Project Title/ID Number 
Benchmarking methods for
Seismic Hazard Ground Motion Representation and their Effects on EDP's—3352003 
Start/End Dates 
10/1/03—9/30/04 
Project Leader 
James Beck (Caltech/F) 
Team Members 
Fatemeh Jalayer (Caltech/PD),
Keith Porter (Caltech/O), John Hall (Caltech/F) 
F=faculty; GS=graduate student; US=undergraduate student; PD=postdoc; I=industrial
collaborator; O=other
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1. Project Goals/Objectives:
Objectives:

To examine the effects of ground motion uncertainty
on both structural response and economic loss using various ground
motion descriptions.

To use the results of this study and specified criteria
to judge the
suitability of each ground motion description for performancebased
earthquake engineering (PBEE).

To predict the uncertainty in specified EDP’s and
DV’s
based on two alternative descriptions of ground motion uncertainty
which are
referred to as options (a) and (b):

A complete probabilistic
description of ground motion constructed by specifying a stochastic
model that depends on seismic source
parameters.

Adopting a parameter (or vector of parameters)
known as the intensity measure (IM) in order to represent the
ground motion
uncertainty.
In this approach, a suite of ground motion records
are used to represent the ground
motion features not captured by IM.

To compare the
differences in the probability distributions of the EDP’s
and DV’s conditional on magnitude M and fault
distance R for the alternative ground motion descriptions
outlined above.

The alternative ground motion descriptions, outlined
as options (a) and (b) above, have been (or
are going to be)
examined in terms
of the
resulting EDP (and DV) predictions for the
Van Nuys testbed structure.

The candidate IM’s are to be selected
from PEER’s proposed
list of IM’s. However, the investigations
are limited to those IM’s
for which attenuation relations are available.

The stochastic ground motion model proposed
by Atkinson and Silva (2000) for California
has been
employed to
provide a complete
probabilistic
description
of the ground motion based on M and
R.

Maximum interstory drift is designated
as the primary EDP.

The expected
repair cost will be chosen as the primary DV. It
will be
calculated
using the
results
of loss
estimation studies
for the Van Nuys
testbed (Porter et al., 2002).
2.
Role of this project in supporting PEER’s mission
(vision):
Performancebased earthquake engineering can be characterized by the
definition of quantifiable performance objectives. These performance
objectives are, implicitly or explicitly, defined as probabilistic statements
that may address various issues affecting structural performance; such
as structural nonstructural and contents damage, and human casualties.
The probabilistic nature of performance objective statements results
from uncertainties in the prediction of loading (i.e., seismic ground
motion), and the modeling of structural behavior and the damage repair
process. Therefore, the representation of the uncertainty in the ground
motion may significantly affect the seismic performance assessments.
The performance assessment methodology adopted by PEER employs a parameter
or a vector of parameters known as the intensity measure (IM) to represent
the uncertainty in the ground motion. In this approach, a suite of real
ground motion records are chosen in order to capture the ground motion
characteristics not already captured by the IM. This representation of
ground motion uncertainty, although computationally very efficient, cannot
provide a complete probabilistic representation of the ground motion.
A complete probabilistic representation of the ground motion uncertainty
can be obtained using simulation techniques based on generating synthetic
ground motion records. Obtaining a complete probabilistic representation
of the ground motion uncertainty is needed in deciding whether the adopted
IM represents properly the ground motion uncertainty and also in choosing
the most suitable IM from a list of candidate IM’s. However, it
is crucial to ensure that the synthetic records can provide a realistic
description of the ground motions expected to happen at the site.
3. Methodology Employed:
The following methods are employed, depending on the description of
GM (ground motion) uncertainty, in order to make the probabilistic EDP
and DV predictions:

When the ground motion is represented by a stochastic
model following option (a), a new efficient stochastic simulation
technique known as
Subset Simulation (Au and Beck, 2003) is used in order to calculate
the probability distribution for the EDP’s for selected values of
magnitude M and distance R over the range of interest. Figure 1 illustrates
(in
thick dashed line) the probability of exceeding a specified value
of the designated EDP, which is the maximum interstory drift ratio
for a scenario earthquake with magnitude M=7 and distance r=20 km for
the
transverse frame of the Van Nuys testbed.

