Technical note
Alternative soil particle-size analysis by gamma-ray attenuation
E.A. Elias
a,*, O.O.S. Bacchi
a, K. Reichardt
a,baLaboratoÂrio de FõÂsica do Solo, CENA, USP, CP 96, CEP 13400-970, Piracicaba, SP, Brazil bDepartamento de Ciencias Exatas, USP, CP 9, CEP 13418-970, Piracicaba, SP, Brazil
Received 12 April 1999; received in revised form 3 August 1999; accepted 3 August 1999
Abstract
In 1992 a new method of soil particle-size analysis was introduced, which coupled sedimentation to gamma-ray attenuation. The theoretical possibility of an alternative for this method is here presented, which includes the necessity of sieving soil samples, but simpli®es the gamma-ray measurements. Advantages and disadvantages of this alternative are discussed.#1999 Elsevier Science B.V. All rights reserved.
Keywords:Granulometry; Soil mechanical analysis; Spectrophotometry
1. Introduction
Vaz et al. (1992) developed a method of soil par-ticle-size analysis by gamma-ray attenuation which, like the pipette method, is based on particle sedimen-tation. It differs, however, from the pipette method for two reasons: (r1) the pipette is replaced by the gamma-ray beam; and (r2) sievingdoes notprecede sedimen-tation. This can be clearly seen in their statement: ``The pipette method estimates sand content indir-ectly, using a sieve (no. 270) of 0.053 mm diameter openings. In the new method all fractions are mea-sured during sedimentation (. . .)'' (Vaz et al., 1992). The advantages of Vaz' method in relation to the pipette method are threefold: (a1) no perturbation of the sedimentation process; (a2) continuous analysis of particle-sizes and (a3) direct observation of all
particle fractions. The theoretical possibility of a ``Vaz' method alternative'' is here presented, in which sieving of coarse particles does precede sedimenta-tion, so that the Vaz' and pipette method would differ due to reason (r1) only. This alternative would miss advantage (a3). However, there are, at least, two additional advantages, shown below.
2. Theoretical
The equation used by Vaz et al. (1992) to estimate particle concentrationCat a time tis
Cln I0=IX pÿw=Dp; (1)
and the relative particle concentration =C0=C/C0is
C0 ln I0=IXC0 pÿw=Dp; (2)
whereI0andIare the count intensities of the gamma-ray beams after passing through the absorbing
med-Soil & Tillage Research 52 (1999) 121±123
*Corresponding author. Tel/fax: 00-55-19-4340021 E-mail address: [email protected] (E.A. Elias)
ium composed of (i) dispersing solution and (ii) dispersing solution plus sedimenting soil particles, respectively; w and p are the mass attenuation coefficients of the used gamma radiation, for water and soil particles, respectively;Dpis the soil particle density (water density is taken as unit); X is the container's inner thickness and C0 the soil particle concentration at the beginning of the sedimentation process.
Vaz et al. (1992) state: ``since measurements ofIare performed in de®nite time interval (t= 3 s in our case), it is dif®cult to measure the initial concentration (corresponding to the start of the sedimentation pro-cesst= 0) through beam attenuation. Therefore, the initial concentration was calculated from soil mass and solution volume''. According to Gee and Bauder (1986), p. 394, the time t at which there are no more particles of diameter d above a chosen depth
his given by
t18h=g DpÿDwd2; (3)
whereis the water viscosity. From Eq. (3), it is easy to recognise thatt< 3 s ford> 0.200 mm,h= 10 cm and at room temperature. If C0includes particles larger than 0.200 mm, then it is, in fact, very difficult to measureC0through beam attenuation. On the other hand, if the soil is previously sieved, so that the largest particles present in the sample are such that
d= 0.053 mm, thent40 s. In this way the concen-tration will remain constant and equal to C0 at
h= 10 cm for 40 s. Consequently, it will be easy to measureC0through beam attenuation. In accordance with Eq. (1),C0will be
C0ln I0=Ico=X pÿw=Dp; (4)
whereIcois the constant count intensity of the gamma-ray beam fromt= 0 tot= 40 s.
Dividing Eq. (1) by Eq. (4) yields
C0 ln I0=I=ln I0=Ico: (5)
If one does not want to calculate the timetthrough Eq. (3), one can refer to the table compiled by Gibbs et al. (1971), p. 15, where the velocity of a 0.050 mm diameter particle is directly given. Then one can easily determinet, dividing hby the velocity.
The Bouyoucos hydrometer method is another method based on the differential rate of settling of
particles during sedimentation, as formulated by Stokes law. According to Bouyoucos (1962), p. 464 and Tan (1996), p. 78, all particles >0.050 mm (sand) settle out after 40 s.
3. Discussion
Interpreting Eq. (5), the ®rst advantage of this alternative over the Vaz' original method is that it does not require the knowledge of parametersw,p,
Dp,XandC0. Hence each researcher would have to decide, according to one's laboratory conditions, whether this alternative is simpler or more compli-cated to be carried out than the Vaz' original method. In other words, one will have to select either the advantage of not sieving or the advantage of avoiding measuring these ®ve parameters.
Vaz' method is quite recent. New methods may always have problems that may take a long time to be detected, so that corrections may eventually be found necessary. The pipette method, on the contrary, has been well established, repeated and cited by several authors. Thus one may hold that such a new method should be as close to the conservative one as possible. Hence the second advantage of the alternative here presented, as it differs from the pipette method for just one reason, not two.
It is interesting to notice that both Vaz' method and spectrophotometry are based on measuring concentra-tion as a funcconcentra-tion of the attenuaconcentra-tion of radiaconcentra-tion.
Eq. (5) is not altered if the exact equation of Elias et al. (1999) is used instead of Eq. (1). This alternative method is also applicable to the improved soil particle-size analysis by gamma-ray attenuation of Oliveira et al. (1997).
Comparing precision and accuracy of both methods Ð the original and the alternative Ð is not within the scope of this theoretical study and should be done by experimental research.
4. Conclusion
A simple and promising theoretical model of an alternative method of soil particle-size analysis has been explained here. The model invites further research for experimental con®rmation and validation.
Acknowledgements
Authors are thankful to Dr. Julio C.M. Oliveira for expert consultation on the subject and to CNPq for ®nancial support.
References
Bouyoucos, J.B., 1962. Hydrometer method for making particle-size analysis of soils. Agronomy J. 54, 464±465.
Elias, E.A., Bacchi, O.O.S., Reichardt, K., 1999. Exact equations for soil particle-size analysis by gamma-ray attenuation. Scientia Agricola. 56(1), 93±96.
Gee, G.W., Bauder, J.W., 1986. Particle-size analysis. In: Klute, A. (Ed.), Methods of Soil Analysis, Part I, 2nd ed., Agron. Monographs, vol. 9, ASA and SSSA, Madison, WI, pp. 383± 411.
Gibbs, R.J., Matthews, M.D., Link, D.A., 1971. The relationship between sphere size and settling velocity. J. Sed. Petrol. 41, 7± 18.
Oliveira, J.C.M., Vaz, C.P.M., Reichardt, K., Swartzendruber, D., 1997. Improved soil particle-size analysis by gamma-ray attenuation. Soil Sci. Soc. Am. J. 61, 23±26.
Tan, K.H., 1996. Soil Sampling, Preparation and Analysis, 1st ed. Marcel Dekker, New York, 408 pp.
Vaz, C.P.M., Oliveira, J.C.M., Reichardt, K., Crestana, S., Cruvinel, P.E., Bacchi, O.O.S., 1992. Soil mechanical analysis through gamma-ray attenuation. Soil Technol. (Cremlingen) 5, 319± 325.
