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Fractal Fract
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Applications of Fractal Analysis in Underground Engineering, Second Edition
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Applications of Fractal Analysis in Underground Engineering, Second Edition

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

Deadline for manuscript submissions: 31 July 2026 | Viewed by 4296

Special Issue Editors

Prof. Dr. Shihao Tu

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Guest Editor
Key Laboratory of Deep Coal Resource Mining (Ministry of Education of China), School of Mines, China University of Mining and Technology, Xuzhou 221116, China
Interests: fractal theory; fractal analysis; fractal characteristics; disaster prevention and control in coal mining; theories and methods in mineral exploitation; intelligent mining; mining planning and sustainability
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Lei Zhang

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Guest Editor
School of Mines, China University of Mining and Technology, Xuzhou 221116, China
Interests: fractal analysis; theories and methods in coal mining; green mining; rock mechanics and rock engineering
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Prof. Dr. Chen Wang

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Guest Editor
School of Mining, Guizhou University, Guiyang 550025, China
Interests: fractal analysis; thin coal seam mining; intelligent mining; green mining; mining system engineering; rock stratum control in karst mountainous area
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Prof. Dr. Cun Zhang

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Guest Editor
State Key Laboratory of Tunnel Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China
Interests: fractional modeling; coal mining; intelligent mining; rock mechanics
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Dr. Defu Zhu

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Guest Editor
Key Laboratory of In-Situ Property-Improving Mining of Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China
Interests: fractal analysis; strata control; numerical calculation; coordinated mining of associated resources in coal measures
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Dr. Kaijun Miao

E-Mail Website
Guest Editor
School of Mines, China University of Mining and Technology, Xuzhou 221116, China
Interests: fractal analysis; stope rock formation control; mining rock mass seepage mechanics; coal mining shallow water resources protection; water inrush disaster prevention and control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractal geometry is an important tool to describe complex natural phenomena. With the development of fractal mechanics, fractal has also been widely applied to the field of rock mechanics and engineering, especially in joints, mining-induced fractures, rock fragmentation, mining-induced rock mass seepage and heat conduction. For many randomly distributed rock parameters, fractal analysis has become an important quantitative characterization method. Due to the differences in fractal dimensions obtained by different fractal measurement methods, there is international controversy in regard to fractal characterization. However, fractal as a new perspective can quantitatively describe the chaos and roughness that has been recognized. Joints, fractures, and voids not only affect the strength of rocks but also are important channels for fluid migration. It is found that the fractal dimension is related to the rock response characteristics of engineering disturbance. The methods of obtaining channel distribution are mainly the physical perspective of small samples, numerical simulation, and similar simulation. The fractal dimension analysis of the later imaging process has become a research hotspot. In addition, in view of the complexity, concealment, and danger of underground engineering, the fractal analysis of massive data provides a new direction for guiding high efficiency and safe production. Therefore, it is necessary to carry out a lot of research work to determine which fractal dimension measurement method is more conducive to understanding the mechanism of rock mechanics and guiding rock mechanics engineering. The scope of this Special Issue includes, but is not limited to, the following topics:

  • Fractal quantitative characterization of natural joints and fractures in rock;
  • Fractal characteristics and engineering application of rock fracture development and crushing processes;
  • Fractal analysis of digital image processing of joints and fractures;
  • Fractal analysis of seepage characteristics of mining rock mass;
  • Fractal characteristics of water/gas/thermal diffusion law in fractured rock mass;
  • Fractal characteristics and evolution law of mining-induced overburden fractures and ground fissures;
  • Fractal analysis of monitoring signals and information of underground engineering disaster prevention and control;
  • Fractal characteristics and application of underground engineering big data.

Prof. Dr. Shihao Tu
Prof. Dr. Lei Zhang
Prof. Dr. Chen Wang
Prof. Dr. Cun Zhang
Dr. Defu Zhu
Dr. Kaijun Miao
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 250 words) can be sent to the Editorial Office for assessment.

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
  • fractal characteristics
  • data fractal processing
  • rock mechanics
  • rock engineering
  • under engineering
  • water/gas/heat conduction
  • joints, fractures and voids
  • fluid migration
  • chaos and roughness
  • image processing process
  • entropy

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Related Special Issue

Published Papers (5 papers)

