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=post-doc; I=industrial collaborator; O=other

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1. Project Goals/Objectives:

Objectives:

  1. To examine the effects of ground motion uncertainty on both structural response and economic loss using various ground motion descriptions.
  2. To use the results of this study and specified criteria to judge the suitability of each ground motion description for performance-based earthquake engineering (PBEE).

Goals:

  1. 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):
    1. A complete probabilistic description of ground motion constructed by specifying a stochastic model that depends on seismic source parameters.
    2. 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.
  2. 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.

Scope:

  1. 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 test-bed structure.
  2. 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.
  3. 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.
  4. Maximum inter-story drift is designated as the primary EDP.
  5. 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 test-bed (Porter et al., 2002).

2. Role of this project in supporting PEER’s mission (vision):

Performance-based 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 non-structural 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:

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 inter-story drift, calculated as explained, by adopting the spectral acceleration Sa(T1) 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 Sa(T1) for is used for the scenario earthquake with M=7 and r=20km.

figure 1
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 IM-based 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:

  1. 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 first-mode 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 first-mode combined with other parameters related to non-linear response and/or spectral information at periods other than the first mode. Pandit et al. (2002) have proposed a class of vector-based IM’s that consist of first-mode spectral acceleration and a non-linear SDOF response parameter. Luco and Cornell (2001) have proposed a scalar IM that combines the bi-linear inelastic response of an (equivalent) SDOF system with second-mode elastic spectral response. Cordova et al. (2000) have proposed a scalar intensity measure that combines the first-mode spectral acceleration with the spectral acceleration at a longer period to account for the period elongation phenomenon.
  2. 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 non-linear 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 non-linear response parameters.
  3. 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 inter-story drift resulting from the following alternative descriptions of ground motion uncertainty:
    1. Using first-mode spectral acceleration Sa as the IM, and,
    2. Using Atkinson and Silva’s stochastic model The proposed project is examining more cases and other IM’s, as well as Sa.

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)

  1. 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.
  2. 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.

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