8 Bulk Density Donald J. Campbell and J. Kenneth Henshall Scottish Agricultural College, Edinburgh, Scotland I. INTRODUCTION The wet bulk density of a soil, r, is its mass, including any water present, per unit volume in the field; its dry bulk density, r s , is the mass per unit volume of field soil after oven-drying. These parameters are related to the soil gravimetric water content, W, as follows: r r ϭ 100 (1) ͩͪ s 100 ϩ W where W is the mass of water expressed as a percentage of the mass of dry soil. The methods available for the measurement of soil bulk density fall into two groups. In the first group are the long-established direct methods, which involve measurement of the sample mass and volume. The mass M s of the oven-dried sample is obtained by weighing, and the total volume, V, of the soil including air and water is obtained by measurement or indirect estimation. The dry bulk density r s is then given by M s r ϭ (2) s V Such methods have been used by both agricultural soil scientists (Freitag, 1971) and civil engineers (DSIR, 1964), and many of them reduce essentially to the problem of the accurate determination of the sample volume. As these meth- ods have not always proved entirely effective, a second group of methods has evolved in which the attenuation or scattering of nuclear radiation by soil is used to give an indirect measurement of bulk density. Radiation methods are capable of Copyright © 2000 Marcel Dekker, Inc. measuring more accurately and precisely than direct methods, but they too have limitations of their own. Thus there is no single measurement method suitable for all circumstances. Sometimes a very crude but quick measurement is all that is required to charac- terize soil conditions, but in other circumstances it may well be appropriate to use a slower method involving expensive equipment, in order, for example, to detect detailed differences between experimental treatments. II. RADIATION METHODS A. Theory Radiation methods involve measuring either the attenuation or the scattering of gamma radiation by the soil, both of which increase with density. Empirical cali- bration relationships are used to relate the magnitude of such effects to soil bulk density. Gamma-ray photons are emitted by radioactive nuclei as they decay to form more stable nuclei of lower excitation. A specific source will emit gamma photons with the characteristic energy of one or more decay transitions. In passing through any medium, the probability that these photons will interact with the atoms of the medium is dependent on the density of the medium, as well as other factors such as the energy of the photon and the chemical composition of the medium. These interactions take the form either of complete absorption of the photon or of scat- tering, where the photon loses energy in relation to the angle of deflection. Since the photons interact principally with the electrons of the medium, the extent of the interaction depends on the electron density, which is related to the bulk density of the medium. There are two main types of gamma-ray density equipment: backscatter gauges, which are designed to detect only scattered photons, and transmission gauges, which detect mainly unscattered photons. Depending on the level of en- ergy discrimination, however, some simpler transmission systems also detect scat- tered photons to different extents. B. Backscatter Gauges In backscatter gauges, the gamma-ray source and detector are fixed relative to, and shielded from, each other in an assembly designed to prevent measurement of directly transmitted photons. This assembly either rests on the soil surface or, in some designs, is lowered into an access hole in the soil (Fig. 1). In either case, any photons incident upon the detector must have been deflected by one or more scat- tering interactions in the medium. Since there is only a low probability that a photon that has travelled an appreciable distance from the source will reach the 316 Campbell and Henshall Copyright © 2000 Marcel Dekker, Inc. detector, it follows that only a restricted volume of the medium close to the source/detector axis will influence the detected photon count rate. In practice, with a probe that is used in an access hole, it is found that the zone of influence does not extend more than about 75 mm from the source/detector axis and that 50% of the photons penetrate soil within only about 25 mm of this axis. The relation between count rate and bulk density is complicated, since the degree of scattering increases with density, thereby increasing the count rate, but absorption of both scattered and unscattered photons also increases with density and so reduces count rate. Thus theoretical calibrations of backscatter gauges are impracticable, and empirical calibrations must be made. Surface backscatter gauges require only that the surface of the soil be made perfectly level in order to exclude air gaps, but they yield little information, merely indicating the average density of the top 50 –75 mm of the soil profile. Their main use is in civil engineering applications where bulk densities which are generally uniform with depth are to be measured. A typical level of accuracy