu, Xiang Sun, Chunwei Ling, Zujun Huang and Hongwei Zhang

Fractal Fract. 2023, 7(1), 45; https://doi.org/10.3390/fractalfract7010045 - 30 Dec 2022

Cited by 3 | Viewed by 1006

Abstract

Coal and rock dynamic disasters occur frequently in deep coal mining. The loading rate affects the mechanical properties and behaviors. Uniaxial compression acoustic emission (AE) tests of bump-prone coal under various loading rates were carried out, and the mechanical properties, AE spatiotemporal evolution, [...] Read more.

Coal and rock dynamic disasters occur frequently in deep coal mining. The loading rate affects the mechanical properties and behaviors. Uniaxial compression acoustic emission (AE) tests of bump-prone coal under various loading rates were carried out, and the mechanical properties, AE spatiotemporal evolution, and spatial fractal characteristics were analyzed. The experimental results indicate that the uniaxial compressive strength is positively related to the loading rate, and the elastic modulus increases before decreasing with the loading rate. The failure strain is positively related to the loading rate, and the percentage of the compaction phase relative to the pre-peak phase decreases with the loading rate. The hit rate, absolute energy, AE events, and amplitude evolution of coal samples under various loading rates are the same, and the maximum of AE absolute energy and hit rate is positively related to the loading rate. The spatial evolution of AE events of coal samples under various loading rates is the same, showing a “slow increase → slow increase → fast increase → rapid increase → slow increase” trend. The spatial fractal dimension ranges from 2.1 to 2.9, and the evolution of coal samples under various loading rates is the same, exhibiting a downward trend. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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15 pages, 4670 KiB

Open AccessArticle

Application of Fractal to Evaluate the Drying Shrinkage Behavior of Soil Composites from Recycled Waste Clay Brick

by Xiaozheng Zhao, Lingchen Li, Binbin Yang and Changde Yang

Fractal Fract. 2023, 7(1), 25; https://doi.org/10.3390/fractalfract7010025 - 26 Dec 2022

Cited by 3 | Viewed by 1240

Abstract

Soil drying cracking is the most common natural phenomenon affecting soil stability. Due to the complexity of the geometric shapes of soil cracks during the cracking process, it has become a major problem in engineering science. The extremely irregular and complex crack networks [...] Read more.

Soil drying cracking is the most common natural phenomenon affecting soil stability. Due to the complexity of the geometric shapes of soil cracks during the cracking process, it has become a major problem in engineering science. The extremely irregular and complex crack networks formed in civil engineering materials can be quantitatively investigated using fractal theory. In this paper, fractal dimension is proposed to characterize the drying cracking characteristics of composite soil by adding recycled waste brick micro-powder. At the same time, the concept of the probability entropy of cracking is introduced to quantify the ordered state of crack development. Correspondingly, the endpoint value of probability entropy was solved mathematically, and the meaning of the probability entropy of cracking was clarified. In this study, the fracture fractal characteristics of composite soil mixed with different materials were first investigated. Then, five groups of composite soil-saturated muds with added recycled waste brick micro-powder of different contents were prepared in the laboratory. Using the evaporation test under constant temperature and humidity, the change rules of the fractal dimensions, probability entropy, crack ratios, and water contents of cracks during the cracking process of the soil samples were obtained. The results show that: (1) on the whole, the fractal dimensions of the soil samples added with recycled waste brick micro-powder of different contents increased over time, and the fractal dimensions of the soil samples without recycled waste brick micro-powder were obviously larger than those of the soil samples with recycled waste brick micro-powder. With the increase in the content of recycled waste brick micro-powder, the maximum fractal dimension decreased in turn. The maximum fractal dimensions of the five groups of soil samples were 1.74, 1.68, 1.62, 1.57, and 1.45. (2) The change trends of the probability entropy and fractal dimensions were similar; both of them showed an upward trend over time, and the probability entropy of the soil samples without recycled waste brick micro-powder was greater than that of the soil samples with recycled waste brick micro-powder. With the increase in the contents of recycled waste brick micro-powder, the probability entropy decreased in turn. The maximum values of the crack probability entropy of the five groups of soil samples were 0.99, 0.92, 0.87, 0.83, and 0.80. (3) Under the action of continuous evaporation, the moisture contents of the soil samples gradually decreased over time, while the crack ratios increased over time. To sum up, both from the perspective of the development process of the cracks of the soil samples and from the perspective of the final stable crack networks of the soil samples, the geometric shapes of the cracks of the soil samples without recycled waste brick micro-powder were the most complex. With the increase in the content of recycled waste brick micro-powder, the fractal characteristics of the cracks gradually changed from complex to simple. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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17 pages, 7352 KiB

