Civil Engineering Reference
In-Depth Information
of dealing with structural redundancies. These examples show that it is
simply not good enough to equate, and hence model, all uncertainties as a
variability of a number of random variables. Uncertainty is more than mere
random variability.
The second restriction is that all of the risks due to soft issues (such as
human error and organisational problems which we will discuss in detail
later) are simply not included. FEMA (2009, 2011) and PEER (2010) defi ne
systems that are entirely technical and seem not to acknowledge that human
and organisational factors have any part to play in why infrastructure
systems fail in an earthquake. It could be argued that this may not matter
if these softer uncertainties are independent of the technical uncertainties,
because they are dealt with elsewhere - by project management and other
decision makers. Unfortunately, many of the important hard and soft risks
are not independent. Many studies (Blockley, 1980; Reason, 1990; Turner
and Pidgeon 1998) have shown that many risks lie at the interface between
the technical and human and do directly infl uence technical outcomes and
the total risk. A report by IAEA (2001) shows that operational and fi nancial
performance is closely related to safety. The report calls for an integrated
approach. One only has to compare the seismic performance of buildings
in Haiti with that in more developed countries to understand that political,
social and human factors are crucially important in managing all risks to
infrastructure. This means that current systems boundary in PBE must be
widened.
Within reliability theory and PBE, fragility is the conditional probability
that the structural capacity C in a stated limit state fails to resist the struc-
tural demand D given the seismic intensity SI.
(
)
pC
<
DSI
=
x
[9.1]
The three performance levels used in PBE (Ellingwood et al. , 2004) are
immediate occupancy (IO) , life safety (LS) , and collapse prevention (CP) .
Immediate occupancy is the limit below which the structure can be occu-
pied safely without signifi cant repair. Life safety is a level above which there
is signifi cant damage but a substantial margin remains against collapse. Col-
lapse prevention is the level above which either the strength of structural
members or connections is lost or there are signifi cant permanent
deformations.
The problems of partiality become apparent as we unpack the sources of
uncertainty in this formulation. Some authors use the word aleatoric to
describe the uncertainties due to randomness. The word aleatoric means
'dependent on chance or accidental events or other contingencies'. It is
unclear how this is different from randomness in a stochastic process and
so in this chapter we will consider aleatory, random and stochastic processes
as equivalent. The other source of uncertainty is often described as epis-
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