Size distribution functions for rock fragments

The capacity of 17 functions to represent the size distribution of fragmented rock is assessed on 1234 data sets of screened fragments from blasted and crushed rock of different origins, of sizes ranging from 0.002 to 2000 mm. The functions evaluated are Weibull, Grady, log-normal, log-logistic and Gilvarry, in their plain, re-scaled and bi-component forms, and also the Swebrec distribution and its bi-component extension. In terms of determination coefficient, the Weibull is the best two-parameter function for describing rock fragments, with a median R2 of 0.9886. Among re-scaled, three-parameter distributions, Swebrec and Weibull lead with median R2 values of 0.9976 and 0.9975, respectively. Weibull and Swebrec distributions tie again as best bi-component, with median R2 of 0.9993. Re-scaling generally reduces the unexplained variance by a factor of about four with respect to the plain function; bi-components further reduce this unexplained variance by a factor of about two to three. Size-prediction errors are calculated in four zones: coarse, central, fines and very fines. Expected and maximum errors in the different ranges are discussed. The extended Swebrec is the best fitting function across the whole passing range for most types of data. Bimodal Weibull and Grady distributions follow, except for the coarse range, where re-scaled forms are preferable. Considering the extra difficulty in fitting a five-parameter function with respect to a three-parameter one, re-scaled functions are the best choice if data do not extend far below 20% passing. If the focus is on the fine range, some re-scaled distributions may still do (Weibull, Swebrec and Grady, with maximum errors of 15-20% at 8% passing), but serious consideration should be given to bi-component distributions, especially extended Swebrec, bimodal Weibull and bimodal Grady.