* The “Design Wave Philosophy’’ * Calculation of the design wave

The “Design Wave Philosophy’’ ***** The “Design Wave Philosophy’’ ***** Calculation of the design wave Wave forces on semi-submersible platforms Wave forces and bending moments in FPSO-ships Platform movements in large waves Examples of heavy weather damage What is a Rogue Wave ? Why, where and when ? Shall we design against Rogue and Freak Waves ? What can a platform master do against Rogue and Freak Waves ? Remote-sensing of sea conditions Search And Rescue and emergency operations Decision making in an emergency

The “Design Wave Philosophy’’

The “Design Wave Philosophy’’ • Standards, class societies, rules and regulations • Consequence-based design, safety factors, reliability • Design wave vs. design sea state • Statistics and extreme value theory • Meaning of the 100-year (or 10000-year) wave

The “Design Wave Philosophy’’ • Everything started in a way similar to the Oklahoma rush in the Conquest of the West, but: • Hurricane Anita in the Gulf of Mexico • The design wave increased by 1 meter each year from return of experience in the late 70’s North Sea • The ”Alexander Kielland” accident occurred in 1980

The “Design Wave Philosophy’’ • National requirements and shipping regulations from a large amount of actors: • National Agencies (Oljedirektoratet, HSE, ...) • Classification Societies (DNV, API, Lloyds, BV, …, IACS) • Standardisation bodies (ISO, Bnpé, DIN, …) • Professional bodies (OGP)

The “Design Wave Philosophy’’ …ended up into a “philosophy for design”. In the North Sea, design is determined by extreme waves, and at the time (80’s), for fixed platforms with quasi-static response, by the single largest wave that would break the platform. At that time, one would compute what happens with a 100-year wave and add a safety margin.

The “Design Wave Philosophy’’ A 100-year wave is the wave height that is exceeded in average once every century over a large number of centuries. It is NOT exactly the same as having a 100-year average interval between two exceedances, and NOT AT ALL the same as being able to expect a duration of the order of magnitude of 100 years before the next after a given exceedance.

The “Design Wave Philosophy’’ • Standards, class societies, rules and regulations • Consequence-based design, safety factors, reliability (some points made by Markku Santala - Exxon) • Design wave vs. design sea state • Statistics and extreme value theory • Meaning of the 100-year (or 10000-year) wave

Identification of controlling design conditions Failure to identify controlling conditions may impact project schedule or lead to unacceptable performance Design practices that are over-conservative may not be cost effective For floating systems the maximum environment is not always sufficient for design Maximum environment  maximum response Response-based methods provide an approach for identification of controlling design conditions Implementation details key to effectiveness Design Method Effectiveness

Fixed Platforms Response = f(Hmax) + secondary contributions (ws, v) Specifying the 100-year wave plus associated parameters leads to the 100-year response approximately. Floaters Response=f(Hs, Tp,, ws, v, ) + secondary contributions Specifying the 100-year wave (or any other single parameter) plus associated parameters DOES NOT necessarily lead to the 100-year response. Example limitations In central GoM where offset can be dominated by Loop Current in a VIV lock-in condition. In western GoM responses can be dominated by wind plus associated conditions Traditional procedures and limitations

Specify a set of 100-year cases and look for the dominant response. Minimal specification might include: 100-year significant wave + associated wind and current Range of associated spectral wave periods 100-year wind + associated wave and current 100-year current + associated wind and wave Develop contours in Hs-Tp, Hs-ws, ws-v space to search for dominant responses. Multi-dimensional parameter contours —though theoretically possible— are not necessarily practical or sufficient. Common “Patches”

Methodology Determine limit state for critical systems Formulate response functions for each critical system element Realistic characterization effects of wind, wave, and current Computationally efficient Develop long-term characterization of the environment Simulate long-term response time history Evaluate extreme response statistics Identify environments that produced design response Assess design for controlling environments Consideration Factors other than environmental conditions may have comparable contribution Response-Based Approach

