**RECURRENCE INTERVALS OF ENVIRONMENTAL
CONDITIONS**

By Arne Kvitrud, Sondre Nordheimsgate 9, 4021 Stavanger.

Paper
presented in 1997, but put on Internet 25.9.2002.

The figures
are not presented here.

** **

**Introduction**

The ISO 13819-1 is stating
that an annual probability of occurrence of 10^{-2} or a return period
of 100 year should be selected for environmental actions. The paper will
describe how the characteristic values of environmental actions can be determined.
Further the presentation will describe some requirements to environmental
extreme values necessary to obtain a structure with a consistent and high
reliability.

This document is to a large
extent obtained by editing text from the draft B versions of ISO 13819-1. The
paper is collected with the purpose to give information about the content and
the background for the ISO standard for personnel not directly involved in the
process of making the standard.

**Reliability requirements**

The design should give safe
offshore structures for personnel, with a low probability of major pollution
and the structures should be economical. A way of obtaining it is to give a
reliability target for the design, or to give a detailed description of how to
obtain it. The second approach is used in ISO 13819-1 and 13819-2, but a target
is described in the commentary for ISO 13819-2 for information.

**The ultimate limit
states**

The ISO 13819-1 describe a
method where the offshore platforms should resist different limit states. For
the purpose of the determination of the annual probability of occurrence of
environmental actions the ultimate limit states and the accidental limit states
are of interest. For the ultimate limit states a characteristic value of the
action should be selected. For environmental actions an annual probability of
exceedence of 10^{-2} is specified. An action factor should be applied
on the characteristic value to obtain the design action. The strength of the
material or component should be based on characteristic values. The design
strength should be found by dividing the characteristic strength with a
resistance factor or a material factor. For the accidental limit states no
target value of the environmental loading is prescribed in the draft ISO
standard at present, but I will come back to it later in this paper.

The safety format in the
ISO 13819-2 draft have been calibrated in offshore areas, such as the North Sea
and the Gulf of Mexico, where the experience base is very extensive and
satisfactory. These calibrations, and the values obtained from them, can not
necessarily be used worldwide. For the specific case of extreme storm loading,
it is known that the long term distribution of environmental loading is
generally a function of the geographic location, and hence harmonisation in
safety levels would require location dependent action factors. The commentary
to ISO 13819-2 draft C lists the properties of reliability models that may be
used to address the above issues and provides appropriate factors for use with
joint environmental conditions in different geographical locations.

Reliability models can used
to derive values of the action factor for various environments to achieve a
target level of safety. Results are given in the table below for a target annual
probability of failure of 3*10-5/annum for a fixed steel structure. This level
of reliability was considered by Efthymiou et al to be appropriate for a new
permanently manned installation because this risk level is small in relation to
the overall risk to personnel. The environments considered refer to a location
of the north-west shelf of Australia (AUS), a location in the northern part of
the UK sector of the North Sea (NNS) and a location in the UK sector of the
central/southern North Sea. Values of action factor to achieve target less than
3*10-5/yr. for new and manned platforms :

Environment |
Action factor |

AUS |
1.59 |

NNS |
1.40 |

CNS/SNS |
1.26 |

A significant engineering and
statistical knowledge and judgement is necessary to obtain reliability numbers
and action factors as described in the table.

**Fatigue limit states**

The ISO 13819-1 give action
factors and resistance factors for fatigue calculations of 1.0. The safety is
taken care of by using fatigue factors on the expected life of the structure.
The fatigue factors are made as a function of consequences and possibility of
inspection. No description is made in the standard itself on target values. ISO
13819-2 chapter 9.3.2 in draft C has the following fatigue factors:

Classification based on
consequences |
Unavailable for
inspection |
Available for inspection |

Major consequences |
10 |
3 |

Minor consequences |
3 |
1 |

The table can be justified using
a simple approach (from Jonas Odland in 1985). If the probability of fatigue
failure is expressed as:

P = PF * (1-PI) * PB

Where

PF
= the probability of fatigue in one
member.

