Civil Engineering Reference
In-Depth Information
In general, it is diffi cult to know precisely the degree of dependence and
thus an interval number [
ρ
u
] may be used. Where probabilities of two
events A and B are also written as interval number, the following equations
are obtained for the union and intersection of the events (Cui and Blockley
1990):
ρ
l
,
(
)
=
()
+
()
−
(
() ()
)
SA B SA SB
∪
ρ
min
SASB
,
n
n
n
u
n
n
(
)
=
()
+
()
−
(
() ()
)
SA B SA SB
∪
ρ
min
SASB
,
n
n
p
u
n
n
(
)
=
(
() ()
)
SA B
∩
ρ
min
SASB
,
n
l
n
n
(
)
(
)
=
() ()
SA B
∩
ρ
min
SASB
,
p
u
p
p
The assessment of the likelihood of a failure scenario is made by
choosing
•
a measure of evidence that an action is likely to cause damage;
•
a measure of confi dence in that assessment; and
•
a measure of the likelihood (importance) of that action irrespective of
the degree of damage it may cause.
The above measures can be either numeric or linguistic. Single point values
may be available for certain actions that are known precisely (e.g. dead
load). For actions such as earthquake load or snow load, an interval number
may be more appropriate considering the uncertainty in assessing the
extremes. For actions, such as accidental damage or sabotage, one can at
best give linguistic grades for damage. But these linguistic descriptions can
be mapped to an interval number using various schemes. Following the
scheme in Dester and Blockley (1997), judgement of damage extent, for
example, with
little
evidence with
moderate
confi dence may be expressed
as an interval number of [0.13, 0.45]. The higher the confi dence, the smaller
is the interval. Below a certain level of confi dence, the interval gets much
larger. The likelihood (or importance) of an action can also be assessed on
a 0 to 5 scale with extremes being
very high
and
very low
.
8.4.1 Risk calculation
The exploitation of vulnerabilities knowingly or unknowingly could cause
grave harm to the structure, occupants, and possibly to a much bigger
system. Vulnerability together with threat can produce high risks. So long
as there is no undesirable action to exploit the vulnerability, it is only a
potential risk. However, if a threat is active, the combination of the active
threat and the vulnerability creates a real risk to the structure and its users.
Hence, after having identifi ed failure scenarios, it is important to consider
the probability of actions and the likelihood of damage occurring. A con-
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