Open AccessArticle

Seepage-Fractal Characteristics of Fractured Media Rock Materials Due to High-Velocity Non-Darcy Flow

by Xiaoming Zhao, Binbin Yang, Yulong Niu and Changde Yang

Fractal Fract. 2022, 6(11), 685; https://doi.org/10.3390/fractalfract6110685 - 18 Nov 2022

Cited by 1 | Viewed by 1191

Abstract

Under the influence of internal and external factors, a fracture network is easily generated in concrete and rock, which seriously endangers project safety. Fractal theory can be used to describe the formation and development of the fracture network and characterize its structure. Based [...] Read more.

Under the influence of internal and external factors, a fracture network is easily generated in concrete and rock, which seriously endangers project safety. Fractal theory can be used to describe the formation and development of the fracture network and characterize its structure. Based on the flow balance in the node balance field, Forchheimer’s law is introduced to derive the control equation of high-velocity non-Darcy flow in the fracture network. The fracture network is established according to the geological parameters of Sellafield, Cumbria, England. A total of 120 internal fracture networks are intercepted according to 10 dimensions (1 m, 2 m, …, 10 m) and 12 directions (0°, 30°, …, 330°). The fractal dimension, equivalent hydraulic conductivity (K), and equivalent non-Darcy coefficient (

β

) of the fracture network are calculated, and the influence of the fractal dimension on K and

β

is studied. The results indicate that the fractal dimension of the fracture network has a size effect; with the increase in the size, the fractal dimension of the fracture network undergoes three stages: rapid increase, slow increase, and stabilization. In the rapid increase stage, K and

β

do not exist. In the slow increase stage, K exists and is stable, and

β

does not exist. In the stabilization stage, K and

β

both exist and are stable. The principal axes of the fitted seepage ellipses of K and

β

are orthogonal, and the main influencing factors are the direction and continuity of the fracture. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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15 pages, 3296 KiB

Open AccessArticle

Fractal Characteristics of Geopolymer Mortar Containing Municipal Solid Waste Incineration Fly Ash and Its Correlations to Pore Structure and Strength

by Peng Zhang, Xu Han, Jinjun Guo and Hongsen Zhang

Fractal Fract. 2022, 6(11), 676; https://doi.org/10.3390/fractalfract6110676 - 15 Nov 2022

Cited by 13 | Viewed by 1282

Abstract

Compression and mercury intrusion porosimetry (MIP) tests were conducted to analyze the effect of municipal solid waste incineration fly ash (MSWIFA) content on the mechanical performance and pore structure of geopolymer mortar. The MSWIFA weight contents were 0%, 5%, 15%, 25%, and 35% [...] Read more.

Compression and mercury intrusion porosimetry (MIP) tests were conducted to analyze the effect of municipal solid waste incineration fly ash (MSWIFA) content on the mechanical performance and pore structure of geopolymer mortar. The MSWIFA weight contents were 0%, 5%, 15%, 25%, and 35% and the pore diameter distribution, specific surface area, and pore volume were considered to assess the pore structure of the geopolymer mortars. The popular fractal model was used to investigate the fractal features of the geopolymer mortars. Additionally, mathematical models of fractal dimension with pore structural parameters and compressive strength were established. The results showed that the compressive strength of geopolymer mortars decreased while the total pore volume and total specific surface area of mortars increased with the increase in MSWIFA content. As the MSWIFA content increased, the harmless pores (pore diameter < 20 nm) were refined. Specifically, the pores with a diameter of 5–10 nm increased in number but the pores with a diameter of 10–20 nm decreased in number with the increase in MSWIFA content. The pore structure in the mortars showed scale-dependent fractal characteristics. All fractal curves were divided into four segments according to the pore diameter, namely, Region I (<20 nm), Region II (20–50 nm), Region III (50–200 nm), and Region IV (>200 nm). The surface fractal dimension (

