Wave Load and StructuraAnalysis for a Jack-Up Platform In

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Ould el Moctare-mail: [email protected]

Thomas E. Schellin1

e-mail: [email protected]

Thomas Jahnkee-mail: [email protected]

Germanischer Lloyd,Hamburg 20459, Germany

Milovan PericCD-adapco Nürnberg,

Nürnberg 90402, Germanye-mail: [email protected]

Wave Load and StructuralAnalysis for a Jack-Up Platform inFreak WavesThis paper analyzed the effects of freak waves on a mobile jack-up drilling platformstationed in exposed waters of the North Sea. Under freak wave conditions, highly non-linear effects, such as wave run-up on platform legs and impact-related wave loads onthe hull, had to be considered. Traditional methods based on the Morison formula neededto be critically examined to accurately predict these loads. Our analysis was based on theuse of advanced computational fluid dynamics techniques. The code used here solves theReynolds-averaged Navier–Stokes equations and relies on the interface-capturing tech-nique of the volume-of-fluid type. It computed the two-phase flow of water and air todescribe the physics associated with complex free-surface shapes with breaking wavesand air trapping, hydrodynamic phenomena that had to be considered to yield reliablepredictions. Lastly, the finite element method was used to apply the wave-induced loadsonto a comprehensive finite element structural model of the platform, yielding deforma-tions and stresses. �DOI: 10.1115/1.2948952�

Keywords: freak waves, jack-up platform, CFD technique, FEM modeling, wave loads,deformations, stresses

ntroductionLast September, hurricane Katrina scoured the Gulf of Mexico,

reaking havoc among mobile drilling rigs and production plat-orms. Since then, it has been clear that the energy industry mustake offshore structures more hurricane resistant. The key chal-

enge in preventing the failures of marine structures is understand-ng the storm’s forces that must be taken into account duringesign. When structures were first situated in shallow waters, theyere designed for a 25 year return period. Today, offshore struc-

ures must withstand the forces generated by a 100 year storm.o-called freak waves are extreme waves that marine structureseed to be designed for if those waves occur on site. These designonditions not only account for the characteristics of the threaten-ng wave, but also for highly nonlinear run-up on the legs andmpact-related forces on the hull. Consequently, accurate assess-

ent of such loads is essential for the design of marine structures.Of late, modern computational fluid dynamic �CFD� tools, vali-

ated against experimental measurements, successfully predictedmpact-related �slamming� loads on ships �1�. The application ofhese methods needs to be incorporated in the analysis of waveorces on marine structures. Wave impact is a strongly three-imensional nonlinear phenomenon that is sensitive to the relativeotion between the structure and the water surface. Furthermore,

he influence of the compressibility of water and air pockets mayave to be accounted for. Methods that directly solve theeynolds-averaged Navier–Stokes �RANS� equations, including

he two-phase flow of water and air, are better able to describe thehysics associated with impact-related wave loads. Today, meth-ds based on codes that implement interface-capturing techniquesf the volume-of-fluid �VOF� type promise to be most suitable foromputing complex wave-structure interactions.

In this paper, we investigated a typical self-elevating �jack-up�

1Corresponding author.Contributed by the Ocean Offshore and Arctic Engineering Division of ASME for

ublication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manu-cript received July 2, 2007; final manuscript received March 3, 2008; publishednline March 12, 2009. Assoc. Editor: Ge �George� Wang. Paper presented at The6th International Conference on Offshore Mechanics and Arctic Engineering
OMAE2007�, San Diego, CA, June 10–15, 2007.
ournal of Offshore Mechanics and Arctic EngineeringCopyright © 20

ded 07 Apr 2009 to 202.118.71.160. Redistribution subject to ASM

drilling unit subject to freak waves of varying height. Traditionalmethods, such as the IMO Code for Offshore Drilling Units �2�and the SNAME Guidelines for Mobile Jack-Up Units �3�, arebased on the Morison formula to determine wave loads. Here,wave loads were analyzed using CFD techniques. We employedcode COMET �4� as it proved to be most suitable to describe thephysics associated with complex free-surface flow shapes such asleg run-up, breaking waves, and air trapping.

