Page 402 - Marine Structural Design

378 Part 111 Fatigue and Fracture

maximum value with nearly zero probability of occurrence. The calculated stress ranges are
used to evaluate the integral in Eq. (20.20). For each sea-state, the fatigue damage associated
with each current velocity is multiplied by the probability of occurrence of the current velocity.
When stress ranges for all sea-states are obtained through the wave force model, the fatigue
damage is calculated using Eq. (20.20). The advantage of using the time-domain fatigue for
pipeline ad riser assessment is to account for the non-linearity in the drag forces and structural
dynamic response. The other benefit is to reduce the conservatism introduced in the boundary
condition for spectral fatigue analysis. An engineering practice is to derive the ratio of the
predicted fatigue life from these two approaches for a few well-selected and performed
analyses, and then to apply this ratio to similar fatigue scenarios.
20.3.3 Analysis Methodology for Time-Domain Fatigue of Risers
In time-domain analysis, a time domain dynamic analysis is performed for all sea states in the
wave scatter diagram, and for each direction with a non-zero probability of occurrence. In
frequency-domain fatigue analysis of risers, the touch-down point is fixed. The time-domain
analysis is applied when the soil-pipe interaction needs to be accounted for in order to remove
the conservatism introduced in the frequency-domain analysis. Besides, the second order
(drift) motions of the vessel may significantly affect the result of fatigue analysis. It is difficult
to include the second-order motions using stress RAOs to transfer wave spectra into stress
spectra. Based on the stress time histories from the time-domain dynamic analysis, the fatigue
damage may be estimated as follows:
The fatigue damage is estimated based on the moments of spectra (as those used in the
frequency-domain analysis), and the stress-spectra are calculated using the Fast Fourier
Transform algorithm.
The fatigue damage is calculated directly from the stress time-history using a rainflow
counting techniques.
The dynamic simulation should be long enough because the dominant period of second order
motions is of the order of 100 seconds.
20.3.4 Analysis Methodology for Time-Domain Fatigue of Nonlinear Ship Response

Jha and Winterstein (1998) proposed a "Nonlinear Transfer Function (NTF)" method for
efficient prediction of the stochastic accumulation of fatigue damage due to nonlinear ship
loads in random seas. Nonlinear time-domain ship-load analysis may reveal asymmetry in sag
and hog moment at mid-ship. The goal of the NTF method is derive accurate prediction using
only a limited amount of nonlinear analysis based on regular waves. The analysis cost is
reduced because expensive time-domain analysis over many cycles of ir-regular sea is
replaced by a limited number of regular-wave analysis.
The NTF is the generally nonlinear transformation from wave amplitude and period to the load
amplitude measure of interest (e.g., total load range for rainflow-counting). Stochastic process
theory is applied to
Identify a minimal set of regular waves @e., wave heights and associated periods) to be
applied based on a discretized version of the Foristall (1978) wave height distribution and
Longuet-Higgins (1983) model for wave period selection.
Assign an appropriate set of "side-waves" to be spatially distributed along the ship based
on probability theory.