D_{S}

) in Region I and Region IV was between 2 and 3. However, the

D_{S}

in Region II and Region III was greater than 3, indicating the pores in Region II and Region III were non-physical according to the surface geometry because of the presence of ink bottle pores which distorted the result of the MIP. The complexity of pores in Region I and Region IV was reduced by the addition of MSWIFA. The

D_{S}

is a comprehensive parameter that well describes the spatial and morphological distribution of pores in geopolymer mortars and exhibited a good correlation with the specific surface area, pore volume, and compressive strength. A mathematical model based on the

D_{S}

was established to predict the compressive strength of the geopolymer mortar containing MSWIFA. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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12 pages, 1600 KiB

Open AccessArticle

Influence of Geotextile Materials on the Fractal Characteristics of Desiccation Cracking of Soil

by Binbin Yang, Shichong Yuan, Zhenzhou Shen and Xiaoming Zhao

Fractal Fract. 2022, 6(11), 628; https://doi.org/10.3390/fractalfract6110628 - 28 Oct 2022

Cited by 7 | Viewed by 1204

Abstract

In recent years, the irregular cracks formed during the damage evolution of civil engineering materials have been able to be quantitatively described by using fractals. In this study, the fractal characteristics of the desiccation cracking of soil were investigated under different substrate contact [...] Read more.

In recent years, the irregular cracks formed during the damage evolution of civil engineering materials have been able to be quantitatively described by using fractals. In this study, the fractal characteristics of the desiccation cracking of soil were investigated under different substrate contact and permeability conditions through a natural drying test in the laboratory. Three kinds of base contact conditions of soil, namely, grease, geomembrane, and geotextile, were designed, and two samples for each contact condition, including one parallel sample, were used. The continuous drying experiment was carried out at a constant ambient temperature. The crack morphology under different spacings was analyzed quantitatively using digital image processing technology. The fractal dimensions of three soil substrate contact conditions (grease, geomembranes, and geotextiles) were between 1.238 and 1.93. When the crack network on the soil surface stops developing, the fractal dimensions under the three experimental conditions are 1.88, 1.93 and 1.79, respectively. In the final state of crack development, the crack intensity factor of the sample with grease at the bottom is 2.99% and 4.02% higher than that of the sample with geomembranes and geotextiles at the bottom, respectively. The residual water contents of the samples with bottom contact conditions of grease, geomembrane, and geotextile increase successively, which are 3.12%, 5.76% and 9.71%, respectively. The effects of interface friction and permeability on soil cracking behavior are analyzed, and the evolution characteristics and formation mechanisms of cracks in soil are revealed. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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20 pages, 6495 KiB

Open AccessArticle

Strength Analysis of Cement Mortar with Carbon Nanotube Dispersion Based on Fractal Dimension of Pore Structure

by Jinjun Guo, Yanling Yan, Juan Wang and Yaoqun Xu

Fractal Fract. 2022, 6(10), 609; https://doi.org/10.3390/fractalfract6100609 - 19 Oct 2022

Cited by 4 | Viewed by 1410

Abstract

Carbon nanotubes (CNTs) are considered among the ideal modifiers for cement-based materials. This is because CNTs can be used as a microfiber to compensate for the insufficient toughness of the cement matrix. However, the full dispersion of CNTs in cement paste is difficult [...] Read more.

