HAZUS Damage Functions

ST-RISK™ Can Use HAZUS® Damage Functions

ST-RISK™ has been expanded to implement, as a user option, the HAZUS® building damage functions developed by FEMA and NIST (1997).  These damage functions use the Capacity Spectrum Method, which is an equivalent non-linear representation of building response during earthquake shaking.  It accounts for the lengthening of a building’s natural period of vibration as the building undergoes seismic damage, and for the increased vibrational damping associated with cracking, yielding, and other causes of non-linear response.

Buildings are represented by 15 structural systems, as follows:

In addition, the height of each building is represented as low, medium, and high-rise, resulting in 36 building types (some structural systems occur only for low-rise buildings). In addition to these characteristics, the occupancy and code design level are used to estimate the response of each building to seismic shaking. Building response is represented by the initial yield level and ultimate strength, which form the capacity spectrum for that building (see Figure 1). The capacity spectrum can be compared to any specific ground motion to estimate the nonlinear response incurred by the building during that ground motion (Figure 1). The nonlinear response allows us to estimate the probabilities of slight damage, moderate damage, extensive damage, and complete loss (see Figure 2). Each damage level is further characterized by the percent loss to structural systems, nonstructural systems, and contents. Uncertainty in the damage level sustained by the building during any given ground motion is also represented.

HAZUS Capacity Spectrum
Figure 1. Capacity Spectrum
HAZUS Fragility Curve
Figure 2. Fragility Curves

The implementation of HAZUS®-based loss estimates within ST-RISK™ has been verified with results available from published references, including Tobas and Lobo (2008) and Porter (2009, 2010). Thus we are confident that the estimates of structural response to ground motion, the damage estimates given structural response, and the loss estimates given damage of HAZUS® have been accurately implemented.

Sample HAZUS Risk Chart
Figure 3. Risk Curve

ST-RISK™ integrates this loss methodology with its seismic hazard capability, accounting for hundreds of thousands of possible earthquakes and their relative frequencies of occurrence, to derive a risk analysis for the building. The risk analysis accounts for possible earthquakes, uncertainties in the associated ground motions, uncertainties in building response, and uncertainties in damage level, to give a composite risk curve (loss vs. return period). See Figure 3 for an example risk curve that shows Scenario Expected Loss (SEL), Scenario Upper Loss (SUL), and Probable Loss (PL) curves for a vulnerable building in California. Following the HAZUS® method, loss includes structural loss, non-structural loss, and loss to contents.

Advantages of ST-RISK™ over alternative programs