Scaling distribution for grain composition of debris flow
Pubdate:2017-07-14 From: ANDF Views:
We are all familiar with the irregular and multimodal frequency distribution of grain sizes for soils (Fig.1) and we are also used to the numerous graphic parameters for describing the grain composition (e.g., the special sizes such as D10, D30, D60, the coefficients of sorting, uniform and curvature, as well as the skewness and kurtosis), but we are lacking of a universal expression of the grain size distribution; or, we are wondering if there is really such an expression, given the diverse appearances of soils.
Fig.1 Comparison between grain composition of soils and fine part of sediment
Recently Prof. Li Yong and his team from Institute of Mountain Hazards and Environment, Chinese Academy of Sciences (IMHE), have proposed a scaling expression for the grain size distribution (GSD), for a great variety of soils:
with P(D) the exceedance percentage and C, μ and Dc are parameters determined by the grain size frequency data. Eq.1 reduces to the simple exponential curve, P*(D) = exp (–D/Dc), when rescaled by D/Dc and P*(D) = P(D)D μ/C. This means that all the GSD curves for individual samples fall upon the exponential curve, as exemplified by Fig.2 and 3 for soils from different sources.
|Fig.2 Rescaled GSD for sediments from various valleys||Fig.3 Rescaled GSD for soils from forested soils in Finland|
They find that the power-law and exponential part of the expression can be taken as respectively responding to the self-similar and random processes of grain fragmentation and accumulation in soil generation and evolution. More important is that the GSD remains the same even the soil undergoes changes in mass movements or erosions; this enables the GSD to describe the evolution of soils. Roughly speaking, μ rises positively with the increase of fine content and Dc features the grain size range. Thus the GSD is able to describe the dynamical processes of grain comminution, segregation, migration and mixture in mass movements such as sediment transport, avalanches, landslides, and debris flows.
The GSD expression also applies to the pore size distribution (PSD), confirming the grain-pore duality of granular materials. This casts a new light on porous media in that it is possible to employ the percolation theory to treat the water-soil interactions (e.g., fluidization or liquefaction).
Using the GSD they are able to describe the soil body as a field with parametrs varying point to point, and thus the slope processes can be ascribed to the dynamics of the "granular field".
A scaling distribution for grain composition of debris flow. Geomorphology, 2013(192): 30-42, DOI: 10.1016/j.geomorph.2013.03.015.A unified expression for grain size distribution of soils. Geoderma, 2017(288):105-119. http://dx.doi.org/10.1016/j.geoderma.2016.11.011
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