Seismic vulnerability analysis of a complex interconnected civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 484

Both DCI and UBI can be effectively estimated by conditional sample
analysis.
Further examples include the mean annual frequency (MAF) of exceed-
ance of a threshold y based on a performance metric Y :

∑ ∑

() = () = () = ()

λ y λ G yi λ pG yi λ G y

[18.15]

Y 0 , i Y i 0 i Yi 0 Y

i i

∑

0, i /
λ 0 is the probability that given the occurrence of an earthquake the active
source is the i th one.

where λ = λ is the MAF of all earthquakes in the region and p i = λ

0 0 , i

i

18.6.4 Infrastructure-level metrics

Metrics at this higher level usually take the form of a summation over
systems or components. These summations require the assembled conse-
quences to have the same units. Commonly employed quantities are money
and people, who may be injured, dead or displaced. Currently and consis-
tently with its emergency-phase focus, the model evaluates the total number
of casualties, fatalities and the Shelter Seeking Population (SSP), as already
mentioned in Section 18.5.1 and in more detail in Cavalieri et al . (2012).
Assessment of economic loss is actually a much more diffi cult proposi-
tion, since indirect loss is highly uncertain. A relatively large body of litera-
ture is available on the matter, with a variety of functions that try to map
physical damage and its functional consequence (e.g. hourly cost times
driver's delay) into monetary terms. Even these functions, however, are
affected by signifi cant uncertainty (e.g. Franchin et al ., 2006a), and the use
of pre-earthquake reference values (e.g. repair cost per unit of damage) is
questionable in post-earthquake market conditions, when many damaged
sites will compete for a fi xed number of construction sector operators
(demand surge), or government's political decision may alter completely
the scenario (e.g. Calvi and Spaziante, 2009). Besides, the full economic
impact of an earthquake evolves over a period of time that is longer than
the current reference time-frame of the model. For these reasons economic
loss is not yet included.

18.7 Probabilistic assessment of the model

18.7.1 Uncertainties in the problem

The model introduced in the previous sections describes a complex system
of interconnected systems, the infrastructure, immersed in an environment
and subjected to hazards. Uncertainty affects all elements of the model.
Some uncertainties have already been addressed. The following is a com-
plete list of uncertain elements: