Dynamic Response of Fixed Offshore Structures Under Environmental Loads

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11th ICSGE 17-19 May 2005

Cairo - Egypt

Ain Shams University

Faculty of EngineeringDepartment of Structural Engineering

Eleventh International Colloquium on Structural and Geotechnical Engineering

DYNAMIC RESPONSE OF FIXED OFFSHORE STRUCTURES

UNDER ENVIRONMENTAL LOADS

SHEHAB MOURAD1, MOHAMED FAYED

2, MOSTAFA ZIDAN

2,

and MOHAMED HARB3

ABSTRACT

Waves have a nonlinear behavior. Thus, the application of direct dynamic analysis on offshorestructures will face some difficulties. Therefore, some adjustments are required to the static

analysis procedure in order to account for the dynamic nature of the wave–structure system and

to present efficiently the behavior of offshore structures. A practical static approach for the

design has been proposed by calculating dynamic amplification factors that represent the

dynamic characteristics of the structure and the dynamic behavior of waves, so that it can be

applied to static analysis that utilizes the nonlinear theories of waves.

This paper presents a study of the dynamic response of fixed offshore structures under the

effect of the environmental wave forces in order to determine the Dynamic Amplification

Factors (DAFs), which will be applied to the static analysis to account for the dynamic

nonlinear behavior of waves. These factors are determined through a linear dynamic analysis

using different random wave records generated using the standard Pierson-Moskowitz spectrum

are compared. These results are compared with those obtained from a linear static analysis. The

same linear wave theory is utilized for both the dynamic and static analyses. Linear wave

theory is implemented to determine the water particle velocities and accelerations at each time

step and phase angle for each wave heading direction. However, wave forces are calculated

using Morison's equation. Three models of selected real fixed offshore structures are analyzed

to determine the effect of the dynamic nature of wave loads when applied at different angles,

and to determine the corresponding DAFs for both base shear and overturning moments. The

values of DAFs computed by a single sea-surface profile (single seed) and those calculated

using a combination of a number of possible sea surface profiles (multi seeds) were compared.

The obtained DAFs were compared with those determined from the approximate formula. Thestudy includes the effect of marine growth on both the wave response analysis and on the

generated stresses in members obtained from static inplace analysis, and its effect on DAF

values. The results showed that the general tendency of the value of a DAF is to be inversely

proportional to the ratio of the wave period to the platform period. In addition, useful

conclusions were discussed

Keywords: Dynamic Amplification Factors, Dynamic Response, Offshore Structures, Marine

Growth, Wave Spectrum.

1Associate. Professor, Faculty of Engineering, Ain Shams University, Cairo, Egypt.

2 Professor, Faculty of Engineering, Ain Shams University, Cairo, Egypt3 B.Sc, M.Sc, Senior Structural Engineer – Offshore Structures



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1. INTRODUCTION

Offshore structures are designated to those structures that are constructed off the shore in the

sea or the ocean water that are used as platforms for installing the drillers and necessaryequipment for extracting petroleum. A fixed offshore structure is a platform extended from the

sea surface and supported on the sea bed either by deep piles or by gravity footings, API WSD

21st Edition (2000). Jacket type structures are considered the classical configuration used for

offshore platforms; it is suitable up to 200 meters water depths. Jacket structures are formed of

main tubular legs braced by tubular members to transfer the lateral environmental forces to the

foundation piles. Number of legs varies from three up to 8 leg jackets. Piles can be connected to

the jacket by two ways. The first is directly inside the jacket leg which is used for shallow to

moderate water depths. The second method is by using external pile sleeves which is widely

used for deep water jackets, CIRIA (1977). Piles are normally grouted through the inner length

of legs and pile sleeves. In some other cases, piles are only welded at the top of the legs using

what is named ‘crown shim plates”, without being grouted through the legs. A typical fixed

offshore compound – North Sea, UK, is shown in Fig. 1.

