7 P article Size Analysis Peter J. Loveland Cranfield University, Silsoe, Bedfordshire, England W. Richard Whalley Silsoe Research Institute, Silsoe, Bedfordshire, England I. INTRODUCTION This chapter is not a laboratory manual. It is more concerned with the principles underlying the concepts of particle, size, and distribution, the relationships be- tween them, and the methods by which they may be measured. There are now some 400 reported techniques for the determination of particle size (Barth and Sun, 1985; Syvitski, 1991), although the large body of measurements amassed by soil scientists has generally been made using simple methods and equipment, prin- cipally sieving, gravitational settling, the pipet, and the hydrometer. There is also a large body of experience in interpreting these data. However, there is still a surprising lack of uniformity in these simple procedures, and for that reason we consider them in some detail. The classification of soils in terms of particle size stems essentially from the work of Atterberg (1916). He built on the work of Ritter von Rittinger (1867) in relation to rationalization of sieve apertures as a function of (spherical) particle volume, and that of Ode´n (1915), who applied Stokes’ law to soil science for the first time. In 1927 the International Society of Soil Science adopted proposals to standardize the method for the ‘‘mechanical analysis’’ of soils by a combination of sieving and pipeting and, equally important, resolved to analyze (at least for agricultural soils) only the fraction passing a round-hole 2 mm sieve—the so- called ‘‘fine earth’’ (ISSS, 1928). There have been many revisions of the particle size classes promulgated in 1927, and it is now recognized that soil science can make little further headway in Copyright © 2000 Marcel Dekker, Inc. the interpretation of particle size distribution in the submicrometer range, because the simple methods are incapable of further resolution. For that reason we have reviewed a number of less common or more recent instrumental techniques, which are capable of extending our understanding of the distribution of particles in this region. We have also quoted much of the older literature, as this gives the physics and mathematics from which more recent developments have arisen. A large number of standard methods for particle size analysis is available. Many have been published by bodies responsible for national standards*, and others by the ISO* (e.g., AFNOR, 1983c; DIN, 1983, 1996; BSI, 1990, 1998; ISO, 1998). Other key sources are Klute (1986), Head (1992), Carter (1993), USDA (1996), and ASTM (1998b). Readers should consult these publications, especially those by the ISO, for practical details of methods of analysis, as use of them will reduce the divergence of analytical results often found in interlaboratory ‘‘ring-tests.’’ II. BASIC CONCEPTS A. Particles A particle is a coherent body bounded by a clearly recognizable surface. Particles may consist of one kind of material with uniform properties, or of smaller par- ticles bonded together, the properties of each being, possibly, very different. Soils are formed under particular conditions, and the particles are to a greater or lesser extent products of those conditions. If the soil is disturbed, the particles may change: for example, salts and cements can dissolve, organic remains can be fragile, bonding ions can hydrolyze, and bonds thus be weakened. Not all these changes may be desirable if the original material is to be fully and properly char- acterized. AFNOR (1981b) has given a useful vocabulary that defines terms relat- ing to particle size. Few natural particles are spheres, and often the smaller they are, the greater is the departure from sphericity. One method of size analysis may not be enough, and the methods chosen should reflect the information desired; there may be little point in characterizing as spheres particles that are plates. Allen et al. (1996) listed a number of measures of particle size applicable to powders. In soil analysis, the commonest by far is the volume diameter, which is generally equated with Stokes’ diameter. 282 Loveland and Whalley * Throughout this chapter, AFNOR stands for Association Franc¸aise de Normalisation (Paris); ASTM for American Society for Testing and Materials (Philadelphia); BSI for British Standards Institution (London); DIN for Deutsches Institut fu¨r Normung (Berlin); ISO for International Standards Orga- nisation (Geneva). Copyright © 2000 Marcel Dekker, Inc. Sedimentologists often characterize irregular particles in terms of ‘‘spheri- city’’ or, more usually, an index to indicate departure from sphericity, although all the methods involve much labor to acquire enough measurements on enough grains to obtain statistically valid data (Griffiths, 1967). The introduction of im- age-analyzing computers has made the task of size analysis much easier and has extended the techniques beyond the range of the optical microscope (e.g., Ringrose-Voase and Bullock, 1984). Tyler and Wheatcraft (1992) made a useful review of the application of fractal geometry to the characterization of soil par- ticles, and cautioned against the use of simple power law functions for particles as diverse as those found in soils. Barak et al. (1996) went further, and concluded that fractal theory offers no useful description of sand particles in soils and hence doubted the applicability of these methods to soils with large amounts of coarser particles. Grout et al. (1998) came to an almost identical conclusion. However, Hyslip and Vallejo (1997) stated that fractal geometry can be used to describe the particle size distribution of well-graded coarser materials. The utility of fractal mathematics in soil particle size analysis is clearly an area likely to develop further. B. Size and Related Matters Soils may contain particles from Ͼ 1 m in a maximum dimension to Ͻ 1 mm, i.e., a size ratio of 1,000,000 :1 or more. For the larger particles, which can be viewed easily by the naked eye, a crude measure of size is the maximum dimen- sion from one point on the particle to another. In many cases, only a scale for the coarse material is needed—for example, as a guide to the practicalities of plowing land. It is the smaller particles, however, on which most interest focuses, as these have a proportionately greater influence on soil physical and chemical behavior. Size and shape are indissoluble. The only particle whose dimensions can be specified by one number (viz., its diameter) is the sphere. Other particle shapes can be related to a sphere by means of their volume. For example, a 1 cm cube has the same volume as a sphere of 1.24 cm diameter. This is the concept of equivalent sphere (or spherical) diameter (ESD). Thus the behavior of spheres of differing diameters can be equated to particles of similar behavior to those spheres in terms of their ESD. However, the limitations of the equivalent sphere diameter concept are illustrated by the fact that a sphere of diameter 2 mm has a volume of approximately 4 ϫ 10 Ϫ12 cm 3 , but the same volume is occupied by a particle of 100 nm ϫ 2 mm ϫ 20 mm. Most soil scientists are interested in the proportion (usually the weight per- cent) of particles within any given size class, as defined by an upper and lower limit (e.g., 63–212 mm). Size classes are usually identified by name, such as clay, silt, or sand, and each class corresponds to a grade (Wentworth, 1922). It is Particle Size Analysis 283 Copyright © 2000 Marcel Dekker, Inc. common, particularly among sedimentologists, to describe a deposit in terms of its principal particle size class, for example, of being ‘‘sand grade.’’ Soil scientists use a similar system when using the proportions of material in different size frac- tions to construct so-called texture triangles or particle size class triangles (Figs. 1 and 2). There is considerable variation among countries as to the limits of the different particle size classes (Hodgson, 1978; BSI, 1981; ASTM, 1998d), and hence the meaning of such phrases as ‘‘silt loam,’’ ‘‘silty clay loam,’’ etc. Rous- seva (1997) has proposed functions that allow translation between these various particle size class systems. The distribution of particles in the different size classes can be used to con- struct particle size distribution curves, the commonest of which is the cumulative curve, although there are others. Interpolation of intermediate values of particle size from such curves should be undertaken with care. The curves are only as good as the method used to obtain the data and the number of points used to construct them. Serious errors can arise if the latter are inadequate (Walton et al., 1980). Thus curve fitting, especially though software, should only be undertaken with a proper understanding of the underlying mathematics (ISO, 1995a, b; AFNOR, 1997b; ASTM, 1998c). 284 Loveland and Whalley Fig. 1. Triangular diagram relating proportions of sand, silt, and clay to particle size classes as defined in England and Wales. Copyright © 2000 Marcel Dekker, Inc. C. Sampling and Treatment of Data Sampling and treatment of data have been discussed exhaustively by many authors (e.g., Klute, 1986; Webster and Oliver, 1990). The cardinal principle is that the sample must be representative of the soil under study; otherwise, the resulting data will be inadequate or misleading, and no amount of statistical massaging will com- pensate for this. Head (1992) gave recommended minimum quantities of soil to be taken for analysis based on the maximum size of particle forming more than 10% of the soil (Table 1). It is clear that as particle size increases, the problems of represen- tative sampling become formidable. Ideally, laboratory subsamples should be taken from a moving stream of the bulk material (Allen et al., 1996). A rotary sampler or chute splitter is the best tool Particle Size Analysis 285 Fig. 2 Particle size classes drawn as an orthogonal diagram using only clay and sand fractions. Copyright © 2000 Marcel Dekker, Inc. for obtaining relatively small samples of soil of Ͻ 2 mm size from a larger bulk sample (Mullins and Hutchinson, 1982), while riffling can be used up to about 10 cm. The only practicable method thereafter is coning andquartering (BSI,1981). D. Accuracy, Precision and Reference Materials The accuracy of particle size analysis methods for soils is difficult to establish, as there are no natural soils made up of perfectly spherical particles for use as stan- dards. Further, because of the varied shape of naturally occurring particles, there is no general agreement on how the accuracy, i.e., the approach to an absolute or true value, of this shape should be measured and reported. The precision is less difficult to assess. Provided that the technique is followed carefully, then sufficient data can be acquired to perform normal quality control statistics (ISO, 1998), which can be used to express the ‘‘repeatability’’ of a method for a particular class of materials. The latter may have to be more specific than just ‘‘soils,’’ for a particular method of determination, e.g., soils dominated by sand grains may give different performance criteria from soils dominated by clay particles. Synthetic reference materials (obtainable as Certified Reference Materials, CRMs), such as glass beads (‘‘ballotini’’), latex spheres, and so on, are of limited application in assessing the performance of methods for the particle size analysis of natural materials. They may be useful in certain techniques, e.g., image analy- sis, electrical sensing zone methods, and methods dependent on the interaction with radiation (Hunt and Woolf, 1969). However, such applications are less com- mon than the need to assess method performance on a routine basis, e.g., in a teaching or commercial laboratory. 286 Loveland and Whalley Table 1 Minimum Quantities of Soils for Sieve Analysis Maximum size of particle forming more than 10% of soil (mm) Minimum mass of soil for sieve analysis (kg) 63 50 50 35 37.5 15 28 5 20 2 Ͻ20 a 1 a It is recommended that the minimum sample mass be 1 kg, however small the particles. Source: Modified from Head (1992) and ASTM (1998b). Copyright © 2000 Marcel Dekker, Inc. Other CRMs, such as powdered quartz, are also available (Table 2), but any particular CRM covers only a limited size range, is relatively expensive (ca. US$2/g at the time of writing), and is available in relatively small amounts, e.g., 100 g lots. Thus any laboratory using these materials to cover a wide range of particle sizes, using the quantities required by many methods of analysis—10 g is not uncommon—may find the expense of including a standard in every ana- lytical batch (often considered to be the minimum requirement of ‘‘good labora- tory practice’’) unsustainable. An alternative is to use in-house reference materials, which can, if prepared and subsampled carefully, be more than adequate to monitor the long-term perfor- mance of the method of analysis. They have the added advantage that continuity of supply can be ensured by careful selection of the source site(s). Our own ex- perience suggests that ca. 10 kg of each of one material representing fine-textured soils, e.g., a clay or clay loam, and another representing coarse textured soils, e.g., a sandy loam or loamy sand, is adequate for quality control of 25,000 or more routine particle size analyses (ca. 10 g of each reference material for every batch of 30 samples). It should be well within the capabilities of the average soil labo- ratory to obtain, prepare, and subsample such modest amounts of material. There is a widespread view that a few percent error either way in the particle size determination of a specific size class is not very important. This seems to stem from the beliefs that soils are inherently variable and that, in most cases, the analytical data are used only to place a soil in a particle size class. However, size classes have exact numerical boundaries, and major decisions can flow from the class in which a soil is placed. Therefore, the class should be decided on the basis of the best possible data that can be obtained. III. PARTICLE SIZE TECHNIQUES AND APPLICATIONS A. Introduction Methods for determining particle size can be divided into the following broad groups: Direct measurement (ruler, caliper, microscope, etc.) Sieving Elutriation Sedimentation (gravity, centrifugation) Interaction with radiation (light, laser light, x-rays, neutrons) Electrical properties Optical properties Gas adsorption Permeability Particle Size Analysis 287 Copyright © 2000 Marcel Dekker, Inc. Table 2 Suppliers of Equipment, Software, and Other Materials a,b Type of equipment Supplier General equipment (samplers, sieves, shakers, splitters, crushers, elutriators, etc.) Amherst Process Instruments Inc., The Pomeroy Building, 7 Pomeroy Lane, Amherst, MA 01002-2905, USA (www.aerosizer.com/) Dispersion Technology Inc., Hillside Avenue, Mt. Kisco, NY 10549, USA (www.dispersion.com/) Eijkelkamp Agrisearch Equipment, P.O. Box 4, 6987 ZG Giesbeek, The Netherlands (www.diva.nl/eijkelkamp/) ELE International (Agronomics), Eastman Way, Hemel Hempstead, Herts. HP2 7HB, UK (www.eleint.co.uk/) Endecotts Ltd., 9 Lombard Road, London. SW19 3TZ, UK (www.martex.co.uk/) Fritsch Laborgera¨tebau GmbH, Industriestraße 8, D-55743, Idar- Oberstein, Germany (www.fritsch.de/) The Giddings Machine Company, 401 Pine Street, P.O. Drawer 2024, Fort Collins, Colorado 80522, USA (www.soilsample.com/) Gilson Company Inc., P.O. Box 677, Worthington, Ohio 43085-0677, USA (www.globalgilson.com/) Glen Creston Ltd., 16, Dalston Gardens, Stanmore, Middlesex HA7 1BU, UK (www.labpages.com/) Ladal (Scientific Equipment) Ltd., Warlings, Warley Edge, Halifax, Yorks. HX2 7RL, UK (www.members.aol.com/fpsconsult/) Pascal Engineering Co. Ltd., Gatwick Road, Crawley, Sussex. RH10 2RD, UK Seishin Enterprise Co. Ltd., Nippon Brunswick Buildings, 5-27-7 Sendagaya, Shibuya-ku, Tokyo, Japan (www.betterseishin.co.jp/) Wykeham Farrance Engineering Ltd., 812 Weston Road, Slough, Berks. SL1 2HW, UK (www.wfi.co.uk/) Centrifugal analyzers Brookhaven Instruments Corp., 750 Blue Point Road, Holtsville NY 11742, USA (www.bic.com/) Horiba Ltd., 17671 Armstrong Ave., Irvine, CA 92714, USA (www.horiba.com/) Joyce-Loebl Ltd., 390 Princesway, Team Valley, Gateshead, NE11 0TU, UK (www.mjhjl.demon.co.uk/) Digital density meters Anton Paar GmbH., Kaerntner Straße 322, A-8054 Graz, Austria (www.anton-paar.com/) Electrical sensing zone devices Beckmann Coulter Inc., 4300 N. Harbour Boulevard, PO Box 3100, Fullerton, CA 92834-3100, USA (www.coulter.com/) Micromeritics Instrument Corp., One Micromeritics Drive, Norcross, GA 30093-1877, USA (www.micromeritics.com/) Light-scattering devices/ Photosedimentometers Brookhaven Instruments Corp., 750 Blue Point Road, Holtsville NY 11742, USA (www.bic.com/) Beckmann Coulter Inc., 4300 N. Harbour Boulevard, PO Box 3100, Fullerton, CA 92834-3100, USA (www.coulter.com/) Fritsch Laborgera¨tebau GmbH, Industriestraße 8, D-55743, Idar- Oberstein, Germany (www.fritsch.de/) Copyright © 2000 Marcel Dekker, Inc. Table 2 Continued Type of equipment Supplier Light-scattering devices/ Photosedimentometers (continued) High Accuracy Products Corp. (HIAC), 141 Spring Street, Claremont, CA 91711, USA (www.hiac.com/) Honeywell Inc., 16404 N. Black Canyon Road, Phoenix AZ85023, USA (Mictotrac Analyzers) (www.iac.honeywell.com/) LECO Corporation Svenska AB, Lo¨va¨ngsva¨gen 6, S-194 