DESIGN OF OFFSHORE CONCRETE GRAVITY PLATFORMS

DESIGN OF OFFSHORE CONCRETE GRAVITY

PLATFORMS

Amaziah Walter Otunyo

Department of Civil and Environmental Engineering, University of Port Harcourt, PortHarcourt. (Email: [email protected])

Abstract

This technical note reviews the design parameters employed in the design of off-shore concrete gravity platforms for the storage of crude oil and gas in the oil andgas industry. Manufacturing and construction methods are discussed. Currenttrends in construction are also mentioned. The paper carefully illustrates how theprincipal Environmental loads (wind and wave), current forces, loads from ice andloads from earth-quake for (earth-quake prone zones) are deployed to archive thedesign and construction of offshore concrete gravity platforms. Two design meth-ods (Analysis and Design of Shell structures) and the Tangent Modulus Methodsof design of Offshore Concrete Gravity platforms are discussed. Finally, founda-tion design of Offshore Concrete Gravity Platforms, the advantages of concreteoffshore structures over steel platform are discussed The paper is concluded withan example problem by the author to demonstrate the response of concrete gravityplatforms to wave loading.

Keywords: concrete gravity platform, offshore, foundation design, manufacturing,construction

Introduction

Offshore platforms are mainly related tothe provision of services for the oil and gasindustry, the sulphur industry utilizes themalso. The discovery, in 1969 of the Ekofiskoil field in the North Sea, signaled the begin-ning of the development of concrete offshoreoil platforms. The first such gravity platformis the Ekofisk oil storage tank. Off shore plat-forms are used to support production drillingequipment and processing equipment, includ-ing compressors, storage, and pumping equip-ment. Many of the dead loads imposed, there-

fore involve vibratory and dynamic loading.Mass is therefore, a desirable feature in thedeck structure.

Manufacture and Construction

Almost all structures designed for sub-merged or floating service have a commoncharacteristic. They are extremely large andmassive. This poses a serious problem formanufacture and construction. As result con-structors have evolved some extremely inge-nious methods for manufacturing, launching,

Nigerian Journal of Technology Vol. 30, No. 1, March 2011.

Design of offshore concrete gravity platforms 35

Figure 1: Launching.

assembly and final installation. A brief reviewof a number of these methods is as follows:

(a) Construction of the base in a dewateredbasin. Many of the largest concrete struc-tures have been cast in a basin, whichis later flooded and the structure floatedout. In some areas, basins may be ex-cavated, kept dewatered during construc-tion, then flooded and an access channeldug to the waterway.

(b) Submergence to a minimum freeboard inorder to mount the deck which is floatedin over the top. Many methods have beendevised to ease submergence.

(i) Launching: Many concrete barges andcaissons have been constructed onlaunching ways, and slid down the waysto flotation in the water. One methodis to employ a launching cradle, whichrides down the inclined slope, whilekeeping the barge or caisson level. An-other method is to build the barge orcaisson on the level at the head of theslope and then rotate it, by jackingbeams, to the inclination of the ways.(See fig. 1).Tidal launching: A large number of con-crete structures have been launched bymaking use of the tidal rise, either aloneor in conjunction with other methods.

(ii) Successive basins: A system used suc-

cessfully for a number of very large con-crete caissons has been as follows:(a) The first lift, including bottom

plate, is constructed in a tidal zone,so that it may float of as a unit athigh tide. Then it is moved to a pre-pared under-water basin, where it issunk onto a level bed of gravel orsand at a depth just sufficient to ex-pose the top of the walls at low tide.

(b) A second lift is poured, and, if nec-essary, the unit moved again. Thusprogressively the unit is floated athigh tide, sunk in a new basin atlow tide, and then its walls are con-structed to a higher stage (See fig2).

(c) Ballasting down to the sea level.(d) Penetration and final founding by

over-ballasting, and placement ofscour protection.

