Applications of a gradation equation in coarse-grained soils

The gradation equation is used to mathematically express the particle size distribution (PSD) of soils. In this paper, a simple and practicable gradation equation and its applications to coarse-grained soils are discussed. First, the proposed equation can be used as an analytical technique for computing particle breakage factors. Closed forms for two widely used breakage factors are derived and demonstrated using a series of test data on the particle breakage of rockfill materials. Second, two particle size reduction techniques are derived and described by the proposed gradation equation. It is believed that the quantitative relationship between the gradation parameters before and after size reduction could be used to quantitatively and systematically study the particle size reduction effect. In addition, the proposed gradation equation can be used to design specific PSDs for the soils used in discrete-element method analyses and laboratory tests. For example, it is convenient in terms of designing the PSD with a certain coefficient of uniformity, coefficient of curvature and/or specified particle sizes.