The use of advanced CFD tools can be relied on only if theresults have been validated. No experimental data were availablefor the platform under consideration; however, impact-relatedwave �slamming� loads on ships predicted by the employed nu-merical method were validated against experimental model testmeasurements �1,5�. As its application for the prediction of waveloads is not restricted to ships, this numerical technique is suitablealso for the wave load analysis of offshore platforms. Of interesthere are pressure dominated loads obtained by integration of localpressures over structural plate fields, and not local peak pressuresacting over small control volume face areas.

To determine the structure’s stress level, we used the finite el-ement method �FEM� to predict the effects of the computed wave-induced loads on the structure’s strength. We started with a com-prehensive finite element structural model of the platform �Fig. 1�and deployed Version 10.0A1 of the commercial code ANSYS �6�to perform a transient nonlinear finite element analysis of the rig’sstructure subject to the considered wave conditions. By comparingresults with the structure’s rule based design capability �7�, wedetermined the reserve strength capacity still available under freakwave conditions �8�.

Jack-Up RigThe investigated three-legged self-elevating mobile drilling unit

is of triangular construction, containing tubular steel legs at eachcorner that can be jacked up or down by electrohydraulic machin-ery. The elevating mechanism is of the rack-and-pinion type, fea-turing an automatic position lock on power failure. The unit’sthree legs are spaced 39.0 m apart, forming an equilateral triangle.
The FEM model in Fig. 1 shows the overall configuration of the
MAY 2009, Vol. 131 / 021602-109 by ASME

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ig in its elevated drilling position. The short front wall of the hull,ituated ahead of the foremost leg, designated the unit’s bow.able 1 lists principal particulars.Our investigation considered the rig operating in the North Sea

n a 33.5 m water depth location. Realistic loading conditionsomprised gravity loading together with relevant environmentaloading. The unit’s Operating Manual specified a correspondingignificant wave height of 6.24 m, a current velocity of 0.51 m /s,nd a wind speed of 58 knots. Current and wind loads were as-umed acting collinearly with the waves. The wind force of348 kN was determined according to the Rules of Germanischerloyd �7�. This force acted at a height of 23.3 m above calm water

evel.

ave Load PredictionIn high and steep waves, the flow around the unit is associated

ith wave run-up along the legs and impact-related loads on thenderside of the hull. Both of these highly nonlinear phenomenaay significantly increase local wave loads that, in turn, lead to

ecreased global stability of the unit as well as increased localamage to the hull.

The code COMET solves the RANS equations and relies on thenterface-capturing method of the VOF type to determine the in-

Fig. 1 Global structural FEM model of the jack-up rig

Table 1 Principal particulars of the jack-up rig

olded hull length 46.0 molded hull breadth 47.6 molded hull depth 5.5 m

levated height above calm water level 13.5 meg diameter 3.66 mverall leg length 64.0 mnsupported leg length 48.3 mross tonnage 4033 tonset tonnage 3209 tons

21602-2 / Vol. 131, MAY 2009


terface between water and air. This technique accounts for highlynonlinear wave effects in that it computes the two-phase flow ofwater and air to describe the physics associated with complexfree-surface shapes with breaking waves and air trapping.

Conservation equations for mass and momentum in their inte-gral form serve as the starting point. The solution domain is sub-divided into a finite number of control volumes that may be ofarbitrary shape. The integrals are numerically approximated usingthe midpoint rule. The mass flux through the cell face is takenfrom the previous iteration, following a simple Picard iterationapproach. The remaining unknown variables at the center of thecell face are determined by combining a central difference scheme�CDS� with an upwind differencing scheme �UDS� for the con-vective terms. The diffusive terms are discretized using CDS. TheCDS employs a correction to ensure second-order accuracy for anarbitrary cell. A second-order CDS can lead to unrealistic oscilla-tions if the Peclet number exceeds 2.0 and large gradients areinvolved. On the other hand, an UDS is unconditionally stable,but leads to higher numerical diffusion. To obtain a good compro-mise between accuracy and stability, the schemes are blended.

