D-A-CH TAGUNG 2011 - SGEB

The Monte Carlo technique was applied for the generation of correlated PGA values (10,000generations) for every cell using the procedure described above. Examples of realisations ofstrong motion distribution, which were estimated using particular parameters of correlation, areshown in Figure 3.3 DAMAGE AND LOSS ESTIMATIONThe loss estimation was performed using the generation of the correlated ground motionfield. Peak ground acceleration was used to evaluate ground shaking-induced structuraldamage. A set of hypothetical buildings (Figure 3a) mimicking a real building stock wasconstructed based on three types of buildings that are typical for Taiwan (Liao et al. [45]): (1)concrete of one to three stories; (2) steel-braced frames of four to seven stories; (3) frames withshear walls more than eight stories. The whole area of 22 km x 18 km was divided into cells of1 km x 1 km, and different numbers of buildings were assigned, more or less randomly, toevery cell. Figure 4a shows the distribution of buildings along the considered territory. Thetotal number of buildings in the area was 5478.In this study, we use the methodology suggested by FEMA (HAZUS [46]), which is basedon fragility functions, for loss estimation. A fragility function defines the exceedance of adamage state for a given level of ground shaking. Five damage states are considered: None,Slight, Moderate, Extensive and Complete. The probability of being or exceeding a damagestate DS i is modelled with a cumulative lognormal distribution, 1 IM P [ DS i| IM ] , (8)DS SMEDIANwhere IM is the given level of ground shaking, DSis the standard deviation of the naturallogarithm of spectral amplitudes of damage state DS, S MEDIAN is the median value of the groundmotion parameter at which the building reaches the threshold of the damage state DS, and isthe standard normal cumulative distribution function. Every damage state is characterised by arepair and replacement cost ratio RRC i , expressed as a percentage of the building replacementcost RC. If we know the replacement cost RC of every type of building we are considering,then the expected direct loss EDL is the product of the damage factor and the replacement cost:EDL RC RRC P [ DS | IM ](9)all DS iwhere P [ DSi | IM ] is the probability of being in damage state DS i for a given groundmotion level IM.The methodology used in this study for the computation of the direct loss involves severaluncertainties. The total variability of each structural damage state β SDS is modelled by thecombination of the following three contributors to damage variability (see Ref. [46]):uncertainty in the damage-state threshold of the structural system β M(SDS) ; variability in thecapacity (response) properties of the model β C ; and variability in the response due to thevariability of ground motion (seismic demand) β D .iiSDS . (10)22( CONV[C,D, SMEDIAN, DS]) (M ( SDS))Thus, fragility functions include both aleatory uncertainty (e.g., uncertainty of the groundmotion level given the characteristics of the earthquake) and epistemic uncertainty (e.g.,9163