Soil & Tillage Research 123 (2012) 43–49

Representative elementary area (REA) in soil bulk density measurements throughgamma ray computed tomography

Jaqueline A.R. Borges, Luiz F. Pires *

Laboratory of Soil Physics and Environmental Sciences, Department of Physics, State University of Ponta Grossa (UEPG), CEP 84.030-900, Ponta Grossa, PR, Brazil

A R T I C L E I N F O

Article history:

Received 29 December 2011

Received in revised form 20 March 2012

Accepted 22 March 2012

Keywords:

Soil structure

Soil physical properties

Paraffin sealed clod method

Gamma ray attenuation

A B S T R A C T

Gamma ray computed tomography (CT) has recently become a useful tool for non-invasive

characterization of soil physical parameters. Such technique is interesting because it can be used, for

instance, in measurements of representative elementary area or volume (REA or REV) of soil samples

used to assess soil physical properties. Soil scientists are aware that a sample has to be of a certain size in

order to represent certain physical property of that soil in the field. In this study, CT was used to measure

REA of samples of a Brazilian soil of clay texture. The objective of using this technique was to verify the

minimum volume of soil to be collected for bulk density measurements (rs) through the paraffin sealed

clod method (PSC). Results revealed that samples with volumes from 50 to 100 cm3, with minimum cross

section 640.1 mm2 are enough to produce representative rs values.

� 2012 Elsevier B.V. All rights reserved.

Contents lists available at SciVerse ScienceDirect

Soil & Tillage Research

jou r nal h o mep age: w ww.els evier . co m/lo c ate /s t i l l

1. Introduction

The concept of representative elementary size (RES) wasintroduced in continuum mechanics by Jacob Bear, in 1972, as atool to be used to describe the flow in porous media. The approachdeals with the definition of a minimum size or physical point of asample which is needed to represent its characteristics of interest,that is, the size in which the measured parameter becomesindependent from the sample size (Bear, 1972).

The analysis of representative sizes, which might be represen-tative elementary volume, area or length (REV, REA and REL), iscommonly carried out by selecting the consecutive sizes around acentral point in the sample image. Also, adjacent constructionswithin the same image, centered at different points can be used(Baveye et al., 2002; Constanza-Robinson et al., 2011; Vandenby-gaart and Protz, 1999). The representative size is then defined asthe one corresponding to the transition from the microscopiceffects domain (region I) to the porous media domain (region II)(Fig. 1).

The use of samples with representative size is a matter ofconcern due to the relation between certain soil physicalproperties and sample size (Baveye et al., 2002). However,representative sizes are usually investigated regarding propertiesof interest in homogeneous media, such as spherical glass beadsand sands (Al-Raoush and Papadopoulos, 2010; Razavi et al., 2007).Also, REV in particular has become a parameter which indicates the

* Corresponding author. Tel.: +55 42 3220 3044; fax: +55 42 3220 3042.

E-mail addresses: lfpires@uepg.br, luizfpires@gmail.com (L.F. Pires).

0167-1987/$ – see front matter � 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.still.2012.03.008

quality of measurements carried out via third generationcomputed tomography (CT). This is due to the fact that smallersamples have been used to obtain higher resolution tomographyimages. However, the sample size must be enough to produceresults representative of the property under investigation. The REVsize established for any property corresponds to the lower samplevolume employed to obtain representative measurements of suchproperty (Constanza-Robinson et al., 2011).

RES can be determined for different porous media, propertiesand measurement scales. However, previous studies revealedthat it can vary according to its application (Asano and Uchida,2010; Bartoli et al., 2005; Li and Zhang, 2010). For example, formicro morphological analyses of total area and perimeter of soilpores with different diameters, REA varies for each physicalproperty analyzed and also the pores diameter interval(Vandenbygaart and Protz, 1999). It is also important to observethat each porous media has its own characteristics, therefore therepresentative size of certain media parameter is probablydifferent for the same parameter in a different porous media(Muller et al., 2010).

Very little research is available on non-homogeneous media,with porosity and/or density varying in space, as in the case of soil(Baveye et al., 2002; Vandenbygaart and Protz, 1999). In such case,some difficulty is observed to determine the elementary size, sinceit is ‘‘somewhere’’ in region II (Fig. 1), due to mild fluctuations ofthe physical property under analysis.

Some observation carried out by Vandenbygaart and Protz(1999), revealed the lack of suitable techniques for the study ofrepresentative size of undisturbed soil samples. In their study, theauthors estimated REA using the micro morphological analysis.

