Several mathematical models have been proposed previously to describe particle-size distribution (PSD) data, but their characteristics and accuracy have not been investigated for the < 0.002, 0.002–0.05 and 0.05–2.0-mm fractions separately. Therefore, the primary objective of this study was to examine the characteristics of various PSD models and to evaluate the accuracy of fitting to the entire PSD curve and to each of the three fractions separately. Thirty-six PSD models were fitted to the experimental data of 160 soil samples from Iran. The beerkan estimation of soil transfer (BEST), Fredlund unimodal and bimodal, two- and three-parameter Weibull, Rosin–Rammler and van Genuchten, models provided the best fit to the experimental data of the three size fractions above, but with a different order of performance for the different fractions. For all textural fractions, the following models performed substantially less well than the other models: the offset-non-renormalized lognormal, simple lognormal, S-curve, Schuhmann, Yang, Turcotte and Gompertz models. A comparison of the overall accuracy and simplicity of the models indicated that the BEST, two- and three-parameter Weibull and Rosin–Rammler models provided the best fit to the experimental data for the entire curve, which is similar but does not correspond fully to the findings of a similar, earlier study. We found that the number of model parameters and the type of equation did not explain the models’ fitting capabilities. We also found that the iterated function system (IFS) model performed better than the PSD models for all fractions. Comprehensive comparisons of PSD models will be of value to future model users, but it is important to note that such comparisons will remain data-set dependent. This is likely to remain so until tested on a near-infinite synthetic data set that covers all possible data options.
