2008 technical papers

2008

Bulletin Technique

Couv BT 2008:Couv BT 2008 14/10/09 11:01 Page1

Introduction

Welcome to this edition of Bulletin Technique, a unique resource of technical papers delivered by experts from Bureau Veritas during 2008.

It is divided into five sections, grouping the papers underHydrodynamics and Hydro-Structure interaction, Structure, Offshore Engineering & Mooring, Rules and Classification and Risk Engineering.

Each section ranges over a wide range of topics which experts have tackled during the year. The variety and depth of the papers are a testimony to the wide range of expertise and resourcescommitted to research by Bureau Veritas. The papers give full details of the topics and are fully referenced, and the authors would be very happy to discuss their work further with interestedparties.

Pierre BesseResearch Director

Bureau Veritas

Bulletin Technique 2008

Editorial BT2008:Editorial BT2008 05/10/09 20:54 Page1

Hydrodynamics & Hydro -Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

• Computations of low-frequency wave loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7X. B. Chen & F. Rezende

• Simulation of second-order roll motions of a FPSO . . . . . . . . . . . . . . . . . . . . . . . .11F. Rezende, X. B. Chen & M. D. Ferreira

• Consistent hydro-structure interface for evaluation of global structural responses in linear seakeeping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19S. Malenica, E. Stumpf, F. X. Sireta & X. B. Chen

• Effects on sloshing pressure due to the coupling between seakeeping and tank liquid motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27L. Diebold, E. Baudin, J. Henry & M. Zalar

• Steep wave impact onto a complex 3D structure . . . . . . . . . . . . . . . . . . . . . . . . . .31I. Ten, A. Korobkin, S. Malenica ,J. de Lauzon & Z. Mravak

• Second-order wave loads on a LNG carrier in multi-directional waves . . . . . . .35M. Renaud, F. Rezende, O. Waals, X. B. Chen & R. van Dijk

• Diffraction and radiation with the effect of bathymetric variations . . . . . . . . . . .43G. De Hauteclocque, F Rezende & X. B. Chen

• Three-dimensional hydro-elastic Wagner impact using variational inequalities 51T. Gazzola & J. de Lauzon

• Some aspects of 3D linear hydroelastic models of springing . . . . . . . . . . . . . . . . .59S. Malenica, J.T. Tuitman, F. Bigot & F. X. Sireta

• Advanced computations of mooring systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69C. Brun, D. Coache & F. Rezende

• 3DFEM-3DBEM model for springing and whipping analyses of ships . . . . . . . . .77S.Malenica & J. T. Tuitman

• Fluid-structure interaction modeling, relating to membrane LNG ship cargo containment system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87W. S. Kim, B. J. Noh, H. Lee, Z. Mravak, J. de Lauzon, J. R. Maguire, D. Radosavljevic, S. H. Kwon & J. Y. Chung

• Hydroelastic aspects of large container ships . . . . . . . . . . . . . . . . . . . . . . . . . . . .97I. Senjanovic, S. Malenica, S. Tomaševic & M. Tomic

• Some aspects of whipping response of container ships . . . . . . . . . . . . . . . . . . .107J. Tuitman & S. Malenica

• A Comprehensive and Pratical Strength Assessment Methodology for Container Ships Taking Into Account Non Linear and Hydro-Elastic Loading .111G. de Jong & M. Huther

Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121

• Simulation of the behaviour of fatigue cracks: a tool for inspection decision making on a ship’s deck beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123V. Boutillier, M. Serror & G. Parmentier

• Quelques aspects hydrodynamique/structure en conception des porte conteneurs geants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135M. Huther, S. Malenica & F. Mauduit

Bulletin Technique 2008

Contents›

Sommaire BT2008:Sommaire BT2008 12/10/09 18:51 Page1

Offshore Engineering & Mooring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147

• Characterization of polyester mooring lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . .149M. François & P. Davies

• Impact of the use of FullQTF on LNGC moored in shallow water studies . . . .159C. Brun, F. Rezende, D. Coache & J. Mombaerts

• Latest evolution of Metocean analysis practices and their applications . . . . . .167T. Barberon & G. Gourdet

• Connection hull–topsides: principles, designs and returns of experience . . . .187G. Gourdet

• Conversion of Offshore Floating Facilities : How to tackle them with an asset integrity focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205C. Chauviere & J. Esteve

• Influence of fibre stiffness on deepwater mooring line response . . . . . . . . . . .217P. Davies, K. Salomon, C. Bideaud, J. P. Labbé, S. Toumit, M. François, F. Grosjean & T.Bunsell

• Directional wave partitioning and its application to the structural analysis of an FPSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227R. Lawford, J. Bradon, T. Barberon, C. Camps & R. Jameson

• Deepwater Moorings with High Stiffness Polyester and PEN Fiber Ropes . . .237P. Davies, C. Lechat, A. Bunsell, A. Piant, M. François, F. Grosjean, P. Baron, K. Salomon, C. Bideaud, J. P. Labbé & Moysan A.G.

• Lessons learnt from 12 years operations of a huge floating production unit made of pre-stressed high performance concrete . . . . . . . . . . . . . . . . . . . .247B. Lanquetin, H. Dendani, P. Collet & J. Esteve

Rules & Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .263

• Fibre rope deepwater moorings: Complete and consistent design and qualification procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .265F. Legerstee, M. Francois & C. Brun

• Bureau veritas rules for the classification of traditional naval submarines . .283Y. Legal

• Condition assessment scheme for ship hull maintenance . . . . . . . . . . . . . . . . .293C. Cabos, D. Jaramillo, G. Stadie-Frohbös, P. Renard, M. Ventura & B. Dumas

• Développement, Implémentation, Maintenance et Futur des Règlementsstructuraux communs de l’IACS pour les Vraquiers et Pétroliers à Double Coque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .315P. Baumans

Risk enginnering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .329

• Including ergonomics in the design process to address the risks of slips, trips and falls : methodology and application . . . . . . . . . . . . . . . . . . . . . . . . . . .331N. Mery, M. Lassagne & J. McGregor

• Performance assessment of davit-launched lifeboat . . . . . . . . . . . . . . . . . . . .341L. Prat, L. de Vries & A. W. Vredeveldt

• Conception ergonomique et analyse de risque : méthodologie et application aux moyens d’accès à bord des navires . . . . . . . . . . . . . . . . . . . . . .359N. Mery & M. Lassagne

Sommaire BT2008:Sommaire BT2008 12/10/09 18:51 Page2

HYDRODYNAMICS

& HYDRO-STRUCTURE

A detailed understanding of hydrodynamics and the response of complexstructures to liquid forces is at the heart of our ability to ensure ever largerand more complex structures are both safe and efficient. The papersgrouped in this section headline the challenges faced by hydrodynamicresearchers, and the advances made. Special reference is made toadvances in understanding elastic behaviour, particularly for largecontainer ships and to dynamic coupling between vessel and tank liquid and between vessel and offshore unit structure and external fluid loads.

Bulletin Technique - Bureau Veritas 2008

ChapitresBT2008:ChapitresBT2008 05/10/09 20:54 Page1

Paper submitted to the 23rd IWWWFB, Jeju (Korea)

Computations of low-frequency wave loading

X.B. Chen1,2 and F. Rezende1

1Research Department, BV, 92077 Paris La Defense (France)Email: [email protected]

2College of Shipbuilding Engineering, HEU, 150001 Harbin (China)

As the main source of resonant excitations to most offshore moored systems like floating LNG terminals,the low-frequency wave loading is the critical input to motion simulations which are important for the design.Further to the analysis presented by Chen & Duan (2007) on the quadratic transfer function (QTF) of low-frequency wave loading, new developments including numerical results of different components of QTF arepresented here. Furthermore, the time-series reconstruction of excitation loads in the motion simulation ofmooring systems is analyzed and a new efficient and accurate scheme is demonstrated.

1. Formulations of QTF and its approximations

The quadratic transfer function (QTF) of low-frequency wave loads F(ω1, ω2) is composed of two distinctparts : one dependent only on the quadratic products of first-order wave fields and another contributed bythe second-order incoming and diffraction potentials.

F(ω1, ω2) = Fq(ω1, ω2) + Fp(ω1, ω2) (1)

Since the application of low-frequency QTF concerns generally the computation of excitation loading toa moored system whose resonant frequencies are often less than 0.05 rad/s while wave frequencies ω aregenerally larger than 0.30 rad/s, the dynamic behavior of mooring systems is sensitive only to the low-frequency QTF at small values of (ω1−ω2). In Chen & Duan (2007), it is denoted that

∆ω = ω1−ω2 and ω = (ω1+ω2)/2 then (ω1, ω2) = (ω+∆ω/2, ω−∆ω/2) (2)

By assuming ∆ω ≪ 1, the quadratic transfer function (QTF) is developed as an expansion :

F(ω1, ω2) = F0(ω, ω) + ∆ωF1(ω, ω) +O[(∆ω)2] (3)

with the zeroth-order term contributed by the quadratic products of first-order wave fields and formulated :

F0 = F0

q=ρ

2

∫∫

H

ds[

(∇φ · ∇φ∗)n − φ∗n∇φ− φn∇φ∗

]

−ρω2

2g

∮

Γ

dℓ (φφ∗)n (4)

as integration over the hull H and along the waterline Γ in their mean position. In (4), φ stands for thefirst-order velocity potential and φn = ∇φ · n the normal derivative of φ on H . The superscript ∗ indicatesthe complex conjugate. The expression (4) shows that F0 is a pure real function dependent on the wavefrequency ω, which is nothing else than the formulation of drift loads (with a factor 2 of that usually useddue to the convention here).

The O(∆ω) order term in (3) is composed of four components :

F1 = F1

q+ F1

p1 + F1

p2 + F1

p3 (5)

with one due to first-order wave fields :

F1

q= iℑ

ρ

2

∫∫

H

ds[

(∇ϕ · ∇φ∗)n − (2/ω)φ∗n∇φ− φ∗n∇ϕ+ ϕn∇φ∗

]

−ρω2

2g

∮

Γ

dℓ (ϕφ∗)n

(6)

a pure imaginary function of ω. In (6) for F1

q, we have involved the terms (ϕ,∇ϕ) which are defined as the

derivative of (φ,∇φ) with respect to ω. The contribution of second-order incoming waves and diffractionwaves of free wave type is given analytically :

F1

p1= −iρg∀4CS(k/ω)[(1+mxx) cosβ+myx sinβ, (1+myy) sinβ+mxy cosβ] (7)

in which ∀ stands for the buoyant volume, C and S dependent on wavenumber k and waterdepth h are givenin Chen (2006b), while (mxx,mxy,myx,myy) added-mass coefficients in double-body flow, dependent onlyon the hull geometry. To note (β, k, ω) are wave heading, wavenumber and wave frequency, respectively.The component F1

p1 expressed by (7) is pure imaginary dependent on the hull geometry and wave heading.

The component F1p2 is associated with the second-order correction of the boundary condition on H and

written as :

F1

p2 = −iρ

∫∫

H

dsℜ(iωx−∇φ)∧(R∗∧n) − (x·∇)∇φ∗ ·n[ψ]0 (8)

with (x,R) as the displacement vector and rotation vector, respectively. In (8), the real functions [ψ]0 aredefined as the radiation potentials at zero frequency (double-body flow) associated with the components ofthe normal vector on H . Again, F1

p2 given by (8) is a pure imaginary function.

Finally, the component representing the effect of forcing pressure over the free surface F (second-ordercorrection of the boundary condition on F ) is expressed by :

F1

p3= i(ρω/g)

∫∫

F

dsℑ

φ∂2

zzφ∗

P + k2φPφ∗

I

[ψ]0 (9)

in which (φP , φI) represent the diffraction-radiation potential and incoming wave potential, two componentsof the first-order potential φ = φI + φP .

The second-order low-frequency wave loads F(ω1, ω2) defined by (3) in bichromatic waves of frequencies(ω1, ω2) are composed of one component F0(ω) depending on ω = (ω1+ω2)/2 and another ∆ωF1(ω) linearlyproportional to ∆ω = ω1 −ω2. The striking fact is that F0(ω) is a pure real function while F1(ω) apure imaginary function. The usual approximation proposed by Newman (1974) largely used in practiceis based on the use of F0 so that it is O(1) approximation. This study confirms that not only the O(1)approximation can underestimate largely the second-order wave loads but also it provides wrong phasedifferences with respect to incoming waves since the complete QTF is a complex function while that by theO(1) approximation is purely real.

2. Time-series reconstruction of low-frequency loading

In irregular waves represented by wave energy spectrum Sηη(ω) characterized by the parameters like sig-nificant heights, peak periods and form coefficients, the elevation of free surface is written as a Fourierseries :

η(t) = ℜ

E(t)

with E(t) =N

∑

j=1

aj exp(−iωjt) (10)

and the complex amplitude :

aj = exp[ikj(x cosβ + y sinβ) + iǫj ]√

2Sηη(ωj)dωj (11)

associated with (ωj , kj , β, ǫj) the wave frequency, wave number, heading and random phase, and dependenton the position (x, y) with respect to the reference point (0, 0) and the sampling space dωj of the spectrum.The low-frequency wave loading in temporal domain is defined by a double summation :

F (t) = ℜ

N∑

i=1

N∑

j=1

Fijai a∗

j exp[−i(ωi − ωj)t]

(12)

with a∗j being the complex conjugate of aj, and Fij = F(ωi, ωj) the QTF representing the component inone degree of freedoms or a vector of wave load QTF. At each time step, the low-frequency wave loadingis evaluated to perform the time simulation of motions. Due to the double summation, the expression (12)is time-consuming. One approximation largely used in practice is called Newman’s approximation in Molin(2002) which is based on :

Fij = sign(F)√

Fii · Fjj (13)

with sign(F) the sign of wave loading which is assumed to remain the same when ωj varies. Introducing(13) into (12), the time-series reconstruction of low-frequency wave loading becomes

F (t) =

∣

∣

∣

∣

∣

∣

N∑

j=1

√

Fjj aj exp(−iωjt)

∣

∣

∣

∣

∣

∣

2

sign(F) (14)

the square of a single summation which is much more economic than the double summation (12).

Considering the fact that

F0,1(ω, ω) =[

F0,1(ωi, ωi) + F0,1(ωj , ωj)]

/2 +O[

(ωi − ωj)2]

with ω = (ωi + ωj)/2 (15)

the approximation (3) can be rewritten as

Fij = (F0

ii + F0

jj)/2 + i(ωi − ωj)(F1

ii + F1

jj)/2 (16)

with F0

jj = F0(ωj , ωj) and F1

jj = −iF1(ωj , ωj) for j = 1, 2, · · · , N so that both F0

jj and F1

jj are realfunctions.

Introducing above expression (16) into (12), the time-series reconstruction of low-frequency wave loadingcan be obtained by :

F (t) = ℜ

[

N∑

j=1

F0

jja∗

j exp(iωjt)]

E(t)

−d

dtℜ

[

N∑

j=1

F1

jja∗

j exp(iωjt)]

E(t)

(17)

involving only single summations. The derivative d(·)/dt in the compact form (17) is understood to applyonly to the factor exp(±iωjt). The first term in (17) can be considered as the variant of O(1) approximationof QTF, which is, unlike (14), not restricted by the assumption of a unique sign for QTF.

The new formulation (3) of QTF by the O(∆ω) approximation provides a novel method to evaluate thelow-frequency second-order wave loads in a more accurate than O(1) approximation and more efficient waycomparing to the computation of complete QTF. All the more interesting is that the reconstruction of timeseries of wave loads is shown to be single summations (17) by using (3) instead of a double summation (12), ifthe complete QTF (1) is used, to account all pairs of wave interactions which is much more time-consuming.

3. Numerical results and discussions

Among components of F1 in (3), the component F1

qdefined by (6) can be evaluated directly when the

terms ϕ as the derivative of first-order potential with respect to wave frequency are obtained. An indirectway consisting to evaluate the finite difference after having obtained Fq for bichromatic waves and driftcomponent F0

qby (4) can be implemented. The term F1

p1defined by (7) depending on the second-order

potential of incoming waves and hull geometry can be a dominant one for a body of large volume (∀) andin water of small depth since C ≈ (3/4)ka2/(kh)3 for kh → 0 as shown in Chen (2006b). F1

p2 given by (8)depending on first-order motions is simple and easy to evaluate, negligible for large wavenumber. Finally,F1

p3expressed by (9) is represented by an integral over the free surface which can be performed in a limited

area around the body since the integrand decreases rapidly for the radial distance R → ∞, as confirmed bythe numerical computations here.

-

6

0

2

4

6

8

10

0 50 100 150 200 250

0

45

90

90

45

0

Figure 1: Mesh on LNG hull & the free surface (left) and the integrand of F1

p3(9) in function of radial

distances and polar angles (right)

Numerical computations are performed for a standard 138 Km3 LNG vessel with the main dimensions(length, width and draft) =(274m, 44.2m and 11m), respectively. The half hull is represented by a meshcomposed of 2204 planar panels and the area of free surface around the body is meshed in an elliptic formwith a ratio of the major axis (along the axis ~ox) over the minor axis (along the axis ~oy) equal to 2. About4000 to 8000 panels are used for a major axis equal to 200m to 500m. A zoom of the hull mesh and the areaon the free surface is shown on the left part of Figure 1. Along three radial lines corresponding the polar

angles (0, 45 and 90) as indicated on the figure, the integrand of F1p3 (9) is computed for a regular wave

of ω = 0.3 rad/s in water of finite depth (15m), and depicted on the right part of Figure 1. The values ofintegrand (9) indeed decrease rapidly and F1

p3 can be obtained in a relatively easy way. Since the doublederivative φPzz cannot be evaluated with a good accuracy at a point in the vicinity of the waterline, theexpression (9) can be transformed into :

F1

p3= i(ρω/g)ℑ

∫∫

F

ds[

ψ(φxφ∗

Px+φyφ∗

Py)+φ(ψxφ∗

Px+ψyφ∗

Py)−k2φIφ∗

Pψ]

+

∮

Γ

dℓ φψ(φ∗Pxnx+φ∗Pyny)

(18)

by applying Stokes’ theorem. In (9), the line Γ includes the waterline and the exterior border of the area F .The component F1

p3 is evaluated in this way and compared with other components.

-80000

-60000

-40000

-20000

0

20000

40000

60000

80000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-2.5e+006

-2e+006

-1.5e+006

-1e+006

-500000

0

500000

1e+006

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

F0

q

−iF1

q

−iF1

p1

ℑFp1 + Fp2

−iF1

p3

ℜFq

ℑFq

Figure 2: Different components of low-frequency wave loading

The components in (4) and (5) of low-frequency wave load (3) on the LNG vessel are evaluated fora series of wave frequencies associated with ω = 0.3 rad/s and ∆ω varying from 0 to 0.16 rad/s in waterof 15m in depth. They are depicted on Figure 2. The first part dependent on the quadratic products offirst-order wave fields is shown on the left while the second part contributed by the second-order incomingand diffraction waves on the right. The real part of QTF includes only F0

q(solid line) which remains constant

for all ∆ω and is a very good approximation to the exact values - the real part of Fq represented by thecross-dashed line. The imaginary part of QTF contains 4 components. The component F1

q(dashed line)

is shown on the left together with the exact values - the imaginary part of Fq (square-dashed line). Thecomponent F1

p1(dashed line) are depicted on the right with the exact values Fp1 + Fp2 (cross-dashed line).

This indicates that F1p2 is negligible. Finally, the component F1

p3 is shown on the right by the square-dashedline.

The quadratic contribution F1q

is positive while the contribution of second-order potentials F1p1 is

negative. The component associated with the forcing effect on the free surface F1

p3is small comparing to

others. Furthermore, the component F1

p1given by the analytical expression (7) is largely dominant for

∆ω > 0.01 rad/s. Globally, the O(∆ω) approximation of QTF is excellent up to ∆ω = 0.05 rad/s and stillvery good for ∆ω ≤ 0.10 rad/s. The O(∆ω) approximation of QTF is so believed to give much better valuesof second-order low-frequency wave loading in an efficient way as described by (17) involving only singlesummations.

References[1] Chen X.B. & Duan W.Y. (2007) Formulation of low-frequency QTF by O(∆ω) approximation, Proc

22nd IWWWFB, Plitvice (Croatia).

[2] Chen X.B. (2006a) Middle-field formulation for the computation of wave-drift loads, J. Engineering

Math. DOI 10.1007/s10665-006-9074-x. 82, 59:61-82. Published online: Sep 2006.

[3] Molin B. (1979) Second-order diffraction loads upon three-dimensional bodies, Appl. Ocean Res., 1,197-202.

[4] Chen X.B. (2006b) Set-down in the second-order Stokes’ waves, Proc. 6th Intl Conf. on HydroDynam-

ics, Ischia (Italy), 179-85.

[5] Newman J.N. (1974) Second-order, slowly-varying forces on vessels in irregular waves, Proc. Intl Symp.

Dyn. Marine Vehicle & Struc. in Waves, Mech. Engng. Pub., London (UK), 193-97.

[6] Molin B. (2002) Hydrodynamique des structures offshore Editions Technip.

SIMULATION OF SECOND-ORDER ROLL MOTIONS OF A FPSO

Flavia RezendeResearch Department

Bureau Veritas (France)

Xiao-Bo ChenResearch Department

Bureau Veritas (France)Professorship, HEU (China)

Marcos D. FerreiraCENPES

PETROBRAS(Brazil)

Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE2008

June 15-20, 2008, Estoril, Portugal

OMAE2008-57405

c

e

t

ABSTRACT

The roll motions are a key parameter on the design of FPSOthat operate in moderate and severe environmental conditions.To reduce the magnitude of roll motions, some techniques basedon changing the vertical position of gravity center are usedtoput the roll natural period outside of the frequency range ofthelinear waves. However, recent model tests and also numerilcalculations have shown that the vessel may still experience largeroll motions which are considered to be induced by second-orderwave loads.

Further to the work in Rezende et al. (2007) to computthe roll response in frequency domain, new developments to per-form simulations in time domain are presented here. In this newmethod, variations of second-order roll moments dependentonthe roll and heave motions are taken into account consistently. Itis shown that, unlike the horizontal loads, the quadratic transferfunctions of the vertical loads depend on the instantaneouspo-sition of the vessel. The variation of the roll moment with theheave position of the vessel has been considered more imporantthan the variation obtained only with the inclination of thevessel.Furthermore, numerical results of roll simulations are comparedwith model tests results and presented in the paper.

NOMENCLATURE

FPSO Floating Production Storage and Offloading Unit

QTF Quadratic Transfer Function

1

s

a

INTRODUCTIONIt is observed that several FPSOs operating in different ar-

eas around the world experience large roll motions, resulting indelays and production down time. For the new constructions,the optimization of the hull geometry in order to achieve goodmotions characteristics has been an issue of major concern.Onetechnique used to limit the roll response is to design the unit suchthat the roll natural period is outside of the range of linearwaveenergy (roughly from 3s to 20s). However, recent tests for FPSOswith roll resonant periods larger than the maximal linear waveperiod have demonstrated the presence of roll response at theirnatural periods, what is attributed to non-linear mechanisms.

We consider the theory of second-order wave diffraction andradiation within which the wave loads occurring at the differ-ence of wave frequencies can be evaluated. These low-frequencywave loads are considered to be the main source of large pe-riod roll motion. Much work has been done for the prediction ofthe horizontal components of second-order loads and two classesof theories have been developed: far-field formulation based onthe momentum principle and the near-field based on the directsecond-order pressure integration on the hull surface. Thefruit-ful results have been obtained in the application to the designof mooring system. However, few works as in Pinkster et Dijk(1985) and in Chen et Molin (1989) have been pursued on thecomputation of the vertical components of second-order loadsdue to two critical issues associated with their numerical evalua-tion.

One concerns the accurate prediction of second-order wavemoments and another, the coupling of linear and second-ordermotions. Concerning the vertical components (force in the ver-tical direction and moments around the horizontal axis), the far-

Copyright c© 2008 by ASME

field formulation cannot be applied. Furthermore, since diffrac-tion and radiation velocities are singular in the zone of hull closeto sharp corners, the near-field formulation, in most cases,cannotgive convergent results. Recently, a new formulation to evaluatethe second order loads was proposed by Chen (2004), whichobtained by applying the variants of Stokes theorem and Grentheorem to a domain limited by a control surface. As this formu-lation is written on a control surface at a certain distance of thebody it is so called middle-field formulation and applicableto theevaluation of both horizontal and vertical low frequency loads.

Further to the work by Rezende et al. (2007) to computthe roll response in frequency domain, new developments to per-form simulations in time domain are presented here. In this newmethod, variations of second-order roll moments dependentonthe roll motion are taken into account consistently. It is shownthat, unlike the horizontal loads, the quadratic transfer functionsof the vertical loads depend on the instantaneous position of thevessel. The variation of the roll moment with the heave postion of the vessel has been considered more important than tevariation obtained only with the inclination of the vessel.

FORMULATION OF LOW-FREQUENCY LOADSThe low-frequency quadratic transfer function (QTF) is de

fined as the second-order wave loads occurring at the frequencyequal to the difference (ω1 − ω2) of two wave frequencies(ω1,ω2) of bichromatic waves. QTF is composed of two distincparts : one dependent only on thequadratic products of first-order wave fields and another contributed by the second-ordrpotentials of the incoming and diffracted waves. The formula-tion for the second-order forces is presented below. Its extensionto second-order moments is easy and omitted here for the sakeofspace.

F(ω1,ω2) = Fq(ω1,ω2)+ Fp(ω1,ω2) (1)

The first partFq can be written in the way presented in [11] :

Fq =ρ2

ZZ

Hds

[

(∇φ1 ·∇φ∗2)n−ω1

ω2φ∗n2∇φ1−

ω2

ω1φn1∇φ∗2

]

−ρω1ω2

2g

I

Γdℓ(φ1φ∗2)n/|cosθ|+ FS

q (2)

as integration over the hullH and along the waterlineΓ in theirmean position. In (2),φ stands for the first-order velocity poten-tial andφn = ∇φ ·n the normal derivative ofφ on H. The angleθis defined as that between the normal vectorn = (nx,ny,nz) andthe horizontal plane. The subscripts (1, 2) represent the quanti-ties associated with the wave frequencies(ω1,ω2), respectively,while the superscript∗ indicates the complex conjugate. In (2),

2

ise

e

i-h

-

t

e

the termFSq is a special component for vertical forces and mo-

ments around the horizontal axes which is written as :

FSq = −

ρg2

I

Γdℓ

[

(η1η∗2−η1Z∗

2−η∗2Z1) tanθ

− [η1(X∗2 nx +Y ∗

2 ny)+ η∗2(X1nx +Y1ny)]/cosθ

]

k

−K33(α1α∗2+β1β∗

2)Zg/2

−K34(β1γ∗2 + β∗2γ1)/4+ K35(α1γ∗2 + α∗

2γ1)/4 (3)

in which η is the wave elevation and(X ,Y,Z) are displacementsalong the waterline.(α,β,γ) are the rotations and (K33,K34,K35)the components of hydrostatic stiffness matrix. Finally,Zg is thevertical coordinate of the gravity center.

The formulation (2) derived from Eq.27 in [11] obtained byapplying the two variants of Stokes’ theorem given in [8] to theclassical near-field (pressure-integration) formulationas in [9],is compact and used here. It is directly applicable to force com-ponents in horizontal directions. The extension to other compo-nents is direct and omitted here. In (2), we involve the gradient ofvelocity potentials which is sensitive to the singularities presentin the velocity field at sharp corners. In particular, the integrationof terms(∇φ1 ·∇φ∗2) converges slowly or in the worst cases, maybe non-convergent.

In [11], after having the new near-field formulation by ap-plying the variants of Stokes’s theorem, we considered a fluidvolume enclosed by the hull, a control surface at a distance fromthe body and the mean free surface limited by the waterline andthe intersection of the control surface with free surface, and haveobtained the general formulation (Eq.8a & 8b in [11]) of second-order loads by using Gauss’s theorem. This formulation can besimplified if we construct a control surface surrounding thehulltouching the free surface only along the waterline :

Fq = (ω1−ω2)ρ2

ZZ

Hds

(

φn1∇φ∗2/ω1−φ∗n2∇φ1/ω2

)

−ρω1ω2

2g

I

Γdℓ(φ1φ∗2)n

−ρ2

ZZ

Cds

[

(∇φ1 ·∇φ∗2)n−φ∗n2∇φ1−φn1∇φ∗2]

+ FSq (4)

in whichC stands for the control surface defined as an arbitraryone surround the body.

The integration of terms(∇φ1 ·∇φ∗2) in (4) now performedon the control surfaceC converges rapidly sinceC is at some dis-tance from the hull where the velocity field does not present anysingularity. The integration on the hullH is of orderO(ω1−ω2)and as small asφn which tends to zero for large wave frequencies.The middle-field formulation (4) is used for the computationofthe first-part of second-order loadsFq in the following.


The second partFp is expressed in the way [7] :

Fp =−i(ω1−ω2)ρZZ

Hds

φ(2)I n− (φ(2)

In −NH)[ψ]

+ i(ω1−ω2)ρg

ZZ

FdsNF [ψ] (5)

in which the first term in the hull integral corresponds to thesecond-order Froude-Krylov component contributed by the in-

coming wave potentialφ(2)I defined by :

φ(2)I = ia1a2Ag2coshkm(z+h)

coshkmheikm(xcosβ+ysinβ)+i(ε1−ε2)

gkm tanhkmh− (ω1−ω2)2 (6)

with km = k1− k2 and(ε1,ε2) being the phases of first-order in-coming waves associated with(ω1,ω2), respectively. In (6),A iswritten :

A =ω1−ω2

ω1ω2k1k2[1+ tanhk1h tanhk2h]

+12

(

k21/ω1

cosh2 k1h−

k22/ω2

cosh2 k2h

)

(7)

where we have used the notations(a1,a2) and (k1,k2) stand-ing for the wave amplitudes and wavenumbers associated wit(ω1,ω2) via the dispersion equationk1,2 tanhk1,2h = ω2

1,2/g withthe waterdepthh, respectively, while the wave heading with re-spect to the positivex-axis is denoted byβ.

The second term in the hull integral of (5) and the term defined by the integral over mean free surfaceF come from theapplication of Haskind relation and represent the contribution ofthe second-order diffraction potential, as shown in [7]. The terms(NH ,NF ) are the second members of the boundary conditionsatisfied by the second-order diffraction potential on the hull Hand the mean free surfaceF , respectively. They are written as :

2NH =−(x1 ·∇)∇φ∗2 ·n− (x∗2 ·∇)∇φ1 ·n

(iω2x∗2−∇φ∗2) · (R1∧n)− (iω1x1+∇φ1) · (R∗2∧n) (8)

and

NF = i(ω1−ω2)(∇φ1 ·∇φ∗P2+ ∇φP ·∇φ∗I2)

−iω1

2g

[

φ1(−ω22∂z+g∂2

zz)φ∗P2 + gk2

2(1−tanh2 k2h)φP1φ∗I2)]

+iω2

2g

[

φ∗2(−ω21∂z+g∂2

zz)φP1 + gk21(1−tanh2 k1h)φ∗P2φI1)

]

(9)

3

h

-

s

in which x is the displacement vector at a point onH andR thevector of rotations. In (9),φI represents the first-order potentialof incoming waves whileφP = φ−φI stands for that of perturba-tion including the diffraction and radiation components. Finally,[ψ] in (5) represents a vector of first-order radiation potentials os-cillating at the difference frequency(ω1−ω2). They satisfy thehomogeneous condition :

[

−(ω1−ω2)2 + g∂z

]

[ψ] = 0 (10)

on the mean free surfaceF and

∂n[ψ] = n (11)

on the hullH.The full QTF (1) is composed of two parts(Fq,Fp) given

by the formulations (2) and (5), respectively. The formulation(2) for Fq derived in [11] is simpler than that in [9]. The for-mulation (5) forFp by [7] is often calledindirect method sinceit provides a way to evaluate the contribution from the second-order diffraction potential through the Haskind relation such thatthe second-order diffraction potential is not explicitly computed.

SECOND-ORDER ROLL MOTIONSWe are limited to study the roll motion of FPSO in beam

sea and assume that the coupling with other motions affects onlythe excitation moments. The equation of roll motions under anarbitrary excitation containing a convolution of its impulsive re-sponse for taking account of memory effect is written as :

[I + Ia(∞)]θ+

Z t

0Θ(t − τ)θdτ+ Bvθ+ Kθ = M(t) (12)

with the memory functionΘ(t) defined by :

Θ(t) = −2π

Z ∞

0[Ia(ω)− Ia(∞)]sin(ωt)dω (13)

involving the added inertial coefficientIa(ω) due to radiationwave fields. The terms(I,Bv,K) are roll inertia in air, viscousdamping and hydrostatic stiffness, respectively.

In (12), the excitation roll momentM(t) is composedof the first-order momentM(1)(t) and second-order momentM(2)(t,θ,Z0+ζ) which is sensible to the mean position of FPSO,i.e. the roll angleθ and the vertical position including the heavemotionζ :

M(t) = M(1)(t)+ M(2)(t,θ,Z0 + ζ) (14)


with Z0 the mean vertical position. Since the wave frequencieare much higher than the roll resonant frequency, the roll motionis not sensible to the first-order excitation moment. We may takeonly the second-order moment in (14) and the motion equatican be approximated by :

[I + Ia(Ω)]θ + [Br(Ω)+Bv]θ + Kθ = M(2)(t,θ,Z0 + ζ) (15)

with Ω equal to the frequency of roll resonance. The termBr(Ω)is the radiation damping in roll.

Further to the work in frequency domain by Rezende et a(2007), we simulate here the roll motion in time domain. In irreg-ular waves represented by wave energy spectrumSηη(ω) charac-terized by the parameters like significant heights, peak periodsand form coefficients, the elevation of free surface is written as aFourier series :

η(t) = ℜ N

∑j=1

a j exp(−iω jt)

(16)

and the complex amplitude :

a j = exp[ik j(xcosβ + ysinβ)+ iε j]√

2Sηη(ω j)dω j (17)

associated with (ω j,k j,β,ε j) the wave frequency, wave number,heading and random phase, and dependent on the position(x,y)with respect to the reference point(0,0) and the sampling spacedω j of the spectrum.

The heave motionζ(t) involving in the vertical mean posi-tion can be obtained by the Fourier series :

ζ(t) = ℜ N

∑j=1

X3(ω j)a j exp(−iω jt)

(18)

with X3(ω) the heave RAOs.The low-frequency roll moment in temporal domain is de

fined by a double summation :

M(2)(t,θ) = ℜ N

∑i=1

N

∑j=1

F(ωi,ω j,θ,Z0+ζ)ai a∗je−i(ωi−ω j)t

(19)with a∗j being the complex conjugate ofa j, andF(ωi,ω j,θ,Z0+ζ) the QTF of roll moments evaluated by the formulations (4) an(5). In fact, the QTF is pre-computed at several mean positions(θk,Zm) with k,m = 1,2, · · · . in a range of values ofθmin ≤ θk ≤θmax andZmin ≤ Zm ≤ Zmax. At each time step, the low-frequencyQTF depending on (θ,Z0 + ζ) is obtained by interpolation fromthe table ofF(ωi,ω j,θk,Zm).

4

s

on

l.

-

d

NUMERICAL RESULTS AND COMPARISONSIn the following a comparison between the numerical com-

putations and the model tests results is presented for one oftheconcept designs of FPSOBR from Petrobras. The model testswere performed at the University of Sao Paulo-Brazil.

The table 1 presents the dimensions and hydrostatic charac-teristics of the FPSO. The scale of the model was 1:90 and it wasconnected to the basin by means of a horizontal mooring system,designed not to influence the behavior of the unit. Figure 1 belowrepresents the positioning of the model and of the sensors inthebasin, whereA andB are wave probes located close to the wavegenerator and to the model respectively;C are load cells locatedat the extremity of the mooring lines andD are the measurer ofthe model motions.

For the purpose of numerical solution, a frequency domainanalysis has been performed for different positions of the ves-sel, in order to obtain the quadratic transfer functions of roll mo-ment. The low-frequency roll motions of the vessel have beencalculated in time domain by considering the interpolated QTFat each time step depending on the instantaneous position ofthevessel. First, only the inclinations around the mean heave po-sition have been taken into account. Then, the influence of theheave motion on the second order roll moment has been includedby considering inclinations around different heave positions. Ina total, fifteen positions have been considered (five inclinationsaround three drafts).

For the diffraction-radiation calculation, the hull wetted sur-face has been meshed by quadrilateral panels. The total numberof panels used is 4028. A mesh has been generated for each po-sition. Three drafts have been used corresponding to three heavepositions (18.94m, 21.94m and 25.94m), and five inclinationsvarying from -8.0deg to 8.0deg with a step of 4deg. The fig-ure 2 represents the mesh for a given position of the vessel. Forthe calculation of the second order roll moment, the middle fieldformulation has been applied and a control surface has been gen-erated, which is illustrated on Figure 3.

Figures 4 and 5 present the comparison between the RAOsof heave and roll derived from numerical calculations and modeltests.

The figures 6 and 7 present the second order roll moments,real and imaginary parts, calculated at the upright position of theFPSO (solid line) and at inclined positions, 4.0deg and 8.0deg(dashed and dot-dashed lines,respectively), for a draft corre-sponding to the mean position of heave (-0.4m). The figures8 and 9 present the second order roll moments calculated atthree different drafts corresponding to different heave positions(-4.0m, -0.4m and 3.0m), being -0.4m the mean heave positionof the vessel obtained from model tests.

A time domain analysis has been performed in order to cal-culate the second order roll motions of the FPSO. The time se-ries of roll motions with and without considering the effects ofthe varying position of the FPSO are presented on figure 10


by dashed and solid line, respectively. The sea state used inthe calculations is represented by a JONSWAP spectrum, withHs=5.5m, Tp=10.76s andγ = 1.54.

The statistical parameters in table 2 have been derived fromthe computed time series of roll motions and compared to thoseobtained from the model tests.

CONCLUSIONSIn this paper the formulations used to compute the quadratic

transfer functions of second order roll moment in frequencydo-main and roll motions in time domain have been presented.

The application to FPSOBR illustrates well the phe-nomenum of large roll motions ocurring in irregular waves, al-though the roll resonant period is larger than the maximum pe-riod of wave energy such that the linear excitation is negligible.Additionally, it has been shown that, unlike the horizontalloads,the quadratic transfer functions of the vertical loads depend onthe instantaneous position of the vessel. For the specific case ofFPSOBR, the variation of the roll moment with the heave posi-tion of the vessel has been considered more important than thevariation obtained only with the inclination of the vessel.Theagreement between the numerical results with the model tests isgenerally good. Including the effects of the heave motions on theroll motions calculations have significantly improved the results.

REFERENCES[1] REZENDE F., CHEN X.B. & FERREIRA M.D. Second Or-

der Roll Motions for FPSO’s operating in Severe Environ-mental Conditions.Proc. OTC Conf, Houston, USA, paperNo.18906.

[2] PINKSTER J.A.& VAN DIJK A.W (1985) Wave driftforces on large semi-submersiblesJoint Industry ProjectsNSMB,

[3] CHEN X.B. & M OLIN B. (1989) Numerical prediction ofsemi-submersible non-linear motionsIntl Symp. on Num.Ship Hydrodynamics, Hiroshima (Japan).

[4] CHEN X.B. (2004) Hydrodynamics in Offshore and NavalApplications - Part I.Keynote lecture at the 6th Intl Confer-ence on Hydrodynamics, Perth (Australia).

[5] M OLIN B. (1979a) Computations of wave drift forces.Proc. OTC Conf., Houston (USA), paper No.3627.

[6] L IU Y.H. (2003) On second-order roll motions of ships.Proc. OMAE03, Cancun (Mexico).

[7] M OLIN B. (1979b) Second-order drift forces upon largebodies in regular waves.Proc. BOSS’79., London (UK),363-70.

[8] DAI Y.S. (1998) Potential flow theory of ship motions in

waves in frequency and time domain (in Chinese).Press ofthe National Defense Industries, Beijing (China).

[9] PINKSTER J.A. (1980) Low frequency second order waveexciting forces on floating structures.H. Veenman En ZonenB.V. - Wageningen (The Netherlands).

[10] FERREIRA M.D. & L EE C.H. (1994) Computation ofsecond-order mean wave forces and moments in multibodyinteraction.Proc. 7th Intl Conf. Behaviour Off. Structures,BOSS’94, Boston (USA)2, 303-13.

[11] CHEN X.B. (2006) Middle-field formulation for the com-putation of wave-drift loadsJournal of Engineering Math-ematics.

5 Copyright c© 2008 by ASME

Table 1. Main Characteristis of FPSOBR

Description Symbol Unit Magnitude

Length L m 320.00

Breadth B m 51.00

Draft mean T m 21.50

Displacement ∆ tf 308000

Metacentric heightincluding correction FS

GM m 4.50

Radius of Gyration

-transverse Rxx m 19.66

-longitudinal Ryy m 80.38

-vertical Rzz m 82.57

Figure 1. Sketch of the basin

Figure 2. Mesh: Draft 21.94m - Upright

6

Figure 3. Mesh: Control Surface Mesh for Middle Field Computation

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

8 10 12 14 16 18 20 22 24 26

RA

O o

f hea

ve (

m/m

)

Wave Period (s)

NumericalModel Tests

Figure 4. RAO of heave

0

1

2

3

4

5

6

7

8

8 10 12 14 16 18 20 22 24 26

RA

O o

f rol

l (de

g/m

)

Wave Period (s)

NumericalModel Tests

Figure 5. RAO of roll


-30000

-20000

-10000

0

10000

20000

30000

0 0.2 0.4 0.6 0.8 1

Rol

l Mom

ent -

rea

l par

t (kN

.m/m

2)

Wave Frequency (rad/s)

Upright ConditionInclination=4.0degInclination=8.0deg

Figure 6. Second order roll moment - real part: effect of inclination

-40000

-30000

-20000

-10000

0

10000

0 0.2 0.4 0.6 0.8 1

Rol

l Mom

ent -

imag

inar

y pa

rt (

kN.m

/m2)


Upright ConditionInclination=4.0degInclination=8.0deg

Figure 7. Second order roll moment - imaginary part: effect of inclination

-40000

-30000

-20000

-10000

0

10000

20000

30000

0 0.2 0.4 0.6 0.8 1

Rol

l Mom

ent -

rea

l par

t (kN

.m/m

2)


Upright Condition;Heave=-0.4mUpright Condition;Heave=-4.0mUpright Condition;Heave=3.0m

Figure 8. Second order roll moment - real part: effect of heave

7

-40000

-30000

-20000

-10000

0

10000

0 0.2 0.4 0.6 0.8 1

Rol

l Mom

ent -

imag

inar

y pa

rt (

kN.m

/m2)


Upright Condition;Heave=-0.4mUpright Condition;Heave=-4.0mUpright Condition;Heave=3.0m

Figure 9. Second order roll moment - imaginary part: effect of heave

-5

-4

-3

-2

-1

0

1

2

3

4

5

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Rol

l (de

g)

Time (s)

Without effect of instantaneous positionWith effect of instantaneous position (roll and heave)

Figure 10. Time series of roll motions

Table 2. Statistical values of roll motions

Parameter Withoutpositioneffects

WithEffectsof roll

WithEffectsof roll +Heave

ModelTests

Mean(deg)

0.002 0.002 -0.116 -0.39

Stand.Dev.(deg)

0.990 0.985 1.146 1.280

Signif.Value(deg)

3.944 3.922 4.540 4.690

Tz (s) 21.20 21.52 21.18 21.81


CONSISTENT HYDRO-STRUCTURE INTERFACE FOR EVALUATION OF GLOBALSTRUCTURAL RESPONSES IN LINEAR SEAKEEPING

Sime MalenicaResearch Department


Estelle StumpfResearch Department


Francois-Xavier SiretaResearch Department


Xiao-Bo ChenResearch Department




OMAE2008-57077

E

---

-

,

INTRODUCTION

The difficulties related to the equilibration of the 3D Fstructural model, in the context of hydro-structure interactions inlinear seakeeping are discussed. Different philosophies in modeling the structural and hydrodynamic parts of the problem,usually lead to very different meshes (hydro and structure) which results in unbalanced structural model and consequently in dubt-ful results for structural responses. The procedure usually em-ployed consists in using different kinds of interpolation schemeto transfer the total hydrodynamic pressure from hydrodynmicpanels to the centroids of the structural finite elements. This approach is both, very complex for complicated geometriestalso rather inaccurate. The method that we propose here issedon two main ideas:

1. Pressure recalculation instead of interpolation2. Separate transfer of different pressure components (incident

diffraction, radiation & hydrostatic variation)

The first point removes the difficulties related to the interpola-tion techniques, and allows for a very robust method of preuretransfer. The second point ensures the perfect equilibriumbe-cause the body motions are calculated after integration ovr thestructural mesh, which means that the equilibrium is impliitly

M

o

sa

, buba

ss

ec

imposed. It should be noted that this procedure is not completelystraightforward and several numerical ”tricks” need to be intro-duced. However, once these difficulties are solved, the finalnu-merical code is extremely robust and can be easily coupled withany of the general 3D FEM packages.

LINEAR SEAKEEPING ANALYSIS

Before considering the hydro-structure interaction problemin more details, and for the sake of clarity, first we briefly de-scribe the basics of the seakeeping model which is used in mostof the seakeeping tools based on Boundary Integral Equationtechniques.The problem is formulated in frequency domain under the poten-tial flow assumptions. The total velocity potential is decomposedinto the incident, diffracted and 6 radiated components:

ϕ = ϕI +ϕD − iω6

∑j=1

ξ jϕR j (1)

where :


ϕI - incident potential

ϕD - diffraction potential

ϕR j - radiation potential

ξ j - rigid body motions

At the same time, the corresponding dynamic pressure is foundfrom the linear Bernoulli equation, and the similar decomposi-tion is adopted:

p = iωρϕ = pI + pD +6

∑j=1

ξ j pR j (2)

In order to obtain the the total hydrodynamic pressure, the dy-namic variation of the hydrostatic pressure should also be addedto the above expression:

phs = −ρg[ξ3 +ξ4(Y −YG)−ξ5(X −XG)] (3)

where the subscript ”G” denotes the position of the center ofgravity, with respect to which the motion equation is written.

It is important to note that the motion equation is writtenin the so called earth fixed reference system, or in the systemparallel to it, if the body is animated with forward speed. For thatreason the restoring matrix is not obtained directly by integrationof the hydrostatic pressure (3), but also the change of the normalvector should be taken into account.

Fhs = [ C ]ξ =∫ ∫

SHB

[phsn−ρgZΩ∧ndS] (4)

whereΩ denotes the rotational component of the motion vec-tor Ω = (ξ4,ξ5,ξ6), andSH

B denotes the hydrodynamic mesh ofthe wetted body surface. Note that the compact notation is usedthroughout whole the paper, so that the normal vectorn denotes(nx,ny,nz) for i = 1,3 , and(R−RG)∧n for i = 4,6.After integrating the pressure over the wetted body surface, thecorresponding forces are obtained and the rigid body motionequation, in frequency domain, is usually written in the followingform:

(

−ω2([ M ]+ [ A ])− iω[ B ]+ [ C ])

ξ = FDI (5)

where:

[ M ] - genuine mass matrix

[ A ] - added mass matrix

[ B ] - damping matrix

[ C ] - hydrostatic restoring matrix

FDI - excitation force vector

2

The final expressions for the excitation, added mass and dampingcoefficients are:

FDIi = iωρ

∫ ∫

SHB

(ϕI +ϕD)nidS (6)

ω2Ai j + iωBi j = ρω2∫ ∫

SHB

ϕR jnidS (7)

Note also that, in the general case, the total restoring matrix isa sum of the pressure part (4) and the gravity part which is zeroin the present case because the motion equation is written withrespect to the center of gravity.

Solution of the boundary value problems

Within the Bureau Veritas’s numerical code HYDROSTAR,the Boundary Integral Equation (BIE) method based on sourceformulation, is used to solve the Boundary Value Problems(BVP) for different potentials (see Chen(2004)).In the case of zero forward speed, the general form of the BVPis:

∆ϕ = 0 in the fluid

−νϕ +∂ϕ∂ z

= 0 z = 0

∂ϕ∂n

= Vn on Sb

lim[√

νR(∂ϕ∂R

− iνϕ)]

= 0 R → ∞

(8)

whereVn denotes the body boundary condition which dependson the considered potential:

∂ϕD

∂n= −

∂ϕI

∂n,

∂ϕR j

∂n= n j (9)

Within the source formulation, the potential at any point inthe fluid is expressed in the following form:

ϕ =∫ ∫

SHB

σGdS (10)

whereG stands for the Green function, andσ is the unknownsource strength which is found after solving the following inte-gral equation:

12

σ +∫ ∫

SHB

σ∂G∂n

dS = Vn , on SH

B (11)


This equation is solved numerically, after discretizing the wet-ted part of the body into a number of flat panels over whichconstant source distribution is assumed.

LOADING OF THE STRUCTURAL MODEL

The loading of the structural model is composed of twparts:

1. Inertia loads2. External pressure loads

Inertia loads can be included straightforwardly by associating theacceleration vector to each finite element. Concerning the pres-sure loading, most of the methods nowadays use the differenin-terpolation schemes in order to transfer the total hydrodynamicpressure (2,3) from hydro model (centroids of the hydro panls)to the structural model (centroids or nodes of finite elemens).Besides the problems of interpolation, it is important to note thatthe motion amplitudes, which are present in the definition ofthetotal pressure, were calculated after integration over thehydrody-namic mesh. For that reason it is impossible to obtain the c-pletely equilibrated structural model. Indeed, the FEM moelhas its own integration procedure which is usually different.As briefly stated in the introduction, in order to obtain the perfectequilibrium of the structural model we introduce two main ideas:

1. Recalculation of pressure in structural points, insteadof in-terpolation

2. Separate transfer of pressure components, and calculonof hydrodynamic coefficients (added mass, damping, hydstatics & excitation) by integration over the structural mesh

Here below we discuss these two points in more details.

Hydrodynamic pressure

What we propose here for transfer of the pressure fromdrodynamic model to the structural model, is to recalculatethepressure at the required locations instead of interpolating it fromhydrodynamic model (see Blandeau et al.(1999)). This becoespossible thanks to the particularities of the BIE method whchgives the continuous representation of the potential through thewhole fluid domainZ < 0. In this way the communication between the hydrodynamic and structural codes is extremely sm-plified. Indeed, it is enough for the structural code to give the co-ordinates of the points where the potential is required and the hy-drodynamic code just evaluates the corresponding potential by:

ϕ(xs) =∫ ∫

Hσ(xh)G(xh;xs)dS (12)

SB

the

o

t

et

omd

atiro-

hy-

mi

-i

where xs = (xs,ys,zs) denotes the structural point andxh =(xh,yh,zh) the hydrodynamic point.

In the case of linear seakeeping without forward speed, thisoperation is sufficient because the pressure is directly propor-tional to the velocity potential and, within the source formula-tion, the potential is continuous across the body wetted surface.This is very important point because, due to the differencesin thehydrodynamic and structural mesh, the structural points mightfall inside the hydrodynamic meshes.Once each pressure component has been transfered onto thestructural mesh, the ”new” hydrodynamic coefficients are cal-culated by integration over the structural mesh:

FDIS

i = iωρ∫ ∫

SSB

(ϕS

I +ϕS

D)nidS (13)

ω2AS

i j + iωBS

i j = ρω2∫ ∫

SSB

ϕS

R jnidS (14)

where the superscript ”S ” indicates that the quantities are takenon the structural mesh.

Hydrostatic pressure variations

Here we concentrate on the calculation of the hydrostaticrestoring matrix which is obtained after the integration ofthehydrostatic pressure variations due to the body motions (3). Theprocedure is rather similar to the hydrodynamic pressure, and wejust need to integrate the expression (3) over the structural mesh.For the sake of clarity, let us first rewrite the hydrostatic pressurevariations in the following compact form:

phs =6

∑j=1

ξ j phsj (15)

where:

phs1 = 0 , phs

2 = 0 , phs3 = −ρg (16)

phs4 = −ρg(Y −YG) , phs

5 = ρg(X −XG) , phs6 = 0 (17)

With these notations, the first part of the hydrostatic restor-ing matrix becomes:

Cpi j =

∫ ∫

Sphs

j nidS (18)
SB

In order to obtain the complete hydrostatic restoring matrix, oneadditional term accounting for the change of coordinate systemshould be added to the above expression as shown in equat(4). In the earth fixed coordinate system, this additional termis accounted for by the change of the normal vector (4). However, the structural response is calculated in the body fixedcoor-dinate system in which the normal vector do not change. It cabe shown (e.g. see Malenica(2003)) that, in the body fixed cordinate system, the change of normal vector is equivalent to thechange of the gravity action, so that we can write:

Fg = −mgΩ∧ k = [ C ]gξ (19)

where the only non zero elements of the matrix[ C ]g

areCg

24andC

g

15 which will be canceled by the contributions implicitlypresent in[ C ]

p.

The total restoring matrix becomes:

[ C ]S= [ C ]

p+[ C ]

g(20)

where the superscript ”S ” indicates that the pressure related parwas calculated by integration over the structural mesh.

Motion equation and final loading of the structuralmodel

The final motion equation can now be rewritten in the form

(

−ω2([ M ]+ [ A ]S)− iω[ B ]

S+[ C ]

S)

ξS= FDI

S(21)

Solution of this equation gives the body motionsξSso that the

total linear pressure can be written in the form

pS= p

S

I+ p

S

D+

6

∑j=1

ξS

j (pS

R j+ p

hs

j) (22)

In summary the final loading of the structural model will be com-posed of the following 3 parts:

−ω2miξS

i - Inertial loading

pS

i - Pressure loading

−migΩS∧ k - Gravity term

The inertial loading and the gravity term are to be applied oeach finite element. The pressure loading is to be applied onyon wetted finite elements. It is clear that the above structural

4

ion

-

no-

t

:

nl

loading will be in perfect equilibrium because this equilibrium isimplicitly imposed by the solution of the motion equation (21) inwhich all different coefficients were calculated by using directlythe information from the structural FEM model.

Seakeeping problem with forward speed

In the case of the body advancing with forward speed inwaves, the situation is slightly more complicated because the hy-drodynamic pressure is no more directly proportional to thepo-tential but also to its gradient. There are several methods in useto solve the linear seakeeping problem with forward speed, butit seems that, up to now, none of them is fully consistent. Any-way, regardless of the approximations and the method which isused to solve the BVP with forward speed, the main difficultiesrelated to pressure transfer are the same. In order to illustratethem, we choose the simplest case of the so called encounter fre-quency approximation. According to this method the effectsofforward speed are mainly taken into account through the changeof excitation frequency. The body moving with constant speedUin waves with frequencyω coming with incidenceβ , will expe-rience the excitation at the encounter frequencyωe:

ωe = ω −νU cosβ (23)

whereν represents the wave numberν = ω2/g.At the same time, since the problem is described in the coor-dinate system steadily moving with the body speedU , the timederivative in the Bernoulli equation, changes to:

∂∂ t

→DDt

=∂∂ t

−U∂∂x

(24)

so that the expression for linear hydrodynamic pressure be-comes:

p = iωeρϕ +ρU∂ϕ∂x

(25)

The problem with the gradient of the potential, in the contextof source formulation of BIE, is that the gradient is discontinu-ous across the hydrodynamic mesh, so that the recalculationofthe pressure on structural points will likely lead to discontinu-ities in the pressure distribution. This means that a preprocessingof the structural points is necessary i.e. these points needs tobe artificially moved to the exterior of the hydrodynamic model.Strictly speaking, structural points do not change their position


-

s

but the pressure associated to them is calculated in the pointswhich are slightly moved off their original position. The errorintroduced by these manipulations remains negligible within thelimits of the linear theory considered here.

NUMERICAL IMPLEMENTATION

The calculation of the hydrodynamic coefficients (addedmass, damping, excitation & restoring) by integration overthestructural mesh (13,14,18) can be done in different ways anusually depends on the type of finite elements that are used bFEM solver. Here below we propose two methods of integration, the first one which is completely independent of the type ofthe FEM package and the second one which apply for the motypical shell elements.

Fully independent numerical integration over struc-tural mesh

In this method, the hydrodynamic coefficients are obtainedafter solving the additional structural problems for differentpressure loadings. The general scheme is shown in FigureDifferent modules and associated interface files are enumeratedbelow:

AMGHydrodynamic mesh generator.

HYDROSTARHydrodynamic seakeeping code.

NASTRANStructural 3D FEM code.

LISACode for preprocessing of the structural points.

MARGECode for solving the motion equation and for definition ofthe final loading.

<>-H.MSHFile containing the hydrodynamic mesh data.

<>-S.MSHFile containing the structural mesh data.

<>.PPIFile containing the preprocessed structural points.

5

dy

t

1.

<>.PRSFile containing the different pressure components for eachstructural point.

<>.LOAFile containing the final structural loading.

<>.HSIGeneral input file for HYDROSTAR (frequencies, inci-dences, speed ...).

<>.RFOFile containing the reaction forces.

<>.OUTNASTRAN output files.

Figure 1. General coupling scheme for fully independent solution.

Within this method, the structural model is put onto artificial sup-ports and loaded by the external loads corresponding to the dif-ferent pressure parts (diffraction, radiation, hydrostatics). Thehydrodynamic coefficients are deduced from the reaction forcesafter solving corresponding structural response. In total17 load-ing cases need to be considered: 2 for diffraction and incidentpressure, 12 for radiation pressures and 3 for hydrostatic pres-sure variations. The boundary conditions at the supports can bechosen rather arbitrarily, as far as they define an isostaticsystemi.e. only 6 additional unknowns are introduced. For example,referring to the Figure 2 and assuming that the structural modelwas loaded by the real part of the ”pitch pressure”ℜpR5, theadded mass coefficientA35 will be A35 = R1Z +R2Z +R3Z.


Z

Y

X

R1Z

R3Y

R2X

R3Z

R1Y

R2Z

Figure 2. Possible supports definition.

The obvious disadvantage of this approach is the necessity tosolve for additional 17 loading cases by FEM solver. The mainadvantage is the perfect equilibrium of the model regardless ofthe FEM package which is used.

Typical numerical integration over the structural mesh.

Within this method, the pressure integration is still per-formed over the structural mesh, but only the most typical fi-nite elements are considered. The advantage of the method ithat there is no necessity to solve for additional structural load-ing cases and hydrodynamic coefficients are calculated outsidethe FEM package (MARGE module in this case). The disadvan-tage is that the small disequilibrium might persist for the FEMcodes which use a different integration scheme. However, thisdisequilibrium is likely to be very minor so that probably thismethod will remain as the most efficient one. The general cou-pling scheme is shown in Figure 3. As we can see the procedureis significantly simplified and can easily be adapted to any par-ticular FEM package.

NUMERICAL RESULTS AND DISCUSSION

Here below, we present few numerical results showing theefficiency of two proposed approaches. The example which waschosen is the 7800 TEU Container ship. The correspondingstructural and hydrodynamic meshes are shown in Figure 4. InFigures 5 and 6, the added mass coefficients, damping coefficients, excitations and motion RAO’s are presented. FEM-M1denotes the results obtained after integration over the structural

6

s

-

Figure 3. General coupling scheme for typical FEM package.

mesh using the fully independent method, and FEM-M2 thoseobtained using the typical integration method, as explained inthe previous sections.

Figure 4. Hydrodynamic and structural mesh of container ship.


0

1e+008

2e+008

3e+008

4e+008

5e+008

0 0.2 0.4 0.6 0.8 1 1.2 1.4

A_3

3 [k

g]

omega [rad/s]

HydrostarFEM_M1FEM_M2

0

1e+009

2e+009

3e+009

4e+009

5e+009

6e+009

7e+009

8e+009

9e+009

1e+010

0 0.2 0.4 0.6 0.8 1 1.2 1.4

A_4

4 [k

gm^2

]

omega [rad/s]


0

1e+007

2e+007

3e+007

4e+007

5e+007

6e+007

7e+007

8e+007

9e+007

0 0.2 0.4 0.6 0.8 1 1.2 1.4

B_3

3 [k

g/s]

omega [rad/s]


0

5e+008

1e+009

1.5e+009

2e+009

2.5e+009

0 0.2 0.4 0.6 0.8 1 1.2 1.4

B_4

4 [k

gm^2

/s]

omega [rad/s]


Figure 5. Added mass and damping coefficients.

0

2e+007

4e+007

6e+007

8e+007

1e+008

1.2e+008

1.4e+008

0 0.2 0.4 0.6 0.8 1 1.2 1.4

F_3

[N]

omega [rad/s]


0

5e+007

1e+008

1.5e+008

2e+008

2.5e+008

3e+008

0 0.2 0.4 0.6 0.8 1 1.2 1.4

F_4

[Nm

]

omega [rad/s]


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

xi_3

[m/m

]

omega [rad/s]


0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 0.2 0.4 0.6 0.8 1 1.2 1.4

xi_4

[rad

/m]

omega [rad/s]


Figure 6. Excitation forces and RAO’s forβ = 45o.


As we can see the agreement between two method of pres-sure transfer is excellent and the data are on top of each other.This is due to the fact that, in the case of NASTRAN FEM solver,the integration over the structural mesh is performed exactly inthe same way by MARGE and by NASTRAN itself. The dif-ferences which exist between FEM and Hydrostar results are ex-pected and are due to the differences in two meshes (hydro andstructure). These differences are exactly the ones which ensurethe equilibrium of the structural model! The fact that thesedif-ferences are not very important shows that the overall couplingprocedure is very efficient.

CONCLUSIONS

As far as the linear seakeeping analysis is concerned, thefully consistent transfer of hydrodynamic loading from hydrody-namic model to the 3D FEM structural model is never perfect,even if the two meshes coincide. However, depending on themethod of pressure transfer, the coupling can be more or lessef-ficient/consistent. The main difficulty lies in the fact thattwomeshes (hydro and structural) are usually very different, whichends up with the unbalanced structural model if the couplingpro-cedure is not correctly performed. In this paper we presentedtwo methods which both lead to completely equilibrated struc-tural model. They can easily be adapted to any of the structuralFEM packages.

ACKNOWLEDGEMENTS

Important part of this work was done under theMARSTRUCT European project.

REFERENCES[1] BLANDEAU F., FRANCOIS M., MALENICA S. & CHEN

X.B. 1999. : ”Linear and non-linear wave loads on FPSO-s.”, In Proc. of ISOPE99, Brest, France.

[2] CHEN X.B. 2004. : ”Hydrodynamics in Offshore andNaval applications”, Proc. Int. Conf. on Hydrodynamics,Perth, Australia.

[3] M ALENICA S. 2003. : ”Some aspects of hydrostatic cal-culations in linear seakeeping”, In Proc. of NAV Conf.,Palermo, Italy.

[4] M ALENICA S., STUMPF E., DELAFOSSEV., CHEN X.B.& SENJANOVIC I. 2006. : ”Some aspects of hydro-structure interfacing in seakeeping.”, In Proc. of ISOPE06,San Francisco, US.


