Stochastic Fatigue Response Of Jackets Under Intermittent Wave Loading
Authors: Haldar A. , Kanegaonkar H.B. 
Published: October 2008

ABSTRACT
A combination of spectral and probabilistic analysis techniques is proposed to estimate the fatigue damage of jackets subjected to intermittent wave loading. The resulting non-Gaussian response process is considered to be a mixture of Gaussian and shifted exponential. It is shown that the peak density deviates significantly from the Rayleigh, and Gaussian response assumption is unconservative for fatigue damage evaluation at higher sea states.

INTRODUCTION
Spectral analysis techniques are commonly used to predict the fatigue behavior of offshore jacket-platforms. The cyclic wave loading is assumed to be a Gaussian random process. Assuming the structure is behaving linearly, the structural response can be considered to be Gaussian and spectral analysis will thus fully define the stress processes at the joints. However, recent field observations show that the response is a non- Gaussian process. Nonlinearity in the drag and in the wave kinematics and the phenomenon of free surface fluctuation near the mean sea level in the splash zone are the major reasons for this non-Gaussian behavior. The effect of nonlinearity in the drag loading on the fatigue life of jacket-platforms was studied in the past (1, 2). A method is proposed here to estimate fatigue life considering the nonlinearity in wave kinematics and the intermittent nature of the wave loading. Since conventional spectral analysis with information on the second moment is insufficient to describe the probability distribution characteristics of the response, a procedure must be developed to estimate higher-order moments. Furthermore, when the response is non-Gaussian, the probability density of the stress peaks will not be Rayleigh, and the estimates of cumulative damage are expected to be significantly different.
In the proposed method, Stokes1 second order wave theory is used to consider the nonlinearity in the wave loading. Intermittent wave loading is modeled by using a Heaviside step function. For lower sea states (sea-state 1 for the example considered here), the first two moments of the response are calculated using spectral analysis and the third and fourth moments are calculated using probabilistic methods assuming the response in this case is resonance- dominated. For higher sea states (sea states 2 through 7 for the example considered here), the response is considered to be quasi-static. The second moment is calculated using the modified spectral analysis method. The first, third and fourth moments of the response are estimated using the expected value of the first, third and fourth power of the response functions, which are related to the load via flexibility coefficients. Using the third and fourth central moments, the optimal marginal distribution of the response is estimated as a mixture of Gaussian and shifted exponential distributions. The level crossings of such a stress process are estimated by considering it to be a translation process. The double inversion technique is used to map a Gaussian process into the response process. The probability density function of the peaks is calculated numerically. It is shown with an example that the probability density of the stress peaks differs significantly from the commonly assumed Rayleigh, and the fatigue damage estimates are found to be unconservative at higher sea states with traditional spectral analysis.