Fig. 1: Typical fixed offshore compound – North Sea, UK

The nature of such structures makes it different from others in the sense of types of loading

conditions that they are imposed to. In addition to typical dead loads, live loads and equipment

operating loads, it is exposed to different loading conditions that results during transportation,

launching and installation prior to the final positioning and start of operation. In addition,during operation, such structures are imposed to environmental loads that appear in such certain



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environment, as wind loads, wave loads, current loads, and seismic loads. Since such loads

have a cyclic and dynamic nature, fatigue phenomenon can cause significant effects. The

design criteria of offshore structures was originally based on twenty five and fifty years as

operating storm conditions till the early sixties of the last century when HILDA hurricanes

attacked the gulf of Mexico with wave heights reaching 42 feet (12.8 meters) accommodatedwith wind gust speed of 200 mph (89 m/s). As a result of this hurricane more than 11 platforms

were destroyed. Engineering research centers such as the American Petroleum Institution “API”

started to reconsider the design basis of offshore structures and to develop new criteria based on

1 year and 100 years operating storm conditions with appropriate considerations for the applied

factors of safety against each case. Although the applied loads are of dynamic nature, the

practical approach of analysis of fixed offshore structures under the operating environmental

forces is performed using the normal static analysis (in-place analysis) in order to be able to

include the nonlinear foundation effect and to utilize high order nonlinear wave theories.

Therefore, the study of the dynamic behavior of offshore structures and their response to

different dynamic loads applied during the operating lifetime of the platforms, are of great

importance to be able to calculate a proper dynamic amplification adjustment factors which are

applied with the calculated static wave forces to assure that the overall structural integrity will

be able to sustain the dynamic effect of the applied wave and current forces. The study carried

out in this paper is focused on studying the dynamic and static behavior of fixed offshore

jackets under the operating wave and current loading conditions using linear wave theory, to

obtain the Dynamic Amplification Factors (DAFs) due to the response of the structure-wave

system, in order to apply them to in-place static analysis utilizing nonlinear wave theory to get

the final stresses in the structural members. The study is applied to three models of selected

real fixed offshore structures. The effect of marine growth on both the wave response analysis

and the generated stresses in members obtained from static in-place analysis, and its effect on

DAF values, was investigated.

2. WAVE THEORIES

The true water surface profile is complex and nearly impossible to be described mathematically

due to the infinite number of interferences and nonlinearities. Thus, it is not possible to have

one theory that can mathematically describe all the possible conditions of the sea water surface.

Linear wave theory, alternatively known as Airy wave theory, was developed in 1845 based on

Laplace theory. It is considered as the most important of the classical theories because it forms

the basis of the probabilistic spectral description of waves, Fayed (1999). The Linear wave

theory is based on a sinusoidal representation of the wave profile, as shown in Fig. 2, and it

provides a first approximation to the wave motion. In order to approach the complete solution

more closely, consideration of a perturbation procedure through successive approximations was

developed. Such method was used by Stoke’s in 1847, and more recent contributions to the

description of Stoke’s wave theory include those of Yamaguchi and Tsuchiya (1974) and

Barltrop, et al (1991). Stoke’s and others solved the problem by a successive approximation

procedure in which the solution was formulated in terms of a series of ascending order terms.

Solutions are widely available in the open literature, Sarpkaya and Isaacson (1981). Stoke’stheory becomes cumbersome and impractical for long waves of finite heights. Linear wave



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theories cannot be applied on shallow water zones where waves become less sinusoidal.

Numbers of alternative theories were developed for this case; they include the analytical ones

such as Solitary and Cnoidal Wave theories, and the numerical ones such as the Stream

Function Wave theory. However, the numerical theories are also applicable for deep water of

finite height, but they are of special interest for shallow water because of the limitation of smallamplitude wave theories. The Cnoidal theory is suitable for the shallow water depth (d/L < 1/8).