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Research

18 pages, 3757 KB  
Article
Fractal Evolution of Acoustic-Emission Dynamics in Green Sandstone Subjected to Wetting–Air-Drying Cycles: Correlation Dimension and Failure-Mode Transition
by Shuyu Du, Shenggen Cao, Yang Liu, Changzheng Zhao, Chiyuan Che, Jiang Li and Kaifei Wang
Fractal Fract. 2026, 10(4), 212; https://doi.org/10.3390/fractalfract10040212 - 25 Mar 2026
Viewed by 410
Abstract
Wetting–air-drying cycling significantly alters the internal damage evolution and failure behavior of sandstone, and identifying reliable acoustic-emission (AE) precursors during loading is important for understanding the rupture mechanism of water-affected rock. In this study, uniaxial compression tests with AE monitoring were conducted on [...] Read more.
Wetting–air-drying cycling significantly alters the internal damage evolution and failure behavior of sandstone, and identifying reliable acoustic-emission (AE) precursors during loading is important for understanding the rupture mechanism of water-affected rock. In this study, uniaxial compression tests with AE monitoring were conducted on green sandstone subjected to different numbers of wetting–air-drying cycles. Ringing counts, RA–AF parameters, b-value evolution, AE spatial localization, and the correlation dimension D2 were jointly used to characterize mechanical deterioration, failure-mode transition, and fractal dynamic evolution. The results show that increasing cycling causes a progressive decrease in peak stress and elastic modulus, while AE activity evolves from a relatively dispersed state to stronger pre-peak concentration. The RA–AF distributions indicate that the dominant AE population gradually shifts from tensile-feature dominance toward mixed/shear-involved behavior, suggesting increasing shear participation during failure. The b-value captures stage-dependent damage evolution but exhibits relatively strong fluctuations under increasingly nonstationary event distributions. In contrast, D2 shows a clearer pre-peak turning feature, and the corresponding stress level remains relatively consistent among different cycling groups. These results indicate that wetting–air-drying cycling not only accelerates the mechanical degradation of green sandstone, but also substantially modifies its rupture dynamics. The D2 feature may therefore serve as a potential precursor parameter for characterizing pre-peak complexity transition in water-affected sandstone. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering, Second Edition)
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15 pages, 10195 KB  
Article
Fractal Evolution of Mining-Induced Fractures in Thick and Hard Roofs Using Similar Simulation and Fractal Theory
by Xuan Cui, Shengli Yang, Hao Yue, Aoxiang Wang and Yongkai Zhao
Fractal Fract. 2026, 10(2), 110; https://doi.org/10.3390/fractalfract10020110 - 4 Feb 2026
Viewed by 462
Abstract
During coal mining, the development of joint fractures in overlying rock strata is one of the key factors that degrade the mechanical properties of rock masses, form water-conducting fracture zones, and induce safety hazards. To investigate the fracture evolution characteristics of overlying strata [...] Read more.
During coal mining, the development of joint fractures in overlying rock strata is one of the key factors that degrade the mechanical properties of rock masses, form water-conducting fracture zones, and induce safety hazards. To investigate the fracture evolution characteristics of overlying strata during coal extraction under thick and hard roof conditions, this study established a mining physical model based on similarity simulation technology, tracked the fracture evolution process, and performed quantitative analysis using fractal theory. The results show that fracture development is significantly correlated with the mining advance distance: the fractal dimension of fractures is small in the initial mining stage and gradually increases as the working face advances. When the mining width exceeds the ultimate span of the roof, local fractures expand rapidly with a sharp rise in the fractal dimension to 1.436; further increasing the mining width triggers large-scale sudden fracture expansion, resulting in severe degradation of rock mass integrity, with the maximum fractal dimension reaching 1.445. The research findings provide theoretical references for safety management and disaster prevention in coal mining under thick and hard roof conditions. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering, Second Edition)
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20 pages, 8298 KB  
Article
Fractal and CT Analysis of Water-Bearing Coal–Rock Composites Under True Triaxial Loading–Unloading
by Qiang Xu, Ze Xia, Shuyu Du, Yukuan Fan, Gang Huang, Shengyan Chen, Zhisen Zhang and Yang Liu
Fractal Fract. 2025, 9(12), 782; https://doi.org/10.3390/fractalfract9120782 - 1 Dec 2025
Cited by 2 | Viewed by 775
Abstract
To reveal the deformation and failure mechanisms as well as the fracture evolution patterns of water-bearing coal–rock composites under complex stress conditions, this study established a true triaxial stress model for the key load-bearing structure of mined coal pillar dams and developed a [...] Read more.
To reveal the deformation and failure mechanisms as well as the fracture evolution patterns of water-bearing coal–rock composites under complex stress conditions, this study established a true triaxial stress model for the key load-bearing structure of mined coal pillar dams and developed a true triaxial loading apparatus capable of implementing localized unloading paths. True triaxial loading–unloading tests were conducted on coal–rock composites under different water content conditions, and the internal fracture structures were quantitatively characterized using CT scanning combined with fractal analysis. The results indicate that: (1) under a constant axial stress-unloading confining stress path, failure primarily occurs in the coal component, and the extent of failure significantly increases with the water content of the roof rock. For instance, the total fracture volume in the coal body increased by approximately 66% from the dry to the saturated state, while the lateral strain at peak stress decreased by about 65% over the same range, indicating a transition towards more brittle behavior. (2) CT scanning and three-dimensional reconstruction results reveal that the fracture system exhibits pronounced multi-scale polarization, with significant differences in volume, surface area, and morphological parameters between the main fractures and micropores, reflecting strong heterogeneity and anisotropy; (3) fractal dimension analysis of two-dimensional slices indicates that the fracture structures exhibit fractal characteristics in all directions, with the spatial distribution of fractal dimensions closely related to the loading direction. Overall, the XY-direction fractures exhibit the highest complexity, whereas the XZ and YZ directions show pronounced directional anisotropy. As water content increases, the amplitude of fractal dimension fluctuations rises, reflecting an enhancement in the geometric complexity of the fracture system. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering, Second Edition)
