Incremental dynamic analysis (IDA) applied to seismic risk assessment of bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 571

21.6 Development of fragility curves using

incremental dynamic analysis (IDA) results

The fragility curve gives the conditional probability that a certain limit-state
be exceeded (i.e., probability of failure) at a given IM value. Percentile IDA
curves can be used to derive fragility curves. In Fig. 21.6 the probabilities
of failure at different IM levels are derived from the IDA results shown in
Fig. 21.1. The fragility curves were developed for collapse and cover-spalling
damage states. The cover-spalling state was defi ned as exceeding the drift
ratio of 1.85% determined using the equations by Berry and Eberhard
(2007). The fragility curves developed using IDA data are shown by dots,
in which each dot represents a ratio of the number of records that caused
failure to the total number of records at an IM level. In Fig. 21.6, the cumu-
lative lognormal distribution curves developed using the median and stan-
dard deviation of the IDA results at collapse and cover-spalling limit states
are also shown. The fragility curves using IDA data can be estimated using
such curves.
Assuming that the data are lognormally distributed, it is possible to
develop the fragility curves at collapse (or any other limit-state) by comput-
ing only the median collapse capacity and logarithmic standard deviation
of the IDA results at collapse. The fragility curves then can be analytically
computed using Eq. [21.6]:

( )

() −

C

⎡
⎢

ln x ln S ⎤

⎥

a 50 %

( ) =

P failure S = x Φ [21.6]

a

β

RTR

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2

Collapse fragility curve (IDA data)

Spalling fragility curve (IDA data)

Collapse fragility curve
(idealized lognormal)
Spalling fragility curve
(idealized lognormal)

0.1
0

0 0.5 1.0 1.5 2.0 2.5 3.0

S a ( T 1 ) ( g )

21.6 Development of fragility curves for different limit states using
IDA results.