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Quantifying Particle Breakage and Its Evolution Using Breakage Indices and Grading Entropy Coordinates

Leak, James; Barreto, Daniel; Dimitriadi, Vasiliki; Imre, Emőke


Emőke Imre


Particle breakage in soils is a well-recognised behaviour. Conventional methods for quantifying the breakage process rely on calculating the area between the particle size distribution (PSD) curves produced before and after crushing. A key aspect of breakage is understanding the process across the different size/sieve fractions. Grading entropy coordinates allow for the representation of any PSD to be shown as a single point on a Cartesian plane and are able to track grading evolution with relative ease. In this study, grading entropy coordinates are compared to three commonly used breakage indices (Br, Br* and IG). It is shown that grading entropy coordinates are advantageous over the traditional indices in quantifying subtle changes in the PSD evolution and directly provide further insight with regards to the individual fraction sizes. It is also discussed that conventional breakage indices rely on relative measures and are dependent on assumptions of an initial and/or final PSD. In contrast, grading entropy coordinates depend only on the characteristics of the (current) PSD curve. It was also observed that the breakage evolution captured by the entropy coordinates is able to determine the rate at which differently sized particles break as differently sized particles take on stress. Moreover, it is suggested that entropy coordinates may also stress path dependency, a feature not present in conventional indices.

Journal Article Type Article
Acceptance Date Dec 2, 2022
Online Publication Date Dec 10, 2022
Publication Date 2022-12
Deposit Date Dec 15, 2022
Publicly Available Date Dec 15, 2022
Journal Geotechnics
Print ISSN 2673-7094
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 2
Issue 4
Pages 1109-1126
Keywords particle breakage; grading entropy; grading entropy coordinates; PSD; breakage indices
Public URL


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