INFILTRATION

Soils Defined
• Natural Body that Occurs on the Land
Surface that are Characterized by One or
More of the Following:

– Consists of Distinct Horizons or Layers

– The ability to support rooted plants in a natural
environment
– Upper Limit is Air or Shallow Water
– Lower Limit is Bedrock or Limit of Biological Activity
– Classification based on a typical depth of 2 m or
approximately 6.0 feet
Five Soil Formation
Factors
• Organisms
• Climate
• Time
• Topography and
Landscape Setting
• Parent Material

R
 Geologic Time

Time
 Parent Material
• Geological Materials
– Minerals and Rocks
– Glacial Materials
– Loess (wind blown)
– Alluvial Deposits
– Marine Deposits Glacial Material
– Organic Deposits

• Influences
– Minerals Present
– Colors
– Chemical Reactions
– Water Movement
– Soil Development

Bedrock
Fig. 1
 Definitions
Infiltration - The downward entry of water into the immediate
surface of soil or other materials.

Infiltration is the flow of water through the soil surface into a

porous medium under gravity action and pressure effects.

Infiltration Capacity- The maximum rate at which water can

infiltrate into a soil under a given set of conditions.

Infiltration Rate- The rate at which water penetrates the surface of

the soil and expressed in cm/hr, mm/hr, or inches/hr. The rate of
infiltration is limited by the capacity of the soil and rate at which
water is applied to the surface. This is a volume flux of water flowing into the
profile per unit of soil surface area (expressed as velocity).

Cumulative infiltration, F denotes the volume of infiltration from the beginning of time, t
or rainfall event
 INFILTRATION CHARACTERISTICS

Fig. 2 The infiltration process depending on soil type and flow [Musy,2001]
 • Infiltration regime i(t) depends on the supply regime
(irrigation, rain), but also on soil properties.

• The cumulative infiltration I(t), is the total amount of

water infiltrated during a given period.

where:
I(t) the cumulative infiltration during the t period (mm)
i(t) the infiltration regime during the t period (mm/h)

Hydraulic conductivity at saturation ks, is an essential parameter of infiltration. It

represents the limiting value of infiltration if the soil is saturated and homogenous.
 Infiltration Rate and Capacity
Soil Factors that Control Infiltration Rate:
•Moisture Content
- Infiltration capacity at the beginning of a storm is relatively high
or low depending on whether the soil is initially dry or wet
•Soil Texture and Structure
 • Porosity and Permeability

• Soil Bulk Density and Compaction

Compaction of the soil surface results
in reducing infiltration rate.

 Slope, Landscape Position,

 Topography
Vegetative Cover, Root Development and
Organic Content
• Vegetation greatly promotes infiltration:
- a- by retarding surface flow
- b- through foilage which shields the soil
from compaction due to rain droplets
- c- through root system which makes the
soil more pervious
Fig. 4 The infiltration regime depending on time for different types of soil
 Infiltration Rate (Time Dependent)

Decreasing Infiltration

Steady Gravity
Induced Rate

Infiltration with Time Rate is Initially Final Infiltration Capacity

High Because of a Combination of (Equilibrium)- Infiltration
Capillary and Gravity Forces Approaches Saturated
Permeability
 Infiltration Rate (Moisture)
Infiltration Decreases with Time

1) Changes in Surface and Subsurface Conditions

2) Change in Matrix Potential

3) Overtime - Matrix Potential Decreases and Gravity Forces

Dominate - Causing a Reduction in the Infiltration Rate
Determination of the Infiltration rate

• 1. Direct Measurements
 Measuring Infiltration Rate
• (a) Flooding (ring)
Infiltrometers
– Single ring
– Double ring
 Single Rings Infiltrometers

Cylinder - 30 cm in Diameter

Drive 10-50 cm into Soil Surface or Horizon

Water is Ponded Above the Surface

Record Volume of Water Added with Time to Maintain a

Constant Head
 Double Rings Infiltrometers

Outer Rings are 6 to 24 inches in Diameter (ASTM - 12 to 24 inches)

Mariotte Bottles Can be Used to Maintain Constant Head
Rings Driven - 5 cm to 6 inches in the Soil and if necessary sealed
Measure rate of vertical movement from center ring
Exterior ring to offset lateral movement of moisture
 Infiltrometers
• Advantage
– It is portable and easy to install and so multiple
measurements can be made in a short period of
time.
• Drawback:
– Mechanical disturbance of the soil adjacent to the
tube wall. This causes measured infiltration to be
up to 10 times the natural rate.
 (b) Rainfall simulator

