leachate flow in leakage collection layers due to defects in ...

GIROUD et al. D Leachate Flow in Leakage Collection Layers Due to Geomembrane Defects
4.3.6 Surface Area of the Wetted Zone in the Case Where the Leakage Collection Layer
is Full
Combining Equation 17 with Equations 49 to 62 gives the following equations for the
case where the leakage collection layer is full (t o > t LCL ), i.e. when the condition expressed
by Equation 11 (or Equation 12, which is equivalent) is not met:
S When the parabola is complete, i.e. when the following conditions are met:
and
tLCL
4 sinb
tLCL
4 sinb
the latter being equivalent to
F
HG
F
HG
Q
kt
1 +
2
LCL
Q
kt
1 +
2
LCL
I
I
£
KJ
tLCL
0 £ x £ L - +
4 sinb
L
£ X £ L
KJ
F
HG
Q
1
2
ktLCL
the surface area of the wetted zone is expressed by
A
w
L
M
A
w
L
N
M
F
HG
L
N
M
4 32 / tLCL
= X 1 +
3 sinb
F
IO
2
1 tLCL
Q
= 1+
N HG
ktLCLKJ
Q
P 1+
2
6 sinb
t
Q
2
kt
LCL
LCL
I
KJ
IO
KJ
Q
P
12 /
4 x sinb
F Q
1 +
2
kt
S When the parabola is truncated, the surface area of the wetted zone is expressed by:
A
w
L
F
A
w
F
HG
4 tLCL
= +
3 sinb
IO
R
L
S|
M
N
M
T|
2
1 tLCL
Q
= +
N
M 1
HG
ktLCLKJ
Q
P 1+
2
6 sinb
| M
t
Q
kt
1
2
LCL
LCL
I
HG
LCL
X - ( X - L)
KJ
32 / 32 /
O
I
KJ
Q
P
32 /
4 x sin b
4( L - x) sinb
- 1 -
F Q I
Q
+ P
M
F
1
tLCL
1 +
2
2
kt
kt
HG
LCL
O
P
KJ
Q
L
M
N
HG
LCL
O
I
KJ
Q
P
32 / 32 /
Equations 86 and 87 are valid under two different sets of conditions. The first set is:
U
V|
W|
(81)
(82)
(83)
(84)
(85)
(86)
(87)
240 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4