When the uncertainty in
the ground motion is represented using IM’s
following option (b), the probability distribution of EDP’s
is estimated using the calculated EDP sample values corresponding
to the
selected suite of GM records. We assume lognormal PDFs for the
EDP’s
and the PDF parameters are estimated from the samples. Numerical
integration may then be used in the integral over IM expressing
total probability
(see Jalayer and Cornell, 2003). As usual when using IM’s,
a suite of real GM recordings are chosen and empirical IM attenuation
relations
are used to express the IM uncertainty for given M and R. Figure
1 illustrates (in thick solid line) the probability of exceeding
maximum interstory
drift, calculated as explained, by adopting the spectral acceleration
at the fundamental period of the structure S_{a}(T_{1}) and
choosing a suite of 20 GM recordings with 6.5 < M < 7.5 and
10 <R <30
km. The Abrahamson and Silva (1997) attenuation relation is used
to represent
the uncertainty
in S_{a}(T_{1}) for
a scenario earthquake with M=7 and r=20km.
In order to provide
a common basis for comparison between options (a) and (b), the
suite of GM records can also be generated for
the IM approach
by using the Atkinson and Silva (2000) stochastic model for each
of the selected values of (M,R). This stochastic GM model is
also used to construct
synthetic attenuation relations for the candidate IM’s
to be used in option (b). These IM attenuation relations are
developed
using Subset
Simulation (Au and Beck, 2003). The corresponding estimated probability
distributions of the EDP’s and the attenuation relations
can be compared with those using real GM recordings to examine
the appropriateness
of using synthetic ground motion records in option (b). Figure
1. illustrates
(in dotted line) the probability of exceeding maximum interstory
drift, calculated as explained, by adopting the spectral acceleration S_{a}(T_{1}) at
the fundamental period of the structure as IM and using a suite
of
20 synthetic GM recordings with M=7 and r=20 km. The synthetic
attenuation
relation
S_{a}(T_{1}) for
is used for the scenario earthquake with M=7 and r=20km.
Figure 1. Probabilistic representation of EDP using alternative
representations of ground motion uncertainty
Observations: It is observed that the response probability distributions
provided by the two alternative approaches for treating ground motion uncertainty
are very close when they both use stochastic ground motions. However, a
significant difference is observed when the IMbased approach is used with
real ground motion records to represent the ground motion uncertainty. The
apparent implication is that the stochastic ground motion model used in
this study is not capturing some important features of real strong motion
records. We are currently investigating the reason for these deficiencies
in the stochastic ground motion model.
4. Brief Description of past year’s accomplishments
(Year 6) & more detail on expected Year 7 accomplishments:
We have developed a (Matlab) software package for predicting the uncertainty
in the EDP’s using the subset simulation technique. This routine employs
the Atkinson and Silva (2000) stochastic ground motion model in order to
describe the seismic characteristics of the source for a scenario earthquake.
A conference paper has been submitted to 13WCEE on the effects of ground
motion uncertainty representation on predicting the structure response.
5. Other Similar Work Being Conducted Within and Outside
PEER and How This Project Differs:
Some related work done within and outside PEER on intensity measures as
follows:

Proposing new intensity measures (for frame structures): Studies
by Shome and Cornell (1999) suggest that the spectral acceleration
at the first mode is a (practically) suitable IM for EDP predictions
for moment
frame structures of moderate firstmode period. Many researchers within
and outside PEER have investigated alternative IM’s that for
a variety of structures are more suitable for EDP predictions. Most
of these IM’s
consist (in vector or scalar form) of the spectral acceleration at
the firstmode combined with other parameters related to nonlinear
response
and/or spectral information at periods other than the first mode. Pandit
et al. (2002) have proposed a class of vectorbased IM’s that
consist of firstmode spectral acceleration and a nonlinear SDOF response
parameter.
Luco and Cornell (2001) have proposed a scalar IM that combines the
bilinear inelastic response of an (equivalent) SDOF system with secondmode
elastic
spectral response. Cordova et al. (2000) have proposed a scalar intensity
measure that combines the firstmode spectral acceleration with the
spectral acceleration at a longer period to account for the period
elongation phenomenon.

Proposing criteria/methodologies for comparing
alternative IM’s:
Luco and Cornell have proposed “sufficiency” and “efficiency” criteria
for comparing alternative IM’s in terms of their prediction
of the EDP conditioned on a specified level of the IM. Based on these
criteria,
Vamvatsikos and Cornell (2002) have proposed the use of a nonlinear
dynamic analysis procedure known as incremental dynamic analysis
(IDA)
for comparing
various intensity measures. Conte and his research group (2002) have
used a large number of ground motion records in order to compare
the IM’s.
They have based their comparisons on the efficiency criterion and
also the observed correlations between the IM’s and ground
motion source parameters and between the IM’s and SDOF nonlinear
response parameters.

Comparing alternative descriptions of ground
motion uncertainty:
This is the focus of the proposed project and the only work that
we know of
in this area is a preliminary study by Beck et al. (2001) who compared
the probability of exceeding maximum interstory drift resulting
from the following alternative descriptions of ground motion uncertainty:

Using firstmode spectral acceleration S_{a} as
the IM, and,

Using Atkinson and Silva’s stochastic model The proposed project
is examining more cases and other IM’s, as
well as S_{a.}
6. Plans for Year 8 if project is expected to be continued:
It can be observed in Figure 1. that there is a significant difference
between probabilistic descriptions of the EDP obtained by using synthetic
ground motion records versus real records. Currently, we are working on
gaining a better understanding of the observed difference. We are interested
in studying alternative procedures for generating synthetic records that
provide EDP predictions that are closer to those provided by real ground
motion recordings. We believe that this is extremely important with regard
to using simulation techniques for providing a complete probabilistic description
of the EDP’s and the DV’s.
7. Describe any actual instances where you are aware your
results have been used in industry:
8. Expected Milestones & Deliverables:
Phase II  (by June 2004)

Finalizing the studies on the effect
of ground motion uncertainty on the prediction of structural response,
especially explaining the significant
difference observed between using synthetic and real ground motion
records for response predictions.

Predicting the uncertainty in specified
EDP’s by adopting candidate
IM’s from the list of IM’s proposed within PEER, for which
attenuation relations are available, following option (b) outlined
above, and comparing the differences in the probability distributions
of EDP’s
obtained by following options (a) and (b). Deliverables at the end
of Phase II include: a report on the effects of ground motion uncertainty
on the
prediction of the structural response, which is the first part of a
PEER report on ground motion uncertainty, and a (journal) paper.
Phase III 
(by September 2004)
Predicting the uncertainty in the prediction of specified
DV’s by
following options (a) and (b) outlined above and comparing the differences
in the resulting probability distributions of the DV’s. Deliverables
at the end of Phase III include a report on the effect of ground motion
uncertainty on predicting economic losses, which is the second part to
the PEER report on ground motion uncertainty, and (tentatively) a journal
paper.