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The study of flow through the soil is necessary to:
Estimate the quantity of seepage flow
Estimate the hydraulic gradient (i), and to check the
possibility ofboiling orquick condition
Estimate the pore water pressure distribution
Decide on the best locations for cut-off walls, filters,
instrumentation etc.
Compute effective vertical stress
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Velocity of seeping water is usually very small; and,
therefore, velocity head is negligible, i.e,
Therefore,
w
u
h z
2
0
2
v
g
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As water flows from one point to another, some energy is
consumed or some head is lost
11 1
22 2
,&w
w
uh z
uh z
1 2
1 2
1 1
1 1
h h h
h h h
u u
z z hw w
Direction of flow ?
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The set of flow lines and equipotential lines can be obtained by
Mathematical analysis: The solutions are possible only for
simple boundary conditions. For complex conditions we can use
finite difference or finite element methods
Models: Electrical analogy model or fluid model
Graphical method: Drawing a flow net by trial and error
Seepage Theoretical Aspects
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Flow Lines define the physical path of flow Equipotential Lines are lines with constant total head Together, these lines constitutes a Flow Net
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Usually horizontal permeability is greater than vertical permeability
To use Laplace equation, we need to transform coordinates; the coord
can be transformed by using following relation
For example: kx = 4.kz x' = 0.5x
Draw flow net in a transformed section Once the flow net is completed, it can be re-drawn (stretched
horizontally) to the natural scale
In this case, the nets are not squares and the equipotential lines and flow
lines do not intersect at 90
02
2
2
2
z
hkx
hkzx
x
z
kkxx '
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The flow lines will deflect at the interface of layers withdifferent perm abilities
Spacingbetweenflow linesincreases
Spacing betweenflow lines decreases
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The flow lines will deflect at the interface of layers withdifferent perm abilities
The continuity of flow lines is maintained; although there
is an abrupt change in direction of flow
The number of flow channels and equipotential lines must
remain constant throughout the flow net
Soil layer with high permeability dominates the flow
location and quantity Thus flow net can be drawn for soil with high permeability
and extended into soil of low permeability to meet the
other requirements
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Phreatic surface
The phreatic surface connects points at which the pressure head is
zero Atmospheric pressure acts on the phreatic surface Phreatic surface is assumed as a flow line and flow net can be drawn
after locating the phreatic surface
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The drain is made of gravel, which has an infinite hydraulic
conductivity compared to that of the clay The hydraulic gradient in a drain is effectively zero, i.e. the drain is
an equipotential line
Phreatic surface
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30
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31
1. Obtain.
2. Calculate and
then 0.3 .
3. Calculate d
4. With known values
of and d, calculateL.
5. With known valuesof L, calculate q.
A step-by-step procedure to obtain the seepage rate q (per unit length ofthe dam) is as follows:
2sinkLq
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