The Solitary Wave theory can be considered as a special case of the Cnoidal theory since it has

an infinite wave length and the crest lies wholly above the water level. In the Cnoidal theory the

crest becomes more pointed and the trough more flattened, CIRIA (1977). The typical profile of

the Cnoidal wave is shown in Fig.3.

Fig. 2: Sinusodial wave profile Fig. 3: Cnoidal wave profile

The problem of selecting the wave theory for a particular application invariably arises in

engineering situations. This difficulty can not be resolved since for specified values of H, d,

and wave period (T), different wave theories might better reproduce different characteristics of

interest and there can be no unique answer, Reddy and Arockiasamy (1991). API WSD 21st

edition (2000) and API LRFD (1993) present a graphical representation of the zones of

application of different wave theories function on the water depth, the wave height and the

wave period. The graph was modified by API task group. Such graph is widely used in the

analysis and design of fixed offshore structures.

2.1 Linear (Airy) Wave Theory

As shown in Fig. 4, the vertical axis of the equations is measured positive from the mean-water

level upwards. The general potential function ),,( z y xΦ satisfies Laplace equation:

02

2

2

2

=Φ

+Φ

y x δ

δ

δ

δ (1)

The horizontal and vertical velocities can be then expressed respectively as:

yv xu δ

δ

δ

δ Φ

=

Φ

= , (2)



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The Potential equation can be expressed in general as:

)sin()cosh(

))(cosh(

4t xk

kd

d yk T H g ω

π −

+=Φ (3)

where:

H= 2a = wave height in meters

k=(2π /L) = wave number

ω=(2π /T) = wave frequency

T = wave period in seconds.

The equation of the free surface η (t) can be expressed as a function in the time (t) as follows:

Fig. 4: Airy wave equation's parameters

t x H

−=T L

t π η 22

)( cos (4)



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2.2 Random Wave Theories

Random wave theories can model the general properties of the real sea much more closely than

the regular theories. Unfortunately the theories are based on the linear (Airy) wave theory, and

therefore, the nonlinearity, which is usually included in higher order wave theories, is not

included in random wave theories. The designer shall envisage which is more important for a

specific structural analysis, nonlinearity or randomness of the sea, or to envisage a practical

way to compromise between the two analyses. For example, in deep water, the structure may

often be subjected to seas with significant energy at longer period, and in these cases, a random

analysis is not easy to avoid, in addition to the need for better understanding of the behavior of

structures in extreme seas, Barltrop and Adams, (1991). Random Wave theory involves taking a

water surface elevation spectrum and building up the resulting particle kinematics, loadings,

and response, from the summation of the effect of different frequencies. This can be performed

using a time domain or a frequency domain approach which is explained in more details

hereinafter in the wave spectrum section.

3. WAVE SPECTRUM AND FORCES

If a time history is made for waves passing a point in the ocean, the resulting trace can be in

principle be viewed as a summation of a large number of regular sinusoidal wavelets, each

superimposed on the other. Such presentation of wave was found, theoretically and

experimentally, to be a much better model for the real sea surface representation, and in

particularly useful for the dynamic response analysis of offshore structures under

environmental sea loads. Therefore, the water surface and particle kinematics are the

summation of wavelets of various amplitude phases and periods. The amplitude content of various frequencies can be represented by a spectrum. The phases are assumed to be random

and uncorrelated between frequencies.

3.1 Pierson-Moskowitz Spectrum

Pierson-Moskowitz (1964) spectra (B/P-M) is commonly used to determine the wave spectrum

based on known values for the significant wave height (Hs ) and mean zero crossing period (Tz).

The general equation of the PM spectrum is given by Eq. 5 and presented in Fig. 5.