Current Construction Trends

(1) Pre-casting of large segments of base androof structures, these are tied by stirrups,transitions or other means to the cast inplace concrete so as to perform compos-itely.

(2) Prefabrication of piping and mechanicalsystems in modules or packages that canbe set into the structure by cranes or der-ricks during the construction operations.

(3) Integration of various conduits for oil, bal-last water, and ventilating air into theconcrete structure as formed ducts.

(4) In softer and cohesion less soils, sinking ofthe structure into the sea floor by a combi-nation of over-ballasting, jetting and air-lifting.

(5) Use of high strength concrete to reduceweight.

(6) Use of lightweight concrete for certain up-per portions of the structure, e.g. roofs

Nigerian Journal of Technology Vol. 30, No. 1. March 2011.

36 A. W. OTUNYO

and shafts. This should be carefully se-lected for high strength.

(7) Use of internal pressurization to re-duce excessive hydrostatic pressure dur-ing deep immersion for deck mountingand installation at the site.

(8) Use of temporary additional buoyancytanks, either steel or concrete to maintainstability during the critical process of sub-mergence across the top of the base.

Design Considerations

Environmental loads

Waves and winds are the two principal en-vironmental loads considered in the design ofoffshore platforms. The design environmen-tal loads are normally based on environmentalconditions which have a recurrence period of100 years, and the design life time of offshorestructures is about 20 - 30 years. A semi-empirical approach is used to evaluate waveloads on offshore structures. The derivativesof a theoretically derived flow potential func-tion are combined with empirical drag andinertia coefficients to predict wave forces onstructural components relative to the positionof the wave. There are two methods of evalu-ating the wave loads on a fixed offshore struc-ture. (a) design wave method (b) spectralanalysis method.

Wave loads by design wave method

This is a static method. The load valueis derived from the passage of a single regu-lar wave of given height and length past thestructure. The most commonly used wave pe-riod for the North Sea is 15 secs, and the pe-riod which causes the worst loading is used.Currently a 20 secs limit on wave period isrecommended.

Wave loads by wave response spectrummethod

Spectral analysis has frequently been usedto predict maximum wave forces responses asan alternate to the deterministic design wavemethod. This method is very suitable forgravity structures where the initial wave forcesdominate. Spectral methods are useful wherenonlinear, drag loads are small compared tothe linear inertial loads. Therefore, a linearrelationship exists between wave heights andwave force for a given period.

Wind loads

The force exerted by wind on an offshorestructure is a function of three basic parame-ters the wind velocity, the orientation of thestructure, and the aerodynamic characteris-tics of the structure and its members. Thewind force exerted on a structure consists oftwo components, one parallel to the directionof travel of the wind and the other perpendic-ular to the direction of travel of the wind.

FD = C12d ρV

2ZA −→ (force parallel to wind)

This is also called Drag force and this tendsto tilt the structure and is responsible for alarge percentage of the overturning moment.

FL = C12LρV

2ZA −→ (force perpendicular

to wind, tends to lift the structure)

Cd = drag coefficientCL = lift coefficientρ = density of the airVZ = wind velocityA = Area perpendicular to wind velocity.

The wind velocity is not constant because ofthe shear forces with the earth’s surface; itis zero at the surface and increases exponen-tially to a limiting maximum speed known asthe gradient wind. Over water the wind speedat any elevation is represented by the one-seventh power law.



Figure 2: Successive basins.

VZ = Vref

(ZRef

)1/7Vref = the wind speed at a height of 30

ft (Usually the customary elevation for suchmeasurements)

Z = desired elevation in ft.

Ref = the reference height (30ft).

The wind effects on all parts of the above-water structure should be calculated. The twokinds of wind speeds are normally considered.

