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start to dominate the hazard at long return period hazards. Several efforts are in progress to find
improved IMs, ranging from the use of combinations of spectral values at modal periods (Luco and
Cornell, 2001) to the use of vectors that incorporate near-fault parameters such as a an equivalent pulse
period.
Engineering Demand Parameters, EDPs
Engineering demand parameters are the product of response prediction, most appropriately from
inelastic dynamic analysis that considers the soil-foundation-structure system resting on top of bedrock.
The challenge of formulating complete system models, which should incorporate modeling
uncertainties and should account for all important uncertainties inherent in geotechnical and structural
material, component, and system properties, will remain a challenge for many years to come.
Relevant EDPs depend on the performance target and the type of system of interest. They include
story drifts, component inelastic deformations, floor accelerations and velocities, but also cumulative
damage terms such as hysteretic energy dissipation. Once identified, they can be computed from
different procedures such as the by now widely employed incremental dynamic analysis (IDA)
procedure. In this procedure, the soil-foundation-structure system is subjected to a ground motion
whose intensity is incremented after each inelastic dynamic analysis. The result is a curve that shows
the EDP plotted against the M used to control the increment of the ground motion. IDAs can be
earned out for a sufficiently large number of ground motions to perform statistical evaluation of the
results. This implies that for a given value of IM, the median value and a measure of dispersion (e.g.
84 th percentile) of the response EDP values are evaluated, with results as shown in the right part of Fig.
4. This provides the information for dG(EDP\IM) of Eq. (1).
For use in Eq. (1), dG(EDP\IM) must be evaluated for the full range of 1M that contributes
significantly to the final value of DV. The IDA, however, has a limited range of applicability because
the ground motion frequency characteristics change with magnitude, particularly for long return period
events that may be dominated by near-fault ground motions. Thus, caution must be exercised in
defining the range of applicability of an IDA and the associated values of dG(EDP\IM).
Presuming that the IDA curves and their statistics are valid for the full range of interest, the
information shown in Fig. 4 can be used to develop a hazard curve for the EDP, using the equation
*£OP 00 = P[^DP > y \ IM = x] | dX m (x) | (3)
This hazard curve can be obtained from numerical integration of results of the type shown in Fig. 4, or
through a formulation described in Luco and Cornell (1998), which results in the following expression
for the mean annual frequency of EDP exceeding a value y:
X EDP (y) = P(EDP > y} = k t ylar k exp-^£DP|(M (4)
This equation holds if the IM hazard can be described by the widely used equation
l ai (x) = P[lM> X ] = k e x' k (5)
and the following relationship can be fit locally (around the return period of primary interest) to the
median EDP - IM data: