5 HYDRAULIC CONDUCTIVITY

5.1 DEFINITION

The hydraulic conductivity of a soil is a measure of the soil's ability to transmit water when submitted to a hydraulic gradient. Hydraulic conductivity is defined by Darcy's law, which, for one-dimensional vertical flow, can be written as follows:

where U is Darcy's velocity (or the average velocity of the soil fluid through a geometric cross-sectional area within the soil), h is the hydraulic head, and z is the vertical distance in the soil. The coefficient of proportionality, K, in Equation 5.1 is called the hydraulic conductivity. The term coefficient of permeability is also sometimes used as a synonym for hydraulic conductivity. On the basis of Equation 5.1, the hydraulic conductivity is defined as the ratio of Darcy's velocity to the applied hydraulic gradient. The dimension of K is the same as that for velocity, that is, length per unit of time (IT^-1).

Hydraulic conductivity is one of the hydraulic properties of the soil; the other involves the soil's fluid retention characteristics. These properties determine the behavior of the soil fluid within the soil system under specified conditions. More specifically, the hydraulic conductivity determines the ability of the soil fluid to flow through the soil matrix system under a specified hydraulic gradient; the soil fluid retention characteristics determine the ability of the soil system to retain the soil fluid under a specified pressure condition.

The hydraulic conductivity depends on the soil grain size, the structure of the soil matrix, the type of soil fluid, and the relative amount of soil fluid (saturation) present in the soil matrix. The important properties relevant to the solid matrix of the soil include pore size distribution, pore shape, tortuosity, specific surface, and porosity. In relation to the soil fluid, the important properties include fluid density, , and fluid viscosity, . For a subsurface system saturated with the soil fluid, the hydraulic conductivity, K, can be expressed as follows (Bear 1972):

where k, the intrinsic permeability of the soil, depends only on properties of the solid matrix, and g/, called the fluidity of the liquid, represents the properties of the percolating fluid. The hydraulic conductivity, K, is expressed in terms of length per unit of time (lT^-1), the intrinsic permeability, k, is expressed in l², and the fluidity, g/, in l^-1T^-1. By using              

Equation 5.2, Darcy's law can be rewritten explicitly in terms of its coefficient of proportionality (hydraulic conductivity K):

When the fluid properties of density and viscosity are known, Equation 5.3 can be used to experimentally determine the value of the intrinsic permeability, k, and the hydraulic conductivity, K, as will be shown in Section 5.2.

The values of saturated hydraulic conductivity in soils vary within a wide range of several orders of magnitude, depending on the soil material. Table 5.1 lists the range of expected values of K for various unconsolidated and consolidated soil materials. The expected representative values of K for soil materials of different textures are presented in Table 5.2. A more detailed list of expected representative values of K based on the grain size distribution, degree of sorting, and silt content of several soil materials is presented in Tables 5.3 and 5.4. Section 2.1.2 discusses soil textures.

Because of the spatial variability usually found in the geological formation of soils, saturated hydraulic conductivity values also show variations throughout the space domain        

within a subsurface geological formation. Such a geological formation is said to be heterogeneous. If the properties of the geologic formation are invariable in space, the formation is homogeneous. A geological formation is said to be isotropic if at any point in the medium, the values of the saturated hydraulic conductivity (K) are independent of the direction of measurement. Again, because of the usually stratified nature of uncon-solidated sedimentary soil materials, soils are usually anisotropic. Within an anisotropic geological formation, the vertical component of the saturated hydraulic conductivity is usually smaller (one to two orders of magnitude) than the horizontal component.

5.2 MEASUREMENT METHODOLOGY

The saturated hydraulic conductivity of water in soil (or the intrinsic permeability of the soil) can be measured by both field and laboratory experiments. Either way, the experimental measurement of K (or k) consists in determining the numerical value for the coefficient in Darcy's equation.

The methodology used for the experimental determination of K (or k) in either laboratory or field experiments is based on the following procedures (Bear 1972):

1. Assume a flow pattern (such as one-dimensional flow in a porous medium) that can be described analytically by Darcy's law,

2. Perform an experiment reproducing the chosen flow pattern and measure all measurable quantities in Equation 5.4, including fluid density, dynamic viscosity, flow velocity, and the gradient of the hydraulic head; and

3. Compute the coefficient K (or k) by substituting the measured quantities into Equation 5.4 above.

Many different laboratory or field experiments can be used to determine the coefficient K (or k).