(a) Sustained wind speed, which is defined asthe average wind speed during the timeinterval of one minute;

(b) Gust wind speed, which is defined as theaverage wind speed during a time intervalof 3 sec. The gust factor is that multi-plier which must be used on the sustainedwind speed to obtain the gust speed, orthe fastest - mile velocity. The averagegust factor, F10, at the 30ft elevation isin the range 1.35 - 1.45.

Another commonly accepted formula forcalculating the wind force is

F = KV 2CsA

Where,F = wind forceK = constantV = design wind speedCs = shape coefficientA = projected areaK = 0.00256 (lbf,mile/hr, ft2)Typical shape coefficients, for all angles of

wind approach could beBeams Cs = 1.5Slides of Buildings Cs = 1.5Cylindrical Sections Cs = 1.0

Shielding coefficients

Shielding coefficients may be used with carewhen, in the judgment of the designer, an ob-ject lies close enough behind another to war-rant the use of such coefficients.


38 A. W. OTUNYO

Current forces

Two major components of the current areconsidered: tidal current and wind driven cur-rent. It is generally accepted that the winddriven current at the still water surface maybe taken as 1% of the sustained wind speedat 30 ft (10m) above the still water level. Thecurrent velocity should be added vectoriallyto the wave particle velocity before computingthe drag force. Because drag depends on thesquare of the horizontal particle velocity, andbecause the current decreases with slowly withdepth, a comparatively small current can in-crease drag significantly. In design, the max-imum wave height is sometimes increased by3 - 4% to account for the current effects andthe current per se is neglected.

Loads from ice

In areas prone to snow, the structure shouldbe designed to resist all static and impactforces from ice. In all locations where thehazard of floating ice may exist, the thicknessand strength of the ice, and the velocity withwhich the ice may strike the structure shouldbe determined. With pack or sheet ice, themode of failure of the ice should be deter-mined. In some locations, ice may accumu-late on the structure and superstructure. Al-lowance should be made for the effect of thisaccumulation upon the stability of, and uponthe stresses in the structure. The additionalresistance to wind offered by such ice accumu-lation should be included in this allowance.

Loads from earthquakes

Where the site is in an area with a history ofrecorded earthquakes, the structure should bedesigned to resist lateral and vertical forcesand overturning moments arising from seis-mic activities. The information used to es-tablish a design earthquake should be takenfrom data recorded for previous earthquakes

at or near the site, if such data are available.Because there are relatively few recorded sta-tions compared with the number of seismicallyactive regions, the likelihood of selecting a lo-cation having a complete historical descrip-tion of seismic activities is very small. In suchcases the given site should be compared witha site whose geology and tectonics are similarand for which records are available.

Design Methods

Design of offshore concrete structures, isbased on limit (semi probabilistic methods).

Limit State – A structure or structuralmember reaches a Limit state of fitness in acondition where it just ceases to fulfill the re-sistance requirements or other specificationsas regards structural performance for which ithas been designed. See table 1 for the variouslimit states used in design.

As a result of the fact that full statisticalinformation is not available, the main uncer-tainties are included as partial load and ma-terial safety factors. Let

Qc = Characteristic load effects

Rc = Characteristic resistances

These are defined as certain percentiles ofthe distribution functions for load and resis-tance. Qc is the mean of the characteristicload effects distribution plus one or two stan-dard deviations.

Parameter Rc is the mean of the character-istic resistance distribution minus one or twostandard deviations. The design load effect,Qd, is the most unfavorable combination ofa specified set of loads and associated partialload factors, hf i.e.

Qd = effect of∑

hfQc

The design resistance, Rd, is the most unfa-vorable combination of relevant characteristic



and substitutional resistance parameters, Rc

and associated material factors, hm i.e.

Rd = Combination of∑

KRc

hm

in which K = constants defining the geometryand composition of member sections.hm = Material factorsSafety against any limit state requires that

Rd > Qd∑K Rc

hm>

∑hfQc

Analysis and design of shell structures

Concrete gravity platforms consist mainlyof various cylindrical shells of large dimen-sions. These shells are capped with sphericalor conical domes at bottom and top. Further,all these platforms are equipped with concreteor steel skirts in the form of short cylindricalshells, or both as a means of scour protectionand of assuming sufficient resistance againsthorizontal sliding.