In the neighborhood of the platform, the blending factor is cho-sen between 0.8 and 0.9. The Euler implicit method is used tointegrate in time. This first-order fully implicit approximation isstable. Pressure and velocity are coupled by a variant of theSIMPLE algorithm �9�. The system of equations is under-relaxedto dampen changes between iterations. All equations except thepressure correction equations are under-relaxed using a relaxationfactor 0.8. The pressure correction equations are under-relaxedusing a relaxation factor between 0.2 and 0.4 for unsteady simu-lations, finding in each case a suitable compromise between sta-bility and convergence speed.

The two-fluid flow is modeled by a two-phase formulation ofthe governing equations �10�. No explicit free surface is definedduring the computations, and overturning �breaking� waves aswell as buoyancy effects of trapped air are accounted for. Thespatial distribution of each of the two fluids is obtained by solvingan additional transport equation for the volume fraction of one ofthe fluids. To accurately simulate the convective transport of thetwo immiscible fluids, the discretization must be nearly free ofnumerical diffusion and must not violate the boundedness criteria.For this purpose, the high resolution interface capturing �HRIC�scheme is used �11�. The scheme is a nonlinear blend of upwindand downwind discretizations, and the blending is a function ofthe distribution of the volume fraction and the local Courant num-ber. The free surface is typically smeared over one to two controlvolumes. Fluid structure interaction effects are presently not ac-counted for, i.e., the body is assumed to be rigid, and the fluid isassumed to be viscous and incompressible.

The Courant number was almost always less than 0.25 for allsimulations. For the grid density and time step used here, thenumerical diffusion turned out to be sufficiently small.

To assure numerical convergence, at every time step the com-putations were performed until the normalized residuals of allequations to be solved were reduced by three to four powers often. Typically, up to 12 outer iterations for each time step werenecessary for convergence. To assure time convergence, the flowwas simulated until a periodic solution was attained.

We started the analysis by investigating the effect of the designwave specified according to the criterion for the rig under thesurvival condition. A deterministic long-crested wave of 11.6 mheight and 13.0 s period, propagating towards the port bow in thedirection of 60 deg to the longitudinal axis of the hull, describedthis condition. Our VOF computations were not deterministic.Therefore, the wave profile represented a regular wave only at theinlet boundaries of the computational grid, and the propagatingwave reached its intended height and period when its crest arrivedat the rig’s legs. An analysis based on the SNAME �3� guidelinesshowed that these wave parameters resulted in the highest base
shear on the structure. We then considered a series of three epi-
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odic freak waves having the same period and direction. Theireights were 15.8 m, 19.9 m, and 23.7 m. Design guidelines des-gnate the 23.7 m wave height to be the limiting wave heightefore breaking.

low SimulationAn unstructured grid, comprising about 2.5�106 hexahedral

ontrol volumes, surrounded the drilling rig, as shown in Fig. 2.enser H-grids defined control volumes around the legs, in theicinity of the hull, and in the neighborhood of the free surface, ashown in Fig. 3. To avoid flow disturbances at the outer gridoundaries of the numerical domain, domain boundaries extended.1 hull lengths upstream, 15.6 hull lengths downstream, and 7.6ull lengths to each side of the platform. The upper boundary wasocated 2.8 hull lengths above the ocean bottom; the lower bound-ry was the ocean bottom itself.

Grid density was higher in the flow region ahead of the struc-ure to resolve the incident waves, whereas aft of the structure therid became coarse to dampen the waves. No significant waveeflection occurred at the outlet boundary.

We specified our numerical grids on the basis of past experi-nce with similar computations performed earlier �1,5,12,13�.onsequently, we were able to narrow down the discretizationrrors. In the longitudinal direction, 70 control volumes extendingver one wavelength defined our grid. In the vertical direction, 20ontrol volumes extending over the wave height defined our grid.n the vertical direction, this grid was locally refined near the freeurface �Fig. 3�.

