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Ranges of Validity of Some Distribution Functions for Blast-fragmented Rock

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Author J A Sanchidrián
ID P201507082

Description

The general ranges of validity of some distribution functions are assessed from their behaviour with 119 sets of fragmentation data from bench blasting obtained by sieving. The emphasis is on determining the lower size/passing limit that the size-scaled Rosin-Rammler, Grady and Swebrec functions, and their bi-component versions, can represent with reasonable precision. By fitting these functions to the data using different weights, the accuracy of the fit varies in the different size/passing zones, so that an overall knowledge of the capacity of the function is obtained across the whole size range, from the coarse zone to the fines. Reasonable ranges of use of bimodal Rosin-Rammler and extended Swebrec (all of them five-parameter, bi-component distributions) are, in terms of percentage passing p, 99 > p > 2 per cent (up to 100 per cent for the extended Swebrec), or 90 > p > 0.5 per cent, in which the expected error of the calculated size is below 15 per cent in the extremes of the range, and less than five per cent in most of the central range; maximum errors (ie errors that will only rarely be exceeded) are typically less than 50 per cent in the central range, and up to about 100 per cent in the extremes. Ranges of use for the Swebrec and the size-scaled Rosin-Rammler (three-parameter distributions), with only slightly larger errors than the bi-components, are 100 > p > 5 per cent or 80 > p > 2 per cent. The classical two-parameter Rosin-Rammler can be used in the range 95 > p > 20 per cent or 90 > p > 10 per cent, with expected and maximum errors less than about 15 per cent and 100 per cent respectively.

CITATION:

Sanchidrián, J A, 2015. Ranges of validity of some distribution functions for blast-fragmented rock, in Proceedings 11th International Symposium on Rock Fragmentation by Blasting, pp 741–748 (The Australasian Institute of Mining and Metallurgy: Melbourne).