Environmental Engineering Reference
In-Depth Information
Flow Conditions for Analysis
Confined flow refers to the cases where the phreatic surface is known; it commonly occurs
beneath cutoff walls.
Unconfined flow refers to cases where the location of the phreatic line is not known; it com-
monly occurs in Earth dams
(Figure 8.28)
and slopes (
Figure 8.29)
.
In the Earth dam illus-
trated, the rock toe is provided to ensure that the phreatic surface does not emerge along the
slope face, since this could result in high exit seepage forces, erosion, and slope instability.
Flow Net Construction
Flow net construction is a graphical procedure accomplished by trial and error, subdivid-
ing the flow zone of a scaled drawing of the problem as nearly as possible into equidi-
mensional quadrilaterals bounded by
flow lines
and
equipotential lines
crossing at right
angles as shown in Figure 8.28 (for details see Taylor, 1948; Cedergren, 1967).
Assumptions are that Darcy's law is valid, and that the soil formation is homogeneous
and isotropic.
A
flow line
is represented in Figure 8.28 as the path along which a particle of water flows on
its course from point A to point C through the saturated sand mass. Each flow line starts at
some point along AB where it has a pressure head
h
p
; thereafter, the flowing particle gradu-
ally dissipates this head in viscous friction until it reaches line BC. (In this case, the soil above
line AB is a free-draining gravel in which there is assumed to be no head loss.) Along each
flow line there is a point where the water has dissipated any specific portion of its potential.
Equipotential lines
connect all such points of equal piezometric level on the flow lines.
The level may be determined in the field by pyrometers.
B
Phreatic surface
h
= 40/9
∆
h
= 40/9
∆
Flow line
H
= 40 ft
Equipotential
line
Rock
toe
C
D
A
(a)
Impervious
E
Trial failure surface
I
Equipotential
Top flow line
2
h
p3
3
h
p3
Pressure
head
h
p4
4
h
p4
5
6
D
(b)
FIGURE 8.28
Unconfined flow through earth dam with rock toe to control toe seepage: (a) Use of flow net to find seepage
quantity and gradient. Given:
k
0.005 ft/sec,
H
40 ft,
$
f
N
f
/N
e
2.65/9
0.294. Seepage through dam
Q
/
L
0.40. (b) Use of flow net to find pore-water pressures on a failure surface: (1) layoff trial failure surface on flow
net, (2) measure pressure heads as elevation difference between phreatic line and trial failure surface at
equipotential lines, and (3) pore-water pressure
kH$
f
0.0005
40
0.294
59
10
4
ft
3
/min/ft. Gradient in square
I
i
1
h
/
l
1
40/9/11.2
h
p
γ
w
(From Lambe, T.W.
Soil Mechanics,
1969, Wiley,
New York, and Whitman, R. V. Adapted with permission of John Wiley & Sons, Inc.)