The complexity of the various shell com-ponents connected together coupled with thecomplex actions of the environmental loadsand other load combinations renders the anal-ysis and design of such structures difficult.

It is important that the walls of concreteshell be properly proportioned to preventcatastrophic collapse against various periodsof large hydrostatic pressure exposure. Po-tential failure modes to be considered are ma-terial failure and structural stability.

Tangent modulus methods

Research has shown that the tangent mod-ulus buckling concept is proper for the predic-tion of the maximum strength of many typesof columns i.e. centrally located columns.This concept is not adequate for cylindri-cal shells, because the tangent modulus ap-proach pertains to idealized perfect struc-tural members while actual structural mem-

bers contain significant geometric imperfec-tions and/or lateral loads. However, tan-gent modulus approach is a powerful simpli-fied model to an actual structure in that:(1) It takes account of nonlinear stress-strain

behavior of the material.(2) It uses linear elastic buckling analysis.(3) If in-plane forces are dominating, this ap-

proach gives reasonable predictions.(4) The design method proposed by Furnes is

briefly described in the following section.(1) Obtain the linear elastic buckling stress

for an idealized perfect structural memberwith constant modulus Ec

(2) Express critical stress αcr as

αcr = ρEc (1)

ρ = an ideal buckling numberFor the case of a simply supported column

it has the value

ρ =π2

( 1y)2

(2)

1r

= the slenderness ratio. For the case of acomplete cylindrical shell with end enclosuresacting as a simple radial supports and subjectto hydrostatic pressure, it has the value

ρ =q4 + s(q2 +m2)2(q2 +m2 − 1)2

(q2 +m2)2(m2 − 1 + q2/2)(3)

q = πR

L

S =t2

12R2(1− V 2)V = Poissons ratiom and n = buckling waver integer numberst = wall thicknessR = mean radiusL = lengthFor other boundary conditions and loads,

the buckling number may be obtained fromhandbooks, tests or computer analysis.


40 A. W. OTUNYO

(3) Take the nonlinear stress-strain behav-ior for concrete into account by simply replac-ing the Young Modulus Ec by the tangentmodulus Ect, which is a function of concretestress α. Substitution of Ect and Ec in equa-tion above. Equation 1 yields

σcrf ′c

= α =2

1 +√

1 + (εult/ρ)2(4)

For short term loading, εult = strain at f ′cis normally chosen to be 0.002. For long termload εult may be modified by creep factor µ

ε′ult = εult(1 + µ) (5)

To allow for the effect of creep, a range of0.5 6 µ 6 1.0 is found appropriate. The effectof reinforcement may be considered by chang-ing α to

α′ = α

(1 +

fsAsf ′cAc

)(6)

In which α is defined in equation 4. fs = thesteel strength; As and Ac = the steel and con-crete sectional areas, respectively. Magnifica-tion factor (1− σ/σcr) may be used to obtaindesign moment Md by simply multiplying thisfactor to first-order moment Mdo. The designmoment is obtained, i.e.

Md =Mdo

1− 1ρt

σσcr

(7)

Special design considerations

As a result of the fact that offshore con-crete gravity structures are usually very huge,their size, coupled with the large environmen-tal forces, present very difficult design prob-lems. The establishment of a realistic service-ability Limit State (SLS) is very importantbecause of the following reasons.

(a) Oil storage is usually one of the principalfunctional requirements, structural com-ponents containing oil should be designedcompletely tight with respect to oil leak-age, which means that only very limitedcracking of the concrete may be allowed.The Author of this paper is an eye witnessof the consequences of frequent oil-spillagein Nigerian swamps. when oil containerscracked. Vast expanses of land were usu-ally totally destroyed and such areas arethen declared disaster areas.

