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Permeability
Soils are permeable due to the existence of interconnected voids through which wa
ter can flow from points of high energy to points of low energy. The study of the flow
of water through permeable soil media is important in soil mechanics. It is necessary
for estimating the quantity of underground seepage under various hydraulic con
ditions, for investigating problems involving the pumping of water for underground
construction, and for making stability analyses of earth dams and earthretaining
structures that are subject to seepage forces.
6.1
Bernoullil's Equation
From fluid mechanics, we know that, according to Bernoulli's equation, the total head
at a point in water under motion can be given by the sum of the pressure, velocity, and
elevation heads. or
t t t
Pressure
Velocity
Elevation
head
where h
=
total head
u
=
pressure
v
=
velocity
g
=
acceleration due to gravity
y,,,
=
unit weight of water
Note that the elevation head,
Z,
is the vertical distance of a given point above or be
low a datum plane. The pressure head is the water pressure,
u,
at that point divided
by the unit weight of water,
7,.
If Bernoulli's equation is applied to the flow of water through a porous soil
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Chapter 6
Permeability
1
1
Datum
Figure
6.1 Pressure, elevation, and total heads for flow of water through soil
I
medium, the term containing the velocity head can be neglected because the seepage
velocity is small, and the total head at any point can be adequately represented by
I
Figure 6.1 shows the relationship among pressure, elevation, and total heads
for the flow of water through soil. Open standpipes called
piezometers
are installed
at points
A
and B. The levels to which water rises in the piezometer tubes situated at
points
A
and B are known as the
piezometric
levels of points
A
and B, respectively.
The pressure head at a point is the height of the vertical column of water in the pie
zometer installed at that point.
The loss of head between two points,
A
and B, can be given by
The head loss,
Ah,
can be expressed in a nondimensional form as
where i
=
hydraulic gradient
L
=
distance between points
A
and Bthat is, the length of flow over
which the loss of head occurred
In general, the variation of the velocity v with the hydraulic gradient
i
is as
shown in Figure 6.2. This figure is divided into three zones:
1.
Laminar flow zone (Zone I)
2.
Transition zone (Zone
11)
3.
Turbulent flow zone (Zone
111)
6.2
Darcy's
Law
141
A
Zone
111
Turbulent flow zone
Zone
I1
Transition zone
8

Zone I
'
Larninarflow
zone
+
Hydraulic gradient, i
Figure
6.2 Nature of variation of v with hydraulic gradient, i
When the hydraulic gradient is gradually increased, the flow remains laminar in
Zones I and 11, and the velocity, v, bears a linear relationship to the hydraulic gradi
ent. At a higher hydraulic gradient, the flow becomes turbulent (Zone 111). When the
hydraulic gradient is decreased, laminar flow conditions exist only in Zone I.
In most soils, the flow of water through the void spaces can be considered lam
inar; thus,
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This note was uploaded on 02/27/2011 for the course CE 383 taught by Professor Marika during the Spring '07 term at Purdue UniversityWest Lafayette.
 Spring '07
 Marika
 Geotechnical Engineering

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