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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

Unsaturated Flow

Groundwater Hydraulics

Daene C. McKinney

summary
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
distribution of subsurface water
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 flow1
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

field capacity
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

wilting point
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

water content of soil
Water Content of Soil

Saturated Soil

  • Porosity – Pores space in total volume
  • Moisture content – Water in total volume

water

solid

air

Unsaturated Soil

piezometric head
Piezometric Head
  • Capillary Pressure
    • A function of moisture content
  • Capillary Pressure Head
  • Piezometric Head

Air

Note: The Book uses:

so

Solid

Solid

Water

r

soil water characteristic curves
Soil Water Characteristic Curves
  • Capillary pressure head
  • Function of:
    • Pore size distribution
    • Moisture content

Vadose Zone

Porosity

Capillary Zone

example
Example
  • Given - unsaturated hydraulic conductivity
  • Find - Flux of water in the soil

z

Ground

Unsaturated

Zone

z1

z2

1

2

Water Table

Aquifer

example1
Example

z

Ground

Unsaturated

Zone

Use an average head for conductivity between points

z1

z2

1

2

Water Table

Aquifer

soil water characteristic curves1
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
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.)

brooks and corey model
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 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
Threshold Entry Heads for Different Soils

Capillary pressure head (cm)

After Hubbert, 1953

Water content (vol./vol.)

example2
Example

Brooks and Corey

Van Genuchten

cm

cm

Singh, p. 31

infiltration
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

infiltration1
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

infiltration2
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

green ampt infiltration
Green – Ampt Infiltration

Precipitation

Ground Surface

Wet

Zone

Wetting Front

Dry

Zone

green ampt infiltration1
Green – Ampt Infiltration

NOTE: z vertical DOWN for G-A!

Precipitation

Ground Surface

Wet

Zone

Wetting Front

Dry

Zone

green ampt infiltration cont

Ground Surface

Wet Zone

Wetting Front

Dry

Zone

Green – Ampt Infiltration (Cont.)
  • @ Ground surface
  • @ Wetting front

Infiltration Rate

slide25

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

green ampt soil parameters
Green-Ampt Soil Parameters
  • Green-Ampt model requires
    • Hydraulic conductivity
    • Porosity
    • Wetting Front Suction Head

Normalized (effective)

water content

Effective Porosity

green ampt porosity data from table 4 3 1
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

conductivity and suction head data from table 4 3 1
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

ponding time
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

example4
Example
  • Silty-Loam soil
  • 30% effective water content
  • 5 cm/hr rainfall intensity

Normalized (effective)

water content

summary1
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