Issue 5, p. 175 (2015)
Pierre Gy has derived an equation, which can be used to estimate the relative variance of the fundamental sampling error of size distribution results given as mass fractions for each size class. This theory is used in this study. The Heterogeneity Invariant, HI, is the relative variance of the fundamental sampling error extrapolated to a sample size of a unit mass (usually 1 g). HI can be estimated from a sieve analysis for each size class i from Eq. 1.
Here ai. is the mass fraction of size class i, vi the average particle size in class i and ρi the density of particles in size class i. Given HIi, the relative variance of the fundamental sampling error, S2FSE can be estimated for different sample sizes to be sieved from the test material:
Here ms is the sample size to be sieved and mL the size of the lot from which the sample is taken. If the sampling methods performs correctly (unbiased) and is able to minimize the segregation effects, always present when material consisting of fragments or particles having a wide size distribution, the observed variance of replicate samples should be close to that obtained by using the above equations. It is also possible to calculate a confidence intervals for a given size distribution. In this study a newly developed sampler was tested by sampling blast hole chippings from Northland Resources’ Kaunisvaara Iron Ore Mine in northern Sweden and the results were compared to other sampling methods currently in use. A number of the samples were also sent for chemical analysis to see if the analytical results correlate with the size classes. A convenient way to summarize and compare size distribution results and analytical results is to carry out Principal Component Analysis (PCA) on both the size data and the analytical data.