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The Median versus the Mean Fragment Size and Other Issues with the Kuz-Ram Model


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Author F Ouchterlony


Soviet precursors to Cunningham’s Kuz-Ram model from 1983 are described. They are rooted in the mean fragment size and Rosin-Rammler (RR) fits to sieving data and rely on approximations. Three versions of the Kuz-Ram model are presented and all three are de facto based on the median fragment size x50, even if the term mean is used in the papers. This discrepancy caused Spathis in 2004 to suggest a correction procedure for the Kuz-Ram rock factor A, which was said to explain some of the missing fines in the model. This correction, while applicable to Cunningham’s 1983 paper, does not apply to his 1987 paper, in which he presents his own A factor.

Common fixes of the Kuz-Ram model’s fines issue are fragmentation models where the fines are mainly generated in a crushed zone around a blasthole. This is contradicted by careful model blasting tests. The lack of a largest block size in the RR function may lead to spurious values of the uniformity coefficient n, eg in conjunction with image-based fragmentation measurements or crusher modelling. These issues may be solved by using the transformed RR function, which has a largest block size xmax or its replacement by the Swebrec function, such as in the KCO model.

The mean to median issue is investigated in some detail and it is found that using x50 instead of the mean:

has a sounder theoretical background

is less prone to errors

is not contradicted by the original Soviet data.

It is finally suggested that future work on fragmentation prediction equations focus on the use of distribution independent quantities like percentiles, eg x50, x20 and x80. Some previous work in this direction is briefly analysed and one consequence is that the n-value of the Kuz-Ram model should depend on specific charge.


Ouchterlony, F, 2015. The median versus the mean fragment size and other issues with the Kuz-Ram model, in Proceedings 11th International Symposium on Rock Fragmentation by Blasting, pp 109–120 (The Australasian Institute of Mining and Metallurgy: Melbourne).