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Fractal Fract
Special Issues
Fractal Analysis and Its Applications in Rock Engineering
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Fractal Analysis and Its Applications in Rock Engineering

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

Deadline for manuscript submissions: 31 January 2025 | Viewed by 5264

Special Issue Editors

Dr. Lihai Tan

E-Mail Website
Guest Editor
School of Resource Environment and Safety Engineering, University of South China, Hengyang 412001, China
Interests: fractal analysis; rock mechanics; discreet numerical modelling; damage mechanics
Special Issues, Collections and Topics in MDPI journals
Dr. Xiaohan Yang

E-Mail Website
Guest Editor
1. School of Civil, Mining and Environmental Engineering, University of Wollongong, Wollongong 2522, Australia 2. School of Civil Engineering, The University of Queensland, Brisbane 4072, Australia
Interests: fractal analysis; rock mechanics; coal/rock burst; underground mining; geomechanics
Special Issues, Collections and Topics in MDPI journals
Dr. Gaofeng Liu

E-Mail Website
Guest Editor
1. School of Resources and Environment, Henan Polytechnic University, Jiaozuo 454003, China
2. Collaborative Innovation Center of Coalbed Methane and Shale Gas for Central Plains Economic Region, Henan Province, Henan Polytechnic University, Jiaozuo 454003, China
Interests: fractal characteristics; fuel; energy; geology; mining

Special Issue Information

Dear Colleagues,

In rock mechanics, fractal analysis is used to study the behavior of rock fractures and their properties, including size distribution, orientation, and connectivity. This allows researchers to better understand the mechanics of rock fractures and their impact on aspects of rock mass behavior, including deformation, stability, and permeability. Fractal analysis has also been applied to study the fragmentation of rocks, including the study of rock blasting and rock cutting. By analyzing the fractal dimensions of rock fragments, researchers can develop models that predict the size, distribution and shape of rock fragments after blasting, which is crucial for designing mining operations. The application of fractal analysis in rock mechanics and rock engineering has opened up new opportunities for understanding the mechanical behavior of rocks and rock masses at various scales and has the potential to improve the design and safety of rock engineering projects.

The scope of this Special Issue includes, but is not limited to, the following topics:

  • Fractal analysis of rock fractures and their properties, such as size distribution, orientation, and connectivity.
  • Fractal modeling and simulation of rock fragmentation processes, including the study of rock blasting and rock cutting.
  • Applications of fractal analysis in rock engineering, including the characterization of rock mass properties and the prediction of rock mass behavior.
  • Fractal analysis of geomechanical processes, such as faulting, folding, and deformation of rocks.
  • Fractal analysis of rock microstructures, including the study of grain size distribution and pore space characterization.

Dr. Lihai Tan
Dr. Xiaohan Yang
Dr. Gaofeng Liu
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.

Keywords

  • fractal analysis and modeling
  • fragmentation
  • rock mechanics
  • rock fractures
  • rock microstructures
  • rock engineering 
  • geomechanical processes
  • engineering application

Published Papers (6 papers)