Rainfall simulator or sprinkler infiltrometer can be used to

estimate infiltration for areas ranging from a few square
meters to hundreds of square meters.
A site is selected and a framework of overhead sprinklers
installed
Sprinkler nozzles and water pressures are designed to
simulated varying rainfall intensity, drop size and fall velocity
• Using a continuity equation, the simulator allows
infiltration to be determined as the difference
between irrigation, runoff, water detained in flow
across the plot, and water retained in surface
depressions
• infiltration rate = “rainfall” rate - runoff rate

• These devices provide estimates of infiltration for

larger areas than the ring infiltrometers, but they are
expensive and difficult to set up in the field
Determination of the infiltration rate

• Analytical Methods
 (i) Hydrograph analysis
• An approximate method for estimating
infiltration for small drainage basins
• It combines the analysis of rainfall
hyetographs and stream hydrographs from a
basin
• The technique is also called average
infiltration method
 Excess Precipitation

0.9

0.8
Derived unit hydrograph is the
result of approximately 6 hours
Excess Prec. (inches)

of excess precipitation.
0.7

Small amounts of
0.6
excess precipitation at
beginning and end may
0.5
be omitted.
0.4

0.3

0.2

0.1

0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Time (hrs.)
Graphical Representation
Duration of
excess precip.

Lag time

Time of
concentration

Base flow
• A complex storm consisting of multiple
bursts (blocks) of rainfall is identified and at
least three distinct rainfall bursts are
selected.
• Total rainfall for each burst is calculated and
converted into an average rainfall intensity
by dividing by the rainfall duration.
• The corresponding storm runoff for each
event is first converted into a uniform
depth over the basin and then into an
average runoff intensity using the same
duration
• Storm runoff is equal to the total runoff minus
the baseflow.
• Average infiltration during each event is the
difference between the average rainfall
intensity and the average runoff intensity
 Hydrograph analysis-Contd…
• Average infiltration during each event is the
difference between average rainfall intensity
and the average runoff intensity

• Example…..on Hydrograph analysis

Figure (a) The hyetographs for the storm sequence, (b) The runoff
hydrograph
 Data for the hydrograph method
Event Duration (hrs) Precipitation Runoff Infiltration
inch (in hr-1) (inch) (in hr-1) (in hr-1)
1 3.0 1.38 0.46 0.15 0.05 0.41

2 3.5 1.32 0.38 0.17 0.05 0.33

3 2.5 0.61 0.24 0.21 0.08 0.16

 (ii) Φ-index
• Φ-index is defined as the average rainfall
intensity above which the rainfall volume equals
the runoff volume.
• It represents the combined effects of infiltration,
interception and depression storage.
• The index represent the amount of precipitation
retained by the basin divided by the duration of
the storm.
• In other words, it is the average ‘loss’ rate.
Φ-index...contd...

Assumes that infiltration occurs at

some constant or average rate
throughout the storm.

In comparison initial rates are under

estimated and final rates are over
estimated.

For an individual storm, φ, is

calculated as the total storm volume
losses;

Vol. losses = Vol. rain - Vol. runoff

For general application φ must be

correlated with basin characteristics.
• A second somewhat more detailed approach
solves for Φ by trial and error using the
following equation:

D1 (i1 − φ ) + D2 (i2 − φ ) + ... + Dn (in − φ ) = QT

Where: D is the duration of the rainfall intensity,

i is the rainfall intensity in the interval, QT is the total runoff
 Example

The rainfall intensities during each 30-min of a 150-min

storm over a 500-acre basin are 4.5, 3, 1, 3.5, and 2inch/hr,
respectively.

The direct runoff from the basin is 105 acre-ft. Determine

the φ index for the basin

Total rainfall = (4.5)*(1/2)+ 3(1/2)+1*(1/2)+3.5*(1/2)+2*(1/2)

= 7.0 in. or 0.583 ft
Rainfall volume = (500)( 0.583) = 291.5-acre-ft
Runoff volume = 105 acre-ft (given)
Volume under φ index = 291.5 – 105 = 186.5 acre-ft
Infiltration depth = 186.5/500 = 0.373 ft or 4.48 in.
φ index = 4.48/(150min) = 1.79 in./hr
>>>compute revised index excluding 1n./hr
Solution: φ index = 2 in./hr
 (iii) Infiltration Rate by
Soil Group/ Texture

Source: Texas Council of Governments, 2003.