Fig. 1. Representative elementary volume (REV, DU0) of the porosity (f). DUi

represents any volume in the porous media. Representative elementary area (REA)

is defined from the REV concept and presents similar behavior.

Adapted from Bear (1972).

J.A.R. Borges, L.F. Pires / Soil & Tillage Research 123 (2012) 43–4944

However, this method might change the soil structure in theimpregnation process, which does not occur with the tomography.

CT has been proved as an efficient method to study soilstructure, and it has become more important as the newgenerations of tomographs exclusively dedicated to the study ofmaterials. The technique has become so successful due to the factthat it is a non-invasive method, that is, it does not damage thestructure of the sample under analysis. Another advantage is thatCT also provides 2D and 3D images with micro and millimetricresolution which make quantitative as well as qualitative analysespossible (Elliot et al., 2010; Pires et al., 2010; Tippkotter et al.,2009; Tomioka et al., 2010; Tumlinson et al., 2008).

In order to determine physical properties of soil samples, firstgeneration tomographs are usually used, since they enable largersamples (a couple of centimeters) analyses (Cruvinel and Crestana,1997; Pedrotti et al., 2005, 2003b). In the data matrix obtained, it ispossible to select specific areas of different sizes in its interior, forthe measurement of the property of interest (Pires et al., 2007,2005b). Thus, the first generation tomography is the idealequipment to investigate soil samples REA.

In this study, the REA was determined for density measure-ments of a Brazilian soil of clay texture, from data obtained viagamma ray first generation CT. Tomography images with milli-metric resolution were used for both qualitative and quantitativeanalyses. Measurements of such physical property were alsocarried out using the paraffin sealed clod method (PSC), adopted asthe standard method.

2. Materials and methods

2.1. Soil sampling

Eighteen clod samples were collected from an experimentalfield belonging to the Areao Farm at ESALQ/USP, Piracicaba, SP,Brazil (228420S and 478380W, 580 m above sea level). Samples werecollected in triplicate, in the inter-row (space of 1.75 between rowsand 0.75 between plants) of the experimental field cultivated withcoffee (coffea arabica), being selected 6 collection points along atransection of 200 m long. The volumes of the soil clod samplesvaried from 50 to 100 cm3. The sampling was made at the surfacelayer (0 – 15 cm) inside of a small trench. Shortly before theopening of a trench the crop above the soil surface was removed.

The clay soil (43% clay, 24% sand, and 33% silt) was classified asEutric Nitosol (FAO, 1998). It presents a mean soil particle density(rp) of 2.65 � 0.01 g cm�3. As to its chemical characteristics, the soilpossesses 20.2 g dm�3 of organic matter; pH 5.3 (in CaCl2) and 29.0,20.0 and 4.3 mol m�3 of Ca, Mg and K (Pires et al., 2005a).

2.2. Soil bulk density measurements

The tomography equipment used was developed at EMBRAPA/CNPDIA. It is a first generation system, with fixed source anddetector and the samples are submitted to rotation and translationmovements. The tomograph is equipped with a gamma ray source241Am (59.54 keV), approximate activity 3.7 GBq, and a7.62 cm � 7.62 cm NaI(Tl) detector. The lead (Pb) collimators usedat the source output and detector input were 1 mm and 4.5 mmrespectively. The tomographic units (TU) data matrices obtainedwere 80 � 80 for all images. The resolution obtained for the clodsamples was 1.1 mm � 1.1 mm. A 2D image was obtained for eachclod with the scanning of the center of each sample. Therefore, thetomography image presents a 2D cut of a soil sample section. Theerror attributed to the tomography (Eequip) was calculatedaccording to the procedure described in Pedrotti et al. (2003a).

Each pixel of the tomographic image has a characteristic valueof TU, which is proportional to the mean linear attenuationcoefficient m (cm�1). The reference media for the TU is the air,which presents the lowest attenuation. For the soil, the TUcorresponds to the contribution of mineral particles, of the organicmatter, from water and air, generating different m values for eachpath crossed by the radiation (Crestana et al., 1996).

Therefore, in the reconstruction of tomographic images the TUare related to the m of each sample cross section where the scanwas carried out. The relation between TU and different physicalproperties of the soil, such as volumetric soil water content (u), isgiven in Eq. (1) (Fante Junior et al., 2002; Pedrotti et al., 2005; Vazet al., 1989):

TU ¼ aðmmsrs þ mmwrwuÞ (1)

where rw (g cm�3) is the water density, a is the calibration straightline angular coefficient of the tomographic system, mms and mmw

(cm2 g�1) are the soil and water mass attenuation coefficients,respectively. Soil bulk density was calculated for each pixel oftomographic images, from Eq. (1), as follows:

rs ¼1

mms

TU

a� mmwrwur

� �(2)

where ur (cm3 cm�3) represents the residual volumetric soil watercontent.

When calibrating the tomograph, samples of the followinghomogeneous materials were used: acrylic, ethanol, water, nylonand glycerin. 2D images of the central cross sections of sampleswere obtained for calibration. The areas in the TU data matricesselected for the system calibration were chosen away from thesample borders to avoid artifacts. A detailed description of thecalibration process of first generation tomography systems can befound in Crestana et al. (1992).

The paraffin sealed clod method (Blake and Hartge, 1986) wasalso employed to the rs measurements. Results obtained wereadopted as standard, due to the tradition as well as economicalviability of this method.

2.3. REA evaluation procedures

The data matrix obtained via CT was firstly converted in densitymatrix (Eq. (2)). The program ‘‘Microvis’’ (Microvis, 2000) was usedto reconstruct and analyze the tomographic images. This programpresents gray scale where darker regions correspond to lowerdensity values and, consequently, lower TU values. In the currentwork, the darker regions represent larger values of density.

The linear steps in the tomography system were 1.0 – 1.1 mm,which is important due to the selection of equal areas for the

Fig. 2. Schematic drawn of the area construction on the tomographic images and

respective areas adopted for the REA definition. The area next to edge corresponds

to the free area (FA). Darker regions represent higher soil bulk density (rs) values.

Table 1Soil bulk density (rs) values of clod samples (S) obtained through computed

tomography (CT) and paraffin sealed clod (PSC) methods.

S CT PSC S CT PSC

rs (g cm�3) CV (%)a rs (g cm�3) rs (g cm�3) CV (%) rs (g cm�3)

01 1.53 3.9 1.60 10 1.70 3.5 1.79

02 1.66 3.6 1.65 11 1.70 3.5 1.66

03 1.57 3.8 1.56 12 1.73 3.5 1.70

04 1.71 3.5 1.75 13 1.68 3.6 1.67

05 1.73 3.5 1.72 14 1.81 3.3 1.75

06 1.75 3.4 1.72 15 1.70 3.5 1.69

07 1.71 3.5 1.72 16 1.74 3.4 1.65

08 1.67 3.6 1.71 17 1.62 3.7 1.56

09 1.65 3.6 1.63 18 1.78 3.4 1.72

a The coefficient of variation (CV) was obtained taking into consideration the

average standard deviation (s) of the rs matrix or the equipment error (Eequip). The

rs values via CT were obtained considering the free area.

J.A.R. Borges, L.F. Pires / Soil & Tillage Research 123 (2012) 43–49 45

tomographic analysis for all samples. The differences in linearsteps are due to different dimension of the clods analyzed.

In order to determine the rs, the larger possible rectangular areawas delimited in the sample interior, without the bordersinterference in the tomographic image. The borders are avoided,as the interface sample-air usually presents artifacts in images thatmight affect the analysis of soil physical properties (Cruvinel et al.,1990; Kak and Slaney, 1999; Pires et al., 2004).

The points regarding each vortex of the rectangular area wereselected in the tomographic image in the Microvis and, later on,identified and marked in the TU matrix. Then, consecutiveconcentric quadrangular areas were selected without extrapolat-ing the maximum area previously selected. The initial area wasobtained from a square matrix of 1 � 1 (1.1 mm � 1.1 mm). Also,an area comprising almost all the tomographic image was selected,with an irregular shape, called free area (FA) (Fig. 2). The number ofareas delimited in the interior of each sample varied according toits size and irregularities in its shape.

Soil bulk density was determined for each of the quadrangularareas as well as for the FA. Here, the rs obtained via CT correspondsto the average value of this physical property, since the CT enablesits analysis pixel by pixel. From the results obtained via CT and PSC,the REA was determined as a function of the rs. Below are listed thecriteria used (itens i and ii) and also the analyses carried out (itensiii and iv):

i. Relative deviation of rs average value between the last and eachof the other areas not superior to 5%, 4%, 3%, 2% and 1%;

ii. That at least three consecutive areas cannot present different rs

values, using the variation criterion in item i;iii. Elaboration of variation graphs of rs values for the areas of each

sample. In these, the rs value obtained via PSC was inserted as areference line. These graphs also show the delimitation of areasin which REA was reached for different criteria listed in item i;

iv. Elaboration of frequency and cumulative frequency graphs (%)for each area representing the number of samples that reachedREA for deviations 5%, 4%, 3%, 2% and 1%, as a function of thearea selected in the interior of the sample.

