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Fractal Fract
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Fractal and Fractional Models in Soil Mechanics
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Fractal and Fractional Models in Soil Mechanics

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

Deadline for manuscript submissions: 30 August 2025 | Viewed by 1793

Special Issue Editors

Dr. Yi Pik Helen Cheng

E-Mail Website
Guest Editor
Department of Civil, Environmental and Geomatic Engineering, University College London, London WC1E 6BT, UK
Interests: soil mechanics; geosynthetic; discrete element modeling; granular geomechanics
Special Issues, Collections and Topics in MDPI journals
Dr. Luju Liang

E-Mail Website
Guest Editor
Institute of Civil Engineering, Hangzhou City University, Hangzhou 310015, China
Interests: soil arching; tunnelling; discrete element modelling; construction waste

Special Issue Information

Dear Colleagues,

Fractal and fractional models have been widely adopted in solving complex problems in mathematics, computer science, physics, chemistry, biology, medicine, finance, and in the social sciences.  In recent years, fractal and fractional models have served as new useful tools in many research fields of soil mechanics, including particle size distribution, soil–water characteristic curves, constitutive models of soil, particle breakage, and particle/pore shape, amongst others.

The aim of this Special Issue is to collect the recent advances in fractal and fractional models in soil mechanics globally. The submitted manuscripts will be peer reviewed. High-quality papers from different disciplines are cordially welcome. Research topics include but are not limited to the following aspects:

  1. Fractal and fractional models in the analysis of the micro-structure of geomaterials;
  2. Fractal and fractional plastic models for soil;
  3. Fractal- and fractional-based complex network analysis in soil mechanics;
  4. The meso-topological evolution mechanism of granular materials;
  5. Fractal and fractional models combined with other theoretical, numerical, and/or experimental methods, in the evaluation of the mechanical performance of soil;
  6. Fractional-order or integer-order neural networks and graph theory approaches in soil mechanics;
  7. The application of fractal- and fractional-based soil mechanics in geotechnical engineering;
  8. Other fractal- and fractional-based approaches used in soil mechanics.

Dr. Yi Pik Cheng
Dr. Luju Liang
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

  • fractals and fragmentation
  • fractional-order mechanics
  • force network analysis
  • constitutive models
  • analytical and numerical methods
  • particle shape
  • macro- to micromechanical granular behavior
  • particle size effect
  • crushable soil mechanics
  • particle breakage and fragmentation
  • discrete element method

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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

