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Unsaturated Flow

Unsaturated Flow. Groundwater Hydraulics Daene C. McKinney. Summary. Distribution of water in subsurface Unsaturated Flow Field Capacity Wilting Point Water Content Piezometric Head Control Volume Analysis Continuity Equation Darcy’s Law Richard’s Equation

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Unsaturated Flow

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  1. Unsaturated Flow Groundwater Hydraulics Daene C. McKinney

  2. Summary • Distribution of water in subsurface • Unsaturated Flow • Field Capacity • Wilting Point • Water Content • Piezometric Head • Control Volume Analysis • Continuity Equation • Darcy’s Law • Richard’s Equation • Soil Moisture Characteristic Curves • Brooks and Corey Model • Van GenuchtenModel

  3. Distribution of Subsurface Water Moisture Profile Soil Profile Description • Unsaturated Zone • Water held by capillary forces, water content near field capacity except during infiltration • Capillary fringe • Saturated at base • Field capacity at top • Saturated Zone • Fully saturated pores

  4. Unsaturated Flow • Flow of water and water vapor through soil • Void space is partially filled with air • Flow of 2 immiscible fluids (water and air) • Air is almost immobile Unsaturated Soil Saturated Soil water solid air

  5. Field Capacity • After infiltration - saturated • Drainage • Coarse soils: a few hours • Fine soils: a 2-3 days • After drainage • Large pores: air and water • Smaller pores: water only • Soil is at field capacity • Water and air are ideal for plant growth After drying After drainage Saturated

  6. Wilting Point • After drainage • Root suction & evaporation • Soil dries out • More difficult for roots • After drying • Root suction not sufficient for plants – plant wilts • Wilting Point= soil water content when plant dies After drying After drainage Saturated

  7. Water Content of Soil Saturated Soil • Porosity – Pores space in total volume • Moisture content – Water in total volume water solid air Unsaturated Soil

  8. Piezometric Head • Capillary Pressure • A function of moisture content • Capillary Pressure Head • Piezometric Head Air Note: The Book uses: so Solid Solid Water r

  9. Soil Water Characteristic Curves • Capillary pressure head • Function of: • Pore size distribution • Moisture content Vadose Zone Porosity Capillary Zone

  10. Example • Given - unsaturated hydraulic conductivity • Find - Flux of water in the soil z Ground Unsaturated Zone z1 z2 1 2 Water Table Aquifer

  11. Example z Ground Unsaturated Zone Use an average head for conductivity between points z1 z2 1 2 Water Table Aquifer

  12. Soil Water Characteristic Curves • Capillary pressure head • Pore size distribution • Moisture content • Irreducible water content • Water remaining at high capillary head • Critical head • Water won’t drain until this head is reached • Normalized (effective) water content

  13. Soil Water Characteristic Curve 105 1.0 104 0.8 1000 0.6 Capillary pressure head (cm) Hydraulic Conductivity (cm/d) 100 0.4 Critical head 10 0.2 0 1 0 0.3 0.2 0.4 0.5 0.1 Water content (vol./vol.)

  14. Brooks and Corey Model • Water content vs capillary pressure head on log-log plots as straight line • l = pore-size distribution factor (neg. slope of line) • Good for coarse soils with narrow pore size distribution (large l) l Capillary pressure head (cm) Water content (vol./vol.)

  15. Van Genuchten Model • Van Genuchten • m is estimated from data • Works well for most soils Capillary pressure head (cm) Water content (vol./vol.)

  16. Threshold Entry Heads for Different Soils Capillary pressure head (cm) After Hubbert, 1953 Water content (vol./vol.)

  17. Example Brooks and Corey Van Genuchten cm cm Singh, p. 31

  18. Example

  19. Infiltration Precipitation • NOTE: z vertical DOWN! • Precip infiltrating into soil • Factors affecting • Condition of soil surface • vegetative cover • soil properties • hydraulic conductivity • antecedent soil moisture • Four zones • Saturated zone • Transmission zone • Wetting zone • Wetting front Saturation Zone Transition Zone Transmission Zone Wetting Zone Wetting Front z, depth

  20. Infiltration • Infiltration rate • Rate at which water enters the soil at the surface • Cumulative infiltration • Accumulated depth of water infiltrating during given time period Potential Infiltration Infiltration rate, f Rainfall Actual Infiltration Time

  21. Infiltration Precipitation Precipitation Ground Surface Ground Surface Saturation Zone Transition Zone Wet Zone Transmission Zone Wetting Front Wetting Zone Dry Zone Wetting Front Dry Soil depth

  22. Green – Ampt Infiltration Precipitation Ground Surface Wet Zone Wetting Front Dry Zone

  23. Green – Ampt Infiltration NOTE: z vertical DOWN for G-A! Precipitation Ground Surface Wet Zone Wetting Front Dry Zone

  24. Ground Surface Wet Zone Wetting Front Dry Zone Green – Ampt Infiltration (Cont.) • @ Ground surface • @ Wetting front Infiltration Rate

  25. Green – Ampt Infiltration (Cont.) Ground Surface Wetted Zone Wetting Front Dry Zone Infiltration Rate Integrate Cumulative Infiltration Nonlinear equation, requiring iterative solution. See: http://www.ce.utexas.edu/prof/mckinney/ce311k/Lab/Lab8/Lab8.html And: http://www.ce.utexas.edu/prof/mckinney/ce311k/homework/Solutions-F06/Lab8.pdf

  26. Green-Ampt Soil Parameters • Green-Ampt model requires • Hydraulic conductivity • Porosity • Wetting Front Suction Head Normalized (effective) water content Effective Porosity

  27. Green-Ampt Parameters(Data from Applied Hydrology, Table 4.3.1)

  28. Green-Ampt Porosity (Data from Table 4.3.1) 0.45 0.09 • Total porosity ~ 0.45 • Clay soils retain water in ~ 20% of voids when dry • Other soils retain water in ~ 6% of voids when dry 0.03

  29. Conductivity and Suction Head(Data from Table 4.3.1) Conductivity, K (cm/hr) Sand Loamy Sand Sandy Loam Suction Head, ψ (cm) Silt Loam Sandy Clay Loam Loam Silty Clay Loam Clay Loam Silty Clay Sandy Clay Clay

  30. Ponding Time • Up to the time of ponding • all rainfall has infiltrated • i = rainfall rate Potential Infiltration Infiltration rate, f Rainfall Actual Infiltration Time Accumulated Rainfall Cumulative Infiltration, F Infiltration Time

  31. Example • Silty-Loam soil • 30% effective water content • 5 cm/hr rainfall intensity Normalized (effective) water content

  32. Summary • Distribution of water in subsurface • Unsaturated Flow • Field Capacity • Wilting Point • Water Content • Piezometric Head • Darcy’s Law • Soil Moisture Characteristic Curves • Brooks and Corey Model • Van GenuchtenModel • Infiltration • Green-Ampt method

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