Unsaturated FlowGroundwater 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• 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

Soil Profile DescriptionMoisture Profile

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

solid

water

Saturated Soil

air

Unsaturated Soil

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

SaturatedAfter

drainageAfter

drying

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

SaturatedAfter

drainageAfter

drying

• Porosity – Pores space in total volume

• Moisture content – Water in total volume

Water Content of Soil

solid water

Saturated Soil

air

Unsaturated Soil

Piezometric Head

• Capillary Pressure– A function of moisture content

• Capillary Pressure Head

• Piezometric Head

Solid SolidWater

Air

r

Note: The Book uses:

so

Soil Water Characteristic Curves• Capillary pressure head• Function of:

– Pore size distribution– Moisture content

PorosityVadose Zone

Capillary Zone

Example• Given - unsaturated hydraulic conductivity

• Find - Flux of water in the soil

zGround

UnsaturatedZone

AquiferWater Table

1

2

z1

z2

Example zGround

UnsaturatedZone

AquiferWater 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

104

1000

100

10

1

1.0

0.8

0.6

0.4

0.2

00.50.40.30.20.10

Capi

llary

pre

ssur

e he

ad (c

m)

Hydr

aulic

Con

ducti

vity

(cm

/d)

Critical head

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

Capi

llary

pre

ssur

e he

ad (c

m)

Water content (vol./vol.)

Van Genuchten Model• Van Genuchten

• m is estimated from data• Works well for most soils

Capi

llary

pre

ssur

e he

ad (c

m)

Water content (vol./vol.)

Threshold Entry Heads for Different Soils

After Hubbert, 1953

Medium

Mean Grain Size Diameter

(mm)yb

(cm)Clay 0.000 < 0.004 > 1000Silt 0.004 - 0.063 65 - 1000Sand 0.063 - 2.00 2.1 - 65Coarse Sand 2.4 - 4.0 1.0 - 2.1

Capi

llary

pre

ssur

e he

ad (c

m)

Water content (vol./vol.)

ExampleBrooks and Corey Van Genuchten

Singh, p. 31

cm cm

Example

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

25

50

75

100

125

150

Van GenuchtenBrooks-Corey

Moisture Content (vol./vol.)

Capi

llary

Pre

ssur

e He

ad (c

m)

Infiltration• 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

Transition ZoneSaturation Zone

z, depth

Wetting Zone

TransmissionZone

Wetting Front

Precipitation

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

Actual Infiltration

Rainfall

TimeIn

filtr

atio

n ra

te, f

i

Infiltration

Wet Zone

Wetting Front

Ground Surface

Dry Zone

z

Precipitation

Transition ZoneSaturation Zone

depth

Wetting Zone

TransmissionZone

Wetting Front

Precipitation

n

Dry Soil

Ground Surface

Green – Ampt Infiltration

zh

MoistureSoilInitialFront WettingtoDepth

i

L

WetZone

Wetting Front

Ground Surface

DryZone

L

i

z

Precipitation

Green – Ampt Infiltration

zh

WetZone

Wetting Front

Ground Surface

DryZone

L

i

z

PrecipitationNOTE: z vertical DOWN for G-A!

Green – Ampt Infiltration (Cont.)

• @ Ground surface• @ Wetting front

Wet Zone

Wetting Front

Ground Surface

DryZone

L

n

i

z

Infiltration Rate

Green – Ampt Infiltration (Cont.)

Wetted Zone

Wetting Front

Ground Surface

DryZone

L

i

z

Integrate

Infiltration Rate

Cumulative Infiltration

See: http://www.ce.utexas.edu/prof/mckinney/ce311k/Lab/Lab8/Lab8.htmlAnd: http://www.ce.utexas.edu/prof/mckinney/ce311k/homework/Solutions-F06/Lab8.pdf

Nonlinear equation, requiring iterative solution.

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)

TexturePorosity

f

Irriducible water

content 0

Effective Porosity

f-0

Suction Head ψ (cm)

Conductivity K (cm/hr)

Sand 0.437 0.020 0.417 4.95 11.78

Loamy Sand 0.437 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 0.10

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)

Sand

Loamy Sand

Sandy Loam

Loam

Silt Loam

Sandy Clay Loam

Clay Loam

Silty Clay Loam

Sandy Clay

Silty Clay

Clay

0.0 0.1 0.2 0.3 0.4 0.5

Residual Porosity

Effective Porosity

0.09 0.45

0.03

• Total porosity ~ 0.45

• Clay soils retain water in ~ 20% of voids when dry

• Other soils retain water in ~ 6% of voids when dry

Conductivity and Suction Head(Data from Table 4.3.1)

0 5 10 15 20 25 30 350.01

0.10

1.00

10.00

100.00

Suction Head, ψ (cm)

Conductivity, K (cm/hr) Sand

Clay

Silt Loam

Silty Clay Loam

Loamy Sand

Sandy Clay

Sandy Loam

Loam Sandy Clay LoamClay Loam

Silty Clay

Ponding Time

• Up to the time of ponding– all rainfall has infiltrated– i = rainfall rate

)( KiiKt f

p

y

Accumulated Rainfall Infiltration

Time

Cum

ulat

ive

Infil

trat

ion,

F

Potential Infiltration

Actual Infiltration

Rainfall

Time

Infil

trat

ion

rate

, f

i

pt

pp tiF *

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