The rig’s orientation relative to the incident waves representedhe direction of wave propagation investigated here. Waves wereenerated at the front of the computational domain, specified ashe inlet boundary of known velocities and known volume frac-ion distributions defining water and air regions. The back of the

ig. 2 Numerical grid on legs and hull of the rig and on thecean bottom

ig. 3 Higher local grid density for wave-structure interaction

ournal of Offshore Mechanics and Arctic Engineering


computational domain was specified as a pressure boundary. Ve-locities that initialized the flow field arose from the superpositionof wave particle velocities and current speed. Second-order Stokeswave theory described the initial wave particle velocities. Theentire flow field was initialized by the hydrostatic pressure. On therig surfaces, a no-slip condition was enforced on fluid velocitiesand on the turbulent kinetic energy.

The wake flow boundary was specified as a zero-gradient pres-sure boundary �hydrostatic pressure�. On average, the time stepsize was chosen such that about 1000 time steps defined eachwave period. The momentum equations were discretized using85% central differences and 15% upwind differences. About 50 hof CPU time on six standard processors was required for onewave period.

We used turbulence models with wall functions, but the flowwas pressure dominated because here we dealt with wave-inducedloads. Based on the assumed current velocity past the platform’slegs, the flow was characterized by a Reynolds number of about2�106 and a Froude number of about 0.08. However, the influ-ence of friction and turbulence on wave loads was small and,consequently, did not significantly contribute to overall loading.Of course, the form drag caused by the flow past the platform’slegs was accounted for.

The boundary conditions of this field method influenced thesolutions. Wave kinematics at the inlet boundary did not signifi-cantly affect the wave formation. The resulting wave kinematicsaccounted for the finite water depth and caused wave crests to behigher than wave troughs. This is seen in Fig. 4, showing a samplescreen shot of the simulated 19.9 m wave advancing from left toright past the structure. The screen shots in Figs. 5 and 6 show theprofile of the 23.7 m wave passing by the structure just as thewave breaks, demonstrating that the VOF method used was ca-pable of simulating this situation. Wave run-up on legs extendedup to the underside of the hull deck, but the undisturbed wavecrest did not. Wave run-up caused impact-related slamming pres-sures to act on the legs and the underside of the hull. This was thecase for all waves considered. For the 19.9 m wave, Fig. 7 showsa pressure distribution on the rig corresponding to the time ofmaximum base shear and overturning moment. Only the two high-est waves caused wave run-up to reach the hull. Time histories in

Fig. 4 Screen shot of rig in 19.9 m wave

Fig. 5 Screen shot of rig in 23.7 m wave

Fig. 6 Simulated wave profile of 23.7 m wave

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ig. 8 show local slamming pressures as they occurred at the topf the two legs facing the wave crest at locations directly under-eath the hull deck. �The symbol HW in this and other figurestands for wave height.� Although the resulting peak pressuresere high for all wave heights, attaining maxima exceeding00 kPa, hull structural plate scantlings of this rig are more thandequate to withstand these pressures.

Grid size as well as time step size did not significantly affecthe resulting wave-induced forces and moments, because thesealues were obtained by integrating the computed pressures.ome of these pressures were characterized by high pressureeaks. However, these pressure peaks acted only locally over themall control volume face area. To obtain impact-related waveorces, we integrated the computed pressures over a plate fieldith an area that was much larger than the control volume face

rea. We did not perform a sensitivity study specifically for thislatform, because previous investigations �1,5,14� demonstratedhe validity of this procedure.

After each time step, pressures acting on the structure werentegrated to yield forces caused by the incident waves and theuperimposed current. The total horizontal force on all parts of theig is known as the base shear. Summing moments of these forcesbout a horizontal axis that runs normal to the direction of waveropagation and through the center of the tip of the most highly