2.4. Correlation between methods

The analysis of correlation between methods used (CT and PSC)for the determination of the soil clod samples rs was carried outwith the elaboration of the following graphs: rs (PSC) � rs (CT) of18 samples (called S 01, S 02, . . . and S 18), where the rs (CT) valuescorrespond to those obtained through FA; rs (PSC) � rs (CT) for 9samples (S 01, S 04, S 07, S 09, S 10, S 12, S 14, S 17 and S 18) fromthe 18 samples that comprised at least 14 areas and also for FA.

Graphs were adjusted using the linear regression model withcorrelation coefficient used as an index in the REA definition(Downing and Clark, 2005). The computational software used to

construct the graphs and to analyze the data was the MicrosoftExcell.

3. Results and discussion

The correlation coefficient (r) obtained in the tomographycalibration was 0.995. This good correlation between experimentaldata is relevant so that representative measurements of the soilphysical properties are obtained via CT (Pires et al., 2011).

The mms and mmw obtained were 0.3339 � 0.0029 and0.2001 � 0.0004 cm2 g�1, respectively. These values are coherentwith the experimental and theoretical results obtained by otherauthors for water and soil of similar texture (Ferraz and Mansell,1979; Hubbell and Seltzer, 1995).

3.1. Correlation between methods

The rs values obtained via CT and PSC methods, and respectiveCV (Downing and Clark, 2005) via CT, are presented in Table 1. Thedensity average values obtained taking into consideration the 18samples were 1.69 � 0.07 and 1.68 � 0.08 g cm�3, for the CT and PSCmethods, respectively. Here, the deviation presented corresponds tothe average standard deviation.

The mean rs values (CT and PSC) evaluated in this work areoverestimated in comparison to those find in the literature for thesame type of soil (Blainski et al., 2009; Domingos et al., 2009). Apossible explanation for this result is the region (inter-rows of theexperimental field) selected for soil sampling. Since these inter-rows are frequently subjected to human and light vehicles traffic,in order to crop management, it is common to find compacted soilstructures in these places.

As for the CT, Pedrotti et al. (2003a) recommend the use of Eequip

whenever it is higher than the sample standard deviation and viceversa. The biggest error is always taken into consideration. In thiswork, the error associated to the tomography was evaluated in0.06 g cm�3. The main source of errors in CT is in determining the I0

and I, due to the disintegration process of the radioactive sourcebeing statistic (Kaplan, 1963).

The percentual relative deviation taking the PSC as referencewas approximately 0.6%. This result shows good agreementbetween the measurement methods. The CT and paraffin sealedclod methods presented a correlation coefficient of 0.76 (Fig. 3). Itcan be stated that the result obtained presents strong positivecorrelation between data. However, the difference observedbetween these methods can be explained by the fact that theypresent different analysis methodologies (Blake and Hartge, 1986;Timm et al., 2005). In CT the analysis is carried out for a plane (2D)and in PSC for a volume (3D).

Fig. 3. Correlation between soil bulk density (rs) values obtained through computed

tomography (CT) and paraffin sealed clod (PSC) methods. CT results were obtained

considering almost all the sample image scanned area (FA – free area).

Fig. 4. Correlation between soil bulk density (rs) values obtained through paraffin sealed

and the different areas selected in the interior of samples.

J.A.R. Borges, L.F. Pires / Soil & Tillage Research 123 (2012) 43–4946

Another factor that might explain this value of r betweenmethods is that some samples presented macroporous and smallpebbles in the cross section analyzed, under or overestimating thers value obtained via CT.

This spatial variability of samples also explains the variation inrs values obtained in analyses through the same measurementmethod (Table 1). Such characteristics from the interior of eachsample could be seen and quantified in non-invasive tomographicimages, which cannot be accomplished with traditional rs

measurement methods such as PSC and volumetric ring.Spatial variability in different areas selected from the tomog-

raphy images was also evaluated by Pires et al. (2005b). Theseauthors analyzed the TU obtained from within the same sample,divided into 15 adjacent areas. The biggest difference found amongareas in the same sample was 111 TU, and the smallest 40 TU. Inthis case, the variation implies in density difference 0.22 g cm�3,

clod (PSC) and computed tomography (CT) methods. FA and A represent the free area

Fig. 5. Soil bulk density (rs) graphs for each area of samples 03, 09, 11 and 17, and respective representative elementary areas (REA) for the deviations 5%, 4%, 3%, 2% and 1%

(arrows), when those were reached. The tomographic images are in gray scale of tomographic units (TU). The dotted line represents the rs value obtained via paraffin sealed

clod (PSC) method. The error bars represent the scanner error and standard deviation of TU data (quadratic areas data matrices) when higher than the equipment error. FA

represents the free area.