PI
= the probability that fatigue crack is
found and corrected for inspection possibility

PB
= the probability that fatigue cracks on
a member cause total failure of the platform

As a basis for discussion
the following numbers can be used. I have assumed a connection between the
Miner sum and the probability of failure equal to Miner sum = 0,45* lg (PF)
+1,9. The following assumptions can be made in addition:

PI = 0.0 for elements which
can not be inspected

PI = 0.9 for elements which
can be inspected under water

PI = 0.99 for elements
which can be inspected above sea level

PB = 1.0 for elements of
major importance

PB = 0.1 for elements
without major importance

The fatigue factors in ISO
13819-2 will have the following probability of exceedence for an under water
structure:

Classification based on
consequences |
Unavailable for
inspection |
Available for inspection |

Major consequences |
10*10 |
2*10 |

Minor consequences |
2*10 |
1*10 |

The levels are not
completely consistent, but it indicates a probability level with a reasonable
high reliability.

**Environmental actions
with an annual probability of occurrence of 10-2**

**The Data basis**

The environmental actions
should be determined with an annual probability of occurrence of 10^{-2 }for
all environmental actions. All actions as waves, wind, currents**, **icing,
sea ice, icebergs and earthquakes are to be handled in a consistent manner.

A well-controlled series of
measurements at the location of an offshore installation is a valuable
reference source for establishing design and operational criteria. Measurements
taken over a short duration may give misleading estimates of long-term
extremes. Extremes derived from short-term site-specific measurements should
only be used in preference to indicative values presented in ISO standard
guidance documents, if care is taken to adjust the records to reflect
long-period climatology.

Measurements at a location
away from the platform location may be misleading e.g. because of a sharp
gradient in wind speed near a coastline or different water depths at the two
sites. If it is decided to use such measurements because site measurements are
not available, allowance should be made (e.g. by the use of numerical models)
for such effects. Note site specific current measurements should normally not
be used without an investigation of the relevance for the actual
location.

It should also be
recognised that measurements made during a climatologically anomalous period
may dominate the data set and the data may therefore not be typical of the
long-term climate at the location.

To get a reasonable
prediction of the environmental actions it is necessary to have a good data
basis.

There are various
circumstances in which site specific data will need to be analysed in order to
produce extreme metocean criteria, for example where:

- Regional regulatory requirements insist on the use of
site-specific data

- An operator has field data in addition to the data used in
producing the metocean criteria presented in standard guidance documents

- An operator may wish to produce metocean criteria for
return periods other than those available in standard guidance documents

- Metocean criteria are not provided in this document or are
otherwise deemed by an operator to be inappropriate

When extrapolating metocean
databases to small probabilities of exceedence, it is assumed that the database
is stationary. This hypothesis should continue to be tested and if necessary,
suitable allowances may need to be made to incorporate any residual
uncertainty. Climate variations during the lifetime of structures, may result
in changes to:

- The water level (means, tide and/or surge)

- The frequency of severe storms

- The intensity of severe storms; with possible associated
changes in the magnitude and frequency of extreme winds, waves and currents.

For ice borders a similar
long data set (> 15 years) of weekly or biweekly satellite ice border maps
is generally sufficient.

For earthquakes and
icebergs longer data series or information’s of events are usually necessary,
because there will be a need to extrapolate to return periods which is longer
than 100 year. For earthquakes the epicentre and magnitude of the earthquake in
a large area is necessary, together with area specific attenuation information.

**Derivation of extremes**

It is beyond the scope of
ISO standard to provide a detailed procedure to produce reliable extreme
estimates in all cases. However, the draft ISO 13819-2 standard states that it
is important to select an expert with experience in all facets of the process.
This includes the hardware and software associated with data gathering (in-situ
or remote sensing), hindcasting procedures, data sampling and analysis
procedures, and extreme statistical analysis techniques. Uncertainties in the
final extreme estimates of the same order of magnitude can be introduced at any
point in the process.

Reliable estimates of
extremes can be made using a number of different approaches, including analysis
of continuous observations, annual or monthly maximum, peak-over-threshold
events, etc. Use of each of these methods dictates certain assumptions about
the data applied, statistical procedures used, and interpretation of the
results. Again, the metocean expert needs to be familiar with these details.

The approach will often be
dictated by the available data itself (i.e. measured, continuous or storm
hindcasts, ship’s visual observations, satellite, radar, etc.). The critical
aspect is to understand the methods used to record and analyse the data, and
how that may influence the selection of an analysis approach or possibly bias
the result. A sound understanding of this type of information is necessary in
order to account for it during interpretation of the data and applying any
corrections that might be necessary to the final estimates.

**Statistical
distributions**

Given a suitable data base
of measured and/or hindcast data, it is important to investigate the
sensitivity of extreme value estimates to the use of different data sets
(measured or hindcast) and statistical analysis procedures. It is important
that the structural engineer who will use the metocean criteria, is made aware
of the uncertainty (preferably by a quantitative assessment) in the extremes
provided. Relatively small changes in estimates of the design wave height (in
particular) may affect the reliability of a structure by an order of magnitude.
However, given reliable long-term data sets (15+ years), the various
statistical approaches should converge to similar results.

Depending on the problem in
question, different statistical distribution might be used. Analysing wind and
wave data the following approaches are frequently used:

- Data sets of all measurements are
frequently used. The data is divided into classes as each half a meter
significant wave height. For each class the number of events is
calculated. A Weibull distribution is fitted to the data. This method is
in practice limited to be used in non-tropical areas.
- If long data series is available, the
yearly maximum value is calculated. A Gumbel distribution is fitted to the
data, as above.
- In some tropical areas only storm data are
available or relevant to analyse. If all the data is used a lognormal
distribution or a truncated Weibull distribution is used. The annual
maximum can be used as above. The third method is called the Peak over
Threshold (POT) method, and includes a calculation of the maximum value
within each storm. These maximum are than assumed to be statistically
independent and a Gumbel extrapolation is performed. The time between each
storm peak should not be to short, introducing statistical dependence in
the calculations. The POT method is very sensitive to the threshold value
selected, and several values should be used to make sure that the
threshold is so low, that the results are stable.

For ice border calculations
a similar approach can be used. The maximum ice border can be found for each
year along defined latitudes. These data can be fitted to a distribution as
described above. All the data can also be used. POT methods will be attractive
when there is an island, where the ice some years are north and some years
south of the island. Only the ice situations south of the island (threshold)
will than usually be of interest for the statistical analysis.

Given a statistical
distribution and a data set, a fitting between these have to be done. Different
methods are used. Traditionally the plotting position will be to the highest
number in each class, but other more sophisticated methods also exist and are
used. A visual fitting of a plot will usually give the user the best feeling
for the uncertainties in the methods and extrapolations. Several computerised
methods as : the linear least square (LLS), the method of moments (MOM) and the
maximum likelihood methods (MLE) are frequently used. Details about them can be
found in statistical textbooks as in Karl V. Bury: Statistical Models in
Applied Science, Florida, 1986.

**Joint probability**

For some areas, substantial
databases are becoming available with which it is possible to establish
statistics of joint occurrence of wind, wave and current magnitudes and
directions. When such a database is available, it is recommended that this
should be used to develop environmental conditions based on joint probability,
which provides an annual probability of exceedence of 10^{-2} for
environmental action. The action factors used in conjunction with this
environmental action should be determined using structural reliability analysis
principles to ensure that an appropriate structural reliability is achieved.
This approach provides more consistent reliability for different geographic
areas than has been achieved by the practice of using separate (marginal)
statistics of winds, currents and waves.

If the metocean database
allows and a reliable model for crest statistics exists, account may be taken
of the joint probability of tide, surge height and crest heights to estimate
the maximum height of "green water". In this case, a probability of
non-exceedence close to the target failure rate of the sub-structure may be
used but with no additional air-gap allowance added. The statistics of crest
elevation is an area of continuing research. A distribution may be used if it
can be reliably demonstrated to be applicable for a particular location, (e.g.
taking into account the water depth at the site, storm population and
geographical position).

