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

GIROUD et al. D Leachate Flow in Leakage Collection Layers Due to Geomembrane Defects
5.2 Leachate Head on Top of the Secondary Liner Due to Several Defects in the
Primary Liner
5.2.1 Scope of Section 5.2
The size of the wetted zone in the case where there are several defects in the primary
liner was discussed in Section 4.4. In this case, the wetted zone consists of several parabolic
wetted zones, each of these parabolic zones being related to a primary liner defect.
When the frequency of defects (i.e. the number of defects per unit area) is small, the
probability for the various parabolic wetted zones to overlap is small and it may be assumed
that they do not overlap. In contrast, when the frequency of defects is high, the
parabolic wetted zones will likely overlap.
In Section 4.4, the wetted fraction was defined as the ratio between the surface area
of the total wetted zone and the surface area of the leakage collection layer. The wetted
fraction was calculated in the worst scenario, i.e. the scenario where all primary liner
defects are at the high end of the leakage collection layer slope, and in the random scenario,
i.e. the scenario where primary liner defects are distributed at random.
In Section 5.2, the worst scenario and the random scenario will be considered to calculate
the average leachate thickness in the wetted zone. The cases where the wetted
zones, related to different defects in the primary liner, do not overlap are considered first
(Sections 5.2.2 and 5.2.3) followed by the case where the wetted zones overlap (Section
5.2.4). Finally, comments on the influence of primary liner defect frequency on average
leachate thickness will be presented in Section 5.2.5.
5.2.2 Average Leachate Thickness in the Worst Scenario With no Overlap
In the worst scenario (defined in Section 4.4.2), if the primary liner defect frequency
is small enough that the parabolic wetted zones do not overlap, all of the parabolic zones
are identical (Figure 9a). Therefore, the average leachate head in the total wetted zone
in the worst scenario, t avg worst , is identical to the average leachate head in any of the parabolic
zones, hence:
t
avg worst
Combining Equations 159 and 170 gives:
t
avg worst
Combining Equations 165 and 170 gives:
t
avg worst
t
o
= t
avg L
( 3/ 2) L sinb
=
32
( 1+ 2 L sin b / t ) / -1
3
=
2
2 m 1+
m
L
F
NM
HG
o
32 /
I
-
KJ
O
QP
1
(170)
(171)
(172)
264 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4