D-A-CH TAGUNG 2011 - SGEB

damaged at this level. The expected time of bridge outage for this damage level (extensivedamage) is between 3 weeks and 3 months (see Ref. [51]). As can be seen from the figure, inthe considered case of several different bridges located a few kilometres from each other, thesite-to-site correlation plays a more important role in such estimations than the betweenearthquakecorrelation. In estimating the probability that at least one bridge will be damaged(Figure 7a), the possible variations in the between-earthquake correlation may be completelyneglected if the spatially correlated ground motions are used. The between-earthquakevariability reveals a slight influence on the probability only when considering spatiallyindependent ground motion. In contrast, an increase in the correlation distances, as well as anincrease in the between-earthquake correlation, would increase the probability of joint damage(Figures 7ab); however, the relative influences of the correlation characteristics are not thesame.Figure 7. Analysis of damage for critical elements of a network (bridges) that are located within the consideredterritory (Figure 4b). Probabilities that (a) at least one bridge will be damaged (damage ratio of 0.2) and (b, c) allbridges of different types will be damaged simultaneously.By separately comparing the variations of damage probabilities due only to betweenearthquakecorrelation ρ η and to spatial correlation (), it can be observed that variations inthe ()functions (correlation distances) lead to larger changes in the probabilities of jointdamage than variations in the ρ η values. Thus, for example, when the correlation distancechanges from 0.0 km to 30 km, the probability of joint damage for the bridges of Type 4 wouldincrease by 1.77 times, while the change of the between-earthquake correlation from 0.09 to 0.5increases the probability of joint damage only by 1.51 times (Figure 7b). The correspondingchanges in the probability of joint damage of all bridges are about 20 times and 13 times(Figure 7c).5 CONCLUSIONSIn this paper, we compared the effects of variations in the between-earthquake correlationand in the spatial (site-to-site) correlation of seismic ground motion on the uncertainty ofearthquake loss estimations for distributed portfolios and on the probability of damage forseveral critical elements of extended structures, e.g., bridges within a lifeline system. It hasbeen recently found that the parameters of ground motion correlation may vary over wideranges. To describe the variations, we considered the following boundary values that have beenreported in the literature: correlation distances (site-to-site correlation) varying from 0 km to 30km and between-earthquake correlation varying from 0.09 to 0.5. A single event, a so-calledscenario earthquake, was used as the source of seismic influence, and a set of hypothetical17218