directional metocean extremes
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DIRECTIONAL METOCEAN EXTREMES
The 800-year question
Graham Feld
Senior Metocean Engineer
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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
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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
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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
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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
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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.
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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
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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
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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
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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.
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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
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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
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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
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800
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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.
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23.5m
23.5m
22.2m
19.5m
23.5m
23.3m21.0m
23.5m
100
1
187
1
860
1
k6
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k14
1
k16
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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?
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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 )
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Designed resistance a lterna tives
10 0-year environment
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PRACTICAL APPLICATION CLARIFICATION 2)
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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PRACTICAL APPLICATION CLARIFICATION 3)
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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PRACTICAL APPLICATION CLARIFICATION 4)
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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