An extensive discussion on the respective measurement methodologies for laboratory and field experiments is presented in Klute and Dirksen (1986) and Amoozegar and Warrick (1986), respectively. For FUSRAP sites, the standard methods used for determining saturated hydraulic conductivity in soil materials are those prepared by the American Society for Testing and Materials (ASTM 1992a-o), the U.S. Environmental Protection Agency (EPA 1986), the U.S. Department of the Army (DOA 1970), and the U.S. Department of the Interior (DOI 1990a,b). Brief descriptions of these pertinent standard methods are presented in Table 5.5.

Laboratory tests are carried out on small samples of soil materials collected during core-drilling programs. Because of the small sizes of the soil samples handled in the laboratory, the results of these tests are considered a point representation of the soil properties. If the soil samples used in the laboratory test are truly undisturbed samples, the measured value of K (or k) should be a true representation of the in-situ saturated hydraulic conductivity at that particular sampling point.

Laboratory methods may be used to evaluate the vertical and horizontal hydraulic conductivity in soil samples. For instance, in undisturbed samples of either cohesive or cohesionless soils, the values of K obtained through laboratory tests correspond to the direction in which the sample was taken, that is, generally vertical. The conductivity of disturbed (remolded) samples of cohesionless soils obtained in the laboratory can be used to approximate the actual value of K in the undisturbed (natural) soil in the horizontal direction (DOA 1970). For fine-grained soils, the undisturbed cohesive sample can be oriented accordingly, to obtain the hydraulic conductivity in either the vertical or horizontal direction.

In contrast to laboratory methods for measuring conductivity in soil samples, field methods, in general, involve a large region of the soil. Consequently, the results obtained from field methods should reflect the influences of both the vertical and horizontal directions and should represent an average value of K. This situation is especially important in highly                       

stratified soils where the values of K measured from field methods would reflect the domi-nation of the most permeable layer in the soil profile. However, by appropriately selecting the specific method to be used in the field, the in-situ values of the vertical and horizontal components of K could be determined independently in each layer of stratified soils.

Selection of a specific method for a particular application will depend on the objectives to be achieved. Because of the difficulty in obtaining a perfectly undisturbed sample of unconsolidated soil, the K value determined by laboratory methods may not accurately reflect the respective value in the field. Therefore, field methods should be used whenever the objective is to characterize the physical features of the subsurface system in question as accurately as possible. Field methods, however, are usually more expensive than laboratory methods and, consequently, when the question of cost becomes decisive, or when actual representation of field conditions is not of fundamental importance and in-situ hydraulic conductivity is not available, laboratory methods may be used to determine the saturated hydraulic conductivity K.

5.2.1 Laboratory Methods

In the laboratory, the value of K can be determined by several different instruments and methods such as the permeameter, pressure chamber, and consolidometer (DOA 1970). A common feature of all these methods is that a soil sample is placed in a small cylindrical receptacle representing a one-dimensional soil configuration through which the circulating liquid is forced to flow. Depending on the flow pattern imposed through the soil sample, the laboratory methods for measuring hydraulic conductivity are classified as either a constant-head test with a steady-state flow regimen or a falling-head test with an unsteady- state flow regimen.

Constant-head methods are primarily used in samples of soil materials with an estimated K above 1.0 × 10² m/yr, which corresponds to coarse-grained soils such as clean sands and gravels. Falling-head methods, on the other hand, are used in soil samples with estimated values of K below 1.0 × 10² m/yr (DOA 1970). A list of standard laboratory methods for determining K, with variations of the constant-head and falling-head flow conditions, is presented in Table 5.5. Also listed in Table 5.5, as a laboratory method for measuring K, is the grain-size based empirical method, in which the intrinsic permeability, k, of the soil sample is empirically determined from the otherwise laboratory-measured grain-size distribution of the soil sample.

Important considerations regarding the laboratory methods for measuring K are related to the soil sampling procedure and preparation of the test specimen and circulating liquid. The sampling process, if not properly conducted, usually disturbs the matrix structure of the soil and results in a misrepresentation of the actual field conditions. Undisturbed sampling of soils is possible, but it requires the use of specially designed techniques and instruments (Klute and Dirksen 1986).

