Rapid Nondestructive Bulk Density and Soil-Water Content Determinationby Computed Tomography

S. H. ANDERSON,* C. J. GANTZER, J. M. BOONE, AND R. J. TULLY

ABSTRACTComputed tomography (CT) is a promising tool that may help

provide measurements needed to obtain finer resolution in soil-watercontent and bulk density for water uptake studies or detailed inves-tigation of root-soil interactions. A need exists for a unified methodto accurately predict soil bulk density and water content using outputfrom CT. Research was conducted on soil collected from the A ho-rizon of Mexico silt loam (Udollic Ochraqualfs) and the B2t horizonof Crider silt loam (Typic Paleudalfs) to evaluate the relationshipbetween linear attenuation coefficients and volume fraction of soilsolids and water. Air-dry soil (<2 mm) was packed into poly vinylchloride cylinders at densities between 1.2 and 1.6 Mg/m3 and CTslices or tomographs were taken before and after water was added.The relationship between attenuation coefficients and volume frac-tion of soil solids was linear for both of the soils evaluated. Param-eter values for the Mexico soil compared favorably with those de-termined on previous data collected from Metea fine sandy loam(Arenic Hapludalfs). Differences in the parameter values for theMexico and Crider soils were attributed to differences in Fe content.An experiment with Fe added to the Mexico soil was conducted thatverified the effect of Fe content on the attenuation coefficients. Ap-proximately 98% of the variation between the attenuation coeffi-cients and volume fraction of soil water was accounted for by usinglinear regression relationships after correction for swelling. Resultsfrom this study indicate that it may be possible to develop a universalrelationship for computed tomography data vs. soil bulk density andwater content; however, more research is needed to characterize theinfluence of sample size on the calibration relationship.

Additional Index Words: computer assisted tomography (CAT),x-ray attenuation coefficients, Fe content, swelling.

BULK DENSITY AND WATER CONTENT are tWO basicphysical properties essential for characterizing

soil. Bulk density influences fluid and thermal trans-port properties of soils and affects the suitability of asoil for root growth and development. The inabilityof current methods to detect small zones of high den-sity limits the use of bulk density information to pre-dict root penetration and thermal, hydraulic, and aer-ation properties of soil. Current techniques formeasuring bulk density typically use an average den-sity for the volume under consideration and, althoughthe average value is accurate, the bulk density may beaveraged over too great a volume for use in explainingtransport properties that are governed by processes ona smaller scale.

Measurements of soil-water content of small vol-umes are required for a proper understanding of trans-port properties on the microscopic level. Currentmethods for measuring soil-water content also limitthe study of soil-root water transport because the soil-root interface is primarily a 1- to 2-mm-thick rhizo-

S.H. Anderson and C.J. Gantzer, Dep. of Agronomy, and J.M. Booneand R.J. Tully, Dep. of Radiology, Univ. of Missouri-Columbia,Columbia, MO 65211. Contribution from the Missouri Agric. Exp.Stn. Journal Series no. 10194. Received 24 Oct. 1986. *Correspond-ing author.

Published in Soil Sci. Soc. Am. J. 52:35-40 (1988).

sphere zone through which all transport must occur.Therefore a need exists for measurement techniquesthat allow rapid evaluation of bulk density and watercontent of intact cores on a more detailed level.

Recent advances in x-ray technology have alloweddevelopment of computed tomography (CT) methodsfor rapid, nondestructive, three-dimensional analysisof intact biological tissue (Hounsfield, 1972). With x-ray CT, the intensity of a collimated x-ray beam pass-ing through an object is measured by an array of de-tectors located opposite the x-ray source. Computedtomography is a method that uses computer recon-struction of a tomographic plane (slice) of an object.The smallest resolution of current CT scanners is ap-proximately 1 mm wide by 1 mm long by 3 mm thick,thus providing a potential opportunity for evaluatingsoil materials on a similar scale. The precision at thisscale is approximately 0.01% of the attenuation coef-ficient.