 Infiltration Rate
Function of Slope & Texture

Source: Rainbird Corporation, derived from USDA Data

 Infiltration Rate
Function of Vegetation

Source: Gray, D., “Principles of Hydrology”, 1973.

 INFILTRATION MODELS
• Two groups of infiltration models
– Empirical models
– Conceptual models
• Empirical equations model infiltration as a
function of time
• Conceptual models represent infiltration using
physics of flow through porous media
 INFILTRATION MODELS
• Predictive equations allow estimating
infiltration as function of time given a set of
soil properties.
• Equations are typically incorporated into
hydrologic models.
• Allow determining infiltration with limited
measurements.
 HORTON’S MODEL
• One of the earliest and best known empirical
equations is from Horton (1939,1940)
• Robert Horton has made significant
contributions to the science of hydrology in
the areas of infiltration, surface runoff
generation, and drainage basin morphology.
 Horton Equation (1939)
Infiltration is a Function of Time as defined by:

f(t) = fc + (fo – fc)e-kt (1)

f(t) = infiltration rate for any time “t” from beginning of infiltration
fc = infiltration capacity
fo = initial infiltration rate at (t=0)
e = 2.71 =base of natural log
k is a measure of the rate of decrease in infiltration rate
(constant that depends on soil type)
Large Watershed Application - Replaced by Philip and Green-Ampt
Horton Method Used in EPA Storm Water Management Model
Cumulative Infiltration:

dF
= f c + ( f o − f c )e − kt
dt
dF 1 1
F =∫ = f c t − f o e + f c e − kt + c
− kt

dt k k
1 − kt
F = f ct + e ( f c − f o ) + c
k

Initial conditions: at t = 0, F = 0
1
0 = ( fc − fo ) + c
k
1
c = ( fo − fc )
k
 1
F = f ct + ( f o − f c ) 1 − e
k
[
− kt
] (2)

-This model is simple and fits well to the experimental data

-Principal weakness: determination of the parameters fo, fc and
k, these have to be determined by data fitting.

-Taking logarithm of equation (1):

ln( f − f c ) = ln ( f o − f c ) − kt (3)
 Equation (3) is the equation of a straight line in semi-
logarithmic plot, slope = -k,

Intercept ln (fo-fc) can be readily determined.

Example-Horton Model
Infiltration capacity of a soil at an experimental field-site located near the University
was measured. Initial infiltration rate was 4.5 cm/hr. A constant infiltration rate was
measured as 1.2 cm/hr. The best-fit constant for Horton’s model was 12 hr-1

a. Plot Horton’s Infiltration Curve.

b. Determine the cumulative infiltration for a 24-hour storm occurred in that
watershed.
 SOIL MOISTURE CONTENT

• Soil water content is an important and

variable hydrologic property in soils.
– Varies in space within small locations and over
large areas.
– Varies in time with response to rainfall and
evaporation.
– Varies with depth according to soil properties.
 Soil water status: content and potential

• The state of water in soil is described in terms

of the amount of water and the energy
associated with the forces which hold the water
in the soil.
• The amount of water is defined by water
content and the energy state of the water is the
water potential.
 Water content & Potential
• Plant growth, soil temperature, chemical transport,
and ground water recharge are all dependent on the
state of water in the soil.
• While there is a unique relationship between water
content and water potential for a particular soil,
these physical properties describe the state of the
water in soil in distinctly different manners.
• It is important to understand the distinction when
choosing a soil water measuring instrument.
 Water Content
• Soil water content is expressed on a
gravimetric or volumetric basis.
• Gravimetric water content (θg) is the mass of
water per mass of dry soil.
• It is measured by weighing a soil sample
(mwet), drying the sample to remove the
water, then weighing the dried soil (mdry).
• Volumetric water content (θv) is the volume of liquid
water per volume of soil.
• Volume is the ratio of mass to density (ρ) which gives:

• Soil bulk density (ρbulk) is used for ρsoil and is the ratio
of soil dry mass to sample volume.
 Porosity
• Another useful property, soil porosity (ε), is
related to soil bulk density as shown by the
following expression.

• The term ρsolid is the density of the soil solid

fraction and is approximated by the value
2.6 g cm-3.
Volume of solids: Mineral matter and Organic matter
 Water content
• Water content indicates how much water is
present in the soil.

