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
Darcys Law

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

3
Richards Equation

• Recall
• Darcys 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

5
Philips Equation

• Recall Richards 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
T To for x 0, t gt 0
T Tn for t 0, x gt 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/wate
r/4521_deeryd.htm
9
Numerical Solution of Richards Equation
(Ernest To)
http//www.ce.utexas.edu/prof/maidment/GradHydro20
07/Ex4/Ex4Soln.doc
10
Implicit Numerical Solution of Richards Equation
t (j)
j j -1
x (i)
i-1 i i1
11
Implicit Numerical Solution of Richards Equation
12
Matrix solution of the equations
13
T
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 (Richards Equation)
• Green Ampt
• Infiltration model developed from an approximate
  theory to an exact solution

19
Hortonian Infiltration

• Recall Richards 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 Richards 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
Wetting Front

• Apply finite difference to the derivative,
  between
• Ground surface
• 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/ce311
k/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
Ponding Time

• Up to the time of ponding, all rainfall has
  infiltrated (i rainfall rate)

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Example

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