A Version of Gy’s Equation for Gold-bearing Ores

The two methods for calibrating the parameters K and (alpha) for use in Gy’s equation for the Fundamental Sampling Error (FSE)–, Duplicate Sampling Analysis (DSA) and Segregation Free Analysis (SFA)–, are described in detail. A case study using identical broken reef material from a Witwatersrand-type orebody was calibrated using the DSA and SFA methods and the results compared. Classically, the form of Gy’s equation for the FSE raises the nominal size of fragments given by dN to the power of 3. A later modification of Gy’s formula raises dN to the power (alpha), the latter term being calibrated with the coefficient K in the DSA and SFA methods. The preferred value of for low-grade gold ores used by sampling practitioners in the mining industry is 1.5. A review of calibration experiments for low-grade gold ores using the DSA and SFA methods has produced values of K that vary between 70 and 170 and values of in the range 0.97 to 1.30. The average value for is shown to be 1, rather than 3 as originally proposed in the classic form of Gy’s equation or the industry-preferred 1.5. It is suggested that for low-grade gold-bearing ores the equation for the FSE should raise dN to a power of 1. Such an equation for the variance of the FSE greatly simplifies the characterization of gold ores, now requiring only the calibration of K for a given mass and established fragment size. The implications of the simplified equation for the heterogeneity test are that, provided the fragments have been screened to within a narrow size range, any particular size will return a value for K that is acceptable for use in the sampling nomogram.