See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/266617560
Fast Prediction of Fixed Offshore Jacket
Platforms Response to Random Wave Loads
Conference Paper · June 2011
CITATIONS
READS
0
141
3 authors:
Seyed Mehdi Enderami
M. Zeinoddini
Khaje Nasir Toosi University of Technology
Khaje Nasir Toosi University of Technology
4 PUBLICATIONS 3 CITATIONS
94 PUBLICATIONS 444 CITATIONS
SEE PROFILE
SEE PROFILE
Siamak Kakasoltani
4 PUBLICATIONS 3 CITATIONS
SEE PROFILE
All in-text references underlined in blue are linked to publications on ResearchGate,
letting you access and read them immediately.
Available from: Seyed Mehdi Enderami
Retrieved on: 11 October 2016
Proceedings of the ASME 30th International Conference on Ocean, Offshore and Arctic Engineering
OMAE2011
June 19-24, 2011, Rotterdam, The Netherlands
OMAE2011-50251
Fast Prediction of Fixed Offshore Jacket Platforms Response to
Random Wave Loads
S.M.Enderami
M.Zeinoddini
Faculty of Civil Engineering, KNToosi University of
Technology, Tehran, Iran
E-mail: s.m.enderami@gmail.com
Faculty of Civil Engineering, KNToosi University of
Technology, Tehran, Iran
E-mail: zeinoddini@kntu.ac.ir
S.Kakasoltani
Faculty of Civil Engineering, KNToosi University of
Technology, Tehran, Iran
E-mail: siamak.kakasoltani@gmail.com
INTRODUCTION
From a design point of view, wave loads on a fixed
offshore platform can be calculated with incorporating
Morrison equation to regular wave models, such as fifth-order
Stokes wave (in deep water) and stream function (in shallow
water). While this approach is potentially able to consider the
nonlinearity of the wave action, it falls short to take into
account the randomness and irregular nature of the sea level
changes. In fact, in a dynamic analyses assumptions that all the
wave energy is concentrated in a specific frequency, may well
result in under predicting the structural response to wave
actions. A direct time domain dynamic analysis using irregular
wave time series, on the other hand, is the most comprehensive
solution for the wave structure interactions. It is however,
computationally expensive and time consuming. Interpretation
of results from such a long duration analysis, considering
abundant output data, will be troublesome. Hence, a number of
researchers tried to develop short time histories of the water
surface fluctuations, which do not abide by a fixed frequency
but well represent the desirable maximum crest height. Such an
irregular short duration wave has to be able to provide load or
response results in the structure close to those from long-term
irregular wave simulations.
Lindgren [1,2] is the first person who studied the
characteristics of a Gaussian sea state, near a local
maximum (e.g. the highest wave crest). During the years 19811982, Boccotti [3, 4] presented the first formulation of the QD
theory (Quasi-Deterministic) based on linear random waves.
The QD theory provides of necessary and sufficient conditions
for the occurrence of a very large wave at a certain place and
ABSTRACT
The more accurate methods for estimating extreme
responses of offshore structures to wave load are usually based
on pseudo-random time domain simulation of the sea surface.
However, they need many long duration storm inputs and are
computationally very time consuming. Accordingly, many
efforts have been made to introduce new, computationally
efficient, theoretically optimal and simultaneously accurate
methodes for simulating the random nature of the sea surface.
The efficiency and the accuracy of these new methods have
been continually evaluated by different researchers to advance
towards a more integrated and complete approach. NewWave
and Constrained NewWave models are among those techniques
proposed for evaluating the response of structures under
irregular waves.
In the current paper two fast prediction methods for
evaluating the response of a steel jacket platform subjected to
irregular waves are discussed. One approach is based on
incremental dynamic analysis of the structure against a series of
Constrained NewWaves each with scaling wave crest heights.
The results were presented in the form of upper and lower
bounds for the intensity measures against damage measures.
The second approach utilizes the results for the jacket structure
response to a limited number of irregular 3-hours storm water
surface simulations. Once again curves for the intensity
measures against damage measures were produced. Results of
the current study remarked that both proposed fast prediction
methods can provide reasonable results for the response of the
jacket structure to random type waves with significantly lower
computational time.
