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

GIROUD et al. D Leachate Flow in Leakage Collection Layers Due to Geomembrane Defects
1.0
Critical value of R w (dimensionless)
0.8
0.6
0.4
0.2
Crit (R wworst )
Crit (R wrand )
0
10 -3 10 -2 10 -1 1 10 100 1000
Dimensionless parameter, μ
Figure 12. Maximum values of the wetted fractions without overlapping of wetted zones
in the worst scenario, R wworst , and in the random scenario, R wrand .
Notes: Crit (R w worst ) was calculated using Equation 136, and Crit (R w rand ) using Equation 138 for μ ≤ 2and
Equation 140 for μ ≥ 2; μ is defined by Equation 109. Values of Crit (R w worst )andCrit(R w rand )arealso
presented in Table 4.
zone occupies the entire leakage collection layer area in Figure 11, hence the upper
valueof1forCrit(R w worst ) in Figure 12.
Also represented in Figure 12 is the critical value of R w rand ,Crit(R w rand ), which is the
maximum value that R w rand can have without overlapping of the wetted zones related
to the various individual primary liner defects. Selecting the value of the frequency F
to be used in the calculation of Crit(R w rand ) is not easy. For the sake of consistency with
the calculation of Crit(R w worst ), the same frequency (i.e. the frequency given by Equation
134) is used. Accordingly, combining Equations 39, 121 and 134 gives the following
value of Crit (R w rand )forμ ≤ 2:
Crit ( R )
w rand
1 F
=
H G
15
to
L sinb
I LF
+
KJ 1
NM
HG
Combining Equations 109 and 137 gives:
I
2 2 -1/
2
F
HG
2 L sinb
2 L sinb
- 2 1+
to
KJ
to
I
KJ
O
QP
(137)
252 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4