A unified expression for grain size distribution of soils

- A general grain size distribution of P(D) = CD− μexp(− D/Dc) is proposed for soils.
- Various soils can be characterized by parameters μ and Dc.
- (μ, Dc) variation indicates changes in grain composition in mass movements.
- The same distribution applies to the pore size of granular materials.

Grain size distribution (GSD) is fundamental for soils and usually described by a set of graphic parameters (e.g., median size, kurtosis, skewness, uniform and curvature coefficient). Some probability distributions (e.g., lognormal and Weibull distribution) are used for special cases, but no general expression is available. In this paper we propose a general distribution form of P(D) = CD−μexp(− D/Dc) for various soil materials, with P(D) the exceedance percentage and C, μ and Dc are parameters determined by the grain size frequency data. The power-law and exponential part of this expression respectively responds to the self-similar and random processes of grain fragmentation and accumulation in soil generation and evolution. The GSD parameters are distinct in soils and their variation reflects the changes in grain composition, such as the grain migration and segregation in landslides, avalanches, debris flows and sedimentary deposits. In addition, the GSD also fits the pore size of granular materials, confirming the grain-pore duality and suggesting an important role of the GSD expression in dynamics of soils and granular media in general.