1
Copyright © 2011 by ASME
time. In fact, the first theory of QD is the same NewWave
Theory that was given by Tromans et al [5], from the statistical
results. This is a new method for estimating the time-domain
response of offshore structures. It assumes that the sea surface
elevation can be modeled as a Gaussian random process. The
elevation expected at an extreme event (for example a crest)
can be derived theoretically. The surface elevation around this
extreme event is modeled by the statistically most probable
shape associated with its occurrence. Taylor et al. [6] showed
how the NewWave embedded in a stochastic seaway could be
used to estimate the extreme response of a Jack-Up in a severe
sea state in a robust and efficient manner. This sea state,
contains expected elevation of extreme crest, is called
Constrained NewWave (CNW). Many investigators have used
CNW in their researches. [7], [8], [9] and [10] have applied
CNW along with 3-hours simulation to a Jack-Up platform
with different support conditions to derive the dynamic
responses of the structure. They performed statistical analysis
to predict the long term extreme responses of the Jack-Up.
Also, Cassidy et al. [7] introduced a new method for fast
prediction of structure responses subjected to 3-hours storm
waves without many hours simulating based on CNW.
Cassidy et al. [11] obtained Dynamic Amplification
Factors (DAFs) for a Monopod platform using CNW method.
Smith et al. [12] carried out a comprehensive study on the jackup rigs, by implemented second-order three-dimensional
NewWave model. This research was focused on determining
Dynamic
Amplification Factors
(DAF)
in
different
environmental conditions, including three-dimensional
propagation. They found satisfactory predictions from
NewWave theory, for situations when the natural period of
structure (Jack-up) was closed to the maximum wave period.
Cassidy et al. [13] reported a prediction method for deriving
responses of a barge during a float over Deck installation. They
obtained the barge responses under a large number of CNW’s
with different heights and wave attack directions. So, during
the installation operation and under each environmental
condition, barge displacements and impact energy on fenders to
prevent of structural damage can be quickly calculated. These
data were also used to foresee those environmental conditions
which were suitable for installation operation.
In the current study, the CNW method along with irregular
3-hours storm water surface simulations are used. Two methods
for fast prediction of structure response are evaluated, first
method is based on CNW [7] and the second method is based
on 3-hours storm simulation.
Wave kinematics corrections for elevations above MSL
(Mean Sea Level), is one of the important subjects in wave load
evaluation using CNW and linear irregular wave theories on
marine structures. In this research, correction methods to
irregular wave kinematics above MSL were reviewed based on
available experimental results. The results have been
implemented to the analysis performed to predict the fixed
offshore platform response.
To study the response of offshore Jacket type platforms
against extreme wave loads, ABAQUS/Standard was
employed. This is a general purpose finite element code, which
allows for both material and geometric nonlinearities. The
program allows for the modeling of wave forces on structures
and allows for buoyancy, drag, and inertia loads resulting from
submersion in steady current, waves, and wind. The software
models the effects of wave and current on tubular members
with the standard Morrison’s equation. The program includes a
number of standard wave models (Airy and Stoke’s waves). In
this case, a user defined wave model, has been developed to
reproduce irregular wave profiles and kinematics. It calculates
irregular wave kinematics in each step of analysis and
incorporates the results to integration points in the structure
members. For analysis performance, wave kinematics at
integration points are used along Morison equations to obtain
the wave forces.
MODELLING OUTLINES
Jacket Structure
In this paper JUDY platform a jacket type offshore rig
operating in the English part of the North Sea, was considered
for the analysis. The steel Jacket structure provides supports for
a 14,000 ton topside through six legs underside of the
integrated deck. The loads are transferred from the six legged
support to the integrated deck down to four main corner legs of
the Jacket at the seabed. Permanent support at the seabed is
provided at the four Jacket corner legs by groups or tubular
steel skirt piles. These piles were driven to about 93m
penetration depth and convey the deck’s weight and
equipments to seabed. The Jacket structural weight, including
piles, is about 15,400 ton. The water depth is 75 meter. The
extreme wave height with a 50-year return period is 24 meter
and has a predominant west direction. The wave period is 15.7
sec. The extreme current for 50-year return period on MSL is
1.24 m/sec and on seabed is 0.79 m/sec [15].
Around 10 beam elements type Pipe31 were used for each
Jacket members. This element is applicable for tubular sections
and can be used in Aqua and nonlinear analysis. It can
accommodate inertia and drag forces produced by wave and
current regimes. Drag, inertia and added-Mass coefficients
were considered as 0.77, 2 and 1, respectively. Material
properties correspond to BS7191 with σy=355MPa and σu=
460MPa.
2
Copyright © 2011 by ASME
For the individual wave components, k n = ω n2 g is the
wave number obtained from the dispersion relation for deep
water waves. g is the acceleration of gravity, ωn is the wave
frequency and θξ,n is a uniformly distributed random phase
angle between 0-2π. Sξ(ωn) represents the wave spectrum
values.
To simulate a long duration irregular sea elevation, wave
spectrum should be divided into enough components. For this
purpose in present research, the wave spectrum was divided
into 200 components and a stochastic phase angle was assigned
to each sinusoidal wave component [17]. So, free simulated
surface of sea, that is superposition of 200 regular waves,
turned into complete irregular background. Therefore, a file
containing 200 stochastic phase angle between 0-2π was
generated for each simulations. In each analysis, this file was
recalled by subroutine and used in sea surface simulation.
Fig.1 3-D description of Judy jacket platform
For deck modeling, a simplified model with two stories is
generated and the total deck weight is divided on ten points of
it as lumped mass. Also for simulating of Pile-Soil interaction,
two models were compared. In first model, piles were modeled
completely and p-y, t-z and q-z springs was used for Pile-Soil
interactions according to API (2001). In second model a pile
stub with shorter length was applied. Basis on compare of static
analyses under lateral loads and frequency analyses results, in
second model a pile stub with 20m length (equal to 8D; D:
diameter of a leg) was considered. For model validating, the
modal analysis results of two models that mentioned above are
given in Table 1.
The Newwave Profile
NewWave theory models the surface elevation around an
extreme event by the statistically most probable shape
associated with its occurrence. This theory formulates a model
that provides wave kinematics, for a special extreme crest, in
different depths. The results can be used in a structural analysis.
With regard to probable shape and its non-periodic nature, the
NewWave model is singled out from regular wave theories like
Stokes 5th order. The surface elevation is described by two
terms, one deterministic and one random. As a function of time,
the surface elevation η (τ ) can be written as [5]:
Table1. Compared of Judy three lowest frequency
First model
Second model
First mode
2.94 sec
2.87 sec
Second mode
2.7 sec
2.8 sec
Third mode
2.19 sec
2.19 sec
η (τ ) = αρ (τ ) + g (τ )
(a)
(3)
where τ=t-to, α is the crest elevation defined as the vertical
distance between the wave maximum and the mean water-level,
and ρ(t) the autocorrelation function for the ocean surface
elevation.
In Equation 3, term (a) describes the most probable value
of water surface and term (b) is a non-stationary Gaussian
process with a mean of zero and a standard deviation that
increases from zero at the crest to σ, the standard deviation of
the underlying sea at a distance away from the crest. Therefore,
as the crest elevation increases, term (a) becomes dominant and
can be used alone in the derivation of surface elevation and
wave kinematics near the crest.
