DNV-RP-H103

RECOMMENDED PRACTICEDNV-RP-H103MODELLING AND ANALYSISOF MARINE OPERATIONSDRAFTDecember 2008Kindly send your comments and suggestions to:Arne NestegårdENENO713DNV EnergyN-1322 Høvik, NorwayTel: +47 41 41 92 15Arne.Nestegard@dnv.comTormod BøeENENO713DNV EnergyN-1322 Høvik, NorwayTel: +47 67 57 88 34Tormod.Boe@dnv.com

Recommended Practice DNV-RP-H103 Draft December 2008Page 2FOREWORDDET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguardinglife, property and the environment, at sea and onshore. DNV undertakes classification, certification, and otherverification and consultancy services relating to quality of ships, offshore units and installations, and onshoreindustries world-wide, and carries out research in relation to these functions.DNV offshore publications consist of a three level hierarchy of documents:−−−Offshore Service Specifications. Provide principles and procedures of DNV classification, certification,verification and consultancy services.Offshore Standards. Provide technical provisions and acceptance criteria for general use by the offshoreindustry as well as the technical basis for DNV offshore services.Recommended Practices. Provide proven technology and sound engineering practice as well as guidance for thehigher level Offshore Service Specifications and Offshore Standards.DNV Offshore publications are offered within the following areas:A. Quality and Safety MethodologyB. Materials TechnologyC. StructuresD. SystemsE. Special FacilitiesF. Pipelines and RisersG. Asset OperationH. Marine OperationsAmendments and CorrectionsThis document is valid until superseded by a new revision. Minor amendments and corrections will be published ina separate document normally updated twice per year (April and October).For a complete listing of the changes, see the “Amendments and Corrections” document located at:http://webshop.dnv.com/global/, under category “Offshore Codes”.The electronic web-versions of the DNV Offshore Codes will be regularly updated to include these amendments andcorrections.

Recommended Practice DNV-RP-H103, Draft December 2008Page 3INTRODUCTION• BackgroundThis Recommended Practice is developed within a Joint Industry Project, Cost Effective Marine Operations(COSMAR) 2005-08.• AcknowledgementThe following companies have provided funding for this JIP:• StatoilHydro• Shell Technology• Petrobras• Technip• Acergy• Det Norske VeritasRepresentatives from these companies have attended project meetings and provided useful comments to the new RP.DNV is grateful for valuable discussions, cooperations and discussions with these partners. Their individuals arehereby acknowledged for their contribution.Marintek, Norway has provided valuable input to the new RP. Their contribution is highly appreciated.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 4CONTENTS1 General .........................................................................71.1 Introduction .................................................................71.2 Objective .....................................................................71.3 Relationship to other codes .........................................71.4 References ...................................................................71.5 Abbreviations ..............................................................71.6 Symbols....................................................................... 71.6.1 Latin symbols ......................................................71.6.2 Greek symbols .....................................................92 General methods of analysis ....................................112.1 Introduction ...............................................................112.2 Description of waves .................................................112.2.1 General ..............................................................112.2.2 Regular waves ...................................................112.2.3 Modelling of irregular waves ............................122.2.4 Breaking wave limit ..........................................122.2.5 Short term wave conditions ...............................122.2.6 Pierson-Moskowitz and JONSWAP spectra ....122.2.7 Directional distribution of wind sea and swell ..142.2.8 Maximum wave height in a stationary sea state 142.3 Wave loads on large volume structures .....................142.3.1 Introduction .......................................................142.3.2 Motion time scales ............................................142.3.3 Natural periods ..................................................152.3.4 Frequency domain analysis ...............................162.3.5 Time domain analysis ........................................172.3.6 Numerical methods ...........................................172.3.7 Frequency and panel mesh requirements ...........172.3.8 Irregular frequencies .........................................182.4 Wave Loads on small volume structures ...................182.4.1 Small volume 3D objects ..................................182.4.2 Sectional force on slender structures .................182.4.3 Definition of force coefficients .........................192.4.4 Moving structure in still water ..........................192.4.5 Moving structure in waves and current .............202.4.6 Relative velocity formulation ............................202.4.7 Applicability of relative velocity formulation ...202.4.8 Hydrodynamic coefficients for normal flow .....212.5 References .................................................................213 Lifting through wave zone – general ......................233.1 Introduction ...............................................................233.1.1 Objective ...........................................................233.1.2 Phases of a subsea lift ........................................233.1.3 Application ........................................................233.2 Loads and load effects............................................... 233.2.1 General ..............................................................233.2.2 Weight of object ................................................233.2.3 Buoyancy force .................................................233.2.4 Steady force due to current ................................243.2.5 Inertia force due to moving object..................... 243.2.6 Wave damping force .........................................253.2.7 Wave excitation force........................................ 253.2.8 Viscous drag force .............................................253.2.9 Slamming force ................................................. 273.2.10 Equation of vertical motion of lifted object whenlowered into wave zone. ................................... 273.2.11 Slamming on top plate of suction anchor .......... 283.2.12 Water exit force ................................................ 283.2.13 Equation of vertical motion of lifted object whenhoisted out of wave zone. ................................. 293.2.14 Hydrodynamic loads on slender elements ........ 293.3 Hydrodynamic Coefficients ...................................... 313.3.1 General .............................................................. 313.3.2 Added mass and drag coefficients for simplebodies ................................................................ 313.3.3 Added mass and damping for typical subseastructures ........................................................... 313.3.4 Added mass and damping for ventilatedstructures ........................................................... 313.3.5 Drag coefficients for circular cylinders ............ 323.3.6 Estimating added mass and damping coefficientsfrom model tests or CFD analyses .................... 323.4 Calculation methods for estimation ofhydrodynamic forces ................................................ 333.4.1 The Simplified Method ..................................... 333.4.2 Regular design wave approach ......................... 333.4.3 Time domain analyses ...................................... 363.4.4 CFD analyses .................................................... 373.5 Moonpool operations ................................................ 383.5.1 General .............................................................. 383.5.2 Simplified analysis of lift through moonpool ... 383.5.3 Equation of motion ........................................... 383.5.4 Resonance period .............................................. 393.5.5 Damping of water motion in moonpool ............ 393.5.6 Force coefficients in moonpool ........................ 413.5.7 Comprehensive calculation method .................. 423.6 Stability of lifting operations .................................... 423.6.1 Introduction ...................................................... 423.6.2 Partly air-filled objects ...................................... 433.6.3 Effects of free water surface inside the object .. 433.7 References ................................................................ 434 Lifting through wave zone - simplified method ..... 454.1 Introduction .............................................................. 454.1.1 Objective ........................................................... 454.1.2 Application ....................................................... 454.1.3 Main assumptions ............................................. 454.2 Static Weight ............................................................ 454.2.1 General .............................................................. 454.2.2 Minimum and Maximum Static weight ............ 454.3 Hydrodynamic Forces ............................................... 464.3.1 General .............................................................. 464.3.2 Wave periods .................................................... 464.3.3 Crane tip motions .............................................. 464.3.4 Wave kinematics ............................................... 474.3.5 Slamming impact force ..................................... 484.3.6 Varying buoyancy force .................................... 494.3.7 Mass force ......................................................... 494.3.8 Drag force ......................................................... 494.3.9 Hydrodynamic force ......................................... 494.4 Accept Criteria .......................................................... 504.4.1 General .............................................................. 50DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 54.4.2 Characteristic total force ...................................504.4.3 The slack sling criterion ....................................504.4.4 Capacity checks .................................................504.5 Typical Load Cases during Lowering throughWater Surface............................................................ 514.5.1 General ..............................................................514.5.2 Load cases for a protection structure .................514.6 Estimation of Hydrodynamic Parameters ..................524.6.1 General ..............................................................524.6.2 Drag coefficients ...............................................524.6.3 Added mass for non-perforated structures .........524.6.4 Effect of perforation ..........................................534.7 Snap Forces in Slings or Hoisting Line..................... 544.7.1 General ..............................................................544.7.2 Snap force ..........................................................544.7.3 Snap velocity .....................................................544.7.4 Snap force due to start or stop ...........................544.7.5 Snap force due to lift-off ................................... 544.7.6 Stiffness of hoisting system ...............................554.7.7 Application of passive heave compensationsystems with limited stroke length ....................554.8 References .................................................................565 Deepwater lowering operations ...............................575.1 Introduction ...............................................................575.1.1 General ..............................................................575.1.2 Application ........................................................575.2 Static forces on cable and lifted object ......................575.2.1 Stretched length of a cable ................................575.2.2 Horizontal offset due to current .........................575.2.3 Vertical displacement ........................................585.2.4 Vertical cable stiffness ......................................585.2.5 Horizontal stiffness ...........................................595.2.6 Cable payout – quasi-static loads ......................595.3 Dynamic forces on cable and lifted object .................595.3.1 General ..............................................................595.3.2 Dynamic drag forces .........................................605.3.3 Application ........................................................605.3.4 Natural frequencies, straight vertical cable .......605.3.5 Eigenperiods ......................................................605.3.6 Longitudinal pressure waves .............................615.3.7 Response of lifted object in a straight verticalcable exposed to forced vertical oscillations .....625.3.8 Horizontal motion response of lifted object in astraight vertical cable ........................................635.4 Heave compensation .................................................635.4.1 General ..............................................................635.4.2 Dynamic model for heave compensation, examplecase.................................................................... 645.5 References .................................................................656 Landing on seabed and retrieval .............................666.1 Introduction ...............................................................666.1.1 Types of structures and foundation designs ......666.1.2 Geotechnical data ..............................................666.2 Landing on seabed .....................................................666.2.1 Introduction .......................................................666.2.2 Landing impact problem definition ...................666.2.3 Physical parameters and effects to be considered676.2.4 Iterative analysis procedure .............................. 696.2.5 Simplified method for foundations without skirts706.2.6 Simplified method for foundations with skirts onsoft soil ............................................................. 706.2.7 Application of safety factors ............................. 716.2.8 Calculation of skirt penetration resistance ........ 716.3 Installation by suction ............................................... 716.4 Levelling by application of suction or overpressure726.5 Retrieval of foundations ........................................... 726.5.1 Retrieval of skirted foundations ........................ 726.5.2 Retrieval of non-skirted foundations ................ 726.6 References ................................................................ 737 Towing operations ................................................... 747.1 Introduction .............................................................. 747.1.1 General .............................................................. 747.1.2 Environmental restrictions ................................ 747.2 Surface tows of large floating structures .................. 747.2.1 System definition .............................................. 747.2.2 Data for modelling and analysis of tows ........... 747.2.3 Static towline configuration .............................. 757.2.4 Towline stiffness ............................................... 767.2.5 Drag locking ..................................................... 767.2.6 Mean towing force ............................................ 767.2.7 Low frequency motions .................................... 777.2.8 Short towlines / propeller race .......................... 777.2.9 Force distribution in a towing bridle ................. 787.2.10 Shallow water effects ........................................ 787.2.11 Dynamics of towlines ....................................... 797.2.12 Nonlinear time domain analysis ........................ 797.2.13 Rendering winch ............................................... 807.3 Submerged tow of 3D objects and long slenderelements .................................................................... 817.3.1 General .............................................................. 817.3.2 Critical parameters ............................................ 817.3.3 Objects attached to Vessel ................................ 817.3.4 Objects attached to Towed Buoy ...................... 827.3.5 Tow of long slender elements ........................... 827.3.6 System data ....................................................... 837.3.7 System modelling ............................................. 837.3.8 Vortex induced vibrations ................................. 837.3.9 Recommendations on analysis .......................... 847.3.10 Wet anchoring ................................................... 857.4 References ................................................................ 858 Weather criteria and availability analysis ............. 878.1 Introduction .............................................................. 878.2 Environmental parameters ........................................ 878.2.1 General .............................................................. 878.2.2 Primary characteristics ...................................... 878.2.3 Weather routing ................................................ 888.3 Data accuracy ........................................................... 888.3.1 General requirements ........................................ 888.3.2 Instrumental data .............................................. 88DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 8C Dz drag coefficient for vertical flowC d damping coefficientC e water exit coefficientC F force centrec F fill factorC G centre of gravityC L lift coefficientC M mass coefficient (=1+C A )C s , C b moonpool damping coefficientslinearized moonpool damping coefficientsC s1C SC ijddd iDDD cD(θ)EEIE kfff(z)f dragf Nf Lf TF lineF BF D0F ρF CF IF T (t)F wdF WDF dF dF hF wF sF egGM LGM Thslamming coefficienthydrostatic stiffnesswater depthdepth of penetrationdiameter of flow valvediameterdiameter of propeller diskcable diameterwave spectrum directionality functionmodulus of elasticitybending stiffnessfluid kinetic energywave frequency (=ω/2π)friction coefficient for valve sleevesskin friction at depth zsectional drag forcesectional normal forcesectional lift forcesectional tangential forceforce in hoisting line/cablebuoyancy forcehorizontal drag force on lifted objectbuoyancy forcesteady force due to currentinertia forcemarginal distribution of “calm” period twave generation damping forcewave drift forcedrag forcedynamic force in cabledepth Froude numberwave excitation forceslamming forcewater exit forceacceleration of gravitylongitudinal metacentric heighttransverse metacentric heightgap between soil and skirt tipH wave heigth (=A C +A T )H(ω,θ) motion transfer functionH L motion transfer function for lifted objectbreaking wave heightH bH m0H sIkkksignificant wave heightsignificant wave heightarea moment of inertia of free surface in tankwave numberroughness heighttotal towline stiffnessk’ equivalent winch stiffness coefficientk flowk sk ck ck fk tk Vk Ek Ek Gk Gk Hk UKK CKC pork ijK ijLL bL sL sleeveMmpressure loss coefficientstiffness of soft slingstiffness of cranemasterstiffness of heave compensatorskin friction correlation coefficienttip resistance correlation coefficientvertical cable stiffnessvertical elastic cable stiffnesselastic towline stiffnessvertical geometric cable stiffnessgeometric towline stiffnesshorizontal stiffness for lifted objectsoil unloading stiffnessstiffness of hoisting systemKeulegan-Carpenter number“Porous Keulegan-Carpenter number”wave numbermooring stiffnessunstretched length of cable/towlinelength of towed objectstretched length of cablelength of valve sleevesmass of lifted objectmass per unit length of cablem’ equivalent winch massm am cM fM GM ijM nadded mass per unit lengthmass of heave compensatordynamic amplification factormoment of towing forcestructural mass matrixspectral momentstowM mass of towed objectstugM mass of tugsNN cN spnumber of wave maximanumber of “calm” periodsnumber of “storm” periodsperforation ratioDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 10δ vertical soil displacement to mobilize Qmobsd& δ rate of change of soil displacementsoilγγ rγ mpeak shape parameter in Jonswap spectrumrate effect factorsoil material coefficientΓ( ) Gamma functionφ~ηηη&η aη Lκκvelocity potentialvertical motion of lifted objectwave induced motion of objectvertical velocity of lifted objectvertical single amplitude crane tip motionmotion of lifted objectmoonpool correction factoramplification factorµ discharge coefficientνν jν ijλθθψρρ sρ wσσσ ησ vσ rΣτcτsωω jω 0fluid kinematic viscositynatural wave numbers of cablewave numberwave lengthwave directionadjustment factor for mass of hoisting linewave amplification factormass density of watermass density of cablemass density of waterspectral width parameterlinear damping coefficient for cable motionstandard deviation of vertical crane tip motionstandard deviation of water particle velocitystandard deviation of dynamic loadlinear damping coefficient for motion of liftedobjectaverage duration of “calm” periodsaverage duration of “storm” periodswave angular frequencynatural frequencies of cableresonance wave angular frequencyω’ non-dimensional frequencyω ηω pξ jξ Langular frequency of vertical motion of liftedobjectangular spectral peak frequencyrigid body motionhorizontal offset at end of cableξ(z) horizontal offset of lifted objectζ(t) wave surface elevationζ aζ bζ sζ wwave amplitudemotion of body in moonpoolheave motion of shipsea surface elevation outside moonpoolDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 112 General methods of analysis2.1 Introduction2.1.1.1 This chapter is a selective extract of thedescription of wave load analysis given in DNV-RP-C205,ref./1/. For more thoroug discussion of this topic and othermetocean issues, see /1/ and referenced documents listed inSection 2.5.2.2 Description of waves2.2.1 General2.2.1.1 Ocean waves are irregular and random in shape,height, length and speed of propagation. A real sea state isbest described by a random wave model.2.2.1.2 A linear random wave model is a sum of manysmall linear wave components with different amplitude,frequency and direction. The phases are random with respectto each other.2.2.1.3 A non-linear random wave model allows for sumanddifference frequency wave component caused by nonlinearinteraction between the individual wave components.2.2.1.4 Wave conditions which are to be considered forstructural design purposes, may be described either bydeterministic design wave methods or by stochastic methodsapplying wave spectra.2.2.2 Regular waves2.2.2.1 A regular travelling wave is propagating withpermanent form. It has a distinct wave length, wave period,wave height.2.2.2.2 A regular wave is described by the followingmain characteristics;- Wave length: The wave length λ is the distance betweensuccessive crests.- Wave period: The wave period T is the time intervalbetween successive crests passing a particular point.- Phase velocity: The propagation velocity of the waveform is called phase velocity, wave speed or wavecelerity and is denoted by c = λ / T- Wave frequency is the inverse of wave period: f = 1/T- Wave angular frequency: ω = 2π / T- Wave number: k = 2π/λ- Surface elevation: The surface elevation z = η(x,y,t) isthe distance between the still water level and the wavesurface.- Wave crest height A C is the distance from the still waterlevel to the crest.- Wave trough depth A H is the distance from the still waterlevel to the trough.- Wave height: The wave height H is the vertical distancefrom trough to crest. H = A C + A T .2.2.1.5 For quasi-static response of structures, it issufficient to use deterministic regular waves characterized bywave length and corresponding wave period, wave height,crest height and wave. The deterministic wave parametersmay be predicted by statistical methods.λλ2.2.1.6 Structures with significant dynamic responserequire stochastic modelling of the sea surface and itskinematics by time series. A sea state is specified by a wavefrequency spectrum with a given significant wave height, arepresentative frequency, a mean propagation direction and aspreading function. A sea state is also described in terms ofits duration of stationarity, usually taken to be 3 hours.Figure 2-1 Regular travelling wave properties2.2.1.7 The wave conditions in a sea state can be dividedinto two classes: wind seas and swell. Wind seas aregenerated by local wind, while swell have no relationship tothe local wind. Swells are waves that have travelled out ofthe areas where they were generated.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 122.2.2.3 Nonlinear regular waves are asymmetric, A C >A Tand the phase velocity depends on wave height.2.2.2.4 For a specified regular wave with period T, waveheight H and water depth d, two-dimensional regular wavekinematics can be calculated using a relevant wave theoryvalid for the given wave parameters.2.2.2.5 Table 3-1 in DNV-RP-C205, ref./1/, givesexpressions for horizontal fluid velocity u and vertical fluidvelocity w in a linear Airy wave and in a second-order Stokeswave.2.2.3 Modelling of irregular waves2.2.3.1 Irregular random waves, representing a real seastate, can be modelled as a summation of sinusoidal wavecomponents. The simplest random wave model is the linearlong-crested wave model given by;Nη ( t)= ∑ A kcos( ωkt+ εk)k = 1whereε are random phases uniformly distributed between 0kand 2π, mutually independent of each other and of therandom amplitudes which are taken to be Rayleighdistributed with mean square valueE22[ A k] = S(ω ) ∆ω≡ σ2k k kS(ω) is the wave spectrum and ∆ω k= ωk− ω is thek −1difference between succesive frequencies. Use ofdeterministic amplitudes A k = σ k can give unconservativeestimates.2.2.3.2 The lowest frequency interval ∆ω is governed bythe total duration of the simulation t, ∆ω =2π/t. The numberof frequencies to simulate a typical short term sea stateshould be at least 1000. The influence of the maximumfrequency ω max should be investigated. This is particularlyimportant when simulating irregular fluid velocities.2.2.4 Breaking wave limit2.2.4.1 The wave height is limited by breaking. Themaximum wave height H b is given byH b2πd= 0.142tanhλλwhere λ is the wave length corresponding to water depth d.2.2.4.2 In deep water the breaking wave limitcorresponds to a maximum steepness S max = H b /λ = 1/7. Inshallow water the limit of the wave height can be taken as0.78 times the local water depth.2.2.5 Short term wave conditions2.2.5.1 It is common to assume that the sea surface isstationary for a duration of 20 minutes to 3-6 hours. Astationary sea state can be characterised by a set ofenvironmental parameters such as the significant wave heightH s and the peak period T p .2.2.5.2 The significant wave height H s is defined as theaverage height (trough to crest) of the highest one-thirdwaves in the indicated time period.2.2.5.3 The peak period T p is the wave period determinedby the inverse of the frequency at which a wave energyspectrum has its maximum value.2.2.5.4 The zero-up-crossing period T z is the averagetime interval between two successive up-crossings of themean sea level.2.2.5.5 Short term stationary irregular sea states may bedescribed by a wave spectrum; that is, the power spectraldensity function of the vertical sea surface displacement.2.2.5.6 Wave spectra can be given in table form, asmeasured spectra, or by a parameterized analytic formula.The most appropriate wave spectrum depends on thegeographical area with local bathymetry and the severity ofthe sea state.2.2.5.7 The Pierson-Moskowitz (PM) spectrum andJONSWAP spectrum are frequently applied for wind seas(Hasselmann et al. 1976; Pierson and Moskowitz, 1964). ThePM-spectrum was originally proposed for fully-developedsea. The JONSWAP spectrum extends PM to include fetchlimited seas. Both spectra describe wind sea conditions thatoften occur for the most severe seastates.2.2.5.8 Moderate and low sea states in open sea areas areoften composed of both wind sea and swell. A two peakspectrum may be used to account for both wind sea andswell. The Ochi-Hubble spectrum and the Torsethaugenspectrum are two-peak spectra (Ochi and Hubble, 1976;Torsethaugen, 1996).2.2.6 Pierson-Moskowitz and JONSWAP spectra2.2.6.1 The Pierson-Moskowitz (PM) spectrumS (ω) PMis given by;5 2 4 −S PM( ω ) = ⋅ H Sωp⋅ ω165⎛⎜ 5 ⎛ ⎞⎜ωexp ⎟⎜−4⎝ ⎝ ωp ⎠where ω p = 2π/T p is the angular spectral peak frequency−4⎞⎟⎟⎠DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 132.2.6.2 The JONSWAP spectrum S (ω)is formulatedas a modification of the Pierson-Moskowitz spectrum for adeveloping sea state in a fetch limited situation:S ( ω ) = AJ γS PMwhere( ω)γ⎛2 ⎞⎜ ⎛ ⎞⎜ω −ωp ⎟ ⎟exp⎜−0.5⎜ ⎟ ⎟⎜⎟⎝ ⎝ σ ω p ⎠ ⎠S PM (ω) = Pierson-Moskowitz spectrumγ = non-dimensional peak shape parameterσ = spectral width parameterσ = σ a for ω≤ ω pσ = σ b for ω > ω pAγ= 1- 0.287 ln(γ) is a normalizing factor2.2.6.3 The corresponding spectral moment M n , of thewave spectra is;Mn=∫ ∞0nω S( ω ) dωn2.2.6.4 For the JONSWAP spectrum the spectralmoments are given approximately as;MMM012===116116116H2s2 6.8 + γH s ω p5 + γ2 2 11 + γH s ω p5 + γ2.2.6.5 The following sea state parameters can be definedin terms of spectral moments:The significant wave height H s is defined byH = H = 4sm0M0The zero-up-crossing period T z can be estimated by:Tm02= 2πM0M2The mean wave period T 1 can be estimated by:Tm01M= 2π0M1JJONSWAP spectrum reduces to the Pierson-Moskowitzspectrum.2.2.6.7 The JONSWAP spectrum is expected to be areasonable model for3 .6 T p/ H < 5

