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