Report - PEER - University of California, Berkeley

Figure 3. Bridge column component decision fragility curves.For example, an earthquake with intensity of Sa(T 1 ) = 1000 cm/s 2 , there is a 91%probability that the repair cost will exceed 25% of the replacement cost. Thisprobability drops to 65% for exceeding the entire replacement cost. It should be notedthat it may not be possible to obtain a complete distribution function if the givendiscrete damage states do not cover the full range required for the decision variablelimit states. Due to the large amount of uncertainty in the loss model and the lack ofother DV choices, cost data on other bridge components and assessment of systemleveleffects for reinforced concrete highway bridges cannot be done withoutadditional research focused on damage assessment and repair cost modeling.5. BRIDGE-LEVEL DECISION: TRAFFIC FUNCTIONFour methods for predicting post-earthquake damage fragilities from first-shockearthquakes, the corresponding interim models, and interim variables are detailed inMackie (Mackie 2004b) for damage fragilities. Only a brief summary of each methodand their comparison are provided here, followed by extensions from damage todecision fragilities. The loss model, which relates a damage variable to the loss ofcapacity decision variable, proposed herein, is shown Figure 4.5.1 Method A: Direct MethodThe direct method is an application of the PEER framework (Equation 5) directly tobridge-level interim models. Therefore, the approach is the same as the one use forcomponent-level decisions: Equation 5 is evaluated numerically for a range of IM,EDP, DM and DV values to produce the DV fragility surface of Figure 5. Thefragility surface is a convenient method of visualizing numerous decision limit stateson the same plot. Each black line on the surface is a single DV fragility curve. The59