Hydraulic Reliability Diagram and Network Buffer Index as Indicators of Water Distribution Network Resilience - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 117

n

( )

∑

*

Q H − H

i i i

I =

i = 1

5.21

r l k n t

∑ ∑ ∑ ∑

*

Q H + Q h − Q H − Q h

s s p p i i v m . v

s = 1 p = 1 i = 1 v = 1

where H * is the minimum piezometric head required to satisfy the demand in node i , equal to
the sum of nodal elevation and PDD threshold pressure .

Prasad and Park (2004) propose more conservative value of the index by introducing the
weighting of the nodal power, based on possibly larger discrepancies in diameters of
connecting pipes. The multiplier, c i , is expressed as:

m , i

∑ =

D

j

j 1

c =

5.22 i

m max{ D }

i j

where D j are the diameters of m pipes connected in node i . The corresponding network
resilience, I n , will be calculated as in Equation 5.23.

n

( )

∑

*

c Q H − H

i i i i

I =

i = 1

5.23

n l k n t

∑ ∑ ∑ ∑

*

Q H + Q h − Q H − Q h

s s p p i i v m . v

s = 1 p = 1 i = 1 v = 1

After running the hydraulic simulations, the HRD for the two networks from Figure 5.12 will
look as shown in Figure 5.13, with the NBI of 0.234 for net10 , and 0.660 for net16 . Unlike
was the situation with the layouts a and b of these networks, the layouts c show clearly more
buffer and better effect of connectivity from net16 than in case of net10 .

1.00

Underconnected

0.90

0.80

0.70

0.60

net10c
net16c
Branched

0.50

0.40

0.30

0.20

0.10

Overconnected

0.00

0.00 0.20 0.40 0.60 0.80 1.00

1-ADF

Figure 5.13 HRD for adapted nets 10 and 16 (PDD threshold = 20 mwc)