Recommended Practice DNV-RP-H103 Draft December 2008Page 142.2.7 Directional distribution of wind sea and swell2.2.7.1 Directional short-crested wave spectraS(ω,θ) may be expressed in terms of the uni-directionalwave spectra,S ( ω,θ ) = S(ω)D(θ,ω)= S(ω)D(θ )where the latter equality represents a simplification oftenused in practice. Here D(θ,ω) and D(θ) are directionalityfunctions. θ is the angle between the direction of elementarywave trains and the main wave direction of the short crestedwave system.2.2.7.2 The directionality function fulfils therequirement;∫ D( θ,ω)dθ= 1θ2.2.7.3 For a two-peak spectrum expressed as a sum of aswell component and a wind-sea component, the totaldirectional frequency spectrum S(ω,θ) can be expressed asS ( ω,θ ) = S ( ω)D ( θ ) + S ( ω)D ( θ )wind seawind seaswellswell2.2.7.4 A common directional function often used forwind sea is;Γ(1+ n / 2) nD(θ ) = cos ( θ − θ p )π Γ(1 / 2 + n / 2)where Γ isthe Gamma function and |πθ - θp| ≤ .22.2.7.5 The main direction θ p may be set equal to theprevailing wind direction if directional wave data are notavailable.2.2.7.6 Due consideration should be taken to reflect anaccurate correlation between the actual sea-state and theconstant n. Typical values for wind sea are n = 2 to n = 4. Ifused for swell, n ≥ 6 is more appropriate.2.2.8 Maximum wave height in a stationary sea state1 0.2886Expected extreme value ln N (1 + )2 ln NFor a narrow banded sea state, the number of maxima can betaken as N = t/T Z where t is the sea state duration.2.3 Wave loads on large volume structures2.3.1 Introduction2.3.1.1 Offshore structures are normally characterized aseither large volume structures or small volume structures.For a large volume structure the structure’s ability to createwaves is important in the force calculations while for smallvolume structrures this is negligible.2.3.1.2 Small volume structures may be divided intostructures dominated by dragforce and structures dominatedby inertia (mass) force. Figure 2-3 shows the differentregimes where area I, III, V and VI covers small volumestructures.2.3.1.3 The term large volume structure is used forstructures with dimensions D on the same order of magnitudeas typical wave lengths λ of ocean waves exciting thestructure, usually D > λ/6. This corresponds to the diffractionwave force regimes II and IV shown in Figure 2-3 belowwhere this boundary is equivalently defined as πD/λ > 0.5.2.3.2 Motion time scales2.3.2.1 A floating, moored structure may respond towind, waves and current with motions on three different timescales,• wave frequency (WF) motions• low frequency (LF) motions2.3.2.2 The largest wave loads on offshore structures takeplace at the same frequencies as the waves, causing wavefrequency (WF) motions of the structure. To avoid largeresonant effects, offshore structures and their mooringsystems are often designed in such a way that the resonantfrequencies are shifted well outside the wave frequencyrange.2.2.8.1 For a stationary sea state with N independentlocal maximum wave heights, the extreme maxima in the seastate can be taken as:Quantity H max /H s (N is large)Most probable largest1ln2N1 0.1835Median value ln N ⋅ (1 + )2ln NDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 152.3.3 Natural periods2.3.3.1 Natural periods for a large moored offshorestructure in surge, sway and yaw are typically more than 100seconds. Natural periods in heave, roll and pitch of semisubmersiblesare usually above 20 seconds.2.3.3.2 The natural periods T j , j = 1,2,…6 of a mooredoffshore structure are approximately given by⎛ Mjj+ AT = 2 ⎜jπ⎝Cjj+ Kjjjj1⎞⎟⎠2where M jj , A jj , C jj and K jj are the diagonal elements of themass, added mass, hydrostatic and mooring stiffnessmatrices.2.3.3.3 Natural periods may depend on coupling betweendifferent modes and the amount of damping.2.3.3.4 The uncoupled natural period in heave for a freelyfloating offshore vessel isFigure 2-3 Different wave force regimes (Chakrabarti,1987). D = characteristic dimension, H = wave height, λ =wave length.2.3.2.3 A floating structure responds mainly in its sixrigid modes of motions including translational modes, surge,sway, heave, and rotational modes, roll, pitch, yaw. Inaddition, wave induced loads can cause high frequencyelastic response, i.e. springing and whipping of ships.2.3.2.4 Due to non-linear load effects, some responsesalways appear at the natural frequencies. Slowly varyingwave and wind loads give rise to low frequency (LF)resonant horizontal motions, also named slow-drift motions.2.3.2.5 The WF motions are mainly governed by inviscidfluid effects, while viscous fluid effects are relativelyimportant for LF motions. Different hydrodynamic effectsare important for each floater type, and must be taken intoaccount in the analysis and design.⎛ M + A3332 ⎟ ⎞T = π⎜⎝ ρgS⎠12where M is the mass, A 33 the heave added mass and S is thewaterplane area.2.3.3.5 The natural period in pitch for a freely floatingoffshore vessel is;T5= 22⎛⎜Mr55+ Aπ⎝ ρgV GM L55⎞⎟⎠12where r 55 is the pitch radius of gyration, A 55 is the pitchadded moment and GM L is the longitudinal metacentricheight. The natural period in roll isT4= 22⎛⎜Mr44+ Aπ⎝ ρgV GM T44⎞⎟⎠12where r 44 is the roll radius of gyration, A 44 is the roll addedmoment and GM T is the transversal metacentric height.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 162.3.4 Frequency domain analysis2.3.4.1 The wave induced loads in an irregular sea can beobtained by linearly superposing loads due to regular wavecomponents. Analysing a large volume structure in regularincident waves is called a frequency domain analysis.2.3.4.2 Assuming steady state, with all transient effectsneglected, the loads and dynamic response of the structure isoscillating harmonically with the same frequency as theincident waves, or with the frequency of encounter in thecase of a forward speed.2.3.4.3 Within a linear analysis, the hydrodynamicproblem is usually divided into two sub-problems:• Radiation problem where the structure is forced tooscillate with the wave frequency in a rigid bodymotion mode with no incident waves. The resultingloads are usually formulated in terms of addedmass, damping and restoring loadsFd ξ2( r)jk= −Akj2dt− Bkjdξdtj− C ξwhere A kj and B kj are added mass and damping, and C kjare the hydrostatic restoring coefficients, j,k = 1,6, forthe six degrees of rigid body modes. A kj and B kj arefunctions of wave frequency ω.• Diffraction problem where the structure isrestrained from motions and is excited by incidentwaves. The resulting loads are wave excitation loadsFk( d )= f ( ω)ek− iωt; k = 1,62.3.4.4 The part of the wave excitation loads that is givenby the undisturbed pressure in the incoming wave is calledthe Froude-Krylov forces/moments. The remaining part iscalled diffraction forces/moments.2.3.4.5 Large volume structures are inertia-dominated,which means that the global loads due to wave diffraction aresignificantly larger than the drag induced global loads. Somefloaters, such as semi-submersibles, may also require aMorison load model for the slender members/braces inaddition to the radiation/diffraction model, ref. Section 2.4.kjjdrift force and moments are of second order, but depends onfirst order quantities only.2.3.4.8 The output from a frequency domain analysis willbe transfer functions of the variables in question, e.g.exciting forces/moments and platform motions per unit waveamplitude. The first order or linear force/ moment transferfunction (LTF) is usually denoted H (1) (ω). The linear motion(1)transfer function, ξ ( ω), also denoted the responsetransfer function H R (ω) or the Response Amplitude Operator(RAO). The RAO gives the response per unit amplitude ofexcitation, as a function of the wave frequency,(1)(1)ξ ( ω)= H ( ω)L−1( ω)where L(ω) is the linear structural operator characterizing theequations of motion,[ M + A(ω)] + iωB(ω C2L ( ω ) = −ω) +M is the structure mass and inertia, A the added mass, B thewave damping and C the stiffness, including both hydrostaticand structural stiffness. The equations of rigid body motionare, in general, six coupled equations for three translations(surge, sway and heave) and three rotations (roll, pitch andyaw).2.3.4.9 The concept of RAOs is also used for globalforces and moments derived from rigid body motions and fordiffracted wave surface elevation, fluid pressure and fluidkinematics.2.3.4.10 The frequency domain method is well suited forsystems exposed to random wave environments, since therandom response spectrum can be computed directly fromthe transfer function and the wave spectrum in the followingway:S R( ω)= ξwhereωξ (1) (ω)S(ω)S R (ω)(1)2( ω) S(ω)= angular frequency (= 2π /T)= transfer function of the response= wave spectrum= response spectrum2.3.4.6 A linear analysis will usually be sufficientlyaccurate for prediction of global wave frequency loads.Hence, this section focuses on first order wave loads. Theterm linear means that the fluid dynamic pressure and theresulting loads are proportional to the wave amplitude. Thismeans that the loads from individual waves in an arbitrarysea state can be simply superimposed.2.3.4.7 Only the wetted area of the floater up to the meanwater line is considered. The analysis gives first orderexcitation forces, hydrostatics, potential wave damping,added mass, first order motions in rigid body degrees offreedom and the mean drift forces/moments. The mean waveDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 172.3.4.11 Based on the response spectrum, the short-termresponse statistics can be estimated. The method limitationsare that the equations of motion are linear and the excitationis linear.2.3.4.12 A linear assumption is also employed in therandom process theory used to interpret the solution. This isinconvenient for nonlinear effects like drag loads, dampingand excitation, time varying geometry, horizontal restoringforces and variable surface elevation. However, in manycases these non-linearities can be satisfactorily linearised.2.3.4.13 Frequency domain analysis is used extensivelyfor floating units, including analysis of both motions andforces. It is usually applied in fatigue analyses, and analysesof more moderate environmental conditions wherelinearization gives satisfactory results. The main advantageof this method is that the computations are relatively simpleand efficient compared to time domain analysis methods.2.3.5 Time domain analysis2.3.5.1 Some hydrodynamic load effects can belinearised and included in a frequency domain approach,while others are highly non-linear and can only be handled intime-domain.2.3.5.2 The advantage of a time domain analysis is that itcan capture higher order load effects. In addition, a timedomain analysis gives the response statistics without makingassumptions regarding the response distribution.2.3.5.3 A time-domain analysis involves numericalintegration of the equations of motion and should be usedwhen nonlinear effects are important. Examples are• transient slamming response• simulation of low-frequency motions (slow drift)• coupled floater, riser and mooring response2.3.6 Numerical methods2.3.6.1 Wave-induced loads on large volume structurescan be predicted based on potential theory which means thatthe loads are deduced from a velocity potential of theirrotational motion of an incompressible and inviscid fluid.2.3.6.2 The most common numerical method for solutionof the potential flow is boundary element method (BEM)where the velocity potential in the fluid domain isrepresented by a distribution of sources over the mean wettedbody surface. The source function satisfies the free surfacecondition and is called a free surface Green function.Satisfying the boundary condition on the body surface givesan integral equation for the source strength.2.3.6.3 An alternative is to use elementary Rankinesources (1/R) distributed over both the mean wetted surfaceand the mean free surface. A Rankine source method ispreferred for forward speed problems.2.3.6.4 Another representation is to use a mixeddistribution of both sources and normal dipoles and solvedirectly for the velocity potential on the boundary.2.3.6.5 The mean wetted surface is discretized into flat orcurved panels, hence these methods are also called panelmethods. A low-order panel method uses flat panels, while ahigher order panel method uses curved panels. A higherorder method obtains the same accuracy with less number ofpanels. Requirements to discretisation are given in ref./1/.2.3.6.6 The potential flow problem can also be solved bythe finite element method (FEM), discretizing the volume ofthe fluid domain by elements. For infinite domains, ananalytic representation must be used a distance away fromthe body to reduce the number of elements. An alternative isto use so-called infinite finite element.2.3.6.7 For fixed or floating structures with simplegeometries like sphere, cylinder, spheroid, ellipsoid, torus,etc. semi-analytic expressions can be derived for the solutionof the potential flow problem. For certain offshore structures,such solutions can be useful approximations.2.3.6.8 Wave-induced loads on slender ship-like largevolume structures can be predicted by strip theory where theload is approximated by the sum of loads on twodimensionalstrips. One should be aware that the numericalimplementation of the strip theory must include a propertreatment of head sea (β = 180 o ) wave excitation loads.2.3.6.9 Motion damping of large volume structures is dueto wave radiation damping, hull skin friction damping, hulleddy making damping, viscous damping from bilge keels andother appendices, and viscous damping from risers andmooring. Wave radiation damping is calculated frompotential theory. Viscous damping effects are usuallyestimated from simplified hydrodynamic models or fromexperiments. For simple geometries Computational FluidDynamics (CFD) can be used to assess viscous damping.2.3.7 Frequency and panel mesh requirements2.3.7.1 Several wave periods and headings need to beselected such that the motions and forces/moments can bedescribed as correctly as possible. Cancellation,amplification and resonance effects must be properlycaptured.2.3.7.2 Modelling principles related to the fineness of thepanel mesh must be adhered to. For a low-order panelmethod (BEM) with constant value of the potential over thepanel the following principles apply:DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 18• Diagonal length of panel mesh should be less than 1/6 ofsmallest wave length analysed.• Fine mesh should be applied in areas with abruptchanges in geometry (edges, corners).• When modelling thin walled structures with water onboth sides, the panel size should not exceed 3-4 timesthe modelled wall thickness.• Finer panel mesh should be used towards water-linewhen calculating wave drift excitation forces.• The water plane area and volume of the discretizedmodel should match closely to the real structure.2.3.7.3 Convergence tests by increasing number of panelsshould be carried out to ensure accuracy of computed loads.Comparing drift forces calculated by the pressure integrationmethod and momentum method provides a useful check onnumerical convergence for a given discretisation.2.3.7.4 Calculating wave surface elevation and fluidparticle velocities require an even finer mesh as compared toa global response analysis. The diagonal of a typical panel isrecommended to be less than 1/10 of the shortest wavelength analysed. For low-order BEM, fluid kinematics andsurface elevation should be calculated at least one panelmesh length away from the body boundary, preferably closeto center of panels.2.3.7.5 For a motion analysis of a floater in the frequencydomain, computations are normally performed for at least 30frequencies. Special cases may require a higher number. Thisapplies in particular in cases where a narrow-band resonancepeak lies within the wave spectral frequency range. Thefrequency spacing should be less than ζω 0 to achieve lessthan about 5% of variation in the standard deviation ofresponse. ζ is the damping ratio and ω 0 the frequency.2.3.8 Irregular frequencies2.3.8.1 For radiation/diffraction analyses, using freesurface Green function solvers, of large volume structureswith large water plane area like ships and barges, attentionshould be paid to the existence of so-called irregularfrequencies.2.3.8.2 Irregular frequencies correspond to fictitiouseigenmodes of an internal problem (inside the numericalmodel of the structure) and do not have any direct physicalmeaning. It is a deficiency of the integral equation methodused to solve for the velocity potential.2.3.8.3 At irregular frequencies a standard BEM methodmay give unreliable values for added mass and damping.Methods are available in some commercial software tools toremove the unwanted effects of the irregular frequencies.The Rankine source method avoids irregular frequencies.2.3.8.4 Irregular wave numbers ν ij of a rectangular bargewith length L, beam B and draft T are given by the relationsνij=wherekijcoth( k T)ij22k ij= π ( i / L)+ ( j / B); i,j = 0,1,2,...; i + j ≥ 12.4 Wave Loads on small volume structures2.4.1 Small volume 3D objects2.4.1.1 The term small volume structure is used forstructures with dimensions D that are smaller than the typicalwave lengths λ of ocean waves exciting the structure, usuallyD < λ/6, see Figure 2-3.2.4.1.2 A Morison type formulation may be used toestimate drag and inertia loads on three dimensional objectsin waves and current;F( t )1= ρ V(1 + C A ) v&+ ρCD Sv v2wherev = fluid particle (waves and/or current) velocity [m/s]v& = fluid particle acceleration [m/s 2 ]V = displaced volume [m 3 ]S = projected area normal to the force direction [m 2 ]ρ = mass density of fluid [kg/m 3 ]C A = added mass coefficient [-]C D = drag coefficient [-]Added mass coefficients for some 3D objects are given inAppendix A. Drag coefficients are given in Appendix B.2.4.1.3 For some typical subsea structures which areperforated with openings (holes), the added mass maydepend on motion amplitude or equivalently, the K C -number(Molin & Nielsen, 2004). A summary of force coefficientsfor various 3D and 2D objects can be found in Øritsland(1989).2.4.2 Sectional force on slender structures2.4.2.1 The hydrodynamic force exerted on a slenderstructure in a general fluid flow can be estimated bysumming up sectional forces acting on each strip of thestructure. In general the force vector acting on a strip can bedecomposed in a normal force f N , an axial force f T and a liftforce f L being normal to both f N and f T , see Figure 2-4. InDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 19addition a torsion moment m T will act on non-circular crosssections.f Tf NαvFigure 2-4. Definition of normal force, axial force and liftforce on slender structure.2.4.2.2 For slender structural members (cylinders) havingcross-sectional dimensions sufficiently small to allow thegradients of fluid particle velocities and accelerations in thedirection normal to the member to be neglected, wave loadsmay be calculated using the Morison's load formula.Thesectional force f N on a fixed slender structure in twodimensionalflow normal to the member axis is then given by1fN(t)= ρ (1 + CA)Av&+ ρC2whereDDv vv = fluid particle (waves and/or current) velocity [m/s]v& = fluid particle acceleration [m/s 2 ]A = cross sectional area [m 2 ]D = diameter or typical cross-sectional dimension [m]ρ = mass density of fluid [kg/m 3 ]C A = added mass coefficient (with cross-sectional areaas reference area) [-]C D = drag coefficient [-]2.4.2.3 Normally, Morison's load formula is applicablewhen the following condition is satisfied:λ > 5 Dwhere λ is the wave length and D is the diameter or otherprojected cross-sectional dimension of the member.2.4.2.4 For combined wave and current flow conditions,wave and current induced particle velocities should be addedas vector quantities. If available, computations of the totalparticle velocities and accelerations based on more exacttheories of wave/current interaction are preferred.v Nf Lwheref drag= sectional drag force [N/m]ρ = fluid density [kg/m 3 ]Dv= diameter (or typical dimension) [m]= velocity [m/s]2.4.3.2 In general the fluid velocity vector will be in adirection a relative to the axis of the slender member (Figure2-4). The drag force f drag is decomposed in a normal force f Nand an axial force f T .2.4.3.3 The added mass coefficient C A is the nondimensionaladded massCAwherem ama=ρA= the added mass per unit length [kg/m]Α = cross-sectional area [m 2 ]2.4.3.4 The mass coefficient is defined asC M = 1 + C A2.4.3.5 The lift coefficient is defined as the nondimensionallift forceC Lwheref LfL=1ρDv22= sectional lift force [N/m]2.4.4 Moving structure in still water2.4.4.1 The sectional force f N on a moving slenderstructure in still water can be written as1f t ρCAr &AρCdDr&r&N() = − −2wherer& = velocity of member normal to axis [m/s]& r& = acceleration of member normal to axis [m/s 2 ]C d = hydrodynamic damping coefficient [-]2.4.3 Definition of force coefficients2.4.3.1 The drag coefficient C D is the non-dimensionaldrag-force;C Dfdrag=1ρ D v22DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 202.4.5 Moving structure in waves and current2.4.5.1 The sectional force f N on a moving slenderstructure in two-dimensional non-uniform (waves andcurrent) flow normal to the member axis can be obtained bysumming the force contributions in 2.3.2.2 and 2.3.4.1.f ( t)= −ρCNAAr &+ ρ(1+ CA1) Av&+ ρC2D1Dv v − ρCD&r r&d22.4.5.2 This form is known as the independent flow fieldmodel. In a response analysis, solving for r = r(t), the addedmass force ρ C Ar & A= m &aradds to the structural mass m stimes acceleration on the left hand side of the equation ofmotion. When the drag force is expressed in terms of therelative velocity, a single drag coefficient is sufficient.Hence, the relative velocity formulation (2.3.6) is most oftenapplied.10 ≤ V R < 20 Relative velocity may lead to an overestimationof damping if the displacementis less than the member diameter.V R < 10It is recommended to discard the velocityof the structure when the displacement isless than one diameter, and use the dragformulation in 2.4.2.2.2.4.7.3 For a vertical surface piercing member incombined wave and current field, the parameter V R can becalculated usingvv cT n= v c + π H s /T z approximation of particle velocityclose to wave surface [m/s]= current velocity [m/s]= period of structural oscillations [s]2.4.6 Relative velocity formulation2.4.6.1 The sectional force can be written in terms ofrelative velocity;1fN(t)= −ρ CAAr&+ ρ(1+ CA)Av&+ ρCDDvrvr2or in a equivalent form when relative acceleration is alsointroduced;f ( t)= ρ Aa + ρCAa +NwhereAr12ρCDvva = v& is the fluid acceleration [m/s]v r = v − r& is the relative velocity [m/s]a r = v & − & r& is the relative acceleration [m/s 2 ]Drr2.4.6.2 When using the relative velocity formulation forthe drag forces, additional hydrodynamic damping shouldnormally not be included.2.4.7 Applicability of relative velocity formulation2.4.7.1 The use of relative velocity formulation for thedrag force is valid if;r/D > 1where r is the member displacement amplitude andD is the member diameter.2.4.7.2 When r/D < 1 the validity is depending on thevalue of the parameter V R = vT n /D as follows:20 ≤ V R Relative velocity recommendedDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 21fD CWave Forces on Offshore Structures", Van Nostrand,,maxD= KCf π2(1 CReinhold Company, New York, 1981.The formula can be used as an indicator on whether the forceis drag or inertia dominated.2.4.8 Hydrodynamic coefficients for normal flow2.4.8.4 For combined wave and current conditions, thegoverning parameters are Reynolds number based on2.4.8.1 When using Morison's load formula to calculatemaximum velocity, v = v c + v m , Keulegan-Carpenter numberthe hydrodynamic loads on a structure, one should take intobased on maximum orbital velocity v m and the current flowaccount the variation of C D and C A as function of Reynoldsvelocity ratio, defined asnumber, the Keulegan-Carpenter number and the roughness.C D = C D (R e , K C , ∆)α c = v c /(v c +v m )where v c is the current velocity.C A = C A (R e ,K C , ∆)2.4.8.5 For sinusoidal (harmonic) flow the Keulegan-Carpenter number can also be written asThe parameters are defined as:K C= 2πη0/ D• Reynolds number: R e = vD/νwhere η 0 is the oscillatory flow amplitude. Hence, the KCnumber• Keulegan-Carpenter number: K C = v m T /Dis a measure of the distance traversed by a fluid• Non-dimensional roughness: ∆=k/Dparticle during half a period relative to the member diameter.where2.4.8.6 For fluid flow in the wave zone η 0 in the formulaD = Diameter [m]above can be taken as the wave amplitude so that the K Cnumber becomesT = wave period or period of oscillation [s]πHK C=k = roughness height [m]Dv = total flow velocity [m/s]where H is the wave height.ν = fluid kinematic viscosity [m 2 /s]. See appendix F. 2.4.8.7 For an oscillating structure in still water, whichv m = maximum orbital particle velocity [m/s]for example is applicable for the lower part of the riser indeep water, the Keulegan-Carpenter number is given byThe effect of R e , K C and ∆ on the force coefficients is x&mTKC=described in detail in Sarpkaya (1981), ref./5/.D2.4.8.2 For oscillatory fluid flow a viscous frequency where x&mis the maximum velocity of the structure, T is theparameter is often used instead of the Reynolds number. period of oscillation and D is the cylinder diameter.This parameter is defined as the ratio between the Reynoldsnumber and the Keulegan-Carpenter number,β = R e /K C = D 2 /νT = ωD 2 /(2πν)where2.5 ReferencesD = diameter [m]T = wave period or period of structural oscillation [s]/1/ DNV Recommended Practice DNV-RP-C205“Environmental Conditions and Environmental Loads”,ω = 2π/T = angular frequency [rad/s]April 2007ν = fluid kinematic viscosity [m 2 /s]/2/ Faltinsen, O.M. (1990) “Sea loads on ships and offshoreExperimental data for C D and C M obtained in U-tube tests arestructures”. Cambridge University Press.often given as function of K C and β since the period of/3/ ISO/CD 19902 ”Fixed Steel Offshore Structures”oscillation T is constant and hence β is a constant for each(2004).model.2.4.8.3 For a circular cylinder, the ratio of maximum/4/ Newman, J.N. (1977) “Marine Hydrodynamics”. MITdrag force f D,max to the maximum inertia force f I,max is givenPress, Cambridge, MA, USA.by/5/ Sarpkaya, T. and Isaacson, M. (1981), "Mechanics of+I A), maxDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 22/6/ Sumer, B.M and Fredsøe, J. (1997) “Hydrodynamicsaround cylindrical structures”. World Scientific./7/ Øritsland, O. (1989) “A summary of subsea modulehydrodynamic data”. marine Operations Part III.2.Report No. 70. Marintek Report MT51 89-0045./8/ Molin, B. and Nielsen, F.G. (2004) ”Heave added massand damping of a perforated disk below the freesurface”. 19 th IWWWFB, Cortona, Italy, March 2004./9/ Chakrabarti, S.K. (1987): “Hydrodynamics of OffshoreStructures”. Springer Verlag./10/ Faltinsen, O.M., Newman, J.N., Vinje, T., (1995),Nonlinear wave loads on a slender vertical cylinder,Journal of Fluid Mechanics, Vol 289, pp. 179-198./11/ Newman, J.N. (1977) “Marine Hydrodynamics”. MITPress./12/ NORSOK Standard N-003 (2004) “Action and actioneffects”.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 233 Lifting through wave zone – generalF BF cF I= buoyancy force= steady force due to current= inertia force3.1 Introduction3.1.1 Objective3.1.1.1 Design loads need to be established whenlowering subsea structures through the wave zone. Accurateprediction of these design loads may reduce the risk ofexpensive waiting on weather, increase the number ofsuitable installation vessels and also increase the safety levelof the operation.3.1.1.2 The objective of this section is to give guidanceon how to improve the modelling and analysis methods inorder to obtain more accurate prediction of the design loads.3.1.2 Phases of a subsea lift3.1.2.1 A typical subsea lift consists of the followingmain phases:- lift off from deck and manouvering object clear oftransportation vessel- lowering through the wave zone- further lowering down to sea bed- positioning and landing3.1.3 Application3.1.3.1 This section gives general guidance for modellingand analysis of the lifting through the wave zone phase.3.1.3.2 Only typical subsea lifts are covered. Otherinstallation methods as e.g. free fall pendulum installationare not covered.3.1.3.3 A simplified method for estimating thehydrodynamic forces is given in section 4. Topics related tothe lowering phase beneath the wave influenced zone arecovered in section 5 while landing on seabed is dealt with insection 6.3.2 Loads and load effects3.2.1 General3.2.1.1 An object lowered into or lifted out of water willbe exposed to a number of different forces acting on thestructure. In general the following forces should be takeninto account when assessing the response of the object;F line = force in hoisting line/cableF wd = wave damping forceF dF wF sF e= drag force= wave excitation force= slamming force= water exit force3.2.1.2 The force F line (t) in the hoisting line is the sum ofa mean force F 0 and a dynamic force F dyn (t) due to motion ofcrane tip and wave excitation on object. The mean force isactually a slowly varying force, partly due to the loweringvelocity and partly due to water ingress into the object aftersubmergence.3.2.2 Weight of object3.2.2.1 The weight of the object is taken as;W0= Mg [N]whereΜ= mass of object including pre-filled water withinobject [kg]g = acceleration of gravity [m/s 2 ]Guidance NoteThe interpretation of the terms weight and mass is sometimesmisunderstood. Weight is a static force on an object due to gravity.The weight of the object is unchanged when it is submerged in water,but the buoyancy force acts upwards which reduces the static load inthe lifting line. Mass is a dynamic property of an object and isunchanged regardless of where the object is situated. The inertiaforce is the product of the mass and acceleration required toaccelerate the mass.3.2.2.2 Additional water flowing into the (partly or fully)submerged object shall either be included as increasedweight or as reduced buoyancy of the object. See also4.6.3.4.3.2.3 Buoyancy force3.2.3.1 The buoyancy force for a submerged object isequal to the weight of the displaced water,F B( t)= ρgV( t)[N]whereρ = mass density of water [kg/m 3 ]g = acceleration of gravity [m/s 2 ]V(t) = displaced volume of water [m 3 ]W 0= weight of object (in air)DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 24Guidance NoteThe mass density of water varies with salinity and temperature asshown in Table C1 in Appendix C.3.2.3.2 During water entry of an object lowered throughthe free surface, the buoyancy force is given by the weight ofthe instantaneous displaced water.3.2.3.3 For a totally submerged object the buoyancyforce may vary with time in the case of continued wateringress into the object.3.2.3.4 The direction of the buoyancy force is opposite togravity. If the centre of buoyancy is not vertically above thecentre of gravity, the buoyancy force will exert a rotationalmoment on the lifted object.Guidance NoteThe centre of buoyancy x B is defined as the geometrical centre of thedisplaced volume of water3.2.3.5 For a partly submerged object in long waves(compared to characteristic horizontal dimension) thebuoyancy force varies with wave elevation according to3.2.7.3. The time varying part of the buoyancy force due towaves can then be taken as a wave excitation force.3.2.3.6 For a submerged object, the submerged weight Wof the object is defined as;[ M − V ( t ] gW ( t)= W0 − FB ( t)= ρ ) ⋅ [N]3.2.4 Steady force due to current3.2.4.1 The steady force due to ocean current can betaken as a quadratic drag forceFcwhere1( ) 2= ρCDSiApiUcz [N]02C DSi = the steady state drag coefficient in the currentdirection i [-]A pi = projected area in direction i [m 2 ]U c (z 0 ) = current velocity at depth z 0 of object [m/s]3.2.4.2 The steady current force is opposed by thehorizontal component of the hoisting line force.3.2.5 Inertia force due to moving object3.2.5.1 The inertia force in direction i (i = 1,2,3) on anobject moving in pure translation can be calculated from( M ij+ A ij)&xjF I , i= − δ[N]where summation over j is assumed andM= structural mass [kg]δ ij = 1 if i = jA ij& x& j= 0 if i ≠ j= added mass in direction i due to acceleration indirection j [kg]= acceleration of object in direction j (x 1 =x, x 2 =y,and x 3 =z) [m/s 2 ]The added mass is usually expressed in terms of an addedmass coefficient C defined by;ijijARijAA = ρC V [kg]whereρ = mass density of water [kg/m 3 ]V R = reference volume of the object [m 3 ]ijC = added mass coefficient [-]AGuidance NoteIn the absence of body symmetry, the cross-coupling added masscoefficients A 12, A 13 and A 23 are non-zero, so that the hydrodynamicinertia force may differ in direction from the acceleration. Added-masscoefficients are symmetric, A ij = A ji. Hence, for a three-dimensionalobject of arbitrary shape there are in general 21 different added masscoefficients for the 3 translational and 3 rotational modes. Addedmass coefficients for general compact non-perforated structures maybe determined by potential flow theory using a sink-source technique.x , x& , & xiiix 3ζx iv , &iv iSWLFigure 3-1 Submerged object lifted through wave zone3.2.5.2 For objects crossing the water surface, thesubmerged volume V and the vertical added mass A 33 shall betaken to the still water level, z = 0.3.2.5.3 For rotational motion (typically yaw motion) of alifted object the inertia effects are given by the massmoments of inertia M ij and the added moments of inertia A ijwhere i,j = 4,5,6 as well as coupling coefficients withdimension mass multiplied by length. Reference is made toNewman (1977).Guidance NoteFor perforated structures viscous effects may be important and theadded mass will depend on the amplitude of motion defined by theKC-number. The added mass will also be affected by a large volumestructure in its close proximity.3.2.5.4 A general object in pure translational motion maybe destabilized due to the Munk moment which can beDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 25expressed in terms of the translational added masscoefficients, ref. /6/.3.2.6 Wave damping force3.2.6.1 In general when an object moves in vicinity of afree surface, outgoing surface waves will be created. Theenergy of these waves comes from the work done to dampenthe motion of the object. The resulting force on the object isthe wave damping force.3.2.6.2 The wave damping force F wd is proportional tothe velocity of the object;Fwdwhere= B x&[N]ijjB ij = wave generation damping coefficient3.2.6.3 For oscillatory motion of the object, the wavedamping force vanishes for high frequencies and for lowfrequencies. Wave damping can be neglected if;T >> 2πD/ g [s]where T is the period of the oscillatory motion, D is acharacteristic dimension of the object normal to the directionof motion and g is the acceleration of gravity. For transparentstructures composed of several slender elements, thecharacteristic dimension is the cross-sectional dimension ofthe slender elements.3.2.7 Wave excitation force3.2.7.1 The wave exciting forces and moments are theloads on the structure when it is restrained from any motionresponse and there are incident waves.3.2.7.2 When the characteristic dimensions of the objectis considerably smaller than the wave length, the waveexcitation force in direction i on a fully submerged object isfound fromF = ρ V ( δ + C ) v&+ F [N]WiwhereijijAρ = mass density of water [kg/m 3 ]VjDi= submerged volume of object (taken to still waterlevel z = 0) [m 3 ]δ ij = 1 if i = j= 0 if i ≠ jijC = added mass coefficient [-]Av& = water particle acceleration in direction j [m/s 2 ]j3.2.7.3 For a partly submerged object the excitation forcein direction i is found fromFijWi = gAwς( t ) δi3+ ρV ( δij+ CA)ρ v& [N]where the first term is a hydrostatic force (see GuidanceNote) associated with the elevation of the incident wave atthe location of the object and whereg = acceleration of gravity [m/s 2 ]A w = water plane area [m 2 ]ζ(t) = wave surface elevation [m]δ i3 = 1 if i = 3 (vertically)= 0 if i =1 or i =2 (horizontally)Guidance NoteThe hydrostatic contribution in the excitation force for a partlysubmerged object can also be viewed as part of a time dependentbuoyancy force (acting upwards) since in long waves the increase insubmerged volume for the object can be approximated by A wζ(t).Note that this is strictly valid for vertical wall sided objects only.3.2.8 Viscous drag force3.2.8.1 The viscous drag force in direction i can beexpressed by the equationF = ρ C[N]Diwhere12 DApvrvriρ = mass density of water [kg/m 3 ]C D = drag coefficient in oscillatory fluid [-]A p = projected area normal to motion/flow direction [m 2 ]v r = total relative velocity [m/s]v ri = v i - x& = relative velocity component in dir. i [m/s]iGuidance NoteNote that the viscous drag force can either be an excitation force or adamping force depending on the relative magnitude and direction ofvelocity of object and fluid particle velocity.3.2.8.2 If the damping of an oscillating object iscalculated by a quadratic drag formulation as given by3.2.8.1, the drag coefficient C D depends on the oscillationamplitude. The oscillation amplitude is usually expressed interms of the non-dimensional Keulegan-Carpenter (KC)number defined aszmKC = 2π [-]Dwherez m = oscillation amplitude [m]D = characteristic length of object, normally the smallestdimension transverse to the direction of oscillation [m]jF Di = viscous drag excitation force [N] (see 3.2.8)DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 26Guidance NoteFor sinusoidal motion the KC-number can also be defined asKC=v mT/D where v m=2πz m/T and T is the period of oscillation. TheKC-number is a measure of the distance traversed by a fluid particleduring half a period relative to the dimension of the object.3.2.8.3 The dependence of KC-number for forcecoefficients (inertia and damping) also applies to objectsexposed to oscillatory water particle motion in the wavezone. For regular waves, the KC-number can be taken asKC = πH [-]Dwhere H is the regular wave height. For irregular waveconditions the KC-number can be taken asstraight line. The parameter ω’ is the non-dimensionalfrequency of oscillation;ω ' = ω D / 2g [rad/s]where D is the same characteristic length of the object asused in the KC-number.The damping coefficient can then be written as;b1KC = b KC ω[-]'CD + 2These constant parameters can replace the amplitudedependent C D for a realistic range of amplitudes, which isnecessary for dynamic analysis of irregular motion.( 2σv) TzKC = [-]Dwhereσ v = standard deviation of water particle velocity [m/s]T z = zero up-crossing period [s]3.2.8.4 For small KC-numbers (typically less than 10) itmay be convenient to express the drag and damping force asa sum of linear and quadratic damping;Fdi12= ρ C= B v1riDAp+ B v2vriri| vr| vr||[N]CD9876543210C DS0 1 2 3 4 5 6 7 8 9 10K CKC3.2.8.5 The upper graph in Figure 3-2 shows a typicalvariation of C D with KC-number. The drag coefficient forsteady flow is denoted C DS . This corresponds to the value ofC D for large KC-number.Guidance NoteDamping coefficients obtained from oscillatory flow tests of typicalsubsea modules for KC-number in the range 0 < KC < 10 can beseveral times larger than the drag coefficient obtained from steadyflow data. Hence, using steady-flow drag coefficients C DS in place ofKC-dependent drag coefficients C D may underestimate the dampingforce and overestimate resonant motions of the object.3.2.8.6 When estimating damping coefficient and itsdependence on KC-number from oscillatory flow tests, theproduct C D KC is plotted against KC-number. A straight linecan then often be drawn through a considerable part of theexperimental values in this representation. See lower graphin Figure 3-2.Guidance NoteThe effect of KC-number on damping coefficients can also bedetermined by numerical simulation using Computational FluidDynamics (CFD) of the fluid flow past objects in forced oscillation.Guidance on use of CFD is given in 3.4.4.3.2.8.7 The intersection with the vertical axis is given byb 1 /ω’ where b 1 represents a linear damping term, and thequadratic damping term, b 2 , is equal to the slope of theCDKCb 1 /ω’30252015105C DC DS00 1 2 3 4 5 6 7 8 9 10y = 1.6699x + 10.62Figure 3-2 Estimation of damping coefficients fromexperimental values. In this example C D KC=10.62+1.67KC3.2.8.8 When b 1 and b 2 are determined, the coefficientsB 1 and B 2 in the expression in 3.2.8.4 can be calculated fromthe formulas;B2ρAp1 =⋅ b2 1B3π2gD12 A2 p ⋅ b2where[kg/s]= ρ [kg/m]b 2KCK CDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 27A p = projected area normal to motion/flow direction [m 2 ]g = acceleration of gravity [m/s 2 ]Guidance NoteThe linear damping can be associated physically with skin friction andthe quadratic damping with form drag.3.2.9 Slamming force3.2.9.1 The slamming force on an object lowered throughthe free surface with a constant slamming velocity v s(assumed positive) in still water can be expressed as the rateof change of fluid momentum;∞( A v )∞d33 sdA33( t)Fs( t)= = v[N]sdt dtwhere A∞ 33( t ) is the instantaneous high-frequency limit heaveadded mass, ref. Faltinsen (1990).Guidance NoteUsing the high-frequency limit of the added mass is based on theassumption that the local fluid accelerations due to water entry of theobject are much larger than the acceleration of gravity g. Thiscorresponds to the high frequency limit for a body oscillating with afree surface.3.2.9.2 The slamming force can be written in terms of aslamming coefficient C s asF1= [N]22s( t)ρCsApvswhere C s is defined byCs=2ρAvpsdA∞33dt=2ρApand dA ∞ 33/ dh is the rate of change of added mass withsubmergence.dA∞33dhρ = mass density of water [kg/m 3 ][-]A p = horizontal projected area of object [m 2 ]h= submergence relative to surface elevation [m]Guidance NoteThe rate of change of added mass with submergence can be derivedfrom position dependent added mass data calculated by a sinksourcetechnique or estimated from model tests. The high frequencylimit heave added mass for a partly submerged object is half of theadded mass of the corresponding “double body” in infinite fluid wherethe submerged part of the object is mirrored above the free surface,ref. /6/.3.2.9.3 For water entry in waves the relative velocitybetween lowered object and sea surface must be applied, sothat the slamming force can be taken as122F ( ) ρ ( & ς &st = CsAp−η)[N]whereς& = vertical velocity of sea surface [m/s]η& = the vertical velocity of the object [m/s]3.2.9.4 It should be noted that when measuring thevertical force on an object during water entry, the buoyancyforce and a viscous drag force will be part of the measuredforce. However, during the initial water entry, the slammingforce may dominate.3.2.10 Equation of vertical motion of lifted objectwhen lowered into wave zone.3.2.10.1 Combining the expressions for buoyancy, inertia,wave excitation, slamming and drag damping forces valid forwave lengths much longer than the dimensions of the object,the equation of vertical motion η(t) for the lowered objectcan be taken as;(1)(2)( M + A )&&η = B ( v − & η)+ B ( v − & η) ( v − & η)33+ ( ρV+ Awhere33) v&3333∞dA332+ ( & ς − & η)dh333+ ρgV( t)− Mg + F(1)B = the linear damping coefficient [kg/s]33(2)B = the quadratic damping coefficient [kg/m]33ν 3 = water particle velocity [m/s]v& 3 = water particle acceleration [m/s 2 ]F line (t) = force in hoisting line [N]3.2.10.2 The force in the hoisting line is given byFlinewhereKz ctη( t)Mg − ρgV( t)+ K(z −η)=ct= hoisting line stiffness [N/m]= motion of crane tip [m]= motion of object [m]3.2.10.3 The velocity and acceleration of the loweredobject are;& η =~ & η + vc [m/s]& η=&& ~η [m/s 2 ]3line( t)where~ η ( t ) = the wave-induced motion of the object [m/s]v c = a constant lowering velocity (v c is negative duringlowering as positive direction is upwards) [m/s]3.2.10.4 For an object with vertical sidewalls at the meanwater level, the instantaneous buoyancy force ρgΩ can besplit into a slowly varying (mean) component, a waveDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 28excitation part, and a hydrostatic restoring part due to thewave induced motion of the object;[ + A ς ( t)− A~ η ( )]= [N]ρgV( t)ρg V0 twherewV 0 = displaced volume of object in still water [m 3 ]A w = instantaneous water plane area [m 2 ]The instantaneous water plane area A w is a slowly varyingfunction of time, depending on lowering velocity v c .3.2.10.5 Assuming a constant vertical velocity v c of thelowered object and neglecting the motion of the crane tip, theforce in the hoisting line can be taken as;Fline∞dA33( t)= Mg − ρ gV ( t)− ( ρV+ A33) v&3− ( & ς − vc)dh− B ( v − v ) − B ( v − v ) ( v − v )13c23cw3c[ N]Slamming and wave excitation forces can cause slack (F=0)in the hoisting wire followed by high snatch loads.3.2.11 Slamming on top plate of suction anchor3.2.11.1 Slamming on the top plate of a suction anchorwill lead to a change in velocity of the anchor. The change invelocity is given by2A33∆v= ( ς& −M + Acv c ,033whereMA 33ς&v c,0= mass of suction anchor [kg])= mass of water plug (added mass) inside suctionanchor [kg]= vertical velocity of water surface inside suctionanchor before slamming event [m/s]= vertical velocity of suction anchor beforeslamming event [m/s]23.2.12 Water exit force3.2.12.1 The water exit force F e (t) on a fully submergedobject lifted up beneath the free surface with constant liftingvelocity v e (positive upwards) in still water can be expressedby the rate of change of fluid kinetic energy by the relationdEkveFe( t)= − [Nm/s]dtwhere1 0 2Ek= A33v e[Nm]20A33( t ) = instantaneous zero-frequency limit heave addedmass, ref./9/.3.2.12.2 The water exit force can then be written as01 d ⎛ 1 0 2 ⎞ 1 dA33Fe( t)= − ⎜ A33ve ⎟ = − ve[N]v dt ⎝ 2 ⎠ 2 dteGuidance NoteUsing the low-frequency limit of the added mass is based on theassumption that the local fluid accelerations during water exit aremuch smaller than the acceleration of gravity g. This corresponds tothe low frequency limit for a body oscillating beneath a free surface.The exit velocity can be expressed in terms of exit Froude number F n= v e/√(gD) where D is a characteristic horizontal dimension of theobject. Hence the formulation is valid for low Froude number F n

