Vector-Valued Ground Motion Intensity Measures for Probabilistic Seismic Demand Analysis

Quantitative assessment of risk to a structure from earthquakes poses significant challenges to analysts. It is a multi-disciplinary problem, incorporating seismology and geotechnical engineering to quantify the shaking which a structure might experience at its base, structural engineering to quantify the structure's response and the resulting damage, as well as finance, public policy, construction cost estimating, etc., to estimate social and economic consequences of this damage. The uncertainties present in many aspects of this problem also require that the assessment be made in terms of probabilities, adding a further layer of complexity.

A formal process for solving this problem has been developed by the Pacific Earthquake Engineering Research (PEER) Center. There are several stages to this process, consisting of quantifying the seismic ground motion hazard, structural response, damage to the building and contents, and resulting consequences (financial losses, fatalities, and business interruption). Each stage of the process is performed in formal probabilistic terms. The process is also modular, allowing the stages to be studied and executed independently, and then linked back together, as illustrated in Figure 1.1. For this method to be tractable and transparent, it is helpful to formulate the problem so that each part of the assessment is effectively independent. The independent assessment modules are then linked together using intermediate output variables, or "pinch point" variables (Kaplan and Garrick 1981). In the PEER methodology the intermediate variables are termed Intensity Measure (IM), Engineering Demand Parameter (EDP) and Damage Measure (DM). The final consequences, termed Decision Variable (DY), could also be considered a pinch point. An important assumption in this methodology is that what follows in the analysis is only dependent on the values of the pinch point variables, and not on the scenario by which it was reached (e.g., the response of the structure depends only upon the intensity measure of the ground motion, with no further dependence on variables such as the magnitude or distance of the causal earthquake). Further, the relationship between each of the stages is Markovian: given knowledge of EDP, the damage to building elements is independent of IM. This model relies heavily on assumptions of conditional independence between analysis stages, and these assumptions should be verified before the model is applied to a given problem. If the assumptions are not valid, then modifications to the model are required before proceeding. The use of vector-valued intensity measures is one such modification.

This multi-stage methodology has had success in other complex Probabilistic Risk Assessment problems (Kaplan and Garrick 1981, NUREG 1983, Garrick 1984), and a significant effort has been made to prepare this methodology for practical earthquake risk assessment applications (Cornell and Krawinkler 2000, Moehle and Deierlein 2004).