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The purpose of seismic design is to reduce risk to life and property from future earthquakes. Risk is defined as the probability of a loss; normally, an increase in the seismic design load reduces the seismic risk. The current approach toward seismic design is to reduce the risk at individual locations (site-specific risk) to an acceptable level. This approach is reasonable from the perspective of a building owner, but it is not reasonable from the perspective of an entire community, because it does not ensure that the risk to multiple locations affected by the same earthquake (aggregate risk) is also reduced to an acceptable level.

The seismic design should be aimed at reducing both the site-specific and the aggregate risks. Due to the highly random nature of earthquake ground motions and uncertain construction quality, it is not possible to eliminate seismic risk entirely, but it is possible to reduce it to an acceptable level.

The site-specific and the aggregate risks do not always go hand-in-hand. For example, if a region is affected only by small but frequent earthquakes, the probability of significant loss at a given location is high due to the high probability of an earthquake happening close to that location. However, the probability of a significant aggregate loss is low because each small earthquake will affect only a few locations. On the other hand, if the same region is affected only by large but rare earthquakes, the probability of a significant loss at a given location is low due to the low probability of strong shaking at that location, but the probability of a significant aggregate loss is high because the large earthquake will affect many locations simultaneously. This is notwithstanding the fact that the low frequency of earthquakes in the region reduces risk awareness, making risk mitigation less popular and thus further increasing the aggregate risk in the region.

Seismic design should be aimed at reducing both the sitespecific and the aggregate risks. Due to the highly random nature of earthquake ground motions and uncertain construction quality, it is not possible to eliminate seismic risk entirely, but it is possible to reduce it to an acceptable level. Ignoring the uncertainties in construction quality, we can say that the site-specific risk is proportional to the chance of exceeding the seismic design load at a given location, and the aggregate risk is proportional to the chance of exceeding the seismic design load at many locations simultaneously. Therefore, the seismic design load for controlling both the site-specific and the aggregate risks should meet the following two criteria:

- Site-specific criterion. The seismic design load at each site in the region should not be exceeded more than 0.002 times per year (in other words, it should have an exceedance return period of 500 years for each site).
- Aggregate criterion. The seismic design load over any 100- km2 area (contiguous or separated) should not be exceeded more than 0.002 times per year (in other words, it should have an exceedance return period of 500 years for a 100- km2 area anywhere in the region).

The first criterion can be met by performing a site-specific probabilistic seismic hazard analysis of every site in the region and selecting the 500-year return-period ground motions for design. This is the traditional approach for obtaining the design ground motions (hence loads). The second criterion can be met by performing an aggregate hazard analysis of the region. The seismic design load at each site should be the higher of the loads obtained from the two criteria.

Now, I present a couple of examples in which the results of site-specific hazard analysis are counterintuitive when viewed in terms of the aggregate risk. First, the site-specific hazard is very sensitive to the variability (standard deviation) in the ground-motion prediction models. During an earthquake any level of ground motion is possible at a site because of the highly unpredictable nature of the rupture and the propagation of the released seismic energy. There is a chance that a site will experience well-above-average ground motion during an earthquake, but there is small chance that all sites in the region will simultaneously experience well-above-average ground motion during the same earthquake. Whereas the loss at a given site is sensitive to the variability in the ground-motion prediction model, the total (aggregate) loss at all sites in the region is less sensitive to the variability in the ground-motion prediction model. Second, it is sometimes unclear whether the next earthquake on the fault will rupture the entire fault or only a segment of the fault. According to the characteristic model, the fault always ruptures in its entirety, producing only the maximum possible earthquake. According to the Gutenberg-Richter (GR) model, the fault can rupture in smaller segments producing smallerthan- maximum earthquakes. Assuming a constant momentrelease rate, the chance of any earthquake on the fault is higher in the GR model, but the chance of the maximum earthquake is higher in the characteristic model. The site-specific hazard increases when the GR model is used. For someone trying to manage the aggregate risk, it is difficult to understand why the design loads increase when the chance of the big earthquake on the fault actually decreases.

The seismic design loads should be based on a transparent analysis of the site-specific and aggregate hazards without the need for arbitrary adjustments.

The seismic design loads in the International Building Code (IBC) are based on the site-specific hazard analysis carried out by the California Geological Survey (CGS) and the U.S. Geological Survey (USGS). The 475- year return-period site-specific hazard analysis did not capture the effects of rare but large earthquakes, which pose significant aggregate risk in the New Madrid seismic zone, the Pacific Northwest, and the Wasatch region. Therefore, the Building Seismic Safety Council decided to increase the return period of the ground motions in the IBC to 2,475 years but require the design of buildings for only two-thirds of the 2,475-year return-period ground motions. The two-thirds of the 2,475-year return-period ground motions were “too high” in the western United States due to the high occurrence rate of earthquakes. Therefore, the 2,475-year return-period ground motions were truncated by the “deterministic limit” to obtain the MCE (maximum considered earthquake) ground motions. As a result of these arbitrary adjustments and truncations, the seismic design according to the IBC is difficult to articulate.

After Hurricane Katrina it can be easily argued that the aggregate risk is even more important than the site-specific risk, yet aggregate risk is not rationally considered in building codes. The seismic design loads should be based on a transparent analysis of the site-specific and aggregate hazards without the need for arbitrary adjustments. Aggregate hazard analysis cannot be carried out simply by adjusting the results of the site-specific hazard analysis. A new approach is needed to analyze the seismic hazard for the purpose of building codes.

`lastiz [at] ucsd.edu`

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Posted: *29 June 2007*