Particle size distributions in Earth Sciences: a review of techniques and a new procedure to match 2D and 3D analyses

Abstract. Particle size is an essential tool in many research areas spanning from Earth Sciences, Engineering, Material Sciences, Soil Sciences and Pharmacology, among others. Over the last decades, several techniques and methodologies have been developed to calculate particle size distributions on different sample types (i.e., cohesive versus loose), spanning from volumetric (3D) to image-aided (2D) analyses. Here, we (1) present a critical review of most commonly used techniques to calculate particle size distributions from cohesive and loose samples, and (2) we illustrate a new calculation formula to extract reliable 3D grain size distributions from 2D datasets. We propose the use of the “corrected volume-weighted mean diameter” (D_w), as a new particle size descriptor, which results from the summation of products between equivalent particle diameter and particle volume, divided by the total volume of analyzed particles. In this calculation, particles were approximated to perfect circles-spheres, but a shape correction factor was applied to consider deviations from the perfect spherical shape. We tested the accuracy of D_w calculation formula by analyzing 2D datasets acquired from thin sections of 5 selected granular sand samples having different mean grain diameters and grain size distributions (i.e., different sorting degree, grain size distribution width and skewness). Grains were manually digitized, and per each thin section more than 5,000 particles were acquired. Two-dimensional grain size distributions were cross-checked with the results provided via laser diffraction granulometry on the same samples and were compared with previously published and widely used calculation methods. Our promising results encourage the usage of D_w formula as it provides best matching results with 3D laser granulometry and needs basic input parameters that can be easily extracted from any image analysis software.