GEOTECHNICAL

ENGINEERING

ECG 503

LECTURE NOTE 02

LEARNING OUTCOMES

Learning outcomes:

At the end of this lecture/week the students would

be able to:

Draw flow nets below concrete dams and

through earth dams.

Use the flow nets to determine quantity of

seepage flow.

In water retaining dams, unless the

foundations continue down to impervious

rock, a steady flow of water is set up

under the structure owing to the difference

in head. This may lead to an undesirable

amount of leakage and, with an upward

flow of water on the downstream side,

dangerous quicksand conditions may

occur, with possible subsequent failure of

the dam. This seepage can be studied by

the use of flow nets.

SEEPAGE THROUGH SOIL

HYDRAULIC GRADIENT

• Flow of water will occur if there is

a different height between point A

and B at a distance L

A

B

Lh1

i = h1

L

• The 2-Dimensional seepage refers

to the existing of flow in two-axis

(consider x-y plane)

What is a flow net ?

A flow net is a pictorial representation

of the paths taken by water in passing

through a material. It is made of flow

lines and equipotential lines

Flow lines are lines which represent

the path of flow through a soil.

Equipotential lines represent all

points of constant head.

Flow Nets

• Is a graphical construction equipotentials

and flow lines.

• Flow nets that are very complicated and

needs a greater understanding of a seepage

principles; some possible methods of

solution of technique can be used as :

• Finite Different Method

• Finite Element Method

• Electrical Analogy

• Used of Hydraulic Models

FLOW NETS – Construction Procedure

& Boundary Condition

1. The boundary conditions must be satisfied.

2. Flow lines must intersect equipotential lines

at right angles.

3. The area between flow lines and equipotential

lines must be curvilinear squares. A

curvilinear squares has the property that an

inscribed circle can be drawn to touch each

side of the square and continuous bisection

results, in a limit, in a point

4. The quantity of flow through each flow

channel is constant

5. The head loss between each

consecutive equipotential lines is

constant

6. A flow line cannot intersect another flow

line

7. An equipotential line cannot intersect

another equipotential line

By theoretically, any number of flowlines may be drawn and the greater the numbers, the more accurate should be. However, in practical, not more than five of six flow line isnecessary.

CALCULATE PORE WATER

PRESSURE

hz Nd Ndh Hp = Ndh - hz Uz = Hpw

The quantity of seepage can be determined using the following formula :

) //( 3

lengthmetredaymN

NkHQ

d

f

Where :Q = quantity of seepagek = permeability of the soilNf = number of flow intervals (channels)Nd = number of equipotential drops

Flow net below a sheet pile

Flow net under a concrete dam

Flow net under a dam with a cutoff curtain (sheet pile) on the upstream end.

WORK EXAMPLES

• Figure 1 shows the cross-section of a line of sheet piling driven to a depth of 7m into a stratum of homogeneous sandy soil which has a thickness of 12m and it is underlain by an impermeable stratum. From an original depth of 5.5m the water level on one side of the piles is reduced by pumping to a depth of 0.5m. Draw a flow net for the seepage condition and from it determine:

a. The quantity of seepage under the piles per

meter run

b. The pore water pressure in the soil at points P and Q

The coefficient of permeability, k = 7.2 x 10-3 mm/s

Guidelines of Solving Problem

1. Impermeable boundaries : along the

sheet piling BCD and along the

impermeable stratum GG; therefore

BCD and GG is flow lines

2. Permeable boundaries : along B’B the

pressure head is a constant 5.5m and

along DD’ the pressure head is 0.5m;

B’B and DD’ are therefore is

equipotential of a value of 5.5 and 0.5m

respectively.

A sheet pile was driven to a depth of 5 m into a

stratum of homogeneous sandy soil. The ground

thickness is 12.5 m and is underlain by an

impermeable stratum.For the sandy soil, the

coefficient of permeability, k = 3 x 10-4 m/s and its

unit weight, γ = 18.5 kN/m3.

a. What is the pressure head if a piezometer is placed at P, Q,

R and S?

b. Determine the total flow discharge in m3/day per metre run

beneath the piles,

c. Tabulate and plot the distribution of water pressure at points

‘a’ – ‘f’ behind the wall.

d. Determine the maximum exit gradient, and hence the factor

of safety against piping in front of the wall.

WORK EXAMPLES

a

b

c

d

e

f

FRONT OF WALL