Recommended Practice DNV-RP-H103, Draft December 2008Page 293.2.13 Equation of vertical motion of lifted objectwhen hoisted out of wave zone.3.2.13.1 Combining the expressions for buoyancy, inertia,wave excitation and water exit forces the equation of verticalmotion η(t) for the lifted object can be taken as;( M + A33+ ( ρV+ A)&&η =33) v&−3B(1)3312( v3− & η)+ B0dA33( & ς − & η)dh(2)332( v3− & η) ( v− & η)+ ρgV( t)− Mg + F3line( t)Figure 3-3: Water exit of ROV.Courtesy of Marintek.3.2.12.4 The water exit force can usually be neglected on apartly submerged object being lifted out of the water.However, large horizontal surfaces beneath the object maycontribute to the water exit force.3.2.12.5 The water exit force can be written in terms of awater exit coefficient C e as;F1= [N]22e( t)− ρCeApvewhere C e is defined by;Ceand001 dA33 1 dA33= = −[-]ρAv dt ρAdhpep0dA33/ dh = rate of change of added mass with submergence[kg/m]. Note that the rate of change is negative.ρ = mass density of water [kg/m 3 ]A p = horizontal projected area of object [m 2 ]h= submergence relative to surface elevation [m]3.2.12.6 Enclosed water within the object and drainage ofwater during the exit phase must be taken into account.Drainage of water may alter the weight distribution duringexit.3.2.12.7 For water exit in waves the relative velocitybetween lifted object and sea surface must be applied, so thatthe exit force can be taken as;F1= [N]22e ( t ) − ρ CeAp(& ς − & η )whereς&η&= vertical velocity of sea surface [m/s]= vertical motion of the object (positive upwards) [m/s]The velocity of the lifted object is& η =~ & η + ve [N]The force in the hoisting line is given by 3.2.10.2.3.2.14 Hydrodynamic loads on slender elements3.2.14.1 The hydrodynamic force exerted on a slenderobject can be estimated by summing up sectional forcesacting on each strip of the structure. For slender structuralmembers having cross-sectional dimensions considerablysmaller than the wave length, wave loads may be calculatedusing Morison's load formula being a sum of an inertia forceproportional to acceleration and a drag force proportional tothe square of the velocity.3.2.14.2 Normally, Morison's load formula is applicablewhen the wave length is more than 5 times the characteristiccross-sectional dimension.f Tf NαvFigure 3-4 Normal force f N , tangential force f T and lift force f Lon slender structure.3.2.14.3 The sectional normal force on a slender structureis given by;v N1f N = −ρ C A A && xN+ ρ( 1 + C A )A v&N + ρCDD v rN vrN2whereρ = mass density of water [kg/m 3 ]A = cross-sectional area [m 2 ]C = added mass coefficient [-]AC D = drag coefficient in oscillatory flow [-]D= diameter or characteristic cross-sectionalf L[ N/m]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 30dimension [m]& x& N= acceleration of element normal to element [m/s 2 ]v rN = relative velocity normal to element [m/s]v& = water particle acceleration in normal dir. [m/s 2 ]NGuidance note:The relative velocity formulation for the drag force is valid when themotion x N of the element in the normal direction is larger than thecharacteristic cross-sectional dimension D. The use of normalvelocity in the force fomulation is valid if the angle of attack α (Figure3-4) is in the range 45-90 deg. The drag coefficient can be taken asindependent of angle of attack. Ref. DNV-RP-C205 sec.6.2.5.3.2.14.4 The sectional (2D) added mass for a slenderelement is a ij = ρC A A R , i,j = 1,2 where A R is a reference area,usually taken as the cross-sectional area.3.2.14.5 For bare cylinders the tangential drag force f t ismainly due to skin friction and is small compared to thenormal drag force. However for long slender elements with apredominantly tangential velocity component, the tangentialdrag force may be important. More information on tangentialdrag is given in DNV-RP-C205.3.2.14.6 The lift force f L , in the normal direction to thedirection of the relative velocity vector may be due tounsymmetrical cross-section, wake effects, close proximityto a large structure (wall effects) and vortex shedding. Formore information on lift forces for slender cylindricalelements, see ref. /8/.3.2.14.7 The sectional slamming force on a horizontalcylinder can be written in terms of a slamming coefficient C sasf1= [N/m]22s( t)ρCsDvsC s is defined by;C swhere∞2 da33=ρDdh[-]ρ = mass density of water [kg/m 3 ]Dhand= diameter of cylinder [m]= submergence [m]da ∞ 33/ dh [kg/m 2 ]is the rate of change of sectional added mass withsubmergence.Guidance Noteh is the distance from centre of cylinder to free surface so that h = -rat the initial time instant when the cylinder impacts the water surface.1.21.00.80.60.40.20.0rh-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0Figure 3-5 High frequency limit of vertical added masscoefficient and its derivative close to a free surface asfunction of water depth. Solid line: a 33 /ρπr 2 . Dotted line:(da 33 /dh)/ρπr .3.2.14.8 The high frequency vertical added masscoefficient as function of submergence is shown in Figure 3-5. The added mass coefficient is defined by;CA= a / ρ π r [-]3323.2.14.9 The sectional water exit force on a horizontalcylinder can be written in terms of a water exit coefficient C easF1= ρ [N/m]22e( t)− CeDvewhere C e is defined by1 da33= − [-]ρDdhC e00da33/ dh = rate of change of sectional low frequencyadded mass with submergence [kg/m 2 ]A discussion of water exit for circular cylinders is presentedin ref. /9/.Guidance NoteNote that the exit coefficient may depend strongly on the exit Froudenumber F n = v e/√(gD) and the formulation in terms of rate of changeof added mass is valid only for F n

Recommended Practice DNV-RP-H103, Draft December 2008Page 31shown in Figure 3-5.It should be noted that buoyancy effects are included in thisformula so that it should only be used for s/D < 0.5 or h/r