23rd IWWWFB, Jeju, Korea 2008

EFFECTS ON SLOSHING PRESSURE DUE TO THE COUPLING BETWEEN

SEAKEEPING AND TANK LIQUID MOTION

Louis Diebold, Eric Baudin, Jacqueline Henry, Mirela Zalar Bureau Veritas - Marine Division, France

INTRODUCTION The influence of dynamic coupling due to the interactions between ship motions and tank liquid motion on the pressure levels on tank boundaries is here investigated by experimental means, using 6 d.o.f. test rig and 1/70 scaled tank model of standard LNG Carrier. Vessel response, given as “traditional” non-coupled and “realistic” coupled motions are obtained by numerical calculations performed with Bureau Veritas hydrodynamic software HydroStar® in frequency domain, as shown in [1]. First the theoretical background of linear coupling in frequency domain is briefly summarized in the first part of this abstract. Then, the numerical results of coupled vessel response are validated trough the comparisons with basin model-test results using the vessels model with incorporated tanks filled with water [4]. Confidence in our validated model for numerical coupling permits further investigation of more realistic case corresponding to the expected partial filling operation of LNG Carrier in a site specific environmental conditions. For this configuration, sloshing effects induced by coupled and non-coupled vessel motion, introduced as the excitation to 6 d.o.f. small-scale model test rig, are presented in a comparative manner. Statistics of sloshing events recorded for coupled/non-coupled motions and for harmonic/random excitations are presented in this abstract and compared. For a lack of space, the figures of the random excitations results will be presented during the workshop. This work presents the initial stage in investigation of the consequence induced by coupled motion. MOTION CALCULATIONS Recent analyses on the dynamic coupling between liquid motions in ship’s tanks (sloshing) and rigid body motions of the ship (seakeeping) can be categorized in two groups: frequency domain ([1], [6]) and time domain approaches ([7][8]). The frequency domain approach is here considered. The problem is formulated under the classical assumptions of linear potential theory and Boundary Integral Equations method is used to solve both sloshing and seakeeping hydrodynamic part. We consider the sloshing and seakeeping parts separately and after coordinates transformation for the sloshing problem, the motion equation of the coupled system is written.

Seakeeping In the classical linear rigid body seakeeping analysis we end up with the motion equation in the form:

[ ] [ ]( ) [ ] [ ]( ) DIQQQQQQ i FξCBAM =+−+− ωω 2 (1)

ξQ - rigid body ship motions [MQ] - genuine mass matrix of the ship [AQ] - hydrodynamic added mass matrix [BQ] - hydrostatic damping matrix [CQ] - hydrostatic restoring matrix DI

QF - hydrodynamic excitation force where subscript “Q” indicates that quantity is written with respect to the global reference point Q. Sloshing The linear case is considered here. Similar to the seakeeping part, an interior boundary value problem is formulated for the potentials associated with six degrees of freedom of the tank. The final result gives the added mass matrix associated with each tank motion (in the local frame of the tank). Note, that since the linear theory is assumed, no damping can be generated by the liquid motions in the tank (an artificial damping ε will be introduced). Then we transform the action (forces and moments) of the liquid motions from the local (tank) coordinate system to the global (ship) coordinate system. The sloshing has the following motion equation form in the ship’s frame:

[ ] [ ]( ) [ ] [ ]( ) DIQQQTTQT FξCCAA =+++− 2ω (2)

Coupling We can now write the motion equation of the coupled system:

[ ] [ ] [ ] [ ]( )( [ ][ ] [ ] [ ]( ) ) DI

QQTQTQ

QTQTQQ i

FξCCC

BAAAM

=++

+−+++− ωω 2

(3)

Numerical Results and Calibration of ε The calibration of the above described parameter ε is performed through comparisons with experimental results [4]. The numerical calculations are performed with HydroStar. In the selected configuration, two separated prismatic LNG cargo tanks were modeled, located at the fore and aft parts of the vessel. Among the different configurations tested, the following one is of particular interest for our case. The filling ratio is 30% of the height for the both tanks. The mesh used for our hydrodynamic computations is shown below:

Fig. 1: Hydrodynamic mesh with two tanks filled at 30%H

RAO’s in roll (β=90°) is presented for two values of the parameter ε (ε=0.02 and ε=0.1).

Fig. 2: Roll RAO for β=90°

For roll motion, we can observe the two characteristic peaks of a coupled system (ship + tanks). The first peak is associated with the motions of the ship and the second one with the liquid motions in the tanks. The value ε=0.02 gives the best results and will be considered hereafter. APPLICATION TO A REALISTIC CASE Environmental Conditions Environmental conditions applied in this study corresponds to realistic site specific all-directions wave scatter diagram, with 5 m of maximum recorded significant wave height. Wave energy spectrum is generated according to JONSWAP model (derived for seas with limited fetch), with spectral peak parameter assumed 3.0. Hydrodynamic Model A LNG carrier with four tanks is here considered. The filling ratios are 90% of the height for the tanks (1) and (3) and 30% of the height for the tanks (2) and (4). The mesh used for the hydrodynamic computations is presented below:

Fig. 3: Hydrodynamic mesh of the LNG Carrier filled at 90%H in

tanks (1) & (3) and 30%H in tanks (2) & (4). Non Coupled – Coupled Transfer Function In this section, results of hydrodynamic computation are displayed in form of Response Amplitude Operators (RAOs). Moreover, we present the comparison of sway and roll (the most affected degree of freedom due to coupling) RAOs between non coupled and coupled motions. The motions affected by the coupling are the surge, sway, roll and yaw

motions. Particularly, the roll motion is strongly affected with the presence of the two peaks described above instead of one peak in the case of the non coupled motion.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

SW

AY

(m/m

)

Wave frequency (rad/s)

NON-COUPLED - SWAY RAO at COG

180.0°195.0°210.0°225.0°240.0°255.0°270.0°270.0°285.0°300.0°315.0°330.0°345.0°360.0°

0.00

0.20

0.40

0.60

0.80

1.00

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

SW

AY

(m/m

)


COUPLED - SWAY RAO at COG

180°195°210°225°240°255°270°285°300°315°330°345°360°

Fig. 4: RAO in Sway for Non Coupled / Coupled Motion

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

RO

LL (°

/m)


NON-COUPLED - ROLL RAO at COG

180.0°195.0°210.0°225.0°240.0°255.0°270.0°270.0°285.0°300.0°315.0°330.0°345.0°360.0°

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

RO

LL (°

/m)


COUPLED - ROLL RAO at COG

180°195°210°225°240°255°270°285°300°315°330°345°360°

Fig. 5: RAO in Roll for Non Coupled / Coupled Motion Then, spectral analysis has been performed for each combination of associated conditions (Hs, Tp, and heading) using JONSWAP spectrum for site-specific environmental conditions. The amplitudes of 1/10th significant level and response zero-crossing periods for non coupled and coupled motions are detailed. These figures highlight for sway and roll the operational case (Tp, heading) corresponding to the worst motions.

WAVE PERIOD Tp (s)

RE

LATI

VE

WA

VE

HE

AD

ING

(°)

4 5 6 7 8 9 10 11 12 13

180

195

210

225

240

255

270

285

300

315

330

345

360

1.601.441.281.120.960.800.640.480.320.160.00

NON COUPLED - SWAY

AMPLITUDE(m)

5.8

5.8

5. 8

5.8

6.4

6.4

6.4 6.4

7.1

7.1

7.1

7.1

7.5

7.5

7.5

7.5

7.8

7.8

7.8

7.8

8.3

8.3

8.3

8.3

8.3

8.3

10.8

10.8

14. 1

1 4.1

9 14.18 10.87 8.36 8.35 7.84 7.53 7.12 6.41 5.8

TRANSVERSERESONANCE

FILLING TR (s)10%H20%H30%H40%H50%H60%H70%H80%H90%H

9.130%H

9.1

9.1

9.1

WAVE PERIOD Tp (s)

RE

LATI

VE

WA

VE

HE

AD

ING

(°)

4 5 6 7 8 9 10 11 12 13

180

195

210

225

240

255

270

285

300

315

330

345

360

1.601.441.281.120.960.800.640.480.320.160.00

COUPLED - SWAY

AMPLITUDE(m)

5.8

5.8

5.8

6.4

6.4

6.4

7.1

7.1

7.1

7.1

7.5

7.5

7.5

7.5

7.8

7.8

7.8

7.8

8.3

8.38.3

8.3

8.3

8.3

8.3

10.8

10.8

14.1

9 14.18 10.87 8.36 8.35 7.84 7.53 7.12 6.41 5.8

TRANSVERSERESONANCE


9.130%H

9.1

9.1

9.1

Fig. 6: Sway A1/10 & RTZ for Non Coupled / Coupled motion

WAVE PERIOD Tp (s)

RE

LATI

VE

WA

VE

HE

AD

ING

(°)

4 5 6 7 8 9 10 11 12 13

180

195

210

225

240

255

270

285

300

315

330

345

360

3.002.702.402.101.801.511.210.910.610.310.01

NON COUPLED - ROLL

AMPLITUDE(dg)

5.8 5.8

5.8

5.8

6.4

6.4

6.4

6.4

7.1

7.1

7.1

7.1

7.5

7.5

7.5

7.5

7.8

7.8

7.8

7.8

8.3

8.3

8.3

8.3

8.3

8.3

8.3

10.8

10.8

10.8

14.1

14.1

9 14.18 10.87 8.36 8.35 7.84 7.53 7.12 6.41 5.8

TRANSVERSERESONANCE


9.130%H

9.1

9.19.1

WAVE PERIOD Tp (s)

RE

LATI

VE

WA

VE

HE

AD

ING

(°)

4 5 6 7 8 9 10 11 12 13

180

195

210

225

240

255

270

285

300

315

330

345

360

3.002.702.402.101.801.501.200.900.600.300.00

COUPLED - ROLL

AMPLITUDE(dg)

5.8

5.8

5. 8

5.8

6.4

6.4

6.4

6.4

7.1

7.1

7.1

7.1

7.5

7.5

7.5

7.8

7.8

7.8

8.3

8.3

8.3

8.3

8.38.3

8.3

10.810.8

10.8

9 14.18 10.87 8.36 8.35 7.84 7.53 7.12 6.41 5.8

TRANSVERSERESONANCE


9.130%H

9.1

9.1

9.1

Fig. 7: Roll A1/10 & RTZ for Non Coupled / Coupled motion

MODEL TEST DESCRIPTION Sloshing model test practice is based on the measurement of fluid impact pressure on the tank walls. The model corresponds to the tank N°2 of BV reference vessel with standard cargo capacity of 138 000 m3, scaled to 1/70 and made of a 20 mm thick Plexiglas®. The impact pressures are measured by dynamic ICP® pressure sensors which natural frequency is above 100 kHz. Static pressure is not taken into account. A total of 54 points around the model could be used to locate the pressure sensors. A total of 16 pressure sensors is used for the tests. The sampling rate used is 20 KHz on each channel. The acquisition control program has been developed by Bureau Veritas. Several VBA® routines developed by Bureau Veritas are launched to: (i) Extract for each channel, elementary statistics such as:

• Pmax : maximum of impact pressure • 10 Pmax : mean of the 10 higher impacts • P1/10 : mean of the tenth of the higher impacts • P1/3 : mean of the third of the higher impacts • N : number of impacts

(ii) Build graphic comparisons between selected tests. Finally, statistical values of impact pressures are computed using statistical softwares (R® & Dataplot®), aimed to complete the assessment procedure from the impact pressure point of view. EXPERIMENTAL RESULTS Presentation of Results In this section are detailed our experimental results concerning the pressure results for the tank No. (2) described above. The duration of the tests is 5-hours at full scale [5]. The Fig. 8 represents the two sensor configuration used during our experiments. On the left side, the sensors location for β=270° is represented. On the right side, the sensors location for the other headings considered here is represented.

Fig. 8: Sensors Location for β =270° / other headings

First, we consider harmonic excitations obtained after spectral analysis for the case of zero forward speed. The pressure levels caused by non coupled and coupled motions are shown just below and can be compared. For instance, the Fig. 9 shows the maximum pressure recorded among our pressure sensors for Non Coupled/Coupled motions. The Fig. 10 represents the highest average recorded among all the sensors of the ten highest pressure peaks (N.C./C. motions). The Fig. 11 shows the maximum number of impacts recorded among all the pressure sensors (N.C./C.

motions). The Fig. 12 shows the statistical pressure associated at 3 hour-return period (named Pstat in the whole paper), calculated by the probability law which fits the best among Weibull-3 parameters, Log-Normal 3 parameters (N.C./C. motions). For each result, a unique scale is used, selected as the one giving the highest values between (non coupled, coupled) / (harmonic) excitations. Results for random excitations will be presented during the Workshop.

WAVE PERIOD Tp (s)

REL

ATI

VE

WA

VE

HE

ADIN

G(°

)

7.5 8.5 9.5 10.5 11.5 12.5

225

240

255

270

285

3001400126011209808407005604202801400

HARMONIC - NON COUPLED - Pmax

Pmax(mbar)

WAVE PERIOD Tp (s)

RE

LATI

VE

WA

VE

HE

AD

ING

(°)

7.5 8.5 9.5 10.5 11.5 12.5

225

240

255

270

285

3001400126011209808407005604202801400

HARMONIC - COUPLED - Pmax

Pmax(mbar)

Fig. 9: Harmonic – Pmax : Non Coupled / Coupled

WAVE PERIOD Tp (s)

RE

LATI

VE

WAV

EH

EA

DIN

G(°

)

7.5 8.5 9.5 10.5 11.5 12.5

225

240

255

270

285

300700630560490420350280210140700

HARMONIC - NON COUPLED - 10 Pmax

10 Pmax(mbar)

WAVE PERIOD Tp (s)

RE

LATI

VE

WAV

EH

EA

DIN

G(°

)

7.5 8.5 9.5 10.5 11.5 12.5

225

240

255

270

285

300700630560490420350280210140700

HARMONIC - COUPLED - 10 Pmax

10 Pmax(mbar)

Fig. 10: Harmonic – 10 Pmax : Non Coupled / Coupled

WAVE PERIOD Tp (s)

RE

LATI

VE

WAV

EH

EA

DIN

G(°

)

7.5 8.5 9.5 10.5 11.5 12.5

225

240

255

270

285

30016501485132011559908256604953301650

HARMONIC NON COUPLED - N impacts

N impacts

WAVE PERIOD Tp (s)

RE

LATI

VE

WAV

EH

EA

DIN

G(°

)

7.5 8.5 9.5 10.5 11.5 12.5

225

240

255

270

285

30016501485132011559908256604953301650

HARMONIC COUPLED - N impacts

N impacts

Fig. 11: Harmonic – N impacts : Non Coupled / Coupled

WAVE PERIOD Tp (s)

RE

LATI

VE

WAV

EH

EA

DIN

G(°

)

7.5 8.5 9.5 10.5 11.5 12.5

225

240

255

270

285

30010009008007006005004003002001000

HARMONIC - NON COUPLED - Pstat

Pstat(mbar)

WAVE PERIOD Tp (s)

RE

LATI

VE

WAV

EH

EA

DIN

G(°

)

7.5 8.5 9.5 10.5 11.5 12.5

225

240

255

270

285

30010009008007006005004003002001000

HARMONIC - COUPLED - Pstat

Pstat(mbar)

Fig. 12: Harmonic – Pstat : Non Coupled / Coupled Overall Analysis: 5-hour Full-Scale Duration Even if all headings have not been represented on the above graphs, the most prevailing cases are displayed. Indeed, the pressure levels for the headings (β=180°, 195°, 210°) are low compared to those detailed hereunder.

For the harmonic excitation, non-coupled motions represent the critical case for all kind of results considered (Pmax, 10 Pmax, number of impacts, Pstat). Even if the most critical case is difficult to identify since it differs from the parameter studied (Pmax, 10 Pmax, number of impacts or Pstat), the 4 following cases appear to be the most relevant:

• (Tp, β)=(10.5 s, 285°) • (Tp, β)=(9.5 s and 10.5s, 270°) • (Tp, β)=(10.5 s, 255°)

Pressure levels for coupled motions are low compared with those obtained with non-coupled motions. As it will be shown during the Workshop, concerning random excitations, the same tendency between non-coupled and coupled motions is observed. Indeed, non-coupled motions appear to be more critical in terms of pressure levels, except for the number of impacts. Finally, for 5-hour full-scale duration analysis among all the hydrodynamic configurations (non-coupled/coupled; harmonic/random) considered, the most critical one appears to be the non-coupled motion with harmonic excitation. Critical Cases: 30-hour Full-Scale Duration Following these results, a focused analysis from five-hour to sixty-hour full scale has been carried out on four the most severe cases listed here above. Our main concern was to assess statistical pressures Pstat using additional statistical distributions: Pareto and Generalized Extreme Value, selected threshold level, 95% confidence intervals, and the test duration required to collect sufficient size of the data sample allowing the convergence of statistical results. In that regard, our observation is that 30-hours experiment is giving satisfactory steadiness of Pstat (for 3-hours return period) and confidence intervals. This test duration has been selected for all comparisons of critical cases using 4 statistical laws. This detailed analysis of 30-hours full scale leads to the same conclusions as 5-hour full scale cases elaborated here above. CONCLUSION The influence of dynamic coupling due to the interactions between ship motions and tank liquid motion on the pressure levels on tank boundaries is here investigated by experimental means, using 6 d.o.f. test rig and 1/70 scaled tank model of standard LNG Carrier. Among all considered hydrodynamic configurations (non coupled/coupled; harmonic/random), the most critical one for the sloshing pressure appears to be non-coupled motion with harmonic excitation. This first conclusion of the study is very interesting since nowadays, due to the restricted computer resources, the major part of numerical calculations using CFD tools are performed with harmonic excitations. In addition, the state of the art of hydrodynamic computation is based on

classical assumptions of rigid body motion without dynamic effects of free surfaces in tanks. Comparing sloshing effects induced by “traditional” sloshing excitation and the “realistic” one which is the random motion accounting for dynamic coupling with liquid motion in the tanks, it appears that currently used numerical model seems to be conservative, at least for the cases studied herein. Further numerical sloshing analysis are envisaged to be carried in order to verify and confirm the observations from experimental study presented in this paper. For instance, the same kind of results will be presented at the Workshop for two partial fillings of 50%H instead of 30%H considered here. Comparisons between these experimental results and numerical calculations will be presented at the Workshop. In addition, due attention should be given to the statistical adjustment, particularly related to the proper selection of applicable statistical distribution and relevant acceptance criteria. Finally, it is to be underlined that conclusions drawn-out from this study should remain restricted only to the assumed operational case and any extrapolation to other configuration (as other filling or other tank capacity, for instance) may mislead to the erroneous recommendation. REFERENCES [1] MALENICA, Š., ZALAR, M. & CHEN, X.B., “Dynamic

coupling of seakeeping and sloshing”, 13th ISOPE Conference, Honolulu, USA, 2003.

[2] ZALAR, M., CAMBOS, P., BESSE, P., LE GALLO, B.

& MRAVAK, Z., “Partial Fillings of Membrane Type LNG Carriers”, 21st GASTECH Conference, Bilbao, Spain, 2005.

[3] ZALAR, M., MALENICA, Š., & DIEBOLD L.:

"Selected Hydrodynamic Issues in Design of Large LNG Carriers", RINA ICSOT Conference, Busan, Korea, 2006.

[4] GAILLARDE, G., LEDOUX, A & LYNCH, M.

“Coupling Between Liquefied Gas and Vessel’s Motion for Partially Filled Tanks: Effects on Seakeeping”, RINA Conference, London, UK, September 2004.

[5] ZALAR M., DIEBOLD L., BAUDIN E. & HENRY J.:

"Sloshing Effects Accounting for Dynamic Coupling between Vessel and Tank Liquid Motion ", 26th OMAE Conference, San Diego, USA, 2007.

[6] NEWMAN, J.N., “Wave effects on vessels with internal

tanks”, 20th Workshop on Water Waves and Floating Bodies, Spitsbergen, Norway, 2005.

[7] KIM, Y., “Numerical simulation of sloshing flows with

impact load”, Applied Ocean Research, 23, 2001. [8] ROGNEBAKKE, O.F., FALTINSEN, O.M., “Coupling

of sloshing and ship motions”, Journal of Ship Research 47, 2003.

Abstract for 23rd IWWWFB, Jeju, Korea, 2008

Steep wave impact onto a complex 3D structure

Ten I.1, Korobkin A.2, Malenica S.1, De Lauzon J.1 & Mravak Z.1

(1) BUREAU VERITAS - DR, Paris, France ([email protected])

(2) School of Mathematics, University of East Anglia, Norwich, UK

Introduction

The hydroelastic interactions during the impact of steep wave onto a complex structures are discussed.This problem is relevant for sloshing impacts apearing in the tanks of the LNG ships. The overall problemof sloshing impacts being extremely complex, some rational approximations were presented in [2], andthis work represents the specific part related to the steep wave impact. First results for this type ofimpact were presented in [1] for purely 2D case and here we extend it to the impact onto a 3D complexstructures, such as the NO96 boxes of the containement system of the LNG tanks. Indeed, even if thefluid flow can reasonably be approximated as a 2D, the complexity of the containement system structureneed to be considered fully 3D and solved by complex numerical solvers such as Abaqus, Nastran ... Themethod which is presented here uses the so called hybrid approach which means that the fluid flow ismodelled by the 2D strip approach, while the structural behavior is solved using the 3D FEM model.

Mathematical formulation

The basic configuration before impact is shown in Figure 1. The fluid of height H and width L occupiesa region x < 0, 0 < y < L, and 0 < z < H, where the plane z = 0 corresponds to the flat rigid bottom,and the vertical z-axis is directed upward. Before the impact, t < 0, a part of the liquid boundary x = 0,0 < z < H − Hw is in contact with the vertical wall. The boundary part x = 0, H − Hw < z < Hcorresponds to the vertical face of the wave (hydraulic jump), which approaches the wall at constantspeed U and hits the wall at t = 0. Only one part of the vertical wall is elastic, S ≡ [y1, y2]× [z1, z2], andthe rest is rigid.

U

H

Hw

L

U

c ∆φ=φ0 !H

Hw

2

φ =0y

φ=0

φ =0x

φ =-wx t

φ =-U-wx t

φ =-Ux

z1

z2

y1 y2

Figure 1. Formulation of the problem

The fluid flow is studied within the acoustic approximation. At the initial stage of the impact, whichis of short duration, the problem is linearized and the boundary value problem shown in Figure 1 isformulated. The problem is solved in non-dimensional variables which relate to dimensional one, denotedby a prime, as follow

x′ = Hx, y′ = Hy, z′ = Hz, ϕ′ = UHϕ, Hw = Hhw, t′ =H

c0t, p′ = ρUc0p, w′ =

HU

c0w, L = Hl. (1)

where, c0, ρ, ϕ, p, and w are sound speed in the fluid at rest, the fluid density, velocity potential, pressuredistribution, and deflection of the structure, respectively.

Fluid flow

Within the acoustic approximation the flow is potential. Velocity potential ϕ(x, y, z, t) satisfies in non-dimensional variables (1) the wave equation

∆ϕ = ϕtt (x, y, z) ∈ Ω ≡ (−∞, 0]× [0, l]× [0, 1], (2)

boundary conditionsϕy = 0, y = 0 and y = l, (3)

ϕ = 0, z = 1, (4)

ϕz = 0, z = 0, (5)

ϕx = −χ1 + wtχ2, x = 0, (6)

where

χ1(y, z) =

1, 0 < y < L, 1− hw = h1 < z < 1,0, 0 < y < L, 0 < z < h1 = 1− hw,

χ2(y, z) =

1, (y, z) ∈ S,0, (y, z) ∈/ S,

(7)

and initial conditionsϕ(x, y, z, 0) = ϕt(x, y, z, 0) = 0. (8)

The hydrodynamic pressure acting on the wall is given by the linearized Cauchy-Lagrange integral

p(y, z, t) = −ϕt(0, y, z, t). (9)

The solution of the problem (2)-(8) is sought in the form of eigenfunction expansion:

ϕ(x, y, z, t) =∞∑

n=1

Xn(x, t)Vn(y, z). (10)

Vn =2√lcos [λi(n)y] cos [µj(n)z], λi =

πi

l(i = 0, 1, 2, ...), µj =

π

2(2j − 1) (j = 1, 2, ...), (11)

δnm = 1 if n = m and zero otherwise. The eigenfunctions Vn(y, z) satisfy the boundary conditions (3)-(5).Substituting (10) into (2) we obtain equations for the coefficients Xn(x, t) which form boundary-valueproblem with initial conditions provided by (8). The obtained problem is solved with the help of Laplacetransform. Finally, after few algebra, the solution at x = 0 can be written as the following

Xn(0, t) =∫ t

0

Fn(τ)J0(rn(t− τ))dτ, Fn(t) =∫ 1

0

∫ l

0

[−χ1(y, z) + wt(y, z, t)χ2(y, z)] Vn(y, z)dydz, (12)

where J0 is the Bessel function.The pressure distribution p(y, z, t) on the wall, x = 0, is :

p(y, z, t) = −∞∑

n=1

[d

dt

∫ t

0

Fn(τ)J0(rn(t− τ))dτ

]Vn(y, z). (13)

Structural dynamics

The structural deflection at the wall w(y, z, t) is the solution of the structural dynamic equation subjectedto the following initial conditions:

w(y, z, 0) = wt(y, z, 0) = 0. (14)

Regardless of the method (analytical or numerical) which is employed to solve the structural dynamics,the wall deflection is developed in the following series:

w(y, z, t) =∞∑

n=1

an(t)Ψn(y, z), (15)

where Ψn(y, z) are the adequate shape functions.The most natural choice for the shape functions are the structural eigenmodes because they satisfy theboundary conditions by definition, and in addition they are orthogonal. The orthogonal property of theeigenmodes allows the reduction of the structural dynamic problem to the evolution equation for themodal amplitudes an(t):

αnd2an

dt2+ dn

(an + γn

dan

dt

)=

∫

S

p(y, z, t)Ψn(y, z)dS, (16)

with the following initial conditions:

an(0) = 0, an(0) = 0. (17)

The coefficients αn, dn and γn are the normalized mass, stiffness and damping coefficients respectively.In the case of simple elastic structures (uniform beam, plate, ...) these coefficients can be obtainedanalytically, but in the general case the numerical methods are usually employed. The most commonmethod is the finite element method (FEM) which will be used here in the context of the commercialcode Abaqus.

Coupling

In order to solve the coupled hydroelastic problem, we need to express the right-hand side in (16), in termsof the modal coefficients an(t). After some algebra we arrive at the following system of integro-differentialequations with the unknown coefficients an(t):

αnd2an

dt2+ dn

(an + γn

dan

dt

)= Pn(t)− d2

dt2

∞∑m=1

∫ t

0

am(τ)Knm(t− τ)dτ. (18)

Here

Pn(t) = −∞∑

k=1

vkTknJ0(rkt), Knm(t) =∞∑

k=1

TkmTknJ0(rkt), (19)

Tkn =∫

S

Vk(y, z)Ψn(y, z)dS, vk ≡ −∫ 1

1−hw

∫ l

0

Vk(y, z)dydz. (20)

Let us define new unknown function bn(t) as

bn ≡ αnan +∞∑

m=1

∫ t

0

am(τ)Knm(t− τ)dτ. (21)

Then equation (18) takes the form

d2bn

dt2+ dn

(an + γn

dan

dt

)= Pn(t), n = 1, 2, ... . (22)

The system (21) and (22) is solved numerically with the following initial conditions (n > 1):

bn(0) = 0, bn(0) = an(0) = 0. (23)

Numerical Results

In order to validate the coupling procedure for FEM structural modelling, we chose the case of the uniformplate for which the analytical solution is available. In the case of the FEM method, the integral (20)must be evaluated numerically. This is done by fitting Ψ(l)

n , where superscript l denotes the Ψn value atthe l-th node, by B-Spline fitting surface Ψn(y, z) using the IMSL standard Fortran subroutines.We chose the case where the plate occupies the whole wall and the following basic parameters are used:sound speed c0 = 1500m/s, water density ρw = 1000kg/m3, impact velocity U = 1m/s, structuraldamping γ = 0.001s, water height H = 2.0m, wave height Hw = 0.5m Poisson’s ratio ν = 0.3, platedensity ρb = 7800kg/m3, Young’s module E = 0.207e12N/m2, width of the wall L = 2.0m and platethickness h = 0.02m.In Figure 2, the time history of the plate deflection at few representative points is presented. As we can

see the agreement between two class of results is almost perfect which concludes the validation of thenumerical model.Now we chose more complex case of 3D structure representing the rectangular box of 1m width, 1mheight and 0.3m depth. The center of the box is placed at y = 1.0m, z = 1.5m and the channel width isL = 2m. All other parameters are the same. Few snapshots during the impact are presented in Figure 3.There is no results for comparisons in this case, and we can just mention that the calculations are stableboth in space and in time.

Commercial code

Analytical

z = 1.759 m

z = 1.241 m

z = 1.500 m0.003

0.002

0.001

0.000

-0.001

-0.002

-0.003

defl

ecti

on

s, m

time, sec0.00 0.01 0.02 0.03 0.04

Commercial code

Analytical

z = 1.759 m

z = 1.241 m

z = 1.500 m0.003

0.002

0.001

0.000

-0.001

-0.002

-0.003

defl

ecti

on

s, m

time, sec0.00 0.01 0.02 0.03 0.04

Figure 2. Time history of plate deflection for few representative points at y = 1.0m (left) and y = 1.5m (right).

Figure 3. Snapshots during steep wave impact onto rectangular box.

Conclusions

We presented here the semi numerical method able to simulate the steep wave impact onto a complexstructures modelled by the general 3D FEM numerical codes such as Abaqus. The model was validatedon the case of elastic plate for which the analytical solution is available. The future work consist inapplying and validating the method on the real NO96 boxes used in the tanks of LNG carriers.

References

[1] Korobkin, A. & Malenica S., 2007. : “Steep Wave Impact Onto Elastic Wall”, 22nd IWWWFB,Plitvice, Croatia.

[2] Malenica S, Korobkin A.A., Scolan Y.M., Gueret R., Delafosse V., Gazzola T.,Mravak Z., Chen X.B. & Zalar M. 2006. : ”Hydroelastic impacts in the tanks of LNG carriers.”,4th Int. Conference on Hydroelasticity, Wuxi, China.

SECOND-ORDER WAVE LOADS ON A LNG CARRIERIN MULTI-DIRECTIONAL WAVES

Mathieu RenaudResearch Department


Flavia RezendeResearch Department


Olaf WaalsMARIN

(The Netherlands)

Xiao-bo ChenResearch Department


Radboud van DijkMARIN

(The Netherlands)



OMAE2008-57409

ABSTRACTDue to the installation of LNG terminals moored in prox-

imity to the coast, the wave kinematics in shallow water and theconsequence on the behavior of those terminals have recently be-came a major concern of the offshore industry. One key issuesthe accurate simulation of the low-frequency motions of LNGcarriers, specially the surge, for which the vessel presents lowdamping, in order to perform the design of the mooring system.The present paper focuses on the effect of wave directionalityon second-order slow-drift loads and the related response of thevessel.

The paper describes results of model tests in regular crowaves - monochromatic but coming from two directions separated by 90 degrees, as well as bichromatic cross waves. Tnew ”middle field” formulation extended to the case of croswaves, is used to compute the wave drift loads and low-frequencyQuadratic Transfer Function (QTF). The results are comparedwith those from the model tests.

NOMENCLATURELNG Liquefied Natural GasQTF Quadratic Transfer Functionωi Pulsation of the incoming wave coming from directionβi

1

i

ss-hes

φ First-order velocity potentialεi Phases of first-order incoming waves associated with

(ωi,βi)

ai Wave amplitude of incoming waves associated with(ωi,βi)

ki Wavenumber of incoming waves associated with(ωi,βi)

η Elevation of free surfaceE(βi,β j) Phase function : representing the phase difference of

two cross waves

INTRODUCTIONLarge LNG terminals have been designed to operate in off-

shore areas approximate to harbors, where water is of finite depthand waves are multi-directional. In the design of such mooringsystems of LNG terminals in a zone of shallow water, one im-portant concern is the accurate simulation of the low-frequencymotions to which the second-order wave loading is well knownas the main source of excitation. In the last decade, the focus ofthe hydrodynamic research has been on deep and ultra deep wa-ter. Although there have been many works on the estimation ofsecond-order loads for the case of long crested waves, therearerelatively few works on the estimation of second-order loads indirectional waves including the works in [2], [3] and [5].

In [6], the formulations of second-order wave loads were


presented, in particular, the new formulation based on the use ofcontrol surface was shown to provide results as accurate ahefar-field formulation and as general as the pressure-integrationformulation. The excellent agreement of second-order drift loadsin cross waves with the semi-analytical results validates the de-velopment.

Further to the work in [6], the formulations of second-ordlow-frequency loads in cross waves are presented here. The-sults of model tests of a LNG carrier in regular cross waand bichromatic cross waves and the comparison with numcal computations are illustrated and analyzed.

FORMULATION OF LOW-FREQUENCY LOADSThe low-frequency quadratic transfer function (QTF) is d

fined as the second-order wave loads occurring at the frequcyequal to the difference (ω1 − ω2) of two wave frequencies(ω1,ω2) of bichromatic waves. Furthermore, the wave directiorelative to the positivex-axis are denoted by(β1,β2). It is under-stood that the bi-directional bichromatic wave is characterizedby, at the first order, one regular wave of(ω1,β1) and another of(ω2,β2), without loss of generality.

QTF is composed of two distinct parts : one dependent oon thequadratic products of first-order wave fields and anotcontributed by the second-orderpotentials of the incoming anddiffracted waves.

F(ω1,ω2,β1,β2) = Fq(ω1,ω2,β1,β2)+ Fp(ω1,ω2,β1,β2) (1)

The first partFq can be written in the way presented in [10

Fq =ρ2

ZZ

Hds

[

(∇φ1 ·∇φ∗2)n−ω1

ω2φ∗n2∇φ1−

ω2

ω1φn1∇φ∗2

]

−ρω1ω2

2g

I

Γdℓ(φ1φ∗2)n (2)

as integration over the hullH and along the waterlineΓ in theirmean position. In (2),φ stands for the first-order velocity potential andφn = ∇φ · n the normal derivative ofφ on H. The sub-scripts (1, 2) represent the quantities associated with the wfrequencies and directions(ω1,β1) and (ω2,β2), respectively,while the superscript∗ indicates the complex conjugate.

The formulation (2) derived from Eq.27 in [10] obtainedapplying the two variants of Stokes’ theorem given in [7] to theclassical near-field (pressure-integration) formulationas in [8],is compact and used here. It is directly applicable to force com-ponents in horizontal directions. The extension to other compo-nents is direct and omitted here. In (2), we involve the gradient ofvelocity potentials which is sensitive to the singularities presentin the velocity field at sharp corners. In particular, the integration

s t

ere rveseri-

e-en

ns

nlyher

] :

-

ave

by

of terms(∇φ1 ·∇φ∗2) converges slowly or in the worst cases, maybe non-convergent.

In [10], after having the new near-field formulation by ap-plying the variants of Stokes’s theorem, we considered a fluidvolume enclosed by the hull, a control surface at a distance fromthe body and the mean free surface limited by the waterline andthe intersection of the control surface with free surface, and haveobtained the general formulation (Eq.8a & 8b in [10]) of second-order loads by using Gauss’s theorem. This formulation can besimplified if we construct a control surface surrounding thehulltouching the free surface only along the waterline :

Fq = (ω1−ω2)ρ2

ZZ

Hds

(

φn1∇φ∗2/ω1−φ∗n2∇φ1/ω2

)

−ρω1ω2

2g

I

Γdℓ(φ1φ∗2)n

−ρ2

ZZ

Cds

[

(∇φ1 ·∇φ∗2)n−φ∗n2∇φ1−φn1∇φ∗2]

(3)

in whichC stands for the control surface defined as an arbitraryone surround the body.

The integration of terms(∇φ1 ·∇φ∗2) in (3) now performedon the control surfaceC converges rapidly sinceC is at some dis-tance from the hull where the velocity field does not present anysingularity. The integration on the hullH is of orderO(ω1−ω2)and as small asφn which tends to zero for large wave frequencies.The middle-field formulation (3) is used for the computationofthe first-part of second-order loadsFq in the following.

The second partFp is expressed in the way [4] :

Fp =−i(ω1−ω2)ρZZ

Hds

φ(2)I n− (φ(2)

In −NH)[ψ]

+ i(ω1−ω2)ρg

ZZ

FdsNF [ψ] (4)

in which the first term in the hull integral corresponds to thesecond-order Froude-Krylov component contributed by the in-

coming wave potentialφ(2)I defined by :

φ(2)I = ia1a2Ag2coshkm(z+h)

coshkmhexp[ikm ·x + i(ε1−ε2)]

gkm tanhkmh− (ω1−ω2)2 (5)

with

km ·x = (k1cosβ1−k2cosβ2)x +(k1sinβ1−k2sinβ2)y (6)

(ε1,ε2) being the phases of first-order incoming waves associatedwith (ω1,β1) and(ω2,β2), respectively.


In (5), km is given by :

km =√

k21 + k2

2−2k1k2cos(β1−β2) (7)

andA written :

A =ω1−ω2

ω1ω2k1k2[cos(β1−β2)+ tanhk1h tanhk2h]

+12

(

k21/ω1

cosh2 k1h−

k22/ω2

cosh2 k2h

)

(8)

where we have used the notations(a1,a2) and (k1,k2) stand-ing for the wave amplitudes and wavenumbers associated wit(ω1,ω2) via the dispersion equationk1,2 tanhk1,2h = ω2

1,2/g withthe waterdepthh, respectively, while the wave heading with re-spect to the positivex-axis is denoted byβ.

The second term in the hull integral of (4) and the term defined by the integral over mean free surfaceF come from theapplication of Haskind relation and represent the contribution ofthe second-order diffraction potential, as shown in [4]. The terms(NH ,NF ) are the second members of the boundary conditionsatisfied by the second-order diffraction potential on the hull Hand the mean free surfaceF , respectively. They are written as :

2NH =−(x1 ·∇)∇φ∗2 ·n− (x∗2 ·∇)∇φ1 ·n

(iω2x∗2−∇φ∗2) · (R1∧n)− (iω1x1+∇φ1) · (R∗2∧n) (9)

and

NF = i(ω1−ω2)(∇φ1 ·∇φ∗P2+ ∇φP ·∇φ∗I2)

−iω1

2g

[

φ1(−ω22∂z+g∂2

zz)φ∗P2 + gk2

2(1−tanh2 k2h)φP1φ∗I2)]

+iω2

2g

[

φ∗2(−ω21∂z+g∂2

zz)φP1 + gk21(1−tanh2 k1h)φ∗P2φI1)

]

(10)

in which x is the displacement vector at a point onH andR thevector of rotations. In (10),φI represents the first-order potentialof incoming waves whileφP = φ−φI stands for that of perturba-tion including the diffraction and radiation components. Finally,[ψ] in (4) represents a vector of first-order radiation potentials os-cillating at the difference frequency(ω1−ω2). They satisfy thehomogeneous condition :

[

−(ω1−ω2)2 + g∂z

]

[ψ] = 0 (11)

on the mean free surfaceF and

∂n[ψ] = n (12)

3

h

-

s

on the hullH.The full QTF (1) is composed of two parts(Fq,Fp) given

by the formulations (2) and (4), respectively. The formulation(2) for Fq derived in [10] is simpler than that in [8]. The for-mulation (4) forFp by [4] is often calledindirect method sinceit provides a way to evaluate the contribution from the second-order diffraction potential through the Haskind relation such thatthe second-order diffraction potential is not explicitly computed.

SECOND-ORDER LOADS IN CROSS WAVESIn cross waves of two frequencies (ω1,ω2) with two head-

ings(β1,β2), the first-order elevation of free surface for regularwaves can be expressed by :

η(t) = ℜη1 e−iω1t + η2 e−iω2t (13)

with the complex amplitudes :

η1 = a1eik1(xcosβ1+ysinβ1)+iε1 (14a)

η2 = a2eik2(xcosβ2+ysinβ2)+iε2 (14b)

associated with the real amplitude(a1,a2), wave numbers(k1,k2), coordinates(x,y) of the reference point and the initialphases (ε1,ε2) of each wave component.

The time series of second-order low-frequency wave loadsare then written by :

F(t) = ℜ1

2η1η∗

1F(ω1,ω1,β1,β1)+12

η2η∗2F(ω2,ω2,β2,β2)

+ η1η∗2F(ω1,ω2,β1,β2)e

−i(ω1−ω2)t

(15)

in which F(ω1,ω2) are the QTF given by (1) and computed by(3) for the first part and (4) for the second part.

In the cross waves of unique wave frequency (ω1 = ω2), thelow-frequency load is reduced to the drift loads expressed by :

F(t) = ℜ1

2a2

1F(ω1,ω1,β1,β1)+12

a22F(ω1,ω1,β2,β2)

+ a1a2E(β1,β2)F(ω1,ω1,β1,β2)

(16)

in which (a1,a2) are the real amplitudes of cross waves define in(14) andE(β1,β2) is the phase function :

E(β1,β2) = eik1x(cosβ1−cosβ2)+ik1y(sinβ1−sinβ2)+i(ε1−ε2) (17)


representing the phase difference of two cross waves (14).The first two terms in (16) are the drift forces associate

with each regular wave while the third one is contributed by theinteraction between two waves of different headings. From (17),the interaction term varies with the phase function depending onthe reference position and initial phases of two regular waves.

NUMERICAL AND MODEL TEST RESULTSNumerical computations and model tests are performed for

standard 138000 m3 LNG vessel moored in the waterdepth equato 15m. The main particulars of the LNG vessel are shown iTable 1. The vessel was moored by a soft spring mooring systeThe mooring stiffnesses given in Table 1 were adjusted to obtaina realistic natural period for surge with a target value of 124s.

Table 1. MAIN PARTICULARS OF LNG VESSEL

Designation Sym. Unit Value

Length between perpendicularsLpp m 274.000

Width B m 44.200

Depth D m 25.000

Draft T m 11.000

Displacement ∆ m3 97120

COG above keel KG m 16.300

COB above keel KB m 5.857

COB from Aft perpendicular LCB m 135.676

Metacentric height GM m 4.770

Transverse gyration radius Kxx m 15.200

Longitudinal gyration radius Kyy m 68.500

Longitudinal mooring stiffness Cx KN/m 281.000

Transverse mooring stiffness Cy KN/m 254.000

Several series tests of cross waves have been performedthe Offshore Basin of MARIN. The basin has a movable floowhich is used to adjust the water depth to 15m. In all cases, tworegular waves of headings 135 and 225 relative to the LNGheading are generated from the two sides of the basin. The assystem is shown on Figure 1 The mean drift loads are measurin the cross waves with equal frequencies of 0.4, 0.6 and 1rad/s. Furthermore, the cross waves with a pair of frequenciesequal to 0.60 and 0.65 rad/s are generated and low-frequenwave loads are measured.

4

d

alnm

inr

xied.0

cy

x

y

0

M fpa p

0°

45°90°

135°

180°

225°

270°

315°

Figure 1. DEFINITION OF THE AXIS SYSTEM

Figure 2. CROSS WAVES IN MODEL TESTS AND NUMERICAL COM-

PUTATION


Figure 3. LNG HULL MESH AND CONTROL SURFACE

The numerical modelHydrostar of wave diffraction and ra-diation presented in [1] is used to evaluate the first-order andsecond-order solutions. A picture of model tests of cross waveswith a frequency equal to 1.0 rad/s is presented on Figure 2. Tworegular waves come in front of the vessel with±45 on the port-side/starboard sides. The cross waves are also computed andalsoillustrated on Figure 2 below the picture of model tests.

The mesh used inHydrostar is composed of 4408 flat panelson the wetted part of LNG vessel. For the computation of second-order wave loads by using the middle-field formulation, a controlsurface composed of 3330 flat panels is automatically generatedand presented on Figure 3 together with the hull mesh.

First, the mean drift forcesFx in cross waves of headings(β1 = 135 andβ2 = 225) with the same frequency are com-puted and compared with measurements of model tests. Thesults ofFx(ω,ω,β1,β2) are presented on Figure 4 with the wavefrequencyω in rad/s as the abscissa. Only the real part is illustrated since the imaginary part is zero for the interaction for Fx

between two waves of these headings.

-150000

-100000

-50000

0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Real part of comp.Real part of test

Figure 4. DRIFT LOAD Fx IN REGULAR CROSS WAVES

5

re-

-

The results of model test (circles) are very close to the curveof numerical computations atω = 0.4 and 1.0 rad/s. The re-sults atω = 0.6 are however quite different. As shown by (16),the mean drift forcesFx vary in function of wave phase differ-ence. This variation is illustrated on Figure 5 where the totaldrift forcesFx defined by (16) are presented in function of phasedifference in deg.

-500000

-400000

-300000

-200000

-100000

0

0 30 60 90 120 150 180 210 240 270 300 330 360

w = 0.4 rad/s (HStar)w = 0.4 rad/s (Test)



Figure 5. TOTAL DRIFT LOAD IN FUNCTION OF WAVE PHASES

The drift forcesFx in regular mono-directional waves ofheading equal to 135 are depicted on Figure 6. The dispersionof model test results atω = 0.6 rad/s is quite important. This dis-persion could be explained by the difficulty to interpret themodeltest results. The measured time signal has to be decomposed inorder to separate the forces coming from the first order loadsfrom the forces coming from the second order loads. Globally,the comparison between the results of model tests and numericalcomputations is good, although only few model tests were per-formed. More measurements are expected to fully validate thenumerical models.

In bichromatic cross waves of

(ω1,ω2,β1,β2) = (0.60,0.65,135,225)

the low-frequency loadsFx are depicted on Figure 7. The real andimaginary parts of numerical computations are presented bysolidand dot-dashed lines, respectively while the test measurementsby the symbols (circle and square) for the real and imaginaryparts, respectively.

Finally, we present some results of numerical computations.The real and imaginary parts of drift forcesFx in regular crosswaves are depicted on Figures 8 and 9. The main heading of reg-ular waves is 180 (head waves) and the drift forces due to inter-


-

-200000

-150000

-100000

-50000

0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6


Figure 6. DRIFT LOAD IN OBLIQUE REGULAR WAVES

-150000

-100000

-50000

0

50000

100000

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6


Imag. part of comp.Imag. part of test

Figure 7. LOW-FREQUENCY LOAD Fx IN BICHROMATIC CROSS

WAVES

actions with another regular waves of different headings varyingfrom 120 to 165 are presented.

The low-frequency loadsFx oscillating at∆ω = 0.05 rad/s inbichromatic cross waves are presented on Figures 10 and 11rthe real and imaginary parts, respectively. The main heading ofwaves is 180 so that the QTFs are functions of :

(ω,ω+0.05,180,β)

The wave frequencyω varies from 0.3 to 1.6 rad/s while the second wave headingβ from 120 to 165.

For two fixed headings(135,225), low-frequency waveforces for different difference-frequencies varying from0.0 to0.075 rad/s are presented on Figures 12 and 13 for the real
imaginary parts, respectively.
6

fo

-

and

-150000

-100000

-50000

0

50000

100000

150000

200000

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Real part (165 deg)Real part (150 deg)Real part (135 deg)Real part (120 deg)

Figure 8. REAL PART OF DRIFT LOAD IN REGULAR CROSS WAVES

-150000

-100000

-50000

0

50000

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Imag. part (165 deg)Imag. part (150 deg)Imag. part (135 deg)Imag. part (120 deg)

Figure 9. IMAGINARY PART OF DRIFT LOAD IN REGULAR CROSS

WAVES

CONCLUSIONSThe formulation of quadratic transfer function (QTF) of low-

frequency wave loads in bichromatic cross waves is given inthe paper with the extension of middle-field formulation forthefirst part depending on the quadratic products of first-orderwavefields. The results of numerical computations and experimen-tal measurements are presented. The comparison between numerical computations and model tests is globally good. How-ever, more results from model tests are needed for fully validatethe numerical developments. Although the further analysesareneeded to quantify the impact to practices, it is already shownthat the interaction effect between waves from different headingsis very important and has to be taken into account in the estima-tion of excitation loads to mooring systems.


-150000

-100000

-50000

0

50000

100000

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Real part (165 deg)Real part (150 deg)Real part (135 deg)Real part (120 deg)

Figure 10. REAL PART OF LOW-FREQUENCY LOAD IN BICHRO-

MATIC CROSS WAVES WITH ∆ω = 0.05 rad/s

-200000

-150000

-100000

-50000

0

50000

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Imag. part (165 deg)Imag. part (150 deg)Imag. part (135 deg)Imag. part (120 deg)

Figure 11. IMAGINARY PART OF LOW-FREQUENCY LOAD IN

BICHROMATIC CROSS WAVES WITH ∆ω = 0.05 rad/s

REFERENCES[1] CHEN X.B. (2004) Hydrodynamics in Offshore and Naval

Applications - Part I.Keynote lecture at the 6th Intl Confer-ence on Hydrodynamics, Perth (Australia).

[2] PINKSTER J.A. (1988) The influence of directional spread-ing of waves on mooring forces.Proc. OTC Conf., Houston(USA), paper No.5629.

[3] K ROKSTAD J.R. (1991) Second-order loads in multidirec-tional seas. Ph.D. Phesis, The Norwegian Institute of Tech-nology.

[4] M OLIN B. (1979b) Second-order drift forces upon largebodies in regular waves.Proc. BOSS’79., London (UK),363-70.

[5] M OLIN B. & FAUVEAU (1984) Effect of wave-directionality on second-order loads induced by the set-

7

-100000

-50000

0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Real. part (Dw =0.)Real part (Dw =0.025)Real part (Dw =0.05)

Real part (Dw =0.075)

Figure 12. REAL PART OF LOW-FREQUENCY LOAD IN BICHRO-

MATIC CROSS WAVES WITH (β1,β2) = (135,225)

0

50000

100000

150000

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Imag part (Dw =0.025)Imag part (Dw =0.05)

Imag part (Dw =0.075)

Figure 13. IMAGINARY PART OF LOW-FREQUENCY LOAD IN

BICHROMATIC CROSS WAVES WITH (β1,β2) = (135,225)

down.J. Appl. Ocean Research. Vol.6, No.2, 66-72.[6] REZENDE F., LI X. & C HEN X.B. (2007) Second-order

loads on LNG terminals in multi-directional sea in waterof finite depth.Proc. 26th Intl. Conf. OMAE, San Diego(USA).

[7] DAI Y.S. (1998) Potential flow theory of ship motions inwaves in frequency and time domain (in Chinese).Press ofthe National Defense Industries, Beijing (China).

[8] PINKSTER J.A. (1980) Low frequency second order waveexciting forces on floating structures.H. Veenman En ZonenB.V. - Wageningen (The Netherlands).

[9] FERREIRA M.D. & L EE C.H. (1994) Computation ofsecond-order mean wave forces and moments in multibodyinteraction.Proc. 7th Intl Conf. Behaviour Off. Structures,BOSS’94, Boston (USA)2, 303-13.


[10] CHEN X.B. (2006) Middle-field formulation for the com-putation of wave-drift loadsJournal of Engineering Math-ematics. Published online: 27 Sep 2006, Vol.59, pp61-82.


Diffraction and radiation with the effect of bathymetricvariations

G. de Hauteclocque, F. Rezende & XB ChenResearch Department, Bureau VeritasCourbevoie, Paris La Defenseemail: [email protected]

ABSTRACT: New developments have been performed to study the wave kinematics andseakeeping of floating bodies in an area of variable water depth. It consists of extendingthe classical diffraction/radiation method applicable to the case of constant water depth tobe able to capture the major effects of the bathymetry. The part of sea bottom under thefloating body is modeled as a second fixed body. The formulation of partial transparencyis applied to an extended zone outside the opaque area to eliminate the unexpected dis-turbance due to the otherwise abrupt truncation of sea bottom along the edge of opaquebottom. The good comparison with semi-analytical solutions (GNWave) of wave kinemat-ics along a slopped seabed has been obtained. Numerical results for the case of a bargefloating over a horizontal bathymetry and for a LNG over a slopped seabed show thatthe interference effect of variable bottom on the wave loads is important. The methodcan then be used in the context of LNG terminals in coastal zones where the bathymetricvariation cannot be ignored.

1 INTRODUCTIONThe recent development of LNG terminals has shown the need to extend the capabilityof seakeeping computations to relatively shallow water area. Among the different issuesassociated with the shallow water, there is the influence of a varying bathymetry whichmight induce significant changes on kinematics of waves and on the behavior of the ship.

A classical way to take into account varying bathymetry in diffraction/radiation sea-keeping code is to model the bottom as a fixed second body. However, it has been shownthat this method presents difficulties when the bottom has to be truncated at differentwater depths (Buchner 2006). Indeed, the abrupt truncation of the bathymetry inducesunwanted and strong reflections. A smoothly sloped extension of the boundary does re-duce these reflections but not as much as expected (Buchner 2006). This paper presents anew way to smooth more efficiently the truncation by introducing a partially transparentextension. The theoretical formulation of the transparency is explained in a first part;next the efficiency of the method is tested and discussed on different configurations.

2 THEORYThe potential theory of wave diffraction and radiation around floating or fixed bodies isadopted. A summary of the wave diffraction/radiation theory is given in Chen (2004).The modification on the boundary condition over part of sea bottom is explained here.

2.1 Diffraction and radiation over an uneven bottomA floating body above a globally flat bottom but uneven in a restricted area is considered:

z =

−h (x, y) ⊂ B−h(x, y) (x, y) ⊂ B

(1)

where B represents the unlimited flat bottom of depth h and B the limited area where thedepth is variable. In the fluid domain D limited by the mean free surface F (at z = 0),the hull of the floating body H and bathymetry B ∪ B, the velocity potential can bedecomposed as:

φ = φI + φD + φR (2)

Where φI is the incident wave field, φD the diffraction potential and φR the radiatedpotential induced by the hull motion. The problem can now be written as:

∆φD,R = 0 P ⊂ DφD,R

z − (ω2/g)φD,R = 0 P ⊂ F (z = 0)φD

n = −φIn and φR

jn = nj P ⊂ HφD,R

z = 0 P ⊂ BφD

n = −φIn and φR

jn = 0 P ⊂ B

(3)

In which φRj is the jth component of the radiation potential expressed by φR = −iω

∑6j=1 ζjφ

Rj

with ζj the jth mode of motion.

2.2 Diffraction over an uneven partially transparent bottomWithout loss of generality, we consider the diffraction problem associated with a partiallytransparent uneven bottom, without presence of body. The perturbation potential φP isdefined as

φP = φD + φT (4)

so that

φ = φI + φP (5)

Where φD is associated to the flat bottom B and φT to the partially transparent bottomB. On the boundaries, the components of perturbation potential satisfy the followingequations:

φDn = −φT

n P ⊂ BφT

n = −(1− ε)(φIn + φD

n ) P ⊂ B(6)

Where ε is the transparency coefficient. Thus, if ε = 0 we have φn = 0 on B, the unevenbottom is thus fully opaque. If ε = 1, it can be shown that φD = φT = 0 and the unevenbottom is not taken into account at all, i.e. fully transparent.

For value of ε between 0 and 1, it can be considered that the bottom is partially trans-parent. However, the decomposition of φP in φD and φT is not unique, one way to closethe problem with a source method is to define φT only as the potential associated withthe source at P (x, y, z) while φD comes from the contribution of all the source except ofthose on P (x, y, z).

2.3 Boundary element methodConsidering a source distribution σ(Q) on the hull H and on the bottom B, the pertur-bation potential and its gradient are expressed by:

φP =∫∫

H∪Bds(Q)σ(Q)G(P,Q) and ∇φP =

∫∫H∪Bds(Q)σ(Q)∇G(P,Q) (7)

G(P,Q), which is the Green function representing a potential flow at a field point Pinduced by a source located at Q, satisfies :

Gz − (ω2/g)G = 0 P ⊂ F (z = 0)Gz = 0 P ⊂ B∇2G(P,G) = 4πδ(P −Q) P ⊂ D

(8)

The source distribution σ is determined by the integral equation :

2πσ(P ) + PV∫∫

H∪Bds(Q)σ(Q)Gn(P,Q) = Vn P ⊂ H ∪ B (9)

in which the word “PV” before the integral means to interpret the integral as a Cauchyprincipal value, and :

Vn =

−φIn for φ = φD P ⊂ H

−nj for φ = φRj P ⊂ H

−φIn for φ = φD P ⊂ B

0 for φ = φRj P ⊂ B

(10)

If the bottom B is partially transparent (ε coefficient), the perturbation potential is de-composed as :

φP = φT + φD with φD = φP − φT (11)

Where we choose to associate the potential φT with the source at the point P . If we noted(Q→ P ) as the disc centered at P and with a radius tending to zero, this can be writtenas :

φT (P ) =∫∫

d(Q→P )ds(Q)σ(Q)Gn(Q) (12)

φD(P ) =∫∫

H∪B−dds(Q)σ(Q)Gn(Q) (13)

From equation (6) we have

φTn + (1− ε)φD

n = +(1− ε)Vn P ⊂ B (14)

The coefficient ε can now be introduced in the integral equation:

2πσ(P ) + (1− ε)∫∫

H∪B−dds(Q)σ(Q)Gn(Q) = (1− ε)Vn P ⊂ B (15)

It can be verified that if ε = 1, the panel is thus transparent and if ε = 0, the integralequation is identical to the one obtained with a normal bottom.

3 RESULTS

Three configurations are presented here to validate the efficiency of a partially transparentarea to remove the edge effect. The first one involves a horizontal bathymetry, the secondone the study of wave’s kinematics over a varying bathymetry, and the calculation of astandard LNG RAOs over a sloped bottom.

3.1 Submerged horizontal bathymetry

A barge floating above a circular horizontal bathymetry is considered. The dimension ofthe barge are 80m×20m×4m, the bathymetry diameter is 160m and its depth is set to15m; the water depth is 20m. This case is chosen because of the availability of a referencecomputation which is a classical computation at uniform water depth 15m.

(a) Side view (b) Top view

Figure 1: Barge over a submerged bottom, description of the geometry.

Without partially transparent area, the added mass and damping oscillate around theexact solution. Increasing the size of the bathymetry makes the number of oscillationsdecreases with no change on the amplitude.

With a partially transparent area, where the panels smoothly disappear (cos2 distribu-tion), the amplitude of the oscillations is significantly reduced, especially for high frequen-cies. The distribution of the transparency parameter has to be as smooth as possible, acos2 distribution has been found to be particularly efficient. The next step is to definehow long the transition area should be. Computations with different ”beach” size (80, 160,240, 320 and 400m) are thus performed. As expected, greater the partially transparentarea is, better the results are (Figure 2a). Moreover, as the beach increases, the resultconverges to the reference.

To define a relation between the wavelength and the efficiency of the partially transpar-ent area size, the relative error is plot against the ratio Beach size / Wavelength (Figure2b). Based on this graph, the beach size of one wave length seems to be a criterion (whichseems physically consistent) to reduce the reflection on the edge of the bathymetry to anacceptable level. The result for other added mass and damping terms are similar.

0.0E+00

2.0E+06

4.0E+06

6.0E+06

8.0E+06

1.0E+07

1.2E+07

0.1 0.3 0.5 0.7 0.9Frequency (rad/s)

CA

33

0m80m160m240mreference

(a) Radiation damping

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5Ratio wavelength / Beach length

CA

33 re

lativ

e er

ror (

%)

260m152m99m80m

(b) Relative error on the radiation damping

Figure 2: Barge over a submerged bottom, Radiation damping

3.2 Comparison with a shallow water code GNWaveAs shown in Buchner (2006) the wave kinematics computed without any special treatmentis not realistic, due to strong reflection at the edge of the bathymetry. The purpose ofthis section is to check if the partially transparent area improves the wave kinematicscomputation. The results obtained are compared with a 2D shallow water code, GNWave,based on the Green-Naghdi theory. This theory is very different from the perturbationapproach. Instead of limiting the order of the solution, the assumption on the verticalvelocity shape and the momentum equation is then depth integrated. The calculation ismade in the temporal domain and allows a fully non linear solution of the problem. Detailson this formulation are provided by Demirbilek & Webster (1992).

As non-linearity is not the topics of this paper, for further comparison with HydroStar,which is in frequency domain, the temporal signal from GNWave is treated by a Fouriertransformation and only the first harmonic is studied (Very low wave amplitudes are usedto avoid second order component). In practice, time evolutions of the wave elevation aremeasured at several points of the numerical water channel and an FFT is then performedon each signal. The time selected has to be long enough to reach the established behaviorand short enough to avoid parasite reflected waves (reflection on the wave maker and onthe imperfect opening condition).

The bathymetry used for this test is represented on figure 3a. In order to enlarge thebathymetry impact, the slope is chosen quite steep.

(a) Bathymetry profile

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

500 700 900 1100 1300

X (m)

Am

plitu

de (m

/m)

GNwave

Hydrostar

(b) Wave amplitude

Figure 3: 2D calculation

The comparison obtained in 2D is very satisfactory, two very different theories agreequite well on the test (Figure 3b). The dispersion relationship is well satisfied upstreamwith both codes. The reflected waves computed by HydroStar and GNWave are compara-ble and quite weak. The smoothing area chosen for the HydroStar computation is about2 wavelengths.

(a) 3D mesh with smoothing area

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

500 700 900 1100 1300

X (m)

Am

plitu

de (m

/m)

GNwaveHydrostar 3D averageHydrostar y=0Hydrostar Y=40

(b) Wave amplitude

Figure 4: 3D calculation

Compared to 2D computation which has shown good results, 3D computation shouldnot rise any other problem than mesh size. The mesh has to be wide enough, then, thereis the need of the smoothing area upstream, but also on the sides. It is thus hard to getresults as good as in 2D, because compromises have to be done (panel size, smoothingarea length or width of the opaque bathymetry) to keep an acceptable computation cost(keeping in mind that the aim is to add a floating body to the computation).

The result obtained without using partial transparency presents a strong reflected wavein X direction and also significant oscillations along the Y axis. The wave kinematicspattern is obviously unrealistic (figure 5a) and would induce wrong loads when computinga ship motion above this bottom. The smoothing areas in both X and Y direction allowsthe computation of the wave refraction on the bathymetry almost without unphysicalreflection.

The results with the incidence of 0 are compared to the 2D case. Due to lack of panelon the smoothing area on the side, the reflection from the side is not fully removed, and anaverage along Y is needed to reach the quality of 2D results. Although not perfect becauseof the lack of panel on the sides, the results presented here are considered satisfactory(Figure 4)

(a) Without treatment (b) With smooth truncation

Figure 5: Wave elevation 15

3.3 Standard LNG above a sloped bottomA standard LNG carrier is now considered over a moderated 1:20 slope. The depth goesfrom 30 to 15m, (see Figure 6). The motions of the ship are computed above the slopewith a smooth extension, and also at constant depth for comparison.

