By Lucien Duckstein, Erich J. Plate, Marcello Benedini (auth.), Lucien Duckstein, Erich J. Plate (eds.)
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Extra resources for Engineering Reliability and Risk in Water Resources
13, in which n is now the number of years in the design life, and PE is assumed to be constant, which would be true if all inputs x(t) as well as the catchment parameters of the model were stationary. The hydrologic variable Q(t) is usually not the variable which is to be compared with the resistance in determining the probability of failure. It is transformed through hydraulic calculations into a design variable. A 39 typical design variable to be determined through a hydraulic transformation is the stage in a canal which has to be dimensioned, such as: the stage in an open channel (Duckstein and Bogardi, 1981) the stage at an upstream point in a tidal river under the influence of a tidal surge at the mouth of a river (Plate and Ihringer, 1984) the stage at a downstream point in an open channel when the stage at the channel inlet is given in terms of a flood wave (Kundzewicz and Plate, 1986 the stages ina system of sewers at poi nts wi thi n the system when the statistics of the inputs due to rainfall are given from hydrological calculations.
The most important case of level 3 design is based on the assumption that rand s are uncorrelated. This yields Freudenthal's design concept, from which a formula to calculate the probability of failure can be derived. A detailed explanation of this concept is given in Plate and Duckstein's paper. However, the case of uncorrelated rand s is not a necessary requirement for the applicability of a level 3 design. It is possible to determine the probability of failure by simulation, or to use empirically determined joint pdf's of sand r.
Thi s becomes evi dent if the LP3 distribution is inspected closely, as was done by Bobee (1975); these results show that the shape of the LP3 function agrees with that of the P3 function only in the region 1 < r < 2 for positive values of A! A transformation of the P3 function which allows keeping the three parameters while at the same time preserving more faithfully the shape of the function is given by: dy _ s-l ax - sx Yo = 0 ; (30) which leads to the Kritsky-Menkel distribution: f(x) = s • Ar sr-l -r-rrr x e -AX S (31) 50 for which tables are aVililab1e (Kartvelishvili, 1969) and which is widely used in the USSR.