**Transportation and
installation**

The environmental
conditions used in determining the motions of the tow should be established
taking account of the expected tow route and season. For long duration tow the
extreme environmental conditions will depend on an evaluation of acceptable
risks and consequences. But for situations where there is major consequences to
personnel, pollution or significant consequences for the national or the
company economy, an annual probability of exceedence of 10^{-2} should
be used. For unmanned short duration tows, which can be done with reliable
weather forecasts, the environmental conditions should generally have a return
period not less than 1 year for the season in which the tow takes place.

**Environmental actions
with an annual probability of occurrence of 10-4**

**A consistent safety
level**

From my point of
view, the present draft of ISO 13819-2 does not give a consistent safety level
for all situations. The design using environmental actions with an annual
probability of 10^{–2}, will give a consistent safety level for a
majority of problems, but exemptions exist related to :

- air gap
- earthquakes
- sea ice borders
- collisions with icebergs

For high consequence situations,
the platforms should be designed to resist an environmental action an annual
probability of occurrence of 10^{-4}. This number is intended to be an
indication on order of magnitude, and usually there will not be available
sufficient information to calculate this number with a high degree of accuracy.
In such a situation local damage should be possible, but the wave should not
endanger any safety function related to personnel or pollution. Two levels of
environmental actions are specified in the earthquake chapter of the ISO
13819-2, but not for the remaining parts. Separating between high and low
consequence platforms should give a reasonable safety approach.

**Deck clearance from
waves**

It is necessary to
determine the minimum acceptable elevation of the bottom of the bottom beam of
the lowest deck in order to avoid waves striking the deck. When using only an
annual probability of exceedence of 10^{-2} criteria to set the minimum
deck elevation, a safety margin, or air gap, should be added to the annual probability
of exceedence of 10^{-2} crest. This air gap should allow for expected
platform settlement, water depth uncertainty, any known or predicted long term
sea-floor subsidence, the possibility of extreme waves, and any other effects
that may erode the air-gap. This safety margin should be based on appropriate
reliability considerations or experience or a combination of both. In no case
should the air-gap be less than that required to account for water depth
uncertainty.

In general, no platform
components, piping or equipment should be located below the lower deck in the
designated air gap. However, when it is unavoidable to position such items as
minor sub-cellars, sumps, drains or production piping in the air gap,
provisions should be made for the wave forces developed on these items. These
wave forces may be calculated using the crest pressure of the design wave
applied against the projected area. These forces may be considered on a
"local" basis in the design of the item and its fixings. These
provisions do not apply to vertical members such as deck legs, conductors,
risers, etc, which normally penetrate the air gap.

Haver (Reliability work
shop, London, 1995) have described that with the reliability level assumed for
overloading of the main structure, the probability that the wave would hit the
deck structure significantly higher, using 1,5m air gap. The total force on the
structure increase significantly when the wave forces start acting on the deck.
The 1.5m deck level is in inconsistency with the general target reliability
levels for the standard. Calculating an wave action with an annual probability
of occurrence of 10^{-2} will give a specified value. If the deck is
just above that value, no action factor will give loading on the deck
structure.

At present a wave crest
with an annual probability of occurrence of 10^{-4} is prescribed in
the commentary to the ISO 13819-2, but only for a very specific situation.

**Ice borders**

Calculating an ice border
with an annual probability of occurrence of 10^{-2} will give a
specified border. If a platform is just outside that border, no action factor
will give ice loading on the structure. To get a consistent safety level
environmental actions with lower probabilities should also be evaluated. In
Norway an additional level with an annual probability of occurrence of 10^{-4}
is prescribed.

**Earthquake**

The ISO standard is
describing two levels of earthquake actions to be defined. As it is defined in
Norway and Indonesia a 100-year value is the first level. USA use 200 year. The
use of 100 year will make the document consistent with the metocean description
and a common basis for establishing the safety level can be set.

The other level could be
with an annual probability of occurrence of 10 ^{-4}. In Norway the
difference between an annual probability of occurrence of 10^{-2} and
10^{-4} is typically a factor of 5 on peak ground acceleration. The use
of a very low second level or no second level will give a very unpredictable
safety level. In other parts of the world this difference will be less than the
action and resistance factors used in the ultimate limit states.