Density, as applied to any kind of homogeneous monophasic material of mass M and volume V, is expressed as the ratio of M to V. Under specified conditions, this definition leads to unique values that represent a well-defined property of the material. For heterogeneous and multiphasic materials, however, such as porous media, application of this definition can lead to different results, depending on the exact way the mass and volume of the system are defined.

Soil is a typical heterogeneous multiphasic porous system which, in its general form, contains three natural phases: (1) the solid phase or the soil matrix (formed by mineral particles and solid organic materials); (2) the liquid phase, which is often represented by water and which could more properly be called the soil solution; and (3) the gaseous phase, which contains air and other gases. In this three-phase soil system, the concept of average density can be used to define the following densities: (1) density of solids or soil particle density, s; (2) bulk or dry density, b; and (3) total or wet density, t.

The masses and volumes associated with the three soil phases must be defined before the definitions of the different densities that characterize the soil system can be formalized. Thus, consider a representative elementary volume (REV) of soil that satisfies the following criteria (Bear 1972; Marsily 1986):

1. A sufficiently large volume of soil containing a large number of pores, such that the concept of mean global properties is applicable, and

2. A sufficiently small volume of soil so that the variation of any parameter of the soil from one part of the domain to another can be approximated by continuous functions.

Within a REV, the masses of the phases composing the soil can be defined as follows:

Ms = the mass of solids,

Ml = the mass of liquids,

Mg = the mass of gases (negligible compared with the masses of the solid and liquid phases), and

Mt = Ms + Ml = the total mass.

Similarly, within the REV, the volumes associated with the soil phases can be defined as follows:

Vs = the volume of solids,

Vl = the volume of liquids,

Vg = the volume of gases,

Vp = Vl + Vg = the volume of pore space, and

Vt = Vs + Vl + Vg = the total volume.

These mass and volume definitions can be used to define the concepts of soil particle density, bulk (dry) soil density, and total (wet) soil density. The dimensional unit of soil density is mass per unit of cubic length (M1-3).

2.1.1 Soil Particle Density

The soil particle density, s, or the density of solids, represents the density of the soil (i.e., mineral) particles collectively and is expressed as the ratio of the solid phase mass to the volume of the solid phase of the soil. Soil particle density is defined as follows:

In most mineral soils, the soil particle density has a short range of 2.6-2.7 g/cm3 (Hillel 1980b). This density is close to that of quartz, which is usually the predominant constituent of sandy soils. A typical value of 2.65 g/cm3 has been suggested to characterize the soil particle density of a general mineral soil (Freeze and Cherry 1979). Aluminosilicate clay minerals have particle density variations in the same range. The presence of iron oxides and other heavy minerals increases the value of the soil particle density. The presence of solid organic materials in the soil decreases the value.

2.1.2 Bulk (Dry) Density

The soil bulk or dry density, b, is the ratio of the mass of the solid phase of the soil (i.e., dried soil) to its total volume (solid and pore volumes together) and is defined as follows:

The bulk density, b, is related to the soil particle density, s, by the total soil porosity, pt, according to the following equation:

where 1-pt is the ratio of the solid volume (Vs ) to the total volume (Vl Vg + Vs ). Section 3 discusses total porosity.

From the above definition, it should be obvious that the value of the dry density is always smaller than the value of the soil particle density. For example, if the volume of the pores (Vl Vg ) occupies half of the total volume, the value of dry density is half the value of the soil particle density.

The dry density of most soils varies within the range of 1.1-1.6 g/cm3. In sandy soils, dry density can be as high as 1.6 g/cm3; in clayey soils and aggregated loams, it can be as low as 1.1 g/cm3 (Hillel 1980b). Because of its high degree of aggregation (i.e., small total porosity), concrete has, in general, a higher dry density than soil. Typical values of dry density in different types of soils and in concrete are shown in Table 2.1. Dry density depends on the structure of the soil matrix (or its degree of compaction or looseness) and on the soil matrix's swelling/shrinkage characteristics.

To use Table 2.1 to estimate dry bulk density (or any other soil properties discussed in this handbook), the user needs to know the soil texture type. The common method used in the field to classify a soil is the "feel" method (Brady 1984). This method consists of merely rubbing the soil between the thumb and fingers. Usually it is helpful to wet the sample to estimate plasticity more accurately. The way a wet soil "slicks out," that is, develops a continuous ribbon when pressed between the thumb and fingers, gives a good idea of the amount of clay present. The slicker the wet soil, the higher the clay content. The sand particles are gritty, and the silt has a floury or talcum-powder feel when dry and is only slightly plastic and sticky when wet. Persistent cloddiness is generally the result of the presence of silt and clay. The accuracy of the feel method depends largely on experience. The laboratory method is more accurate but is time-consuming. The laboratory method to classify soil involves particle-size analysis, in which sieves are usually employed for coarser particles and the rate of settling in water for finer particles (Marshall and Holmes 1979). The U.S. Department of Agriculture (USDA) has developed a method for naming soils on the basis of particle-size analysis. The relationship between such an analysis and soil class names is shown diagrammatically in Figure 2.1. The legend in the figure explains the use of this soil texture triangle.

