mektan i 2 flow nets

8/20/2019 Mektan I 2 Flow Nets

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1.

Permeabil ity coefficient in stratified soil

2. Permeability test in the field

3. Seepage and Flow-net

4. Uplift pressure on hydraulic structure

5. Seepage through an earth dam on impervious base

6.

Soil compaction

Soil Mechanics I(T. Faisal Fathani)



SeepageFlow nets:To calculate the flow of water through soil which is not in one direction

only, nor is it uniform over the area perpendicular to the flow.

The concept of flow nets Laplace’s equation of continuity

H1

H2

h

dz

dx

Impermeable layer

Sheet pile

A Single-row sheet piledriven into permeable

layer



Flow at A:

dx

dz

dy

vz dx dy

vx dz dy

Laju perubahan

kecepatan aliran

Assuming the water is incompressible

and that no volume change in soil

mass:

2D seepage continuity equation:

If the volume change:(1)



With Darcy’s Law, discharge velocities:

kx = hydraulic conductivity in horizontal direction

kz = hydraulic conductivity in vertical direction (2)

From Eq (1) and (2):

If the soil is isotropic, kx = kz ; continuity equation for 2D flow:

(1)



Flow nets:- Flow lines: a water particle will travel from upstream

to downstream side in permeable soil medium- Equipotential lines: potential head at all points is

equal.

H1

H2

Impervious layer

Sheet pile

Flow line

Equipotential

line



- Equipotential lines intersect the flow lines at right angles

- The flow elements formed are approximate squares

H1

H2

Impervious layer

Sheet pile

a b

c

d e

f g

Nf = 4Nd = 6



H1

H2

Impervious layer

a d

Nf = 4Nd = 8

H

Flow net under a dam



The rate of seepage through the flow channel per unit length.

Because no flow across the flow lines:

From Darcy’s Law:

Seepage calculation from a Flow Net

(flow channel

square elements)

q

q

h1

h2h3

h4l 1

l 2

l 3

l 1

l 2

l 3

q1q2

q3

h1, h2, h3, hn = piezometric

levels corresponding to the

equipotential lines



H = head difference between upstream and downstream sidesNd = Number of potential drops

Nf = Number of flow channels

Total rate of flow through all the channels per unit length:

Flow elements are drawn as approximate potential drop between

any 2 adjacent equipotential line is the same

The rate of flow through a flow channel per unit length:



The rate of flow through the channel:

q

q

h1h2

h3h4

b1

b2

b3

l 1

l 2l 3

Seepage calculation from a Flow Net

(flow channel

rectangular elements)



H1

H2

Impervious layer

Sheet pile

Channel-1Channel-2

Channel-3



15 m

5 m

Impervious layer

Sheet pile

I II

III

30 m a

b

c

d 1 2 3 4 5

Example-1

(a)

How high (above the ground surface) the water will rise if

piezometers are placed at points a, b, c dan d

From the figure : Nf = 3 dan Nd = 6

Potential drop between 2 equipotential lines: H/Nd = 10/6 = 1,667 m



Point a is located on equipotential line 1

Potential drop at a = 1 x 1,667 m

• Water in piezometer at point a will rise to an elevation of

(15-1,667) = 13,333 m above the ground surface.

Similary, the piezometer levels for:

• Point b = (15 - 2 x 1,667) = 11,67 m above the ground surface

• Point c = (15 - 5 x 1,667) = 6,67 m above the ground surface

•

Point d = (15 - 5 x 1,667) = 6,67 m above the ground surface



(b) The rate of flow through flow channel II per unit length:

(c) Total rate of flow through all the channels per unit length



4,5 m

0,5 m

Impervious layer

Sheet pile

6 m

8,6 m

Datum

h = 4 m h = 0

A

B C

E

D

2. Draw flow nets of the following case:



•

From flow nets:

•

Potential drop between 2 adjacent equipotential lines:

•

Total volume of flow under the sheet pile per length of sheetpile :

•

Total head at every points on the same equipotential line

with number (n

d) =• A piezometer at point P on equipotential line : nd=10. Total

head at point P:

Nf = 4,3

Nd = 12



4 m

Impermeable layer

Sheet pile

4,8 m

Datum

3. Draw net water pressure distribution at the sheet pile.

4,7 m

2,5 m



Total head at the water table (upstream) = 2,5 m

(pressure head = 0; elevation head +2,50 m)

Total heal at the ground surface in front of sheet pile(downstream equipotential) =0 (pressure head = 4,00 m; elevation head = -4,00m)

Nd = 12



Water pressure at both sides of sheet pile no. 1-7

example, at Surface 4, Total head behind the sheet pile:

Total heat in front of sheet pile:

Elevation heat at the surface 4 = -5,5 m

Net pressure behind the sheet pile :

Similar calculation for the other point



Example 4



q = 0,25 m3/hour

per length

Nf = 6,0Nd = 11



• Hydraulic conductivity of sand:

•

Hydraulic gradient below the excavated surface :

Distance (s) between 2 last equipotential line = 0,9 m.

mektan i 2 flow nets

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