The stochastic wave load environment of offshore structures is of such a complicated naturernthat any engineering analysis requires extensive simplifications. This concerns both the transformation of thernwave field velocities and accelerations to forces on the structure and the probabilistic description of the wavernfield itself. In this keynote the last issue is in focus. The modeling follows the traditional structure of subdividingrnthe time development of the wind driven wave process into sea states within each of which the wave process isrnmodeled as a stationary process. The wave process of each sea state is modeled as an affinity in height and timernof a Gaussian process defined by a normalized dimensionless spectrum of Pierson-Moskowitz type. The affinityrnfactors are the so-called significant wave height H_s and the characteristic zero upcrossing time T_z. Based onrnmeasured data of (H_s, T_z) from the North Sea a well fitting joint distribution of (H_s, T_z) is obtained as a socalledrnNataf model. Since the wave field is wind driven, there is a correlation between the time averaged windrnvelocity pressure Q and the characteristic wave height in the stationary situation. Using the Poisson processrnmodel to concentrate on those load events that are of importance for the evaluation of the safety of the structure,rnthat is, events with Q larger than some threshold q_0, available information about the wind velocity pressurerndistribution in high wind situations can be used to formulate a Nataf model for the joint conditional distributionrnof (H_s, T_z,Q) given that Q > q_0. The distribution of the largest wave height during a sea state is of interestrnfor designing the free space between the sea level and the top side. An approximation to this distribution isrnwell known for a Gaussian process and by integration over all sea states given Q > q_0, the distribution isrnobtained that is relevant for the free space design. However, for the forces on the members of the structure alsornthe wave period is essential. Within the linear wave theory (Airy waves) the drag term in the Morison forcernformula increases by the square of the ratio between the wave height and the wave length, and the mass forcernterm increases proportional to the ratio of the wave height and the square of the period. For a strongly narrowrnband Gaussian process Longuet-Higgins has derived a joint distribution of the height and the period. However,rnsimulations show that the Pierson-Moskowitz spectrum does not provide a sufficiently narrow banded processrnfor the distribution of Longuet-Higgins to make a good fit. Surprisingly it turns out that the random time Lrnbetween two consecutive 0-upcrossings and the random wave height H observed between the two 0-upcrossingsrnbehaves such that L and the ratio H/L are practically uncorrelated and both normally distributed except forrnclipping the negative tails. This result is of global nature and is therefore very difficult if not impossible tornobtain by analytical mathematical reasoning. Finally, by combining all the derived distributional models intorna Rosenblatt transformation, a first order reliability analysis of a tubular offshore platform can be made withrnrespect to static pushover. Correction for non-linear wave theory can be taken into account crudely by using therndeterministic 5th order Stokes wave in the limit state formulation. A dynamic analysis will be more complicated,rnof course, but the provided distributional information and the demonstrated modeling principles are judged asrngenerally applicable.
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