Seepage Analysis

Dr. Sayed Mohamed Elaraby

Ain Shams University

Faculty of Engineering

Structural Engineering Dept.

Geotechnical Group

3rd Year Civil

1

Table of Contents

Laplace Equation

Graphical Solution (Flow Nets)

Anisotropic Soils

Seepage Force

Check Heave

Check Piping

Filter Design

Earth Dams Phreatic Line in Earth Dams

Analytical Determination of the Phreatic Line and the Discharge

Flow Net for Earth Dams

2

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th Ed.

Laplace (Continuity) Equation

3

If the soil is isotropic

Solutions to Laplace's Equation

Computer solutions using finite element or

finite difference techniques.

Graphical solutions known as flow nets.

Flow Nets

4

Flow Lines and Equipotential Lines

A flow line is the path a water particle would follow in moving

from upstream to downstream.

An equipotential line is a line along which the total head is a

constant value.

Rules for Flow Net Construction in Isotropic Soils

Draw the situation to scale.

Establish the equipotential boundary conditions.

Establish the flow boundary conditions.

Flow lines and equipotential lines must always intersect at

right angles.

Fields are the spaces in a flow net formed by the intersecting

flow lines and equipotential lines. The fields should be

"square"

5

6

If piezometers were inserted into the ground with their tips on a single

equipotential then the water would rise to the same level in each standpipe

nd= 10

Dh= H/nd = H/10

Datum H 0

0.9H

0.8H

0.7H

0.1H

0.2H

0.3H

0.6H

0.5H

0.4H

nh= 4

No. of head drops

No. of flow channels

7

H 0 nd= 10

Dh= H/nd = H/10

nf= 4

No. of head drops

No. of flow channels

Flow channel

L

L

DQ Dq = K i L 1 = K (DH/L) . L = K . DH

Dq = K . H / nd

Q = Dq . nf = K H (nf / nd)

Shape factor = (nf / nd)

8

Example

= 6m = 9m

= 3m

40m

2m

40m

4.6

7

3.6

7

4.3

3

3.0

0

1m

2.3

3

1.6

7

1.0

0

-5.0

0

-4.0

0

-5.0

0

ht

z

Pressure head (u/gw)= total head - position head

= 10-5 m/sec

q = K H (nf/nd)

q = 10-5 x 6 x (5/9)

= 3.33x 10-5 m3/sec/m

= 2.88 m3/day/m

Pressure head (u/gw)

9.6

7

5.0

0

4.0

0

4.0

0

Anistropic Soils

9

Transformations

10

Seepage force

11 11

H 0

Net seepage force = (P1-P2) L

L

L

P1= gw (h+Dh)

P2= gw h

= gw . Dh . L

Net seepage force per volume = (gw . Dh . L ) / L2

Net seepage force per volume = gw . i

g’s . Volume

gw . i. Volume

H 0

12

Check Heave

13

Example

Datum

gw = 62.4 lb/ft3

nd = 6 Dh = 25/6 = 4.167 ft

25 0

20.833

16.667 12.5 8.33

4.167

7

12.5

iav = [0.5 ( 12.5+7) – 0] / 20 = 0.488

FOS = [(112-62.4) / 62.4] / 0.488 = 1.62

14

Check Piping

15

exitexit L

hi

Dexit

critical

i

iFOS

wcriticali g

g '

Lexit

Lexit

Filter design

16

Uncontrolled seepage accounts for approximately 50% of all dam failures in USA.

Erosion piping (aka., suffusion / suffosion: fines are washed away by seepage) may be responsible for up to 30% of all piping failures.

Filter allows drainage without suffusion.

17

18

Retention criteria:

D15, F < 4 to 5 D85, s

Permeability criteria:

D15, F > 4 to 5 D15, S

The size of the voids in the filter material should be small enough to

hold the larger particles of the protected material in place.

The filter material should have a high hydraulic conductivity to

prevent buildup of large seepage forces and hydrostatic pressures in

the filters.

Diameter (mm)

Pa

ssin

g (

%)

A

5A B 5B

19

Diameter (mm)

Pa

ssin

g (

%)

A

5A B 5B

Additional Filter requirements:

Fines % < 5 %

Maximum grain size = 75 mm

U ifor ity coefficie t ≤ 3

Phreatic Line in Earth Dams

20

m

0.3m

Focus

The phreatic line is the groundwater

surface with the pressure head = 0

The total head = the position head

Phreatic line is a flow line

21 2 3 1

22

23

a

Da

b

Da + a Da

Da + a

Da

24

Casagrade 1st graphical approximation b < 30

25

Casagrade 2nd graphical approximation b < 60

(it remains a good approximation to b < 90)

26

b b b b b b b b

Analytical Determination of the Phreatic

Line and the Discharge

27

28

Flow Net for Earth Dams

29

30

Questions ?