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### CE 394K.2 Hydrology

Infiltration

Reading AH Sec 5.1 to 5.5

Some of the subsequent slides were prepared by Venkatesh Merwade

Darcy’s Law

- K = hydraulic conductivity
- q = specific discharge
- V = q/n = average velocity through the area

Richard’s Equation

- Recall
- Darcy’s Law
- Total head

- So Darcy becomes
- Continuity becomes

Soil water diffusivity

Saturation Zone

Transition Zone

Transmission

Zone

Wetting Zone

Wetting Front

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

Philips Equation

- Recall Richard’s Equation
- Assume K and D are functions of q, not z

- Solution
- Two terms represent effects of
- Suction head
- Gravity head

- Two terms represent effects of
- S – Sorptivity
- Function of soil suction potential
- Found from experiment

Infiltration into a horizontal soil column

Boundary conditions

Θ = Θo for x = 0, t > 0

Θ = Θn for t = 0, x > 0

x

0

Equation:

Measurement of Diffusivity by Evaporation from Soil Cores

Air stream

q

x

q = soil water flux = evaporation rate

Measurement of Diffusivity by Evaporation from Soil Cores

http://www.regional.org.au/au/asa/2006/poster/water/4521_deeryd.htm

Numerical Solution of Richard’s Equation

(Ernest To)

http://www.ce.utexas.edu/prof/maidment/GradHydro2007/Ex4/Ex4Soln.doc

Definitions

Element of soil, V

(Saturated)

Pore with

water

solid

Pore with

air

Element of soil, V

(Unsaturated)

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

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 q or z

- Solve for moisture diffusion at surface

f0 initial infiltration rate, fc is constant rate and k is decay constant

Philips Equation

- Recall Richard’s Equation
- Assume K and D are functions of q, not z

- Solution
- Two terms represent effects of
- Suction head
- Gravity head

- Two terms represent effects of
- S – Sorptivity
- Function of soil suction potential
- Found from experiment

Green – Ampt Infiltration (Cont.)

Ground Surface

Wetted Zone

- Apply finite difference to the derivative, between
- Ground surface
- Wetting front

Wetting Front

Dry Soil

Green – Ampt Infiltration (Cont.)

Ground Surface

Wetted Zone

Wetting Front

Dry Soil

Evaluate the constant of integration

Integrate

Green – Ampt Infiltration (Cont.)

Ground Surface

Wetted Zone

Wetting Front

Dry Soil

Nonlinear equation, requiring iterative solution.

See: http://www.ce.utexas.edu/prof/mckinney/ce311k/Lab/Lab8/Lab8.html

Soil Parameters

- Green-Ampt model requires
- Hydraulic conductivity, Porosity, Wetting Front Suction Head
- Brooks and Corey

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)

Infiltration

Infiltration rate, f

Rainfall

Actual Infiltration

Time

Accumulated

Rainfall

Infiltration

Cumulative

Infiltration, F

Time

Ponding Time- Up to the time of ponding, all rainfall has infiltrated (i = rainfall rate)

Example

- Silty-Loam soil, 30% effective saturation, rainfall 5 cm/hr intensity

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