Incremental dynamic analysis (IDA) applied to seismic risk assessment of bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 579

1.2

1

16% DM IM

0.8

50% DM IM

0.6

0.4

84% DM IM

0.2

0

0 0.02 0.04 0.06 0.08 0.1

Maximum drift ratio

21.9 IDA results developed for the case of a regular bridge with
H 1 = H 2 = H 3 = 7 m and D = 2 m (adapted from Tehrani and Mitchell,
2012d).

models may overestimate the overall capacity of the structure. More
research is required to investigate the differences between the 2D and the
3D analyses for performing the IDA especially for the case of bridges.
Fragility curves can be developed using the IDA results as discussed in
Section 21.6. The record-to-record variability can be obtained from the IDA
results at different damage states as reported in Table 21.4. Although there
is little research on this subject, the quality of test data and modelling were
assumed as good and the quality of the design requirements was considered
to be superior in this study to estimate the total uncertainty, using the
judgemental method described in Section 21.4.
The IDA results presented in Table 21.4 can be used along with Eq. [21.7]
to develop the fragility curves at different damage states, as shown in Fig.
21.10. In the horizontal axis of the fragility curves in Fig. 21.10 the spectral
acceleration at the fundamental period, S a ( T 1 ), is normalized by the spec-
tral acceleration at the MCE level, S aMCE . The fragility curves can be better
compared for different structures with different periods, when S a ( T 1 ) is
normalized. For example when S a ( T 1 ) is twice the S aMCE , the probability of
collapse is around 15%. To predict the probability of collapse or the prob-
ability of exceeding different damage states at different hazard levels, Eq.
[21.7] is used with S a ( x ) set as the value of the UHS at the corresponding
hazard level (i.e., UHS for 2% or 10% probability of exceedance in 50 years
given in Fig. 21.8). The probability of collapse as well as exceeding different
damage states at the MCE level (i.e., 2% in 50 years), given in Table 21.4,
is reasonably low and the performance of the bridge is satisfactory.