INFILTRATION
Classification: Internal
INFILTRATION
Flow of water into the ground through the soil surface
Classification: Internal
FACTORS OF INFILTRATION CAPACITY
▸ SOIL CHARACTERISTICS
▸ CONDITION OF THE SOIL SURFACE
▸ VEGETATIVE COVER
▸ CURRENT MOISTURE CONTENT
▸ SOIL TEMPERATURE
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Classification: Internal
HORTON
INFILTRATION
CAPACITY
The capacity decreases with time and
ultimately reaches a constant rate,
caused by filling of soil pores with water,
which reduces capillary suction.
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Classification: Internal
HORTON INFILTRATION CAPACITY
▸ 𝑓𝑓 = 𝑓𝑓𝑓𝑓 + 𝑓𝑓0 − 𝑓𝑓𝑓𝑓 𝑒𝑒 −𝑘𝑘𝑘𝑘
where
f = infiltration capacity (in./hr),
f 0 = initial infiltration capacity (in./hr)
f c = final capacity (in./hr)
k = empirical constant (hr –1 )
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Classification: Internal
SAMPLE PROBLEM
The initial infiltration capacity f 0 of a watershed is
estimated as 1.5 in./hr, and the time constant is taken to
be 0.35 hr –1. The equilibrium capacity f c is 0.2 in./hr. Use
Horton’s equation to find (a) the values of f at t = 10 min,
30 min, 1hr, 2 hr, and 6 hr, and (b) the total volume of
infiltration over the 6-hr period.
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Classification: Internal
SAMPLE PROBLEM
f 0 = 1.5 in./hr
f c = 0.2 in./hr
k = 0.35 hr - 1
a.) f at 10, 30, 1hr, 2hrs, 60
hrs
b.) total volume
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Classification: Internal
SAMPLE PROBLEM
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Classification: Internal
Φ-INDEX
METHOD
It is simplest infiltration method and
is calculated by finding the loss
difference between gross
precipitation and observed surface
runoff measured as a hydrograph
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Classification: Internal
SAMPLE PROBLEM
For the rainfall data below, determine the runoff volume
if φ index is 1.0 in/hr. The watershed area is 0 .875 mi2.
Time (hr) Rainfall (in./hr)
0 -2 1.4
2-5 2.3
5-7 1.1
7-10 0 .7
10 -12 0 .3
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Classification: Internal
SAMPLE PROBLEM
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Classification: Internal
GREEN-AMPT
METHOD
Developed by William Heber Green
and Gustav Adolph Ampt. Infiltration
is modeled as unsaturated flow.
Used the Richard’s Equation and
Darcy’s Law
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Classification: Internal
RICHARD EQUATION
𝜕𝜕𝜕𝜕 𝜕𝜕 𝜕𝜕𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕(𝜃𝜃)
▸ 𝜕𝜕𝜕𝜕
= − 𝜕𝜕𝜕𝜕 [𝑘𝑘(𝜃𝜃) 𝜕𝜕𝜕𝜕
] − 𝜕𝜕𝜕𝜕
where
θ = volumetric moisture content (cm 3 /cm 3 )
z = distance below the surface (cm),
𝜓𝜓𝜓𝜓 = capillary suction (pressure) (cm of water)
𝐾𝐾(𝜃𝜃) = unsaturated hydraulic conductivity (cm/s)
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Classification: Internal
DARCY’S LAW
𝜕𝜕𝜕
▸ q = −𝐾𝐾(𝜃𝜃) 𝜕𝜕𝜕𝜕
where
q = Darcy velocity (cm/s),
z = depth below surface (cm),
h = potential or head = z + Ψ (cm),
c = suction (negative cm),
K(𝜃𝜃) = unsaturated hydraulic conductivity (cm/s),
𝜃𝜃 = volumetric moisture content. 14
Classification: Internal
5 Pr inciple Assumpt ions on G-A Met hod
▸ The soil under consideration is homogeneous and stable, implying that
macropores and preferential migration pathways should not be considered.
▸ The supply of ponded water at the surface is not limited.
▸ A distinct and precisely definable wetting front exists, and as water
continues to infiltrate, the wetting front advances at the same rate with
depth.
▸ The capillary suction just below the wetting front is uniform throughout the
profile and constant in time during the infiltration event.
