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

GIROUD et al. D Leachate Flow in Leakage Collection Layers Due to Geomembrane Defects
t
avg II
t
o
tavg lim
t
ª a + ( 1 - a)
t
t
o
avg L
o
(166)
where t avg lim is defined by Equation 164, t avg L by Equation 165, and α by:
a =
t
o
L - x 2 ( L - x) sinb
=
/( 2 sin b)
t
o
(167)
The dimensionless parameter α is related to the location of the primary liner defect
as illustrated in Figure 15. It should be noted that Equations 166 and 167 are valid only
if:
0 £ a £ 1
(168)
This condition is met if the conditions required for Case II to exist are met (Figure 13b).
Numerical values of Equation 166 are given in Table 5. It should be noted that both
Equations 164 and 165 approach the same limit when μ approaches 0:
Lim
F
HG
t
avg lim
t
o
I
F t
= Lim
KJ H G
t
avg L
m = 0 o m = 0
I
3 m
= =
KJ
4 2
0.
530
m
(169)
In Table 5, one may expect to see the value t avg /t o = 1/3, which is the classical value
for the average height of a cone (see Equation 151), since the phreatic surface has been
assumed to be a cone (see Figures 1 and 4). In fact, the value t avg /t o = 1/3 appears only
once in Table 5: for α =1andμ = 2. This case is illustrated in Figure 14b. This is the
only case where the truncation does not affect the cone volume. In all other cases, the
phreatic surface is a truncated cone and the average height of a truncated cone is not
equal to one third of its total height.
t o /(2 sinβ)
α
0.0
0.2
0.4
0.6
0.8
1.0
t o /(2 sinβ)
x
Primary liner defect
L
Figure 15. Definition of the dimensionless parameter α used in Equation 166 and in
Table 5.
Note: In the case illustrated above, α = 0.43.
262 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4