Recommended Practice DNV-RP-H103 Draft December 2008Page 32wherez m = oscillation amplitude [m]p = perforation ratio 0 < p < 1µ = discharge coefficient [-]The perforation ratio p is defined as the open area divided bythe total area. The discharge coefficient µ is usually between0.5 and 1.0, see ref./2/ and /3/.3.3.4.3 Figure 3-7 shows model test results for addedmass of 5 ventilated structures representing typical protectionstructures, with perforation ratio varying from 0.15 to 0.47.The added mass A 33 is normalized with the added mass of asolid structure, A 33,0 (with same dimensions perpendicular tothe motion direction). The variation of added mass withamplitude of oscillation is considerable (by a factor of 2-3)for all the objects.3.3.4.4 The asymptotic value for A 33 in the limit of zeroamplitudes (KC=0) can be found from potential theory andcalculated by a sink-source panel program. The followingapproximated formula has been found by curve fittingthrough results for plates with circular holes, and has beenfound applicable for plates with ventilation openings;AA3333,0 KC = 0p−0.28= e [-]3.3.5 Drag coefficients for circular cylinders3.3.5.1 The drag coefficient for circular cylindersdepends strongly on the roughness k of the cylinder. For highReynolds number (R e > 10 6 ) and large K C number, the steadydrag-coefficient C DS may be taken asCDS⎧⎪( ∆)= ⎨⎪⎩0.65( 29 + 4⋅log ( ∆))1.0510/ 20; ∆ < 10; 10−4; ∆ > 10−4(smooth)< ∆ < 10−2−2(rough)where ∆=k/D is the non-dimensional roughness. The abovevalues apply for both irregular and regular wave analysis.3.3.5.2 The variation of the drag coefficient withKeulegan-Carpenter number KC for circular cylinders can beapproximated by;CD= C ⋅ψ( KC ) [-]DSwhere C DS is the drag coefficient for steady flow past acylinder and;ψ (KC) [-]is an amplification factor. The shaded area in Figure 3-8show the variation in ψ from various experimental results.Note that surface roughness vary.However, as seen in figure 3-7, this asymptotic value atKC=0 may give inaccurate values for structures inoscillatory fluid flow.2.52Wake amplification factorAmAm33aa/a033,0 a 00.60.50.40.30.20.10.0Hatch 20, pr=0.15Hatch 18, pr=0.25Roof #1, pr=0.267Roof #2, pr=0.47Roof #3, pr=0.3750 0.5 1 1.5 2µz(1-r)/(2Dr^2) µK KC,porµKC porCD/CDS1.510.500 2 4 6 8 10 12 14KCRodenbusch (1983), CDS=1.10, random directionalMarin (1987), CDS=1.10Sarpkaya (1986), CDS=1.10Bearman (1985), CDS=0.60Marin (1987), CDS=0.60Garrison (1990), CDS=0.65Rodenbusch (1983), CDS=0.66, sinusoidalRodenbusch (1983), CDS=0.66, random directionalGarrison (1990), CDS=1.10Sarpkaya (1986), CDS=0.65Rodenbusch (1983), CDS=1.10, sinusoidalIwaki (1991), CDS=1.10Figure 3-7 Added mass of 5 perforated objects compared,ref. /7/.Figure 3-8 Wake amplification factor, ref. /11/.3.3.6 Estimating added mass and damping coefficientsfrom model tests or CFD analyses3.3.6.1 In forced oscillation tests the structure is forced tooscillate sinusoidally at a frequency ω.3.3.6.2 Time series for motion z(t) and force F(t) areanalyzed and the total oscillating mass (M+A 33 ) and theDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 33linearized damping B can be estimated by a least-squaresmethod, using the equation;F = −(M + A )z & − Bz&[N]3.3.6.3 The added mass, A, is found by subtracting thestructural mass of the structure and the suspension elementsfrom the total oscillating mass. The added mass coefficient isextracted from the added mass by;CAA= [-]ρVR3.3.6.7 Having established drag coefficents for a numberof oscillation amplitudes, the linear and quadratic dampingterms, B 1 and B 2 , may be derived as described in 3.2.8.7 (if astraight line is obtained).3.3.6.8 These methods are more robust than estimatingthe two damping coefficients in one single step. A similarapproach is applied for estimating added mass and dampingfrom CFD analyses.3.3.6.9 In a free motion decay test the total mass is foundfrom the period of each oscillation cycle, and the damping isderived from the decaying amplitudes of oscillation.whereρ = mass density of water [kg/m 3 ]V R = reference volume of the object [m 3 ]C A = added mass coefficient [-]3.3.6.4 The derived linearized damping , B, may beplotted as function of the oscillation amplitude, z. If a fairlystraight line can be fitted, the damping may be split into alinear and quadratic term by:B 1 = B at z = 0 [kg/s]3T= ( B − B ) [kg/m]16 zB2 1 ⋅whereTz= oscillation period [s]= oscillation amplitude [m]B 1 = linear damping, ref. 3.2.8.4 [kg/s]B 2 = quadratic dampin, ref. 3.2.8.4 [kg/m]3.3.6.5 Alternatively, a better fit may be obtainedapplying;F = −(M + A )z & − Bz&z&[N]3.3.6.6 The drag coefficient is then extracted from thedamping factor B by;CDwhereA p2B=ρA[-]p= projected area of object normal to the direction ofoscillation [m 2 ]3.4 Calculation methods for estimation ofhydrodynamic forces3.4.1 The Simplified Method3.4.1.1 The Simplified Method as described in Section 4may be used for estimating characteristic hydrodynamicforces on objects lowered through the water surface anddown to the sea bottom.3.4.1.2 The Simplified Method may also be applied onretrieval of an object from sea bottom back to the installationvessel.3.4.1.3 The intention of the Simplified Method is to givesimple conservative estimates of the forces acting on theobject.3.4.1.4 The Simplified Method assumes that thehorizontal extent of the lifted object is small compared to thewave length. A regular design wave approach or a timedomain analysis should be performed if the object extensionis found to be important.3.4.1.5 The Simplified Method assumes that the verticalmotion of the structure is equal to the vertical motion of thecrane tip. A time domain analysis is recommended ifamplification due to vertical resonance is present.3.4.2 Regular design wave approach3.4.2.1 Lifting and lowering operations may be analysedby applying a regular design wave to the structure using aspreadsheet, or a programming language, as described in thissection.3.4.2.2 Documentation based upon this method should bethoroughly described in every detail to such extent that thecalculations are reproducible.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 343.4.2.3 Shallow water effects are for simplicity notincluded in this section.Guidance NoteA finite water depth, d, may be taken into account by deriving thewater particle velocity v = grad φ and acceleration α = ∂v/∂t from thevelocity potential for linear Airy waves;( z + d )gζcosh kφ = acos( ωt− kx cos β − ky sin β ) [m 2 /s]ω cosh kdDetailed expressions for water particle velocity and acceleration aregiven in DNV-RP-C205.3.4.2.4 The global structure geometry should be dividedinto individual main elements both horizontally andvertically, each of which contributes to the hydrodynamicforces, see Figure 3-8.3.4.2.5 Separate calculations are made for each definedwave direction and for each defined load case where the stillwater level is positioned either beneath a slamming area orjust above the top of a main item.3.4.2.6 A regular wave is applied. Calculations are madeto obtain acceptance limits for both significant wave heightand zero-crossing wave period.BLeft SB Left Hook SideSideCDzyTop ViewFront ViewβAADyPort Right Hook SideFigure 3-8 Example of subsea module. Main elements,coordinate system and wave direction3.4.2.7 The regular wave height should not be less thanthe most probable largest wave height. If the loweringthrough the wave zone are to be performed within 30minutes, the largest characteristic wave height may beassumed equal to 1.80 times the significant wave height, see3.4.2.11.x3.4.2.8 The applied regular wave height should be 2.0times the significant wave height in cases where the plannedoperation time (including contingency time) exceeds 30minutes.3.4.2.9 The regular wave period should be assumed equalto the zero-crossing period, T z , of the associated sea state.3.4.2.10 Figure 3-8 shows the definition of the coordinatesystem for the wave description given in 3.4.2.11. The wavespropagate in a direction β relative to the x-axis. The origin ofthe coordinate system is in the still water level.Guidance NoteThe structure may in this case roughly be divided into four suctionanchors ( A, B, C and D) and two manifold halves (Left Side andRight Side).3.4.2.11 The regular wave is given by:( ωt− kx cos β − ky sin β )ζ = ζ sin[m]whereζ a =awave amplitude, i.e. ζ a =0.9H s for operations less than30 minutes and ζ a =H s for operations exceeding 30minutes. [m]ω = wave angular frequency, i.e. ω=2π/T where theregular wave period, T, should be assumed equal tothe applied zero-crossing period T=T z [rad/s]t = time varying from 0 to T with typical increments of0.1 [s]k = wave number, i.e. k=ω 2 /g for deep water, where g isthe acceleration of gravity [m -1 ]x, y = horizontal CoG coordinates for the individual mainitems of the lifted object [m]β = wave propagation direction measured from the x-axisand positive counter-clockwise [rad]Guidance NoteIn shallow water the wave number is given by the general dispersionrelation;ω 2 = gk tanh(kd)3.4.2.12 The vertical wave particle velocity andacceleration can be taken as:kzv = ω ζ e cos ωt− kx cos β − ky sin β [m/s]anda2kz( )( ωt− kx cos β − ky sin β )v& = − ω ζ e sin[m/s 2 ]whereav = vertical water particle velocity [m/s]v& = vertical water particle acceleration [m/s 2 ]z = vertical CoG coordinate for the individual main itemsof the lifted object (negative downwards) [m]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 353.4.2.13 The vertical motion of the lifted object is in thiscalculation method assumed to follow the motion of thecrane tip. The vertical crane tip motion is assumed tooscillate harmonically with an amplitude, η a , and a regularperiod T ct .Guidance NoteA time domain analysis is recommended in cases where thisassumption is not valid.3.4.2.14 The most probable largest vertical singleamplitude crane tip motion, η a , for the applied T z waveperiod can be taken as:ηa = 3. 6σ η[m] for operation durations less than 30 min.ηa = 4. 0σ η[m] for operation durations above 30 min.where σ η is the standard deviation of the vertical crane tipmotion response spectrum.3.4.2.15 The vertical motion, velocity and acceleration ofthe lifted object is then given by:( ω ε )η = η sin t + [m]ηa( ω ε )& η = ωη η cos a ηt+ [m/s]and( ω ε )2& η= − ω ηasin t [m/s 2 ]whereη =η& =η η+vertical motion of lifted object [m]vertical velocity of lifted object [m/s]η& & = vertical acceleration of lifted object [m/s 2 ]η a = vertical single amplitude motion of lifted object,assumed equal the most probable largest crane tipsingle amplitude, see 3.4.2.14 [m]ω η = angular frequency of the vertical motion of the liftedobject, i.e. ω η =2π/T ct where T ct is the peak period ofthe crane tip motion response spectrum for the appliedT z wave period [rad/s]t = time varying from 0 to T with typical increments of0.1 [s]ε = phase angle between wave and crane tip motion, see3.4.2.16 [rad]3.4.2.16 The phase angle that results in the largestdynamic tension amplitudes in the lifting slings and hoistingline should be applied.Guidance NoteThis can be found by applyting a set of phase angles in a range fromε = 0 to ε = 2π with increments of e.g. 0.1π. The phase angles thatresults in the highest risk of slack sling or the largest DAF conv shouldbe applied, ref. 4.2.4.3 and 4.2.5.1.3.4.2.17 The characteristic vertical hydrodynamic forceacting on each of the structure main items can be found by:F = F ρ+ F + F + F [N]hydwheremF ρ = varying buoyancy force [N]F m = hydrodynamic mass force [N]F s = slamming impact force [N]F d = hydrodynamic drag force [N]sd3.4.2.18 The varying buoyancy force for items intersectingthe water surface can be found by:F ρ = ρ g δV( ζ −η)[N]whereδV(ζ-η) = change in displacement due to relative verticalmotion, ζ-η, (see 3.2.10.2 and Figure 3-9) [m 3 ]ζ = water surface elevation in the applied regular waveas defined in 3.4.2.11 [m]η = vertical motion of lifted object, see 3.4.2.15 [m]ρ = density of sea water, normally = 1025 [kg/m 3 ]g = acceleration of gravity = 9.81 [m/s 2 ]zyη = 0ζ = 0yyδV( ζ −η)ζηzyη > 0ζ > 0Figure 3-9 The displacement change δV(ζ-η)yyζ-η3.4.2.19 The mass force is in this simplified regular designwave approach estimated by:F mwhere( v&− && η ) − M & η= ρ Vv&+ A[N]33M = mass of object item in air [kg]A 33 = added mass of object item [kg]ρ = density of sea water, normally = 1025 [kg/m 3 ]V = volume of displaced water of object item [m 3 ]v& = vertical water particle acceleration as found in3.4.2.12 [m/s 2 ]η& & = vertical acceleration of lifted object, see 3.4.2.15[m/s 2 ]The mass force as defined above is the sum of the inertiaforce (3.2.5.1) and the wave excitation force (3.2.7.2).Guidance NoteFor items intersecting the water surface, the volume of displacedwater should be taken as the volume at still water level.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 363.4.2.20 The slamming impact force on object items thatpenetrate the water surface may be taken as:( &) 2Fs = 0.5ρCsAsv −η[N]whereρ = density of sea water [kg/m 3 ]C s = slamming coefficient which may be determined bytheoretical and/or experimental methods. For smoothcircular cylinders C s should not be taken less than 3.0.Otherwise, C s should not be taken less than 5.0. Seealso DNV-RP-C205.A s = slamming area projected on a horizontal plane [m]v = vertical water particle velocity at slamming area, z=0if slamming area is situated in the still water level, see3.4.2.12 [m/s]η& = vertical velocity of lifted object [m/s]3.4.2.21 The drag force may be taken as:F( v − & η) − & η= 0 . ρ C A v [N]d5whereDpC D = drag coefficient of object item [-]A P = area of object item projected on a horizontal plane[m 2 ]and otherwise as defined in 3.4.2.20.Guidance NoteAlternatively, the drag force can be estimated by:( v − & η ) + B ( v − & η ) − & η= BvF d 2where1[N]B 1 is the linear damping of the object [kg/s]B 2 is the quadratic damping of the object [kg/m]3.4.2.22 The performed analyses should cover thefollowing zero-crossing wave period range for a givensignificant wave height H s :H [s]S8.9⋅ ≤ TZ≤g133.4.2.23 A more limited T z range may be applied if this isreflected in the installation criteria in the operationprocedures.3.4.2.24 The vertical crane tip motion is found accordingto Section 4.3.3.3.4.2.25 The motions, velocities and accelerations arecalculated for each time step at each defined main item.3.4.2.26 Some motion response analysis computerprograms are able to define off-body points on the wavesurface and generate relative motion directly. In such case,these values may be applied.3.4.2.27 The varying buoyancy force, mass force,slamming force and drag force are calculated for each timestep at each defined main item.3.4.2.28 The forces are then summed up. The static weightis applied as a minimum and maximum value according toSection 4.2.2. Reaction forces in slings and crane hooks arefound applying the force and moment equilibrium. The slacksling criterion as described in Section 4.4.3 should befulfilled. The structure and the lifting equipment should bechecked according to Section 4.4.4.3.4.3 Time domain analyses3.4.3.1 Computer programs applying non-linear timedomain simulations of multibody systems may be used formore accurate calculations.3.4.3.2 If applicable, a full 3 hour simulation period foreach load case is recommended in the analyses.3.4.3.3 In sensitivity analyses a number of shortersimulations may be performed, e.g. 30 minutes.3.4.3.4 The largest and smallest observed loads in e.g.slings and fall during simulation time should be stated.3.4.3.5 Assuming that the dynamic loads can be Rayleighdistributed, the most probable largest maximum load, R max ,may be found applying the following relation:⎛ t ⎞R =⎜⎟maxσr2ln[N]⎝ T ⎠wherezσ r = standard deviation of the dynamic load [N]t = duration of operation including contingency time,minimum 30 minutes [s]T z = zero up-crosing period of the dynamic load [s]The zero up-crossing period of the dynamic load is definedbyM0T z= 2π[s]M2where M 0 and M 2 are the zeroth and second moments of theload spectrum (Ref. DNV-RP-C205)Guidance NoteIn most dynamic non-linear cases the response does not adequatelyfit the Rayleigh distribution. The estimated maximum load shouldtherefore always be compared with the largest observed load in thesimulation.3.4.3.6 If analyses are based upon selected wave trains ofshort durations, the selections should preferably be basedupon maximum vertical relative motion between crane tipand water surface. Both relative motion amplitude, velocityand acceleration should be decision parameters in theselection of wave trains.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 373.4.3.7 If analyses are based upon a continuous loweringsimulation of short duration a minimum of 10 simulationsshould be performed for each sea state. The minimum andmaximum observed values for all 10 simulations should beincluded in the documentation. In irregular sea, selection ofwave trains should be performed according to 3.4.3.6.3.4.3.8 Damping and added mass values should becarefully chosen in the analyses, ensuring that also themoment of inertia values are correctly modelled.3.4.4 CFD analyses3.4.4.1 Wave load analyses based on ComputationalFluid Dynamics (CFD) may be performed on subsea lifts.The fluid motion is then described by the Navier-Stokesequations.3.4.4.2 Examples of numerical methods applicable forsimulation of wave-structure interaction including waterentry (slamming) and water exit are- Volume-of-Fluid (VOF) method- Level Set (LS) method- Constrained Interpolation Profile (CIP) method- Smooth Particle Hydrodynamics (SPH) methodGuidance NoteGeometry approximations may give an inadequate representation oflocal forces and pressures. Convergence tests should always beperformed.3.4.4.10 Additional buoyancy due to modelapproximations should be taken into account whenevaluating computed total vertical forces.3.4.4.11 The computed slamming loads may beoverestimated when single phase modelling is applied. Forwave impact problems it is recommended to use two-phasemodelling.3.4.4.12 Computed forces, pressures and velocities shouldbe checked and compared with approximate handcalculations.3.4.4.13 If model test results are available, numericalsimulation results should be compared and validated with themodel test.3.4.4.14 Figure 3-10 shows an example of prediction ofadded mass and damping coefficients for model mudmatgeometries with 3 different perforation ratios (0%, 15% and25%). Calculations are carried out using 2 different CFDmodels and are validated with experimental results.3.4.4.3 The first three methods (VOF, LS, CIP) are gridmethods while SPH is a particle method where a grid is notneeded.3.4.4.4 The applied boundary conditions and the size ofthe computational domain should ensure that reflections fromthe boundaries of the domain do not influence thehydrodynamic forces on the object.3.4.4.5 Convergence tests should be performed verifyingadequacy of applied number of cells or particles (for particlemethods) in the model.3.4.4.6 Stretching of cells may influence the incomingwave. Hence, this should be thoroughly tested.3.4.4.7 The distance from inflow boundary to thestructure may in some cases influence the wave action on thestructure.3.4.4.8 For simulations where generated waves start fromrest, a sufficient number of subsequent waves should begenerated in order to avoid transient effects.3.4.4.9 Approximations of actual structure geometry dueto limitations in available computer capacities should beperformed applying correct total areas. Holes andpenetrations may be summarized in fewer and largeropenings.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 38ζζ sζ bζ wC sC b= motion of water plug [m]= heave motion of the ship [m]= motion of body in moonpool [m]= sea surface elevation outside moonpool [m]= damping coefficient for relative motion betweenwater plug and ship [kg/m]= damping coefficient for relative motion betweenwater plug and body [kg/m]K = ρgA water plane stiffness [kg/s 2 ]F(t) = wave excitation force on water plug [N]Figure 3-10: Example of use of CFD for prediction of addedmass and drag coefficients for model mudmat geometries.Courtesy of Acergy.3.5 Moonpool operations3.5.1 GeneralFor small subsea modules and tools, installation through themoonpool of the vessel is often preferred. This may reducethe dynamic forces, increase the limiting seastate and thusreduce the costs of installation and intervention operations. Atypical application area is maintenance and repair operationsof subsea production plants.3.5.2 Simplified analysis of lift through moonpoolThe ship heave motion is related to the sea surface elevationby a transfer function G s (amplitude and phase),ζ = G ζ [m]sswThe hydrodynamic pressure force acting on the water plugcan also be related to the sea surface elevation by a transferfunction G w (amplitude and phase),F( t)= ζ [N]G ww3.5.3.3 Both G s and G w can be found by integrating thepressure p obtained by a sink-source diffraction programover the cross-section of the moonpool at z = -D. G s and G ware functions of wave frequency and wave direction.3.5.2.1 The simplified analysis described in thissubsection is based on the following limiting assumptions, The moonpool dimensions are small compared to thebreadth of the shipOnly motion of the water and object in vertical directionis consideredThe blocking effect of the lifted object on the water inthe moonpool is moderate.Cursors prevent impact into the moonpool walls. Onlyvertical forces parallel to the moonpool axis areconsidered.zDζ sA(z)ζζ bζ w3.5.3 Equation of motionp3.5.3.1 A body object suspended inside a moonpool isconsidered, see Figure 3-11. The moonpool may havevarying cross-sectional area A(z). The draught of the ship isD. The vertical motion of the lifted body may differ from thevertical ship motion due to the winch operation and/ordynamic amplification in the hoisting system.Figure 3-11 Suspended body in a moonpool.3.5.3.2 The equation of motion for the water plug can bewritten as( M + A ) &&33ζ + C & ζ − & ζ & ζ − & ζwhereΜΑ 33+ Cbs& ζ − & ζbs(s)( & ζ − & ζ ) + Kζ= F(t)= mass of water plug [kg]= added mass of water plug (see 3.5.4.3) [kg]bDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 393.5.4 Resonance period3.5.4.1 The natural period of vertical oscillations of thewater plug and the damping conditions given by themoonpool design are important for the dynamic forces on anobject inside the moonpool.3.5.4.2 In general the cross-sectional area of themoonpool is a function of the vertical position z. Assumingthe moonpool walls do not move, the requirement ofcontinuity yieldsA ( z)⋅ & ζ ( z)= A(0)⋅ & ζ (0) [m 3 /s]3.5.4.3 The requirement of energy conservation gives,ddt( E kE ) = 0where+ p[Nm/s]3.5.4.7 The energy-equivalent mass (mass plus addedmass) moving with the surface velocity & ζ (0)is;⎧D⎫E⎪⎪=kA(0 ) A(0 )Meq = ⎨ + ⋅ A( −D)2⎬1⎪∫& ρA(0 ) dz κζ (0 )A( z ) A( −D )⎪2⎩0⎭3.5.4.8 If the moonpool has a constant cross-sectionalarea A(z) = A, the above expressions simplify to thefollowing;2πT0=gMeq= ρ AD + κ A[ s]( D + κ A ) [ kg][ kg]0E = 1k ρ A(2 ∫−Dz )2⋅ & ζ (z )dz⎧ 0⎪= 1 2 A(0 )ρ A(0 ) ⋅ & ζ ( 0 )2⎨⎪∫ A(⎩−Dand+dzz )1 2A33⋅ & ζ ( −D )22E = 1 ρ g A(0)⋅ ζp(0) [Nm]2⎫A(0 ) A ⎪+ ⋅33⎬A( −D ) ρ A( −D ) ⎪⎭[ Nm]3.5.5 Damping of water motion in moonpool3.5.5.1 The amplitude of the water motion in themoonpool, in particular for wave excitation close to theresonance period T 0 , depends on the level of damping. Inaddition to inviscid damping due to wave generation,damping is provided by viscous drag damping caused byvarious structures like guidance structures, fittings,cofferdam or a bottom plate.3.5.4.4 A 33 is the added mass for vertical oscillation ofthe water plug, which can be expressed asA= ρ κ A(−D)A(− ) [kg]33D3.5.4.5 The parameter κ has been found to be within 0.45and 0.47 for rectangular moonpools with aspect ratiosbetween 0.4 and 1.0. Thus κ = 0.46 can be used for allrealistic rectangular moonpools. For a circular moonpool κ =0.48.3.5.4.6 The resonance period is found from the energyconservation expression,02 ⎧ A(0)A(0)⎫ω0 ⎨ ∫ dz + ⋅κA(−D)⎬ − g = 0 [m/s 2 ]⎩−DA(z)A(−D)⎭or3.5.5.2 In model tests of several offshore diving supportvessels and work vessels with different damping devices, thewater motion inside a moonpool has been investigated. Inthese tests the relative motion between the water plug and theship at the moonpool centre axis has been measured. Anamplitude RAO for the relative motion is defined as;RAOwhereζζ sζ wζ − ζs= [m/m]ζ w= motion of water plug [m]= heave motion of the ship [m]= sea surface elevation outside moonpool [m]3.5.5.3 Figure 3-12 shows the measured RAO fordifferent structures causing damping of water motion inmoonpool.T2πA(0)A(0)00= ∫ dz + ⋅κA(−D)−DA(z)A(−D)g[s]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 403Relative water elevation in moonpool3.5.5.6 To obtain a relationship between transferfunctions G w and G s , some simplifying assumptions aremade,RAO2.521.510.5−−−−The moonpool dimensions are small compared to theship breadthExcitation force due to incoming waves, F 1 , and due toship motion, F 2 , can be assessed as for a ship withoutmoonpoolThe fluid pressure expressions valid for long waves canbe usedDeep water is assumed00.4 0.6 0.8 1 1.2 1.4T/T0Naked moonpoolGuidance structureGuid.+ 50% bottom plateMinor fittingsCofferdamFigure 3-12 Measured relative water elevation in a moonpoolper unit incoming wave amplitude. Courtesy of Marintek.3.5.5.4 The water plug is excited both by the incomingwaves and by the vertical ship motion. Hence it is notstraightforward to derive damping data directly from suchcurves. An approximated approach has been used in order toestimate the damping given by the various dampingarrangements. An approximate linearized complex equationof motion of the water plug in an empty moonpool (without alifted object) is;M ζ( & ζ − & ζ ) + K F()& + Cs 1 s ζ = t [N]⇓2− M ζ + iωCs1( ζ − Gsζw ) + KζGwζwω =whereM = ρ A( D + κ A)= total mass of water plug,including added mass [kg]K = ρgA = waterplane stiffness [kg/s 2 ]C s1 = 2 η KM = linearized damping [kg/s]η = damping ratio (relative to critical damping) [-]G s = transfer function for vertical moonpool motion[m/m]G w= transfer function from wave elevation toexcitation force [N/m][N]The following approximate expressions for the excitationforce can then be used;F( t ) = F ( t ) + F ( t )= pFK= ρ A= ρ A1⋅ A +A332⋅ && ςgζw− kDe + κ ρ A Aζsζ wss&−kD2( g e − ω κ AG ) [ N]where= the undisturbed (Froude-Krylov) dynamic fluidpFKpressure [N/m 2 ]A 33 = the added mass of the water plug as given in 3.5.4.4[kg]Hence,F( t )Gw= = ρ Aζ w2where k = ω / g .−kD2( g e − ω κ A Gs)[N/m]3.5.5.7 The amplitude ratio of relative water plugelevation to incoming wave elevation is then given byζ − ζ sRAO =ζw=ζζw− Gs3.5.5.5 The ratio between the motion of the water plugand the sea surface elevation outside the moonpool is;ζ=ζ wiωCs1Gs+ Gw2− ω M + iωCs1+ KGwω+ 2i GsηρgAω=02⎛ ω ⎞ ω1 − ⎜ ⎟+ 2iηω⎝ 0 ⎠ ω0[-]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 413.5.5.8 In Figure 3-13 an example case of the relativewater elevation inside moonpool is plotted. The motiontransfer functions of a typical 80 m long diving supportvessel have been used. G s for vertical moonpool motion hasbeen inserted in the above expressions, and the RAO curveshave been computed for varying relative damping, η.3.5.5.9 The results are uncertain for the shortest waveperiods (T/T 0 < 0.8), where the curve shapes differ from themodel test results.3.5.5.10 The maximum RAO values, found at resonance,are shown as a function of the relative damping, for the caseswithout bottom plate, in Figures 3-13 and 3-14.Elevation / wave amplitude9876543210Relative water elevation inside moonpool0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00T / T0Relativedamping =0.030.050.070.100.150.200.300.50Figure 3-13: Calculated relative water elevation, no bottomplate (β = 1).Minor fittings: η = 13 - 14 %Guidance structure: η = 18 - 19 %Guidance structure + 50% bottom plate: η = 40 - 45 %Cofferdam: η ≈ 45 %3.5.5.12 The quadratic damping coefficient C s can beestimated from the relative damping and the motion. Thefollowing approximation may be used,C s= 3πωζ02ηKM8⋅ ⋅[-]where ζ is the amplitude of relative motion.03.5.6 Force coefficients in moonpool3.5.6.1 Restricted flow around the object inside amoonpool leads to increased hydrodynamic forces. Increaseddrag coefficient C D and added mass coefficient C A to be usedin the calculation can be taken asCC1−0.5A/ A= for A b /A < 0.8Db2D0 (1 − Ab/ A)A094CA ⎛ Ab⎞= 1+1.9⎜⎟ for A b /A < 0.8C ⎝ A ⎠whereC D0 = drag coefficient for unrestricted flow [-]C A0 = added mass coefficient for unrestricted flow [-]A b = solid projected area of the object [m 2 ]A= cross-sectional area of the moonpool(at the vertical level of the object) [m 2 ]Max. relative elevation / Wave amplitude1098765432100.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50Relative dampingFigure 3-14: Calculated relative water elevation at resonance.3.5.5.11 Approximate relative damping values for thecases without bottom plate have been found by a comparisonbetween Figure 3-12 and Figure 3-13. The followingapproximate relative damping values have been assessed,Naked moonpool: η = 8 - 9 %DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 423.5.6.2 For A b /A > 0.8 it is recommended to calculate theadded mass coefficient C A of the lifted object inside themoonpool by a wave diffraction panel program. To assessthe effect of constrained flow in the moonpool on the dragcoefficient C D Computational Fluid Dynamics can beapplied.3.5.6.3 The dynamic behaviour of the lifted object whenleaving the lower moonpool end during lowering or prior toentry at lifting, should be analysed by a time domaincalculation method, in irregular waves.3.5.6.4 For an object close to the lower end of themoonpool, a conservative approach is to analyse thedynamics, using hydrodynamic forces based on the wavekinematics of undisturbed waves and hydrodynamiccoefficients for unrestricted flow condition.3.5.6.5 Realistic impact forces between lifted body andmoonpool walls require accurate stiffness data for the cursorsystem.3.5.7 Comprehensive calculation methodA more comprehensive calculation method should be used,either if the solid projected area covers more than 80% of themoonpool section area, or if the vertical motion of the liftedobject differs from the vertical motion of the vessel atmoonpool, i.e.:−−if a motion control system is applied when the liftedobject is inside the moonpool, orif the object is suspended in soft spring, such as apneumatic cylinder.3.5.7.1 The following calculation steps are defined,1) Calculate the first order wave pressure transfer functionsat the moonpool mouth, using a wave diffraction theoryprogram with a panel model of the ship with moonpool.Emphasis should be put on obtaining numerical stabilityfor the moonpool oscillation mode.2) Carry out a non-linear time domain analysis of thesystem, with a model as described below. The analysisshould be made for relevant irregular wave sea states.Calculate motion of the lifted object and forces in liftinggear.d) The water body should be excited by the water pressuremultiplied by the section area of the moonpool opening.e) The interaction between the water plug and themoonpool walls should be modelled a a quadraticdamping coupling in vertical direction.f) The interaction force between the water plug and thelifted object is found as:( ρV+ A )& ςwA &3333ςbF = [N]where1 ρ CDAbvrv−2r+v r = relative velocity between lifted objectand water plug [m/s]A b = solid projected area of the lifted object [m 2 ]V = volume of lifted body [m 3 ]A 33 = added mass of lifted body [kg]& = vertical acceleration of the water plug [m/s 2 ]ς& wς& & b= vertical acceleration of lifted object [m/s 2 ]3.5.7.3 A wave diffraction panel program can be used tocalculate the fluid motion in the moonpool by solving for themotion of a mass-less lid on the top of the water plug as ageneralized mode of motion in addition to the 6 degree offreedom rigid body motions of the vessel.3.6 Stability of lifting operations3.6.1 IntroductionSituations where stability during lifting operations isparticularly relevant include,−−Tilting of partly air-filled objects during loweringEffects of free water surface inside the object3.5.7.2 The following analysis model is proposed,a) The lifted object is modeled, with mass andhydrodynamic mass and damping.b) The lifting system is modeled, with motion compensatoror soft spring, if applicable.c) The water plug inside the moonpool is modeled as afluid body moving only in vertical direction, with massequal to the energy-equivalent mass given in 3.5.4.7.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 433.6.2 Partly air-filled objects3.6.2.1 This case is also relevant for lifting of objectswhere the buoyancy is distributed differently from the mass.Figure 3-16 shows a submerged body where the centre ofgravity C G and the centre of buoyancy C B do not coincide.I = area moment of inertia of the free surface [m 4 ]The area moment of inertia I varies with filling, geometryand tilt angle.ρgVρgVCCB BC GC FCFMg - ρgVMgC BCBCG C GFigure 3-16 Definition of C G , C B and C F .CGMgFigure 3-17 Lifting with free surface inside the object3.6.2.2 The force centre is found from momentequilibrium;Mg ⋅ xC− ρgV⋅ x − α ⋅GCxB CxGCBxC==[m]FMg − ρgV1−αwhereρgVα = [-]Mgx , x , x are the horizontal coordinates of the centreCGCBCFof gravity, centre of buoyancy and the force centrerespectively.3.6.2.3 If no other forces are acting on the object, it willrotate until C B is vertically above C G . If the object issuspended, the liftwire must be attached vertically above C Fin order to avoid tilting.3.6.2.4 The adjustments of sling lengths required for ahorizontal landing on seabed may thus give a tilt angle whenthe object is in air (due to the horizontal distance C F - C G ).3.6.3 Effects of free water surface inside the object3.6.3.1 In case of a free water surface inside the body, thevertical distance z GB between C G and C B must be largeenough to give an uprighting moment larger than theoverturning moment provided by the free water surface.Figure 3-17 illustrates this.Mg zGB > ρgI⋅ [Nm]wherez = vertical (positive) distance between centre ofGBbuoyancy and centre of gravity [m]M = object mass [kg]3.7 References/1/ DNV Recommended Practice DNV-RP-C205“Environmental Conditions and Environmental Loads”,April 2007/2/ Molin B. (2001) "On the added mass and damping ofperiodic arrays of fully or partially porous disks". J.Fluids & Structures, 15, 275-290./3/ Molin, B. and Nielsen, F.G. (2004) “Heave added massand damping of a perforated disk below the freesurface”, 19 th Int.Workshop on Water Waves andFloating Bodies, Cortona, Italy, 28-31 March 2004./4/ Faltinsen, O.M.; “Sea Loads on Ships and OffshoreStructures”, Cambridge University Press, 1990./5/ Greenhow, M. and Li, Y. (1987) “Added masses forcircular cylinders near or penetrating fluid boundaries –Review, Extension and application to water entry, exitand slamming.”. Ocean Engng 14 (4) 325-348./6/ Newman, J.N. (1977) “Marine Hydrodynamics”. MITPress./7/ Sandvik, P.C., Solaas,F. and Nielsen, F.G. (2006)“Hydrodynamic Forces on ventilated Structures" ISOPEPaper no. 2006-JSC-322, San Francisco, May 2006./8/ Sumer, B.M. and Fredsøe, J. (1997) “Hydrodynamicsaround cylindrical structures”. World Scientific./9/ Zhu, X.Y., Faltinsen, O.M. and Hu, C.H. (2005) “Waterentry and exit of a circular cylinder”. Proc. 24 th OMAEConference, Halkidiki, Greece./10/ Campbell, I.M.C. and Weynberg, P.A. (1980)“Measurement of parameters affecting slamming”. FinalDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 44Report, Rep. No. 440,Technology Reports Center No.OT-R-8042. Southampton University: Wolfson Unit forMarine Technology./11/ ISO 19902 (2001), “Petroleum and Natural GasIndustries – Fixed Steel Offshore Structures”, AnnexeA9.6.2.3.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 454 Lifting through wave zone - simplifiedmethod4.1 Introduction4.1.1 Objective4.1.1.1 This section describes the Simplified Method forestimating characteristic hydrodynamic forces on objectslowered through the water surface and down to the seabottom.4.1.1.2 The intention of the Simplified Method is to givesimple conservative estimates of the forces acting on theobject.4.1.2 Application4.1.2.1 Calculation results based upon the SimplifiedMethod may be used as input in DNV-OS-H205, Lifting,ref./3/.4.1.2.2 The Simplified Method supersedes therecommendations for determination of environmental loadeffects given in DNV Rules for Marine Operations, 1996,Pt.2 Ch.6, ref./5/.4.1.2.3 The sign of the motion, velocity, acceleration andforce terms in the Simplified Method should always beapplied as positive unless denoted otherwise.4.1.2.4 In general, the Simplified Method describesforces acting during lowering from air down through thewave zone. The method is however also applicable for theretrieval case.4.1.3 Main assumptions4.1.3.1 The Simplified Method is based upon thefollowing main assumptions;• the horizontal extent of the lifted object (in the wavepropagation direction) is relatively small compared to thewave length.• the vertical motion of the object follows the crane tipmotion.• the load case is dominated by the vertical relative motionbetween object and water – other modes of motions canbe disregarded.4.1.3.2 More accurate estimations are recommended ifthe main assumptions are not fulfilled, see, Section 3.4.1.3.3 Increased heave motion of the lifted object due toresonance effects is not covered by the Simplified Method,see 4.3.3.3.4.2 Static Weight4.2.1 General4.2.1.1 The static weight of the submerged object isgiven by:F static = Mg − ρVg [N]whereM = mass of object in air [kg]g = acceleration due to gravity = 9.81 [m/s 2 ]ρ = density of sea water, normally = 1025 [kg/m 3 ]V = volume of displaced water during different stageswhen passing through the water surface [m 3 ]4.2.1.2 The static weight is to be calculated with respectto the still water surface.4.2.1.3 A weight inaccuracy factor should be applied onthe mass of the object in air according to DNV-OS-H102Section 3, C200.4.2.2 Minimum and Maximum Static weight4.2.2.1 Flooding of subsea structures after submergencemay take some time. In such cases, the static weight shouldbe calculated applying both a minimum value and amaximum value.4.2.2.2 The minimum and maximum static weight forobjects being flooded after submergence should be taken as:F static-min = M min g − ρVg [N]F static-max = M max g − ρVg [N]whereM min = the minimum mass is equal the mass of object in air(i.e. the structure is submerged but the flooding hasnot yet started) [kg]M max = the maximum mass is equal the mass of object in airincluding the full weight of the water that floods thestructure (i.e. the structure is fully flooded aftersubmergence) [kg]Guidance NoteThe volume of displaced water, V, is the same for both cases.4.2.2.3 The weight inaccuracy factor should be applied asa reduction of the minimum mass and as an increase in themaximum mass.4.2.2.4 Water that is pre-filled before lifting should betaken as part of the mass of object in air.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 464.2.2.5 Water that is retained within the lifted objectduring recovery should be taken as part of the mass of objectin air.4.2.2.6 The possibility of entrapped air should beevaluated and included in calculations when relevant. Bothloss of stability, risk of implosion and risk of slack slingsshould be investigated.4.3 Hydrodynamic Forces4.3.1 General4.3.1.1 This section describes the Simplified Method forestimation of the environmental loads and load effects.4.3.1.2 Only characteristic values are included.Implementation of safety factors in the capacity check ofstructure and lifting equipment should be performed asdescribed in DNV-OS-H102, ref./2 and DNV-OS-H205,ref./3/.4.3.1.3 For further explanation of the term“characteristic”, see DNV-OS-H102 Section 1, C100.4.3.2 Wave periods4.3.2.1 The influence of the wave period may be takeninto account. The performed analyses should then cover thefollowing zero-crossing wave period range for a givensignificant wave height H s :H8.9⋅ s≤ Tz≤gwhere13[s]g = acceleration of gravity = 9.81 [m/s 2 ]H s = Significant wave height of design sea state [m]= Zero-crossing wave periods [s]T zGuidance NoteT z values with increments of 1.0s are in most cases sufficient.Guidance NoteA lower limit of H max=1.8·H s=λ/7 with wavelength λ=g·T z2 /2π is hereused.Guidance NoteThe relation between the zero-crossing wave period, Tz, and thepeak wave period, Tp, may be taken according to DNV-RP-C205,ref./6/, Section 3.5.5, applying a JONSWAP spectrum. For a PMspectrum the relation can be taken as Tp=1.4·Tz.4.3.2.2 Applied T z -ranges or concluded allowable Tzrangesdeviating from 4.3.2.1 should be reflected in theweather criteria in the operation procedures.4.3.2.3 Alternatively, one may apply the wave kinematicequations that are independent of the wave period. Theoperation procedures should then reflect that the calculationsare only valid for waves longer than the followingacceptance limit, i.e. :Tz≥ 10. 6 ⋅Guidance NoteHgS[s]As zero-crossing wave periods less than the above acceptance limitvery rarely occur, this operation restriction will for most cases notimply any practical reduction of the operability.Guidance NoteA lower limit of H max=1.8·H s=λ/10 with wavelength λ=g·T z2 /2π is hereused.4.3.3 Crane tip motions4.3.3.1 In order to establish the relative motion betweenthe waves and the lifted structure, it is necessary to find themotions of the vessel’s crane tip.4.3.3.2 The Simplified Method assumes that the verticalmotion of the structure is equal to the vertical motion of thecrane tip. More accurate calculations should be made ifamplification due to vertical resonance is present.4.3.3.3 Resonance amplification may be present if thecrane tip oscillation period or the wave period is close to theresonance period, T 0 , of the hoisting system:M + A33+ θ ⋅ mLT0 = 2 π [s]Kwherem = mass of hoisting line per unit length [kg/m]L = length of hoisting line [m]M = mass of object in air [kg]A 33 = heave added mass of object [kg]K = stiffness of hoisting system, see 4.7.6.1 [N/m]θ = adjustment factor taking into account the effect ofmass of hoisting line and possible soft springs(e.g. cranemaster), see 5.3.5.2.Guidance NoteIn most cases, T 0 is less than the relevant wave periods. Waveinduced resonance amplification of an object located in the wavezone may in such cases be disregarded if the peak wave period, T P,is significantly larger than the resonance period of the hoistingsystem, typically:T> 1.6 ⋅P T 0Guidance NoteResonance amplification due to the crane tip motion may bedisregarded if the peak period of the response spectrum for thevertical motion of the crane tip, T p-ct, is larger than the resonanceperiod of the hoisting system, typically:Tp−ct> 1.3 ⋅T0where T p-ct is calculated for a T z range as described in 4.3.2.1.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 47Guidance NoteThe resonance period of the hoisting system, T 0 , increase with thelength of the hoist line. Resonance amplification due to crane tipmotion may therefore occur during deployment of objects down tovery deep water. This should be given special attention, see Section4.7.7 and Section 5.4.3.3.4 Active or passive heave compensation systemsshould normally not be taken into account in the SimplifiedMethod when calculating hydrodynamic loads, see, Section 3for more accurate time-domain simulations.Guidance NoteThe effect of passive heave compensation systems may beimplemented as soft springs in the stiffness of the hoisting systemwhen performing snap load calculations and when checking risk ofresonance amplification.4.3.3.5 The characteristic vertical crane tip motions onthe installation vessel should be calculated for theenvironmental design conditions, either by a refined analysis,or by acceptable documented simplified calculations.4.3.3.6 For subsea lift operations dependent on a fixedvessel heading, vessel responses for all wave directionsshould be analysed.4.3.3.7 For subsea lift operations that may be performedindependent of vessel headings, vessel response should beanalysed for wave directions at least ±15° off the vesselheading stated in the procedure.4.3.3.8 Long crested sea may be applied in the analysis.See however the guidance note below.Guidance NoteIn some cases it may be appropriate to apply short crested sea inorder to find the most critical condition. Vertical crane tip motion maye.g. be dominated by the roll motion in head sea ±15°. Roll motionmay then be larger for short crested sea than for long crested sea. Itis hence recommended to investigate the effect of short crested seain such cases, see also DNV-OS-H101 Section 3, C800.Guidance NoteIf long crested sea is applied for simplicity, a heading angle of ±20° isrecommended in order to account for the additional effect from shortcrested sea. A heading angle of ±15° combined with long crestedsea should only be applied if the vertical crane tip motion is notdominated by the roll motion, or if the vessel can document that it isable to keep within ±10° in the design sea state.4.3.3.9 The computed heave, pitch and roll RAOs for thevessel should be combined with crane tip position in thevessel’s global coordinate system in order to find the verticalmotion of the crane tip.4.3.3.10 The applied values for the crane tip velocity andacceleration should represent the most probable largestcharacteristic single amplitude responses.4.3.3.11 If the lowering through the wave zone (includingcontingency time) is expected to be performed within 30minutes, the most probable largest characteristic responsesmay be taken as 1.80 times the significant responses.4.3.3.12 The performed motion response analyses shouldcover a zero-crossing wave period range as described insection 4.3.2.4.3.4 Wave kinematics4.3.4.1 The lowering through the wave zone (includingcontingency time) is in this subsection assumed to beperformed within 30 minutes.4.3.4.2 If the duration of the lifting operation is expectedto exceed the 30 minutes limit, the significant wave height,Hs, in the below equations for wave amplitude, wave particlevelocity and wave particle accelerations should be multipliedwith a factor of 1.10.4.3.4.3 The characteristic wave amplitude can be takenas:ζ = 0. 9 ⋅ [m]aH S4.3.4.4 In this Simplified Method the followingcharacteristic wave particle velocity and acceleration can beapplied:4π2d−2⎛ 2π⎞ T z gvw= ζ a ⋅⎜⎟eT⋅[m/s]⎝ z ⎠and4π2d2 −2⎛ 2π⎞ T z gaw= ζ a ⋅ ⎜ ⎟⋅ eT[m/s 2 ]⎝ z ⎠wherev w = characteristic vertical water particle velocity [m/s]a w = characteristic vertical water particle acceleration [m/s 2 ]ζ a = characteristic wave amplitude according to 4.3.4.3[m]g = acceleration of gravity = 9.81 [m/s 2 ]d= distance from water plane to centre of gravity ofsubmerged part of object [m]H s = Significant wave height of design sea state [m]T z = Zero-up-crossing wave periods, see 4.3.2.1 [s]4.3.4.5 Alternatively, one may apply the followingwavekinematic equations that are independent of the waveperiod;v waw0.35d−= 0.30 π g Hs ⋅ e Hs [m/s]0.35d−= 0.10π g ⋅eHs[m/s 2 ]with definition of parameters as given in 4.3.4.4 and a T zapplication limit as described in 4.3.2.3.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 48Guidance NoteA lower limit of H max=1.8·H s=λ/10 with wavelength λ=g·T z2 /2π is hereused.4.3.4.6 It should be clearly stated in the analysesdocumentation whether or not the influence of the waveperiod is included. The two alternatives for the SimplifiedMethod should not be interchanged within the analyses.4.3.5 Slamming impact force4.3.5.1 The characteristic slamming impact force on theparts of the object that penetrate the water surface may betaken as:F slam = 0.5 ρ C s A s v s2where[N]ρ = density of sea water [kg/m 3 ]C s = slamming coefficient which may be determined bytheoretical and/or experimental methods. For smoothcircular cylinders C s should not be taken less than 3.0.Otherwise, C s should not be taken less than 5.0. Seealso DNV-RP-C205.A s = slamming area, i.e. part of structure projected on ahorizontal plane that will be subject to slammingloads during crossing of water surface [m 2 ]v s = slamming impact velocity [m/s]Figure 4-1 Top-plate of suction anchor crossing the watersurface. Water spray from ventilation hole.4.3.5.2 The slamming impact velocity may be calculatedby:v = v + v + v [m/s]swherev cc2ct2w= hook lowering velocity, typically 0.50 [m/s]v ct = characteristic single amplitude vertical velocity of thecrane tip [m/s]v w = characteristic vertical water particle velocity as foundin 4.3.4.4 or 4.3.4.5 applying a distance, d, equal zero[m/s]4.3.5.3 Increased slamming impact velocity due toexcitation of the water column inside suction anchors can bespecially considered.Guidance NoteA simplified estimation of the local slamming impact velocity inside asuction anchor may be to apply:⋅κ2 2 2vs= vc+ vct+ v[m/s]wwherev c = hook lowering velocity, typically 0.50 [m/s]v ct = characteristic single amplitude vertical velocity of the crane tip[m/s]v w = characteristic vertical water particle velocity [m/s]κ = amplification factor, typically 1.0 ≤ κ ≤ 2.0 [-]Guidance NoteCompression and collapse of air cushions are disregarded in thissimplified estimation. The air cushion effect due to limited evacuationof air through ventilation holes may contribute to reduced slammingforce.Figure 4-2 Internal slamming on top-plate of foundationbucket. From CFD analysis. Bucket dim. 3.5xØ4.0m.Ventilation holes Ø0.8m. Regular wave H=3.5m, T=5.5s.Lowering speed 0.25m/s. One second between snapshots.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 494.3.6 Varying buoyancy force4.3.6.1 The static weight of the object is related to thestill water surface. The change in buoyancy due to the wavesurface elevation may be taken as:Fρ = ρ ⋅δV⋅ g [N]whereρ = density of sea water, normally = 1025 [kg/m 3 ]δV = change in volume of displaced water from still watersurface to wave crest or wave trough4.3.6.2 The change in volume of displaced water may beestimated by:~ 2 2δ V = A w ⋅ ζ a + ηct[m 3 ]whereA ~ = mean water line area in the wave surface zone [m 2 ]wζ a = characteristic wave amplitude, see 4.3.4.3 [m]η ct = characteristic single amplitude vertical motion of thecrane tip [m]4.3.6.3 The change in volume of displaced water may beasymmetric about the still water surface.Guidance NoteIf the change in displacement is highly nonlinear, a direct calculationof the volume from still water surface to wave crest or to wave troughmay be performed applying a water surface range of:δζ ζ a+ η ct2 2= ±[m]4.3.7 Mass force4.3.7.1 The characteristic mass force on an object itemdue to combined acceleration of object and water particlesmay be taken as:FMiwhere2[( M i + A ) ⋅ a ] + [( Vi+ A ) ⋅ a ] 2= ρ [N]33ctM i = mass of object item in air [kg]A 33i = heave added mass of object item [kg]a ct = characteristic single amplitude vertical acceleration ofcrane tip [m/s 2 ]ρ = density of sea water, normally = 1025 [kg/m 3 ]V i = volume of displaced water of object item relative tothe still water level [m 3 ]a w = characteristic vertical water particle acceleration asfound in 4.3.4.4 or 4.3.4.5 [m/s 2 ]Guidance NoteThe structure may be divided into main items. The mass, addedmass, displaced volume and projected area for each individual mainitem are then applied in 4.3.7.1 and 4.3.8.1. Mass forces and dragforces are thereafter summarized as described in 4.3.9.6.33wGuidance NoteThe term “mass force” is here to be understood as a combination ofthe inertia force and the hydrodynamic force contributions fromFroude Kriloff forces and diffraction forces (related to relativeacceleration). The crane tip acceleration and the water particleaccelerations are assumed statistically independent.4.3.7.2 Estimation of added mass may be performedaccording to 4.6.3 – 4.6.5.4.3.8 Drag force4.3.8.1 The characteristic drag force on an object itemmay be taken as:F Di = 0.5 ρ C D A Pi v r2[N]whereρ = density of sea water, normally = 1025 [kg/m 3 ]C D = drag coefficient in oscillatory flow of submerged partof object [-]A Pi = area of submerged part of object item projected on ahorizontal plane [m 2 ]v r = characteristic vertical relative velocity between objectand water particles, see 4.3.8.3 [m/s]4.3.8.2 Estimation of drag coefficients may be performedaccording to 4.6.2.4.3.8.3 The characteristic vertical relative velocitybetween object and water particles may be taken as:v v + v + vr= [m/s]c2ct2wwherev c = hook hoisting/lowering velocity, typically 0.50 [m/s]v ct = characteristic single amplitude vertical velocity of thecrane tip [m/s]v w = characteristic vertical water particle velocity as foundin 4.3.4.4 or 4.3.4.5 [m/s]4.3.9 Hydrodynamic force4.3.9.1 The characteristic hydrodynamic force on anobject when lowered through water surface is a timedependent function of slamming impact force, varyingbuoyancy, hydrodynamic mass forces and drag forces.4.3.9.2 The following combination of the various loadcomponents is acceptable in this Simplified Method:22Fhyd = ( FD+ Fslam) + ( FM− Fρ) [N]whereF D = characteristic hydrodynamic drag force [N]F slam = characteristic slamming impact force [N]F M = characteristic hydrodynamic mass force [N]F ρ= characteristic varying buoyancy force [N]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 50Guidance NoteDuring lowering through the water surface, the structure may haveboth fully submerged parts and items in the splash zone. Theslamming force acting on the surface crossing item is then in phasewith the drag force acting on the fully submerged part. Likewise, themass and varying buoyancy forces are 180° out of ph ase.4.3.9.3 The slamming impact force on a structure partthat is hit by the wave surface may be taken as the only loadcomponent acting on that structure part, see 4.5.2.4.3.9.4 This method assumes that the horizontal extent ofthe lifted object is small compared to the wave length. Amore accurate estimation should be performed if the objectextension is found to be important, see Section 3.4.3.9.5 The structure may be divided into main items andsurfaces contributing to the hydrodynamic force.4.3.9.6 The water particle velocity and accelerationshould be related to the vertical centre of gravity for eachmain item when calculating mass and drag forces. Theseforce contributions should then be found by:F M = ∑F M i and F D = ∑F Di [N]iiwhereF Mi and F Di are the individual force contributions from eachmain item, see 4.5.2.4.4 Accept Criteria4.4.1 General4.4.1.1 This section describes the accept criteria for thecalculated hydrodynamic forces.4.4.2 Characteristic total force4.4.2.1 The characteristic total force on an object loweredthrough water surface should be taken as:F total = F static + F hydwhere[N]F static = static weight of object, ref. 4.2.2 [N]F hyd = characteristic hydrodynamic force, ref. 4.3.9 [N]4.4.2.2 In cases where snap loads occur the characteristictotal force on object should be taken as:F total = F static + F snapwhere[N]F static = static weight of object, ref. 4.2.2 [N]F snap = characteristic snap force, ref. 4.7.2 [N]4.4.3 The slack sling criterion4.4.3.1 Snap forces shall as far as possible be avoided.Weather criteria should be adjusted to ensure this.4.4.3.2 Snap forces in slings or hoist line may occur ifthe hydrodynamic force exceeds the static weight of theobject.4.4.3.3 The following criterion should be fulfilled inorder to ensure that snap loads are avoided in slings and hoistline:Fhyd ≤ 0 . 9 ⋅ F static −min[N]Guidance NoteA 10% margin to the start of slack slings is here assumed to be anadequate safety level with respect to the load factors and loadcombinations stated in the ULS criteria.Guidance NoteHydrodynamic forces acting upwards are to be applied in 4.4.3.3.Guidance NoteIn cases involving objects with large horizontal extent, e.g. longslender structures like spool pieces, more refined analyses areneeded in order to establish loads in individual slings. In general, timedomain analyses are recommended for this purpose. A simpler andmore conservative approach may be to apply the Regular DesignWave Approach as described in Section 3.4.2. In this method thewave induced motion response of the lifted object is assumednegligible.4.4.3.4 The minimum static weight of the object shouldbe applied as described in 4.2.2.4.4.4 Capacity checks4.4.4.1 In addition to the slack sling criterion, thecapacity of lifted structure and lifting equipment should bechecked according to DNV-OS-H205, Lifting, ref./3/.4.4.4.2 The characteristic total force on the object shouldbe calculated applying the maximum static weight.4.4.4.3 The capacity checks described in DNV-OS-H205,Lifting relates to the weight of the object in air. Hence, aconverted dynamic amplification factor (DAF) should beapplied equivalent to a factor valid in air. The followingrelation should be applied in the equations given in DNV-OS-H205:FDAFtotalconv = Mg[-]whereDAF conv = is the converted dynamic amplification factorM = mass of object in air [kg]g = acceleration of gravity = 9.81 [m/s 2 ]F total = is the largest of: F total = F static-max + F hyd orF total = F static-max + F snap [N]4.4.4.4 The maximum static weight of the object shouldbe applied as described in 4.2.2.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 514.5 Typical Load Cases during Lowering throughWater Surface4.5.1 General4.5.1.1 There will be different hydrodynamic loads actingon different parts of the structure during lowering throughwater surface. The operation should therefore be analysedcovering a number of different load cases.4.5.1.2 When establishing load cases one should identifymain items on the object contributing to hydrodynamicforces. The still water levels may be positioned according tothe following general guidance:• Varying buoyancy force F ρ , mass force F M and dragforce F D are negligible assuming the horizontal projectedarea of the skirt walls is small.4.5.2.3 The second load case is when buckets are fullysubmerged, figure 4-4:Load Case 2 – Still Water Level above Top ofBuckets≥ 1.0m4.5.1.3 the still water level is located just beneath theslamming area of the main item.CoGd4.5.1.4 the still water level is located just above the topof the submerged main item.4.5.1.5 Examples of typical load cases are given in 4.5.2.These are merely given as general guidance. Typical loadcases and load combinations should be established for allstructures individually.4.5.1.6 The total hydrodynamic force on the structureshould be calculated as specified in 4.3.9.2.4.5.2 Load cases for a protection structure4.5.2.1 The lowering through water surface of a typicalprotection structure with roof, legs and ventilated bucketsmay be divided into four load cases as shown in figures 4-3to 4-6.Figure 4-4 Typical loadcases for a protection structure.where• Slamming impact force, F slam , is zero.• Varying buoyancy force F ρ , mass force F M and dragforce F D are calculated. The characteristic verticalrelative velocity and acceleration are related to CoG ofsubmerged part of structure.4.5.2.4 The third load case is when the roof cover is justabove the still water level, figure 4-5:Load Case 3 – Still Water Level beneath RoofCover≤ 1.0m4.5.2.2 The first load case is slamming on the mudmats,figure 4-3:Load Case 1 - Still Water Level beneath Top ofVentilated BucketsCoG LegsCoG Bucketd Legsd BucketsFigure 4-5 Typical loadcases for a protection structure.Figure 4-3 Typical loadcases for a protection structure.where≤ 1.0m• Slamming impact force, F slam , acts upwards on top-plateinside the buckets. Only the mudmat area of bucketssimultaneously affected need to be applied. Typically, ifthe object has four buckets, it may be sufficient to applytwo.where• Slamming impact force, F slam , is calculated on the roofcover.• Varying buoyancy force, F ρ , in the wave surface zone iscalculated.• Mass forces, F Mi , are calculated separately for bucketsand legs, applying the characteristic vertical waterparticle acceleration for CoG of buckets and legsindividually. The total mass force is the sum of the twoload components, see 4.3.9.6.• Drag forces, F Di , are also calculated separately forbuckets and legs applying correct CoGs. The total dragforce is the sum of the two load components.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 524.5.2.5 The fourth load case is when the whole structureis fully submerged, figure 4-6:Load Case 4 – Still Water Level above RoofCoverd Roof ≥ 1.0mCoG Roof4.6.2 Drag coefficients4.6.2.1 Hydrodynamic drag coefficients in oscillatoryflow should be used.4.6.2.2 The drag coefficient in oscillatory flow, C D , varywith the Keulegan-Carpenter number and can be typicallytwo to three times larger than the steady flow dragcoefficient, C DS , see e.g. Ref./6/ and /7/.CoG LegsCoG Bucketd Legsd Buckets4.6.2.3 Waves, current or vertical fluid flow due tolowering speed may partly wash away some of the wake.This may reduce the oscillatory drag coefficient compared tomodel test data obtained without this influence.Figure 4-6 Typical loadcases for a protection structure.where• Slamming impact force, F slam , is zero.• Varying buoyancy force F ρ , is zero.• Mass forces, F Mi , are calculated separately for buckets,legs and roof, applying the characteristic vertical waterparticle acceleration for CoG of buckets, legs and roofindividually. The total mass force is the sum of the threeload components.• Drag forces, F Di , are also calculated separately forbuckets, legs and roof, applying correct CoGs. The totaldrag force is the sum of the three load components, see4.3.9.6.4.6 Estimation of Hydrodynamic Parameters4.6.1 General4.6.1.1 The hydrodynamic parameters may bedetermined by theoretically and/or experimental methods.4.6.1.2 The hydrodynamic parameters may be dependenton a number of factors, as e.g.:- structure geometry- perforation- sharp edges- proximity to water surface or sea bottom- wave height and wave period- oscillation frequency- oscillation amplitude4.6.1.3 The drag coefficients and added mass valuesgiven in this simplified method do not fully take into accountall the above listed parameters.4.6.1.4 Model tests have shown that the added mass maybe highly dependent on the oscillation amplitude of typicalsubsea structures, see e.g. Ref./11/.Guidance NoteBeneath the wave zone, the drag coefficient decreases withincreasing lowering speed. The reason for this is that the loweredstructure will tend to enter more undisturbed fluid. If the loweringspeed exceeds the maximum oscillation velocity, the drag coefficientwill tend to approach the value of the steady flow drag coefficient.4.6.2.4 Unless specific CFD studies or model tests havebeen performed, the following guideline for drag coefficientson typical subsea structures in oscillatory flow is given:C D ≥ 2.5 [-]4.6.2.5 For long slender elements a drag coefficient equalto twice the steady state C DS may be applied provided thathydrodynamic interaction effects are not present, see app.B.4.6.2.6 Sensitivity studies of added mass and dampingare in general recommended in order to assess whether or notmore accurate methods as CFD studies or model tests shouldbe performed.Guidance NoteThe drag coefficient may be considerable higher than therecommended value given in 4.6.2.4. In model tests and CFDanalyses of complex subsea structures at relevant KC numbers,oscillatory flow drag coefficients in the range C D ≈ 4 to 8 may beobtained when wake wash-out due to waves, current or loweringspeed is disregarded.Guidance NoteIt should be noted that for extremely low KC numbers the dragcoefficient as applied in 4.3.8.1 goes to infinity as the fluid velocitygoes to zero.4.6.3 Added mass for non-perforated structures4.6.3.1 Hydrodynamic added mass values for differentbodies and cross-sectional shapes may be found in DNV-RP-C205, ref./6/.4.6.3.2 The heave added mass of a surface piercingstructure may be taken as half the heave added mass (in aninfinite fluid domain) of an object formed by the submergedpart of the structure plus its mirror about the free surface.Guidance NoteThis approximation is based upon the high frequency limit and ishence only applicable in cases where the radiated surface waves arenegligible.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 534.6.3.3 The following simplified approximation of theadded mass in heave for a three-dimensional body withvertical sides may be applied:⎡2 ⎤1A ⎢ − λ33 ≈ 1 + ⎥ ⋅ A⎢2 33o2(1 )⎥⎢+ λ⎣⎥⎦andλ =whereh +ApAp[-][kg]A 33o = added mass for a flat plate with a shape equal to thehorizontal projected area of the object [kg]h= height of the object [m]A P = area of submerged part of object projected on ahorizontal plane [m 2 ]4.6.3.4 A structure that contains a partly enclosed volumeof water moving together with the structure may be taken asa three-dimensional body where the mass of the partlyenclosed water volume is included in the added mass.Guidance NoteFor example, a bucket shaped suction anchor with a diameter equalthe height will according to 4.6.3.3 have an added mass equal 1.57times the added mass of a circular disc plus the mass of the watervolume inside the bucket.Guidance NoteIn this Simplified Method flooded items as e.g. tubular frames orspool pieces should be applied in the static weight calculationsaccording to 4.2.2. The mass of this water volume should not beincluded in the added mass as it is already included in the bodymass.4.6.3.5 Added mass calculations based upon panelmethods like the sink-source technique should be used withcare (when subject to viscous fluid flow). It may giveunderestimated values due to oscillation amplitudedependency and proximity to the free water surface.Guidance NoteMethods based upon potential theory assumes non-viscous fluid andsmall oscillation amplitudes and can be suitable for determiningfrequency dependency on deeply submerged bodies in infinite fluiddomain.4.6.3.6 Added mass calculations based upon summationof contributions from each element is not recommended ifthe structure is densely compounded. The calculated valuesmay be underestimated due to interaction effects and theoscillation amplitude dependency.Guidance note:Interaction effects can be neglected if the solid projected area normalto the direction of motion (within a typical amplitude of either bodymotion or wave particle motion) is less than 50 %.4.6.4 Effect of perforation4.6.4.1 The effect of perforation on the added mass mayroughly be estimated by the following guidance:A A33S= A ⋅ ( 0.7 + 0.3cos[ ( p 5) / 34])= 33 if p< 5ASπ if 5 < p < 34A33 33−33where33S10−p28= A ⋅ e if 34 < p < 50A 33S = solid added mass (added mass in heave for a nonperforatedstructure) [kg]p = perforation ratio (percentage) [-]Guidance NoteFor example, a bucket shaped suction anchor with a ventilation holecorresponding to 5% perforation will have an added mass equal thesolid added mass, i.e. the added mass is in this case unaffected bythe ventilation hole.Guidance NoteThis guidance is based upon a limited number of model test data andincludes hence a safety margin. It is not considered applicable forperforation ratios above 50%.Guidance NoteThe recommended DNV-curve is shown as the upper curve in figure4-7. The shadowed area represents model test data for differentsubsea structures at varying KC-numbers. The exp(-p/28) curve isderived from numerical simulations (based on potential flow theory) ofperforated plates and included in the figure for reference. As shown,the exp(-p/28) curve may give non-conservative values.Added Mass Reduction Factor10.90.80.70.60.50.40.30.20.10Effect of perforation on added massPerforation0 10 20 30 40 50e^-P/28BucketKC0.1-H4D-NiMoBucketKC0.6-H4D-NiMoBucketKC1.2-H4D-NiMoBucketKC0.5-H0.5D-NiMoBucketKC1.5-H0.5D-NiMoBucketKC2.5-H0.5D-NiMoBucketKC3.5-H0.5D-NiMoPLET-KC1-4Roof-A0.5-2.5+Hatch20-KCp0.5-1.8Hatch18-KCp0.3-0.8BucketKC0.1BucketKC0.6BucketKC1.2RoofKCp0.1-0.27RoofKCp0.1-0.37DNV-CurveMudmat CFDFigure 4-7 Added mass reduction factor A 33 /A 33S asfunction of the perforation ratio (percentage).4.6.4.2 The intention of this guidance is to ensure aconservative estimate of the perforation ratio influence onthe added mass. As seen in figure 4-7 (shaded area) theactual reduction factor may vary a lot depending ongeometry and oscillation amplitude. The recommendedguidance in 4.6.4.1 will in most cases significantlyoverestimate the added mass. CFD studies or model tests arerecommeded if more accurate estimations are needed.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 544.7 Snap Forces in Slings or Hoisting Line4.7.1 General4.7.1.1 Snap forces shall as far as possible be avoided.Weather criteria should be adjusted to ensure this.4.7.1.2 Snap forces may occur if the slack sling criterionis not fulfilled, see 4.4.3.3.4.7.2 Snap force4.7.2.1 Characteristic snap load may be taken as:( M )Fsnap vsnapK ⋅ + A 33= [N]wherev snap = characteristic snap velocity [m/s]K = stiffness of hoisting system, see 4.7.6 [N/m]M = mass of object in air [kg]A 33 = heave added mass of object [kg]4.7.2.2 The characteristic snap load should be applied asdescribed in 4.4.2.2 and 4.4.4.3.4.7.3 Snap velocity4.7.3.1 The snap velocity may be taken as:v snap = v ff + C · v r [m/s]wherev ff = free fall velocity, see 4.7.3.5 [m/s]v r = characteristic vertical relative velocity between objectand water particles, see 4.7.3.2, [m/s]C = Correction factor, see 4.7.3.4 [-]4.7.3.2 The vertical relative velocity between object andwater particles may be taken as:v = v + v + v [m/s]rwherec2ct2wv c = hook hoisting/lowering velocity, see 4.7.3.3 [m/s]v ct = characteristic single amplitude vertical velocity of thecrane tip [m/s]v w = characteristic vertical water particle velocity as foundin 4.3.4.4 or 4.3.4.5 [m/s]4.7.3.3 Two values for hook lowering velocity should beapplied; v c = 0 m/s and v c = typical lowering velocity. Inaddition, a retrieval case should be covered applying a v cequal to a typical hoisting velocity. The highest snap velocityfor the three options should be applied in the snap forcecalculation.Guidance NoteIf the typical hoisting/lowering velocity is unknown, a value of v c = ±0.50m/s may be applied.4.7.3.4 The correction factor should be taken as:C = 1⎡ ⎛ vC = cos⎢π⎜⎢⎣⎝ vandC = 0forforffrvffvff< 0.2v⎞⎤− 0.2⎟⎥⎠⎥⎦r> 0.7vrfor0.2v< vrff< 0.7v4.7.3.5 The free fall velocity of the object may be takenas:vffwhere2F=static[m/s]ρ A CpDF static = The minimum and maximum static weight asdefined in 4.2.2.2 [N]ρ = density of sea water, normally = 1025 [kg/m 3 ]A P = area of submerged part of object projected on ahorizontal plane [m 2 ]C D = drag coefficient of submerged part of object4.7.3.6 If the snap load is caused by a slamming impactforce while the object is still in air, the snap velocity may beassumed equal the slamming impact velocity given in4.3.5.2.Guidance NoteIt is here assumed that the maximum free fall velocity after impact willnot exceed the maximum relative velocity between object and watersurface.4.7.4 Snap force due to start or stop4.7.4.1 Snap force due to start or stop may be calculatedaccording to 4.7.2.1, applying a characteristic snap velocityequal to:v snap : maximum lowering velocity, typically v snap = 1.0 [m/s]4.7.5 Snap force due to lift-off4.7.5.1 Snap forces due to lift off from e.g. a bargeshould be taken into due considerations. The calculatedDAF conv as specified in 4.4.4.3 should be applied in theequations given in DNV-OS-H205, ref./3/, Section 2, D200.4.7.5.2 Snap loads during lift off may be calculatedaccording to 4.7.2.1, applying a characteristic snap velocityequal to:v snap = v c + v rctwhere[m/s]v c = hook hoisting velocity, typically 0.50 [m/s]v rct = characteristic vertical relative velocity between objectand crane tip [m/s]rDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 554.7.5.3 The characteristic vertical relative velocitybetween object and crane tip should be calculated applyingdesign sea states according to 4.3.2.1 and using the sameguidelines as given in 4.3.3.4.7.6 Stiffness of hoisting system4.7.6.1 The stiffness of the hoisting system may becalculated by:1 1=K kwhererigging+1kline+1ksoft+1kblock+1kboom1+kotherK = total stiffness of hoisting system [N/m]k rigging = stiffness of rigging, spreader bar, etc.k line = stiffness of hoist line(s)k soft = stiffness of soft strop or passive heave compensationsystem if used, see 4.7.7k block = stiffness of multiple lines in a block if usedk boom = stiffness of crane boomk other = other stiffness contributions, if any4.7.6.2 The line stiffness may be calculated by:EAk line = [N/m]LwhereE = modulus of rope elasticity [N/m 2 ]A =effective cross section area of line(s), see 4.7.6.3. Theareas are summarized if there are multiple parallellines. [m 2 ]L = length of line(s). If multiple lines the distance fromblock to crane tip is normally applied [m]4.7.6.3 The effective cross section area of one wire line isfound by:A2⋅ Dwire = π ⋅ cF[m 2 ]4wherec F = fill-factor of wire rope [-]D = the rope diameter [m]Guidance NoteThe value of the fill factor c f needs to be defined in consistence withA wire, D, and E. Typical values for e.g. a 6x37 IWRC steel core wirerope could be C F=0.58 and E=85 ·10 9 N/m 2 .4.7.7 Application of passive heave compensation systemswith limited stroke length4.7.7.1 Passive heave compensation systems may have acertain available stroke length. This stroke length must notbe exceeded during the lift.4.7.7.2 Dynamic motions of lifted object exceedingavailable stroke length may cause huge peak loads andfailure of the hoisting system.Guidance NoteA more accurate calculation of the lifting operation is recommended ifthe Simplified Method indicates risk for snap loads.4.7.7.3 Estimation of available stroke length should takeinto account the change in static weight as lifted object istransferred from air to submerged. The smallest availablesingle amplitude stroke length at each load case should beapplied.Guidance NoteThe equilibrium position (and thereby the available stroke length) willchange during the lifting operation as the static weight of the objectchange when lowered through the water surface.Guidance NoteAlso the recovery load cases should be verified.4.7.7.4 Entrapped water causing increased weight in airduring recovery should be taken into account.4.7.7.5 Changes in equilibrium position of pressurizedpistons due to increased water pressure may be taken intoaccount if relevant.4.7.7.6 A simplified check of the available singleamplitude stroke length, δx , may be to apply the followingcriterion:soft2stroke( M + A33) ⋅ vδ x >k[m]whereM = mass of object in air [kg]A 33 = heave added mass of object[kg]v stroke = stroke velocity, to be assumed equal the relativevelocity, v r (see 4.7.3.2) unless snap forces occur atwhich the snap velocity, v snap , should be applied, seee.g. 4.7.3.1 or 4.7.5.2. [m/s]k soft = stiffness of the passive heave compensation system[N/m]Guidance NoteA more accurate estimation of available stroke length isrecommended if the system characteristics are known, e.g. inpressurized pistons the energy loss due to flow resistance is notincluded in 4.7.7.6.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 575 Deepwater lowering operations5.1 Introduction5.1.1 General5.1.1.1 For lifting operations in deep water the followingeffects should be considered,• stretched length of cable due to cable own weight andweight of lifted object• horizontal offset due to current where the currentvelocity may be time-dependent and its magnitude anddirection may vary with water depth• dynamics of lifted object due to wave induced motion ofcrane tip on vessel• methods for controlling vertical motion of lifted object5.1.1.2 The term “cable” is in the following used todenote the lifting line from crane to lifted object. Cable canconsist of steel wire, fibre rope, chain, or a combination ofthese.5.1.2 Application5.1.2.1 Calculation results based upon the method andformulas given in this section may be used as input in DNV-OS-H205, Lifting, ref./1/.5.1.2.2 The sign of the motion, velocity, acceleration andforce terms in this section should always be applied aspositive unless denoted otherwise.5.1.2.3 In general, this section describes forces acting onthe vertical cable and the lowered object from beneath thewave zone down to the sea bed. The method and formulasare also applicable for the retrieval case. Forces on liftedobjects in the wave zone is covered in Sections 3 and 4.5.1.2.4 Static and dynamic response of lowered or liftedobjects in deep water can be predicted by establishedcommercial computer programs. The analytic formulaspresented in this section may be used to check or verifypredictions from such numerical analyses.5.2 Static forces on cable and lifted object5.2.1 Stretched length of a cableA vertical cable will stretch due to its own weight and theweight of the lifted object at the end of the cable. Thestretched length L s of a cable of length L is;L s⎡ 1 ⎤⎢ W + wL ⎥= L⎢1+2⎥⎢ EA ⎥⎢⎣⎥⎦whereL sLWwM[m]= stretched length of cable [m]= original length of cable [m]= Mg – ρgV = fully submerged weight of liftedobject [N]= mg – ρgA = fully submerged weight per unitlength of cable [N/m]= mass of lifted object [kg]m = mass per unit length of cable [kg/m]g = acceleration of gravity = 9.81 m/s 2ρ = density of water [kg/m 3 ]E = modulus of elasticity of cable [N/m 2 ]A = nominal cross sectional area of cable [m 2 ].See Guidance Note in 5.2.4V = displaced volume of lifted object [m 3 ]5.2.2 Horizontal offset due to current5.2.2.1 For an axially stiff cable with negligible bendingstiffness the offset of a vertical cable with a heavy weight W 0at the end of the cable in an arbitrary current withunidirectional (in x-direction) velocity profile U c (z) is givenby;z10 D0Dn c−L∫ [z W + w(z1+∫[ U ( z )]F + (1/ 2) ρ C Dc 2dz2ξ ( z)=] dz [m]1L)whereF1= ρ [ U ( −L] 2 [N]2D0 CDxAxc)is the hydrodynamic drag force on the lifted object. Theparameters are defined as;ξ(z)ξ LL= horizontal offset at vertical position z [m]= horizontal offset at end of cable z = - L [m]= unstretched length of cable [m]C Dn = drag coefficient for normal flow past cable [-]C DxD c= drag coefficient for horizontal flow past liftedobject [-]= cable diameter [m]A x = x-projected area of lifted object [m 2 ]U c (z)z 1, z 2Guidance Note:= current velocity at depth z [m/s]= integration variables [m]It is assumed that the sum of the weight wL of the cable and thesubmerged weight W of the lifted object are so large that the anglebetween cable and a vertical line is small. See Figure 5-1.2DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 58Guidance Note:The cable diameter D c(z) and drag coefficient for normal flow C Dn(z)may vary with depth. This variation must be taken into account whencalculating the offset.Uzξ(z)ξ LxwqWF D0Figure 5-1: Horizontal offset ξ(z) due to uniform current.Parameters are defined in 5.2.2. Curvature of cable determinedby F D /W 0 < q/w.5.2.2.2 For a uniform current U c and cable properties D c ,C Dn the horizontal offset can be derived by;⎡ z ⎤1q ⎢ κ + +⎛ ⎞ L⎥ qξ ( z ) = L ⎜ κ − λ ⎟ ln ⎢⎥ − z [m] (1)⎝ w ⎠ ⎢ κ + 1 ⎥ w⎢⎣⎥⎦where the top of the cable is at z = 0 and the lifted object is atthe end of the cable at z = −L. See Figure 5-1. Thehorizontal offset of the lifted object is obtained by settingz = −L in the expression for ξ(z);⎛ q ⎞ ⎡ κ ⎤ qLξL= L ⎜ κ − λ ⎟ ln + [m] (2)w ⎢ ⎥⎝ ⎠ ⎣ κ + 1⎦wwhere κ is the ratio between the weight of the lifted object,W, and the weight of the cable;Wκ = [-] (3)wLand λ is the ratio between the drag on the lifted object, F DO ,and the weight of the cable;F D0λ = [-] (4)wLThe hydrodynamic drag force per unit length of cable, q, isgiven by;12q = ρCDnDcU[N/m] (5)c2Guidance Note:A correction to account for the vertical component of drag is toreplace w by (w – qξ L/L) in formula (1) for the horizontal offset, whereξ L is the uncorrected offset at the end of the cable as calculated byformula (2).5.2.2.3 When the current velocity direction and cableproperties vary with water depth a static analysis using aFinite Element methodology with full numerical integrationis recommended to find the offset.5.2.3 Vertical displacement5.2.3.1 For installation of modules on seabed it isimportant to control the distance from the seabed to thelower part of the lifted object at the end of the cable. Thedifference ∆z of vertical position of the lower end of thecable between the real condition and a vertical unstretchedcondition has two contributions∆z =∆z G + ∆z Ewhere∆z G = vertical geometric displacement due to curvature ofthe cable∆z E = vertical elastic displacement due to stretching of cableThe geometric effect increase the clearance to seabed whilethe stretching descrease the clearance to seabed.5.2.3.2 For constant unidirectional current and constantcable properties along the length of the cable, the verticaldisplacement due to curvature of the cable my be taken as;∆ zLG≈qw⎧⎪⎛ q ⎞⎡⎜ κ − λ ⎟⎨lnw⎢⎝ ⎠⎪⎣⎪⎩κ ⎤+κ + 1⎥⎦12⎡ λw⎤⎫⎢1−q⎥⎪⎢κ⎥1 ⎛⎬ + ⎜⎢ 1 + κ ⎥⎪2 ⎝⎢ ⎥⎣ ⎦⎪⎭where the parameters q, w, κ and λ are defined in 5.2.2.1 and5.2.2.2.5.2.3.3 The vertical displacement due to stretching of thecable may be taken as;∆ zL1 ⎡ 1⎤≈ − ⎢W+ ( wL − q )EA⎥⎣ 2⎦Eξ L5.2.3.4 When the current velocity direction and cableproperties varies with water depth a three-dimensional staticanalysis using a Finite Element methodology isrecommended to find the offset.5.2.4 Vertical cable stiffness5.2.4.1 The vertical cable stiffness k V is the vertical forcethat has to be applied to the lifted object at the lower end ofthe cable per unit vertical displacement;dFVkV = [N/m]dz[-]qw⎞⎟⎠2[-]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 595.2.4.2 The vertical stiffness is the sum of twocontributions, the elastic stiffness k E and the geometricstiffness k G . The vertical stiffness k V is given by;1k11= +V kEk[m/N]G5.2.4.3 The elastic stiffness k E is given by;EAk E= [N/m]LwhereE = modulus of elasticity [N/m 2 ]A = cross-sectional area of cable [m 2 ]L = length of cable [m]Guidance Note:A is the nominal cross-sectional area of the cable defined as A=S·c Fwhere S is the cross-sectional area (of circumscribed circle) and c F isthe fill factor. See also Section 4 and 7.5.2.4.4 The non-linear geometric stiffness k G is given by1kG∂(∆ z= −∂WG)= −qwq λ 1+22w κ ( κ + 1)Guidance Note:23⎡ ⎛⎢ln⎜⎢⎣⎝+κ ⎞⎟ +κ + 1 ⎠1w212κ + 3( κ + 1)⎛ λ ⎞ 2κ+ 1⎜ ⎟2⎝ κ ⎠ 2( κ + 1)2⎤⎥⎥⎦[ m/N]The vertical cable stiffness defined above is valid for static loads, andgives the change in position of the lower end of the cable for a unitforce applied at the end.Guidance Note:The geometric stiffness decreases with increasing current speed at arate of Uc -4 . Hence, the geometric stiffness becomes rapidly moreimportant at higher current speeds.5.2.5 Horizontal stiffness5.2.5.1 The horizontal stiffness k H of lifted object is thehorizontal force that has to be applied to the lower end of thecable per unit horizontal displacement.dFHkH = [N/m]dx5.2.5.3 When the lifted object is much heavier than theweight of the cable the horizontal cable stiffness reduces tothe stiffness of the mathematical pendulum,WWκ = >> 1 ⇒ kH = wκ= [N/m]wLL5.2.6 Cable payout – quasi-static loadsThe quasi-static tension T(s) at the top end of the cableduring payout for a deepwater lowering operation is given byT(s )where12= W + ws + ρ CDfπDcsvcvc+ ρCDzApvcvc[N]s = length of cable payout [m]ρ = water density [kg/m 3 ]C Df = cable longitudinal friction coefficient [-]C Dz = drag coefficient for vertical flow past liftedobject [-]D c = cable diameter [m]A p = horizontal projected area of lifted object [m 2 ]v c = constant cable payout velocity, hauling beingpositive and lowering negative [m/s]w = submerged weight per unit length of cable[N/m]W = submerged weight of lifted object [N]For a cable payout length s, the necessary payout velocity toproduce a slack condition is found by setting T = 0 in theequation above. Note that the formula above neglects theeffect of current and water particle velocity due to wavesand is therefore only valid for still water.Guidance noteData describing friction coefficients for flow tangentially to a cablemay be found in e.g. DNV-RP-C205, ref./6/.5.3 Dynamic forces on cable and lifted object5.3.1 General5.3.1.1 For a typical lifting operation from a floatingvessel it is normally acceptable to assume that the motion ofthe vessel is not affected by the motion of the object. Thissimplification is based on the following assumptions:125.2.5.2 The horizontal stiffness k H is given by1kH=∂ξL1 ⎡ κ + 1⎤= ln∂Fw⎢ ⎥⎣ κ ⎦DO[m/N]Note that the horizontal stiffness is not influenced by thecurrent drag on the cable and the lifted object. It should alsobe noted that this expression for horizontal stiffness is validfor static loads only.−−−−mass and added mass of lifted object is much smallerthan the displacement of the vesselthe objects contribution to moment of inertia aroundCoG/centreplane of vessel is much smaller than thevessels moment of inertiathe motion of the crane tip is verticalthe effect of current can be neglectedDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 60Guidance Note:Typically, applying uncoupled vessel RAOs will give conservativeresults as the object in most cases tend to reduce the vertical cranetip motion.5.3.2 Dynamic drag forces5.3.2.1 Due to the motion of crane tip and lifted object,dynamic drag forces will act on the cable. The drag forcesrestrict the change of shape of the cable. As thevelocity/accelerations of the crane tip increases, the elasticstiffness becomes increasingly important.5.3.3 Application5.3.3.1 For lifting and lowering operations in deep waterthe dynamic response of the object depends on its verticalposition (depth). In order to perform a controlled lowering ofthe object in a given sea state, an assessment of the dynamicresponse of the lifted object at all depths should be carriedout in the planning of the operation.5.3.4 Natural frequencies, straight vertical cable5.3.4.1 The natural frequencies of a straight vertical cable(Figure 5-4) is given byEAωj= ν [rad/s] ; j = 0,1,2,..jm5.3.4.2 The exact solution for wave numbers ν j are givenby the equation (assuming undamped oscillations);mLνjL tan( vjL)= ε =[-]M + Awhereω jΤ jν jL= 2π/Tj = angular natural frequencies [rad/s]= eigenperiods [s]= corresponding wave numbers [1/m]= length of cable [m]E = modulus of elasticity [N/m 2 ]A = nominal cross-sectional area of cable [m 2 ]mMA 33= mass per unit length of cable [kg/m]= mass of lifted object in air [kg]33= added mass for motion in vertical direction [kg]ε = mL/(M+A 33 ) = mass ratio [-]Guidance noteThe vertical added mass for three-dimensional bodies in infinite fluidis defined as A 33 = ρC AV R where C A is the added mass coefficient andV R is a reference volume, usually the displaced volume. The addedmass of the lifted object is affected by proximity to free surface andproximity to sea floor. It should be noted that for complex subseamodules that are partly perforated, the added mass also depends onthe oscillation amplitude, which again affects the eigenperiod of thelifted object. Reference is made to sections 3 and 4. Added masscoefficients for certain three-dimensional bodies are given inAppendix A, Table A2.5.3.4.3 For small mass ratios, ε, the fundamental wavenumber is given by the approximation1 / 2⎛ ε ⎞ν0L = ⎜ ⎟ [-]⎝1+ε / 3⎠Guidance Note:The difference between the exact solution and the approximatesolution is shown in Figure 5-2. The figure shows that the aboveapproximation is close to the exact solution even for mass ratios,ε, up to 3.0. Hence, the eigenperiod stated in 5.3.5.1 (derived from5.3.4.3) should be valid for most practical cases.ν0L1.41.21.00.80.60.40.20.00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0mL/ (M+A 33 )Figure 5-2: Exact solution and approximated solution of thefundamental wave number ν 0 L as function of mass ratio(corresponding to the first natural frequency of verticaloscillations). Solid line is exact solution while the dotted line isthe approximation for small mass ratio ε.5.3.4.4 The higher natural frequencies can for small massratios, ε, be estimated by the corresponding wave numbers,ν j , given by;mLν j L ≈ jπ+jπ( M + A33)[-] ; j = 1,2,..Guidance Note:The fundamental frequency is normally related to the oscillation of thelifted object (with modifications due to the mass of the cable), whilethe higher modes are related to longitudinal pressure waves in thecable (Ref. 5.3.6).5.3.5 Eigenperiods5.3.5.1 The first (fundamental) eigenperiod forundamped oscillations of the lifted object in the presence ofcranemaster and/or soft slings (Figure 5-3) may be taken asT2= =ωM + A + θ ⋅ mLπK0 π 2330where1K⎛ 1 1=⎜ + +⎝ kcksLEA⎞⎟⎠[s]K = stiffness of total hoisting system [kg/s 2 ]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 61k c = stiffness of cranemaster at top of cable [kg/s 2 ]k sθ= stiffness of soft sling or cranemaster at lifted object[kg/s 2 ]= adjustment factor to account for the cable mass5.3.5.2 The adjustment factor to account for the cablemass is given by the general formulaθ =where21+c + c / 32(1 + c + c / s)zLk cm, EAkcLc = andEAksLs =EAk s5.3.5.3 The following limiting values for the adjustmentfactor may be applied:• θ ~ 1/3 if the line stiffness EA/L is the dominant softstiffness (c and s are both large numbers)• θ ~ 0 if the dominant soft spring is located just above thelifted object (s 1)• θ ~ 1 if the dominant soft spring is located at the cranetip (c 1)In the case of soft springs at both ends of the cable (s