(b) The internal pressure of the stored oilshould always be kept below the exter-nal pressure of the surrounding water, inwhich case somewhat less severe require-ments may be used. Sometimes a separatewater-containing chamber is provided be-tween the stored oil chamber and the out-side ocean water.

(c) As a means of checking cracks in the off-shore concrete gravity structures, the au-thor suggests the installation of probesor strain gauges that will measure cracksaround potential crack regions and con-stant monitoring of such probes to detectunusual signs of danger.

Other important design problems

The following additional important designconsiderations should not be overlooked.

(a) Cumulative fatigue damage at the columnbases.

(b) Temperature stresses within the caissoncaused by storage of hot oil.

(c) Structural instability of the columns andthe inner walls of the caisson.

(d) Local earth pressures on the base raft.(e) Impact load capacity of reinforced con-

crete.(f) Ultimate load carrying capacity in com-

plex regions where structural members ofvarious geometry are connected.



(g) Potential instability of the structural sys-tem during tow-out operation due to top-sided structural weight.

Foundation Design for Offshore Con-crete Platforms

Soil parameters of the soil should be ob-tained by thorough investigation because thefoundation design depends entirely on them.The site investigations should include a sur-vey of sea bottom topography, site geology,geophysical investigations, in-situ determina-tion of soil parameters by means of soundings,vane shear and cone penetration tests, andsampling in boreholes with laboratory inves-tigations, of the samples.

The stability of the foundations is the mostimportant problem often encountered in foun-dation design. Several possible modes of fail-ure for a typical gravity structure is shown inFig. 3. The simplest mode of failure is slid-ing between the base of the structure and thesea floor. This is critical if the shear resis-tance at the interface is smaller than that inthe soil mass. Sliding is checked by addingsteel skirts to the bottoms of the concretecells of the caisson and by adding several steeltubular dowels that extend below the skirts.During de-ballasting for placement the dowelscontact the soil first. Both dowels and steelskirts penetrate the soil and preclude sliding.The second mode of failure occurs if the shearstrength of the soil is exceeded. This failuremode is typical for foundations of clay. Theanalysis should consider the possible reduc-tion in shear strength due to repeated load-ings. For large foundations on sand the pos-sibility for a bearing capacity failure for tran-sient wave loading depends on the un-drainedshear strength of the soil. In this case a bear-ing capacity failure like that in clay soil is notlikely. However, a high stress level may lead

to large deformations with high hydraulic gra-dients along the rim of the foundation and re-peated loading may lead to softening of thesoil and rocking failure. Liquefaction is an-other mode of failure for gravity structures onsandy soil. This mode of failure would mostlikely occur during a storm wherein repeatedshear stress applications lead to a gradual in-crease in pore water pressure which causes areduction or possibly a complete loss of shearstrength of the sand so that it behaves like aheavy liquid. If there is eccentric loading onthe deck, the structure sinks into the fluidizedsoil, tilting at the same time. To account forsuch defects in the design, tests on the actualsoil have to be carried out.

Advantages of concrete offshore struc-tures over steel platforms(1) Concrete structures, not relying on piles

require great mass to stay put in the faceof sea storms even severe storms. TheEkofisk platform tank weighs 212,000metric tons exclusive of its extra ballastof lean concrete and oil and/or water thatfill its tanks at all times. It must be men-tioned that the concrete structures areso massive that they include oil storagetanks at little or no extra cost.

(2) Because the concrete tanks are so massive,they can carry heavy oil production plat-forms up top. So if North Sea platformis going to extract oil at a high rate say300,000 bpd (barrels per day) a concretestructure may be less costly.

(3) Steel structures offshore tend to be harderto inspect than concrete, steel structuresconsist of many tubes and joints, manyof them at locations which are not eas-ily accessible. The few, large pieces in aconcrete structure can be more easily in-spected visually from a diving bell or sub.

