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Fractal Fract
Special Issues
Applications of Fractal Dimensions in Rock Mechanics and Geomechanics
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Applications of Fractal Dimensions in Rock Mechanics and Geomechanics

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 576

Special Issue Editors

Prof. Dr. Hai Pu

E-Mail Website
Guest Editor
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China
Interests: seepage mechanics; rock dynamics; coal mining; fractal
Special Issues, Collections and Topics in MDPI journals
Dr. Kangsheng Xue

E-Mail Website
Guest Editor
State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China
Interests: fluid mechanics coupling; fractal; fluid flow mechanism; unconventional reservoirs simulation; geological reservoir modeling; multiphase flow

Special Issue Information

Dear Colleagues,

Fractal geometry has emerged as a powerful tool to quantify the complexity of irregular structures and scale-invariant patterns in geological media. In rock mechanics, fractal dimension provides critical insights into multiscale phenomena, ranging from microcrack networks to macroscopic rock mass behavior. This Special Issue aims to consolidate cutting-edge research on fractal dimension-based characterization, modeling, and predictive analytics for rock systems. We invite contributions that bridge theoretical innovations with engineering applications, addressing challenges such as nonlinear deformation, fracture propagation, fluid flow in fractured reservoirs, and seismic hazard assessment.

Finally, we would like to thank Dr. Dejun Liu (State Key Laboratory of Intelligent Construction and Healthy Operation & Maintenance of Deep Underground Engineering, China University of Mining and Technology) for his valuable work in assisting us with this Special Issue.

Topics of interest include (but are not limited to) the following:

  • Fractal characterization of rock fracture networks and damage evolution;
  • Fractal dimension-based permeability modelling in fractured porous media;
  • Multifractal analysis of acoustic emission/earthquake catalogues;
  • Machine learning-enhanced fractal dimension quantification from imaging data;
  • Scale effects in rock strength and fragmentation processes;
  • Fractal dimension applications in unconventional reservoir geomechanics;
  • Coupled THMC processes in fractal rock systems;
  • Digital rock physics with fractal descriptors.

Prof. Dr. Hai Pu
Dr. Kangsheng Xue
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 dimension
  • rock mechanics
  • multiscale phenomena
  • fracture networks
  • nonlinear deformation
  • geomechanical applications