Computed tomography applications have not beenlimited to the field of medicine. Hopkins et al. (1981)showed how CT could be used to analyze plastics,wood, concrete, steel, and electronic components.Onoe et al. (1983) illustrated the use of a portable x-ray CT scanner for measuring annual growth rings oflive trees. Several investigators (Petrovic et al., 1982;Hainsworth and Aylmore, 1983; Crestana et al., 1985;Hainsworth and Aylmore, 1986) have already illus-trated the use of x-ray CT for the nondestructive eval-uation of soils. Petrovic et al. (1982) used a CT scan-ner for investigating the precision, linearity, spatialresolution, and limitations of CT determined bulkdensity. Their studies indicated that CT output waslinearly related to bulk density of glass spheres overthe range of 0.14 to 1.64 Mg/m3. They showed thatthe relationship between CT output and bulk densityof soil from the surface horizon of Metea fine sandyloam was linear over the range of 1.2 to 1.6 Mg/m3.Densities were determined on volumes as small as1.25 by 1.25 by 2 mm in soil of heterogeneous bulkdensity. The sensitivity to density changes for the Me-tea soil was about 0.02 Mg/m3, with a maximum ob-served deviation from predicted of 0.07 Mg/m3. Pre-cision was lost when size and composition of thesample container varied, and when stones or relativelylarge air-filled holes or channels were present. Petrovicet al. mentioned that work was underway to determinethree-dimensional measurements of soil-water con-tent; however, work at that time did not yield con-sistent results.

Hainsworth and Aylmore (1983) conducted prelim-inary studies to examine the possibility of using CTto measure spatial changes in soil-water content re-lated to soil-root water transport. They modified agamma attenuation unit and found results that com-pared favorably with the CT scanner. Later, Hain-sworth and Aylmore (1986) used the CT to show theeffect of a single root on the removal of soil water.Crestana et al. (1985) showed that CT scanners could

35

36 SOIL SCI. SOC. AM. J., VOL. 52, 1988

be used to measure the movement of water in soils atrates of 1.6 mm/s. They developed a calibration be-tween the CT output and soil bulk density and soil-water content for two coarse-textured soils. Theyshowed different parameter values for the relation-ships of the two soils but did not explore the theoret-ical justification for the differences.

The objectives of this study were (i) to compare therelationships of linear attenuation coefficients and bulkdensity measured by CT for two Missouri soils andthe soil used by Petrovic et al. (1982), (ii) to comparethe relationships of linear attenuation coefficients andsoil-water content for the two soils, and (iii) to eval-uate the effects of swelling and Fe content on the at-tenuation coefficients.

THEORYAlthough several articles have been developed that pres-

ent the theory used by CT (Brooks and DiChiro, 1975,1976;Budinger and Gullberg, 1974), we include a brief discussionof the theory.

For monoenergetic radiation, the attenuation of a x-raybeam of intensity /,„ as a result of passing through a sampleof material of thickness D, yields an attenuated intensity 7behind the sample (Fig. 1) described by

1 = I0exp(-nD) [1]where n is the linear attenuation coefficient that dependsprimarily upon the electron density of the material, the en-ergy of the radiation, and the packing density. Use of Eq.[1] assumes the material is homogeneous in compositionand density over the distance D. Since soils are rarely ho-mogeneous even over short distances, the attenuation coef-ficient will be variable in the region of interest. As a result,the attenuated intensity behind the sample is

/ = /„ ex f r:p - PL Jodx [2]

where x is the distance from the x-ray source and variesbetween 0 and D, the thickness of the sample (Fig. 1). Al-though Eq. [2] is theoretically correct, the distribution of theattenuation coefficients, which is usually unknown, cannotbe estimated when only a single beam is attenuated andmonitored. However, if many beams are passed through thesample at various angles (0-360°), the distribution of theattenuation coefficients at discrete points within a materialcan be determined. This is the basis of CT.

