Structural vulnerability analysis of civil infrastructure facing seismic hazards - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 221

of the whole network. Vulnerability analysis of water pipe networks (Pinto
et al. 2010) follows a similar procedure to that described above for struc-
tures. Clusters of connected pipes are formed using head loss as a measure
of well-formedness. This relates to the properties of a pipe (e.g. length,
diameter and friction factor) and the confi guration of the pipe network.
Other sources of head loss are also considered. A smaller total head loss
indicates a better formed cluster. Where head losses are the same, nodal
connectivity and damage demand are used as secondary clustering criteria.
Nodal connectivity measures the degree of connection of a cluster with the
rest of the network, and damage demand measures the effort needed to
introduce a deteriorating event. A deteriorating (i.e. initial failure) event
occurs when a pipe bursts or it fails to supply good quality water to a
demand point. Currently damage demand is assumed to be proportional to
the strength of pipe. Separateness measures the failure consequences and
it is obtained as the ratio of total head losses in the damaged network and
that of the original network. Vulnerability index measures the dispropor-
tionateness of the consequences in relation to the initial damage and is
determined as before i.e. the ratio of separateness and damage demand.
Figure 8.8 gives an example water pipe network which is adapted from
EPA (2000). A hydraulic analysis was carried out to determine the relative
head losses for different pipe segments. Using head losses as the well-
formedness measure, damage demand, nodal connectivity, and distance
from sources, clustering hierarchy shown in Fig. 8.8b was obtained. A search
through this hierarchy suggests a high vulnerability index for the loss of
segments p121 and p122.

T

C13

2 Tank

p110

C12 Source

Source

p10 p11 p12

9 11 12 1

C11 Tank

Pump

C9

C10

p 111 p 112 p113

p10 p111

C8 C7

p21 p22

21 22 2

p111 p122

C6 C5

p112 p31 p121

C4

p121 p122

C3 C2

p12 p110 p113

C1

31 p31

32

p21 p22

(a)

(b)

8.8 (a) An example water pipe network (adapted from EPA (2000)) and
(b) its hierarchical representation.