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Some Notes on Granular Mixtures with Finite, Discrete Fractal Distribution


Emoke Imre


Maria Datcheva

Wiebke Baille

Ivan Georgiev

Stephen Fityus

Vijay P. Singh

Francesca Casini

Giulia Guida

Phong Q. Trang



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.


Imre, E., Talata, I., Barreto, D., Datcheva, M., Baille, W., Georgiev, I., …Lőrincz, J. (2022). Some Notes on Granular Mixtures with Finite, Discrete Fractal Distribution. Periodica Polytechnica Civil Engineering, 66(1), 179-192.

Journal Article Type Article
Acceptance Date Sep 12, 2021
Online Publication Date Oct 11, 2021
Publication Date 2022
Deposit Date Dec 21, 2021
Publicly Available Date Jan 6, 2022
Journal Periodica Polytechnica Civil Engineering
Electronic ISSN 0553-6626
Publisher Budapest University of Technology and Economics
Peer Reviewed Peer Reviewed
Volume 66
Issue 1
Pages 179-192
Keywords grading curve, grading entropy, finite fractal distribution, degradation, breakage
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