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Fractal Fract
Special Issues
Applications of Fractal Analysis in Underground Engineering
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Applications of Fractal Analysis in Underground Engineering

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

Deadline for manuscript submissions: 1 May 2025 | Viewed by 10561

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: disaster prevention and control in coal mining; theories and methods in mineral exploitation; intelligent mining; mining planning and sustainability
Prof. Dr. Lei Zhang

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

E-Mail Website
Guest Editor
School of Mining, Guizhou University, Guiyang 550025, China
Interests: thin coal seam mining; intelligent mining; green mining; mining system engineering; rock stratum control in karst mountainous area
Special Issues, Collections and Topics in MDPI journals
Dr. Cun Zhang

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Guest Editor
School of Energy and Mining Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China
Interests: mine pressure and strata control; mine water resources utilization; coal and gas co-mining; abandoned mine reuse
Special Issues, Collections and Topics in MDPI journals
Dr. Defu Zhu

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

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

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 controversy about fractal characterization internationally. However, fractal as a new perspective can quantitatively describe the chaos and roughness 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 physical perspective of small samples, numerical simulation and similar simulation. The fractal dimension analysis of the later image processing 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 process.
  • 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
Dr. Cun Zhang
Dr. Defu Zhu
Dr. Kaijun Miao
Guest Editors

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Published Papers (7 papers)