(a) Side view

(b) LNG mesh

Figure 6: LNG over a slope 15

If it is incontestable that the depth has an impact on the motion of the vessel, it is notobvious to predict whether or not the bathymetry variation has a significant impact on thebehavior of the ship. The RAOs of the ship are compared with the modeled bathymetryand at the mean depth (Figure 8a). For the surge motion, the variation of the bathymetrydoes not change the response, however, for heave motion; the slope does have an influence,especially if the incidence differs from 0 (Figure 9).

This change of motion is not only caused by the modified kinematics of the incidentwave, but also from the modification of the added mass and damping of the ship (seeFigure 8b). In this configuration, that is to say with the LNG perpendicular to the coast,the added mass and damping term of heave and roll are the most sensible to the slopedbottom.

0.0E+00

1.0E-01

2.0E-01

3.0E-01

4.0E-01

5.0E-01

6.0E-01

7.0E-01

8.0E-01

9.0E-01

1.0E+00

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency (rad/s)

Surg

e (m

/m)

Water depth 22.5mSloped bottom

(a) Surge 0

7.6E+09

7.8E+09

8.0E+09

8.2E+09

8.4E+09

8.6E+09

8.8E+09

9.0E+09

9.2E+09

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency (rad/s)

CA

44


(b) Roll radiation damping

Figure 7: RAOs with and without sloped bottom

0.0E+00

1.0E-01

2.0E-01

3.0E-01

4.0E-01

5.0E-01

6.0E-01

7.0E-01

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency (rad/s)

Hea

ve (m

/m)


(a) Heave 0

0.0E+00

1.0E-01

2.0E-01

3.0E-01

4.0E-01

5.0E-01

6.0E-01

7.0E-01

8.0E-01

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency (rad/s)

Hea

ve (m

/m)


(b) Heave 15

Figure 8: Heave RAO

4 CONCLUSIONThe smoothing of the bathymetry truncation by the introduction of a partially transparentarea successfully attenuates unexpected reflections. Added mass, damping terms andincident wave kinematics are better computed. The minimum size for the smoothing areahas been found to be about one wavelength. A well dimensioned bottom then results inmore accurate seakeeping calculations in area of variable waterdepth.

However, computing the incident wave field in a wide area with a potential code iscomputationally expensive and remains linear. As the non-linearity could be significantin shallow water, it would be valuable to combine the advantages of a non-linear shallowwater code with radiation/diffraction software. The shallow water code (Boussinesq orGreen-Naghdi for instance) would be used to provide the incident wave kinematics asan improved input for the diffraction/radiation code, which would then use the localbathymetry to compute the added mass and damping term of the ship.

References

[1] Chen Xiao-Bo (2004) Hydrodynamics in offshore and Naval Application - Part 1,Keynote lecture at the 6th International Conference on Hydrodynammics, The Uni-versity of Western Australia, Perth, Australia

[2] Buchner Bas, (2006) The motion of a ship on a sloped seabed, OMAE2006-92321,Hamburg, Germany

[3] Molin Bernard & Betous (1993) Attenuation de la houle par une dalle horizontaleimmergee et perforee, Actes des Quatriemes Journees de l’Hydrodynamique, Nantes.(inFrench)

[4] Teigen.P (2005) Motion response of a spread moored barge over a sloping bottom,Proc of the fifteenth International Offshore and Polar Engineering Conference, Seoul,Korea.

[5] Demirbilek Zeki & Webster William (1992) Application of the Green-Naghdi theoryof fluid sheets to shallow-water wave problems.

[6] Bingham H.B. (2000) A hybrid Boussinesq-panel method for predicting the motionof a moored ship

THREE-DIMENSIONNAL HYDRO-ELASTIC WAGNER IMPACTUSING VARIATIONAL INEQUALITIES

Thomas Gazzola & Jérôme de Lauzon

Research Department, Bureau VeritasCourbevoie, Paris La Défense, Franceemails: [email protected], [email protected]

ABSTRACT

We propose an hydro-elastic impact model for fluid-structure flat impacts.The fluid is assumed potential, and the structure is considered linear. The impact is solved through

the Wagner approximations, using the displacement potential and a variational inequality method.The coupling algorithm is validated against the semi-analytical solution of an elastic cone falling

into calm water. The numerical simulation gives precise results.The method is also tested on an inclined clamped plate, falling into water at constant imposed

velocity. This case illustrates the differences between coupled and uncoupled impacts, and needs tobe validated with experiments and measurements.

INTRODUCTION

In order to deal with flat fluid structure impacts, a simplifiedmodel was developped in 1932 by Wagner[Wag32]. To be able to simulate violent impacts - for examplein LNG carriers tanks - we propose inthis article a way to solve the three-dimensional hydro-elastic impact.

1 HYDRO-ELASTIC FORMULATION

1.1 Fluid formulation

We suggest to solve the three dimensional Wagner problem by using a variational inequality method(details may be found in [Kor82] and [GKMS05]). These methods make use of thedisplacementpotentielφ, which is the integration with respect to time of the velocity potentielϕ.

φ =

∫ t

0ϕ dτ. (1)

The Wagner approximation linearises the wet and free surfaces on the planz = 0, assumingfluid and structure make a flat impact.

The problem was first solved for rigid body impacts (see [GKMS05]). For the issue of flexiblestructure impact, it is necessary to take into account the deflection of the structure (see figure 1).

uz(x, y, t)

x

y

z

Figure 1:Water impact for a flexible structure. The vertical deformation of the structureuz must be taken into account.

The vertical derivative∂zφ of the displacement potential on the planz = 0 characterises theelevation of water(seee.g. [GKMS05]). The position of the structure on the wet surfaceΓw isf − h + uz, wheref describes the structure shape,h is the penetration depth anduz is the verticaldeformation of the structure.

On the free surfaceΓf , the Wagner approximation leads toφ = 0. The boundary value problemsatified byφ is

∆φ = 0 in Ω = z < 0φ = 0 onΓf

∂zφ = f(~x) − h(t) + uz(~x, t) onΓw

φ → 0 in the far field.

(2)

Γf andΓw are unknown, and must be determined as part of the solution.The boundary value problem (2) can be transformed into variational inequalities (see [GKMS05]).

a(φ, v − φ) > l0f (v − φ) + l1f (~u, v − φ),∀v ∈ K. (3)

The proper definition of functional spaceK can be found in [GKMS05].a, l0f andl1f are

l0f (v) =

∫∫

z=0(f(x, y) − h(t)) · v dx dy, (4)

l1f (~u, v) =

∫∫

z=0~ez · ~u(x, y, t) · v dx dy, (5)

and

a(u, v) =1

2π

∫∫

(x,y)∈D

∫∫

(x0,y0)∈D

∇2u(x, y) · ∇2v(x0, y0) ·dx0 dy0 dx dy

√

(x − x0)2 + (y − y0)2. (6)

Bilinear form a is the Laplacian bilinear form, and is transformed using boundary element method.The integration domainD is a part ofz = 0 large enough, such that we are sure that it contains thewet surface (see [GKMS05] for details).

The fluid variational formulation of the hydro-elastic Wagner impact is very similar to its formula-tion for the uncoupled case. The only difference is the terml1f (~u, v) which translates the flexibility ofthe structure into the variational problem. Anyway, for agiven deflection~u, the mathematical formu-lation for the coupled and uncoupled fluid problems are equivalent, and the hydro-elastic inequalitycan be transformed into a constrained minimisation question.

φ = arg minv∈K

(

1

2a(v, v) − l0f (v) − l1f (~u, v)

)

. (7)

1.2 Structure model

Writing the variational formulation of a linear elastic structure under the small displacement assump-tion is classical; details may be found in [Aub00]. The behavior law is σij = Rijkl · εkl, with σ, Randε respectively the stress, Hooke and strain tensors.

The principle of virtual power (within the small perturbations approximation) is

∫∫∫

Ωs

ρs

∂2~u

∂t2· ~v dΩ +

∫∫∫

Ωs

Rijkl · εkl(~u) · εij(~v) dΩ

=

∫∫

z=0(p · ~n) · ~v dΣ, ∀~v ∈ H1(Ωs)

3. (8)

where~u is the displacement andp is the fluid pressure.In order tokeep the symmetry with the fluid problem, we divide the classical mass and stiffness

bilinear forms by the fluid volumic massρf . This leads to the definition of bilinear formsm (mass),k(stiffness) andls (right hand side).

m(~u,~v) =

∫∫∫

Ωs

ρs

ρf

· ~u · ~v dΩ,

k(~u,~v) =

∫∫∫

Ωs

1

ρf

· Rijkl · εkl(~u) · εij(~v) dΩ,

ls(~f,~v) =

∫∫

z=0

~f · ~v dΣ.

(9)

1.3 Hydro-elastic system of equations

Bilinear formsls and l1f are adjoint of each other.l1f is then linked to operatortR, and ls will beassociated to operatorR.

ls andl1f will also play the crucial role in the information transfertbetween incompatible fluid andstructure meshes.

In the end, we define

a(u, v) = (Au, v),m(u, v) = (Mu, v),k(u, v) = (Ku, v),l0f (v) = (L0, v),

l1f (~u, v) = (tR~u, v).

(10)

And the operatorH attached to the constrained minimisation problem:

H(L1) = arg minΦ60

(

1

2tΦ · A · Φ − tL0 · Φ − tL1 · Φ

)

. (11)

Hence the following relation between the structure deflection and the displacement potential:

Φ = H tR(X). (12)

The pressure is linearised asp = −ρ ∂2t φ. The hydro-elastic is then written as the following system

M∂2X

∂t2+ KX = −R

∂2Φ

∂t2Φ = H t

R(X)(13)

2 TIME DISCRETISATION

The hydro-elastic system (13) is discretised in time using asecond order central finite differencescheme, with a constant time step∆t.

We note as an exponent the time step numbern (with t = n ·∆t). For example,Xn−1 is thestructure displacement at timet = (n − 1)·∆t.

MXn+1 − 2Xn + Xn−1

∆t2+ K

Xn+1 + Xn−1

2

= −RΦn+1 − 2Φn + Φn−1

∆t2+ O(∆t2),

Φn+1 = H tR(Xn+1).

(14)

At each time step, we are searching forXn+1 andΦn+1; the vectorsXn−1, Xn, Φn−1 andΦn beginknown and written on the right hand side.

Φn+1 = H tR(Xn+1),

(M +1

2∆t2K)Xn+1 + RΦn+1 = Gn,

(15)

whereGn = M(2Xn − Xn−1) + R(2Φn − Φn−1) − 12∆t2KXn−1. We define the structure operator

S =

(

M +1

2∆t2K

)−1

. (16)

The discretised hydro-elastic system (14) is rewritten as

S−1Xn+1 + RΦn+1 = Gn,

Φn+1 = H tR(Xn+1).

(17)

This system of two equations can be reduced to one single equation, by substituting the second relationinto the first one.

S−1Xn+1 + FXn+1 − Gn = 0, (18)

where the fluid operatorF was defined as

F = R H tR. (19)

3 SOLVING THE HYDRO-ELASTIC PROBLEM

The non-linear hydro-elastic equation (18) is considered under the from

N(Xn+1) = 0. (20)

Equation (20) can be seen as a multidimensional root-findingproblem. Using the Newton method tosolve this equation leads to the iterative process

Xn+1p+1 = Xn+1

p − JN(Xn+1p )−1 N(Xn+1

p ), (21)

whereJN(Xn+1p ) is the Jacobian of operatorN at point(Xn+1

p ).

The main issue for the Newton resolution method is the computation of the JacobianJN of theconsidered operatorN.

N is defined as the sum of three operators:X 7→ S−1(X), X 7→ F(X) and the constant operatorX 7→ G. Since the derivation operation is linear, the Jacobian of the sum is the sum of the Jacobians.

First, the operatorX 7→ G is constant, and thus its Jacobian is zero.In a second time, we need to compute the Jacobian of the structure operator. A linear elastic

structure is considered. In this precise case, the operatorS−1 defined in equation (16) is linear. Andthen, its Jacobian isS−1 itself.

JS−1 = S−1. (22)

In the end, the Jacobian of the fluid operatorF must be computed too.F is defined in equation(19). The Jacobian of this composed function at pointX is

JF(X) = JR(H tR(X)) · JH(tR(X)) · JtR(X) (23)

Hence, the aim is to compute the Jacobians ofR, tR andH. R andtR are linear; their Jacobians areR and tR themselvesJR = R andJtR = tR. The crucial issue is then to compute the derivative ofoperatorH defined in equation (11).

The main difficulty is thatH is not derivable everywhere, due to theconstraints in the minimisationprocess.

Let us suppose that the optimisation process in the operatorH is unconstrained. Then operatorHwould be the affine functionL1 7→ A−1L1 + A−1L0. The Jacobian of this function isA−1.

In our case, theconstrainedoptimisation is equivalent to anunconstrainedminimisation inside thecone of constraintsC.Of course, theC is unknown, and has to be determined as a part of the solution.

Assuming the cone known, then the Jacobian ofH could be computed, and would be the inverseof the restriction ofA to the coneC, i.e. JH = (A|C)

−1.For every structure deformationXn+1

p , it is possible to compute the displacement potential, andto deduce the cone of constraintsCp (which is where the displacement potential is not zero).

As a conclusion, the Jacobian of operatorN is

JN = S−1 + R (A|C)

−1 tR. (24)

where the termR (A|C)−1 tR can be considered as anadded mass matrixfor the fluid structure

interfaceC.By defining the Jacobian in this way, we skip the problem of derivating along the constraints.

4 VALIDATION CASE

The Wagner problem for anelastic conehas been solved in [Sco04]. The cone has a radiusR =0.128m, and is made of aluminium (E = 1.2 · 102 N/m2, ν = 0.3, ρ = 2700 kg/m3). The thicknessof the plate is 1.5mm, and it is clamped in the center and on the boundaries. The dead rise angle is6. It enters calm water at imposed velocity 8.3m/s.

A modal approach was used. Figure 2 shows the modal generalised displacements for the firstthree modes of the structure during the impact process.

The numerical simulation was performed withnoassumption of the axisymmetry of the case. Theresults show fairly good agreement with the semi-analytical simulation.

−0.01

−0.008

−0.006

−0.004

−0.002

0

0.002

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016

gen

eral

ized

dis

pla

cem

ents

time [s]

Scolan − mode 1

Scolan − mode 2

Scolan − mode 3

Figure 2:Generalised displacements for the first three modes of the cone, during the impacting process. Continuous linesare the simulations provided in [Sco04]. The crosses are theresult of the method described in this article.

5 CLAMPED PLATE SIMULATION

Variational inequalities used to solve Wagner problem are now coupled with a commercial finite ele-ment software.

Eigen-modes are first calculated with the FEM software and then imported in Bureau Veritas’s in-house code to simulate hydro-elastic impacts. For example,following figures show results of coupledsimulation for a square clamped plate. Realistic industrial structures could be considered too.

The plate is1 m× 1 m and its thickness is20 mm; it is made of steel with linear isotropic elasticbehavior (volumic massρ = 7800kg · m−3, Young modulusE = 2.1 · 105MPa, Poisson’s ratioν = 0.3). 10 eigen-modes were used.

Parameters for the impact simulations are impact velocityV = 10m · s−1 and angleβ = 5.Comparison is made with an uncoupled simulation (comparingdisplacement and von Mises stressesat the center of the plate).

CONCLUSIONS

A three-dimensionnal hydro-elastic impact model has been described. Numerical resolution has beencarefully studied, and the process has been validated with respect to semi analytical solutions. Com-parisons with respect to the experiments are now needed to validate the theoretical model.

-4

-2

0

2

4

6

8

10

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

disp

lace

men

t (m

m)

time (sec)

CoupledUncoupled

Figure 3:Displacement at the center of the plate, for both coupled anduncoupled cases.

0

50

100

150

200

250

300

350

400

450

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Str

ess

(MP

a)

time (sec)

CoupledUncoupled

Figure 4:Von Mises stress at the center of the plate, for both coupled and uncoupled cases.

References

[Aub00] D. Aubry. Mécanique des milieux continus. École Centrale Paris, 2000.

[GKMS05] T. Gazzola, A.A. Korobkin, S. Malenica, and Y.-M. Scolan. Three-dimensional Wagnerproblem using variational inequalities. Inproceedings of the International Workshop onWater Waves and Floating bodies, volume 20, 2005.

[Kor82] A.A. Korobkin. Formulation of penetration problemas a variational inequality.Din.Sploshnoi Sredy, 58:73–79, 1982.

[Sco04] Y.-M. Scolan. Hydroelastic behaviour of a conical shell impacting on a quiescent-freesurface of an incompressible liquid.Journal of Sound and Vibration, 277, Issues 1-2:163–203, 2004.

[Wag32] H. Wagner. Über Stoß-und Gleitvorgänge an der Oberfläche von Flüssigkieten.Zeitschriftfür Angewandte Mathematik und Mechanik, 12:192–215, 1932.

SOME ASPECTS OF 3D LINEAR HYDROELASTIC MODELS OFSPRINGING

Malenica S.1, Tuitman J.T.2, Bigot F.1 & Sireta F.X.1


(2) Delft University of Technology, Netherlands.

ABSTRACT

The paper deals with the modeling of the linear wave induced ship vibrations called springing.The presented method is based on the full coupling of 3DFEM structural model and 3DBEMhydrodynamic model. Only linear springing in frequency domain is considered. The so calledmodal approach is used, which means that the total structural response is presented as a series ofthe dry structural modes precalculated by the 3DFEM structural code. The coupling with 3DBEMhydrodynamic model is performed by defining the additional boundary value problems for radiationpotentials associated with those structural modes. Finally the dynamic modal equation is solvedwhich makes the strains and stresses RAO’s available in any part of the ship structure.

The total structural response is decomposed into quasi static and dynamic part, in order to clearlyevaluate the influence of springing on the overall ship structural response. The decomposition intothe quasi static and dynamic part also allows superimposing the springing response to the existingquasi static fatigue calculation methods and ensures the proper convergence of the results.

1 Introduction

Springing is usually defined as the entertained global ship structural vibrations induced by waterwaves. Springing is a resonant phenomenon in contrast to the whipping which is the transient shipvibrational response induced by impulsive loading (slamming, green water, underwater explosion,...). A typical springing and whipping responses are shown in Figure 1, where we can clearlyobserve the fundamental difference between the two phenomena.

Figure 1: Typical springing (left) and whipping (right) ship structural response. Top - total signal, bottom- filtered signal.

The springing type of ship hydro-elastic structural response is usually not considered in the designprocess of the conventional seagoing ships. The main reason is the significant gap between theship wet natural frequencies and the wave frequencies encountered by the ship in the commonsea states. This does not means that the conventional ships are not experiencing the springingduring their service, but springing amplitudes are believed to be quite small. However, this is notnecessarily true and the evidences of the important non-linearly induced springing response were

recently reported for some bulk carriers (e.g. [7]). Non linear hydroelastic springing modeling isextremely difficult and, it is fair to say that, no efficient numerical model exists up to now. Thisis mainly due to the complicated non linear hydrodynamics which, in the case of ship advancingin waves with a forward speed, is still not solved properly and that even in the linear case.

In the present context, it is also important to recall the case of the springing response of thetendons of the Tension Leg Platforms (TLP), e.g. [5], where the non linear wave excitation wasmore or less successfully explained by the so called second order diffraction theories, which werenumerically possible thanks to the fact that the TLP is stationary floating body (no forward speed).In principle, the same kind of methods should be applied in the case of the ships but, as alreadyexplained, this seems to be beyond the state of the art of the nowadays numerical methods.

Figure 2: Ultra large container ship and its typical midship section.

The springing type of ship structural response was reactualized recently, in the context of theUltra Large Container Ships (Fig. 2). Indeed, due to their huge dimensions (length close to 400m) which reduce the structural natural frequencies and particular operating conditions (speed upto 27 knots) which increase the excitation frequencies, a linearly induced springing becomes pos-sible. On the other hand, due to their complex structure with open midship section, these shipscan hardly be modeled by the equivalent beam models, which was the usual practice for spring-ing/whipping calculations, and complete 3DFEM model is necessary. All these facts represent themain motivation for the present study.

2 Linear hydroelastic model in frequency domain

The general methodology for hydroelastic seakeeping model is rather well known and the firstdevelopments can be attributed to Bishop & Price [1]. In their work they used the simplified, socalled Timoshenko beam model for structural modeling and strip theory for seakeeping part. Sincethen several more or less sophisticated models were proposed (e.g. [2, 8, 9, 10]).Below we briefly recall the basic principles of the model used in this study. The 3DBEM model forthe seakeeping is coupled to a 3DFEM model of the ship structure. A more detailed descriptionof the applied 3DBEM model can be found in [3] and [6].

In contrast to the well known rigid body seakeeping model, the hydroelastic model basically extendsthe motion representation with the additional modes of motion/deformation chosen as a series ofthe dry structural natural modes. We write:

H(x, y, z, t) =

N∑

i=1

ξi(t)hi(x, y, z) =

N∑

i=1

ξi(t)[hix(x, y, z)i + hi

y(x, y, z)j + hiz(x, y, z)k] (1)

where hi(x, y, z) denotes the general motion/deformation mode which can be either rigid or elastic.The above decomposition leads to the additional radiation boundary value problems (BVP) forelastic modes, with the following change in the body boundary condition:

∂ϕRj

∂n= hjn (2)

After solving the different BVP-s the resulting pressure is calculated using Bernoulli’s equationand integrated over the wetted surface in order to obtain the corresponding forces, so that the

following coupled dynamic equation can be written:

−ω2

e([ m ] + [ A ]) − iωe [ B ]+ [ k ] + [ C ]

ξ = FDI

(3)

where:

[ m ] - modal genuine mass

[ k ] - modal structural stiffness

[ A ] - hydrodynamic added mass

[ B ] - hydrodynamic damping

[ C ] - hydrostatic stiffness

ξ - modal amplitudes

FDI

- modal excitation

The solution of the above equation gives the motion amplitudes and phase angles ξi and theproblem is formally solved. Note that the motion equation includes both 6 rigid body modes anda certain number of elastic modes.Several technical difficulties need to be solved before arriving to the above motion equation (3).Certainly the most difficult one is the solution of the corresponding hydrodynamic BVP. In thispaper we do not enter into the detailed description of the methods used to solve the seakeepingproblem at forward speed and we just mention that these difficulties remain the same, both forthe rigid and elastic body. It is fair to say that the numerical methods which are used to solvethe seakeeping problem nowadays, are not fully ready yet for a general combination of speed,heading and frequency. However, most of the methods have approximate solutions to accountfor the forward velocity. The method used in this paper is the so called encounter frequencyapproximation which was reasonably well validated for rigid body case.The second technical difficulty is related to the evaluation of the hydrostatic restoring matrixwhich, in the most general case, takes quite complicated form:

Cij = CHij + Cm

ij (4)

CHij = −g

∫ ∫

SB

(Z∇ · hj + hjz)h

in + Z[(hi∇)hj − (hj∇)hi]ndS (5)

Cmij = g

∫∫∫

V

(hj∇)hiz dm (6)

As we can see from these expressions, the calculation of the restoring matrix requires the knowledgeof the different gradients of the modal shape functions which are not trivial to evaluate using the3DFEM structural models. However, some simplifications of the above expressions seem to bepossible and they are under investigation.The third important technical difficulty concerns the application of the body boundary condition(2) for the general mode of motion. In the next section we briefly explain how this was done inthe present work.

2.1 Body boundary condition

In the case of the simplified beam structural model, the transfer of the modal displacements of thebeam onto a hydrodynamic mesh can be done relatively easy, but in the case of 3DFEM structuralmodel this transfer requires very careful attention. Indeed, the modal displacements are known onthe structural 3DFEM mesh which is usually completely different from the hydrodynamic mesh,so that a special interpolation procedure is necessary. In the present work, the following procedureis adopted.For each hydrodynamic point (panel center) the following steps are performed, these steps areillustrated in figure 3:

yesh(p) = h(s1)

p project on elements

s1

s3

s2

pd

no

s1

s3

s2

yes

Select closets

h(p) =fintp(h(s1), h(s2))

p

p project on linesno

p

s4

s5

s6

select closets point

h(p) = h(s5)

no

ps1

s3

s2

yes

Select closets

h(p) =fintp(h(s1), h(s2), h(s3))

d < ǫ

Figure 3: Mapping procedure

1. Looking for the 3 closest structural points. In the case that one of the 3 points is withinsmall enough distance (ǫ) from the considered hydrodynamic point, we retain that structuralpoint for interpolation.

2. The list of the structural finite elements containing at least one of the above defined pointsis created.

3. The hydro point is projected onto the surfaces created by the retained structural elements. Ifthe projection falls inside the element, the corresponding distance is calculated. The elementwith smallest distance from the hydro point is retained for interpolation.

4. In the case when the hydro point do not project on any element from the list, the projectionon the sides of the considered elements is performed. If the projection falls onto the side,the corresponding distance is calculated. The side with the smallest distance from the hydropoint is retained for interpolation.

5. In the case when there is neither point at ǫ distance, nor element nor the element side on whichpoint project, the structural point closest to the hydro point is retained for interpolation.

6. The interpolation using the shape functions of the retained finite element, of the structuraldisplacements is performed on the projection of the hydro point and the calculated displace-ments are associated to the hydro point.

This procedure was verified on several ship types and showed to be very efficient. In Figure 4 wepresent one example for the first torsional mode of typical ULCS.

Figure 4: First torsional mode of ULCS and the transfer of modal displacements from structural tohydrodynamic model.

2.2 Calculation of the stresses in frequency domain

The solution of the hydroelastic motion equation (3) includes the linear springing response auto-matically. Indeed, once this motion equation solved, all necessary quantities (motions, accelera-tions, stresses, ...) can be easily calculated because the modal decomposition remains valid forany particular quantity. This means that, for example, we can write for the stress distributionΣ(x, y, z, ω):

Σ(x, y, z, ω) =

N∑

i=1

ξi(ω)σi(x, y, z) (7)

where σi(x, y, z) represents the spatial distribution of the stresses corresponding to each mode ofmotion/deformation and ξi(ω) are the modal amplitudes i.e. solution of the motion equation (3).

2.3 Separation of the quasi static and dynamic contributions

In the present context, it is important to note that the rigid body modes do not contribute to anystress, and that the above expression (7) is slowly convergent in general. This is especially true forthe structural details which are affected by the local structural effects. A good example of suchdetail is a hatch corner of the container ship. The longitudinal response is well described by the firstfew longitudinal flexible modes. However, in order to obtain any contribution of the transversal(side shell) loading, one needs to include natural mode shapes which describe the deformation intransversal direction. The 3DFEM methods calculate the structural natural frequencies of theship from the lowest natural frequency. By using a proper 3DFEM model of ship it is relativelyeasy to obtain the first few torsional and longitudinal modes. However, after these lowest globalstructural modes, the numerous local modes with similar natural frequencies will quickly ”pollute”the solution and it will be almost impossible to obtain the subset of modes necessary for accuraterepresentation of the transversal stresses of the hatch corner. Fortunately, the global structuraldynamic response is well described by the first few lowest modes. In order to obtain the convergedstress distribution, the total structural response should be properly separated into the quasi staticand dynamic parts. The stresses due to the quasi static ship response will be calculated, afterseparation, by the so called direct method which calculates the structural response after the ”rigidbody” hydrodynamic pressure is transferred on the wetted finite elements (see section 2.4). It isalso important to note that the decomposition into the quasi static and dynamic response is madewith respect to the structural response, which means that the quasi static structural response doesalso includes the dynamic rigid body response and the dynamic response includes the dynamicstructural response only.In the present approach the decomposition of the different parts of the response is done by firstschematically rewriting the motion equation (3) in the following form:

([

[ RR ] [ RE ][ ER ] [ EE ]

]

+

[

[ 0 ] [ 0 ][ 0 ] [ k ]

])

ξR

ξE

=

F R

F E

(8)

where R stands for the rigid body parts, E for the elastic ones and k is the structural modalstiffness matrix.At the same time we separate the total response amplitudes into the quasi static and dynamicparts:

ξR = ξR0

+ ξRd , ξE = ξE

0+ ξE

d (9)

The quasi static part of the responses is defined by the following equations:

[ RR ]ξR0 = F R (10)

[ k ]ξE0 = F E − [ ER ]ξR

0 (11)

After inserting (9), (10) and (11) into (8), the following linear system of equations for dynamicparts is obtained:

([

[ RR ] [ RE ][ ER ] [ EE ]

]

+

[

[ 0 ] [ 0 ][ 0 ] [ k ]

])

ξRd

ξEd

= −

[ RE ]ξR0

[ EE ]ξE0

(12)

As mentioned before, the above procedure was adopted in order to be able to keep the classicaldirect approach for the quasi static part [4] and to clearly identify the dynamic part as a correctionof the quasi static one. Anyhow, the proposed decomposition completely removes the convergenceproblems discussed before.

2.4 Practical evaluation of the quasi static contribution

The direct approach is used to obtain the converged quasi static response. The hydrodynamicpressures are applied to the structural model and the response is calculated using FEM. Thedirect approach described in this section ensures perfect balance between the hydrodynamic andstructural models.

The final loading of the structural model is composed of two parts:

1. Inertia loads2. External pressure loads

Inertia loads can be included straightforwardly by associating the acceleration vector to each finiteelement. Concerning the pressure loading, most of the methods nowadays use the different inter-polation schemes in order to transfer the total hydrodynamic pressure from hydro model (centroidsof the hydro panels) to the structural model (centroids or nodes of finite elements). Besides theproblems of interpolation, it is important to note that the motion amplitudes, which are present inthe definition of the total pressure, were calculated after integration over the hydrodynamic mesh.For that reason it is impossible to obtain a completely balanced structural model. Indeed, theFEM model has its own integration procedure which is usually different.In order to obtain the perfect equilibrium of the structural model we use two main ideas [4]:

• Recalculation of the pressure in structural points, instead of interpolation• Separate transfer of pressure components, and calculation of hydrodynamic coefficients (added

mass, damping, hydrostatics & excitation) by integration over the structural mesh

The recalculation of the hydrodynamic pressure on the structural points, is possible thanks tothe particularities of the BIE method which gives the continuous representation of the potentialthrough the whole fluid domain Z < 0. In this way the communication between the hydrodynamicand structural codes is extremely simplified. Indeed, it is enough for the structural code to give thecoordinates of the points where the potential is required and the hydrodynamic code just evaluatesthe corresponding potential by:

ϕ(xs) =

∫ ∫

SH

B

σ(xh)G(xh;xs)dS (13)

where xs = (xs, ys, zs) denotes the structural point and xh = (xh, yh, zh) the hydrodynamic point.

In the case of linear seakeeping without forward speed, this operation is sufficient because thepressure is directly proportional to the velocity potential and, within the source formulation, thepotential is continuous across the body wetted surface. This is very important point because, dueto the differences in the hydrodynamic and structural mesh, the structural points might fall insidethe hydrodynamic meshes.In the case of the body advancing with forward speed in waves, the situation is slightly morecomplicated because the hydrodynamic pressure is no more directly proportional to the potentialbut also to its gradient. The problem with the gradient of the potential, in the context of sourceformulation of BIE, is that the gradient is discontinuous across the hydrodynamic mesh, so that therecalculation of the pressure on structural points will likely lead to discontinuities in the pressuredistribution. This means that a preprocessing of the structural points is necessary i.e. these pointsneeds to be artificially moved to the exterior of the hydrodynamic model. The procedure similar tothe one presented in Figure 3 is used to obtain these projection points. Strictly speaking, structuralpoints do not change their position but the pressure associated to them is calculated in the pointswhich are slightly moved off their original position. The error introduced by these manipulationsremains negligible within the limits of the linear theory considered here.

Anyhow, once each pressure component has been transfered onto the structural mesh, the ”new”hydrodynamic coefficients are calculated by integration over the structural mesh:

FDIS

i = iω

∫ ∫

SS

B

(ϕS

I + ϕS

D)nidS (14)

ω2AS

ij + iωBS

ij = ω2

∫ ∫

SS

B

ϕS

RjnidS (15)

where the superscript ” S ” indicates that the quantities are taken on the structural mesh.

A similar procedure is applied for the variation of the hydrostatic pressure in order to obtain therestoring matrix and after that the ”new” motion equation is written:

(

−ω2([ M ] + [ A ]S

) − iω[ B ]S

+ [ C ]S)

ξ0

S

= F DIS

(16)

Solution of this equation gives the rigid body body motions ξ0

S

so that the total linear pressurecan be calculated. In summary the final loading of the structural model will be composed of thefollowing 3 parts:

−ω2miξS

i0 - Inertial loading (to be applied on each finite element)

pS

i - Pressure loading (to be applied only on wetted finite elements)

−migΩS

∧ k - Gravity term (to be applied on each finite element)

It is clear that the above structural loading will be in perfect equilibrium because this equilibriumis implicitly imposed by the solution of the motion equation (16) in which all different coefficientswere calculated by using directly the information from the structural FEM model. In that respectand in order to ensure full consistence between the results of the direct approach as described inthis section and the quasi static part of the modal approach described in the previous sections, thehydrodynamic coefficients in equation (3) should also be obtained by integration over the structuralmesh as explained in this section.Let us also mention that, in practice, the pressure part of the loading can be applied in terms ofthe nodal forces instead of the pressure which proved to be more efficient.

2.5 Top down analysis of structural details

Springing hydroelastic analysis is usually performed using the relatively coarse structural meshand some additional manipulations are necessary in order to obtain the local stresses in the critical

structural details. Usually the so called top down analysis is applied. The top down analysis is welldeveloped for the classical quasi static structural responses. The principles are relatively simple

Figure 5: Typical structural details and their position on the ship structure.

and the calculations are performed in two steps:

1. Calculation of the global structural response on the coarse mesh

2. Application of the structural deformations of the coarse mesh on the fine mesh and calculationof the local stresses

One typical situation is shown in Figure 5. As already mentioned before, in the case of the quasistatic structural analysis, the loading case for the structural FEM model is built by consideringthe ship as a rigid body. After solving the rigid body seakeeping boundary value problems, theresulting pressure is applied on the FEM mesh together with the inertia loads resulting from therigid body accelerations. Since, in the rigid body case, the hydrodynamic and structural parts ofthe problem are independent they can be performed separately and the transfer, of the resultingdeformations of the coarse mesh, onto the fine mesh is relatively straightforward. In the case ofdynamic structural analysis, which is of main concern here, the additional loading cases for finemeshes need to be created. These additional loading cases correspond to each structural naturalmode deformations. The resulting local stresses should be added to the quasi static ones, afterbeing previously multiplied by the associated dynamic modal amplitudes ξE

d .

3 Numerical results and discussions

First we present few results related to the convergence of the modal representations for the struc-tural response in terms of the global internal loads and the local structural stresses. Figure 6 showsthe RAO’s for these quantities calculated using different number of mode shapes and the directapproach. Note that only the static response is considered here as it is very difficult to calculatethe real dynamic response by the direct approach. As is clearly visible in figure 6 and true for mostof the cases, the convergence in terms of the global quantities, such as vertical bending momentor sectional shear forces is much better, than the convergence of the local stresses. This resultappears to be in line with the intuition because the local stresses are likely to be influenced, muchmore, by the higher structural modes while the global quantities will normally filter these localcontributions in most of the cases. All this implies that, in order to ensure proper convergence, thequasi static part of the structural response should be calculated using the classical direct approachfor rigid body hydrodynamics, and only the dynamic part should be calculated using the modalapproach. In this way, the number of the dry structural modes which are necessary for dynamic

analysis is reducing to a few global modes only and these modes can be calculated relatively easilyby any commercial 3DFEM software.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

M_y

[GN

m]

Omega_e [rad/s]

Nf=8 Nf=16 Nf=32 Nf=48 Nf=64 Direct

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Sig

ma

[MP

a]

Omega_e [rad/s]

Nf=8 Nf=16Nf=32Nf=48Nf=56Nf=64Direct

Figure 6: Convergence of the modal representation for vertical bending moment (left) and local structuralstresses (right).

In Figure 7, the results for the local stresses in the hatch corner of the ULCS are presentedand decomposed into quasi static and dynamic parts, and in Figure 8 the local stresses for twodifferent ship speeds are illustrated. It is interesting to observe that the dynamic part of the

0

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5

Sig

ma

[MP

a]

Omega_e [rad/s]

Quasi staticDynamic

Total

Figure 7: Typical stress RAO decomposed into quasi static and dynamic parts.

response contributes to the stresses even for the frequencies well away from the structural naturalfrequency. This might seem a bit strange, but one should remind that these are very flexibleships. The static deformation of the structure, due to the still water bending, between midshipand the fore perpendicular is of the order of 1m for the ULCS. The wave bending moment is of thesame order as the still water bending moment and will cause the same order of deflections. Thisdeflection will influence the heave response and the total bending moment.On the other hand, the influence of ship speed on dynamic springing response is evident. Indeedhigher speed will induce the higher stresses because the encounter frequency will be increased sothat the corresponding wave lengths will increase too, and the modal excitation will become moreimportant.

4 Conclusions

We presented here an efficient linear model for springing calculations. The main advantage ofthe model, as compared to more classical equivalent beam models, lies in the fact that a 3DFEMstructural model is used. This allows for an easy and fast access to the local stresses at any position

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5 3

Sig

ma

[MP

a]

Omega_e [rad/s]

v=0.6Vmaxv=Vmax

Figure 8: Typical stress RAOs for different ship speeds.

of the ship. Furthermore, the response decomposition into the quasi static and dynamic parts isproposed in order to ensure the proper convergence of the results.

Some preliminary results which are presented here, stress the importance of utilizing a hydroelasticanalysis for ULCS’s even when springing is not explicitly considered.

The remaining work will include more thorough validation of the model by comparisons with modeltests and full scale measurements, as well as the proper integration of the springing responses intothe design procedures.

ACKNOWLEDGEMENTS

Authors acknowledge the support of the MARSTRUCT European project.

References

[1] Bishop, R.E.D. & Price, W.G., 1979. : ”Hydroelasticity of ships”, CUP.

[2] Jensen J.J. & Wang Z., 1999. : ”Wave induced hydroelastic response of high speed monohulldisplacement ship.”, 2nd. Int. Conf. on Hydroelasticity, Fukuoka, Japan.

[3] Malenica S., Molin B., Remy F. & Senjanovic I., 2003. : ”Hydroelastic response of abarge to impulsive and non impulsive wave loads.”, 3rd. Int. Conf. on Hydroelasticity, Oxford.

[4] Malenica S., Stumpf E., Sireta F.X. & Chen X.B., 2008. : ”‘Consistent hydro-structureinterface for evaluation of global structural responses in linear seakeeping.”, 26th OMAE Conf.

[5] Molin B., 2003. : ”Hydrodynamique Off shore.”, Technip.

[6] Newman, J.N., 1994. : ”Wave effects on deformable bodies”, Applied Ocean Research, Vol.16, pp.47-59.

[7] Perunovic J.V. & Jensen J.J., 2005. : ”Non linear springing excitation due to a bidirec-tional wave field.”, Marine Structures 18, pp. 332-358.

[8] Wu M.K. & Moan T., 1996. : ”Linear and nonlinear hydroelastic analysis of high speedvessels.”, J. of Ship Res., Vol.40/2, pp.149-163.

[9] Wu Y. & Price W.G., 1986. : ”A general form of the interface boundary condition of fluidstructure interaction and its applications.”, CSSRC Rep. 86010.

[10] Xia J. & Wang Z., 1997. : ”Time domain hydroelasticity theory of ships responding towaves.”, J. of Ship Res., Vol.41/4, pp.286-300.

Advanced computations of mooring systems

C. Brun, D. Coache & F. Rezende

Research Department, Bureau Veritas

5-6, Place de l’Iris, 92400 Courbevoie, Paris La Defense

email: [email protected]

ABSTRACT: The analysis of mooring systems is becoming more and more complex withthe emergence of large floating units like LNG terminals anchored in deepwater or in waterareas of relatively small depth. Depending on the site characteristics and environmentalconditions, the design of mooring systems needs more and more aides from advancedcomputations to simulate the motion of floating units and the variation of mooring linestensions. Based on the classical quasi-dynamic formulation developed since more than 20years in Bureau Veritas, new developments have been recently performed. They consist ofthe accurate simulation of second-order wave loading by involving full QTF, the interactionbetween two vessels and the modelling of their connections of different types. Furthermore,the optimisation of temporal simulations and the development of user friendly interfacemake more efficient the practical applications. To illustrate the powerful features of ourmodel, an example of detailed analysis will be included in the paper.

1 INTRODUCTION

Floating units are used increasingly to drill and store the offshore oil and gas. Becauseof the offshore environment diversity depending on location and time, the design of thesemoored structures has to be studied intensively and in an accurate way.

Nowadays, floating offshore units are installed in areas of different water depths. SomeFPSO are anchored by more than 1500m of water depth and recent examples of LiquefiedNatural Gas (LNG) terminals anchored in shallow water depth (around 30m). Both,deep and shallow water operations, present different particularities to the mooring systemdesign and the calculation methods shall be chosen accordingly.

In addition, side-by-side operations are starting to be routinely used for both oil andgas offloading. Normally, limiting weather conditions are defined based on operationalexperience. However, it is very important to access those values by means of numericalcomputations. Moreover, the hydrodynamic and mechanical interactions of two bodies inclose proximity are not trivial and need to be evaluated carefully.

Furthermore, considering that more and more environmental data are available, exten-sive calculations may be now performed based on hindcast model results or measurements.Taking into account the improvement of the computers efficiency, computation time is stilla limiting parameter, especially for models based on a full coupling between mooring andstructure.

It is important in Bureau Veritas activities to be able to perform mooring analysis aspart of an independent verification of engineering designs. In this context, the ARIANE

mooring software is in continuous development. This paper deals with aspects of multi-body modelling and wave low-frequency loads computations, that both constitute one ofthe latest research topics. As an example of application, a multi-body system duringoffloading operations in side-by-side is studied and some numerical results are presented.

2 GENERAL METHODOLOGY

There are basically two types of analyses that are generally accepted in the commonpractice:

• Fully coupled analyses: the lines are modelled using the finite element method. Themotions of the vessel are calculated accounting for the contribution of the lines (dragforce, damping and stiffness). The problem may be solved either in frequency domainor time domain.

• Weakly coupled analyses: For these analyses, two models are necessary. In the firstmodel the lines are modelled as non-linear springs without mass. The drag anddamping forces coming from the mooring lines shall be pre-calculated and appliedto the vessel as external data. The motions of the vessel are calculated either infrequency or time domain and the tensions in the mooring lines are given by thedisplacement at the fairlead point (quasi-dynamic analysis). In the second modelthe dynamic behaviour of the mooring lines are calculated by finite element and thedisplacements at the fairlead are prescribed.

Fully coupled analyses (lines + vessel) are very time consuming. That’s why it’s inter-esting to perform a weakly coupled analysis where the dynamics of the mooring lines areevaluated only for the critical cases identified in the quasi-dynamic analysis.

3 MULTI-BODY CALCULATIONS

More and more studies are dedicated to multi-body configurations. Thus, the interactionsbetween multiple bodies has become a key issue for the analysis of complex mooringsystems or offloading operations, which main configurations are in tandem (two vesselslocated one behind the other) and in side by side (two vessels parallel to each other).Another multi-body application could be turrets modelling. Indeed, instead of modellingthe turret by one single point where all lines are connected, the turret and the vessel canbe modelled as two different bodies. Thus, mooring lines between the seabed and theturret can be correctly located around the turret and loads between the turret and thevessel estimated.

The interactions between two bodies can be divided into two classes: mechanical (dueto the connection system) and hydrodynamic/aerodynamic (waves, wind and current). Incase the vessels are sufficiently far from each other (for example in most part of tandemconfigurations), the hydrodynamic/aerodynamic interactions may be neglected. However,when the vessels are close from each other, those interactions shall be taken into accountproperly. In the present paper, only the aspects regarding the mechanical interactionsbetween two vessels in side-by-side configuration are considered.

3.1 Multi body specific elements

In order to simulate correctly multi-body situations, some particular elements should beadded. In side by side configurations for example, hulls are protected by fenders.

The characteristic of a fender is highly non-linear and the contact point between a fenderand a vessel is not constant during the simulation. One way to calculate fender loads isto model a fender attached to one vessel and acting with another vessel. In this case, thepoint of application of the fender loads on the second vessel is calculated at each timestep. In the same way as for a mooring line, the characteristic of the fender should alsobe given as a curve representing horizontal tension in function of the effective distance,being the effective distance equal to the diameter of the fender.

Figure 1: ARIANE fender module a) Fender display b) Fender modelling

3.2 Mooring stiffness matrix

A main parameter in multi-body simulations is the global stiffness matrix which is com-posed of that of mooring lines linked to the sea bottom and that due to the connectionbetween two vessels. This matrix gives valuable information of the resonant modes ofthe system, for a given position of the vessels, in particular at the equilibrium position ofthe moored system. Additionally, one may be interested in investigating how this matrixvaries as the vessels positions change. An example of stiffness matrix for a side-by-sideconfiguration is given in section 5.

4 WAVES LOW-FREQUENCY LOADS

The wave low-frequency loads are the second-order loads that excite the vessel at a fre-quency equal to the difference of two wave frequencies (ω1−ω2). As the resonant frequencyof the mooring systems is often very low (∆ω < 0.05rad/s), the waves low-frequency loadsrepresent one of the main sources of the system excitation. The accurate estimation ofthose loads is crucial for the correct estimation of the lines tension.

In the common practice, the design of moored systems is made using the Newmanapproximation, which is based on a very low resonance frequency of the system (∆ω (ω1 + ω2)/2) and small contribution of the second order wave fields. The advantage ofthis formulation is that it only requires the computation of the diagonal terms of the QTF(Quadratic Transfer Function) matrix and the time series reconstruction is made usingsingle sums only. This type of approximation is satisfactory for systems moored in deepwater but can underestimate the drift loads in shallow water or for stiff mooring systems.In these cases, in order to estimate correctly the second order loads, the full QTF matrixshall be computed. The disadvantage of the FullQTF method concerns the time seriesreconstruction by means of double sums which increases significantly the computationtime.

Recently, a new formulation has been presented in [1] and [2]. Considering ∆ω 1, theQTF can be developed in an expansion depending on ∆ω. The quadratic transfer functionT (ω1, ω2) is then composed of one component T 0(ω) depending on ω = (ω1 + ω2)/2 andanother component ∆ωT 1(ω) linearly proportional to ∆ω = (ω1 − ω2). This formulation,hereafter called BV approximation, presents very good results for systems which resonancefrequencies are below 0.05 rad/s and for any water depth. The main advantage of thisformulation concerns the time series reconstruction of loads that can be done by means ofsingle sums in the same way as Newman approximation.

In figure 2 the comparison between the three methods of computation of waves second-order loads is made for a LNG vessel at a water depth of 15m in head waves condition

(Pierson-Moscowitz, Hs = 3m, Tp = 10s). It can be noted that the results given by theBV approximation match quite well with the ones given by the full QTF, while Newmanapproximation dramatically underestimates the loads.

Figure 2: Comparison of the vessel’s surge motions according to different calculationmethods in shallow water

5 NUMERICAL EXAMPLE AND DISCUSSIONS

A multi-body system has been chosen as case study, where one of the vessels is anchoredto the ground and the other is moored to the first one in side-by-side configuration. Thebehaviour of both vessels in such configuration is discussed and some numerical resultsare presented.

5.1 Description of the mooring system

The system is composed of two bodies linked together in a side-by-side configuration. Oneof the two vessels is moored to the seabed by means of a spread mooring system, whilethe other is linked to the first one using synthetic ropes (see figure 3). The anchoring linesare composed by chains in catenary configuration at a water depth of 500m.

Figure 3: Representation of the mooring system used in the example

In addition to the lines between the two vessels, two fenders are modelled between thevessels. Their characteristic is given in figure 4.

Figure 4: Representation of the fenders reaction force against the effective distance be-tween the vessels

5.2 Resonant periods of the system

Before performing the mooring analysis in presence of all the environmental loads, it’sinteresting to evaluate the resonant periods of the system and if/how those periods changewith respect to the position of the vessels. This analysis can bring valuable information tothe choice of the calculation method. It can be performed in both frequency domain, usingthe stiffness matrix calculated at different positions of the vessels, and in time domain,using decay tests performed around different mean positions.

5.2.1 Stiffness matrix and resonant modes

The stiffness matrix of a multi-body system is a n×n matrix with n equal to the numberof modes times the number of bodies. The table 1 presents an example of stiffness matrixcalculated at the equilibrium position (without loads) of the above described mooringsystem.

surge b1 sway b1 yaw b1 surge b2 sway b2 yaw b2surge b1 5.36E+02 9.44E−02 -1.37E+04 -4.44E+02 -9.44E−02 1.37E+04sway b1 8.98E−02 2.76E+03 -3.67E+00 -8.98E−02 -2.67E+03 3.67E+00yaw b1 -1.36E+04 -3.67E+00 2.33E+07 -1.20E+04 -5.12E−01 -1.96E+07

surge b2 -4.44E+02 -9.44E−02 -1.20E+04 4.44E+02 9.44E−02 1.20E+04sway b2 -8.98E−02 -2.67E+03 -6.73E−01 8.98E−02 2.67E+03 6.73E−01yaw b2 1.36E+04 3.67E+00 -1.96E+07 1.20E+04 5.12E−01 2.03E+07

Table 1: Stiffness matrix at the equilibrium position of the multi-body system (given inkN/m, kN, kN.m)

The terms in the matrix represent the force/moment on the body i given by the dis-placement of the body j. When i 6= j, then we have the mechanical interaction betweenthe bodies. In this example it’s interesting to notice that the term ∗ b1 × ∗ b1 correspondto the stiffness given by both the mooring system between the vessels and the anchoringsystem, while all the other terms are only contributed by the mooring between the vessels.The stiffness of the anchoring system only is given by the difference between the totalstiffness presented for body 1 (anchoring + mooring) and the stiffness presented for body2 (mooring) for a given mode.

With the stiffness matrix, the Eigen modes of the system can be calculated in frequency

domain. For a system composed by two vessels, twelve eigen modes are calculated. Differ-ently from the single body analysis, it’s difficult to attribute one mode to a single motion.Sometimes a mode is contributed by a combination of motions of the two vessels. Thetable 2 presents the twelve resonant modes of the system. The first six modes are givenby the hydrostatic stiffness of the vessels and the last six modes are given by the mooringstiffness of the system. The DoFs presented are the motions that contribute the most tothe mode. It can be noticed that for very small displacements around the equilibriumposition, all the modes due to the mooring/anchoring system are outside the range of thewaves periods. However the out-of-phase modes are excited by difference frequences (∆ω)considerably high comparing to the in-phase modes. In that case, the full QTF matrix isrequired for the accurate calculation of the relative motions of the vessels.

Mode Frequency (rad/s) Period (s) DoF1 0.63 9.95 pitch b 22 0.61 10.29 heave b 23 0.53 11.82 pitch b 14 0.491 12.792 heave b 15 0.456 13.788 roll b 16 0.388 16.209 roll b 27 0.177 35.503 out-of-phase sway/yaw8 0.136 46.031 out-of-phase sway9 0.082 76.265 out-of-phase surge10 0.03 209.439 in-phase yaw11 0.015 407.671 in-phase surge12 0.014 460.071 in-phase sway

Table 2: Resonant modes of the system at the equilibrium position

The modal analysis may be repeated for stiffness matrices calculated at different po-sitions of the vessels in order to obtain the variation of the modes with respect to theposition.

5.2.1 Decay tests

Another way to evaluate the resonant periods of the system is by means of decay tests.The decay tests are performed by applying an initial offset to one of the vessels and lettingthe vessels move until they achieve the equilibrium. In the same way as for the frequencydomain, where we calculate the stiffness matrices for different positions, we may alsoperform decay tests around different equilibrium positions by applying constant loads toone of the vessels all along the simulation. Doing so, different periods are found if themooring system stiffness is non-linear.

The figure 5 presents the sway decay tests for different mean positions of the body 2,while the body 1 is kept fixed all during the simulation. It can be noticed that the out-of-phase sway period changes significantly with the relative position of the two vessels. Whenthe relative motion is significant, the period starts to decrease and may even come to rangeof the waves periods in case of very large relative motions (order of 2m). This is due tothe non-linear characteristics of the lines and fenders. This means that when large relativemotions are expected an analysis where both first- and second-order hydrodynamics arecoupled properly in time-domain may be required.

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500 600 700 800 900 1000

Sway

mot

ion

- B

ody

2

Time (s)

Mean offset= 0.0m / Tn=52sMean offset=-0.5m / Tn=55sMean offset=-1.0m / Tn=36sMean offset= 0.4m / Tn=49sMean offset= 1.0m / Tn=34s

Figure 5: Sway decay tests

5.2 Time domain simulations

In order to evaluate qualitatively the behaviour of the vessels in presence of waves, atime domain analysis has been performed for a quartering sea state with HS = 3.0m andTp = 10.0s.

In figure 6 a) it can be observed that the vessels move globally together oscillatingat the natural period of the anchoring system between the body 1 and the ground (in-phase motions). The mooring lines connecting the two vessels are not sensitive to thein-phase motions but to the out-of-phase motions. Figure 6 b) presents the out-of-phasesway motions of the vessels for a time window of 1000s. It’s interesting to observe thatthose motions are given by a combination of first and second order motions. The secondorder motions however can have very low natural period (around 40s) which requires thecalculation of the low-frequency wave loads for ∆ω up to 0.20.

5

6

7

8

9

10

11

12

13

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Sway

mot

ion

(m)

Time (s)

Sway motions - Body 1Sway motions - Body 2

-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Out

-of-

phas

e sw

ay(m

)

Time (s)

out-of-phase sway - low-frequency onlyout-of-phase sway - low-frequency + wave frequency

Figure 6: a) Vessels sway motions b) Out-of-phase motions

6 CONCLUSIONS

The latest developments made in Bureau Veritas on mooring system analysis have beendescribed, which are mainly linked to shallow water applications and/or multi-body con-figurations. Those developments have been implemented in the new version of the softwareAriane that has been used for the analysis in this paper.

For the evaluation of second order loads, different methods have been discussed. Ithas been shown that the Newman approximation, commonly used, does not provide anaccurate estimation of the low-frequency wave loads for shallow water and/or stiff mooringsystem. The new O(∆ω) approximation may be a good alternative for mooring systemswith resonant frequencies up to 0.06rad/s at any water depth, presenting as advantage

the same computation time as Newman approximation. For resonant periods greater than0.06rad/s, no choice is currently available other than the full QTF computation.

For the multi-body configurations, the focus has been on the hydrodynamic and mehan-ical interactions between the vessels. As an example of application a side-by-side mooringsystem has been presented. It has been shown the importance of performing a modalanalysis of the system at different positions prior to the definition of the methodologyto be employed, for example, for the evaluation of the second order loads (Newman,O(∆ω) approximation or full QTF). The time-domain simulations with environmentalloads demonstrate that in side-by-side configuration, the relative motions between thevessels are due to a combination of first and second order loads. The second order mo-tions however can have very low natural period (around 40s) which requires the calculationof the low-frequency wave loads for ∆ω up to 0.20rad/s.

References

[1] Chen X.B & Duan W.Y. (2007) Formulation of low-frequency QTF by O(∆ω) ap-proximation, 22nd IWWWFB,Plitvice (Croatia).

[2] Chen X.B & Rezende F. (2008) Computations of low-frequency wave loading, 23rd

IWWWFB, Jeju (Korea).

[3] Brun C.,Rezende F.,Coache D., Mombaerts J. (2008) Impact of the use of FullQTF on LNGC Moored in Shallow Water Studies, OTC.

[4] Chen X.B. (1994) Approximation on the Quadratic Transfer Function of Low-Frequency Loads, BOSS.

[5] Newman J.N. (1974) Second Order, slowly-varying forces on vessels in irregular waves,Intl. Symp. Dyn. Marine Vehicle & Struc. In Waves, Mech. Engng. Pub., London (UK)

[6] Chen X.B. (2006) Hydrodynamic analysis for offshore LNG terminals 2nd InternationalWorkshop on Applied Offshore Hydrodynamics

[7] Naciri M. (2007) Time domain simulations of side-by-side moored vessels; Lessonslearnt from a benchmark test, 26th OMAE.

[8] Naciri M., Buchner B., Huijsmans R., Andrews J. (2004) Low Frequency Motionsof LNG Carriers Moored in Shallow Water, 23rd OMAE.

3DFEM-3DBEM MODEL FOR SPRINGING AND WHIPPING ANALYSES OF

SHIPS

S. Malenica, Bureau Veritas, France

J. T. Tuitman, Delft University of Technology, The Netherlands

SUMMARY

The paper deals with the modeling of the wave induced ship structural vibrations. The presented method is fully integrated

in both the linear frequency domain and non-linear time domain seakeeping calculations. Due to the transient non-linear

nature of slamming loading, the corresponding whipping response is calculated in the time domain only, while the non

impulsive springing response is evaluated both in frequency and time domain. A method based on the full coupling of

3DFEM structural model and 3DBEM hydrodynamic model is presented. The choice of the full coupling with the 3DFEM

structural model is necessary due to the particular structural characteristics of the container ships, in particular their open

midship section, which is hard to model using non-uniform beam model. In addition, the 3DFEM model gives the direct

access to the structural response (stresses and strains) at any required location.

The stresses at the structural details are investigated using a so called top-down analysis, and the total stress response is

separated into quasi static and dynamic parts in order to improve the convergence.

1 INTRODUCTION

Increased size of the recent Ultra Large Container Ships

(ULCS) and LNG ships, reactualizes the hydroelastic wave

induced type of ship structural responses. Usually the hy-

droelastic ship response is separate into springing and whip-

ping types, springing being defined as the steady ship vibra-

tions induced by non-impulsive wave loading and whipping

as a transient vibratory ship response induced by impulsive

loading such as slamming. In this paper only slamming

induced whipping is considered.

2 FREQUENCY DOMAIN HYDROELAS-

TIC SEAKEEPING MODEL

The general methodology for hydroelastic seakeeping

model is rather well known and the first developments can

be attributed to Bishop & Price2)

. In their work they

used the simplified, so called Timoshenko beam, model for

structural modeling and strip theory for seakeeping part.

Since then several more or less sophisticated models were

proposed (e.g.4, 12, 13, 14)

).

Below we briefly recall the basic principles of the model

used in this study. The 3DBEM model for the seakeep-

ing is coupled to a 3DFEM model of the ship structure. A

more detailed description of the applied 3DBEM model can

be found in6)

and9)

.

2.1 Hydroelastic model

In contrast to the well known rigid body seakeep-

ing model, the hydroelastic model basically extends the

motion representation with the additional modes of mo-

tion/deformation chosen as a series of the dry structural

natural modes. We write:

H(x, y, z, t) =

NX

i=1

ξi(t)hi(x, y, z) (1)

=

NX

i=1

ξi(t)[hix(x, y, z)i + h

iy(x, y, z)j + h

iz(x, y, z)k]

where hi(x, y, z) denotes the general motion/deformation

mode which can be either rigid or elastic.

The above decomposition leads to the additional radiation

boundary value problems (BVP) for elastic modes, with the

following change in the body boundary condition:

∂ϕRj

∂n= h

jn (2)

After solving the different BVP-s the resulting pressure is

calculated using Bernoulli’s equation and integrated over

the wetted surface in order to obtain the corresponding

forces, so that the following coupled dynamic equation can

be written:

˘

−ω2

e([ m ] + [ A ]) − iωe [ B ]+ [ k ] + [ C ]¯

ξ = FDI

(3)

where:

[ m ] - modal genuine mass

[ k ] - modal structural stiffness

[ A ] - hydrodynamic added mass

[ B ] - hydrodynamic damping

[ C ] - hydrostatic stiffness


FDI

- modal excitation

The solution of the above equation gives the motion am-

plitudes and phase angles ξi and the problem is formally

solved. Note that the motion equation includes both 6 rigid

body modes and a certain number of elastic modes.

Several technical difficulties need to be solved before arriv-

ing to the above motion equation (3). Certainly the most

difficult one is the solution of the corresponding hydrody-

namic BVP. In this paper we do not enter into the detailed

description of the methods used to solve the seakeeping

problem at forward speed and we just mention that these

difficulties remain the same, both for the rigid and elastic

body. It is fair to say that the numerical methods which

are used to solve the seakeeping problem nowadays, are not

fully ready yet for a general combination of speed, heading

and frequency. However, most of the methods have approx-

imate solutions to account for the forward velocity. The

method used in this paper is the so called encounter fre-

quency approximation which was reasonably well validated

for rigid body case.

The second technical difficulty concerns the application of

the body boundary condition (2) for the general mode of

motion. In the next section we briefly explain how this was

done in the present work.

2.2 Body boundary condition

In the case of the simplified beam structural model,

the transfer of the modal displacements of the beam onto

a hydrodynamic mesh can be done relatively easy, but in

the case of 3DFEM structural model this transfer requires

very careful attention. Indeed, the modal displacements

are known on the structural 3DFEM mesh which is usu-

ally completely different from the hydrodynamic mesh, so

that the special interpolation procedure is necessary. In the

present work, the following procedure is adopted.

For each hydrodynamic point (panel center) the following

steps are performed, these steps are illustrated in figure 1:

1. Looking for the 3 closest structural points. In the

case that one of the 3 points is within small enough

distance (ǫ) from the considered hydrodynamic point,

we retain that structural point for interpolation.

2. The list of the structural finite elements containing

at least one of the above defined points is created.

3. The hydro point is projected onto the surfaces created

by the retained structural elements. If the projection

falls inside the element, the corresponding distance is

calculated. The element with smallest distance from

the hydro point is retained for interpolation.

4. In the case when the hydro point do not project on

any element from the list, the projection on the sides

of the considered elements is performed. If the pro-

jection falls onto the side, the corresponding distance

is calculated. The side with the smallest distance

from the hydro point is retained for interpolation.

5. In the case when there is neither point at ǫ dis-

tance, nor element nor the element side on which

point project, the structural point closest to the hy-

dro point is retained for interpolation.

6. The interpolation using the shape functions of the re-

tained finite element, of the structural displacements

is performed on the projection of the hydro point and

the calculated displacements are associated to the hy-

dro point.

yesh(p) = h(s1)

p project on elements

s1

s3

s2

pd

no

s1

s3

s2

yes

Select closets

h(p) =fintp(h(s1), h(s2))

p

p project on linesno

p

s4

s5

s6

select closets point

h(p) = h(s5)

no

ps1

s3

s2

yes

Select closets

h(p) =fintp(h(s1), h(s2), h(s3))

d < ǫ

Fig. 1: Mapping procedure

This procedure was verified on several ship types and

showed to be very efficient. In Figure 2 we present one

example for the first torsional mode of typical ULCS.