π−

π= −ηη 4

z54z

2

s )fT(1expf T4

H)f (S ( 5 )

Fig. 5: Pierson-Moskowitz spectrum



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3.2 Morison's Equation

The wave induced loading on a structure is a result of pressure field produced by the wave. A

number of separate mechanisms have been identified within this phenomenon. There is the drag

force, which is proportional to the first approximation of the frontal area of the body and the

square of the flow velocity. There is the inertia force that is proportional to the acceleration of

flow and volume of the structure. Morison’s equation application is limited to the assumptionthat water motion is unaffected by the presence of the structure itself. Morison’s Equation can

be expressed in the following form:

( ) •∗∗∗+∗∗∗∗= U AC U U DC F md ρ ρ 2/1

(6)

where: F = The force in the direction of velocity per unit member length. ρ = The water mass density.U = The water particle velocity normal to the member.

•U = The water acceleration normal to the axis of the member.

D = The member outer diameter.

A = The area of the member = π D2

/4.Cd = The drag coefficient

Cm = The inertia coefficient

4. ANALYSIS OF MODELS

Three models of fixed jackets are selected form real projects approved and installed in the

desired offshore locations. The configurations of models are shown in Figs. 6-8, while the

description of models is summarized in Table 1. It can be noted that only the third model

has 15 drilled conductors of 660 mm diameter each. The analysis of this study is divided

into linear dynamic response analysis compared with linear static analysis using Linear wave theory, to determine the proper DAF values. Then, a final static in-place analysis,

using Stoke’s high order wave theory and applying the calculated DAF, is carried out to

obtain the final member stresses under the applied wave and current loads. The software

used in analyzing the mathematical models is SACS commercial software release 5 which

is widely used in the analysis of offshore structures. SACS-IV program is capable of

performing various types of analysis starting from normal static in-place analysis and

ending with the sophisticated types of analysis such as fatigue analysis, transportation,

nonlinear collapse, and dynamic response analyses. Wave and current parameters are

extracted as per the installation zone meteorological data of each jacket location. The Cd and Cm values are considered as per API (2000) to be 0.65 and 1.6, respectively. The same

values of wave parameters are applied in three directions ±0o, ±45o and ±90o (X, XY, and

Y) with the associated current parameters having the same direction of wave application.

For each wave direction, five different generated wave records (seeds) were applied to each

model, and the results of each seed is extracted and tabulated, calculating the vector base

shear and base moment for the dynamic and static forces at each time step. The Dynamic

Amplification Factor “DAF” at each time step is determined by dividing the dynamic base

shear and moments by the static base shear and moments. Then, the median value is

calculated for the whole set of time steps for each wave record, which will give the DAF

value for this specific applied wave and direction.



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Fig. 6: Model 1 Fig. 7: Model 2 Fig. 8: Model 3

Table 1: Models Description

Model 1 Model 2 Model 3Water

depth:90 m 59 m 59.5 m

N u m b e r o f l e g s ,

a n d l e g d i a m e t e r

Four vertical legs (no leg

inclination) with an average

diameter of 1400 mm.

Four battered (inclined) legs

with slope 1:10 of average

diameter of 1180 mm.

Four legs, of averagediameter of 1330 mm, 2 of

them are battered in both

directions with slope 1:10

and the other 2 legs are

inclined in one direction

with a slope of 1:8

D i m e n s i o n s 22.5 x 22.5 m overall

dimension at Deck junction

elevation +22.0m above sea

water level, Pile sleeves are

spaced 45 x 45 m

16 x 16 meters overall

dimension at Deck junction

elevation +7.50 m above sea

water level, and 29 x 29 m at

sea bed

14 x 14 meters overall

dimension at Deck

junction elevation +7.50 m

above sea water level, and

22 x 22 m at sea bed

F o u n d a t i o n

Pile soil interaction is

represented by four

prismatic equivalent pile

stubs having: Length = 25

m, Section Area = 9000

cm2, Inertia Iz = Iy =

3.213x107cm

4


represented by four


stubs having: Length = 9 m,

Section Area = 297.62 cm2,

Inertia Iz = Iy = 1429700cm4


represented by four


stubs having: Length =

13.4m, Section Area =

524.82 cm2, Inertia Iz = Iy

= 3222500.0 cm

4

Jacket

steel

weigh29400 kN (without piles) 8177.79 kN (without piles)

15472.55 kN

(without piles) )

Deck

weight 191296 kN 1564 kN 14824 kN



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dynamic and static results are computed and given in Table 3 for each wave direction applied

on each model.

