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CE 394K.2 Hydrology. Infiltration Reading AH Sec 5.1 to 5.5 Some slides were prepared by Venkatesh Merwade Slides 2-6 come from http://biosystems.okstate.edu/Home/mkizer/C%20Soil%20Water%20Relationships.ppt. Soil Water Measurement. Neutron scattering (attenuation) - PowerPoint PPT Presentation
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CE 394K.2 Hydrology
InfiltrationReading AH Sec 5.1 to 5.5
Some slides were prepared by Venkatesh MerwadeSlides 2-6 come from http://biosystems.okstate.edu/Home/mkizer/C%20Soil
%20Water%20Relationships.ppt
• Neutron scattering (attenuation)Neutron scattering (attenuation)– Measures volumetric water content (Measures volumetric water content (vv))– Attenuation of high-energy neutrons by hydrogen nucleusAttenuation of high-energy neutrons by hydrogen nucleus– Advantages: Advantages:
• samples a relatively large soil sphere samples a relatively large soil sphere • repeatedly sample same site and several depths repeatedly sample same site and several depths • accurateaccurate
– Disadvantages: Disadvantages: • high cost instrument high cost instrument • radioactive licensing and safety radioactive licensing and safety • not reliable for shallow measurements near the soil surfacenot reliable for shallow measurements near the soil surface
• Dielectric constantDielectric constant– A soil’s dielectric constant is dependent on soil moistureA soil’s dielectric constant is dependent on soil moisture– Time domain reflectometry (TDR)Time domain reflectometry (TDR)– Frequency domain reflectometry (FDR)Frequency domain reflectometry (FDR)– Primarily used for research purposes at this timePrimarily used for research purposes at this time
Soil Water MeasurementSoil Water Measurement
Soil Water MeasurementSoil Water MeasurementNeutron AttenuationNeutron Attenuation
• Tensiometers– Measure soil water potential (tension)– Practical operating range is about 0 to 0.75
bar of tension (this can be a limitation on medium- and fine-textured soils)
• Electrical resistance blocks– Measure soil water potential (tension)– Tend to work better at higher tensions (lower
water contents)• Thermal dissipation blocks
– Measure soil water potential (tension)– Require individual calibration
Soil Water MeasurementSoil Water Measurement
Tensiometer for Measuring Soil Water PotentialTensiometer for Measuring Soil Water Potential
Porous Ceramic Tip
Vacuum Gauge (0-100 centibar)Vacuum Gauge (0-100 centibar)
Water ReservoirWater Reservoir
Variable Tube Length (12 in- 48 in) Based on Root Zone Depth
Electrical Resistance Blocks & MetersElectrical Resistance Blocks & Meters
Infiltration• General
– Process of water penetrating from ground into soil
– Factors affecting• Condition of soil surface,
vegetative cover, soil properties, hydraulic conductivity, antecedent soil moisture
– Four zones• Saturated, transmission,
wetting, and wetting front
depth
Wetting Zone
TransmissionZone
Transition ZoneSaturation Zone
Wetting Front
Richard’s Equation
• Recall – Darcy’s Law– Total head
• So Darcy becomes
• Continuity becomes
zhKqz
Kz
D
Kz
K
zzKqz
KD
Soil water diffusivity
K
zD
zzq
t
Kz
Kqz
Philips Equation• Recall Richard’s
Equation– Assume K and D are
functions of , not z• Solution
– Two terms represent effects of
• Suction head• Gravity head
• S – Sorptivity– Function of soil suction
potential– Found from experiment
K
zD
zt
KtSttF 2/1)(
KSttf 2/1
21)(
Infiltration into a horizontal soil column
x0
Θ = Θn for t = 0, x > 0
Θ = Θo for x = 0, t > 0
zD
xt
Equation:
Boundary conditions
Measurement of Diffusivity by Evaporation from Soil Cores
Air stream
q = soil water flux = evaporation rate
xDq
q
x
