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Research Paper
Comparison between grain-size analyses using laserdiffraction 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
a r t i c l e i n f o
Article history:
Received 3 December 2009
Received in revised form
15 March 2010
Accepted 18 March 2010
* Corresponding author.E-mail address: [email protected] (V. Ferro
1537-5110/$ e see front matter ª 2010 IAgrEdoi:10.1016/j.biosystemseng.2010.03.013
A comparison between laser diffraction method (LDM) and the sieve-hydrometer method
(SHM) was carried out for 228 soil samples representing a different texture classification
sampled in a Sicilian basin. The analysis demonstrated that the sand content measured by
SHM can be assumed equal to that determined by LDM technique, while the clay fraction
measured by LDM was lower than that measured by the SHM. A set of equations to
transform LDM results to SHM results was proposed. The influence of the LDM measure-
ments 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
Particle-size distributions (PSDs) are fundamental physical
properties of soil and are typically presented as the percentage
of the total dry weight of soil occupied by a given size fraction.
This property is commonly used for soil classification and for
the estimation of some hydraulic properties (Campbell &
Shiozawa, 1992).
Over recent decades, various new methods for grain-size
analysis have been developed. These new methods, (electro-
resistance particle counting, time of transition, laser diffrac-
tion (LD), optical determination of the PSD using image
analysis) (Goossens, 2008; McCave & Syvitski, 1991) generally
have the advantage of covering a wide range of grain sizes,
and rapidly analysing small samples.
Particles of sand size (0.05e2.00 mm) are usually deter-
mined using sieving. The sieve defines a particle diameter
as the length of the side of a square hole through which the
particle can just pass (Allen, 1990). Finer particles are usually
determined by classical sedimentation methods such as
hydrometer or pipette (Gee & Bauder, 1986). Sieving combined
).. Published by Elsevier Lt
international standard to determine quantitatively the PSD of
soils (Allen, 1990; Cooper, Haverland, Hendricks, & Knisel,
1984). With similar pretreatment techniques, the pipette
method (PM) and hydrometer method (HM) - give comparable
results (Liu, Odell, Etter, & Thornburn, 1966; Walter, Hallberg,
& Fenton, 1978); however the PM requires that clay and silt
fractions (<0.05 mm) are separated from the sand fraction
using wet sieving.
Sedimentationmethods are time consuming, especially for
the determination of the particles having a size less than 2 mm,
since they require relatively large samples (10e20 g for the
pipette and 50 g for the hydrometer). They also give unreliable
results for particles 1 mm because of the effect of Brownian
motion on the rate of sedimentation.
A particle diameter obtained by the laser diffraction
method (LDM) is equivalent to that of a sphere giving the same
diffraction as the particles. A laser diffraction particle size
analyser “sees” the particle as a two-dimensional object and it
gives its grain size as a function of the cross-sectional area of
the particle.
d. All rights reserved.
Nomenclature
Symbol or abbreviation
SHM sieve-hydrometer method
LDM laser diffraction met
PSD particle-size distribution
PM pipette method
HM hydrometer method
RI refractive index
PM-clay clay determined by pipette method
HM-clay clay determined by hydrometer method
nr real part of RI
ni imaginary term of RI
l wavelength of light
SASHM sand content determined with SHM
SALDM sand content determined with LDM
CLSHM clay content determined with SHM
CLLDM clay content determined with LDM
SIE estimate of silt percentage
RMSE root mean square error
K soil erodibility factor
f percentage of silt þ very fine sand particles
g percentage of sand coarser than very fine sand
d soil particle diameter
fE estimate of f
a coefficient Eq. (5)
b i o s y s t em s e n g i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5206
Using a laser particle analyser the following assumptions
are made (Konert & Vandenberghe, 1997): (i) the analytical
transformation of diffraction patterns to grain sizes is based
on matrices, which are calculated for spheres. Thus, the
diffraction along the cross-sectional area of the particles is
assigned to diffraction of spheres; (ii) particle orientation is
assumed to be randomly distributed, even if the laser
measurements are carried out in a continuous suspension in
which the particles may be oriented with respect to its shape.
Determination of PSD by an LDM has interested soil scien-
tists for some time (Beuselinck, Govers, Poesen, Degraer, &
Froyen, 1998; de Boer, de Weerd, Thoenes, & Goossens, 1987;
Buurman, Pape, & Muggler, 1997, 2001; Eshel, Levy, Mingelgrin,
& Singer, 2004; McCave, Bryant, Cool, & Coughanowr, 1986;
Pieri, Bittelli, & Rossi Pisa, 2006) but its application has not
generally replaced the labour-intensive classical methods (i.e.