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Research

13 pages, 12921 KiB  
Article
Fractal Evolution Characteristics on the Three-Dimensional Fractures in Coal Induced by CO2 Phase Transition Fracturing
by Zhen Zhang, Gaofeng Liu, Jia Lin, George Barakos and Ping Chang
Fractal Fract. 2024, 8(5), 273; https://doi.org/10.3390/fractalfract8050273 - 4 May 2024
Viewed by 324
Abstract
To analyze the transformed effect of three-dimensional (3D) fracture in coal by CO2 phase transition fracturing (CO2-PTF), the CO2-PTF experiment under a fracturing pressure of 185 MPa was carried out. Computed Tomography (CT) scanning and fractal theory were [...] Read more.
To analyze the transformed effect of three-dimensional (3D) fracture in coal by CO2 phase transition fracturing (CO2-PTF), the CO2-PTF experiment under a fracturing pressure of 185 MPa was carried out. Computed Tomography (CT) scanning and fractal theory were used to analyze the 3D fracture structure parameters. The fractal evolution characteristics of the 3D fractures in coal induced by CO2-PTF were analyzed. The results indicate that the CO2 phase transition fracturing coal has the fracture generation effect and fracture expansion-transformation effect, causing the maximum fracture length, fracture number, fracture volume and fracture surface area to be increased by 71.25%, 161.94%, 3970.88% and 1330.03%. The fractal dimension (DN) for fracture number increases from 2.3523 to 2.3668, and the fractal dimension (DV) for fracture volume increases from 2.8440 to 2.9040. The early dynamic high-pressure gas jet stage of CO2-PTF coal influences the fracture generation effect and promotes the generation of 3D fractures with a length greater than 140 μm. The subsequent quasi-static high-pressure gas stage influences the fracture expansion-transformation effect, which promotes the expansion transformation of 3D fractures with a length of less than 140 μm. The 140 μm is the critical value for the fracture expansion-transformation effect and fracture generation effect. Five indicators are proposed to evaluate the 3D fracture evolution in coal caused by CO2-PTF, which can provide theoretical and methodological references for the study of fracture evolution characteristics of other unconventional natural gas reservoirs and their reservoir stimulation. Full article
(This article belongs to the Special Issue Fractal Analysis and Its Applications in Rock Engineering)
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18 pages, 7062 KiB  
Article
Compressive Failure Characteristics of a Coal–Rock Combination at Different Angles: Experimental Study and Fractal Analysis
by Long Tang, Shihao Tu, Hongsheng Tu, Kaijun Miao, Wenlong Li, Hongbin Zhao, Jieyang Ma and Lei Zhang
Fractal Fract. 2024, 8(4), 240; https://doi.org/10.3390/fractalfract8040240 - 20 Apr 2024
Viewed by 464
Abstract
In order to explore the influence of dip angles on the deformation and failure of a coal–rock combination, uniaxial compression experiments were carried out on a coal–rock combination with different dip angles, and the acoustic emissions (hereinafter referred to as AE) responses during [...] Read more.
In order to explore the influence of dip angles on the deformation and failure of a coal–rock combination, uniaxial compression experiments were carried out on a coal–rock combination with different dip angles, and the acoustic emissions (hereinafter referred to as AE) responses during loading were collected. Based on the damage mechanics theory and fractal theory, the fractal dimensions of different damage degrees were calculated. The results show that, with the increase in the inclination angle, the compressive strength and elastic modulus of the coal–rock combination gradually decreased, while the AE ringing count gradually increased first and then decreased. At the initial loading stage of the specimen, the greater the damage degree of the coal–rock combination under the same strain condition, the larger the value of its overall fractal dimension. The AE fractal dimension of the coal–rock combination increases gradually between 10% and 20% of the damage degree. It suddenly decreased between 50% and 60%, then increased slightly before gradually decreasing to the minimum between 80% and 100%. The sudden decrease in fractal dimension, a slight increase, and then a continuous decrease can be used as the precursor information for the instability and failure of the coal–rock combination. Full article
(This article belongs to the Special Issue Fractal Analysis and Its Applications in Rock Engineering)
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15 pages, 5652 KiB  
Article
Experimental Study on the Butterfly Shape of the Plastic Zone around a Hole near Rock Failure
by Wenlong Zhang, Jiajia Yu, Jianju Ren, Chen Li and Ji Ma
Fractal Fract. 2024, 8(4), 215; https://doi.org/10.3390/fractalfract8040215 - 7 Apr 2024
Viewed by 564
Abstract
The precursor of rock failure around a hole has always been one of the research hotspots in the field of rock mechanics, and the distribution of the plastic zone is often adopted to reflect the location and form of rock failure. The shape [...] Read more.
The precursor of rock failure around a hole has always been one of the research hotspots in the field of rock mechanics, and the distribution of the plastic zone is often adopted to reflect the location and form of rock failure. The shape of the plastic zone around a hole before rock failure can guide the mechanism of and early warning methods for geotechnical engineering disasters, while previous theoretical research and numerical simulation results show that the shape of the plastic zone around the hole is butterfly shaped under specific stress, which is referred to as butterfly failure theory. Studies also indicate that the butterfly shape of the plastic zone around a hole is considered to be the main cause of many disasters, which signifies the importance of studying the morphology of the plastic zone near rock failure. Therefore, this study is committed to finding the specific shape of the plastic zone near rock failure through relatively accurate and a high number of AE event location results, and the final experimental results show that the plastic zone around the hole is basically a butterfly shape near rock failure. This study verifies the correctness of the butterfly failure theory and provides an important reference for the study of geotechnical engineering disaster mechanisms and monitoring methods. The fact that the plastic zone in the early stage of rock failure in this study tends to be butterfly shaped preliminarily indicates the fractal law of rock failure. In the moment before rock failure, the distribution of AE events is more regular, which leads to large-scale collapse type failure. Full article
(This article belongs to the Special Issue Fractal Analysis and Its Applications in Rock Engineering)
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15 pages, 5769 KiB  
Article
