An Automated Approach to the Heterogeneity Test for Sampling Protocol Optimization

Abstract

The fundamental sampling error is one of the sampling errors defined by Pierre Gy’s Theory of Sampling and is related to the constitution heterogeneity of the mineralisation. Even if a sampling procedure is considered ideal or perfect, this error will still exist and, therefore, cannot be eliminated. A key input into Gy’s fundamental sampling error equation is intrinsic heterogeneity. The intrinsic heterogeneity of a fragmented lot can be estimated by the “calibrated” formula of Gy, which can be written as a function of the sampling constants K and α. These constants can be calibrated by the standard heterogeneity test, originally developed by Pierre Gy and Francis Pitard. This method is based on the selection of rock fragments, individually and randomly, in an equiprobabilistic way from a lot of particulate material, aiming to estimate the intrinsic heterogeneity of the lot. This test, in addition to demanding time and space, can be influenced by human biases, and is difficult to quantify or measure. Aiming to simplify the test execution and eliminate the variance generated by human biases, a prototype called the intrinsic heterogeneity tester was developed as an automated alternative for heterogeneity testing. This prototype selects fragments from a falling stream, one by one, by means of a predefined laser count. To evaluate the prototype, a study was carried out, using painted chickpeas to simulate mineralisation grades and, sequentially, processing the same lot in the intrinsic heterogeneity tester prototype several times. The statistical and mineral content analysis, and comparisons between the intrinsic heterogeneity tester and the standard heterogeneity test sampling constants and constitution heterogeneities were undertaken. As a result, the authors conclude that the intrinsic heterogeneity tester prototype can be used as an alternative to the manual selection of individual fragments and for estimating the intrinsic heterogeneity of particulate material lots to support sampling protocol optimization.