Comparison Between Grain-Size Analyses Using Laser Diffraction and Sedimentation Methods

biosystems engineering 106 (2010) 205e215

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Research Paper Comparison between grain-size analyses using laser diffraction and sedimentation methods

C. Di Stefano, V. Ferro*, S. Mirabile

Dipartimento di Ingegneria e tecnologie Agro-Forestali, Universita` di Palermo, Viale delle Scienze, 9018 Palerrmo, Italy article info A comparison between laser diffraction method (LDM) and the sieve-hydrometer method Article history: (SHM) was carried out for 228 soil samples representing a different texture classification Received 3 December 2009 sampled in a Sicilian basin. The analysis demonstrated that the sand content measured by Received in revised form SHM can be assumed equal to that determined by LDM technique, while the clay fraction 15 March 2010 measured by LDM was lower than that measured by the SHM. A set of equations to Accepted 18 March 2010 transform LDM results to SHM results was proposed. The influence of the LDM measurements of clay on the estimated percentage of silt þ very fine sand particles (particle diameter ranging from 0.002 mm to 0.1 mm), which is useful for estimating soil erodibility, was also studied. ª 2010 IAgrE. Published by Elsevier Ltd. All rights reserved.

1. Introduction with hydrometer method (SHM) has been adopted as an international standard to determine quantitatively the PSD of Particle-size distributions (PSDs) are fundamental physical soils (Allen, 1990; Cooper, Haverland, Hendricks, & Knisel, properties of soil and are typically presented as the percentage 1984). With similar pretreatment techniques, the pipette of the total dry weight of soil occupied by a given size fraction. method (PM) and hydrometer method (HM) - give comparable This property is commonly used for soil classiﬁcation and for results (Liu, Odell, Etter, & Thornburn, 1966; Walter, Hallberg, the estimation of some hydraulic properties (Campbell & & Fenton, 1978); however the PM requires that clay and silt Shiozawa, 1992). fractions (<0.05 mm) are separated from the sand fraction Over recent decades, various new methods for grain-size using wet sieving. analysis have been developed. These new methods, (electro- Sedimentation methods are time consuming, especially for resistance particle counting, time of transition, laser diffrac- the determination of the particles having a size less than 2 mm, tion (LD), optical determination of the PSD using image since they require relatively large samples (10e20 g for the analysis) (Goossens, 2008; McCave & Syvitski, 1991) generally pipette and 50 g for the hydrometer). They also give unreliable have the advantage of covering a wide range of grain sizes, results for particles 1 mm because of the effect of Brownian and rapidly analysing small samples. motion on the rate of sedimentation. Particles of sand size (0.05e2.00 mm) are usually deter- A particle diameter obtained by the laser diffraction mined using sieving. The sieve deﬁnes a particle diameter method (LDM) is equivalent to that of a sphere giving the same as the length of the side of a square hole through which the diffraction as the particles. A laser diffraction particle size particle can just pass (Allen, 1990). Finer particles are usually analyser “sees” the particle as a two-dimensional object and it determined by classical sedimentation methods such as gives its grain size as a function of the cross-sectional area of hydrometer or pipette (Gee & Bauder, 1986). Sieving combined the particle.

* Corresponding author. E-mail address: [email protected] (V. Ferro). 1537-5110/$ e see front matter ª 2010 IAgrE. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.biosystemseng.2010.03.013 206 biosystems engineering 106 (2010) 205e215

Nomenclature l wavelength of light

SASHM sand content determined with SHM

Symbol or abbreviation SALDM sand content determined with LDM

SHM sieve-hydrometer method CLSHM clay content determined with SHM

LDM laser diffraction met CLLDM clay content determined with LDM

PSD particle-size distribution SIE estimate of silt percentage PM pipette method RMSE root mean square error HM hydrometer method K soil erodibility factor RI refractive index f percentage of silt þ very ﬁne sand particles PM-clay clay determined by pipette method g percentage of sand coarser than very ﬁne sand HM-clay clay determined by hydrometer method d soil particle diameter

nr real part of RI fE estimate of f

ni imaginary term of RI a coefﬁcient Eq. (5)