PM or HM). According to Buurman et al. (1997), this reluctance
mainly depends on three factors: (i) insufficient confidence in
the results of LDMs: studies on correlations of laser-clay deter-
minationswith clay determined by pipettemethod (PM-clay) or
clay determined by hydrometer method (HM-clay) are still
rare, and their correlations usually deviate from1:1; (ii) inmany
countries PMs or HMs are accepted as standard for particle size
analysis of soils; (iii) many available relationships/interpreta-
tions have been established with HM/PM textures and (iv) the
high cost of the laser-diffraction equipment.
Theuse of LDMs raises thequestionof howsimilar the laser
grain-size measurements are to those obtained by classical
techniques such as SHM. Thework of Buurman et al. (1997) and
Muggler, Pape, and Buurman (1997), which was carried out
usingsoil profiles, suggested that the relationshipbetweenPM-
clay and LDM-clay may depend on the properties of the clay
fraction itself. Loizeau, Arbouille, Santiago, and Vernet (1994),
using samples of fluvial and lacustrine sediments, found that
the laser grain-size distribution underestimated the clay
content with respect to the classic sedimentationmethod and
that this underestimation increased with increasing clay
content. They were not able to establish if the clay underesti-
mation derived from its mineralogical composition which is
related to the particle shape and no conclusion was made
about the effects on the other size classes.
Buurman et al. (2001) also noted that sand-size particles are
measured more or less equally by LDMs and PSMs while
measurement of the clay-size fraction by the LDM usually
results in smaller percentages than those obtained by PSM.
This means that the lower percentages of the clay fraction
measured by the LDM must be compensated for higher
percentages in the silt-size fraction.
According to Bah, Kravchuk, and Kirchhof (2009) the
differences between the two methods are attributable to the
heterogeneity of soil particle density and the deviation of
particle shapes from sphericity. Sedimentation methods
assume a single particle density, which is a major source of
error, whereas LDM measurements are independent of
particle density.
Deviations from sphericity affect both methods. In the case
of the LDM, an irregular shaped soil particle reflects a cross-
sectional area greater than that of a sphere having the same
volume. Thus, particles are assigned to larger size fractions of
the PSD underestimating the clay fraction. Nonspherical parti-
cles in SHMs have longer settling times than their equivalent
spheres,which results in anoverestimation of the clay fraction.
Taking into account that SHM is an accepted and certified
method, and that LDMprovidesmore information and ismore
efficient than SHM, a relevant question is to establish whether
a correlation exists between the fine sizes fractions obtained
by both methods.
Laser-diffraction instruments have different ranges of
measurement and use a different number of detectors to
cover this range (size classes). Since the accuracy of the
particle size distribution obtained by an LDM depends on the
number of detectors used for a specific size-range, then it is to
be expected that themeasurements in the fine fraction will be
specific for a given LD analyser (Buurman et al., 2001).
Recently Goossens (2008) carried out a comparative study of
ten instruments for measuring the grain-size distribution of
loamy sediments (clay percentage ranging from 2 to 15%) sus-
pended in water. The grain-size analyses were carried out on
four sediments with a particle size-range<90 mm. In particular,
four LDanalysers (MalvernMastersizer S,Coulter LS200, Fritsch
Analysette22CandHoribaParticaLA-950)wereused.According
to thevariouscriteriaconsidered inGoussensstudy (cumulative
grain-size curve, median diameter, grain-size histograms,
skewness and kurtosis), the LD instruments produced the best
results. Althoughno “ideal”method canbedefinedand thefinal
choice of a grain-size technique depends onmany factors (type
of sediments, quantity of sediment available, speed of
measurement, specific aims of the study, etc.), Goossens (2008)
b i o s y s t em s e ng i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5 207
summarised that instruments based on LDM as offering many
advantages and generally work adequately.
In this paper, following a review of the LDM and some asso-
ciated effects (i.e. ultrasonic duration, pretreatment of the soil
sample and diffraction theory used), we test the method and
then compare the particle size distributions obtained by SHM
andbytheLDM.Wealsopresentsacomparative textureanalysis
using hydrometer measurements as a reference for the LDM.
The analysis is carried out using 228 soil samples, all
sampled in Sicily, representing a wide range of textures and
the Fritsch A22-Economy version of the laser diffraction
analyser. Therefore the paper is also the first comparative
analysis between SHM and LDM measurements carried out
using soil samples collected in Italy.
