Department of Civil Engineering
College of Engineering, UNITEN
Chapter 4
Subsurface Water
Unsaturated Flow
Infiltration
Groundwater
Unsaturated Flow
Subsurface water flows beneath the land surface.
Subsurface flow processes and the zones in which they
occur are shown in the figure.
Subsurface water zone and processes.
Unsaturated Flow
Three important processes are
Infiltration of surface water into the soil to become
soil moisture.
Subsurface flow (Unsaturated flow through the soil).
Groundwater flow (Saturated flow through the
soil/rock strata).
Unsaturated Flow
Soil and rock strata which permit water flow are
called “Porous Media”.
Flow is unsaturated when the porous medium still has
some of its voids occupied by air, and saturated
when the voids are filled with water.
The water table is the surface where the water in a
saturated porous medium is at atmospheric pressure.
Unsaturated Flow
Below the water table, the porous medium is
saturated and at greater pressure than atmosphere.
Above the water table, the porous medium is usually
unsaturated except following rainfall, when
infiltration from the land surface can produce
saturated conditions temporarily.
Subsurface and groundwater outflow occur when
subsurface water emerges to become surface flow
in a stream.
Soil moisture is extracted by ET as the soil dries out.
Unsaturated Flow
Cross section through unsaturated porous medium.
A portion of cross section is occupied by soil particles
and voids (air & water)
Unsaturated Flow
The Porosity () is defined as
=
Porosity
Volume of Voids
Total Volume
The range of  is approximately 0.25<<0.75 for soils,
the value depending on the soil texture.
Porosity is a measure of
how much of a rock/soil
is open space. This
space can be between
grains or within cracks
or cavities of the rock.
Unsaturated Flow
Soil Moisture Content
A part of the voids is occupied by water and the
remainder by air, the volume occupied by water
being measured by the Soil Moisture Content ()
=
Volume of Water
Total Volume
0.25< < ; the soil moisture content is equal to the
porosity when the soil is saturated.
Unsaturated Flow
Darcy Flux
Its sides have length dx, dy, dz in the
coordinate directions.
Volume
= dx.dy.dz
The volume of water contained in the
control volume = .dx.dy.dz
The flow of water through the soil is
measured by the “Darcy Flux” (q)
Q
q=
A
Control volume containing
unsaturated soil
Unsaturated Flow
Darcy’s Law
Darcy’s Law was developed to relate
the Darcy flux, q to the rate of head
loss per unit length of medium, Sf
q = KSf
Consider flow in the vertical direction
and denote the total head of the
flow by h
Sf = −
Control volume containing
unsaturated soil
h
z
h
q = −K
z
The negative sign
indicates that the total
head is decreasing in
the direction of flow
because of friction,
Darcy’s Equation
Hydrologic Processes - Infiltration
• Infiltration is the water that soaks into the surface of the
soil.
• The infiltration capacity, the maximum rate at which water
can infiltrate into a given soil at a given time, depends on
the soil physical properties and the depth of water that has
already infiltrated.
• The actual rate of infiltration depends also on the rainfall
intensity or the depth of water ponded on the catchment
surface.
• For impervious catchment surfaces, such as paved areas,
the infiltration capacity is so small that it can be neglected,
but for highly pervious surfaces, such as sands or lateritic
soils, most of the precipitation on the land surface may be
lost to infiltration.
(A) Cover and Storage
of a Natural
Watershed
(B) Cover and Storage
of an Urbanized
Watershed
(C) Flood Frequency
Curves for Natural
and Urbanized
Watershed
(D) Hydrographs for
Natural and
Urbanized
Watershed
12
Changes in Hydrology and Runoff Due to
13
Hydrologic Processes – Soil Moisture
• Soil Moisture is the water contained in the soil above the water table. It
is depleted by evaporation from the ground surface and by transpiration
through vegetation.
• The availability of soil moisture plays a key role in supporting natural
vegetation and agricultural crops.
• The amount of useful soil water varies between the ‘wilting point’ (the
lowest soil moisture content beyond which plant roots can no longer
extract water from the soil) and ‘field capacity’ (the maximum amount of
water a soil can hold against the action of gravity).
• Interflow (or sub-surface storm flow) is water that percolates in a nearly
horizontal direction through the soil and seeps out into stream channels
relatively quickly during or shortly after a storm period, without having
reached the ground water reservoir.
• Percolation is the movement of water (particularly in the vertical
direction) under hydrostatic pressure through rock or soil, excluding
turbulent flow through large openings (macropores).
