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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 - PowerPoint PPT Presentation
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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