J.A.R. Borges, L.F. Pires / Soil & Tillage Research 123 (2012) 43–49 47

which reflects changes in the soil structure resulting from naturalor artificial processes.

Particular characteristics of each sample might impede resultsof physical properties evaluated for certain soil being representa-tive of this soil, depending on the size of the samples used. For thisreason, rs was also evaluated in different areas selected in theinterior of each sample (Fig. 2). In Fig. 4 graphs of rs correlationvalues are presented of each area obtained through PSC for the 9samples that comprised at least 14 areas.

The correlation analyses presented in Fig. 4 were carried outas an attempt to create an initial parameter for the REAdefinition. The idea is based on the fact that as the REA getscloser, the r value becomes closer to 1. It can be seen that rincreases gradually reaching 0.63 in the 14th area, which is closeto the value obtained for FA for the 9 samples that comprise 14quadratic areas.

However, the r value still indicates the existence of relativelyhigh dispersion of experimental data. For example, the differencebetween correlation coefficients of areas 14th and 11th was 0.10;while the difference between the 14th and 9th areas was 0.25. Thisresult provides an idea of the rs variability with the area selected toanalyze it. There r value is over twice as high for a difference of only3 areas (9th–11th areas). When comparing the r value obtained forthe FA of samples 9 and 18, the difference is only 2%, whichindicates that this analysis carried out with 9 samples can beextended to all 18 samples.

In the correlation graphs, it is possible to observe that mostrs values in the PSC are overestimated in relation to the CT. Thisresult can be explained by the fact that the soil clods arenaturally denser at the edges. Soil bulk density measurementsthrough PSC require stable clods, which resist to transportation,manipulation and the waterproofing process (Blake and Hartge,

5%-REA

4

3

1

0

11

2

1

0

3

2

000000

2

4

6

8

104%-REA

1

3

0

2

0

3

1

2

11

22

00000

20

40

60

80

100

REA - 3%

0

2

00011

5

2

1

2

1

3

0000

2

4

6

8

10

1513110907050301

Area (mm2)

2%-REA

00001

00

22

3

2111

00

1513110907050301

(mmArea2)

0

20

40

60

80

100

1%-REA

000001

000111

00000

2

4

6

8

10

1513110907050301

(mmArea2)

0

20

40

60

80

100

Fre

qu

ency

Cu

mu

lati

ve

freq

uen

cy (

%)

Fig. 6. Frequency and cumulative frequency (%) of soil bulk density (rs) data for the different areas selected in samples and for the different criteria used for the representative

elementary area (REA) definition.

Table 2Areas in which each sample reached the representative elementary area (REA) for

the soil bulk density (rs).

S REA S REA S REA

01 06 07 12 13 07

02 02 08 02 14 08

03 06 09 11 15 10

04 12 10 11 16 06

05 02 11 01 17 04

06 08 12 04 18 09

J.A.R. Borges, L.F. Pires / Soil & Tillage Research 123 (2012) 43–4948

1986; Pires et al., 2005a; Silva et al., 2000). Such edges are takeninto consideration when the clod total area is calculated.However, for smaller areas selected in the interior of clods,the edge is not included. FA, on the other hand, includes valuesthat are part of the edge or are very close to it.

3.2. REA determination for rs measurements

In Fig. 5, rs variation graphs are presented regarding thedifferent areas selected (Fig. 2) for 4 of the 18 soil clod samples.

Qualitatively analyzing the particularities in the cross sectioninvestigated in the tomography images presented, it can beobserved that the three first samples have small regions withdensity values more/less elevated, regarding the pebbles/macro-pores in their interior. However, when compared to the S 17, suchsamples are still more homogeneous.

S 17 has a large macropore, probably a biopore. This is thesample with the higher values of density standard deviation. This isexplained by the qualitative analysis of the tomography image.When comparing the rs result through CT and PSC for this samplethe relative difference between methods was 3.9% (PSC as areference method). However, S 17 reached REA even for the 2% and1% criteria. The homogeneity of S 11 is corroborated in the fastachievement of REA for all variation criteria, including for thestricter criterion (1% variation) still in the 6th area selected (area11).

