Estimation of Extreme Response - in a Jack-up Platform by Application of Stochastic Methods
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- Institutt for marin teknikk 
Abstract This thesis investigates different stochastic methods for estimating the extreme response on a jack-up platform in the North Sea. The extreme response of jack-ups is often heavily affected by dynamics and thus dynamic effects must be accounted for. In this thesis the Equivalent Dynamic Amplification Factor (EDAF) has been calculated based on time domain simulations of sea states decided by the Environmental Contour Method. A metocean report was created based on 57 years of hindcast data of the Ekofisk-field, with a focus on finding the extreme sea states and waves. The long-term variation of the environment is described by the joint probability distribution of significant wave height (Hs) and spectral peak period (Tp). The environmental contour lines in the Tp-Hs plane have been constructed based on their annual probability of exceedance. Estimates for the 100 and 10 000 year largest crests and wave heights were found using their respective Forristall distributions. These results are used as input for the extreme response analyses. For structures acting quasi-statically it is common practice to estimate the extreme response by using the Design Wave Method. Previously the Stoke 5th wave was designed based on the extreme wave height, but using the extreme crest with the same return period gives larger responses. The crest height should therefore be the deciding parameter of the Design Wave Method. Long-term analysis of the dynamic response based on an all sea states approach has been illustrated and conducted using time domain simulations in the nonlinear finite element program USFOS. The extreme response for deck displacement, base shear and overturning moment was calculated based on annual probabilities of exceedance of 10-2 and 10-4. The focus of the thesis has been on using the Environmental Contour Method to calculate the extreme (Gumbel) distribution for both static and dynamic response. The EDAFs and the α-percentiles were found by comparing the Gumbel distribution with the responses of the Design Wave Method and the Long-Term Analysis. The time domain simulations in USFOS are based on linear (Airy) wave theory and Wheeler stretching is used to account for wave kinematics up to the free surface. By comparing the static time domain simulations with Stokes 5th regular waves in USFOS, the results show that Wheeler stretching doesn t adequately account for higher order wave kinematics and hence cannot correctly predict the extreme response. This means that second order wave theory should be used for drag-dominated structures such as jack-ups in regard to extreme response estimation.