• It can be used to estimate the amount of

stored water in a profile or how much
irrigation is required to reach a desired
amount of water.
Soil Moisture
 Infiltration & Soil Moisture Processes

once water reaches the earth’s surface it either

runs off, is evapotranspired or infiltrates the
surface by permeating into cracks, grooves, root
canals, animal/insect burrows or small pores in
the soil matrix…
once in the soil matrix, water is redistributed in
all directions as it is acted upon by many
forces… dominant forces control directions of
movements and are defined by soil energy
(pressure) potentials (Ψ)
 Infiltration & Soil Moisture Processes

for instance, high ET at soil surface can cause

water to move up from within soils to the surface
via exfiltration as driven by heat gradients &
vapour pressure gradients between the soil &
atmosphere
soil water can also move upward from the
saturated zone to the unsaturated zone via
capillary action which results from surface
tension force of water molecules to the walls of
thin pore channels (sediment surfaces)
 Infiltration & Soil Moisture Processes

soil water can also percolate downward under

it’s own weight (if pores are large or moisture
content is great) & drain to the water table,
thereby contributing to groundwater recharge
soil water may also flow laterally in the
unsaturated zone downslope to re-emerge at
the surface as return flow or as groundwater
baseflow in river systems
infiltration rates controlled by: soil texture,
structure, porosity, specific surface area
available for water adhesion & surface tension
 Soil Water types

• Each is distinguished by the amount of energy

(pressure or tension) required to hold it in the
soil/sediment matrix
1. Hygroscopic water: a very thin (microscopic)
layer of water held (adhered) tightly on the
surfaces of mineral grains
– stored at very high tension (-ve pressure) & is lost
only as vapour… thus, essentially ‘unavailable’ for
redistribution & for plant use… defines the
permanent wilting point (θpwp)
 Soil Water types

2. capillary water: water held by surface tension

in smaller pore spaces… due to a fairly high
tension, capillary water is resistant to
gravitational drainage but can flow upward
(and to some extent laterally) via capillary
action
3. gravitational water: stored in largest pores &
drains readily under it’s own weight…defines
the field capacity (θfc)
• managing these 3 types of water has important implications for:
runoff, groundwater recharge, nutrient &/or pollutant transport,
crop irrigation & drainage management…
 Soil Moisture Energy & Potential

• Terzaghi (1942) first noted that if gravity

were the only force acting on soil water,
soils would drain completely after each PPT
event… thus, soil water would only be
found below the water table
• under such conditions, plant growth would be limited to
areas where rainfall occurred frequently or to areas with
shallow groundwater tables… however, most soils (even in
very dry climates) always contain some amount of
moisture in their matrix that is held in place against gravity
via additional forces
 Soil Moisture Energy & Potential

• Essentially 4 main forces responsible for soil

moisture retention & movement:
1. adsorption force: generated by electrostatic
charges between polar water molecules &
charged surfaces of mineral grains (e.g.,
clays)… water molecules held (adhered)
very tightly (i.e., held with high tension)
 Soil Moisture Energy & Potential

2. capillary force: upward force generated by

surface tension between air & soil water
such that in smaller pores water is able to
rise further because cohesive force between
molecules (i.e., surface tension) + adhesion
to mineral surfaces > air pressure + gravity
acting down on pore water
• upward (& to some extent lateral) movement
against gravity & air pressure
 Capillary Force

• height of capillary rise inversely proportional

to pore radius & fluid density (viscosity)…
doubles with ½ reduction in radius
• rate controlled by porosity, pore orientation
& shape, air pocket
• finer soils (with smaller pores) have ↑ rise of
water but at slower rates due to greater
surface contact (friction)
 Ground surface 0 +ve
+ve -ve 0 +ve
Soil water zone
Unsaturated
or Vadose

Intermediate
zone

zone

Capillary fringe

depth
Water table
Saturated

Groundwater
zone

(a) (b) (c)

(a) Zones of subsurface water, (b) profile of moisture content θ, and (c) profile of pressure head
 versus depth.
 SurfaceTension

• As a result of surface tension water molecules at

the water table are subject to an upward attraction
(capillarity).
• An expression for the height of capillary rise in
unsaturated soils is usually arrived at by utilising
an approach similar to that used in classical
physics for the analysis of the binding of water in a
glass capillary.
• The phenomenon of capillarity may be illustrated
by inserting one end of a fine glass tube of radius r
into water. As a result of capillarity, water will rise in
the tube to a height hc.
 cos

hc

Water

Illustration of capillary rise using a glass tube

 Attraction Forces

• The rise of the water in contact with the tube is attributed to

the attraction between the sides of the tube and the water
molecules (adhesive forces).
• In contrast, the rise of the water not directly in contact with
the walls of the tube is due to cohesive forces between
water molecules.
• Water will eventually stop rising when the downward pull of
gravity exactly equals the sum of the adhesive and
cohesive forces.
 Adhesion