In CT, many thousands of line integral projections aremeasured and used to reconstruct the image. The contri-bution of each point (Fig. 2) to the attenuation of an x-raybeam /„ is denoted by

I,j = Ia exp - , y) ds [3]

where i is the detector position in the detector array, j is theposition of the center of the detector array, and i is thedistance from the radiation source, which varies from 0 toS. We can rearrange Eq. [3] to obtain the projection valueP

P,v,= In (/„//,,)= n(x,y)ds.=/: [4]

In Eq. [4], n(x, y) can be determined using many indepen-dent views or projections through the object. Projection dataare acquired at many positions and angles through the object

using the geometry outlined in Fig. 2. The data are acquiredin a fan beam, allowing many projections to be measuredat any instance due to the multiple detector array. The fanbeam data is then shuffled by the computer into sets of pro-files where parallel ray geometry is approximated. The in-dividual profiles are convolved with an appropriate math-ematical filter and backprojected onto an image space. Thesum of the filtered backprojections from all the profiles ateach point (x, y) is normalized and displayed as the CTimage. The CT image is essentially a "map" of linear atten-uation coefficients, n(x, y).

In most cases, knowledge of the distribution of the linearattenuation coefficients in the material is of interest but oftennot the desired end product in using CT. Generally, infor-mation about the density distribution or composition of thematerial is desired. This is obtained by using theoretical orempirical relationships between the linear attenuation coef-ficients and the parameters of interest. McCullpugh (1975)showed how the average mass attenuation coefficient is equalto the sum of the weighted mass attenuation coefficients ofthe constituent elements of the material;

[5]

where (M/P) is the average mass attenuation coefficient (M isthe linear attenuation coefficient and p is the physical den-sity), m, is the mass fraction of the /th constituent element,(M/P), is the mass attenuation coefficient for the rth constit-uent element, and n is the number of constituent elements.Multiplying Eq. [5] by the average density and rearranginggives

M = [6]

where n is the average linear attenuation coefficient (oftenreferred to as just the attenuation coefficient), f, is the vol-ume fraction of the /th constituent element, M, is the linearattenuation coefficient for the rth constituent element, andn is the number of constituent elements. Equation [6] canbe expanded to the following:

M = fji, + fo» [7]where fs and /, are the volume fractions of the soil solidsand water, respectively, and fts and nu. are the attenuationcoefficients of the soil solids and water, respectively. In orderto experimentally obtain the relationship between \i andfs,the soil material must be oven-dry. Once the relationshipbetween /u and fs has been obtained, the attenuation due tofs may be subtracted to obtain a relation between a newvariable M* and /,.

M* = p - fstis = /„,/!„. [8]where M* is the portion of the attenuation coefficient due toattenuation by water. (Note that/J is equivalent to the bulkdensity divided by the particle density and /,, is equal to 8,the volume fraction of soil water.)

MATERIALS AND METHODSSoil from the A horizon of Mexico silt loam and the B2t

horizon of Crider silt loam was obtained from continuousfallow runoff plots (Jamison et al., 1968; Wendt et al., 1986)at the McCredie Claypan Res. Farm near Kingdom City,MO, and from a field near Farmington, MO, respectively.The soil was brought to the lab, air-dried, and passed througha 2-mm sieve. Particle density was determined on six rep-licates for each soil using the method of Blake and Hartge(1986). The particle size distribution for each soil was eval-

ANDERSON ET AL.: RAPID NONDESTRUCTIVE BULK DENSITY AND SOIL-WATER CONTENT 37

1=1 exp( - \i D)

I = I e x p < - d

c

dx)

Fig. 1. Schematic representation of the attenuation of an x-ray beam of initial intensity /„ through a material of thickness D and (a) constantattenuation coefficient n; (b) variable attenuation coefficients, M;» for discrete units of thickness d; and (c) variable attenuation coefficients,MJ? over the distance from the source x.

uated using the pipette method of Gee and Bauder (1986).The Fe content of each soil was determined using energydispersive spectroscopy (Smart and Tovey, 1982).

A Philips Tomoscan 310 (Philips, Holland), housed in theUniv. of Missouri Medical Hospital, was used in this in-vestigation. This scanner is a third generation (rotate/rotate)CT with 576 Xenon ionization detectors in the detector ar-ray. A 120-peak kV x-ray beam was used. Approximately900 profiles were acquired in 4.8 s; and using a reconstruc-tion field of view of 320 mm, each pixel in the resultant 256X 256 pixel image corresponded to a volume element of1.25 by 1.25 by 12 mm. The reconstruction algorithm wasfiltered back-projection.