The autocorrelation function is proportional to the inverse
Fourier Transform of the surface energy spectrum [5]:
Irregular Wave Model
An irregular time history of sea elevation could be
generated from linear superposition of several regular waves
with different heights and phase angles. A wave spectrum may
be used for construction of this wave train. As a function of
time, the wave elevation Z ( x, t ) can be defined as [16]:
N
Z ( x, t ) = ∑ cξ ,n cos(k n x − ωnt + θξ , n )
(b)
(1)
n =1
where N is large and the expected value of amplitude cξ,n is
given by:
cξ , n = 2 S ξ (ω n ) ∆ω
ρ (τ ) =
1 ∞
σ ∫0
2
Sξ (ω )eiωτ dω
(4)
With the time history of the extreme wave group
proportional to ρ(t) at the region around τ=0. For a time lag of
(2)
3
Copyright © 2011 by ASME
τ=0 the autocorrelation function of Equation 4 reduces to one,
allowing the surface elevation of the NewWave to be scaled
efficiently. The NewWave shape can be described by a finite
number (N) of component sinusoidal waves, which when
including spatial dependency can be to the discrete form [5]:
η( X , t) =
α
N
S (ωn )∆ω ]cos( k n X − ωn t )
2 ∑ n =1[ ξ
σ
the extreme input surface elevation, and the extreme response
might very well correspond to a combination of the local
extreme wave with unfavorable background structural memory
effect. It means that the extreme dynamic response of structure
under wave effects can be generated by waves with lower
height and different frequencies and also a long and high wave
in wave process. Therefore, using regular wave theories such as
stokes 5th order with a single frequency, possibly does not lead
to the extreme response of structure. So, with methods such as
CNW, which is considerably shorter than 3-hours simulations,
the structural responses can be estimated and used in a design
process.
(5)
X=x-x0, is the distance relative to the initial position with X=0
representing the wave crest. This allows the positioning of the
spatial field such that the crest occurs at a user-defined position
relative to the structure and is a useful tool for time domain
analysis. Only linear NewWaves have been implemented
allowing the water wave particle kinematics to be easily
obtained once the water surface has been established.
The hydrodynamic loads on a structure can be estimated
using the Morison equation with the velocity and acceleration
values from the NewWave. Fig.2 shows typical NewWave
surface elevations as a function of time at X=0.
To construct a proper NewWave profile, knowledge about
some environmental conditions for the platform location is
necessary. First of all, the design wave spectrum for the region
and the crest elevation (α) should be determined. In fact, α
represents the distance between the wave crest level to MSL.
For the Judy platform, the design wave height is 24m.
Considering a water depth of 75m and a wave period of
Tz=15s, around 56% of the wave height was assumed to stay
above MSL (α = 13.5m).
The constrained surface elevation ηc(t) could be considered
as [11]:
ηc (t) = ηr (t ) + Qe(t ) + Rf (t )
(6)
where ηr(t) is any random surface elevation from a given
spectrum, Q and R are random constants and e(t) and f(t) are
two non-random functions define as [11]:
N
e(t ) = ∑ cn . cos(ωn t )
(7)
n =1
N
f (t ) = ∑ d n . sin(ωnt )
(8)
n =1
From equations 6 to 8, with some mathematical
calculations as describe in details in [11], a solution for the
constrained surface elevation can be derived:
. . N 
N


2
2
− ρ (t ) 


η c (t ) = η r (t ) + ρ (t ) α − ∑ An + ( 2 ) α − ∑ Bn  (9)


λ
n =1
n =1




Time of Hmax
0.56
1
2
3
4
5
6
7
where the terms have the following meanings:
0.44
term 1- the original random surface elevation;
term 2- the unit NewWave;
term 3- the predetermined constrained amplitude ( α );
term 4- the original random surface elevation at t=0 (or ηr(0));
term 5- the slope of the unit NewWave;
term 6- the predetermined constrained slope; for a crest, α& =0;
term 7 - the original random surface’s slope at t=0 (orη&r (0) ).
Fig.2 The NewWave profile as a function of time
The Cnw Profile
Taylor et al. [6] showed that the NewWave can be
embedded in a stochastic time history of sea surface and be
used to estimate the extreme response of a Jack-Up in a severe
sea-state. This irregular time history of the sea surface is called
CNW (Constrained NewWave). For dynamically responding
structures, the extreme response does not always correspond to
A proper design spectrum that presents environmental sea
conditions with a certain return period should be defined for
CNW modeling and 3-hours simulations. The JONSWAP is the
most suitable spectrum for North Sea. With regard to extreme
50-years return wave period (with 24m height on west
4
Copyright © 2011 by ASME
Fig.3 NewWave with 13.5m elevation constrained in irregular wave surface
components which is represented in shorter waves riding on the
longer waves [21].
