# permeability .ppt

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```					        Seepage Through Porous Media
W.T.

Impervious Soil

)h = hA - hB

W.T.

hA = total head

Impervious Soil
Datum
W.T.

Impervious Soil

)h = hA - hB

q = v . A = k i A = k DhA
W.T.

hA
Water In
L
Impervious Soil

Datum
hB

or Energy Loss
)h =hA - hB

i = Hydraulic Gradient
hA
(q)
Water
out
hB

ZA                                                                                             ZB

Datum
Bernouli’s Equation:
Total Energy = Elevation Energy + Pressure Energy + Velocity Energy

or

htotal =      Z        +      P     +    V2
g          2g

Darcy’s Law:
v%i             v = discharge velocity & i = hydraulic gradient
v=ki            k = coefficient of permeability

v = k )h/L
To determine the rate of flow, two parameters are needed

* k = coefficient of permeability
* i = hydraulic gradient

k can be determined using
1-     Laboratory Testing          [constant head test & falling head test]
2-     Field Testing               [pumping from wells]
3-     Empirical Equations

i can be determined
1-    from the head loss
2-    flow net
Seepage Through Porous Media
Water In

L = Drainage Path                      Head Loss or
or Energy Loss
i = Hydraulic Gradient
)h =hA - hB

hA
Water
out
hB
Soil                                          Datum
A                                   B

Porous                                             Porous
Stone                     L                        Stone
Seepage Through Porous Media
Water In

L = Drainage Path                      Head Loss or
or Energy Loss
i = Hydraulic Gradient
)h =hA - hB

hA
Water
out
hB
Soil
A                                   B

Porous                                               Porous
ZA    Stone                     L                          Stone            ZB
Datum
No Seepage                                      Piezometer
In
Flow
3 ft

D
Out
Flow
2 ft
C

u = 6 x 62.4
4 ft

14 ft
B
u = 14 x 62.4

W
s
W
12 ft   s
W
s

W        W
s
s

Buoyancy
8 ft

A

3 ft                                                           3 ft             Datum
Upward Seepage    In
Flow                                              Piezometer

3 ft
Du
D
Out

u = 6 x 62.4 + Du
Flow
2 ft
C

4 ft

17 ft
B
u = 17 x 62.4
12 ft
W
s
W              W
s              s

8 ft                   W   W
s
s

Buoyancy + Seepage Force
A

3 ft                                                                  3 ft                    Datum
Downward Seepage                                         Piezometer

3 ft
In
D    Flow

2 ft
C

u = 6 x 62.4 - Du
Out
Flow                                                      4 ft

B
u = 17 x 62.4

10 ft                                                             12 ft

Seepage Force

8 ft
W
s
W                       W
s                       s

W        W
s
s

A                     Buoyancy - Seepage Force

3 ft                                                             3 ft                         Datum
No Seepage

1                            1
g1 =110 pcf
W.T.   3 ft
2                                 2

4 ft

3                                     3

-                                                   6 ft
=
4                                         4

12 ft

5                                                5

Total Stress           Pore Water         Effective Stress
Pressure
Total Stress                         Pore Water Pressure          Effective Stress
u1 =                          s1 =
s1 =                                                                                                                         W
u2 =                              s2 =                                                 s
s2 =                                                                                                          W                    W
s
u3 =                              s3 =                                                       s
s3 =                                                                                                                W        W
u4 =                              s4 =                                        s
s4 =                                                                                                                         s

s5 =                                   u5 =                             s5 =
Buoyancy
No Seepage

W.T.
1
g1 =110 pcf
3 ft

4 ft

2

-                                                 6 ft
=
3

12 ft

4
Total Stress           Pore Water       Effective Stress
Pressure

W
s
W                    W
s                    s

W        W
s
s

Buoyancy
No Seepage                                  W.T.
1

3 ft
2
g1 =110 pcf
3 ft

4 ft

3

-                                                 6 ft
=
4

12 ft

5
Total Stress           Pore Water       Effective Stress
Pressure

W
s
W                    W
s                    s

W        W
s
s

Buoyancy
Upward Seepage

5 ft                       1
g1 =110 pcf
W.T.   3 ft
2

4 ft

3

-                =                                   6 ft

4

12 ft

54                                            4
Total Stress            Pore Water
Effective Stress
Pressure
W
s
W             W
Total Stress   Pore Water Pressure                   Effective Stress                                s             s

W   W
s
s

Buoyancy + Seepage Force
Downward Seepage

g1 =110 pcf
W.T.   3 ft
1                              1

3 ft
4 ft

2                              2

-                        =                                  6 ft

3                               3

12 ft

4                            4
Total Stress                   Pore Water
Effective Stress
Pressure                                                     Seepage Force

Total Stress            Pore Water Pressure            Effective Stress
W
s
W                       W
s                       s

W        W
s
s

Buoyancy - Seepage Force
g1 =110 pcf
W.T.   3 ft    W.T.   3 ft

4 ft           4 ft

6 ft           6 ft

12 ft          12 ft
q = A k i = A k Dh
L

Equipotential
Lines
Flow Lines
Principles of the Flow Net

Equipotential Lines

Flow Element
Principles of the Flow Net

)h = head loss = one drop

Piezometer

1

2
3

4

5

Flow Element

Equipotential Lines
Total heads along this
line are the same

Datum
In
Flow
)h
)h
)h
)h                   3 in
)h
)h
)h
)h

Out        2 in
Flow
8

Feff =     *(soil + * (water - ( - )h) * (water
7

14 in        6

u = [14 - (3. )h)].(water
5

4
Ws

3                              Ws                Ws

Ws
2                                        Ws

1   2

Buoyancy + Seepage Force
Seepage Through Porous Media
IN
qx(in) = dz . dy kx (Mh/Mx)
qx(in) = dx . dz ky (Mh/My)

OUT
qx (out) = dz . dy kx (Mh/Mx + M2h/Mx2 dx
)
qx (out) = dx . dz ky (Mh/My + M2h/My2 dy
)

Equating q in and q out

Two sets of curves
Rate of Discharge = qout

Z                                                     Rate of Discharge = qin
dy
X
dZ
Y

Rate of Discharge = qin                                      Rate of Discharge = qout
dx

Rate of Discharge = qin
(Rate of Discharge)in = (Rate of Discharge)out

Rate of Discharge = qin

```
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 views: 222 posted: 3/17/2012 language: English pages: 20
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