22 pages, 11068 KiB  
Article
Relationship Between Pore-Size Distribution and 1D Compressibility of Different Reconstituted Clays Based on Fractal Theory
by Yanhao Zheng, Tanfang Zhu, Junqi Chen, Kun Shan and Junru Li
Fractal Fract. 2025, 9(4), 235; https://doi.org/10.3390/fractalfract9040235 - 9 Apr 2025
Viewed by 274
Abstract
This paper first examines the evolution of pore-size distribution (PSD) in four types of reconstituted clays during one-dimensional (1D) compression, utilising mercury intrusion porosimetry. Central to this work, fractal theory is then applied to quantify the complexity of the pore structure through fractal [...] Read more.
This paper first examines the evolution of pore-size distribution (PSD) in four types of reconstituted clays during one-dimensional (1D) compression, utilising mercury intrusion porosimetry. Central to this work, fractal theory is then applied to quantify the complexity of the pore structure through fractal dimensions, followed by being correlated with 1D compressibility. The key findings are as follows: (1) The 1D compressibility of the four clays exhibits significant variability, with montmorillonite demonstrating the highest compressibility and Shenzhen clay, dominated by chlorite, the lowest. This is associated with distinct pore size evolution patterns under 1D loading while also emphasising the crucial role of mesopores in macroscopic clay deformation. (2) Fractal dimensions increase with loading, reflecting the progressive refinement of the pore structure, with natural Shenzhen clay demonstrating the most pronounced change. (3) A mathematical relationship between fractal dimension and 1D compressibility is established for each clay type, providing a quantitative tool for predicting 1D compressibility based on fractal dimensions. (4) The testing procedures and methods to ensure the representativeness of pore structure analysis are elaborated, ensuring reliable PSD data. By employing fractal theory, this study provides new insights into the correlation between pore structure complexity and compressibility in reconstituted clays. Full article
(This article belongs to the Special Issue Fractal and Fractional Models in Soil Mechanics)
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18 pages, 5864 KiB  
Article
Revisiting the Consolidation Model by Taking the Rheological Characteristic and Abnormal Diffusion Process into Account
by Tao Feng, Yongtang Yu and Tao Zeng
Fractal Fract. 2025, 9(4), 233; https://doi.org/10.3390/fractalfract9040233 - 8 Apr 2025
Viewed by 172
Abstract
With the increasing construction of engineering structures on soft soils, accurately assessing their consolidation behavior has become crucial. To address this, Terzaghi’s one-dimensional consolidation model was revisited. The elastic behavior of soil skeleton was modified by incorporating viscous effects using the fractional derivative [...] Read more.
With the increasing construction of engineering structures on soft soils, accurately assessing their consolidation behavior has become crucial. To address this, Terzaghi’s one-dimensional consolidation model was revisited. The elastic behavior of soil skeleton was modified by incorporating viscous effects using the fractional derivative Merchant model (FDMM), while the linear Darcy’s law governing flux–pressure relations was extended by introducing time memory formalism through the fractional derivative Darcy model (FDDM). The governing equation is derived by incorporating the resulting constitutive behavior of both the soil skeleton and water flow into the Terzaghi’s formulation of the poroelasticity problem. The proposed rheological consolidation model is solved by a forward time-centered space scheme (FTCS). After verifying the numerical procedure with published data, the influence of parameters on both the average degree of settlement and the pressure was comprehensively studied. Full article
(This article belongs to the Special Issue Fractal and Fractional Models in Soil Mechanics)
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17 pages, 4370 KiB  
Article
Discrete Element Study of Particle Size Distribution Shape Governing Critical State Behavior of Granular Material
by Mingdong Jiang, Daniel Barreto, Zhi Ding and Kaifang Yang
Fractal Fract. 2025, 9(1), 26; https://doi.org/10.3390/fractalfract9010026 - 6 Jan 2025
Viewed by 973
Abstract
Granular soil is a porous medium composed of particles with different sizes and self-similar structures, exhibiting fractal characteristics. It is well established that variations in these fractal properties, such as particle size distribution (PSD), significantly influence the mechanical behavior of the soil. In [...] Read more.
Granular soil is a porous medium composed of particles with different sizes and self-similar structures, exhibiting fractal characteristics. It is well established that variations in these fractal properties, such as particle size distribution (PSD), significantly influence the mechanical behavior of the soil. In this paper, a three-dimensional (3D) Discrete Element Method (DEM) is applied to study the mechanical and critical-state behavior of the idealized granular assemblages, in which various PSD shape parameters are considered, including the coefficient of uniformity (Cu), the coefficient of curvature (Cc), and the coefficient of size span (Cs). In addition, the same PSDs but with different mean particle sizes (D50) are also employed in the numerical simulations to examine the particle size effect on the mechanical behavior of the granular media. Numerical triaxial tests are carried out by imposing axial compression under constant mean effective pressure conditions. A unique critical-state stress ratio in p′-q space is observed, indicating that the critical friction angle is independent of the shape of the PSD. However, in the e-p′ plane, the critical state line (CSL) shifts downward and rotates counterclockwise, as the grading becomes more widely distributed, i.e., the increasing coefficient of span (Cs). Additionally, a decrease in the coefficient of curvature (Cc) would also move the CSL downward but with negligible rotation. However, it is found that the variations in the mean particle size (D50) and coefficient of uniformity (Cu) do not affect the position of the CSL in the e-p′ plane. The numerical findings may shed some light on the development of constitutive models of sand that undergo variations in the grading due to crushing and erosion, and address fractal problems related to micro-mechanics in soils. Full article
(This article belongs to the Special Issue Fractal and Fractional Models in Soil Mechanics)
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