Ce 394k 2 hydrology
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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

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Ce 394k 2 hydrology l.jpg

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 l.jpg
Darcy’s Law

  • K = hydraulic conductivity

  • q = specific discharge

  • V = q/n = average velocity through the area


Richard s equation l.jpg
Richard’s Equation

  • Recall

    • Darcy’s Law

    • Total head

  • So Darcy becomes

  • Continuity becomes

Soil water diffusivity


Infiltration l.jpg

q

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 l.jpg
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

  • S – Sorptivity

    • Function of soil suction potential

    • Found from experiment


Infiltration into a horizontal soil column l.jpg
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 l.jpg
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 cores8 l.jpg
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 l.jpg
Numerical Solution of Richard’s Equation

(Ernest To)

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






Slide14 l.jpg

f


Slide15 l.jpg

F


Definitions l.jpg
Definitions

Element of soil, V

(Saturated)

Pore with

water

solid

Pore with

air

Element of soil, V

(Unsaturated)


Infiltration17 l.jpg
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 l.jpg
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 l.jpg
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 equation21 l.jpg
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

  • S – Sorptivity

    • Function of soil suction potential

    • Found from experiment


Green ampt infiltration l.jpg
Green – Ampt Infiltration

Ponded Water

Ground Surface

Wetted Zone

Wetting Front

Dry Soil


Green ampt infiltration cont l.jpg
Green – Ampt Infiltration (Cont.)

Ground Surface

Wetted Zone

  • Apply finite difference to the derivative, between

    • Ground surface

    • Wetting front

Wetting Front

Dry Soil


Slide24 l.jpg

Green – Ampt Infiltration (Cont.)

Ground Surface

Wetted Zone

Wetting Front

Dry Soil

Evaluate the constant of integration

Integrate


Green ampt infiltration cont25 l.jpg
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 l.jpg
Soil Parameters

  • Green-Ampt model requires

    • Hydraulic conductivity, Porosity, Wetting Front Suction Head

    • Brooks and Corey

Effective saturation

Effective porosity


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Ponding time

  • Elapsed time between the time rainfall begins and the time water begins to pond on the soil surface (tp)


Ponding time28 l.jpg

Potential

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 l.jpg
Example

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


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