Rapid Nondestructive Bulk Density and Soil-Water Content Determination by Computed Tomography

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


    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 (

  • 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 Jo dx [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;


    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-


    1=1 exp( - \i D)

    I = I e x p < - d



    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.





    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!


    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



    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 so...


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