2.3 Springing

The solution of the hydroelastic motion equation (3)

includes the linear springing response automatically. How-

ever, there is no clear justification for considering springing

as a linear phenomena, at least as far as the wave excita-

tion part is considered. Indeed, experience shows that many

type of ship suffer from more or less important structural re-

sponse around their first structural natural frequencies even

if there is no important wave energy around these frequen-

cies. The explication for existence of the structural response

can be explained only by introducing the nonlinearity into

the hydrodynamic model. The well known example is the

springing of the tendons of the TLP platforms where the hy-

drodynamic excitation was successfully explained using the

weakly non-linear second order theory. In principle similar

Fig. 2: First torsional mode of ULCS and the transferof modal displacements from structural to hydrodynamicmodel.

kind of methods should also be applied in the case of the

ships, but unfortunately the state of the art in ship hydro-

dynamics do not allow for that so that only approximate

and empirical methods can be used.

However, due to their huge dimensions and particular struc-

tural properties, the case of ULCS is quite particular be-

cause their first structural natural frequencies become quite

low so that it can be excited in a linear sense too! This

means that the linearity excited springing might become

dominant which justify the linear model for its assessment.

The non-linear hydroelastic model in time domain which

will be presented in section 3 does also include the linear

springing response. The Froude Krylov loading is the only

non-linear wave excitation in this model. Some non-linear

springing due to this Froude Krylov is observed in the re-

sults of the time domain calculations, but to the authors

opinion a more sophisticated non linear model is necessary

to correctly calculate the non-linear springing response.

2.4 Calculation of the stresses in frequency domain

Once the motion equation (3) solved, all necessary

quantities (motions, accelerations, stresses, ...) can now

be calculated. Indeed, the modal decomposition remains

valid for any quantity and, in particular, we can write for

the stress distribution Σ(x, y, z, ω):

Σ(x, y, z, ω) =

NX

i=1

ξi(ω)σi(x, y, z) (4)

where σi(x, y, z) represents the spatial distribution

of the stresses corresponding to each mode of mo-

tion/deformation. Equation similar to (4) remains valid in

the time domain model too, (10). The only change concerns

the replacement of ω by t.

2.5 Separation of the quasi static and dynamic con-tributions

In the present context, it is important to note that the

rigid body modes do not contribute to any stress, and that

the above expression (4) is slowly convergent in general.

This is especially true for the structural details which are

affected by the local structural effects. A good example of

such detail is a hatch corner of the container ship. The

longitudinal response is well described by the first few lon-

gitudinal flexible modes. However, in order to obtain any

contribution of the transversal (side shell) loading, one need

to include natural mode shapes which describes the defor-

mation in transversal direction. The 3DFEM methods cal-

culates the structural natural frequencies of the ship from

the lowest natural frequency. By using a proper 3DFEM

model of ship it is relatively easy to obtain the first few tor-

sional and longitudinal modes. However, after these lowest

global structural modes, the numerous local modes with

the similar natural frequencies will quickly ”pollute” the

solution and it will be almost impossible to obtain a sub-

set of modes necessary for accurate representation of the

transversal stresses of the hatch corner. Fortunately, the

global structural dynamic response is well described by the

first few lowest modes. In order to obtain the converged

stress distribution, the total structural response should be

properly separated into the quasi static and dynamic parts.

The stresses due to the quasi static ship response will be

calculated, after separation, by the so called direct method

which calculates the structural response after the ”rigid

body” hydrodynamic pressure is transferred on the wetted

finite elements8)

. It is also important to note that the de-

composition into the quasi static and dynamic response is

made with respect to the structural response, which means

that the quasi static structural response does also includes

the dynamic rigid body response and the dynamic response

includes the dynamic structural response only.

In the present approach the decomposition of the different

parts of the response is done by first schematically rewriting

the motion equation (3) in the following form:

„»

[ RR ] [ RE ]

[ ER ] [ EE ]

–

+

»

[ 0 ] [ 0 ]

[ 0 ] [ k ]

–«

ξR

ξE

ff

=

F R

F E

ff

(5)

where R stands for the rigid body parts, E for the elastic

ones and k is the structural modal stiffness matrix.

At the same time we separate the total response amplitudes

into the quasi static and dynamic parts:

ξR

= ξR0

+ ξRd , ξ

E= ξ

E0

+ ξEd (6)

The quasi static part of the responses is defined by the

following equations:

[ RR ]ξR0 = F R (7)

[ k ]ξE0 = F E − [ ER ]ξR

0 (8)

After inserting (6), (7) and (8) into (5), the following linear

system of equations for dynamic parts is obtained:

„»

[ RR ] [ RE ]

[ ER ] [ EE ]

–

+

»

[ 0 ] [ 0 ]

[ 0 ] [ k ]

–«

ξRd

ξEd

ff

= −

[ RE ]ξR0

[ EE ]ξE0

ff

(9)

As mentioned before, the above procedure was adopted in

order to be able to keep the classical direct approach for the

quasi static part8)

and to clearly identify the dynamic part

as a correction of the quasi static one. Anyhow, the pro-

posed decomposition completely removes the convergence

problems mentioned before.

2.6 Top down analysis of structural details

Springing hydroelastic analysis is usually performed us-

ing the relatively coarse structural mesh and some addi-

tional manipulations are necessary in order to obtain the

local stresses in the critical structural details. Usually the

so called top down analysis is applied. The top down analy-

sis is well developed for the classical quasi static structural

responses. The principles are relatively simple and the cal-

culations are performed in two steps:

1. Calculation of the global structural response on the

coarse mesh

2. Application of the structural deformations of the

coarse mesh on the fine mesh and calculation of the

local stresses

One typical situation is shown in Figure 3. As already

Fig. 3: Typical structural details and their position on theship structure.

mentioned before, in the case of the quasi static structural

analysis, the loading case for the structural FEM model is

built by considering the ship as a rigid body. After solving

0

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5

Sig

ma

[MP

a]

Omega_e [rad/s]

Quasi staticDynamic

Total

Fig. 4: Typical stress RAOs.

the rigid body seakeeping boundary value problems, the re-

sulting pressure is applied on the FEM mesh together with

the inertia loads resulting from the rigid body accelerations.

Since, in the rigid body case, the hydrodynamic and struc-

tural parts of the problem are independent they can be per-

formed separately and the transfer, of the resulting defor-

mations of the coarse mesh, onto the fine mesh is relatively

straightforward. In the case of dynamic structural analy-

sis, which is of main concern here, the additional loading

cases for fine meshes need to be created. These additional

loading cases corresponds to each structural natural mode

deformations. The resulting local stresses should be added

to the quasi static ones, after being previously multiplied

by the associated dynamic modal amplitudes ξEd . One typ-

ical example of the local stresses in the hatch corner of the

classical ULCS are shown in Figure 4.

2.7 Hydroelasticity

It is interesting to observe that the dynamic part of

the response contributes to the stresses even for the fre-

quencies well away from the natural frequency. This might

seems a bit strange, but one should remind that these are

very flexible ships. The static deformation of the structure,

due to the still water bending, between midship and the

fore perpendicular is of the order of 1m for the ULCS. The

wave bending moment is of the same order as the still water

bending moment and will cause the same order of deflec-

tions. This deflection will influence the heave response and

the total bending moment.

All this suggests the importance to utilize a hydroelastic

analysis for ULCS’s even when springing and whipping are

not explicitly considered.

3 NON LINEAR TIME DOMAIN SIMULA-

TIONS

In contrast to the linear springing calculations which

can be performed in frequency domain, the nonlinear

springing and whipping simulations require the time do-

main simulations. The procedure used in this paper is based

on the method proposed in Cummins3)

and elaborated in

Ogilvie10)

. This method uses the frequency domain hydro-

dynamic solution and transfers it to the time domain using

the inverse Fourier transform. In this way the following

time domain motion equation is obtained:

([ m ]+[ A∞

])ξ(t) + ([ k ]+[ C ])ξ(t) (10)

+

Z t

0

[ K(t − τ) ]ξ(τ)dτ = FDI

(t) + Q(t)

where overdots denote the time derivatives and:

[ A∞

] - infinite frequency added mass matrix

[ K(t) ] - matrix of impulse response functions

It was shown by Ogilvie10)

, that the impulse response

functions can be calculated from the frequency dependent

damping coefficients:

Kij(t) =2

π

Z

∞

0

Bij(ω) cos ωt dω (11)

After the impulse response functions Kij have been calcu-

lated, the motion equation (10) is integrated in time using

the Runge Kutta 4th order scheme.

The main advantage of the time domain method lies in the

fact that we can introduce non-linear components in the

excitation forces Q(t). There are many non linear effects

which are missing in the linear model and the state of the

art in the numerical seakeeping, do not allows for the con-

sistent inclusion of all of them. In this paper we include the

so called Froude Krylov correction for the wave excitation

and the non linear slamming forces. Here below we briefly

explain the way in which the Froude Krylov and slamming

loads are calculated.

3.1 Froude Krylov approximation

It is well known that the linear hydrodynamic model

evaluate the pressure up to z = 0 only so that we can end

up with the negative pressure close to the waterline, as well

as with zero pressure above the waterline and below the

wave crest which is unphysical. The so called Froude Krylov

approximation is usually employed to correct this pressure

distribution close to the waterline. The ”simplest” Froude

Krylov variant is rather intuitive and consists in adding

the hydrostatic part of the pressure (−gz) below the wave

crest (in the linear sense) and by putting zero total pressure

above the wave trough. Even if the methodology might ap-

pear quite simple, the correct practical implementation in

the numerical codes might become very tricky. To the au-

thors knowledge, the details of the numerical implementa-

tion of the Froude Krylov method are usually not discussed

in the literature and that is why we are briefly elaborating

on it here below. It is also important to note that some

other extrapolation procedures, like Wheeler stretching, for

the pressure close to the waterline are sometimes employed,

but we do not discuss them here.

According to the linear theory the linear hydrodynamic

pressure at any point below z = 0, is composed of two

parts:

• pure hydrodynamic part associated with the velocity

potential and its derivatives

• hydrostatic pressure variation due to ship motions

For the wave of unit amplitude we can write:

p(x, y, z, t) = ℜ[iωeϕ − U∇(φ − x)∇ϕ]e−iωet

+ℜ−gζve−iωet (12)

where ϕ(x, y, z) is the linear unsteady potential, φ(x, y, z)

is the steady potential due to the forward speed in calm

water, and ζv is the vertical displacement of the considered

point on the ship surface.

In order to simplify the notations, it is useful to express the

pressure in meters of water height and write:

p(x, y, z, t) =Ap(x, y, z, t)

g= p

z(13)

In this way the relative wave elevation (usually denoted by

ηR) is equal to p at z = 0

ηR(x, y, t) = p

0(14)

Now we consider separately the case p0

> 0 and p0

< 0. In

Wave profile

Total pressure (>0)

z=0 z=0

Hydrostatic pressure (>0)

Hydrodynamic pressure (>0)

Ξ (>0)

Fig. 5: Modified pressure distribution for p > 0.

the case of p > 0 (Fig. 5) we can identify two different wet-

ted regions with the following total pressure distribution:

P (z, t) =

(

p0 − z for 0 < z < Ξ

pz − z for z < 0(15)

The choice of the maximal wetted point Ξ is quite natural:

Ξ = p0 (16)

In the case of p < 0 (Fig. 6) the situation is more com-

plicated and we need to be careful. As far as the pressure

z=0

Wave profile

Hydrostatic pressure (>0)

Hydrodynamic pressure (<0)

Ξ (<0)

Total pressure (>0)

z=0

Fig. 6: Modified pressure distribution for p < 0.

distribution is concerned, the situation is similar to the pre-

vious case, and the choice is quite natural (even if, strictly

speaking, not fully consistent):

P (z, t) =

(

0 for 0 > z > Ξ

pz − z for z < Ξ(17)

The main problem appears to be the choice of the minimal

wetted point Ξ. The usual choice for Ξ is the same as in

the previous case:

Ξ = p0 (18)

The problem is that this choice introduce the jump in the

pressure distribution because:

p0 6= p

z, for z = Ξ (19)

which means that the pressure at the point imediatly below

the wave profile will not be zero but:

P (Ξ, t) = pΞ − Ξ = pΞ − p0 (20)

The reason for this is the inconsistency of the adopted ap-

proach which do not include all non-linear terms, so that all

necessary conditions can not be satisfied at the same time

and we need to ”sacrify” something.

Let us now choose the value of Ξ as a solution of the fol-

lowing equation:

Ξ = pΞ (21)

It is important to note that an iterative procedure should

be used to obtain the solution of this equation. It is easy

to see that this choice eliminates the jump in the pressure

distribution. The disadvantage is that we have to solve the

equation (21). The ”physical” consequence of the above

choice is that the wave profile is changed from the assumed

one (ηR). However, this slight move of the free surface is

within the order of the approximations we adopted at the

begining. Strictly speaking both choices are not fully con-

sistent but the second one has the advantage to allow for

more physical pressure distribution.

In summary, we can say that the Froude Krylov approxi-

mation is not so clear and we need to be very careful in the

implementation and in the interpretation of the results. In-

deed, as we have seen, several approximations are involved

in the above described procedure and, in spite of the quite

complicated considerations, it is impossible to remain fully

consistent. It is also important to note that several variants

of the Froude Krylov method are in use and the simplest

one consists in taking only the incident wave part of ele-

vation in the definition of the relative wave elevation ηR.

This choice highly simplify the numerical implementation

and that is the reason why it is most often employed. In

that case we need to be extremely careful when interpreting

the results. This, lets call it incident wave Froude Krylov

approximation, is likely to be valid only in the case of rather

long waves where the diffraction and radiation parts play

less important role in the overall contribution to relative

wave elevation ηR. However, in the case of ULCS which

have quite a low block coefficient i.e. rather slender form

the incident wave Froude Krylov approximation can be rea-

sonably justified for head or almost head wave conditions

for which the springing and especially whipping are most

likely to occur.

3.2 Course keeping

The non-linear part of the force in equation (10) will

cause a mean loading at the ship. The ship will not hold

course and speed due to this mean force. This mean force

is not an error in the calculation. The mean force by the

Froude Krylov calculation is a part of the added resistance

in waves (RAW) and slamming forces cause also a loading

in the horizontal direction.

The drift of the ship in the time domain calculation should

be compensated in order to obtain a proper calculation.

Springs and dampers are often added to keep the ship at

the correct positions. An other solution is to model the

compete resistance, propulsion and maneuvering system of

the ship. Both method require quite some tuning to be able

to make a realistic simulation. To the authors opinion the

correct non-linear surge, sway and yaw response will not

affect the structural loading much. Also one could ques-

tion if using a spring, damper system would give the cor-

rect non-linear horizontal motions. In the present approach

Lagrange multipliers are added to equation (10). These

Lagrange multipliers impose the surge, sway and yaw mo-

tions as is calculated using the frequency domain solution

(3). This gives a reasonable horizontal motions without any

tuning.

3.3 Slamming induced whipping

The time domain calculation will automatically include

the linear and non linear springing. In order to calculate

the slamming induced whipping response, the slamming

forces should be calculated during the seakeeping calcula-

tion. This forces are added to the force vector Q(t) of

equation (10).

3.3.1 Slamming force

The hydrodynamic modeling of slamming is extremely

complex and still no fully satisfactory slamming model ex-

ists. However, the 2D modeling of slamming is well mas-

tered today and 2D models are usually employed to assess

the slamming loads on ships. Within the potential flow

approach, which is of concern here, several more or less

complicated 2D slamming models exist, starting from sim-

ple von-Karman model and ending by the fully nonlinear

model. In between these two models there are several in-

termediate ones such as Generalized Wagner Model (GWM)11)

and Modified Logvinovich Model (MLM)5)

which are

implemented in the presented method. We will not go into

too much details of these models and we refer to7)

. The

advantage of the MLM method when compared to GWM

method lies in the lower requirements of CPU time. Most

often, at least when rigid body impact is concerned, two

methods give comparable results as shown in Figure 7 The

GWM method is used for the presented examples because

this method has a wider range of validity and the number

of slamming calculations remains limited. If many calcula-

tions, for example a complete scatter diagram, have to be

preformed the MLM method might become more attrac-

tive. The validity of the MLM calculation can be checked

0

1000

2000

3000

4000

5000

6000

0 0.2 0.4 0.6 0.8 1 1.2 1.4

F_z

[KN

]

t [s]

section_3

GWMMLM

Fig. 7: Slamming forces on typical 2D section obtained byGWM and MLM method.

using the GWM results for the some cases.

The use of 2D methods implicitly requires the employment

of the so called strip approach for 3D simulations. The usual

procedure consist in cutting the 3D mesh into a certain

number of 2D sections as shown in Figure 8. For each par-

Fig. 8: 3D hydrodynamic mesh and corresponding 2Dsections.

ticular section, independent calculation of slamming loading

are performed and the overall slamming is obtained by sum-

ming up different contributions. The implementation of this

procedure is different for, the most often used, beam struc-

tural model and for 3DFEM model. Indeed, in the case of

the nonuniform Timoshenko beam model, only the overall

slamming force on the slamming sections is required, while

in the case of the 3DFEM model the transfer is slightly more

complicated. Here below we briefly describe the method

which is likely to be very efficient for 3DFEM case.

The general expression for pressure excitation force pro-

jected on the motion/deformation mode hi, can be written

in the following form:

Fi=

ZZ

S

phindS (22)

where S denotes the part of the ship surface on which the

pressure is applied and that regardless if the pressure is

calculated using the 2D or 3D methods. In the present case,

and since the slamming pressure is calculated on the 2D

sections, the above expression is rewritten in the following

form:

Fi=

NsX

i=1

ZZ

Ss

pshisnsdSs (23)

where Ss denotes the surface associated with the corre-

sponding slamming section, ns the associated normal vec-

tor, ps the calculated 2D slamming pressure and his the

projection of the 3D deformation mode hionto 2D slam-

ming section. The differential element of the surface of the

slamming section can be rewritten as:

dSs = bs(l)dls (24)

where b(l) is the normalized width of the section:

bs(l) =dSs

dls(25)

which can be easily calculated from the 3D sectional mesh

extracted from 3D mesh (Figure 8). The same is true for

the associated normal vector, so that the following final ex-

pression, for the slamming induced modal excitation force,

can be written:

Fi=

NsX

i=1

Z

Ls

pshisnsbsdls (26)

This expression can be easily implemented into the existing

rigid body slamming 2D module based on GWM or MLM

method.

We note here that, due to the lack of time, for the examples

presented in this paper a simplified method is used. The

modal excitation is calculated by multiplying the 2D slam

force with the area of the 3D section and the average mode

shape over the sections. This methods works well for the

first longitudinal modes

3.3.2 Whipping

One typical whipping event from full scale measure-

ments is shown in Figure 9 (taken from1)

). The curve

represents the time history of the vertical bending moment

after slamming event. Two important points should be ob-

served: whipping can increase the wave bending moment

significantly and the transient whipping vibrations can last

for quite a long time because of low damping. This is very

important because it implies that whipping will be rele-

vant both for extreme structural response as well as for

the fatigue loading. Anyway, once the above procedure im-

plemented, it is possible to calculate the time history of

the stresses at any particular finite element. The decom-

position into quasi static and dynamic contribution do not

seems to be straightforward. The most practical way is to

perform two separate simulations: one purely quasi static

and another with the structural dynamics included. The

above described procedure is applied on 11400 TEU ship

sailing with speed U = 10m/s in the irregular head waves

Fig. 9: Whipping from full scale measurements.

(Jonswap spectrum Hs = 5m and Tp = 16s). The typical

situation at one particular time instant is shown in Figure

10 and the typical stress time history around a slamming

event in Figure 11. Typical transitory whipping behavior

can be observed. It should be noted that only modal super-

position is used for this figure and no separation into quasi

static and dynamic parts as only the longitudinal loading

will contribute to the stress for this element. In the present

case the local structural stress is presented but the exactly

same procedure can be applied for the global quantities as

well. In particular the vertical bending moment at a partic-

ular ship section can be evaluated. Calculation of the ver-

tical bending moment is usually required in order to have

quick idea of the influence of whipping on the overall ship

design. In Figure 12 one typical simulation result for ver-

tical bending moment is presented. This example is very

illustrative and shows that, even if the whipping usually

appears in sagging conditions, the vertical bending moment

in hogging conditions is also affected due to relatively low

structural damping. The stress in the structural detail is

Fig. 10: Stress distribution in the ship structure at oneparticular time instant. The total stress includes the linearand non linear quasi static, springing and whipping contri-butions at the same time.

calculated for 2000 second in the same sea state to obtain

a better quantification of the effect of whipping. The non-

linear calculation is run with and without slamming using

the same wave train. Figure 13 shows the probability distri-

bution of the stress in the structure. The rainflow cycles and

the fatigue damage calculated using a standard SN-curve is

shown in figure 14. The slamming induced whipping clearly

increase the amplitude of the stress and reduces the fatigue

life of the structural detail.

20

25

30

35

40

45

50

55

60

65

70

75

415 420 425 430 435 440 445

Sig

ma

[MP

a]

Time [s]

With slammingWithout slamming

-8

-6

-4

-2

0

2

4

6

415 420 425 430 435 440 445

Sig

ma

[MP

a]

Time [s]

Fig. 11: Typical stress time history during the whippingevent (top - total, bottom - filtered).

-500000

0

500000

1e+006

1.5e+006

2e+006

2.5e+006

3e+006

3.5e+006

4e+006

8160 8180 8200 8220 8240

Ver

tical

ben

ding

mom

ent a

t fra

me

88 [K

Nm

]

Time [s]

Elastic - with slammingRigid - no slamming

Fig. 12: Typical time history of the vertical bending mo-ment during the whipping event.

4 CONCLUSION

The method for hydroelastic analysis using the 3DFEM

3DBEM coupling procedure is presented. Both frequency

and time domain approaches are discussed. The overall

problem is extremely difficult and only approximate solu-

tion is possible up to now. In spite of numerous technical

difficulties the present model seems to produce quite real-

istic results. More detailed validations and calibrations are

necessary before employing the method in practice.

REFERENCES

1. Aalberts P.J. & Nieuwenhuijs M., 2006. : ”Full

scale wave and whipping induced hull girder loads.”,

0.001

0.01

0.1

1

50 55 60 65 70 75 80 85

Pro

babi

lity

of e

xcee

denc

e

Stress [MPa]

With slamNo slam

Fig. 13: Probability of exceedence of stress in the struc-tural detail

1

10

100

1000

0 10 20 30 40 50 60 70 80 0

2e-06

4e-06

6e-06

8e-06

1e-05

1.2e-05

Num

ber

of c

ycle

s

Fat

igue

dam

age

per

hour

Stress [MPa]

cycles with slamcycles no slam

damage with slamdamage no slam

Fig. 14: Rainflow count and fatigue damage of the struc-tural detail

4th. Int. Conf. on Hydroelasticity, Wuxi, China.

2. Bishop, R.E.D. & Price, W.G., 1979. : ”Hydroe-

lasticity of ships”, Cambridge University Press.

3. Cummins W.E., 1962. : ”The impulse response func-

tion and the ship motions.”, Schiffsctechnik, Vol. 47,

pp.101-109.

4. Jensen J.J. & Wang Z., 1999. : ”Wave induced

hydroelastic response of high speed monohull dis-

placement ship.”, 2nd. Int. Conf. on Hydroelasticity,

Fukuoka, Japan.

5. Korobkin A.A., 2005. : ”Analytical models of water

impact.”, Euro Journal on Applied Mathematics.

6. Malenica S., Molin B., Remy F. & Senjanovic I.,

2003. : ”Hydroelastic response of a barge to impulsive

and non impulsive wave loads.”, 3rd. Int. Conf. on

Hydroelasticity, Oxford, UK.

7. Malenica S. & Korobkin A.A., 2007. : ”Some as-

pects of slamming simulations in seakeeping.”, 9th.

Int. Conf. on Numerical Ship Hydrodynamics, Ann

Arbor, USA.

8. Malenica S., Stumpf E., Sireta F.X. & Chen

X.B., 2008. : ”‘Consistent hydro-structure interface

for evaluation of global structural responses in linear

seakeeping.”, 26th OMAE Conf.

9. Newman, J.N., 1994. : ”Wave effects on deformable

bodies”, Applied Ocean Research, Vol. 16, pp.47-59.

10. Ogilvie T.F., 1964. : ”Recent progress toward the

understanding and prediction of ship motions.”, 5th

Symposium on Naval Hydrodynamics.

11. Zhao R., Faltinsen O.M. & Aarsnes J.V., 1996.

: ”Water entry of arbitrary two dimensional section

with and without flow separation.”, 21st Symposium

on Naval Hydrodynamics.

12. Wu M.K. & Moan T., 1996. : ”Linear and nonlinear

hydroelastic analysis of high speed vessels.”, J. of Ship

Res., Vol.40/2, pp.149-163.

13. Wu Y. & Price W.G., 1986. : ”A general form of

the interface boundary condition of fluid structure in-

teraction and its applications.”, CSSRC Rep. 86010.

14. Xia J. & Wang Z., 1997. : ”Time domain hydroelas-

ticity theory of ships responding to waves.”, J. of Ship

Res., Vol.41/4, pp.286-300.

Paper No. ISOPE-2008-TPC-269 First author’s last (family) name: Kim Total number of pages: 10

Fluid-structure interaction modeling, relating to membrane LNG ship cargo containment system

W S Kim1, B J Noh1, H Lee2, Z Mravak3, J de Lauzon3, J R Maguire4, D Radosavljevic4, S H Kwon5, J Y Chung5 1Shipbuilding Division, Hyundai Heavy Industries Co., Ltd., Ulsan, Korea

2Technology, Research and Product development Group, American Bureau of Shipping, Houston, USA 3Marine Division, Bureau Veritas, Paris, France

4Technical Investigations, Lloyd’s Register EMEA, London, England 5Department of Naval Architecture & Ocean Engineering, Pusan National University, Busan, Korea

ABSTRACT Over the period 2006-07, a JDP (joint development project) for LNG cargo containment system (CCS) was carried out by HHI, ABS, BV, LR and PNU. The aim of the project was to develop “best current practice” for the analysis of fluid-structure interaction (FSI) events, in particular relating to sloshing impact loads in membrane type LNG CCS, which could lead to the improved evaluation of the structural safety of GTT Mark III type CCS. KEY WORDS: Liquefied Natural Gas (LNG); Cargo Containment System (CCS); Fluid-Structure Interaction (FSI); Wet Drop Test INTRODUCTION In recent years, the needs for natural gas (NG) have been quickly and steadily increasing, due to the fast growth of world energy usage and NG’s environment-friendly nature. The demand for building of LNG (liquefied natural gas) carriers with bigger cargo capacity has been also increasing to economically transport LNG. In cargo tanks of membrane type LNG carriers, because there is no internal supporting structure such as partial bulkheads, sloshing loads by LNG is one of the most important factors for the safety of insulation system and supporting hull structure. Therefore, to design a new-size LNG carrier safely, it is needed evaluating the sloshing impact load and assessing the structural response to that impact load. A dynamic structural analysis considering fluid-structure interaction (FSI) under sloshing impact load is the most essential for assessment of the structural safety of cargo containment system (CCS) in a membrane type LNG carrier (Nam et al., 2005 and 2006). Till now, however, a single method to predict the structural response of CCS on absolute basis has not been validated yet.

In early 2006, Hyundai Heavy Industries (HHI) commissioned Pusan National University (PNU) to carry out physical wet drop tests of Mark III type LNG tank insulation specimens, to clarify the impact pressure acting on the insulation membrane and the strains developed in the insulation system. In parallel, HHI proposed a joint development project (JDP) to major classification societies to carry out the numerical simulation of the wet drop test by each own manner. The main purpose of the JDP was to develop the best practice of analytical solution for the evaluation of structural safety of CCS in membrane type LNG carriers in consideration of FSI under sloshing impact loads. Three classification societies of American Bureau of Shipping (ABS), Bureau

Veritas (BV) and Lloyd’s Register Asia (LR) participated in the JDP of “Wet Drop Test Simulation” initiated by HHI.

This paper summarizes the simulation works carried out by four participants of HHI, ABS, BV and LR, including wet drop tests carried out by PNU. WET DROP TEST The tests were carried out at Slamming research laboratory in PNU. Figure 1 illustrates the test facility. The test specimen is guided by four linear motion (LM) sliders installed at main vertical columns. Transverse and rotational motions of the specimen are restrained for strict vertical drop maintaining the inclined (incident) angle. The test rig is placed on a water basin of 3 meter depth and the maximum drop height is 4.3 meter (Chung et al., 2006). The drop unit where the test specimen is to be attached is shown in Fig. 2. The drop unit consisted of steel housing for the test specimen, supporters and jigs connected to LM guide sliders.

Fig. 1 Test rig for wet drop test Total three types of specimens were tested; flat membrane (Flat), corrugated membrane (Light) and corrugated membrane with added weight (Heavy). The distinction of types comes mainly from shape of the membrane and weight of the specimen. Test specimens of Flat and Light are shown in Fig. 3. Both specimens consisted of plywood, reinforced poly-urethane foam (RPUF), rigid triplex, mastics and

stainless-steel membrane. For Heavy specimen, additional weight of 500 Kg was welded inside of steel housing as shown in Fig. 4. Total weight of the assembled specimen was about 1,000 Kg for Flat and Light, and 1,500 Kg for Heavy.

Fig. 2 Configuration of drop unit

Housing

Flat & Corrugated membrane

R - PUF & mastic

Fig. 3 Drop specimens (Flat and Light)

Light condition Heavy condition Fig. 4 Inside of housing for Light and Heavy Three pressure sensors were located on the membrane surface along the flow direction, which were denoted by P1, P2 and P3, as shown in Fig. 5. Uni-axial strain gauges of 5 mm length were placed on the mastic and the plywood, whose locations were denoted by SM1, SM2, SP1, SP2, ---, SP10. The sampling rate of the pressure and strain signal was 20 kHz. Motion of the dropped unit was monitored by a high-speed camera, and dropping velocity was obtained by digitizing captured images. As given in Table 1, total 20 cases of the drop test (9 cases for Flat and Light, and 2 cases for Heavy) were carried out. For each case, two tests were performed to confirm the repeatability of measured data.

(a) Sensor layout

MARK III Corrugation membrane

340

340

940

940

940

120 120

Flow direction

Diameter = 6mmThickness = 2mm

(b) Pressure sensors

(c) Strain gauges

Fig. 5 Sensor layout and locations Table 1. Test case matrix for wet drop

Incident Angle (degree) Drop Height (meter) ItemModel 0 4 8 2 3 4

Flat √ √ √ √ √ √

Light √ √ √ √ √ √

Heavy √ − − √ √ −

SIMULATION In this section, the method how to simulate the wet drop tests numerically by each participant is introduced in brief.

Methodology

HHI MSC/DYTRAN was used for both of fluid and structure models adopting General coupling. FSI was carried out by solving equations of motion for the structure and the fluid simultaneously at each time step. ABS At the first stage, pressure distribution history on the drop specimen

Inner hull Mastic

Strain gauge(plywood)

Strain gauge (mastic)

Pressure gauge

R-PUF

Primary barrier (STS 304L)

was computed by using FLUENT under the assumption of the rigid body. The computed impact pressure, which was subdivided into 4 by 4 patch loads, was used as the input loads on the structural model coupled with the fluid element, to consider FSI effect in indirect way, for the dynamic structure analysis (ABS, 2006). MSC/DYTRAN was used for the dynamic structure analysis adopting Euler coupling between the structure and fluid elements.

BV A modal method was used to perform hydro-elastic coupled analysis of impact calculation. At the first stage, eigen-modes of the structure were calculated using ABAQUS to be transferred to BV’s in-house program for hydro-elastic coupling, which was based on the Wagner’s impact theory and variational inequality method (Gazzola et al., 2006 and Malenica et al., 2006). Then for each time step of the simulation, BV’s in-house solver iterated to find the mutually dependent hydrodynamic load and structural response; convergence was achieved using Newton’s algorithm. Using this technique and programs the required CPU time and data storage capacity necessary for the calculation of hydro-elastic problems were significantly reduced

LR Three approaches were examined. The first one was FEA-only approach by using ABAQUS. The fluid and the structure were entirely modeled by finite elements and calculated simultaneously. The second one was 1-way coupled approach by linking STAR-CD to ABAQUS via MpCCI. STAR-CD calculated pressure distribution on the drop specimen surface at each time step under assumption of the rigid body, and ABAQUS calculated dynamic structure response under the transmitted pressure history. The third one was 2-way coupled approach by linking STAR-CD and ABAQUS each other via MpCCI. STAR-CD calculated pressure distribution on the drop specimen surface at certain time step under the assumption of the rigid body, and ABAQUS calculated deformation of structural body for calculation of STAR-CD at the next time step. Then, STAR-CD calculated pressure distribution on the drop specimen surface again at the next time step with the deformed rigid body, and this calculated pressure distribution was transmitted to ABAQUS for calculation of structure response at the next time step. This procedure of calculation and transmission was repeated during the whole calculation period. Only two cases of drop tests were selected to illustrate the effect of coupling methods, namely Flat specimen cases dropped at 4 meter height with incident angles of 0 and 4°. Model

HHI Figure 6 shows the drop structure model of Light specimen, partly cut for visibility, with the membrane up and the housing down (a) and in the drop position with the membrane down and the housing up (b). The exact complex corrugation geometry was replaced by simplified corrugation geometry. A contact was defined between the membrane and the top plywood. Rigid connections were defined between the secondary barrier and the primary insulation foam. Other bonding and welding connections were modeled by having common nodes. A contact was defined between the primary/secondary insulation foam and the housing. All 16 hinge lugs, which were welded to the eight corners on two sides of the steel housing, were modeled. Supporting brackets and LM guide sliders were not directly modeled, but their mass was divided into 16 lugs as concentrated mass. The restraining effect of supporting brackets and LM guides was modeled by restraining the motion in X and Y global directions at the hinge axis of each lug. Figure 7 shows the fluid model. A special consideration for air flow between membrane corrugation and water surface, as well as

water behavior in the impact area was taken account. Fluid domain dimensions were taken 5 x 5 x 4 meters in breadth x width x height. The lower 3 meters were filled with water as in the actual basin, and the upper 1 meter was filled with air. To keep the possible minimum number of elements for calculation efficiency, mesh size was gradually increased (biased) from the center towards corners. 1 bar boundary condition was applied at out 5 faces of air region. Outer boundaries of water region were closed. Air was assumed to be an ideal gas with a gas constant γ of 1.4 and density of 1.18 kg/m3. Water was modeled as compressible fluid using a polynomial equation of state. Density was taken as 1,000 kg/m3 and bulk modulus was taken as 2.2 GPa. The total number of fluid elements was about 370,000.

(a)

(b)

Fig. 6 Drop structure model of HHI

Pressure=1bar

Rigid wall

Fig. 7 Fluid model of HHI

ABS Figure 8 shows a typical CFD model of FLUENT to calculate the pressure time history of Light/Heavy specimen with 0 incident angle. In consideration of symmetry, half or one-forth of the fluid and the structure was modeled. The structure was a rigid body. Water was modeled as incompressible fluid and air was modeled as compressible ideal gas. Material properties of air and water were provided within FLUENT material database. Grid sizes were 6.25 ~ 20 mm depending on the type of specimens and incident angles. Figure 9 shows the FE model. The top surface of the structure was contacting with the fluid, which was modeled by isotropic elastic fluid element. Corrugation of the membrane was not considered for the structure analysis.

Fig. 8 CFD model of ABS (corrugated membrane with 0 indent angle)

(a) Steel casing (b) Mastics

(c) RPUF & Plywood (d) Membrane

Fig. 9 FE model of ABS BV Figure 10 shows the FE model of Light/Heavy specimens. In consideration of the structure and load symmetry, only one half of the specimen was modeled and analyzed. The interaction of the analyzed part with the test rig structure was defined as fix boundary conditions at four specimen hinge points. The rig structure was assumed as rigid during the impact phase. The mutual interaction between the different structural parts could be characterized as tie and therefore the following pairs were defined in FE model: mastic rope-housing, mastic rope-secondary plywood, secondary plywood-secondary foam, primary foam-primary plywood, primary membrane edges-housing, vertical housing plates-RPUF vertical surfaces and primary membrane-primary plywood surface. Different mesh size was tested to determine the

proper finite elements dimension which allowed enough stabile and precise results and also reasonable computing time and required data storage capacity. The utilized FE mesh size for the insulation structure was about 30 x 30 mm and total number of elements in FE model was about 15,000.

Fig. 10 FE model of BV For the discretization and analysis of the fluid domain, the finite boundary elements method was used. Therefore only the contact surface of the fluid domain had to be meshed. To properly calculate pressure distribution on the impact surface a very fine mesh should be defined in the proximity of contact line during the whole duration of impact. To successfully follow the contact line displacement over the impact surface, extremely fine mesh should be defined over the whole surface. This would require a significant number of elements, as well as computing time and data storage capacity. To avoid these difficulties an adaptive meshing technique could be applied. At each calculation time step, a new mesh for the fluid domain was generated having the smallest element size in the proximity of contact line. For the illustration of applied adaptive meshing technique, the mesh of impact surface for two instant t1 and t2 (with t1<t2) is given in Fig. 11. It could be noted that the mesh refinement follows the evolution of the contact line.

Fig. 11 Mesh on the impacted surface at instant t1 and instant t2

LR Figure 12 shows the FE model, which was used for FEA-only approach. Characteristics of the dropping unit model are similar to those of ABS, except the corrugated membrane. Geometry of the corrugated membrane was modeled precisely by using very fine mesh. Water was modeled by elements with very small shear viscosity value of 1.0E-10 Ns/mm2. Air was not modeled. Figure 13 shows CFD model of STAR-CD for 1-way and 2-way coupled approach. A pressure boundary condition was applied to the upper most part of the domain. All other boundaries were no slip walls. In CFD model, compressibility of both water and air was taken into account.

Fig. 12 FE model of LR for FEA-only approach

Computational domain with Local mesh refinement around

moving mesh setup the box and corrugation surface

Fig. 13 CFD model of LR Material Properties All participants agreed to use exactly the same material data. Material properties used in simulations are listed in Table 2. Table 2. Material properties

Unit: MPa, ton/mm3 Plywood RPUF Triplex Mastics Membrane Steel

En 8900 142 13133 2934 200000 206000 Es 7500 142 - 2934 200000 206000 Et 520 84 9100 2934 200000 206000 nns 0.17 0.24 0.3 0.3 0.27 0.3 nnt 0.17 0.18 - 0.3 0.27 0.3 nst 0.17 0.18 - 0.3 0.27 0.3 Gns 196 12.2 - - - - Gnt 196 12.2 - - - - Gst 196 12.2 - - - -

Density 7.10E-10 1.25E-10 2.50E-09 1.50E-09 7.85E-09 7.85E-09 Model Ortho Ortho Iso Iso Iso Iso

Simulation Cases

HHI All 20 test cases of wet drop given in Table 1 and the static load test were simulated.

ABS Four cases of following drop tests were simulated. - Flat and Light specimens with 0 incident angle at 2 meter drop height

(Pressure only) - Flat specimen with 4° incident angle at 2 meter drop height (Pressure

only) - Heavy specimen with 0 incident angle at 2 meter drop height BV Twelve cases of following drop tests and the static load test were simulated. The further development of hydrodynamic code which is in progress needs to cover impact with 0° incident angle. - Flat specimen with 4° and 8° incident angles at drop height equal to 2

,3 and 4 meters - Light specimen with 4° and 8° incident angles at drop height equal to

2, 3 and 4 meters LR Nine cases of following drop tests and the static load test were simulated. - Flat specimen with 0 incident angle at 3 meter drop height - Flat specimen with 0 incident angle at 4 meter drop height

(including 2-way coupled approach) - Flat specimen with 4° incident angle at 3 meter drop height - Flat specimen with 4° incident angle at 4 meter drop height

(including 2-way coupled approach) - Light specimen with 0 and 4° incident angles at 3 and 4 meters drop

height - Heavy specimen with 0 incident angle at 2 meter drop height

CUT-UP OF SPECIMENS After drop tests, internal damages and fabrication quality of all specimens were checked by dismantling steel housing and slicing CCS by 50 mm interval, as shown in Fig. 14. Some damages were found at corrugated membranes as shown in Fig. 15. In case of Light specimen, large corrugations were buckled due to pressure and small corrugations were bent due to jet flow. In case of Heavy specimen, however, large corrugations only were buckled and there was no damage in small corrugations because the drop test with an incident angle was not carried out. Some cracks on RPUF underneath mastics were found, as shown in Fig. 16, in case of Flat specimen. The main cause of the crack is assumed to be stress concentration under pressure loading and repeated drop tests. Figure 17 shows bonding status of the mastic to the plywood at the middle part of three specimens. Due to poor craftsmanship, there were a lot of cavities in the mastic. In case of Flat specimen, bonding between the mastic and the bottom plywood was protruded quite a lot, which was expected to affect the bending response of the plywood near to the mastic. In case of Light specimen, the bonding status was worse than the one of Flat specimen. There were noticeable defects of bonding between the mastic and the plywood. Among three specimens, the bonding in Heavy specimen was comparatively quite good. EVALUATION OF SIMULATION RESULTS

Static Load

Fig. 14 Slicing CCS

(a) Light specimen (b) Heavy specimen

Fig. 15 Damaged membrane of Light and Heavy specimens

Fig. 16 Cracks on RPUF of Flat specimen

(a) Flat specimen

(b) Light specimen

(c) Heavy specimen

Fig. 17 Bonding status of mastic to plywood

After all drop tests, static load tests were carried out and strain distributions on the bottom plywood of specimens were measured to check the integrity of the physical specimens and measuring gauges. Figure 18 shows how to carry out the static load test. The static load tests with Flat and Heavy specimens only were carried out. In case of Light specimen, the static load test could not be carried out because the signal cables were already removed after the drop tests. HHI, BV and LR simulated the static load test by using each own method and structure model. Since the numerical models were identical except for the membrane and the mass, which should not have a large effect on

results, each party’s simulation was carried out for only one model of either Flat or Heavy. Figure 19 shows the comparison of measurements and simulations at the static load weight of 1,440 Kg. The measurement result of Flat specimen shows very strange strain distribution comparing to those of Heavy specimen and simulations. This seems mainly due to poor bonding and quality of the mastic, as described previously. In Heavy specimen, the measured strain values and distribution closely correspond to those obtained in simulations, although they are not symmetry. These results, in line with those obtained by cut-up specimens, indicate that comparisons of simulated strains with measured results during drop tests may be meaningful only in case of Heavy specimen.

(a) 0 Kg (b) 40 Kg (c) 540 Kg

(d) 1,040 Kg (e) 1,440 Kg Fig. 18 Weight set up for static load test (Heavy specimen)

- 300

- 200

- 100

0

100

200

300

- 200 - 160 - 120 - 80 - 40 0 40 80 120 160 200

Distance(mm)

Stra

in(μ

ε)

Flat- measuredHeavy- measuredHHI- simulationLR- simulationBV- simulation

Positionof

m astic

Fig. 19 Comparison of strains at plywood under static load of 1,440 Kg

Wet Drop

During drop tests, velocity of drop specimens was calculated using tracking points in pictures taken by a high speed camera and bundled software. To get the drop accelerations in drop tests, the slope of the obtained velocity time histories were calculated. The averaged acceleration was 8.787 m/s2 and the averaged final entry velocity was

94.6% of the free fall theoretical value calculated from the gravitational acceleration assuming no resistance or friction. Accordingly, it was decided to take the velocity as 95% of the free fall theoretical velocity for simulations.

Pressure Time History Figures 20 and 21 show typical comparisons of pressure time histories at the membrane center (P2) of Flat and Light specimens with the incident angle of 4° at drop height of 2 and 4 meters, respectively. Due to differences between time zero in simulations of each party and time zero in drop tests, all results are shifted on the time axis such that the time of maximum pressure at P2 in measurements is matched with the time of that pressure in simulations. HHI Peak pressures in simulations are generally close to or a little lower than those in measurements. Pressure durations in simulations are about 20% longer in general than those in measurements. Especially, quick rising of pressure is not as apparent as that of measurements. These differences between the results of simulations and measurements seem to be mainly owing to the size of meshes in the simulation model. The mesh size in simulations was 20 x 20 mm for the structure model and 30 x 30 mm for the fluid model, whereas the pressure gauge in measurements was 6 mm diameter. Further research work will be carried out to verify the effect of the mesh size. ABS The simulated pressure shows good agreement in magnitude and shape with the measured pressure for the most of the cases. It is of interest to note that simulated pressure agrees well with the experimental value although fluid-structure interaction was not considered in the CFD simulation. BV When the problem is strongly hydro-elastic, measured/calculated pressure seems not proper value for the evaluation and comparison. Structural response during the impact in hydro-elastic coupled analysis has to be expressed and compared based on the structural deformation and induced stresses. The load, i.e. pressure is the value which doesn’t have particular meaning in this kind of analysis. Even measurements of pressure, in particular pressure peak value is extremely difficult and could be influenced by many local phenomena. For the purpose of this project and for the demanded comparison, pressure as one intermediate result was extracted from calculations. Comparison of calculated results with measurements is shown in Fig. 20. For the cases with flat primary membrane calculated values have fairly good agreement with measurements. In general, calculated peak values are higher than measured. For the cases with corrugated primary membrane, calculated peak values were much higher than measured.

LR It is clear from Figs. 20 and 21 that, as expected, CFD prediction of the flow field and the resulting pressures are much more accurate than the FEA simplified approach. Furthermore it was not possible to obtain direct reading of pressure within the FEA code and therefore it had to be obtained indirectly via stresses in the vertices nearest to the position of the pressure gauges during experiment. This was furthermore complicated by the noise in the results from the explicit solver which required filtering. The resulting pressure plots exhibit several spikes in the curve which are not observed in the measurements. Taking all results into consideration, it is clear that the ABAQUS simplified water model is not very accurate in reproducing local fluid behavior in any great detail. CFD, on the other hand, generally shows excellent

agreement between predictions and measurements, both in terms of the magnitude and in terms of the behavior of pressure. This accuracy was achieved by taking all elements of the drop into consideration: the drop started at the appropriate height (3 or 4 meters) and was fully tracked until the point of impact when coupling with ABAQUS was engaged. Compressibility of both water and air was taken into account. Fine mesh in the vicinity of the membrane allowed for high resolution of water surface deformation during the impact and accurate pressure distribution across the whole of the surface. The drawback in achieving this accuracy was the relatively long run-time. Some compromises have therefore to be made to keep run-times within practical limits, but, as figures demonstrate, little is sacrificed in terms of accuracy. Strain Time History As described previously, it was hard to compare the structural responses one by one between simulations and measurements, due to poor bonding and quality of the mastics in specimens. Among signals of gauges, values of SP8 rather seemed to show close relation to results of simulations, because it was located between mastics. In this regard, comparisons of strain time histories at SP8 position only are presented in this paper. Figures 22 and 23 show typical comparisons of strain

0.01 0.02 0.03 0.04time [sec]

-4

0

4

8

12

16

20

24

28

32

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ssur

e [b

ar]

Pressure P2- flat, 2m, 4dPNUHHIABSBV

(a) Drop height 2 meter

(b) Drop height 4 meter

Fig. 20 Pressure time history at P2 of Flat specimen (incident angle 4°) time histories at SP8 position of the bottom plywood of Flat and Light specimens with the incident angle of 4° at drop height of 2 and 4 meters, respectively. Figure 24 shows comparison of strain time histories at SP8 position of the bottom plywood in Heavy specimen at the drop height of 2 meter with 0 incident angle. As the case of pressure time history, all results are shifted on the time axis such that the time of maximum pressure at P2 in measurements is matched with the time of that pressure in simulations. HHI All results of simulations show good agreement with those of measurements in general according to comparisons of strain time histories at SP8. ABS Both magnitude and shape of the simulated strain response show good agreement with the measured results.

BV The strain results of simulations show good agreement with those of measurements. Calculated strains are in general slightly higher than measured values; this might be due to the structural FE model which doesn’t have defined damping materials property.

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-4

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4

8

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0.01 0.02 0.03 0.04time [sec]

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ssur

e [b

ar]

Pressure P2- flat, 4m, 4dPNUHHILR(FEA-only)LR(CFD-1way)LR(CFD-2way)BV

Fig. 21 Pressure time history at P2 of Light specimen (incident angle 4°) LR What the results show for the cases with the incident angle of 0 is the following: - Both FEA-only (simplified water model) and CFD 1-way coupling

over-predict the measured strains. - The simplified water model in FEA does not cope well with the 0

degree impact and produces unrealistic spikes in the filtered data which are visible both in pressure results and resulting strains.

- CFD 1-way predicts pressure well, providing the correct input to stress calculations which results in the smooth strain curves similar in character to those measured. However, strain magnitude is over-predicted compared with measurements to about the same level as the FEA-only model. This suggests that spikes generated by the FEA water model do not have an important influence on the maximum strain values. It also suggests that the structural response is less sensitive to the prediction accuracy of local pressure variations.

- Calculated strains with CFD 2-way coupling are much closer to those measured. For point SP8, predicted strain magnitudes match measurements quite well, although the measured values show sharper rise and fall. This is an encouraging result and the outcome, which one would hope to see when the full feedback of “2-way” coupling is introduced. Unfortunately, “2-way” coupling has a dramatic effect on the predicted pressures by reducing the peak magnitude by about

0.01 0.02 0.03 0.04time [sec]

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-1000

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2000

3000

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5000

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8000

Mic

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Strain of backplywood - SP8, flat, 4m, 4dPNUHHILR(FEA-only)LR(CFD-1way)LR(CFD-2way)BV


Fig. 22 Strain time history at SP8 of Flat specimen (incident angle 4°) 40%. This in effect means that in order to match measurements, the solid stress model has to ‘see’ much lower pressures than the experimental measurements show.

To assess whether the same findings are applicable to any of other cases, the cases with the incident angle of 4° are run “2-way” coupled (Fig. 22). While the outcome agrees with the previous case in most points, one significant difference is observed: strains are over-predicted compared to measurements even with a “2-way” coupling although pressures again show a clear drop to below measured values. These findings indicate that there may be a mismatch between the stress model and the tested physical sample. Due to the complex structural design of the Mark III corrugated section, it is difficult to ascertain what has the biggest influence, but the computed strains suggest that the models need to be generally stiffer in order to predict lower strains in response to recorded pressures. A stiffer model would results in the lower deformations being passed over to CFD model and, one would expect, a smaller drop in the 2-way coupled pressure prediction. Potential issues with material properties could also be linked to static tests. From Fig. 19, it is clear that strain over-prediction can be observed for a static load condition although this is much less pronounced than for the actual drop case (dynamic impact). All this ties

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Strain of backplywood - SP8, light, 4m, 4dPNUHHILR(FEA-only)LR(CFD-1way)BV


Fig. 23 Strain time history at SP8 of Light specimen (incident angle 4°)

0.01 0.02 0.03 0.04time [sec]

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Strain of backplywood - SP8, heavy, 2m, 0dPNUHHIABSLR(FEA-only)LR(CFD-1way)

Fig. 24 Strain time history at SP8 of Heavy specimen

(drop height 2 meter, no incident angle) in with the overall impression that the complexity of the Mark III section and inherent difficulty in assigning accurate material properties could result in the solid model not being accurate enough to allow good prediction of strains. CONCLUDING REMARKS To establish a reliable prediction method of LNG CCS response to sloshing loads, physical wet drop tests of CCS specimens and their numerical simulations were carried out by four parties of HHI, ABS, BV and LR using each party’s own method, under the name of JDP for Wet Drop Test Simulation. Three types of the specimen were fabricated and drop-tested by PNU. Flat and Light specimens were tested at drop heights of 2, 3 and 4 meter in combination with incident angles of 0, 4° and 8°. Heavy specimen was tested at drop heights of 2 and 3 meter only without an incident angle. Comparison works of pressure and strain time histories between the results of measurements and simulations were performed.

According to comparisons of pressure time histories on the membrane,

results of each party’s simulation show good agreement with those of measurements in general, even though some parties’ results require some further consideration. In case of strain time histories, it was verified through static load tests and cutting-up specimens that results of measurements were not so reliable due to poor craftsmanship in mixing and bonding mastics during fabrication of specimens. Notwithstanding errors in measurements, comparisons of strain time histories at a typical location of the bottom plywood between mastics, where strain signals in static load tests showed relatively close relation to results of simulations, were performed. All results of each party’s simulations present reasonable response of strain time histories.

In line with findings and outcomes through this JDP, it is highly recommended to proceed with next stage of a development project to establish more practical and rational assessment procedure for CCS and supporting hull structures of LNG carriers under sloshing loads. REFERENCES American Bureau of Shipping (2006). Guidance Notes on “Strength

assessment of Membrane-Type LNG Containment Systems under Sloshing Loads”

Chung, JY, Lee, JH, Kwon, SH, Ha, MK, Bang, CS, Lee, JN, and Kim, JJ (2006). “Wet Drop Test for LNG Insulation System,” Proc 16th (2006) Int Offshore and Polar Eng Conf, Vol III, pp 199-204, San Francisco

Gazzola, T, Korobkin, A, and Malenica, S (2006). “Hydro-elastic Wagner Impact using Variational Inequalities,” Proc Int Workshop on Water Waves and Floating Bodies, Loughborough

Malenica, S, Korobkin, A, Gueret, R, Delafosse, V, Gazzola, T, Mravak, Z, and Zalar, M (2006). “Hydro-elastic Impacts in the Tanks of LNG Carriers,” Proc 4th (2006) Int Conf on Hydroelasticity, Wuxi

Nam, SK, Kim, WS, Noh, BJ, Shin, HC, Choe, IH, Park, KH, Kim, DE, and Rashed S (2005). “Structural Response of Membrane Tanks to Sloshing Load in a Mark III Type LNG Carrier,” Proc 19th (2005) TEAM Conf, pp 347-352, Singapore

Nam, SK, Kim, WS, Noh, BJ, Shin, HC and Choe, IH, (2006). “The Parametric Study on the Response of Membrane Tanks in a Mark III Type LNG Carrier Using Fully Coupled Hydro-elastic Model,” Proc Int Conf on ICSOT 2006: Design, Construction & Operation of Natural Gas Carriers & Offshore Systems, pp 147-154, Busan

HYDROELASTIC ASPECTS OF LARGE CONTAINER SHIPS

Ivo Senjanović

University of Zagreb Faculty of Mechanical Engineering

and Naval Architecture I. Lucica 5, 10000 Zagreb

Croatia

Šime Malenica Bureau Veritas

17 bis, Place des Reflets, La Défense 2

Paris La Defense Cedex 92077 France

Stipe Tomašević, Marko Tomić

University of Zagreb Faculty of Mechanical Engineering

and Naval Architecture I. Lucica 5, 10000 Zagreb

Croatia



OMAE2008-57111

ABSTRACT The importance of hydroelastic analysis of large and flexible

container ships of today is pointed out. A methodology for

investigation of this challenging phenomenon is drawn up and a

mathematical model is worked out. It includes definition of ship

geometry, mass distribution, structure stiffness, and combines ship

hydrostatics, hydrodynamics, wave load, ship motion and vibrations.

Based on the presented theory, a computer program is developed and

applied for hydroelastic analysis of a flexible segmented barge for

which model test results of motion and distortion in waves have been

available. A correlation analysis of numerical simulation and

measured response shows quite good agreement of the transfer

functions for heave, pitch, roll, vertical and horizontal bending and

torsion. The developed tool is furthermore used for hydroelastic

analysis of a large container ship.

1. INTRODUCTION Large container ships are very flexible and their structural natural

frequencies can fall into the range of the encounter frequencies in an

ordinary sea spectrum. Therefore, the wave induced hydroelastic

response becomes an important issue especially for improving the

classification rules and ensuring ship safety. For container ships, due

to open cross-section, the lowest elastic natural modes are those of

coupled horizontal and torsional vibrations. This coupling is highly

pronounced due to the fact that the shear (torsional) centre is below

the keel, i.e. far from the centre of gravity. The classical approach to

determine ship motions and wave loads is based on the assumption

that the ship hull acts as a rigid body [1]. That approach is not

reliable enough for ultra large ships due to mutual influence of the

wave load and structure response. Therefore, a reliable solution

requires analysis of wave load and ship vibrations (springing and

whipping) as a coupled hydroelastic problem.

The hydroelastic theory has been established by Bishop and Price as

the unified strip-beam theory [2]. The hull model is represented by

the Timoshenko beam and the fluid action by the strip theory [3]. The

1

hydroelastic theory is extended to general floating structures in such a

way that the space structural modes are obtained by the finite element

method and the fluid action is determined by a three-dimensional

potential theory [4].

One of the most recent detailed investigations of ship hydroelasticity

in case of bulk carrier is elaborated in [5]. Timoshenko beam

idealization and 3D FEM model combined with potential flow theory

are applied. The vertical bending responses obtained from one- and

three-dimensional models are in good agreement, while differences

are observed for the horizontal bending and twisting responses. This

may be due to inadequate modelling of the highly non-prismatic hull

girder, discontinuities between open and closed cross-section

segments, and warping effects [6].

The above state-of-the-art gave incentive to further investigation of

this challenging problem. The present paper is intended to propose

the consistent theory for hydroelastic coupling between the structural

model, represented by either 1D beam model or 3D FEM model, and

3D hydrodynamic model. The well known principles of the modal

superposition method are employed. However, the proposed model is

slightly different: namely in the way in which hydrostatics is taken

into account and in the way the coupling with 3D hydrodynamic

model is performed.

The methodology of hydroelastic analysis, which includes definition

of the structural model, ship and cargo mass distributions, and

geometrical model of ship surface, is shown in Fig. 1 according

to [7]. First, dry natural vibrations are calculated, and then modal

hydrostatic stiffness, modal added mass, damping and modal wave

load are determined. Finally, wet natural vibrations are obtained as

well as the transfer functions (RAO-response amplitude operator) for

determining ship structural response to wave excitation.

Copyright © 2008 by ASME

FIGURE 1. METHODOLOGY OF HYDROELASTIC ANALYSIS

2. STRUCTURAL MODEL The hydroelastic problem can be solved at different levels of

complexity and accuracy. The best, but highly time-consuming way,

is to consider 3D FEM structural model and 3D hydrodynamic model

based on the radiation-diffraction theory. Such an approach is

recommended only for the final strength analysis of ship structures.

However, in the preliminary strength analysis, it is more rational and

convenient to couple 1D FEM model of ship hull with 3D

hydrodynamic model.

1D FEM procedure for vertical ship hull vibrations is well known in

literature [1]. Coupled horizontal and torsional vibrations are a more

complex problem. The matrix finite element equation for coupled

natural vibrations yields [8]

[ ] [ ] ee ee e

f k mδ δ= + , (1)

where

fe – nodal forces vector

δe – nodal displacements vector

[k]e – stiffness matrix

[m]e – mass matrix.

These quantities consist of flexural and torsional parts

e e

e e,

P Uf

R Vδ

= =

(2)

[ ] [ ]e e0

, .0

bs sb st

wt ts tw

k m mk m

k m m

= =

(3)

Vectors of nodal forces and displacements are

(0)(0)

(0)(0), ,

( )( )

( )( )

w

w

TQ

BMP R

T lQ l

B lM l

−−

− = = −

(4)

2

(0) (0)

(0) (0), .

( ) ( )

( ) ( )

w

U Vw l l

l l

ψ

φ ϑ

ψ

φ ϑ

= =

(5)

In the above formulae symbols Q, M, T and Bw denote shear force,

bending moment, torque and warping bimoment, respectively. Also,

, , andw ϕ ψ ϑ are deflection, rotation of cross-section, twist angle

and its variation, respectively. The submatrices have the following

meaning:

[kbs] – bending - shear stiffness matrix

[kwt] – warping - torsion stiffness matrix

[msb] – shear - bending mass matrix

[mtw] – torsion - warping mass matrix

[mst] = [mts]T – shear - torsion mass matrix.

It is evident that coupling between horizontal and torsional vibrations

is realised through the mass matrix due to eccentricity of the centre of

gravity and shear centre.

Before assembling of finite elements it is necessary to transform Eq.

(1) in such a way that all the nodal forces as well as nodal

displacement, Eqs. (4) and (5), are related to the first and then to the

second node. Furthermore, Eq. (1) has to be transformed from local

to global coordinate system. The origin of the former is located at the

shear centre, and of the latter at the base line.

Regardless of the FEM approach for the structural model, the

governing matrix equation of dry natural hull vibrations yields [9]

[ ] [ ]( ) 2 0Ω− =K M δ , (6)

where

[K] - stiffness matrix

[M] - mass matrix

Ω - dry natural frequency

δ - dry natural mode.

As solution of the eigenvalue problem (6), Ωi and δi are obtained

for each i-th dry mode, where i = 1,2...N, N is total number of degrees

of freedom. Now the natural modes matrix can be constituted

[ ] , ... ...1 2 i N

= δ δ δ δ δ , (7)

and the modal stiffness and mass can be determined [9]

[ ] [ ] [ ][ ] [ ] [ ] [ ][ ],T T

= =k δ K δ m δ M δ . (8)

Since the dry natural vectors are mutually orthogonal, matrices [k]

and [m] are diagonal. Terms ki and 2

i imΩ represent deformation

energy and kinetic energy of the i-th mode, respectively.

Note that generally the first six natural frequencies Ωi are zero with

corresponding eigenvectors representing the rigid body modes. As a

result, the first six diagonal elements of [k] are also zero, while the

first three elements in [m] are equal to structure mass, the same in all

directions x, y, z, and the next three elements represent the mass

moment of inertia around the coordinate axes.


3. GEOMETRICAL MODEL OF WETTED SURFACE For determining pressure forces acting on the wetted surface it is

necessary to specify panels and their position in space. Wet surface is

given by offsets of waterline ordinates at body plan stations. If the

strip method is used for pressure calculation, then the panels bounded

with two close stations can be used.

If 3D radiation-diffraction theory is used for hydrodynamic pressure

determination, the wetted surface mesh can be created in such a way

that panels of more regular shape and refined subdivision in the area

of the free surface are achieved [10]. Such a rational mesh is shown

in Fig. 2, where the panel rows follow the ship body diagonals

similarly to the structural elements of ship outer shell. In this way, the

efficiency of hydrodynamic calculation is increased.

FIGURE 2. RATIONAL MESH OF WETTED SURFACE

4. DRY MODES OF WETTED SURFACE As mentioned in Section 2, structural dry modes can be determined

by 1D or 3D FEM analysis. If 1D analysis is used, the beam modes

are spread to the ship wetted surface as follows.

Vertical vibration

d( )

d

wv Z z w

v N vx= − − +h i k , (9)

horizontal vibration

d

d

wh Y w

h hx= − +h i j , (10)

torsional vibration

( )Z z Yt S

ψ ψ= − −h j k , (11)

where w is hull deflection, ψ is twist angle, Y and Z are coordinates of

the point on ship surface, and zN and zS are coordinates of neutral line

and shear centre respectively.

If strong coupling between horizontal and torsional vibration occurs,

as in the case of container ships, the coupled mode yields

d d( )

d d

wh Y u w Z z Y

ht h Sx x

ψψ ψ

= − + + + − −

h i j k , (12)

where ( , , )u u x Y Z= is the cross-section warping function reduced

to the wetted surface [11].

