Page 401 - Marine Structural Design

Chapter 20 Spectral Fatigue Analysis and Design 377

20.3 Time-Domain Fatigue Assessment

20.3.1 Application
Similarity between Time-Domain Fatigue Analysis (TFA) and Spectral Fatigue Analysis
(SFA): Both procedures are based on wave-scatter diagram.
Difference between Time-Domain Fatigue Analysis and Spectral Fatigue Analysis: TFA is
a deterministic analysis, and includes the effect of non-linearity. SFA is a stochastic
approach based on linear analysis.
Time-domain fatigue assessment is mainly applied to the following scenarios:
Fatigue of pipelines and risers due to wave-induced forces (Bai, 2001)
Fatigue of TLP tethers (Fylling and Larsen, 1989)
Fatigue of Spar structures due to low frequency motions (Luo, 2001)
20.3.2 Analysis Methodology for Time-Domain Fatigue of Pipelines
In the following, a fatigue damage equation will be derived for fatigue of pipelines and risers
due to wave forces. The number of cycles n, corresponding to the stress range block Si is
given by

P(.) is the probability of a combined wave and current induced flow event. f, is the
dominating vibration frequency of the considered pipe response and q# is the time of
exposure to fatigue load effects. Using Miner‘s law and a S-N curve, Eq.(20.3), the fatigue
damage may be evaluated for each sea-state of the scatter diagram in terms of H, , T, and 8,
as below.

(20.20)

where:
P() is the joint probability of occurrence for the given sea state in terms of
significant wave height H, , wave peak period T, , mean wave direction.

dFur denotes the long term distribution function for the current velocity. The notation
“ma” denotes that the mode associated with the largest fatigue damage must
be applied when several potential modes may exist at a given current velocity.
In the time domain analysis, the long-term irregular wave condition is divided into
representative sea-states. For each sea-state, a time history of the wave kinematics is generated
from the wave spectrum. Hydrodynamic loads are then predicted using the wave kinematics
and applied to the structures. Stress ranges are calculated through structural analysis. Fatigue
damage is then calculated using Miner’s law.
In Bai (2001), the stress range is calculated in the time domain model for each sea-state with a
constant value of wave-induced velocity but for a range of current velocities, from zero to a