Using a laser particle analyser the following assumptions results in smaller percentages than those obtained by PSM. are made (Konert & Vandenberghe, 1997): (i) the analytical This means that the lower percentages of the clay fraction transformation of diffraction patterns to grain sizes is based measured by the LDM must be compensated for higher on matrices, which are calculated for spheres. Thus, the percentages in the silt-size fraction. diffraction along the cross-sectional area of the particles is According to Bah, Kravchuk, and Kirchhof (2009) the assigned to diffraction of spheres; (ii) particle orientation is differences between the two methods are attributable to the assumed to be randomly distributed, even if the laser heterogeneity of soil particle density and the deviation of measurements are carried out in a continuous suspension in particle shapes from sphericity. Sedimentation methods which the particles may be oriented with respect to its shape. assume a single particle density, which is a major source of Determination of PSD by an LDM has interested soil scien- error, whereas LDM measurements are independent of tists for some time (Beuselinck, Govers, Poesen, Degraer, & particle density. Froyen, 1998; de Boer, de Weerd, Thoenes, & Goossens, 1987; Deviations from sphericity affect both methods. In the case Buurman, Pape, & Muggler, 1997, 2001; Eshel, Levy, Mingelgrin, of the LDM, an irregular shaped soil particle reflects a cross- & Singer, 2004; McCave, Bryant, Cool, & Coughanowr, 1986; sectional area greater than that of a sphere having the same Pieri, Bittelli, & Rossi Pisa, 2006) but its application has not volume. Thus, particles are assigned to larger size fractions of generally replaced the labour-intensive classical methods (i.e. the PSD underestimating the clay fraction. Nonspherical parti- PM or HM). According to Buurman et al.(1997), this reluctance cles in SHMs have longer settling times than their equivalent mainly depends on three factors: (i) insufficient confidence in spheres, which results in an overestimation of the clay fraction. the results of LDMs: studies on correlations of laser-clay deter- Taking into account that SHM is an accepted and certified minations with clay determined by pipette method (PM-clay) or method, and that LDM provides more information and is more clay determined by hydrometer method (HM-clay) are still efficient than SHM, a relevant question is to establish whether rare, and their correlations usually deviate from 1:1; (ii) in many a correlation exists between the fine sizes fractions obtained countries PMs or HMs are accepted as standard for particle size by both methods. analysis of soils; (iii) many available relationships/interpreta- Laser-diffraction instruments have different ranges of tions have been established with HM/PM textures and (iv) the measurement and use a different number of detectors to high cost of the laser-diffraction equipment. cover this range (size classes). Since the accuracy of the The use of LDMs raises the question of how similar the laser particle size distribution obtained by an LDM depends on the grain-size measurements are to those obtained by classical number of detectors used for a specific size-range, then it is to techniques such as SHM. The work of Buurman et al. (1997) and be expected that the measurements in the fine fraction will be Muggler, Pape, and Buurman (1997), which was carried out specific for a given LD analyser (Buurman et al., 2001). using soil profiles, suggested that the relationship between PM- Recently Goossens (2008) carried out a comparative study of clay and LDM-clay may depend on the properties of the clay ten instruments for measuring the grain-size distribution of fraction itself. Loizeau, Arbouille, Santiago, and Vernet (1994), loamy sediments (clay percentage ranging from 2 to 15%) sus- using samples of fluvial and lacustrine sediments, found that pended in water. The grain-size analyses were carried out on the laser grain-size distribution underestimated the clay four sediments with a particle size-range <90 mm. In particular, content with respect to the classic sedimentation method and four LD analysers (Malvern Mastersizer S, Coulter LS 200, Fritsch that this underestimation increased with increasing clay Analysette 22 C and Horiba Partica LA-950) were used. According content. They were not able to establish if the clay underesti- to the various criteria considered in Goussens study (cumulative mation derived from its mineralogical composition which is grain-size curve, median diameter, grain-size histograms, related to the particle shape and no conclusion was made skewness and kurtosis), the LD instruments produced the best about the effects on the other size classes. results. Although no “ideal” method can be defined and the final Buurman et al. (2001) also noted that sand-size particles are choice of a grain-size technique depends on many factors (type measured more or less equally by LDMs and PSMs while of sediments, quantity of sediment available, speed of measurement of the clay-size fraction by the LDM usually measurement, specific aims of the study, etc.), Goossens (2008) biosystems engineering 106 (2010) 205e215 207

