Advances in the simulation and automated measurement of well-sorted granular material: 2. Direct measures of particle properties

• Published in: Journal of Geophysical Research: Earth Surface Vol. 117; no. F2
• Main Authors: Buscombe, D., Rubin, D. M.
• Format: Journal Article
• Language: English
• Published: Washington, DC Blackwell Publishing Ltd 01-06-2012; American Geophysical Union
• Subjects: Arithmetic; Automation; Coefficients; Corrections; Diameters; Earth sciences; Earth, ocean, space; Empirical analysis; Exact sciences and technology; Fourier analysis; Fractions; Geophysics; grain size analysis; Grains; Granular materials; Gravel; High performance computing; Interstices; Marine geology; Mathematics; Methods; Mineralogy; Particle size; Petrology; powder; Probability theory; random field; Sediment; Sedimentary geology; Sediments; Simulation; Transition probabilities; two-phase media; Void fraction; models; Particle size; geologic sections; Bias; simulation; testing; Particle properties; silt; slopes; graded bedding; grains; gravel; sand; depth; corrections; Severe weather; new methods; Transition probability; prediction; granular materials; particles; populations; Diameter; standard deviation
• ISSN: 0148-0227; 2169-9003; 2156-2202; 2169-9011
• DOI: 10.1029/2011JF001975

In this, the second of a pair of papers on the structure of well‐sorted natural granular material (sediment), new methods are described for automated measurements from images of sediment, of: 1) particle‐size standard deviation (arithmetic sorting) with and without apparent void fraction; and 2) mean particle size in material with void fraction. A variety of simulations of granular material are used for testing purposes, in addition to images of natural sediment. Simulations are also used to establish that the effects on automated particle sizing of grains visible through the interstices of the grains at the very surface of a granular material continue to a depth of approximately 4 grain diameters and that this is independent of mean particle size. Ensemble root‐mean squared error between observed and estimated arithmetic sorting coefficients for 262 images of natural silts, sands and gravels (drawn from 8 populations) is 31%, which reduces to 27% if adjusted for bias (slope correction between observed and estimated values). These methods allow non‐intrusive and fully automated measurements of surfaces of unconsolidated granular material. With no tunable parameters or empirically derived coefficients, they should be broadly universal in appropriate applications. However, empirical corrections may need to be applied for the most accurate results. Finally, analytical formulas are derived for the one‐step pore‐particle transition probability matrix, estimated from the image's autocorrelogram, from which void fraction of a section of granular material can be estimated directly. This model gives excellent predictions of bulk void fraction yet imperfect predictions of pore‐particle transitions.
Key Points
New methods for estimation of the standard deviation of particle sizes (sorting)
New method for mean particle size in a granular section with known void fraction
Methods are completely automated, requiring no calibration or tunable parameters