Recommended Practice DNV-RP-H103 Draft December 2008Page 625.3.7 Response of lifted object in a straight vertical cableexposed to forced vertical oscillations5.3.7.1 When a deeply submerged object is lifted from avessel in waves, the vertical motion of the object is governedby the motion of the top of the cable, fixed to the oscillatingvessel.Guidance noteThe motion of top of the cable, or motion of crane tip in a given seastate is derived from the motion characteristics of the crane vessel bylinear combination of vessel RAOs determined by the location of thecrane tip relative to centre of rotation of the vessel. The resultingmotion RAOs in x-, y- and z-directions for crane tip may be combinedwith a wave spectrum to obtain time history of motion of crane tip. Fordeep water lowering operations only the vertical motion is of interest.See also 5.3.3.1.5.3.7.2 The vertical motion of a straight vertical cablewith the lifted object at vertical position z = -L caused by aforced oscillation of top of the cable with frequency ω andamplitude η a is given by;2[ k(z + L)] + ( −ωM ' + iωΣ)sin[ k(z + L)]η ( z)kEAcos=[m/m]2η kEAcos(kL)+ ( −ωM ' + iωΣ)sin(kL)awhere | | means the absolute value (or modulus) of a complexnumber and the mass M’ = M +A 33 (ref. 5.3.4.2).5.3.7.3 The complex wavenumber k is given byk = kr+ iki=mEA⎛ σ ⎞ω 2 − iω⎜⎟ [m -1 ]⎝ m ⎠where the positive square root is understood. i = −1is theimaginary unit and m is the mass per unit length of cable.The functions cos(u) and sin(u) are the complex cosine andsine functions of complex numbers u = u r + iu i as defined inAbramowitz and Stegun (1965).σ and Σ are linear damping coefficients for cable motion andmotion of lifted object respectively defined by equivalentlinearization.5.3.7.4 The linear damping coefficient for cable motionis defined by;σ = 2π ρC ωη [kg/ms]DfD caand the longitudinal cable friction force per unit length isgiven by;fv1= ρ C πD& η &Dfη [N/m]2where the vertical motion along the cable is given by;η& = ∂η/ ∂t [m/s]5.3.7.5 The linear damping coefficient for motion oflifted object is defined by;2Σ = ρCDzA pωη [kg/s]aπand the vertical drag force for lifted object is given byFv1= ρ CDzA &pη &Lη [N]L2and whereM = structural mass of lifted object [kg]A 33 = added mass of lifted object [kg]M’ = M+A 33 = the total mass [kg]m = mass per unit length of cable [kg/m]L = length of cable [m]E = modulus of elasticity [N/m 2 ]A = nominal cross-sectional area of cable [m 2 ]C Df = cable longitudinal friction coefficient [-]C Dz = vertical drag coefficient for lifted object [-]ρ = mass density of water [kg/m 3 ]D c = cable diameter [m]A p = z-projected area of lifted object [m 2 ]η L = η(-L) = motion of lifted object [m]Guidance noteSince the linearized damping coefficients depend on the amplitude ofmotion η a, an iteration is needed to find the actual response.5.3.7.6 The amplitude of the vertical motion of the liftedobject caused by a forced oscillation of top of the cable withfrequency ω and amplitude η a is given by η where η(z) isLdefined in 5.3.6.2,ηLkEA=2η kEAcos(kL)+ ( −ωM ' + iωΣ) sin( kL)a[m/m]5.3.7.7 The ratio between the motion of the lifted objectand the motion at the top of the cable, is the motion transferfunctionηLH L( ω ) = [m/m]ηaGuidance noteAn example response curve of a lifted object in deep water is shownin Figure 5-4, plotted with respect to oscillation period T= 2π/ω. Thefollowing parameters were used in the calculations:M’ = M+A 33 = 48000 kgm = 7.26 kg/mL = 3000 mEA = 1.00E+08 Nρ = 1025 kg/m 3D c = 0.04 mC Df = 0.02C Dz = 1.0 – 2.0A p = 25 m 2η a= 1mDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 63For long oscillation periods, the combined system of cable and liftedobject is oscillating like a rigid body where the lifted object follows themotion of the top of the cable, |η L/η a |~ 1.35.3.8 Horizontal motion response of lifted object in astraight vertical cable5.3.8.1 The first (fundamental) eigenperiod forundamped oscillations of the lifted object may be taken as:|η L |(m)2.521.5C Dz =1.0⎛ mL ⎞⎜ M + A11+ ⎟ ⋅ L⎝ 3 ⎠T0h≈ 2π [s]W + 0.45wLwhere10.5C Dz =2.000 2 4 6 8 10 12 14 16 18 20Period, [s]Period T (s)Figure 5-4: Example response amplitude of a lifted object indeep water due to a forced motion η a = 1 m at top end of cablefor two different drag coefficients C Dz=1.0 and C Dz=2.0. Largeresponse is observed close to eigenperiod T 0 = 8.1 s (as given bythe formula in 5.3.5.1 for undamped oscillations). Enhancedresponse at eigenperiod T 1 = 1.6 s can also be observed.5.3.7.8 The amplitude of the dynamic force F d (z) in thecable at position z is given by;[ k(z + L)] + ( kL)h(ω) cos[ k(z + L)]2Fd( z)− ( kL)kEsin=η k( kL)k cos( kL)+ h(ω) sin( kL)aEELWwMmA 11= length of cable [m]= Mg – ρgV = submerged weight of liftedobject [N]= mg – ρgA = submerged weight per unitlength of cable [N/m]= mass of lifted object [kg]= mass per unit length of cable [kg/m]= surge added mass of lifted object [kg]5.3.8.2 Applying added mass in sway, A 22 , in equation5.3.8.1 will give the eigenperiod for sway motion of liftedobject.5.3.8.3 If the ocean current energy spectrum is non-zeroin a range of frequencies close to f 0 = 1/T oh horizontaloscillations of the lifted object can be excited. Likewise, theoscillations may be excited by horizontal motion of crane tip.Such oscillations may be highly damped due to viscous dragon cable and lifted object.where2h(ω)= −ωM ' + iω∑kE= EA / L5.3.7.9 The dynamic force varies along the length of thecable. If the amplitude of the dynamic force exceeds thestatic tension in the cable, a slack wire condition will occur.The amplitude of the dynamic force F d0 at the top of thecable is obtained by setting z=0 in the expression above,Likewise, the amplitude of the dynamic force F dL at thelifted object is obtained by setting z=L in the expressiongiven in 5.3.7.8.5.3.7.10 The motion of the lifted object due to a generalirregular wave induced motion of top of the cable is obtainedby combining transfer functions for motion of lifted objectand motion of top of cable at crane tip position. The responsespectrum of the lifted object is given by2[ H ( ω)H ( ω)] S(ω)SL( ω)= [m 2 s]L a5.4 Heave compensation5.4.1 General5.4.1.1 Various motion control devices may be used tocompensate for the vertical motion of the vessel. The mostcommonly used device is a heave compensator.5.4.1.2 A heave compensator may be used to control themotion of the lifted object and tension in cable during alifting operation.5.4.1.3 Heave compensators may be divided into threemain groups:−−−passive heave compensatorsactive heave compensatorscombined passive/active systemswhere H a (ω) is the transfer function for crane tip motion,S(ω) is the wave spectrum and H L (ω) is defined in 5.3.7.7.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 645.4.1.4 A passive heave compensator is in principle apure spring – damper system which does not require input ofenergy during operation. An active heave compensator mayuse actively controlled winches and hydraulic pistons. Theactive system is controlled by a reference signal. In acombined system the active system is working in parallelwith the passive.5.4.1.5 Examples of input reference signals to an activeheave compensator are:−−−−−−wire tensioncrane top motionwinch or hydraulic piston motionposition of lifted objectvessel motionwave heigth/current velocity5.4.2 Dynamic model for heave compensation, examplecase5.4.2.1 As an example case, a simplified dynamic modelfor a passive heave compensator situated at crane tip isshown in Figure 5-5. The equations of motion at top of wire,η 3P , and at lifted object, η 3, can be taken as;m && ηc3P( M+ c & ηc+ A333P+ k η+ k ( η−η) = F)&&η + c & η + k ( η −η) = F3c3P3ww3P33P33T3Mη 3T( t )( t )wherem ck cc cMA 33k wcη 3Pη 3η 3T= Mass of heave compensator [kg]= Stiffness of heave compensator [N/m]= Linear damping of heave compensator [kg/s]= Mass of lifted object [kg]= Added mass of lifted object [kg]= Wire stiffness = EA/L [N/m]= Linear damping of lifted object [kg/s]= Vertical motion at top of wire (i.e. belowcompensator) [m]= Vertical motion of lifted object [m]= Vertical motion at crane tip (i.e. at top ofcompensator) [m]F3 T( t)= Vertical force at crane tip (i.e. at top ofcompensator) [N]F M( ) = Vertical force at lifted object [N]3tGuidance noteNote that the damping of compensator and lifted object is in generaldue to quadratic viscous damping and the compensator stiffness is ingeneral nonlinear. Linear damping estimates can be obtained byequivalent linearization. Compensator stiffness may be due tocompression of gas volume in pneumatic cylinders.5.4.2.2 For forced motion of top of heave compensatordue to vessel motion, the force on compensator is given by( = η & η c [N]F3 Tt)3Tkc+3Tc5.4.2.3 The vertical force F 3M (t) on the lifted object isrelated to the motion of top of wire η 3P = η a by the transferfunction as given in 5.3.7.2.k cC c5.4.2.4 In a lowering operation the length of the wirechanges with time hence the wire stiffness k w will be afunction of time.η 3Pm c5.4.2.5 For given time series of F 3T (t) and F 3M (t) theequations of motion in 5.4.2.1 can be integrated in time byreplacing the two equations by four first order differentialequations and using a standard integration scheme, i.e 4 thorder Runge-Kutta technique.η 3k wCM+mL5.4.2.6 For harmonic excitation of the top of heavecompensator, we have that;Ft)= η cos( ω ) [N]3T(3Tat5.4.2.7 The ratio between the response of the lifted objectand the excited motion can be expressed through a complextransfer functionηη3T= G() [m/m]3ωwhere the efficiency of the heave compensator is defined asFigure 5-5:compensatorSimplified dynamic model of a passive heaveDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 65e = 1−G(ω)[-]5.4.2.8 Active heave compensation systems generally useinformation from vessel motion reference unit (MRU) tocontrol payout of winch line. The heave motion at crane tipis calculated from the vessel motions in six degrees offreedom and signal sent to compensator unit.5.4.2.9 Motion measurements and control systeminevitably introduces errors and time delays. Hence, atheoretical model of active heave compensation will have totake into account physical imperfections in order to producerealistic results. Such imperfections must be based onoperating data for the actual system.5.4.2.10 Deviations due to imperfect motionmeasurements and tracking control may result in residualmotion of the lifitng cable at suspension point on ship. Thisresidual motion may cause low amplitude oscillations of thelifted object at the resonance frequency.5.4.2.11 An active heave compensator is generally notequally effective in reducing motions at all frequencies. Atsome frequencies it will be more effective than at others.5.5 References/1/ DNV Offshore Standard DNV-OS-H205, “MarineOperations, Lifting Operations” (planned isssued 2009see ref./4/ until release)./2/ Abramowitz, M. and Stegun, I.A. (1965) “Handbook ofMathematical Functions”. Dover Publications./3/ Nielsen, F.G. (2007) “Lecture notes in marineoperations”. Dept. of Marine Hydrodynamics, NTNU./4/ DNV Rules for Planning and Execution of MarineOperations (1996). Pt.2 Ch.5 Lifting – Pt.2 Ch.6 SubSea Operations./5/ Sandvik, P.C. (1987) “Methods for specification ofheave compensator performance”. NTNF ResearchProgramme “Marine Operations”. Marintek Report No.511003.80.01./6/ DNV Recommended Practice DNV-RP-C205“Environmental Conditions and Environmental Loads”,April 2007.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 666 Landing on seabed and retrieval6.1 Introduction6.1.1 Types of structures and foundation designs6.1.1.1 This chapter gives recommendations forevaluating seabed landing and retrieval of any subseastructure with permanent or temporary foundation consistingof plate foundations that may or may not be equipped withskirts. This includes the foundation solution of suctionanchors, also called bucket foundations. Installation orretrieval of driven piles or drilled and grouted piles is nottreated. Structures with piles as permanent pile foundations,however, go through a temporary phase supported on platefoundations or “mudmats”.6.1.2 Geotechnical data6.1.2.1 Geotechnical data required for these evaluationswill normally be covered by the data gathered andestablished for the foundation design. Reference torequirements for soil investigations are the DNVClassification Note 30.4 “Foundations” and NORSOK G-001“Soil investigation”.6.2 Landing on seabed6.2.1.4 In the following sections a problem definition ofthe landing impact is given including a description of thephysical effects and the parameters involved. Then an‘optimal’ solution taking account for the relevant effects isdescribed. Finally, simplified methods are suggested to checkout landing impact of a foundation without skirts on hard soiland required water evacuation for skirted foundations onvery soft soil.6.2.2 Landing impact problem definition6.2.2.1 The following describes a methodology forsimulating the landing of a bucket on the seabed. Themethod considers one degree of freedom only, i.e. verticalmotion.6.2.2.2 This methodology can also be used to solve thevertical impact of structures with several foundations, as longas centre of gravity and centre of reaction for other forcescoincides with the geometrical centre of the foundations. Inthat case masses and forces can be divided equally onto eachof the foundations and the impact can be analysed for onefoundation.6.2.2.3 A mudmat foundation without skirts can beconsidered a special case of the method described for abucket foundation. The model to be analysed is illustratedon Figure 6-1.6.2.1 Introduction6.2.1.1 The aim of evaluating the landing on seabed shallbe to assure that• Foundation failure does not take place during thelanding• Damage does not occur to acceleration sensitiveequipmentAcceptance criteria should thus be available to compare withthe analysed/evaluated responses related to allowabledisplacements or allowable accelerations (retardations).Q wireA hHatch for waterevacuation, area A h.6.2.1.2 Whether or not the foundation solution (i.e. sizeof plate foundations) is equipped with skirts, stronglydepends on the type and characteristics of the subseastructure and the soil characteristics. This again hasinfluence on the challenges for the landing and how this shallbe considered.LD6.2.1.3 Some foundations on hard soils have amplecapacity to carry the submerged weights without skirts,whereby the landing evaluation should focus on the dynamicimpact force and maximum retardations. Other foundationson soft soil may require a significant penetration of skirtsbefore the soil can resist even the static submerged weight ofthe structure. In that case the main design issue is to assuresufficient area of holes for evacuation of entrapped waterwithin the skirt as they penetrate in order for the waterpressure not to exceed the bearing capacity of the soil.δ soilFigure 6-1 Model for impact analysishDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 676.2.2.4 The anchor is lowered down to seabed in a slingfrom an installation vessel being exposed to wave action.6.2.2.5 During lowering the vertical motion of the anchoris given by a constant downwards velocity plus an oscillatoryheave motion caused by the wave induced motion of theinstallation vessel.6.2.2.6 The geometry of the bucket is simplified to avertical cylindrical surface of diameter D and height L. Ahatch for water evacuation is located on the top of theanchor.6.2.2.7 The impact is to be solved by time integration ofthe general equation of motion, which may be performed astime integration assuring energy preservation.All relevant forces acting upon the foundation shall beconsidered in the time integration with their instant timedependent values. Such forces are gravity, buoyancy, slingforces, dynamic water pressure from within the bucket andsoil resistance acting upon the skirts as they penetrate.6.2.3 Physical parameters and effects to be considered6.2.3.1 The following physical parameters are involvedin the simulation modelAssuming bucket consists of only steel volume we get asubmerged weight W given by,ρs− ρW = M ⋅ g ⋅ [N]ρwhereM = structural mass [kg]ρ s = mass density of steel [kg/m 3 ]ρ = mass density of water [kg/m 3 ]g = acceleration of gravity [m/s 2 ]6.2.3.2 The structural mass, M, shall include mass ofstructural elements and equipment on top of the anchor.6.2.3.3 The added mass including mass of waterentrapped within the skirts may for a typical foundationbucket be taken as;⎛ 2 D ⎞A33 = ρ ⋅ Ab⋅ L ⎜1+ ⎟ [kg]⎝ 3 L ⎠whereA 33= added mass for vertical motion [kg]D = diameter of bucket [m]L = length of bucket [m]A b = πD 2 /4 = bucket area [m 2 ]Additional added mass may have to be added to representadded mass caused by structural elements and equipment ontop of the anchor.Guidance NoteBucket height and size of ventilation hole may affect the heave addedmass. See section 4.6.3 for more accurate estimation.6.2.3.4 The total dynamic mass is:M ' = M + A 33[kg]and the initial kinetic energy is:E1= [Nm]22k 0⋅ M ' ⋅v c 0where v c0 is the initial velocity at start of the calculations.6.2.3.5 For vertical motion of an object very close to theseabed the added mass will vary with distance to seabed. Theeffect is an upward force of;20.5(33/ dh)Lwhereη&LhdA η& [N]= velocity of the object [m/s]= distance to the seabed [m]dA 33 / dh = rate of change of added mass vs. h [kg/m]Guidance NoteThis estimation of hydrodynamic force uses the same approach foradded mass as for water exit, ref. 3.2.11.3.6.2.3.6 The hydrodynamic water pressure increases as thebucket approaches the seabed, and the area for waterevacuation decreases. The development of the waterpressure also depends on the interaction with the soil(mobilisation of soil bearing capacity). The increase inbearing capacity with skirt penetration must be accountedfor, and penetration resistance as skirt starts to penetratemust be included in the calculations.6.2.3.7 The sum of the penetration resistance and theforce from water pressure inside the bucket, shall be limitedby the bearing capacity.6.2.3.8 The hydrodynamics force from the water pressurebeneath and within the bucket is calculated using Bernoulli’sequation:pwwhere12= kflow⋅ ρ ⋅v[N/m 2 ]flow2p w = hydrodynamic pressure within the bucket [N/m 2 ]v flow = velocity of water out of the bucket [m/s]ρ = mass density of water [kg/m 3 ]k flow = pressure loss coefficient [-]6.2.3.9 In the case of valve sleeves with high length todiameter ratio, the pressure loss coefficient can bedetermined as;flowDET NORSKE VERITAS2 2[ − ( di/ D)] + f ⋅ n ⋅ Lsleevedik = 1+1/ 21/ [-]

Recommended Practice DNV-RP-H103 Draft December 2008Page 68whered i= diameter of flow valves [m]f = friction coefficient for valve sleeves [-]n= number of flow valvesL sleeve = length of the valve sleeves [m]6.2.3.10 Alternatively, k flow for different outlet geometriesare given by Blevins (1984), ref./3/.k u1k u1Q sdQ soilδ soil6.2.3.11 The velocity of water out of the bucket can beexpressed asqflowvflow= [m/s]Aflowwhereq flow= flow of water out of the bucket [m 3 /s]A flow = A h + πD·h [m 2 ]A h = area of available holes in the bucket [m 2 ]h = gap between the soil and the skirt tip, whichreduces as the bucket approaches theseabed [m]6.2.3.12 Assuming incompressible water, the water flowthat escapes at any time from within and beneath the bucketis taken as;qflowb( v − & δ )= A ⋅[m 3 /s]csoilv c is the vertical velocity of the bucket and;& δ = δ dt [m/s]soild soil/where dδ soil is the change in soil displace-ment due to thechange in bearing pressure taking place during time step dt.6.2.3.13 The total force Q soil transferred to the soil at anytime can be written as;Q = Q + Q [N]soilwskirtwhich is the sum of the force Q w = p w A b resulting from thehydrodynamic water pressure and the force Q skirt transferredfrom the penetrating skirts to the soil.6.2.3.14 The relation between Q soil and δ soil is illustrated inFigure 6-2. As a simplified solution it is suggested thatmobilisation of soil resistance follows a parabolic function.The following relation between Q soil and δ soil can thus beapplied,Qsoil = Q sd⋅ δsoil/ δ for δmobsoil< δmobQsoil= Q sdfor δsoil≥ δmob∆ Q = ⋅ ∆δfor unloadingwhereQ sdδ mobk usoil= the design bearing capacity for loading within areaA p at seabed or at skirt tip level [N]= the vertical soil displacement to mobilise Q sd [m]k = the unloading stiffness [N/m]uδ mobFigure 6-2 Mobilisation of soil bearing capacity6.2.3.15 The characteristic static soil resistance, Q sc is inthe calculations transferred to a ‘design soil resistance’ bythe following relationQ= ⋅γ γ [N]sdQ scwhereγ rrm= rate effect factor to account for increased shearstrength due to rapid loading [-]γ m = soil material coefficient [-]6.2.3.16 The soil bearing capacity can be determinedbased on bearing capacity formulae, or computer programsusing limit equilibrium or finite element methods, asdescribed in DNV Class Note 30.4 Foundations. The skirtpenetration resistance can be calculated as described in 6.2.8.6.2.3.17 The bucket impact problem can be solved by atime integration with an iterative solution at each time step.The calculations should start at a distance above the seabedwhere the build-up of hydrodynamic pressure is moderate,with correspondingly moderate soil displacements.6.2.3.18 The interaction with the string is taken as aprescribed lowering velocity combined with a sinusoidalheave motion given by its amplitude and period. The phaseangle for start of calculations is an input. The clearance withthe seabed at start of calculations is related to a givenminimum clearance and to the heave amplitude and a phaseangle of start as illustrated in Figure 6-3.h h + η ⋅(1+ sin ϕ)[m]start=min Lwhereh start = clearance at start of calculations, t = 0 [m]h min = required minimum clearance for start ofcalculation [m]η L = heave amplitude of the foundation (at the end of thecrane wire, of length L) [m]ϕ = phase angle at t = 0 [-]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 69hi= h −1− ∆z+ ∆δ[m] where ∆ z = v,⋅ ∆t[m]iisoilic iNote that h i has negative values when skirt penetrates3. Calculate area for escape of water;A= A + max( π ⋅ D ⋅ h ,0) [m 2 ]flow, i hiFigure 6-3 Situation for start of analysis4. Calculate corresponding water pressure reaction on thesoil and bucket6.2.3.19 Conservatively the heave motions can be takeninto account by analysing the impact for a constant loweringvelocity, taken as the sum of the crane lowering velocity andthe maximum heave velocity of the foundation. This willrepresent the worst phasing of the heave motions, which isalso relevant to consider, since a beneficial phasing is notlikely possible to control.6.2.3.20 When the impact lasts long, as when skirtspenetrate deeply before the peak impact is reached, it may bebeneficial and relevant to account explicitly for the combinedcrane lowering and heave motions. In that case several phaseangles of the heave motions should be considered.6.2.3.21 For the analysis method described it is assumedthat the heave motions relates to the motion η L of thefoundation close to seabed, which is to be observed andcontrolled during installation. In order to include theinteraction with the crane wire the motion at the vessel endof the wire η a can be set considering an undamped oscillationof the modelled total dynamic mass in the wire.ηL= Mηawheref1=2⎛ ω ⎞⎜ ⎟1 −2⎝ ω0⎠Μ f = dynamic amplification factor [-]ω = angular frequency of the heave motions [rad/s]= angular eigen-frequency [rad/s]ω 0Dynamic response of a lowered object due to wave actions isdescribed in Section 5.Qw,i= sign( v= sign( vc,ic,i) ⋅ k) ⋅ kflowflowv⋅2flow,i⋅ ρ⋅ Ab2Ab⋅ ρ ⎛⎜⎛⋅ ⋅ ⎜v2 ⎜⎝⎝5. Calculate total reaction on soil;Qsoil , iQw,i+ Qskirt,i= [N]c,i∆δ−∆tsoil,i⎞ A⎟⋅⎠ A6. Calculate soil displacements δ andsoil, i∆ δ soil,;ia) For Qsoil i< Qsd,;( Q Q ) 2δ = δ ⋅[m]soil, i mob i s∆δ = δ − δ [m]soil, i soil,i soil,i−1bflowb) For Qsoil≥ Q orsd( Qsoil− Qsd) / Qsd≥ −0.0001;• When h i > 0 (i.e. skirts are not yet penetrated);∆δ = −h + ∆z+ h [m]hisoil,i=Aflow,ii−1π ⋅ D− Ahii[m]⎞⎟⎟⎠2[ N]6.2.4 Iterative analysis procedure6.2.4.1 For each time step in the suggested time domainanalysis the following iteration procedure is suggested inorder to account for the non-linear behaviour of the soilresistance.Aflow,i⎛=⎜v⎝c,i∆δ−∆tsoil,i⎞⎟ ⋅ Ab⋅⎠kflow⋅ A ⋅ ρ2⋅Qbsd[m 2 ]Note that iteration on ∆δ soil, i is required to solve forthe unknown A flow,i .;δsoil , iδsoil,i 1+ ∆δsoil,i=−[m]1. Assume an incremental soil displacement ∆ δsoil[m]2. Calculate the clearance h i between the skirt tip and theseabed as;• When h ≤ 0 (i.e. skirts are penetrating);∆δsoil,ii⎛= ⎜v⎜⎝c,iA−Aflow,ib⋅2⋅( Q − Q )ksdflowbskirt,i⋅ A ⋅ ρ⎞⎟ ⋅ ∆t⎟⎠[m]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 70c) For unloading:( Qsoil,i− Qsoil,i 1) ku∆δ =[m]soil, i−7. Repeat steps 1. – 6. until convergencewater cushion underneath the mud mat and the beneficialeffect of the work performed by the crane wire.6.2.5.2 Applied boundary conditions for the problem arethen a structure with a given dynamic mass and submergedweight, a velocity at the impact with the seabed and a nonlinearmobilisation of the bearing capacity. A simplifiedequation to solve landing impact problem then becomes;12M ' ⋅v2imp+ W ⋅δsoil=δ soil∫0Qsoil( δ ) dδ[Nm]8. Calculate total change in crane wire length;δ⎡ 1⎤= ∑ ∆zi− ⎢vc⋅t+ d0⋅ ⋅(sin(ωt+ ϕ)− sin ) ⎥⎢⎣Mf⎥⎦wire, iϕwhere v c is the crane lowering velocity[m]6.2.5.3 Assuming the non-linear soil resistance beingdescribed as on Figure 6-2, the right side of equation 6.2.5.2becomes;23Q sdδ 3soil⋅ [Nm] for δsoil≤ δ [m]mobδmob9. Calculate new wire force;Q Q + k ⋅δ 0 [N]wire , i=wire ,0 wire wire , i≥where k wire is the crane wire stiffness as defined in Section 5.10. Calculate loss in kinetic energy;∆E⎛A − Ab hi = ⎜Qw,iQskirt,iQsling,iW ⎟⋅ + + − ⋅ ∆ziA[Nm]b⎝It is assumed that the retardation from dynamic waterpressure within the bucket does not act on the evacuationholes in the top plate, A h .Ek , iEk, i 1− ∆Ek, i=−[Nm]11. Calculate new velocity;vc, i 1= 2 ⋅ Ek,im [m/s]+ d6.2.4.2 As the skirts penetrate, the penetration resistanceand the global soil resistance should be updated to accountfor the increased resistance with increased penetration.6.2.4.3 It should be noticed that a requirement for usingthe above method is that the crane lowering velocity is keptconstant until the foundation comes to rest and is notincreased when skirts start to penetrate.6.2.5 Simplified method for foundations without skirts6.2.5.1 In a simplified approach to check the foundationcapacity for the seabed landing situation for a foundationwithout skirts one may neglect the beneficial effects of⎞⎠andQ sdδmob⋅ ( δsoil− ) [Nm] for δsoil> δ [m]mob36.2.5.4 Loads coefficients should be included in thedesign dynamic mass and submerged weight, and materialcoefficients in the soil resistance as relevant. Normally theacceptance criteria would be;δsoil≤ δ mob[m]in which case the requirements to the landing impact velocitybecomes;vimp( 4 Q − 2W )3 sd ⋅δmob≤ [m/s]M'6.2.5.5 Other criteria may however be used based on anevaluation of consequences.6.2.6 Simplified method for foundations with skirts onsoft soil6.2.6.1 For skirted foundations on soft soil where it isrequired that the skirts penetrate before the soil can resist thedynamic landing impact (or even the submerged weight ofthe installed subsea structure with foundation), it is necessarythat sufficient areas for escape of water are provided so thatthe hydrodynamic pressure never exceeds the bearingcapacity.6.2.6.2 A conservative design can be performed byneglecting the beneficial effects on the impact fromflexibility of crane wire and soil. The boundary conditionsfor the problem then becomes the impact velocity as theskirts start to penetrate, the gross foundation area, the areafor escape of water, and the soil bearing capacity for aDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 71surface loading on the gross foundation area. The relationbetween impact velocity and required area for escape ofwater is then given by the following equation;Q12sd22≥ pw= kflow⋅ ρ ⋅vimp⋅(Ab/ Ah) [N/m 2 ]bA6.2.6.3 The requirements to area for escape of water for adesired landing velocity becomes;Ah≥kflow⋅ ρ ⋅v2⋅Q2impsd⋅ A3b[m 2 ]or if the area for escape of water is set, requirements tolanding velocities becomes;vimp≤2 ⋅ Qkflowsd⋅ A⋅ ρ ⋅2h3Ab[m/s]6.2.7 Application of safety factors6.2.7.1 Application of safety factors should be evaluatedin relation to the consequences of exceeding selected limits.Load coefficients may be applied to masses andcorresponding submerged weights, and material coefficientsshould be applied to the soil resistance. When consequencesare considered serious a load coefficient γ f =1.3 and amaterial coefficient γ m =1.25 should be applied.6.2.8 Calculation of skirt penetration resistance6.2.8.1 Calculation of skirt penetration resistance isrequired as input to seabed landing analyses, but is alsorequired in order to evaluate the need for suction aidedpenetration and in order to determine the suction required.6.2.8.2 The skirt penetration resistance shall becalculated as the sum of the vertical shear resistance, oftennoted as skin friction, along both sides of the skirts and theresistance against the skirt tip;d6.2.8.3 Q = A ⋅ ∫ f ( z)dz + A ⋅ q ( d)[N]whereQ skirtdA sskirts= skirt penetration resistance [N]= depth of penetration [m]0= friction area per meter depth [m 2 /m]A t = skirt tip area [m 2 ]f(z) = skin friction at depth z [N/m 2 ]q t (d) = tip resistance at the depth of penetration [N/m 2 ]tt6.2.8.4 In sand and over-consolidated clays the skinfriction and tip resistances may most reliably be predicted bycorrelations to cone penetration resistance as;f ( z)= k q ( z)[N]f⋅q ( z)= k ⋅ q ( z)[N]twheretccq c (z) = cone penetration resistance as measured in a conepenetration test (CPT) [N]k f = skin friction correlation coefficient [-]k t = tip resistance correlation coefficients [-]6.2.8.5 The most probable and highest expected valuesfor the skin friction correlation coefficient k f and tipresistance correlation coefficient k t for clay and sand (NorthSea condition) are given in Table 6-1.6.2.8.6 Alternatively in less over consolidated clays theskin friction may be taken equal to the remoulded shearstrength. The uncertainties should be accounted for bydefining a range for the remoulded shear strength. The tipresistance may in clays be taken as 7.5 times the intactundrained shear strength of the clay.CorrelationcoefficientMostprobableClayHighestexpectedMostprobableSandHighestexpectedSkinfriction, k f0.03 0.05 0.001 0.003Tip resistance,k t0.4 0.6 0.3 0.6Table 6-1: Correlation coefficients for skin friction andtip resistance in sand and over-consolidated clay.6.3 Installation by suction6.3.1.1 When suction is required to install skirtedfoundations it is important that the range for expectednecessary suction is calculated in order to provide adequateequipment and to design the skirted foundation to resist thesuction.6.3.1.2 The skirt penetration resistance may be calculatedas prescribed in 6.2.8 and may be applied in the estimation ofrequired suction in order to provide the necessary penetratingforce (in excess of the submerged weight).6.3.1.3 The skirts as well as the mud mat shall bedesigned with respect to buckling for the upper estimate ofthe required suction.6.3.1.4 As part of the foundation design it shall bechecked that when applying suction, a soil plug failure is notachieved. Such failure will take place when the total skinfriction on the outside of the skirts exceeds the reversedbearing capacity at the skirt tip level. This may be the caseDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 72for suction anchors with high length to diameter ratio, alsooften called ‘suction piles’.6.3.1.5 The actual suction applied during installationshould be continuously monitored and logged as adocumentation of the installation performance.6.4 Levelling by application of suction oroverpressure6.4.1.1 A subsea structure supported by three or more(typically four) individual skirted foundations may belevelled by applying pressure into the void between the mudmat and the soil at low corners, or by applying suction athigh corners.6.4.1.2 The procedures should be well planned, and thenecessary suction and or overpressure to accomplish thelevelling should be calculated.6.4.1.3 When levelling a subsea structure with fourfoundations application of suction or overpressure should beperformed at two neighbouring foundations at a time to avoidrestraining of the structure.6.4.1.4 The righting moment to achieve the levellingcomes from differential pressures within the skirt foundation.The resistance to overcome is;• The vertical soil skin friction and tip resistance dueto penetration or rising of skirts.• The resistance to rotate the skirts within the soil• The structural weight that contributes to increasedoverpressure or reduction in suction6.4.1.5 The vertical soil skin friction and tip resistancecan be calculated, as described in 6.2.8. Skin friction may betaken equal in both directions. In clay a suction contributionbelow the tip should be considered when the skirts aremoved upwards.6.4.1.6 The resistance to rotate a skirt foundation withinthe soil will be the least of a ‘local’ mode where soilresistance is mobilised on each side of the skirt walls and a‘global’ mode where the skirt foundation is rotated as a pilewith the soil plug following the motions of the pile. Bothmodes can be studied using a simple pile model where at anylevel above skirt tip the maximum horizontal resistanceequals the integrated resistance around the skirt periphery ofpassive and active pressures and horizontal shear resistance.6.4.1.7 For the local mode resistance to both sides of theskirt wall should be included, whereas for the global moderesistance only to the outside should be included. For theglobal mode a horizontal resistance at the skirt tip reflectingshear off of the soil plug at skirt tip level should be included.The resistance can be implemented as p/y-curves. Theboundary condition for the analysis should be appliedmoment with no horizontal force at the ‘pile top’.6.4.1.8 Alternatively the resistance to rotate the skirtswithin the soil could be analysed with finite elementanalyses.6.4.1.9 The skirt foundation including the mud matshould be checked structurally for the maximum foreseensuction or overpressure. Likewise the possible soil plugfailure mode of a reversed bearing failure for high suction ora downward bearing failure for high overpressure should bechecked.6.4.1.10 For foundations with long skirts requiring suctionto penetrate, levelling should normally be performedfollowing the stage of self penetration, with a subsequentfrequent adjustment of the level during the furtherpenetration.6.4.1.11 The levelling process should be carefullymonitored and logged as a documentation of the installationperformance.6.5 Retrieval of foundations6.5.1 Retrieval of skirted foundations6.5.1.1 Retrieval of skirted foundation may be achievedby a combination of lifting and application of pressureunderneath the mud mat. The total force to be overcome isthe sum of submerged weights and soil resistance.6.5.1.2 Skirted foundations intended to be removedshould be equipped with a filter mat attached to theunderside of the mud mat in order to prevent adhesion to thesoil and to assure a distribution of applied pressure on thetotal area between the mud mat and the soil. The soilresistance will then only be vertical resistance towards theskirts.6.5.1.3 The initial outside and inside skin friction may becalculated using methods developed for calculation of axialcapacity of driven piles. In clay also a downwards tipresistance should be included. After the motion is initiated,the soil resistance may drop towards that used for calculationof skirt penetration.6.5.2 Retrieval of non-skirted foundations6.5.2.1 When retrieving non-skirted foundations thesuction from the soil will have to be considered. Even onsandy soils suction will occur for a rapid lifting. Dependingon the size of the area and the permeability of the sand, someDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 73seconds or minutes may be required to release the suction.This should be considered when establishing liftingprocedures.6.5.2.2 When lifting non-skirted foundations off clayeyseabed, the suction will last so long that it will normally beunrealistic to rely on suction release. In addition to liftingthe submerged weight of the structure, one will then have toovercome a reversed bearing failure in the soil. Themagnitude of this additional soil resistance will be at leastequal to the submerged weight of the structure.6.5.2.3 If the structure has been installed with a high setdown velocity, the resistance to overcome may be close tothe dynamic impact load onto the soil during installation.This impact load may e.g. be evaluated by the methodsuggested in 6.2.5. If e.g. the impact load is twice thesubmerged weight of the structure, the required lifting loadto free the structure will be three times the submergedweight. This should be taken into account when choosingand designing lifting equipment. The required lifting forcemay be reduced by lifting at one end of the structure or byuse jetting in combination with the lifting.6.6 References/1/ DNV Classification Note CN-30.4 (1992)“Foundations”/2/ NORSOK G-001 (2004) “Marine soil investigation”/3/ Blevins, R.D. (1984) “Applied Fluid DynamicsHandbook”. Krieger publishing Company.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 747 Towing operations7.1 Introduction7.1.1 General7.1.1.1 Towing is one of the most common marineoperations. Most offshore development projects involvetowing in one or several of its phases. Examples of tows are:−−−−−rig movetransport to site and positioning of large floatingstructuretransport of objects on bargewet tow of subsea moduleswet tow of long slender elements7.1.1.2 Classical surface tow of large volume structuresis covered in section 7.2. Subsurface (or wet) tow of smallvolume structures or long slender structures is covered insection 7.3.7.1.2 Environmental restrictions7.1.2.4 For operations with T R >72 hours, the operationnormally needs to be defined as an unrestricted operation.Environmental criteria for these operations shall be based onextreme value statistics (see DNV-OS-H101 ref./1/).7.2 Surface tows of large floating structures7.2.1 System definition7.2.1.1 Dynamic analysis of a tow requires informationon geometry and mass properties of towed object and tug,towline data (weight, diameter, stiffness, bridle etc) andoperational data including information on environmentalconditions (wave, wind and current).7.2.1.2 Figure 7-1 shows local and global co-ordinatesystems and definition of angles for orientation of tug, towedobject and towline to be used for static and dynamic analysisof towline in waves propagating in direction β.7.2.1.3 The wave induced response of tug and towedobject (and hence the dynamic tension in the towline) is afunction of wave direction relative to the objects.7.1.2.1 A tow operation may take several days due to thelow transit speed, and the operation may either be classifiedas weather restricted or as unrestricted. Reference is given toDNV-OS-H101, ref./1/. A short description is however givenin the following paragraphs.7.1.2.2 For operation reference period, T R , less than 72hours a weather window can be established (weatherrestricted operation). Start of the operation is conditional toan acceptable weather forecast.Guidance NoteThe operation reference period should include both the plannedoperation period and an estimated contingency time;T R = T POP + T CwhereT R = Operation reference periodT POP = Planned operation period= Estimated contingency timeT CFigure 7-1: Definition of angles for orientation of tug,towed object and towline relative to global axes (X G ,Y G ).7.1.2.3 For T R > 72 hours the operation can be defined asweather restricted provided that:−−−Continuous surveillance of actual and forecastedweather is specified in the operation proceduresSafe conditions for the towed object is established alongthe route (e.g. set down at seabed)The system satisfies ALS requirements for unrestrictedweather conditions7.2.2 Data for modelling and analysis of tows7.2.2.1 Input data for analysis of surface tows areclassified as tug and tow data, towline data and operationaldata as given below.Tug and towed object data:tugHjtowHj( ω,θ )( ω,θ )= Motion transfer function in six degrees offreedom (j=1,6) for tug [-]= Motion transfer function in six degrees offreedom (j=1,6) for towed object [-]tugr = Local position of towline end on tug [m]0DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 75towr = Local position of towline end on tow [m]0BL bT b7.2.2.2Towline data:D= Breadth of towed object [m]= Length of towed object [m]= Draft of towed object [m]= Hydrodynamic diameter of towline [m]C D = Hydrodynamic drag coefficient [-]C M = Hydrodynamic inertia coefficient [-]A = Nominal area of towline (area of steel) [m 2 ]S = Area of circumscribed circle = πD 2 /4 [m 2 ]c F = A/S = Fill factor [-]E = Modulus of elasticity of towline [N/m 2 ]ρ s = Density of steel [kg/m 3 ]mm awW= Mass per unit length of towline [kg/m]= Added mass per unit length of towline [kg/m]= Submerged weight per unit length of towline [N/m]= Total submerged weight of towline [N]T 0Lα= Towline tension [N]= Length of towline [m]= Towline direction [deg]H s = Significant wave height [m ]T pS(ω,θ)β= Spectrum peak period [s]= Wave spectrum= Mean wave direction [deg]7.2.3 Static towline configuration7.2.3.1 For a towing cable where the towline tension ismuch larger than the weight of the cable, T 0 /W > >1, thehorizontal x(s) and vertical z(x) coordinates along the towlinecan be approximated by the following parametric equations⎛ T ⎞ 1 ⎛ w ⎞x( s)⎜ + ⎟ sEA 6⎜T⎟⎝ ⎠ ⎝ 0 ⎠=031 s −[m]21 ws ⎛ T ⎞= − + ⎜ +0z( s)zm1 ⎟2 T ⎝ EA[m]⎠02where s is the coordinate along the towline (-L/2 < s < L/2)and z m is the sag of the towline,L ⎛ wL ⎞ ⎛ T ⎞⎜⎟ ⎜ +0zm= 1 ⎟ [m]8 ⎝ T0⎠ ⎝ EA ⎠7.2.3.2 The approximate fomulas in 7.2.3.1 give goodestimates even when T 0 is comparable to the weight W of thetowline. Usually T 0