Adhesion
Cohesion

Gravity
b

Diagram showing the forces acting on a column of water in a glass tube

 Capillary Rise
• An equation for the height of capillary rise hc may
be written by considering the forces acting on the
column of water in the glass tube. The force acting
downward Fd is the weight of the column of water
and is given by

Fd=hcπr2ρw g

• Where ρw is the density of water and g is the

acceleration due to gravity.
 Upward Force
The force acting upward Fu is the vertical component
of the surface tension φ which acts around the
circumference of the tube
Fu=2πr φ cosθ
Where θ is the angle of wetting between the liquid
and the glass. At the point of maximum capillary rise
Fd must be equal to Fu.

Thus
hc=2 φ cosθ/(ρw gr)
 Soil Moisture Energy & Potential
3. gravitational force: downward force acting
on water mass stored in largest pores in the
soil matrix (i.e., only effective if moisture is
not held via capillarity or adhesion)
4. osmotic force: force caused by
concentration gradients in soil solution
(e.g., salts)…often small except in arid
environments
 Soil Moisture Energy & Potential

• forces of attraction in soil matrix (i.e.,

adsorption, capillary surface tension,
osmotic) serve to reduce the energy of
water to flow ‘freely’ as it would above the
soil surface (i.e., by gravity only)
• capillary & adhesion forces are said to exert
tension or suction force (i.e., a negative
pressure) on soil water compared to
atmospheric pressure
 Soil Moisture Energy & Potential
• as such, under unsaturated conditions water
will flow from H → L energy (or pressure)
along this negative (favourable) pressure
gradient…
– e.g., from atmosphere into soil, or within soil
matrix from wet → dry, large pores → small
pores, etc.
• often referred to as soil moisture pressure
potential, Ψp, measured as:
– F L-2 in Pa or N m-2… or bars (where 1 bar = 0.99
standard atmosphere at 101.3 kPa)… or pressure
head
 Soil Moisture Energy & Potential
• thus, Ψp describes force with which water is
attracted into (&held within the soil matrix)…
• amount of absorptive (capillary) force
available in soil matrix can be estimated
using:
– Ψm = 2 σ * cos θ / g r
where: Ψm = matric or capillary water pressure (suction head in
mm)
σ = surface tension of water (72.4 mN m-1 @ 10 °C)
θ = contact angle between water & soil grain surface (measure of
capillarity… usually 1 for water – sand contact)
g = specific weight of water (9.81 kN m-3 )
r = pore radius (mm)
 Soil Moisture Energy & Potential

 for average soil conditions, this simplifies to Ψm =

14.76 / r
 thus, for a sandy soil with pore radius ≈ 0.01mm,
Ψm = 1476 mm of potential suction head → a
‘thirsty’ soil indeed!
 this relates to the specific surface available for
capillary action (Table 1 below) & in general,
increases with finer grain sizes
Table 1Specific surface areas according to mineral type and
particle size

(Source: White, 1987)

Soil Moisture Energy & Potential

• total soil moisture potential, φ: a measure

of total available energy for soil water
movement relative to atmospheric pressure
• φ = Ψg + Ψp + Ψo (in cm or mm H20)
where Ψg = gravitational potential = g h → +ve
(downward) (h = height above datum… usually sea-level)…
Ψg drains water from upper horizons, recharges
groundwater
Ψp = pressure potential = -ve matric suction pressure
potential
 Soil Moisture Energy & Potential

• Ψo = osmotic potential = driven by solute

concentration gradients (salts, organic compounds)
in soil solution… generally negative as solutes move
from [H] → [L] via dissolution… often assumed
negligible.
 Example

Assume you bought a rose plant planted in a gallon-pot at local nursery. Your
“engineering brain” wanted to know the “soil-water status” of the soil in the pot. So,
you took a small soil core out of the soil container to experimentally determine the
gravimetric water content.

Your results from the experiment are:

Wet soil weight = 110 g

Dry soil weight = 100 g
Volume of the soil sample core = 75 cm3
a. What is the gravimetric water content of the soil?
b. What is the volumetric water content of the soil?
c. What is the porosity of the soil if the particle density of the soil is 2.6 g/cm3?
d. What is the amount of water in soil available for the rose plant? Present your result
in litres. (1 gallon = 3.79 liters)