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20 pages, 8324 KB  
Article
Development Characteristics of Mining-Induced Fractures in Weakly Cemented Overburden During the First Layer Mining of Ultra-Thick Coal Seam: Similar Simulation and Field Measurement
by Yupei Deng, Weidong Pan, Shiqi Liu, Bo Cui and Kunming Zhang
Fractal Fract. 2025, 9(11), 718; https://doi.org/10.3390/fractalfract9110718 - 7 Nov 2025
Cited by 1 | Viewed by 931
Abstract
Focusing on the mining-induced fracture development characteristics of Weakly Cemented Overburden (WCO) in Ultra-Thick Coal Seam (UTCS) extraction, this study, based on the 1101 first mining face in Xinjiang’s Zhundong Coalfield, systematically investigates the dynamic evolution law of the water-conducting fracture zone (WCFZ) [...] Read more.
Focusing on the mining-induced fracture development characteristics of Weakly Cemented Overburden (WCO) in Ultra-Thick Coal Seam (UTCS) extraction, this study, based on the 1101 first mining face in Xinjiang’s Zhundong Coalfield, systematically investigates the dynamic evolution law of the water-conducting fracture zone (WCFZ) in WCO by employing similarity simulation, quantitative characterization using Fractal Dimension (D), and surface borehole exploration and borehole imaging technology. The results show that existing prediction equations for the WCFZ have poor applicability in the study area, with significant fluctuations in prediction outcomes. Similarity simulation reveals that Thick Soft Rock Layers (TS) guide and control fracture development, with the D exhibiting a “step-like” evolution. After the first rupture of TS1, the peak D reaches 1.49, stabilizing between 1.36 and 1.37 after full extraction. The height of the WCFZ increases non-linearly with the advance of the working face, reaching a maximum of 189 m, with a fracture-to-mining ratio of 10.5. Based on D fluctuations and extension patterns, the fracture development is divided into three stages, initial development, vertical propagation, and stabilization, clarifying its spatial evolution. Field measurements indicate a WCFZ height ranging from 161 to 178 m, with a fracture-to-mining ratio of 9.73–12.18, showing only a 6.2% error compared to the simulation results, which verifies the reliability of the experiment. This study reveals the evolution mechanism of the WCFZ during mining in UTCS and WCO in the Zhundong area, providing a theoretical basis and practical guidance for mine disaster prevention and control, as well as safe and efficient mining. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering, Second Edition)
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20 pages, 6947 KB  
Article
Fractal Evolution Characteristics of Weakly Cemented Overlying Rock Fractures in Extra-Thick Coal Seams Mining in Western Mining Areas
by Cun Zhang, Zhaopeng Ren, Jun He and Xiangyu Zhao
Fractal Fract. 2025, 9(8), 531; https://doi.org/10.3390/fractalfract9080531 - 14 Aug 2025
Cited by 5 | Viewed by 1220
Abstract
Coal mining disturbance induces progressive damage and fracturing in overlying rock (OLR), forming a complex fracture network. This process triggers groundwater depletion, ecological degradation, and severely compromises mine safety. Based on field drilling sampling and mechanical experiments, this paper reveals the occurrence properties [...] Read more.
Coal mining disturbance induces progressive damage and fracturing in overlying rock (OLR), forming a complex fracture network. This process triggers groundwater depletion, ecological degradation, and severely compromises mine safety. Based on field drilling sampling and mechanical experiments, this paper reveals the occurrence properties and characteristics of weakly cemented overlying rock (WCOLR). At the same time, similar simulation experiments, DIC speckle analysis system, and fractal theory are used to explain the development and evolution mechanism of mining-induced fractures under this special geological condition. The OLR fracture is determined based on the grid fractal dimension (D) distribution. A stress arch-bed separation (BS) co-evolution model is established based on dynamic cyclic BS development and stress arch characteristics, enabling identification of BS horizons. The results show that the overlying weak and extremely weak rock accounts for more than 90%. During the process of longwall face (LF) advancing, the D undergoes oscillatory evolution through five distinct stages: rapid initial growth, constrained slow growth under thick, soft strata (TSS), dimension reduction induced by fracturing and compaction of TSS, secondary growth from newly generated fractures, and stabilization upon reaching full extraction. Grid-based D analysis further categorizes fracture zones, indicating a water conducting fracture zone (WCFZ) height of 160~180 m. Mining-induced fractures predominantly concentrate at dip angles of 0–10°, 40–50°, and 170–180°. Horizontally BS fractures account for 70.2% of the total fracture population, vertically penetrating fractures constitute 13.1% and transitional fractures make up the remaining 16.7%. The stress arch height is 314.4 m, and the stable BS horizon is 260 m away from the coal seam. Finally, an elastic foundation theory-based model was used to predict BS development under top-coal caving operations. This research provides scientific foundations for damage-reduced mining in ecologically vulnerable Western China coalfields. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering, Second Edition)
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