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Research

15 pages, 7611 KiB  
Article
Experimental Study on the Impact of High-Frequency Vibration Excitation on Coal Fracturing
by Lei Zhang, Xufeng Wang and Zhijun Niu
Fractal Fract. 2024, 8(9), 546; https://doi.org/10.3390/fractalfract8090546 - 19 Sep 2024
Viewed by 665
Abstract
The ultrasonic vibration rock-breaking method has been successfully applied to hard rock due to its high efficiency and controllable energy, providing a novel approach for the development of a more efficient, intelligent, safe, and environmentally friendly reconstruction method for coal and rock reservoirs. [...] Read more.
The ultrasonic vibration rock-breaking method has been successfully applied to hard rock due to its high efficiency and controllable energy, providing a novel approach for the development of a more efficient, intelligent, safe, and environmentally friendly reconstruction method for coal and rock reservoirs. By subjecting the rock to ultra-high frequency (>15 kHz) vibration load, rapid fatigue damage can be induced within a short period of time, thereby enhancing the extent of cracking in hard rock. In order to investigate the impact of high-frequency vibration excitation on coal cracking, this study conducted exploratory tests using an independently designed ultrasonic vibration excitation system. These tests were combined with nuclear magnetic resonance (NMR) and permeability measurements to compare and analyze the pore fracture structure and permeability changes in coal samples under resonant and non-resonant conditions. Additionally, multifractal characteristics of the coal samples were investigated. The results demonstrate that high-frequency vibration excitation leads to significant expansion of micropores and mesopores in coal samples. Moreover, there is a strong exponential relationship between coal porosity/permeability and excitation time. After 40 s of stimulation, both porosity and permeability increase by 32.4% and over 8400%, respectively; these increases are five times higher for resonance-state compared to non-resonance-state conditions. Furthermore, water-saturated coal samples exhibit multifractal characteristics in their NMR T2 spectrum distribution, and multifractal parameters ΔD(q)and Δα show positive correlations with the proportion of mesoporous/macropores but negative correlations with the proportion of micropores; conversely, Δf shows an opposite trend relative to pore proportions. The pore structure of coal exhibits intricate multi-scale characteristics, and the heterogeneity at various scales is quantified through multifractal analysis. This study confirms the feasibility of utilizing high-frequency vibration excitation for cracking coal rocks while also providing valuable insights for further expanding its application. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering)
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21 pages, 62211 KiB  
Article
Damage Law and Reasonable Width of Coal Pillar under Gully Area: Linking Fractal Characteristics of Coal Pillar Fractures to Their Stability
by Zhaopeng Wu, Yunpei Liang, Kaijun Miao, Qigang Li, Sichen Liu, Qican Ran, Wanjie Sun, Hualong Yin and Yun Ma
Fractal Fract. 2024, 8(7), 407; https://doi.org/10.3390/fractalfract8070407 - 11 Jul 2024
Viewed by 742
Abstract
The coal pillar is an important structure to control the stability of the roadway surrounding rock and maintain the safety of underground mining activities. An unreasonable design of the coal pillar size can result in the failure of the surrounding rock structure or [...] Read more.
The coal pillar is an important structure to control the stability of the roadway surrounding rock and maintain the safety of underground mining activities. An unreasonable design of the coal pillar size can result in the failure of the surrounding rock structure or waste of coal resources. The northern Shaanxi mining area of China belongs to the shallow buried coal seam mining in the gully area, and the gully topography makes the bearing law of the coal pillar and the development law of the internal fracture more complicated. In this study, based on the geological conditions of the Longhua Mine 20202 working face, a PFC2D numerical model was established to study the damage characteristics of coal pillars under the different overlying strata base load ratios in the gentle terrain area and the different gully slope sections in the gully terrain area, and the coal pillar design strategy based on the fractal characteristics of the fractures was proposed to provide a reference for determining the width of the coal pillars in mines under similar geological conditions. The results show that the reliability of the mathematical equation between the overlying strata base load ratio and the fractal dimension of the fractures in the coal pillar is high, the smaller the overlying strata base load ratio is, the greater the damage degree of the coal pillar is, and the width of the coal pillar of 15 m under the condition of the actual overlying strata base load ratio (1.19) is more reasonable. Compared with the gentle terrain area, the damage degree of the coal pillar in the gully terrain area is larger, in which the fractal dimension of the fracture in the coal pillar located below the gully bottom is the smallest, and the coal pillar in the gully terrain should be set as far as possible to make the coal pillar located below the gully bottom, so as to ensure the stability of the coal pillar. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering)
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24 pages, 16242 KiB  
Article
Investigation into the Failure Characteristics and Mechanism of Rock with Single Elliptical Defects under Ultrasonic Vibrations
by Zhijun Niu, Xufeng Wang, Lei Zhang, Jiyao Wang, Zechao Chang, Chenlong Qian and Xuyang Chen
Fractal Fract. 2024, 8(5), 261; https://doi.org/10.3390/fractalfract8050261 - 27 Apr 2024
Cited by 2 | Viewed by 988
Abstract
In order to investigate the effects of elliptical defects on rock failure under ultrasonic vibrations, ultrasonic vibration tests and PFC2D numerical simulations were conducted on rocks with single elliptical defects. The research results indicated that the fracture fractal dimension, axial strain, and [...] Read more.
In order to investigate the effects of elliptical defects on rock failure under ultrasonic vibrations, ultrasonic vibration tests and PFC2D numerical simulations were conducted on rocks with single elliptical defects. The research results indicated that the fracture fractal dimension, axial strain, and crack depth of specimens with elliptical defects at 45° and 90° were the smallest and largest, respectively. The corresponding strain and fractal dimension showed a positive linear and logarithmic function relationship with time. The maximum crack depth of 46.50 mm was observed on the specimens with an elliptical defect angle of 90°. Specimens with elliptical defects at 0°, 30°, 75°, and 90° exhibited more dense and frequent acoustic emission events than those with elliptical defects at 15°, 45°, and 60°. During the ultrasonic vibration process, the maximum total energy (87.86 kJ) and energy consumption coefficient (0.963) were observed on specimens with elliptical defect angles of 30° and 45°, respectively. The difference in the stress field led to varying degrees of plastic strain energy in the specimens, resulting in different forms of crack propagation and triggering differential acoustic emission events, ultimately leading to specimen failure with different crack shapes and depths. The fractal dimensions of elliptical defect specimens under ultrasonic vibration have a high degree of consistency with the changes in axial strain and failure depth, and the fractal dimension of defect specimens is positively correlated with the degree of failure of defect specimens. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering)
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14 pages, 5303 KiB  
Article
Pore-Type-Dependent Fractal Features of Shales and Implications on Permeability
by Qian Zhang, Yanhui Dong and Shaoqing Tong
Fractal Fract. 2023, 7(11), 803; https://doi.org/10.3390/fractalfract7110803 - 4 Nov 2023
Cited by 1 | Viewed by 1503