3

5. HYDRODYNAMIC MODEL 5.1. General The fully consistent and efficient seakeeping model with forward

speed, even for rigid body, does not exist yet and only the

approximate models are employed for the time being. These

approximated models spread from the so called 2D strip theories,

over so called encounter frequency approximation (main effect is put

on the change of frequency due to speed) and different 3D

approximations based on the exact forward speed Green function

with or without coupling with the ship steady flow, to non-linear time

domain seakeeping models. However, according to the authors’

knowledge, none of the above methods has been validated enough,

and the problem is still open.

The most widely used method, the one based on the encounter

frequency approximation, is applied in this study, even if the method

utilizing the exact forward speed Green function (together with so

called Neuman-Kelvin approximation) is also implemented in the

software used [12].

The choice of hydrodynamic model is not likely to change the

general conclusions of this paper, because the experience shows that,

in the case of a rigid body, the encounter frequency method agrees

quite well with more complicated methods, at least for the global ship

loadings. This, however, does not mean that we should forget this

important assumption, and that point should be kept in mind when

more detailed correlations with experiments and full scale results will

be undertaken.

Anyhow, the coupling procedure does not depend on the used

hydrodynamic model, and is therefore described here for the zero

speed case, as the simplest one.

5.2. Theoretical Background The harmonic hydroelastic problem is considered in frequency

domain and therefore we operate with amplitudes of forces and

displacement. In order to perform coupling of the structural and

hydrodynamic models, it is necessary to subdivide the external

pressure forces in a convenient manner [13]. First, the total

hydrodynamic force Fh has to be split into two parts: the first part FR

depending on the structural deformations, and the second one FDI

representing pure excitation

h R DIF F F= + . (13)

Furthermore, the modal superposition method can be used. The

vector of the wetted surface deformations H (x, y, z) can be presented

as a series of dry natural modes hi (x, y, z)

( , , ) ( , , )

1

( , , ) ( , , ) ( , , ) ,

1

Nx y z x y z

i ii

Ni i i

h x y z h x y z h x y zi x y z

i

ξ

ξ

= ∑=

= + +∑

=

H h

i j k

(14)

where ξi are unknown modal coefficients. Vectors hi (x, y, z) related

to wetted surface are obtained from the structural dry modes as

explained in the previous section.

As far as the hydrodynamic part of the hydroelastic problem is

concerned, the potential flow theory is adopted. Within this approach

the fluid is assumed inviscid and fluid flow irrotational, so that the

velocity potential can be defined and the corresponding boundary


value problem can be formulated. The general seakeeping problem

for ship advancing with forward speed in waves is an extremely

difficult problem and only approximate solutions exist today. In this

paper we do not enter into the details of the pure hydrodynamic

analysis and we concentrate on the coupling principles only. Indeed,

the coupling procedure remains the same regardless of the

complexity of the boundary value problems for velocity potentials.

Thus, this coupling procedure is illustrated for the seakeeping

problem without forward speed. The total velocity potential ϕ , is

defined with the Laplace differential equation and the given boundary

values

0 within the fluid

0 at the free surface, 0

on the wetted body surface, ,

zz

i Sn

φ

φνφ

φω

∆ =

∂− + = =

∂

∂= −

∂

Hn

(15)

where ν is the wave number, 2/ gν ω= , ω is wave frequency, n is

the wetted surface normal vector, and i is the imaginary unit.

Furthermore, the linear wave theory enables the following

decomposition of the total potential

1

Ni

I D j Rjj

φ φ φ ω ξ φ= + − ∑=

, (16)

where

( )e

gA z ixi

Iν

φ

ω

+= − (17)

- incident wave potential

- diffraction wave potential

- radiation wave potential

A - wave amplitude

I

D

Rj

φ

φ

φ

Now, the body boundary conditions (15) can be deduced for each

potential

,RjD I

jn n n

φφ φ ∂∂ ∂

= − =

∂ ∂ ∂

h n . (18)

It is necessary to point out that the diffraction and radiation potentials

should also satisfy the radiation condition at infinity.

Once the potentials are determined, the modal hydrodynamic forces

are calculated by pressure work integration over the wetted surface.

The total linearised pressure can be found from Bernoulli's equation

p i gzωρφ ρ= − . (19)

First, the term associated with the potential ϕ is considered and

subdivided into excitation and radiation parts (16)

( ) dDIF i Si I D i

S

ωρ φ φ= +∫∫ h n , (20)

2 d

1

NR

F Si j Rj i

j S

ρ ω ξ φ= ∑ ∫∫=

h n . (21)

Thus, (20) represents the modal pressure excitation. Now one can

decompose (21) into the modal inertia force and the damping force

associated with acceleration and velocity respectively

2Re( ) , Re d

1

Na R

F F A A Si i j ij ij Rj i

j S

ω ξ ρ φ= = =∑ ∫∫=

h n , (22)

Im( ) , Im d

1

Nv R

F F B B Si i j ij ij Rj i

j S

ω ξ ρ ω φ= = =∑ ∫∫=

h n , (23)

where Aij and Bij are elements of added mass and damping matrices,

respectively.

Determination of added mass and damping for rigid body modes is a

well-known procedure in ship hydrodynamics [1]. Now the same

procedure is extended to the calculation of these quantities for elastic

modes.

The hydrostatic part of the total pressure, – ρgz in (19) is considered

within the hydrostatic model.

6. HYDROSTATIC MODEL 6.1. Pressure Forces Hydroelastic analysis is performed by the modal superposition

method. Modal forces represent work of actual static and dynamic

forces on rigid body and elastic mode displacements. Thus, modal

restoring forces consist of time-dependent modal pressure forces and

modal gravity forces. In order to specify the contribution of the

hydrostatic part of the total pressure, –ρgz in (19), to hydrostatic

stiffness it is necessary to determine the change of the modal

hydrostatic force as the difference between its instantaneous value

and the initial value for the vibration mode hi of the body wetted

surface Z = Z (x, y) [14]

d dHF g Z S g Z Si i i

SS

ρ ρ= − +∫∫ ∫∫h n h n

. (24)

Each of the above quantities can be presented in the form,

( )

( ) ( )... ... ...δ= + where δ denotes the variation. By neglecting small

terms of higher order, one can write for the modal hydrostatic

force (24)

( )d .HF g Z Z Z Si i i i

S

ρ δ δ δ= − + +∫∫ h n h n h n (25)

Variation of the particular quantity can be determined by applying the

notion of directional derivative ∇H , where H is given with (14)

and ∇ is Hamilton differential operator

1 1

N N j j jh h h

j j j x y zx y zj j

ξ ξ ∂ ∂ ∂

∇ = ∇ = + +∑ ∑ ∂ ∂ ∂ = =

H h . (26)

Copyright © 2008 by ASME 4

As a result

( ) , ( ) , ( )Z Zi i

δ δ δ= ∇ = = ∇ = ∇H Hk h H h n H n . (27)

Determining the variation of the body surface normal vector, δn,

according to (27) is a rather difficult task. Therefore, a relatively

simpler procedure, taken from [14], is applied. By using Eqs. (26),

(27) and δn from [14], the modal hydrostatic force (25) can be

presented in the following form:

1

NH H

F Ci j ij

j

ξ= − ∑=

, (28)

where

HpH Hh HnC C C C

ij ij ij ij= + + (29)

is the i,j-th element of the hydrostatic stiffness matrix, composed of

static pressure, surface mode and normal vector contributions,

respectively

( )dHp j i i i

C g h h n h n h n Sij z x x y y z z

S

ρ= + +∫∫ , (30)

d ,

i i ih h hj j jHh x x xC g Z h h h n

ij x y z xx y zS

i i ih h h

y y yj j jh h h nx y z yx y z

i i ih h hj j jz z zh h h n S

x y z zx y z

ρ

∂ ∂ ∂

= + + +∫∫ ∂ ∂ ∂

∂ ∂ ∂

+ + + ∂ ∂ ∂

∂ ∂ ∂

+ + ∂ ∂ ∂

(31)

d

j jj jh hh hy yHn iz zC g Z n n n hij x y z xy z x x

S

j j j jh h h h

ix x z zn n n hx y z yy x z y

j jj jh hh hy y ix xn n n h Sx y z zz z x y

ρ

∂ ∂∂ ∂

= + − − +∫∫ ∂ ∂ ∂ ∂

∂ ∂ ∂ ∂

− − + − + ∂ ∂ ∂ ∂

∂ ∂∂ ∂

− − − + ∂ ∂ ∂ ∂

.

(32)

Note that the wetted surface coordinate Z is measured from the

waterplane. Based on the constitution of the above coefficients, it is

evident that the hydrostatic stiffness matrix is not diagonal.

In literature, various definitions of hydrostatic stiffness matrix can be

found [15], [16]. The advantage of the present method is that the

derived formulae are general and applicable for a complex body, as

well as for its parts. This is important for determining the local

hydrostatic action as internal loads, transfer of load to a FEM

structural model, etc.

6.2. Gravity forces The above expressions represent only the action of the hydrostatic

pressure, and the gravity part has to be added in order to complete the

total restoring coefficients. Similarly to the pressure part, Eqs. (24)

and (25), a change of the generalised modal gravity force associated

with a particular mode yields [14]

dmF g mi i

V

δ= − ∫∫∫ h k , (33)

where V is body volume and dm is differential mass.

By employing (27) and further (26) one can write

( ) d

1

Nm i m

F g h m Ci z j ij

jV

ξ= − ∇ = − ∑∫∫∫=

H , (34)

where

d

i i ih h hj j jm z z zC g h h h m

ij x y zx y zV

∂ ∂ ∂

= + +∫∫∫ ∂ ∂ ∂

. (35)

6.3. Restoring Stiffness Finally, the complete restoring coefficients read

H mC C C

ij ij ij= + . (36)

It is important to point out that the above expressions for the

hydrostatic and gravity coefficients are general and therefore valid

not only for the elastic modes but also for the rigid body modes as

well as for their coupling [14].

7. HYDROELASTIC MODEL After the structural, hydrostatic and hydrodynamic models have been

determined, the hydroelastic model can be constituted. For that

purpose, let us impose modal hydrodynamic forces (21), (22) and (23) and hydrostatic and gravity forces (28), (33) to the modal

structural model, Section 2

[ ] [ ]( ) 2 DI a v H m

ω− = + + + +k m ξ F F F F F . (37)

Furthermore, all terms dependent on unknown modal amplitudes, ξi,

can be separated on the left hand side. Thus, the governing matrix

differential equation, which combines rigid body motions and

vibrations, is deduced

[ ] [ ] [ ] [ ]( ) [ ] [ ]( ) 2

( ) ( ) .iω ω ω ω+ − + − + =k C d B m A ξ F (38)

where all quantities are related to the dry modes:

[k] - structural stiffness

[d] - structural damping

[m] - structural mass

[C] - restoring stiffness

[B(ω)] - hydrodynamic damping

[A(ω)] - added mass


F - wave excitation

ω - encounter frequency.


Structural damping can be given as a percentage of the critical value

based on experience with similar ships. As it is well-known, added

mass and hydrodynamic damping depends on the frequency. The

solution of (38) gives the modal amplitudes ξi and displacement of

any point of the structure obtained by retracking to (14).

The wet natural modes can also be determined by solving the

eigenvalue problem extracted from (38)

[ ] [ ] [ ] [ ]( ) 2 ( ) 0ω ω+ − + =k C m A ξ . (39)

Now damping is neglected since its influence on the eigenpair is very

small. The solution of (39) gives natural frequencies of ship motion

and vibration in water and the corresponding so-called wet natural

modes. Since added mass is a frequency dependent function, it is

evident that an iteration procedure has to be employed to solve (39).

Therefore, the wet modes are not orthogonal. Also, there are no more

zero natural frequencies and pure rigid body modes due to their

coupling with the elastic modes [13].

8. HYDROELASTICITY OF A FLEXIBLE BARGE The implementation of the structural model in hydroelastic analysis is

checked in case of a flexible barge, for which test results are

available [7], [13]. The barge consists of 12 pontoons, which are

connected by a steel rod above the deck level, Figure 3.

FIGURE 3. BARGE IN WAVES

The deformation centre is above the gravity centre and strong

coupling between horizontal and torsional vibrations is achieved as in

case of container ships. For illustration, Figures 4 and 5 show

correlation of the calculated and the measured transfer function of

horizontal bending moment and torque, respectively, as function of

wave period T, [13], [17].

FIGURE 4. TRANSFER FUNCTION OF BARGE

HORIZONTAL BENDING MOMENT, cccc=60°

FIGURE 5. TRANSFER FUNCTION OF BARGE TORQUE,

cccc =60°

Also, convergence of the applied modal superposition method in

hydroelastic analysis is confirmed in the case of the same flexible

barge with no forward speed. Figure 6 shows absolute amplitude

values ξi of normalized modes. The first three modes are related to

sway, roll and yaw, while the remaining modes are elastic. All

diagrams are determined for heading angle χ=120o, and each of them

is a result of single wave length in the range λ/L=0.5-2.

FIGURE 6. MODAL AMPLITUDES OF COUPLED HORIZONTAL AND TORSIONAL VIBRATIONS OF

FLEXIBLE BARGE, U=0 kn, cccc=120°

9. HYDROELASTICITY ANALYSIS OF CONTAINER SHIP 9.1. Ship Particulars The application of developed theory is illustrated in case of a 7800

TEU VLCS (Very Large Container Ship), Figure 7. The main vessel

particulars are the following:

Length overall Loa = 334 m

Length between perpendiculars Lpp = 319 m

Breadth B = 42.8 m

Depth H = 24.6 m

Draught T = 14.5 m

Displacement, full load ∆f = 135336 t

Displacement, ballast ∆b = 68387 t

Engine power P = 69620 kW

Ship speed v = 25.4 kn .


FIGURE 7. 7800 TEU CONTAINER SHIP

The ship hull stiffness properties are calculated by program STIFF,

based on the theory of thin-walled girders [11]. The geometrical

properties rapidly change values in the engine and superstructure area

due to closed ship cross-section. This is especially pronounced in

case of torsional modulus, which takes quite small values for open

cross-section and rather high for the closed one [18].

9.2. Natural Vibrations Dry natural vibrations are calculated by program DYANA [18]. The

ship hull is divided into 50 beam finite elements. Finite elements of

closed cross-section (6 d.o.f.) are used in the ship bow, ship aft and in

the engine room area. Dry natural frequencies for vertical vibrations,

and coupled horizontal and torsional vibrations for full load and

ballast conditions are listed in Table 1. Their values for ballast

condition are higher due to the lower mass. The lowest frequency

value, which plays the main role in wave excitation, is detected for

coupled vibrations. As a result of rather low torsional stiffness, this

value belongs to primarily torsional mode.

TABLE 1 . DRY NATURAL FREQUENCIES, ωωωωi [rad/s]

Full load Ballast Mode

no. Vertical

Horizontal +

torsional Vertical

Horizontal +

torsional

1 4 2.18 5.59 3.98

2 8.41 4.23 11.6 6.79

3 13.22 7.08 17.85 11.55

4 18.07 9.23 25.02 14.9

5 23.04 13.19 32.52 20.59

6 28.09 15.37 39.21 23.03

7 32.77 18.22 46.29 27.98

8 37.22 22.65 53.25 32.64

9 41.73 23.75 60.4 36.33

10 42.27 28.38 66.96 40.38

Once the dry natural modes of ship hull are determined it is possible

to transfer the beam node displacements to the ship wetted surface for

the hydrodynamic calculation, Eqs. (9) and (12). The first two dry

natural modes of the ship wetted surface in case of vertical and

coupled horizontal and torsional vibrations for full load are shown in

Figures 8, 9, 10 and 11.

7

FIGURE 8. THE FIRST NATURAL MODE OF VERTICAL VIBRATIONS, ω1=4 rad/s

FIGURE 9. THE SECOND NATURAL MODE OF VERTICAL VIBRATIONS, ω2=8.41 rad/s

In addition, the values of natural frequencies of wet ship in full load

condition are listed in Table 2. By comparing them to those of dry

ship in Table 1, one sees that vertical vibration frequencies are more

reduced than those of coupled horizontal and torsional vibrations.

TABLE 2. WET NATURAL FREQUENCIES, ωωωωi [rad/s]

Full load

Mode no. Vertical

Horizontal +

torsional

1 3.07 2.04

2 6.33 3.65

3 10 6.57

4 13.96 8.28

5 18.09 11.73

6 22.18 13.46

7 26.23 16.34

8 30.48 20.38

9 35.01 21.51

10 41.23 25.88

FIGURE 10. THE FIRST NATURAL MODE OF COUPLED HORIZONTAL AND TORSIONAL VIBRATIONS,

ω1 = 2.18 rad/s


FIGURE 11. THE SECOND NATURAL MODE OF COUPLED HORIZONTAL AND TORSIONAL VIBRATIONS,

ω2 = 4.23 rad/s

9.3. Ship Response Numerical calculation of ship response to waves is performed for full

load and ballast condition, unit harmonic wave amplitude, and set of

heading angles, ship speed and wave length [18]. Here, only some

selected results for full load and ship speed of U = 25 kn are

presented. Vertical response is shown for head sea, c = 180°, and

coupled horizontal and torsional response for quartering sea,

c = 120°. In all figures hydroelastic response is correlated to rigid

body response determined by program HYDROSTAR [12], where

the so called encounter frequency approximation was used for the

solution of the seakeeping problem with forward speed. Due to the

lack of measured data on large container vessels, modal damping that

is usually used in global vibration calculations of merchant ships, i.e.

2% of the critical value, is applied in the analysis [19]. Figure 12

shows the transfer function of the vertical bending moment at the

midship section. Heave resonance occurs at encounter frequency

ωe = 0.83 rad/s, while bending resonance is achieved at

ωe = 3.74 rad/s. In the former case, bending moments determined by

hydroelasticity and rigid body motion are almost the same, Figure 13.

In the latter case, the hydroelastic bending moment takes very high

values compared to the rigid body one, Figure 14.

FIGURE 12. TRANSFER FUNCTION OF VERTICAL

BENDING MOMENT, x=161.35 m, cccc=180°, U=25 kn

8

FIGURE 13. VERTICAL BENDING MOMENT,

ωe=0.83 rad/s, λλλλ=246.55 m, cccc=180°, U=25 kn

FIGURE 14. VERTICAL BENDING MOMENT,


The results of coupled horizontal and torsional ship response are

presented in Figures 15 to 20. Figures 15 and 16 show transfer

functions of horizontal bending moment and torque referred to the

shear (torsional) centre, at the midship section, respectively.

Hydroelastic effect is more pronounced in torsional than in bending

response.

FIGURE 15. TRANSFER FUNCTION OF HORIZONTAL

BENDING MOMENT, x=168.57 m, cccc=120°, U=25 kn


FIGURE 16. TRANSFER FUNCTION OF TORQUE,

x=168.57 m, cccc=120°, U=25 kn

Large relative discrepancies between the hydroelastic and rigid body

torque in low frequency domain in Figure 16 might be the result of

ill-conditioning of the former. In hydro-rigid-body analysis, namely,

sectional forces are determined by pressure integration over wetted

surface, while in hydroelastic analysis sectional forces are obtained

by derivation of hull displacements, which are predominantly rigid

body ones in low frequency domain. Looking through the modal

decomposition, derivatives of rigid body modes are zero, while those

of elastic body are quite small with decreased accuracy.

FIGURE 17. HORIZONTAL BENDING MOMENT,


Distributions of bending moment in case of rigid body and elastic

resonance are shown in Figures 17 and 18. In the former case

hydroelastic and rigid body bending moments are quite close, while

in the latter case the elastic bending moment is much higher than the

rigid body one. Similar situation occurs with torques, Figures 19 and

20. When elastic response is in resonance with wave excitation the

hydroelastic torque takes very high values.

FIGURE 18. HORIZONTAL BENDING MOMENT,


FIGURE 19. TORQUE, ωe=1.3236 rad/s, λ=85.31 m, cccc=120°,

U=25 kn

FIGURE 20. TORQUE, ωe=2.0169 rad/s, λ=46.61 m, cccc=120°,

U=25 kn

9.4. Validation Of 1D FEM Model For this purpose, the light weight loading condition of dry ship with

displacement ∆=33692 t is considered. The first dominantly torsional

mode and the second dominantly horizontal flexural mode of the

wetted surface are quite similar to those shown in Figures 10 and 11,

obtained for the full load. The reliability of 1D FEM analysis is

verified by 3D FEM analysis of the considered ship [17]. The first

two 3D dry natural modes are similar to those of 1D analysis, Figures

10 and 11. The corresponding natural frequencies obtained by 1D and

3D analyses are compared in Table 3. Quite good agreement is

achieved. Values of natural frequencies for higher modes are difficult

to correlate, since strong coupling occurs between global hull modes

and local substructure modes of 3D analysis.

TABLE 3. NATURAL FREQUENCIES OF CONTAINER SHIP

IN LIGHT WEIGHT CONDITION, ω [rad/s]

Mode no. 1 (T+HB) 2(HB+T)

1D FEM 5.39 9.23

3D FEM 5.41 9.42


10. CONCLUSION Ultra large container ships are quite flexible and stretch the bounds of

present classification rules for reliable structure design. Therefore,

hydroelastic analysis has to be performed. One of the basic steps is

dry natural vibration analysis of ship hull. Vertical vibration

calculation is performed in a standard way, while the coupled

horizontal and torsional vibration is rather complex.

The performed vibration analysis of the 7800 TEU Container ship

shows that the developed hydroelasticity theory, utilizing 1D FEM

structural model and 3D hydrodynamic model, is an efficient tool for

application in ship hydroelastic analyses. The obtained results point

out that the transfer functions of hull sectional forces in case of

resonant vibration (springing) are much higher than in resonant ship

motion. This is the main issue of the paper, which requires further

investigation.

In order to complete hydroelastic analysis of container ships and

confirm its importance for ship safety, it is necessary to proceed

further to ship motion calculation in irregular waves for different sea

states, based on the known transfer functions. This includes

determination of global wave loads, i.e. bending and torsional

moments and their conversion into stresses, stress concentration in

critical areas of ship structures, especially in hatch corners due to

suspended warping, and fatigue of structural details. The same

numerical procedures, which are used in hydro-rigid-body analysis,

are at disposal and are applicable in this case.

The used beam model of ship hull is a reasonable choice for

determining wave load. However, stress concentration in hatch

corners calculated directly by the beam model is underestimated

[20,21]. This problem can be overcome by applying substructure

approach, i.e. 3D FEM model of substructure with imposed boundary

conditions from beam response. In any case, 3D FEM model of

complete ship is preferable from the viewpoint of determining stress

concentration.

Another aspect of hydroelasticity is slamming and whipping, which

are related to vertical bending. This impulsive load is considered in

time domain and is outside the scope of this paper. However, it must

be considered within general container ship problematic.

At the end of a complete investigation, which also has to include

model tests and full scale measurements, it will be possible to decide

on the extent of the revision of Classification Rules for the design and

construction of ultra large container ships. Also, operational

conditions for this type of ships, i.e. reduction of ship speed and

change of heading angle for some sea states due to resonant flexural

and torsional response (as well as parametric rolling) have to be

reconsidered.

ACKNOWLEDGMENT The authors would like to express their gratitude to Ms. Estelle

Stumpf, research engineer of Bureau Veritas, Marine Division –

Research Department, for performing the 3D FEM vibration analysis

of container ship and kind permission to publish the valuable results.

REFERENCES

[1] Principles of Naval Architecture. SNAME, 1988.

10

[2] Bishop RED, Price WG. Hydroelasticity of Ships.

Cambridge University Press, 1979.

[3] Salvensen N, Tuck EO, Faltinsen O. Ship motion and sea

loads. Transactions, SNAME 1970; Vol. 70, p. 250-287.

[4] Price WG, Wu Y. Hydroelasticity of Marine Structures,

in Theoretical and Applied Mechanics, Eds. Niordson FI

and Olhoff N. Elsevier Science Publishers B.V. (North

Holland), 1985.

[5] Hirdaris SE, Price WG, Temarel P. Two- and three-

dimensional hydroelastic modelling of a bulker in regular

waves. Marine Structures 2003; 16, p. 627-658.

[6] ISSC, Technical Committee II.2. Proceedings of the 16th

ISSC, 2006.

[7] Remy F, Molin B, Ledoux A. Experimental and

numerical study of the wave response of a flexible barge.

Hydroelasticity in Marine Technology. Wuxi, China,

2006. p. 255-264.

[8] Senjanović I, Grubišić R. Coupled horizontal and

torsional vibration of a ship hull with large hatch

openings. Computers & Structures 1991; Vol. 41, No. 2,

p. 213-226.

[9] Bathe KJ. Finite Element Procedures. Prentice Hall,

1996.

[10] Malenica Š, Senjanović I, Chen XB. Automatic mesh

generation for naval and offshore hydrodynamic

simulations. SORTA'04, Plitvice Lakes, Croatia, 2004.

[11] Senjanović I, Fan Y. A higher-order theory of thin-walled

girders with application to ship structures. Computers &

Structures 1992; 43(1), p. 31-52.

[12] Hydrostar, User's manual. Bureau Veritas, Paris, 2006.

[13] Malenica Š, Molin B, Remy F, Senjanović I. Hydroelastic

response of a barge to impulsive and non-impulsive wave

load. Hydroelasticity in Marine Technology. Oxford, UK,

2003, p. 107-115.

[14] Malenica Š. Some aspects of hydrostatic calculations in

linear seakeeping. The 14th NAV Conference, Palermo,

Italy, 2003.

[15] Newman JN. Wave effects on deformable bodies.

Applied Ocean Research 1994; 16, p. 47-59.

[16] Huang LL, Riggs RR. The hydrostatic stiffness of

flexible floating structure for linear hydroelasticity.

Marine Structures 2000; 13, p. 91-106.

[17] Malenica Š, Senjanović I, Tomašević S, Stumpf E. Some

aspects of hydroelastic issues in the design of ultra large

container ships. The 22nd IWWWFB, Plitvice Lakes,

Croatia, 2007.

[18] Tomašević S. Hydroelastic model of dynamic response of

Container ships in waves. Ph. D. Thesis, FSB, Zagreb, (in

Croatian), 2007.

[19] Kumai T. Damping factors in the higher modes of ship

vibrations. European Shipbuilding 1958; Vol. 7, No. 1, p.

29-34.

[20] Pedersen PT. Torsional response of containerships.

Journal of Ship Research 1985, Vol. 29, No. 3, p. 194-

205.

[21] Senjanović I, Fan Y. Pontoon torsional strength analysis

related to ship with large deck openings. Journal of Ship

Research 1991; Vol. 35, No. 4, p. 339-351.


Abstract for 23rd IWWWFB, Jeju, Korea, 2008

Some aspects of whipping response of container ships

Tuitman J1 & Malenica S2

(1) Delft University of Technology, Netherlands ([email protected])


Introduction

Whipping is usually defined as a transient hydroelastic ship structural response due to impulsive loadingsuch as slamming, green water, underwater explosion, etc. Here we concentrate on the slamming inducedwhipping. Slamming induced whipping is observed both in experiments and in full scale measurementsfor any kind of ships as far as they encounter heavy seas in which the slamming type of loading is likelyto occur. One example of the typical whipping event is shown in figure 1 (taken from [1]). This figurerepresents the time evolution of the vertical bending moment, following severe slamming event, at themidship of the relatively small (Lpp = 124m) general cargo/container vessel. As we can see, the whippingcontribution to the overall vertical bending moment is not only very important but it also last for arelatively long time due to the low structural damping. One slam event increases multiple extremes inthe bending moment which makes the whipping phenomena to be relevant both for extreme and fatigueloading of the ship structure.

However, up to the authors knowledge, the hydroelastic whipping effects are not properly accountedfor in the ship design. This is mainly due to the difficulties in the correct modelling of whipping and theneeded calculation time. Indeed, in order to calculate the whipping response, one should combine severalaspects (seakeeping in large waves at forward speed, slamming, hydroelasticity, etc.) which are difficultto model even independently. In spite of all these difficulties, there is a lot of research on whipping goingon nowadays, especially in the context of the ultra large container ships. There are several reasons whythe whipping is likely to be more important for the large container ships: high ship speed (close to 30knots) and large bow flare induce higher slamming loads, large ship size reduce the natural frequencies.In this paper we present the recent numerical developments related to whipping and we apply them totwo container ships different in size (Lpp ≈ 260m and Lpp ≈ 360m). Both extreme loading and fatigue isdiscussed.

Figure 1: Typical whipping event.

Numerical model

Numerical model that we use is based on the coupling in between the 3D diffraction radiation seakeepingcode for hydrodynamic part and the Timoshenko beam model for structural part. The so called modalapproach is adopted which means that the ship motions and deformations are represented in a series of6 rigid body modes and several (5 to 10) dry structural modes. The basics of the theory are presentedin [5] and [8] and here below we present just the final dynamic modal equation:

([ m ]+[ A∞ ])ξ(t)+[ b ] ˙ξ(t)+([ k ]+[ C ])ξ(t)+

∫ t

0

[ K(t− τ) ]ξ(τ)dτ = F (t)+Q(t) (1)

where ξ is the vector of modal amplitudes, [ m ] is the modal mass matrix, [ A∞ ] is the infinitefrequency added mass matrix, [ b ] is the damping matrix, [ k ] is the structural stiffness matrix, [ C ] isthe hydrostatic restoring matrix, [ K(t) ] is the matrix of the hydrodynamic memory functions, F is thevector of the non-impulsive wave loading (linear and nonlinear) and Q is the vector of impulsive loads.The dimension of all the above matrices is (6 + Nf ) × (6 + Nf ) where Nf represents the number of drystructural modes. This equation is integrated in time using the 4th order Runge Kutta method.

It is important to note that the linear hydrodynamic coefficients in the above equation are derivedfrom the frequency domain calculations, using the well known method proposed in [3, 7]. The nonlinearpart of the loading includes non-impulsive and impulsive parts. The non impulsive part represents theso called Froude Krylov loads which basically corrects the hydrostatics and pressure distribution aroundthe waterline while the impulsive part represents the slamming loads. The slamming part is probablythe most difficult part to evaluate numerically. A very robust method is needed and the calculationof the slamming force should not take to much CPU time to be able to preform long time whippingsimulations. The only fast and reliable methods for evaluation of the slamming forces which are availabletoday are based on the so called 2D strip approach. The bow is modeled by multiple 2D sections and theslamming force is evaluated at these sections. In this paper we use two different methods for evaluationof the slamming loads at each 2D section: the Generalized Wagner Model (GWM) [9] and the ModifiedLogvinovich Model (MLM) [4]. The advantage of the second method is much lower CPU time, but thedisadvantages is the lower domain of validity. We do not discuss these methods in details here and werefer to [6].The above described procedure was integrated into a single numerical tool able to perform the long timewhipping simulations for any prescribed irregular sea state. These simulations allows for determinationof the probability of exceedence of the maxima and for determination of fatigue damage.

Numerical results

As already mentioned, two container ships of different size were chosen for illustration of the overallprocedure and for demonstration of the importance of whipping in container ship design. The first ship(S1) has the length between perpendiculars of 360m and the second one (S2) 260m. Only the case of headwaves and zero forward speed is investigated which means that the vertical modes only will participate.The first few structural natural frequencies in vertical plane, corresponding natural mode shapes for

Mode S1 S21 0.432 0.6002 0.905 1.2253 1.445 1.9504 2.008 2.7385 2.606 3.631

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

w

Time [s]

1st2nd3rd4th5th

Figure 2: Structural natural frequencies and mode shapes.

S1 and transfer of the first mode onto hydrodynamic mesh, are shown in Figure 2. Only five naturalmodes are used in the calculations because the tests showed that the higher modes do not participatesignificantly, and because the mode with the highest frequency determines the stable time step.

The midship bending moment is calculated using different approaches to investigate the effect ofwhipping. The same wave trains are used for the different calculations for the same sea condition tomake comparison more valid. The fist approach is using linear theory only with a rigid ship. Thecontribution of the non-linear Froude Krylov forces is investigated using a rigid model with the non-linear seakeeping code without slamming. The last approach is a flexible ship using non-linear seakeepingcode and applying the slamming loads. For every sea condition six halve hour runs using 250 wavecomponents are glued to obtain enough statistical information.

Example of typical output is presented in Figure 3 where the zoom on the typical whipping event isalso shown. As we can see from this figure, the slamming usually occurs in sagging conditions but it lastlong enough to influence the maximum hogging moment too. These signals are rich of informations and

can be used for determination of the maximum expected values as well as for the determination of thefatigue damage by using the rain-flow counting method.

-4-2 0 2 4 6 8

10 12 14 16

0 2000 4000 6000 8000 10000

My

[GN

m]

Time [s]

-4

-2

0

2

4

6

8

10

12

14

16

8840 8860 8880 8900 8920

My

[GN

m]

Time [s]

Elastic - with slammingRigid non linear

Rigid linear

Figure 3: Typical time history of the vertical bending moment and zoom around a whipping event.

The probability of exceedence of the midship bending moment is shown in figure 4 for the differentapproaches. Even if the relatively mild sea states were chosen, (Hs = 9m, Tz = 11s for S1, and Hs = 10m,Tz = 13.95s for S2), the influence of whipping is clearly visible. The non linear Froude Krylov forcesincrease the sagging moment significantly and the whipping response does increase it even more. Figure5 shows the cycle count of the bending moment using the rainflow method and the calculated fatiguedamage of the deck. The whipping increase the fatigue damage significantly by increasing the amplitudeof the large cycles.

0.001

0.01

0.1

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pro

babi

lity

of e

xcee

denc

e

My [GNm]

Elastic - with slamming - HoggingRigid nonlinear - no slamming - Hogging

Elastic - with slamming - SaggingRigid nonlinear - no slamming - Sagging

Rigid linear - no slamming

0.001

0.01

0.1

1

0 2 4 6 8 10 12

Pro

babi

lity

of e

xcee

denc

e

My [GNm]

Elastic - with slamming - HoggingRigid nonlinear - no slamming - Hogging

Elastic - with slamming - SaggingRigid nonlinear - no slamming - Sagging


Figure 4: Probability of exceedence of the midship bending moment (S1-left, S2-right).

1

10

100

1000

10000

0 2 4 6 8 10 12

Num

ber

of c

ycle

s

Bending moment [GNm]

Elastic - with slammingRigid nonlinear - no slamming


0

2e-06

4e-06

6e-06

8e-06

1e-05

1.2e-05

1.4e-05

0 2 4 6 8 10 12

Fat

igue

dam

age

Bending moment [GNm]

Elastic - with slammingRigid nonlinear - no slamming


Figure 5: Rainflow count of bending moment and fatigue damage of the deck for S1.

To obtain design values many sea states have to be evaluated. The sagging moment with a probabilityof 10−5 calculated using a Weibull extrapolation and the fatigue damage per hour are shown in figure6 for a limited number of sea states. In this case the slamming and whipping occurs only in the verysevere sea states. When a non zero velocity would be used, the number of cells where whipping occurswill increase.

6 8 10 12 14 16 18 6 7 8 9 10 11 12 13 14

1e+06 2e+06 3e+06 4e+06 5e+06 6e+06 7e+06 8e+06 9e+06 1e+07

Rigid linearRigid non-linear

Elastic - with slamming

Tz [s]

Hs [m] 6 8 10 12 14 16 18 6 7 8 9 10 11 12 13 14

0 5e-05

0.0001 0.00015

0.0002 0.00025

0.0003 0.00035

0.0004 0.00045

Rigid linearRigid non-linear

Elastic - with slamming

Tz [s]

Hs [m]

Figure 6: The 10−5 probability sagging moment (left) and the fatigue damage per hour (right).

Conclusions

We presented here the numerical method which can be used in ship design for determination of theinfluence of whipping on wave loadings and ship structural responses. The method was demonstrated ontwo container ships of different size and in both cases the influence of whipping was found to be importantnot only for the maximum values but also for fatigue. It should be mentioned that the examples whichwere chosen are just demonstrative ones, and the general methodology should include more complex setof calculations namely the model should include the effects of forward speed, heading, different loadingconditions (full, ballast, etc.) and different sea states. At the same time the sensitivity to some otherparameters such as damping, direction of 2D slamming strips, aft slamming, l ength of runs, number ofwave components, etc. should be properly investigated. Maybe the most critical point in the analysis isthe determination of slamming loads which are extremely difficult to evaluate. In this work we used twodifferent methods GWM and MLM and even if there are some differences in the evaluation of the localforces the final results in terms of maximum values and fatigue seem to be in good agreement. This isimportant because the MLM method requires much less CPU time. It should also be kept in mind thatboth methods are limited to the 2D calculations and some 3D correction coefficients need to be employed.How this should be done is not clear yet.

References

[1] Aalberts P.J. & Nieuwenhuijs M. 2006. : ”Full scale wave and whipping induced hull girderloads.”, 4th. Int. Conf. on Hydroelasticity, Wuxi, China.

[2] Bishop, R.E.D. & Price, W.G., 1979. : ”Hydroelasticity of ships”, Cambridge University Press.

[3] Cummins W.E., 1962. : ”The impulse response function and ship motions.”, Schiffstecknik

[4] Korobkin A.A., 2005.: ”Analytical models of water impact.”, Euro. J. Applied Mathematics, 16,pp. 1-18.

[5] Malenica S., Molin B., Remy F. & Senjanovic I., 2003. : ”Hydroelastic response of a bargeto impulsive and non impulsive wave loads.”, 3rd. Int. Conf. on Hydroelasticity, Oxford, UK.

[6] Malenica S. & Korobkin A.A., 2007. : ”Some aspects of slamming calculations in seakeeping.”,9th. Int. Conf. on Numerical Ship Hydrodynamics, Ann Arbor, USA.

[7] Ogilvie T.F., 1964. : ”Recent progress toward the understanding and prediction of ship motions.”,5th. Symp. on Naval Hydrodynamics.

[8] Tuitman J. Aanhold H 2007: Using generalized modes for time domain seakeeping calculations,22th IWWWFB, Croatia

[9] Zhao R., Faltinsen O.M. & Aarsnes J.V., 1996. : ”Water entry of arbitrary two dimensionalsections with and without flow separation.”, 21st Symp. on Naval Hydrodynamics, Trondheim, Nor-way.

A COMPREHENSIVE AND PRACTICAL STRENGTH ASSESSMENT METHODOLOGY FOR CONTAINER SHIPS TAKING INTO ACCOUNT NON LINEAR AND HYDRO-ELASTIC LOADING G de Jong and M Huther, Bureau Veritas, France SUMMARY The drive for economy of scale effects has fuelled the strong growth in size and capacity of new container ships. The combination of relatively low hull girder stiffness and high speed (decreased natural frequency of hull girder vibrations and increased wave encounter frequency) may cause phenomena which are of second order for average size vessels to become of high importance for these large vessels. This is particularly the case for vibratory structural response and associated fatigue damage caused by whipping and springing. Making use of experience feedback with calculations and full scale measurements this paper presents a methodology to estimate the consequences of these phenomena during the design stage of the vessel. Practical application of the methodology has been made possible by further developing the Bureau Veritas in-house hydrodynamic suite HydroSTAR to take into account hydro-elasticity and non linear time domain simulations. The software has been validated against model tests, while a full-scale measurement campaign is ongoing. Application of the methodology to ultra large container ships confirms that stress levels are indeed increasing. As a consequence, a significant increase both hull girder loads and fatigue damage accumulation is found, which can no longer be ignored when analysing the ship structure. When considering future designs for even larger container ships of 400 m in length and beyond, the effects of whipping and springing will become even more important. 1. INTRODUCTION Over the past five years the maximum size of Post-Panamax container ships has increased dramatically to achieve economy of scale effects. Together with the rapid growth in trade volume and mileage between the emerging production economies in the Far East and the established economies (mainly Europe), as well as a firm belief that market share is the key for future success, an unprecedented surge in new orders for ultra large container ships (ULCS, 10 000+ TEU) has been created. According to data published by Clarkson, the world orderbook for this segment stood at 187 vessels at the end of the first quarter of 2008. The majority of these giant boxships are expected to be delivered in 2009 (17%), 2010 (29%) and 2011 (43%). Although the turmoil in the financial markets and uncertainty regarding economic growth (possible slowdown in China, fear for recession in the US, high oil price) have drastically reduced the amount of new orders in the first quarter of 2008, there is no reason to believe that the drive for increasing the vessel size will come to a halt at the present maximum of 13 300 TEU for a ship overall length of about 370 m1. Therefore, realizing that a new upheave in container ship ordering would probably produce designs of well over 400 m in length, it is of key importance to reflect on the technical challenges associated with scale enlargement of ultra large boxships.

1 The only exemption is the E-class series of Maersk, with an estimated capacity of 15 200 TEU and a length of 397 m according to data from AXS Alphaliner.

In fact, if the increase in size is achieved through extrapolation of existing ship dimensions and application of environmental loads estimated from dimensional analysis, it may be expected that phenomena which are of second order for average size vessels can become important for large vessels. This is particularly the case for vibratory structural response and associated fatigue. Experience feedback shows that two dynamic phenomena affecting the hull girder require specific attention when considering large container ships: whipping (transitory hull girder vibrations caused by hydrodynamic impact at the bow) and springing (excitation of the first natural modes of vibration of the hull girder). Indeed, increasing the size of ships with large deck openings will decrease the natural frequencies of hull girder vibrations, while an increase in service speed will result in a higher wave encounter frequency. Consequently the wave encounter frequency may be in the same range as the lowest hull girder natural frequencies, causing important dynamic amplification effects. As it is not fully clear to what extent these phenomena are covered by the implicit and explicit safety margins of classical rules and regulations, the effect of the dynamic behaviour of large container ships in a seaway is to be studied by direct calculations. In this paper the two phenomena and their impact on ship structures are analysed. In addition, the methodology recently developed by Bureau Veritas to assess whipping and springing effects in large container ship is presented, as well as the implementation into the in-house developed hydrodynamic simulation suite HydroSTAR.

2. WHIPPING Whipping can be characterised as transitory response of the hull girder in the first natural mode caused by hydrodynamic impact at the bow due to re-entry of the foreship into the water (slamming) or violent wave impact at the stem (slapping), see figure 1. Figure 1: Container ship experiencing slamming The first natural mode of the hull girder could be simulated by a system with one degree of freedom damped at the corresponding frequency. The associated forces are extremely high but of short time duration, similar to an impulse [1] and consequently infer transitory damped vibrations. 2.1 SHIP STRUCTURAL RESPONSE Slamming and slapping are known to occur in head seas when the vertical (relative) motions are highest. The deformations associated with the hull girder vibration caused by hydrodynamic impact are superimposed on the wave induced hull girder deformations, see figure 2. Figure 2: Full scale measurements of stresses in the deck of the vessel Marcel Bayard It has been known for several years that ships with large deck openings are prone to sustaining damages as a result of whipping. First of all, the design value of the vertical bending moment can be exceeded, causing permanent deformation of the hull girder. Secondly, high frequent stress cycles can be generated, causing premature fatigue cracks in structural details [2, 3]. The understanding and analysis of the phenomenon of exceeding the acceptable bending moment is relatively straightforward, while the prediction of the occurrence of fatigue cracks is much more difficult. However, the risk for fatigue damages has been clearly demonstrated on the vessel Marcel Bayard. In fact, the full scale measurement campaign [2] was initiated after the appearance of fatigue

cracks when the vessel was only three years in service. The study showed that, although the vessel length is only 110 m, the cracks could be explained by frequent occurrence of whipping as a result of particular operating conditions for this type of vessel and large deck openings causing high stress concentrations in the deck. Therefore, it is important to be able to estimate effects of whipping on the stresses in the deck during the design stage. This requires the combined simulation of the behaviour of the vessel under wave loading and hydrodynamic impact caused by slamming and slapping. 2.2 CALCULATION METHODS Direct calculations on a ship in a seaway in order to determine the extreme hull girder loads and the fatigue life of structural details have been common practice for some decades. The methods used are based on the fast spectral approach and are, after calibration, sufficiently accurate for the classical checks. As whipping is a non linear impulsive phenomenon, the (linear) spectral approach does not longer hold. Instead, time domain methods have been developed which can solve the coupling problem between the 3D hydrodynamic diffraction-radiation calculations and the dynamic deformation of the hull girder modelled as a Timoshenko beam or a 3D finite element model. For this modal approach the motions and deformations of the vessel are represented by a series of six rigid modes and five to ten dry structural modes [4]. It is to be noted that the linear hydrodynamic coefficients in the time step equations are obtained from the classical frequency domain calculations [5, 6]. There are two methods available for the determination of the slamming and slapping loads (dynamically exciting the hull girder), which are essentially 2-dimensional: the ‘Generalized Wagner Model’ and ‘Modified Logvinovich Model’. The determination of the structural response to whipping is possible by combined application of calculation tools for the rigid ship in the frequency domain and for the elastic ship in the time domain (non linear). This set of tools was successfully verified on vessels of 260 m and 360 m of length [7], see figures 3 and 4. Figure 3: Example of time history of non linear bending moment time including whipping

Figure 4: Zoom of figure 3 at the instant of hydrodynamic impact (response types: elastic non-

linear, rigid non linear and rigid linear) The calculations are performed according to the scheme shown in table 1. Table 1: Step-by-step procedure for estimating the

extreme hull girder loads

1 Selection of the sea states and their probability of occurrence for the relevant operational profile of the vessel (standard: North Atlantic)

2

Calculation of the linear response and determination of the possible extreme navigation conditions for the incident waves (ship speed, wave height)

3 Determination of navigation conditions for which slamming could occur (wave incidence, ship speed, wave height)

4 Calculation of the non linear behaviour for navigation conditions with high risk of slamming

Cwp∆SwCwp∆Sw

=+

2.3 EXTREME HULL GIRDER LOADS Observation of the elastic response shows that whipping increases the extreme values of the vertical bending moment. Therefore, it is necessary to take this effect into account for checking the ultimate strength of the hull girder. The performed calculations [7] and full scale measurements [2] show that whipping occurs when the ship is in sagging condition. Therefore, for the most severe navigation conditions the extreme slamming loads and consequently the increase of the sagging wave bending moment are calculated. Full scale measurements show that the damping of the vibratory response is small (of the order of ξ=1.5%), which means that whipping is still important half a wave period later when the vessel is in hogging condition and that the ultimate strength check is also to be carried out for this condition 2. This check can be done in analogy with the class rules for the bending moment corrected for the whipping effect as described [8].

2 Especially since container ships normally operate in hogging condition, thus providing the extreme hull girder bending moment.

Application on a 250 m container ship shows that the increase of the total bending moment can reach 20 to 30% for severe navigation conditions, which is in agreement with full scale measurements [2]. The calculations performed for ultra large container ships show that a similar percentage of increase may be expected for these ships. 2.4 FATIGUE Observation of the whipping response (figures 3 and 4) reveals two effects regarding fatigue: • Increase of amplitude of the wave frequent hull girder

stresses • Creation of high frequent damped stress cycles at the

first natural frequency of hull girder bending For welded details it is considered that the residual stresses due to the heat input create a high level of tension in zones where cracks may be expected, resulting in a high R coefficient (minimum stress divided by maximum stress, R > 0.5). For these high R values variation of the average stress level has little influence on the fatigue lifetime. For details without welding there are no residual stresses and analysis becomes somewhat more delicate. In order to simplify matters, in first instance the same approach as for welded structures is applied. As this means that a high level of residual stress is presupposed, this is a conservative simplification. Application of Miner’s law, which is linear by nature, allows for separating the low frequency (wave) and high frequency (whipping) contributions and add both individual effects to obtain the total result, see figure 5. Figure 5: Separation of whipping effects for fatigue calculation Knowing the stress range of the first whipping cycle and the damping it is possible to determine the distribution of cycles and their associated stress ranges as depicted in figure 6. Figure 6: Distribution of high frequent, whipping induced, stress cycles

The associated equations are

( )⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

−−=∆

23j4

21expAjSwp π

ξ

ξ (1)

with j designating the nth whipping cycle

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−−

∆=

21exp

SwCwpA

2

π

ξ

ξ (2)

The short term distribution is obtained by noticing that for every single whipping response there is only one cycle at every level and that there will be a whipping response associated to every wave cycle, i.e., at each level the number of cycles is equal to the total number of waves, see figure 7. Figure 7: Short term distribution of whipping stresses for a given wave amplitude Miner’s sum can be computed by superimposing the short term distributions of the stress ranges. Every cycle can be considered as a response to a regular wave of constant amplitude, while non linear response calculations to regular waves can be utilised as well. For a given wave frequency in head seas (being the dominant wave condition for slamming to occur) it is possible to determine the response function for a wave height H and a threshold wave height Hth below which there is no risk of slamming:

( )HfSwCwp =∆ (3) thHH > An overview of the step-by-step calculation method is presented in table 2. A study performed for an ultra large container ship shows that whipping effectively causes amplification of the hull girder bending stresses, as well as a measurable contribution to the accumulation of fatigue damage. In short term head sea condition the correction of the low frequency stress range can yield a very significant increase of up to 100% for some navigation conditions. Considering that whipping disappears for non-severe sea states, which are far more numerous than severe sea states, and that there is no whipping for transverse and following seas, the total long term increase of the Miner sum due to whipping is estimated to be of the order of 3 to 5%.

Table 2: Step-by-step procedure for estimating the

whipping induced fatigue damage

1

Determination of the maximum speed of the vessel as function of the wave height for the considered wave frequencies and incidence angles (maximum bearable navigation condition on the bridge)

2 Calculation of the transfer functions and associated short term response spectra without whipping

3

Determination of the whipping response in head seas as function of the wave height according to the wave frequencies of the considered sea states and taking into account the whipping threshold

4 Approximation of a linear rule giving the amplitude of the first whipping cycle as a function of the amplitude of the rigid body response

5 Approximation of the variation on the linear rule as a function of the wave incidence angle

6 Identification of the short term sea states for which whipping is likely to occur

7 Correction of the low frequent (wave) stress range distributions for the whipping effect

8 Calculation of the Miner sum for all short term low frequent distributions

9 Determination of the high frequent whipping responses and associated Miner sums for every short term distribution for which whipping occurs

10 Calculation of total Miner sum taking into account low frequency contributions corrected for whipping and high frequency contributions

Following the analysis it can be concluded that the Miner sum associated to the high frequent part has a relatively small contribution for the following reasons: • Whipping occurs only in a limited number of sea

states (head seas, wave height above threshold value) • The reduction of the stress amplitudes due to

damping puts the majority of the cycles under the changing point of the slope of the S-N curve used (due to the random character of the phenomenon a 2-slope S-N curve is used for calculating the Miner sum).

3. SPRINGING Springing can be described as enforced wave induced hull girder vibrations. The calculation of the natural frequency of the two node hull girder bending mode for vessels with a length up to 350 m shows values above the frequency of the shortest observed waves. For instance, North Atlantic wave tables give a lower period Tz=3.5 s (0.28 Hz), while the natural frequency including added mass of a 300,000 dwt tanker has been calculated at 0.5 Hz (T=2.0 s). Springing was identified in 1972 during a full scale study on board a 340 m tanker [9], see figure 8. The response of the first natural mode of hull girder vibration, in spite of the high frequency, can be explained by the fact that for a given wave period the energy is distributed over a broad bandwidth. Using a Pierson-Moskowitz spectrum, the energy associated to a wave

period of 3.5 s is distributed over a bandwidth of 0.12 to 0.65 Hz, while for a wave period of 8.5 s this is 0.05 to 1.7 Hz. In addition, for head seas the encounter frequency is increased by the ship speed as follows:

Vg

2H

Heω

ωω += (4)

Figure 8: Response spectrum deck longitudinal stresses on a tanker in head seas for rigid mode and including springing [9] For the referenced tanker, sailing at a speed of 15 kn (7.7 m/s), the energy for a wave period of 3.5 s will be distributed over a bandwidth of 0.19 to 2.73 Hz, while for a wave period of 8.5 s this bandwidth is 0.06 to 16 Hz. These data clearly show that it the natural mode at 0.5 Hz is effectively excited. On vessels ranging from 300 to 350 m in length, if springing is at all visible from the spectral analysis, the level will be very weak and without effect on the structural resistance. When the length of the vessel increases or when the deck contains large openings the structural rigidity and therefore the first natural frequency mode decrease. When the ship speed increases, the encounter frequency increases as well. In both cases the frequency band associated with springing moves towards the region where the spectral density of wave energy is higher, thus amplifying the springing response (the springing associated peak in figure 8 moves to the left). This effect was noticed when performing design analysis for tankers of 550,000 dwt (414 m in length) and later confirmed during a four year full scale measurement campaign [10, 11]. When considering the characteristics of a typical ultra large container ship, with a length of over 360 m, speed of about 25 kn and large open deck structure, it becomes clear that springing is a phenomenon to be considered during the design of the ship structure. 3.1 SHIP STRUCTURAL RESPONSE A typical time series of measured longitudinal stress in the deck is presented in figure 9, which shows a high frequent springing signal of nearly constant amplitude superimposed on the low frequent (wave) component.

Figure 9: Measurement of deck longitudinal stress with visible springing effect Studies and measurements performed on 550,000 dwt tankers show that springing is sensitive for sea states with short wave periods. For these periods the maximum wave height is generally low, see table 3. Table 3: Maximum significant wave heights for North Atlantic wave environment according to IACS

Tz (s) 3.5 4.5 5.5 6.5 7.5 8.5 Hs (m) 1.5 4.5 9.5 13.5 14.5 14.5

Due to the weak damping, ξ=1.5% obtained from full scale measurements [2, 11], the available energy for the whipping response is limited and the amplitude remains small compared to the wave frequent response. Therefore, the influence of springing on the extreme hull girder loads, corresponding to severe sea states (higher natural period and very high significant wave height), is not significant. On the other hand, the high frequency and character of the enforced vibration (a quasi permanent phenomenon in sea states with relatively small waves, which are the most frequent during the life of the vessel) yield a non negligible springing induced contribution to the accumulated fatigue damage. This is confirmed by experience feedback of the 550,000 dwt tankers [11]. 3.2 CALCULATION METHODS Taking into consideration that the springing induced deformations are much smaller than the rigid body motions of the hull girder, it can be assumed that the problem can be treated in a linear sense and that the total response can be obtained by summation of the separately calculated rigid and elastic contributions [10]. Therefore it is possible to apply the linear tools developed for hydrodynamic and structural response calculations [13]. First of all, a classical calculation can be performed to determine the linear hydrodynamic coefficients, in particular the added mass and the transfer functions of the rigid body responses (figure 10). Secondly, the natural frequencies for the elastic hull and the associated transfer functions for springing are calculated (figure 11).

Figure 10: Calculation of rigid body transfer functions Figure 11: Calculation of transfer function for springing in torsional mode (elastic hull) In this way the transfer functions for the quasi static, springing and total response are obtained for the selected navigation conditions (figure 12).

= + = + Figure 12: Transfer function of peak stress in hot spot (welded detail) in a container ship (springing, wave and total) The calculations are performed according to the scheme shown in table 4. Table 4: Step-by-step procedure for springing analysis


2


3 Determination of navigation conditions for which springing could occur (wave incidence, ship speed, wave height)

4 Calculation of the linear elastic behaviour for wave incidences where springing occurs

3.3 FATIGUE Observation of the springing response for a given sea state (figure 9) shows that, on top of the wave frequent response, a time series of stress cycles with nearly constant amplitude at the first natural frequency of the hull girder is generated. The calculation of the short term fatigue damage accumulation requires the determination of the distribution of the high frequent stress cycles. The exact method for achieving this would be Rainflow counting. In order to do that a time history needs to be available, which is impractical for the spectral approach. By considering the same hypothesis as for the whipping and the using the linearity of Miner’s rule, it is possible to separate both the high frequent and low frequent contributions as depicted in figure 13 superimpose them to obtain the total result. As shown for whipping, the range of the wave frequent stress cycles needs to be corrected for the springing effect as well. As only the navigation conditions with a risk for the occurrence of springing need to be considered, it is important to take into account speed reduction in case the wave height increases, because this can cancel the springing effect altogether. Figure 13: Separation of springing effects for fatigue

calculation For each of the contributions corresponding to a signal with narrow banded spectrum, the fatigue accumulation can be computed according the methodology for wave frequent fatigue assessment [12]. The short term distribution of the stress range ∆Si can be described by a Rayleigh distribution, where the coefficient m0 is determined by the area under the response spectrum:

( ) ⎥⎦

⎤⎢⎣

⎡ ∆−=∆>∆

0

2i

i m8S

expSSprob (5)

For a given structural detail with known S-N curve it is possible to calculate the Miner sums separately and add them, taking into account the probability of occurrence of each short term navigation condition (wave height and period, vessel speed and wave incidence angle):

springingcorrected,wavetotal DDD += (6) An overview of the step-by-step calculation method is presented in table 5.

Table 5: Step-by-step procedure for estimating the springing induced fatigue damage

1


2 Calculation of the transfer functions and associated short term response spectra without springing

3 Determination of the frequency bands with high energy density within the wave spectra for the considered navigation conditions

4 Calculation of the natural frequencies of the hull girder, taking into account the added mass

5 Identification of the short term sea states for which springing is likely to occur

6 Calculation of the transfer functions for springing and associated short term response spectra for the considered sea states

7 Calculation of total Miner sum taking into account low frequency contributions corrected for springing and high frequency contributions

The method has been checked at short term level against the considered exact method, i.e. the Rainflow counting of the stress time history. To do so, a time history has been generated from the short term 2-peak response (see figure 12) using specific software. Then a Rainflow counting according to the AFNOR standard procedure has been performed and the Miner sum calculated. Two typical cases have been identified. For sea states with Tz above 5 s the low frequent wave stress is dominant over the high frequent springing, while for smaller Tz the situation is reversed, see figure 14. Figure 14: Stress time histories for Tz = 6.5 s (above) and Tz = 3.5 s (below) (First modal period T1 = 2.15 s) The comparison between the methods confirms that the proposed procedure provides acceptable short term Miner sum values. However, the correction factor for the

low frequent wave stress range has to be adjusted to the typical cases to prevent underestimations. A study performed for an ultra large container ship shows that, due to the large deck openings, the first natural mode of the hull girder is a torsional mode, which is followed by a number of vertical bending and torsional modes, see table 6. Table 6: Wet natural hull girder modes and frequencies ultra large container carrier Hull girder vibration mode f (Hz) 1-node torsional 0.37 2-node vertical bending 0.47 2-node torsional 0.50 3-node vertical bending 0.90 An investigation of the navigation conditions with a risk for springing occurrence showed that the torsional modes are to be considered for wave incidence angles of 120 and 90 degrees, while the flexural modes are to be considered for wave incidence angles of 180 and 120 degrees (180 degrees corresponding to head seas). The fatigue lifetime of a structural detail in the deck experiencing high dynamic loading has been calculated according applying North Atlantic scatter diagram, see figure 15. Figure 15: Fatigue analysis of hatch corner detail of an

ultra large container ship The springing response has been calculated for all wave heights and periods of the wave data table until a significant wave height of 5 m. For greater wave heights it is assumed that the vessel speed will be reduced and, consequently, that the shifted encounter frequency will yield only irrelevant springing response. The calculation of the short term Miner sum including springing shows that, compared to the situation excluding high frequent springing part, an increase in fatigue damage of up to a factor 3 can be reached for small period sea states. However, as small period sea states represent only a limited part of the long term total Miner sum, and taking into account that springing does not occur for transverse and following seas, the total long term increase of the Miner sum due to springing is estimated to be of the order of 4 to 10%.