West AfricaGoMcentral N. Sea Hs 3.9 m 12.6 m 13.6 m Tp, associated 15-17 s 14.6 s 15.5-19.4 s ws, 1hr,10m 8 m/s* 46 m/s 35 m/s * 3-second gust is 30m/s. (due to West Africa squall conditions) Traditional 100-yr Environments(as per ISO regional annexes)

GOM – 100 YR Wave West Africa - Swell Why is the issue different for W. Africa? • Response may be highly resonant near its natural frequency. • In the Gulf of Mexico, which is a semi-enclosed sea, there are no long period waves to excite the heave resonance. • In environments like West Africa where there are long period swells it may be possible to excite this resonance. • This comparison shows a heave response more than 10 times greater in a 1m, 25s swell than in the 100-year GoM hurricane.

Assembling a long-term environmental database can be problematic. Wind and Waves - Hindcast data provided a 45-year time history of continuous 6-hourly “normal” winds and waves. Squalls – Only one year of measured wind data on the seasonal frequency and intensity. Currents - A long-term synthetic time-series of current based on a year of measurements. For this region, squalls and currents have little correlation to the swell dominated wave environment. Assembling long-term databases would be more straight-forward in mature areas such as the GoM or N. Sea but must still be done with care. Long-Term Characterization for Environment 45-Year Wave Hindcast 45-Year Squall Distribution

Simulate Long-Term Response Time History Initialize & load environmental database Analyze next seastate Compute mean forces & moments Compute offset & resulting mooring stiffness Compute slow-drift, wave-frequency and wind-induced motions at the keel Compute min/max stroke in seastate no Last seastate ? yes Archive results as input to extreme value analysis

With a 45-year sequence of responses, extrapolation to a 100-year extreme is straightforward. If our response functions were perfect we could use the results of the analysis directly. However, the response model used was an approximation and we can only use the analysis as a screening tool to determine input conditions. In past analyses in the GoM where we have used extremely long synthetic time-series (500 years+), the 100-year response can simply be picked out of the input database. In this case we need to “back out” conditions which lead to the 100-year response. Extrapolation of Response to Extremes Peak-Over-Threshold Analysis

To determine the environmental conditions which give rise to the 100-year response we examine the conditions which generated the largest peak responses. None of the responses occurred in the region of the 100-year Hs plus the “conservative” range on the associated Tp. In fact the 100-year response was more than 50% greater than the response in the worst part of the 100-year Hs and associated Tp range. In this case the top ten responses were all caused by conditions with long wave periods, modest wave heights and negligible winds and currents. The environmental conditions driving the 100-year stroke response were backed out of the region of the top ten responses using the response function. Determining the 100-Year Stroke Input Condition • This result could have also been • determined by examining 100-year • Hs-Tp contours. And, for this case with a • known sharp resonance, a prudent design • team would explore this option in the • absence of having performed a response • analysis.

The conditions determined by the response analysis are dependent on the system configuration. In a subsequent design cycle where the DDCV geometry and mass distribution was changed the response analysis was re-run. A case unrelated to swells emerged as the peak case. A large tilt response to extreme wind caused a large pull-down (right). Design Cycle Considerations • Here simply using Hs-Tp contours does not yield the critical response. Relying contours requires examining other contour dimensions to ensure identification of other conditions that may govern the extreme response.

Traditional methods based on SPJ experience are clearly dated and most of industry has made some effort to move ahead with specifications of metocean conditions more appropriate for floaters. Specifying a limited set of cases (e.g. wind-dominated, wave dominated etc) in the absence of any knowledge of the structure to be used is a first step but does not guarantee that the 100-year response of every critical system element has been considered. Judicious use of environmental contours and careful consideration of system resonance and damping on various components of the system may lead to an acceptable range of design cases. In cases where damping or VIV lock-in are an important part of the response it is not assured that the contour approach will identify the critical cases. Response-based analyses require designers and metocean specialists work together in a collaborative (rather than sequential) mode to identify critical cases. Success requires : the appropriate responses being screened, a good input database, good response models, appropriate updates of response analysis as design matures. Satisfying the above conditions is not easy and requires a non-trivial analysis and data gathering effort. Summary

