## Seismic Hazard Assessment

The analysis of a structure under a given ground motion is a relatively simple task that may be accomplished using well-established principles of structural dynamics. However, as discussed in previous chapters, earthquake ground motions may be radically different from one earthquake to another and from one site to another. Furthermore, it is impossible to forecast how strong a future earthquake will be and when and where it will occur. Therefore, the characteristics of future earthquake ground motions are, for the most part, unpredictable and, hence, the selection of the ground

motion characteristics for which structures should be designed constitutes a diffi cult and elaborate undertaking that involves the use of historical information, statistical data, geological inferences, probabilistic models, empirical correlations, and, more often than not, engineering judgment. This process of evaluating for the purpose of seismic design the likely characteristics of future earthquake ground motions in a given seismic area is a critical step in the seismic design of structures called seismic hazard assessment.*

As seen in the preceding chapter, several parameters may be used to characterize earthquake ground motions, but by far the most widely used have been peak ground acceleration, peak ground velocity, and response spectrum ordinates. As a result, the objective of a seismic hazard assessment in the past has been, and still is, an estimation of the peak ground acceleration, peak ground velocity, or response spectrum ordinates of the ground motions expected at a given site as a result of the earthquakes that can be generated, within a given time interval, in the vicinity of the site. Thus, in general terms, an assessment of the seismic hazard at a specifi c site involves the following steps:

1. Identifi cation and characterization of all earthquake sources capable of producing signifi - cant ground motions at the site

2. Estimation of the magnitude and the frequency of the earthquakes that can be generated at these sources

3. Evaluation of the distance and orientation of each source with respect to the site 4. Establishment of statistical correlations between earthquake magnitude, earthquake

source characteristics, distance from source to site, and ground motion intensity (e.g., peak ground acceleration, peak ground velocity, or response spectrum ordinates)

5. Estimation of the expected ground motion intensity at the site using these correlations in terms of (a) the expected earthquake magnitudes at the identifi ed sources, (b) the known characteristics of these sources, and (c) the estimated distances from the sources to the site

There are obviously several ways by which such an assessment can be made. In the early days of earthquake engineering, it was made deterministically without due consideration of all the uncertainties involved in the evaluation process and the fact that earthquakes are, for the most part, random events. That is, an assessment of the seismic hazard at a particular site was made by assuming the occurrence of an earthquake of a presumed possible largest magnitude at a nearby, previously known, earthquake fault. Today, these assessments are invariably made, explicitly or implicitly, within a probabilistic framework. In one approach, called in this text the semi probabilistic approach, some variables, such as distance to seismic source, are assumed deterministic while some others, such as frequency of occurrence, are assumed random with a given probability distribution. In another approach, referred herein as the probabilistic approach, all variables are considered to be random and are defi ned in terms of given probability distributions.