summarised that instruments based on LDM as offering many measurements had higher percentages of fine particles than advantages and generally work adequately. LDM. Similarly Konert and Vandenberghe (1997), comparing In this paper, following a review of the LDM and some asso- the results obtained by pipette analysis and laser-diffraction ciated effects (i.e. ultrasonic duration, pretreatment of the soil technique, concluded that particle size distributions were sample and diffraction theory used), we test the method and comparable for “blocky” quartz particles but significantly then compare the particle size distributions obtained by SHM different for “platy” clay particles. Recently, Lu, Ristow, and andby theLDM. Wealso presentsa comparative texture analysis Likos (2000) carried out a theoretical analysis for deter- using hydrometer measurements as a reference for the LDM. mining the settling velocity of disk-shaped and rod-shapes The analysis is carried out using 228 soil samples, all particles. Their analysis showed that for disk-shaped and rod- sampled in Sicily, representing a wide range of textures and shapes particles, in sizes ranging from 0.1 mm to 100 mm, the Fritsch A22-Economy version of the laser diffraction Stokes’ law underestimates the maximum particles dimen- analyser. Therefore the paper is also the first comparative sion by up to two orders of magnitude. The experimental analysis between SHM and LDM measurements carried out results of Lu et al. (2000), using various techniques, also using soil samples collected in Italy. confirmed the underestimate errors of particle size inherent The results obtained in this paper have to be considered as in hydrometer analysis. being apparatus specific because the measurement accuracy For soil and earth materials, particle density is commonly is dependent on the number of detection cells (e.g. 31 in the taken constant and equal to 2.65 Mg m 3 Clifton, McDonald, Fritsch instrument and 116 in the Coulter LS 230) even though Plater, and Oldfield (1999) suggested that density of sediment Goossens (2008) obtained similar results using different types particles can vary between 1.66 and 2.99 Mg m 3. A soil is of laser analyser. composed of particles with different densities, which are mainly determined by their mineral compositions. The 1.1. Sieving e hydrometer method uncertainty of particle density may strongly bias the particle size distribution (Wen et al., 2002). The PM or the HM defines a particle diameter as equivalent to The effects due to both particle-to-particle interference and that of a sphere settling in the same liquid with the same the column walls, which limits the applicability of Stokes’ law speed as the unknown sized particles, the so-called “Stokes can be avoided limiting the maximum concentration of soil in diameter” (Allen, 1990; Konert & Vandenberghe, 1997). The the suspension (50 g of dry soil in 1000 ml of suspension). sphere is usually assigned the density of quartz. Assumption (4) from above is verified for an upper limit of the Hydrometer analysis uses a hydrometer having a gradu- Reynolds number value ranging from 0.1 to 1 (Allen, 1990; ated stem and weight bulb, to measure the specific density of Bernhardt, 1994); these values correspond to free-falling the suspension. The specific density depends on the weight of spherical quartz particles 2 mm in diameter (Lu et al., 2000). soil particles in the suspension at the time of measurement The classical technique SHM represents a “standard” for (Wen, Aydin, & Duzgoren-Aydin, 2002). soil particle size analysis and many available relationships, The HM is based on Stokes’ law that establishes the such as pedotransfer functions, were established using velocity at which particles settle in suspension assuming that: hydrometer/pipette texture measurements. (1) soil particles are rigid, spherical and smooth; (2) soil particles have similar densities; (3) particle-to-particle inter- 1.2. Laser diffraction method ference and boundary effects from the walls of the sedimentation column are negligible; (4) particle sizes are small The principle of LDM is that particles of a given size diffract enough to ensure that the induced fluid flow is well within the light through a given angle. The angle of diffraction is inversely laminar flow regime. A particle size calculated by Stokes’ law proportional to particle size, and the intensity of the diffracted is the quartz equivalent spherical sedimentation diameter beam at any angle is a measure of the number of particles with (McCave & Syvitski, 1991) a specific cross-sectional area in the optical path. Deviations from Stokes’ law are expected when particles A parallel beam of monochromatic light passes through are irregular in shape, as most silt particles, or are platy or a suspension contained in a sample cell, and the diffracted tubular in shape as are most clay particles. The particle-shape light is focused onto detectors. For calculating particle sizes effect is due to the circumstance that the most stable position from light intensity sensed by detectors, two diffraction of a settling, non-spherical particle is the one in which the theories are commonly used: the Fraunhofer diffraction maximum cross-sectional area is perpendicular to the direc- and the Mie theory (Gee & Or, 2002). Both theories assume that tion of motion. As a consequence, this position increases the the particles have a spherical shape; in other words, the expected particle drag resistance and reduces the settling particle dimension is the optical spherical diameter, i.e. the velocity. In other words the particle-shape effect results in diameter of the sphere having a cross-section area equivalent a so-called “overestimation” of the fine size fraction which to the measured one by laser diffraction. depends on at which size the platy particles appear. Fraunhofer theory is based on the approximation that the The validity of the spherical assumption (1) has been laser beam is parallel and the detector is at a distance that is examined in many papers in the past. Nettleship, Cisko, and very large compared with the size of the diffracting particle. Vallejo (1997) established that the standard hydrometer Fraunhofer theory becomes inapplicable when the particle analysis should not be recommended for submicron mate- diameter is close to the wavelength of light (l) as the refraction rials. Vitton and Sadler (1997), examining eleven soil by of particles in this size range becomes appreciable (Loizeau hydrometer and laser measurements, found that hydrometer et al., 1994). 208 biosystems engineering 106 (2010) 205e215