A detailed guide on the standard methods for soil sampling is presented in ASTM D 4700-91, Standard Guide for Soil Sampling from the Vadose Zone (ASTM 1992l). Relatively undisturbed soil samples, suitable for the determination of hydraulic conductivity in the laboratory, could be obtained, for example, by using the thin-walled tube sampling method in ASTM D 1587-83, Standard Practice for the Thin-Walled Tube Sampling of Soils (ASTM 1992c). In this technique, a relatively undisturbed soil sample is obtained by pressing a thin-walled metal tube into the soil, removing the soil-filled tube, and sealing its ends to prevent physical disturbance in the soil matrix.

Selecting the test fluid is also of fundamental importance for the laboratory determination of the saturated hydraulic coefficient. The objective is to have the test fluid mimic the actual properties of the soil fluid as closely as possible. When an inappropriate test fluid is selected, the test sample can get clogged with entrapped air, bacterial growths, and fines. To avoid such problems, a standard test solution such as a deaerated 0.005-mol calcium sulfate (CaSO₄) solution, saturated with thymol (or sterilized with another substance such as formaldehyde) should be in the permeameter, unless there are specific reasons to choose another solution (Klute and Dirksen 1986).

5.2.1.1 Constant-Head Method

The constant-head test with the permeameter is one of the most commonly used methods for determining the saturated hydraulic conductivity of coarse-grained soils in the laboratory. The test operates in accordance with the direct application of Darcy's law to a soil liquid configuration representing a one-dimensional, steady flow of a percolating liquid through a saturated column of soil from a uniform cross-sectional area. In this method, a cylindrical soil sample of cross-sectional area A and length L is placed between two porous plates that do not provide any extra hydraulic resistance to the flow. A constant head difference, H₂ - H₁, is then applied across the test sample. By measuring the volume V of the test fluid that flows through the system during time t, the saturated hydraulic conductivity K of the soil can be determined directly from Darcy's equation:

To improve the results, it is recommended that the test be performed several times under different head differences, H₂ - H₁. It is also recommended that the quantity of liquid collected should be sufficient to provide at least three significant figures in the measured volume. In a simple version of the constant-head permeameter, the lower limit of the measurement of K is approximately 1 × 10¹ m/yr, which corresponds to the lower limit of the conductivity of sandy clay soils. For lower values of K, it is recommended that either an enhanced version of the constant-head permeameter (i.e., one that has a more sensitive method of measuring the volume flow rate) or the falling-head permeameter be used (Klute and Dirksen 1986). Table 5.5 presents variations of the constant-head method for measuring saturated hydraulic conductivity of soil materials in the laboratory.

5.2.1.2 Falling-Head Method

The falling-head test with the permeameter is primarily used for determining the K (or k) value of fine-grained soils in the laboratory. Like the constant-head method, the falling-head test also operates in accordance with direct application of Darcy's law to a one-dimensional, saturated column of soil with a uniform cross-sectional area. The falling-head method differs from the constant-head method in that the liquid that percolates through the saturated column is kept at an unsteady-state flow regimen in which both the head and the discharged volume vary during the test. In the falling-head test method, a cylindrical soil sample of cross-sectional area A and length L is placed between two highly conductive plates. The soil sample column is connected to a standpipe of cross-sectional area a, in which the percolating fluid is introduced into the system. Thus, by measuring the change in head in the standpipe from H₁ to H₂ during a specified interval of time t, the saturated hydraulic conductivity can be determined as follows (Klute and Dirksen 1986):

The lower limit of K, which can be measured in a falling-head permeameter, is about 1 × 10^-2 m/yr. This value corresponds approximately to the lower limit of conductivity of silts and coarse clays (Klute and Dirksen 1986).

A common problem encountered in using either the constant-head or falling-head test with the permeameter is related to the degree of saturation achieved within the soil samples during the test. Air bubbles are usually trapped within the pore space, and although they tend to disappear slowly by dissolving into the deaerated water, their presence in the system may alter the measured results. Therefore, after using these instruments to measure K, it is always recommended that the degree of saturation of the sample be verified by measuring the sample's volumetric water content and comparing the result with the total porosity calculated from the particle density.

For a more accurate laboratory measurement of K in soil samples in which the presence of air bubbles becomes critical, the conductivity test with back pressure is recommended. In this method, additional pressure (back pressure) is applied to the pore fluid of the soil sample, which reduces the size of the gas bubbles in the pores, and, consequently, increases the degree of water saturation.

