The Median Versus the Mean Fragment Size and Other Issues with the Kuz-Ram Model (8c6eb78e-36ab-4850-9d6b-ecb1792625f3)

Soviet precursors to Cunningham’s Kuz-Ram model from 1983 are described. They are rooted in the mean fragment size and Rosin-Rammler (RR) fits to sieving data and rely on approximations. Three versions of Kuz-Ram model are presented and all three are de facto based on the median fragment size x50, even if the term mean is used in the papers. This discrepancy caused Spathis in 2004 to suggest a correction procedure for the Kuz-Ram rock factor A, which was said to explain some of the missing fines in the model. This correction, while applicable to Cunningham’s 1983 paper, does not apply to his 1987 paper in which he presents his own A factor. Common fixes of the Kuz-Ram model’s fines issue are fragmentation models where the fines are mainly generated in a crushed zone around a blast hole. This is contradicted by careful model blasting tests. The lack of a largest block size in the RR function may lead to spurious values of the uniformity coefficient n, e.g. in conjunction with image based fragmentation measurements or crusher modeling. These issues may be solved by using the transformed RR function, which has a largest block size xmax or its replacement by the Swebrec function such as in the KCO model.