Principles, Methods, and    
Application of Particle Size 
Analysis

James P. M. Syvitski (Ed.)

Cambridge University Press, Cambridge,     
368 pp., 1991.            
$70 (hbI). ISBN 0 – 521 – 36472 – 8.

At last, a comprehensive, state-of-the-art treatment of granularity for geoscientists! This book fills an important gap in the literature on this topic – it approaches the level of Krumbein & Pettijohn (1938), a classic of its time, and I am especially pleased to see it appear. The relevance of the quotation from Marcel Proust used as the motto of this book has been amply demonstrated: old problems are really seen with new eyes.

The chief contribution of this volume is its presentation of the principles and the theory behind the technology of particle size analysis, as well as applications. It is of interest to anyone involved in this area of geoscience, and it will be of value even to some civil and chemical engineers. The editor is to be commended for assembling the major thematic groups in a logical manner, for attempting to unite 24 chapters (34 authors) in 5 sections into one coherent volume, and for writing the outstanding Preface and Prologues to each section. Indeed, he has been an important contributor to almost every area in this volume.

The book presents a complex array of topics in granularity, but does not favour any one particular method or interpretation over another. The reader will not be forced to accept any specific point of view; rather the evaluations are presented in an impartial manner. However, this liberal treatment has lead to a few inconsistencies in some chapters. For example, the very important chapter l (written by the editor as a co-author) advocates ”the plotting of size in μm or mm increasing to the right on the lower side of a diagram and the phi parameter increasing to the left along the top” (p. 7), but in the next two chapters, his chapter 4 etc., these diagrams are plotted in the opposite manner, with coarse size to the left (p. 23: fig. 2.2 [but not fig. 2.1 above it!], pp. 24, 30, 38 – 58). I also noticed that the level of complexity varies widely from chapter to chapter; some understanding of mathematical procedures such as differential equations is required, which might pose some difficulties for those uninitiated in medium-level mathematics.

Section 1 introduces the basic principles and methods of geological grain size analysis. I highly recommend chapter l, even to those who are interested only in the more specialized chapters of this book. The appendix to this chapter presents a valuable list of 21 manufacturers of instruments, mostly fine size analysers but from few countries (12 USA, 7 UK, 1 France, 1 Germany), without detailing the specific products. Many of those companies are merely importers in the UK or USA, and the parent

companies are not given; for example, the parent companies of Wild-Leitz UK Ltd are Wild Heerbrugg AG, Switzerland, and Ernst Leitz Wetzlar GmbH, Germany (Leitz – and Micromeritics – is misspelled on p. 21). This list should be as distinct and comprehensive a directory as the list of references or authors and subject index, with all appended to the book as a whole rather than to a single chapter.

The two other chapters are by Matthews, the developer of the popular settling rate formula for spheres (Gibbs et al.). The first shows the effect of shape and density on size measurement – the fundamental problem of all methods since natural particles are irregular bodies frequently consisting of several minerals. However, the chapter would behave dramatically simplified if the author had considered a hydraulic reference shape other than spherical, close to the shape of natural particles, such as a shape-factor-specified ellipsoid (Brezina 1979): then the conceptual particle size would be closer to the real physical size, and the investigator who attempts ’to think in terms of physical size rather than conceptual size’ (p. 26) would not be so far out. Since the author ignores any non- spherical shape as a hydraulic reference, his statements are true but only in reference to the spherical shape used for settling (using an equation for sedimentation of spheres). Two examples: ’non-streamlined distortions of a sphere cause increased drag; this decreases the settling velocity, resulting in a hydraulic (or sedimentation) diameter smaller than the particle’s true nominal diameter’ (p. 26). Settling, similar to sieving, ’underestimates the true nominal size of a grain’ (p. 31). However, sieving, in contrast to settling, normally measures non-spherical particles (e.g. mica) as being larger, and therefore it usually overestimates their size. This chapter is based on dry sieving using square screen holes (woven sieves); however, it should also include the most accurate and precise wet sieving with circular screen holes. Moreover, a microscope with the usual short- focus objective lens is one of the most inaccurate methods of measuring particle size: extreme care is required to make the accuracy approach the most accurately measurable sedimentation time. The results are expressed as smooth curves in terms of the rarely used Zingg’s diagram (figs 2.3 – 2.6), without showing the individual data as dots to see the goodness-of-fit of the curves. Some documentation is desirable for presenting experimental work such as this, particularly in constructing the 8 diagrams mentioned above, notably fig. 2.4. The chapter concludes that joining size distributions measured by two different techniques (e.g. sieving of sand, settling of the finer remainder) involves the depletion (p. 31 – 32) of the particles immediately coarser than the separation size. The second chapter by Matthews touches upon a problem rarely addressed in the literature; the definition of composite grains. A size analysis pre-treatment may easily change (usually reduce) the size of aggregates; whether they are authigenic or diagenetic in origin will have major bearing on pre-treatment and subsequent interpretations.