5.2.2 Field Methods

The several methods developed for in-situ determination of saturated hydraulic conductivity of soils can be separated into two groups: (1) those that are applicable to sites near or below a shallow water table and (2) those that are applicable to sites well above a deep water table or in the absence of a water table. More specifically, these groups are applicable to sites located, respectively, in the saturated and unsaturated zones of the soil. In either group (similar to the laboratory methods), the determination of K is obtained from Darcy's law after measuring the gradient of the hydraulic head at the site and the resulting soil water flux. Table 5.5 lists several standard methods used for in-situ determination of K in saturated and unsaturated regions of the soil.

5.2.2.1 Field Methods Used in Saturated Regions of the Soil

Many in-situ methods have been developed for determining the saturated hydraulic conductivity of saturated soils within a groundwater formation under unconfined and confined conditions. These methods include (1) the auger-hole and piezometer methods, which are used in unconfined shallow water table conditions (Amoozegar and Warrick 1986), and (2) well-pumping tests, which were primarily developed for the determination of aquifer properties used in the development of confined and unconfined groundwater systems (EPA 1986).

5.2.2.1.1 Auger-Hole Method. The auger-hole method is the field procedure most commonly used for in-situ determination of saturated hydraulic conductivity of soils. This method has many possible variations (Amoozegar and Warrick 1986). In its simplest form, it consists of the preparation of a cavity partially penetrating the aquifer, with minimal disturbance of the soil. After preparation of the cavity, the water in the hole is allowed to equilibrate with the groundwater; that is, the level in the hole becomes coincident with the water table level. The actual test starts by removing the entire amount of water from the hole and by measuring the rate of the rise of the water level within the cavity.

Because of the three-dimensional aspect of the flow pattern of the water near the cavity, there is no simple equation for accurately determining the conductivity. Numerous available semiempirical expressions, however, can be used for approximating the saturated hydraulic conductivity for different soil configurations. These expressions are functions of the geometrical dimensions of the auger hole and the aquifer and the measured rate at which the water level in the hole changes with time (Amoozegar and Warrick 1986).

The auger-hole method is applicable to an unconfined aquifer with homogeneous soil properties and a shallow water table. In its simplest form, this method provides an estimate of the average horizontal component of the saturated hydraulic conductivity of the soil within the aquifer. Enhanced variations of the method have been developed to account for layered soils and for the determination of either horizontal or vertical components of saturated hydraulic conductivity. Results obtained by the auger-hole method are not reliable for cases in which (1) the water table is above the soil surface, (2) artesian conditions exist, (3) the soil structure is extensively layered, and (4) highly permeable small strata occur.

5.2.2.1.2 Piezometer Method. The piezometer method, like the auger-hole method, is applicable for determining the saturated hydraulic conductivity of soils in an unconfined aquifer with a shallow water table level. Unlike the auger-hole method, however, the piezometer method is appropriately designed for applications in layered soil aquifers and for determining either horizontal or vertical components of the saturated hydraulic conductivity.

This method consists of installing a piezometer tube or pipe into an auger hole drilled through the subsurface system without disturbing the soil. The piezometer tube should be long enough to partially penetrate the unconfined aquifer. The walls of the piezometer tube are totally closed except at its lower extremity, where the tube is screened open to form a cylindrical cavity of radius r and height h_c within the aquifer. The water in the piezometer tube is first removed to clean the system and is then allowed to equilibrate with the groundwater level.

Similar to the auger-hole method, the piezometer method is conducted by removing the water from the pipe and then measuring the rate of the rise of the water within the pipe. The saturated hydraulic conductivity is then evaluated as a function of the geometrical dimension of the cavity in the piezometer tube, the dimensions of the aquifer, and the measured rate of rise of the water table in the tube. The value for the conductivity is calculated with the help of a nomograph and tables (Amoozegar and Warrick 1986).

Depending on the relative length (h_c) of the cavity as compared with its radius (r), the piezometer method can be used to determine the horizontal or vertical component of the saturated hydraulic conductivity. Thus, if h_c is large compared to r, the results obtained reflect the horizontal component of K. Otherwise, if h_c is small compared to r, then the vertical component of K is estimated.

The piezometer method is especially suitable for determining the conductivity of individual layers in stratified subsurface systems.

5.2.2.1.3 Well-Pumping (Slug) Methods. The well-pumping (slug) test is applicable for in-situ determination of the saturated hydraulic conductivity in soil materials of unconfined and confined aquifers. This method consists of removing a slug of water instantaneously from a well and measuring the recovery of the water in the well. Variations of the well-pumping test, called single-well tests (EPA 1986), are listed in Table 5.5.