Several researchers attempted solving this problem by
methods such as Stretching and Extrapolation to rectify the
velocity and acceleration profiles of fluid. The most recognized
method is Wheeler stretching method [18]. In this research, for
selecting a suitable exact and fast method to determine the fluid
kinematics on top of MSL, available investigations were
reviewed. In some studies some Stretching method and the
linear Extrapolation method have been correlated against
available experimental data ([19, 20 and 21]). They found that
Wheeler stretching method gave velocity profiles that were
lower than the experimental results. The discrepancy was
increasing by the increase in the wave steepness. They reported
that linear extrapolation was giving results closer to the
experiments. However, the latter was very sensitive to the cutoff frequency of the wave spectrum used for generating the
irregular wave.
A simple comparison is given in Figure 4, between the
horizontal particle velocity predicted by the Airy and Stokes 5th
order regular wave theories (with no correction) and from the
NewWave predictions using Extrapolation and Wheeler
correction methods. The wave spectrum and conditions
correspond to that in the Judy Platform location and the crest
height for three theories is 15m.
Based on the discussions made above, in the current study,
the Extrapolation method was considered for calculation of
CNW and 3-hours storm irregular wave kinematics.
direction), a JONSWAP spectrum with Hs=15m and Tp=12sec
was selected as design spectrum. The same wave spectrum was
used to generate both the CNW and 3-hours simulation sea
states. In this research, 800 CNW simulations for four crest
elevations were carried out.
Correctons to the Velocity and Acceleration Profiles
While the theoretical analysis of regular waves and
hydrodynamic loading in general are fairly matured subject
areas linear waves and Stokes waves are based on perturbation
theory and provide directly wave kinematics below MSL. The
underlying kinematics of regular waves and a random sea is not
very clear in the region above the MSL. An irregular sea is
assumed to be comprised of individual linear waves randomly
super-imposed on each other. As an example, in a deep water
the horizontal particle velocity, u(t), at time t is given by:
N
u (t ) = ∑ a jω j e
kjz
cos(ω jt + θ j )
(10)
j =1
Where aj, ωj, kj , θj, and z are the amplitudes, frequencies,
wave-numbers, phases and vertical elevation of the jth wave
respectively.
However, the ek z term increases very rapidly above MSL
and can give rise to the phenomenon of “high frequency
contamination”. This inherent problem in applying linear
theory to irregular waves is well known and results in the
exponential velocity profile being highly biased towards the
higher frequency components above MSL, thereby giving
extremely large and spurious velocities further up the wave
crest. This is because the exponential term becomes very large
at higher frequency and spuriously so at higher elevations as
the baseline for all the elevation of any frequency component is
taken to be the MSL. This is true on the assumption that all
components are free. However in reality, this is not strictly so
as there exist varied degrees of interaction between the
j
Crest Occurance Time in CNW
One parameter in analyzing a structure against a CNW is
the minimum warm up time, which is necessary for the
structure and the CNW. This is the time duration from t=0 in
the structural analysis to the time that the NewWave crest
occurs (tHmax). The crest occurrence time depends on the crest
height and the dynamic sensitivity of the structural. A
5
Copyright © 2011 by ASME
MSL
Fig.5 Variations in the maximum deck displacement
against time of Hmax
then mathematically extended to reproduce the cumulative
probabilistic distribution for 100 maximum structural responses
(called here a pseudo 100 cpdf). It was assumed that the
cumulative probabilistic distribution functions of n different
simulations (FX i (x) ) are identical to each other.
Fig.4 comparison of regular & irregular wave
horizontal velocities with the same crest heights
sensitivity analysis has been performed on the Judy Platform
using CNWs to study the effects from variations in the crest
occurrence times. Four different CNWs were examined on the
platform. The maximum deck displacement was used as a
comparative index. The results are given in Figure 5 which
shows that the structural response was converged and did not
experience much change, when the crest occurrence times
exceeded 60 seconds. .
