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Chapter 3 Loads and Dynamic Response for Offshore Structures 65

Jensen's formulation are obtained. Subsequently, upon substituting the most probable extreme
value of U in Eq.(3.36) or Eq.(3.37), the MPME of the responses will be determined. The
procedure of Jensen appears perfectly simple.
Ochi (1 973) presented the expression for the most probable value of a random process that
satisfies the generalized Rayleigh distribution (Le. the wide-banded Rayleigh). The bandwidth,
E, of this random variable is determined from the zeroth, 2"d and 4th spectral moments. For E
less than 0.9, the short-term most probable extreme value of U is given by
(3.38)

For a narrow-banded process, E approaches zero and the preceding reduces to the more well-
known expression:
U=JZiZ7 (3.39)
Comparison of Eq. (3.38) and Eq.(3.39) clearly indicates that the consideration of bandwidth
effect for a Gaussian process, U, results in a reduction of the most probable value.
Lu et a1 (2001,2002) compared the above four methods recommended in the SNAME Bulletin,
investigated the random seed effect on each method, and presented the impact on the dynamic
response due to various parameters, e.g. leg-to-hull flexibility, P-delta effect and foundation
fixity. The structural models employed in this investigation were constructed to reflect the
behavior of two jack-up rigs in service. These rigs were purposely selected to represent two of
the most widely used jack-up designs, which are of different leg types, different chord types,
and designed for different water depth. Comparison of the four methods was presented in
terms of the calculated extreme values and the respective dynamic amplification factors (DAF).
WintersteidJensen method is considered preferable from the design viewpoint. Gumbel fitting
Method is theoretically the most accurate, if enough amount of simulations are generated. Ten
simulations are minimum required, which may however, not be sufficient for some cases.

3.6 Concluding Remarks
This chapter gave an overall picture of the environmental conditions and loads for offshore
structural design, and detailed the recent developments in the prediction of extreme response.
A systematic method for structural analysis of offshore structures has been developed to
predict extreme response and fatigue assessment under wave conditions. For the convenience
of structural analysis, vibration frequency analysis was also briefly outlined. This Chapter
concludes the following:
Design of offshore structures is highly dependent on wave conditions. Both extreme
response and fatigue life can be affected significantly by site-specific wave environments.
Collecting accurate wave data is an important part of the design.
Wave spectral shapes have significant effects on the fatigue life. Choosing the best
suitable spectrum based on the associated fetch and duration is required.
The bandwidth parameter E of responses is only dependent on the spectral (peak) period.
The effect of H, on E is negligible.
The long-term approach is preferred when predicting extreme responses, because it has
less uncertainty. However, using the long-term approach is recommended along with the
short-term approach for obtaining a conservative result.