Recommended Practice DNV-RP-H103 Draft December 2008Page 767.2.4 Towline stiffness7.2.4.1 The towline stiffness can be split into twocomponents, one due to elastic elongation of the line and onedue to the change of geometry of the towline catenary.7.2.4.2 The stiffness due to elastic elongation of thetowline is given by;EAk E= [N/m]LwhereA = Nominal cross-sectional area of towline [m 2 ]E = Modulus of elasticity of towline [N/m 2 ]L= length of towline [m]7.2.4.3 The stiffness due to change of geometry is givenby;312T0= [N/m]( wL)Lk G 2whereT 0wL= towline tension [N]= submerged weight per unit length of towline [N/m]= length of towline [m]7.2.4.4 The total stiffness k is given by the formula;1 1 1= + [m/N]k k Ek GorkGkEk =k + kGEk=1 +kEEkG[N/m]For very high towline tension, k G >> k E , and the totalstiffness can be approximated by the elastic stiffness k ≈ k E .7.2.4.5 It should be noted that the force – displacementratio given by the combined stiffness above is only valid forslow motion of the end points of the towline. For typicaltowlines this means motions with periods above 30 sec. Forwave frequency motions, dynamic effects due to inertia anddamping will be important.7.2.5 Drag lockingWhen towing in waves the resulting oscillatory verticalmotion of the towline may be partly restricted due to dragforces on the line, as if the towline was restricted to movewithin a narrow bent pipe. Hence, the geometric elasticity is“locked”. This phenomenon is called “drag-locking”. Draglockingcauses the apparent stiffness of the line to increaseand the dynamic force is approximately the force which isobtained considering the elastic stiffness only.7.2.6 Mean towing force7.2.6.1 At zero velocity and in the absence of wind,waves and current, the tug will have maximum towing forceequal to the continuous bollard pull. When the tug has aforward velocity some of the thrust is used to overcome thestill water resistance of the tug. This resistance is partly dueto viscous skin friction drag, pressure form drag and wavemaking drag. The available towing force decreases withforward velocity. Also, if the tug is heading into waves, windor current, the net available towing force is reduced due toincreased forces on the tug itself.7.2.6.2 The towed object is in addition to wind forces andcalm water resistance subject to wave drift forces F WD , whichmay give an important contribution to the towing resistance.Wave drift force on a floating structure can be calculated bya wave diffraction program using a panel discretization of thewetted surface.7.2.6.3 The effect of waves can be taken into account bymultiplying the continuous bollard pull by an efficiencyfactor (see DNV-OS-H202, ref./2/) depending on length oftug and significant wave height.7.2.6.4 The wave drift force at zero towing speed can beapproximated by the following simplified expression;F182 2WD = ρwg R B ⋅ H [N]swhere typical reflection coefficients, R, are;Table 7-1: Typical reflection coefficients.Square faceCondeep baseVertical cyllinderBarge with raked bowBarge with spoon bowShip bowR=1.00R=0.97R=0.88R=0.67R=0.55R=0.45andρ w = density of sea water, typically 1025 [kg/m 3 ]g = acceleration of gravity, 9.81 [m/s 2 ]H sBGuidance Note= the significant wave height [m]= breadth of towed object [m]This simplified expression for wave drift force will in most cases giveconservative results. Calculation by a wave diffraction program isrecommended if more accurate results are needed.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 777.2.6.5 The wave drift force increases linearly with thetowing speed according to the formulaFWD( U)= F (0) + U ⋅ B [N]WD11where B 11 is the wave drift damping. For more informationon wave drift damping reference is made to DNV-RP-C205.ref./4/.7.2.7 Low frequency motions7.2.7.1 The tug and the towed object may experience lowfrequency (slow drift) motions due to slowly varying waveand wind forces. For the low frequency motions the towlinewill behave as a spring.7.2.7.2 The eigenperiod of the slow drift motion is givenbyT0wheretug tugMs+ A11= 2π [s]tug tug⎛ M + ⎞sA11k ⎜⎟1 +tow tow⎝ Ms+ A11⎠k = towline stiffness defined in 7.2.4.4 [kg s -2 ]MtowstowA 11= structural mass of towed object [kg]= added mass of towed object in towline direction [kg]tugMs= structural mass of tug [kg]tugA 11= added mass of tug in direction of towline [kg]7.2.7.3 In most cases, for surface tows, the mass andadded mass of the towed object is much larger than the massand added mass of the tug so that the eigenperiod can beapproximated byTtug tugMs+ A11= π [s]k02Guidance noteThe formulas for the eigenperiod of slow drift motion assume that themass of the towline is much smaller than the mass of the tug andtowed object.Guidance noteGuidelines for estimation of the actual slow-drift motion may be foundin e.g. DNV-RP-C205, ref./4/ and DNV-RP-F205, ref./5/.7.2.8 Short towlines / propeller racetowed structure can be estimated from the local flow velocitytaking into account the increased velocity in the propellerrace and drag force coefficients for normal flow.7.2.8.3 For deeply submerged thrusters the propeller racecan be approximated by an axi-symmetric turbulent jet with aradial velocity distribution2 −[ 1 + 0.4142( r / r ( ) ] 2U ( r;x)= Um( x)x [m/s]where−[ 0.89 + 0.149x] 10/0 .5)U m( x)= UD [m/s]andr ( x)= 0.39D0. 0875x[m]0 .5+r is the radial distance from the centre of the jet at x = -4.46Dwhere D is the diameter of the propeller disk and U 0 is theflow velocity through the propeller disk, considered to beuniform. See Figure 7-4. Reference is made to /11/ and /15/for details.x = - 4.46DrPropeller planexr = r 0.5 (x)U m /2Figure 7-4 Propeller race modelled as an axisymmetricjet7.2.8.4 For towlines longer than 30 m, the effect of thepropeller race is taken into account by reducing the availablebollard pull by an interaction efficiency factor (ref. DNV-OS-H202);α−[ + 0.015A / ] ηint= 1expL [-]whereα int = interaction efficiency factorA exp = projected cross sectional area of towed object [m 2 ]L = length of towline in metres [m]η = 2.1 for typical barge shapesU m7.2.8.1 When short towlines are applied the tug propellermay induce flow velocities at the towed structure whichincreases the towing resistance significantly.7.2.8.2 When the towed structure is small compared tothe propeller race the force on each structural member of theDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 787.2.8.5 When the towed object is large compared to thedimensions of the propeller on the tug, a large part of thepropeller race may be reversed by the towed object, hencereducing the net forward thrust on the system. Actually, thenet forward thrust can become negative by this effect, so thatthe system of tug and tow move backward. Detailedcalculation of this effect can be done by use of CFD.7.2.9 Force distribution in a towing bridle7.2.9.1 When the towed structure is rotated an angle α,the forces in each of the bridle lines will be different. SeeFigure 7-4. Assuming each bridle line forms an angle β withthe towing line, and the towing force is T 0 , the distribution offorces in each bridle line for small rotation angles, is givenby;TTTT0sin( β + α γ )=sin 2β1 +0sin( β − α γ )=sin 2β2 −whereT 0T 1T 2LRαβγ= towing force [N][N/N][N/N]= force in port bridle [N] (for rotation of towed objecttowards port. See figure 7-5)= force in starboard bridle [N] (for rotation of towedobject towards port. See figure 7-5)= length of towline, measured from bridle [m]= distance from centre of gravity of towed structure toend of bridle lines [m]= angle of rotation of towed structure [rad]= angle between each of the bridle lines and thevessel centreline [rad]R= α [rad]Lα2βRFigure 7-5 Layout of towline and bridle linesγLT 07.2.9.2 The force in starboard bridle line becomes zerowhenLβα = [rad]L + R7.2.9.3 For rotation angles greater than this value, onebridle line goes slack and only the other bridle line will takeload.7.2.9.4 The moment of the towing force around therotation centre of the towed structure is given as;RM G= T0R(1+ )α [Nm]Land the rotational stiffness due to the towing force is givenby;RC66= T0R(1+ ) [Nm/rad]LHence, the bridle contributes with a substantial increase inthe rotational stiffness, improving the directional stability ofthe tow.7.2.10 Shallow water effects7.2.10.1 The towed object will be subject to a set downeffect (sinkage) because of the increased velocity past theobject causing the pressure on the wetted surface to bedecreased. This effect may be greatly increased in shallow,restricted water, such as a canal- or trench-type channel. Thetrim of the object will also be modified. This combined effectof sinkage and trim in shallow water is called the squateffect.A semi-empirical relation for squat of a shipliketowed object iszTmaxwhere2CbFh= 2.4[m/m]L / B 1−F2hz max = squat (combined sinkage and trim) at bow orstern [m]L = length of object [m]B = beam of object at the maximum area [m]T = draught of object [m]C b = ∇ / LBT [-] , where ∇ is the displaced water volume.F h = the depth Froude number: F h= V / gh [-]V = U-U c is the relative speed [m/s]g = gravitational acceleration [m/s 2 ]h = water depth [m]U = towing speed [m/s]U c = current velocity (in e.g. a river) being positive in thedirection of the tow route [m/s]DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 797.2.11 Dynamics of towlines7.2.11.1 Analysis of towline dynamics involvesindependent motion analysis of tug and towed object in agiven sea state and the resulting towline response. A winchcan be used on the tug to reduce tension in the towline. Theresponse of the winch and the towline is strongly non-linearand coupled (ref. 7.2.13).7.2.11.2 Analysis of towline dynamics can be done in thefrequency domain or time domain. A frequency domainmethod is computational efficient, but requires a linearizedmodel of the system. A time-domain method can account fornonlinearities in the system, nonlinear wave inducedresponse as well as nonlinear towline dynamics.7.2.11.3 Wave induced response of towed object and tug iswell described by linear equations. Neither tug nor towedobject is significantly influenced by the towline with respectto first order wave induced response. A frequency domainanalysis can be used to obtain relative motion between tugand tow.7.2.11.4 The following frequency domain solution methodcan be applied:• First the static towline configuration is calculated. Staticconfiguration is the basis for calculation of dynamictowline dynamics. Maximum sag depth is obtained fromstatic analysis.• The motion transfer functions for the line attachmentpoints are calculated on tug and towed objectrespectively and the transfer function for the relativemotion of the towline attachment points can beestablished. If the towed object is much larger than thetug, the relative motion will be dominated by the tugresponse, and the towed object transfer functions may beomitted.7.2.11.5 The transfer function for relative motion ηbetween tug and towed object in the towline secant directionis obtained by a linear transformation. See Figure 7-1.HTU TU TOη ( secsecω,β ) = H ( ω,β ) − H ( ω,β ) [m/m]TOfunctions. The transfer function for motion in the secant (towline)direction is the component of the motion vector in this direction.7.2.11.7 From the response spectrum an extremerepresentation of the relative motion can be generated. Themost probable extreme value for the relative motion in a timeinterval T, usually taken as 3 hours, is;η ≈ 2ln( T / T ) [m]maxwhereσ ησ η = M0T z = 2πM n =∞∫0MMz= standard deviation of the relative motion [m]02= zero up-crossing period [s]nω S(ω)dω= spectral moments [m 2 /s n ]7.2.11.8 An estimate of the extreme towline tension whentowing in waves can be obtained by assuming drag locking(7.2.5) so that the effective stiffness is the elastic stiffness,Tmax= T + η k [N]0maxwhere T 0 is the mean towing force and k is the towlinestiffness as given in 7.2.4.4. Hence, the extreme towlinetension decreases with increasing towline length.7.2.12 Nonlinear time domain analysis7.2.12.1 An alternative approach to the frequency domainmethod described above is to model the towline in a nonlinearFEM analysis program and prescribe forced motionsof the towline end points on tug and towed objectrespectively.7.2.12.2 Time histories for the motions of the towline endpoints x p (t), y p (t), z p (t) are obtained by proper transformationof the rigid body motion transfer function for each of the tugand towed object and combining with a wave spectrum. Forexample, the time history of the motion in the x-direction ofend point p is given by;px ( t)= ∑ A H ( ω ) cos( ω t + ε ) [m]pwherekkxkkk7.2.11.6 The relative towline motion transfer function iscombined with the wave spectrum characterizing the actualsea state. The response spectrum for relative motion in thesecant direction of the towline is obtained from;S ( ω)= H ( ω,β ) S(ω)[m 2 s]ηηwhere S(ω) is the wave spectrum.Guidance note2Assuming small wave induced rotations (roll, pitch and yaw) of tugand towed object, the motion transfer function for end point of towlineis given by a linear combination of the rigid body motion transferADET NORSKE VERITASk= 2 S(ω ) ∆ω[m]kkand H x p (ω) is the transfer function for motion in x-directionof end point p. Examples of simulated motions of towlineend points at tug and towed object for head waves and nocurrent are shown in Figures 7-6 and 7-7. Resulting towlinetension at tug and towed object are shown in Figure 7-8.Minor differences between the two curves at peaks are due todynamic effects in towline.

Recommended Practice DNV-RP-H103 Draft December 2008Page 8027.2.13 Rendering winchAxialX-disptension[m][N]10-1-27.2.13.1 An automatic rendering winch (Figure 7-9) canbe designed to reduce extreme towline tension. The winch isdesigned to start rendering when the towline tension exceedsa specified limit. A detailed analysis of a coupled towlinewinchsystem during forced excitation was presented in Ref./13/.-3-4-5200 210 220 230 240 250 260 270 280 290 300Time [s]Figure 7-6: Example of simulated horizontal motion oftowed object (upper curve) and tug (lower curve) in agiven sea state.15Figure 7-9: Coupled towline – winch model (from Ref./13/).Axial tension [N]Z-disp [m]1050-5-10-15-20200 210 220 230 240 250 260 270 280 290 300Time Time [s]Figure 7-7 Example of simulated vertical motion of towedobject (lower curve) and tug (upper curve) in a given seastate.Axial Tension7.2.13.2 A simplified towline model is based on theassumption that the shape of the dynamic motion is equal tothe change in the static towline geometry. Mass forces arenegelected. This leads to the following equation for the linemotion;c* u&u&+ k * u = kwhereuEx[N]= displacement of the towline [m]c* = generalised line damping [kg/m]k* = k E + k G = generalised towline stiffness [N/m]k E = elastic stiffness [N/m] (7.2.4.2)k G = geometric stiffness [N/m] (7.2.4.3)x= tangential motion exitation at end of towline [m]1800000Axial tension [N]Axial Tension [N]16000001400000120000010000008000006000004000002000000200 210 220 230 240 250 260 270 280 290 300Time [s]Figure 7-8: Example of simulated axial towline tension atendpoints. Mean tension is T 0 = 1.0 MN (i.e. ≈100 tonnesbollard pull).7.2.13.3 The rendering winch is modelled by an equivalentmass, damping and stiffness with the equation of motion;m' & x+ c'x&+ k'x = T0 T ( t)[N]w w w+when the winch is rendering, and whereT 0T d (t)x w= static tension [N]= dynamic tension [N]= winch pay-out coordinate [m]m’ = equivalent winch mass (= I/r 2 where I is thewinch mass moment of inertia and r is theradius of the winch) [kg]c’ = equivalent velocity dependent winch dampingcoefficient (= c w /r 2 where c w is the winchdamping coefficient) [kg/s]k’ = equivalent position dependent winch stiffnesscoefficient (= k w /r 2 where k w is the winchstiffness coefficient) [N/m]dDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 81When the winch is stoppedx& = 0 [m/s]w7.3.1.3 Surface or sub-surface tow of long slenderelements are established methods for transportation to field.Acceptably low risk for damage during the transportationphase must be ensured.7.2.13.4 The winch starts rendering when the total tensionT 0 + T d (t) exceeds the winch rendering limit F.7.2.13.5 Assuming the towline leaves the winchhorizontally, the tangential motion of the towline end isgiven by;x = η − x w[m]where η is the relative motion between tug and tow. Thetowline dynamic tension can be expressed as;Td= k ( x − u) [N]EFigure 7-10. The configuration of a submerged tow controlledby a leading tug and a trailing tug.7.2.13.6 Combining the equations in 7.2.13.2 and 7.2.13.3yields the equations of motion for the coupled towline-winchmodel& + &[N]m ' x c'x + ( k'+ k)x =wheref ( t)f ( t)= kEu(t)+ m'& η( t)+ c'& η(t)+ k'η(t)− T [N]This equation is coupled with the towline response model(FEM) giving the towline response u as a function of the endpoint displacement x.7.3 Submerged tow of 3D objects and long slenderelements7.3.1 General7.3.1.1 Three different tow configurations will becovered in this chapter;1) Submerged tow of objects attached to Vessel2) Submerged tow of objects attached to Towed Buoy3) Surface or sub-surface tow of long slender elements, e.g.pipe bundles7.3.1.2 Submerged tow of objects is an alternative tooffshore lift installation. Reasons for selecting suchinstallation method may be;• to utilise installation vessels with limited deck space orinsufficient crane capacity• to increase operational up-time by avoiding offshoreoperations with low limiting criteria such as lifting offbarges and/or lowering through the splash zone07.3.1.4 The following steps are involved in the towoperation:• Inshore transfer to towing configuration• Tow to offshore installation site• Offshore transfer to installation configurationThis chapter covers the tow to offshore installation site.7.3.2 Critical parameters7.3.2.1 Examples of critical parameters to be consideredin modelling and analysis of a submerged tow could be:• vessel motion characteristics• wire properties• towing speed• routing of tow operation (limited space for manoeuvring,varying current condition)• directional stability of towed object as function ofheading• forces in hang-off wire, slings and towing bridle• clearance between object and tow vessel• clearance between rigging and vessel• VIV of pipe bundles and slender structures (e.g. spools,structure/piping)• Lift effects on sub-surface towed structures• Wave loads on surface towed bundles (extreme andfatigue loading)In order to calculate/simulate these effects a time domainanalysis is necessary.7.3.3 Objects attached to Vessel7.3.3.1 Objects attached to vessel in e.g. a hang-off frame(Figure 7-11) are mainly influenced by forward speed andDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 82the vertical wave frequency motion (heave, roll and pitch) ofthe installation vessel.Figure 7-12(not to scale)Submerged object attached to towed buoy7.3.3.2 Initially one should determine whether longcrested or short crested sea is conservative for the analysis inquestion. For head sea short crested sea will give increasedroll motion compared to long crested sea, while long crestedsea will give increased pitch motion compared to shortcrested sea (ref. DNV-OS-H102).7.3.3.3 From simulations it is seen that coupling effectsmay be important even for small objects. The object tends todampen the vessel motions with reduced force in hoist wireas a result. An uncoupled analysis will therefore beconservative.7.3.3.4 With increased size of object (mass, added massetc.) the discrepancies can be large and a coupled analysiswill thus describe the vessel behaviour more correctly.7.3.3.5 If the object is located in e.g. a hang-off frame onthe side of the vessel the weight of the object will make thevessel heel. This heeling can be counteracted by including arighting moment in the analyses. In effect this models theballasting that will be performed to keep the vessel on evenkeel.7.3.3.6 If the object is hanging in a rigging arrangementthrough the moon pool of the vessel, particular attentionshould be given to check clearance between rigging andmoon pool edges.7.3.4 Objects attached to Towed Buoy7.3.4.1 For objects attached to Towed Buoy (Figure 7-12) the dynamic forces on object and rigging is not affectedby wave induced vertical vessel motions.7.3.4.2 The buoy itself can be designed with a smallwater plane area relative to its displacement reducing thevertical wave induced motion of the buoy.7.3.4.3 Since vessel roll motions do not influence thebehaviour of the buoy, long crested sea will be conservativefor this analysis.7.3.4.4 Changes in the buoyancy of the towed object dueto hydrostatic pressure and/or water density should beinvestigated.7.3.5 Tow of long slender elements7.3.5.1 Examples of slender objects that may be towed tofield are;• Pipelines, bundles, spools• TLP tethers• Riser towers / hybrid risersSeveral slender objects may be towed together as a bundle(strapped together or within a protective casing).7.3.5.2 Tow of long slender elements are normallyperformed by one of the following methods:1) Off-bottom tow uses a combination of buoyancy andballast chains so that the towed object is elevated abovethe seabed. Ballast chains are used to keep the tow nearthe seabed and provide sufficient submerged weight andstability.Figure 7-11 Submerged object attached to vessel2) Deeply submerged, or Controlled Depth Tow (CDT)method is a further development of the off-bottom towmethod. By careful design of towline length, holdbacktension, buoyancy, ballast and drag chains with theirspecific hydrodynamic properties, the towed object willbe lifted off the seabed at a critical tow speed to betowed at a ‘controlled depth’ above obstructions on seabed, but below the area with strong wave influence.3) Surface or near-surface towing methods for transport oflong slender elements over short or long distances. Forsurface tows the towed object will be influenced bywave loads. Buoyancy elements are often used. SeeFigure 7-12.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 83−−−Rigging data: Mass properties (mass, buoyancy) of anylumped masses such as crane hook. Geometry andstiffness.Tow line/bridle data: Mass properties (mass, buoyancy),any lumped masses, geometry and stiffness.Operational data: Towing speed, vessel heading, currentspeed/heading, wave heading and sea states.7.3.7 System modellingFigure 7-13 Different methods for tow of long slenderobjects7.3.5.3 The tow configuration is dependent on:• Submerged weight in water• Use of temporary buoyancy/weight• Tow speed and towline length• Back tension provided by trailing tug• Drag loading due to current7.3.5.4 Lift effects and stability may impede the controlof a sub-surface towed bundle. Particular attention should begiven to non-axisymmetrical cross section, tow-heads orother structures attached to the bundle7.3.5.5 It is important to minimize fatigue loading on thepipe due to tug motions and direct wave action. In order tominimize direct wave action the tow depth of the towedobject should be deeper when towing in sea-states with highpeak periods since long waves have an effect further down inthe water column.Guidance noteThe wave induced velocity is reduced with a factor e kz downwards inthe water column, where k=2π/λ is the wave number and λ is thewave length. Hence, at tow depth equal to λ/2 the energy is only 4%of the value at the surface.7.3.6 System data7.3.6.1 The following system data is necessary in orderto perform a time domain analysis for a submerged towconcept:−−−Vessel data: Mass properties (mass, buoyancy, COG,radius of inertia, draught, trim) and hull geometry. Thesedata will be input to 3D diffraction analysis.Buoy data: Mass properties (mass, buoyancy, COG,radius of inertia, draught) and hull geometry.Towed object data: Mass properties (mass, buoyancy,COG, radius of inertia) and General Arrangement (GA)drawing (incl. size of structural members) forestablishment of analysis model, stiffness properties,drag and lift effects.7.3.7.1 Vessel force transfer functions and hydrodynamiccoefficients for all 6 degrees of freedom should be calculatedby 3D wave diffraction analysis.7.3.7.2 For the buoy, in the towed-buoy concept, it isimportant to apply a model that describes the combinedsurge/pitch motion correctly. Further, the effect of trim onthe heave motion should also be included. In order to capturethese effects a Morison model may be suitable. This is validfor long and slender buoys. Possible forward speed effectsshould be included.7.3.7.3 For towed objects attached to vessel or towedbuoy, a Finite Element (FE) model of the rigging (slings andhoist wire) and/or the tow line and bridle is normally notnecessary. In such cases it may be sufficient to model thelines using springs.7.3.7.4 In most cases it is recommended that the towedobject is modelled by Morison elements with added mass anddrag properties for the different basic elements such ascylinders, plates etc. It is important to assure that correctmass and buoyancy distribution is obtained. The towedobject should be modelled as a 6DOF body with the Morisonelements distributed over the structure to capture the correctdynamic load distribution between the slings.7.3.7.5 For tow of long slender objects like bundles, thestructure should be modelled in a finite element (FE)program. In this case, fatigue loading can be decisive, andthe global behaviour of the structure under dynamic loadinghas to be assessed.7.3.8 Vortex induced vibrations7.3.8.1 For slender structures such as bundles, spools,piping etc. special consideration should be given to identifywhether vortex induced vibrations (VIV) will be a problem.7.3.8.2 Eigenmodes for the slender structures can becalculated in a FE program. The eigenmodes are the “wet”eigenmodes including the effect of added mass fromsurrounding water. If one of the eigenfrequencies f n of thestructure are close to the vortex shedding frequency, vortexinduced vibrations may occur and possible fatigue due toVIV during the tow-out operation should be furtherevaluated.Guidance noteDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 84For long slender structures submerged in water, vortex inducedvibrations may occur if the 3 < V R < 16, whereV RUf nD= U/(f nD) is the reduced velocity= Relative velocity between tow speed and current [m/s]= natural frequency [Hz]= Slender element diameter [m]Further guidance on calculating VIV response is given in DNV-RP-C205.Guidance noteThe first natural frequency of a simply supported beam may be takenas;2EI ⎡ ⎛ ⎞ ⎤f1 = 1.57 ⎢1+ 0. 84⎜ ⎟ ⎥m'⋅L⎢⎣⎝ D ⎠ ⎥⎦δ[s -1 ]where EI is the bending stiffness, m’ is the total mass per unit length(including added mass), L is the span length, δ is the static deflection(sag) and D is a characteristic cross-sectional dimension (diameter).7.3.8.3 If it is found that the towed object is susceptibleto VIV, one should either document that the resultingdamage is acceptable, or alter the configuration in such away that the eigenperiods are reduced to avoid VIV. This canbe done by supporting the structure or part of it which issusceptible to VIV to make it stiffer.Guidance noteUnless otherwise documented, it is recommended that no more than10 % of the allowable fatigue damage is used in the installationphase, irrespective of safety class. This is according to industrypractice.7.3.9 Recommendations on analysis7.3.9.1 It is recommended to use a time domain analysisin order to capture the important physical effects (ref.7.3.2.1). Frequency domain analysis may be used in planningphase for parameter studies and to obtain quick estimates ofthe response for various towing configurations. Frequencydomain analysis may also be used for fatigue analysis of longduration tows encountering different seastates during thetow.7.3.9.2 The duration of the time simulation should besufficient to provide adequate statistics. It is recommended toperform 3 hour simulations in irregular sea states.7.3.9.3 Some analysis programs may require very longsimulation time for a full 3 hour simulation, and full timesimulations for a wide range of sea states and wave headingsmay therefrore not be practical. For these programs a methodwith selection of characteristic wave trains can be applied.7.3.9.4 A consistent selection is to compute time series ofthe vertical motion at the suspension point (e.g. the hang offframe) and then select wave trains that coincide with theoccurrence of maximum vertical velocity and maximumvertical acceleration.7.3.9.5 Special considerations should also be given to theselection of wave trains for calculation of minimumclearance to vessel side and moon pool edges.7.3.9.6 It is recommended to perform one 3 hour checkfor the worst limiting cases in order to verify that theselection method give results with approximately correctmagnitude.7.3.9.7 It is important to establish the operationallimitations for each weather direction.7.3.9.8 A heading controlled vessel will not be able tokeep the exact same direction continuously. It is thereforeimportant that the analyses are performed for the intendeddirection ±15 degrees.Guidance NoteIf long crested sea is applied, a heading angle of ±20° isrecommended in order to account for the additional effect from shortcrested sea.7.3.9.9 It is important to check the results versusestablished acceptance criteria, such as:• Minimum and maximum sling forces• Clearance between object and vessel• Stability during tow• VIV of slender structures. For bundles VIV maycause significant fatigue damageDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 857.3.9.10 For long slender elements an important resultfrom the analyses will be to determine the optimal towconfiguration (tow depth, use of temporary buoyancy/weight,tension in the bundle etc.).7.3.9.11 Visualisation of results is beneficial. In this wayunphysical behaviour, such as large deflections from initialposition and large rotations, can be detected.7.3.10 Wet anchoringOff-bottom tows of long slender objects over long distancesmay be abrupted due to adverse weather conditions and thebundle left in anchored position close to sea bed. See Figure7-15. Anchors are usually attached to the end of the bundle.In anchored position the bundle will be exposed to currentforces. The bundle is stabilized by the friction forcesbetween ballast chains and the sea bed. Typical frictioncoefficients for anchor chain is given in Table 7-2.Table 7-2: Friction coefficients between chain and seabed.Sea bedFriction coefficientcondition Static SlidingSandMud with sandFirm mudSoft mudClay0.980.921.010.901.25Figure 7-14 Ballast chains during tow0.740.690.620.560.81Figure 7-15 Bundle with ballast chains in off-bottommode.7.4 References/1/ DNV Offshore Standard DNV-OS-H101, “MarineOperations, General” (planned isssued 2009, see ref./3/until release)./2/ DNV Offshore Standard DNV-OS-H202, “MarineOperations, Sea Transports” (planned isssued 2009, seeref./3/ until release)./3/ DNV Rules for Planning and Execution of MarineOperations (1996)./4/ DNV Recommended Practice DNV-RP-C205“Environmental Conditions and Environmental Loads”,April 2007./5/ DNV Recommended Practice DNV-RP-F205 “GlobalPerformance Analysis of Deepwater FloatingStructures”, October 2004./6/ Binns, J.R., Marcollo, H., Hinwood, J. and Doctors, L.J.(1995) “Dynamics of a Near-Surface Pipeline Tow”.OTC 7818, Houston, Texas, USA./7/ Dercksen A. (1993) “Recent developments in thetowing of very long pipeline bundles using the CDTMmethod”. OTC 7297, Houston, Texas, USA./8/ Fernandez, M.L. (1981) “Tow techniques for offshorepipelaying examined for advantages, limitations”. Oil &Gas Journal, June 22, 1981./9/ Headworth, C., Aywin, E. and Smith, M. (1992)“Enhanced Flexible Riser Installation – ExtendingTowed Production System Technologies”. MarineStructures 5, pp. 455-464./10/ Knudsen, C. (2000) “Combined Riser-Bundle-TemplateInstalled by Controlles Depth Tow Method”. Proc. 10 thInt. Offshore and Polar Eng. Conf., Seattle, May 28-June 2, 1990./11/ Lehn, E. (1985) “On the propeller race interactioneffects”. Marintek Report P-01, 85. Trondheim, 1985./12/ Ley, T. and Reynolds, D. (2006) “Pulling and towing ofpipelines and bundles”. OTC 18233. OffshoreTechnology Conference, Houston, Texas, USA, 1-4May 2006./13/ Moxnes, S. and Fylling, I.J. (1993) “Dynamics ofOffshore Towing Line Systems”. Offshore 93 –Installation of Major Offshore Structures andEquipment./14/ Moxnes, S. (1993) “Dynamikk i slepeliner under slep avoffshore konstruksjoner”. Norske SivilingeniørersForening. (In Norwegian)/15/ Nielsen, F.G (2007) ”Lecture notes in marineoperations”. NTNU, Trondheim./16/ Risøy, T., Mork, H., Johnsgard, H. and Gramnæs, J.(2007) “The Pencil Buoy Method – A SubsurfaceTransportation and Installation Method”. OTC 19040,Houston, Texas, USA, 30 April – 3 May 2007, 2007.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 86/17/ Rooduyn, E. (1991) “Towed Production Systems –Further developments in design and installation”.Subsea International’91, 23 April 1991, London, UK./18/ Song, R., Clausen, T. and Struijk, P. (2001) “Designand Installation of a Banded Riser System for a NorthSea Development”. OTC 12975. Houston, Texas, USA./19/ Watters, A.J., Smith, I.C. and Garrett, D.L. (1998) ”Thelifetime dynamics of a deep water riser design”. AppliedOcean Research Vol 20., pp. 69-81.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 878 Weather criteria and availabilityanalysis8.1 Introduction8.1.1.1 Information about weather conditions required forcarrying out marine operations depends on the type ofoperation, e.g. drilling, pipeline installation, offshoreoffloading, installation of a platform, crane operations orsubsea installation.8.1.1.2 Relevant environmental parameters for carryingout marine operations as well as recommendations andrequirements for description of environmental conditions aregiven in DNV-OS-H101, ref. /7/.8.1.1.3 Marine operations consist of two phases:1) design and planning2) execution of the operations8.1.1.4 The design and planning phase shall selectseasons when the marine operations can be carried out andprovide weather criteria for starting and interrupting theoperations (the availability analysis). The analysis shall bebased on historical data covering a time period of at least 5-10 years.8.1.1.5 Execution of marine operations shall be based onthe weather forecast, the Near Real Time (NRT) data (datawith a time history 1-5 hours) and, if justified, on Real Time(RT) data (data with a time history 0-1 hours).8.2 Environmental parameters8.2.1 General8.2.1.1 For marine operations the time history of weatherconditions and duration of weather events are the keyparameters. Weather criteria and availability analysis shallinclude identified environmental parameters critical for anoperation and provide duration of the events for exceedingand not exceeding the threshold limits of these parameters.8.2.1.2 Threshold limits of environmental parameterscritical for carrying out an operation and its sub-operations,time for preparing the operation as well as the duration ofeach sub-operation need to be specified prior to the start ofan operation. These values will depend upon the type ofoperation and on critical responses.Guidance NoteIf a maximum response limit (X max) is defined for an operation, thecorresponding significant wave height limits (threshold values) mustbe found, for varying wave period and wave direction. Assuming thePierson-Moskowitz spectrum, a linear response and a constant zerocrossingwave period, T z, and wave direction, the response will beproportional to the significant wave height H s. Then the response canbe calculated for H s.= 1m for all zero-crossing wave periods observedin the statistical data. The maximum H s for each T z is then scaledaccording to:XmaxHs, max( Tz) = ⋅ Hs( T ) [m]z H S = 1X ( Tz)H s = 18.2.2 Primary characteristics8.2.2.1 Often the significant wave height exceeding agiven threshold level, as shown in Figure 8-1, will be theprimary parameter. Threshold limits for other environmentalparameters (e.g. corresponding wave periods) relevant forcarrying out a marine operation may be established based onjoint probabilities.H s(m)H s’t 1 t 2 t 3 t 4 t 5 t 6 t 7Time (hours)Figue 8-1 Example of significant wave height variationwith time.8.2.2.2 The duration of a weather event is defined as thetime between a crossing of a level for that parameter and thenext crossing of the same level. See Figure 8-1. The eventcan be defined as above the level (from t 1 to t 2 , H S > H S ’ )or below the level (from t 2 to t 3 , H S

