Environmental Engineering Reference
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the events of no buffer in the network i.e. the situation when the failure of any pipe will cause
the loss of demand, which is the case with serial/branched networks, or GA-optimised looped
networks reflecting the least-cost design. The other extreme, the reliability index having the
value of one, depicts the situation where no single pipe failure will cause the loss of demand
in the network, whatsoever. The reliability index derived from the position of all the dots on
the graph, including proportional weighting to the pipes carrying more flow under normal
condition, has been proposed as the network buffer index (NBI), which takes only into
consideration the consequences of the failure and not the chance that it would happen.
The conducted analysis and the comparisons done between the NBI and two resilience
indices from the literature make clear that no easy conclusion can be drawn based on a single
index whatever is the value it takes. Moreover, no direct conclusion could have been drawn
from the pipe connectivity alone; the pipe diameters and supplying heads play important role
for network reliability, too. Hence, one number can hardly describe the complexity of
hydraulic performance in irregular supply scenarios, which is determined by both geometric
and hydraulic parameters.
Nevertheless, giving a visual i.e. graphical interpretation of the index, in this case by having
the NBI value 'explained' with the HRD, gives better idea how this index has been influenced
i.e. what is the source of the loss of demand. Moreover, the HRD gives impression about the
buffer in the network, possible loss of service level resulting for insufficient supply heads (no
pipe failure), and the source of reliability achieved either by increased connectivity, and/or
increased pipe diameters, and as such can be seen as useful diagnostics tool.
As far the computational tool, the PDD software developed in C++ using the EPANET
toolkit function library for the purpose of network diagnostics and calculation of ADF has
proven to be pretty robust and fast. For example, the calculation of ADF values for all the
pipes of the Amsterdam North network was taking anything between five and 10 minutes for
one demand scenario, depending on the PC that was used for this purpse.
Finally, all the results showed clear correlation between the three indices. Nevertheless, the
NBI index appears to be more responsive towards the changes of network configuration i.e.
the pipe connectivity and diameters, compared to the resilience indices that are mostly driven
by the change of piezometric heads. Those will therefore occasionally show unreasonably
low or high values compared to NBI.
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