2.1.3 Total (Wet) Density

The total, or wet, density of soil, t, is the ratio of the total mass of soil to its total volume and can be defined as follows:

Total density differs from dry density in that it is strongly dependent on the moisture content of the soil. For a dry soil, total density approximates the value of dry density.


For use in RESRAD, only the dry densities of five distinct materials (cover layer, contaminated zone, unsaturated and saturated zones, and building foundation material) are needed as input parameters. However, because information on both soil particle and bulk (i.e., dry) density is required for the calculation of total porosity of the soil material, descriptions of the techniques and procedures for measuring both types of densities follow.

The standard methods used on Formerly Utilized Sites Remedial Action Program (FUSRAP) sites for determining the particle density and the dry density in soil materials are those prepared by the American Society of Testing Materials (ASTM 1992a-o) and the U.S. Department of the Army (DOA 1970), as listed in Table 2.2. A general discussion on these measurement methodologies is also presented in Blake and Hartge (1986a,b).

2.2.1 Soil Particle Density Measurement

The soil particle density of a soil sample is calculated on the basis of the measurement of two quantities: (1) Ms, the mass of the solid phase of the sample (dried mass) and (2) Vs, the volume of the solid phase (Blake and Hartge 1986b). Assuming that water is the only volatile in a soil sample, the mass (Ms) can be obtained by drying the sample (usually at 110 ± 5C) until it reaches a constant weight, Ws. This method may not be valid for organic soils or soils with asphalt.

The solid phase volume, Vs, can be measured in different ways. One way is to measure the volume directly by observing the resulting increase in the volume of water as the sample of dried soil is introduced into a graduated flask that initially contains pure water (or another liquid). After making sure that the soil/water mixture is free from air bubbles,  

the observed expansion in volume (i.e., the replaced volume of water) should be equal to Vs, the solid phase volume. The problem with this approach is that the techniques used to eliminate air bubbles from the mixture (such as heating) can also disturb the total volume and thus introduce errors into the calculations.

Another way to measure the solid phase volume (Vs) is based on evaluating the mass and density of water (or another fluid) displaced by the sample (after being oven-dried). This second approach has been used for quite some time and is simple, direct, and accurate     

TABLE 2.2 Standard Methods for Measuring Particle Density and Bulk

(Dry) Density in Soil Materials at FUSRAP Sites

Parameter Measured

Type of Measurement

Standard Test Method





Soil sample testing

Appendix IV: Specific Gravity

ASTM D 854-91: Standard Test Method for Specific Gravity of Soils

DOA (1970)

ASTM (1992a)

Bulk (dry)



Soil sample


Appendix II: Unit Weights, Void Ratio, Porosity, and Degree of Saturation

DOA (1970)

In-situ near



ASTM D 1556: Standard Test Method for Density and Unit Weight of Soil in Place by the Sand-Cone Method

ASTM (1992b)
ASTM D 2167-84: Standard Test Method for Density and Unit Weight of Soil in Place by the Rubber Balloon Method

ASTM (1992d)

ASTM D 2922-91: Standard Test Methods for Density of Soil and Soil-Aggregate in Place by Nuclear Methods (shallow depth)

ASTM (1992g)

ASTM D 2937-83: Standard Test Method for Density of Soil in Place by the Drive-Cylinder Method

ASTM (1992h)

ASTM D 4564-86: Standard Test Method for Density of Soil in Place by the Sleeve Method

ASTM (1992k)

In-situ below



ASTM D 5195-91: Standard Test Method for Density of Soil and Rock In-Place at Depths below the Surface by Nuclear Methods

ASTM (1992n)

if done carefully (Blake and Hartge 1986a). It is based on the fact that if Vdw, the volume of water displaced by the solids, is equal to Vs, then


where Mdw is the mass of the displaced water and w is the water density. Therefore, to obtain the soil particle density, it is necessary to evaluate the water density at the specific pressure and temperature conditions and to measure Ms and Mdw (DOA 1970, Appendix IV; ASTM 1992a).

The value of Mdw is obtained by using a graduated volumetric flask and by taking the following measurements:

Mf = mass of the empty flask;

Mfs = mass of the flask plus the dried soil sample;

Mfsw = mass of the flask plus the soil and filled with water up to a fixed volume, Vf; and

Mfw = mass of the flask filled with pure water up to the fixed volume Vf.

