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INFILTRATION

INFILTRATIONINFILTRATIONInfiltration is the process of water penetrating from the ground surface into the soil.

Many factors influence the infiltration rate, including the Condition of the soil surface and its vegetative cover, the properties of the soil, such as its porosity and hydraulic conductivity, and the current moisture content of the soil.soil, such as its porosity and hydraulic conductivity, and the current moisture content of the soil.

Moisture zone during Infiltration

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Slow water movement in Slow water movement in Slow water movement in Slow water movement in a small diameter ofa small diameter ofa small diameter ofa small diameter of soilsoilsoilsoil

Unsaturated soil tends to Unsaturated soil tends to Unsaturated soil tends to Unsaturated soil tends to Unsaturated soil tends to Unsaturated soil tends to Unsaturated soil tends to Unsaturated soil tends to draw the water (down)draw the water (down)draw the water (down)draw the water (down)

Infiltration rate: varies Infiltration rate: varies Infiltration rate: varies Infiltration rate: varies (not constrant)(not constrant)(not constrant)(not constrant)

INFILTRATIONINFILTRATION• Horton’s equation: infiltration begins at some rate f0 and exponentially decreases until it reaches a constant rate fc

f(t) = fc + (f0 – fc)e-kt

Phillip’s equation: cumulative infiltration F(t):F(t) = St1/2 + Ktcumulative infiltration F(t):F(t) = St1/2 + KtS = sorptivityK = hydraulic conductivity

Green-Ampt Method

INFILTRATIONINFILTRATION• Green-Ampt Method

If the soil was initially of moisture content θi throughout its entire depth, the moisture content will increase from θi to η (the porosity) as the wetting front passes.

The moisture content θ is the ratio of the volume of water to the total The moisture content θ is the ratio of the volume of water to the total volume within the control surface, so the increases in the water stored within the control volume as a result of infiltration is L(η – θi).

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INFILTRATIONINFILTRATION• Green-Ampt Method

Green-Ampth equation for cumulative infiltration. Once F is found from equation:F(t)- ψ∆θ ln (1 + F(t)/ψ∆θ) = Kt

the infiltration rate f can be obtained from:the infiltration rate f can be obtained from:

F(t) = K [(ψ∆θ/F(t) + 1)]

Ψ = wetting front soil suction head∆θ = the change in the moisture content when the

wetting front passes = (1 – se)θe

θe = effective porosity

INFILTRATIONINFILTRATION• Green-Ampt Method

Compute the infiltration rate f and cumulative infiltration F after one hour of infiltration into a silt loam soil that initially had an effective saturation of 30%. Assume water is ponded to a small but negligible depth on the surface.surface.

Effective saturation, Se = θ- θr/(η- θr)is the ratio of the available moisture (θ- θr) to the masimum possible available moisture content (η- θr).

The residual moisture content of the soil after it has been thoroughly drained is denoted by θr

Change in moisture content, ∆θ = (1-Se)θe

INFILTRATIONINFILTRATION• Green-Ampt Method

Compute the infiltration rate f and cumulative infiltration F after one hour of infiltration into a silt loam soil that initially had an effective saturation of 30%. Assume water is ponded to a small but negligible depth on the surface.surface.

From the table: for a silt loam soil θe =0.486, ψ=16.7 cm, and K = 0.65 cm/h, se =0.3

F(t)= Kt + ψ∆θ ln (1 + F(t)/ψ∆θ)

∆θ = (1-Se)θe

∆θ = (1-0.3) (0.486) = 0.34and ψ∆θ = 16.7 x 0.340 = 5.68 cm

The cumulative infiltration at t=1 hour is calculated employing the method of successive substitution. F(t)= Kt + ψ∆θ ln (1 + F(t)/ψ∆θ)

INFILTRATIONINFILTRATIONRawls, Brakensiek, and Miller (1983) used the method to analyze approximately 5000 soil horizons across the United States and determined average values of the Green-Ampt parameters η, θe, ψ, and K for different soil classes, as shown in Table.

As soil becomes finer moving from sand to clay the wetting front soil suction head increases while the hydraulic conductivity decreases. As soil becomes finer moving from sand to clay the wetting front soil suction head increases while the hydraulic conductivity decreases.

