Empirical determination of sieve size statistics from grain measurement

Abstract

Relationships between sieve grain size and thin section grain size have been determined empirically from the study of 72 artificially created sendstone samples. Modern sands were sieved into size fractions, which were recombined in a log normal distribution to give samples with a range of means and standard deviations, but with similar individual grain properties. Sample splits of these were impregnated with resin, and the size distribution of grain long axes selected by point counter in thin section was compared with that found by sieving the remaining sample. This method attempts to minimise the effects of factors that influence apparent size in thin section. The results have been compared with those of (1958, 1962) who studied the same size relationships in 38 natural sandstones, e.g. This work: Sieve size from Folk = 1.078(thin section mean) + 0.200 phi graphical mean 1/3(Ø16+Ø50+Ø84) Friedman (1958): Sieve size mean from = 0.903(thin section mean) + 0.381 phi combined quartile measures Ø25, Ø50,Ø75 The regression coefficients differ from those of Friedman, probably because of the range of mean sizes investigated in the present work was twice as large (5.7 phi units vs. 2.6 phi units). The correlation coefficient relating sieve to thin section analysis decreases progressively, as Friedman found, from mean (0.992) to standard deviation (0.958), skewness (O.536), and kurtosis (0.249). The correlation for skewness and kurtosis is not significant. The size range was extended to -3.5 phi by the study of the mean size of selected gravel samples measured in sawn slabs. The resulting regression line has a slope of one and an intercept of 0.4 phi and is close to that found for the sands. Grain size in grain mount is also closely related to sieve and thin section size, and a preliminary study of pebble size measured from photographs suggests that this may also be converted to an equivalent sieve size. On qualitative grounds the relationships between the various mean size statistics should involve the simple addition of a constant phi value. However the slopes of the regression equations found in the present work differ slightly from a slope of one. This difference is shown to represent a progressive shape change with size. For a constant b/a ratio of 0.73 or 0.70 conversion of thin section mean size (in phi units) to an equivalent sieve value should therefore be made by the simple addition of a 0.33 or 0.40 phi constant respectively.