1. 1 Workshop on GMSM for Nonlinear Analysis, Berkeley CA, October 26, 2006 ATC-63 Selection and Scaling Method Charles Kircher Curt B. Haselton Gregory G. Deierlein

2. 2 Workshop on GMSM for Nonlinear Analysis, Berkeley CA, October 26, 2006 Ground Motion Objectives and Considerations  Objectives of ATC-63 Project:  Develop a far-field set that is independent of site and building period  Use set to assess collapse of 70 buildings with various period  Use set as part of an assessment process to validate new building systems for inclusion in building code  Minimize required scaling factors at collapse levels (PGA, PGV limits)  Maintain enough records to do meaningful statistics with collapse predictions  Consideration of spectral shape:  For rare ground motions, spectral shape ( ε ) is extremely important (Baker and Cornell).  Our selection does not account for this proper spectral shape.  We account for this by adjusting the collapse capacity distribution (mean and sigma) after running the collapse simulations (forthcoming paper on this method).

3. 3 Workshop on GMSM for Nonlinear Analysis, Berkeley CA, October 26, 2006 Selection of Far-Field Ground Motion Set  Selection Criteria:  M > 6.5  R > 10km  PGA > 0.2g AND PGV > 15 cm/sec  Vs > 180 m/s (NEHRP A-D)  ≤ 2 records per event  Lowest useable frequency < 0.25 Hz (4 seconds)  Strike-slip and thrust faults (consistent with California)

4. 4 Workshop on GMSM for Nonlinear Analysis, Berkeley CA, October 26, 2006 Summary of Far-Field Ground Motion Set - 22 records - 14 events - Mechanisms: - 9 strike-slip - 5 thrust

5. 5 Workshop on GMSM for Nonlinear Analysis, Berkeley CA, October 26, 2006 Ground Motion Scaling Method  Scaling method developed by C. Kircher (details included in last slide)  Scaling steps:  Compute the average [Sa(T 1 )/PGV] for the full set of ground motions  Compute record scale factors:  SF = [ average [Sa(T 1 )/PGV] of set ] * RecordPGV  Further scale the records by anchoring the mean Sa(T 1 ) to the target value

6. 6 Workshop on GMSM for Nonlinear Analysis, Berkeley CA, October 26, 2006 Scaled Far-Field Ground Motion Set  Records scaled to Sa(1s) = 0.9g

7. 7 Workshop on GMSM for Nonlinear Analysis, Berkeley CA, October 26, 2006 Dispersion in Scaled Ground Motion Set  Dispersion in scaled record set 0.4-0.6

8. 8 Workshop on GMSM for Nonlinear Analysis, Berkeley CA, October 26, 2006 Closing  Thank you for your attention.  Questions?

9. 9 Workshop on GMSM for Nonlinear Analysis, Berkeley CA, October 26, 2006 Ground Motion Scaling Method A Method for Scaling Horizontal Earthquake Time Histories Kircher & Associates Consulting Engineers March 28, 1996 Definitions (Input Data): N Number of pairs of horizontal time history components that make up the set of earthquake records for each of site soil conditions (e.g., rock/rear- source, soil near-source, rock/far-source and soil/far-source. PGVji Peak ground velocity, PGV, of time history, THji, (note: PGV values are provided by USGS/CDMG with processed time history and response spectra data), Rsji Response spectrum (5%-damping) of time history, THji, Thji Time history of the ith pair in the jth horizontal direction (i.e., j = 1 or 2), TRS Target response spectrum (defined as 1.4 times the DBE, Z = 0.4, N=1.0) Teff Effective period of structure in seconds at intersection of capacity/demand curves. Definitions (Calculated Data): ARS Response spectrum shape of time histories taken as the mean of composite response spectra, CRSi, normalized by composite peak ground velocity, CPGVi, CPGVi Composite peak ground velocity of the ith horizontal time history pair, CRSi Composite response spectrum of the ith horizontal time history pair, MARS Response spectrum multiplier used to fit the response spectrum shape, ARS, to the target response spectrum, TRS, STHji Scaled time history of the ith pair in the jth horizontal direction. Calculation Steps: 1.For near-source records, rotate each pair of horizontal components to fault normal and fault parallel directions (note: rotation affects all parameters, including time histories, THij, response spectra, RSij, and peak ground velocity, PGVij). 2.For each pair of earthquake components, calculate the composite spectrum, CRSi, and the composite peak ground velocity, CPGVi: CRSi = (RS1i2 + RS2i2)1/2 CPGVi = (PGV1i2 + PGV2i2)1/2 3.Find the average value of composite spectra normalized by composite peak ground velocity: 4.Determine the response spectrum multiplier, MARS, that is required to increase (or decrease) the response spectrum shape, ARS, such that it matches the target response spectrum, TRS, at the period(s) of interest (e.g., 1.4 times 0.60g for soil sites and 1.4 times 0.40g for rock sites at 1 second): MARS  TRS/ARS (ARS  1/T at Teff  1 second) 5.For each pair of earthquake time histories, scale both horizontal components by the ratio of the response spectrum multiplier to the composite peak ground velocity: STH1i = (MARS/CPGVi)TH1i STH2i = (MARS/CPGVi)TH2i