Soil bulk density (p6, Mg m-3) is the ratio of the mass of dry solids to a bulk volume of soil (Blake and Hartge, 1986). Its determination is essential to calculate the mass of soil organic carbon (SOCm, Mg C m-3) from SOC concentration (SOCc, Mg C Mg-1):

Although p6 is a relatively straightforward measurement, its evaluation can be subject to errors. Blake and Hartge (1986) and Culley (1993) offer excellent descriptions of the various methods that can be used to determine p6. In the extractive methods, a soil sample of known (core method) or unknown volume (clod and excavation methods) is extracted, dried, and weighed (Blake and Hartge, 1986). Bulk density can also be determined in situ with the use of gamma radiation methods (Blake and Hartge, 1986). Instrument cost and radiation hazard may limit the utilization of gamma radiation methods in carbon sequestration projects.

For determination of p6 at various depths, which will be the case for carbon sequestration projects, Blake and Hartge (1986) recommend the use of hydraulically driven probes mounted on pickup trucks, tractors, or other vehicles, but certainly, hand-driven samplers are appropriate as well. The obvious goal with any sampling method for determining pb is to avoid compressing the soil in the confined space of the sampler. Challenges are encountered when trying to determine pb in soils containing coarse fragments, soils with large swell-shrink capacity, or high organic matter content (Lal and Kimble, 2001). Each of these challenges must be answered with specific solutions. Lal and Kimble (2001) briefly review these and other cases and recommend solutions. For example, the excavation method might work best for determining pb in soils containing significant amounts of coarse fragments or soils with high organic matter content. The clod method might be the best method for soils that develop large cracks upon drying.

Can pb be estimated by in situ measurements other than the gamma radiation probe? Time domain reflectometry (TDR), a technique originally designed for detecting failures in coaxial transmission lines, was first applied in soil science to measure soil water content (Topp et al., 1980). Theory and applications for TDR technology have expanded quickly since then as a way to measure mass and energy in soil (Topp and Reynolds, 1998). Ren et al. (2003) used a thermo-TDR probe to make simultaneous field determinations of soil water content, temperature, electrical conductivity, thermal conductivity, thermal diffusivity, and volumetric heat capacity. Knowledge of volumetric heat capacity (pc) and soil water content (n) further allowed them to calculate other soil physical parameters such as pb, air-filled porosity, and degree of saturation. They calculated pb, as in Ochsner et al. (2001):

where cs is the specific heat capacity of soil solids (kJ kg-1 K-1), pw is the density of water (kg m-3), and cw is the specific heat of water (kJ kg-1 K-1). They tested their procedure in the laboratory with six column-packed soils ranging in texture from sand to silty clay loam with pb ranging from 0.85 to 1.52

Mg m-3. The p6 predicted with the thermo-TDR was able to explain slightly more than half of the variation in measured p6, which suggests a method that, when improved, could deliver rapid measurements of p6 in the field.

Soil bulk density is a dynamic property; its value changes in response to applied pressure, soil water content, and SOM content. Up to a 20% change in p6 can occur with changes in soil water potential from 0.03 to 1.5 MPa (Lal and Kimble, 2001). Reporting p6 at standardized soil water content of 0.03 MPa is recommended. SOM content has a strong effect on p6. Adams (1973) developed an equation to estimate p6:

0- 244 p m where %OM is percent SOM, pm is mineral bulk density (Mg m-3), and the value 0.244 is the bulk density of organic matter (Mg m-3). The bulk density of organic matter is fairly constant. However, the formula is difficult to apply because pm is not usually known. Mann (1986) rearranged Adams's equation to calculate pm from 121 pairs of soil samples with known values of SOM and p6.

The Adams equation is difficult to solve directly because it has two unknowns (p6, pm). In principle, p6 could be estimated from knowledge of soil texture, soil particle density (ps), and the packing arrangement of mineral particles. Here, a simple method is proposed for estimation of p6 based on soil texture, ps, and packing arrangement information. Soil particle density is usually assumed to be 2.65 Mg m-3, but there are slight variations depending on the textural composition. While the sand fraction has a ps of 2.65 Mg m-3, the clay and silt fractions have ps of about 2.78 Mg m3.

If the fractional values of sand (sandf), silt (siltf), and clay (clayf) are known, then ps can be calculated as:

where psa is the soil particle density of sand, while psc is the soil particle density of silt and clay. The next problem is to estimate a possible arrangement of these particles in the soil matrix.

Assuming a spherical shape for soil particles, there are various geometrical arrangements in which these particles can accommodate when packed. Sphere packing can be done in two and three dimensions, but only three-dimensional packing applies to soils. The densest packing is provided by the cubic close and the hexagonal close geometries (http://mathworld.wol-fram.com/SpherePacking.html). These and other types of packing are defined by the packing density (n), which is the fraction of a volume filled by a given collection of solids. The packing density can be solved analytically for some types of arrangements; for others it cannot. For example, n for a cubic lattice arrangement is 0.524; it is 0.64 for a random arrangement, and 0.74 for a hexagonal close packing arrangement. (See http://mathworld.wolfram.com/SpherePacking.html for additional information on this topic.)

After selecting a value for n, mineral bulk density can be estimated as:

A modified Equation 19.1 is then used to calculate p6 at a given SOC concentration:

0.2^141 pm

where 1.724 is the conversion factor generally used to convert SOC into SOM. A theoretical example is shown in Figure 19.1 for three types of sphere packing (cubic lattice, random, and hexagonal). A test of the model is shown in Figure 19.2 against soil taxonomy data (U.S. Department of Agriculture, 1999). Gupta and Larson (1979) described a model that uses the same principles of sphere packing described here. This model is theoretically very good because it accounts for various particle sizes, but it requires complete information on soil fractions (very coarse sand, coarse sand, medium sand, fine sand, very fine sand, coarse silt, fine silt, and clay).

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Figure 19.1 Soil bulk density estimated with three packing density models at different soil organic carbon concentrations and constant texture (0.33 clay, 0.33 silt, and 0.34 sand).

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