Geotechnical Engineering

DHARM

SEEPAGE AND FLOW NETS 183

downstream slope are designated G and E respectively, EF and GE are designated a and ∆a
respectively. The underdrainage case is defined by value of 180° for α. The top flow line meets
the downstream face tangentially at the breakout point E.

The top flow lines for typical inclinations of the discharge faces are shown in Fig. 6.17.

a

S/2

Dh

Dh

Da

S

a

Top flow

line

Discharge

face

Top flow

line

Discharge

face

a

Dh

Dh

Da

Rock

toe

S/2

Dh

Dh

a

S/2

Da

Rock

toe

S

Top flow line

Discharge

face

Top flow line

Vertical

S Horizontal filterunder the dam

Focus S/2

(a)a< 90° (b)a= 90°

(c) 90° <a< 180° (d)a= 180°

Fig. 6.17 Exit conditions for different slopes of discharge faces

The values of

∆

∆

a

()aa+

for different values of α, as given by A. Casagrande, are plotted

in Fig. 6.18.

30 60 90 120 150 180

0.4

0.3

0.2

0.1

0

DDa/(a + a)

a° DDa/(a + a)

30

60

90

120

135

150

180

0.36

0.32

0.26

0.18

0.14

0.10

0

a°

Fig. 6.18 Relation between α and ∆a/(a + ∆a) (after A. Casagrande)