Table 3: Wave Response Results

Wave

Direction

Wave

heightH s (m)

Dominant

period Tz (sec)

Number of Air

wave components(linear wavelets)

Number of

response analysistime points

0o 13.2 10.5 261 525

45o 14.7 11.1 276 555

First

Model

90o 16.1 11.6 289 580

90o

8 9 449 900

137o

6.8 8 399 800

Second

Model

180o

5.8 7.5 374 750

180o 8 9 449 900Third

Model 230o

6.8 8 399 800

5. ANALYSIS RESULTSThe results of the first six free vibration periods are given in Table 4 for the three models. The

highest 25 values of base shear and overturning moments from both dynamic and static analysis

for the five seeds for each direction and model were obtained. Figure 9 shows those values for

the first model when the wave direction was zero

Table 4: Modal Analysis ResultsModel 1 Model 2 Model 3

Mode Freq. Hz

(CPS)

Period T

(sec)

Freq. Hz

(CPS)

Period T

(sec)

Freq. Hz

(CPS)

Period T

(sec)

1 0.399 2.508 0.703 1.422 0.379 2.637

2 0.399 2.506 0.726 1.377 0.455 2.196

3 0.526 1.901 1.072 0.933 0.803 1.2464 0.847 1.181 1.700 0.588 1.275 0.784

5 0.848 1.179 1.777 0.563 1.313 0.762

6 1.468 0.681 3.289 0.304 2.008 0.498

Fig. 9: Dynamic & static base shear and overturning moments for 5 seeds of first model withwave angle 0o

DYNAMIC AND STATIC BASE SHEAR - 5 SEEDS - MODEL 1 SW - 0 DEG

0

500

1000

1500

2000

2500

3000

3500

1 5 9 1 3 1 7 2 1 2 5 2 9 3 3 3 7 4 1 4 5 4 9 5 3 5 7 6 1 6 5 6 9 7 3 7 7 8 1 8 5 8 9 9 3 9 7 10 1 1 05 10 9 1 13 1 17 12 1 1 25

POINTS OF MAXIMUM BASE SHEAR FROM 5 SEEDS

B

A

S

E

S

H

E

A R

( K

N

)

Dyn . BS S tc . BS

Dynamic & static Base Shear, 5 Seeds

DYNAMIC AND STATIC MOMENTS - 5 SEEDS - MODEL 1 SW - 0 DEG

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125

POINTS OF MAXIMUM OVER TURNING MOMENT FROM 5 SEEDS

M

O

M

E N (

K N

. M

)

D yn . M S tc . M

Dynamic & static overturning moment, 5 Seeds



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The Dynamic Amplification Factors "DAFs" are calculated by dividing the base shear or the

overturning moments resulted from the dynamic analysis by those resulted from static analysis

for each time step, for each seed. It was observed that the DAF value can reach a high value as

50, as shown in Fig. 10. However, that does not reflect the case that forces generated from the

dynamic nature of waves can reach 50 times those resulted from static wave force, since suchhigh value can occur due to outliers that results at an instant of time where the static base shear

or overturning moment is very low whereas that resulted from dynamic analysis is within an

average value. Therefore, if the "arithmetic mean" of the DAFs is chosen to represent the

whole values of DAF from a certain seed, that will result in an unrealistic value due to the

presence of outliers.

DAF Base Shear - SEED1 - Model 2 PP1 - 180o

0.000

5.000

10.000

15.000

20.000

25.000

30.000

35.000

40.000

45.000

50.000

1 28 55 82 109 136 163 190 217 244 271 298 325 352 379 406 433 460 487 514 541 568 595 622 649 676 703 730 757 784 811 838 865 892

Analysis Time Steps

D A F

=

( D y n .

