Hydraulic Reliability Diagram and Network Buffer Index as Indicators of Water Distribution Network Resilience - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 101

Q = Q ( − ADF ) 5.2

j tot j

Q tot in Equation 5.2 is the total network demand intended to be supplied from the source(s).
In this respect, the drop of demand at no-failure condition, resulting from insufficient source
head leading to the pressures below the threshold, would also be considered as a violation of
the service level. Equally, the failure of any single pipe causing any loss of demand means
that the buffer capacity of serial/branched networks that could be utilised during irregular
supply scenarios is practically void.

Looped networks designed on the least-cost pipe diameters, by using genetic algorithms
(GA), will show similar tendency. GA optimisers normally tend to develop a tree-like
skeleton of secondary mains, towards the areas/nodes of higher demand, and then close the
loops with the pipes of the least diameter available. From the perspective of reliability, these
small pipes will serve little purpose as they carry low flows during regular supply and will
therefore not be capable to convey surplus flows redirected after the failure of larger pipes,
whatsoever. Figure 5.1 shows the layouts of 16 simple networks illustrating this point. The
GA optimisation was conducted by optiDesigner software developed by OptiWater
(http://www.optiwater.com) for the threshold pressure of 20 mwc and using the following list
of available diameters (in mm): 50, 80, 100, 125, 150, 200, 250, 300, 350, 400, 500 and 600.
Variable pipe lengths, nodal elevations and demands were assigned, as well as arbitrary head
was set at the supplying point. The only fixed parameter was the absolute roughness set at 0.5
mm for all pipes/networks.

The results for flows and pressures are shown in Figure 5.2. The GA optimisation has been
further repeated using two other programmes: GANetXL from Exeter University in UK
(Savić et al., 2007), and Evolving Objects (EO) distributed under the GNU Lesser General
Public License by SourceForge (http://eodev.sourceforge.net). The obtained results have been
almost identical, which makes Equation 5.2 mostly valid for the least-cost designed looped
networks in the sample.

The consequences of pipe failures in the four serial/branched networks from Figure 5.1a are
shown in the diagram in Figure 5.3 where the loss of demand, 1 - ADF , is plotted against the
relative pipe flow Q j /Q tot under regular operation. Obviously, all the dots will be placed on
the diagonal of the diagram, which results from the flow continuity i.e. the linearity of
Equation 5.2.

The ADF of the 12 looped network configurations from Figures 5.1b-d has been calculated in
the PDD mode. The results of ADF calculations at uniform PDD threshold of 20 mwc are
shown in Figure 5.4. All of these dots are laid very close to the diagonal, matching the
situation in Figure 5.3.

Creating additional buffer in the network, by adding extra pipes i.e. increasing the
connectivity and/or the pipe diameters (also by reducing the demand, in theory) will result in
migration of the dots towards the Y-axis; by increasing the connectivity significantly, all the
dots will start converging towards the origin of the diagram. From the moment all of the dots
have landed on the Y-axis, further increase of the diameters and/or connectivity makes no
difference because the network has already achieved the level of buffer in which any failure
causes no loss of the demand, whatsoever. This is the opposite extreme compared to the
position of the dots on the diagonal of the diagram in Figures 5.3 and 5.4.