for these gauges is Ϯ0.16 Mg m Ϫ3 (Carlton, 1961). Bulk Density 317 Fig. 1 Schematic diagrams of backscatter gamma-ray gauges in which the source and detector assembly either lies on the soil surface (left) or is lowered into an access hole in the soil (right). Copyright © 2000 Marcel Dekker, Inc. Single-probe backscatter gauges are normally lowered into lined access holes in a manner similar to neutron moisture probes (Chap. 1) and are available in combination with such probes. The major failing of these gauges results from the bias of their zone of influence close to the source/detector axis. This means that both the clearance gap of the probe in the liner tube and the tube itself influ- ence the measurements unduly. The measurements are also very susceptible to any disturbance of the soil during installation of the liner tube. C. Transmission Gauges In transmission gauges (Fig. 2), the sample to be tested is located between the source and the detector of the gauge, and ideally only unattenuated photons passing directly from source to detector are counted. In this ideal case, where none of the photons has been degraded, the detected photon count rate, I, obeys Beer’s law, I ϭ I exp[Ϫmrx] (3) 0 318 Campbell and Henshall Fig. 2 Schematic diagrams of transmission gamma-ray gauges in which the detector ei- ther remains on the soil surface and the source is lowered into an access hole in the soil (left) or in which both the source and detector are lowered into separate access holes (right). Copyright © 2000 Marcel Dekker, Inc. where I 0 is the photon count rate in the absence of a sample, m is the mass attenu- ation coefficient for the specific photon energy and sample material concerned, r is the wet bulk density of the sample, and x is the sample length. The bulk density of the sample can then be calculated as Ϫ1 I r ϭ ln (4) ͩͪ mxI 0 if values are available for m, x and I 0 . In practice, several factors make such a theoretical calculation of density impracticable. The most important of these are 1. Inclusion in the count of some scattered photons 2. Determination of a single mass attenuation coefficient for soils of vari- able composition 3. Estimation of the photon count rate in the absence of a sample 1. Scattered Photons With the exception of laboratory equipment in which a high degree of both colli- mation and energy discrimination is possible, scattered photons will always be included to some extent in the detected count rate. Scattered and unattenuated photons have different mass attenuation coefficients, and the presence of scattered photons therefore affects the linearity of the relationship between r and ln I/I 0 . The reduced energy of these scattered photons also increases the dependence of the detected count rate on the chemical composition of the soil sample, as will be discussed later, and reduces the spatial resolution of the gauge by increasing the volume of soil, which influences the count rate. While it is possible to reduce the number of scattered photons by collima- tion, limited space prevents this in field gauges. An alternative is to use an energy- discriminating detector, set to exclude photons with energies lower than the emission energy of the source. Gauges with this facility generally use a scintilla- tion detector, such as a sodium iodide crystal, linked to a photomultiplier tube and pulse height analyzer. Energy-discriminating detectors need to be stabilized against temperature changes. Simpler transmission gauges use Geiger–Mu¨ller detectors, which are not capable of energy discrimination and hence are susceptible to scattered photons. In effect, these gauges operate in both the transmission and backscatter modes simultaneously. Provided such a gauge is calibrated empirically, its only major disadvantage, other than a slight dependence on the chemical composition of the soil, is its low spatial resolution, which can affect measurements close to distinct boundaries such as the soil surface or a plow pan. For example, Henshall and Campbell (1983) found that a Geiger–Mu¨ller based gauge overestimated the den- sity of water by 35% at a depth of 20 mm below an air/water interface and contin- ued to overestimate the density by more than 5% to a depth of 90 mm. Bulk Density 319 Copyright © 2000 Marcel Dekker, Inc. Gauges employing energy discrimination can be adjusted to give high spa- tial resolution limited only by the dimensions of the detector, which can be as small as 10 ϫ 10 mm cross-section. However, the need to ensure sufficiently high count rates forces lower resolution settings which, by including some scattered photons, results in the need for empirical calibration as with simpler gauges. 