3.1 DEFINITION
The total porosity of a porous medium is the ratio of the pore volume to the total volume of a representative sample of the medium. Assuming that the soil system is composed of three phases -- solid, liquid (water), and gas (air) -- where V_{s} is the volume of the solid phase, V_{l} is the volume of the liquid phase, V_{g} is the volume of the gaseous phase, V_{p} = V_{l} + V_{g} is the volume of the pores, and V_{t} = V_{s} + V_{l} + V_{g} is the total volume of the sample, then the total porosity of the soil sample, p_{t}, is defined as follows:
Porosity is a dimensionless quantity and can be reported either as a decimal fraction or as a percentage. Table 3.1 lists representative total porosity ranges for various geologic materials. A more detailed list of representative porosity values (total and effective porosities) is provided in Table 3.2. In general, total porosity values for unconsolidated materials lie in the range of 0.25-0.7 (25%-70%). Coarse-textured soil materials such as gravel and sand tend to have a lower total porosity than fine-textured soils such as silts and clays. The total porosity in soils is not a constant quantity because the soil, particularly clayey soil, alternately swells, shrinks, compacts, and cracks.
TABLE 3.1 Range of Porosity Values | |
Soil Type | Porosity, p_{t} |
Unconsolidated deposits | |
Gravel | 0.25 - 0.40 |
Sand | 0.25 - 0.50 |
Silt | 0.35 - 0.50 |
Clay | 0.40 - 0.70 |
Rocks | |
Fractured basalt | 0.05 - 0.50 |
Karst limestone | 0.05 - 0.50 |
Sandstone | 0.05 - 0.30 |
Limestone, dolomite | 0.00 - 0.20 |
Shale | 0.00 - 0.10 |
Fractured crystalline rock | 0.00 - 0.10 |
Dense crystalline rock | 0.00 - 0.05 |
Source: Freeze and Cherry (1979). |
TABLE 3.2 Representative Porosity Values | |||||
Total Porosity, p_{t} | Effective Porosity,^{a} p_{e} | ||||
Material | Range | Arithmetic Mean | Range | ArithmeticMean | |
Sedimentary material |
|||||
Sandstone (fine) | -^{b} | - | 0.02 - 0.40 | 0.21 | |
Sandstone (medium) | 0.14 - 0.49 | 0.34 | 0.12 - 0.41 | 0.27 | |
Siltstone | 0.21 - 0.41 | 0.35 | 0.01 - 0.33 | 0.12 | |
Sand (fine) | 0.25 - 0.53 | 0.43 | 0.01 - 0.46 | 0.33 | |
Sand (medium) | - | - | 0.16 - 0.46 | 0.32 | |
Sand (coarse) | 0.31 - 0.46 | 0.39 | 0.18 - 0.43 | 0.30 | |
Gravel (fine) | 0.25 - 0.38 | 0.34 | 0.13 - 0.40 | 0.28 | |
Gravel (medium) | - | - | 0.17 - 0.44 | 0.24 | |
Gravel (coarse) | 0.24 - 0.36 | 0.28 | 0.13 - 0.25 | 0.21 | |
Silt | 0.34 - 0.51 | 0.45 | 0.01 - 0.39 | 0.20 | |
Clay | 0.34 - 0.57 | 0.42 | 0.01 - 0.18 | 0.06 | |
Limestone | 0.07 - 0.56 | 0.30 | ~0 - 0.36 | 0.14 | |
Wind-laid material |
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Loess | - | - | 0.14 - 0.22 | 0.18 | |
Eolian sand | - | - | 0.32 - 0.47 | 0.38 | |
Tuff | - | - | 0.02 - 0.47 | 0.21 | |
Igneous rock |
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Weathered granite | 0.34 - 0.57 | 0.45 | - | - | |
Weathered gabbro | 0.42 - 0.45 | 0.43 | - | - | |
Basalt | 0.03 - 0.35 | 0.17 | - | - | |
Metamorphic rock |
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Schist | 0.04 - 0.49 | 0.38 | 0.22 - 0.33 | 0.26 | |
^{a} Effective porosity is discussed in Section 4. ^{b} A hyphen indicates that no data are available. Source: McWorter and Sunada (1977). |
3.2 MEASUREMENT METHODOLOGY
The standard method used on FUSRAP sites for determining the total porosity of soil materials is described in Appendix II of DOA (1970). Further discussion on this methodology is also presented in Danielson and Sutherland (1986).
On the basis of the definition of total porosity, a soil sample could be evaluated for total porosity by directly measuring the pore volume (V_{p}) and the total volume (V_{t}). The total volume is easily obtained by measuring the total volume of the sample. The pore volume can, in principle, be evaluated directly by measuring the volume of water needed to completely saturate the sample. In practice, however, it is always difficult to saturate the soil sample exactly and completely and, therefore, the total porosity of the sample is rarely evaluated by a direct method. Usually, the total porosity is evaluated indirectly by using the following expression (DOA 1970, Appendix II; Danielson and Sutherland 1986):
where p_{t} is given as a decimal fraction, V_{s} is the soil particle volume, V_{t} is the total volume, _{s} is the solid phase (soil particle) density, and _{b} is the dry bulk density of the sample. (Equation 3.2 can be obtained by rearranging Equation 2.3.) Under this approach, the values of _{s} and _{b} are evaluated by laboratory or in-situ measurements (Section 2.2) and are then used to calculate the total porosity p_{t}.
