The ellipsoidal form of clasts with practical applications to fabric and size analyses of fluvial gravels

Abstract

The widespread assumption that most water-worn gravel clasts approximate ellipsoids is confirmed by a statistical analysis of available data. The analysis demonstrates a Gaussian distribution of V/Ve ratios, centred on unit ratio, where V is clast volume and Ve the volume of a symmetric ellipsoid with equivalent triaxial dimensions. For internally isotropic and unbroken clasts, ellipsoidal form evolves as the rounding due to abrasion reaches its final stages. There appears to be no other major control on the tendency towards ellipsoidal geometry. The ellipsoidal tendency assists the interpretation of fluvial gravel deposits, which depends greatly on accurate description of clast size and fabric.Firstly, it facilitates calculation of Ap, the plane area projected upstream by clasts, a key parameter in bed–flow interactions such as preferred fabric. Formulae are derived to calculate Ap for ellipsoidal clasts with any configuration relative to flow direction. Viewing fabric in terms of the Ap variable supports and explains earlier conclusions concerning the controls on variability of imbrication angle.Secondly, an investigation of the relative merits of six size measures as descriptors of areal trends and predictors of nominal diameter, dn, concludes that (abc)1/3(the formula for dn of an ellipsoid) is superior. Other measures, namely, a, b, c, (a + c)/2, and (a + b + c)/3, are all subject to error in proportion to the degree of shape variation. Also, since downstream fining is typically accompanied by a changing proportion of oblate, bladed, prolate, and equant forms, dn is subject to inconsistent levels of under- or overestimation. The commonly used b dimension is endorsed as an acceptable predictor of dn, but a severely overestimates dn and should be abandoned. Information on errors in size analysis is presented as nomograms in the form of contoured c/b versus b/a plots and as probability distributions based on the typical range of shape variation in fluvial gravel.