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Conductivity Testing of Unsaturated Soils A Presentation to the Case Western Reserve University May 6, 2004 By Andrew G. Heydinger Department of Civil Engineering

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2 Purpose of Presentation Present fundamental concepts necessary for understanding mechanics of unsaturated flow. Discuss conductivity testing of unsaturated soils.

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3 Some Fundamental Concepts Some Fundamental Concepts

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4 Mechanics of Unsaturated Soils Mechanics of Unsaturated Soils Unsaturated soils are distinguished from saturated soils by negative pore water pressures, soil suction, that develop. The negative pore pressures affect soil properties and behavior.

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5 Matric Suction Defined Component of the soil moisture suction associated with the capillary head. Matric suction = (u a - u w ) u a = soil air pressure u w = soil water suction pressure.

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6 Importance of Matric Suction Soil matric suction is a primary stress state variable used to characterize unsaturated soil behavior. Relationships required to model flow in unsaturated soils are given as functions of pore water pressure or matric suction.

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7 Mass Balance Equation for Water Phase Derived assuming homogeneous, isotropic non-deforming medium and incompressible, homogeneous fluid. Volumetric water content depends on pore water pressure, ( ).

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8 Darcy’s Law A flow law relating the flow rate to the driving potential is needed. Flow depends on a coefficient, hydraulic conductivity ( ), and the total head gradient ( ).

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9 Hydraulic Conductivity Hydraulic conductivity is the coefficient obtained from a flow or conductivity test. Hydraulic conductivity depends on medium and fluid properties. Hydraulic conductivity depends on fluid pressure, K( ).

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10 Flow Equation The two required functions are K( ) and ( ) where is the pressure head. The functions can be given in terms of pore water pressure, pressure head or matric suction.

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11 Soil-Water Retention Function After Mualem (1976)

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12 Conductivity Function After Mualem (1976)

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13 Relative Conductivity After Brooks and Corey (1964)

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14 Modeling With the Functions Both functions exhibit hysteresis during drying and wetting processes. Mathematical expressions are used to approximate the experimental curves, using the boundary drying or wetting curve.

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15 van Genuchten (1980) Equations The curve fitting parameters, n and m, and other parameters are obtained from the curves.

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16 Laboratory Testing

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17 Variation of Matric Suction in the Laboratory To vary matric suction, both the soil air and soil water pressures are increased (axis translation technique). Matric suction is computed as the difference between the two pressures, always positive.

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18 High Air Entry Ceramic Material A ceramic material is used to prevent flow of air from the soil. Once the material is saturated, the capillary pressure in the material prevents air from flowing through the material and out of the soil.

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19 Direct Measurement of Soil Moisture Suction Tensiometers. Directly measure pore water pressures but are limited to 90 centibars pressure. Thermocouple Psychrometers. Measure relative humidity of the soil to compute the total suction, to high suction values.

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20 Indirect Measurement of Soil Moisture The physical properties of soil minerals do not vary significantly, but they differ significantly from the properties of pure water. Consequently, soil moisture content or matric suction are correlated to physical properties of soil.

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21 Indirect Measurement Sensors The types of sensors include: o thermal conductivity sensors o time domain reflectomety or frequency domain sensors (dielectric properties) o electrical resistivity sensors

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22 Measurement Accuracy Sensor calibrations are nonlinear. At low moisture contents, large changes in matric suctions occur with only small changes in water content, so the accuracy of the sensors is reduced.

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23 Modified Triaxial Cell Triaxial cells were modified by adding two ports and a load cell in line with the loading piston.

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24 Water Volume Change Indicator Four burettes and a gang of zero volume change valves are used to measure flow.

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25 Diffused Air Volume Indicator A burette is used to collect and measure air volume. An exit tube maintains constant pressure.

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26 Steady State Conductivity Test Matric suction is varied and steady state flow is induced to measure conductivity. Soil air and water pressures and outflow rates are measured. Tests are very difficult and time consuming for fine grained soils.

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27 Instantaneous Profile Test Water or air is injected into the soil at steady rates and water content or pore water pressures are measured at several locations at various times. Water content and hydraulic conductivity calculations depend on the test procedure and type of measurements.

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28 Single-Step and Multi-Step Outflow Tests The soil air pressure is varied and the water outflow or inflow rates are measured. The use of sensors is optional. Hydraulic functions are computed using an analytical or numerical solution.

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29 Geo-centrifuge Testing Geo-centrifuge Testing Centrifuges are used for evaluating petroleum yields from rock cores, for measuring hydraulic properties of soils and contaminant transport in soil. Large and small-scale geo-centrifuges are used. Include sensors and different methods of analysis to compute hydraulic properties.

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30 Laboratory Tests at the University of Toledo Multi-step tests are conducted using the modified triaxial apparatus. Hydraulic conductivity is computed from analytical solution that uses soil diffusivity and that accounts for the system impedance.

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31 Analytical Solution for Diffusivity Analytical Solution for Diffusivity The governing equation for 1-D flow is Hydraulic conductivity is computed from

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32 Analysis Procedure Normalized outflow is plotted versus a non-dimensional time factor. Parameters are varied in the equation for theoretical outflow until there is good agreement between theoretical and experimental curves. Hydraulic conductivity is computed from the diffusivity used in the calculation.

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33 Comparison of Measure and Theoretical Outflow

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34 Soil-Water Retention Curve

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35 Hydraulic Conductivity Function 2.00E-10 1.20E-09 2.20E-09 3.20E-09 4.20E-09 5.20E-09 6.20E-09 7.20E-09 0100200300400500 Matric Suction (kPa) Conductivity (cm/sec)

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36 Inverse Modeling Numerical solutions that use finite difference or finite element procedures are used to back calculate the hydraulic functions using inverse modeling techniques. Parameters required for the curve fitting equations are obtained using optimization techniques.

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37 Vadose Zone Models

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38 Future Work

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39 Laboratory Procedures Procedures for multi-step outflow tests that do not require instrumented samples. Measurement of system impedance. Measurement of saturated/unsaturated hydraulic conductivity.

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40 Data Analysis Comparison of hydraulic functions determined from analytical solution with known system impedance to numerical modeling of multi-step outflow tests using inverse modeling. Use of numerical modeling to investigate hysteresis effects.

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41 Beyond the Laboratory Modeling flow in the vadose zone using programs that couple heat and moisture flow and contaminant transport. Investigation of the movement of both liquid and vapor transport in the vadose zone.

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z = -50 cm, ψ = -100 cm, h = z + ψ = -50cm + -100cm = -150 cm Which direction will water flow? 25 cm define z = 0 at soil surface h = z + ψ = 0 + -200cm.

z = -50 cm, ψ = -100 cm, h = z + ψ = -50cm + -100cm = -150 cm Which direction will water flow? 25 cm define z = 0 at soil surface h = z + ψ = 0 + -200cm.

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