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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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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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