It was observed that FA presents standard deviation valuesclose to the smaller areas, which is probably due to the fact thatthis area comprises almost all the sample, balancing thediscrepancies. It could be also seen that there is a tendency ofrs average values to the PSC value, considered the standard, withthe increase in the area under study.

Fig. 6 shows frequency and cumulative frequency graphs (%) perarea representing the number of samples that reached REA for eachof the deviations and for each area.

With the definition of 5% for the rs maximum variation betweenselected areas in the image, the 18 samples analyzed reached REAup to an area value of 533.6 mm2 (area 11). For 4%, the REA wasobtained up to 640.1 mm2 (area 12) and, for 3%, 756.3 mm2 (area13). For the 2% and 1% criteria, only 13 and 4 samples reached REA,respectively.

It was observed that the stricter the rs variation criterion is, thelarger the area needed to reach REA. For the 2% and 1% cases, only72% and 22% of samples reached REA. This happened because somesamples are smaller and, therefore, lower is the number of areasselected in their interior. The size of areas selected was not enoughfor the variations to occur within the pre-established criteria.

The rs measurements through the paraffin sealed clod methodpresented CV 3.8%. In this study, this value was used as a referenceto determine the REA. It was observed that samples with crosssection areas over 640.1 mm2 provided representative values ofthis soil physical property. In Table 2 are the areas in which eachsample reached REA.

J.A.R. Borges, L.F. Pires / Soil & Tillage Research 123 (2012) 43–49 49

The variation criterion adopted in this study is stricter whencompared to that adopted by Vandenbygaart and Protz (1999).However, the micro morphological soil properties evaluated bythese authors presented higher spatial variability than the rs, amacroscopic parameter.

4. Conclusions

Using 2D images of soil clod samples, it was possible todetermine the REA for rs measurements with 4% reliability, basedon the rs CV measurements obtained through the paraffin sealedclod method, adopted as a standard method. For the Eutric Nitosolof clay texture, cross section areas of 640.1 mm2 are enough toprovide representative values of this soil physical property.

The first generation gamma ray CT was proved an excellenttechnique to determine REA for rs measurements. The tomographyenables qualitative as well as quantitative studies in different areasselected in the tomographic image, and has the advantage of notchanging the physical structure of the samples, enabling furtheranalyses using the same samples.

Acknowledgments

Many thanks are owed to the Brazilian Federal FundingAgencies: CNPq for the provision of the productivity fellowshipin research and CNEN/CAPES for the PhD Scholarship, as well as toDr. Osny O. S. Bacchi from the Laboratory of Soil Physics of theCenter for Nuclear Energy in Agriculture, Piracicaba, Brazil, for theinfra-structure used to obtain the tomographic images.

References

Al-Raoush, R., Papadopoulos, A., 2010. Representative elementary volume analysisof porous media using X-ray computed tomography. Powder Technol. 200, 69–77.

Asano, Y., Uchida, T., 2010. Is representative elementary area defined by a simplemixing of variable small streams in headwater catchments? Hydrol. Process.24, 666–671.

Bartoli, F., Genevois-Gomendy, V., Royer, J.J., Niquet, S., Vivier, H., Grayson, R., 2005.A multiscale study of silty soil structure. Eur. J. Soil Sci. 56, 207–223.

Baveye, P., Rogasik, H., Wendroth, O., Onasch, I., Crawford, J.W., 2002. Effect ofsampling volume on the measurement of soil physical properties: simulationwith X-ray tomography data. Meas. Sci. Technol. 13, 775–784.

Blainski, E., Goncalves, A.C.A., Tormena, C.A., Folegatti, M.V., Guimaraes, R.M.L.,2009. Intervalo hıdrico otimo num nitossolo vermelho distroferrico irrigado.(-Least limiting water range of an irrigated dystroferric red nitosol). Rev. Bras. Ci.Solo 33, 273–281 (in Portuguese, with English abstract).

Bear, J., 1972. Dynamics of fluids in porous media. American Elsevier Pub. Co., NewYork.

Blake, G.R., Hartge, K.H., 1986. Bulk density. In: Klute, A. (Ed.), Methods of SoilAnalysis. Part 1: Physical and Mineralogical Methods. American Society ofAgronomy, Soil Science Society of America Book Series, No. 9, Madison, pp.371–373.