45 Upp- lands, Va¨sby, Sweden (www.lecoswe.se/) Malvern Instruments Ltd., Enigma Business Park, Grovewood Road, Malvern, Worcs. WR14 1XZ, UK (www.malvern.co.uk/) Quantachrome Corp., 1900 Corporate Drive, Boynton Beach, FL 33426, USA (Cilas Analyzers) (www.quantachrome.com/) Sequoia Scientific, Inc., PO Box 592, Mercer Island, WA 98040, USA (www.sequoiasci.com/) (includes submersible instruments) X-ray sedimentation equipment (Sedigraph) Micromeritics Instrument Corp., One Micromeritics Drive, Norcross, GA 30093-1877, USA (www.micromeritics.com/) Software Most electronic instruments come with built-in software to process, display, or output data. Many earth science and civil engineering departments of universities offer software for aspects of particle size analysis, and the following also supply more general-purpose software: Fritsch Laborgera¨tebau GmbH, Industriestraße 8, D-55743, Idar- Oberstein, Germany (www.fritsch.de/) (sieve analysis) SPSS Inc., 233 S. Wacker Drive, 11th Floor, Chicago, IL 60606-6307, USA (www.spss.com/) (image analysis) Fine Particle Software, 6 Carlton Drive, Heaton, Bradford, W. York- shire, BD9 4DL, UK (www.members.aol.com/lsvarovsky/) (most areas of particle size data manipulation) Texture Autolookup (www.members.xoom.com/drsoil/tal.html) (places particle size analysis data in USDA and UK ‘‘texture’’ classes; see also Christopher & Mokhtaruddin, 1996) Advanced American Biotechnology and Imaging, 116 E. Valencia Drive, #6C, Fullerton, CA 93831, USA. (www.aabi.com/) (image analysis, including shape factors) Certified Reference Materials (CRMs) Many National Standards’ Organisations (but not ISO) produce, or participate in the production of, Certified Reference Materials for en- vironmental analysis. The following have particularly wide coverage, but a search of the WWW will reveal very many more: Community Bureau of Reference—BCR, Commission of the European Communities, rue de la Loi 200, B-1049 Brussels, Belgium Promochem GmbH, Postfach 101340, 46469 Wesel, Germany a This list is not claimed to be exhaustive. We give manufacturers/suppliers only of items specific to particle size analysis, and generally give the headquarters’ address and world wide web site. All addresses were checked at the time of writing, and all quoted web-sites visited to test that they existed and were working. The mention of any company or product is not a recommendation or warranty of any kind, but is given merely for information. b All world wide web site addresses given between brackets are assumed to start with: http://. Copyright © 2000 Marcel Dekker, Inc. Some procedures make use of combinations of these methods. This chapter touches on some of the techniques available. We aim to discuss the principles, origins, and limitations of some standard methods and to point to newer methods that may provide more and/or better information as to how particles in soils can be characterized, and hence how soil behavior can be better predicted. Table 2 gives commercial sources of some of the instrumentation. B. Direct Measurement Although soil scientists generally concentrate on the soil fraction passing a 2 mm aperture sieve, many soil classification systems categorize soils according to the amounts of particles greater than a given size (e.g., ASTM 1998d). Engineers faced with moving much soil may find its complete grading to be essential (BSI, 1981). Although even large particles may be sized by sieving, it is often more practical to resort to direct measurement in situ. The very largest particles can be measured with a tape, and those up to some tens of cm in size by wooden or light alloy templates into which are cut holes of differing shapes and dimensions (Billi, 1984). Caroni and Maraga (1983) used an adjustable caliper connected to a tape-punch so that the results could be fed directly to a computer back at the laboratory; nowadays an electronic caliper and data-logger would be possible. Hodgson (1997) gave a method by which the volume of particles above a particu- lar sieve size may be estimated by means of plastic balls. Laxton (1980) has used a photographic technique for estimating the grading of the boulder- and cobble- grade material in exposed working faces of quarries. Buchter et al. (1994) found good correlation between the amounts of very coarse material in a rendzina, as measured by volume, conventional