Experiments were conducted on (i) dry soil, (ii) wet soil,and (iii) dry soil with added Fe. Using air-dry soil, 11 coreseach were packed at bulk densities of 1.2, 1.3, 1.4, and 1.5Mg/m3 with the Mexico soil and 11 soil cores each werepacked at bulk densities of 1.3, 1.4, 1.5, 1.6 Mg/m3 with theCrider soil. Higher bulk densities were used for the Cridersoil because of its greater particle density. The air-dried soilwas packed into 52-mm i.d. by 48-mm high polyvinyl chlo-ride (PVC) cylinders using a hydraulic press. One of the 11cores for each bulk density from each soil was dried in theoven at 105 °C and immediately stored in a dessicator untilscanned. To fill the aperture-stage of the CT scanner withmass, a group of four cores were analyzed together. A waterbag was wrapped around the group of cores to provide ad-ditional mass. Cores were arranged with two upper corescentered on top of two bottom cores, separated by a 25-mmstyrofoam jig. The mean attenuation coefficient and stan-dard deviation were determined for a 13 950-mm3 volumein the center of each core. Regression relationships betweenattenuation coefficients and volume fraction of solids for theoven-dry cores and the air-dry cores adjusted to an oven-dry basis (subtracting the attenuation due to water) were notsignificantly different. Therefore, the attenuation coefficientsfor the air-dry cores were adjusted to an oven-dry basis insubsequent analyses.

ROTATION

X-RAYSOURCE

DETECTORARRAY

ROTATION

Fig. 2. Schematic of how a CT scanner measures the attenuated x-ray beams passing through a detection aperature containing a soilcore. The x-ray source and detector array rotate clockwise aroundthe detection zone. The diagram represents the pattern for a fanbeam CT unit.

The wet soil experiment used exactly the same soil coresas the dry soil experiment. Distilled water was slowly addedto nine of the cores of each density group for both the Mex-ico and Crider soils. Water contents ranged from air-dry tosatiated values. Water was added with a syringe over an 8-h period. After wetting, the bottom and top of the cores weresealed with paraffin. Cores were then placed on their side inhumid chambers and equilibrated for 2 wk. Cores were ro-tated 180° every day for the 2-wk period. After water in thesoil cores had equilibrated, tomographs were taken using thesame procedure as described for the dry soil experiment.

Swelling was noted for both the Mexico and Crider soilsupon addition of water. Therefore, swelling behavior wasevaluated on separate cores using a point gauge to measurechanges in vertical swelling of laterally confined samples.Three soil cores were hydraulically packed for each selectedbulk density used for the Mexico and Crider soils. The height

38 SOIL SCI. SOC. AM. J., VOL. 52, 1988

Table 1. Selected physical and chemical properties for the Mex-ico silt loam A and Crider silt loam B2t horizons.

Hori- Textural Particle Fe,OjSoil zon Depth class density Sand Silt Clay content!

40

Mg/m3 kg/kgMexico A 0-0.15 Silt loam 2.63 0.033 0.743 0.224 0.0143Crider B2t 0.45-1.00 Silty clay 2.75 0.043 0.474 0.483 0.0536

t Fe,03 content was calculated from total Fe determined by energy disper-sive spectroscopy with an electron microscope.

of the top-center of the soil in the core above a referenceplate was measured using a point gauge. Distilled water wasadded to each core to achieve a degree of saturation of 20%using a syringe. The cores were then placed in humid cham-bers and equilibrated for 2 d. The height of the top-centerof the core above the reference plate was again measuredusing the point gauge. This procedure was repeated for de-grees of saturation of 40, 60, 80, and 90%. The core volumewas subsequently calculated for each water content assum-ing only vertical swelling and related to water content foreach bulk density. Regression equations were developed andused to calculate exact bulk density and volumetric soil-water contents for soil cores in the wet soil experiment.

For the third experiment, Fe metal (electrolytic powder)was added to Mexico soil to give values of 3.3, 6.7, 10.0,13.3, and 16.7% (w/w) Fe added. Four cores were preparedfor each Fe content including the original soil. Sufficient soilwas packed to give a volume fraction of soil solids of 0.496m3/m3. (Particle density increased as Fe was added, there-fore, the soil was packed to higher densities for soil mixeswith greater iron content.) Computed tomography scans weretaken of these soil cores using the same procedure as usedduring the dry soil experiment.