(4) Concrete itself performs well under lowtemperature conditions. It is well known


42 A. W. OTUNYO

Figure 3: Possible failure modes for foundation oftypical gravity platform.

that the strength of concrete increaseswith lower temperature. This featuregives concrete advantages as a buildingmaterial for vessels carrying LNG (Liq-uefied Natural Gas) or working in arcticareas.

(5) Concrete vessel construction time is 18months steel vessel construction time is36 months.

(6) Concrete vessel costs U.S.$33 millionbased on 1975 cost proposals as againststeel vessel - $40 million, based on thesame 1975 cost proposals.

(7) Constructions of concrete vessel in a drydock makes use of traditional civil engi-neering materials and less skilled labor,steel vessel require skilled welders and alot of other costly materials for connec-tions.

Response of concrete gravity platformto wave loading

An example problem will be used to illus-trate how the design engineer can incorpo-rate all the factors so far mentioned in thispaper. In this example, the problems aris-ing during the analysis of gravity type struc-tures are investigated. The example, apart

from showing how all the factors mentionedin this paper are usually incorporated in thedesign, will show how the soil structure in-teraction is included and secondly will illus-trate the use of spectral methods for handlingthe dynamic analysis solely in the frequencydomain that is considered. Let us consider astructure, 50m diameter by 100m high circulartank which is typical of an offshore soil storagetank. As shown in Fig. 4. The structure is tobe analyzed completely in the frequency do-main using the spectral method. For simplicityonly two degrees of freedom will be assumed,namely the rocking and translative motion ofthe rigid structure on the soil springs.

The equation of motion is

M(X) + C(X) +KX = F (t),

Where the vector C = {X, 0} is the horizontaltranslation and angle of rocking of the system.Considering the first terms in the left handside of the equation, then the forcing terms.

Mass: Three component masses must beincluded, namely, the mass of the structureand contents, the added water mass and theeffective mass of the soil participating in themotion. The position of the centre of grav-ity and the moment of inertia must also becalculated.

The calculations shown for the componentsparts below, the centre of gravity is given inmetres from the mudline (positive upwards)and the moments of inertia are about the in-dividual component mass centres.

(i) Structural MassMass = 2.4× 108KgMoment of Inertia = 2.04× 1011kgm2Centre of gravity = 43.05m

(ii) Added MassThe added mass of the water which be-comes entrapped and moves with thestructure is calculatedAdded Mass = 1.62× 108kg


Design of offshore concrete gravity platforms 43�

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Figure 4: Mass of structure and contents = 2.4×108 kg; Distance of c.g from base = 43.05m; Mo-ment of inertia of structure and contents about G= 2.04 ×1011 kg m; Water depth = 80m; Den-sity of sea water = 1030kg/m; Density of soil =2000kg/m; Coefficient of subgrade modulus forsoil = 7 ×107 N/m

Moment of Inertia = 8.64× 1010kgm2

Centre of gravity = 40.00m(iii) Soil Mass

Effective Horizontal Mass =ρ0.76R3/(2− v)

R =BL

π= Radius of foundation

ρ = soil densityB = width of rectangular foundationL = Length of rectangular foundationSoil Mass = 1.58× 107 Kg.Effective rocking inertia of soil =0.64ρR5/(1− v)= 2.5× 1010Kgm2

Centre of gravity = -5.84m(It is assumed that the 1.58 ×107 Kg ofsoil is contained within a hemisphere be-low the base radius of which is calculateddirectly as 15.6 m for the specified soildensity).It is interesting to note that the soil massis less than 1/10th of the structure andadded mass, therefore, even if it is ne-glected entirely, the influence in naturalfrequency is small.


