Some Notes on Granular Mixtures with Finite, Discrete Fractal Distribution

Authors

  • Emőke Imre
    Affiliation

    EKIK HBM Systems Research Center, Bánki Donát Faculty of Mechanical and Safety Engineering, Óbuda University, Bécsi út 96/B, 1034 Budapest, Hungary

    AIAM Doctoral School, Óbuda University, Bécsi út 96/B, 1034, Budapest, Hungary

  • István Talata
    Affiliation

    Ybl Faculty, Óbuda University, Bécsi út 96/B, 1034, Budapest, Hungary

  • Daniel Barreto
    Affiliation

    School of Engineering and the Built Environment, Edinburgh Napier University, Merchiston Campus, EH10 5DT, Edinburgh, UK

  • Maria Datcheva
    Affiliation

    Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., 1113 Sofia, Bulgaria

  • Wiebke Baille
    Affiliation

    Department of Civil and Environmental Engineering, Ruhr University Bochum, Universitätsstraße 150, 44801 Bochum, Germany

  • Ivan Georgiev
    Affiliation

    Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev St., 1113 Sofia, Bulgaria

  • Stephen Fityus
    Affiliation

    School of Engineering, University of Newcastle, University Drive, NSW 2308, Callaghan, Australia

  • Vijay P. Singh
    Affiliation

    Department of Biological and Agricultural Engineering, Texas A & M University, Scoates Hall, Suite 321, 2117 TAMU, 333 Spence St, College Station, TX 77843, USA

  • Francesca Casini
    Affiliation

    Department of Civil and Informatics Engineering, University of Roma Tor Vergata, Via del Politecnico, 1, 00133 Roma, Italy

  • Giulia Guida
    Affiliation

    Department of Civil and Informatics Engineering, University of Roma Tor Vergata, Via del Politecnico, 1, 00133 Roma, Italy

  • Phong Q. Trang
    Affiliation

    Department of Engineering Geology and Geotechnics, Budapest University of Technology and Economics, Műegyetem rkp. 3, 1111 Budapest, Hungary

    Bachy Soletanche, 126 Nguyen Thi Minh Khai St., Dist. 3, Ho Chi Minh City, Vietnam

  • János Lőrincz
    Affiliation

    Department of Engineering Geology and Geotechnics, Budapest University of Technology and Economics, Műegyetem rkp. 3, 1111 Budapest, Hungary

https://doi.org/10.3311/PPci.19103

Abstract

Why fractal distribution is so frequent? It is true that fractal dimension is always less than 3? Why fractal dimension of 2.5 to 2.9 seems to be steady-state or stable? Why the fractal distributions are the limit distributions of the degradation path? Is there an ultimate distribution? It is shown that the finite fractal grain size distributions occurring in the nature are identical to the optimal grading curves of the grading entropy theory and, the fractal dimension n varies between –¥ and ¥. It is shown that the fractal dimensions 2.2–2.9 may be situated in the transitional stability zone, verifying the internal stability criterion of the grading entropy theory. Micro computed tomography (μCT) images and DEM (distinct element method) studies are presented to show the link between stable microstructure and internal stability. On the other hand, it is shown that the optimal grading curves are mean position grading curves that can be used to represent all possible grading curves.

Keywords:

grading curve, grading entropy, finite fractal distribution, degradation, breakage

Published Online

2021-12-21

How to Cite

Imre, E., Talata, I., Barreto, D., Datcheva, M., Baille, W., Georgiev, I. “Some Notes on Granular Mixtures with Finite, Discrete Fractal Distribution”, Periodica Polytechnica Civil Engineering, 66(1), pp. 179–192, 2022. https://doi.org/10.3311/PPci.19103

Issue

Vol. 66 No. 1 (2022)

Section

Research Article