infiltration reading ah sec 4.3 to 4.4
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Infiltration
Reading AH Sec 4.3 to 4.4
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
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
Nonlinear equation, requiring iterative solution.
Soil Parameters
• Green-Ampt model requires – Hydraulic conductivity, Porosity, Wetting Front
Suction Head
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
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