A universal grain‐size distribution of soil with scaling invariance

TL;DR: In this paper , the authors proposed a universal GSD function for a general form of P(D)~D−μexp(−D/Dc)n, which introduces a new exponent n for the grain size scale.

Abstract: Soils are composed of wide‐ranged grains and grain size distribution (GSD) is the fundamental characteristic determining the physical and hydraulic properties. Previously we have proposed a GSD function for various soils. However, the remarkable discrepancy in the distribution occurs in some soils, which not only limits the applicability of the function but also raises doubt as to the possibility of a universal GSD function. In this study we modify the GSD function to a general form of P(D) ~ D−μexp(−D/Dc)n, which introduces a new exponent n for the grain size scale. It turns out that this modification has eliminated the discrepancies and universally applies to a great variety of soils from around the world (hence to be a universal GSD function, UGSD). The exponent n is proved to be a scaling factor of grain size in log‐scale and divides soils into three categories of n < 1 n > 1, and n = 1. Furthermore, soils of surface processes (e.g., erosion, tillage, desertification, landslides, avalanches, deposition, and sediment transportation) remain in the same category and preserve the UGSD function. Thus, the UGSD not only provides parameters μ and Dc as synthetic indices for soil properties (e.g., as indices for spatial heterogeneity or variables for pedotransfer functions), but also describes texture changes in dynamic processes. The UGSD function represents a ‘conservative law’ underlying soil genesis and processes, which fills the knowledge gaps related to the lack of universally applicable indices for soil properties, and thus has universal applications in soil classification, spatial variability, as well as dynamical processes.