It is worth mentioning that in the analyses performed on
the platform, it has been noticed that the maximum structural
responses happened less than 10 seconds beyond the NewWave
crest occurrence. So, for the CNW analysis performed on this
platform, the NewWave crests were chosen to occur 60 seconds
behind the analyses beginning, while the total time length of
CNW analysis was considered 70 seconds.
FX 1 ( x ) = FX 2 ( x ) = FX 3 ( x ) LL = FX n ( x )
(11)
The cumulative probabilistic distributions of extreme
responses from n separate simulations ( FY ( y ) ), or the pseudo n
i
cpdf, will then be:
FYn ( y) = P[Yn ≤ y] = P[ X1 ≤ y, X 2 ≤ y, X 3 ≤ y,KK, X n ≤ y ]
[
⇒ FYn ( y ) = FX1 ( y)
]
(12)
n
The cpdf of each 3-hours simulations for the deck
displacement was obtained. For this purpose, different
probability distribution functions such as Weibull and lognormal by statistical methods Chi-square, LevenbergMarquardt and Kolmogorov-Smirnov were tested against all
responses to decide which one fits the data.The cpdfs from
separate 3-hours simulations were then compared to each other.
In general, separate cpdfs were found to be virtually identical.
Then for each cpdfs with using probabilistic method, cpdfs of n
maximum responses are generated. The 50% response
exceedence value of cpdfs was then considered as the
maximum structural response out of n 3-hours irregular storm
wave simulations. Obviously more accurate responses could be
obtained if the number of the 3-hours simulations is increased.
Probabilistic Analysis Model
Probabilistic analysis was performed to evaluate the
maximum structural responses to irregular waves. Usually
maximum structural responses of several simulations are
determined and cumulative probabilistic distribution function
(cpdf) is generated for obtaining the maximum structural
response. Then the certain response exeedence value with
engineering judgment on existing conditions obtained as the
maximum response of structure.
FAST PREDICTION METHODS
CNW Model
To avoid numerous time consuming 3-hours simulations, a
cumulative probabilistic distribution function was defined for
structural responses of a simulation. This cumulative
probabilistic distribution against single 3-hours simulation was
As it was previously stated, short duration CNW models
have found able to provide results reasonably well comparable
to those from time-consuming many hours of sea elevation
simulating. The CNW model results have then been used in a
6
Copyright © 2011 by ASME
fast predicting approach to obtain the response of the structure
to different irregular wave conditions. The method incorporates
the CNW simulation outputs and produces probabilistic nonlinear response amplitude operators. These data can then be
used for “fast prediction” of the structural response against
different wave climates. The results have seemed comparable to
those provided by scores of 3-hour simulations of irregular
storm waves. In this method, firstly a number of CNW
simulations with various wave crests, 100 simulating per each
wave crest height, are performed. The maximum structural
response (say the maximum lateral topside displacement) from
each "CNW simulation"/"wave crest height" are identified. For
each wave crest height the probabilities of various responses
(that is, responses with the likelihood 10, 20, 30,..., 90 percent)
can then be plotted to obtain probabilistic non-linear response
amplitude operator curves. Each response curve corresponds to
specific probabilities. So, the structural response against the
wave crest elevation in an irregular wave climate can
be obtained by selecting a desirable wave crest height and
introducing a random number between 0-100. The structural
response is calculated by interpolating between "probability
lines"/"crest heights" in top and down of random number.
Figure 6 indicates a sample of fixed probability displacement
response lines for the Judy platform, obtained from FPCNW
(Fast Predict of CNW) method.
response time series. This have resulted in several hundred
"wave crest height"/"response amplitude" pairs out of each 3hour simulations. It is noted that in general there exists a time
lag between the wave crest and the maximum response
incidences. The data pairs have been arranged in crest height
bins (for example elevation 4m is considered for a crest height
range between 3.5m to 4.5m). This is different from that
explained for the CNW model, where each CNW was
representing an exact wave height (crest). Once again, for each
wave crest height bin the probabilities of various response
amplitudes have been plotted to obtain probabilistic non-linear
response amplitude operator curves. Figure 7 shows the lines
with the fixed probability displacement response of the Judy
platform obtained from the FPTHS (Fast Predict of Time
History Simulation) method.
Fig.7 Constant probability lines generated from three
time history simulation results
RESULTS AND DISCUTIONS
In previous section, two fast response prediction methods
FPCNW and FPTHS have been discussed. The FPCNW
method, incorporates the CNW simulation outputs to produce
probabilistic non-linear response amplitude operators. In this
method, firstly a number of CNW simulations with various
wave crests are performed. For each wave crest height the
probabilities of various responses are then plotted to obtain
probabilistic non-linear response amplitude operator curves.
The structural response against the wave crest elevation, in an
irregular wave climate, can be obtained by selecting a desirable
wave crest height.
Fig.6 Constant probability lines generated from CNW
results with different crest
3-Hour Simulations Model
Based on the results from 3-hour simulations, another
approach has also been examined in this paper for rapid
predicting the structure response. Instead of performing 800 to
1000 CNW simulations, results from a small number of 3-hour
simulations have been used to produce probabilistic non-linear
response amplitude operators. The response time history,
resulting from an individual 3-hour simulation, has been
analysed to relate wave crest heights in the irregular water
surface time series to its concurring response amplitude in the
The FPTHS method introduced in this paper is based on
result of three 3-hours simulations. Outputs from a small
number of 3-hour simulations have been used to produce
probabilistic non-linear response amplitude operators.
In figure 8, cumulative probabilistic distribution of
displacement responses from two fast predict methods,
FPCNW and FPTHS, are compared with that from actual data
(obtained from ten full 3-hours irregular storm simulations).
7
Copyright © 2011 by ASME
Fig.8 Comparison of displacement cumulative probabilistic distribution of ten time history simulations from
Actual, FPCNW and FPTHS results
8
Copyright © 2011 by ASME
REFRENCES
These probabilistic distributions have then been used to provide
predictions for the maximum lateral displacement of the
structure subjected to a wave with 13.5 crest height. Results are
summarized in Table 2.
[1]
[2]
[3]
Table.2 Displacement response of time history
simulations from probabilistic and fast predict
methods and maximum of actual response
[4]
[5]
Displacement
R P(x)=50% from
R P(x)=50% from R P(x)=50% from
number of
pseudo 100 cpdf
pseudo 100 cpdf pseudo 100 cpdf
3-hours storms
from cpdf each
FPCNW
FPTHS
TH
maximum of
actual
response
[6]
[7]
1
0.53
0.5
0.57
0.55
2
0.55
0.48
0.4
0.36
3
0.45
0.46
0.45
0.39
4
0.52
0.49
0.55
0.63
5
0.55
0.5
0.45
0.39
6
0.58
0.47
0.54
0.45
7
0.52
0.49
0.56
0.62
8
0.52
0.48
0.53
0.61
9
0.58
0.5
0.53
0.58
10
0.56
0.48
0.4
0.42
mean of them
0.54
0.49
0.50
0.50
[8]
[9]
[10]
[11]
[12]
Table 2 shows that the predictions provided by the two fast
methods (FPCNW and FPTHS) are well close to the maximum
responses obtained from ten 3-hours simulations. In general
FPCNW, has provided predictions around 8% higher than that
from ten 3-hours simulations.
[13]
[14]
[15]
CONCLUSION
Different irregular wave simulation approaches such as 3hours storm waves and Constrained NewWave (CNW) have
been examined to predict the response of a jacket offshore
structure to the wave action. Then two fast prediction methods,
FPCNW and FPTHS, have been presented. They incorporates
the CNW and 3-hours simulation outputs respectively to
produce probabilistic non-linear response amplitude operators.
[16]
[17]
[18]
[19]
Cumulative probabilistic distribution responses of FPCNW
and FPTHS have been found to be very similar to that from ten
full 3-hours simulation results.
Predictions provided by the two fast methods (FPCNW and
FPTHS) for the maximum response under an extreme wave
event have been reasonably close to the maximum responses
obtained from ten 3-hours simulations. FPCNW, predictions
have been around 8% higher than that from ten 3-hours
simulations while FPCNW, predictions have fallen around 2%
bellow.