A sensitivity study shows that if the maximum significant wave height is increased from 5 to 6 m, the springing related Miner sum increases by 20%. However, the effect on the total Miner sum is of second order. 4. HYDROSTAR The described methodology to assess the effects of whipping and springing during the design stage of ultra large container ships has been made practically applicable within the Bureau Veritas in-house hydrodynamic simulation suite HydroSTAR, which has been developed and validated for more than 20 years to support new technological challenges. Originally started as a linear 3D diffraction-radiation scheme for floating offshore units, today HydroSTAR is a multi disciplinary hydrodynamic package widely used in the marine and offshore industry. Typical issues like irregular frequencies, forward speed effect, roll damping, automatic mesh transfer, second order wave loads and multi body interactions are accounted for. In order to simulate whipping and springing hydro-elastic and non linear effects are to be accounted for. Hydro-elastic effects are handled using the modal approach, for which the equation of motion can be written as [13]:

[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) DIFξCkbBAm =+++−+− ωω i2 (7) where [m] is the structural mass, [b] the structural damping, [k] the structural stiffness, [A] the hydrodynamic added mass, [B] the hydrodynamic damping, [C] the hydrodynamic restoring, ξ the modal amplitudes and FDI the modal hydrodynamic excitation. The hydro-elastic coupling is visualised in figure 16. Figure 16: Hydrodynamic mesh following the structural deformation of the hull (first modal period) The non linear time domain simulations make use of the procedure proposed by Cummins (1962), for which the equation of motion can be written as follows [13]: [ ] [ ]( ) ( ) [ ] [ ]( ) ( )

( )[ ] ( ) ( ) ( ) ttdtt

ttt

0

QFξK

ξCkξAm

+=−+

+++

∫

∞

ττ &

&&

(8)

where [A∞] is the infinite frequency added mass matrix and [K(t)] the matrix of impulse response functions, which can be calculated from the frequency dependent damping coefficients [5, 13]:

( ) ( ) ωωωπ

dtcosB2tK0

ijij ∫∞

= (9)

This method enables the introduction of non linear components in the excitation forces F(t) and Q(t) [13]. As an example, for the calculation of the extreme hull girder bending moment including whipping effect a (weakly) non linear Froude-Krylov model is applied, see figure 17. Figure 17: Non linear time domain simulation using Froude-Krylov approach (loads on finite element model) The resulting overall computation scheme of the software called HydroSTAR++ is depicted in figure 18. Figure 18: Computation scheme of HydroSTAR++ for

hydro-structural simulation of container ships 4.1 MODEL TESTING In order to validate and calibrate the methodology for the hydro-elastic and time domain simulations, several model tests have been carried out and compared to the calculation results. In figure 19 depicts the torsional response of an elastic barge, showing good agreement between measurements and calculation results [13]. Figure 19: Elastic barge in torsion (impression of test left,

RAO of torsional angle right): comparison between experiments and calculation results

In figure 20 the initial deformation and the time history of the vertical displacement after releasing it from the original position are depicted. Again, there is good agreement between calculations and experiments. Figure 20: Elastic decay test (initial position left, time

history right): comparison between experiments and calculation results

4.2 FULL SCALE MEASUREMENTS Within the scope of the Joint Industry Project Lashing@Sea full scale measurements are carried out on board the BV class 9,400 TEU container ship CMA-CGM Rigoletto. Motion and acceleration sensors have been distributed over the hull and two cross sections have been equipped with strain sensors to record the dynamic response in terms of accelerations and internal hull girder loads. In order to study the behaviour of stacked containers and lashing equipment a dedicated measurement container has been installed above the aft deck. An example of a time series of measured accelerations in the container is shown in figure 21. Figure 21: Time series of full scale measurement in

transverse accelerations in container (normalised)

The results of the measurement campaign can be used to study the ‘real life’ behaviour of large container ships and to further validate and calibrate the developed numerical tools. 5. CONCLUSIONS An increase in the size and speed of container ships importantly changes the behaviour in a seaway. Phenomena already known for smaller size vessels can be amplified to reach levels high enough to have an impact on the design of the hull. This is particularly true for the cases of whipping and springing. The springing phenomenon was first studied during the construction of the 550,000 dwt tankers in 1975, for which time domain calculations have been performed. At that time the whipping phenomenon was also known, specifically in relation to ships with large deck openings, but computer simulation was not yet feasible. Recent developments in computer computation power and

efficient algorithms allow performing non linear hydro-structural calculations in the time domain. A methodology has been proposed to estimate the effects of whipping and springing on the extreme hull girder loads and fatigue lifetime of structural details. In order to be able to study the fatigue related effects during the design stage of a vessel, it is assumed that the low frequent and high frequent contributions can be dealt with separately. This simplification importantly reduces the required amount of non linear time domain simulations. The application of the methodology has been made possible by further development of the Bureau Veritas in-house hydrodynamic simulation suite HydroSTAR to solve hydro-elastic and non linear time domain problems. Extensive validation has been done by model testing, while the ongoing full scale measurement campaign will provide additional valuable feedback. Application of the methodology to ultra large container ships confirms that the stress levels are indeed increasing. As a consequence, a significant increase both hull girder loads and fatigue damage accumulation is found, which can no longer be ignored when analysing the ship structure. Whipping effects can cause an increase of about 20% in total vertical bending moment, for which the hull girder ultimate strength is to be checked. For current container ship designs of about 350 m with extremely large open deck structure, whipping can cause an increase in short term fatigue damage accumulation by a factor of up to 100% for some head sea navigation conditions. The increasing effect on the long term whipping induced fatigue damage accumulation is estimated to be in the range of 3 to 5%. With regard to springing, as a consequence of the flexibility of the hull girder and high vessel speed, current designs of about 350 m in length show an increase in short term fatigue damage accumulation by a factor of up to 3 for small period sea states, which is superior to the referenced tankers of 414 m. The increasing effect on the long term springing induced fatigue damage accumulation is estimated to be in the range of 4 to 10%. It is expected that full scale measurements results will provide valuable insight into the real dynamic behaviour of large container ships, as well as the accuracy of the calculations. In addition, further development of the methodology and hydro-structural computation schemes are ongoing and are expected to further enhance prediction capabilities. When considering future designs for even larger container ships of 400 m in length and beyond, it is

certain that with similar hull structural design the increase of fatigue damage accumulation due to whipping and springing will become even more important. By realizing that springing is a forced vibration phenomenon with little damping and that the whipping response is of non linear character, the dynamic phenomena and associated consequences will have to be analysed with greater attention. 6. ACKNOWLEDGEMENTS The models and results presented in this paper require strong interaction of many technical competencies. Therefore, the authors would like to thank all the people involved in the research and application of the developed methodologies, in particular Š. Malenica, F. Mauduit, N. Germain, F. Bigot, F.X. Sireta, S. Maherault, E. Stumpf, V. Bouitillier, J. Henry and G. Parmentier. 7. REFERENCES 1. Huther M, Ket N, ‘Water impact risk estimation

during ship design’, Ship Behaviour at Sea, International Symposium on Ship Hydrodynamics and Energy Saving, ISSHES, Madrid, September 1983

2. Osouf J, ‘Etude expérimentale du comportement dynamique dur houle du navire câblier Marcel Bayard’, Revue NTM, 1973 (in French)

3. Drummen I, Moan T, Storhaug G, Moe E, ‘Experimental and full scale investigation of the importance of fatigue damage due to wave-induced vibration stress in a container vessel’, Design & Operation of Container Ships, RINA, London, November 2006

4. Malenica Š, Molin B, Remy F, Senjanovic I, ‘Hydroelastic response of a barge to impulsive wave loads’, 3rd International Conference on Hydroelasticity, Oxford, 2003

5. Cummins WE, ‘The impulsive response function and ship motions’, Schiffstechnik, 1962

6. Ogilvie TF, ‘Recent progress toward the understanding and prediction of ship motions’, 9th International Conference on Numerical Ship Hydrodynamics, Ann Arbor (USA), 2007

7. Tuitman J, Malenica Š, ‘Some aspects of whipping response of container ships’, 23rd IWWWFV, Jegu (Korea), 2008

8. Bureau Veritas, ‘Rules for the Classification of Steel Ships’, November 2007

9. Planeix JM, ‘Wave loads, A correlation between calculations and measurements’, Revue International Shipbuilding Progress, August 1972

10. d’Hautefeuille B, Huther M, Baudin M, Osouf J, Calcul de springing par équations intégrales’, Revue NTM, 1977

11. Huther M, Osouf J, ‘SEFACO, Four years of experience in ship hull girder stress monitoring’, MARINTEC, Shanghai, October 1983

12. Huther M, Beghin D, Mahérault S, ‘A fatigue strength guidance note for welded ship structure assessments’, IIW/IIS doc XIII-111742-98/XV-992-98, 1998

13. Malenica Š, ‘Hydro structure interaction in seakeeping, International Workshop on Coupled methods in numerical dynamics IUC, Dubrovnik, September 2007

8. AUTHORS’ BIOGRAPHIES Gijsbert de Jong holds the current position of product manager at Bureau Veritas. He is responsible for the international business development in the field of container ships. Gijsbert joined Bureau Veritas in 2001 after obtaining an MSc in Naval Architecture & Marine Engineering from Delft University of Technology. Before moving to the sales and marketing management team in Paris, he has worked as hull surveyor and department manager in the plan approval office in Rotterdam. Michel Huther is a graduate Mechanical Engineer (Ecole Centrale de Lyon, 1965) and Naval Architect & Marine Engineer (Ingénieur Civil du Génie Maritime, 1967). Michel joined Bureau Veritas in 1969 and has worked as research engineer and department head for the ship research and rule development department, with many contributions to European R&D projects. In 2000 he was promoted deputy to the director of the marine technical management. After his retirement in 2003 Michel is holding the position of technical advisor to the Bureau Veritas marine technical management. He is a member of SNAME, ATMA & SF2M and has published over 200 scientific and technical papers on ship structural behaviour and safety.

STRUCTURE

Managing structural fatigue onboard ships requires either fittedapproaches for existing fleet and new tools to prevent the emergence ofnew fatigue sources such as whipping or springing. The papers in thissection focus on risk based maintenance versus crack propagation andprediction of fatigue loads resulting from hydrodynamic structuralinteraction in large containerships.



1

SIMULATION OF THE BEHAVIOUR OF FATIGUE CRACKS: A TO OL FOR INSPECTION DECISION MAKING ON A SHIP’S DECK BEAM V. Boutillier, M. Serror, G. Parmentier, Bureau Veritas, 17 bis place des Reflets, La Défense 2, 92400 COURBEVOIE

ABSTRACT To assess the condition of ships and FPSOs, it is necessary to fit the inspection process to the safety targets. By using the knowledge gained from the inspection data, failure of the ship’s structural components may be avoided. Crack propagation is an important issue to consider when devising an appropriate inspection plan; this is particularly true for ships and FPSOs that operate in regions with high sea states. On some types of ships, it can be very difficult to perform inspections due to certain structural arrangements, for example wall fascias that hide the structural members, and the time required to perform this task leads to heavy costs. Thus, it is important to know the exact behaviour of how cracks propagate in order to determine, as far as possible, if the inspection process may be delayed. The original feature of the methodology is the use of Line Spring Method to calculate the stress intensity factors. Based on this approach, we have developed a probabilistic analysis using Monte Carlo simulation. The main benefit of this assessment technique is the added flexibility in the development of an inspection plan that best suits the ship or FPSO considered. This approach may help operators and engineers to make decisions for inspections, repairs and maintenance processes, in order to have the lowest cost whilst complying with the required safety targets. Finally, an example is provided on a ship’s deck beam, which shows us the effects of inspection parameters on the probability of failure and probability of detection.

1. INTRODUCTION

The aim of a fatigue analysis on ships or offshore structures is to evaluate the damage due to cracks propagation, leading sometimes to the failure of parts of the structure. Ship structures are submitted to cyclical forces, such as wave actions, as well as loading and unloading sequences. On some types of ships, it can be very difficult to perform inspections due to certain structural arrangements, (for example wall fascias that hide the structural members), and the time required to perform this task leads to heavy costs. Therefore, in order to help operators and engineers to make decision for inspections, maintenance and repairs, a probabilistic crack propagation approach based on a new crack propagation method has been developed. This probabilistic approach is based on SAPHIRS [1] which evaluates crack propagation and a Monte Carlo simulation for the probabilistic part. That methodology gives us probability of failure.

2. SAPHIRS 2.1 METHODOLOGY The aim of the methodology is to forecast as accurately as possible the fatigue crack initiation and the fatigue crack growth in ships or offshore structures components that have been submitted to fluctuated and repeated loads. These loads can be represented by a combination of unitary loads or modes if the response of the component is linear elastic. To take into account the discontinuity of the presence of a crack which induces non-linearity effects, the mathematic models generally use the contour integral evaluation related to the energy release rate. That action implies re-meshing after each propagation step. Re-meshing is very time consuming. The stress intensity factor is one of the most important parameter responsibilities of the crack propagation. It depends on the notch geometry and on the stresses on the crack lips. It is well known that the fatigue crack propagation varies exponentially with it.

2

Therefore, with the use of both Line-Spring and the stress intensity factors to determine the stress field, success is achieved accompanied with very easy implementation. This method allows taking into account the stiffness variation during crack propagation, impossible with analytical solutions or finite element methods without re-meshing. 2.2 POSITION OF THE CRACKS The finite element model must be carefully performed with shell elements including all the directions of loads that the structure encounters. This first and very important step establishes stress cartography. From these results with the use of the concept of hot spot, we are able to define the position of one or several cracks. The experience showed that the position of the cracks is more commensurate with the structural geometry, rather than the forces directions. However, the software leaves open the ability for a crack possibly growing due to a force’s direction, and somewhere else, growing from another force’s direction. But most importantly is the software which has the ability to consider the interactions between several cracks (Figure n°1).

Figure n°1: Two cracks

Our process needs to know a priori the crack path. So it has to be determined [2], and the simplest method is to use the principal stresses directions (Figure n°2). The main assumption consists of setting the crack path in a direction perpendicular to the maximum principal stresses whose directions are the eigenvectors of the stress tensor.

So the first step is to determine the stress field of the component to be able to draw the path of the hot spots.

Figure n°2: Principal stress directions

Often, the hot spots appear at an intersection of two sheets, and the crack must be defined at the weld toe position, even if no weld has been modeled. Wherever the hot spots take place, we build one or several part-through cracks, by one or several lines of coupled nodes.

2.3 THE LINE SPRING METHODOLOGY The Line Spring model was introduced in 1972 by Rice and Levy [3] to estimate stress intensity factors due to tension and bending in large plates containing part-through surface cracks. He essentially reduced the three-dimensional problem to a two-dimensional one, in mode I. This model has been extended to the modes II and III by Desvaux [4]. The idea was to analyze the part-through crack as a several single edged specimen, the cracked structure part (Figure n°3).

Figure n°3: A several single edge specimen

The crack is defined as a line of couple of nodes, with same coordinates, and separated. The both nodes simulate the crack, each node located on each crack lip.

The Line-Spring model is based on the fact that there is a relationship at each point along the cut,

Two cracks

Principal stress directions

3

between local displacements and the loadings, the compliance coefficients. Then, from the point of view of the plate, the surface crack is represented by a through-crack with a continuous distribution of generalized springs connected across the line of discontinuity, the Line Spring (Figure n°4).

Figure n°4: Line-Spring

After the crack has been defined as upper, the keystone of the software can be set up. The compliance coefficients, the Sij

pq matrix, are defined by the additional relative displacements and rotations due to the crack’s presence. Thanks to a finite element calculation, the second one’s being the displacements of the crack lips, di

p are determined for each couple of nodes i, in the direction p, resulting in an unitary force Fj

q, exerted on the couple node j in the direction q, in order to build the compliance matrix. It is the same to evaluate the displacements of the crack lips on each couple of node i, di

p∞ due to external loads, Fext, which are applied on the fully-cracked component. These loads may be unitary and exerted on any point on the structure and according to any direction. The displacements will be then worked out by an easy linear combination.

Thus, for the desired crack shape, the resolution kernel of the software SAPHIRS, is to find loads F, and di

p to solve:

dip - di

∞ = - Sijpq . Fj

q (1)

This first equation lets us verify the loads along the virtual crack, when there are no cracks yet, i.e., di

p =0.

The stresses on the intact structure are again evaluated from the equation:

di∞ = Sij

pq . Fjq (2)

At the end of this step, all the behavior of the structure followed by the behavior of the crack is condensed in the Sij matrix.

2.4 CRACK INITIATION The propagation crack process always begins by the crack initiation. This step is fundamental for the next propagation step. The shape of the crack front is drawn by the stress field distribution. If the stress gradient is important, the initiation and then the propagation will occur in the hot spot and its neighborhood. If the stress gradient is small, the initiation will go off gradually, and the crack will extend first along the surface. It leads to a multi-initiation of the crack. All these phenomena are taken into account in the software. In this phase, the damage is cumulated cycle after cycle, either by a local approach or by an SN curve approach.

2.4 (a) Local approach

The module CALEND stems from Petitpas’s [5] works. It uses the local stresses determined by the precedent step. For designing welded components, it allows you to take into account stress concentration factors Kt to evaluate the stress tensor at the weld toe. Residual stresses can be included, too. As the local stresses are often greater then the yield stress, a plastic correction has to be done. Then a fatigue stress criterion is calculated on different planes of the stress tensor (using Dang Van criterion [6]) and damage is accumulated (using Miner’s rule and Basquin’s law) on extracted cycles (using Rainflow counting). Finally, damage is taken as the maximum damage obtained on all planes of the stress tensor, and the crack initiation occurs when damage at a node is given and overestimated critical value.

In each point where the damage is an upper critical damage, it is assessed as an initial flaw, generally the 1/10th of the sheet thickness. After that, the propagation may occur.

2.4 (b) SN curve approach

This treatment of the initiation phase is built on the initiation SN curves, which supply the probability to get an initial flaw, after Ni solicitations under the stresses, Sij, on the couple j. This probability is supposed following a Weibull

Lower crack tip

Line Spring Upper crack tip

ddddip

4

distribution, with two parameters a and b.

βα )(exp1

1 ij

ni

ij

KS

NP

−−= ∑=

=

(3)

The crack initiation occurs when the probability at a node is over a given critical value.

Those critical values may be different if the non- homogenous surface weld toe is taken into account

This step allows initiating the crack by laying an initial flaw with a given size, a0 (Figure n°5).While the crack growths on this node (Figure n°6), the other nodes will initiate at their turn. So, this phase allows the crack propagating through the thickness of the sheet, but also, in the direction parallel to the sheet. The crack propagation diagram may be summarized as follows:

Figure n°5: Multi-Initiation

Figure n°6: Propagation through thickness

2.5 CRACK PROPAGATION: PART THROUGH THICKNESS

The crack grows from each point where the initiation has occurred. The Tada coefficients Aij, depend only on the ratio l/h, (l: crack depth and h: plate thickness), and vanish when l=0.These coefficients set up relations between the forces acting upon the crack lips and the crack lips opening displacements.

dip = Aij

pq . Fjq (4)

Then, for any crack depth, it is easy to find the displacements di, and the forces Fj

q, by solving both (1) and (4). Now the Irwin’s (1967) relation in potential energy accompanying a variation of crack depth and the stress intensity factor are employed as a basis for calculating the stress intensity. The stress intensity factors, first in mode

I, K I from Tada (1973) [7] and then extended to the modes II and III, KII, KIII by Desvaux (1983) may be expressed as follows, in every cracked point, j:

)6

()(2

,,

h

gM

h

gNhjK

MIjNIjI += (5)

),(),()(

)),((2

)2/tan(/24),(

)),((2

)2/tan(2),(

TjKQjKjK

hlfh

hlhTTjK

hlfh

hlQQjK

IIIIII

II

II

+=

−=

=

π

π

(6)

τπτ ,)( IIIII ghjK = (7)

)1983(,

),,(

:

:

:

:

:

:

5

3

1

4

2

DesvauxbygivenxII

ghlfwith

FmomenttwistingantiplaneT

FshearforceantiplaneQ

Fsshearstrestransverse

FmomentbendingM

FtensionN

with

→

→

→

→

→

τ

Then, for every crack depth on each node belonging to the crack line, the three stress intensity factors are evaluated according to the loads acting on the structure. In the structures, we study the mode I because it is the most preponderant crack propagation. Then, the crack propagation rate, in the software SAPHIRS follows the Paris law:

,)(/ msI KKCdNdl ∆−∆= (8)

With ∆Ks: the threshold stress intensity factors, and

∆K I =KI,max- KI,min

The crack propagation through the plate thickness goes cycle after cycle until a failure criterion occurs. After every propagation step, an update of the defect size is performed, and the equations (3) and (4) are solved again.

The software proposes three failure criteria:

• Ductile criterion

• Brittle criterion

• Critical size

When one of these criteria is realized, the ligament

Plate thickness

Flaws on the surface

Plate thickness

5

breaks and the crack becomes a through thickness crack.

2.6 THROUGH CRACK BOX: THE CRACK BOX TECHNIQUE

It is important to emphasize that the stress intensity factors calculated with Tada coefficients are available for cracks propagation in the depth of a plate. When the ligament rupture occurs, the crack propagation extends in a longitudinal direction parallel to the plate (Figure n°7).

Figure n°7: Three crack configurations

The Crack Box idea, developed by Lebaillif (2005) [8], is set to use the technique of sub-modeling: the displacements of nodes located in the neighborhood of the cracks, determined in the same way of the crack lips displacements, are used to drive a 3D sub-model of the structure, including the crack tip which is meshed using fracture mechanics elements (Figure n°8).

Figure n°8: Crack Box Technique

Thus, the stress intensity factors are previously calculated at all the crack tip nodes of the sub-model, with unitary displacements applied at its border. Next, the three stress intensity factors are calculated using a linear combination with the displacements in each mode.

3. PROBABILISTIC APPROACH 3.1 METHODOLOGY A sensitivity study has helped us to determine the random parameters (such as material characteristics, initial crack length, etc.) which govern crack propagation. These parameters are described here after respectively with their density function [9].

Random parameter

Density function

Yield stress

minimum Weibull law - 355=thresholdε MPa

- 411=u - 1.2=k

Ultimate strength

minimum Weibull law - 490=thresholdε MPa

- 558=u - 1.2=k

Paris law parameter: K threshold

normal law

- Mean = 10 MPa m

-Standard deviation=2.5 MPam

Toughness minimum Weibull law

- 40=thresholdε MPa m

- 106=u - 3.3=k

We have to notice that we didn’t take loads as random parameter. For each simulation, we observed the detail behaviour, considering the ship used 80% of 30 years in navigation. During this span time, we inspect the ship considering one inspection plan. Each plan is described by its type and the time interval between each inspection. SAPHIRS evaluates the crack propagation and gives the crack length at each step. At the end of each simulated inspection, two possibilities exist. The first one, no crack is detected, so the simulation goes on. The other possibility is, a crack is detected. Therefore, we repaired the structure (without redesign). Thereby, a new detail is done, so we make a new Monte Carlo simulation in order to give new material

Plate thickness

A through thickness crack

u j

6

characteristics’ for the considered detail. If a failure appends during the simulation, we do not repair, we stop the simulation. Inspection type is defined by a probability of detection (pod). This pod helps us to know either the surveyor detect the crack or not during the inspection. In fact, thanks to this pod, we were able to determine the probability the surveyor had to detect this crack length. Next, we choose a random value between 0 and 1, if this value is lower than the probability to detect the crack, that means we detect it, however if the random value is greater than the probability to detect the flaw, the crack propagation goes on until the next inspection or a failure.

We have decided to look at two different inspection types. Therefore, we defined two pod represented by two lognormal laws whose parameters are defined below:

• Visual inspection: - mean = 20 - standard deviation = 10

• NDT (Non Destructive Testing) inspection:

- mean = 2.87 - standard deviation = 1.03

The total number of simulation depends on the wanted accuracy. After each inspection, probability of failure and confidence interval are calculated. Probability of failure, p, is evaluated by:

With: n: the total number of simulations k: the total number of failure Confidence interval is calculated by:

( )212/1 ,ννα−F : is a Fisher-Snedecor law α−1 : is a confidence interval

This confidence interval is used to limit the parameter estimation. In our case, this interval corresponds to 95%. The following figure shows us the program mechanism.

Figure n°9: program mechanism 4. A SHIP’S DECK BEAM SIMULATION 4.1 HYPOTHESIS The loading histories are all the sea states significant heights encountered by the ship during its life. Each sea cycles is supposed to last 6 hours, i.e. 1 800 cycles. The diagram below shows the significant height distribution state, HS1.

New random simulation

Monte Carlo simulation

Planning inspection Detail description

Crack propagation SAPHIRS

Monte Carlo simulation

Visual Crack ⇒ Repair required

No Visual Crack ⇒ The crack keeps going

Yard inspection

Inspection Critical length crack reached

⇒ Failure

n

kp =

nksip ==1sup

( ) ( ) ( )( )( ) ( ))(2),1(21

2,121

5.97

5.97sup knkFkkn

knkFkp

−+++−−−+=

00inf == ksip

( ) ( ))(2),1(21 5.97inf kknFknk

kp

+−+−+=

7

Sea states HS1

0

2

4

6

8

10

12

1 32 63 94 125 156 187 218 249 280 311 342 373 404 435 466 497

Hs

num

erou

s of

the

sea

stat

es

Initiation after the step 61

73200 cycles

Figure n°10. Significant heights of loading histories

4.2 EFFICIENCY OF INSPECTION PLAN ON FAILURE PROBABILITIES Time interval influence On these simulations, we show the time interval influence on the failure probabilities. The first one is visual inspection every 6 year, the second one is annual visual inspection and finally the last one is visual inspection every 6 month. Table 1: failure probabilities for visual inspection plan Failure Probabilities

Lower boundary

Mean estimation

Upper boundary

Visual Inspection Every 6 year

3.15*10-1 3.93*10-1 4.76*10-1

Visual Annual Inspection

4.71*10-3 1.17*10-2 2.39*10-2

Visual Inspection Every 6 month

1.41*10-2 2.5*10-2 4.09*10-2

The following diagrams show the failure probabilities evolution after each simulation of 80% of 30 years.

1.00E-03

1.00E-02

1.00E-01

1.00E+003 24 45 66 87 108 129 150

Figure n°11. failure probabilities - visual inspection every 6

year

1.00E-03

1.00E-02

1.00E-01

1.00E+003 24 45 66 87 108 129 150 171 192 213 234 255 276 297 318 339 360 381 402 423 444 465 486 507 528 549 570 591

Figure n°12. failure probabilities - visual annual inspection

1.00E-03

1.00E-02

1.00E-01

1.00E+003 54 105 156 207 258 309 360 411 462 513 564

Figure n°13. failure probabilities - visual inspections every 6

month

The upper diagrams show that we run only 150 simulations for visual inspection every 6 year against 600 simulations for visual annual inspections and visual inspection every 6 month. Nevertheless, we may notice that the confidence interval is rather large for inspection every 6 month or every year than for inspection every 6 year.

8

The reason is that during annual inspection, the number of failure decreases and therefore the confidence interval is more difficult to evaluate. It is the reason why we carry out more simulations when inspections are close together than for every 6 year inspections. Inspection type influence On this calculation, we show the influence of inspection type. We changed visual inspections by NDT inspections. As we may predict, NDT inspections give better results than visual inspections. Table 2: failure probabilities for NDT inspection plan Failure Probabilities

Lower boundary

Mean estimation

Upper boundary

NDT inspection Every 6 year

2.34*10-1 3.07*10-1 3.87*10-1

NDT Annual inspection

6.89*10-3 1.50*10-2 2.83*10-2

NDT inspection Every 6 month

1.82*10-3 6.67*10-3 1.70*10-2

Here again, it can be observed, as for visual method, that if we carry out every 6 month inspections, it didn’t provided better results than annual inspections. Failure results depend either on the probability of the structure to resist to fatigue and crack propagation and on the performance of inspection process. The selected detail was known as ill designed for the applied loads. Therefore, the question was how a reinforced inspection planning would improve or not, the structural reliability, and show the limit of inspection versus inspection methods and inspection periods. These failure probabilities show us that the time interval has much influence than the type. In fact, reducing the time interval will supply better results than changing the inspection type.

4.3 EFFICIENCY OF INSPECTION PLAN FOR DETECTING CRACKS BEFORE FAILURE We evaluated two different probabilities of detection. The first one is the probability to detect a flaw leading to a repair (table 3 & 4). The second one is the probability to detect a crack before a failure (table 5 & 6). Table 3: Probabilities to detect a flaw leading to a repair for visual inspection plan Probability to detect a flaw leading to a repair

Lower boundary

Mean estimation

Upper boundary

Visual inspection Every 6 years

1.98*10-1 2.31*10-1 2.66*10-1

Visual inspection Annual

8.22*10-2 8.65*10-2 9.10*10-2

Visual inspection Every 6 month

4.86*10-2 5.11*10-2 5.36*10-2

Table 4: Probabilities to detect a flaw leading to a repair for NDT inspection plan Probability to detect a flaw leading to a repair

Lower boundary

Mean estimation

Upper boundary

NDT inspection Every 6 years

2.51*10-1 2.48*10-1 3.19*10-1

NDT inspection Annual

1.08*10-1 1.13*10-1 1.18*10-1


5.13*10-2 5.37*10-2 5.63*10-2

Table 3 and 4 show no significant discrepancies between visual inspection and inspection carried out with the help of NDT methods.

9

This is due to the fact that the probability to detect a flaw depends mainly on the probability that a flaw exists. Table 5: Probabilities to detect a crack before a failure for visual inspection plan Probability to detect a crack before a failure

Lower boundary

Mean estimation

Upper boundary

Visual inspection Every 6 years

5.3*10-1 6.13*10-1 6.92*10-1

Visual inspection Annual

6.72*10-1 7.1*10-1 7.46*10-1

Visual inspection Every 6 month

7.53*10-1 7.88*10-1 8.20*10-1

Table 6: Probabilities to detect a crack before a failure for NDT inspection plan Probability to detect a crack before a failure

Lower boundary

Mean estimation

Upper boundary

NDT inspection Every 6 years

5.44*10-1 6.27*10-1 7.04*10-1

NDT inspection Annual

7.16*10-1 7.53*10-1 7.87*10-1


6.87*10-1 7.25*10-1 7.60*10-1

Table 5 and 6 show us that increasing the number of inspection (for example performing inspection every 6 month instead of every 6 year) increases the probability of crack detection before failure. In the same way, help of NDT methods increases the probability of crack detection before failure. Increasing the number of simulation would probably shows that inspection every 6 month would be better that every year. Nevertheless, the lower boundary of simulation shows that the efficiency to this improvement is

limited. This is mainly due to the probability to miss a crack of a large size. In fact, failure happens because we repair identically after we detect it. Therefore, the crack will propagate as the same as before. Furthermore, the surveyor could miss a crack during inspection (due to the chosen pod), and this is that crack which is going to fail. 4.4 CRITICAL LENGTH INFLUENCE ON STRUCTURAL RELIABILITY For previous simulations the critical length was equal to 114 mm, but for these simulations, it was taken equal to 54 mm. Considering a visual inspection every 6 year and this new critical length, we may compare results with those obtain for the former one. Table 7: probabilities for visual inspection plan function of the critical length Visual inspection every 6 year – ac = 54mm

Lower boundary

Mean estimation

Upper boundary

Probability of failure

5.71*10-1 6.53*10-1 7.29*10-1

Probability to detect a flaw leading to a repair

1.66*10-1 2.02*10-1 2.41*10-1

Probability to detect a crack before a failure

3.53*10-1 4.33*10-1 5.17 *10-1

Regarding the probability of failure, if we consider that the failure is happening with a smaller critical length (54 mm instead of 114mm), the probability of failure will increase. However, concerning the both probabilities of detection, we can see that the critical length has no influence.

10

Table 8: probabilities for visual inspection plan function of the critical length Annual visual inspection – ac = 54mm

Lower boundary

Mean estimation

Upper boundary

Probability of failure

1.48*10-2 4.00*10-2 8.50*10-2

Probability to detect a flaw leading to a repair

9.16*10-2 1.01*10-1 1.11*10-1

Probability to detect a crack before a failure

7.86*10-1 8.53*10-1 9.06*10-1

The same conclusions may be done for annual inspection with (ac = 54mm) (table 8). We may explain this because the crack grows up quickly when it is possible to see it. In other terms, the crack grows slowly at the beginning and will grow very quickly after. In fact, probabilities are almost the same, either with a critical length of 54mm or 114mm. It means that we consume a lot of cycles to arrive at 54 mm. 5. CONCLUSION For the considered ship, wall fascias lead to high inspection costs. Relative improvement of inspection every 6 month is not sufficient to justify additional cost and time lost of operating availability resulting from this additional inspection. Monte Carlo approach is very effective to simulate successive inspection and repair due to a poor detail design. To justify the reliability and inspection planning of a well design detail, Monte Carlo approach will lead to a very large number of simulations. Nevertheless, alternative approach based on FORM-SORM methods will better suit for design stage, due to the fact that the design is made in order to avoid failure.

An overall methodology has been introduced to forecast crack initiation and propagation without re-meshing. This method rounds up a lot of strong points: realistic stresses, local approach initiation, easily calculable stress intensity factors, several cracks with their interactions. It has been applied on a ship deck beam, and we have seen that lots of data are accessible to monitor the crack propagation. The fundamental idea is that the perfect knowledge of the crack lips displacements allows for determining the stress intensity factors which govern the crack propagation. Taking into account realistically the propagation phenomena seems the right way to lead to a life span close to reality.

These results performed with this probabilistic crack propagation approach have shown that the code is efficient and easy to carry out.

It proved that the tool may helps operators to make decisions for inspection, repair and the maintenance process. In fact, we can determine, function of how cracks propagate if the inspection process may be delayed or not. REFERENCES

1. Serror M., Lebaillif D., Huther I., 2007, ‘Simulation of behavior of fatigue cracks: A complete industrial process on a ship deck beam’, PRADS 2007

2. Lebaillif D., Ma S., Huther M., Lieurade H.P, Petitpas E., Recho N., 2003, ‘Fatigue Crack Propagation and Path Assessment in Industrial Structures’, International Conference on Fatigue Crack Paths / FCP 200318-20 Sept. 2003, Parma (Italy)

3. Rice J.R. and Levy N, 1972 ’The Part-Through Surface Crack in an Elastic Plate’, Journal of Applied Mechanics, March 1972, 185-184 4. Desvaux G.J., 1985 ‘The Line Spring Model for Surface Flaw, an extension to mode II and mode III’, Master of Science in Mechanical Engineering at the MIT, June 1985

5. Petitpas E., Lebrun B., de Meerleer S., Fournier P., Charrier A., Pollet F., 2000, Use of the local

11

approach for the calculation of fatigue strength of welds. IIW, Florence, 9-14/07/2000

6. Recho N., 2008, ‘Calculation tools for fatigue’ in french ‘Outils de calcul pour la fatigue’, EPF-etude bibliographique, Feb 2008

7. Tada H., Paris P.C. & Irwin G.R., ‘The stress analysis of cracks handbook- DEL Research Corporation’

8. Lebaillif D., Huther I., Serror M., Recho N., 2005, ’Fatigue Crack initiation and propagation: a complete industrial process compared with experiments on industrial welded structure’, Fatigue Design. Cetim, Senlis, Nov. 2005

9. Parmentier G., 2007, Internal Bureau Veritas report

ATMA 2008

QUELQUES ASPECTS HYDRODYNAMIQUE/STRUCTURE EN CONCEPTION DES PORTE-CONTENEURS GEANTS

Šime MALENICA, Florence MAUDUIT, Michel HUTHER BUREAU VERITAS – Division Marine – Paris (France)

SOMMAIRE La nouvelle tendance à accroître la taille des porte-conteneurs (jusqu'à 400m de longueur) fait apparaître en conception et en procédures de vérification des thèmes nouveaux en calculs hydrodynamiques et de structures concernant les vérifications en résistance ultime et en fatigue. Certains thèmes concernent la réponse hydroélastique qui devient importante en raison des périodes propres structurelles relativement basses des ces navires et des fortes contraintes opérationnelles (vitesse maximale de l'ordre de 27 nœuds). Effectivement, la combinaison de la diminution des fréquences propres et l'augmentation des fréquences d'excitation peut conduire à l'excitation forcée des vibrations de la poutre navire par la houle appelé "springing", vibrations qui peuvent affecter de manière significative la durée de vie du navire. En sus de ce phénomène, la vibration transitoire engendrée par le "slamming" ("whipping") peut affecter aussi bien la résistance ultime que la fatigue. Dans ces conditions, les règles classiques des sociétés de classification atteignent leurs limites pour ces navires et ainsi il est nécessaire de faire appel à une approche dite calculs directs. Cette communication présente et discute la procédure complète du Bureau Veritas basée sur des calculs directs

SUMMARY SOME ASPECTS OF HYDRO STRUCTURAL ISSUES

IN THE DESIGN OF ULTRA LARGE CONTAINER SHIPS Recent trends in increasing the size of the container ships (up to 400m in length), raise the new hydro structural issues in their design and verification process, both from ultimate strength and fatigue points of view. Some of these issues are related to the hydroelastic structural responses which become important due to the relatively low structural natural frequencies of these ships, and due to the strong operational requirements (maximum speed around 27 knots). Indeed, the combination of the reduced natural frequencies and increased excitation frequency can lead to the forced wave induced hull girder ship vibrations called springing, which might significantly affect the ship fatigue life. In addition to this, the slamming induced transient vibration (whipping) can affect both the ultimate strength and fatigue. In any case, the classical classification society’s rules are reaching their limits for these ships and the so called direct calculation approach is needed. In this paper the over-all Bureau Veritas procedure based on direct calculations is presented and discussed.

1. INTRODUCTION Plus grand semble aujourd'hui synonyme de plus rentable, mais en fait le gigantisme a toujours fasciné l'homme. L'histoire nous apporte de nombreux exemples depuis la plus haute antiquité et la construction navale de notre époque n'échappe pas à ce phénomène.

Les 40 dernières années ont été fertiles en projets et constructions de navires géants. Dans les années 60 les pétroliers ont doublés de taille tous les 2 ans jusqu'à atteindre en 1975 550.000 tdw pour une longueur de 414m [1], puis ce furent les navires de croisières qui passèrent de 2000 passagers dans les années 60 à 5000 passagers pour le dernier navire en construction [2].

Aujourd'hui c'est au tour des porte-conteneurs qui de 6.000 TEU dans les années 60 ont atteint 11.000 et 11.400 TEU en 2007 [3] avec aujourd'hui des projets de 14.000 TEU et une longueur de l'ordre de 400m.

Si l'augmentation de taille peut être obtenue par extrapolation des dimensions de navires existants et les sollicitations de houle évaluées par analyse dimensionnelle, des phénomènes dynamiques de second ordre pour des tailles moyennes peuvent devenir importants pour de grandes dimensions. C'est en particulier le cas pour les réponses structurelles vibratoires et la fatigue.

Il suffit de regarder le passé pour s'en convaincre. Deux exemples peuvent illustrer l'apparition au premier plan de phénomènes antérieurement secondaires, l'avion Comet (1954), premier grand avion commercial à réaction, qui a fait apparaître l'importance de la fatigue en aéronautique et le pétrolier Magdala (1968), premier 250.000 tdw, qui a mis en lumière les risques de flambement des composants primaires[4]. Le retour d'expérience conduit à considérer deux phénomènes dynamiques affectant la poutre navire avec une attention toute particulière pour les porte-conteneurs géants, le

whipping1 (mise en vibration transitoire due aux chocs hydrodynamiques à l'avant – slamming et slapping), le springing (excitation entretenue du premier mode de vibration libre).

En effet, la taille croissante des navires et leur pont ouvert diminuent les fréquences propres de la poutre navire alors que la vitesse augmente les fréquences de rencontre avec les houles les amenant dans la même gamme avec des effets dynamiques amplifiés.

Il apparaît alors que les règles classiques des sociétés de classification atteignent leurs limites rendant nécessaire des approches faisant appel à des calculs directs de comportement dynamique sur houle.

Nous allons analyser ces deux phénomènes, leur impact sur les structures des navires, les moyens disponibles pour les aborder et leur incidence sur la conception des navires.

2. WHIPPING Le whipping est la réponse transitoire du premier mode de la poutre navire aux chocs hydrodynamiques sur les fonds à l'avant du navire après déjaugeage (slamming) ou sur un fort dévers d'étrave (slapping) (figure 1).

Figure 1: Retour violent dans l'eau de l'avant

d'un navire après déjaugeage

Le comportement du premier mode de la poutre navire peut être simulé par un système à un degré de liberté amorti de même fréquence. Les efforts sont de courte durée mais très

1 Les termes tossage et fouettement sont utilisés en français pour slamming et whipping mais slapping et springing n'ayant pas d'équivalent français, nous utiliserons la terminologie anglaise dans le texte

élevés, similaires à une impulsion [5] et induisent ainsi des vibrations transitoires amorties.

2.1. Incidence sur la tenue de la structure

Les slamming et slapping sont connus pour se produire par mer de l'avant, lorsque les mouvements verticaux sont les plus forts.

La déformation de vibration de la poutre navire engendrée par le choc se superpose à celle engendrée par la houle (figure 2).

Figure 2: Navire Marcel Bayard, mesures à la

mer des contraintes au pont, houle plus whipping

Les risques de dommage dus au whipping sur des navires à pont ouvert ont été identifiés depuis de nombreuses années, le premier effet étant un moment vertical supérieur à celui d'échantillonnage et engendrant une déformation permanente de la poutre navire, le second étant la génération de cycles de contraintes pouvant conduire à des fissurations de fatigue prématurées[6 , 7].

Si le dépassement du moment maximum de flexion admissible entraînant la déformation de la poutre navire est aisé à comprendre, l'apparition de fissure de fatigue est plus difficile à admettre.

Cependant, le navire Marcel Bayard illustre bien ce risque. Les mesures à la mer rapportées en [6] ont été décidées suite à l'apparition de fissures au bout d'un temps anormalement court, 3 ans. Les mesures et l'étude ont montré que malgré sa taille moyenne, 110m longueur, les avaries pouvaient s'expliquer par le whipping fréquent provenant des conditions d'opération particulières à ce type de navire et les grandes écoutilles entraînant de fortes concentrations de contraintes au pont.

Au niveau du projet d'un navire il est donc important de pouvoir évaluer l'incidence du whipping sur les contraintes au pont, ce qui requiert le calcul du comportement du navire

sur houle puis celui de la structure aux efforts impulsifs engendrés par les slamming et slapping.

2.2. Moyens de calcul et méthode

Depuis quelques décennies le calcul direct sur houle d'un navire est devenu courant pour les analyses en effort extrême et de cumul de fatigue.

Les méthodes utilisées par les bureaux d'études reposent sur l'approche spectrale, rapide à mettre en œuvre, et ayant après calibration une précision suffisante pour les vérifications classiques.

Par contre le whipping étant un phénomène impulsif non linéaire, l'approche spectrale devient insuffisante. Il a donc été développé des méthodes de calculs à pas de temps permettant de résoudre le problème de couplage entre la diffraction/radiation 3D hydrodynamique et la déformation dynamique du navire modélisé par une poutre suivant Timoshenko.

Dans cette approche modale, les mouvements et déformations du navire sont représentés par une série de 6 modes de corps rigides plus 5 à 10 modes structurels sans masse d'eau ajoutée [8]. Mais il est à noter que les coefficients hydrodynamiques linéaires dans les équations à pas de temps sont obtenus à partir de calculs dans le domaine fréquentiel classique [9 , 10].

Les méthodes de détermination des efforts de slamming/slapping, excitations de la réponse dynamique, correspondent aux deux méthodes disponibles aujourd'hui "Generalized Wagner Model" et "Modified Logvinovich Model", toutes deux basées sur des approches 2D.

Les calculs de réponse de whipping sont ainsi possibles par la mise en œuvre de la chaîne de logiciels de calcul de comportement du navire rigide dans le domaine fréquentiel et un calcul à pas de temps non linéaire de la poutre navire élastique. L'ensemble a été vérifié avec succès sur des navires de 260 et 360 m de longueur [11] (figure 3 et 4).

Figure 3:Exemple de moment de flexion non linéaire avec whipping sur un état de mer fixé

Figure 4: Zoom à l'instant d'un choc de

slamming (réponses: élastique, rigide non linéaire, rigide linéaire)

La méthode de calcul se déroule alors suivant les étapes ci-dessous:

1. sélection des états de mer et de leur fréquence d'existence suivant les zones d'opération du navire (standard: Atlantique Nord)

2. calcul de comportement linéaire avec détermination des conditions extrêmes possibles suivant l'incidence de la houle (vitesse du navire, hauteur de houle)

3. détermination des conditions de navigation avec possibilité de slamming (incidence de houle, vitesse, hauteur de houle)

4. calcul de comportement non linéaire pour les conditions de navigation avec slamming

2.3. Effets sur efforts extrêmes

L'observation des réponses élastiques montrent que le whipping augmente les valeurs extrêmes du moment de flexion vertical de la poutre navire. Il est donc nécessaire de prendre en compte cet accroissement pour les vérifications de la structure à l'état ultime.

Les calculs effectués [11] et les mesures à la mer [6] montrent que le whipping apparaît lorsque le moment de houle est en contre-arc.

A partir de la condition de navigation la plus sévère, force de slamming extrême, il est déterminé l'augmentation du moment réglementaire maximal en contre-arc.

Les mesures à la mer montrent que l'amortissement de la vibration transitoire est faible, de l'ordre de ζ=1,5%, aussi la vibration de whipping est encore sensible lorsque le moment de houle passe en arc (figure 4). La valeur du moment réglementaire en arc peut donc aussi nécessiter une augmentation.

Les calculs de structure peuvent alors être effectués suivant le règlement de classification en utilisant les moments réglementaires corrigés des accroissements dus au whipping.

L'application sur un porte conteneurs de 250m de longueur montre que l'accroissement du moment de flexion maximal total (houle plus eau calme) pouvait atteindre 20 à 30 % pour des conditions de navigation sévères, en accord avec les mesures à la mer [6].

Les calculs effectués sur des porte-conteneurs géants conduisent à considérer que cet ordre de grandeur reste valable pour ces navires

2.4. Effets sur la fatigue

L'observation de la réponse en whipping (figure 4) montrent deux effets en fatigue:

• accroissement de l'étendue de contrainte poutre navire rigide à la fréquence relative de la houle

• génération de cycles d'amplitudes décroissantes à la fréquence du premier mode de la poutre navire élastique.

Pour les détails soudés, on considère que les contraintes résiduelles de soudage entraînent un niveau de traction élevé dans les zones d'apparition des fissures permettant d'admettre pour les calculs un rapport R (contrainte min divisée par contrainte max) élevé (R>0.5).

Les essais de fatigue montrent que ce rapport élevé efface l'influence des variations de contrainte moyenne sur l'estimation de la durée de vie en fatigue.

Pour des détails sans soudure il n'y a pas de contraintes résiduelles, aussi le traitement

devient très délicat. Pour simplifier on applique cependant la même approche que pour les détails soudés ce qui revient à considérer qu'il existe un niveau élevé de contrainte moyenne en traction, en fait hypothèse du côté de la sécurité, donc acceptable.

L'utilisation de la règle linéaire de Miner permet alors de séparer les deux composantes, basse fréquence (houle) et haute fréquence (whipping) et de calculer les dommages séparément, puis de les sommer (figure 5).

=+

Figure 5: Séparation des effets de whipping en

vu du calcul de fatigue

Ayant déterminé par un calcul de réponse de la poutre navire l'étendue du premier cycle d'une réponse de whipping (noté Cwp∆Sw sur la figure 6), il est possible de déterminer la distribution transitoire amortie des étendues (figure 6):

Cwp∆SwCwp∆Sw

Figure 6: Composante haute fréquence

transitoire de whipping

Les équations sont alors:

∆Swpj = A⎥⎥⎦

⎤

⎢⎢⎣

⎡−

−−

2)34(

1exp

2

π

ξ

ξ j (1)

avec j n° d'ordre du cycle

A =

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−−

∆

21exp

2

π

ξ

ξ

SwCwp (2)

La distribution à court terme est obtenue en remarquant que pour une réponse il n'y a que 1 cycle à chaque niveau et qu'il y a une réponse à chaque cycle de houle (figure 7).

n

∆Swp

Cwp∆Sw

n

∆Swp

Cwp∆Sw

Figure 7: Distribution des contraintes de

whipping pour une amplitude de houle donnée

Le calcul de la somme de Miner peut s'effectuer à partir des distributions à court terme des étendues de contraintes. Chaque palier d'une distribution peut être assimilé à la réponse sur une houle régulière d'amplitude constante, aussi on peut utiliser des calculs de réponses non linéaire sur houle régulière.

Pour une houle de fréquence donnée mer de l'avant, puisque le slamming ne se produit pratiquement que mer de l'avant, il est possible de déterminer les réponses fonction de la hauteur de houle H et la hauteur de houle seuil Hth au dessous de laquelle il n'y a plus de risque de slamming:

Cwp∆Sw = f(H) H > Hth (3)

La méthode de calcul devient alors la suivante:

1. détermination, pour les fréquences de houle de la table des états de mer et les incidences retenues, de la vitesse du navire maximale suivant la hauteur de houle (conditions de navigation extrêmes supportables à la passerelle)

2. calcul des fonctions de transfert et des réponses court terme sans whipping

3. détermination, mer de l'avant et pour les fréquences de houle de la table des états de mer retenue de la hauteur de houle seuil et des réponses en whipping en fonction de la hauteur de houle

4. approximation d'une loi linéaire donnant l'amplitude du premier cycle de whipping fonction de l'amplitude de la réponse en mode rigide

5. approximation de la variation de la loi linéaire en fonction de l'angle d'incidence de la houle

6. identificatioon des états court terme avec possibilité de whipping

7. correction de whipping de l'étendue de

contrainte des distributions court terme basse fréquence concernées

8. calcul des sommes de Miner pour tous les court termes (avec et sans whipping)

9. pour chaque court terme avec whipping, détermination des distributions de la composante haute fréquence de whipping et somme de Miner

10. somme de Miner totale, basse fréquence corrigée du whipping et haute fréquence de whipping.

Une évaluation effectuée pour un porte-conteneurs géant montre que le whipping concerne essentiellement les contraintes engendrées par le moment de flexion vertical et a une incidence mesurable sur le cumul de fatigue.

La correction d'étendue de contrainte basse fréquence entraîne une augmentation de l'ordre de 3% de la somme de Miner totale, avec 100% d'accroissement pour les mers de l'avant seules.

La somme de Miner de la composante haute fréquence par contre est négligeable, principalement du aux faits que:

• le whipping n'apparaît que sur un nombre limité d'état de mer (mer de l'avant, houles de hauteur supérieur au seuil)

• la décroissance des amplitudes des cycles entraînent la majorité des cycles sous le niveau de changement de pente de la courbe S-N utilisée en raison du caractère aléatoire des phénomènes.

3. SPRINGING Le springing est une vibration de réponse forcée de la poutre navire excitée par la houle.

Des calculs de fréquence propre du mode à deux nœuds de la poutre navire effectué sur des navires de taille jusqu'à 350m de long conduisent à des valeurs bien supérieures à celles des plus courtes houles observées. Les tables de l'Atlantique Nord donnent comme plus basse période Tz=3,5s (0,28Hz) et le calcul pour un pétrolier de 300.000tdw donne comme fréquence propre avec masse d'eau ajoutée 0,5Hz (T=2,0s).

Cependant le springing a été identifié dès 1972 lors du dépouillement de mesures à la mer sur un pétrolier de 340m [12] (figure 8).

La réponse du 1er mode de vibration de la poutre navire, malgré sa fréquence élevée, s'explique par le fait que pour une période de houle donnée, l'énergie est répartie sur une large bande de fréquence. En utilisant la représentation de Pierson-Moskowitz, pour une houle de 3,5s on peut considérer une énergie dans la bande de [0,12-0,65]Hz et pour une houle de 8,5s dans la bande de [0,05-1,7]Hz.

Figure 8:Spectre de réponse de la contrainte de flexion au pont d'un pétrolier, mer de l'avant,

mode rigide et springing [12]

En outre mer de l'avant, en raison de la vitesse du navire, la fréquence d'excitation ωe est supérieure à celle de la houle ωH. Cette fréquence d'excitation (fréquence de rencontre) est donnée par la formule:

ωe = ωH + VgH2ω (4)

ce qui pour le pétrolier mentionné, avec une vitesse de 15nd (7,7m/s), donne l'énergie pour une houle de 3,5s dans la bande de [0,19-2,73]Hz et pour une houle de 8,5s dans la bande de [0,06-16,0]Hz. Comme on le constate, le mode à 0,5Hz est effectivement excité.

Sur les navires de 300 à 350m de longueur, si le springing est visible sur une analyse spectrale, son niveau est très faible et sans incidence sur la résistance de la structure.

Lorsque la longueur du navire augmente ou si le pont principal comporte de grandes ouvertures, sa rigidité diminue et la fréquence propre du 1er mode diminue. Lorsque la vitesse augmente, les fréquences d'excitation augmentent. Dans les deux cas la fréquence de springing se déplace vers la région des spectres

à plus forte densité d'énergie accroissant la réponse (figure 8, le pic de springing se déplace vers la gauche).

Cet effet a été constaté lors des études des projets des pétroliers de 550.000tdw (longueur 414m) puis confirmé par 4 années de mesures à la mer [13,14].

Lorsque l'on considère les caractéristiques des porte-conteneurs géants, longueur 363m, vitesse 24nd, pont très largement ouvert [15], il apparaît clairement que le springing est un phénomène à prendre en considération pour la conception de la coque.

3.1. Incidence sur la tenue de la structure

La réponse temporelle de la contrainte au pont a la forme de la figure 9, un signal haute fréquence d'amplitude quasi constant (springing) sur une porteuse basse fréquence (houle)

Figure 9: Mesure de la contrainte au pont avec

springing apparent

Les études et mesures effectuées sur les pétroliers de 550.000tdw montrent que le springing est sensible pour les états de mer à plus faible période. Pour ces périodes, les tables d'observations montrent que les hauteurs de houle maximales sont faibles (tableau 1).

Tz (s) 3.5 4.5 5.5 6.5 7.5 8.5

Hs (m) 1,5 4,5 9,5 13,5 14,5 14,5

Tableau 1: Hauteurs significatives maximales pour l'Atlantique Nord (table IACS)

Due au très faible amortissement, ζ=1.5% obtenu par mesures à la mer [6,14], l'énergie totale de la réponse reste très limitée, et l'amplitude est faible par rapport à celle de la houle (figure 9).

Ainsi l'influence du springing ne sera pas significative sur les valeurs extrêmes qui correspondent aux fortes houles de période importante.

Par contre la haute fréquence et le caractère vibration forcée, donc quasi permanente du phénomène sur les faibles houles qui sont les plus fréquentes au cours de la vie du navire, entraîne un cumul de fatigue non négligeable, confirmé par le retour d'expérience des pétroliers de 550.000tdw [14].

3.2. Moyens de calcul et méthode

Si l'on considère les mouvements verticaux de la poutre navire et sa déformation due au springing, il est possible de faire l'hypothèse des petits mouvements pour le springing ce qui permet d'effectuer un calcul linéaire en séparant les deux phénomènes, réponse rigide, réponse élastique [13].

Il est ainsi possible d'utiliser les outils linéaires développés pour les calculs hydrodynamiques et de comportement des structures [17].

Un premier calcul, classique de comportement sur houle, permet de déterminer en linéaire les coefficients hydrodynamiques, en particulier les masses d'eau ajoutées, et la fonction de transfert de la réponse de la poutre navire rigide (figure 10).

Figure 10: Calcul de la fonction de transfert

poutre navire rigide

Un deuxième calcul de poutre navire élastique permet de déterminer les fréquences propres poutre navire, et la fonction de transfert de springing (figure 11).

Figure 11: Calcul de la fonction de transfert de

springing en torsion de la poutre navire élastique

On obtient ainsi les fonctions de transfert quasi-statiques, springing et totales pour les conditions de navigation sélectionnées pour les calculs de structure (figure 12)

La détermination des fonctions de transfert permet de calculer les réponses sur spectres de houle et les distributions à court terme sur chaque état de mer correspondant aux conditions de navigations retenues pour le projet avec les outils classiques mis au point pour les effets de houle navire rigide.

Figure 12: Fonctions de transfert de la

contrainte au point chaud d'un détail soudé de porte-conteneurs (springing, houle, totale)

La méthode de calcul se déroule alors suivant les étapes ci-dessous:

1. sélection des états de mer et de leur fréquence d'existence suivant les zones d'opération du navire (standard: Atlantique Nord)

2. calcul de comportement linéaire avec détermination des conditions extrêmes possible suivant l'incidence de la houle (vitesse du navire, hauteur de houle)

3. détermination des conditions de navigation avec possibilité de springing (incidence de houle, vitesse, période de houle)

4. calcul de comportement linéaire élastique pour les incidences de houle avec springing

3.3. Effets sur la fatigue

L'observation de la réponse en springing sur un état de mer donné (figure 9) montrent une génération de cycles d'amplitude quasi constante à la fréquence du premier mode de la poutre navire élastique sur la réponse à la fréquence de houle.

Le calcul de cumul de fatigue à court terme requiert la détermination de la distribution des étendues de contrainte. La méthode exacte serait un comptage Rainflow, mais pour ce faire il est nécessaire d'avoir un historique temporel, ce qui est peu pratique à partir d'une approche spectrale.

En considérant les mêmes hypothèses que dans le cas du whipping et la règle de cumul linéaire de Miner, il est possible de séparer les deux composantes (figure 13), basse fréquence (houle) et haute fréquence (springing), et de calculer le dommage par somme de Miner.

Comme pour le whipping, l'étendue de contrainte de vague doit être corrigée de l'amplitude de springing. Seules les conditions de navigation avec risque de springing sont à considérer, il est donc important de prendre en compte les réductions de vitesse lorsque la hauteur de houle augmente car elle réduit ou même supprime le phénomène de springing.

= + = +

Figure 13: Séparation des effets de springing

en vu du calcul de fatigue

Chacune des composantes, houle seule et springing seul, correspondant à un signal à spectre étroit il peut être appliqué la méthodologie du calcul de fatigue sur houle [16]. La distribution de l'étendue de contrainte ∆Si à court terme est représentée par une distribution de Rayleigh dont le coefficient est déterminé à partir de l'aire du spectre de réponse m0:

prob∆S > ∆Si= ⎥⎥⎦

⎤

⎢⎢⎣

⎡ ∆−

0

2

8exp

mSi (4)

Lorsque le nombre de cycles total du court terme est connu Nt (durée du court terme divisé par la période moyenne de passage par zéro), pour chaque ∆Si il peut être calculé le nombre de cycles ni:

ni = (pi – pi-1)Nt

en notant pi = prob∆S > ∆Si

Pour un détail de structure donné, connaissant le courbe S-N, il est possible de calculer séparément les sommes de Miner puis de les

sommer en tenant compte des probabilités d'existence de chaque condition court terme (période et hauteur de houle, vitesse du navire, incidence de la houle):

Dtotal = Dhoule/corrigée+ Dspringing

La méthode de calcul devient alors la suivante:

1. détermination, pour les fréquences de houle de la table des états de mer et les incidences retenues, de la vitesse du navire suivant la hauteur de houle (conditions de navigation extrêmes supportables à la passerelle)

2. calcul des fonctions de transfert sans springing et des réponses court terme

3. détermination des domaines de fréquences des spectres de densité d'énergie pour les conditions de navigation de calcul

4. calcul des fréquences propres de la poutre navire avec masses d'eau ajoutées

5. détermination des états court terme avec risque de springing

6. calcul des fonctions de transfert de springing et des réponses à court terme pour les états court terme concernés

7. somme de Miner totale, basse fréquence de houle corrigée du springing et haute fréquence de springing.

Une évaluation effectuée pour un porte-conteneurs géant montre que, en raison du pont très largement ouvert, la fréquence propre de poutre navire la plus basse est celle en torsion, suivi par celle de flexion vertical (tableau 2). Mode de vibration de la poutre f (Hz)

mode en torsion 1 noeuds 0,37

mode en flexion 2 noeuds 0,49

mode en torsion 2 noeuds 0,50

mode en flexion 3 noeuds 0,90

Tableau 2: Fréquences propres de la poutre navire avec masses d'eau entraînée

La détermination des conditions de navigation avec risque de springing a conduit à considérer le springing de torsion pour les incidences de 120° et 90° et le springing de flexion pour les

incidences de 180° et 120° (180° correspond à une mer de l'avant).

Sur un détail de structure au pont (figure 14), région la plus sollicitée en dynamique d'ensemble, une analyse de la durée de vie en fatigue a été effectuée suivant la méthode décrite.

Figure 14: Détail de structure de pont d'un

porte-conteneurs géant: coin d'écoutille

La réponse de springing a été calculée pour toutes les périodes de houle et les hauteurs de la table d'observation jusqu'à 5m significatif. Pour les hauteurs supérieures il a été considéré qu'il y avait réduction de vitesse et que la modification des fréquences de rencontre rendait le springing négligeable.

Les sommes de Miner ont été calculées à court terme. Le springing entraîne une augmentation de l'ordre de 4% à 10% de la somme de Miner totale.

Une analyse de la sensibilité à la hauteur de houle maximale montre que le passage de 5m à 6m significatif augmente le cumul de Miner de springing de 20%, mais a un impact du second ordre sur la somme totale.

Une étude en cours analyse une alternative plus précise à l'approche ci-dessus. Pour ce faire un signal temporel de la contrainte est généré par transformée de Fourrier inverse à partir du spectre de réponse global (houle plus springing) sur lequel le comptage des étendues de contraintes est effectué par la méthode Rainflow. Le cumul de fatigue par somme de Miner est alors considéré plus précis.

Les résultats obtenus montrent des écarts entre les deux approches mais confirment la validité de l'approche simplifiée utilisée.

4. CONCLUSION L'augmentation des tailles et vitesses des navires, en particulier des porte-conteneurs, modifie les comportements sur houle.

Des phénomènes connus sur les navires de plus petites tailles peuvent être amplifiés jusqu'à atteindre des niveaux impactant la conception des coques. C'est en particulier, pour la poutre navire, le cas du whipping, réponse vibratoire transitoire suite à un slamming ou slapping, et du springing, vibration forcée par la houle irrégulière.

Le phénomène de springing avait été analysé puis vérifié à la mer lors de la construction des pétroliers de 550.000tdw en 1975, avec les moyens de calcul de l'époque.

Le whipping est aussi connu depuis cette même époque avec des conséquences gênantes sur des navires à pont ouvert, mais alors sans possibilité de calcul en raison de la faiblesse des moyens informatiques.

Le développement des outils informatiques ayant permis la mise en œuvre de méthodes complexes d'hydrodynamique navale dans le domaine non linéaire et avec couplages fluide/structure, il a été possible de développer une approche d'estimation de ces phénomènes et de leurs conséquences sur les contraintes extrêmes et la fatigue en service.

La mise en application pour des projets de porte-conteneurs géants a confirmé que leur taille et disposition générale conduisent à des accroissement des niveaux de contrainte et du cumul de fatigue significatif, ne permettant plus de les ignorer pour l'échantillonnage des structures.

Les effets de whipping peuvent entraîner un accroissement de l'ordre de 20% du moment de flexion vertical total, important pour les vérification à l'état ultime.

Concernant le springing, les projets actuels de 350m de long, en raison de la flexibilité due à un pont très ouvert et de la vitesse élevée, montrent un niveau d'accroissement en fatigue supérieur à ceux des pétroliers de 414m, restant cependant limité et se mesurant en pour cents.

Pour des projets de plus grande taille, 400m et au-delà, il est certain qu'avec des dispositions de coques similaire, l'accroissement de fatigue

deviendra plus important. En se rappelant qu'il s'agit d'un phénomène de vibration forcée très peu amorti, les réponses ne sont pas linéaires et devront donc être analysées avec une plus grande attention.

5. REFERENCES [1] Bureau Veritas 1828/1978 - A record of

150 years - PEMA 2B Publishing, 1978

[2] Another Genesis for Aker - The MotorShip review - May 2007, p 6

[3] H.J. REUSS et J. BARNES, Maersk takes world biggest and fastest - The MotorShip review - November 2006, p 16-17

[4] P. de Livois et B. Parizot – Le gigantisme en construction navale, ses conséquences sur la sécurité des navires – Revue Navigation – Avril et juillet 2007

[5] M. Huther et N. Ket – Water impact risk estimation during ship design – Ship Behaviour at Sea, International Symposium on Ship Hydrodynamics and Energy Saving, ISSHES 83 – Madrid, September 1983

[6] J. Osouf – Etude expérimentale du comportement dynamique dur houle du navire câblier "Marcel Bayard" – Revue NTM 1973

[7] I. Drummen, T. Moan, G. Storhaug, E. Moe – Experimental and full scale investigation of the importance of fatigue damage due to wave-induced vibration stress in a container vessel – Design & Operation of Container Ships, Royal Institution of Naval Architects, London, November 2006

[8] Š.Malenica, B. Molin, F. Remy, I. Senjanovic – Hydroelastic response of a barge to impulsive and non impulsive wave loads – 3rd International Conference on Hydroelasticity – Oxford, 2003

[9] W.E. Cummins – The impulse response function and ship motions – Schiffstecknik, 1962

[10] T.F. Ogilvie – Recent progress toward the understanding and prediction of ship motions – 9th International Conference on Numerical Ship Hydrodynamics – Ann Arbor (USA), 2007

[11] J. Tuitman,S. Malenica – Some aspects of whipping response of container ships – 23rd IWWWFV – Jegu (Korea), 2008

[12] J.M. Planeix – Wave loads, A correlation between calculations and measurements – Revue International Shipbuilding Progress, August 1972

[13] B. d'Hautefeuille, M. Huther, M. Baudin, J. Osouf – Calcul de springing par équations intégrales – Revue NTM, 1977

[14] M. Huther et J. Osouf – SEFACO, Four years of experience in ship hull girder stress monitoring – MARINTEC – Shangai, October 1983

[15] L. Gérard - De 6 500EVP à 11 400EVP sur un même concept, jusqu’où sera-t-il possible d’aller ? – ATMA, juin 2007

[16] M. Huther, D. Beghin, S. Mahérault – A fatigue strength guidance note for welded ship structure assessment – IIW/IIS doc XIII-111742-98 / XV-992-98, 1998

[17] S. Malenica – Hydro structure interaction in seakeeping – International Workshop on Coupled methods in numerical dynamics IUC – Dubrovnik (Croatia), September 2007

OFFSHORE ENGINEERING & MOORING

Finding the right site for an offshore unit, understanding the localconditions and then designing moorings which will hold it in place are thethree apparently simple but in practice complex problems which many ofthe papers in this section address. There is a strong focus on moorings,and also papers which summarise the long experience of Bureau Veritaswith offshore concrete floating structures.