Constanza-Robinson, M.S., Estabrook, B.D., Fouhey, D.F., 2011. Representative ele-mentary volume estimation for porosity, moisture saturation, and air–waterinterfacial areas in unsatured porous media: data quality implications. WaterResour. Res. 47 12 pp.

Crestana, S., Cruvinel, P.E., Vaz, C.M.P., Cesareo, R., Mascarenhas, S., Reichardt, K.,1992. Calibracao e uso de um tomografo computadorizado em ciencia dosolo.(Calibration and use of a computerized tomography in soil science). Rev.Bras. Ci. Solo 16, 161–167 (in Portuguese, with English abstract).

Crestana, S., Cruvinel, P.E., Mascarenhas, S., Biscegli, C.I., Neto, L.M., Colnago, L.A.,1996. Instrumentacao Agropecuaria: Contribuicoes no Limiar do Novo Seculo.(Agricultural instrumentation: Contributions on the Threshold of New Centur-y).EMBRAPA-SPI, Brasılia.

Cruvinel, P.E., Crestana, S., 1997. The use of X and gamma rays dedicated comput-erized minitomography scanner in agriculture due to the limitations imposedby medical computerized tomography scanners. In: Proceedings Workshop OnCybernetic Vision, IEEE Comput. Soc. Los Alamitos., pp. 208–212.

Cruvinel, P.E., Cesareo, R., Crestana, S., Mascarenhas, S., 1990. X-ray and gamma-raycomputerized minitomograph scanner for soil science. IEEE Trans. Instrum.Meas. 39, 745–750.

Domingos, M.M.M., Gasparetto, N.V.L., Nakashima, P., Ralisch, R., Filho, J.T., 2009.Estrutura de um nitossolo vermelho latossolico eutroferrico sob sistema plantiodireto, preparo convencional e floresta.(Evaluation of the structure of a eutroferric

red nitosol under no-tillage, conventional tillage and forest). Rev. Bras. Ci. Solo 33,1517–1524 (in Portuguese, with English abstract).

Downing, D., Clark, J., 2005. Estatıstica Aplicada. (Applied Statistics).Saraiva, SaoPaulo.

Elliot, T.R., Reynolds, W.D., Heck, R.J., 2010. Use of existing pore models and X-raycomputed tomography to predict saturated soil hydraulic conductivity. Geo-derma 156, 133–142.

Fante Junior, L., Oliveira, J.C.M., Bassoi, L.H., Vaz, C.M.P., Macedo, A., Bacchi, O.O.S.,Reichardt, K., Cavalcanti, A.C., Silva, F.H.B.B., 2002. Tomografia Computador-izada na avaliacao da densidade de um solo do semi-arido brasileiro.(ComputedTomography for the soil density evaluation of samples of semi-arid Braziliansoils). Rev. Bras. Ci. Solo 26, 835–842 (in Portuguese, with English abstract).

FAO, 1998. World Reference Base for Soil Resources. FAO, ISRIC and ISSS, World SoilResources Report No. 84, Rome, 88 pp.

Ferraz, E.S.B., Mansell, R.S., 1979. Determining water content and bulk density ofsoil by gamma ray attenuation methods. IFAS, Technical Bulletin, No. 807,Florida, 51 pp.

Hubbell, J.H., Seltzer, S.M., 1995. Tables of X-ray mass attenuation coefficients andmass energy-absorption coefficients 1 keV to 20 MeV for elements Z = 1 to 92and 48 additional substances of dosimetric interest. NISTIR, US Department ofCommerce, National Institute of Standards and Technology, Physics Laboratory,Ionizing Radiation Division, No. 5632, Gaithersburg, 111 pp.

Kak, A.C., Slaney, M., 1999. Principles of Computerized Tomography Imaging. IEEPress, New York.

Kaplan, I., 1963. Nuclear Physics. Addison-Wesley Pub. Co., Massachusetts.Li, J.H., Zhang, L.M., 2010. Geometric parameters and REV of a crack network in soil.

Comput. Geotech. 37, 466–475.Microvis, 2000. Manual do Programa de Reconstrucao e Visualizacao de Imagens

Tomograficas. (Program Manual for Reconstruction and Visualization of tomo-graphic images).Embrapa Instrumentacao Agropecuaria, Sao Carlos, 18 pp.

Muller, C., Siegesmund, S., Blum, P., 2010. Evaluation of the representative elemen-tary volume (REV) of a fractured geothermal sandstone reservoir. Environ. EarthSci. 61, 1713–1724.

