Sampling of particulate materials with significant spatial heterogeneity - Theoretical modification of grouping and segregation factors involved with correct sampling errors: Fundamental Sampling Error and Grouping and Segregation Error.

There has been an extensive abuse of Gy's Formula during the entire history of applied TOS (Theory of Sampling), it being applied too liberally to almost any aggregate material conceivable for many material classes of extremely different compositions with significant (to large, or extreme) fragment size distribution heterogeneity, for example many types of municipal and industrial waste materials. This abuse regimen is for the most part characterized by lack of fundamental TOS competence and the historical context of Gy's formula. The present paper addresses important theoretical details of TOS, which become important as sampling rates increase at the conclusion of the full 'lot-to-analysis sampling pathway regarding finer details behind TOS' central equations linking sampling conditions to material heterogeneity characteristics allowing the estimation of Total Sampling Error (TSE) manifestations. We derive a new, complementary understanding of the two conceptual factors, y the grouping factor and, z, the segregation factor, intended to represent the local (increment scale) and long-range (increment to lot-scale) heterogeneity aspects of lot materials, respectively. We contrast the standard TOS exposé with the new formulation. While the phenomenological meaning and content of the new proposed factors (y and z) remains the same, their numerical values and bracketing limits are different with z now representing more realistic effects of liberation and segregation combined. This new formulation makes it easier to get a first comprehensive grasp of TOS' dealings with sampling of significantly heterogeneous materials. We believe this may present a slightly easier path into the core issues in TOS when sampling and sub-sampling gets closer to the final aliquot scale.