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

24 pages, 4026 KiB  
Article
Quantitative Analysis of Multi-Angle Correlation Between Fractal Dimension of Anthracite Surface and Its Coal Quality Indicators in Different Regions
by Shoule Zhao and Dun Wu
Fractal Fract. 2025, 9(8), 538; https://doi.org/10.3390/fractalfract9080538 - 15 Aug 2025
Abstract
The nanoporous structure of coal is crucial for the occurrence and development of coalbed methane (CBM). This study, leveraging the combined characterization of atomic force microscopy (AFM) and Gwyddion software, investigated six anthracite samples with varying degrees of metamorphism (Ro = 2.11–3.36%). [...] Read more.
The nanoporous structure of coal is crucial for the occurrence and development of coalbed methane (CBM). This study, leveraging the combined characterization of atomic force microscopy (AFM) and Gwyddion software, investigated six anthracite samples with varying degrees of metamorphism (Ro = 2.11–3.36%). It revealed the intrinsic relationships between their nanoporous structures, surface morphologies, fractal characteristics, and coalification processes. The research found that as Ro increases, the surface relief of coal decreases significantly, with pore structures evolving from being macropore-dominated to micropore-enriched, and the surface tending towards smoothness. Surface roughness parameters (Ra, Rq) exhibit a negative correlation with Ro. Quantitative data indicate that area porosity, pore count, and shape factor positively correlate with metamorphic grade, while mean pore diameter negatively correlates with it. The fractal dimensions calculated using the variance partition method, cube-counting method, triangular prism measurement method, and power spectrum method all show nonlinear correlations with Ro, moisture (Mad), ash content (Aad), and volatile matter (Vdaf). Among these, the fractal dimension obtained by the triangular prism measurement method has the highest correlation with Ro, Aad, and Vdaf, while the variance partition method shows the highest correlation with Mad. This study clarifies the regulatory mechanisms of coalification on the evolution of nanoporous structures and surface properties, providing a crucial theoretical foundation for the precise evaluation and efficient exploitation strategies of CBM reservoirs. Full article
(This article belongs to the Special Issue Applications of Fractal Dimensions in Rock Mechanics and Geomechanics)
17 pages, 4064 KiB  
Article
Study on Multi-Scale Damage Evolution of Sandstone Under Freeze–Thaw Cycles: A Computational Perspective Based on Pore Structure and Fractal Dimension
by Jianhui Qiu, Keping Zhou, Guanglin Tian and Taoying Liu
Fractal Fract. 2025, 9(8), 534; https://doi.org/10.3390/fractalfract9080534 - 15 Aug 2025
Abstract
Understanding the intrinsic relationship between microscopic structures and macroscopic mechanical properties of rock under freeze–thaw (F-T) conditions is essential for ensuring the safety and stability of geotechnical engineering in cold regions. In this study, a series of F-T cycle tests, nuclear magnetic resonance [...] Read more.
Understanding the intrinsic relationship between microscopic structures and macroscopic mechanical properties of rock under freeze–thaw (F-T) conditions is essential for ensuring the safety and stability of geotechnical engineering in cold regions. In this study, a series of F-T cycle tests, nuclear magnetic resonance (NMR) measurements, and uniaxial compression tests were conducted on sandstone samples. The mechanisms by which F-T cycles influence pore structure and mechanical behavior were analyzed, revealing their internal correlation. A degradation model for peak strength was developed using mesopore porosity as the key influencing parameter. The results showed that with increasing F-T cycles, the total porosity and mesopore and macropore porosities all exhibited increasing trends, whereas the micropore and different fractal dimensions decreased. The compaction stage in the stress–strain curves became increasingly prominent with more F-T cycles. Meanwhile, the peak strength and secant modulus decreased, while the peak strain increased. When the frost heave pressure induced by water–ice phase transitions exceeded the ultimate bearing capacity of pore walls, smaller pores progressively evolved into larger ones, leading to an increase in the mesopores and macropores. Notably, mesopores and macropores demonstrated significant fractal characteristics. The transformation in pore size disrupted the power-law distribution of pore radii and reduced fractal dimensions. A strong correlation was observed between peak strength and both the mesopore and mesopore fractal dimensions. The increase in mesopores and macropores enhanced the compaction stage of the stress–strain curve. Moreover, the expansion and interconnection of mesopores under loading conditions degraded the deformation resistance and load-bearing capacity, thereby reducing both the secant modulus and peak strength. The degradation model for peak strength, developed based on changes in mesopore ratio, proved effective for evaluating the mechanical strength when subjected to different numbers of F-T cycles. Full article
(This article belongs to the Special Issue Applications of Fractal Dimensions in Rock Mechanics and Geomechanics)
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22 pages, 4572 KiB  
Article
Effects of Organic Matter Volume Fraction and Fractal Dimension on Tensile Crack Evolution in Shale Using Digital Core Numerical Models
by Xin Liu, Yuepeng Wang, Tianjiao Li, Zhengzhao Liang, Siwei Meng and Licai Zheng
Fractal Fract. 2025, 9(8), 518; https://doi.org/10.3390/fractalfract9080518 - 8 Aug 2025
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Abstract
Organic matter plays a vital role in shale reservoirs as both a hydrocarbon storage medium and migration pathway. However, the quantitative relationship between the microstructural features of organic matter and the macroscopic mechanical and failure behaviors of shale remains unclear due to rock [...] Read more.
Organic matter plays a vital role in shale reservoirs as both a hydrocarbon storage medium and migration pathway. However, the quantitative relationship between the microstructural features of organic matter and the macroscopic mechanical and failure behaviors of shale remains unclear due to rock heterogeneity and opacity. In this study, high-resolution three-dimensional digital core models of shale were reconstructed using Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) imaging. The digital models captured the spatial distribution of silicate minerals, clay minerals, and organic matter. Numerical simulations of uniaxial tensile failure were performed on these models, considering variations in the organic matter volume fraction and fractal dimension. The results indicate that an increased organic matter volume fraction and fractal dimension are associated with lower tensile strength, simpler fracture geometry, and reduced acoustic emission activity. Tensile cracks preferentially initiate at interfaces between minerals with contrasting elastic moduli, especially between organic matter and clay, and then propagate and coalesce under loading. These findings reveal that both the volume fraction and fractal structure of organic matter are reliable predictors of tensile strength and damage evolution in shale. This study provides new microscale insights into shale failure mechanisms and offers guidance for optimizing hydraulic fracturing in organic-rich formations. Full article
(This article belongs to the Special Issue Applications of Fractal Dimensions in Rock Mechanics and Geomechanics)
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