The shape of rock particles, a critical review

Abstract

An attempt was made to distinguish aspects of the shape of rock particles, and to discover by analysis and empirical considerations the most appropriate parameters for describing these aspects. The shape of a rock particle can be expressed in terms of three independent properties: form (overall shape), roundness (large‐scale smoothness) and surface texture. These form a three‐tiered hierarchy of observational scale, and of response to geological processes. Form can be represented by only two independent measures from the three orthogonal axes normally measured. Of the four pairs of independent measures commonly used for bivariate plots, the two sphericity/shape factor pairs appear to be more efficient discriminators than simple axial ratios. Of the two, the most desirable pair is the maximum projection sphericity and oblate‐prolate index for both measures show an arithmetic normal distribution for the range investigated. A measure of form that is independent of the three orthogonal axes, and measures derived from them, is the angularity measure of Lees. Roundness has measures of three types, those estimating average roundness of corners, those based on the sharpest corner, and a measure of convexity in the particle outline. Although each type measures a different aspect, they are not independent of each other. Only roundness from corners is considered in detail. As neither average nor sharpest corner measures are inherently more objective or more quantitative, purpose should determine which is more appropriate. Of the visual comparison charts for average roundness, Krumbein's appears best. The Modified Wentworth roundness is the most satisfactory for estimating roundness from the sharpest corner. The Cailleux Roundness index should not be used because it includes aspects of roundness and form. Shape is a difficult parameter to use for solving sedimentological problems. Even the best of the commonly used procedures are limited by observational subjectivity and a low discriminating power. Unambiguous interpretation of particle shape in terms of source material and processes will always be made difficult by the large number of natural variables and their interactions. For ancient sediments satisfactory results can be expected only from carefully planned studies or rather unusual geological situations.

A composite particle model for non-spherical particles in DEM simulations

“…In general, the motions of granular materials are resisted by the sliding friction and geometrical interference [1,2], when grains slide along the adjacent particle surfaces. This frictional effect is characterized by the internal friction angle of granular materials which depends mainly on the particle surface roughness and interlocking, while it is independent of the confining stress and density [3]. From a microscopic point of view, both the particle rotation and grain length scale structure can influence the mechanical behaviour of soil [4,5], which can be investigated numerically by the discrete element method (DEM) [6].…”

Particle Shape and Crushing Effects on Direct Shear Behavior Using DEM

“…According to the previous studies, particle shape has been evaluated quantitatively using various roughness parameters such as sphericity, roundness, smoothness, etc (Wadell, 1932;Krumbein, 1941;Power, 1953;Krumbein and Sloss, 1963;Barret, 1980). Based on the literature review, the concepts of circularity and convexity were selected in this study and the particle roughness was evaluated and expressed with the values in the range of 0¿1.0.…”

Failure behavior of single sand grains: Theory versus experiment

“…Roundness reflects grain angularity or surface roughness caused by variations in radii of curvature of edges, corners and faces. It may be quantified as (S(r i /R in ))/n [Wadell, 1932] or r s /R in [Dobkins and Folk, 1970;Folk, 1978], where r i is the radius of curvature of the ith grain corner (of a total n) and r s is the radius of curvature of the sharpest corner [Barrett, 1980]. Sphericity and roundness defined as above can be quantified in the context of the present investigation using a simple geometric model implying the following relations Figure 9 shows sphericity and roundness data compiled from morphology studies on dune sands of various grain size (d) converted into r g versus d plots.…”

“…[42] Second, it is important to consider that in sedimentary petrology the shape or external morphology of quartz sand grains is characterized by independent properties of form, roundness and surface texture distinguishable by their different scales with respect to grain size [Barrett, 1980]. Form can be estimated by elongation parameters based on ratios involving orthogonal principal axes (a e > b e > c e ) of assumed ellipsoidal grains.…”