Influences of Different Acid Solutions on Pore Structures and Fractal Features of Coal
by Jingshuo Zhang, Xiaoming Ni, Xiaolei Liu and Erlei Su
Fractal Fract. 2024, 8(2), 82; https://doi.org/10.3390/fractalfract8020082 - 26 Jan 2024
Cited by 1 | Viewed by 849
Abstract
The effect of different acids on the pore structure and fractal characteristics of micropores and mesopores was determined with the help of low-temperature liquid nitrogen adsorption, X-ray diffraction, and the Frenkel–Halsey–Hill (FHH) model by using Yuwu coal as a sample and placing it [...] Read more.
The effect of different acids on the pore structure and fractal characteristics of micropores and mesopores was determined with the help of low-temperature liquid nitrogen adsorption, X-ray diffraction, and the Frenkel–Halsey–Hill (FHH) model by using Yuwu coal as a sample and placing it in acidic environments, such as HF, HCl, HNO3, and CH3COOH. The results show that the acidization effects of HF and CH3COOH are separately dominated by the micropore and mesopore formation effects, while HCl and HNO3 mainly play their roles in expanding mesopores. After acidization, the surface fractal dimensions D1 and D1′ of micropores and mesopores in coal are always negatively correlated with the total specific surface area SBET, specific surface area Smic of micropores, and specific surface area Smes of mesopores. After being acidized by HF, D2 is negatively correlated with the total volume Vtot and the corresponding micropore volume Vmic, while acidization with HCl and HNO3 leads to the opposite result. After being acidized by CH3COOH, D2 has a negative correlation with Vtot and a positive correlation with Vmic. The structural fractal dimensions D2′ of mesopores in samples acidized by HF and CH3COOH are positively correlated with both the volume Vtot and mesopore volume Vmes, while it is the opposite for samples acidized by HNO3. D2′ of coal samples acidized by HCl is negatively correlated with Vtot while positively correlated with Vmes. Full article
(This article belongs to the Special Issue Fractal Analysis and Its Applications in Rock Engineering)
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28 pages, 11882 KiB  
Article
A Binary Medium Constitutive Model for Frozen Solidified Saline Soil in Cold Regions and Its Fractal Characteristics Analysis
by Xinrui Kang, Hongbo Li, Gang Zhang, Sheng Li, Long Shan, Jing Zhao and Zhe Zhang
Fractal Fract. 2024, 8(1), 33; https://doi.org/10.3390/fractalfract8010033 - 2 Jan 2024
Cited by 1 | Viewed by 1097
Abstract
In addressing the issue of strength degradation in saline soil foundations under the salt-freeze coupling effects, a binary medium constitutive model suitable for un-solidified and solidified frozen saline soil is proposed considering both bonding and friction effects. To verify the validity of the [...] Read more.
In addressing the issue of strength degradation in saline soil foundations under the salt-freeze coupling effects, a binary medium constitutive model suitable for un-solidified and solidified frozen saline soil is proposed considering both bonding and friction effects. To verify the validity of the constitutive model, freezing triaxial tests are carried out under different negative temperatures, confining pressures, and water contents. The pore structure and fractal characteristics of saline soil are analyzed using mercury intrusion porosimetry (MIP) and the fractal dimension D qualitatively and quantitatively, which shed light on the strength enhancement mechanism during the solidification of frozen saline soils. The results show that the constitutive model for frozen solidified saline soil based on binary medium theory aptly captures the stress–strain relationship before and after the solidification of frozen saline soil. The stress–strain relationship of frozen saline soil before and after solidification can be delineated into linear elasticity, elastoplasticity, and strain-hardening or -softening phases. Each of these phases can be coherently interpreted through the binary medium constitutive model. The un-solidified and solidified frozen both show pronounced fractal characteristics in fractal analysis. Notably, the fractal dimension D of the solidified saline soil exhibits a significant increase compared to that of un-solidified ones. In Regions I and III, the values of D for solidified saline soil are lower than those for untreated saline soil, which is attributed to the filling effect of hydration products and un-hydrated solidifying agent particles. In Region II, the fractal dimensions DMII and DNII of the solidified saline soil exhibit a “non-physical state”, which is mainly caused by the formation of a significant number of inkpot-type pores due to the binding of soil particles by hydration products. Full article
(This article belongs to the Special Issue Fractal Analysis and Its Applications in Rock Engineering)
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25 pages, 7143 KiB  
Article
Energy Transfer and Destabilizing Impulse Inducing Mechanism of Coal–Rock System in Roadway through Coal Seam in Deep Zone
by Jiazhuo Li, Wei Zhou, Jiaqi Chu, Wentao Ren, Linming Dou and Shikang Song
Fractal Fract. 2023, 7(7), 550; https://doi.org/10.3390/fractalfract7070550 - 16 Jul 2023
Cited by 1 | Viewed by 946
Abstract
Aiming at the problem of the unclear rock burst generation mechanism and anti-impact measures of a large roadway through a coal seam in a deep panel area, taking the rock burst of a large roadway in the first panel area of Gaojiapu Coal [...] Read more.
Aiming at the problem of the unclear rock burst generation mechanism and anti-impact measures of a large roadway through a coal seam in a deep panel area, taking the rock burst of a large roadway in the first panel area of Gaojiapu Coal Mine as the engineering background, this paper adopts the comprehensive research methods of theoretical analysis, experiments, numerical simulation, fragmentation fractal analysis, and field monitoring, to discuss the mechanical characteristics of the loading process of the assemblage and the energy transfer law and its difference in the deformation and failure process. The possibility and strength of the impact failure of coal under the grip of rock masses with different stiffness are related to the γ value. The smaller the γ value is, the higher the impact possibility is, and the more severe the impact degree is. The assemblage under the grip of soft rock is more prone to system instability. Energy relief and impact reduction are adopted to reduce the post-peak stiffness and elastic strain energy of the coal body in a short distance, avoid the energy transfer and concentration of the roadway surrounding the rock system under the disturbance of a long-distance dynamic load, and reduce the likelihood of impact pressure occurring and the extent to which an impact manifests. Full article
(This article belongs to the Special Issue Fractal Analysis and Its Applications in Rock Engineering)
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