Recommended Practice DNV-RP-H103 Draft December 2008Page 888.2.2.4 Planning and design of marine operations shall bebased on an operation reference period defined as;T = T + TRwhereT RT POPT CPOPC= operation reference period= planned operation period= estimated contingency time.8.2.2.5 Reference periods less than 12 hrs, shall bespecially considered.8.2.2.6 The start and termination points for the intendedoperation shall be clearly defined.8.2.2.7 If required time for contingency situations are notassessed the reference period may be taken as twice theplanned operation, but not less than 6 hrs.8.2.3 Weather routing8.2.3.1 For marine operations involving transportation,e.g. towing, an optimal route is recommended to be decided.Environmental conditions necessary for evaluating criticalresponses along different alternative routes shall be providedand used in the analysis. Usually they will represent scatterdiagrams of significant wave height and zero-crossing wave(or spectral peak) period.8.2.3.2 In the design and planning phase an optimal routeis recommended to be selected based on evaluation ofresponses and fatigue damage along different alternativeroutes, ref. /2/. Global environmental databases may beutilized for this purpose.8.2.3.3 Weather routing may also be performed duringthe execution of the transportation itself on the basis ofweather forecasting. Bad weather areas or critical weatherdirections may then be avoided by altering speed anddirection of the vessel. Due to the implicit possibilities ofhuman errors or forecast errors, there is however a certainrisk of making wrong decisions, ref. /22/. On-route weatherrouting should therefore be used with care.8.3 Data accuracy8.3.1 General requirementsThe weather criteria and availability analysis shall be basedon reliable data and accuracy of the data shall be indicated.The data applied shall be given for a location or an oceanarea where an operation takes place. It is recommended touse reliable instrumental data, if available, or data generatedby recognized weather prediction models. Further, it isrecommended that the data are sampled at least each 3 rd hourand interpolated between the sampling intervals.8.3.2 Instrumental data8.3.2.1 Accuracy of environmental data may vary widelyand is very much related to the observation mode.8.3.2.2 The common wind observations include meanwind speed, mean wind direction and maximum wind speedwithin the observation interval. The standard wind datarepresent measured or calibrated 10-minute average speed at10 m above ground or mean sea level. Wind instruments onbuoys are usually mounted approximately 4 m above sealevel. The systematic instrumental error in estimating meanwind speed and direction can be regarded as negligible, ref./1/. Satellite scatterometers data may be utilized.8.3.2.3 The instrumental accuracy of wave observationsdepends on the type of instrument used. Wave buoys areregarded as being highly accurate instruments, and error inthe estimated significant wave height and zero-crossing waveperiod may be considered as negligible for most sea states,ref. /1/. During severe sea conditions, the presence of strongsurface current or external forces on the buoy (e.g., breakingwaves, mooring) may cause the buoy measurements to bebiased.8.3.2.4 Several investigations carried out in the last yearsindicate very promising results that support use of satellitealtimeter data. Ref. /6/ demonstrates that over the range ofsignificant wave heights 1 m - 8 m satellite altimeter derivedsignificant wave heights were nearly as accurate as the onesobtained from surface buoy measurements, ref. /19/.8.3.2.5 In steep waves, the differences between seasurface oscillations recorded by a fixed (Eulerian) probe orlaser, and those obtained by a free-floating (Lagrangian)buoy can be very marked, see e.g. ref. /10/ and ref. /18/. Thewave buoy data shall not be used for estimation of waveprofiles in steep waves. For monitoring a wave profile a laseris recommended to be used.8.3.2.6 Platform mounted wave gauges and other wavesensing devices have the advantage that they measuredirectly sea surface displacement rather than the accelerationas the buoys do. The position of the wave gauge may affectaccuracy of data, ref. /5/.8.3.2.7 Ship Borne Wave Recorder (SBWR) makes directwave height measurements but provides no directionalinformation. The main uncertainty is the response of a shipto the waves. Comparison with the wave buoy data suggestswave height accuracy on average of about 8-10%. TheSBWR significant wave height are on average higher thanthe buoy wave heights, with a greater percentage differenceat low wave heights and less at high wave heights, ref. /9/.The zero-crossing periods from the two instruments areapproximately the same.8.3.2.8 Marine radars (e.g. WAVEX, WAMOS) providedirectional wave spectra but infer wave height indirectly.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 89Initial analysis of WAVEX data shows that the WAVEXmay significantly over-estimate wave heights for swelldominatedconditions, ref. /21/. Technology used by marineradars for recording the sea surface is under continuousdevelopment and the accuracy is continuously improved.Accuracy of a marine radar shall be indicated prior to using itin a marine operation.8.3.2.9 For instrumentally recorded wave data, samplingvariability due to a limited measurement interval constitutesa significant part of the random errors. For the JONSWAPand Pierson-Moskowitz spectrum the sampling variabilitycoefficient of variation of the significant wave height andzero-crossing wave period are approximately 4-6% and 1.5-2.5% respectively for a 20-minute measurement interval, /1/.8.3.2.10 An instrumentally recorded ocean current data setmay be erroneous due to instrument failure, such as loss ofrotor or marine growth. Before application of a data set inplanning and execution of marine operations, it is importantto make sure that a data quality check has been carried out.Current data uncertainty is specified e.g. in ref. /1/.8.3.2.11 Water level data are collected either by usingmechanical instruments or by using pressure gauges, wavebuoys, wave radars, and lasers. The accuracy of theserecordings is 2-3 cm. For use of the computed water leveldata it is necessary to know the assumptions and limitationsof the models. The data are usually given as residual seawater levels, i.e., the total sea water level reduced by the tide.8.3.3 Numerically generated data8.3.3.1 Numerically generated wave data are produced onroutine basis by major national meteorological services andare filed by the data centers. The accuracy of these data mayvary and depends on the accuracy of a wave predictionmodel applied as well as the adopted wind field. Thehindcast data can be used, when the underlying hindcast iscalibrated with measured data and accuracy of the data isdocumented.8.3.3.2 The Global Wave Statistics (GWS) visualobservations (BMT (1986)) collected from ships in normalservice all over the world since 1949 are often applied. Thedata represent average wind and wave climate for 104 oceanwave areas. They have a sufficiently long observationhistory to give reliable global wind and wave climaticstatistics. Accuracy of these data is, however, stillquestioned, especially concerning wave period, confer e.g.ref. /15/ or ref. /2/. It is recommended to use the data withcare, and if possible to compare with other data sources.8.3.3.3 Recently several global environmental databaseshave been developed. They include numerical wind andwave data (some provide also current and/or sea water level)calibrated by measurements (in-situ data, satellite data), amixture of numerical and instrumental data or pureinstrumental (satellite) data. Accuracy of a data basis shall bedocumented before applying the data.8.3.4 Climatic uncertainty8.3.4.1 Historical data used for specification ofoperational weather criteria may be affected by climaticuncertainty. Climatic uncertainty appears when the data areobtained from a time interval that is not fully representativefor the long-term variations of the environmental conditions.This may result in overestimation or underestimation of theoperational weather criteria. The database needs to cover atleast 20 years of preferably 30 years or more in order toaccount for climatic variability.8.3.4.2 If data from 20 to 30 years are available, it isrecommended to establish an environmental description, e.g.a distribution of significant wave height, for return periods of1, 3, 5, 10 and 25 years.8.3.5 Sources of data8.3.5.1 Because of data inaccuracy it is recommended touse several data sources in the analysis (if available),specifying weather criteria for comparison. Particularattention shall be given to ocean areas where data coverage ispoor.8.4 Weather forecasting8.4.1 Weather restricted operations8.4.1.1 Marine operations with a reference period lessthan 72 hours may be defined as weather restricted. Theseoperations may be planned with weather conditions selectedindependent of statistical data, i.e. set by an owner, anoperator, etc. The starts of a weather restricted operation isconditional on a reliable weather forecast as given in DNV-OS-H101, ref. /7/.8.4.2 Uncertainty of weather forecasts8.4.2.1 For weather restricted operations uncertainties inweather forecasts shall be considered. Operational limits ofenvironmental parameters (e.g. significant wave height, windspeed) shall be lower than the design values. This isaccounted for by the alpha factors as specified in DNV-OS-H101, ref. /7/. The requirements are location specific andshall be used with care for other ocean locations. It isrecommended to apply location specific and, if justified,model specific corrections when used outside the areasprovided in DNV-OS-H101.Guidance NoteAt present, the given alpha-factors in DNV-OS-H101 are derived fromNorth Sea and Norwegian Sea data only.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 908.5 Persistence statistics8.5.1 Weather unrestricted operations8.5.1.1 Marine operations with a reference periodexceeding 72 hours are normally defined as unrestrictedoperations, see DNV-OS-H101, ref. /7/. These operationsshall be planned based on extreme value statistics establishedfrom historical data or time domain simulations.8.5.1.2 Persistence statistics shall be establishedaccording to specified a priori operational design criteria.8.5.1.3 A non-stationary stochastic modelling, suitablefor the analysis and simulation of multivariate time series ofenvironmental data may be used as a supporting tool forgenerating the long–term data, ref. /17/.8.5.1.4 For limited time periods like months the statisticsshall follow the DNV-OS-H101 requirements and be basedon events that start within the period and are followed to thenext crossing. The average duration of events will depend onthe averaging period and sampling interval of the data.Guidance NoteNote that certain operations require a start criterion althoughdesigned for unrestricted conditions.8.5.2 Statistics from historical data8.5.2.1 It is recommended that duration statistics includesthe following parameters (ref. /16/):T totN cN sτcτT cT ssHence;T cT stotN= c∑i=1N= c∑i=1= total time period of an environmental timeseries under consideration= number of “calm” periods= number of “storm” periods= average duration of “calm” periods= average duration of “storm” periods= total duration of all “calm” periods= total duration of all “storm” periodsτ [hours]ciτ [hours]csiT = T + T [hours]s8.5.2.2 Unless data indicate otherwise, a 2-parameterWeibull distribution can be assumed for the marginaldistribution of “calm” period t (ref. /9/ and ref. /14/);β⎡ ⎛ t ⎞ ⎤F⎢⎜⎟τ( t)= 1−exp − ⎥ [-]⎢⎣⎝ t c ⎠ ⎥⎦wheret cβ= scale parameter= shape parameterThe distribution parameters are determined from site specificdata by some fitting technique.8.5.2.3 The average duration is expressed as∞∫0τ = t ⋅ dF (t) [hours]CτFor the 2-parameter Weibull distribution it reads;τ=1⋅ Γ( + 1)βctc[hours]where Γ ( ) is the Gamma function.8.5.2.4 If the cumulative distribution of H s is known thenthe average duration of periods with significant wave heightlower than h can be approximated byT= F h)totτ ( [hours]C H sNCalternatively, ref /9/;1−[ − ln( F ( ))] βτc= AHh [hours]swhere A and β are established based on location specificdata, and FH s(h)is a cumulative distribution of significantwave height. For the North Sea, A=20 hours and β=1.3 maybe adopted, ref. /9/.8.5.2.5 The distribution for h < H s' and duration t

Recommended Practice DNV-RP-H103, Draft December 2008Page 918.5.2.6 The number of periods when h < H s' and t

Recommended Practice DNV-RP-H103 Draft December 2008Page 92three months and a shorter period of time according to therequirements given in DNV-OS-H101, ref. /7/. Several returnperiods are recommended to be considered.8.6.3 Monitoring of responses8.6.3.1 Monitoring of responses shall be carried out byapproved reliable instruments.8.6 Monitoring of weather conditions andresponses8.6.1 Monitoring of environmental phenomena8.6.1.1 For marine operations particularly sensitive tocertain environmental conditions such as waves, swell,current, tide, etc., systematic monitoring of these conditionsprior to and during the operation shall be arranged.8.6.1.2 Monitoring shall be systematic and follow therequirements given in DNV-OS-H101. Responsibilities,monitoring methods and intervals shall be described in aprocedure. Essential monitoring systems shall have back upsystems. Any unforeseen monitoring results shall be reportedwithout delay.8.6.1.3 Carrying out marine operations can be assisted bya Decision Support System installed on board of marinestructures if reliability of the system is described andapproved by an authority or by a Classification Society. TheDecision Support System may be based on the Near RealTime (NRT) and/or Real Time (RT) data which can beprovided by met-offices, private company or researchinstitutes. The NRT and RT data may represent numericallygenerated data, a mixture of numerical and instrumental data(in-situ measurements, marine radar and satellite data) orpure instrumental data if sampling frequency of the latter issufficient for an operation under consideration. Vesselmotions may be utilized by a Decision Support System andenvironmental conditions can be evaluated from measuredvessel motions, ref. /16/. Attention shall be given toaccuracy of prediction of combined seas (wind sea andswell).8.6.1.4 A required sampling interval for time monitoringwill depend upon the type of operation and its duration, andis recommended to be considered carefully.8.6.2 Tidal variations8.6.2.1 Tidal variations shall additionally be monitoredduring a period with the same lunar phase as for the plannedoperation.Guidance NoteTidal variations shall be plotted against established astronomical tidecurves. Any discrepancies shall be evaluated, duly consideringbarometric pressure and other weather effects.8.6.4 Alpha factor related monitoring8.6.4.1 Uncertainties related to monitoring of weatherconditions shall be taken into considerations according to therequirements given in DNV-OS-H101.8.7 References/1/ Bitner-Gregersen, E.M. and Ø. Hagen (1990),"Uncertainties in Data for the Offshore Environment",Structural Safety, Vol. 7., pp. 11-34./2/ Bitner-Gregersen, E. M., Cramer, E., and Løseth, R.,(1995), “Uncertainties of Load Characteristics andFatigue Damage of Ship Structures”, J. MarineStructures, Vol. 8, pp. 97-117./3/ Bitner-Gregersen, E. M., Cramer, E. H., and Korbijn, F.,1995. “Environmental Description for Long-term LoadResponse of Ship Structures”. Proceed. ISOPE-95Conference, The Hague, The Netherlands, June 11-16./4/ British Maritime Technology (Hogben, N. Da Cunha,L.F., and Oliver , H.N.) (1986), Global Wave Statistics,Unwin Brothers Limited, London, England./5/ Cardone, C.J. Shaw and V.R.Swail (1995),“Uncertainties in Metocean Data”, Proceedings of theE&P Forum Workshop./6/ Carter, D.J.T., Challenor, P.G. and M.A. Srokosz,(1992), “An Assessment of GEOSAT Wave Height andWind Speed Measurements”, J. Geophys. Res. Vol.97(C7)./7/ DNV Offshore Standard ”Marine Operations General”,DNV-OS-H101 (planned issued 2009)./8/ Graham, C.G., Verboom, G. and Shaw, C.J. (1978)“Comparison of Ship Born Wave Recorder andWaverider Buoy Data used to Generate Design andOperational Planning Criteria”. Proc. CoastalEngineering, Elsevier, Amsterdam, pp. 97-113./9/ Graham, C., (1982), ”The Parametrisation andPrediction of Wave height and Wind Speed persistenceStatistics for Oil Industry Operational PlanningPurposes”. Coastal Engineering, Vol 6, pp. 303-329./10/ Marthinsen T. and S.R. Winterstein (1992), On theskewness of random surface waves, Proc. of the 2 ndInternational Offshore and Polar EngineeringConference, San Francisco, pp 472-478, ISOPE./11/ Nielsen, F. G., (2007) , “Lecture Notes in MarineOperations”. Department of Marine Hydrodynamics,Faculty of Marine Technology, Norwegian UniversityDET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 93of Science and Technology, Trondheim/Bergen January2007./12/ Nielsen, U.D. (2006), Estimations of On-siteDirectional Wave Spectra from Measured ShipResponses, Marine Structures, Vol. 19, no 1./13/ Kleiven, G. and Vik, I. (1984) “Transformation ofCumulative Probability of Significant Wave height intoEstimates of Effective Operation Time”. Norsk HydroResearch Centre, Bergen July./14/ Houmb, O.G. and Vik, I. (1977), “On the Duration ofSea State”. NSFI/NTH Division of port and Ocen Eng.Report./15/ Guedes Soares, C. and Moan, T., (1991). “ModelUncertainty in a Long Term Distribution of WaveinducedBending Moments for Fatigue Design of ShipStructures, Marine Structures, Vol. 4./16/ Nielsen, U.D. (2006), Estimations of On-siteDirectional Wave Spectra from Measured ShipResponses, Marine Structures, Vol. 19, no 1./17/ Stefanakos, Ch. N and Belibassakis, K.A. ,(2005),“Non-stationary Stochastic Modelling of MultivariateLong-term Wind and Wave data”, Proc. OMAE’2005Conf., Halkidiki, Greece, 2005./18/ Vartdal, L., Krogstad, H. and S.F. Barstow (1989),“Measurements of Wave Properties in Extreme SeasDuring the WADIC Experiment” , Proc. 21 st AnnualOffshore technology Conference, Houston, Texas./19/ deValk, C. Groenewoud, P., Hulst S. and Kolpman G.(2004), “Building a Global Resource for RapidAssessment of the Wave Climate”, Proc. 23 rd OMAEConference, Vancouver, Canada, June 20-25, 2004./20/ Vik, I. and Kleiven, G., (1985) “Wave Statistics forOffshore Operation”. 8 th Inter. Conference on Port andOcean Enfigeering under Arctic Conditions (POAC 85),Narssarssuaq, Greenland, Sept. 6-13./21/ Yelland, M.J., Bjorheim, K., Gommenginger, C., PascalR.W. and Moat, B.I. (2007) “Future Exploition of InsituWave Measurements at Station Mike”. Poster at theGLOBWAVE Workshops, Brest, September 19-21./22/ Aalbers, A.B. and van Dongen, C.J.G., (2008) “WeatherRouting: Uncertainties and the Effect of DecisionSupport Systems”. Marine Operations SpecialtySymposium – MOSS2008, pp.411-423.DET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 94APPENDIX A ADDED MASS COEFFICIENTSTable A1: Analytical added mass coefficient for two-dimensional bodies, i.e. long cylinders in infinite fluid (far fromboundaries). Added mass (per unit length) is A ij =ρC A A R [kg/m] where A R [m 2 ] is the reference area.Section through bodyDirection ofmotionC A A RAdded mass moment ofinertia [(kg/m)*m 2 ]1.02π a 02bVertical 1.0Horizontal 1.02π a2π bπρ (82 2 2b − a )Vertical 1.02π aπρ8 a42abCircularcylinder withtwo finsVertical 1.0Horizontal2π aa24⎞ ⎛ a2⎛ ⎞1−⎜ ⎟ + ⎜ ⎟⎝ b ⎠ ⎝ b ⎠π b4 42ρa(csc α f ( α)− π ) / 2πwheref ( α ) = 2α2 −αsin 4α2+ 0.5 sin 2α and2 2sinα= 2ab /( a + b )π / 2 < α < π2aHorizontal orVertical1.02π a2 ρa4π2aa / b = ∞a / b = 10a / b = 5a / b = 2a / b = 1a / b = 0.5a / b = 0.2a / b = 0.1Vertical1.01.141.211.361.511.701.982.232π aβ or41ρπaβ42ρπba/b β 1 β 20.1 - 0.1470.2 - 0.150.5 - 0.151.0 0.234 0.2342.0 0.15 -5.0 0.15 -∞ 0.125 -4βρπ ad / a = 0.05d / a = 0.10d / a = 0.25Vertical1.611.722.192π ad / a0.050.100.10β0.310.400.69DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 95Section through bodyDirection ofmotionC A A RAdded mass moment ofinertia [(kg/m)*m 2 ]a / b = 2a / b = 1a / b = 0.5a / b = 0.2Vertical0.850.760.670.612π a 0.059 ρπa 4 for a = b onlyHorizontal −13π 22π aHorizontalh 22a2⎛ ⎞1+⎜ − ⎟⎝ 2ah ⎠π abb/ac/a0.1 0.2 0.4 1.00.5 4.7 2.6 1.3 -cabVertical1.0 5.2 3.2 1.7 0.61.5 5.8 3.7 2.0 0.72.0 6.4 4.0 2.3 0.93.0 7.2 4.6 2.5 1.14.0 - 4.8 - -2abA2adB2aA movingB fixedHorizontald/a = ∞d/a = 1.2d/a = 0.8d/a = 0.4d/a = 0.2d/a = 0.11.0001.0241.0441.0961.1601.2242π aab2 2Cylinder withinb apipe2 2b − a+ 2π asyθrxCross section issymmetricabout r and saxesa a 2m = m sin θ + myyrrassa a 2m = m cos θ + mxxrrass2cos θ2sin θ1 a arr− mssamxy= ( m2)sin 2θDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 96Section through bodyDirection ofmotionC A A RAdded mass moment ofinertia [(kg/m)*m 2 ]dShallow water2bcb 2 2 2bb 2− ln 4ε+ − + ε + ε2cεπ π c c 3πdc= 1 − ε where ε

Recommended Practice DNV-RP-H103, Draft December 2008Page 97Body shapeDirection ofmotionC AV REllipsoid2b2c2aAxialCAwhereα0=2 −α0∞−3/ 2 2 −1/ 2 2 − 2= ∫ + + +1/0εδ 1 u)( ε u)( δ u)0α( du4π abc3Axis a > b > cε = b / a δ = c / aSquare prismsVerticalb/a1.02.03.04.05.06.07.010.0b/2aC A0.680.360.240.190.150.130.110.08C Aa 2bRight circularcylinderabVertical1.22.55.09.0∞0.620.780.900.961.00πa 2 bDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 98APPENDIX B DRAG COEFFICIENTSTable B1: Drag coefficient on non-circular cross-sections for steady flow C DS . Drag force per unit length of slenderelement is f = ½ρC DS Du 2 . D = characteristic width [m]. R e = uD/ν = Reynolds number. Adopted from Blevins, R.D.(1984) Applied Fluid Dynamics Handbook. Krieger Publishing Co.Geometry1. Wire and chains2. Circular cylinder with thin finDDrag coefficient, C DSType (R e = 10 4 - 10 7 )Wire, six strandWire, spiral no sheatingWire, spiral with sheatingChain, stud (relative chain diameter)Chain studless (relative chain diameter)C DS1.5 - 1.81.4 - 1.61.0 - 1.22.2 - 2.62.0 - 2.4T 10 35. Rectangle with rounded cornersL/D R/D C DS L/D R/D C DS0.5 00.0210.0830.2502.52.21.91.62.0 00.0420.1670.501.61.40.70.41.0 00.0210.1670.3332.22.01.21.0R e ~ 10 56.0 00.50.890.29DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 99Geometry6. Inclined squareDrag coefficient, C DSθ 0 5 10 15 20 25 30 35 40 45C DS 2.2 2.1 1.8 1.3 1.9 2.1 2.2 2.3 2.4 2.4R e ~4.7 x 10 47. Diamond with rounded corners8. Rounded nose sectionL 0 /D 0 R/D 0 C DS0.5 0.0210.0830.1671.0 0.0150.1180.2352.0 0.0400.1670.335L/D1.81.71.71.51.51.51.11.11.1R e ~ 10 50.51.02.04.06.0C DS1.160.900.700.680.64Fore and aft cornersnot roundedLateral corners notrounded9. Thin flat plate normal to flowC DS = 1.9, R e > 10 410. Thin flat plate inclined to flowC No⎧ 2πtanθ,θ < 8⎪⎨ 1⎪⎩ 0.222 + 0.283/sinθo= , 90 ≥ θC L = C N cos θC DS = C N sin θ> 12o11. Thin lifting foilC DS ~ 0.01C L = 2π sin θC M = (π/4) sin 2θ (moment about leading edge)C M = 0 about point D/4 behind leading edgeDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 100Geometry12. Two thin plates side by sideDrag coefficient, C DSE/D C DS0.51.02.03.05.010.015.01.42 or 2.201.52 or 2.131.9 or 2.102.01.961.91.9multiple valuesdue tojet switchDrag on each plate.13. Two thin plates in tandem14. Thin plate extending part wayacross a channelR e ~4 x 10 3E/D C DS1 C DS22346102030∞1.4CDS=2.85(1 − D / H )1.801.701.651.651.91.91.91.9R e ~ 4 x 10 30.100.670.760.951.001.151.331.90for 0 < D/H < 0.2515. EllipseR e > 10 3 D/L C DS (R e ~10 5 )0.1250.250.501.002.00.220.30.61.01.616. Isosceles triangle17. Isosceles triangleθ C DS (R e ~ 10 4 )30 1.160 1.490 1.6120 1.75θ C DS (R e = 10 4 )30 1.960 2.190 2.15120 2.05DET NORSKE VERITAS

Recommended Practice DNV-RP-H103, Draft December 2008Page 101Table B2: Drag coefficient on three-dimensional objects for steady flow C DS . Drag force is defined as F D =½ρC DS Su 2 . S = projected area normal to flow direction [m 2 ]. R e = uD/ν = Reynolds number where D = characteristicdimension.Geometry Dimensions C DSRectangular plate normal to flow directionB/HuH1510∞1.161.201.501.90BR e > 10 3Circular cylinder. Axis parallel to flow.L/DuLD012471.120.910.850.870.99R e > 10 3Square rod parallel to flowL/DuLDD00.51.01.52.02.53.04.05.01.251.251.150.970.870.900.930.950.95Re = 1.7·10 5Circular cylinder normal to flow.L/DSubcritical flowR e < 10 5Supercritical flowR e >5·10 5uL2510204050100κ0.580.620.680.740.820.870.98κ0.800.800.820.900.980.991.00DC κ C∞DS=DSκ is the reduction factor due to finite length.coefficient.∞CDSis the 2D steady dragDET NORSKE VERITAS

Recommended Practice DNV-RP-H103 Draft December 2008Page 102APPENDIX C PHYSICAL CONSTANTSTable C1: Density and viscosity of fresh water, sea water and dry airTemperatureDensity, ρ, [kg/m 3 ] Kinematic viscosity, ν, [m/s 2 ]deg [C] Fresh water Salt water Dry air Fresh water Salt water Dry air051015202530999.81000.0999.7999.1998.2997.0995.61028.01027.61026.91025.91024.71023.21021.71.2931.2701.2471.2261.2051.1841.1651.79 · 10 -61.521.311.141.000.890.801.83 · 10 -61.561.351.191.050.940.851.32 · 10 -51.361.411.451.501.551.60- o0o -DET NORSKE VERITAS