B S

/ S t c B S )

Fig. 10 : DAF for base shear against time step form single seed

In order to remove the effect of the outliers different statistical representation for the central

tendency of the results, the median is to be implemented. The "median" is calculated instead of

the arithmetic mean as it represents the middle value of the array of numbers, i.e. half of thevalues which are greater than or equal to the median, and the other half of the values are less

than or equal to it. In this way, the effect of outlier will be eliminated. Three cases of study for

a descriptive statistical normality test has been performed on the results of the first SEED

applied on the second model results, using Anderson-Darling normality test to verify that the

median lies within a proper confident interval. The confident interval indicates how certain

does the calculated parameter represent the specific percentage of the population. i.e. 95%

confident interval for the median means that the upper and lower limits of this interval

represents not less than 95% of the results. The results are summarized in Table 5. The median

value of all time steps is calculated for each seed to represent the overall DAF of a single particular seed (a seed is a particular group of Linear Airy wave components that represents



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Table 5: Median values of DAFs and confidence intervals for first SEED at different

angles for second model

Study CaseNo. of

pointsMean

Standard

DeviationMedian

95%

Lower

95%

Upper

PP1-90-BS-STUB 747 2.425 4.955 1.327 1.261 1.3956

PP1-137-BS-STUB 800 2.228 7.033 1.157 1.108 1.201

PP1-180-BS-STUB 900 1.907 3.618 1.114 1.0737 1.1504

the random sea surface profile). The ''Max 25x5'' value for the DAF is calculated by selecting

the highest 25 values of DAFs for base shear and overturning moment from each seed and

determining the median for those highest values, that will represent ''Max 25x5''. It can be noted

that this method produce more conservative results for DAF values. The calculated DAF values

for both base shear and overturning moment for each seed, direction, and model, with the

corresponding ''Max 25x5'' DAF values are given in Tables 6-8.

Table 6 : DAF values for model 10

o45

o90

o

Seed DAF for

moment

DAF for

base shear

DAF for

moment

DAF for

base shear

DAF for

moment

DAF for

base shear

1 1.184 1.219 1.084 1.085 1.092 1.089

2 1.178 1.164 1.065 1.060 1.109 1.082

3 1.151 1.150 1.079 1.084 1.122 1.113

4 1.208 1.206 1.082 1.081 1.083 1.077

5 1.185 1.152 1.058 1.050 1.105 1.093

Max 25x5 1.218 1.238 1.11 1.122 1.129 1.142

Table 7 : DAF values for model 2180

o137

o90

o

Seed DAF for

moment

DAF for

base shear

DAF for

moment

DAF for

base shear

DAF for

moment

DAF for

base shear

1 1.119 1.114 1.133 1.157 1.225 1.327

2 1.139 1.137 1.141 1.162 1.219 1.285

3 1.139 1.155 1.111 1.121 1.252 1.331

4 1.095 1.116 1.13 1.142 1.264 1.347

5 1.136 1.13 1.132 1.137 1.313 1.406

Max 25x5 1.147 1.16 1.15 1.171 1.456 1.565

Table 8 : DAF values for Model 3180

o230

o

Seed DAF for

moment

DAF for

base shear

DAF for

moment

DAF for

base shear

1 1.484 1.370 1.614 1.483

2 1.415 1.352 1.711 1.591

3 1.396 1.320 1.619 1.524

4 1.437 1.324 1.742 1.608

5 1.422 1.300 1.626 1.496

Max 25x5 1.550 1.499 1.618 1.572



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The results of the main analysis shows that the general tendency of the values of the DAFs

is to be inversely proportional to the ratio between the wave periods (Tz) to the platform

fundamental period (T p) as presented in Table 9, that shows the values of DAFs for base

shear of the three models with different wave periods.

