Figure 2.21. Smoothed displacement spectra for El Centro earthquake.

Figure 2.22. Tripartite response spectra for El Centro earthquake (5% damping, north-south component).

• For long-period buildings, the maximum spectral displacements approach the maximum ground displacements.

• For intermediate values of period, the maximum spectral velocity is several times the input velocity.

Thus, in the short-period range, the variation of the spectrum curve tends to show correlation with the line of maximum ground acceleration. In the medium-period range, the correlation is with maximum ground velocity while in the higher-period range, the correlation is with the displacement.

Because of the aforementioned characteristics, it is possible to represent an idealized upper-bound response spectrum by a set of three straight lines, as shown in Fig. 2.22. Also shown in the same figure are the values of ground acceleration (a = 0.348g), maximum velocity (V = 1.10 ft), and displacement (d = 0.36 ft/sec) experienced during the El Centro earthquake.

Site-Specific Response Spectrum. For especially important structures or where local soil conditions are not amenable to simple classification, the use of smooth spectra curves is inadequate. In such cases, site-specific studies are performed to determine more precisely the expected intensity and character of seismic motion. The development of site-specific ground motions is generally the responsibility of geotechnical consultants. However, it is important for the structural engineer to be aware of the procedure used in the generation of site-specific response spectrum. This is considered next.

Procedure for Developing Site-Specific Response Spectra. The seismicity of the region surrounding the site is determined from a search of an earthquake database. A list of active, potentially active, and inactive faults is compiled from the database along with their nearest distance from the site.

The predicted response of the deposits underlying the site and the influence of local soil and geologic conditions during earthquakes are determined based on statistical results of studies of site-dependent spectra developed from actual time-histories recorded by strong motion instruments.

Several postulated design earthquakes are selected for study based on the characteristics of the faults. The peak ground motions generated at the site by the selected earthquakes are estimated from empirical relationships.

The dynamic characteristics of the deposits underlying the site are estimated from the results of a nearby downhole seismic survey, from the logs of borings, static test data, and dynamic test data.

The causative faults are selected from a list as the most significant ones along which earthquakes are expected to generate motions affecting the site.

Several earthquakes with different probabilities of occurrence that may be generated along the causative faults are selected. The maximum capable earthquake (MCE), for example, constitutes the largest earthquake reasonably likely to occur. Since the probability of such an earthquake occurring during the lifetime of the subject development is low, the ground motions associated with the MCE events are estimated to have 10% probability of being exceeded in 250 years.

The slip rates of the faults are estimated from published data. Using the slip rates, the accumulated slip over an approximate 475-year period (corresponding to 10% probability of being exceeded in 50 years) and over an approximate 72-year period (corresponding to 50% probability of being exceeded in 50 years) are determined.

Using a statistical analysis approach, the peak ground motion values (acceleration, velocity, and displacement) anticipated at the site are estimated. By applying structural amplification factors to these values, the spectral bounds for acceleration, velocity, and displacement are obtained for each desired value of structural damping, most often 2, 5, and 10% of critical damping. The ground motion values for a given site thus vary with the magnitude of the earthquake and distance of the site from the source of energy release.

These values provide a basis by which site-dependent response spectra are computed. For each of the six site classes, spectral bounds are obtained by multiplying the ground motion values by damping-dependent amplification factors.

Use of Tripartite Response Spectra. Site-specific spectra are shown in Fig. 2.23. Tripartite response spectra for four seismic events characterized as earthquakes A, B, C, and D for a downtown Los Angeles site are shown in Fig. 2.24a-d. Response spectrum A is for a maximum capable earthquake of magnitude 8.25 occurring at San Andreas fault at a distance of 34 miles while B is for a magnitude 6.8 earthquake occurring at Santa Monica-Hollywood fault at a distance of 3.7 miles from the site. Response spectra C and D are for earthquakes with a 10 and 50% probability of being exceeded in 50 years.

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