Carbon nanotubes (CNTs) are considered among the ideal modifiers for cement-based materials. This is because CNTs can be used as a microfiber to compensate for the insufficient toughness of the cement matrix. However, the full dispersion of CNTs in cement paste is difficult to achieve, and the strength of cement material can be severely degraded by the high air-entraining property of CNT dispersion. To analyze the relationship between the gas entrainment by CNT dispersion and mortar strength, this study employed data obtained from strength and micropore structure tests of CNT dispersion-modified mortar. The fractal dimensions of the pore volume and pore surface, as well as the box-counting dimension of the pore structure, were determined according to the box-counting dimension method and Menger sponge model. The relationship between the fractal dimensions of the pore structure and mortar strength was investigated by gray correlation. The results showed that the complexity of the pore structure could be accurately reflected by fractal dimensions. The porosity values of mortar with 0.05% and 0.5% CNT content were 15.5% and 43.26%, respectively. Moreover, the gray correlation between the fractal dimension of the pore structure and strength of the CNT dispersion-modified mortar exceeded 0.95. This indicated that the pore volume distribution, roughness, and irregularity of the pore inner surface were the primary factors influencing the strength of CNT dispersion-modified mortar. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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14 pages, 8554 KiB

Open AccessArticle

Fractal Dimension Analysis of Structure and Bending Strength of Porous Alumina Prepared Using Starch and Carbon Fiber as Pore-Forming Agents

by Chang Chen, Xuecheng Ding, Yubin Wang, Zhixing Luo and Peiyu Zhai

Fractal Fract. 2022, 6(10), 574; https://doi.org/10.3390/fractalfract6100574 - 09 Oct 2022

Cited by 5 | Viewed by 1320

Abstract

Porous alumina was prepared via a sacrificial template method using alumina as the matrix and starch and carbon fibers as the pore-forming agents. After sintering, no residual pore-forming agents were present. The density, porosity, and pore structure of the samples were measured using [...] Read more.

Porous alumina was prepared via a sacrificial template method using alumina as the matrix and starch and carbon fibers as the pore-forming agents. After sintering, no residual pore-forming agents were present. The density, porosity, and pore structure of the samples were measured using the Archimedes’ method and mercury intrusion porosimetry (MIP). The results showed that the pore size distribution of porous alumina was double-peak when the content of the pore-forming agent was 20, 30, or 50 vol.%, but was single-peak when the content was 40 vol.%. A fractal model based on the measured MIP data was used to calculate and evaluate the fractal dimension (D_s) of porous alumina. The D_s values decreased with an increase in the pore-forming agent content. Furthermore, D_s was negatively correlated with porosity, most probable pore size, and median pore diameter and positively correlated with the bending strength of porous alumina. Since porous alumina has obvious fractal characteristics, the fractal theory can be used to quantitatively describe its complex distribution. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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16 pages, 6505 KiB

Open AccessArticle

Carbon Fibers and Graphite as Pore-Forming Agents for the Obtention of Porous Alumina: Correlating Physical and Fractal Characteristics

by Litong Fang, Chang Chen and Yubin Wang

Fractal Fract. 2022, 6(9), 501; https://doi.org/10.3390/fractalfract6090501 - 06 Sep 2022

Cited by 4 | Viewed by 1338

Abstract

Porous alumina ceramics with different porosities were prepared via atmospheric pressure sintering using a sacrificial template method with alumina powder as the raw material and carbon fiber (CF) and graphite as pore-forming agents. The effects of the contents and ratios of the pore-forming [...] Read more.

Porous alumina ceramics with different porosities were prepared via atmospheric pressure sintering using a sacrificial template method with alumina powder as the raw material and carbon fiber (CF) and graphite as pore-forming agents. The effects of the contents and ratios of the pore-forming agents and the aspect ratios of CF on the microstructure, mechanical properties, pore size, and pore-size distribution of the porous alumina samples were investigated. In addition, the surface fractal dimension (D_s) of porous alumina samples with different pore-forming agents was evaluated based on the mercury intrusion porosimetry data. The pore-size distribution of the prepared porous alumina samples showed single, double, or multiple peaks. The pore structure of the samples maintained the fibrous shape of the original CF and the flake morphology of graphite with a uniform pore-size distribution, but the pore structure and morphology were different. With the increase in the content of the pore-forming agent, the porosity of the samples gradually increased to a maximum of 63.2%, and the flexural strength decreased to a minimum of 12.36 MPa. The pore structure of the porous alumina samples showed obvious fractal characteristics. D_s was closely related to the pore structure parameters of the samples when the content of the pore-forming agent was 70 vol.%. It decreased with an increase in the sample porosity, most probable pore size and median pore size, but increased with an increase in the sample flexural strength. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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14 pages, 1534 KiB