In contrast to the auger-hole and piezometer methods, the results of which reflect an in-situ average of a relatively small region of soil around the created cavity in the soil, well-pumping tests also provide an in-situ representation of the soil hydraulic conductivity, but averaged over a larger representative volume of the soil. The measured results of K primarily reflect the value in the horizontal direction. (Further references for these methods can be found in EPA [1986], Freeze and Cherry [1979], and Amoozegar and Warrick [1986].)

5.2.2.2 Field Methods Used in the Unsaturated Region of the Soil

Measuring the saturated hydraulic conductivity of unsaturated soils located above the water table (or in the absence of a water table) by in-situ methods is more difficult than measuring K for saturated soils. The important difference is that the original unsaturated soil must be artificially saturated to perform the measurements. An extra large quantity of water may be needed to saturate the medium, which results in a more elaborate and time-consuming measurement. The results of these in-situ measurements of K are commonly called the field-saturated hydraulic conductivity.

Many in-situ methods have been developed for determining the field-saturated hydraulic conductivity of soil materials within the unsaturated (vadose) zone of the soil. As listed in Table 5.4, the available standard methods for measuring field-saturated K include (1) the shallow-well pump-in or dry auger-hole, (2) the double-tube, (3) the ring infiltrometer, (4) the air-entry permeameter, and (5) the constant-head test in a single drill hole. A complete guide for comparing these standard methods is presented in ASTM D5126-90, Standard Guide for Comparison of Field Methods for Determining Hydraulic Conductivity in the Vadose Zone (ASTM 1992n). Further detailed discussion on these standard methods can also be found in Amoozegar and Warrick (1986).

5.3 RESRAD DATA INPUT REQUIREMENTS

In RESRAD, the user is requested to input a saturated hydraulic conductivity value in units of meters per year (m/yr) for three soil materials: contaminated, unsaturated, and saturated zones.

The vertical infiltration of water within the contaminated zone and through the unsaturated region of the soil, the subsequent vertical leaching, and the transport of contaminants into the underlying aquifer are the important aspects of the problem being modeled. Consequently, in RESRAD, the saturated hydraulic conductivity values related to the contaminated and unsaturated zones of the soil should represent the vertical component of K. For isotropic soil materials, the vertical and horizontal components of K are the same; for anisotropic soils, however, the vertical component of K is typically one or two orders of magnitude lower than the horizontal component.

The major concern within the saturated zone is related to the horizontal transport of the contaminants that have infiltrated through the unsaturated zone and reached the aquifer. Therefore, the input value for the saturated hydraulic conductivity (K) of the soil material in the saturated zone should reflect the horizontal component of K.

The estimation of the values of K to be used in RESRAD can be performed at different levels of site-specific accuracy, depending on the amount of information available. For generic use of the code, a set of default values of K is defined as 10 m/yr for the contaminated and unsaturated zones and 100 m/yr for the saturated zone. These values approximately represent the condition of an anisotropic sedimentary soil material, that is, silt, loess, or silty sand, in which the vertical component of K is one order of magnitude lower than the horizontal component.

If the geological stratigraphy and the soil textures at the site are known, a better (i.e., more accurate and site-specific) estimation of K can be performed with the help of Tables 5.1, 5.2, 5.3, or 5.4. However, if values in the literature are used in place of actual site data, no more than one significant digit is appropriate.

For an accurate site-specific estimation of the input data for RESRAD, the values of K should be measured either in the laboratory or in field experiments according to one of the standard methods listed in Table 5.5.

Because of the intrinsic difficulties of the methods available for in-situ measurements of field-saturated K in unsaturated regions of the soil, it is recommended that laboratory methods be used for determining the vertical component of K in the contaminated and unsaturated zones. In these cases, either variation of the constant-head or falling-head method can be used, depending solely on the actual values of K being measured. As mentioned previously, the constant-head method is more applicable for large values of K (in the range of 10⁰-10⁶ m/yr), and the falling-head method is more applicable for lower values of K (in the range of 10^-2-10² m/yr).

Determination of the horizontal component of K in the saturated zone of the soil can be accomplished either by laboratory (i.e., constant-head and falling-head) or field methods (i.e., auger-hole, piezometer, and well-pumping). In the laboratory, the value of the horizontal component of K in cohesionless soil materials can be approximated by the conductivity of a disturbed soil sample obtained by the permeameter method. For cohesive soil materials, the undisturbed cohesive soil sample can then be oriented in the horizontal direction to obtain the appropriate value of K. In the field, most of the methods available for the determination of K in the saturated zone will reflect the value in the horizontal direction.