http://www.regional.org.au/au/asa/2006/poster/water/4521_deeryd.htm
Measurement of Diffusivity by Evaporation from Soil Cores
Numerical Solution of Richard’s Equation
(Ernest To)
http://www.ce.utexas.edu/prof/maidment/GradHydro2007/Ex4/Ex4Soln.doc
Implicit Numerical Solution of Richard’s Equation
x (i)
t (j)
i-1 i i+1
jj -1
Implicit Numerical Solution of Richard’s Equation
Matrix solution of the equations
Θ
f
F
Definitions
solid
Pore withair
Pore withwater
Element of soil, V(Saturated)
Element of soil, V(Unsaturated)n0content;moisturenS
VV
S0;saturationVVS
porosityVVn
waterofvolumeVsolidsofvolumeVporesofvolumeV
elementofvolumegrossV
w
v
w
v
w
s
v
1
Infiltration
• Infiltration rate– Rate at which water enters the soil at the surface
(in/hr or cm/hr)• Cumulative infiltration
– Accumulated depth of water infiltrating during given time period
t
dftF0
)()(
)(tf
dttdFtf )()(
InfiltrometersSingle Ring Double Ring
http://en.wikipedia.org/wiki/Infiltrometer
Infiltration Methods
• Horton and Phillips – Infiltration models developed as approximate
solutions of an exact theory (Richard’s Equation)
• Green – Ampt– Infiltration model developed from an
approximate theory to an exact solution
Hortonian Infiltration• Recall Richard’s
Equation– Assume K and D are
constants, not a function of or z
• Solve for moisture diffusion at surface
K
zD
zt
zK
zD
t
2
2
02
2
zD
t
ktcc effftf )()( 0
f0 initial infiltration rate, fc is constant rate and k is decay constant
Hortonian Infiltration
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2Time
Infil
trat
ion
rate
, f
k1
k3
k2
k1 < k2 < k3
fc
f0
Philips Equation• Recall Richard’s
Equation– Assume K and D are
functions of , not z• Solution
– Two terms represent effects of
• Suction head• Gravity head
• S – Sorptivity– Function of soil suction
potential– Found from experiment
K
zD
zt
KtSttF 2/1)(
KSttf 2/1
21)(
Green – Ampt Infiltration
Wetted Zone
Wetting Front
Ponded WaterGround Surface
Dry Soil
0h
L
n
i
z
LLtF i )()(
dtdL
dtdFf
Kz
Kf
fzhKqz
MoistureSoilInitialFront WettingtoDepth
i
L
Green – Ampt Infiltration (Cont.)
• Apply finite difference to the derivative, between – Ground surface– Wetting front
Kz
Kf
Wetted Zone
Wetting Front
Ground Surface
Dry Soil
L
i
z0,0 z
fLz ,
KL
KKz
KKz
Kf f
00
FL
LtF )(
1
FKf f
Kz
Kf
1
LK
dtdL f
1
FKf f
dtdLf
Green – Ampt Infiltration (Cont.)
LtF )(
Wetted Zone
Wetting Front
Ground Surface
Dry Soil
L
i
z
LdL
dLdtK
f
f
CLLtKff
)ln(
Integrate
Evaluate the constant of integration
)ln( ffC
0@0 tL
)ln(L
LKtf
ff
Green – Ampt Infiltration (Cont.)
)ln(L
LKtf
ff
)1ln(f
fFKtF
1
FKf f
Wetted Zone
Wetting Front
Ground Surface
Dry Soil
L
i
z
See: http://www.ce.utexas.edu/prof/mckinney/ce311k/Lab/Lab8/Lab8.html
Nonlinear equation, requiring iterative solution.
Soil Parameters
• Green-Ampt model requires – Hydraulic conductivity, Porosity, Wetting Front
Suction Head– Brooks and Corey
Soil Class Porosity Effective Porosity
Wetting Front
Suction Head
Hydraulic Conductivity
n e K (cm) (cm/h) Sand 0.437 0.417 4.95 11.78 Loam 0.463 0.434 9.89 0.34 Clay 0.475 0.385 31.63 0.03
re n
ees )1(
e
res
Effective saturation
Effective porosity
Ponding time
• Elapsed time between the time rainfall begins and the time water begins to pond on the soil surface (tp)
Ponding Time
• Up to the time of ponding, all rainfall has infiltrated (i = rainfall rate)
if ptiF *
1
FKf f
1
* p
f
tiKi
)( KiiKt f
p
Potential Infiltration
Actual Infiltration
Rainfall
Accumulated Rainfall
Infiltration
Time
Time
Infil
trat
ion
rate
, fC
umul
ativ
e In
filtr
atio
n, F
i
pt
pp tiF *
Example
• Silty-Loam soil, 30% effective saturation, rainfall 5 cm/hr intensity 30.0
/65.07.16486.0
e
e
shrcmK
cm
340.0)486.0)(3.01()1( ees
340.0*7.16
hr17.0))(65.00.5(0.5
68.565.0)(
KiKiiKt f
p