CE 394K.2 Hydrology

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. 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

5. 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

6. 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:

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

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

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 t (j) j j -1 x (i) i-1 i i+1

11. Implicit Numerical Solution of Richard’s Equation

12. Matrix solution of the equations

13. Θ

14. f

15. F

16. Definitions Element of soil, V (Saturated) Pore with water solid Pore with air 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 q or z • Solve for moisture diffusion at surface f0 initial infiltration rate, fc 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 q, 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 Ponded Water Ground Surface Wetted Zone Wetting Front Dry Soil

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

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

25. 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

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 (tp)

28. 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)

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