Environmental Engineering Reference
In-Depth Information
By adding the weighting proportional to the pipe flows under regular supply conditions, the
NBI will be calculated as in Equation 5.17.
Q
Q
−
(
−
ADF
)
Q
Q
m
m
Q
∑
∑
j
tot
j
j
j
NBI
=
=
+
ADF
−
1
tot
5.17
j
m
m
Q
Q
Q
∑
∑
j
=
1
Q
j
=
1
Q
j
tot
tot
j
j
j
=
1
j
=
1
For serial- and branched networks, Equation 5.17 yields the NBI value of 0 (after plugging
Equation 5.1), while in case of
1
-
ADF
j
= 0 for all the pipes, the NBI will equal 1.
Applying Equation 5.17, the networks from Figure 5.5 have the following values of
NBI
:
net10
- 0.050,
net10a
- 0.270,
net10b
- 0.499,
net16
- 0.060,
net16a
- 0.216 and
net16b
-
0.370. The trend of increase is obvious as the diameters have also been increased in
a-
and
b
alternative, whilst the index values for optimised networks are very low: 0.05 and 0.06,
respectively, reflecting very low buffer capacity. Furthermore, the indices for
a-
and
b
alternative of
net16
are lower than those of
net10
; based on the pipe connectivity alone, this
might look peculiar, but
net16
is supplying much higher demand with lower supplying head
than
net10
(155 l/s and 60 msl, against 70 l/s and 90 msl, respectively). Moreover, the GA-
optimisation has minimized the connectivity effect on the reliability by forming branched
skeletons in both networks. Alternative
a
and
b
also maintain this skeleton as all pipe
diameters have been uniformly increased. In fact, the position of the dots in Figure 5.5
suggests the poorer connectivity of
net16
compared to
net10
, which based on the selection of
diameters is actually a valid conclusion. All this makes the NBI values fairly logical
reflection of the layout and hydraulic performance of both networks.
With additional derivation, Equation 5.17 transforms into a simpler form:
m
m
(
)
∑
∑
Q
−
Q
∆
Q
tot
tot
,
j
tot
,
j
m
Q
∑
j
=
1
j
=
1
5.18
NBI
=
1
−
(
−
ADF
)
tot
=
1
−
=
1
−
j
m
m
m
∑
∑
∑
j
=
1
Q
Q
Q
j
j
j
j
=
1
j
=
1
j
=
1
where
Q
tot,j
is the total demand in the network that is available after the failure of pipe
j
and
ΔQ
tot,j
is the corresponding loss of demand.
5.6
COMPARISON OF NBI WITH THE RESILIENCE INDICES
The network buffer index has been compared with two other indices from the literature: the
resilience index
,
I
r
, of Todini (2000) and its upgrade named the
network resilience
,
I
n
, which
was defined by Prasad and Park (2004). The initial layouts of the networks
net10
and
net16
have been modified by introducing more looped skeletons of secondary mains i.e. reducing
the range of used diameters. Furthermore, the supply heads and nodal elevations have been
set for both networks at 75 msl (in
R1
) and 45 msl (in all other nodes), respectively. The
remaining input data, namely the nodal demands, pipe lengths and k-values are kept the same
as in the initial network. Figure 5.12 shows the layout and the hydraulic performance of the
adapted
net10
and
net16
.
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