CHARACTERIZATION OF POLYESTER MOORING LINES

Michel FRANÇOIS Bureau Veritas, Paris

Peter DAVIES IFREMER Brest Centre



OMAE2008-57136

ABSTRACT Fibre ropes are extensively used in marine applications.

One critical area of interest is their application as mooring lines for floating offshore platforms, for which primarily polyester is now employed in various regions (offshore Brazil - now for 10 years, West Africa, Gulf of Mexico). Evaluating the response of the system requires a description of the load-elongation properties of the rope.

A practical model involving two sets of stiffness data is currently used, and procedures for their measurement are available. This paper presents an overview of this model, then focuses on recent work on the quasi-static stiffness of polyester ropes. This is addressing the variations of the mean tension in the lines, at a very slow rate, under changing weather conditions.

Extensive tests were performed, principally on polyester sub-rope samples. Some tests were also performed on a full size 800-ton MBS rope. Besides standard tests, specific tests were performed over an extended range of loading, to cover the situations that may be found in a wide range of systems and design conditions. The factors (measurement accuracy, test conditions, etc…) affecting the values are discussed along with the presentation of tests and results.

Results are interpreted to provide practical data for mooring analysis, in the form of a quasi-static load-elongation characteristic. These results also give a better insight into the visco-elasto-plastic response of polyester fibre ropes.

For the dynamic stiffness of polyester ropes, an overview of recent and earlier test data is presented. The dependence of dynamic stiffness on testing parameters is discussed, highlighting mean load as the principal parameter under real stochastic loading, and confirming the current practice for modelling dynamic stiffness in design.

1 INTRODUCTION Fibre ropes are extensively used in a number of marine

applications. One critical area of interest is their application as mooring (anchoring) lines for the station-keeping of floating offshore platforms in deep-water. Following a development period, and now ten years after the first installations of floating production systems by Petrobras in Brazil, this technology has reached a stage of maturity: fibre rope station keeping systems are now employed commonly offshore Brazil, and also in other regions around the world (in West African waters, in the Gulf of Mexico, …). Polyester, the material primarily used in this application, is addressed in this paper.

Evaluating the response of the system, and then the adequacy of maximum offset and line tensions with the relevant acceptance criteria, requires a description of the load-elongation properties of the rope. However, these properties are rather complex to evaluate and specify, in comparison with the linear elastic behaviour of equivalent steel components, as they are non-linear and time dependent. Besides, the loading regimes of a rope in an anchoring line are quite specific with respect to usual service conditions of fibre ropes.

A first insight into the load-elongation properties of fibre rope lines was given in [1]. Within the French CLAROM fibre rope projects, since 1997 [2], extensive testing has been carried out. This resulted, in 2000, in a practical (Engineering) model for the load-elongation characteristics of polyester ropes, that was presented and documented in [3] and [4], and is currently in use within several State of the Art mooring analysis and line dynamics software packages. Tests performed since on other materials [5] have generally confirmed the applicability of this model.

In the meantime, testing procedures have been developed for rope qualification (see [6]), that are now available with the ISO standard for rope qualification [7] and the BV Guidance Note [8]. The model for engineering and analysis of fibre rope mooring systems and the testing procedures in these documents define rope properties in a consistent manner. This model

1 Copyright © 2008 by ASME

involves a separation into several terms. One of these terms is the “Quasi-static stiffness”, that is the focus of the present paper.

The tests were performed principally on polyester sub-rope samples. Some tests were also performed on a full size parallel construction 800-ton MBS rope. In addition to the standard tests, an extended series of test sequences was performed, to get an understanding of rope behaviour under a wider range of load and elongation, and to cover the particular situations that may be found in some systems or design conditions.

Besides the interpretation of results to provide practical data for analysis, these results also gave a better insight into the visco-elasto-plastic response of polyester fibre ropes. As correct measurement and interpretation of test data are essential for platform safety, the factors affecting the values are discussed (measurement accuracy, test conditions, …) along with the presentation of tests.

For the dynamic stiffness, a discussion on the dependence of dynamic stiffness on testing parameters is made, based on the comprehensive data from recent tests and on earlier data.

2 FIBRE ROPES LOAD-ELONGATION PROPERTIES AND MODEL

Issues The load-elongation properties of fibres and fibre ropes

exhibit a non-linear and time dependent (visco-elasto-plastic) behaviour. This is primarily the result of the load and time dependence of the materials forming the filaments (a complex assembly of long chains of organic molecules), and to a lesser extent from the effects of rope construction [9]. As a result these properties cannot be reduced to a load-elongation “characteristic”, even a non linear one, and particularly, NOT to the load elongation curve of a new sample under monotonic loading (as obtained from a standard breaking test).

In the lines of a station-keeping system, once the system is deployed/installed and set under tension, the rope will be maintained under a sustained tension for months, even years or decades in the case of a deep-water permanent mooring, then subjected to the random loads induced by the environment (wind, waves, current). It is then convenient for the evaluation of system response, as proposed in [8], to separate the response into three terms, related to the time scale of actions, and matching the typical steps of a mooring analysis (be it frequency or time domain) : • Mean elongation (system pretension, permanent load), • Visco-elastic response to slow variations of mean load

under changing weather, modelled by the quasi-static stiffness, as further discussed in sections 3 and 4 below,

• Response to dynamic actions (both low frequency and wave frequency) modelled by the dynamic stiffness (see section 5 below). A particularly important aspect, quite specific to fibre

ropes, is the modification of the properties of a rope during the first loading(s) and during the early stages of rope service. This process, called “bedding in”, is primarily due to changes at a

molecular level within fibres. It results in a stabilisation of the rheological properties of the rope, and in an essentially permanent - not recoverable - elongation with respect to the rope initial length at the time of manufacturing. The length of a finished rope is thus defined in [7] as a bedded-in length at a specified tension.

Besides, as a noteworthy consequence of time dependence, it is important to consider in the definition of test sequences and the derivation of engineering data that the time scale of actions on a test bench is much smaller than for a line in-situ: this time dependence (also bedding-in) will thus affect somewhat differently the response.

Quasi-Static stiffness Following the concept proposed in [1], a “quasi-static

stiffness” was defined, ten years ago, in order to model the visco-elastic response of ropes to slow variations of mean load, under the effect of changing weather conditions, i.e. a time scale of several hours or days, where the tension in the line, initially the line pre-tension, increases (in the "windward" lines) or decreases (in the "leeward" lines), at a very slow rate.

In this test (see [7], [8] and below), after a proper bedding-in, the rope is cycled between two tension levels, with a constant load plateau at each level, during which creep or recovery is measured. Several cycles are needed to get rid of the initial condition of the rope on the test bench (which is not representative of actual conditions), and to obtain stabilised results. Typically, 3 cycles of twice ½ hour each are used, keeping the duration of the test within a practical time frame.

In order to get a stiffness that is more representative of the real loading duration of the events intended to be modelled (see below), cycles of longer duration can be simulated as follows from test results (load and elongation versus time).

1) The elongation L( t ) along each creep (or recovery) plateau can be written, by a three parameter fit (see [8] ), as : L( t ) = L( tp ) + ac . log [ 1 + ( t - tp ) / ta ] (1)

This fit (on ac , ta, and L(tp)) is independent of time unit and origin, and the result does not depend on the selection of tp, the time at any point along the load plateau.

2) From L( t ) , the elongation Lτ at the end of each ½ cycle of duration τ can be obtained as : Lτ ≈ L( tp ) + ac . log [ τ / ta ] (2)

3) The (linearised) quasi-stiffness is then taken as a secant stiffness between the end points of the last successive ½ cycles of duration τ . Normalising loads by rope MBS, the non-dimensional quasi-static stiffness KrS is obtained.

The two load levels are normally taken as 10% and 30% of MBS, and the duration τ is normally taken as 12 h, providing values for typical storm conditions. Different levels or durations could apply to some design or metocean conditions (e.g. a damaged system, a loop current event). The tests presented in this paper were performed to get an understanding of rope behaviour under a wider range of load and elongation, and in order to provide data for such conditions.


3 ROPE TESTING

General : The CLAROM French Mooring Line project has been

working on fibre rope moorings over the last ten years and has generated a large database of material properties. Tests have been performed at scales from single filament [9] up to 800-ton break load ropes [10], including the intermediate yarn, assembled yarn and sub-rope levels. Here only results from the sub-rope and full scale ropes will be discussed, but it is important to underline that by working on filaments and yarns the material and rope construction contributions to overall rope behaviour can be quantified and modelled. This provided also some light on the underlying mechanisms at molecular level, if not yet a definitive interpretation.

Experimental set-up Sub-rope tests were performed at the IFREMER test

facilities in Brest. A 9-meter long 100-ton capacity test frame was used, equipped with a 1.5-meter course hydraulic piston (see Figure 1). A programmable controller enables loading sequences to be pre-programmed, so that long, complex test sequences lasting several days can be defined and run. Full size rope tests were run at the LCPC test laboratory in Nantes, on the 2400-ton test frame (see e.g. [10]).

Figure 1 . Sub-rope on test frame

Both series of tests used the same instrumentation to measure strains in the central rope section away from the splices : wire transducers clamped to the rope for stiffness measurements and digital cameras linked to an image analysis system for break tests and to check wire transducer measurements. The tension in the rope is measured by the strain-gages load cell system of the test frame. All measurements are recorded, at a high data acquisition rate (up to 5 Hz for dynamic stiffness), and stored on a PC for subsequent analysis. Accurate and continuous time series of load and elongation are thus available for analysis.

Materials The tests described here were performed on 8-strand

braided polyester sub-rope samples, with a 70 t breaking strength, and on test lengths of a full size (800 t MBS) parallel construction rope based on the same sub-ropes. The fibre is a standard high tenacity grade with marine finish. Oliveira Sá, Portugal supplied all samples.

Test sequences The standard test to measure quasi-static stiffness

described in [7] consists of three 1-hour load-unload cycles between 10% and 30% (of the break strength), applied to a rope which has been fully bedded-in (i.e. an initial loading to 50% , with the load maintained constant for 30 minutes, then 100 cycles between 10 and 30%).

In order to widen the scope of this characterisation, an extended quasi-static stiffness test was developed : As shown in Figure 2, a series of load-unload cycles is applied, similar to those of the standard test, all with the same 20% range but at different sets of load levels, starting and ending with a set of cycles at 10-30%. Four cycles are applied at each load condition, in order to verify stabilisation.

0

100

200

300

400

500

600

0 5 10 15 20 25 30 35 40 45 50Time, h

Forc

e, k

N Linear density

Figure 2 . Extended quasi-static stiffness sequence Force versus time applied to sub-rope samples 3 and 4

On two samples , an extended sequence was applied to a

rope that has been previously subjected to bedding-in cycles following the standard procedure quoted before, or equivalent (on one of them). On two other samples, a sequence was applied to a rope with a lower degree of bedding-in cycles, obtained by applying instead the procedure defined in [7] for the “linear density test” (i.e. an initial loading to 20%, then 100 cycles between 15 and 25%, ending at a 20% load). Samples were then loaded to failure. A fifth sample was used for dynamic stiffness measurements (see section 5 below).


Test results - stiffness Figure 3 shows an example of the resulting force-strain

plot during the extended quasi-static stiffness test (continuous record over 48 h).

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7 8 9 10Strain, %

Forc

e, k

N

Figure 3 . Extended quasi-static stiffness sequence, sub-rope samples 3 and 4.

From the elongations at the end of the last two half cycles, a secant stiffness is obtained (without extrapolation at this stage). The quasi-static stiffness is found to be increasing with mean load, with a trend similar to that of the dynamic stiffness (see Figure 5). As shown in Figure 4, there is a close match between the results of all four samples, and a very limited effect of previous bedding-in : stiffness for the samples with mild bedding-in are only marginally lower than for well bedded-in samples, the lowest point corresponding to the very first load set after measurement of L20 .

0

8

16

24

32

0 10 20 30 40 50 60 70 80Mean Load (% of MBS)

KrS

Figure 4 . Quasi-static stiffness versus mean load, all four samples.

Comparing (see Figure 5) the results of the measurements performed on sub-ropes with those from full size 800 ton break load ropes, an excellent agreement is found for both the quasi-static and the dynamic stiffness when expressed in tenacity unit (N/Tex), as on Figure 5. Same result would be found if these stiffnesses are expressed as a non-dimensional Kr, using a normalisation by MBS of the full size rope (see [8]).

Influence of mean load

0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60 70Mean load, %

Stif

fnes

s, N

/tex

Rope DYNSub-rope DYNRope QSSub-rope QS

Figure 5 . Correlation between results for sub-rope and full size ropes; quasi-static and dynamic stiffness.

Test results - mean elongation The tests also provided information on the mean

elongation of the rope, and its dependence on the loading history.

On the samples to which the “linear density test” sequence was applied, the elongation at a 20% load, at the end of the sequence provides the reference length L20 for rope purchasing, according to the length measurement method in the standard [6].

Besides, a mean elongation at 20% can be obtained from each set of 10-30 cycles (indeed taken as the mean between the elongation at the end of the last 10% and 30% ½ cycles), or inferred from the fully relaxed condition (see 4 below). As shown in Figure 6, a very good agreement between the results of each group of two ropes is found.

20

30

40

50

60

70

80

90

0.0 0.5 1.0 1.5 2.0 2.5elongation (% ) above L20

Fmax

(% o

f BS) OL1 OL2

OL3 OL4

Figure 6 . Mean elongation at a 20% load all four samples.

The mean elongation of well-bedded-in samples is stable,

about 1.6% higher than L20, for all loads up to 40%. For higher maximum loads, further (delayed) permanent elongation is observed, increasing almost linearly until 70% (the maximum


load for these two samples).

For the samples with a milder bedding-in, the elongation increases quickly when the load exceeds the maximum seen during bedding-in, confirming that L20 is a lower-bound of the installed length, and is always lower than for well bedded-in ropes, up to 70% load. Given the time frame of the test (within 48h of the very first loading of the rope, i.e. much less than the time required to install a system and to have it actually operating) the resulting permanent elongations may be also considered as a very lower bound.

4 INTERPRETATION

QS stiffness From the fitting of creep and recovery plateau’s (greatly

facilitated by the very good accuracy of load control) and the extrapolation of last cycle plateau’s, the elongation’s for different levels and duration’s can be obtained : the standard duration of 12h and 7 days, that would be more representative of slowly growing events, such as loop currents, are considered here. When normalising loads by full size rope MBS and elongations by the length at 20%, including permanent elongation), the quasi static stiffness for the standard levels (10 and 30%) is found, , to be about 14.5 for 12h (i.e. 17% less than for the 1/2h duration in test), and about 12.5 for 7 days, i.e. 12 % lower than for 12h. This decay is consistent with earlier findings, as shown in Figure 7 .

Q-S PRACTICAL characteristics For other loads, a stiffness between two levels could be

calculated in the same way, but this is not very representative of the situation in a station-keeping system, where line tension

will generally not oscillate between such levels : Together with vessel offset, the tension will gradually increase (or decrease) more or less monotonically in most cases, and over the same period of time, from initial tension to a maximum (or minimum) value which will be different in each line.

Then, by considering the relevant points, a practical characteristic for the specified loading time can be obtained, that is shown in Figure 8. This characteristic was derived from data from the different samples: a very consistent behaviour was found.

10

11

12

13

14

15

16

0 1 10 100 1000loading time (hours)

KrS

10-

30

OL1

Clarom 2000

Figure 7 . Q-S stiffness KrS10-30 , blue : data from reference [3] (corrected).

0

10

20

30

40

50

60

70

80

90

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0elongation (% ) above L20

Tens

ion

(% o

f BS)

Xij 12h

Xij 7d

QS 12h

QS 7d

included Xp

fully relaxed

oliv1 Xtrap2 f

Figure 8 . Q-S PRACTICAL characteristics included Xp, and fully relaxed characteristic (see text)


A first observation is that, for the 12h (standard) loading time, this characteristic is almost linear, i.e. the standard quasi-static stiffness derived from tests between 10 and 30 % is valid over a large range, from about 7 to above 70%.

For the 7 days loading time, the slope of the characteristic (dX/dT = 1/Kr ) is higher between 10 and 30 % (as per the lower stiffness noted above) but, above 30%, is the same as for 12h.

Taking the pre-tension T0 as a start point, this characteristic (elongation versus load) can be written as : X(T) - X(T0) = ( T - T0 ) / Krsτ for T between 10 and 30% (3)

X(T) - X(T0) = ( 30 - T0 ) / Krsτ + ( T - 30 ) / Krs12h

for T above 30% (4) where Krsτ is the 10-30 stiffness for loading time considered (12h or 7 days).

For tensions below 10%, there is a clear increase of compliance with decreasing load. From a fitting between available data points, the characteristic may be taken as : X( T ) = X( 10 ) - 10 / Krsτ * ( u + 1.8 * u^3.6 ) where u = 1 - T / 10 (5)

In a system working at low tensions in leeward lines, this effect will have a similar effect as the catenary effect in weighty components of the line.

Fully relaxed condition During the test, at a given load, either creep can be

observed, or recovery from a larger elongation. There should be a stable point in between. As discussed below, this point can be obtained by extending the loading duration τ to t∞, the time at the intersection point of elongation versus (log) time of two ½ cycles terminating at same level, and correcting for the permanent elongation (when applicable).

Taking t∞ as 4 107 s , i.e. about 15 months, all points converge to a single curve, that is the non linear, but elastic (reversible) fully relaxed characteristic, i.e. the characteristics Xrx(T) for “infinitely slow” rate of loading , also shown (round dots) on Figure 8.

Arriving at or approaching a point on the fully relaxed characteristic in a shorter time than t∞ is possible, but requires some specific test sequences.

Discussion - Toward a rheological model Based on the above fully relaxed characteristic Xrx(T), the

load-elongation relation around this condition could be written as follows in order to address, if needed, more complex cases than the practical QS characteristic presented above can handle: L= L20 * ( 1 (+ Xpe) + Xrx ( T0 )) (6)

X( T ) - X( T0 ) = Xrx( T ) - Xrx( T0 ) + Xdpe - Xv (7) In this equation, Xpe is the permanent elongation at T0, if

not included in Xrx, and Xdpe is the delayed permanent elongation : Xdpe = Xpe ( Tmax ) – Xpe( T0 ) if T > T0 else 0 (8)

where Tmax is the maximum between tension T and the maximum reached before (since last re-tensioning).

Xdpe for a well bedded-in rope (maximum 0.8% at 80%) is indeed included in the practical characteristic above. It could be that for particular situations a lower initial bedding-in level, thus higher Xdpe, needs to be considered, but as discussed before, considering data from the samples with milder bedding-in would be unduly over-conservative.

The term Xv is the (remaining) un-developed visco-elastic elongation : Xv is positive in a situation where the rope tend to creep, i.e. X is lower than Xrx, and negative in the opposite case (relaxation).

For the 12h standard duration, the amount of Xv (also included in the practical characteristic above) is below 0.2% but, towards low tensions, is going from - 0.2% to - 0.5% for loads going from 20 to 2%. The values for 7 days are 40% lower.

On the other hand, if neither cycling nor load holding time was applied in the tests, Xv would have been of the order of 0.5 to 1%, or more : this highlights the importance of time scale in such tests.

For a constant load, i.e. creep or recovery, Xv could be modelled as the response of a non-linear spring and damper system. With an adequate (argsinh) damper function, a solution can be found, that can be approximated by: Xv = ac log ( t∞ / τ ) for τ << t∞ (9)

Xv = 0 for τ >> t∞ (with a transition over one or two decades around t∞ ). where ac is the creep (or recovery, then < 0) per decade. This supports the method above to determine t∞ . However ac is not an intrinsic material constant but depends on load history, and the spring and damper model suggested above does not fully address the growth of Xv. Besides, a closer look at time traces shows that Xpe is not only a function of Tmax, but depends also on the time under load (as also shown by Figure 6), so Xp and Xv are likely not fully separable.

The characteristics above are thus given for the Designer, as PRACTICAL Q-S characteristics. Development of a true “time domain” rheological model still requires further effort.

5 DYNAMIC STIFFNESS The “Dynamic stiffness” is modelling the near-elastic

response of the rope to cyclic actions (both low frequency and wave frequency) induced by the environment.

In tests (see [7] and [8]), after bedding-in, the rope is cycled around a pre-set mean tension. For harmonic (constant amplitude, sinusoidal) loading, at least 100 cycles are typically used today and, as the load-elongation graph converges to a fairly linear relation, a stiffness can be defined. This is taken as the mean slope over several cycles at the end of the sequence (i.e. 500 data points, in the results below). Normalising loads by rope MBS, the non-dimensional dynamic stiffness KrD is then obtained.


In order to complement the characterisation work performed earlier (see [3]), a number of dynamic stiffness tests were performed, on the same sub-ropes and full size ropes as those above. Similar tests were also performed on another full size rope with a different polyester fibre (see [11]). Results will be briefly summarised, together with a discussion of the dependence of dynamic stiffness on testing parameters.

Cycling period A series of tests was performed with the same mean load

and amplitude, and cycling periods from 12.5 s to 500 s. Results confirmed that the effect of this parameter on dynamic stiffness is negligibly small (1.4% variation over the above range). This is in accordance with earlier findings from bi-harmonic loading, and those of stochastic loading below.

Load history During tests with harmonic loading, at a constant mean load, the stiffness quickly increases in the first cycles, then tends to stabilise (at least apparently), and 100 cycles minimum are typically used today to obtain results in a practical time frame. There is however some effect of previous load history affecting the results. Indeed, the increase of stiffness during cycling is quite linear with log of time, as is the variation of mean elongation (be it creep or recovery) over the same time: From different tests, it seems that the stabilisation of the dynamic stiffness (toward the maximum stiffness for applied mean load) and that of mean elongation (towards the fully relaxed condition) are closely related.

Load range, stochastic loading From a series of tests under harmonic loading, with

different mean load and range, the effect of both parameters can be identified. Figure 9 shows the influence of load range, with the dynamic stiffness normalised by the value at a 5% range (obtained from a fit of data) . The dynamic stiffness is clearly decreasing when range is increased, more sharply towards higher amplitudes and lower mean loads. This may be due, at least in part, to the increase in rope temperature observed during such tests (see [12]).

However, the real loading is not harmonic. Series of tests were thus performed on the two full size ropes, using 1-hour time series obtained by mooring analysis (i.e. a wide band signal, with realistic low frequency and wave frequency contents), and different combinations of mean load and amplitude. Figure 10 shows an example of applied time series and resulting load-elongation plot. It is noteworthy that the load-elongation is very close to a single overall linear relation (linear regression over 18000 points). A closer look to signals clearly shows effect of neither the amplitude of individual cycles, nor the period of underlying (low and wave frequency) components.

Besides, from different tests it is apparent (see Figure 9) that this stiffness is almost independent of the overall (min to max) amplitude of the signal, and is slightly higher (within -1 to +5%) than the stiffness under harmonic loading at a 5%

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

0 2 4 6 8 10 12 14Amplitude (range/2) (% of BS)

KrD

/ K

rD2.

5

Figure 9 . Influence of load range on dynamic stiffness harmonic loading (10 , 20, 30, 40% light to dark blue),

stochastic loading (red and pink)

1500

2000

2500

0 10 20 30 40 50 60time, minutes

Forc

e, k

N

1500

1750

2000

2250

2500

3 3.1 3.2 3.3 3.4

Strain, %

Forc

e, k

N

Figure 10 Example of stochastic loading (1h) a) time trace;

b) resulting load-elongation and linear regression

range. In this respect, it must be observed that in such realistic stochastic signals, the energy, being related to the standard deviation of the signal, is 5 to 10 times lower than in an harmonic signal having the same range. Besides, it seems that a better stabilisation, i.e. closer to real conditions, was achieved by these sequences.

Thus, there is no point in taking into account an effect of load range in analysis.


Mean Load Mean load has been identified before as the dominant

parameter affecting the dynamic stiffness, and a linear relation is currently used. As an update of [3] (where a comparison with the relation in [1] and those by other authors was shown), Figure 11 shows the variation of dynamic stiffness with mean loads, for 11 different ropes from 6 rope manufacturers, including the results of recent tests.

Besides the overall trend for an increase of stiffness (about linearly) with mean load, some scatter is observed that can be attributed to several reasons. A first set is the effect of the parameters noted above : load range (10% maximum on this figure), load regime and effect of previous history/stabilisation. There is also some small effect of measurement inaccuracy and small discrepancies between the testing laboratories (three, in addition to IFREMER), along the measurement and data processing chain.

The principal reason is, however, the differences between the ropes themselves (material and construction), that are reflected in the dynamic-stiffness-at-end-of-bedding-in Krebi. For the ropes in Figure 11, Krebi (shown by bigger marks, at 20% mean load) is in the range of 18.5 to 23, i.e. the range of a “normally stiff” rope according to A1-5.7 in [8].

Normalising data by Krebi, for each rope, significantly reduces the scatter, but does not lead to a single relation, due to the other reasons quoted.

Values for Analysis. As shown in Figure 11, all data points are lying within the

envelope formed by the design (upper-bound) stiffness and the minimum stiffness, as proposed in [8] : KrD = 18.5 + 0.33 ML (design) KrDm = 15 + 0.25 ML (lower bound), where ML is mean load (in % of MBS).

Only a few points are marginally outside. Towards low mean loads, results now available confirm

that stiffness is decreasing, and that the linear relation is on the conservative side. Therefore, the minimum value proposed earlier has been dropped. Towards higher mean loads, there is a trend for the stiffness to increase less than predicted by the linear relation. This was attributed to an insufficient number of cycles in earlier test procedures, and does not appear in some results, therefore was not considered.

The envelope given above is thus adequate for the design of a mooring system, i.e. typically some significant time in a project before a particular product is selected and manufactured. This envelope covers the possible range of stiffness of a “normally stiff” rope. Then the standard measurements during rope qualifications will confirm that the purchased product has properties within the range used for Design. This envelope should be adjusted if stiffer ropes are considered. Besides, for some cases (e.g. a site assessment) where the rope is already known, a more accurate relation could be defined. This will however require that further measurements are made, e.g. using stochastic loading, and that due care is taken is the derivation of engineering values, that cannot be simply taken as the raw results of a few tests.

15

20

25

30

35

40

0 10 20 30 40 50 60Mean load ( % MBS )

KrD

Krebi

Figure 11 . Dynamic stiffness as a function of mean load : test data from [3] (blue and green), recent (red and pink), and relations in ref [8]


CONCLUSION Within the French CLAROM fibre rope project, tests have

been performed to confirm and complement the currently used practical engineering model that was derived from earlier work. This work focused principally on the response of ropes to slow variations of mean load, under the effect of changing weather conditions, usually modelled by the “Quasi-static stiffness”. In addition to the standard tests described in [7], extended test sequences were defined. From these specific sequences, and the number of data points provided, an interpretation can be given that overcomes the discrepancy between the time scale of tests (one or two days), and the real world.

Tests reported in this paper were principally performed on sub-ropes. Some full size rope test results are also reported. The scalability of results, an already known fact, was shown. Due attention was given to the accuracy of load and elongation measurement methods. Continuous time traces were obtained : this is also an important factor for interpretation of test data.

Based on the interpretation of test results, a practical Q S

characteristic can be defined, addressing monotonic changes of line mean load, from around the line pre-tension. This characteristic is an extension of the current Quasi-Static stiffness KrS. Two characteristics are proposed for the 12h (standard) loading time, and for 7 days, a loading time more appropriate for some other design conditions (e.g. the effect of a loop current). Both are scaleable by KrS.

A first observation is that, for the 12h loading time, the quasi-static stiffness (Krs10-30) derived from standard tests is valid over a large range of tensions, from about 7 to above 70%, i.e. the characteristic is linear over this range.

Another significant observation is that, for tensions below 10%, the characteristics show a clear increase of compliance with decreasing load : this should be considered for systems working at low tensions in leeward lines.

As background to the above characteristics, further separation of the rope response is presented, based on the derivation of a fully relaxed characteristic (the characteristic for “infinitely slow” rate of loading), and two additional terms : a permanent (non recoverable) elongation, and a (remaining) un-developed visco-elastic elongation, modelling the effect of loading rate. Nevertheless, development of a true “time domain” rheological model and a definitive understanding of underlying mechanism will require further effort.

For the dynamic stiffness, the discussion of the

dependence of dynamic stiffness on testing parameters, based on recent data, highlighted mean load as the principal parameter under real stochastic loading. This confirmed the adequacy of current practice in the analysis of a system, of modelling the dynamic stiffness as a linear function of mean load only. Besides, for a particular rope, it is important to note that load history and other effects will always affect the test results, thus due care is to be taken in the derivation of engineering values that cannot be simply taken as the raw

results of a few tests. Using stochastic loading time series for the testing appears an efficient method in this respect.

ACKNOWLEDGEMENTS The work presented in this paper was performed within the

framework of the CLAROM group, the French Club for research activities on offshore structures. The contributions of project partners are gratefully acknowledged.

The authors wish also to thank Oliveira Sá for providing test ropes, their colleagues that contributed to performing tests and analysing results, and their respective companies for permission to publish this paper.

The views expressed are those of the authors, and do not necessarily reflect those of their respective companies.

REFERENCES [1] Del Vecchio CJM (1992), “Light weight materials for

deep water moorings”, PhD thesis University of Reading

[2] Grosjean F, Davies P, Francois M, (2005), “Synthetic Fiber Ropes mooring: technical status and stiffness prediction”, Proc CMOO4

[3] François M, Davies P, (2000), “Fibre rope deep water mooring : a practical model for the analysis of polyester mooring systems” , IBP 247 00, Rio Offshore 2000

[4] François M, Giulivo R, (2000), “Practical procedures for fibre rope moorings”, Continuous Advances in Mooring & Anchoring, Aberdeen

[5] Davies P et al., (2002), “Synthetic mooring lines for depths to 3000 meters”, OTC14246

[6] François M. (2005), “Fiber ropes for Station-keeping : Engineering properties and qualification procedures”, OCEANS 2005, Washington

[7] ISO 18692:2007, Fibre ropes for offshore station keeping - Polyester

[8] Bureau Veritas, (2007), Certification of fibre ropes for Deep water offshore services, NI432R01

[9] Lechat C, Bunsell AR, Davies P, Piant A, (2006), “Mechanical behaviour of polyethylene terephthalate & polyethylene naphthalate fibres under cyclic loading”, Journal of Materials Science, Vol. 41, pp 1745-1756

[10] Davies P, Baizeau R, Grosjean F, François M, (1999), “Testing of large polyester cables for mooring line applications”, Proc ISOPE, Brest, p360

[11] Davies P, Lechat C, Bunsell A, Piant A, François M, Grosjean F, Baron P, Salomon K, Bideaud C, Labbé JP, Moysan AG., (2008), “ Deepwater Moorings with High Stiffness Polyester and PEN Fiber Ropes” OTC 19315

[12] Davies P et al, (2008), “Infuence of fibre Stiffness on Deepwater Mooring Lines” , OMAE2008-57147


OTC-19450-PP

Impact of the use of FullQTF on LNGC Moored in Shallow Water Studies Cédric BRUN, Flávia REZENDE, Damien COACHE, Johan MOMBAERTS (Bureau Veritas)

Copyright 2008, Offshore Technology Conference This paper was prepared for presentation at the 2008 Offshore Technology Conference held in Houston, Texas, U.S.A., 5–8 May 2008. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract

The prediction of slow drift motions for the design of a mooring system is usually made using the Newman approximation [1], based on the assumption of a very low resonance frequency of the system and small contribution of the second order wave fields. This hypothesis is commonly satisfied for most parts of the mooring systems in deep water. However, this is not the case for LNG terminals moored in shallow water.

Unlike the Newman approximation, the FullQTF formulation to compute the low frequency wave loads is more accurate but requires much longer time of computation, which presents limitations in practice when a large quantity of simulations is needed.

Further to the work presented in [2] on the quadratic transfer function (QTF) of low-frequency loading, a new approximation has been developed in [3]. The F1 approximation gives comparable results to the FullQTF and presents the interesting aspect that the loads time series can be reconstructed by means of simple summations, presenting the same efficiency in computation time as Newman approximation.

In this paper, main parameters of mooring systems are analyzed to evaluate the impact of the choice of each method, Newman, F1 or FullQTF. Indeed, this choice is a compromise between calculation time and accuracy of results. The conclusions raised are underlined in the study of an LNG terminal.

2 OTC OTC-19450-PP

Introduction More and more LNG carriers are built across the world to transport the liquefied gas from a location to another. These

locations sometimes propose LNG terminals in the proximity of the harbors, thus in shallow water. For those terminals, the accurate prediction of low-frequency wave loads is a key issue in the design of mooring systems.

The approximation proposed by Newman (1974) is generally used for the simulations of low frequency loading due to the fact that it is based only on the diagonal terms of the QTF (Quadratic Transfer Functions). Those terms, the mean drift loads, are contributed only by the first-order wave field and body motions and are easily calculated once the first order solution is obtained. In moderate and deep water depths it can be shown that the second order wave field contribution is small comparing to the first order one. This way, the assumptions applied to the Newman approximation are satisfied and the results obtained through this approximation can be considered adequate. However, this is not the case in shallow water, where the contribution of the second order wave field can not be neglected.

The use of the complete QTF matrix gives more accurate estimations of the low-frequency loads, but it requires the solution of the second order problem and the time series reconstruction is more time-demanding. Recently, a new approximation has been presented in [2] and [3] considering that the resonant frequencies of mooring systems are often small (<<1). This approximation consists in developing the QTF as an expansion of difference frequency ω∆ and keeping the terms dependent on the first order quantities T0 and another term T1 linearly proportional to ω∆ . From this expansion two approximations can be derived: the F0 approximation, which is equivalent to the Newman approximation, and the F1 approximation.

In this paper the F0 (Newman) and F1 approximations are compared to the FullQTF considering the influence of the water depth and mooring stiffness. The time efficiency of each method is also addressed.

Finally, the conclusions raised are highlighted in an LNG terminal example, under specific environmental conditions. QTF Formulations

The full quadratic transfer function (QTF) of low-frequency loads is composed of two parts: one depends on the quadratic product of the first-order quantities and another is contributed by the second-order potentials:

( ) ( ) ( )21221121 ,,, ωωωωωω TTT += (1)

The Newman approximation is obtained by disregarding the second term of equation (1). This approximation is based on

the assumption that Ω→0, where Ω = ω1- ω2. For shallow water applications, however, the second-order potentials contributions can not be neglected and the Newman approximation may largely underestimate the low frequency loading.

Recently, a new approximation has been presented in [4]. Assuming Ω<<1, the QTF is developed as an expansion: ( ) ( ) ( ) ( )210

21 ,,, ΩΟ+Ω+= ωωωωωω TiTT (2)

The quadratic transfer function T(ω1,ω2) is then composed of one component T0(ω) depending on ω=( ω1+ ω2)/2 and

another Ω T1(ω) linearly proportional to Ω = ω1- ω2. From this expansion two approximations are derived. The F0 approximation, which is equivalent to the Newman approximation, is based only on the use of T0(ω) so that is of )1(Ο and the F1 approximation that consider also the term Ω T1(ω) so that is of )(ΩΟ .

Considering the fact that:

( ) ( ) ( )[ ] [ ]21/01/01/0 ,,21, ΩΟ++= jjii TTT ωωωωωω with

2ji ωω

ω+

= (3)

The F1 approximation in [3] can be rewritten as:

( ) ( ) ( )[ ] ( ) ( ) ( )( )[ ]jjiijijjiiji TTiTTT ωωωωωωωωωωωω ,,21,,

21, 1100 +⋅−++= (4)

OTC OTC-19450-PP 3

Time series reconstructions

For an irregular sea, the wave elevation can be noted as follows:

( ) ( )

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

ℜ= +⋅−⋅

=∑ ϕωη xkti

N

jjeat

1

with jjj dSa ωω ⋅⋅= )(.2 (5)

Where S(ω) is the irregular wave spectral density and dω is the sampling space of the spectrum. The low frequency loads can now be defined in time domain as below.

FullQTF formulation FullQTF is a two dimensions complex matrix. The Real part of the matrix is symmetrical whereas the Imaginary one is

anti-symmetrical. The low-frequency drift loads time signal using the FullQTF formulation is obtained by a double summation:

( ) ( ) ( ) ( )( )[ ]⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⋅ℜ= ∑∑= =

−+⋅−−⋅−N

i

N

j

xkktijijiFullQTF

ijijijeaaTtF1 1

..,)( ϕϕωωωω (6)

F0 approximation (Newman)

This method consists in approximating |T(ωi, ωj)|² by a function of T(ωi, ωi) and T(ωj, ωj). Thus, the FullQTF double summation can be transformed into the simple following formulation:

( ) ( ) ( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⋅⋅ℜ= ∑∑=

+⋅−⋅⋅

=

+⋅−⋅⋅−N

j

xktij

N

j

xktijjj

jjjjjj eaeaTtF11

00 ..,)( ϕωϕωωω (7)

F1 approximation

Introducing (4) into (6), the time series reconstruction for the F1 approximation presented in [3] can be obtained as follow:

( ) ( ) ( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⋅⋅ℜ−= ∑∑=

+⋅−⋅⋅

=

+⋅−⋅⋅−N

j

xktij

N

j

xktijjj

jjjjjj eaeaTdtdtFtF

11

101 ..,)()( ϕωϕωωω (8)

Remarks

The FullQTF formulation is the most accurate method to describe the physical phenomenon. However this kind of calculation is very time consuming due to the double summation on the frequencies and the calculation of the FullQTF matrix. The F1 approximation is a new method that provides more accurate results comparing to the F0 approximation and presents the advantage that the time series reconstruction can be described as simple summations instead of double summations, hence faster to compute. Numerical results

Different parameter influences are studied before computing a complete example of LNG terminal. Thus, varying water depth, wave period and mooring stiffness, differences between the three methods are evaluated in terms of accuracy and time efficiency. Influence of water depth and peak period of sea state

In this case, numerical calculations are performed for a standard 138km3 LNG vessel with main dimensions (Length, Breadth and Draft) = (274m, 44.2m and 11m), respectively. The half hull mesh is composed of 2204 panels. At a first stage, the vessel is considered fixed and the low-frequency loads are calculated in frequency domain for different water-depths and for sea states with Hs=2.0m and peak periods varying from 6s to 18s. Figures 1 to 6 present the spectral density of low-frequency loads. For each peak period the left bar is used for F0 approximation, the middle bar for F1 approximation and the right bar for the FullQTF. Two differences of frequencies (Ω) are evaluated, 0.025 rd/s and 0.05 rd/s, which are directly linked to the resonance of the mooring system. It can be noticed that the F0 approximation largely underestimates the loads in shallow water comparing to the FullQTF. For moderate water

4 OTC OTC-19450-PP

depth, such like 60m, the F0 approximation may give conservative results except for very long waves. In all the cases the F1 approximation presents results which are comparable to those obtained through the FullQTF.

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

4.50E+05

Tp=6s Tp=8s Tp=10s Tp=12s Tp=14s Tp=16s Tp=18s

Spec

tral

den

sity

(kN

^2.m

^2.s

)

F0 Approximation F1 Approximation Full QTF

0.00E+00

2.00E+05

4.00E+05

6.00E+05

8.00E+05

1.00E+06

1.20E+06

1.40E+06


Spec

tral

den

sity

(kN

^2.m

^2.s

)

F0 Approximation F1 Approximation Full QTF Figure 1 – LF spectral density – WD 15m – Tn ~251s Figure 2 - LF spectral density – WD 15m – Tn ~126s

0.00E+00

2.00E+09

4.00E+09

6.00E+09

8.00E+09

1.00E+10

1.20E+10

1.40E+10

1.60E+10


Spec

tral

den

sity

(kN

^2.m

^2.s

)


0.00E+00

5.00E+09

1.00E+10

1.50E+10

2.00E+10

2.50E+10

3.00E+10

3.50E+10

4.00E+10

4.50E+10

5.00E+10


Spec

tral

den

sity

(kN

^2.m

^2.s

)

F0 Approximation F1 Approximation Full QTF Figure 3 - LF spectral density – WD 30m – Tn ~251s Figure 4 - LF spectral density – WD 30m – Tn ~126s

0.00E+00

1.00E+09

2.00E+09

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6.00E+09

7.00E+09

8.00E+09


Spec

tral

den

sity

(kN

^2.m

^2.s

)


0.00E+00

1.00E+09

2.00E+09

3.00E+09

4.00E+09

5.00E+09

6.00E+09

7.00E+09

8.00E+09


Spec

tral

den

sity

(kN

^2.m

^2.s

)

F0 Approximation F1 Approximation Full QTF Figure 5 - LF spectral density – WD 60m – Tn ~251s Figure 6 - LF spectral density – WD 60m – Tn ~126s

Regarding the two resonance periods studied from Figure 1 to Figure 6, it is shown that the differences between the three methods increase for smaller resonance periods. To highlight this phenomenon, the mooring stiffness influence is studied in time domain. Mooring stiffness influence

LNG carrier motions are analyzed using different mooring system stiffnesses. To study the mooring stiffness influence, a typical reference characteristic shown in Figure 7 is multiplied by coefficients from 0.2 to 2.0 with a step of 0.2.

OTC OTC-19450-PP 5

-10000

-5000

0

5000

10000

15000

20000

25000

0 5 10 15 20 25 30 35 40 45 50 55

Horizontal distance (m)H

oriz

onta

l ten

sion

(kN

)

Figure 7: Mooring system characteristic

In each study case, the same environment is imposed. It is composed of waves (Jonswap spectrum with Hs=3m, Tp=10s

and γ=3.3). Only surge motion direction has been studied for head sea condition. Figure 8 and Figure 9 give a comparison of the vessel motions time series for three different mooring stiffnesses, (from

the softest on the left to the stiffest on the right), comparing respectively F0/FullQTF and F1/FullQTF. 20% of reference stiffness

-6

-4

-2

0

2

4

6

8

-1000 1000 3000 5000 7000

Time (s)

Vess

el p

ositi

on (m

)

Reference stiffness

-6

-4

-2

0

2

4

6

0 1000 2000 3000 4000

Time (s)

Vess

el p

ositi

on (m

)

F0 FullQTF

200% of reference stiffness

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1000 2000 3000

Time (s)Ve

ssel

pos

ition

(m)

Figure 8: Vessel position time series under F0 and FullQTF drift loads

With reference to Figure 8, it can be clearly shown that changing the global mooring stiffness accentuates the differences

between the F0 and FullQTF calculations. Indeed, when the mooring system is very soft, the two resulting signals from F0 and FullQTF are quite similar. On the contrary, when the stiffness is increasing, the time series become more and more different. 20% of reference stiffness

-8

-6

-4

-2

0

2

4

6

8

-1000 1000 3000 5000 7000

Time (s)

Vess

el p

ositi

on (m

)

Reference stiffness

-6

-4

-2

0

2

4

6

0 1000 2000 3000 4000

Time (s)

Vess

el p

ositi

on (m

)

F1 FullQTF

200% of reference stiffness

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1000 2000 3000

Time (s)

Vess

el p

ositi

on (m

)

Figure 9: Vessel position time series under F1 and FullQTF drift loads

Figure 9 shows that the differences in the vessel motions time series when using the F1 approximation or FullQTF

formulation are not as consequent as when using the F0 approximation. Indeed, it seems to suggest that the F1 expression gives suitable results even for the stiffest mooring stiffness evaluated.

In case the F0 approximation is used with a very soft mooring system, the ratio between the F0 and FullQTF time series standard deviation of loads is about 0.8 whereas it could be less than 0.4 for a stiff mooring system (see Figure 10). In fact, the stiffer is the mooring system, the bigger the difference between the F0 and FullQTF time series.

However the ratio between F1 and FullQTF time series standard deviation is less than 1.10 for most of the mooring stiffnesses, except for the stiffest mooring system with a maximum of 1.25 (see Figure 10). In addition, it can be seen that the ratio is always greater than 1.00, which seems to suggest that the F1 approximation is conservative.

6 OTC OTC-19450-PP

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200

Stiffness rate (%)R

atio

of S

td. D

ev.

F0/FullQTF F1/FullQTF

Figure 10: F0 and FullQTF time series standard deviation relative difference function of the stiffness rate Computation efficiency in time domain reconstruction

As shown in equations (6), (7) and (8), the FullQTF reconstruction is based on a double summation on frequencies whereas F0 and F1 are based on simple summations. Figure 11 shows an example of comparison between the methods when irregular waves are reconstructed by 200 elementary airy waves.

0%

20%

40%

60%

80%

100%

FullQTF F0 F1Cal

cula

tion

time

rate

(% o

f max

)

Figure 11: Calculation time comparison between FullQTF, F0 and F1

A solution to make FullQTF calculations faster is to reduce the number of terms of the “double summation”. Thus, a new

parameter called maxΩ is introduced, considering that the vessel is less sensitive to the difference frequency greater than

maxΩ . Only terms of the FullQTF matrix that satisfy the following inequality are taken into account:

maxΩ<− ji ωω (9)

Remark: if Ωmax > ωN - ω0, the complete drift load is calculated whereas if Ωmax = 0. only the mean drift load is computed.

Figure 12 shows that the computation time decreases significantly when Ωmax < 0.4.

020406080

100120

0 0.2 0.4 0.6 0.8 1 1.2

Ωmax (rad/s)

Tim

e ra

te (%

of m

ax)

Figure 12: Double summation time consumption in function

of maxΩ

020406080

100120

0 0.2 0.4 0.6 0.8 1 1.2

Ωmax (rad/s)

Erro

r rat

e (%

)

Figure 13: F(t) standard deviations error rate

Choosing Ωmax = 0., there is no more time dependency, meaning that the time series is a constant signal, and standard deviation is logically 100%. In Figure 13, it is possible to see that the wave drift load time series is well recomposed for

srad /3.0max >Ω , that gives about 20% reduction of the calculation time. This conclusion is set for this particular example. The main notion is that it is possible to analyze a mooring system and

quickly determine a maxΩ in function of its resonance frequency.

OTC OTC-19450-PP 7

Study case: LNG terminal in shallow water In this section, one practical example is used to compare the different low frequency wave loads calculation methods in

order to illustrate the results previously obtained. The selected mooring system is a typical configuration for LNG terminals in shallow water. This system, called Soft

Yoke (SY) is composed of a fixed structure, mooring legs and the yoke (see Figure 14)[5].

Figure 14: SY for LNG terminals (Cortesy of SBM)

The mooring system is modeled by its characteristic horizontal distance/horizontal tension used as the reference one for

the stiffness influence study (see Figure 7). The neutral point is 30 meters from the yoke nose. The mooring system is symmetrical. The LNG carrier can turn around the fixed structure and around the yoke nose. As previously presented, the main properties of the 138km3 LNG carrier are respectively (Length, Breadth and Draft) = (274m, 44.2m and 11m). The water depth is 15 meters and studies are done with 3 hours time series of vessel motions and SY tensions.

In order to be able to compare correctly the different temporal signals, the same wave spectrum is imposed. The selected spectrum is a Jonswap one defined by respectively (Hs, Tp, γ) = (3m, 10s, 3.3). The wave spectrum is discretized into two hundred elementary Airy waves.

A current load is applied in order to change the vessel azimuth with respect to the wave. Different incidences are studied, thus different relative wave headings. Current is supposed to be constant with a velocity of 1.2m.s-1.

Table 1: Simulation results under different environmental conditions

F0 F1 FullQTF F0 F1 FullQTF F0 F1 FullQTF F0 F1 FullQTF

Azimuth std. dev. (deg) 0.00 0.00 0.00 2.88 2.85 3.16 1.47 1.65 1.69 2.27 2.45 2.50North std. dev. (m) 0.63 2.19 2.03 3.58 3.67 4.39 4.74 5.42 5.48 6.83 7.40 7.64East std. dev. (m) 0.00 0.00 0.00 2.35 2.43 2.44 3.01 3.18 3.19 3.52 3.85 4.01Std. Dev. (kN) 167.37 602.91 555.28 125.40 412.72 359.72 185.95 397.28 456.42 323.93 574.88 660.10Relative diff. / FullQTF 0.30 1.09 0.35 1.15 0.41 0.87 0.49 0.87

SY horizontal tension

Vessel position

Wave: 0°, current: 30°Wave: 0°

Wave relative heading at mean position (deg)

Wave: 295°, current: 90°Wave: 0°, current: 60°

0.0 42.128.517.0

Table 1 illustrates the differences between the drift loads calculation methods varying the relative heading between the wave and the vessel. The first point that could be underlined is that for all simulations, F0 approximation underestimates the loads on the mooring system. Indeed, this difference is always over 50% on the standard deviation of loads and is more important in head sea (70%).

Moreover, the F1 approximation presents comparable results to the FullQTF ones. The maximum difference observed is 15%, and F1 could underestimate the loads as well as overestimating them. Conclusions

This paper presents a comparison between different formulations for the calculation of slow drift loads for the applications in shallow water. It has been shown that the F0 approximation, commonly used in practice, largely underestimates the low-frequency loads for shallow water depths (below 60m) or when the mooring system is stiffened.

The FullQTF method, in spite of giving more accurate results, is less efficient in computation time due to the fact that the time reconstruction of the loads is made by double summations instead of simple summations as in the case of F0 approximation. The F1 approximation is a new method to evaluate the low-frequency loads in a more accurate way than F0 approximation. The most interesting aspect of this approximation is that the time reconstruction can be done by simple summations, thus it presents the same calculation time efficiency as the F0 formulation.

8 OTC OTC-19450-PP

Acknowledgments The authors wish to thank SBM for providing mooring system information for this study.

Nomenclature SY = Soft Yoke QTF = Quadratic Transfer Function LNG = Liquefied Natural Gas References

[1] NEWMAN J.N. (1974) – Second Order, slowly-varying forces on vessels in irregular waves, Intl. Symp. Dyn. Marine

Vehicle & Struc. In Waves, Mech. Engng. Pub., London (UK). [2] CHEN X.B & DUAN W.Y. (2007) – Formulation of low-frequency QTF by O(∆ω) approximation, 22nd IWWWFB,

Plitvice (Croatia). [3] CHEN X.B. & REZENDE F. (2008) - Computations of low-frequency wave loading, 23rd IWWWFB, Jeju (Korea) [4] CHEN X.B. (1994) – Approximation on the Quadratic Transfer Function of Low-Frequency Loads, BOSS [5] NACIRI M. & QUEAU J.P. (2003) - The Soft Yoke Mooring and Offloading System for LNG Offloading

Applications, OMAE, Cancun (Mexico)

Tables Table 1: Simulation results under different environmental conditions...........................................................................................7

Figures

Figure 1 – LF spectral density – WD 15m – Tn ~251s .......................................................................................................................4 Figure 2 - LF spectral density – WD 15m – Tn ~126s ........................................................................................................................4 Figure 3 - LF spectral density – WD 30m – Tn ~251s ........................................................................................................................4 Figure 4 - LF spectral density – WD 30m – Tn ~126s ........................................................................................................................4 Figure 5 - LF spectral density – WD 60m – Tn ~251s ........................................................................................................................4 Figure 6 - LF spectral density – WD 60m – Tn ~126s ........................................................................................................................4 Figure 7: Mooring system characteristic............................................................................................................................................5 Figure 8: Vessel position time series under F0 and FullQTF drift loads........................................................................................5 Figure 9: Vessel position time series under F1 and FullQTF drift loads.........................................................................................5 Figure 10: F0 and FullQTF time series standard deviation relative difference function of the stiffness rate .............................6 Figure 11: Calculation time comparison between FullQTF, F0 and F1............................................................................................6 Figure 12: Double summation time consumption in function of maxΩ .........................................................................................6 Figure 13: F(t) standard deviations error rate ....................................................................................................................................6 Figure 14: SY for LNG terminals..........................................................................................................................................................7

Latest evolution of Metocean analysis

practices and their applications Thomas Barberon – Hydrodynamic and Mooring technical department –

Bureau Veritas

Guillaume Gourdet – Offshore Project Engineer – Bureau Veritas

1. Abstract

Lately hydrodynamic analysis performed for moored floating units have known a little

revolution. From the typical Metocean data in directional scatter diagrams format, the industry is

moving to the regular use of hindcast data. These data are presented as a list of sea-states,

including swell, wind sea or secondary swell, wind and current data. The combination of these

effects allows a proper estimation of heading analysis for a turret moored vessel. Thus wave

loads effects can be assessed more accurately, in particular the occurrence of beam and

quartering sea conditions. As results of heading analysis one’s get the common wind and wave

directions with regards to the ship’s heading which may lead to important information regarding

safety and marine operations.

Firstly, the paper details the methodology for heading analysis and the typical required site data..

Secondly, it presents the effect of such analysis of the wave loads applied onto the vessel hull

and some applications in hull structural and fatigue calculations.

The paper follows the different steps of a typical project: review and analysis of Metocean data,

heading analysis, hydrodynamic and spectral assessment. Finally, typical structural classification

finite elements computations are described with ways to adapt them for site conditions.

2. Hindcast data analysis

The first step of every project is the environmental conditions analysis. The results of these

analysis will then be used by most of the different studies done during the project.

In design reports, Metocean data may be given in two forms. The first one is the statistical form

(e.g. intensity versus return period), that eliminates information of simultaneous occurrence of.

waves, wind, and current. The second one is the form of “n” years hindcast data base issued by

meteorological companies.

Time series of environmental parameters are provided for 5, 10, 25 years at 3-hourly (most of the

time) intervals and include the following Metocean parameters:

- Parameters corresponding to the lowest frequency spectral peak (sometime referred to

as swell),

- Parameters corresponding to the highest frequency spectral peak (sometime referred

to as wind-sea),

- Wind speed and direction,

- Current speed and direction.

In reference [9] is presented one solution for the partitioning of waves into swells and wind-sea.

Before processing into hydro/mooring analysis, the assumptions made by the companies

provinding data should be analysed.

- Wave described by an uni-modal or bi-modal / bi-directional spectrum (each part

representing respectively swell and wind seas),

- Spectrum used,

- Wave, wind and current heading (coming from or going to) and characteristics.

As some seastates present some spurious data, these ones have to be removed from the hindcast

data.

Based on the cleaned database, plots are used to assess the validity of the data. One of the most

usefull plot is steepness curves (see Figure 1). This reveals the partitioning between waves and

allows the comparison with steepness curves (ratio Hs/Tz²).

Figure 1: Hs vs. Tz (Swell front) and Hs vs. Tz (Wind Sea front)

Next, in order to assess the validity of the partitioning, a plot Tp_swell vs. Tp_windsea (see

Figure 2) may be investigate. Following example shows typical results where peak periods of the

swell are higher than peak periods of the wind sea.

Figure 2: Tp swell vs. Tp WindSea

After checking the partitioning of the waves, correlation between environmental parameters

should be looked for. An obvious correlation is the wind sea with respect to the wind. Shape of

the plot close to median line indicates a connection between elements. The graph shown on

Figure 3 could also be split according to the seasons (Figure 4 and Figure 5).

Figure 3: Hs Wind sea vs. Wind

Speed


Speed - Winter


Speed - Summer

In case partitioning is well done, a weak correlation between swell intensity and wind intensity is

obtained as shown in Figure 6.

Figure 6: Hs Swell vs. Wind Speed

Relation between a parameter (intensity, period …) versus the direction allows to validate the

data with respect to geographical parameters.

Figure 7: Hs Swell vs. Swell Direction Figure 8: Hs Swell vs. Swell Direction

Figure 7 for example indicates that point is located far from the coast with a prevailing direction

from swell (in a channel for example). Figure 8 shows a sector without swell. This could be close

to a coast. It should be underlined that points in the sector 220°-360° are probably spurious wind

sea seastates.

Directional plots between correlated parameters allow to determine the “intensity” of this

connection. The sharpest the plot is, the closest the parameters are (see Error! Reference source

not found.).

1000Y Scatter Diagram

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14

Tz [s]

Hs

[m

]

Steepness 1/7

Steepness 1/10

Steepness 1/15

Steepness 1/18

Steepness 1/20

1-Y

10-Y

100-Y

Figure 9: Wind Sea vs. Relative

Wind Sea direction

Figure 10: 1000 Year graph

For some Metocean analysis, 1000 years (or 10000 years) data are available. Plotting the couples

(Hs,Tz) for all data allows to get information on the extrapolation of the extreme values. On

Error! Reference source not found., it is clear that extreme values have been computed only

based on steepness curves.

3. Heading Analysis

Heading Analysis are usually performed to obtain the heading of the vessel with respect to global

axis and then to extract the relative heading of the vessel with respect to the environmental

parameters.

Results of these calculations are used for long term and short term computations of

hydrodynamic parameters (wave bending moment, wave shear forces, relative wave elevations,

accelerations, motions ...). Actual link between heading analysis and hydrodynamic computation

is performed by the mean of Fata, BV in house software. The heading analysis itself is performed

by the help of Ariane 3-Dynamic software, which allow to combine wind, current and waves

loads.

Description of the mooring pattern is not fundamental for the simulation of each seastate but

recommended. However, as heading is computed over 3-hours duration (mean heading computed

for each seastate of the hindcast data base), real stiffness of the mooring pattern could avoid

some errors.

Mandatory required data are generally the wind coefficients, wind areas, current coefficients, the

characteristics of the vessel (draft, length, beam …), QTFs (coming from hydrodynamic

software, such as BV-Hydrostar), Added mass, Damping, Metocean parameters…

Optional data could also be required such as mooring lines description (length, composition, …),

anchors positions, pretension in lines at fairlead, water depth, position of the fairlead

Time domain simulation

All environmental parameters (swell, wind sea, current and wind) are taken into account during

the simulations. Mean heading is computed for each seastate based on low frequency time

simulation over 3-hours after a transient time depending of the studied vessel.

As mean drift force are of interest, effect of the seed for wave or wind spectrum is not to be

considered.

Heading Analysis Results

Attention must be given on the fact that software could give equilibrium position that is not the

most stable. In the case of turret moored vessel (majority of mooring pattern encountered in

heading analysis), some “wrong” static position can be found at the beginning of the simulation.

For example, static position with all environmental parameters in line coming from stern can be

found instead of parameters coming from bow.

In some cases, after a time simulation (variable), the vessel could turn around its mooring point

to reach the “normal” steady position.

In the worst case, the “wrong” initial static position can subsists during a long time simulation

(more than 3 hours). That is the reason why it is recommended not to use only the static position

given by mooring software to perform heading analysis.

Result of the total heading analysis is a time serie of heading of the vessel relative to global axis

system (generally North, depending of the model).

Then, this time serie - one result per seastate (time step depending on the database) – is extracted

to be post treated relatively to waves heading.

After having performed the heading analysis, some graphs are interesting to be plotted.

Among these, heading of the vessel relative to environmental parameter is probably the most

important.

Figure 11: Vessel Heading Relative to North Figure 12: Vessel Heading Relative to Wind

Direction

Figure 11 could be compared to the site position. For previous example, the position of the vessel

on a west coast gives parameters to check results.

In Figure 12, it is important to precise how relative heading is computed. Such graph could

permit to give information such as position of the flare, position of equipment onboard.

Figure 13 and Figure 14 represent the heading of the vessel relative to swell and wind-sea

direction. Conclusion is that vessel is governed by wind-sea and not by swell (in this case).

Figure 13: Vessel heading vs. swell direction Figure 14: Vessel heading vs. wind sea direction

Another interesting graph to be plotted is the absolute heading of the vessel in polar coordinate.

All lines connecting two following time step results should be in the vicinity of the circle and not

crossing the circle (large change of direction probably due to wrong heading result or spurious

seastate).

Figure 15: Heading Analysis with sudden change (inversion)

– Probably wrong

Figure 16: Heading Analysis with smooth variation –

Probably correct

For some projects, on-site records are available and should be compared with heading analysis

results. Some examples are given hereafter:

Figure 17: Comparison Heading analysis vs.

Excursion monitoring system

Figure 18: Comparison Heading Analysis vs. Excursion

monitoring system

Previous comparison Figure 17 gives correct results. It should be underlined that some data are

missing around the 24 of July for the on-site data. Moreover, on-site data are given every minute

and heading analysis is performed every 3-hour (due to database time step).

Example Figure 18 shows some spurious cases due to inverted heading of the vessel.

Attention should be care on the fact that vessel could have some temporary periods with heading

forced by tug (for maintenance for example), offloading sequences...

Analysis of parameters time series

The results of the heading analysis are often used to compute motion time series. Motion

response can be computed for each sea-state. Then, motion time serie over 10 (or 20, 25) years

can be analysed.

Figure 19: Roll response over several years Figure 20: Roll response over 12 days

Figure 19 shows the roll response of the vessel over several years. Analysis of the maxima can

be correlated with the season (depending of the hemisphere).

Time serie over lower time duration (1 week) give information on the continuity of the results. If

points are not in accordance with previous and following, results of the heading analysis is

probably wrong (see Figure 20).

Disambiguation of spurious points

When plotting Metocean parameters in function of relative heading, some spurious points can

occur (for example, points surrounded in red in Figure 21).

Figure 21: Wind Velocity vs. Vessel Heading

These points can have a statistical significance and correspond to exceptional events in the

distribution of the values of the Metocean parameters. They can correspond to spurious or odd

events in the hindcast data. First, the Metocean conditions must be recomputed to determine the

validity of the odd points. Afterward, one way to determine whether these points have a

statistical significance is to examine the distribution of the value of the analyzed parameter per

heading.

4. Hydrodynamic Analysis

In this paper, the hydrodynamic computation itself will not be detailed. By hydrodynamic

computations we mean the way to assess hull specific behaviour (motions, accelerations &

waveloads) of the hull using radiation-diffraction methods. The outputs of such analysis are

RAOs (Response Amplitude Operator). These RAOs are then analysed through spectral analysis

in order to get the site and hull specific waveloads. Additional information can be found in [11].

5. Spectral analysis

The structural analysis needs as input the response of the ship at a certain Return Period (RP). In

principle, the response should be obtained by cumulative Long Term (LT) statistics requiring

extrapolation of Metocean data. In lieu of such analysis, Short Term analysis is carried out using

the short term extremes sea-states in each direction.

Short Term & Long term calculation

In the philosophy of a short term calculation, a single sea state is considered representative of the

Metocean condition to be encountered, and the response of the unit of this sea-state is considered

representative of the extreme response. In a long term calculation, each sea state is taking into

account in the unit response.

This type of study in necessary for fatigue study and is generally considered more accurate for

extreme response.

The LT response is then obtained by cumulative long term statistics with BV software, FATA.