This circumstance could explain why clay detection is often problematic for laser grain-size measurements. The Fraunhofer diffraction model gives inaccurate results for particles <10 l (de Boer et al., 1987). Matrices based on Fraunhofer theory are calculated from diffraction by the particles and differences in absorption and refraction indices have no effect on the calculated grain-size distribution. This hypothesis is not completely correct for organic matter since it may absorb some light. The Mie theory is a solution of the Maxwell equations describing propagation of the electromagnetic wave of light in space. This theory provides a solution for the case of plane wave on a homogeneous sphere of any size (Eshel et al., 2004). Mie theory takes into account phenomena of transmission through the particle and therefore requires knowledge of the refractive index (RI) of the tested soil. The RI of a material is a function both of particle size and the composition of the material. Taking into account that soils are generally multi- sized and poly-mineralic in nature, this can make it difficult to choose a representative RI for a given soil. The RI is a complex number (Eshel et al., 2004) comprising a real part nr, representing the change in the velocity of light through the tested material compared with the velocity of light in vacuum, and an imaginary term ni which represents the transparency and absorptivity of the tested material. According to Konert and Vandenberghe (1997) the Fraunhofer theory is well suited for non-spherical clay particles. However, de Boer et al. (1987) suggest that the Fraunhofer model is not accurate enough for the determination of the clay-size fraction. Different authors (Beuselinck et al., 1998; Konert & Vandenberghe, 1997; Loizeau et al., 1994) have concluded that the Fraunhofer theory overestimates the clay fraction with respect to the Mie model. Loizeau et al. (1994) also established that the Fraunhofer theory detects a significantly larger proportion of the clay measured by the sieving-pipette method than does the Mie theory. The LDM analyses small samples in a short period of time (5e10 min per sample), so it is suitable for rapid and accurate Fig. 1 e Distribution by USDA texture using the percentage analysis of a large number of samples (e.g. soil samples sampled of clay, sand and silt determined by SHM (a) and by LDM in a basin, suspension samples caught during soil erosion events). (b). LDM also covers a wide range of grain sizes and may also be used to analyse non-dispersed samples (Muggler et al., 1997). Although the fully dispersed size distribution (i.e. the ultimate grain-size distribution) is important with respect to certain soil For each analysed soil sample, 50 g was used for the SHM chemical and physical properties, other relevant processes, analysis and 10 g was used for the LDM. Each sample was such as soil erosion and sediment transport by overland flow, treated with H2O2 (concentration equal to 30%) to assure are dependent on the size distribution of soil aggregates complete removal of organic material and was dispersed to (effective grain-size distribution)(Buurman et al., 1997; Di Stefano remove aggregates by adding a sodium hexametaphosphate & Ferro, 2002; Foster, Young, & Neibling, 1985). solution over night (Gee & Or, 2002). A volume of 100 ml of sodium hexametaphosphate solution, having a concentration equal to 50 g l 1, was used. The treated sample was mixed 2. Materials and methods overnight using an end e over e end shaking. For the SHM analysis the pretreated sample (50 g) was wet Soil samples were taken at various locations in a Sicilian sieved through a 0.075 mm sieve. The fine fraction (<75 mm) basin, Imera Meridionale, which has an area of 2000 km2. The collected after wet sieving was transferred to standard cylin- 228 samples were selected to represent a large variety of soil ders for hydrometer analysis. The cylinders were inserted into textures based on the SHM (Fig. 1a). a water bath at a constant temperature. Corrections for the For both the SHM and the LDM, soil samples were dried at temperature effects on density and viscosity of suspension 105 C and were gently crushed and dry sieved at 2-mm mesh-size. were carried out. A standard hydrometer, ASTM no. 152 H, biosystems engineering 106 (2010) 205e215 209

with Bouyoucos scale (g l 1) was used. The suspension was mixed using an end-over-end shaking for 1 min (Gee & Or, 2002). The hydrometer analysis was carried out by multiple readings at 2, 5, 15, 30, 60, 180, 1440 and 2880 min (Gee & Or, 2002). The coarse fraction retained by the 75 mm sieve was oven-dried at 105, weighed and sieved at 0.075, 0.106, 0.250, 0.425, 0.85 and 2 mm. The adopted sieve sizes belong to the series R 40/3 of the standard ISO 3310-1. For the LDM analysis, in the range 0.1e600 mm, the pretreated sample (10 g) was ﬁrstly wet sieved through a 710 mm sieve. A pretreated sub-sample, having a volume of 1.5 ml, was then introduced into the dispersion unit device of the laser particle analyser for measurement; it contained 400 ml of deionised water, for the measurement. The Fritsch Laser Particle Sizer Analysette 22 e Economy version measures 31 grain-size classes in the working range of 0.1e600 mm. For the LDM analysis a sub-sample was introduced into the dispersion unit device where, to maintain the random orientation of particles in suspension, automatic ultrasonication was applied during the measurement. Ultrasonication is an efﬁcient dispersion method but it can be critical for the particle size distribution because, although the clay coatings are quickly removed, the quartz grain can be also broken up. According to Chappel (1998) a 3-min duration of ultrasound is appropriate for samples suspended in tap water. Taking into account that the samples were pretreated with sodium hexametaphosphate, less than 3-min duration could be appropriate. Fig. 3 e Cumulative particle size distributions of two samples, having a different organic matter content, with

and without H2O2 pretreatment.