Hydrologic Processes -Groundwater
• Groundwater is the water contained in saturated soil
(i.e. below the water table). The total volume of
groundwater storage may be very large compared to
the other components of the water balance.
• Groundwater flow, in general terms, is the flow within,
between or from groundwater systems.
• Baseflow is a general term for that portion of the
streamflow that seeps into the stream channels from
below the ground surface.
• Mostly, it is taken to include both groundwater flow and
interflow, but sometimes is used to mean only
groundwater flow, i.e. the outflow from the groundwater
store to streams that may continue for several months
after a storm event, and that is thus responsible for the
dry-weather flow in streams.
Typical Loss Model for Estimating Rainfall
Excess
Loss
Rainfall, Loss
Rainfall, Loss
Rainfall
Time
Time
(b) Constant Loss Rate
Rainfall, Loss
Rainfall, Loss
(a) Constant Fraction
Time
Time
Runoff
(c) Initial Loss-Loss Rate
(d) Infiltration curve
Curve
Rainfall
(e) U.S. SCS relations
Recommended Infiltration Models Parameters based on MSMA Manual
Note: Well drained sandy soils – A; Poorly drained clayey soils - D
Infiltration
Infiltration is a process of water penetrating from the
ground surface into the soil.
The factor influences the infiltration rate
1) condition of soil surface and its vegetative
cover
2) the properties of the soil: porosity and
hydraulic conductivity
3) the current moisture content of the soil.
Hydraulic Conductivity/Permeability is a measure of the ease with which
a fluid (water in this case) can move through a porous media.
Infiltration
The distribution of soil moisture
within the soil profile during
the downward movement of
water is illustrated in the
figure.
There are 5 moisture zones
1) Saturated zone
2) Transition Zone
3) Transmission zone
4) Wetting zone
5) Wetting front
Moisture zones during infiltration.
Infiltration
1) Saturated Zone :
near the surface, extending up to about 1.5 cm below the
surface and having a saturated water content.
2) Transition Zone :
which is about 5 cm thick and is located below the
saturated zone. In this zone, a rapid decrease in water content
occurs.
3) Transmission Zone :
the water content varies slowly with depth as well as time.
Infiltration
4) Wetting Zone :
in which sharp decrease in water content is observed.
5) Wetting Front :
a region of very steep moisture gradient. This represents
the limit of moisture penetration into the soil.
The infiltration rate, f expressed in inches per hour or
centimeters per hour, is the rate at which water
enters the soil at the surface.
If water is ponded on the surface, the infiltration
occurs at the Potential Infiltration Rate.
Infiltration
If rainfall at the surface is less than the potential infiltration rate
then the actual infiltration rate will also be less than the potential
rate.
Most infiltration equations describe the potential rate.
The cumulative infiltration, F is the accumulated depth of water
infiltrated during a given time period and is equal to the integral of
the infiltration rate over that period.
t
F(t) =  f()d
 is variable of time in the integration.
0
dF(t)
f(t) =
dt
The infiltration rate is the time derivative
of the cumulative infiltration.
Horton’s Equation
Horton’s
Equation
•
•
•
•
•
•
Infiltration process of movement of water into soil under gravity and capillary
forces.
A simple infiltration model was suggested by Horton (1933)
It state that the rate of infiltration of rain water into soil decrease exponentially
with time during a storm event.
Some hours during the storm, the infiltration rate maybe closed to zero as the soil
becomes saturated.
The concept of infiltration based on Horton model which relates between
infiltration capacity, f and rainfall duration, t is as shown :
When i > f at all times, Horton’s equation can be written as
f = fc + (f0 – fc ) e-kt
Where
f 0 is the initial infiltration rate
fc is the final infiltration rate
f is the infiltration rate at a time
k is the empirical constant for time
Horton’s Equation
Horton’s
Equation
•
•
•
•
•
In Horton’s equation, k is a function of surface texture where k decrease with
increasing vegetation.
Also, fo and fc are function of soil types and covers.
The figure shows the variation of infiltration rate with soil cover, rainfall
intensity and slope.
The figure indicates that low rainfall intensity will have a lower proportion of its
rainfall infiltrates than a high rainfall intensity event.
Another important parameter is the cumulative infiltration, F. It represents the
volume of infiltration from the beginning of rainfall to the end of rainfall. It is
sometimes called infiltration volume or accumulated infiltration.
Example – Horton’s Eq
Infiltration capacity data obtained in a flooding type infiltration test in given in Table
below.