particle size analysis, and thin section. For particles between about 10 cm and 1 mm, there is little practical alter- native to sieving (Sec. III.C), as the particles are too numerous for the methods outlined above. Between 1 mm and about 20 mm, optical microscopic methods are suitable, while for smaller particles electron microscopy can be used. The advantage of microscopy is that it allows full consideration of shape factors. Mi- croscopy requires careful sampling for the measurement of many individual par- ticles to obtain statistically valid results (Griffiths, 1967; Kiss and Pease, 1982; AFNOR, 1988). The use of automatic image analysis can also speed matters. All microscopic techniques, but especially those for very small particles, require good dispersion of the material. This usually means destruction of organic matter, sol- vation with a particular cation, commonly sodium, with subsequent removal of excess salt, and/or dissolution of cementing agents (Klute, 1986). The basic tech- niques for sizing by microscopy were reviewed by Allen et al. (1996). Many Stan- dards give specific procedures for optical microscopy (e.g., AFNOR, 1990; BSI, 1993). Tovey and Smart (1982) covered electron microscopy techniques in detail, 290 Loveland and Whalley Copyright © 2000 Marcel Dekker, Inc. [...]... Analysis 309 640; and subsequent documents: 1981a: NF-X-1 1-6 83; 1981b: NF-X-1 1-6 30; 1982: NF-X-1 1-6 42; 1983a: NF-X-1 1-6 85; 1983b: NF-X-1 1-6 93; 1983c: NF-X-3 1-1 07; 1984: NF-X-1 1-6 82; 1990: NF-X-1 1-6 61; 1992: NF-X-1 1-6 67; 1997a: NF-X-11 671 ; 1997b: NF-X-1 1-6 36 Paris: AFNOR Allen, T., Davies, R., and Scarlett, B., eds 1996 Particle Size Measurement (2 vols.) London: Chapman and Hall Anon 19 97 Macmillan Encyclopedia... 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London: Soc Anal Chem., pp 133 –146 Copyright © 2000 Marcel Dekker, Inc Particle Size Analysis 311 Hodgson, J M 1 978 Soil Sampling and Soil Description London: Oxford Univ Press Hodgson, J M 19 97 Soil Survey Field Handbook Technical Monograph No 5 Silsoe, U.K.: Soil Survey and Land Research Centre, pp 112 –115 Hunt, C M., and Woolf, A R 1969... Laboratory Methods Manual Soil Survey Investigations Report No 46, Version 3.0 Washington, DC.: Soil Conservation Service Vitton, S J., and Sadler, L Y 19 97 Particle-size analysis of soils using laser light scattering and x-ray absorption techniques Geotech Test J 20 : 63 73 Walker, P H., and Hutka, J 1 971 Use of the Coulter Counter (Model B) for Particle-Size Analysis of Soils Div of Soils Tech Paper No... Characterisation and control of fine particles involved in drilling J Petrol Technol 37 : 1622 –1632 Muller, R N., and Tisne, G T 1 977 Preparative-scale size fractionisation of soils and sediments and an application to studies of plutonium geochemistry Soil Sci 124 : 191–198 Mullins, C E., and Hutchinson, B J 1982 The variability introduced by various subsampling techniques J Soil Sci 33 : 5 47 561 Nadeau,... T P., and Durney, T E 1985 Sieve data—Size and shape information J Sedimentol Petrol 55 : 356 –360 Kiss, K., and Pease, R N 1982 Quantitative analysis of particle sizes: Estimation of the most efficient sampling scheme J Microsc 126 : 173 – 178 Klute, A., ed 1986 Methods of Soil Analysis, Part I Physical and Mineralogical Methods 2d ed Madison, WI: Am Soc Agron Konert, M., and Vandenberghe, J 19 97 Comparison... D., and Hutka, J 1 974 Particle size measurements by Coulter counter of very small deposits and low suspended sediment concentrations in streams J Sedimentol Petrol 44 : 673 – 679 Copyright © 2000 Marcel Dekker, Inc 314 Loveland and Whalley Walton, E K., Stephens, W E., and Shawa, M S 1980 Reading segmented grain-size curves Geol Mag 1 17 : 5 17 524 Webster, R., and Oliver, M A 1990 Statistical Methods . in soils. Barak et al. (1996) went further, and concluded that fractal theory offers no useful description of sand particles in soils and hence doubted the applicability of these methods to soils. of these methods. This chapter touches on some of the techniques available. We aim to discuss the principles, origins, and limitations of some standard methods and to point to newer methods that. hard-won infor- mation, and is misleading: sieves of, for example, 50 mm aperture are nowhere used in soil analysis. Most standards organizations nowadays strongly support the 292 Loveland and