Ground motion selection for seismic risk analysis of civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 104

( )

dim
IM

λ

( )

IM j

( ) =

∫

λ edp P edp im

j

dIM [4.18]

EDP EDP IM j j

j

j

IM

j

where λ EDP ( edp ) is the seismic demand curve of EDP , and quantifi es the

rate of exceedance of various values of the seismic responses considered;
λ IM j ( im j ) is the rate of exceedance of the conditioning intensity measure,
IM j , obtained from PSHA; and P EDP | IM j ( edp | im j ) is the probability of the
vector of seismic responses, EDP , exceeding specifi c values edp , which is
obtained from the set of seismic response analyses conducted using ground
motions selected by the aforementioned methodology for IM j im j . The

assumption behind the computation of the seismic demand curve as given
by Equation (4.18) are elaborated upon in Bradley (2012a), but can be
considered to be consistently satisfi ed if ground motions are selected using
the discussed methodology, which practically requires six key steps (Bradley,
2012a):

=

• Selection of the set of intensity measures IM , which suffi ciently repre-

sent the ground motion severity.

• Choose a conditioning intensity measure, IM j , from IM and compute

the ground motion hazard

λ IM j ( im j ).
• Selection of ground motions based on the GCIM distribution
f IM | IM J ( im | im j ) in Equation (4.1).

• Perform seismic response analysis and use the results to parametrize

P EDP | IM j ( edp | im j ) (e.g. Bradley, 2012a).

• Ensure that the considered IM , is suffi cient with respect to EDP .

• Compute the seismic demand curve via Equation (4.18).

Because of its simplicity in implementation, the IM -based approach is
the most common methods for computation of the seismic demand curve
(as given by Equation (4.18)). One observed detrimental consequence of
the IM -based approach is that the practical computation of the seismic
demand curve appears to be dependent on the intensity measure used in
its computation (Bradley, 2012a). Bradley (2012a) demonstrated theoreti-
cally the independence of the seismic demand curve on the choice of con-
ditioning intensity measure, and noted that inconsistent seismic demand
curves would be obtained, if ground motions selected were inconsistent
with the GCIM distribution, f IM | IM J ( im | im j ), and the seismic response analy-
ses are sensitive to such intensity measures.
Figure 4.11 presents examples of the seismic demand curve for the case
study structure computed using six different conditioning intensity mea-
sures for peak pile head displacement, U PH , and peak deck acceleration, a D
(Bradley, 2012a). It can been seen that the demand curves computed via
different IM j s are the same in a qualitative sense, consistent with the theory
previously presented. Furthermore, the majority of the differences between