The “Design Wave Philosophy’’ • Main problems with the 100-year wave + safety factor approach: • Failures occur for sub-extreme wave height combined with other factors • Actual level of safety is not known, not consistent over different structures, and with sometimes costly overconservativeness and sometimes dangerous unconservativeness

The “Design Wave Philosophy’’ • New “goal-based” approaches: • Define target levels of reliability • Probability of failure = Overall probability that simultaneously “stochastic” action exceeds “stochastic” resistance • Targets: • 10-2 yearly: unmanned, no danger to environment • 10-3 yearly: evacuatable, no danger to environment • 10-4 yearly: manned, or danger to environment • 10-4 yearly is similar to a 10000-year wave, it is also different.

The “Design Wave Philosophy’’ For many kinds of structures, wave height is not the only wave characteristic leading to failure. Steepness, wavelength, wave groups, ringing, springing, beam waves, etc. lead to consider one or several sea states (durations of, say, 3 hours) as the design conditions.

The “Design Wave Philosophy’’ • Two ways to arrive to the “design wave”: • Extrapolate the maximum waves measured in each sea state • Find the distribution of the largest Hs’s, and perform convolution with the distribution of the ratio Hmax/Hs • The two methods should yield the same final value… if assumptions are verified and database is sufficient.

Statistics and extreme value theory How can one extrapolate a few years of data to yearly probabilities of occurrence of 10-4 ? Extreme values theory is a very powerful tool Using measured or hindcast data of a few decades, and the “independent identically distributed” assumption, it allows to determine the likely distribution of 10000 year extremes

Statistics and extreme value theory Extreme values theory is a very powerful tool

Statistics and extreme value theory ..., and not forgetting the “independent identically distributed” assumption, ...

Statistics and extreme value theory What does “independent identically distributed” mean ? Independent, in practice, means that a single event should not be counted more than once. Designers are very concerned about independence, and tend to accept higher uncertainties in order to ensure independence. Often, they use POT (Peak Over Threshold) to retain only one value per storm, and may even consider that 2 storms 3 days apart should be taken as a single one. In fact, statisticians have shown that many kinds of slight dependence do not spoil extreme value extrapolation.

Statistics and extreme value theory What does “independent identically distributed” mean ? Identically distributed means that events are of a single kind. A typical case where it is not verified is locations where hurricanes occur once in, say, 10 years. Extrapolation from the main bulk of measurements is thus useless. Identically distributed is very difficult to verify, so designers have assumed it in many cases. Hence the question whether rogue waves are “normal” extremes or “ones from nowhere”, and its crucial importance.

The “Design Wave Philosophy’’ • Standards, class societies, rules and regulations • Consequence-based design, safety factors, reliability • Design wave vs. design sea state • Statistics and extreme value theory • Meaning of the 100-year (or 10000-year) wave (Some points made by Sverre Haver - Statoil)

Jacket structure in the North Sea

Target Safety Level of Offshore Structures By designing according to Norwegian Rules and Regulations, it is tacitly assumed that the nominal annual probability of structural failure is 10-4 – 10-5 or lower.  A structure should resist all wave events or wave induced load events corresponding to an annual exceedance probability of 10-4 with a proper margin (i.e. in worst case some local damage damage may be experienced).  Quantity of concern regarding ultimate safety is therefore the very, very upper tail of the annual distribution function of wave events and loads.

Target Safety Level of Offshore Structures Regarding overload failures, industry aims to fulfill target by the followingdesign controls:i) Ultimate Limit State (ULS)Component based control ensuring that the 10-2 – annual probability loadsmultiplied by a load factor are lower than a low percentile of the elasticcomponent capacity divided by a material factor. ii) Accidental Limit State (ALS)System based control ensuring that the 10-4 annual probability load is smallerthan the the system capacity.

Governing limit state (introducing the ugliness property) ALS governs design ULS governs design

If freak waves exist – what is the problem? For ship and platforms, freak waves will mainly represent a problem if their crest hits a structural element which is not designed for wave loads.

* The “Design Wave Philosophy’’ * Calculation of the design wave