The mass of the displaced water, Mdw, can then be calculated as follows:

Substituting Mdw into the expression for soil particle density, s, yields

This method is very precise, but it requires careful measuring of volumes and masses and consideration of the effects of pressure and temperature conditions on the water density. Possible errors can result not only from determining the masses and volumes but from nonrepresentative sampling.

2.2.2 Dry Density Measurement

The dry (bulk) density (b) of a soil sample is evaluated on the basis of two measured values: (1) Ms, the oven-dried mass of the sample and (2) Vt, the field volume or the total volume of the sample. As stated previously, for the calculation of soil particle density (s), mass (Ms) is measured after drying the sample at 110 ± 5 C until a near constant weight is reached. This laboratory technique directly determines the dry density of a soil sample (DOA 1970, Appendix II). Possible direct methods of measuring the dry density include the core and excavation methods, which essentially consist of drying and weighing a known volume of soil.

Variations of these methods are related to different ways of collecting the soil sample and measuring volume. In the core method (Blake and Hartge 1986a; ASTM 1992h), a cylindrically shaped metal sampler is introduced into the soil, with care to avoid disturbing the sample. At the desired depth in the soil, a known field volume (Vt) of soil material is collected as it exists in-situ. The sample is then oven-dried and weighed to obtain the mass. The value of the dry density is calculated by dividing the mass by the volume. Problems in using this technique include sampling difficulties, such as the presence of gravels in the soil, and the possibility of disturbing the structure of the soil during the sampling process when the sampler is introduced into the ground.

In the excavation method (Blake and Hartge 1986a), the dry density of the soil is determined by excavating a hole in the ground, oven-drying and weighing the amount of soil removed from the ground to determine the mass, and measuring the volume of the excavation. The volume (Vt) can be determined in different ways. One is to use the sand-funnel method (ASTM 1992b) in which a selected type of sand with a known volume per unit mass is used to completely fill the hole. Then, by measuring the total mass of sand needed to fill the hole, the volume can be determined. Another possible way to measure the volume (Vt) is to use the rubber-balloon method (ASTM 1992d). In this technique, a balloon is placed within the hole and filled with a liquid (water) up to the borders of the hole. The volume of the excavated soil sample is then equal to the volume of the liquid in the balloon.

An advantage of using the excavation method to measure dry densities of soils other than the core method is that it is more suitable for heterogeneous soils with gravels.

An indirect method of measuring soil density, applicable for in-situ rather than laboratory determinations, is called the radiation method or gamma-ray attenuation densitometry (Blake and Hartge 1986a; ASTM 1992g,o). This method is based on the principle that the amount of gamma radiation being attenuated and scattered in the soil depends on the soil properties, including the combined densities of the solid/liquid components of the medium. By measuring the radiation that is transmitted through the medium or that is scattered by soil components and reaches a detector placed away from the source and by using proper calibration, the wet density of the soil, t, can be determined. To determine the dry density, b, a correction of the result is needed to delete the contribution from the liquid phase of the soil.

The radiation method used for measuring soil density has several advantages over other related laboratory techniques: (1) it yields an in-situ evaluation of soil density, (2) it causes minimum disturbance of the soil, (3) it requires a relatively short measurement time, (4) it is more applicable for deeper subsoil determinations because it requires minimal excavation, and (5) it is a nondestructive technique because continuous or repeated measurements can be performed at the same spot. The radiation method also has some disadvantages compared with the other methods. Because it is a more sophisticated technique, it requires expensive equipment and highly trained operators who must be able to handle the frequent calibration procedures, the electronics, and the sampling equipment. The system operator must be trained in the radiation aspects and radiological protection procedures of the entire operation.


In RESRAD, one variable is assigned to represent the dry density, measured in units of grams per cubic centimeter, of each of the following five materials: (1) cover material, (2) contaminated zone, (3) unsaturated zone, (4) saturated zone, and (5) building foundation material (i.e., concrete). For the first four types of soil, a default value of 1.5 g/cm3 is assigned for the dry density, a value that is representative of a sandy soil. Although the building foundation material (i.e., concrete) has a solid phase density (i.e., particle density) similar to that of the soil, because of its small total porosity, concrete has, in general, a higher dry density than soils. In RESRAD, a default value of 2.4 g/cm3 is assigned for the dry density of the foundation building material. This default value is provided for generic use of the RESRAD code. For more accurate use of the code, site-specific data should be used.

If the type of soil is known, then Table 2.1 can be used for a slightly more accurate determination of the input data values for dry density. If no information about the type of soils is available, however, then the values for dry density should be experimentally determined by using one of the methods described in Section 2.2.2.