Groundwater Hydraulics Daene C. McKinney 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 Soil Moisture Characteristic Curves Brooks and Corey Model Van Genuchten Model

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

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 Saturated Soil Unsaturated Soil water solid air

Field Capacity After infiltration - saturated Drainage After 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

Wilting Point After drainage Soil dries out After drying 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

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

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

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

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

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

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

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 1 0.1 0.2 0.3 0.4 0.5 Water content (vol./vol.)

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.)

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

Threshold Entry Heads for Different Soils Medium Mean Grain Size Diameter (mm) yb (cm) Clay 0.000 < 0.004 > 1000 Silt 0.004 - 0.063 65 - 1000 Sand 0.063 - 2.00 2.1 - 65 Coarse Sand 2.4 - 4.0 1.0 - 2.1 Capillary pressure head (cm) After Hubbert, 1953 Water content (vol./vol.)

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

Example

Infiltration NOTE: z vertical DOWN! Precip infiltrating into soil Transition Zone Saturation Zone z, depth Wetting Zone Transmission Zone Wetting Front 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

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

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

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

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

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

Green – Ampt Infiltration (Cont.) Wetted Zone Wetting Front Ground Surface 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

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

Green-Ampt Parameters (Data from Applied Hydrology, Table 4.3.1) Texture Porosity f Irriducible water content q0 Effective Porosity f-q0 Suction Head ψ (cm) Conductivity K (cm/hr) Sand 0.437 0.020 0.417 4.95 11.78 Loamy Sand 0.036 0.401 6.13 2.99 Sandy Loam 0.453 0.041 0.412 11.01 1.09 Loam 0.463 0.029 0.434 8.89 0.34 Silt Loam 0.501 0.015 0.486 16.68 0.65 Sandy Clay Loam 0.398 0.068 0.330 21.85 0.15 Clay Loam 0.464 0.155 0.309 20.88 0.10 Silty Clay Loam 0.471 0.039 0.432 27.30 Sandy Clay 0.430 0.109 0.321 23.90 0.06 Silty Clay 0.470 0.047 0.423 29.22 0.05 Clay 0.475 0.090 0.385 31.63 0.03

Green-Ampt Porosity (Data from Table 4.3.1) 0.09 0.45 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

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

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

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

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 Genuchten Model Infiltration Green-Ampt method