Post on 02-Jan-2016
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
• 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
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
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
)()(
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 *