Abstract
Pore structure features govern the capacity of gas storage and migration in shales and are highly dependent on the types of pores, i.e., interparticle (InterP) pores, intraparticle (IntraP) pores and organic matter (OM)-hosted pores. However, fractal features in terms of pore types and [...] Read more.
Pore structure features govern the capacity of gas storage and migration in shales and are highly dependent on the types of pores, i.e., interparticle (InterP) pores, intraparticle (IntraP) pores and organic matter (OM)-hosted pores. However, fractal features in terms of pore types and their respective contributions to permeability have been rarely addressed. On the basis of high-resolution imaging, fractal dimensions (Ds) have been determined from both pore size distributions and digital rock to quantify the heterogeneity in pore morphology and spatial textures. Overall, OM-hosted pores are smaller in size and more abundant in quantity, corresponding to a relatively high D, while IntraP pores are mainly isolated and scarce, translating into lower D values. Additionally, crack-like InterP pores with a moderate level of porosity and the D can play a pivotal role in shale seepage potential. A comparison of the estimated permeability among different pore types highlights that the contribution of interconnected OM pores to the overall permeability remains constrained unless they can link neighboring pore clusters, as commonly observed in organo-clay composites. Furthermore, the pore morphology and fractal features of shale rocks can exhibit noteworthy variations subjected to sedimentology, mineralogy, diagenesis and OM maturation. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering)
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17 pages, 7599 KiB  
Article
Evolution Law of Shallow Water in Multi-Face Mining Based on Partition Characteristics of Catastrophe Theory
by Yujiang Zhang, Bingyuan Cui, Yining Wang, Shuai Zhang, Guorui Feng and Zhengjun Zhang
Fractal Fract. 2023, 7(11), 779; https://doi.org/10.3390/fractalfract7110779 - 26 Oct 2023
Cited by 17 | Viewed by 1417
Abstract
It is of great significance for ecological environment protection to clarify the regional evolution characteristics of shallow water under the disturbance of multi-working face mining. In this paper, the catastrophe theory method, GIS spatial analysis function and FEFLOW numerical calculation method were comprehensively [...] Read more.
It is of great significance for ecological environment protection to clarify the regional evolution characteristics of shallow water under the disturbance of multi-working face mining. In this paper, the catastrophe theory method, GIS spatial analysis function and FEFLOW numerical calculation method were comprehensively used to study the instability risk and evolution law of shallow water systems in the Zhuan Longwan Coal Mine. The results show that: the Zhuan Longwan Coal Mine is divided into five areas (small risk area, light risk area, middle risk area, heavy risk area and special risk area) based on catastrophe theory, among which the middle risk area has the largest area of 16,616,880 m2, and the special risk area has the smallest area of 1,769,488 m2. Based on the results of catastrophe zoning, the evolution law of shallow water under multi-surface disturbance in different zones is expounded. In the middle-risk area, the water level drop at measuring point 4 is the largest, which is 0.525 m, and the water level drop at measuring point 5 is the smallest, which is 0.116 m. The study aims to provide a basis for regional coal development planning and research on the method of water-retaining coal mining. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering)
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20 pages, 7668 KiB  
Article
Study on Uniaxial Compression Deformation and Fracture Development Characteristics of Weak Interlayer Coal–Rock Combination
by Shun Lei, Dingyi Hao and Shuwen Cao
Fractal Fract. 2023, 7(10), 731; https://doi.org/10.3390/fractalfract7100731 - 2 Oct 2023
Cited by 2 | Viewed by 1575
Abstract
With increases in mining depth and intensity, disasters such as stress concentration, slab failure, and coal body dynamic outbursts at the coal–rock interface have become more serious. Therefore, it is important to analyze the stress–strain behavior of coal–rock combinations to explore the deterioration [...] Read more.
With increases in mining depth and intensity, disasters such as stress concentration, slab failure, and coal body dynamic outbursts at the coal–rock interface have become more serious. Therefore, it is important to analyze the stress–strain behavior of coal–rock combinations to explore the deterioration process and failure characteristics of coal–rock combinations. In this study, we used field survey, theoretical analysis, and numerical simulation methods to explore the microstructure characteristics of the coal–rock interface and the influence of interlayer thickness on the composite body. The results show that with the increase in interlayer thickness, the compressive strength of the composite body gradually decreases. This reduction is mainly due to the interlayer dividing the coal sample, resulting in a decrease in the equivalent elastic modulus of the composite body, weakening of the overall integrity, and a decrease in carrying capacity. In addition, the failure mode and mechanical properties of the coal–rock combination are influenced by the interlayer position. Different “soft layer” positions can lead to changes in the overall carrying and failure modes of the coal–rock composite. The position of the interlayer also has a significant influence on the failure mode and fracture propagation of the composite body. This study provides an important theoretical reference for the control of coal–rock deformation and instability and regional rock mass modification in underground engineering. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering)
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15 pages, 9271 KiB  
Article
Fractal Characteristics of Overburden Rock Fractures and Their Impact on Ground Fissures in Longwall Coal Mining
by Chunwei Ling, Bin Liu, Cun Zhang, Teng Teng, Kangning Zhang, Bo Sun and Jinlong Zhou
Fractal Fract. 2023, 7(10), 699; https://doi.org/10.3390/fractalfract7100699 - 23 Sep 2023
Cited by 1 | Viewed by 1300
Abstract
Ground fissures are generated during the coal mining process due to overlying strata migration, which provides gas and water seepage channels and usually contributes to coal mining accidents in shallow buried coal seams with larger mining height working faces. Thus, the evolution features [...] Read more.
Ground fissures are generated during the coal mining process due to overlying strata migration, which provides gas and water seepage channels and usually contributes to coal mining accidents in shallow buried coal seams with larger mining height working faces. Thus, the evolution features of ground fissures in large mining height working faces and shallow buried coal seams were explored by considering field observation data, similar simulation, and numerical simulations. The results show that the weathered rock layer above the thin bedrock inhibits fracture growth caused by coal mining. Overlying strata fracture expansion can be quantitatively divided into three stages based on fractal dimension: the overburden fracture formation stage, the overburden deformation fracture expansion stage, and the overburden fracture stable development stage. The movement deformation region of the ground fissure can be described by three characteristic zones: the boundary tension zone, the central compression zone, and the central dynamic tension and compression zone. Central dynamic fissures usually have 3–5 fissure counts with 2–5 m intervals between each group of fissures; central fissures develop twice from open to closed widths; the time period for two central fissures to reach their with maximum widths is 11–20 days; and border fissures expand rapidly with maximum values in a time period of 5–6 days. Full article
(This article belongs to the Special Issue Applications of Fractal Analysis in Underground Engineering)
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