▸ The soil is uniformly saturated above the wetting front, and the volumetric
water contents remain constant above and below the advancing wetting
front.
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Classification: Internal
G-A Simplificat ion
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Classification: Internal
G-A Simplificat ion
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Classification: Internal
G-A Der ivat ion
𝜕𝜕𝜕
▸ 𝑞𝑞 = −𝐾𝐾(𝜃𝜃) 𝜕𝜕𝜕𝜕
𝐾𝐾 ℎ −ℎ
▸ 𝑞𝑞 = −𝑓𝑓 ≅ − 𝑠𝑠𝑧𝑧 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠− 𝑧𝑧 𝑤𝑤𝑤𝑤
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑤𝑤𝑤𝑤
Note that hsurf = 0
𝐾𝐾𝑠𝑠(0−(𝜓𝜓+ −𝐿𝐿 )
▸ −𝑓𝑓 = − (0 −(−𝐿𝐿)
𝐾𝐾 (𝐿𝐿−𝜓𝜓)
▸ −𝑓𝑓 = − 𝑠𝑠 𝐿𝐿
𝜓𝜓
▸ 𝑓𝑓 = 𝐾𝐾𝑠𝑠(1 − 𝐿𝐿 )
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Classification: Internal
G-A Der ivat ion
▸ Total Infiltration, F
▸ 𝐹𝐹 = 𝐿𝐿 𝜃𝜃𝑠𝑠 − 𝜃𝜃𝑖𝑖 = 𝐿𝐿𝐿𝐿𝐿𝐿
▸ 𝐿𝐿 = 𝐹𝐹/𝑀𝑀𝑑𝑑
𝜓𝜓
▸ 𝑓𝑓 = 𝐾𝐾𝐾𝐾(1 − 𝐿𝐿 )
𝜓𝜓𝑀𝑀𝑑𝑑
▸ 𝑓𝑓 = 𝐾𝐾𝐾𝐾(1 − )
𝐹𝐹
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Classification: Internal
3 Infilt r at ion-Rainfall
▸ Case 1: i < Ks. The rainfall intensity is less than the maximum downward
hydraulic conductivity, meaning that runoff will never occur and
all rainfall will infiltrate regardless of the duration.
▸ Case 2: K s <i < f . The rainfall intensity is greater than the saturated
hydraulic conductivity but less than the infiltration rate. The time to
ponding varies for different rainfall intensities.
▸ Case 3: i > f . The rainfall intensity is greater than the infiltration rate
and runoff can occur.
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Classification: Internal
Volume of Infilt r at ion at Sur face
Sat ur at ion (Fs)
𝜓𝜓𝑀𝑀𝑑𝑑 ▸ We require i > Ks and remember that
▸ 𝑓𝑓 = 𝐾𝐾𝐾𝐾(1 − 𝐹𝐹 ) capillary suction c is negative. The Green–
Ampt infiltration method will predict the
▸ At surface saturation, i = f following results for various intensities of
𝜓𝜓𝜓𝜓𝜓𝜓 rainfall i:
▸ 𝑖𝑖 = 𝐾𝐾𝐾𝐾 1 − 𝐹𝐹𝑠𝑠 ▹ 1. If i ≤ Ks, then f = i
𝑖𝑖 ▹
▸ 𝐹𝐹𝑠𝑠 = 𝜓𝜓𝜓𝜓𝜓𝜓/(1 − 𝐾𝐾 ) 2. If i >Ks, then f = i until F = it s = Fs,
𝑠𝑠 ▹ 3. Following surface saturation,
𝜓𝜓𝜓𝜓𝜓𝜓
𝑓𝑓 = 𝐾𝐾𝐾𝐾(1 − ) for i>Ks and f=i ≤Ks
𝐹𝐹
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Classification: Internal
G-A Infilt r at ion Par amet er s for Var ious Soil Text ur e
Classes
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Classification: Internal
SAMPLE PROBLEM
For the following soil properties, develop a plot of infiltration rate f vs.
infiltration volume F using the Green and Ampt equation:
Ks = 1.97 in./hr,
θs = 0 .518,
θi = 0 .318,
ψ = -9.37 in.,
i = 7.88 in./hr.
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Classification: Internal
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Classification: Internal
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Classification: Internal