Fig. 7 Pressure distribu

Fig. 8 Slamming pressures on underside of hull deck

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loaded �starboard aft� leg resulted in the overturning moment. Forthe four wave heights considered, Figs. 9 and 10 show time his-tories of the structure’s base shear and overturning moment, re-spectively, and Fig. 11 shows time histories of the base shear ofone of the two legs facing the wave crest. Negative values of baseshear represent horizontal forces acting in the direction of wavepropagation; positive values, forces acting against the direction of

n on rig in 19.9 m wave

Fig. 9 Time histories of base shear

Fig. 10 Time histories of overturning moment



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ave propagation. The corresponding values of overturning mo-ent are based on moment arms measured positively upward

rom the ocean bottom.Base shear and overturning moment are the dominant safety

riteria against sliding and capsizing of the rig, respectively. Fromigs. 9 and 10, we see that only for the 11.6 m wave height are

he computed time histories almost sinusoidal with negative non-ero mean values. For higher waves, the functions are character-zed by peaks in the negative direction, corresponding to waverests attacking the structure. Peak �absolute� values increase non-inearly with wave height, as seen by the plots of maximum valuesf base shear and overturning moment versus wave height shownn Fig. 12. However, this nonlinearity is less pronounced betweenhe two highest waves, indicating that the increase in the wettedreas of the legs decreased when the highest wave started toreak. Positive peak values of these time histories are nearly equalor all four wave heights, indicating that the wave troughs wereearly the same for all four waves. Profiles of waves when reach-ng the legs of the rig no longer represented regular waves, be-ause the VOF computations were not deterministic. Only at inletoundaries did wave profiles represent regular waves.

Peak values of base shear and overturning moment occurred athe same instants of time. This was expected because the over-urning moment was a direct result of multiplying the horizontaloads with their respective moment arms.

Wave loading on the two legs simultaneously facing the waverest was split nearly equally between each of these legs, as seeny the time histories of base shear on one of these legs �Fig. 11�.his result was expected because we simulated long-crestedaves.We then calculated wave loads using the Morison formula, with

oefficients as recommended in the SNAME design guidelines forobile jack-up units �3�. For the four wave heights considered,

Fig. 11 Time histories of base shear on a single leg

ig. 12 Maxima of base shear and overturning moment versus
ave height


Figs. 13–20 show time series of the resulting base shear and over-turning moment together with comparative results from ourRANS computations.

Regarding base shear, both methods predicted nearly equalpeak values for the three lower wave heights of 11.6 m, 15.8 m,and 19.9 m �Figs. 13–15�. Only for the highest �breaking� wave�23.7 m� did peak values from the Morison formula exceed peakvalues from RANS by about 15% �Fig. 16�. Regarding overturn-ing moment, both methods yielded nearly equal peak values onlyfor the 19.9 m wave �Fig. 19�. For the 11.6 m wave, peak valuesfrom the Morison formula are about 15% greater than peak valuesfrom RANS �Fig. 17�, whereas for the 15.8 m and 23.7 m waves,the peak values from the Morison formula are about 25% greaterthan values from the RANS �Figs. 18 and 20, respectively�.

The basics of the two approaches resulted in these differences.Only the RANS technique was able to account for wave kinemat-ics associated with breaking waves and, therefore, predicted waveloads more realistically, especially for the two highest waves con-sidered. The deviation between the time histories from the twoapproaches at higher waves confirmed this.

Fig. 13 Comparative results of base shear for the 11.6 m wave



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Morison results were steady as they repeated themselves fromycle to cycle, indicating that incident Morison waves were regu-ar. This was not the case for RANS results, where the differencesn peaks from wave to wave of up to 30% were observed. Theariation of predicted impact pressures caused these differences.he VOF computations, simulating breaking waves splashinggainst a solid structure, were not deterministic. Our RANSethod did not resolve small-scale fluctuations that turbulenceodels consider; however, our transient simulations did resolveuctuations that took place on a larger time scale. Only if the freeurface would have remained smooth, would our RANS simula-ions have produced a perfectly periodic behavior. In principle, weolved the unsteady Reynolds-averaged Navier–Stokes �URANS�quations. This procedure was justified because the frequencies ofhe resolved unsteadiness, here caused by wave breaking andplashing, were sufficiently far away from the higher frequenciesf turbulent fluctuations.

Generally, Morison peak values turned out to be larger thaneak values from RANS computations. This was because the less

ig. 16 Comparative results of base shear for the 23.7 m wave

ig. 17 Comparative results of overturning moment for the1.6 m wave

ig. 18 Comparative results of overturning moment for the
5.8 m wave
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accurate Morison formulation had to rely on predetermined hy-drodynamic force coefficients and harmonic wave profiles.

