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Mathematical Geosciences

, Volume 48, Issue 2, pp 211–232 | Cite as

Calibrating K and Alpha in Gy’s Formula: A New Approach

  • Richard MinnittEmail author
Article

Abstract

Application of Gy’s formula to the determination of the fundamental sampling error is critically based on the calibration of the parameters K and alpha (\(\alpha \)) in his equation. Typical calibration methods include the heterogeneity test (HT) and the duplicate sampling analysis (DSA). Concerns relating to these methods are that the HT is applicable to only one size fraction, whereas the DSA method may introduce grouping and segregation errors (GSE) during sample splitting, thus casting suspicion on the values derived for K and \(\alpha \). The segregation free analysis (SFA) approach involves crushing and screening approximately 100–200 kg of mineralised ore through a nest of 14 different sieve sizes. Narrowly classified ore fragments from each screen size are split into a series of 32 samples and assayed for gold. The log\(_\mathrm{e}\) product of variance and average mass of the 32 samples is plotted against the log\(_\mathrm{e}\) of fragment sizes to produce a calibration curve from which values for K and alpha are derived. Advantages are the simplicity of the method, absence of the GSE, and the ability to calculate the liberation size. Sichel’s t estimate for the mean of the different size fractions overcomes the instability associated with the calculation of the mean of lognormal distributions. Theoretical objections to the SFA method are that the single stage of comminution of the parent lot is insufficient to expose the variability that is captured by other methods, as the individual series are successively crushed from one size to the next.

Keywords

Gy’s formula Fundamental sampling error Calibration K and alpha (\(\alpha \)

Notes

Acknowledgments

A version of this work was published by RCA Minnitt, D Francois-Bongarçon and FF Pitard in 2011 under the title “Segregation Free Analysis for calibrating the constants K and \(\alpha \) for use in Gy’s formula”, in the proceedings of the Fifth World Conference on Sampling and Blending WCSB5, 25-28 October 2011. M. Alfaro, E. Magri and F.F. Pitard (Eds.), Gecamin Ltda., Paseo Bulnes 197, Piso 6, Santiago, Chile. pp 133-150. Permission to publish this paper was obtained from Gecamin Publications, March 16, 2015.

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Copyright information

© International Association for Mathematical Geosciences 2015

Authors and Affiliations

  1. 1.School of Mining EngineeringUniversity of the WitwatersrandJohannesburgSouth Africa

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