The results obtained in this paper have to be considered as
being apparatus specific because the measurement accuracy
is dependent on the number of detection cells (e.g. 31 in the
Fritsch instrument and 116 in the Coulter LS 230) even though
Goossens (2008) obtained similar results using different types
of laser analyser.
1.1. Sieving e hydrometer method
The PM or the HM defines a particle diameter as equivalent to
that of a sphere settling in the same liquid with the same
speed as the unknown sized particles, the so-called “Stokes
diameter” (Allen, 1990; Konert & Vandenberghe, 1997). The
sphere is usually assigned the density of quartz.
Hydrometer analysis uses a hydrometer having a gradu-
ated stem and weight bulb, to measure the specific density of
the suspension. The specific density depends on the weight of
soil particles in the suspension at the time of measurement
(Wen, Aydin, & Duzgoren-Aydin, 2002).
The HM is based on Stokes’ law that establishes the
velocity at which particles settle in suspension assuming that:
(1) soil particles are rigid, spherical and smooth; (2) soil
particles have similar densities; (3) particle-to-particle inter-
ference and boundary effects from the walls of the sedimen-
tation column are negligible; (4) particle sizes are small
enough to ensure that the induced fluid flow is well within the
laminar flow regime. A particle size calculated by Stokes’ law
is the quartz equivalent spherical sedimentation diameter
(McCave & Syvitski, 1991)
Deviations from Stokes’ law are expected when particles
are irregular in shape, as most silt particles, or are platy or
tubular in shape as aremost clay particles. The particle-shape
effect is due to the circumstance that the most stable position
of a settling, non-spherical particle is the one in which the
maximum cross-sectional area is perpendicular to the direc-
tion of motion. As a consequence, this position increases the
expected particle drag resistance and reduces the settling
velocity. In other words the particle-shape effect results in
a so-called “overestimation” of the fine size fraction which
depends on at which size the platy particles appear.
The validity of the spherical assumption (1) has been
examined in many papers in the past. Nettleship, Cisko, and
Vallejo (1997) established that the standard hydrometer
analysis should not be recommended for submicron mate-
rials. Vitton and Sadler (1997), examining eleven soil by
hydrometer and laser measurements, found that hydrometer
measurements had higher percentages of fine particles than
LDM. Similarly Konert and Vandenberghe (1997), comparing
the results obtained by pipette analysis and laser-diffraction
technique, concluded that particle size distributions were
comparable for “blocky” quartz particles but significantly
different for “platy” clay particles. Recently, Lu, Ristow, and
Likos (2000) carried out a theoretical analysis for deter-
mining the settling velocity of disk-shaped and rod-shapes
particles. Their analysis showed that for disk-shaped and rod-
shapes particles, in sizes ranging from 0.1 mm to 100 mm,
Stokes’ law underestimates the maximum particles dimen-
sion by up to two orders of magnitude. The experimental
results of Lu et al. (2000), using various techniques, also
confirmed the underestimate errors of particle size inherent
in hydrometer analysis.
For soil and earth materials, particle density is commonly
taken constant and equal to 2.65 Mg m�3 Clifton, McDonald,
Plater, and Oldfield (1999) suggested that density of sediment
particles can vary between 1.66 and 2.99 Mg m�3. A soil is
composed of particles with different densities, which are
mainly determined by their mineral compositions. The
uncertainty of particle density may strongly bias the particle
size distribution (Wen et al., 2002).
The effects due to both particle-to-particle interference and
the columnwalls, which limits the applicability of Stokes’ law
can be avoided limiting the maximum concentration of soil in
the suspension (50 g of dry soil in 1000 ml of suspension).
Assumption (4) from above is verified for an upper limit of the
Reynolds number value ranging from 0.1 to 1 (Allen, 1990;
Bernhardt, 1994); these values correspond to free-falling
spherical quartz particles �2 mm in diameter (Lu et al., 2000).
The classical technique SHM represents a “standard” for
soil particle size analysis and many available relationships,
such as pedotransfer functions, were established using
hydrometer/pipette texture measurements.
1.2. Laser diffraction method
The principle of LDM is that particles of a given size diffract
light througha given angle. The angle of diffraction is inversely
proportional to particle size, and the intensity of the diffracted
beamat any angle is ameasure of the number of particleswith
a specific cross-sectional area in the optical path.
A parallel beam of monochromatic light passes through
a suspension contained in a sample cell, and the diffracted
light is focused onto detectors. For calculating particle sizes
from light intensity sensed by detectors, two diffraction
theories are commonly used: the Fraunhofer diffraction
and theMie theory (Gee & Or, 2002). Both theories assume that
the particles have a spherical shape; in other words, the
particle dimension is the optical spherical diameter, i.e. the
diameter of the sphere having a cross-section area equivalent
to the measured one by laser diffraction.
Fraunhofer theory is based on the approximation that the
laser beam is parallel and the detector is at a distance that is
very large compared with the size of the diffracting particle.
Fraunhofer theory becomes inapplicable when the particle
diameter is close to thewavelength of light (l) as the refraction
of particles in this size range becomes appreciable (Loizeau
et al., 1994).
Fig. 1 e Distribution by USDA texture using the percentage
of clay, sand and silt determined by SHM (a) and by LDM
(b).
b i o s y s t em s e n g i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5208
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 canmake 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, repre-
senting 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 parti-
cles. 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 claymeasured by the sieving-pipettemethod
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
analysis of a large number of samples (e.g. soil samples sampled
inabasin, suspensionsamplescaughtduringsoil erosionevents).
LDMalso covers awide range of grain sizes andmay 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
chemical and physical properties, other relevant processes,
such as soil erosion and sediment transport by overland flow,
are dependent on the size distribution of soil aggregates
(effective grain-size distribution) (Buurman et al., 1997; Di Stefano
& Ferro, 2002; Foster, Young, & Neibling, 1985).
2. Materials and methods
Soil samples were taken at various locations in a Sicilian
basin, Imera Meridionale, which has an area of 2000 km2. The
228 samples were selected to represent a large variety of soil
textures based on the SHM (Fig. 1a).
For both the SHM and the LDM, soil samples were dried at
105 �Candweregentlycrushedanddrysievedat2-mmmesh-size.
For each analysed soil sample, 50 g was used for the SHM
analysis and 10 g was used for the LDM. Each sample was
treated with H2O2 (concentration equal to 30%) to assure
complete removal of organic material and was dispersed to
remove aggregates by adding a sodium hexametaphosphate
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
overnight using an end e over e end shaking.
For the SHM analysis the pretreated sample (50 g) was wet
sieved through a 0.075 mm sieve. The fine fraction (<75 mm)
collected after wet sieving was transferred to standard cylin-
ders for hydrometer analysis. The cylinders were inserted into
a water bath at a constant temperature. Corrections for the
temperature effects on density and viscosity of suspension
were carried out. A standard hydrometer, ASTM no. 152 H,
Fig. 3 e Cumulative particle size distributions of two
b i o s y s t em s e ng i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5 209
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 pre-
treated 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
versionmeasures 31 grain-size classes in the working range of
0.1e600 mm. For the LDM analysis a sub-sample was intro-
duced 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 dispersionmethod 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. 2 e Cumulative particle size distributions for samples
22 and 44 corresponding to different durations of
ultrasound.
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 LDMwere 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 shows, as an example for two tested soil samples
(number 22 and 44), the effect of the duration of ultrasound.
Samples 22 and 44 were selected because they had the highest
Fig. 4 e Comparison between clay (a) and silt (b) fractions
with and without H2O2 pretreatment.
Fig. 5 e Comparison between cumulative particle size
distributions obtained by the Fraunhofer model and Mie
theory.
b i o s y s t em s e n g i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5210
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
pretreatment can be recognised in the particle size distribu-
tion for soil particles ranging from 0.002 mm to 0.1 mm.
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. 6 e Comparison between cumulative particle size distributions obtained by SHM and LDM.
b i o s y s t em s e ng i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5 211
Fig. 7 e Relationship between sand fraction obtained by
LDM and by SHM.
Fig. 9 e Comparison between f percentage estimated by Eq.
(4) and by SHM.
b i o s y s t em s e n g i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5212
oxides has to be considered a nr value of 1.6 should be
employed (CRC Press, 2002).
Fig. 5 shows that no significant differences could be
detected for the two investigated diffraction models applied to
the selected samples. For the same soil samples, the analysis
showed that the variability of the imaginary term of the
refraction index (0.1e0.2) does not produce appreciable effects
on the cumulative grain-size distribution. Accordingly, the
cumulative grain-size distributions of the investigated samples
were determined using the Fraunhofer diffraction model.
Fig. 6 shows the comparison, as an example for eight soil
samples having a different United States Department of
Agriculture (USDA) texture classifications, between the PSD
determined by SHM (for d < 75 mm by HM and for d � 75 mm by
sieving) and LDM (for d � 600 mm by LD and for d > 750 mm by
Fig. 8 e Relationship between clay fraction obtained by
LDM and by SHM.
sieving). This figure shows that for each sample appreciable
differences were detected between the two methods used to
determine the particle size distribution. In particular, for all
samples, the sand content determined by SHM was similar to
the one obtained by LDMwhile the so-called “overestimation”
of the clay percentage measured by SHM as compared to LDM
was confirmed.