RESULTS AND DISCUSSIONMeasured data for selected physical and chemical

properties for the soil material from the A horizon ofthe Mexico silt loam and B2t horizon of the Cridersilt loam are given in Table 1. The principal differ-ences between the two soil materials are the higherclay and iron oxide content in the Crider soil. Thegreater iron oxide content in the Crider is the probablecause of its higher particle density.

Dry Soil ExperimentThe relationship between the CT attenuation coef-

ficient and volume fraction of solids (/J) for the Mexicoand Crider soils is shown in Fig. 3. Both functions arelinear over the range of fs evaluated. The higher CTattenuation coefficients for the Crider soil are attrib-uted to its higher Fe content. Because the x-ray atten-uation coefficient is dependent upon electron density(McCullough, 1975), higher electron densities causelarger attenuation coefficients. The electron density forSi (atomic no. = 13) and Al (14) is about half that ofFe (26). Therefore, a small difference in Fe contentbetween the two soils causes a significant change inthe linear attenuation coefficients.

To compare the results of Petrovic et al. (1982) withthose of the two soils in this paper, we converted therelationship between Hounsfield units and bulk den-sity for the Metea soil to attenuation coefficients andfs assuming a particle density of 2.65 Mg/m3. Houns-field units are defined with reference to water as fol-lows: H = (ji, — MH) X 1000/ju,v The resulting rela-tionship from Petrovic et al. (1982) is

30

25

CRIDER DY = 3.5 + 58.0 xr2 = 0.990

MEXICO +Y = 5.8 + 49.1 xr* = 0.992

0.4 0.5 0.6w /

Fig. 3. Relationship between M (attenuation coefficient) and f, (vol-ume fraction of soil solids) for the Mexico and Crider soils.

M = 5.9 + 46.7 / r2 = 0.969. [9]This regression relationship is quite similar to that forthe Mexico soil, which suggests that the electron den-sity of the Metea soil used by Petrovic et al. (1982) issimilar to that of the Mexico. It also suggests that itmay be possible to obtain CT calibration relationshipsfor different soils with similar electron densities.

From Fig. 3, it appears that the two lines are notparallel. The slope for the Crider soil is about 18%higher than that for the Mexico. It is not known whythis occurs because theory says the two lines shouldbe parallel. Crestana et al. (1985) also obtained non-parallel slopes for two coarse textured soils.

It is also apparent from Fig. 3 that the interceptsfor both soils are nonzero, which is contrary to theory(Eq. [7]). This may be due to the relatively small range(in terms of absolute density) in bulk densities usedfor the experiment, suggesting a nonlinear relationshipat lower densities.

Wet Soil ExperimentThe relationship between the attenuation coeffi-

cients and /,, as influenced by bulk density for theMexico and Crider soils is illustrated in Fig. 4. Thereason for the nonparallel lines for both soils is swell-ing since these values have not been corrected forswelling effects. However, even uncorrected, the cor-relation coefficients are all >0.93. Some nonlinear be-havior was present for each of the bulk density rela-tionships in Fig. 4.

Because these soils swelled when water was added,the water contents and bulk densities were correctedusing experimentally determined relationships. The R2

for the equations expressing the corrections were all>0.95. Attenuation coefficients were corrected for/using the relationships obtained in Fig. 3. This pro-cedure was equivalent to using Eq. [8]. The n* (cor-rected for^) are plotted vs./,, in Fig. 5. About 98% ofthe variation in attenuation coefficients due to watercontent was explained by /,,. It is interesting to notethat the slopes of the lines for each soil are almostidentical (17.7 m"' for Mexico and 17.9 m~' for Cri-der). However, the values are <19 m~', a value oftenused as the standard attenuation coefficient of water.It is also noted that the intercept for the Mexico soil(—0.2 m~') is not significantly different from zero,whereas the intercept for the Crider soil (0.6 m~') issignificantly different from zero. These differences may

ANDERSON ET AL.: RAPID NONDESTRUCTIVE BULK DENSITY AND SOIL-WATER CONTENT 39

45

40

35

30

25

Symbol

MEXICO

6

0.6

Fig. 4. Relationship between n (attenuation coefficient) and /„. (vol-ume fraction of soil water) for selected bulk densities of the (a)Mexico and (b) Crider soils. The/,, are not corrected for swelling.

be attributed to slight errors in the determination ofthe fs relationships and/or the swelling relationships.

