CE 394K.2 Hydrology

Infiltration

Reading 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

z

hKqz

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivity

Kz

Dzz

q

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

Kz

Dzt

KtSttF 2/1)(

KSttf 2/1

2

1)(

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

V

V

S0;saturationV

VS

porosityV

Vn

waterofvolumeV

solidsofvolumeV

poresofvolumeV

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

dt

tdFtf

)()(

Infiltrometers

Single 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

Kz

Dzt

z

K

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 2

Time

Infi

ltra

tio

n r

ate,

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

Kz

Dzt

KtSttF 2/1)(

KSttf 2/1

2

1)(

Green – Ampt Infiltration

Wetted Zone

Wetting Front

Ponded Water

Ground Surface

Dry Soil

0h

L

n

i

z

LLtF i )()(

dt

dL

dt

dFf

Kz

Kf

fz

hKqz

MoistureSoilInitial

Front 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

Kff

0

0

F

L

LtF )(

1

FKf

f

Kz

Kf

1

LK

dt

dL f

1

FKf

f

dt

dLf

Green – Ampt Infiltration (Cont.)

LtF )(

Wetted Zone

Wetting Front

Ground Surface

Dry Soil

L

i

z

L

dLdLdt

K

f

f

CLLtK

ff

)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

fF

KtF

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

fp

Potential Infiltration

Actual Infiltration

Rainfall

Accumulated Rainfall

Infiltration

Time

Time

Infi

ltra

tion

rate

, f

Cu

mu

lati

ve

Infi

ltra

tion

, F

i

pt

pp tiF *

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

68.565.0

)(

KiKiiKt

fp