Nonlinear Analysis
6.2 Input Ground Motions
Nonlinear dynamic response of index archetypes is evaluated for a set of pre-defined ground motions that are systematically scaled to increasing
intensities until median collapse is established. The ratio between median collapse intensity,SˆCT, and Maximum Considered Earthquake (MCE) ground motion intensity, SMT, is defined as the collapse margin ratio, CMR, which is the primary parameter used to characterize the collapse safety of the structure.
6.2.1 MCE Ground Motion Intensity
Collapse performance is evaluated relative to ground motion intensity associated with the MCE, as defined in ASCE/SEI 7-05, and related to the seismic criteria used for design of index archetypes in Chapter 5.
As described in Chapter 5, the Methodology defines DE and MCE ground motion intensities for three ranges of spectral acceleration associated with Seismic Design Categories B, C and D. Table 6-1 summarizes MCE spectral acceleration for maximum and minimum ground motions for these Seismic Design Categories, and Figure 6-1 shows MCE response spectra for the corresponding ground motion intensities.
Table 6-1 Summary of Maximum Considered Earthquake Spectral Accelerations And Transition Periods Used for Collapse Evaluation of Seismic Design Category D, C, and B Structure Archetypes, Respectively
Seismic Design Category Maximum Considered
Earthquake Transition
Period Maximum Minimum SMS (g) SM1 (g) Ts (sec.) D 1.5 0.9 0.6 C D 0.75 0.30 0.4 B C 0.50 0.20 0.4 B 0.25 0.10 0.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0 0.5 1 1.5 2 2.5 3 3.5 4
Period (seconds)
Spectral Acceleration (g)
MCE SDC D (maximum) MCE SDC D (min)/SDC C (max) MCE SDC C (min)/SDC B (max) MCE SDC B (minimum)
Figure 6-2 MCE response spectra required for collapse evaluation of index archetypes designed for Seismic Design Category (SDC) B, C, and D.
MCE ground motion intensity, SMT, is defined for short-period archetypes (T ≤ Ts) as:
MS MT S
S (6-2)
and for long-period archetypes (T > Ts) as:
T
SMT SM1 (6-3)
where values of SM1 and SMS are given in Table 6-1, and T is the fundamental period of an index archetype as defined in Equation 5-5.
6.2.2 Ground Motion Record Sets
The Methodology provides two sets of ground motion records for collapse assessment using nonlinear dynamic analysis, referred to as the Far-Field record set and the Near-Field record set. The Far-Field record set includes twenty-two component pairs of horizontal ground motions from sites located greater than or equal to 10 km from fault rupture. The Near-Field record set includes twenty-eight component pairs of horizontal ground motions
recorded at sites less than 10 km from fault rupture. The record sets do not include the vertical component of ground motion since this direction of earthquake shaking is not considered of primary importance for collapse evaluation, and is not required by the Methodology for nonlinear dynamic analysis.
The ground motion record sets each include a sufficient number of records to permit evaluation of record-to-record (RTR) variability and calculation of median collapse intensity, SˆCT. Explicit calculation of record-to-record variability, however, is not required for collapse evaluation of index archetypes. Instead, an estimate of record-to-record variability, based on previous research and developmental studies, is built into the process for calculating total system collapse uncertainty in Chapter 7. The record sets, along with selection criteria and background information on their selection, are provided in Appendix A.
The Methodology specifies use of the Far-Field record set for collapse evaluation of index archetypes designed for Seismic Design Category (SDC) B, C or D criteria (i.e., structures at sites that are located away from active faults). The Near-Field record set is provided as supplemental information, and is used in special studies of Appendix A to evaluate potential differences in the CMR for SDC E structures. Figure 6-3 shows the 44 individual response spectra (i.e., 22 records, 2 components each) of the Far-Field record set, the median response spectrum, and spectra representing one standard deviation and two-standard deviations above the median.
0.01 0.1 1 10
0.01 0.1 1 10
Period (seconds)
Spectral Acceleration (g)
Median Spectrum - Far-Field Set + 1 LnStdDev Spectrum - FF Set + 2 LnStdDev Spectrum - FF Set
Figure 6-3 Far-Field record set response spectra.
Both ground motion record sets include strong-motion records (i.e., records with PGA > 0.2 g and PGV > 15 cm/sec) from all large-magnitude (M > 6.5) events in the Pacific Earthquake Engineering Research Center (PEER) Next-Generation Attenuation (NGA) database (PEER, 2006a). Large-magnitude events dominate collapse risk and generally have longer durations of shaking, which is important for collapse evaluation of nonlinear degrading models.
The sets include records from soft rock and stiff soil sites (predominantly Site Class C and D conditions), and from shallow crustal sources
(predominantly strike-slip and thrust mechanisms). To avoid event bias, no more than two of the strongest records are taken from each earthquake.
The primary function of the Far-Field record set is to provide a fully-defined set of records for use in a consistent manner to evaluate collapse across all applicable Seismic Design Categories, located in any seismic region, and founded on any soil site classification. Actual earthquake records are used, in contrast with artificial or synthetic records, recognizing that regional variation of ground motions would not be addressed. In the United States, strong-motion records date back to the 1933 Long Beach Earthquake, with only a few records obtained from each event until the 1971 San Fernando Earthquake. Large magnitude events are rare, and few existing earthquake ground motion records are strong enough to collapse a large percentage of modern, code-compliant buildings.
Even with many instruments, existing strong motion instrumentation networks (e.g., Taiwan and California) provide coverage for only a small fraction of all regions of high seismicity. Considering the size of the earth and period of geologic time, the available sample of strong motion records from large-magnitude earthquakes is still quite limited, and potentially biased by records from more recent, relatively well-recorded events. Due to the limited number of very large earthquakes, and the frequency ranges of ground motion recording devices, the ground motion record sets are
primarily intended for buildings with natural (first-mode) periods less than or equal to 4 seconds. Thus, the record set is not necessarily appropriate for tall buildings with long fundamental periods of vibration greater than 4 seconds.
6.2.3 Ground Motion Record Scaling
Ground motion records are scaled to represent a specific intensity (e.g., the collapse intensity of the index archetypes of interest). Record scaling involves two steps. First, individual records in each set are “normalized” by their respective peak ground velocities, as described in Appendix A. This step is intended to remove unwarranted variability between records due to inherent differences in event magnitude, distance to source, source type and site conditions, without eliminating overall record-to-record variability.
Second, normalized ground motions are collectively scaled (or “anchored”) to a specific ground motion intensity such that the median spectral
acceleration of the record set matches the spectral acceleration at the fundamental period, T, of the index archetype that is being analyzed.
The first step was performed as part of the ground motion development process, so the record sets contained in Appendix A already reflect this normalization. The second step is performed as part of the nonlinear dynamic analysis procedure. This two-step scaling process parallels the ground motion scaling requirements of Section 16.1.3.2 of ASCE/SEI 7-05.
Figure 6-4 shows the median spectrum of the Far-Field record set anchored to maximum and minimum MCE response spectra of Seismic Design Categories B, C and D, at a period of 1 second.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0 0.5 1 1.5 2 2.5 3 3.5 4
Period (seconds)
Spectral Acceleration (g)
FF Record Set Scaled to MCE SDC Dmax FF Set Scaled to MCE SDC Dmin/Cmax FF Set Scaled to MCE SDC Cmin/Bmax FF Record Set Scaled to MCE SDC Bmin
Figure 6-4 Median spectrum of the Far-Field record set anchored to maximum and minimum MCE response spectra of Seismic Design Categories B, C and D, at a period of 1 second.