In order to prevent the formation of gas bubbles during the movement of suspension into the dispersion unit device, the stirrer velocity was set to 60e70 revolutions/s. The suspension was then pumped through a sample cell placed in the convergent laser beam where the forward scattered light fell onto the 31 photosensitive sensor rings. Each run was set for 60 s. Prior to each run, the detectors were aligned, the back- ground measured and the sample dilution controlled (to test that the used sub-sample volume allowed a correct analysis). All operations were controlled by a personal computer.

3. Results

Some factors affecting the LDM were tested before comparing the PSD obtained by the two techniques. In particular the following effects were considered:

i) the duration of ultrasoniﬁcation

ii) the pretreatment of the soil sample using H2O2 and iii) the diffraction theory applied.

Fig. 2 e Cumulative particle size distributions for samples Fig. 2 shows, as an example for two tested soil samples 22 and 44 corresponding to different durations of (number 22 and 44), the effect of the duration of ultrasound. ultrasound. Samples 22 and 44 were selected because they had the highest 210 biosystems engineering 106 (2010) 205e215

Adding of H2O2 produces a shift in the PSD towards ﬁner particles; in other words for a given particle diameter d the

particle size distribution corresponding to H2O2 pretreatment is characterised by a frequency value F(d ) greater than that of

the PSD corresponding to “no H2O2 pretreatment”. Removal of organic material shows that some soil particles which are originally aggregated become free from aggregation links. For the seven considered samples, Fig. 4a clearly demon-

strates that the absence of the H2O2 pretreatment gives a small underestimation of the clay fraction. Taking into account that three data pairs of Fig. 4b lie on the 1:1 line, and that the slope of the relationship is almost equal to one, silt

fraction is assumed not affected by the H2O2 pretreatment.

Taking into account that the effect of the H2O2 pretreatment is not negligible for the clay fraction, all samples analysed in this investigation were pretreated. For testing the effect of the diffraction theory used, the grain-size distribution was determined using both the Fraunhofer diffraction model and Mie theory. The ﬁrst comparison was carried out using a refraction index charac-

terised by a real part nr assuming two different values typical

for the tested soils (1.5 and 1.6) and an imaginary term, ni,

equal to 0.1. The used, nr, values (1.5 and 1.6) were selected taking into account that for most minerals a value of approximately 1.53 is suitable (Eshel et al., 2004). Also, if the effect of coating clay-sized particles by organic matter and

Fig. 4 e Comparison between clay (a) and silt (b) fractions with and without H2O2 pretreatment.

clay content of their data set and their grain-size distribution could be appreciably affected by clay particle aggregation. Fig. 2 shows the cumulative particle size distribution, for each tested sample, corresponding to ultrasound duration of 1, 2 and 3 min. The PSD without the dispersion action of ultrasound was also measured as a reference. Because no signiﬁcant difference was determined between the three particle size distributions corresponding to ultrasoniﬁcation for 1, 2 and 3 min n, a duration of 2 min was used in all the investigations. To investigate the effect of a pretreatment of the soil sample by H2O2, seven samples having different organic matter contents (0.32, 0.36, 1.64, 2.11, 3.03, 4.03 and 7.18%) were examined. Fig. 3 shows results from two typical agri- cultural soils (OM < 4%) and demonstrates that an effect of the Fig. 5 e Comparison between cumulative particle size pretreatment can be recognised in the particle size distribu- distributions obtained by the Fraunhofer model and Mie tion for soil particles ranging from 0.002 mm to 0.1 mm. theory. biosystems engineering 106 (2010) 205e215 211

Fig. 6 e Comparison between cumulative particle size distributions obtained by SHM and LDM. 212 biosystems engineering 106 (2010) 205e215

Fig. 7 e Relationship between sand fraction obtained by Fig. 9 e Comparison between f percentage estimated by Eq. LDM and by SHM. (4) and by SHM.

oxides has to be considered a nr value of 1.6 should be sieving). This figure shows that for each sample appreciable employed (CRC Press, 2002). differences were detected between the two methods used to Fig. 5 shows that no significant differences could be determine the particle size distribution. In particular, for all detected for the two investigated diffraction models applied to samples, the sand content determined by SHM was similar to the selected samples. For the same soil samples, the analysis the one obtained by LDM while the so-called “overestimation” showed that the variability of the imaginary term of the of the clay percentage measured by SHM as compared to LDM refraction index (0.1e0.2) does not produce appreciable effects was confirmed. on the cumulative grain-size distribution. Accordingly, the Fig. 7, which compares the sand content determined with cumulative grain-size distributions of the investigated samples SHM, named SASHM, with the LD measured sand content, were determined using the Fraunhofer diffraction model. SALDM, shows that the two values can be assumed equal. Fig. 6 shows the comparison, as an example for eight soil y samples having a different United States Department of SASHM SALDM (1) Agriculture (USDA) texture classifications, between the PSD The relationship plotted in Fig. 7 is characterised by a root determined by SHM (for d < 75 mm by HM and for d 75 mmby mean square error (RMSE) equal to 2.16 (expressed as %). sieving) and LDM (for d 600 mm by LD and for d > 750 mmby For the clay fraction the following equation was established:

CLSHM ¼ 1:91CLLDM (2)

where CLSHM and CLLDM are, respectively, the clay percentage determined by the SHM and the LDM (Fig. 8). The relationship plotted in Fig. 8 is characterised by RMSE ¼ 9.27.

Use of Eqs. (1) and (2) allows the following estimate of SIE or silt percentage to be obtained:

SIE ¼ 100 1:91CLLDM SALDM (3)

This is characterised by appreciable scatter (RMSE ¼ 9.05). Taking into account that SHM has been adopted as an international standard to determine quantitatively the PSD of soils (Cooper et al., 1984), the use of Eqs. (1) and (2) allows the sand and clay percentage measured by LDM to be referred to the SHM standard. The K soil erodibility factor is an integrated long-term average soil response to the erosive power of rainstorms. Its estimation by nomograph of Wischmeier, Johnson, and Cross Fig. 8 e Relationship between clay fraction obtained by (1971) requires knowledge of the soil grain distribution, soil LDM and by SHM. organic matter, soil structure and permeability. In particular biosystems engineering 106 (2010) 205e215 213

To derive equations useful to transform measurements obtained from the LDM to the SHM, comparisons between LDM and SHM measurements were carried out grouping soils with respect to their USDA classiﬁcation. Fig. 1b shows the textural classiﬁcation of the sampled soils using the silt content (SI), sand content (SA) and clay content (CL) percentage measured by LDM. For comparing the CL percentage measured by the two different methods the soil samples were merged into three textural groups: loamy sand þ sandy loam (group 1, 19 samples), loam (group 2, 23 samples), silt loam þ silty clay loam (group 3, 186 samples). The selected textural groups represent homogeneous zones of the USDA triangle characterised by sand content SA greater than 50% (loamy sand þ sandy loam), quasi equal to 50% (loam) and less than 50% (silt loam, silty clay loam). Figs. 10, 11 and 12 show, for each considered textural group, the relationship between clay percentage determined

Fig. 10 e Relationship between sand and clay fractions obtained by LDM and by SHM for the textural group “loamy sand D sandy loam”.

the particle size distribution needed to calculate K is the percentage f of silt þ very fine sand particles (0.002 mm < d < 0.1 mm, being d the particle diameter) and the percentage g of sand coarser than very fine sand (0.1 mm < d < 2 mm) as defined by Wischmeier et al. (1971) and used in their nomograph. Taking into account the definition of the percentages f and g and Eq. (2), the following equation for þ estimating the percentage of silt very fine sand particles fE is obtained: fE ¼ 100 1:91 CLLDM g (4)

Fig. 9 shows the comparison between the percentage of þ silt very ﬁne sand particles fE estimated by Eq. (4) and the same percentage f calculated by the measurements carried Fig. 11 e Relationship between sand and clay fractions out by SHM. This comparison shows that fE is similar to f even obtained by LDM and by SHM for the textural group ¼ if the scattering of the pairs ( f, fE) is appreciable (RMSE 9.56). “loam”. 214 biosystems engineering 106 (2010) 205e215

As a consequence, the improved estimate of clay percentage by Eq. (5) allows a more accurate estimate of silt percentage by use of the following equation:

SIE ¼ 100 aCLLDM SALDM (6) þ and of the percentage of silt very ﬁne sand particles fE by the following equation:

fE ¼ 100 aCLLDM g (7)

The calibration equations (5) and (6) by particle size (SA > 50% and SA 50%) presented in this paper are not universal. As stated earlier, correlations of the LDM with the SHM may vary for a variety of reasons related to laser diffraction analyser used, particle shape, mineralogy, RI, etc. Poor correlations between LDM results and SHM results may occur if the calibration equations (5) and (6) are applied outside the range tested here.

