Directional Metocean Extremes

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Copyright of Shell Global Solutions (UK)

DIRECTIONAL METOCEAN EXTREMES

The 800-year question

Graham Feld

Senior Metocean Engineer

1December 2012

N

NW NE

W E

SW SE

S


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AGENDA

Context and definitions Directional extremes in ISO and API

Traditional approa ch to directional extremes

Approach consistent with ISO 19901

The 800-year solution

The optimum solution

Some comments on practical application

Clarification addendum

December 201 2 2


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CONTEXT AND DEFINITIONS

Discussion applies to any directional metocean parameters that loadoffshore structures, typically winds, waves, currents

For most structures:

waves tend to dominate

most-probable maximum individua l wave is critical pa rameter

For simplicity, the slides focus on the derivation of return values of

significant wave height, Hs, from which the maximum individualwave is derived

3December 2012


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CONTEXT AND DEFINITIONS 2)

Target return period is 100 yea rs

100-year Hs value, Hs100,is defined as the:

Hs that is expected to be exceeded once in 100 yearsHs that has an annual probability of exceedance of 0 01

4December 2012


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DIRECTIONAL EXTREMES IN ISO

ISO19901-1:2005 Metocean design and operating considerationsFor design different wave, wind, and/ or current magnitudes may be used for

different approach directions [as long as] the overall reliability of the structure

is not compromised by the use of such lower directional environmental conditions

Environmental conditions should be scaled up such that the combined event from allsectors has the same probability of exceedance as the target return period

Method is expla ined in FORRISTALL, G.Z., On the use of directiona l wave criteria , J.

Waterway, Port, Coastal and Ocean Engineering, 2004

ISO19902:2007 Fixed steel offshore structuresThe environmental conditions should be scaled up such that the most severe sector is no

less severe than the omni-directional 100 year condition.

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DIRECTIONAL EXTREMES IN API

API RP-2A Recommended Practice for Planning, Designing andConstructing Fixed Offshore Platforms - Working Stress DesignProvides factors to apply to omni-directional extremes in GoM

No basis given for the derived factors

API RP 2RD Design of Risers for Floating Production Systems FPSs)and Tension-Leg Platforms TLPs)No explicit advice I could find

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TRADITIONAL APPROACH TO DIRECTIONAL EXTREMES

Omni Hs100 Hs100,dir

Directional extremes are scaled up by ratio of:

Omni Hs100:maxHs100,dir) Result:

There is no definitive statistical relationship between directional and

omni-directional extremes

Consistent with ISO 19902 but not 19901-1

7December 2012

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APPROACH CONSISTENT WITH ISO 19901

Ensure that combined event from all sectors has the same probabilityof exceedance as the ta rget return period.

Requires a clear statistical relationship between Hs100a nd Hs100,dir

The overall probability of failure must not be dependent upon the

choice of sectors, e.g. 1, 2, 4 or 8 sectors.

8December 2012

Omni

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HYPOTHETICAL EXAMPLE 1 ISO-DIRECTIONAL

Completely symmetrical climate from all directions in terms of:Storm severity

Storm occurrence rate

Storms in each sector are independent and affect only one sector each

Weibull distribution:

Scale pa rameter = 6

Shape pa rameter = 2

Omni-directional Hs100is 16.5m

9December 2012


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HYPOTHETICAL EXAMPLE 1 OMNI AND 2 SECTORS

Omni-directional case:P(Hs >16.5m) = 1 in 100 years

= 1/ 100

2-sector case: only half the number of events in each sector, so takes

twice a s long to reach 16.5m, i.e.

P(HsNorth>16.5m) = 1in 200 years

P(HsSouth>16.5m) = 1in 200 years

P(HsSouth>16 .5m or HsNorth>16.5m) = 1/ 200 + 1/ 200 = 1/ 100

10December 2012

Omni

North

South


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HYPOTHETICAL EXAMPLE 1 4 AND 8 SECTORS

4-sector case:P(HsN>16.5m) = 1/ 400

P(HsE>16.5m) = 1/ 400

P(HsS>16.5m) = 1/ 400

P(HsW>16.5m) = 1/ 400

P(HsNor HsEor HsSor HsW>16.5m) = 4 *1/ 400 = 1/ 100

8-sector case

P(Hsany direction >16.5m) = 8 *1/ 800 = 1/ 100

11December 2012

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HYPOTHETICAL EXAMPLE 1 SUMMARY

Whatever sectors we choose, the composite probability of exceeding16.5m is once in 100 years.

This cant be achieved by taking the 100-year independent extreme

from ea ch sector, which a re:

So, for 8 sectors, the hypothetical solution is using 800-year extremes.

Should we always take the 800-year solution for 8 sectors?

12December 2012

16.5m

15.8m

15.8m

15.0m

15.0m

15.0m 15.0m

14.1m14.1m

14.1m

14.1m

14.1m

14.1m14.1m

14.1m


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HYPOTHETICAL EXAMPLE 2 HIGHLY DIRECTIONAL

100-yea r omni-directiona l is 22 .3m. Directional extremes are:

Hs100,dir Hs800,dir

Surely, the 800-year solution doesnt make sense in this context.