2. Soil Composition As used in Eq. 3, the mass attenuation coefficient, m, is an overall value for the bulk material examined. A theoretical value of m would be the mean of the indi- vidual mass attenuation coefficients for each of the constituent elements, weighted according to the mass fraction of each element in the sample. Differences in the chemical composition of the soil can therefore affect the overall mass attenuation coefficient. The mass attenuation coefficient of a chemical element varies with the atomic number of the element, Z, and the incident photon energy. Coppola and Reiniger (1974) showed that m increased with increasing photon energy but that, for photon energies above about 0.3 MeV, there was little dependence of m on Z below Z ϭ 30, with the exception of hydrogen, which is discussed below. Caesium-137, which emits mono-energetic photons of 0.662 MeV, is the radio- active source most commonly employed in soil bulk density gauges. At this pho- ton energy, calculations based on theoretical values of mass attenuation coefficient for nine different soils show that the error in estimated density due to the effect of composition is of the order of 0.5% in the most extreme case (Reginato, 1974). An energy-discriminating system set to exclude photons of energy lower than the caesium-137 emission energy would therefore not show a significant dependence on chemical composition of the soil. In contrast, Geiger–Mu¨ller detectors, which do not employ energy discrimination, are sensitive to photon energies as low as 0.04 MeV (Soane, 1976). Consequently, a significant proportion of the detected count rate will include scattered photons with energies that are below 0.3 MeV and so are susceptible to composition effects. Nevertheless, only a small propor- tion of the detected photons will have been scattered through angles large enough to result in such low energies so that the effect of composition on count rate is unlikely to be serious except in backscatter gauges, where it is only the less ener- getic scattered photons that are counted. Generally, transmission gauges, espe- cially those with energy discrimination, are not susceptible to soil composition effects except in soils that have a large proportion of heavy elements, such as iron (Gameda et al., 1983). 3. Photon Count Rate in the Absence of a Sample In order to apply Beer’s equation (Eq. 3), it is necessary to know the photon inten- sity I 0 in the absence of a sample. The theoretical relation assumes an ideal situ- 320 Campbell and Henshall Copyright © 2000 Marcel Dekker, Inc. ation where none of the detected photons in I or I 0 are attenuated or scattered. Although a measurement of I 0 directly, i.e., in the absence of any attenuation by the soil, would be very similar to this ideal situation, safety considerations make it impracticable. The normal method therefore is to make a reference measurement using a material of constant density such as a steel plate. The reference count rate, I r , can be written as I ϭ I exp[mrx] (5) r0 rr where r r is the mean density, over the sample length, of the reference plate and air gap, and m r is the corresponding mass attenuation coefficient. This, combined with Eq. 3, gives I ϭ exp[Ϫx(mr Ϫ mr)] (6) rr I r thereby eliminating I 0 . Relating test measurements to reference measurements in this way also allows for the gradual decrease with time in the activity of the source and any gradual change in the efficiency of the detection system. D. Calibration When a gauge is calibrated relative to a standard reference plate, Eq. 6 can be rearranged to give an expression for bulk density, namely 1 I r r ϭ ln Ϫ mrx (7) ͫͩͪ ͬ rr mxI or I r r ϭ A ln ϩ B (8) ͩͪ I where A and B are empirically determined constants. Since the gauge measures only wet bulk density, an independent measurement of gravimetric water content is required to give the dry bulk density r s from Eq. 1. Hydrogen, which in soil is most abundant in the water, does not conform with other elements in its attenuation of gamma photons, as it possesses only one nucleon per electron, whereas other atoms typically possess approximately two. While the gamma-ray attenuation system effectively measures the number of elec- trons per unit volume, bulk density is related to the number of more massive nu- cleons per unit volume, and so the density of hydrogen is overestimated by a factor of approximately two. Consequently, if the greater attenuation coefficient of hy- drogen were not corrected for, the bulk density would be slightly overestimated. For samples with gravimetric water contents of 10, 25, and 100%, the theoreti- Bulk Density 321 Copyright © 2000 Marcel Dekker, Inc. cal overestimate would be 1, 2, and 5%, respectively. In many applications, this level of accuracy may be considered acceptable, but, if required, the error can be corrected for during calibration. Separating the effects of water and soil, Eq. 3 becomes I ϭ I exp[Ϫx(mr ϩ mr)] (9) 0ssww where r w is the mass of water per unit total sample volume, and m s and m w are the mass attenuation coefficients for soil and water, respectively. Expressing r w as (r s W/100) and incorporating a reference standard as in Eq. 6, we have IW ϭ exp Ϫx rmϩ m Ϫ mr (10) ͭͫͩ ͪ ͬͮ ss w rr I 100 r which leads to ln(I /I) ϩ mrx rrr r ϭ (11) s x(m ϩ m W/100) sw which again can be simplified to A ln(I /I) ϩ B r r ϭ (12) s 100 ϩ CW where constants A, B, and C are determined empirically. E. Gauge Design 1. Radioactive Source The primary requirements of a radioactive source for a soil density gauge are that it should have a single energy peak at an energy sufficiently high to reduce com- position effects, that the emitted photons should have a suitable penetration range into the soil sample, and that the half-life should be long enough not to affect any series of experimental measurements and should preferably exceed the expected life of the gauge. Caesium-137, with a mono-energetic peak of 0.662 MeV and a half-life of 30 years, is the source most suited to these requirements. The optimum soil sample length for gamma photons of this energy has been suggested as 100 to 250 mm (Ferraz and Mansell, 1979). The rate of emission of gamma photons from a radioactive source is not perfectly constant but subject to random fluctuations about a mean value. The resulting fractional error in count rate is inversely proportional to the square root of the total number of photons counted (Ferraz and Mansell, 1979), and so it is preferable to count as many photons as possible to achieve the highest level of precision. This can be achieved by counting for long periods of time and by using the highest possible activity of source. However, for portable field gauges, the 322 Campbell and Henshall Copyright © 2000 Marcel Dekker, Inc. practical limit of activity is set by safety considerations. The maximum source activity that can be shielded to give the statutory levels of safety without the gauge becoming unacceptably heavy for field use is of the order of 0.4 GBq (10 mCi). In laboratory gauges, larger shields allow much larger sources to be used, in which case the upper limit to source activity is determined by the dead time of the detec- tion system. This results from the inability of the detector to respond within a fixed time after detecting a photon, thereby imposing a count rate limit irrespective of source strength. With gauges based on NaI(T1) detectors this limits source activity to about 7 GBq (200 mCi). Although it has been suggested (Herkelrath and Miller, 1976) that this could be increased to 70 GBq (2000 mCi) where plastic scintilla- tors are used, this proposal has never been adopted. 2. Probe Design Portable field transmission gauges are of either single or twin probe design (Fig. 2). In single-probe gauges, the radioactive source is lowered through the body of the gauge into a preformed access hole, normally to a depth of about 300 mm (Fig. 2). The detector, which is generally of the nondiscriminating type, is located on the base of the gauge body at a fixed distance from the source probe axis, so that it is in contact with the surface of the soil. The count rate at each depth then relates to the average bulk density between the source depth and the surface. Such a gauge avoids some operational problems common to twin-probe gauges but suffers from an inability to examine soil layers and also requires a separate calibration for each measurement depth. Commercial gauges are nor- mally supplied with factory calibrations, but users generally find that recalibration is necessary (Gameda et al., 1983). The probes of twin-probe gauges (Fig. 2) are normally clamped rigidly at a fixed separation of between 140 and 300 mm so that, after they have been lowered to any desired depth in the soil, horizontal layers of soil can be examined (Fig. 2). These gauges are more suited to the study of soils in the context of agriculture, forestry, and the natural environment, where considerable variation in bulk den- sity with depth is usually found. Conversely, in civil engineering applications, the soil is likely to be more uniform with depth, since only subsoils, either in situ or excavated and subsequently compacted as fill material, are of concern. In such applications, single-probe gauges have proved more popular. Because of the fixed probe separation in twin-probe gauges, a single cali- bration relationship is applicable to all depths, but it is essential either that the access holes remain parallel or that any deviation is corrected for. Most popular commercial gauges incorporate nondiscriminating detectors and are therefore sus- ceptible to problems of lack of resolution close to either air/soil interfaces or abrupt soil density changes with depth. However, detectors that employ energy discrimination are available (Fig. 3). Bulk Density 323 Copyright © 2000 Marcel Dekker, Inc. Fig. 3 Gamma-ray transmission gauge developed at the former Scottish Centre of Agri- cultural Engineering, complete with transport box which incorporates material for making a reference measurement and a scaler in the lid. Copyright © 2000 Marcel Dekker, Inc. [...]... savannah soils in relation to land use and pore size distribution Soil Tech 11 : 185 –195 McBratney, A B., and R Webster 1 983 How many observations are needed for regional estimation of soil properties? 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The poor correlation in loamy soil was attributed to the presence of stones in the soil and its high iron. inaccuracies in the gamma gauge. King and Parsons (1959) found reasonable agreement (Ϯ3%) between a single-probe gamma gauge and the sand replacement method in sandy and clay soils but unacceptably large. repacking field soils into bins and determining their density independently from measurements of sample mass and volume (Henshall and Campbell, 1 983 ; Soane et al., 1971). Both types of calibra- tion are