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Fractal Fract
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Fractal and Fractional in Geomaterials, 2nd Edition
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Fractal and Fractional in Geomaterials, 2nd Edition

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

Deadline for manuscript submissions: 15 January 2026 | Viewed by 2921

Special Issue Editor

Dr. Yifei Sun

E-Mail Website
Guest Editor
College of Civil and Transportation Engineering, Hohai University, Nanjing 210024, China
Interests: fractional plasticity; fractional viscoelasticity; fractals in particle breakage; geomechanics; heat conduction

Special Issue Information

Dear Colleagues,

Geomaterials are some of the most common materials in the world. Based on their function, there can be different types of geomaterials, e.g., soft soils, granular aggregates, and composite materials. However, no matter what kind of geomaterials are used, fractal laws can always be observed in the material’s responses. For example, the pore size or contact force network within granular aggregates can obey fractal distribution, which can be described using fractional calculus or other advanced mathematical tools. In recent years, the application of fractal theory and fractional mechanics in characterizing the micro-to-macro behavior of geomaterials has attracted worldwide attention.

The aim of this Special Issue is to present state-of-the-art research on fractal or fractional approaches for geomaterials. Therefore, high-quality review papers, full-length research articles, and technical notes from different disciplines are cordially welcome. Research topics include, but are not limited to, the following topics:

  1. Fractal laws for contact networks/pore structures in geomaterials;
  2. Fractional mechanics modeling of geomaterials;
  3. Local/nonlocal deformation in geomaterials;
  4. Non-Fourier/non-Fickian/non-Darcy laws for geomaterials;
  5. Other nonconventional approaches for geomaterials.

Dr. Yifei Sun
Guest Editor

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 media
  • fractional mechanics
  • micro-to-macro. geomaterials
  • nonconventional approach

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Related Special Issue

Published Papers (2 papers)

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Research

22 pages, 3539 KiB  
Article
Multifractal Methods in Characterizing Pore Structure Heterogeneity During Hydrous Pyrolysis of Lacustrine Shale
by Xiaofei Liang, Qinhong Hu, Xiugang Pu, Wei Li, Qiming Wang, Mengdi Sun and Wenzhong Han
Fractal Fract. 2024, 8(11), 657; https://doi.org/10.3390/fractalfract8110657 - 11 Nov 2024
Viewed by 1295
Abstract
By using gas physisorption and multifractal theory, this study analyzes pore structure heterogeneity and influencing factors during thermal maturation of naturally immature but artificially matured shale from the Kongdian Formation after being subjected to hydrous pyrolysis from 250 °C to 425 °C. As [...] Read more.
By using gas physisorption and multifractal theory, this study analyzes pore structure heterogeneity and influencing factors during thermal maturation of naturally immature but artificially matured shale from the Kongdian Formation after being subjected to hydrous pyrolysis from 250 °C to 425 °C. As thermal maturity increases, the transformation of organic matter, generation, retention, and expulsion of hydrocarbons, and formation of various pore types, lead to changes in pore structure heterogeneity. The entire process is divided into three stages: bitumen generation stage (250–300 °C), oil generation stage (325–375 °C), and oil cracking stage (400–425 °C). During the bitumen generation stage, retained hydrocarbons decrease total-pore and mesopore volumes. Fractal parameters ΔD indicative of pore connectivity shows little change, while Hurst exponent H values for pore structure heterogeneity drop significantly, indicating reduced pore connectivity due to bitumen clogging. During the peak oil generation stage, both ΔD and H values increase, indicating enhanced pore heterogeneity and connectivity due to the expulsion of retained hydrocarbons. In the oil cracking stage, ΔD increases significantly, and H value rises slowly, attributed to the generation of gaseous hydrocarbons further consuming retained hydrocarbons and organic matter, forming more small-diameter pores and increased pore heterogeneity. A strongly negative correlation between ΔD and retained hydrocarbon content, and a strongly positive correlation with gaseous hydrocarbon yield, highlight the dynamic interaction between hydrocarbon phases and pore structure evolution. This study overall provides valuable insights for petroleum generation, storage, and production. Full article
(This article belongs to the Special Issue Fractal and Fractional in Geomaterials, 2nd Edition)
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18 pages, 4586 KiB  
Article
The Spatial Variation of Soil Structure Fractal Derived from Particle Size Distributions at the Basin Scale
by Yujiang He, Borui Peng, Lei Dai, Yanyan Wang, Ying Liu and Guiling Wang
Fractal Fract. 2024, 8(10), 570; https://doi.org/10.3390/fractalfract8100570 - 29 Sep 2024
Viewed by 885
Abstract
The accurate characterization of soil structure is fundamental to groundwater science, environmental ecology, and Earth systems science. To address the challenge of quantifying the high spatial variability of large-scale soil structures, this study used a laser particle size analyzer to measure the distribution [...] Read more.
The accurate characterization of soil structure is fundamental to groundwater science, environmental ecology, and Earth systems science. To address the challenge of quantifying the high spatial variability of large-scale soil structures, this study used a laser particle size analyzer to measure the distribution of soil particle size in 207 samples from ten profiles across the Daqing and Ziya River basins in the North China Plain. The quantified soil structure, expressed as soil fractal dimension D, was derived using monofractal theory. Various spatial analysis techniques, including Moran’s I index, correlation analysis heat maps, the Kolmogorov–Smirnov one-sample test, and geostatistical semivariogram function, were jointly applied to investigate the spatial variability of soil structural fractals across different depths in the piedmont plain–coastal areas of the two river basins. The results indicate the following: (1) Quantitative analysis confirms that under the influence of piedmont alluvial and fluvial dynamics, soil D values homogenize from the piedmont to the coastal areas, with decreasing particle size differences closer to the coast. However, the spatial variability of the soil structural fractals in the Ziya River Basin was greater than that in the Daqing River Basin. (2) The combined effects of climate change, regional differences, and human activity led to greater spatial variability in the soil structural fractals in the Ziya River Basin than in the Daqing River Basin. The correlation between D values and burial depth was strongest in the Xianxian profile (−0.78), whereas the spatial correlation was strongest in the Hengshui and Dacheng profiles (−0.47). (3) The greatest spatial variability in soil D values occurred at depths of 1–2 m, with a coefficient of variation of 23.595%, which was significantly higher than those at depths of 0–1 (14.569%) and 2–3 m (16.284%). Full article
(This article belongs to the Special Issue Fractal and Fractional in Geomaterials, 2nd Edition)
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