Structural vulnerability analysis of civil infrastructure facing seismic hazards - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 219

member is shorter than m2 or m6 and therefore has a higher damage
demand (or higher buckling load capacity) it is not the one chosen by this
analysis. Clearly however were m1 to be signifi cant in terms of loading or
response analysis or for any non-structural reason, then it is a possible
failure scenario with high risk.
A qualitative analysis of the likelihood of the failure scenarios in the
above example is done and the results are given in Table 8.2. Different
actions are considered and a linguistic assessment of damage to members
(column c in the table) is made. For the purpose of this illustration, damage
assessment of members and evaluation of the likelihood of actions are
based on a simplifi ed quantitative analysis and/or engineering judgement.
But these results can be improved by carrying out a rigorous quantitative
analysis for different actions. Support for the likelihood of a scenario is
summarized in column i. Here actions are assumed to be independent of
each other though it will not be the case always. Where a scenario has more
than one event, careful consideration has to be given to the degree of
dependency between them. Vulnerability of different scenarios (column j )
and their likelihood (column i ) can be plotted in the form of a risk map.
Here only three failure scenarios are discussed but in general there would
be a large number of failure scenarios and appropriate actions can be taken
to mitigate critical failure scenarios.

8.5 Vulnerability of infrastructure networks

Structural vulnerability theory has been generalized into a vulnerability
theory applicable to infrastructure systems that can be represented as a
graph. Complementary variables, called 'across variables' and 'through vari-
ables', together with equivalents of Kirchhoff's laws form the basis of the
generalization. These variables can be envisaged as cause and effect or
driver and change. For structures, they are force and displacement, and the
structural rings developed in structural vulnerability analysis are circuits of
force and displacement. Analogous variables for water pipes and traffi c
networks, which also suffer damage during earthquakes, are defi ned in
Agarwal et al. (2001b). The across and through variables are related through
component equations. The through variables balance across any section
through the circuit and the across variables balance around the circuit.

8.5.1 Water pipe networks

A typical water distribution network is formed with pipes, reservoirs, pumps
and control elements. The interconnected pipe network transmits water
from reservoir(s) to consumers. However, pipes or other elements are sus-
ceptible to failure causing a drop in downstream pressure or performance