Open AccessArticle

The Influence of Fly Ash Dosages on the Permeability, Pore Structure and Fractal Features of Face Slab Concrete

by Lei Wang, Shihua Zhou, Yan Shi, Yajun Huang, Feng Zhao, Tingting Huo and Shengwen Tang

Fractal Fract. 2022, 6(9), 476; https://doi.org/10.3390/fractalfract6090476 - 28 Aug 2022

Cited by 40 | Viewed by 1737

Abstract

Concrete-face slabs are the primary anti-permeability structures of the concrete-face rockfill dam (CFRD), and the resistance of face slab concrete to permeability is the key factor affecting the operation and safety of CFRDs. Herein, the influences of five fly ash dosages (namely 10%, [...] Read more.

Concrete-face slabs are the primary anti-permeability structures of the concrete-face rockfill dam (CFRD), and the resistance of face slab concrete to permeability is the key factor affecting the operation and safety of CFRDs. Herein, the influences of five fly ash dosages (namely 10%, 20%, 30%, 40% and 50%) on the permeability property of face slab concretes were investigated. Moreover, the difference in the permeability caused by the fly ash dosage variations is revealed in terms of the pore structure and fractal theory. The results illustrate that: (1) The inclusion of 10–50% fly ash lowered the compressive strength of face slab concretes before 28 days of hydration, whereas it contributed to the 180-day strength increment. (2) The incorporation of 10–50% fly ash raised the average water-seepage height (D_m) and the relative permeability coefficient (K_r) of the face slab concrete by about 14–81% and 30–226% at 28 days, respectively. At 180 days, the addition of fly ash improved the 180-day impermeability by less than 30%. (3) The permeability of face slab concretes is closely correlated with their pore structures and D_s. (4) The optimal fly ash dosage in terms of the long-term impermeability and pore refinement of face slab concretes is around 30%. Nevertheless, face slab concretes containing a high dosage of fly ash must be cured for a relatively long period before they can withstand high water pressure. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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13 pages, 2839 KiB

Open AccessArticle

Surface Cracking and Fractal Characteristics of Cement Paste after Exposure to High Temperatures

by Li Li, Yang Zhang, Yuqiong Shi, Zhigang Xue and Mingli Cao

Fractal Fract. 2022, 6(9), 465; https://doi.org/10.3390/fractalfract6090465 - 25 Aug 2022

Cited by 23 | Viewed by 1500

Abstract

Destruction pattern analysis of building materials subjected to fire provide the basis for strengthening, restoring the bearing capacity, and optimizing the function of the building structure. The surface cracking and fractal characteristics of calcium carbonate whisker-reinforced cement pastes subjected to high temperatures were [...] Read more.

Destruction pattern analysis of building materials subjected to fire provide the basis for strengthening, restoring the bearing capacity, and optimizing the function of the building structure. The surface cracking and fractal characteristics of calcium carbonate whisker-reinforced cement pastes subjected to high temperatures were studied herein. The test results showed that at 400 °C, the surface crack area, length, and fractal dimension of cement pastes specimen increases from 0 to 35 mm², 100 mm, and 1.0, respectively, due to the increase of vapor pressure. When the temperature is above 900 °C, the calcium carbonate whisker (CW) and other hydration products in the specimen begin to decompose, causing the surface crack area, length, and fractal dimension of the cement paste specimen to increase from 0 to 120 mm², 310 mm, and 1.2, respectively. Compared with the length and width of cracks, the area, and fractal dimension of cracks are less affected by the size and shape of specimen. This paper uses image processing methods to analyze the cracking patterns and fractal characteristics of specimens after high-temperature treatment. The aim is to elucidate the quantitative relationship between concrete material, temperature, and cracking characteristics, providing theoretical basis for structural evaluation after exposure to high temperature. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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16 pages, 16461 KiB

Open AccessArticle

Fractal Analysis of Porous Alumina and Its Relationships with the Pore Structure and Mechanical Properties

by Xufu Wang, Chang Chen and Yubin Wang

Fractal Fract. 2022, 6(8), 460; https://doi.org/10.3390/fractalfract6080460 - 21 Aug 2022

Cited by 7 | Viewed by 1379

Abstract

Porous alumina was prepared by the sacrificial template approach using 30 vol.%, 50 vol.%, and 70 vol.% of carbon fibers and graphite as pore formers. In order to determine the pore size distribution, porosity, most probable pore size, and median pore size, a [...] Read more.

Porous alumina was prepared by the sacrificial template approach using 30 vol.%, 50 vol.%, and 70 vol.% of carbon fibers and graphite as pore formers. In order to determine the pore size distribution, porosity, most probable pore size, and median pore size, a mercury intrusion porosimeter (MIP) was used. The surface fractal dimensions (D_s) of porous alumina with various pore formers were assessed based on MIP data. The findings revealed that the pore size distribution of the prepared porous alumina was either bimodal or trimodal at 50 vol.% of the pore formers, and unimodal at 30 vol.% and 70 vol.% of the pore formers in the raw materials. The porous alumina’s pore structure and morphology varied depending on the volume content of the pore formers and their shapes. The porosity and pore size of the porous alumina increased with the increase in carbon fiber content because the carbon fiber was unfavorable to the densification of the initial billet before sintering. After sintering, there were no residual pore formers other than alumina in the samples. The pore structure of the porous alumina samples showed prominent fractal characteristics, and its D_S decreased with the increase in the pore former content. The samples’ D_s was highly negatively correlated with the pore structure parameters, and was positively correlated with the flexural strength. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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18 pages, 4948 KiB

Open AccessArticle

Fractal Analysis on Pore Structure and Modeling of Hydration of Magnesium Phosphate Cement Paste

by Yuxiang Peng, Shengwen Tang, Jiasheng Huang, Can Tang, Lei Wang and Yufei Liu

Fractal Fract. 2022, 6(6), 337; https://doi.org/10.3390/fractalfract6060337 - 17 Jun 2022

Cited by 81 | Viewed by 2977

Abstract

Magnesium phosphate cement (MPC) paste is hardened by the acid–base reaction between magnesium oxide and phosphate. This work collects and evaluates the thermodynamic data at 25 °C and a pressure of 0.1 MPa and establishes the hydration reaction model of MPC pastes. The [...] Read more.

Magnesium phosphate cement (MPC) paste is hardened by the acid–base reaction between magnesium oxide and phosphate. This work collects and evaluates the thermodynamic data at 25 °C and a pressure of 0.1 MPa and establishes the hydration reaction model of MPC pastes. The influence of the magnesium–phosphorus molar (M/P) ratio and water-to-binder (W/B) ratio on the hydration product is explored by the thermodynamic simulation. Following this, the initial and ultimate states of the hydration state of MPC pastes are visualized, and the porosity of different pastes as well as fractal analysis are presented. The result shows that a small M/P ratio is beneficial for the formation of main hydration products. The boric acid acts as a retarder, has a significant effect on lowering the pH of the paste, and slows down the formation of hydration products. After the porosity comparison, it can be concluded that the decreasing of M/P and W/B ratios helps reduce porosity. In addition, the fractal dimension D_f of MPC pastes is positively proportional to the porosity, and small M/P ratios as well as small W/B ratios are beneficial for reducing the D_f of MKPC pastes. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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20 pages, 3451 KiB

Open AccessArticle

Effects of Fly Ash Dosage on Shrinkage, Crack Resistance and Fractal Characteristics of Face Slab Concrete

by Lei Wang, Zhiqiang Yu, Bo Liu, Feng Zhao, Shengwen Tang and Minmin Jin

Fractal Fract. 2022, 6(6), 335; https://doi.org/10.3390/fractalfract6060335 - 16 Jun 2022

Cited by 53 | Viewed by 2985

Abstract

The crack resistance of face slab concretes to various shrinkages is crucial for the structural integrity and the normal operation of concrete-faced rockfill dams (CFRDs). In this work, the effects of fly ash with four dosages (i.e., 10%, 20%, 30% and 40%) on [...] Read more.

The crack resistance of face slab concretes to various shrinkages is crucial for the structural integrity and the normal operation of concrete-faced rockfill dams (CFRDs). In this work, the effects of fly ash with four dosages (i.e., 10%, 20%, 30% and 40%) on the drying shrinkage, autogenous shrinkage and the cracking resistance of face slab concrete were studied. Besides, the difference in shrinkage behavior due to fly ash addition was revealed from the viewpoint of the pore structure and fractal dimension of the pore surface (D_s). The findings demonstrate that (1) the incorporation of 10–40% fly ash could slightly reduce the drying shrinkage by about 2.2–13.5% before 14 days of hydration, and it could reduce the drying shrinkage at 180 days by about 5.1–23.2%. By contrast, the fly ash addition could markedly reduce the autogenous shrinkage at early, middle and long-term ages. (2) Increasing fly ash dosage from 0 to 40% considerably improves the crack resistance of concrete to plastic shrinkage. Nevertheless, the increase in fly ash dosage increases the drying-induced cracking risk under restrained conditions. (3) The pore structures of face slab concrete at 3 and 28 days become coarser with the increase in fly ash dosage up to 40%. At 180 days, the pore structures become more refined as the fly ash dosage increases to 30%; however, this refinement effect is not as appreciable as the fly ash dosage increases from 30% to 40%. (4) The D_s of face slab concrete is closely related with the concrete pore structures. The D_s of face slab concrete at a. late age increases from 2.902 to 2.946 with increasing of the fly ash dosage. The pore structure and D_s are closely correlated with the shrinkage of face slab concrete. (5) The fly ash dosage around 30% is optimal for face slab concretes in terms of lowering shrinkage and refining the pore structures, without compromising much mechanical property. However, the face slab concretes with a large fly ash dosage should be well cured under restrained and evaporation conditions at an initial hydration age. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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15 pages, 3334 KiB

Open AccessArticle

Experimental Investigation of the Relationship between Surface Crack of Concrete Cover and Corrosion Degree of Steel Bar Using Fractal Theory

by Weiwen Li, Meizhong Wu, Tiansheng Shi, Pengfei Yang, Zejie Pan, Wei Liu, Jun Liu and Xu Yang

Fractal Fract. 2022, 6(6), 325; https://doi.org/10.3390/fractalfract6060325 - 12 Jun 2022

Cited by 8 | Viewed by 1547

Abstract

Conventionally, crack width is used to assess the corrosion level, whereas other important characteristics such as the variation in crack width at different locations on the surface are disregarded. These important characteristics of surface crack can be described comprehensively using the fractal theory [...] Read more.

Conventionally, crack width is used to assess the corrosion level, whereas other important characteristics such as the variation in crack width at different locations on the surface are disregarded. These important characteristics of surface crack can be described comprehensively using the fractal theory to facilitate the assessment of the corrosion level. In this study, the relationship between steel corrosion and the fractal characterization of concrete surface cracking is investigated. Reinforced concrete prisms with steel bars of different diameters and with different corrosion rates were evaluated. High-resolution images of cracks on the surfaces of these specimens were captured and processed to obtain their fractal dimensions. Finally, a relationship between the fractal dimension, steel bar diameter, and the corrosion rate is established. The results show that the fractal dimension is associated closely with the corrosion rate and steel bar diameter. This study provides new ideas for evaluating corroded reinforced concrete structures. Full article

(This article belongs to the Special Issue Investigation and Application of Fractals in Civil Engineering Materials)

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