To compare the results for the Crider and Mexicosoils with previous work, we adjusted the numbers ofthe regression equations for the water content rela-tions of the Crestana et al. (1985) work to attenuationcoefficients assuming ju,,, = 19 m~'. The slopes of theirequations (32.1-34.4 m~') were almost twice as largeas those for the Mexico and Crider soils. The cause ofthe disparity between the slopes for the two studiesmay be attributed to differences in the total samplemass analyzed during scans. We also adjusted thenumbers of the regression equation for the water con-tent relation from more recent work of Crestana et al.(1986) where the total sample mass evaluated in a scanwas comparable to the amount used in our study. Theadjusted slope is 17.0 m~' , which is similar to theslopes determined in our study.

Added Iron ExperimentBecause the difference in the dry soil attenuation

coefficients between the Mexico and Crider soils wasthought to be attributed to Fe content differences, anexperiment was conducted to evaluate the effect ofadding Fe to a soil on the linear attenuation coeffi-cient. The relationship between the attenuation coef-ficient and Fe content, which was linear over the rangeof Fe contents evaluated, explained 99% of the vari-ation in /a (Fig. 6). The standard deviation was higherfor Fe contents >0.05 kg/kg than for those below,which may be due to the difficulty in obtaining a well-mixed sample because of particle size differences be-

10

8

2

0

10

8

e^ 6

x3. 4

2

0

MEXICOY = -0.2 + 17.7 )r* = 0.976

0 0.1 0.2 0.3 0.4 0.5f u . u / v

CRIDERY = 0.6 + 17.9 Xr* = 0.980

0 0.1 0.2 0.3 0.4 0.5f u • v/u

Fig. 5. Relationship between M* (adjusted attenuation coefficient)and /„, (volume fraction of soil water) for the (a) Mexico and (b)Crider soils. The attenuation coefficients are adjusted for /, andthe/, are corrected for swelling.

50

45

40

35

30

25

MEXICO +CRIDER DY = 28.8 + 109 xr* = 0.991

0.05FE

0.1 0.15K g / K g

0 .2

Fig. 6. Relationship between n (attenuation coefficient) and Fe (Fecontent) for Mexico soil with selected amounts of Fe added with/ = 0.496 m'/m3. The attenuation coefficient for the Crider soilwith/ = 0.496 mYm1 is also plotted.

tween the soil and Fe powder. The data for the Cridersoil are also shown in Fig. 6, which correlate well withthe expected value. This suggests that the main dif-ference betweeen the attenuation coefficients for thedry soil experiment for the Mexico and Crider soilswas due to the difference in Fe content.

SUMMARYResults from the study show that x-ray CT can be

used to determine the bulk density and water contentof intact soil cores. Over 99% of the variation in CTattenuation coefficients for the 40 dry soil cores foreach of two soils were accounted for by linear regres-sion relationships with fs. Approximately 98% of thevariation in CT attenuation coefficients for the 40 wetcores for each of the two soils were accounted for byregression relationships with /,, after correcting for

40 SOIL SCI. SOC. AM. J., VOL. 52, 1988

swelling effects and fs. Results from the added Fe ex-periment suggested that the differences in attenuationcoefficients for the two soils were due primarily to Fecontent differences. Results for the Mexico soil werevery similar to the Metea soil used by Petrovic et al.(1982), which suggests that it may be possible to de-velop a universal relationship between x-ray CT datavs. soil bulk density and water content if differencesin the electron density of the soils are known. Resultsfrom the added Fe experiment also suggest this pos-sibility. However, comparisons of calibrations be-tween experiments should account for differences intotal sample mass used during a scan. This concern isespecially pertinent for experiments using much largersoil volumes than those used in this study. Furtherresearch is needed to characterize the effect of soil coresize on computed tomography results.

ACKNOWLEDGMENTThe authors would like to acknowledge John M. Brown

of the Horticulture Dep. at North Carolina State Univ. forthe introduction to computed tomography. They would alsolike to thank Patricia Remley for preparing the soil cores.