Background
Within the preparation of HAZUS, FEMA developed capacity curves for 36 building types (being representative for the United States) in four earthquake load regimes (reflecting the variation in building regulations as a function of time across the United States). These 144 capacity curves were analytically developed, but are adjusted so that empirical knowledge is incorporated in the curves whenever possible. The building capacity curve is described by three control points representing design, yield and ultimate capacity. Up to the yield point, the building’s capacity curve is assumed to behave linearly (ideal elastic). From the yield point to the ultimate point, the capacity curve changes from an ideal elastic to a fully plastic state (curved form), and the curve is assumed to remain fully plastic past the ultimate point (linear form). A bilinear representation (two linear parts) is sometimes used to simplify the model. The vulnerability curves (also called fragility curves) are developed as lognormal probability distributions of damage from the capacity curves.
Using inventory data from Oslo (Norway) with 902 reinforced-concrete (RC) buildings from the district Grünerløkka, a simple classification of the buildings yields fragility curves as shown in the figure below, for Damage Limit States 1 to 3 (1: no damage, 2: slight damage, and 3: moderate damage).
Fragility curves for 902 reinforced-concrete buildings (1- to 3-story) in Oslo
for Damage Limit States 1, 2, and 3 using a displacement-based approach.
There are two approaches commonly followed in vulnerability estimation:
Through dynamic analysis of single structures and building types, the earthquake shaking performance can be computed. A typical example to this side is HAZUS (Risk estimation software developed by the Federal Emergency Management Agency, FEMA).
Based on post earthquake surveys data on damage for various building classes are collated and related to estimated or measured ground motion.
NORSAR can provide consulting and research into seismic vulnerability, and provide results based on deterministic methods and empirical data.
Damage and loss estimation
Currently, SELENA computes seismic losses using the capacity spectrum method. The losses are computed as aggregates of the inflicted damages to each building type within a predefined area (a city quadrant, census tract or any user-specified area). The damage to the physical environment can then be converted to monetary damages as well as to estimates of casualties using empirical relations. The damages are presented in tabular form and any appropriate mapping or graphing software can be used to display the results in easy understandable figures.
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