(a) For this data plot the curves of (i) infiltration capacity vs time (ii) infiltration
capacity vs cumulative infiltration and (iii) cumulative infiltration vs time
(b) Obtain the best values of the parameters in Horton’s infiltration capacity
equation to represent this data set.
Time since start (minutes)
Cumulative Infiltration
depth (cm)
5
1.75
10
3.00
15
3.95
25
5.50
45
7.25
60
8.30
75
9.30
90
10.20
110
11.28
130
12.36
The best fit straight line through the plotted points could be expressed as
ln(fp – fc) = 2.8868-2.6751t
-K=slope of the best fit line = -2.6751
Thus K = 2.675/h and
Ln(fo – fc) = intercept = 2.8868 giving (fo – fc) = 17.94;
Since fc = 3.24 cm/h, fo = 17.94 + 3.24 = 21.18 cm/h
Infiltration
Horton’s Equation
One of the earliest infiltration equations was developed by Horton
(1933, 1939) who observed that
“infiltration begins at some rate, fo and exponentially
decreases until it reaches a constant rate, fc”
f(t) = fc + (f0 − fc )e
−kt
K = a decay constant having
dimensions [T-1]
Infiltration by Horton’s Equation.
Location plan and layout of HTC Kuala Lumpur
134
SEK SYEN 60
K AWASAN BANGUNAN PARLI M EN
84
782
SEK SYEN 97
128
FIGURE 2.1 : LOCATION PLAN AND
AND HTC LAYOUT PLAN
ZHL ENGINEERS SDN BHD
PROPOSED WSUD COMPONENTS
Grey Water Treatment System
Porous
Pavement
Toilet
Cabin
Garaj
Office
Building
Garden
Surau
Office
Building
Bio
Retention
Green Roof
Rainwater Tank
Porous
Pavement
Bio
Retention
Detention Pond /
Wetland
• Based on MSMA Volume 12 (Chapter 32 Infiltration section 32.2.1), one of the general limitations for suitability
of soil for quality infiltration is the minimum infiltration rate fc
is 13 mm/hr.
Soil Properties Classified by Soil Texture (Source: Puget Sound,
1992)
ZHL ENGINEERS SDN BHD
• The method used for this testing is by using the
Hand Auger Test Pit/Boring Method based on
MSMA Volume 8 Chapter 21 (Appendix 21.A –
Soil Infiltration).
Table 1: Infiltration Testing Summary (Source: MSMA Volume 8
Table 21.A1
Type of Facility
Initial Feasibility Test
Trench
1 field infiltration test, test pit not required
Concept Design Testing
1 field infiltration test & 1 test
pit per 15m of trench
1 field infiltration test & 1 test
Basin
1 field infiltration test, test pit not required
pit per 50m2 of basin area
1 field infiltration test & 1 test
Biofiltration
1 field percolation test, test pit not required
pit per 15m of filter area
(no under drains required)
ZHL ENGINEERS SDN BHD
Soil exploration using
hand auger
Water filled into the hole
Water level is measured
Infiltration Curve (Infiltration
Rate and Cumulative Depth vs.
Time
ZHL ENGINEERS SDN BHD
Summary of the results:
Parameters (Average)
Point A – Bio
Retention
Point B Wetland
Point C – Porous
Pavement
Initial Rate of Infiltration (f0)
(mm/hr)
130.43
246.58
789.63
Constant Rate of Infiltration (fc)
(mm/hr)
4
13
13.43
Shape factor (k) (hr-1)
6.511
4.354
9.448
Ratio f0/fc
34.17
26.48
73.07
Horton Equation
f = fc+(f0 – fc)e-kt
f = 3 + (130.43 –
4)e-6.65t
f = 9 + (246.58 –
13)e-4.354t
f = 13.43 + (789.63
– 13.43)e-9.448t
ZHL ENGINEERS SDN BHD
Infiltration
Phillip’s Equation
Philip (1957, 1969) solved the equation to yield an infinite series for
cumulative infiltration, F(t), which is approximated by
F(t) = St1/ 2 + Kt
S = a parameter called sorptivity (which is a function of the
soil suction potential)
K = hydraulic conductivity
By differentiation
1 1/ 2
f(t) = St + K
2
As t → , f(t) tends to K
For a horizontal column of
soil, soil suction is the only
force drawing water into
the column
F(t) = St1/ 2
Infiltration
Infiltration Rate (cm/hr)
Cumulative Infiltration, cm
Phillip’s Equation
Infiltration Time (hr)
Variation of infiltration rate and
cumulative infiltration with time
Green Ampt’s Equation
Green Ampt’s Equation
▪It is a very old model proposed by Green and Ampt (1911). This model is based on
Darcy’s Law.