Strength AnalysisTo investigate the structure’s strength, we performed a transient

finite element analysis of the rig’s structure subject to wave con-ditions, current, and wind forces. The analysis accounted for non-linear large structural deformations, but the material propertieswere assumed to be linear. For this strength analysis, we consid-ered only the three lower wave heights and not the 23.7 m wave�8�. This was done because it turned out that the 19.9 m highwave was already a breaking wave.

The global FEM comprised stiffened plates with eight-nodeshell elements and three-node beam elements to idealize hull, jackhouses, living quarters, and legs �Fig. 1�. Modeling of the struc-ture with stiffened shells and beams simulated the complete stiff-ness distribution of the rig. Concentrated masses modeled the he-lideck and the cantilevered drill floor. Shell elements modeledplane plating of hull bottom, side shells, transoms, decks, andinternal structural bulkheads. Shell elements also modeled thefloors. Beam elements idealized webframes, deck girders, and pil-lars. Beam elements also modeled the longitudinal framing systemof decks, bottom, bulkheads, and shell elements. Profiles weregrouped together to limit the mesh size. Shell elements modeledthe cylindrical shells of the legs and the spud wells. For the ringstiffeners inside the legs, we used beam elements. Plane shellelements with a mean height of the tooth profile idealized theelevator racks.

For the legs, we used a nonlinear material model because highstresses were expected to occur at the positions of the lower legguides. Pin supports idealized the boundary condition of the legtips on the mudline. Nonlinear spring elements surrounding thelegs were located at the levels of the leg guides, namely, at thehull bottom and at the top of the jack houses. These spring ele-

Fig. 19 Comparative results of overturning moment for the19.9 m wave

Fig. 20 Comparative results of overturning moment for the
23.7 m wave


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ents transmitted mainly compressive loads. Truss elements, ex-ending from the top of the legs to the three pinions on each sidef the legs, served as vertical supports between hull and legs.

When transforming the wave and current induced loads ontohe structure, we determined spatial mean wave-induced loads byntegrating computed local wave-induced pressures over the areasf the finite elements that idealized the exposed surfaces of thetructure’s legs and hull. The resulting loads were transformed toquivalent nodal forces on the FEM of the structure. To minimizeransient effects, a sinusoidal ramp function was used to graduallypply wave- and current-induced loads for the first half of a waveeriod �6.5 s�. A consequence of using this ramp function was thathe time histories of stresses in Figs. 22 and 23 no longer corre-ponded to the time histories of base shear in Fig. 9.

We used three criteria to assess the global safety of the unit:rst, the resulting stress level in the shell underneath the hull for

he most loaded leg; second, the vertical holding capacity of theacking gears; third, the rig’s overturning stability.

The rig’s safety margin or reserve strength was based on safetyactors for the survival condition according to Ref. �3�. For allow-ble stresses, the safety factor of equivalent stress against yieldas 1.1; against axial/bending stress, 1.25. For the required legolding capacity of the jacking system, the safety factor againstaximum leg design load was 1.3. The safety factor against over-

urning was 1.3.To analyze the resulting stresses in the most loaded �starboard

ft� leg, we selected two points, both situated on the outer shell ofhis leg. As shown in Fig. 21, Point 1 was located on the outerhell directly underneath the hull; Point 2 was located 1.5 m be-

Fig. 21 Stress distribution at Points 1 and 2 for 15.8 m wave

Fig. 22 Equivalent stresses at Point 1



low Point 1. At point 1, equivalent von Mises stresses were su-perimposed on local stresses caused by the action of the legguides. At this point, the overloaded structure was most likely toexperience plastic deformation. At Point 2, the predicted stressesrepresented the undisturbed global bending stresses in the leg.

Figures 22 and 23 show the resulting time histories of stressesin the most loaded �aft starboard� leg. It is seen that the higher19.9 m wave caused disproportionately larger stresses that ex-tended into the plastic range. However, even for the highest wave,the resulting stresses were within allowable limits according toclassification society rules �7�.

