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

GIROUD et al. D Leachate Flow in Leakage Collection Layers Due to Geomembrane Defects
4.4.3 Wetted Fraction in the Worst Scenario
In the worst scenario (Figure 9a), the leachate flow through each defect generates a
wetted zone whose surface area is A wmax (Figure 7) given by Equation 62 (which is
equivalent to Equation 97 or 80 depending on whether the leakage collection layer is
full or not, respectively). Therefore, the surface area of the total wetted zone for the scenario
where all the defects are at the high end of the leakage collection layer slope is
expressed as follows, if all of the leaks are assumed to be equal, which is generally the
case in design:
n=
N
∑ Aw
=
n = 1
N A
wmax
(101)
Combining Equations 99 and 101 with R w = R w worst gives:
R
w worst
NA
=
A
wmax
LCL
(102)
Combining Equations 100 and 102 gives:
R
w worst
= FA
w max
(103)
Combining Equations 62 and 103 gives the following equation for the wetted fraction
in the worst scenario:
R
wworst
2F to
2 L sinb
1
3 sinb
t
=
F H G
I LF
+
KJ NM
HG
o
/
I
-
KJ
2 3 2
O
QP
1
(104)
Combining Equations 80 and 103 gives the following equation for the worst scenario
when the leakage collection layer is not full (t o < t LCL ), i.e. when the condition expressed
by Equation 11 (or Equation 12, which is equivalent) is met:
2 FQ
32 /
R L
wworst= 1+ 2L k Q -1O
2 d sin b / i
(105)
3k
sin b
NM
Combining Equations 97 and 103 gives the following equation for the worst scenario
when the leakage collection layer is full in a certain area around the primary liner defect
(t o > t LCL ), i.e. when the condition expressed by Equation 11 (or Equation 12, which is
equivalent) is not met:
R
wworst
L
F
IO
R
L
S|
M
N
M
T|
2
F tLCL
Q
= +
N
M 1
HG
ktLCLKJ
Q
P 1+
2
6 sinb
| M
t
LCL
4 L sinb
F Q
1 +
2
kt
HG
LCL
QP
O
I
KJ
Q
P
32 /
- 1
U
V|
W|
(106)
244 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4