1. INFILTRATION
PRESENTED BY
KARUNAKAR KEMA

2. 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
Transmission
Zone
Transition Zone
Saturation Zone
Wetting Front


3. 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
dftF
0
)()( 
)(tf
dt
tdF
tf
)(
)( 

4. Infiltrometers
Single Ring Double Ring

5. 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

6. 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
z
D
zt 

z
K
z
D
t 




2
2


0
2
2
z
D
t 




kt
cc effftf 
 )()( 0
f0 initial infiltration rate, fc is constant rate and k is decay constant

7. Hortonian Infiltration
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2
Time
Infiltrationrate,f
k1
k3
k2
k1 < k2 < k3
fc
f0

8. 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
z
D
zt 

KtSttF  2/1
)(
KSttf   2/1
2
1
)(

9. Green – Ampt Infiltration
Wetted Zone
Wetting Front
Ponded Water
Ground Surface
Dry Soil
0h
L

n
i

z
  LLtF i )()(
dt
dL
dt
dF
f 
zh 
K
z
Kf 


f
z
h
Kqz 


MoistureSoilInitial
FrontWettingtoDepth


i
L


10. Green – Ampt
Infiltration (Cont.)
 Apply finite difference to the
derivative, between
 Ground surface
 Wetting front
K
z
Kf 




Wetted Zone
Wetting Front
Ground Surface
Dry Soil
L


i

z
0,0  z
fLz   ,
K
L
KK
z
KK
z
Kf
f







0
0







F
L
LtF )(








 1
F
Kf
f
K
z
Kf 



11. 





 1
L
K
dt
dL f









 1
F
Kf
f
dt
dL
f 
Green – Ampt
Infiltration (Cont.)
 LtF )(
Wetted Zone
Wetting Front
Ground Surface
Dry Soil
L


i

z
L
dL
dLdt
K
f
f


 


CLLt
K
ff 

)ln(

Integrate
Evaluate the constant of integration
)ln( ffC 
0@0  tL
)ln(
L
LKt
f
f
f






12. Green – Ampt Infiltration
(Cont.)
)ln(
L
LKt
f
f
f





)1ln(
f
f
F
KtF












 1
F
Kf
f
Wetted Zone
Wetting Front
Ground Surface
Dry Soil
L


i

z
Nonlinear equation, requiring iterative solution.

13. 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
r
es

 
 Effective saturation
Effective porosity

14. Ponding time
 Elapsed time between the time rainfall begins and the time water begins to
pond on the soil surface (tp)

15. Ponding Time
 Up to the time of ponding,
all rainfall has infiltrated (i
= rainfall rate)
if  ptiF *








 1
F
Kf
f










 1
* p
f
ti
Ki

)( Kii
Kt
f
p




Potential
Infiltration
Actual Infiltration
Rainfall
Accumulated
Rainfall
Infiltration
Time
Time
Infiltrationrate,f
Cumulative
Infiltration,F
i
pt
pp tiF *

16. Example
 Silty-Loam soil, 30% effective
saturation, rainfall 5 cm/hr
intensity
30.0
/65.0
7.16
486.0




e
e
s
hrcmK
cm

340.0)486.0)(3.01()1(  ees 
340.0*7.16
hr17.0
))(65.00.5(0.5
68.5
65.0
)(






KiKii
Kt
f
p