Section 2, which deals with theory, methods and

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calibration provides details of a spectrum of modern and some classical methods. The background information for modern theory behind settling tubes, sieves, image analysis, electro-resistance, laser diffraction, X-ray attenuation and light scattering is well presented in chapters 4 – 11. The Preface states that chapter 12 presents thin-section analysis of sedimentary rocks. However, it does not deal either with theory or application of the effects of random sectioning of bodies, which greatly influences size distribution from thin or polished sections not only of sedimentary, but also of igneous and metamorphic rocks, ores, alloys, plastics, etc. A comprehensive survey and evaluation of the extensive literature on random sectioning effects is desirable. Because this chapter actually deals with interpreting textural maturity from size and shape features, it would suit Section 5 (Applications) better.

Based on my experience, settling tubes (chapter 4), if properly designed, are capable of far higher accuracy than any other method; properly designed in this context means having the capability to weigh the smallest samples quickly to avoid concentration errors. There is a minor misunderstanding in presenting formulae of the grain size and settling rate relationship [p. 47 (and 12)]: Brezina (1979) developed a general equation for drag coefficient as a function of Reynolds’ number and Corey’s Shape Factor and entirely independently of the equations of Gibbs et al. (1971) and Komar & Reimers (1978.), not as a continuation of the work of these authors. Moreover, a graphical comparison of the formulae presented would be helpful. The reader should be aware that a simple formula on grain concentration effects (p. 48 – 49) which fully agrees with the referred studies by Gibbs (1972) and Kranenburg & Geldof (1974), defines a grain concentration limit; above this streaming may cause serious errors, through a minimum grain distance of 3.6 mm (valid for 0.12 – 0.8 mm quartz grains falling in water; Brezina, 1972, p. 265 – 266; 1979, p. 15 – 16, fig. 9). This grain distance in the uppermost 3.5 cm of the settling tubes defines the number of grains per cross sectional area to be a maximum of 109 grains cm^-2. In order to maintain a good statistical representation, 18,000 grains are satisfactory (Kolmogorov, 1933; Kol- mogorov – Smirnov test, 0.99 level of significance), requiring a settling tube diameter of at least 15 cm; then the suitable mass, in grams, of a quartz sample is proportional to the grain-size d in millimeters cubed, i.e. 25d³, giving a sample mass from 0.05 g for finest to 10 g for coarsest sand grains.

The outstanding chapter 11 on light scattering provides a good explanation of background optics not readily found in the geological literature. I am happy to see that the author cites ‘a physicist who says about the horse: let’s assume it is a sphere!’ and says ’irregular particles do scatter light differently than do spheres’ (p. 147). Ignorance of shape leads to distortions of size measured not only by light scattering but also by sedimentation.

Readers new to the subject should consider critically many statements in chapter 12. The sorting index (p. 169, eq. 12.2) is a misinterpretation of Trask (1932): the square root should be calculated; or, if phi is used instead of mm

(Table 12.4, p. 172), a half difference instead of a ratio of phi-quartile values is proper, otherwise the ’sorting index’ is size-dependent; if the phi-quartile difference equals l (So_ø=0.5), then the ’sorting index’ varies from – ∞ (= – 1/0) for the coarsest grains of 2 mm (= – 1 phi) to the maximum of 0.83 ( = 5/6) for the finest grains (6 phi). A roundness formula (eq. 12.4, p. 165) is the arithmetic mean of 5 rounding classes of grains, the amount of which is given by their number instead of by volume or mass. Therefore, a great number, but a negligible volume, of fine grains will over-evaluate the rounding of fine grains. Similar distortion is involved in the so-called ’corrected roundness formula’ (egs 12.5 and 12.6, p. 165). Both the comprehensive textural coefficients T (p. 164) and Td (eq. 12.7, p. 166) include the ’sorting index’ and the average roundness, which are both size-dependent.

In chapter 13, the calibration experiment shows that each method has distinct inaccuracies and recommends reporting size information in the scientific literature. Even though I have continually developed settling tubes and dealt with related problems for more than two decades, I cannot share the view that settling tubes should replace sieving (as also recommended in chapter 4). The tubes sense distributions of settling rate which controls particle occurrence in a space – time unit; relative change of this variable is subject to sedimentational stochastic processes. This is why the psi settling. rate may be suitable variable for sedimentological interpretation of granularity. How- ever, errors caused by inferior settling tubes, such as a positive phi-skewing (its misinterpretation was correctly criticized by Folk 1962) cannot be excused by genetic consistency and thus considered to be harmless and ’natural’. Sieving is not less valuable than settling tubes: a combination of both can reveal valuable information. Psi-settling rate distributions of narrow sieve fractions assembled into a three-dimensional plot disclose a density and/or shape distribution; in this manner heavy to light mineral components (including porous microfossils) can be computed (and isolated without heavy liquids by the Sand Sedimentation Separator™; Brezina, 1992). However, both the sieving and settling tubes require effort to assure precision and accuracy, and cheap efforts are wasted efforts. Minor corrections to chapter 13 (p. 192) include the fact that the MacroGranometer™ settling tube indicated by ’ST3’ has an inner diameter of 20 cm (not 18.5 cm), and the settling tube indicated by ’ST4’ has an inner diameter of 17.5 cm (not 15 cm) and a settling distance of 1.65 m (not 1.5 m).

