Hydraulic Reliability Diagram and Network Buffer Index as Indicators of Water Distribution Network Resilience - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 100

5.1 INTRODUCTION

Hydraulic reliability of water distribution networks is commonly considered against a
threshold pressure indicating sufficient service level. Below this value, the reduction of
demand will occur to a certain degree and, combined with the probabilities of failure, an
overall reliability index will be calculated that normally takes value between 0 and 1. Such
approach is proposed by Ozger and Mays (2003) who introduced the term available demand
fraction (ADF) to express the demand proportion still available in the network after a pipe
failure event. Consequently, the loss of demand i.e. the drop in service level can be correlated
to 1 - ADF . If taken alone, this figure will reflect only the impact of the failure. Combined
with the probability P j that the failure of pipe j will happen, the reliability index R for the
network of m pipes is calculated according to Equation 5.1:

1

m

∑ =

R = 1 − ( − ADF ) P

5.1

j j

m

j 1

Practical considerations assume a series of snapshot hydraulic simulations for particular
demand scenario, starting with no-failure condition and then failing the pipes, one by one,
and calculating the ADF in the network for each pipe, eventually obtaining the mean value
for the entire network. To accomplish this analysis, the hydraulic simulation will switch into
the pressure driven demand (PDD) mode and the outcome of the calculation will be the
demand that is available in the network under stress conditions.

Having a PDD mode built into the hydraulic solver and adding computational loop that will
break all the pipes in a sequence, makes the calculation of R relatively easy. Nevertheless, the
obtained average value of ADF says much neither about the area affected by the failure i.e.
the impact coverage, nor about the extent of the failure i.e. the impact intensity. The same
value of ADF can be in theory a result of large network area affected to a lesser extent, or a
small network portion that is affected severely. Furthermore, little can be grasped from the
index about the buffer capacity of the network, and consequently no viable investment
decision can be made purely based on the increase of ADF and overall reliability index, as
long as it is not clear what it adds in practical terms i.e. to the improvement of the service
level in irregular supply conditions.

The concept of resilience introduced by Todini (2000) and upgraded by Prasad and Park
(2004) throws more light on the network buffer and its capacity to withstand a certain degree
of stress but equally lacks insight about the impact coverage and intensity; the indices used to
express the resilience will again be averaged values representing the entire network and
possibly hiding the implications of some critical pipe failures.

5.2 HYDRAULIC RELIABILITY DIAGRAM

Serial- and branched networks have straight-forward calculation of ADF; the failure of any
pipe j will mean the loss of all the demand downstream of that pipe, which equals the pipe
flow Q j under regular conditions. Hence: