The project is structured into two phases:

Phase I:     Investigate whether "non-stationary" characteristics of seismograms, in addition to more conventional ground motion intensity measures (e.g., spectral values), can improve the accuracy in the prediction of structural seismic performance.

Phase II:     Three tasks:

1. to provide the quantitative technical basis to establish the threshold limits beyond which earthquake record scaling introduces bias in the nonlinear response of structures (issue of particular interest to the PEER Lifelines Program's Design Ground Motion Library study).
2. to provide the tools necessary for the synthetic time history validation criteria currently being developed by the PEER Lifelines Program (NGA Working Group #3). These criteria will consider the issue of nonlinear structural response.
3. to provide a technical basis for some of the assumptions used in the PEER Lifelines Project 507 entitled "The Advanced Seismic Assessment Guidelines," which provided recommendations for "tagging" of buildings damaged by a mainshock and susceptible to an aftershock. These assumptions are also relevant to the follow-up applications PEER Lifelines Projects 508 and 509.

This project supports the PEER methodology for performance-based earthquake engineering by providing new information related to ground motion intensity measures that may correlate well with structural response. It also supports the PEER Lifelines Program with issues relevant to practical applications (e.g., use of scaled or synthetic time history for structural evaluation and design, tagging of damaged buildings after earthquakes – see description of Phase II above).

Phase I.      First we used a signal processing technique known as Empirical Mode Decomposition (Norden E. Huang, NASA Goddard Space Flight Center) to decompose numerous earthquake ground motion records for which the response of several building models had previously been computed via nonlinear dynamic analysis (by Nicolas Luco as a Research Assistant at Stanford University). In looking for a correlation between the "modes" of the earthquake records and the drift response of the building models, we found that it was difficult to see beyond the correlation attributable to the response spectra of the ground motions. For this reason, we subsequently switched to a set of 31 earthquake records that were "spectrum-matched" to the median response spectrum of the original earthquake records (by Norm Abrahamson and his colleagues). With this set of earthquake records that have the same response spectrum (but different time-history signals) we were able to remove the effect of the response spectrum from our search for time-domain features of ground motions that correlate well with the drift response of buildings.

We were also able to investigate the effect of the spectrum-matching process on:

1. time-domain features of the ground motions, and
2. the average structural drift response (i.e., a bias), and
3. the record-to-record variability of drift response, all relative to the original records and/or their amplitude-scaled versions. In addition to a SMRF building model, we considered numerous inelastic SDOF oscillators of various periods and yield strengths to give breadth to our results.

Phase II.     The last objective of Phase II, i.e., regarding the assessment of aftershock capacity as a criterion for guiding the tagging of damaged buildings, was tackled first. The work in the first two tasks has not started yet. In Task 3 we intend to estimate the residual capacity of damaged structures via nonlinear dynamic analyses of multiple nonlinear SDOF systems and of a 3-story SMRF building subject to back-to-back ground motion records simulating the effect of a mainshock followed by an aftershock. For a few of the SDOF systems, we have gone through this exercise with a suite of 30 ground motion records that were used both as mainshocks and aftershocks, creating a matrix of 900 cases (30 x 30). The results of these analyses are compared with those obtained by applying the Guidelines developed by the PEER Lifelines Project 507. The latter results were based on assumptions and less accurate response analyses that we are testing.

Phase I.      By computing the response of structures of different yield strengths to the spectrum-matched earthquake records, we have discovered that, even knowing the response spectrum of a given earthquake record, it is inappropriate to ask whether that ground motion is, in general, severe or benign in terms of the drift response it induces. In fact, the record can be both severe and benign, depending on the strength (and, as one might expect, the period) of the structure considered. This is demonstrated in the figure below, which is a plot of the maximum inter-story drift angle response to each of the 31 spectrum-matched earthquake records for a nine-story SMRF building of, effectively, two different strengths (the case with R=4 has half the strength of the building with R=2).

Because the relative severity of the drift response depends on the strength of the particular structure of interest, measures of ground motion intensity that do not consider the strength are not likely to correlate well with the drift response of structures of a wide ranges of strengths. We have demonstrated that this can be true for the ground motion measures of duration and pulse period/amplitude/# of cycles, for example. Other measures of ground motion intensity that do consider the strength of the structure of interest, such as inelastic spectral displacement, are found to correlate reasonably well with structural drift response, even after the elastic response spectrum of the earthquake record has been accounted for. As a proxy for inelastic spectral displacement, we have also discovered that the first "significant" (relative to the yield displacement) displacement excursion of an elastic SDOF oscillator correlates reasonably well with the drift response of the building model considered. Unlike inelastic spectral displacement, this measure makes use of time-domain features of the same analysis results that are used to define an elastic response spectrum.

Phase II.     No definitive results are available at this point.

Phase I.     There are many researchers, within and outside of PEER, who are investigating alternative parameterizations of ground motion that correlate well with nonlinear structural response and damage. However, to our knowledge, this PEER project is unique in that it looks at features of ground motion that correlate well with structural response/damage when considered in conjunction with the elastic response spectrum of the ground motion.

Phase II.    We are not aware of other projects with the same objectives and statistical flavor as those outlined in Tasks 1 and 2. Task 3 is also based on a novel idea for tagging damaged buildings.

No plans at this moment to continue the project.

We have encountered significant interest from a group of engineers and seismologists from Caltrans who are interested in explicitly considering inelastic response in future bridge designs and who are concerned with the effect of near-source ground motions on inelastic structures. Great interest in our results has also been expressed by professors at Stanford University and by colleagues in the industry (e.g., Ron Hamburger of SGH and Joe Maffei of R&C).

Phase I.      the four quarterly milestones have been completed.

Phase II.     June, September, and December 2003 are the three remaining milestones.

Phase I.     The final report will be completed by June 2003. Based on this report, we plan to write two journal papers.

Phase II.    The deliverables consist of a report with the findings of the three tasks, and a computer program to be used by seismologists to compute nonlinear response spectra of SDOF systems.