INFILTRATIONINFILTRATIONGreen-Ampt infiltration parameters for various soil classes

Soil class Porosity

η

Effective porosity

θe

Wetting front soil suction head (cm),

ψ

Hydraulic conductivity (cm/h),

K

Sand 0.437 0.417 4.95 11.78

Loamy sand 0.437 0.401 6.13 2.99Loamy sand 0.437 0.401 6.13 2.99

Sandy loam 0.453 0.412 11.01 1.09

Loam 0.463 0.434 8.89 0.34

Silt loam 0.501 0.486 16.68 0.65

Sandy clay … … … …

Clay loam

…….

INFILTRATIONINFILTRATION

Material Porosity Hydraulic conductivity (cm/h),

η K

Gravel 25-40% 10-1 -102

Sand 25-50% 10-5 -1

Silt 35-50% 10-7 -10-3

Clay 40-70% 10-9 -10-5

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Darcy’s Darcy’s LawLaw

Water is percolating through a fine sand aquifer withhydraulic conductivity 10-2 cm/s and porosity 0.4 toward a stream 100 m away. If the slope of the water table is 1%, calculate the travel time of water to the stream.

SolutionThe Darcy flux q = K.Sf

With K =0.01 cm/s = 8.64 m/day and Sf = 1%; hence q = 8.64 x 0.01 = 0.086 m/day.The water velocity va = q/η = 0.086/0.4 = 0.216 m/day.The travel time to the stream 100 m away is 100/va = 100/0.216 = 463 days = 1.3 years.

Soil Water

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Cumulative Infiltration

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Soil Particle Aggregates Conceptual Diagrams

INFILTRATIONINFILTRATIONCompute the infiltration rate f and cumulative infiltration F after one hour of infiltration into a silt loam soil that initially had an effective saturation of 30 percent. Assume water is ponded to a small but negligible depth on the surface.

Ponding TimePonding TimeThe ponding time tp is the elapsed time between the time rainfall begins and the time water begins to pond on the soil surface.

Ponding begins when the rainfall intensity exceeds the potential infiltration rate. At this time (t = tp), the soil surface is saturated. As rainfall continues (t > tp), the saturated zone extends deeper into the soil and overland flow occurs from the ponded water. (t > tp), the saturated zone extends deeper into the soil and overland flow occurs from the ponded water.

Porosity

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Shape

Sorted

Porosity

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Permeability

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ClayClayClayClayWater likes to stick to waterMore surface area of clay for water to stickwater to stick

Soil Texture Triangle

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Soil Texture Triangle

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HIDROLOGI BAHASAN

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Composition:

•Clay – 21%

• Sand – 66%

• Silt – 13%

Soil Property Range

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Soil-water Pressure (Tension)

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Tension is much

higher in finer-higher in finer-

grained than in

coarser-grained soils

Water Movement in Unsaturated Zone

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Water that does not Water that does not

infiltrate becomes

overland flow

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Field capacity – minimum soil water content after indefinite gravitational drainage

Permanent wilting point– natural vegetation cannot remove enough water to

match moisture loss to atmosphere

Hygroscopic water – water forms thin layers around soil particles. Tightly held, not

available to plants.

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Water penetration into the soil

Rate of infiltration depends on

– Conditiion of soil surface

-Vegetative cover

- Soil properties: porosity, hydraulic conductivity, moisture content

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Darcy’s Law

Studying the performance of sand filters in

treating drinking water, Darcy measured the

flowrate of water through sand.

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Darcy’s LawWater is percolating through a fine sand aquifer with

hydraulic conductivity 10-2 cm/s and porosity 0.4 toward

a stream 100 m away. If the slope of the water table is

1%, calculate the travel time of water to the stream.

Solution

EnvironmentalEngineeringInstitut Teknologi BandungEnvE

Darcy’s Law

Water is percolating through a fine sand aquifer with

hydraulic conductivity 10-2 cm/s and porosity 0.4 toward

a stream 100 m away. If the slope of the water table is

1%, calculate the travel time of water to the stream.

Solution

The Darcy flux q = K.Sf

With K =0.01 cm/s = 8.64 m/day and Sf = 1%; hence

q = 8.64 x 0.01 = 0.086 m/day.

The water velocity va = q/η = 0.086/0.4 = 0.216 m/day.

The travel time to the stream 100 m away is 100/va =

100/0.216 = 463 days = 1.3 years.

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Darcy’s Law

EnvironmentalEngineeringInstitut Teknologi BandungEnvE

Darcy’s Law

A ‘fine sand’ has

hydrualic conductivity

of 3 m/d. What flow

rate would be expected rate would be expected

through a 1 m long, 25

cm diameter column of

soil where the head

differential is 35 mm?