Section 3, which deals with in situ methods in two chapters is a fine example of the actualistic approach to interpreting past environments. This section is a pioneering contribution concerning analysis of sediments in vivo (’live sediment’ in the process of being modified and deposited), as opposed to in vitro (taken out of natural context and analysed in the laboratory). Relatively few workers have attempted to solve problems in this manner, largely, I suspect, for logistical reasons. Nonetheless, these techniques, including laser holography and high-frequency

Book Reviews
 

acoustic remote sensing, represent a beginning that should be encouraged strongly.

Section 4 on data interpretation deals with the ultimate purpose of all efforts in grain-size analyses: to give them meaning. Chapter 16 on suite statistics emphasizes the importance of a group of samples rather than single samples, criticizes bivariate plots, yet continues to use them. Chapter 17 describes hyperbolic distributions thoroughly. The authors, both representatives of the Aarhus hyperbolic school, believe that the better fit of a hyperbola to natural, particularly asymmetrical, distributions is evidence in favour of its suitability. Chapter 18 shows how to find significant distribution features among large (grain-size) data sets using Q-mode factor analysis. Chapter 19 which is similarly good and well-founded mathematically, demonstrates the hydrodynamic generation of Gaussian and hyperbolic distributions by flume experiments. All chapters in this section deal with specific aspects of grain size interpretation. However, I had hoped to see a general chapter on interpreting distributions. The book leaves the impression that size distributions can only be fitted by a hyperbola (chapter 17) or described by bivariate plots (chapter 16). However, these concepts fail when applied to the commonly seen inhomogeneous size populations due to mixing, both of materials and of generating processes. The mixture components combine in random proportions. This is why a universal model such as the hyperbolic distribution can fit mixed distributions only approximately; the bivariate plots of moments or similar parameters must suffer from irregularities and overlaps even after averaging them from sample groups (’suite statistics’). Because we tend to prefer fewer numbers rather than many, we try to substitute or at least approximate the frequency – size data by a possibly universal distribution model, apparently in the desire to obtain a magic combination of numbers such as a cabala. I recommend that Basin Research readers should consider separating components from the observed distributions (Curray 1961) as suggested on p. 7. Plotting of component means on a map, supported by the component percentages and standard deviations, may reflect basin palaeogeography with transportation pathways. The mixture components are not the segments of probability plots as assumed by Visher: they must be determined by a suitable computer program (this paper is currently in preparation). Only rigid distribution models, such as the Gaussian used on phi, psi or any other suitable function of

the independent variable, should be used for homogeneous distributions, and for single components of mixed distributions. Parameters of flexible, possibly universal, models (such as the hyperbolic one) are influenced by neighbour components and render the separation of these components incorrect. Therefore, these distribution models give distorted results from mixed populations and are not suitable for component separation.

Section 5 (Applications) closes the volume with five chapters as examples of five major applications from among myriads of other themes; chapter 20, ’suite statistics’ of chapter 16 on stratigraphy, chapter 21 on glacial geology, chapter 22 on marine geochemistry, chapter 23 on oceanography, and chapter 24 on marine geotechnical studies.

The only index for this voluminous book amounts to 5½ three-column pages of 825 carefully selected subject items. An authors’ index would be valuable because the references are appended after each article, with a few in prologues to each of the five sections. It is good to see that the 24 chapters have 1104 citations altogether (including repeats); the prologues to each section call attention to a total of 32 citations. I was somewhat surprised that the fundamentally important Small Particle Statistics by Herdan & Smith (1960) was not used in this volume.

This book, sponsored and encouraged by the International Union of Geological Sciences, is an impressive first step in dealing with an area of geoscience largely ignored for about the past decade. Granularity should again be a powerful and invaluable tool of geoscientists. This book is a must to own for all who are involved in the field and is well worth the price. I am certain that in the next edition the flaws outlined will be overcome, and this volume will thereby attain the classical status worthy of the natural successor to Krumbein & Pettijohn.

Jiri Brezina

REFERENCES

Folk, R. L. (1962) Of skewnesses and sands. J. sedim. Petrol. 32, p.145-146.

HERDAN, G. & SMITH, M. L. (1960) Small Particle Statistics, 2nd edn. Butterworths, London, 418 pp.

Kolmogorov, A. N. (1933) Sulla determinatione empirica di una legge di distributione. Giornale Inst. 1tal. Attuari, 4.

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