Environmental Engineering Reference
In-Depth Information
m
m
1
m
∑ ∑
0
j
net
jk
net
A
=
ADF
MA
+
ADF
u
+
ADF
u
2.14
net
j
jk
j
=
1
j
=
1
k
=
j
+
1
where ADF 0 is the available demand fraction with fully functional network, ADF j is the
available demand fraction after the failure of pipe j , and ADF jk is the available demand
fraction after the simultaneous failure of pipes j and k . Furthermore, MA stands for the
mechanical availability of the system that can be calculated as:
n
=
MA
=
MA
2.15
j
j
1
which is the probability that all n pipes are operational. The mechanical availability of pipe j
is defined as:
MTTF
j
MA
=
2.16
j
MTTF
+
MTTR
j
j
where MTTR j is the mean time to repair and MTTF j is the mean time to failure of this pipe,
which is given by:
1
MTTF
=
2.17
j
λ
L
j
j
Furthermore, in Equation 2.14, the probability of a failure of the j th pipe and all other
components remaining fully functional is given as:
MU
j
u =
MA
2.18
j
MA
j
For simultaneous failure of pipes j and k :
MU
MU
j
u =
MA
k
2.19
jk
MA
MA
j
k
In both equations, MU stands for the mechanical unavailability that equals 1-MA .
Yoo et al. (2005) tested this method on the sample network taken from Khomsi et al. (1996),
shown in Figure 2.5. The Hazen-Williams coefficient and the length of all pipes were set at
130 and 1000 m, respectively. The diameter of pipe 3 is 100 mm, pipes 7 and 8 = 150 mm,
pipes 4 and 5 = 200 mm, pipes 1 and 2 = 250 mm and pipe 6 = 300 mm. A hypothetical
MTTF was specified for each pipe, in the range of 0.039 and 0.329 bursts per km per year,
and the threshold pressure and MTTR were set at 20 mwc and one day, respectively. Figure
2.5 clarifies the procedure to calculate ADF , which has six steps:
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