The total required holding capacity for a selected load wasevaluated by summing the internal forces of all truss elementsrepresenting the jacking system of one leg. Again, the most loadedleg turned out to be the aft starboard leg. As a representativesample, Fig. 24 shows the computed time series of the jackinggear forces for the 19.9 m wave height. In this figure, symbolsPS-Aft, SB-Aft, and CL-Fwd designate the rig’s portside aft leg,starboard side aft leg, and centerline forward leg, respectively.

We investigated overturning in the sense of rule based require-ments, that is, when the reaction force of at least one leg loses itsdownward support loads on the mudline. As a representativesample, Fig. 25 shows the resulting time series of vertical leg tipreaction forces of all three legs for the 19.9 m wave height. In thisfigure, symbols PS-Aft, SB-Aft, and CL-Fwd again designate theunit’s portside aft leg, starboard side aft leg, and centerline for-ward leg, respectively.

The severe environmental loads investigated here caused siz-able global deformations of the rig. To illustrate, Fig. 26 showsthe computed time series of deformations for the center bottomnode of the hull. The maximum deflection in the horizontalx-direction turned out to be about 1.2 m as the 19.9 m wave wentby the rig. Symbols x, y, and z in this figure refer to the axes of the

Fig. 23 Bending stresses at Point 2 for 15.8 m and 19.9 mwaves

Fig. 24 Jacking system forces for 19.9 m wave

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ig-bound right-handed coordinate system, with the x-axis point-ng towards the bow, the y-axis to port, and the z-axis verticallypward.

At the outer shell directly underneath the hull of the mostoaded �starboard aft� leg �Point 1�, the material deformed plasti-ally. The computed time series reflect this behavior, consideringhe rig had a natural frequency of about 5.0 s. Because the result-ng deformations were large, it would have been appropriate toccount for these deformations when applying loads to the FEM.

Although plastic deformation occurred in the most loaded legor the 19.9 m wave height �Fig. 22�, the overall structural integ-ity was still assured as far as leg strength is concerned. If thisase were classified as an accident, plastic deformation wouldave been acceptable.

The jacking system of the rig was designed for a maximumolding capacity of 32,000 kN per leg. This value was exceededlready for the 19.9 m wave �Fig. 24�. With the rule based safetyactor of 1.3 and the maximum design leg load for the survivalondition �11.6 m wave height�, the required holding capacity ofhe jacking system is 1.3�21,345 kN=27,750 kN for this rig.his means that the jacking system turned out to be the weak link

n the design of this rig.With a mass of 5438 tons and a lever of about 21 m, the up-

ighting moment was about 1120 MN m. The maximum overturn-ng moment, equal to the sum of the maximum wave- and current-nduced moment for the 23.7 m wave �330 MN m, see Fig. 10�nd the wind-induced moment �250 MN m�, was 580 MN m.ence, the safety factor against overturning turned out to be120 MN m /580 MN m=1.9, well in excess of the rule requiredafety factor of 1.3.

onclusionsThe combined use of CFD and FEM techniques proved to be

ffective to assess the structural integrity of the investigatedack-up mobile offshore drilling platform. By analyzing freak

Fig. 25 Vertical leg tip reaction forces for 19.9 m wave

Fig. 26 Rigid body hull deformation for 19.9 m wave

21602-8 / Vol. 131, MAY 2009


waves, we demonstrated that this rig possesses sufficient reservestrength to withstand freak wave conditions in excess of the re-quired design wave specified for its survival condition. Our analy-sis, however, considered a considerably higher hull elevation thanthe required elevation based on the rule based minimum airgap.We specifically selected this higher hull elevation for our analysisbecause most operating assignments for this kind of rig call for ahigh hull elevation.

Our comparative results of base shear and overturning momentof the platform subject to freak waves revealed that predictionsbased on the use of the Morison formula differed by not more than25% from predictions obtained from CFD techniques. Peak valuesof overturning moment differed more than peak values of baseshear. This was brought about by the more accurate distribution ofCFD based wave forces acting on the platform legs, especially forthe higher �breaking� waves.