4. Conclusions

Taking into account the fact that LDM provides more information and is more efficient than the SHM although the latter is an accepted and certified method, this paper has tried to solve the question of how similar are the results from the two methods. This study was developed using 228 soils sampled in Sicily, having a variety of texture and the Fritsch A22-Economy version laser analyser. Goossens (2008) obtained similar results using different types of laser analyser, but the results obtained in this paper have to be considered as being apparatus specific because measurement accuracy for the LDM is dependent on the number of detection cells. This study showed that there was no significant difference in the particle size distribution using different ultrasound

durations. The absence of the H2O2 pretreatment gave a small underestimation in the clay fraction while the silt fraction can be assumed not affected by the pretreatment. The choice of Fig. 12 e Relationship between sand and clay fractions the Fraunhofer or Mie diffraction models for the LDM gave no obtained by LDM and by SHM for the textural group “silt appreciable differences for the soils investigated. loam D silty clay loam”. Analysis of all samples showed that the sand content determined by SHM was similar to that obtained by the LDM while the so-called “overestimation” of the clay percentage of by the two different methods. According to these figures, for SHM with respect to LDM was confirmed. the clay fraction the following equation can be established: Finally, a set of equations useful to refer LDM measurements to the SHM results, the latter is used as an international CL ¼ aCL (5) SHM LDM standard, was proposed. where a is a coefficient equal to 2.18 for the textural group 1 The analysis demonstrated that for improving the trans- (SA > 50%), 1.91 for the textural group 2 ðSAy50%Þ and equal to formation of the clay measurements from the LDM to the SHM 1.91 for the textural group 3 (SA < 50%). three textural groups (sand content greater than 50% (loamy The relationship Eq. (5) calibrated for each textural group is sand þ sandy loam), almost equal to 50% (loam) and less than characterised by RMSE ¼ 3.1 for the textural group 1, 50% (silt loam, silty clay loam)) have to be distinguished. For RMSE ¼ 6.4 for the textural group 2, RMSE ¼ 10 for the textural each textural group a more reliable estimate of clay group 3 which is lower than or similar to that obtained by Eq. percentage can be obtained using a specific coefficient. (2) (RMSE ¼ 9.27). In other words, even if in some case (Figs. 11 Even if for transforming the clay measurements from the and 12) the number of samples used is small, for transforming LDM to the SHM a more reliable estimate of clay percentage clay measurements from the LDM to the SHM a more reliable can be obtained using a coefficient specific for each textural estimate of clay percentage can be obtained using a coefficient group, the calibration equations (5) and (6) by particle size specific to each textural group. (SA > 50% and SA 50%) presented in this paper are not biosystems engineering 106 (2010) 205e215 215

