1. CE 394K.2 Hydrology Infiltration Reading AH Sec 5.1 to 5.5 Some of the subsequent slides were prepared by Venkatesh Merwade

2. Darcy’s Law K = hydraulic conductivity q = specific discharge V = q/n = average velocity through the area

3. Richard’s Equation Recall –Darcy’s Law –Total head So Darcy becomes Continuity becomes Soil water diffusivity

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 Transmission Zone Transition Zone Saturation Zone Wetting Front 

5. 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

6. Infiltration into a horizontal soil column x 0 Θ = Θ n for t = 0, x > 0 Θ = Θ o for x = 0, t > 0 Equation: Boundary conditions

7. Measurement of Diffusivity by Evaporation from Soil Cores Air stream q = soil water flux = evaporation rate q x

8. http://www.regional.org.au/au/asa/2006/poster/water/4521_deeryd.htm Measurement of Diffusivity by Evaporation from Soil Cores

9. Numerical Solution of Richard’s Equation (Ernest To) http://www.ce.utexas.edu/prof/maidment/GradHydro2007/Ex4/Ex4Soln.doc

10. Implicit Numerical Solution of Richard’s Equation x (i) t (j) i-1 i i+1 j j -1

11. Implicit Numerical Solution of Richard’s Equation

12. Matrix solution of the equations

13. Θ

14. f

15. F

16. Definitions solid Pore with air Pore with water Element of soil, V (Saturated) Element of soil, V (Unsaturated)

17. 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

18. 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

19. Hortonian Infiltration Recall Richard’s Equation –Assume K and D are constants, not a function of  or z Solve for moisture diffusion at surface f 0 initial infiltration rate, f c is constant rate and k is decay constant

20. Hortonian Infiltration

21. 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

22. Green – Ampt Infiltration Wetted Zone Wetting Front Ponded Water Ground Surface Dry Soil

23. Green – Ampt Infiltration (Cont.) Apply finite difference to the derivative, between –Ground surface –Wetting front Wetted Zone Wetting Front Ground Surface Dry Soil

24. Green – Ampt Infiltration (Cont.) Wetted Zone Wetting Front Ground Surface Dry Soil Integrate Evaluate the constant of integration

25. Green – Ampt Infiltration (Cont.) Wetted Zone Wetting Front Ground Surface Dry Soil See: http://www.ce.utexas.edu/prof/mckinney/ce311k/Lab/Lab8/Lab8.htmlhttp://www.ce.utexas.edu/prof/mckinney/ce311k/Lab/Lab8/Lab8.html Nonlinear equation, requiring iterative solution.

26. Soil Parameters Green-Ampt model requires –Hydraulic conductivity, Porosity, Wetting Front Suction Head –Brooks and Corey Effective saturation Effective porosity

27. Ponding time Elapsed time between the time rainfall begins and the time water begins to pond on the soil surface (t p )

28. Ponding Time Up to the time of ponding, all rainfall has infiltrated (i = rainfall rate) Potential Infiltration Actual Infiltration Rainfall Accumulated Rainfall Infiltration Time Infiltration rate, f Cumulative Infiltration, F

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