TY - JOUR

T1 - The Case for the Median Fragment Size as a Better Fragment Size Descriptor than the Mean

AU - Ouchterlony, Finn

PY - 2015/3/15

Y1 - 2015/3/15

N2 - Cunningham’s use of x50, the median fragmentsize, instead of the mean hxi in the main prediction equationof the Kuz–Ram model has several times been pointedout as a mistake. This paper analyses if this mistake isimportant using dimensional analysis and by reanalyzingthe historical Soviet data behind Kuznetsov’s originalequation for the mean. The main findings in this paper arethat: (1) Cunningham’s mistake has no proven effect inpractice and would only be relevant as long as he usedKuznetsov’s equation for the rock factor A, i.e. till 1987.(2) Kuznetsov’s equation has its roots in the characteristicsize of the Rosin–Rammler (RR) functions fit to the sievingdata as a way to determine the mean, not only in the meanitself. (3) The key data set behind Kuznetsov’s equationjust as easily provides a prediction equation for x50 with thesame goodness of fit as the equation for the mean. (4) Useof x50 instead of the mean hxi in a dimensional analysis offragmentation leads to considerable mathematical simplificationsbecause the normalized mass passing at x50 is aconstant number. Non-dimensional ratios like x50/xmaxbased on two percentile sizes also lead to such simplifications.The median x50 as a fragment size descriptor thushas a sounder theoretical background than the mean hxi. Itis normally less prone to measurement errors and it is notrejected by the original Soviet data. Thus, Cunningham’smistake has led the rock fragmentation community in theright direction.

AB - Cunningham’s use of x50, the median fragmentsize, instead of the mean hxi in the main prediction equationof the Kuz–Ram model has several times been pointedout as a mistake. This paper analyses if this mistake isimportant using dimensional analysis and by reanalyzingthe historical Soviet data behind Kuznetsov’s originalequation for the mean. The main findings in this paper arethat: (1) Cunningham’s mistake has no proven effect inpractice and would only be relevant as long as he usedKuznetsov’s equation for the rock factor A, i.e. till 1987.(2) Kuznetsov’s equation has its roots in the characteristicsize of the Rosin–Rammler (RR) functions fit to the sievingdata as a way to determine the mean, not only in the meanitself. (3) The key data set behind Kuznetsov’s equationjust as easily provides a prediction equation for x50 with thesame goodness of fit as the equation for the mean. (4) Useof x50 instead of the mean hxi in a dimensional analysis offragmentation leads to considerable mathematical simplificationsbecause the normalized mass passing at x50 is aconstant number. Non-dimensional ratios like x50/xmaxbased on two percentile sizes also lead to such simplifications.The median x50 as a fragment size descriptor thushas a sounder theoretical background than the mean hxi. Itis normally less prone to measurement errors and it is notrejected by the original Soviet data. Thus, Cunningham’smistake has led the rock fragmentation community in theright direction.

KW - Blast fragmentation Prediction equation

U2 - 10.1007/s00603-015-0722-1

DO - 10.1007/s00603-015-0722-1

M3 - Article

VL - 49.2016

SP - 143

EP - 164

JO - Rock mechanics and rock engineering

JF - Rock mechanics and rock engineering

SN - 0723-2632

IS - 1

ER -