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Hydraulic conductivity Learning Objectives: 1. Know the definition of soil hydraulic conductivity 2. Know the dependency of the unsaturated hydraulic conductivity on soil water content and pressure head 3. be able to identify proper procedures for measuring saturated and unsaturated hydraulic conductivity 4. Know the difference between intrinsic permeability and hydraulic conductivity Hydraulic conductivity, dimensional units of L/T (e.g., m/s, in/h), is the proportionality factor in Darcy's law as applied to viscous flow of water in soil (i.e., the flux of water through a unit cross sectional area of the soil per unit time under a unit hydraulic gradient). Hydraulic conductivity can be defined as a measure of the ability of soil to transmit water. When the soil is saturated, hydraulic conductivity is called saturated hydraulic conductivity and is generally denoted by Ks or Ksat. For any given position in the soil and at a given time Ksat is a constant. The unsaturated hydraulic conductivity (Kunsat), on the other hand, depends on soil water content and soil water pressure head [K(h), K(Θ)]. Figure 31 shows the hydraulic conductivity as a function of soil water tension (soil water pressure head with a positive value) of four different soils. Because of soil water hysteresis, Kunsat depends on whether a soil is wetting or drying (Kunsat hysteresis). The soil intrinsic permeability is independent of the properties of the fluid flowing through the soil. 2 2 Intrinsic permeability has the dimensional units of L (e.g., cm ), and is given by k = Kη/ρg where K is the saturated hydraulic conductivity, η is the viscosity of water [units of poise, g/(cm s), or 2 3 2 dyne s/cm ], ρ is the water density (g/cm ), and g is the gravitational acceleration (980 cm/s ). Figure 31. Hydraulic conductivity as a function soil water tension for four soils (after Bouma, 1975). A. Measuring infiltration and saturated hydraulic conductivity A number of methods are available for measuring infiltration rate in situ (in the field), and saturated (Ksat) and unsaturated (Kunsat) hydraulic conductivities in situ or in the laboratory using intact or repacked samples. In general, the available methods for measuring Kunsat are more difficult and time consuming than the procedures for measuring Ksat. Furthermore, to be useful, Kunsat must be determined at a number of soil water contents or pressure heads (see Fig. 31). [NOTE: 1. A number of procedures for measuring Ksat and Kunsat are presented in: Amoozegar A., and G. W. Wilson. 1999. Methods for Measuring Hydraulic Conductivity and Drainable Porosity. p. 1149-1205. In Skaggs and van Schilfgaarde (ed). Drainage Monograph No. 8. ASA, CSSA, and SSSA, Madison, WI. 2. It has been shown that saturated hydraulic conductivity for a given soil horizon within a field is generally log normally distributed (for examples see Warrick and Nielsen, 1980). Furthermore, an analysis of the statistical distribution of K sat requires a relatively large number of measurements. Because of the relative difficulty and cost associated with measuring Ksat, the number of measurements at any given site may be limited. In analyzing the Ksat data for a field, one should keep in mind the variability of other soil properties that were determined as part of the soil/site evaluation. ] Only selected number of procedures for measuring Ksat will be discussed here. To learn about the procedures listed below see Chapter 37 of the Drainage Monograph handout. INFILTRATION RATE: Intake rate infiltrometer o Single-Cylinder (Ring) Infiltrometer o Double-Cylinder Infiltrometer (Fig. 32) o Only suitable for flat areas Figure 32. Schematic diagram of a double cylinder infiltrometer. Rainfall Simulator Infiltration can also be measured in a relatively large area using a rainfall simulator. In this procedure a border is placed around an area and a rainfall simulator is used to spray water at a rate slightly above the infiltration rate of the soil. Runoff from the plot inside the border is collected and the infiltration rate is measured by subtracting the volume of runoff from the amount of water applied to the plot. HYDRAULIC CONDUCTIVITY: o Saturated Hydraulic Conductivity -- Ksat, Ks Field method for below a water table (saturated zone) Do not need water Quality and temperature of water Water flow analysis is complicated Sample size and variability Auger-hole method Piezometer method Field method for above the water table (unsaturated zone) Reasons for measuring Ksat of the unsaturated zone Water flow analysis for designing drainage systems during the time when water table is low Ground water mounding analysis for waste disposal systems (e.g., large septic systems) Need water Need special equipment Water flow analysis is complicated Sample size and variability Quality of water Temperature of water Constant-head well permeameter method (also Known as borehole permeameter method) Air-entry permeameter method Cylinder infiltrometer method Laboratory Techniques Intact sample - Repacked sample Sample size Length and cross sectional area Variability of measured Ksat values Variation in flow rate and Ksat during measurement period Advantages Water flow analysis is relatively simple (use Darcy's law directly) Disadvantages May require special apparatus Sample size may be too small, variability may be high o Unsaturated Hydraulic Conductivity -- Kunsat, K(Θ), K(h) Depends on soil water content and potential Need to measure it at different soil water content or potential Field and laboratory techniques Difficult to perform and time consuming Requires special apparatus Using the values for design purposes Field (in situ) Techniques Instantaneous profile method Tension infiltrometer method Crust method Laboratory Techniques One-step outflow method Hot-air method Two-plate method Crust method o Methods for measuring saturated hydraulic conductivity of landfill liners: Test Pad Laboratory Methods Fixed wall permeameter Triaxial permeameter Field Methods Sealed double-cylinder (ring) infiltrometer Two stage borehole test (Boutwell Method) REMARKS: o Understanding the reasons for measuring e.g., Confirming loading rates for septic system e.g., Permeability rating o Selection of an appropriate method for measuring hydraulic conductivity Unsaturated zone (above water table) Saturated zone (below water table) Capillary fringe (Is it saturated or unsaturated?) o Following the procedure for the selected method Use of the right equipment Use of the right (or Known) diameter hole or sample size Reaching steady-state o Selecting an appropriate model for calculating Ksat Complicated models Simplifying assumptions Required parameter(s) Average hydraulic conductivity for layered soils: Consider a soil to be composed of n layers, with thicK ness and saturated hydraulic conductivity of each layer denoted by Li and Ki, where i = 1, 2, ..., n, respectively. When the flow is perpendicular to the layering of the soil (series flow), the net flux for water passing through each of the horizons under steady-state condition is equal to the flux through all the horizons combined. The average Ksat in the direction of the flow (referred to as harmonic mean) is obtained by (Luthin, 1978) Ksat = L/(L1/K1 + L2/K2 + ... +Ln/Kn)  where L = L1 + L2 + ... +Ln. If the flow direction is parallel to the layers (parallel flow), the average Ksat in the direction of the flow is the weighted average of the Ksat values (K1, K2 ...KMn) for all the layers (referred to as arithmetic mean) given by Ksat = (L1K1 + L2K2 + ... + LnKn)/L  For cases where the flow is not necessarily parallel or perpendicular to the layers, Ksat in the direction of the flow is somewhere between the average of the Ksat values for parallel and series flows. The geometric mean falls somewhere between the arithmetic and harmonic mean values, and for equally thick layers the geometric mean defined by 1/n Ksat-g = (K1K2...Kn)  can be used for obtaining an average Ksat value for the soil (Bouwer and Jackson, 1974).
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