How should jack-up operators determine the appropriate airgap when faced with varying environmental loads?
Jack-ups are often required to remain on location for many weeks and in places where the distance to shore may mean that they cannot quickly or easily move to shelter during adverse conditions.
In such situations, they are elevated for safety reasons, this is known as “survival mode”.
Overturning the survival mode problem
While in an elevated mode a jack-up is more exposed to the environmental loads (winds, waves, currents) which contribute to an overturning moment. Of these environmental loads the wave contribution is usually dominant.
The weight of the jack-up along with seabed stability and leg penetration combine to counter these overturning forces, creating a stabilising moment.
Ideally the centre of gravity should be as low as safely possible. This means elevating the deck area high enough to safely avoid the major destabilising forces without excessively doing so.
With wave inundation of the deck area (a negative airgap) environmental loading steeply increases. This additional loading is through the obvious horizontal wave motions as the wave crest impacts the deck creating an overturning moment (‘O’ in Figure 1), but also the vertical wave or buoyancy loads (‘B’) which reduce the stabilising, gravity based, forces (‘S’). For a typical jack-up a 3m deck inundation can produce vertical loads equivalent to 40% of the entire structural dead weight.
The safety of the elevated jack-up depends, in part, on the stabilising moment exceeding the overturning moment (seabed stability and leg penetration being other critical factors).
When there is a positive airgap, the stabilising forces only need to out-compete the wave and current loadings on the jack-up legs.
Figure 1. Wave in deck (negative airgap) main loadings
Calculating survivability air gaps
To avoid the increased environmental loading, and the associated reduced stability, it is essential that a sufficient air gap is maintained between the hull structure and the total water level - the combination of astronomical tides, storm surge (combining to give a still water level, ‘SWL’) plus wave crest elevation.
The key word here is ‘sufficient’, largely a compromise between achieving a low centre of gravity (stabilising) and the risk of deck impacts from waves (destabilising).
Depending on the selected wave crest return period used an additional airgap (at least equal to a predefined minimum value) may be required. The purpose of the extra safety margin is to allow the structure to withstand extremely rare, but highly consequential events such as wave inundation.
The hull elevation in survival mode is often set to the 50 or 100-year extreme wave condition with an additional safety margin of 1.5 m. This arbitrary type of definition is rather unsatisfactory as any fixed safety margin is proportionally larger in benign environments than in severe ones. For example, a safety air gap of a fixed 1.5 m added to the 100-year condition in the North Sea still usually comes out as much lower than the 10,000-year condition. In a more benign, potentially upper wave limited environment, an additional 1.5 m may far exceed the 10,000-year event. Using suitably conservative fixed return periods eliminates the need for arbitrary additional safety factors.
The uncertainty factor
Extrapolating from limited duration datasets can lead to significant statistical uncertainties. The conversion from sea state extremes (e.g. significant wave heights) to individual wave extremes (e.g. crest elevations) also creates uncertainty.
Traditional, extreme, individual wave calculations deal with the ‘most probable’ magnitude of the maximum individual waves so have a relatively large probability of being exceeded.
Storm-based methodologies that involve the convolution of long and short-term wave distributions significantly reduce this exceedance issue (e.g. Tromans and Vanderschuren, 1995).
Of course, when estimating survivability air gaps, we are not only interested in the wave climate. As mentioned earlier, the total water level comprises waves, tides and storm surges. The joint probability of these components also needs to be considered.
Tidal predictions are mostly well established and we can have a high degree of faith in the data. Storm surge suffers the same uncertainties of any extreme value extrapolation, but is often based on less data than that of waves.
The ABPmer Metocean team’s approach always depends on the task in hand. Pragmatic solutions often suffice for preliminary assessments, whereas more statistically robust approaches are required at later project stages.
For jack-up survivability investigations the concentration of effort is, for most locations, clearly required in the derivation of the extreme wave crest.
Our approach to the determination of wave crest extremes deals with the likelihood of the highest individual waves occurring in sea states other than the highest.
In reasonably deep, non-complex environments, we use empirical combinations of tide, surge and wave crest (e.g. ISO-19902, 2007) with knowledge of the associations between storm surge and wave crest.
In more complex situations, a true bivariate approach to the association of various water level components (e.g. Heffernan and Tawn, 2004) is used.
Prepared by Ian Wade, Metocean Consultant
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Header image (c) Seajacks, used with permission