44 A. W. OTUNYO

(iv) Total MassThe total mass, centre of gravity andmoment of inertia (about the compositec.g.) for the vibrating system are:Mass = Mhoriz = 4.18× 108KgCentre of gravity = Lg =40.0m (above mudline)Moment of Inertia = Mrock = 3.51 ×1011Kgm2

Stiffness: In this example, the structureis taken as rigid. The only flexibility is thehorizontal and rocking resilience of the soil.For modeling the soil stiffness the lumped ele-ment technique is used. The subgrade modulusmethod is considered more appropriate to thissize of structure.

Horizontal Spring Stiffness:

Khoriz = 0.5CVA = 6.87× 1010N/m

Rotational Spring Stiffnes:;

Krock = 1.7CV I = 3.65× 1013NmM/rad

A = area of horizontal contact betweenfoundation and soil.I = Rocking inertia of foundationCV = Subgrade modulusTo ensure a lower bound to the natural fre-

quency for this example, 50% of the horizon-tal stiffness and 33% of the rocking stiffness istaken in the analysis.

Damping: The damping ratio of the soil iscalculated from equations. Horizontal Damp-ing ratio = 0.31B′

B′ =M

ρR3

M = Mass of foundationρ = soil densityR = effective radiusEhoriz = 0.086Rocking Damping Ratio = ξrock

= 0.05 +0.1

B′(1 +B/4)

ξrock = 0.055Arrange the mass and stiffness in the mass

and stiffness matrices and the natural frequen-cies and calculate normal modes. The originis taken at the centre of gravity.

Mass Matrix:

M =

[Mhoriz 0

0 Mrock

]

=

[4.18× 108 0

0 3.51× 1011

]Stiffness Matrix:

K =

[Khoriz −Lg Khoriz

−Lg Hhoriz Lg2 Khoriz +Krock

]

=

[3.44× 1010 −1.37× 1012

−1.37× 1012 6.70× 1013

]Natural Frequencies:The natural frequencies are found from the

roots of the frequency determinant.

−M2w +K = 0 W12

W22

=

10.754

262.156

rad/sec2

Or N1

N2

=

0.52

2.56

Hz

Normal Modes:The normal modes are found by substitut-

ing the values of W1 and W2 back into thefrequency determinant to find relative magni-tudes of X and θ (The absolute values cannotyet be found until the forcing terms are con-sidered).

Mode 1: X = 1.00, θ = 2.173x10−2

Mode 2: X = 1.00, θ = −5.472x10−2



So that

φ =

[1 1

2.173× 10−2 −5.472× 10−2

]Using orthogonality to decouple the equa-

tions of motion

φTMφ =

5.837× 108 0

0 1.47× 109

=

M1 0

0 M2

φTKφ =

6.278× 109 0

0 3.853× 1011

=

K1 0

0 K2

Introducing Damping at this stage,

C =

Chorizant −Lg Choriz

−Lg Choriz Lg2 Choriz + Crock

But φT Cφ would not be diagonal and the

equations would not decouple. To overcomethis limitation for this example, the dampingis included on a modal basis bearing in mindthat the first mode is predominantly rockingand the second mode ground translation.

Thus, damping ratio relevant to rocking isassociated with the first uncoupled mass termand that for translation with the second massterm. Therefore the decoupled damping ma-trix is taken as

φT Cφ =

C1 0

0 C2

And Cn = 2ξnMnWn

For n = 2So that

Ci, 2 = i, 2 M1,2W1,2

C1 = 2× (.055)× (5.837× 108)

×√

10.754= 2.106× 108Ns/m

C2 = 2× (.086)× (1.470X109)

×√

262.156= 4.093× 109Ns/m

The modal transfer functions are

H1(jf) =1

K1 −M1(2πf)2 + jC1(2πf)

H2(jf) =1

K2 −M2(2πf)2 + jC2(2πf)

Assuming a Spectrum of the JONSWAPform

Snn(f) =αg2

(2π)41

f5exp(−1.25(

fm

f)4)Υ

α = Philips empirical constant ( =0.00081)g = Acceleration due to gravityfm = frequency at which mps. Spectral

energy is maximum.The force may be computed from the water

surface elevation as follows. For a large body,such as an offshore concrete platform underconsideration, the force is largely dependenton the water particle inertia terms with smallcontribution from the velocity dependent dragterms. The water particle acceleration at anyhorizontal co-ordinate, x, and depth, y, maybe related to water surface elevation by equa-tion below.

