By Lucien Duckstein, Erich J. Plate, Marcello Benedini (auth.), Lucien Duckstein, Erich J. Plate (eds.)
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The higher the level, the more data are required. However, the complexity of analytical tools does not necessarily vary in the same direction. Levell design is based on the concept of a safety factor. If rO (for example, the minimum stress to which a structure can be subjected in its critical section) is specified by standards, then it is necessary to dimension the structure so that sD ~ n • r D where n is the safety factor and So is the calculated stress due to the worst-case load. The concept is based on experience and risk averse decision-making and leads to a selection of nand rO that yield an economically acceptable design.
With this expression one obtains: ! e. PF reduces to the hydraulic exceedance probability PH' (23) 47 A second observation is that the integration of Eq. 22 depends on those values of Fr ( s) whi ch usually over 1ap with the extreme part of the asymptotic "tail" of f s(s). This again has two consequences: usually only that part of fs(s) is required which is not well defined by data, because an extreme value is a rare event and only few data points exist to determine empirically fs(s) for large values of s.
The long-term variability of the hazard function is of great significance and requires careful consideration. Although there have not been enough dam failures on record to establish conclusively how the hazard function changes in the long run, it is reasonable to expect the pattern shown in Figure 4, which is the shape of the typical "bath-tub" curve well known in reliability engineering (see for example Dhillon and Singh, 1981, p. 28). \Pit) \ , ' ... 'I-------i I ~/ / / I I------~I-- I 1-------+------'-- t(yearsl 1 - - - - - - - design life TO - - - - - - - i Figure 4: Standard "bath-tub" type failure rate (hazard function) S(t).