Lecture 18
Unsaturated Flow Theory
Fetter 6.6-6.7
Darcy’s Law is valid for unsaturated flow of water
K depends on 
(Volumetric moisture content) and 
(Matric) Moisture Potential (
) tension on the pore water in the unsaturated
zone due to attraction of soil water interface ® Negative pressure.
Gravity Potential (Z) potential due to position.
Soil-Water Retention Curve-
| f - Total soil water potential | |
f  |
Typical Soil- water retention curve-
Experimentally
dry a saturated soil  |
||
| Bubbling pressure (hb) = point on a curve where water starts to drain. | ||
| Residual moisture content -point on curve minimum water content unequal to field capacity. | ||
Effects of sorting on a retention curve
The bubbling pressure in relation to sorting
| Usually construct Drying Curve apply suction. | |
| Wetting Curve resaturate sample. | |
| Typically the curves are not the same. | |
Caused by
| (1) Geometry of pores- harder to refill some pores than to drain, | |
| " ink bottle effect" | |
| (2) Air trapped in pores during wetting, eventually air is dissolved | |
| May be aided by shrinking and swelling of soils. |
Therefore, to know must know if soil is wetting or drying.
Example of wetting front
 (given) |
Rainfall event infiltration starts.
Infiltration stops, vertical flow in soil.
Unsaturated flow -K(Ov) controls flow.
Field capacity = 0.06 (
)
Important to know when there is flow in the Vadose Zone.
Hard to monitor if no flow
Different soil-water sampling devices work at different ranges.
Porous Ceramic cup lysimeter - 0-60 centibars
Typically measure Ks Double ring infiltrometers.
Measure Ks and K(
)
| Guelph permeameter. |
Hualapai Reservation
| 0.1 inch recharge per year. |
| Average rainfall 9-13 inches, potential ET = 72-76 inches per year. | |
| Measured Spring outflow of 4cfs distributed over 600 mi2 surface recharge area of recharge. | |
| Assume: | |
| (1) Springs and seeps account for all discharge, | |
| (2) Negligible losses to ET on steeps slopes. | |
| (3) Q represents long term data. |
Summary Information on Vadose Hydraulic Conductivity Techniques
Technique |
Kb or Kunsat |
K Directionb |
Other Parameters Measured |
| Infiltration | |||
| Seepage Meters | Saturated | Undefined | I |
| Instantaneous Rate | Saturated | Undefined | I |
| Impoundment Water Budget | Saturated | Undefined | I |
| Sprinkler Infiltrometer | Saturated | Vertical | I |
| Infiltration Test Basins | Saturated | Undefined | I |
| Watershed Average | Undefined | Undefined | I |
| Watershed Empirical Relations | Undefined | Undefined | I |
| Infiltration Equations | Both | Vertical | I |
| Unsaturated Hydraulic Conductivity | |||
| Instantaneous Profile | Unsaturated | Vertical | D, F, K(f ), R |
| Draining Profile Methods | Unsaturated | Vertical | D, F, K(f ), R, S |
| Tension infiltrometers | Both | Vertical | I, D, F, K(f ), R, S |
| Crust-Imposed Steady Flux | Unsaturated | Vertical | I, F, K(f ) |
| Sprinkler/Dripper Methods | Unsaturated | Vertical | I, F, K(f ), R, S |
| Entrapped Air Method | Unsaturated | Vertical | I, F |
| Parameter Identification | Both | Undefined | R |
| Empirical Equations | Both | Undefined | Varies |
| Column-Crust | Both | Vertical | F, K(f ) |
| Saturated Hydraulic Conductivity Above Shallow Water Tablec | |||
| Cylinder Infiltrometers | Saturated | Vertical | I, S |
| Constant Head Borehole Infiltration | Saturated | Horizontal | S |
| Guelph Permeameter | Both | Vert./Hor. | K(f ), S |
| Air-Entry Permeameter | Both | Vertical | I, K(f ), S |
| Double Tube | Saturated | Vertical | -- |
| Cylinder Permeameter | Saturated | Vertical | -- |
| Infiltration Gradient | Saturated | Verticald | -- |
| Cube | Saturated | Vert./Hor. | -- |
| Column/Monoliths | Saturated | Vertical | -- |
| Boutwell Method | Saturated | Vert./Hor. | -- |
| Velocity Permeameter | Saturated | Vertical | -- |
| Percolation Test | -- | -- | -- |
| CP Porous Probe | Saturated | Horizontal | -- |
| Collection Lysimeter | Saturated | Vertical | F |
| Saturated Hydraulic Conductivity Above Deep Water Tablee | |||
| USBR single Well | Saturated | Undefined | -- |
| USBR Multiple-Well | Saturated | Horizontal | -- |
| Stephens-Neuman Single Well | Saturated | Undefined | -- |
| Air Permeability | Saturated | Undefined | -- |
| Packer Tests | Saturated | Vert./Hor. | -- |
D = diffusivity; F = Flux; I = Infiltration; K(f ) = hydraulic conductivity-pressure head relationship;
R = Retention (pressure-moisture relationship); S = Sorptivity.
aMost methods for measuring or estimating unsaturated hydraulic conductivity also can
be used to measure water flux in the vadose zone. Section 7.5 discusses the application
of these and other methods for measuring soil water flux.
bDirectional ratings are qualitative in nature. Different references might give different
ratings depending on site conditions and criteria used to define directionality.
cThese methods measure field-saturated or satiated hydraulic conductivity (Ks),
which is lower than saturated hydraulic conductivity, due to the presence of
entrapped air.
dDifferentiation of vertical and horizontal is possible when used with double tube
method.
eThe percolation test does not provide an accurate measure of saturated hydraulic
conductivity.
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ENV 302 - Lectures