Incremental dynamic analysis (IDA) applied to seismic risk assessment of bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 556

the large amount of data obtained through all IDA curves by quantifying
the randomness introduced by the records. Appropriate techniques should
be used to reduce the entire data to the probability distribution of DM
given IM and to the probability of exceeding any specifi c limit-state given
the IM level. The use of percentiles (fractiles) are the most appropriate
approach to summarize the IDA, since at the point of dynamic instability,
introduced by fl atlines in the IDA curves, the DM values are infi nite and
therefore the use of mean values or similar parameters is not possible
(Vamvatsikos and Cornell, 2002).
In order to evaluate the IDA result the median responses are determined
along with the predicted dispersion of the results from different ground
motion records. The IDA results thus can be summarized in percentiles,
including median (50% percentile), 16% and 84% percentiles. With the
assumption of a lognormal distribution of maximum drift ratio as a function
of S a ( T 1 ), the median (i.e., 50% percentile) is the natural 'central value' and
the 84% and 16% percentiles correspond to the median times e ±dispersion ,
where 'dispersion' is the standard deviation of the logarithm of the values
(Jalayer and Cornell, 2003). These percentile curves are much smoother
than the individual IDA curves and can better represent the overall behav-
iour of a structure.
A summary of the IDA curves can be expressed either by the values of
DM given IM or the values of IM given DM. The fi rst method provides the
distribution of DM in the structure at a given IM level, while the second
approach provides the distribution of IM that causes a given level of DM
in the structure. It has been shown that the line connecting the x % percen-
tiles of DM given IM is similar as the one connecting the (100 x )% per-

centiles of IM given DM (Vamvatsikos and Cornell, 2004). However for
some cases with signifi cant waiving and structural resurrection behaviour
the two methods may result in different predictions (Tehrani and Mitchell,
2012d). An example of IDA curves summarized into 16%, 50% and 84%
percentiles is shown in Fig. 21.1.

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21.3 Structural modelling for incremental dynamic

analysis (IDA)

In IDA, the intensity of the ground motion records is increased until they
cause structural instability which is referred to as structural collapse. There-
fore, the structural models in the IDA should be capable of simulating
structural collapse and should directly or indirectly consider all signifi cant
deterioration modes that contribute to collapse including the stiffness,
strength and inelastic deformations under reversed cyclic loading. The most
important structural parameters that infl uence the IDA predictions include
the plastic deformation capacity,

θ cap , and the post-capping rotation capacity,