Page 447 - Pipelines and Risers

414 Chapter 22

To fully account for the fatigue damage from all seastates and all directions of loading,
linearisation of riser response is required. Linearisation is the process by which the fluctuation
of stresses along the riser length in one loading condition is assumed to be related to that of
another loading condition.
Linearisation can be conducted in a number of ways such as:
- Lumping of seastates
- Lumping of loading direction
- Assuming riser response is proportional to wave height
When linearisation is implemented, it should be demonstrated that the chosen approach errs
on the side of conservatism. The extent to which linearisation is used should therefore be
limited to an extent which avoids undue conservatism. This will generally preclude extensive
use of the first two methods identified above. The third method, which is commonly used,
requires splitting of the scatter diagram into windows. A single seastate from each window is
analyzed to determine the response transfer function, or stress RAO, along the riser length for
each of the windows. The transfer function for a given window are then used to determine
riser response in the other seastates of the window, assuming the transfer function is constant
across the window. Fatigue damage from each seastate can then be determined based on an
assumed statistical distribution of response and the total fatigue damage across the scatter
diagram summed.
Careful consideration must be given to the method of scatter diagram windowing, accounting
for variation in wave height and period and the effects of selecting different parameters. The
mean slow drift offsets of individual seastates must also be considered as these can have a
significant influence on TDP fatigue damage distribution. Hence, the linearisation analysis
must use wave height, period and offset representative of the window. Typically, 5 or 6
windows may be required. A preliminary assessment of the scatter diagram can be conducted
to identify seastates, which provide the greatest contribution to total fatigue damage.

2. Analysis method

A spectral fatigue analysis approach can be applied for first order fatigue analysis. Fatigue
damage is based on time domain random sea analyses since the non-linearity’s of the system
can be large, particularly around the critical touch down point. The fatigue seastates are split
into a number of windows and one seastate selected from each window for the purpose of
response linearisation. Mean second order motions are accounted for as part of first order
fatigue analysis by use of appropriate floater offsets when conducting linearisation analyses.
Time-domain random sea analysis is carried out on each of the 3 linearisation seastates, for 3
directions of loading (far, near and transverse). Timetraces of tension and bending variations
in the riser are combined to provide transfer functions of total axial stress variation for each of
the linearisation seastates, at each of 8 points around the riser circumference. The fatigue
damage resulting from each seastate is then determined using the total stress transfer function
obtained from the relevant linearisation seastate and initially assuming that stress peaks are
Rayleigh distributed. The damage from different seastates is summed using the Miner rule.
The assumption that response is Rayleigh distributed is calibrated by calculation of fatigue
damage from riser total stress response timetraces. Fatigue life estimates along the riser length
are made using both a statistical (Rayleigh) approach and by stress cycle counting, and the
differences evaluated.