U(t) = (2πf)2 H Cosh[(2πt)2(y + d)]

Sin

[2π(

x

t− t

T)

]Sinh[(2πf)2d]

g

H = wave height


46 A. W. OTUNYO

L = g/2πf 2 , the wave heightd = water depthy is positive upwards from the m.w.1.The force over a length of cylinder dy, may

be related to the water particle accelerationsbyF (t) = ρπR2 dy Cm U(t) = Acceleration ×

volumeCm = inertia coefficient which for a large

body should be calculated by diffraction the-ory.

Conclusion

In the early eighties, the ACI Committee357 on Offshore Structures issued a reporton Recommended Practice for Fixed OffshoreConcrete Structures. This report was issuedin the anticipation of the forthcoming usageof large fixed concrete sea structures all overthe world. Apart from going by the designmethods presented in this paper, a survivalstrength analysis is needed in order to preventthe structure from catastrophic collapse in theevent of rare natural or man-made events suchas ductility level earthquake, adverse ice con-dition, collisions or explosion.

Finally, all aspects of the installation of thestructure, including its immersion and placingon the sea bed, should be planned and carriedout with the greatest care. The arrangementsmade for installation should ensure that thestructure is placed in position with the giventolerances. For large structures, lifting and re-placing should be considered only as an emer-gency.

References

Bury, M.R., and Domone, P.L. The Role of Re-search in the Design of Concrete, Offshore Struc-tures. Proceedings of Offshore Technology Con-ference. Paper No. 1949, 1974, (Articles).

Gerwick (Jr.), B. C. Concrete Ships and Float-ing Structures.Berkeley Campus University ofCalifornia. September 15th 19th ,1975, (Arti-cles).

Furnes, O. Shell Structures in Offshore plat-form design and application, Engineering Struc-tures, Elsevier, 1981, (Articles).

Guide for the Design and Construction ofFixed offshore Concrete Structures. AmericanConcrete Institute Committee 357 on OffshoreConcrete Structures, Journal of the AmericanConcrete Institute. Vol. 75 No. 12, 1978, pp684 709, (Articles). .

Hallam M.G.,Holm, N.J., and Wootton, L.R.Dynamics of Marine Structures. Offshore Tech-nology Conference Vol. III, 1975, (Articles).

Meyers, J.J. Holm, C.H. and McAllister, R.F.The Handbook of Ocean and Underwater Engi-neering. Section 12. McGraw-Hill Book Co. Inc,New York, N.Y., 1969, (Book).

Moan, T., and Graff, W.J. Structural Analysisand Design of Steel and Concrete Fixed OffshoreStructures. Lectures on Offshore Engineering:Combined Proceedings of a One-Day ConferencePlus Eight Weekly Seminars, Aalborg UniversityCentre, Aalborg, Denmark, 1978, (Articles).

MoKsnes, J. Condeep Platforms for the NorthSea: Some Aspects of Concrete Technology. Pa-per No. 2369, Proceedings of Offshore Technol-ogy Conference, 1975, (Articles).

Recommendations for the Design and Con-struction of Sea Structures. Federation Interna-tionale de la Precontraint, 2nd ed., Nov. 1974,(Articles).

William J. G. and Wai F. C. Bottom-

Supported Concrete Platforms: Overview. Pro-

ceedings of the American Society of Civil Engi-

neers. Journal of the Structural Division, 1981,

(Articles).


DESIGN OF OFFSHORE CONCRETE GRAVITY PLATFORMS

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