13December 2012

14.1m

14.1m

14.1m

14.1m

14.1m

14.1m14.1m

22.3m16.5m

16.5m

16.5m

16.5m

16.5m

16.5m

16.5m

26.2m


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HYPOTHETICAL EXAMPLE 3 MORE REALISTIC CASE

Omni-directional extreme 23.5m 8 sectors, each with different Weibull description.

Hs100,dir

14December 2012

21.1m

18.8m

16.4m

14.1m

20.0m

17.6m15.3m

22.3m

5.121

1001

1001

1001

1001

1001

1001

1001

1001 =+++++++


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HYPOTHETICAL EXAMPLE 3 TRADITIONAL SOLUTION

Tra ditiona l solution scaled up Hs100,dirby ra tio ofOmni Hs100/ maxHs100,dir)

23.5/ 22.3 = 1.05

Traditional scaled Hs100,dir

15December 2012

22.3m

19.8m

17.3m

14.8m

21.0m

18.6m16.1m

23.5m

5.23

1

185

1

190

1

192

1

190

1

190

1

186

1

180

1

190

1=+++++++


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HYPOTHETICAL EXAMPLE 3 800-YEAR SOLUTION

800-yea r solution

Hs800,dir

16December 2012

100

1

800

1

800

1

800

1

800

1

800

1

800

1

800

1

800

1=+++++++

24.8m

22.1m

19.3m

16.5m

23.4m

20.7m17.9m

26.2m


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HYPOTHETICAL EXAMPLE 3 AN ALTERNATIVE SOLUTION

Ensuring that no Hs100,dir> Hs100to the nea rest 0.1m

Other a lterna tives a re possible if you are prepa red to increa se la rgest

sector by 0.1m, 0.2m etc.

17December 2012

23.5m

23.5m

22.2m

19.5m

23.5m

23.3m21.0m

23.5m

100

1

187

1

860

1

k6

1

k14

1

k16

1

k10

1

k2

1

376

1=+++++++


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HYPOTHETICAL EXAMPLE 3 COMPARISON

Comparison of some solutions

In fact, any solution is possible as long as the sum of probabilities is

1/ 100.

What is the optimum solution?

18December 2012

13.0

15.0

17.0

19.0

21.0

23.0

25.0

27.0

N NE E SE S SW W NW

m]

Alterna tive #1

Alterna tive #2

Alterna tive #3

800-Year

Trad itiona l

100-Year


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THE OPTIMUM SOLUTION

. it depends . .. but will almost certainly not be the 800-year solution.

Some thoughts:

Optimum solution can only be found by relating it to the structure.

Likely to be one tha t has no direction much more severe than the

100-year omni-directional value.

The more variable the climate by direction, the more the optimum

solution is likely to depart from the 800-year solution

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PRACTICAL APPLICATION

The optimum solution is often hard to define Need to decide wha t criterion you want to use to determine wha t is

optimal

Is it practical to make an asymmetrical structure?

Probably best to use omni-directional for new designs

Reliability approaches can use the independent 100-year directionalvalues as probability of failures ARE combined at the end of theanalysis.

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PRACTICAL APPLICATION CLARIFICATION 1)

For a new structure that is yet to be built, you have some freedom inhow you want to resist the environment at the location in question.

There a re a n infinite number of ways tha t the environment can be

resisted to target return period and you can define exactly how you

would like to do this. Two examples are depicted below structural

resistance in blue, 100-yea r environment (red dots )

December 2012 21

Designed resistance a lterna tives

10 0-year environment


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For an existing structure, you have no freedom as the structuralresistance already exists (blue dashed line).

You need to try to find whether the resistance (blue dashed line) gives

overa ll 100 years or better. You can do this in two ways:

A push-over ana lysis Directional code checks

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In-place resistance

10 0-year environment


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Option 1: Push-over analysisCalculate probability of failure in each direction

Shown as green dots in the figure - all at different return periods as

output from the analysis but all lie on actual line

Combine to get the overall probability of failure

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In-place resistance

Directional failure probabilities


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Option 2: Directional code checkCould try 800-yea r in ea ch direction (yellow dots)

Some pass (inside the blue line), some fail (outside the blue line)

If all pass, then success

If not, must try another combination that combines to100 years, e.g.the cyan dots.

Repeat until you find any set where all points are on the line or

inside, e.g. the cyan dots work in this case.

There is an infinite number of combinations

tha t you can try. You only have to find one

set that works but it is trial and error.

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CONCLUSION

When designing a new structure:

You ca n design to resist the environment in infinite number of ways

The 800-year solution is ra rely, if ever, optimal

For pre-existing structures. Test using either push-over or code check:

Push-over a pproaches

use independent 100-year directional values, combine probabilities of failure at the

end

Code checks are trial and error there is no single definitive set of directional criteria

use of either traditional or independent 100-yea r extremes is insufficient for testing

aga inst an overa ll ta rget return period a s neither combine to 100 years or better.

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