Fig. 7, which compares the sand content determined with
SHM, named SASHM, with the LD measured sand content,
SALDM, shows that the two values can be assumed equal.
SASHMySALDM (1)
The relationship plotted in Fig. 7 is characterised by a root
mean square error (RMSE) equal to 2.16 (expressed as %).
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 inter-
national 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
(1971) requires knowledge of the soil grain distribution, soil
organic matter, soil structure and permeability. In particular
Fig. 10 e Relationship between sand and clay fractions
obtained by LDM and by SHM for the textural group “loamy
sand D sandy loam”.
Fig. 11 e Relationship between sand and clay fractions
obtained by LDM and by SHM for the textural group
“loam”.
b i o s y s t em s e ng i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5 213
the particle size distribution needed to calculate K is the
percentage f of silt þ very fine sand particles
(0.002mm< d< 0.1mm, being d the particle diameter) and the
percentage g of sand coarser than very fine sand
(0.1mm< d< 2mm) as defined byWischmeier 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
estimating the percentage of siltþ very fine sand particles fE is
obtained:
fE ¼ 100� 1:91 CLLDM � g (4)
Fig. 9 shows the comparison between the percentage of
silt þ very fine sand particles fE estimated by Eq. (4) and the
same percentage f calculated by the measurements carried
out by SHM. This comparison shows that fE is similar to f even
if the scattering of the pairs ( f, fE) is appreciable (RMSE¼ 9.56).
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 charac-
terised 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. 12 e Relationship between sand and clay fractions
obtained by LDM and by SHM for the textural group “silt
loam D silty clay loam”.
b i o s y s t em s e n g i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5214
by the two different methods. According to these figures, for
the clay fraction the following equation can be established:
CLSHM ¼ a CLLDM (5)
where a is a coefficient equal to 2.18 for the textural group 1
(SA> 50%), 1.91 for the textural group 2 ðSAy50%Þ and equal to
1.91 for the textural group 3 (SA < 50%).
The relationship Eq. (5) calibrated for each textural group is
characterised by RMSE ¼ 3.1 for the textural group 1,
RMSE ¼ 6.4 for the textural group 2, RMSE ¼ 10 for the textural
group 3 which is lower than or similar to that obtained by Eq.
(2) (RMSE ¼ 9.27). In other words, even if in some case (Figs. 11
and 12) the number of samples used is small, for transforming
clay measurements from the LDM to the SHM a more reliable
estimate of clay percentage can be obtained using a coefficient
specific to each textural group.
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)
and of the percentage of siltþ 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 infor-
mation 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 appa-
ratus 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
the Fraunhofer or Mie diffraction models for the LDM gave no
appreciable differences for the soils investigated.
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
SHM with respect to LDM was confirmed.
Finally, a set of equations useful to refer LDM measure-
ments to the SHM results, the latter is used as an international
standard, was proposed.
The analysis demonstrated that for improving the trans-
formation of the claymeasurements from the LDM to the SHM
three textural groups (sand content greater than 50% (loamy
sand þ sandy loam), almost equal to 50% (loam) and less than
50% (silt loam, silty clay loam)) have to be distinguished. For
each textural group a more reliable estimate of clay
percentage can be obtained using a specific coefficient.
Even if for transforming the clay measurements from the
LDM to the SHM a more reliable estimate of clay percentage
can be obtained using a coefficient specific for each textural
group, the calibration equations (5) and (6) by particle size
(SA > 50% and SA � 50%) presented in this paper are not
b i o s y s t em s e ng i n e e r i n g 1 0 6 ( 2 0 1 0 ) 2 0 5e2 1 5 215
universal. Further measurements carried out contemporane-
ously by the LDM and the SHM could allow the results
obtained in this investigation to be confirmed and the
proposed scale equations to be improved.
Acknowledgements
The research was set up by Prof. V. Ferro and Dr. C. Di Stefano,
the measurements were carried out by Dr. S. Mirabile. All
authors analysed the results and contributed to the writing of
the paper.
The research was supported by a grant of Ministero del-
l’Istruzione, dell’Universita e della Ricerca scientifica, Governo
Italiano, PRIN 2007 “Monitoraggio e modellazione dei processi
erosivi a differenti scale spaziali nell’area sperimentale di
Sparacia” and Progetto FEROS.
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