The case for the median fragment size as a better fragment size descriptor than the mean

Finn Ouchterlony

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11 Citations (Scopus)


Cunningham’s use of x50, the median fragment
size, instead of the mean hxi in the main prediction equation
of the Kuz–Ram model has several times been pointed
out as a mistake. This paper analyses if this mistake is
important using dimensional analysis and by reanalyzing
the historical Soviet data behind Kuznetsov’s original
equation for the mean. The main findings in this paper are
that: (1) Cunningham’s mistake has no proven effect in
practice and would only be relevant as long as he used
Kuznetsov’s equation for the rock factor A, i.e. till 1987.
(2) Kuznetsov’s equation has its roots in the characteristic
size of the Rosin–Rammler (RR) functions fit to the sieving
data as a way to determine the mean, not only in the mean
itself. (3) The key data set behind Kuznetsov’s equation
just as easily provides a prediction equation for x50 with the
same goodness of fit as the equation for the mean. (4) Use
of x50 instead of the mean hxi in a dimensional analysis of
fragmentation leads to considerable mathematical simplifications
because the normalized mass passing at x50 is a
constant number. Non-dimensional ratios like x50/xmax
based on two percentile sizes also lead to such simplifications.
The median x50 as a fragment size descriptor thus
has a sounder theoretical background than the mean hxi. It
is normally less prone to measurement errors and it is not
rejected by the original Soviet data. Thus, Cunningham’s
mistake has led the rock fragmentation community in the
right direction.
Original languageEnglish
Pages (from-to)143-164
Number of pages22
JournalRock mechanics and rock engineering
Issue number1
Early online date17 Feb 2015
Publication statusPublished - Jan 2016


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