Characterization of two- and three-dimensional morphological properties of fragmented sand grains

•A numerical framework was proposed to obtain vertical projections of grains after freefalls.•Correlations between two- and three-dimensional morphological properties were explored.•Promising equations were developed to estimate three-dimensional properties from two-dimensional measurements.•Interpretation of grain flatness from multiple grain freefalls was discussed.•Developed equations were applied to determine the specific surface area and permeability of soils.