Incremental dynamic analysis (IDA) applied to seismic risk assessment of bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 581

Yielding Serviceability Bar-buckling Collapse

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 1 2

S a ( T 1 ) / S aMCE

3 4 5

21.10 Fragility curves for different damage states (Adapted from
Tehrani and Mitchell 2012d).

The probability of collapse at the MCE level is typically limited to 10%
(and to 20% for rare cases) (ATC-63, 2008). These limits are currently based
on judgement and accordingly different limits on the maximum probability
of collapse may be accepted for different types of structures. For bridges
different criteria might be accepted for seismic evaluations according to the
functionality and importance of the bridge.
The computed probability of exceeding different damage states reported
in Table 21.4 and Fig. 21.10 are conditional probabilities predicted at a given
intensity level. To predict the seismic risk associated with exceeding differ-
ent damage states (i.e., the total probability of failure in a period of time),
the results obtained from the fragility curves should be combined with the
results from the seismic hazard analysis (i.e., hazard curves) using the 'total
probability theorem' (Benjamin and Cornell, 1970). The hazard curves
provide the mean annual frequency that a certain level of seismic intensity
is exceeded. The hazard curve obtained at T 1.09 s for Montreal using the

updated seismic hazard data provided by Atkinson and Goda (2011) is
shown in Fig. 21.11.
Following the determination of the hazard curve, the mean annual prob-
ability of exceeding any particular damage state,

=

λ DS , can be estimated using

Eq. [21.8] (e.g., Jalayer and Cornell 2003):

IM =+∞

∫

( ) ( )

λ DS = f IM H IM d IM [21.8]

R

IM = 0