Table 9: Effect of wave periods on the DAF values

Model 1 Model 2 Model 3

Tz / Tp DAF Tz / Tp DAF Tz / Tp DAF

4.2 1.238 6.33 1.16 3.40 1.499

4.4 1.122 5.62 1.171 3.03 1.572

4.63 1.142 5.27 1.565

5.1 Comparison of DAF Values

The obtained DAF values from the previous analysis were compared with those obtained from

the approximate equation that is usually used in practice when the jacket first natural period is

less than 2.5 sec. The approximate equation is based on the fact that waves has a dominate

period (T) and the jackets vibrate mainly in the first mode with a period (T P ), with a damping

ratio (β) that is usually taken 0.02. The approximate equation is given by;

=

−=

+=

T Tp B

T Tp A

B A DAF β 2,1,1

2

22(7)

Table 10, presents the variation in the DAF values calculated by the approximate equation as

compared to the DAF values obtained from the analysis for the Overturning Moment (OTM)

and Base Shear (BS). These values are based on the results of a single seed. It can be noted that

the values obtained from the analysis are higher than those obtained by the equation, even for

the second model whose fundamental period (1.42 sec) is less than 2.5 sec, a case for which

the approximate equation is applicable. It is clear that there is a difference in case of simple

hydrodynamic configuration (jackets without conductors or boat-landing) such as models 1 and2, that can reach up to about 15%, while there is a significant difference for jackets having

hydrodynamic force collectors such as boat-landings and conductors which is the case of model

3, and can reach up to about 35%.

Table 10: Comparison of DAF values calculated by various methods.

DAF

(from analysis)Model H T Tp

DAF

(Approximate

Equation)DAF

OTM

%

difference

DAF

BS

%

difference

1 13.2 10.5 2.508 1.061 1.184 11.6 1.219 14.8

2 8 9 1.422 1.026 1.119 9.11 1.114 8.573 8 9 2.637 1.094 1.484 35.6 1.378 25.2



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5.2 Effect of Marine Growth

The marine growth phenomenon was not considered in the main analysis as it was preferred to

be studied as a separate case in order to demonstrate its effect on the jacket stresses and the

DAF values. Tables 11 and 12 summarize the stresses Unity Check (U.C.) ratios of the jacket

members with and without marine growth. Table 11 presents the (U.C.) calculated considering

the marine growth against the (U.C.) without marine growth. As can be noted from Table 11,

the marine growth can cause an increase in the stress Unity Check (U.C.) ratio for splash zone

members that can reach up to 6% in model 1. However, due to the existence of conductors that

attract more hydrodynamic forces in model 3, the unity check stress increased to 13% for

members at plash zone in model 3, Table 12. The increase in marine growth has insignificant

effect on DAF values for overturning moments and base shear, as can be noted from Table 13.

Table 11 : Stress U.C. comparison with marine growth for model 1

Face LocationU.C.

without marine

growth

U.C. withmarine

growth

% increasedue to marine

growth

Lower leg part 0.24 0.28 4%1

Splash zone members 0.08 0.14 6%







Table 12: Stress U.C .with and without marine growth for Model 3

Face Location

U.C.

without

marine growth

U.C. with

marine

growth

% increase due to

marine growth

Lower leg part 0.14 0.2 6%

Lower x brace 0.11 0.17 6%1













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Table 13: Effect of marine growth on the DAF values

With marine growth Without marine growth

Model DAF for Overturning

moment

DAF for

Base shear

DAF for Overturning

moment

DAF for

Base shear

1 1.153 1.153 1.150 1.1502 1.091 1.073 1.090 1.070

3 1.410 1.320 1.401 1.310

6. CONCLUSIONS

The effect of the dynamic nature of wave loads on fixed offshore structures was investigated on

three different real models. The wave records were generated to have a matched spectrum to