[20]
[21]
[22]
9
Lindgren, G, 1970: ‘‘Some properties of a normal process near a local
maximum’’ .Ann. Math. Stat., 41(6), pp. 1870–1883.
Lindgren, G, 1972: ‘‘Local maxima of Gaussian fields’’ Ark.
Mathematic, 10, pp. 195–218.
Boccotti P, 1981: “On the Highest Waves in a Stationary Gaussian
Process,” Atti Accad. Ligure Sci. Lett., Genoa, 38, pp. 271–302.
Boccotti P, 1982: ‘‘On ocean waves with high crests’’ Meccanica, 17,
pp. 16–19.
P.S. Tromans, A.R. Anatruk and P. Hagenmeijer, A New Model for
the Kinematics of Large Ocean Waves–Application as a Design
Wave, Proceedings of the First International Offshore and Polar
Engineering Conference, volume 3: Pages 64-71, 1991
P.H. Taylor, P. Jonathan and L.A. Harland, Time Domain Simulation
of Jack-Up Dynamics With Exteremes of a Gaussian Process, OMAE
Preceedings, Offshore Technology, volume IA: Pages 313-319, 1995
M.J. Cassidy, R.E. Taylor and G.T. Houlsby, Analysis of Jack-Up
Units Using a Constrained NewWave Methodology, Applied Ocean
Research, volume 23: Pages 221-234, 2001
G.T. Houlsby, Modelling of Shallow Foundations for Offshore
Structures, Department of Engineering Science, Oxford University,
2001
M.J. Cassidy, P.H. Taylor, R.E. Taylor and G.T. Houlsby, Evaluation
of Long-Term Extreme Response Statistics of Jack-Up Platforms,
Applied Ocean Engineering 29 (2002) 1603–1631
B. Bienen and M.J. Cassidy, Advances In The Three-dimensional
Fluid–Structure–Soil Interaction Analysis of Offshore Jack-up
Structures, Applied Marine Structures 19 (2006) 110–140
M. Cassidy and R. Pinna, Dynamic Analysis of a Monopod Platform
Using Constrained NewWave, Proceeding of OMAE, Vancouver,
British Columbia, 2004
Smith S.F, Hoyle M.J.R and Ahilan R.V, Noble Denton Consultants
Ltd.; R.J. Hunt, Shell U.K. Ltd.; and M.R. Marcom, Rowan
Companies, 2006: “3D Nonlinear Wave Spreading on Jack-up
Loading and Response and Its Impact on Current Assessment
Practice”.Offshore Technology Conference, Houston, Texas.
M. Cassidy, L. O’Neill and E. Fakas, A Methodology to Simulate
Floating Offshore Operations Using a Design Wave Theory,
Proceeding OMAE 2006
Hibbitt, Karlsson & Sorensen, Inc. (2007) "ABAQUS Manual".
P.Broughton, L.Silva, Design of JUDY Steel Piled Jacket Structure,
Proceeding Structural and Building Board, Structural Panel, Paper
10830, 1996
J.J. Jensen, Load and Global Response of Ships, Elsevier Ocean
Engineering Book Series, volume 4, Elsevier Science Ltd, Oxford,
UK, 2001
S.K. Chakrabarty, Hydrodynamics of Offshore Structures, Hardcover
–Jan 1, 2003
JD. Wheeler, Method for Calculating Forces Produced by Irregular
Waves, J petrol Technol, Pages: 359-367, 1970
S.F. Smith and C. Swan, Extreme Two-dimensional Water Waves:
An Assessment of Potential Design Solutions, Applied Ocean
Engineering 29 (2002) 387–416
H.J. Choi, Kinematics Measurements Of Regular Irregular And
Rogue Waves By PIV/LDV, PHD Dissertation, Texas A&M
University, 2005
N.C. Ojieh and N. Barltrop, Theoretical Modelling Of The
Kinematics of Extreme Random-Wave Event generated by Focusing,
Proceedings of the Eighteenth (2008) International Offshore and
Polar Engineering Conference Vancouver, BC, Canada, July 6-11,
2008
DNV – RP – C205, Environmental Conditions and Environmental
Loads, April 2007 Recommended Practice
Copyright © 2011 by ASME