1. Selection of Time Series for Seismic Analyses
Jennie Watson-Lamprey
Norm Abrahamson
University of California at Berkeley

2. Typical Approach Specified Design Event
M, R, Site, Spectrum
Engineers Request: Provide small set of representative ground motions time series
e.g. 1-7 sets of time series
Ground Motion Analyst
Select ground motions with similar M, R, site, style-of-faulting, directivity condition
Modify the ground motion to be consistent with the design spectrum
Preference for less scaling

3. Basis for this Approach
The response of the structure depends on more parameters than just the spectral acceleration
e.g. Duration, peak velocity, Arias intensity, root mean square of acceleration, epsilon, spectral shape …
These other unspecified parameters are captured in the time histories
Select time histories
Similar seismological & geotechnical conditions
Use time series with a scale factor close to one because they will have the appropriate combination of these other unspecified parameters

4. Selection Should Consider Structure Properties
“Just give me the ground motions”
This approach does not work for small numbers of ground motions
Need to consider non-linear behavior of the structure
Best set of ground motions will be different for different types of structures
e.g. dam vs building
We need to determine the unspecified parameters that affect nonlinear response

5. Development of an Objective Method of Time Series Selection
Use a simplified model of the non-linear system
Identify the vector of record properties that control the response of the simplified model
Choose scaled records that have record properties expected to produce an average response

6. Evaluation of Proxy Response
Proxy Selection
Structure - Bilinear Oscillator Displacement
Dam - Newmark Displacement
NGA PEER Database
Model Proxy Response using record properties
Structure - Sa(T1), Sa(2T1), Uniform Duration, PGV
Dam - ARMS, PGA, Uniform Duration, PGV

7. Example Structure Application
R = 10 km
Sa(1sec) = 1.08g
Sa(2)|Sa(1) = 0.40g
ky = 0.2g
Calculate
PGV = 77 cm/s
DurUNI = 11.5sec
Calculate
Average Expected Design Event Gamma = 1.00

8. Select Candidate Records
NGA PEER dataset
7075 ground motions
Scale to Spectral Value
Scale all records to Sa(1sec)
Reject Bad Fits
9 s < DurUNI < 15 s
62 cm/s < PGV < 95 cm/s

9. Repeat for R values of 1.5R, 2R and R/1.5
Calculate the expected Gamma for each scaled record
Calculate the difference between the expected gamma and the Design Event Gamma
Select the seven records with the smallest difference for all R values.

10. Top Seven Scaled Records

11. Summary
By identifying the record properties that affect response and selecting time series based on those properties the effects of Magnitude and distance on nonlinear response are reduced and the effects of scale factors are reduced. This allows for wider Magnitude and distance bins and larger scale factors to be employed in selection.

12. Spectrum Compatible Ground Motions
Used to reduce variability of structural response.
Their use generates estimates of median response conditioned on the elastic response spectral values that are matched to.

13. Spectrum Compatible Ground Motions
RSPMatch
Adds small wavelets to the time series to increase or decrease the peaks that generate the points on the elastic response spectrum
The goal is to maintain the nonstationary record properties, those other record properties that we know influence response, but we aren’t explicitly using for selection.
You shouldn’t be able to tell that anything has happened to the time series.

14. Spectrum Compatible Ground Motions
For this application I am matching to an elastic response spectrum conditioned on spectral acceleration at 1 second.
For Estimate II
Matching to a red:
For Estimate IV
Matching to blue:

15. Thank You
Questions?