3.3 RESRAD DATA INPUT REQUIREMENTS
To use RESRAD, the user is required to define or use the default values of the total porosity of five materials: (1) cover material, (2) contaminated zone, (3) unsaturated zone, (4) saturated zone, and (5) building foundation material (i.e., concrete). In RESRAD, the total porosities are entered as decimal fractions rather than as percentages. RESRAD adopts the following values as defaults: n = 0.4 for the first four materials listed above and n = 0.1 for the building foundation (i.e., concrete). These default values are provided for generic use of the RESRAD code. For more accurate use of the code, site-specific data should be used.
If site-specific data are not available and the type of soil is known, Tables 3.1 and 3.2 can be used for estimating total porosity. However, if no information is available on the type of soils, then the values for total porosity should be experimentally determined according to the method presented in Section 3.2.
4.1 DEFINITION
The effective porosity, p_{e}, also called the kinematic porosity, of a porous medium is defined as the ratio of the part of the pore volume where the water can circulate to the total volume of a representative sample of the medium. In naturally porous systems such as subsurface soil, where the flow of water is caused by the composition of capillary, molecular, and gravitational forces, the effective porosity can be approximated by the specific yield, or drainage porosity, which is defined as the ratio of the volume of water drained by gravity from a saturated representative sample of the soil to the total volume of the sample.
The definition of effective (kinematic) porosity is linked to the concept of pore fluid displacement rather than to the percentage of the volume occupied by the pore spaces. The pore volume occupied by the pore fluid that can circulate through the porous medium is smaller than the total pore space, and, consequently, the effective porosity is always smaller than the total porosity. In a saturated soil system composed of two phases (solid and liquid) where (1) V_{s} is the volume of the solid phase, (2) V_{w} = (V_{iw} + V_{mw}) is the volume of the liquid phase, (3) V_{iw} is the volume of immobile pores containing the water adsorbed onto the soil particle surfaces and the water in the dead-end pores, (4) V_{mw} is the volume of the mobile pores containing water that is free to move through the saturated system, and (5) V_{t} = (V_{s} + V_{iw} + V_{mw}) is the total volume, the effective porosity can be defined as follows:
Another soil parameter related to the effective soil porosity is the field capacity, _{r}, also called specific retention, irreducible volumetric water content, or residual water content, which is defined as the ratio of the volume of water retained in the soil sample, after all downward gravity drainage has ceased, to the total volume of the sample. Considering the terms presented above for a saturated soil system, the total porosity p_{t} and the field capacity _{r} can be expressed, respectively, as follows:
and
Therefore, the effective porosity is related to the total porosity and the field capacity according to the following expression:
Several aspects of the soil system influence the value of its effective porosity: (1) the adhesive water on minerals, (2) the absorbed water in the clay-mineral lattice, (3) the existence of unconnected pores, and (4) the existence of dead-end pores. The adhesive water in the soil is that part of the water present in the soil that is attached to the surface of the soil grains through the forces of molecular attraction (Marsily 1988). The sum of the volumes of the adhesive and absorbed water plus the water that fills the unconnected and dead-end pores constitute the volume of the adsorbed water, V_{iw}, that is unable to move through the system.
A detailed list of representative porosity values (total porosity and effective porosity) is presented in Table 3.2.
4.2 MEASUREMENT METHODOLOGY
Determination of the effective porosity, p_{e}, of soils can be accomplished indirectly by measuring the total porosity, p_{t}, and the field capacity, _{r}, and then calculating p_{e} from Equation 4.4. The total porosity is obtained indirectly by measuring the soil densities according to the method described in Section 3.2. To determine the field capacity of the soils, the soil sample is first saturated with water and is then allowed to drain completely under the action of gravity until it gets to its irreducible saturation. The value of _{r} can then be obtained according to the methods used for measuring volumetric water content (Section 6.2).
4.3 RESRAD DATA INPUT REQUIREMENTS
To use RESRAD, the user is required to define (or to use the default values) of the effective porosity of three distinct materials: (1) contaminated zone, (2) saturated zone, and (3) unsaturated zone. In RESRAD, the effective porosity values are entered as decimal fractions rather than as percentages. As a default value, RESRAD adopts the value of p_{e} = 0.2 for all three materials. These default values are provided for generic use of the RESRAD code. For more accurate utilization of the model, site-specific data should be used.
If site-specific data are not available and the soil type is known,
Table 3.2 can be used for estimating effective porosity. However, if no
information is available on soil type, then the values of effective porosity
should be experimentally determined according to the method presented in
Section 4.2. Effective porosity values should not be greater than total
porosity values. Total porosity is discussed in Section 3.