These comparative results demonstrated the general usefulnessof the Morison formula approach to assess strength related safetyaspects although only for cases of high hull elevation. At lowerhull elevations with waves attacking the hull directly, it wouldhave been necessary to rely on methods such as this CFD tech-nique to predict wave loads.

This CFD approach is just as effective to reliably predict aero-dynamic loads. Because of large moment arms, wind loads actingon the above-water parts of the rig can be critical. They can causewind-induced moments that are of the same order of magnitude aswave-induced moments. However, as wind forces were separatelydetermined, we did not employ this method to compute thesewind forces.

The complexity of modeling wave loads and their interactionwith a finite element structural model forced us to make simpli-fying assumptions. For instance, we considered waves to be long-crested although this was not necessary as we employed this CFDtechnique routinely to simulate sea loads on many ships. Also, werelied on linear strain displacement relationships. However, thestructural finite element analysis accounted for a bilinear materialbehavior and compression only spring elements. Only the treat-ment of long-crested waves was a conservative assumption. Thestructural analysis resulted in large horizontal hull deformationsthat would have justified accounting for these deformations whenapplying loads to the finite element structural model.

References�1� el Moctar, O., Brehm, A., and Schellin, T. E., 2004, “Prediction of Slamming

Loads for Ship Structural Design Using Potential Flow and RANSE Codes,”Proceedings of the 25th Symposium on Naval Hydrodynamics, St. John’s.

�2� International Maritime Organization �IMO�, 1989, Code for the Constructionand Equipment of Mobile Offshore Drilling Units, IMO MODU Code.

�3� Society of Naval Architects and Marine Engineers �SNAME�, 2002, Guide-lines for Site Specific Assessment of Mobile Jack-Up Units, Technical & Re-search Bulletin 5-5A, Jersey City, 1st ed., Rev. 2.

�4� CD-adapco, 2002, User Manual COMET, Version 2.0, Nürnberg.�5� Schellin, T. E., and el Moctar, O., 2006, “Numerical Prediction of Impact-

Related Wave Loads on Ships,” ASME J. Offshore Mech. Arct. Eng., 129, pp.39–47.

�6� Müller, G., and Groth, C., 2002, Practical Application of FEM Code ANSYS,Vol. 1: Basics, 7th ed., Expert Verlag, Renningen, in German.

�7� Germansicher Lloyd, 2007, Rules for Classification and Construction, IV In-dustrial Services, 6 Offshore Technology, Hamburg.

�8� Schellin, T. E., Jahnke, T., and Künzel, J., 2007, “Consideration of FreakWaves for Design of a Jack-Up Structure,” Proceedings of Offshore Technol-ogy Conference, Houston, TX, Paper No. OTC-18465.

�9� Ferziger, J., and Peric, M., 1996, Computational Methods for Fluid Dynamics,Springer-Verlag, Berlin.

�10� Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S., and Zanetti, G., 1994,



J

Downloa

“Modeling Merging and Fragmentation in Multiphase Flows With SURFER,”J. Comput. Phys., 113, pp. 134–147.

�11� Muzaferija, S., and Peric, M., 1998, “Computation of Free Surface FlowsUsing Interface-Tracking and Interface-Capturing Methods,” Nonlinear WaterWave Interaction, O. Marenholtz and M. Markiewicz, eds., ComputationalMechanics, Southampton, Chap. 3.

�12� el Moctar, O., Schellin, T. E., and Priebe, T., 2006, “CFD and FE Methods to



Predict Wave Loads and Ship Structural Response,” Proceedings of the 26thSymposium on Naval Hydrodynamics, Rome, Italy.

�13� el Moctar, O., and Bertram, V., 2001, “RANSE Simulations for High-Fn,High-Re Free Surface Flows,” Proceedings of the Fourth Numerical TowingTank Symposium, Hamburg, Germany.

�14� Klemt, M., 2004, “Motion Simulation of Floating Bodies in Viscous Flow,”Ph.D. thesis, Hamburg University, Hamburg.

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Wave Load and StructuraAnalysis for a Jack-Up Platform In