Validation of the Iterative Component Addition (ICA) formulas for the damage assessment of multimodal loading spectra
Type  Contract report  

Date  2009  
Language  English  
Ref.  R06/HO/09  
Author(s)  Guede Zakoua^{1}, Olagnon Michel^{1}, Pineau Hélène^{2}  
Affiliation(s)  1 : Ifremer, Brest, France 2 : Actimar, Brest, France 

Publisher  Ifremer  
Abstract  The purpose of this study is to validate the use of the socalled Iterative Component Addition (ICA) formulas for the assessment of fatigue damage of marine structures subjected to complex (multimodal) wave loading conditions, as prevail in West Africa areas where the sea states are usually described as combinations of three wave systems (e.g. main swell, secondary swell and wind sea). In this context, operators specifications require to consider a very large set of fatigue loading cases, which lead to excessive computation times if the conventional procedure is used for fatigue assessment. The use of the ICA formulas is expected to simplify the evaluation of the damage and to allow a drastic reduction of computation time, keeping a slight level of conservatism. The present work intends to validate those formulas on an industrial application. One is especially interested in the accuracy of the ICAbased approach for fatigue damage assessment, the ease of use of this approach and the computation times it involves. The scope of the study is limited for simplicity purposes to cases where the structural dynamic response is linear. Its actual industrial application deals with the assessment of the fatigue damage induced by the vertical bending moment of an FPSO hull girder subjected to wave loading in a West Africa area. In this report, we define the occurrence probabilities of all the fatigue loading cases to be applied as required by the operator specifications. Then, to validate the use of the ICA formula, the fatigue damage is estimated according to two main approaches. The first one, which serves as a reference solution, uses a conventional method and computes the damages of the sea states from the metocean data base only. The other one uses ICA formulas and compute the damages of all possible sea states defined by the operator specifications. For this last approach, a full application of ICA formulas based on a partition of wave systems response spectra is also carried out and some analytical formulas for the damage of unimodal spectra are set up. Between both approaches, some intermediate computations are made to estimate the individual effects of the approximations introduced. The occurrence probabilities of the fatigue loading cases derived from the metocean specifications exhibit some significant discrepancies from the statistics of the metocean database. Namely, they provide a lower significant height for the sea states with only a main swell and a larger one for sea states with the three wave systems. As to the application of ICA formulas, it is shown to provide accurate results. We can note that the ICA results are close to the reference solution and that most of the conservatism comes from the discretization defined for the statistical analysis. Moreover, the implementation of the ICAbased approach is simple on the actual industrial application. With appropriate change of programming language and optimization of the procedure, dramatic improvements have been obtained in the computation time, with nearly 2 million combinations of sea states processed in less than one minute. Two main difficulties were encountered in this study. The first one concerns the twoslopes SN curve, as a combined spectrum may have cycles amplitudes that are larger than the stress thres hold of the SN curve while its individual components do not. That was solved by providing a method to estimate twoslope damage from the two singleslope ones. The second difficulty stems from the discrepancies observed between the statistics on the metocean database and the sea states probabilistic model derived from the metocean specifications, which raises some questions on the construction of fully relevant metocean specifications. Though some progress was made, that second difficulty is not yet satisfactorily solved. However, this study appears as a mighty step in the development of a global framework for fatigue damage assessment under multimodal loading conditions with the ICA formulas. 

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