Civil Engineering Reference
In-Depth Information
instead should be considered as an integrated part of the design process.
There is now a new fundamental way of looking at all problems. The build-
ing is not considered alone, but as a
group of buildings
using the 'portfolio
approach' which will allow regional loss analysis. This concept is borrowed
from the fi nancial industry, where modern portfolio theory (MPT) was
developed in the 1950s through the early 1970s and was considered an
important advance in the mathematical modelling of fi nance (Elton and
Gruber, 1997). MPT is defi ned as a theory of investment which attempts to
minimize risk for a given level of expected return, by carefully choosing the
proportions of various assets. MPT is a mathematical formulation of the
concept of
diversifi cation
in investing, with the aim of selecting a collection
of investment assets that has collectively lower risk than any individual
assets. Analogously, the concept of diversifi cation can be applied in the fi eld
of disaster resilience, where the
diversifi cation
in retrofi t of different build-
ings in a given region can increase resilience collectively more than any
individual retrofi ts. In other words, RBD attempts to fi nd a method that
addresses the concern of minimizing the risk of low-probability-high-
consequence (LPHC) extreme events that can potentially result in multiple
losses and fatalities.
MPT models an
asset's return
as a normally distributed function, defi nes
risk as the standard deviation of return, and models a portfolio as a weighted
combination of assets so that the return of a portfolio is the weighted com-
bination of the assets' returns. Analogously in RBD, the
weight aggregated
losses
of the
building portfolio
in a community is equivalent to the portfolio
asset's return in MPT, and the
risk of losses
at the community level is the
aggregated conditional probability of exceeding certain damage D
of the
building portfolio. Furthermore the
conditional probability of exceeding
certain damage
of the building portfolio is a weight combination of the
conditional probabilities of exceeding certain damage
for individual units. In
other words, at the community level, analytically the global vulnerability of
a community
P
COM
is a weight combination of conditional probabilities
associated to a
j
th unit and it is given by the following equation:
∑
(
)
=
(
)
PDH
wPDH
j
[11.2]
COM
j
j
where
D
is the probability of
exceeding a certain damage level associated with the
j
th unit; and
w
j
=
=
damage state;
H
=
hazard level;
P
j
( )
=
weight parameter.
The risk at the community level
Risk
COM
is a weight combination of
aggregated conditional probabilities:
∑
∑
(
)
(
)
Risk
=
P
L D P
D H
λ
[11.3]
COM
COM
COM
H
H
D
where
L
earthquake hazard
level of a given community. For instance, in RBD group of buildings having
=
exposure level of a given community;
λ
H
=
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