Some Notes on Granular Mixtures with Finite, Discrete Fractal Distribution

István Talata,Ivan Georgiev,Daniel Barreto,Francesca Casini,Emoke Imre,Maria Datcheva,Phong Q Trang,Vijay P Singh,János Lőrincz,Wiebke Baille,Giulia Guida,Stephen Fityus

doi: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.

Highlights

1.1 Natural soils and fragmentation The fragmentation phenomena are described by a power law distribution [1]
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

Summary

Introduction

1.1 Natural soils and fragmentation The fragmentation phenomena are described by a power law distribution [1]. 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 ¥.

Results

Conclusion