Pierson-Moskowitz Spectrum with different significant wave heights and a mean zero crossing

period that are applied at different angles. Both static in-place analysis and dynamic analysis

was carried out to determine the Dynamic Amplification Factor (DAF) for both overturning

moment and base shear. The effect of marine growth was investigated on both the stress unity

of members and the DAF values. From the results of the presented study in this paper, the

following conclusions can be drawn:

1- The general tendency of the value of the DAF is to be inversely

proportional to the ratio between the wave period to the platform

fundamental period. the dynamic effect of waves with shorter periods

is significantly greater than waves with longer period, considering that

the probability of occurrence of such short period waves is higher thanlonger period waves. Therefore, the study of the dynamic behavior of

the structure under such waves is of significant importance regarding

the degree of dynamic amplification expected rather than static stresses

which will be much less than the stresses generated from longer period

waves.

2- Comparing the DAF values obtained from the approximate equation

and those obtained from the dynamic analysis, it was noted that the

approximate equation underestimates the DAF values by about 15%

and 10% for first model and second model, respectively, while there isa significant underestimation that can reach 35% for jackets having

quite complex hydrodynamic configuration such as the third model.

3- Calculation of the Dynamic Amplification Factors using multi Seeds

by selecting the maximum forces from each seed gives more

conservative values than the ones calculated from a single Seed.

4- The Use of the median values of the resulted DAFs from a single seed

gives a better representation for the DAF, since it was proven that the

median value lies within a 95% confidence interval, rather than the

arithmetic mean, that can represent a misleading value due to theexistence of outliers.



E05SR26 16

5- The existence of marine growth that can be accumulated with time has

a significant effect on increasing stress check unity, especially for

members at splash zone. In case of jackets that has complex

hydrodynamic configurations, however, it was found that the marine

growth has insignificant effect on the DAF values.

REFERENCES

[1] API (American Petroleum Institute) recommended practice 2A-WSD (RP 2A-WSD) 21st

edition (2000) for design of offshore structures, USA.

[2] API (American Petroleum Institute) recommended practice RP 2A-LRFD – Load

Resistance Factor Design - First edition, July 1993 for design of offshore structures, USA.

[3] Barltrop, N. D. and Adams, A. J. (1991), “Dynamics of Fixed Marine Structures”, 3rd

edition, Marine Technology Directorate Limited, Epsom, U.K.

[4] CIRIA (1977) “Dynamics of Fixed Marine Structures”, methods of calculating the dynamicresponse of fixed structures subjected to wave and current action, Underwater Engineering

Group report, UR8, U.K.

[5] Fayed, M. N., (1999), “Static and Dynamic Response of Offshore Structures to

Environmental Loading”, State of the Art Report – Faculty of Engineering, Ain Shams

University - Cairo.

[6] Pierson, W. J., and Moskowitz, L. (1964), “A Proposed Spectral form For Fully Developed

Wind Seas Based on the Similarity Theory of S.A. Kitaigorodskii” J. of Geophysical

Research, December, Vol. 69.

[7] Reddy, D. V., and Arockiasamy, M. (1991), “Offshore Structures”, Krieger Publishing

Company, Malabar, Florida, USA.

[8] SACS-IVTM (Structural Analysis Computer System). A computer software for design andanalysis of offshore structures by Engineering Dynamics Incorporated (EDI), Ver. 5.1,

2004. For more details, consult http://www.sacs-edi.com/.

[9] Sarpkaya, T. and Issacson, M. (1981), “Mechanics of Wave Forces on Offshore Structures”

Chapter 4, Van Nostrand Reinhold Co., The Netherlands, 1981.

[10] Yamaguchi, M., and Tsuchiya, Y. (1974), “Relation between Wave Characteristics of

Cnoidal Wave Theory”, Derived by Latione and Chappelear, Bull. Disaster Prev. Res. Inst.,

Kyoto Univ., Vol. 24, PP. 217-231, Japan.

Dynamic Response of Fixed Offshore Structures Under Environmental Loads

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