Pedrotti, A., Pauletto, E.A., Crestana, S., Cruvinel, P.E., Vaz, C.M.P., Naime, J.M., Silva,A.M., 2003a. Tomografia computadorizada aplicada a estudos de um Planosso-lo.(Computer-assisted tomography for studies of an Albaqualf). Pesq. Agropec.Bras. 38, 819–826 (in Portuguese, with English abstract).

Pedrotti, A., Pauletto, E.A., Crestana, S., Cruvinel, P.E., Vaz, C.M.P., Naime, J.M., Silva,A.M., 2003b. Planosol soil sample size for computerized tomography measure-ment of physical parameters. Sci. Agric. 60, 735–740.

Pedrotti, A., Pauletto, E.A., Crestana, S., Holanda, F.S.R., Cruvinel, P.E., Vaz, C.M.P.,2005. Evaluation of bulk density of Albaqualf soil under different tillage systemsusing the volumetric ring and computadorized tomography methods. Soil Till.Res. 80, 115–123.

Pires, L.F., Bacchi, O.O.S., Reichardt, K., 2004. Damage to soil physical propertiescaused by soil sampler devices as assessed by gamma ray computed tomogra-phy. Aust. J. Soil Res. 42, 857–863.

Pires, L.F., Bacchi, O.O.S., Reichardt, K., 2005a. Gamma ray computed tomography toevaluate wetting/drying soil structure changes. Nucl. Instrum. Methods Phys.Res. B 229, 443–456.

Pires, L.F., Bacchi, O.O.S., Reichardt, K., Timm, L.C., 2005b. Application of gamma-raycomputed tomography to the analysis of soil structure before density evalua-tions. Appl. Radiat. Isot. 63, 505–511.

Pires, L.F., Arthur, R.C.J., Bacchi, O.O.S., Reichardt, K., 2007. Application of gamma-ray computed tomography to evaluate the radius of influence of soil solutionextractors and tensiometers. Nucl. Instrum. Methods Phys. Res. B 259, 969–974.

Pires, L.F., Borges, J.A.R., Bacchi, O.O.S., Reichardt, K., 2010. Twenty-five years ofcomputed tomography in soil physics: a literature review of the Braziliancontribution. Soil Till. Res. 110, 197–210.

Pires, L.F., Arthur, R.C.J., Bacchi, O.O.S., Reichardt, K., 2011. Representative gamma-ray computed tomography calibration for applications in soil physics. Braz. J.Phys. 41, 21–28.

Razavi, M.R., Muhunthan, B., Hattamleh, O., 2007. Representative elementaryvolume analysis of sands using X-ray computed tomography. Geotech. Test.J. 30, 212–219.

Silva, V.R., Reinert, D.J., Reichert, J.M., 2000. Comparacao entre os metodos docilindro e do torrao na determinacao da porosidade e da densidade do solo.(-Comparison between the core and clod methods for the determination of soilporosity and bulk density). Ci. Rural 30, 1065–1068.

Timm, L.C., Reichardt, K., Roveratti, R., Oliveira, J.C.M., Bacchi, O.O.S., Pires, L.F., 2005.Soil bulk density evaluation by conventional and nuclear methods. Aust. J. SoilRes. 43, 97–103.

Tippkotter, R., Eickhorst, T., Taubner, H., Gredner, B., Rademaker, G., 2009. Detectionof soil water in macropores of undisturbed soil using microfocus X-ray tubecomputerized tomography (CT). Soil Till. Res. 105, 12–20.

Tomioka, S., Kozaki, T., Takamatsu, H., Noda, N., Nisiyama, S., Kozai, N., Suzuki, S.,Sato, S., 2010. Analysis of microstructural images of dry and water-saturatedcompacted bentonite samples observed with X-ray micro CT. Appl. Clay Sci. 47,65–71.

Tumlinson, L.G., Liu, H., Silk, W.K., Hopmans, J.W., 2008. Thermal neutron computedtomography of soil water and plant roots. Soil Sci. Soc. Am. J. 72, 1234–1242.

Vandenbygaart, A.J., Protz, R., 1999. The representative elementary area (REA) instudies of quantitative soil micromorphology. Geoderma 89, 333–346.

Vaz, C.M.P., Crestana, S., Mascarenhas, S., Cruvinel, P.E., Reichardt, K., Stolf, R., 1989.Using a computed tomography miniscanner for studying tillage induced soilcompaction. Soil Technol. 2, 313–321.