universal. Further measurements carried out contemporane- Di Stefano, C., & Ferro, V. (2002). Linking clay enrichment and ously by the LDM and the SHM could allow the results sediment delivery processes. Biosystems Engineering, 81, e obtained in this investigation to be confirmed and the 465 479. Eshel, G., Levy, G. J., Mingelgrin, U., & Singer, M. J. (2004). Critical proposed scale equations to be improved. evaluation of the use of laser diffraction for particle-size distribution analysis. Soil Science Society of America Journal, 68, 736e743. Foster, G. R., Young, R. A., & Neibling, W. H. (1985). Sediment Acknowledgements composition for nonpoint source pollution analyses. Transactions of the ASAE, 28, 133e146. The research was set up by Prof. V. Ferro and Dr. C. Di Stefano, Gee, G. W., & Bauder, J. W. (1986). Particle-size analysis. In J. H. the measurements were carried out by Dr. S. Mirabile. All Klute (Ed.), Methods of soil analysis. Part 1 (2nd ed.).Agron. e authors analysed the results and contributed to the writing of Monogr., Vol. 9 (pp. 383 411) Madison, WI: ASA and SSSA. Gee, G. W., & Or, D. (2002). Particle-size analysis. In: J. H. Dane & G. the paper. C. Topp (Eds.), Soil Science Society of America Book Series: Vol. 5, The research was supported by a grant of Ministero del- Methods of soil analysis. Part 4. Physical methods (pp. 255e293). l’Istruzione, dell’Universita` e della Ricerca scientifica, Governo Madison, WI. Italiano, PRIN 2007 “Monitoraggio e modellazione dei processi Goossens, D. (2008). Techniques to measure grain-size erosivi a differenti scale spaziali nell’area sperimentale di distributions of loamy sediments: a comparative study of ten Sparacia” and Progetto FEROS. instruments for wet analysis. Sedimentology, 55,65e96. Konert, M., & Vandenberghe, J. (1997). Comparison of laser grain size analysis with pipette and sieve analysis: a solution for the references underestimation of the clay fraction. Sedimentology, 44, 523e525. Liu, T. K., Odell, R. T., Etter, W. C., & Thornburn, T. H. (1966). Comparison of clay contents determined by hydrometer and Allen, T. A. (1990). Particle size measurement (4th ed.). London: pipette methods using reduced major axis analysis. Chapman and Hall. Proceedings e Soil Science Society of America, 30, 665e669. Bah, A. R., Kravchuk, O., & Kirchhof, G. (2009). Fitting performance Loizeau, J. L., Arbouille, D., Santiago, S., & Vernet, J. P. (1994). of particle-size distribution models on data derived by Evaluation of a wide range laser diffraction grain size analyzer conventional and laser diffraction techniques. Soil Science for use with sediments. Sedimentology, 41, 353e361. Society America Journal, 73, 1101e1107. Lu, N., Ristow, G. H., & Likos, W. I. (2000). The accuracy of Bernhardt, C. (1994). Particle size analysis: Classification and hydrometer analysis for fine-grained clay particles. sedimentation methods. London, UK: Chapman and Hall. Geotechnical Testing Journal, GTIODI, 23, 487e495. Beuselinck, L., Govers, G., Poesen, J., Degraer, G., & Froyen, L. McCave, I. N., Bryant, R. J., Cool, H. F., & Coughanowr, C. A. (1986). (1998). Grain-size analysis laser diffractometry: comparison Evaluation of a laser-diffraction-size analyser for use with with the sieve-pipette method. Catena, 32, 193e208. natural sediments. Journal of Sedimentary Petrology, 56, de Boer, G. B., de Weerd, C., Thoenes, D., & Goossens, H. W. (1987). 561e564. Laser diffraction spectrometry: Fraunhofer versus Mie McCave, I. N., & Syvitski, J. P. M. (1991). Principles and methods of scattering. Particle Characteristics, 4,14e19. geological particle size analysis. In J. M. P. Syvitski (Ed.), Buurman, P., Pape, Th., & Muggler, C. C. (1997). Laser grain-size Principles, methods and application of particle size analysis (pp. determination in soil genetic studies. 1. Practical problems. 3e21). Cambridge, UK: Cambridge University Press. Soil Science, 162, 211e218. Muggler, C. C., Pape, Th., & Buurman, P. (1997). Laser grain-size Buurman, P., Pape, Th., Reijneveld, J. A., de Jong, F., & van determination in soil genetic studies: 2. Clay content, clay Gelder, E. (2001). Laser-diffraction and pipette-method grain formation, and aggregation in some Brasilian Oxisols. Soil sizing of Dutch sediments: correlations for fine fractions of Science, 162, 219e228. marine, fluvial and loess samples. Netherlands Journal of Nettleship, I., Cisko, L., & Vallejo, L. B. (1997). Aggregation of clay Geosciences, 80,49e57. in the hydrometer test. Canadian Geotechnical Journal, 34, Campbell, G. S., & Shiozawa, S. (1992). Prediction of hydraulic 621e626. properties of soils using particle-size distribution and bulk Pieri, L., Bittelli, M., & Rossi Pisa, P. (2006). Laser diffraction, density data. In M. T. van Genuchten, F. J. Leij, & L. J. Lund (Eds.), transmission electron microscopy and image analysis to Indirect methods for estimating the hydraulic properties of unsatured evaluate a bimodal Gaussian model for particle size soils (pp. 317e328). Riverside: University of California. distribution in soils. Geoderma, 135, 118e132. Chappel, A. (1998). Dispersing sandy soil for the measurement of Vitton, S. J., & Sadler, L. Y. (1997). Particle-size analysis of soils particle size distributions using optical laser diffraction. using laser light scattering and X-ray absorbition technology. Catena, 31, 271e281. Geotechnical Testing Journal, 20,63e73. Clifton, J., McDonald, P., Plater, A., & Oldfield, F. (1999). An Walter, N. F., Hallberg, G. R., & Fenton, T. S. (1978). Particle size investigation into the efficiency of particle size separation analysis by the Iowa State Univ. Soil Survey Lab. In G. R. Hallberg using Stokes’ law. Earth Surface Processes and Landforms, 24, (Ed.), Standard procedures for evaluation of quaternary materials in 725e730. Iowa (pp. 61e74). Iowa City: Iowa Geological Survey. Cooper, L. R., Haverland, R. L., Hendricks, D. M., & Knisel, W. G. Wen, B., Aydin, A., & Duzgoren-Aydin, N. S. (2002). A comparative (1984). Microtac particle-size analyzer: an alternative particle- study of particle size analyses by sieve-hydrometer and laser size determination method for sediment and soils. Soil Science, diffraction methods. Geotechnical Testing Journal, 25, 434e442. 138, 138e146. Wischmeier, W. H., Johnson, C. B., & Cross, B. V. (1971). Soil CRC Press. (2002). Handbook of Chemistry and Physics (83rd ed.). erodibility nomograph for farmland and construction sites. Boca Raton, FL: CRC Press. Journal of Soil and Water Conservation, 26, 189e193.