An Approach to Probabilistic Fatigue Analysis of Offshore Structures
Authors: Wallis J.R. , Bayazitoglu Y.O. , Chapman F.M. , Mangiavacchi A.R. 
Published: October 2008

ABSTRACT
As the offshore industry moves into deeper water, the dynamic behavior of structures becomes a very important parameter in the overall design procedures. In particular, the cyclic nature of wave loads has a significant effect on the fatigue life of the structure.
This paper presents a procedure for fatigue analysis where the dynamic response of the structure is analyzed through a spectral approach. The sea waves which constitute the forcing function acting on the structure are represented as energy spectra; the response is obtained in spectral terms and is subsequently interpreted according to probabilistic concepts.
As part of this study we have considered the characteristics of the distribution of the response. In the usual approach to fatigue analysis one assumes that the peaks of the response follow a Rayleigh distribution. This assumption is valid if the Cartwright-Longuet-Higgins' measure of bandwidth (E) is equal to zero. However, in practical fatigue applications, this idealization is rarely, if ever, encountered. Thus, in order to better characterize narrow banded phenomena, we have investigated descriptions which do not assume ? = o. An investigation of caisson designs indicates that fatigue results using the more accurate response distributions can differ appreciably from those obtained with the Rayleigh distribution.

INTRODUCTION
The critical loading conditions for design of an offshore platform are primarily dependent on water depth and prevailing meteorological conditions such as waves, currents and winds. If dynamic amplification is not a major consideration, the static applied force due to the largest single wave is traditionally used as the critical or design load conditions for fixed offshore structures. In the corresponding fatigue analysis the sea surface is represented by a discrete set of waves characterized by period, amplitude and percentage of occurrence. The expected fatigue life is then obtained by applying each wave to the structure and summing the individual effects.
Due to the dynamic amplification of wave-induced response this approach is not adequate for deep water structures where fatigue may, be a controlling factor in design. In this case distribution of the frequencies of wave loadings over a much larger range is needed to give a more realistic description of the sea surface. In practice, this is accomplished by statistically modeling the sea surface elevation. It has been shown that the time history of sea surface elevation over a period of several hours (i. e. a sea state) can be represented as a stationary random process with Gaussian probability distribution and narrow banded power spectrum. Present work discusses a fatigue analysis procedure based on these considerations.
The paper is divided into six sections. The first three sections describe a fatigue analysis procedure in which the spectral density of member end stresses is obtained by a frequency domain solution using existing dynamic analysis and space frame static analysis programs. The fourth section discusses narrow band approximations for the stress range distribution and their effect on fatigue analysis. Fatigue results for a caisson structure are presented in section five; conclusions and observations are given in the sixth section.