▪It is meant for infiltration into uniform soil to uniform initial moisture content due to a
pool of water whose depth can be neglected.
▪The water is assumed to infiltrate into the soil and there is a distinctly definable
wetting front of the water as shown in following figure.
▪The wetting can be considered as a plane separating a uniformly wetted infiltrated
zone from a totally unwetted zone.
▪Once the soil is wetted, the moisture content does not change with time as long as infiltration
continuous.
▪The Green-Ampt model can be written as :
f = Ks (L +H+S )/L
where :
L is the distance from the ground surface to the wetting front,
H is the depth ponding above the soil surface normally taken as zero,
S is the capillary suction at the wetting front,
Ks is the saturated hydraulic conductivity of the soil.
Negligible ponded
Green Ampt’s Equation
Depth of water
Green Ampt’s ’s Equation
Negligible ponded
Depth of water
H
L
Wetted soil
Wetting front
Unwetted soil
Parameters Ks and S can be determined from laboratory and analysis on
soil samples.
Infiltration
Soil Texture
Porosity (%)
Basic Infiltration Rate (cm/hr)
Sand
32-42
2.5-25
Sandy Loam
40-47
1.3-7.6
Loam
43-49
0.8-2.0
Clay Loam
47-51
0.25-1.5
Silty Clay
49-53
0.03-0.5
Clay
51-55
0.01-0.1
Based on MSMA Manual – min infiltration rate is 13 mm/hr.
Example 1
In a 10 hour storm event, the following rainfall intensity were observed
over the catchment. Surface runoff resulting from the storm is equivalent
to 20 cm of depth over the catchment.
Time (h)
Rainfall intensity
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
(cm/h)
1.0
1.5
5.0
6.0
10.5
8.5
9.0
7.0
1.5
10.0
1.5
Total
51.5
Determine:
1. Infiltration capacity, fi
2. Infiltration rate, f
Example 1 - Solutions
Total rainfall in 10 hours = 51.5 cm
Total runoff in 10 hours = 20.0 cm
Therefore,
Total infiltration in 10 hours = 51.5-20.0 = 31.5 cm
Then,
Infiltration capacity, f = 31.5 /10 = 3.15cm/h.
It is obvious that, the rainfall is less then the average infiltration capacity during
first, second, ninth, and tenth hour and the infiltration rate is equal to the rainfall
intensity.
During third to eight hour, the rainfall is more than the infiltration thus resulting in
runoff occurrence.
Let fi be the infiltration rate during these 6 hours,
Therefore,
1.0 + 1.5 + 6fi + 1.5 + 1.5 = 31.5 cm.
Thus, the infiltration rate fi = (31.5-5.5)/6
= 4.33 cm/h.
Example 2 – Horton’s Eq
The following infiltration characteristic are meant for particular catchment area:
f0, = 100 mm/h ; fc , = 10mm/h ; k= 0.35/h
Calculate infiltration rate at 1 hour, 2 hours and 6 hours for the catchment .
Solutions:
Using equation ;
f = fc + (f0 – fc ) e-kt
f= 10 + 90 e-0.35t
For t =1h ; f = 73.4mm/h
For t = 2h ; f = 54.6mm/h
For t = 6h ; f = 21.0 mm/h
Example 3
A small tube with a cross-sectional area of 40 cm2 is filled with soil
and laid horizontally. The open end of the tube is saturated, and
after 15 minutes, 100 cm3 of water have infiltrated into the tube. If
the saturated hydraulic conductivity of the soil is 0.4 cm/hr,
determine how much infiltration would have taken place in 30
minutes if the soil column had initially been placed upright with its
upper surface saturated.
The cumulative infiltration depth in the horizontal column is F = 100
cm3/40 cm2 = 2.5 cm.
For horizontal infiltration, cumulative infiltration is a function of soil
suction alone so that t = 15 min = 0.25 hr
F(t) = St1/ 2
F(t) = 2.5 cm, t = 0.25 hr , therefore S = 5 cm.hr-1/2
Example 3
For infiltration down a vertical column, applies with K=0.4 cm/hr.
Hence, with t = 30 min = 0.5 hr.
1 1/ 2
f(t) = St + K
2
S = 5 cm.hr-1/2, t = 0.5 hr, K = 0.40
F = 3.74 cm