The summation over all spectrums is made. Given a sea-state and assuming a Rayleigh

distribution of maximum, the probability associated to a response level S is equal to:

( )( )

−=

2

,2exp,

PSS

PSTHR

STHSp

And then the number of cycle associated to a response level S is:

( ) ( )( )PT

ref

PSPSTR

TTHSpTHSN ,, =

The number of cycle, over all the seastates, associated to a given response level S is equal to:

( ) ( ) ( )( )

∑=

ji PT

ref

PSPS

jZ

jiji TR

TTHpTHSpSN

,

,,

Where:

- T the average duration of a sea-state (3h)

- ),( PS THSp the probability of a given stress level S within a sea-state characterize

by the wave significant height Hs and the peak period Tp

- ( )ji PS THp , the probability to encounter the sea-state Hsi, Tpj

- ( )jE PT TR the mean period of the response for a sea-state with a peak period of Tpj

6. Bureau Veritas FPSO Structural methodology

Once the final waveloads computed we can start structural loading. This first chapter gives an

overview of structural computation in BV. The next chapter will make the link with

hydrodynamic loads.

Bureau Veritas approach is based on the analysis of the stress level acting in the structure (for

yielding, buckling and fatigue strengths) and on its verification according to permissible stresses

ratios. The evaluation is carried out including:

3D FEM coarse mesh models to evaluate stresses and buckling behaviour.

3D fine meshes analysis to complete the necessary structural analysis of primary structural

members from 3D coarse mesh.

Fatigue analysis for connections details

It should be noted that definition of coarse mesh is changing now in Bureau Veritas Rules in

order to harmonize offshore Rules with Common Structural Rules for bulk carriers and double

hull tankers (IACS).

Typical FPSO loading patterns from loading sequences are used for fatigue analysis. While

yielding and buckling analysis can be performed for special loading conditions (inspection,

repair LC…)

For all FPSO calculations, site conditions are applied.

At the end, the following criteria will be considered to identify elements which do not comply

with the Rules criteria for intended operation as FPSO:

Elements with stress ratio above 1.00 do not comply with the applied criteria.

Elements with stress ratio between 0.975 and 1.00 are considered as suspects areas.

Elements with ratio less than 0.975 comply with applied criteria.

Calculations are performed at both tanker and FPSO stages. Tanker phase gives an overview of

the structural integrity of the original vessel against the newest set of Rules. The conclusions of

such study can lead the pre-dry-dock inspections directly to the most critical areas. This study

may also help to determine the level of criticality of elements found critical in FPSO or tanker

phase.

As part of tanker phase, an accumulated damage is also calculated, based on the available trading

history of the ship.

On the other hand, the FPSO assessment enables to define where renewals or reinforcements will

be needed either because of ageing of the structure (corrosion, accumulated damage…) either

because of its new use of FPSO (loading/unloading sequence, site conditions…)

This VeriSTAR approach is generally preceded of a 2D analysis, performed in Mars BV

software. Mars enables to check longitudinal elements and transverse bulkhead against BV Rules

for both hull girder and local scantlings.

Figure 22: 2D Sections

The 3D models can be either a set of partial models (called 3-holds models) to assess separately

each tank either a Complete Ship Model (CSM).

3-holds models are used at first stage of project, to quickly and efficiently assess the strength of

the cargo region. They are generally linked to fix load cases defined in the Classification

Societies Rules.

However offshore engineers are used to adapt these load cases to offshore projects and their

particular wave behaviour (like spread or turret mooring, specific site conditions, etc…)

Finally it is now a common practise to model the whole unit, from transom to bow. These

models generally tolerate a higher flexibility for the loads to use. If this flexibility allows a better

representation of the actual wave loads, it is also synonymous of a lot more of loading conditions

to run, increase the time of the computations and post-treatment.

Figure 23: 3-holds coarse mesh model

(including deck fine mesh)

Figure 24: Complete Ship coarse mesh model

7. Hydro to Structure

Once hydrodynamics waveloads computed with the state of the art methods, hydrodynamic

engineers and structural engineers need to decide how these waveloads should be used in the

structural assessment.

Several types of analysis are performed using direct waveloads computations:

Hull structure analysis

Topsides structure analysis

These two cases include both extreme conditions for yielding and buckling check and fatigue

conditions

Sloshing loads on hull structure

Green waters effects

Slamming

These 3 analyses may also require hydro-elastic methods. This means that stiffness of the

structure should be taken into account in the hydrodynamic analysis. These methods if already

applied for several ship and offshore designs are still quite exceptional studies.

Mooring and offset analysis

Motions analysis

Etc…

Wave loads as described in ship Rules

On the contrary of traditional offshore engineering, naval architects are not used to apply directly

computed wave loads on hull structure. The common way to design a hull is to apply wave loads

from Rules (Classification Rules, mainly based on IACS unified requirements with regards to

wave loads).

These loads are issued from North Atlantic waves conditions, recognised as the worst area for a

ship to sail. A hull design with these loads should then be able to sail all around the world

without any restrictions.

It should however be noted that a few exceptions exist, mainly for shuttle tankers operating

continuously in harsh conditions like in North Sea, or in North Pacific.

For ships sailing in mild environment, classification societies also developed navigation

notations, which limit the areas where the ship is able to sail (tropical waters, sheltered waters,

etc…). These navigation notations are simple coefficient applying to the IACS North Atlantic

waveloads.

The Rules always define a set of load cases to be applied on the hull structure. For example

Bureau Veritas Rules defined 4 basic load cases which combine the following effects of the

waves:

- Vertical bending moment

- Horizontal bending moment

- Vertical shear forces

- Torsion

- Accelerations

- Elevation of the waves as view per the hull

The difficulty of the combination is to know which loads are correlated with the other. For

example, it is quite obvious that maximum vertical accelerations will not happen at the same

time than maximum horizontal acceleration. While vertical bending moment is maximum at the

same time than the crest wave pressure on the side shell.

Wave loads in load case “Acrest” & “Atrough”

Wave loads in load case “B”

Wave loads in load case “C”

Wave loads in load case “D”

Figure 25: BV Combinations of waveloads.

Extracted from the Offshore Rules, Part D, Chapter 1, Section 5

It is also a challenge to define the values of secondary wave loads when trying to maximise one

of them. For example to evaluate the wave vertical bending moment to be applied, when

maximising wave horizontal bending moment. Rules defines default coefficient for these

combinations.

Application of hydrodynamic wave loads on structural models

As for all engineering studies, it is possible to define different methods, depending of course of

what it is the purpose of the study or of the schedule of the project. But it may also depend of the

quality of available data.

BV keeping Rules load cases.

The simplest methods keep the Rules load cases for basis. These methods are quick to put in

place, using Rules Finite Element Software like VeriSTAR Hull.

They do not require complex interactions between structural and hydrodynamic analysis.

At first stage of FPSO projects, it is quite common to perform structural analysis by just applying

a single coefficient to Rules wave loads. This can even be done without hydrodynamic

computations, based on the experience of offshore engineers for well-known areas (like West

Africa, Brazil).

These methods should be used with care and only to pre-project analysis, before any better

hydrodynamic results are available.

When hydrodynamic results are known, it is then possible to tune the Rules load cases wave

loads by wave loads.

For example in the load case maximising the transversal accelerations, the site transversal

accelerations is combined with the site vertical accelerations multiply with the Rules coefficient

for this load case.

This method is known as conservative for extreme computations. However it presents limitations

mainly in 2 cases:

Fatigue issues, because of the difficulties to combine load cases results on a long term

approach.

Exceptional waves, like cyclones when Rules combination of waves loads may not be

realistic.

Direct transfer of wave loads on the structural model is then the next possible step.

Direct transfer

The most common direct transfer is used for Spectral fatigue analysis. In this method, basic data

from radiation-diffraction analysis are applied directly to the structural model: accelerations and

pressure of waves.

At the end of the structural we get stresses RAOs, exactly like RAOs define in the first part of

this paper.

It is then possible to follow the spectral computation defines in the section 5 to get probability of

each stress cycle. These stress cycles and their probabilities are then summed using Miner-

Palmgren formula to get final damage of the details and so fatigue life.

The Spectral Fatigue Analysis takes into account the exact site conditions and the relative

heading of the vessel. It is known as the most up-to-date fatigue methods for ship details.

Apart from the huge numbers of calculations to define stresses RAOs, this methodology is

limited by the linear assumptions done in spectral domain. Even if corrective methods exist, it is

still difficult to interpret results on side shell area, where the wave pressure discontinuity has not

a negligible effect on stress repartition.

Figure 26: Example of stress RAOs for representative heading. Each node required hydrodynamic computation, transfer to structural model and run of FEM.

It is also possible to perform time domain analysis. This is mainly used for extreme

computations, or with specific waves.

In this case the first is to define the wave, defined by its height, length and phase that should be

computed. Then hydrodynamic software can issue wave pressure all along the hull and hull

girder accelerations to be applied on the structural FEM.

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Omega (rad/s)

Str

es

s R

an

ge

(M

Pa

/m)

180°

225°

270°

315°

360°

This methodology avoids spectral assumptions which are not always easy to apply on a structural

model. The main point of this methodology is to select the wave to be run. It is always easy to

use RAOs to select the most critical wave for one effect. However it is much more difficult to be

sure that this wave will be the most critical once combining all the loads it generates.

Limit of transfer

The main point of transferring hydrodynamic results to structural is the difference of

fundamental assumptions in both methodologies. They are particularly critical for

Viscosity, which is difficult to take into account in structural FEM models

Linearity again wave height, which basic assumptions in hydrodynamics, but quite

difficult to apply on structural assessment of side shell area.

Viscosity

While hydrodynamic analysis take into account the viscosity of the liquid, viscosity is not easily

added to structural finite element models (FEM). If the viscosity can be omitted for longitudinal

waveloads, it is an important input for beam sea cases, where roll motion and acceleration are the

some of the main parameters for the computation of

Transversal acceleration,

Wave pressure on side shell in beam sea cases,

Horizontal bending moment.

Viscosity and in particular roll damping calibration is already a challenge for hydrodynamic

analysis. It becomes even more complicated when transferring to structural finite element model,

which in naval architecture does generally not include viscosity capabilities.

For a structural computation it is reasonable assumptions to neglect the viscosity (except in way

of particular appendix such as bilge keel). However in case of direct transfer of wave loads from

hydrodynamic to structural FEM the loads will not be equilibrated, which is not acceptable.

Several methods have been developed to solve this problem. Bureau Veritas spectral fatigue

methodology is applying equivalent forces on the bilge keel to model viscosity effect.

Linearity with regard to wave height

Another point is the linear assumptions of hydrodynamic computation versus the wave height.

Most of the hydrodynamic calculations are not time simulation but spectral simulations (for

computation time reasons). They consider the waveloads as a linear function of the wave height.

Applying such assumptions for a structural model would lead to wrong results in way of side

shell, where the wave pressure is not proportional to the wave height. The following picture

shows the two types of waves.

However this assumption is relatively correct for details far from the side shell.

Linear wave pressures as used in spectral

hydrodynamic analysis

Non linear pressure as needed for time domain

structural analysis

Several methods exist to compensate this assumption. In particular Bureau Veritas recommends

to compute the effect of the missing pressures on a separate model. The stress correction

obtained is then applied to the stress RAOs.

8. Conclusions

To conclude this paper the authors would like to highlight the increase and generalization of high

level technical computation for offshore projects, including fast track conversion projects. This

increase in the number of studies has transferred existing tools and methodologies from research

departments to engineering common practice. It has also highlighted points where the industry

need to improve its standard like for Metocean data, whose quality is not always at the level of

the expected following studies , or areas where research and returns of experience are still to be

gathered.

Nowadays tools and methodologies are available to analyze site data and compute accurate

waveloads for a specific hull design. And these waveloads are now used at different levels in

structural extremes and fatigue computations.

9. Acknowledgement

The authors wish to thank Bureau Veritas for permission to publish this paper. The views

expressed are those of the authors and do not necessarily reflect those of Bureau Veritas.

10. Reference

[1] C. Bran, R. Veyer « Feedback on structural issues from FPSOs purpose built or converted

from oil tankers » OMC2007

[2] Bureau Veritas « Rules for classification of steel ships» 2007

[3] C. Chauviere, J; Esteve « Conversion of offshore floating facilities - How to tackle them with

an asset integrity focus » OSEA 2008

[4] Bureau Veritas « Rules for offshore units» 2007

[5] P. Biasotto, V. Bonniol, P. Cambos « Selection of trading tankers for FPSO conversion

projects » OTC2005

[6] G. Gourdet« Connection hull-topsides: principles, design and return of experience »

DOT2008

[7] IACS « Common structural rules for double oil tanker» 2008

[8] Bureau Veritas NI 493 R01 E, July 2008

[9] R.Lawford, J.Brandon, T.Barberon, C.Camps, R.Jameson “Directional Wave Partitioning and

its Application to the Structural Analysis of an FPSO”, OMAE2008-57041

[10] M.François, C.Morandini, P.Gorf, M.Lewin “Relative Wave Heading of an FPSO in Harsh

Environment” OMAE-FPSO’04-0043

[11] HYDROSTAR FOR EXPERT “Reference guide and Tutorial for Naval and Offshore

Hydrodynamic Application (Summary)”; X-B C, Research Department Bureau Veritas.

[12] Xiao-Bo Chen “Hydrodynamics in offshore and naval application”, Part I, Keynotes lecture

at the 6th Intl Conf Hydrodynamics, Perth, Australia, 2004.

Connection hull–topsides:

principles, designs and returns of experience

Guillaume Gourdet - Bureau Veritas - Naval and Offshore Engineer

I. Abstract

In the 7 last years several findings have highlighted the importance of the system connecting the

topsides structure to the hull. This area at the border between hull design and topsides design is of

uttermost importance for the production integrity. Based on this observation, this paper will

present different existing designs of connection of the topsides to the hull, from stiff stools, to

sliding support. It will then focus on the way to assess such connections in order to insure the

integrity of the connection but also of the hull structures below the deck and of the topsides first

level structures. Interaction between the hull and the topsides will be developed. The paper

finishes on the challenges regarding inspection, maintenance and repairs of these connections. All

along the paper, feedbacks from existing units will be used to illustrate the speech, for converted

and new built units in mild and severe environment. There are approximately 170 Floating Unit

systems in operation or available worldwide. If about 45% of them are FSO with none or limited

topsides, about 55% are FPSO concerned by the question of the connection between their hulls

and their more or less complex topsides.

II. Introduction

There are approximately 170 Floating Unit systems in operation or available worldwide. About

55% are FPSO. FPSO combines the refinery technologies for the topsides and the naval

architecture for the hull. One of the challenges in a FPSO project is to design, assess and validate

the structure between the topsides structure and the hull structure. The hull is under continuous

deformation due to the passing waves and these deformations should be “absorbed” by topsides

structures.

Since the first FPSO in the world, more than 20 years of experience have been gathered. Several

designs have been proved inefficient, expensive to build or on the contrary satisfactory choice.

And if the first FPSO were equipped with light topsides, the topsides are still becoming heavier

and heavier, and not limited to mild environment. Following the technology needs, the structural

assessment of FPSO is increasing in complexity, accuracy and quickness. Nowadays integrated

models, including hull and topsides, are a standard tool of validation of FPSO design for yielding

and spectral fatigue analysis.

This paper describes the different steps to assess the interface between topsides and hull

structure; starting by identifying the different loads to be taken into account, continuing on a

review of design of these interfaces and finishes the presentation of the different ways to assess

them.

III. Topsides loads and hull accelerations

Initially we can considered the hull as a rigid structure, to identified the first set of load than

apply to the interface hull-topsides. The effects of the elasticity of the hull will be described in

section IV.

III.1/ Topsides loads

The first aim of the interface hull-topsides is to transmit the topsides weights to the hull structure!

If topsides weights are generally well known when the project enter in the structural design

phase, their distribution on the topsides structure is known only after a first design analysis.

Moreover the loads distribution between the different support between the hull and the topsides

also depend of the design engineering of the topsides structure. To correctly assess these loads it

is needed to know:

the topsides main structure

the weight and centre of gravity of main equipements

the weight, centre of gravity and inertia of the rest of the topsides (both structure and

smaller equipments)

Depending of the stage of the project, the accuracy of the estimation of these data can lead to

different assumptions regarding the interface assessment. From a basic vertical weight to be

applied on each topsides supports to a fully coupled model. This will be detailed in section VI.

Of course the topsides loads to be transmitted to the hull are also depending of the hull on-site

motions and accelerations. These results are coming from the hydrodynamic analysis.

III.2/ Hull motions and accelerations from hydrodynamic analysis

Hull motions and accelerations are the first results of hydrodynamic computations. It takes into

account the unit shape, weight and inertia to get Response Amplitude Operators (RAOs) for each

of the motions and accelerations. These RAOs are specific to the unit and to the loading

conditions analysed.

Short terms accelerations can then be easily assessed for specific wave types.

However, it is recommended to perform long term calculations based on extended site condition

data. Such site data are now quite common and can be obtained either by on-site measurements

over several years, either by hindcast data.

In particular in case of units equipped with a weathervaning system (such as a turret) correlated

data of waves, wind and current are necessary to estimate the real heading of vessel with regards

to the waves. These heading calculations allow to determine the wave directions as seen by the

unit, depending of the wave heights and periods, but also of the wind and current speed and

direction. This is particularly relevant to assess the quartering and beam sea cases and estimate

how much transversal accelerations (and others transversal effects) will happen on the

weathervaning unit.

Once this heading analysis performed, long term analysis for defined return periods can be done

based on spectral computations.

These accelerations, computed at the centre of gravity of the unit can then be translated to any

point of the unit, considered as a rigid body.

Hydrodynamic analysis taking into account the real stiffness of the hull body, are now being

developed in research department, papers are mentioned in the references.

IV. Hull deformations

As said previously, the main reason of specificity of the interface hull-topsides is that the hull is

far from a rigid structure. The hull, much more than moving to follow the incoming waves, is

also continuously deformed under the wave loads and the internal pressures.

IV.1/ Hull girder deformations

The hull girder deformations can be divided in three main deformations:

Vertical bending moment

Horizontal bending moment

torsion

Those 3 deformations are always a combination of both mass distribution in the hull girder and

wave effect on the hull. Their RAOs are the next results of hydrodynamic analysis, after motions

and accelerations RAOs. Short and long term vertical and horizontal bending moment and torsion

are then computed with similar spectral computation then described for accelerations.

In ship engineering the terms “static” or “still water” analysis are used when assessing the self-

weight of the unit versus the buoyancy. The buoyancy is defined by the hull shape, draft and trim.

The self-weigh is a combination of lightship distribution (steel, piping, equipments, topsides

weights) and compartment fillings. The hull girder effects due to still water loads are known as

accurately as the self-weight distribution is known using stability software, as the on-board

loadmaster (at least for vertical bending moment). At early design stage a maximum still water

vertical bending is defined called permissible. All loading patterns used during the life of the unit

should then stay below this value.

Torsion is traditionally not computed for oil tankers and considered as negligible. However

recent FSO studies lead to such extreme inspection/repair loading pattern, that torsion was no

longer negligible

The wave types of effect on the hull girder depend of:

Waves and ship relative heading

wave length

The amplitude of the effect induced is then linked also to the wave height, the hull shape and

inertia.

The 2 following sections will illustrate each effect separately. But it should be kept in mind, that

the hull always sees a combination of them.

IV.1.1/ Vertical Bending Moment

Static vertical bending moment is generally maximized homogenous loading pattern.

Wave vertical bending moment is maximized in head sea sea-states, for waves about as long as

the length of the ship.

FPSO model in trough of waves

This effect is the one that creates the greater hull girder deflections. And due to the stiffness of

the hull compared to the topsides structure, the topsides are working under forced displacement.

Naval engineers say that elements longer than the tenth of the unit length are fully contributed to

the hull girder vertical bending moment. Even if class societies have generally in their Rules a

more refined way to estimate this participation, finite element models are often the only way to

determine exactly this participation.

For the interface hull topsides, it means that special care is to be paid to stiff modules, if they are

close or longer than the tenth of the hull length.

IV.1.2/ Torsion

Static torsion is generally negligible. When not, it is due to specific loading patterns, such as the

one on the following picture. This type of loading pattern is not common in shipping industry and

so, should be analyzed with the greatest care during FPSO project.

Wave torsion is maximized in quartering sea sea-states. It is strongly linked to the hull shape. It

should be noted than to assess directly the wave torsion, hydrodynamic assessment should know

the centre of torsion.

Deformation under both torsion and bending moment

(pictures of container vessel is used because torsion is easier to show on open-deck vessel)

Torsion is said negligible for ship with a complete deck. (On the contrary torsion is critical for

ships like container vessel with large deck openings). However FPSO loading pattern are

generally more severe than on a ship and it has been shown on several cases than torsion should

not be disregarded.

IV.1.3/ Horizontal bending moment

In ship design, horizontal bending is the moment around the vertical axis. Static horizontal

bending moment is null, since there is no transversal loads in stillwater conditions. This remark is

also applicable in case of pure head sea condition.

On the contrary, when the waves come transversally (beam or quartering seas) the gradient of

pressure between each side of fore and aft parts of the hull can generate a horizontal bending

moment.

View from below of a converted unit

beam sea wave loads inducing horizontal bending moment

Horizontal bending moment should be assessed particularly when wind sea and swell directions

are not directly associated, like for Campos Basin, offshore Brazil. In such case the hull is most

of the time seeing both head and side seas.

IV.2/ Effects leading to deck stresses concentration

Effects described in the previous sections were hull girder effects, affecting the whole ship. In

this section we will detail the effects than can locally modify the deck deformations, being

generated either globally on the hull or locally.

IV.2.1/ Effects of alternate filling

Cargo tank fillings have a direct effect on the hull deformations and so, on the deck structure. In

case of alternate filling the deck and the structures below will be sensible to the global

deformations of transverse and longitudinal bulkheads.

IV.2.2/ Poisson effect

When put in tension a steel piece will of course lengthen, but it will also transversally shorten.

The same thing happens for the deck. When the ship is in hogging, the deck is in tension. So it

will also have the tendency to retract itself transversally. This effect can create non-negligible

transverse effects in pure head sea conditions. Combined with the alternate filling between wing

and center tanks, this is one of the critical effects for the design of deck transverse web frames in

ships.

Typical section of single hull FPSO, under hogging moment and crest of waves

deck transverse webs are under transversal compression

IV.2.3/ Steel dilatation

Dilatation due the variation of temperature between the outside air, the fluid (air, sea water, oil)

below the deck and the temperature of the structure will also generate additional deformations.

This is particularly the case if the oil is warmed, or in tropical area (where the sun is harsh, but

the nights can be cold) or close to the flare tower…

If the dilation is quite easy to estimate at first stage, a refine assessment is much more

complicated due to the number of heating sources and the complexity of screen effect of topsides

elements.

IV.2.4/ Effect of attached structures

Last but not least, the deck deformations are locally depending of the close by structures. The

hull girder effects are generally considered as a forced displacement, due the high stiffness of the

hull. However, it should not be forgotten than the local deformations can be significantly

influenced by the local structure such as:

longitudinal or transverse bulkhead;

Under deck secondary structure;

Under deck reinforcements for the hull equipment;

And, of course, the topsides stools…

The stools arrangement and design depend of the several factors, it will also influence the type of

assessment to be performed.

Typical longitudinal and transverse deformations of ship with super-structures under bending

Discussion regarding the effects of super-structure on neutral fiber of hull section and hull girder

stresses can be found in reference [2]

V. Main interfaces hull topsides:

V.1/ Topsides supports philosophy

Topsides supporting stools arrangements and designs are almost as numerous as FPSOs. They

depend of the topsides equipments needed, of the weather severity of the site and of the hull.

Without trying to be exhaustive here are some criteria to class and assess the stools arrangements.

Number of stools

A high number of stools has the advantage to limit the loads by stools and so limiting the stresses

in the stool and the need for under-deck structure reinforcements. On the other hand that means

that the hull deformations will be much more transmit to the topsides “pallet”, which will have to

sustain it. In harsh environment it can appear to be difficult to design, particularly if the topsides

pallet are long compared to the unit length (around and more than one tenth of Lpp).

This picture highlights the effect of long modules combined with stiff stools: the fore and aft

stools are taking all the deformations

Length of the topside modules

The number of stool has very few effects on the stress concentration in way of first and last stool

at deck level. These stress concentrations are much affected by the length of the modules

compared with the unit length, as already mentioned in this paper.

Stool stiffness

The stool stiffness will generate the stress concentration at the connection with the deck. The

more stiff the design is the more their will be stresses between the hull and the topsides. Several

level of stiffness can be found from the complete stiff stools, which are generally large stools,

with heavy brackets in longitudinal and transversal direction in order to smooth the stress

concentration factor. These brackets should be backed by under-deck deck structure. This type of

stool allows to transmit heavy loads. Then there are some stools stiff in only one direction,

generally done with transverse or longitudinal bracket on the deck. These stool are less efficient

in case of heavy topsides. Stools stiffness can also be determined with the help of sliding joints.

In this case no stiffness will be seen by the connection in the sliding direction.

Example of four stiff stools module topsides.

Four stools, iso-static design

This arrangement aims to be quasi-isostatic. If one stool is generally stiff in every direction the

three others one are sliding in one or two directions in order to avoid too much hyperstatic. These

sliding arrangements allow the deck of the hull to move and be slightly deformed without

transferring too much displacement at the topsides level. Separate like this hull and topsides is

quite satisfying from structural point of view, however the sliding joints and their aging are still a

major engineering piece of work for huge topsides. Nevertheless some of the heaviest topsides in

the world are supported using such stools design.

It should be noted that a critical design load case for sliding joint is a damaged load case with a

lot of heel. Several degrees of heel can happen very quickly on a floating unit, as a recent

example remind us. If these cases are generally not critical for the hull (damaged stability should

be checked by Class Society) the topsides supports should also be designed for such extreme load

cases.

On the left, view of stools of a FPSO, under sagging conditions.

On the right, a view of deformed 4 stools iso-static support.

No real stools, but an integrated deck.

For mild environment, it can also be found a design of “integrated deck”, which allows a large

flexibility in term of topsides module integration on a deck linked to the main deck of the hull by

a series of transversal supports. These transversal supports let the hull move around its

transversal axis without transferring too much displacement on the integrated deck.

Double plate

In some designs, double plates are welded on the deck. Then the topsides stools are welded on

this double plate. If from structural point of view, double plate could be easily assess, in

particular in way of the weld which should transfert most of the loads, from integrity point of

view, this design is not recommended. In fact it leads to risk of undetectable problem such as root

cracking or corrosion between double plate and deck. This 2 damage could both lead to an

unexpected breach on deck and the linked risk of explosion.

Whatever the stools arrangement their integration within the hull structure is a critical point.

V.2/ Integration with hull

Looking at general arrangement of a ship, several points appear to be more adapted to support

high weight, in particular the connection between transverse web frames and longitudinal

bulkheads. Due to the hull girder loads this area is generally strong enough to support heavy

loads. On the contrary this are will support high longitudinal stresses. The stools welded above

such longitudinal primary members should be designed to support theses stresses.

However it is not possible to put all the stools on such areas, and most of them are put above

typical transverse web frames. Of course the deck transverse webs should be assessed for

yielding and buckling due to the additional loads but also local calculations should be performed

for stress concentration areas.

Generally thick insert plates are put in the deck below the stools. However, great care should be

taken to the under-deck structure. This area is quite difficult to inspect and even more difficult to

repair on site due to the necessity of scaffolding. The connection between deck longitudinal

stiffeners and transverse web can be critical in fatigue due to bending. In way of topsides stools

stresses longitudinal stresses can be increased at longitudinal bracket toes increasing this risk of

low fatigue life.

Cut-out on deck transverse web around deck longitudinal stiffeners are very common in shipping

industry. The deck is not loaded and such cut-outs are not critical. But in way of topsides stool

the shear can be significantly increased and the cut-outs may become critical in shear and fatigue

due to shear. In such cases they will need to be closed by collar plates.

It should also be noted than the structure below the deck is generally found very corroded on

older F(P)SOs. This gaseous corrosion has already leaded to on-site steel renewal. It is strongly

recommended to paint this area.

Before detailing the different ways to assess structural integrity of this integration of the stool

topsides within the hull structure in section VII; the next section will introduce typical hull

structural analysis for FPSO.

VI. Hull structural analysis

Bureau Veritas approach is based on the analysis of the stress level acting in the structure (for

yielding, buckling and fatigue strengths) and on its verification according to permissible stresses

ratios. The evaluation is carried out including:

3D coarse mesh models to evaluate stresses and buckling behaviour.

3D fine meshes analysis to complete the necessary structural analysis of primary

structural members from 3D coarse mesh.

Fatigue analysis for connections details

This VeriSTAR approach is generally preceded of a 2D analysis, performed in Mars. Mars

enables to check longitudinal elements and transverse bulkhead against BV Rules for both hull

girder and local scantlings.

Typical FPSO loading patterns from loading sequences are used for fatigue analysis. While

yielding and buckling analysis can be performed for special loading conditions (inspection, repair

LC…)

For all FPSO calculations, site conditions are applied.

At the end, the following criteria will be considered to identify elements which do not comply

with the Rules criteria for intended operation as FPSO:

Elements with stress ratio above 1.00 do not comply with the applied criteria.

Elements with stress ratio between 0.975 and 1.00 are considered as suspects areas.

Elements with ratio less than 0.975 comply with applied criteria.

Calculations are performed at both tanker and FPSO stages. Tanker phase gives an overview of

the structural integrity of the original vessel against the newest set of Rules. The conclusions of

such study can lead the pre-dry-dock inspections directly to the most critical areas. This study

may also help to determine the level of criticality of elements found critical in FPSO or tanker

phase.

As part of tanker phase, an accumulated damage is also calculated, based on the available trading

history of the ship.

On the other hand, the FPSO assessment enables to define where renewals or reinforcements will

be needed either because of ageing of the structure (corrosion, accumulated damage…) either

because of its new use of FPSO (loading/unloading sequence, site conditions…)

VII. Structural Assessment of the interface

The following sections will detail the different ways to assess the interface hull-structure

regarding yielding, buckling and fatigue. They are classed from the most basic to the most

complex one. Each of them can be relevant depending of the status of the project (particularly of

the knowledge of the topsides main structure and weight distribution), but depending of what is

the question to answer, from the easiest: “can the hull structure support my topsides loads?” to

the most difficult: “is my design able to stay 20 years on site?”

For each of the different assessment types, we will try to highlight the advantages and

disadvantages. Of course this list is not exhaustive; project needs and specificities on one hand

and engineer imagination and subtlety on the other hand could lead to slightly different

calculations. But the main methods are summarized here:

VII.1/ Hull partial models and topsides loads

The hull structure is analyzed trough 3-holds FEM models.

Topsides loads are distributed on deck structure by mean of

forces. The lower of the topsides can be modeled or not. For

such analysis the topsides loads are generally obtained through

basic assumptions.

This first level of analysis is particularly adapted for a quick estimation of the global yielding and

buckling capacities of the primary members under the deck:

Upper strakes of longitudinal bulkheads

Upper plates of transversal bulkheads

Deck transverse web and brackets.

For a local assessment of the connection between the stool and the deck structure, the lower part

of the stool can be modeled, and the concentrated loads from topsides analysis input on top of the

modeled stools. With such models, the local design of topsides stools support can be checked,

regarding yielding and buckling.

However these models do not take into account the topsides stiffness between stools. Most of the

time the topsides loads are also maximum topsides loads, combining gravity and hull

accelerations) which are not relevant for fatigue analysis.

Fatigue analysis based on such model will only assess the fatigue due to the hull

dynamic effects.

VII.2/ Hull partial models and main structure of topsides

The hull structure is still analyzed trough 3-holds

model. But this time the topsides are modeled up to the

first main structural level. Topsides weights and inertia

are them distributed either by mean of concentrated

loads on the model, either by an additional weight at

the centre of gravity of the topsides modules.

Based on such models, the effect of hull deformations

on the interaction hull-topsides can be analyzed, and

relevant yielding and fatigue assessment can be done.

VII.3/ Complete models and main structure of topsides

The next level of analysis corresponds to a similar hull-topside interface modelling, but extended

on the whole ship length.

These models increase the accuracy of the hull

girder deformations, in particular in the fore and aft

part of the cargo area, where the hull scantlings and

the topsides design show discontinuities. These

areas are generally more difficult to analyze using

3-holds models.

These models can also better assess the secondary hull girder effects such as horizontal bending

moment and torsion, described previously.

Nevertheless, these models are longer to build than a 3-holds model, due the complexity of the

hull design in the fore and aft part.

VII.4/ Integrated models

The higher level of analysis is a coupled model,

including the whole ship model, the complete

topsides main structures and weight distribution.

The main advantage of these models is that the

topsides weight distribution and inertia is directly

including in the model. The load distribution on topsides stools is then directly calculated by the

software, using an accurate modeling of hull and topsides and the wave induced effects.

These models allow to assess the effect of the interaction hull topsides even in the higher

structural nodes.

Whatever the level used the global weight of topsides and their longitudinal weight distribution is

taken into account for hull girder still water load. For 3-holds, the results from stability or load

master calculations are input in the model. For complete ship model, the hull girder loads are re-

calculated for each load cases.

Wave loads computed trough hydrodynamic studies, will always take into account the topsides

and superstructures mass, centre of gravity and inertia to determine on site accelerations. Wave

bending moment, wave shear and relative wave elevation computation will also use the total

weight distribution.

VIII. Conclusions

To conclude this paper, which was focused on design, here are a few remarks regarding the

inspection/maintenance of the interface hull/tospides. Without carrying out a full risk analysis, it

appears that the interface hull/topsides is a critical area regarding both stress concentrations and

possible consequences. In case of damage and due to the proximity of the deck, the risks of gas

leaking (and so explosion) or hull weakening are quite high. Generally repairs will require hot

works.

On the other hand, in most cases stresses at the deck and topsides level can be reduced by adapted

loading and unloading sequence. It should also be noted that if the part above the deck is easy to

inspect regularly, others part such as under-deck structure are difficult to access, particularly if no

passageways is put in place, but not less critical.

Finally, behind the complexity of FPSO the connection between the hull and topsides structure, at

the border between the hull and the topsides, the marine engineers and the offshore engineers, the

shipyard and the oil industry, should not be neglected. Using the up-to-date naval and offshore

tools, it is now possible to build effective coupled models, integrating both the complete hull

structural mode and the complete topsides structure. These models can then be used to assess

accurately the yielding and fatigue of these connections, under realistic wave loads.

IX. Acknowledgements

The author wishes to thank Bureau Veritas for permission to publish this paper. The views

expressed are those of the authors and do not necessarily reflect those of Bureau Veritas.

Thank also to all of my colleagues of the VeriSTAR team who participated to the various studies

which inspired and guided the writing of this paper. In particular: Cristian Bran and Nolwenn

Lorans, who put in place the fully integrated model methodology; Jose Esteve, who took the time

to read and comment this paper.

X. References:

[1] Owen F. Hughes, “Ship Structural Design: A rationally-based, computer-aided optimization approach”, 1988

[2] Babinet J-N, “Passenger Ships: Contribution of superstructures to overall bending strength”, Bulletin Technique Bureau Veritas, 4 - 1995

[3] Bureau Veritas, “Rules for the Classification of Steel Ships”, July 2007 [4] Bureau Veritas, “Rules for Offshore Units”, June 2007 [5] Arselin E, Cambos P, Frorup U. – Bureau Veritas : “New FPSO rules based on return of

experience” , OMAE FPSO 2004 [6] Malenica Š – Bureau Veritas ; “Hydro-structure interactions in sea seakeeping”, International

Workshop on Coupled Numerical Dynamics 2007. [7] Blandeau F., François M., Malenica Š, Chen X.B. – Bureau Veritas, “Linear and non-linera

wave loads on FPSO”, ISOPE 1999

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INFLUENCE OF FIBRE STIFFNESS ON DEEPWATER MOORING LINE RESPONSE

Peter Davies / IFREMER 29280 Brest, France, [email protected]

Patrice Baron / Doris Engineering 75013 Paris, France

Karine Salomon / Saipem 13321 Marseille, France

Charles Bideaud / Technip 92973 La Défense, France

J-P Labbé / Acergy 92156 Suresnes, France

Stéphane Toumit / Principia 13600 La Ciotat, France

Michel Francois / Bureau Veritas 92400 La Défense, France

Francois Grosjean / IFP 69390 Solaize, France

Tony Bunsell / ENSMP 91003 Evry, France

A-G Moysan / Total 92069 La Défense, France

ABSTRACT ::;



OMAE2008-57147

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:

DIRECTIONAL WAVE PARTITIONING AND ITS APPLICATION TO THE STRUCTURAL ANALYSIS OF AN FPSO

Ruth Lawford Fugro GEOS, Wallingford, UK

Jill Bradon Fugro GEOS, Wallingford, UK

Thomas Barberon Bureau Veritas, Paris, France

Claude Camps Bureau Veritas, Paris, France

Richard Jameson Hess Limited, Aberdeen, UK

ABSTRACT



OMAE2008-57341

A full characterisation of the individual components of a

sea-state is key to enabling the response of an offshore structure to be accurately calculated. This paper discusses the partitioning of a time series of directional wave spectra into wind-sea and swell components with distinct frequency and direction characteristics. Once the wave data have been partitioned, JONSWAP or Pierson-Moskowitz parameters can be fitted to each spectrum using ‘best-fit’ techniques. The result of the partitioning and fitting analyses is a time series of wave parameters defining the wave spectrum for each component of the sea state.

A 10-year site specific time series of directional wave

spectra has been partitioned in this way and used in the analysis of the Triton FPSO, a turret moored FPSO in the central North Sea. The representation of the directionality and magnitude of each environmental force acting simultaneously on the vessel, allows the relative heading of the vessel to be determined and the mooring and hydrodynamic analyses to be performed. These analyses provided input to a structural analysis of the FPSO, which resulted in an inspection plan for monitoring the effects of the metocean conditions on the unit.

1. INTRODUCTION

There is increasing interest among offshore operators and classification societies in performing hydrodynamic and mooring analyses in the time domain, i.e. for several years duration. To calculate the response of a vessel at each time step it is necessary to define the parameters of wave spectra that represent the wave conditions at a particular location. At any one point in time a wave climate consists of a combination of locally-generated

1

Figure 1. Triton FPSO

wind sea, plus swells which have travelled to the site from distant storms. The wind sea and the swells often approach the vessel from different directions and hence it is important to be able to separate these components before fitting analytical spectra to the wave data.

Directional wave data for the vessel location can be in the

form of hindcast or measured data. Typically, hindcast data provides spectral energy values for a range of wave frequencies and directions at 6-hourly time intervals. The spectral data are read into partitioning software which identifies the spectral peaks and then fits a JONSWAP spectrum to each peak using a least-squares fitting procedure. The output from the program is a time series of Hs, Tp, direction and spectral parameters α and γ for each identified seastate. σa and σb may also be provided if required.


Hindcast data such as this has a variety of applications. Here it is applied to the case of the Triton FPSO seen in Fig. 1. Triton is a turret moored FPSO operated by Hess Limited in the central North Sea, see Fig. 2. The vessel is free to weather-vane around the turret in response to the wave, wind and current forces acting on it. Depending on the magnitudes and directions of the applied forces the vessel will take up a heading relative to prevailing environmental conditions.

Figure 2. Location of Triton FPSO in the central North Sea: 57°05’N, 000°53’E

During late 2006 Hess decided that a cost effective, proactive development program to monitor vessel integrity would be advantageous. Analyses were performed by Bureau Veritas to assess the current state of the unit, focusing on the mooring system and the vessel structure. FPSO responses are based on a hydrodynamic analysis, performed by combining the environmental loads at the appropriate headings with the response amplitude operators of the vessel. Key to this analysis is the ability to describe analytically the wave spectra approaching the vessel from different directions. Current and wind effects may also be a factor. Fugro GEOS provided a ten year hindcast metocean time series containing wave spectral parameters for the bimodal spectrum along with wind and current, speed and direction data.

2. PARTITIONING AND FITTING DIRECTIONAL

WAVE SPECTRA

2.1 DATA SOURCE

Hindcast directional wave spectra and wind time series data are obtained from the Fugro Oceanor Worldwaves database. The database is derived from the European Centre for Medium Range Weather Forecasts (ECMWF) Wave Model (WAM) and calibrated against satellite data. Model output may be provided in the form of integrated wave parameters or for a more complete set of information on the sea state a spectral output is available. Bidlot et al [1], provide an overview of recent changes to the ECMWF model and the ongoing

improvement of spectral information. The model currently assimilates wave heights from the ENVISAT satellite altimeter mission launched by the European Space Agency (ESA). Previous to October 2003 the ERS-2 altimeter was used, also an ESA mission. In order to provide spectral output the model utilises more comprehensive, two dimensional observations from Synthetic Aperture Radars (SAR). Since 2000, directional spectra from the model have been available for a range of 24 directions and 30 frequencies. Data from the wa ve model are available on a global grid and for the purpose of this work, ten years of spectral data from the nearest point on the model grid were utilised.

Homogeneity changes in the model present challenges for

the provision of continuous long term hindcast data. For example the failure of an altimeter has been shown to cause changes in the bias and variance when compared to wave buoy data (Bidlot et al [1]). Each satellite mission has a set length and may be replaced from time to time with a more sophisticated altimeter or SAR.

In order to combat these difficulties and provide a fully integrated source of wave data, Fugro Oceanor AS perform bespoke calibration of the model with a range of further satellite data and, if available, in-situ buoy networks. The main source of altimeter data for the calibration has been the Topex/Poseidon mission, which ran from 1992 to 2002 before replacement with the Jason mission. Topex 2 was introduced to follow ground tracks midway between Jason tracks, increasing the amount of data from 2001. The satellite data are reorganised from individual tracks to data contained within a 10° x 10° square areas. All data are retained and no averaging is undertaken. The wave height and wind speed data are corrected to remove bias relative to a large satellite/buoy matched data set and are run through a carefully designed automatic data control. The closest along-track locations for each satellite mission to each grid point are found and time series of the calibrated satellite wave heig hts are extracted. Scatter plots are then produced for the matched wave model against satellite significant wave heights. Any inhomogeneities occurring in the data are investigated and corrected if necessary. This method of calibration has regularly yielded high quality results throughout the North Sea when compared to sources of in-situ data such as that from the Ekofisk and K13 platforms. The wind speed is also calibrated using an analgous procedure. Global comparison statistics for the model against satellite data are presented in Barstow et al [2].

Calibration of this type is applied to each grid point on a

global grid both for the integrated parameters and for the spectrum as a whole. In order to obtain a data set unique to the Triton site, a further site specific calibration was undertaken using data from the closest satellite tracks; Topex and Geosat Follow-On. The resulting calibrated values of significant wave height (Hs) from the wave model are plotted against the closest satellite data in Fig. 3, demonstrating the high quality of these data.


Data are provided as a sequence of spectral matrices for each time step ready for input to the partitioning process. A concurrent time series of integrated wave parameters, wind speed and wind direction is also required as an output from this process

Figure 3. Calibrated model significant wave height (Hm0) against satellite (Hs). 2.2 PARTITIONING PROCEDURE

An established partitioning algorithm detailed in work by Hanson and Phillips [3] and Aarnes and Krogstad [4] which in turn used ideas from Hasselmann et al [5] and Gerling [6] is used to identify the peaks within the spectra for each time step and assign the energy to wind-sea or swell components. Partitioning may be undertaken using spectra from numerical model hindcast data or measured wave buoy data, or to allow comparison between the two, as described in Feld and Mork [7]. A summary of the partitioning methodology is provided in the following sections. 2.2.1 Peak Isolation and Partitioning

Each value or point in the spectral matrix represents a frequency-direction combination. Before analysis begins the number of peaks required is specified. In the North Sea two peaks, one wind-sea and one swell, is usually sufficient to capture the dominant conditions. However the same methodology may be applied to more complex systems where additional swell peaks are expected. The spectral matrix is analysed using the ‘steepest ascent’ method to find the local energy maxima. This is achieved by comparing the spectral energy at each point in the matrix, to each adjacent point and assessing which energy ‘belongs’ to which local peak. If the number of required peaks has been correctly estimated then the number of local peaks should be equivalent to the number of required peaks. In some cases there may be additional local peaks but these are likely to contain small amounts of energy. All energy belonging to that peak will be reassigned to a more

3

dominant peak or discarded according to whether or not it meets certain criteria detailed in the following sections.

2.2.2 Identify and Combine Wind Sea Peaks

After the peaks have been identified they are assigned as either a wind-sea or swell component. Concurrent wind speed and direction data are required to assess whether each peak meets the following criterion:

cp = γw U10 cos δ (1)

where cp is the phase speed of the spectral

component. γw is a factor applied to the wind speed to ensure all possible wind peaks are included.

U10 is the wind speed at 10m elevation. δ? is the angle between the wind and the wind sea (0 = δ ?=? ?π?/2)

Or in deep water: fp = g/2π . [γw U10 cosδ]-1 (2) where fp is the peak wave frequency

The factor γw is variable although is usually specified between 1 and 1.5. A typical value is 1.33.

Any partition whose peak falls within the parabolic boundary defined in the criterion is considered to be forced by the local wind, and all peaks within this region are combined and defined as wind-sea. 2.2.3 Combine Swell Peaks

All peaks not assigned as wind-sea are considered to be swell. If more than one peak is assigned to swell then the peaks are analysed to assess whether or not they are part of the same swell system. If either of the following criteria are met, then the peaks are combined. The factors ?κ and v are variable user-input thresholds.

• Peak separation: Two peaks are combined if the spread of either peak satisfies:

∆f2 = κ.δf2 (3)

where ∆f2 is the distance between the peaks δf2 is the spread of each individual peak κ ???? is the spread function

• Minimum height between peaks: Two peaks are combined if the lowest point between them is greater than the peak minimum factor, ν, times the smaller of the two peaks: s > ν . m (4)


2.2.4 Energy Threshold Check

Low energy peaks are negligible in comparison to the total energy contained within the dominant peaks and these partitions are therefore removed. When working with measured data this step also serves to remove spectral noise belo w a certain energy threshold.

The threshold is calculated from the peak frequency fm

and two user-defined parameters a and b: e = a / (b + f m

4) (5) 2.2.5 Evaluation of Partitioning Method

The Hansen and Phillips partitioning method was compared with wave spectra measured off the west coast of New Zealand by Ewans et al [8]. The comparison showed that in general the method performed well, although in a few cases small low frequency swells were missed because a maximum of two partitions had been specified. Ewans et al also present results using a bimodal spectral fitting method proposed by Guedes Soares [9], which gave a good fit to the measured spectra. However, this method only partitions the data in the frequency domain, and so cannot separate sea states coming from different directions if they have similar peak frequencies.

2.3 FITTING PROCEDURE

2.3.1 Calculation of JONSWAP or Pierson-

Moskowitz Spectra

The partitioning methodology allows identification of the dominant peaks within the wave spectra for each time step. In order to use this information, omni-directional spectra for each peak must be calculated by summing the amount of energy in each partition. Then each omni-directional spectra is approximated using the JONSWAP spectrum, or the Pierson-Moskowitz spectrum if the calculated peak enhancement factor γ is less than or equal to 1. In the North Sea case this will result in one or two spectra for each time step according to the number of peaks identified during the partitioning process.

The aim of the fitting procedure is to obtain values of the

JONSWAP parameters alpha (α)???, gamma (γ), sigma-a(σa) and sigma-b(σb) for each peak. The enhancement widths may be fitted along with alpha and gamma or may be fixed at the accepted values 0.07 and 0.09.

Approximation to the JONSWAP spectra is achieved using the Gunther method. A parabola is fitted to the highest spectral density estimate and one point either side to identify the peak frequency. Alpha is calculated by assuming that the spectrum in the range 1.35fm to 2.00fm can be approximated by

4

the Pierson-Moscowitz spectrum. Given this information it is possible to use a least squares fitting procedure to find the remaining parameters, gamma, sigma -a and sigma-b or just gamma ,? if? sigma-a and sigma-b are fixed values. This involves the input of initial values for the parameters and iterating until the closest match to the function is found.

An example result for one time step is presented in Fig. 4. The dark and light blue areas illustrate how the spectrum is partitioned across the range of frequency and direction. The bottom left hand plot shows the omni-directional spectrum for each of the two peaks, the associated Hs values and whether the peak has been assigned as wind-sea or swell. The bottom right hand plot shows the full omni-directional spectrum of the total seastate and how the combined fitted spectrum compares to the original omni-directional spectrum before partitioning. In this case a good fit has been achieved and the total energy within the sea state is conserved. 2.3.2 Large Gamma Cases

In cases where two spectra are fitted and one of these is a small swell with a low significant wave height, this spectrum will often have a high gamma. As the time series of parameters is prepared for entry to engineering software it is sometimes necessary to enforce a sensible range of values. Typically gamma will be limited to a value of 10. However, limiting gamma will reduce the total wave energy represented by the calculated spectral parameters unless some adjustment is made to conserve the energy in the sea state.

If significant wave height values are calculated from a

peak with reduced gamma then they would be reduced and in turn extreme wave height values derived from the output time series would be underestimated. Therefore a routine has been developed in order to allow limitation of gamma values without loss of energy from the sea state.

This method is undertaken for each time step where one

of the peaks has a gamma value greater than 10 and has been refitted using a gamma equivalent to 10. Alpha must be adjusted in order to compensate for the reduction in energy caused by setting a limit on gamma. The key considerations are the accuracy of the significant wave height and zero-crossing period for the entire sea state. These may be assessed by comparing the original time series data for the sea state as a whole, to the new values calculated from the fitted omni-directional spectrum. Adjustments are made to the alpha value of one of the peaks for that time step so that the correct significant wave height for the total wave energy is obtained and the total mean zero -crossing period value is as close as possible to the required value.


Figure 4. Partitioning and fitting the spectrum.

2.3.3 Quality Control

The rigorous fitting procedure is the starting point for a high level of quality control within the output time series of spectral parameters. In addition for each spectral fit, a normalised rms error and a bias are calculated so that the goodness of fit may be assessed and unacceptable fits may be removed. Each fit is identified in terms of the spectrum used; JONSWAP or Pierson Moskowitz, and whether it has been designated wind sea or swell.

The rms error and bias are available for each peak and if

the values fall outside of an acceptable defined range then individual sea states are flagged or discarded. High error values are most commonly found in the smallest sea states where it is a challenge to fit spectra using standard methods. Error values will also be higher if sigma values are fixed rather than found using the least squares method. If treated as free parameters then sigma values are limited a maximum of 1 and 2 respectively. 2.4 DATA FORMAT

Data are presented in time series format for each of the required parameters. The wave parameters are provided in two components, or more depending on the number of peaks specified. Component one contains the parameters defining the first spectral peak and component two the parameters defining the second peak. Presentation of results is such that

component one corresponds to high frequency spectral peaks and component two corresponds to low frequency spectral peaks. For the majority of records component one will be the wind-sea peak and component two will be the swell peak. In periods of lesser wind influence there may be no wind-sea peak. In this case the spectrum may contain one or two swell peaks. In the case of two swell peaks, component one will contain the higher frequency of the two peaks and component two, the lower.

Further quality control must be applied to maintain

continuity of spectral peaks. This may be achieved by applying an algorithm to track each peak as it grows and decays through time and to ensure continuity in the presentation of the parameters in the two components.

Table 1 lists the parameters that are available from the

analysis. Sigma values for each peak may also be provided if they are not specified as fixed.

The procedure described in this section may be applied to any site using any number of required peaks. For example in areas exposed to swell waves from more than one direction at the same time, more than one swell peak would be required to accurately describe conditions. The approach may then be extended to track individual swells to their original source.


Column Heading Definition

Time Time stamp (GMT)

Hs 1 Significant Wave Height (m) for low frequency spectral peak

Tp 1 Peak Wave Period (s) for low frequency spectral peak

Alpha 1 JONSWAP Equilibrium Range Constant for low frequency spectral peak

Gamma 1 JONSWAP Peak Enhancement Factor for low frequency spectral peak

WavDir 1 Mean Wave Direction (°T, from) for low frequency spectral peak

Hs 2 Significant Wave Height (m) for high frequency spectral peak

Tp 2 Peak Wave Period (s) for high frequency spectral peak

Alpha 2 JONSWAP Equilibrium Range Constant for high frequency spectral peak

Gamma 2 JONSWAP Peak Enhancement Factor for high frequency spectral peak

WavDir 2 Mean Wave Direction (°T, from) for high frequency spectral peak

WindSpd 10-minute Mean Wind Speed at 10m above sea level (m/s)

WindDir 10-minute Mean Wind Direction at 10m above sea level (°T, from)

Table 1. Parameters in the hindcast data set. 3. TRITON FPSO

3.1 METOCEAN REGIME

Directional spectral wave data, partitioned into wind-sea and swell components and approximated to omni-directional spectra, allow the comprehensive study of vessel response in the time domain. It is important that each wave energy source is identified and represented analytically so that all cases are included within calculation of vessel motion and mooring response. If omni-directional or single peak spectra alone are used then the resulting responses could be over conservative. Conversely, important design cases could be missed. Fitted spectral parameters alpha and gamma (and optionally sigma-a and sigma-b) are available for each time step providing a much more accurate description of the sea state than if a typical or average value of gamma were used.

The North Sea is a wind-sea dominated environment. The strongest winds typically come from the sectors between North-West and South-West and conditions are dominated by the passage of anti-cyclonic systems often resulting in strong storms. However, the North Sea also experiences longer period swell waves especially in the more exposed Northern region. In the central and southern North Sea the fetch is more limited in most directions and significant wave heights are lower, although storm waves are steeper with short periods. The Triton FPSO is located in the central area and as such experiences both wind sea and swell effects, although conditions are dominated by the wind. Therefore within the

6

hindcast data set, the sea state for each time step is represented by up to two peaks. Figure 6 plots all wind sea and swell peaks against the peak wave direction (° from). As expected, the data show that the highest waves were generated by the wind-sea peak. The wind-seas approached from all directions with a fairly consistent magnitude apart from the North-East sector. The highest significant wave heights are generated by westerly winds. The swells wave heights were much lower, with the largest swells coming from the north.

Figure 6: Significant wave heights with direction for 2 peaks (each dot represents a sea state).

For the Triton analysis, 10-year hindcast data were provided containing wave spectral parameters for up to two peaks. In addition, a concurrent time series of wind speed, wind direction, current speed and current direction were provided, all of which may impact the heading of the vessel.

The following analyses, similar to a previous study

undertaken by Bureau Veritas [10], were undertaken for the Triton FPSO using the hindcast data:

• Calculation of vessel heading, and hence the heading

of swell and wind-sea relative to the vessel. • Mooring analyses including calculation of fatigue. • The 100 year response of wave bending moments,

wave shear forces, accelerations and relative wave elevation using a long term approach.

• Structural analyses. • Comparison with in-situ measurements.

3.2 HEADING ANALYSIS

Heading analyses were completed using the Bureau Veritas ARIANE-3Dynamics software package. The availability of the time series of partitioned wind-sea and swell, with associated wind and current data allowed vessel heading to be calculated for each sea state at each time step. Further inputs required for this analysis are first order motion


response amplitude operators (RAO’s), quadratic transfer functions, wind and current vessel response characteristics (obtained from wind tunnel tests) and total mooring pattern description in the model.

Results of the heading analysis are presented in Figure 7

below. Each dot represents one three-hour seastate. The study showed that the vessel heading is generally governed by the wind-sea and by the wind directions when intensities are important. However, the Triton FPSO can face wind-sea with Hs equivalent to 4 metres from all directions. There is a weak correlation between vessel heading and swell directions. High intensities of these parameters can occur from almost all incidences.

3.3 HYDRODYNAMIC ANALYSIS

Once the vessel heading, and hence the relative headings of each environmental force, are known the hydrodynamic responses of the vessel can be computed. The computation used the spectral parameters fitted to the partitioned wave data at each time step. The RAOs for the vessel at the relevant headings were combined with the wave spectra to compute the 100-year vessel response at three-hourly intervals. Figure 8 shows the RAO for the vertical wave bending moment amidships compared to a typical energy density spectrum for the site.

The parameters of interest for structural assessment are

wave bending moments, wave shear forces, accelerations and relative wave elevation at any point on the structure. The long-term distribution of each parameter was calculated based on the whole hindcast database. Figure 9 represents the long-term distribution of the vertical wave bending moment amidships and the 100-year extremes. The same approach was repeated along the vessel in order to obtain the 100-year response (Fig. 10). Checks were then made to compare the actual stress levels against the design values in order to monitor vessel integrity. In addition, knowledge of the actual load ranges experienced by the hull enabled fatigue calculations to be carried out with a higher accuracy.

The final aim of the analysis was to ensure vessel

integrity for the future. This included consideration of the possible evolution of the weight of the vessel, for example the addition of topsides, and the extension of the operating life of the vessel. To meet this objective, calculations needed to be as refined as possible to allow an accurate description of the unit to be drawn-up. The availability of hindcast data enabled the conditions that the vessel had experienced over the past 10 years to be reproduced and analysed. It also allowed a good estimate to be made of what the vessel will have to face in the future. Practically, the results from the Bureau Veritas study have yielded a plan for inspections of both the structural elements of the FPSO, and also the mooring lines, prioritizing areas where high stresses are expected. Further work involves long term in-situ measurement aboard the vessel which may be cross-checked with the results obtained using metocean data. This will allow the actual vessel responses to be predicted and ensure that the model and the vessel are in accordance.

Figure 7 (left). Relative headings between each

element incidence and the vessel heading. 180° means that the element is going towards the vessel bow (head waves).


0.0E+00

5.0E+07

1.0E+08

1.5E+08

2.0E+08

2.5E+08

3.0E+08

3.5E+08

4.0E+08

4.5E+08

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2


VWBM (N.m/m)

0.00

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0.08

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0.24

0.28

0.32

0.36

S(w) (m²/s)

VWBM RAO amidships -head seasEnergy density spectrumHs=1m, Tp=12s, gamma=2

Figure 8.Vertical wave bending moment RAO

Long-term distribution of vertical wave bending moment amidships

0.0E+00

5.0E+08

1.0E+09

1.5E+09

2.0E+09

2.5E+09

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1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

Number of cycles

N.m

LT distribution - full LT distribution - intermediate LT distribution - ballast100Y - full 100Y - intermediate 100Y - ballast

Figure 9. Long-term distribution of vertical wave bending moment amidships for different drafts and 100-year extremes.

Vertical wave bending moment along the vessel

0.0E+00

5.0E+05

1.0E+06

1.5E+06

2.0E+06

2.5E+06

3.0E+06

3.5E+06

4.0E+06

0 25 50 75 100 125 150 175 200 225 250

x from aft perpendicular (m)

kN.m

Full Intermediate Ballast

Figure 10. 100-year long-term response of vertical wave bending moment along the vessel for different drafts.


4. CONCLUSION

A time series of wave spectral output from the ECMWF WAM model was obtained and passed through a bespoke calibration procedure using various satellite altimeter data sets. Each individual spectrum from the calibrated time series was analysed using partitioning software. The spectra were partitioned into 1 or 2 peaks using a steepest ascent algorithm and then fitted using the JONSWAP or Pierson-Moscowitz spectrum to give time step specific values of the defining spectral parameters alpha and gamma. This in addition to the usual parameters Hs, Tp and peak wave direction. Quality control checks were applied to the parameters and the data were presented so that parameters associated with a wind-sea peak were contained within the first component of the presentation and parameters associated with the swell peak were contained in the second.

The data were then applied to the case of the Triton FPSO, located in the central North Sea. The partitioned data showed that the highest waves were caused by wind-sea dominated sea-states and that these may originate from a range of direction sectors. Swell waves were highest when originating from the North sector, as a result of the fetch length. Heading analyses were completed for each time step and showed that the heading was governed by the wind-sea and by the wind. Swell waves and current had little effect on the vessel’s heading. Headings were then combined with the wave spectra and motion RAO’s of the vessel to assess vessel response, specifically for the 100-year case. Stress levels were compared with design values. These analyses have resulted in a comprehensive view of vessel integrity providing an inspection plan for monitoring the effects of the metocean conditions on the unit.

ACKNOWLEDGMENTS The authors would like to thank their respective

companies and in particular Hess Limited, for permission to publish the paper. The views expressed are those of the authors and do not necessarily reflect those of their companies.

Thanks are due to Gunnar Mørk and Stephen Barstow at

Fugro OCEANOR AS, for advising on and undertaking the site specific calibration of wave model data with available satellite data for the Triton site.

REFERENCES [1] Bidlot, J.R., Janssen, P.A.E.M., and Abdalla, S., 2005. “On the Importance of Spectral Wave Observations in the Continued Development of Global Wave Models ”, Paper 207, Ocean Wave Measurements and Analysis, Fifth International

Symposium WAVES 2005, Madrid, Spain.

[2] Barstow, S.F., Mørk, G., Lønseth, L., Mathisen, J.P., and Schjølberg, P., 2005. “The Role of Satellite Wave Data in the Worldwaves Project”, Paper 206, Ocean Wave Measurements and Analysis, Fifth International Symposium WAVES 2005, Madrid, Spain. [3] Hanson, J.L., and Phillips, O.M., 2001. “Automated Analysis of Ocean Surface Directional Wave Spectra”, J. Atmos. Oceanic Technol., 18, 277-293. [4] Aarnes, J.E., and Krogstad, H.E., 2001. “Partitioning Sequences for the Dissection of Directional Ocean Wave Spectra: A Review”, Part of work package 4 (Wp4) of the EnviWave (EVG-2001-00017) research programme under the EU Energy, Environment and Sustainable Development programme. [5] Hasselmann, S., Hasselmann, K., and Bruning, C., 1994. “Extraction of Wave Spectra from SAR Image Spectra”, Dynamics and Modelling of Ocean Waves, G. Komen (ed.), Cambridge University Press, Cambridge, UK, 391-401. [6] Gerling, T.W., 1992. “Partitioning Sequences and Arrays of Directional Wave Spectra into Component Wave Systems ”, J. Atmos. Oceanic Technol., 9, 444-458. [7] Feld, G. , and Mørk, G., 2004. “A Comparison of Hindcast and Measured Wave Spectra”, The 8th International Workshop on Wave Hindcasting and Forecasting, Hawaii.

[8] Ewans, K. C., Bitner-Gregersen, E. M. and Guedes Soares, C., 2006. “Estimation of Wind-Sea and Swell Components in a Bimodal Sea State”. Journal of Offshore Mechanics and Arctic Engineering., 128, 265-270.

[9] Guedes Soares, C., 1984. “Representation of Double-

Peaked Sea Wave Spectra”. Ocean Eng. 11(2) 185-207. [10] Francois, M., Morandini, C., Gorf, P. and Lewin., M,

2004. “Relative Wave Heading of an FPSO in a Harsh Environment”, OMAE-FPSO’04-0043, Proc. OMAE-FPSO 2004,Houston,USA.


OTC 19315

Deepwater Moorings with High Stiffness Polyester and PEN Fiber Ropes Davies P /IFREMER Brest, Lechat C, Bunsell A, Piant A /ENSMP, François M /BV, Grosjean F / IFP, Baron P/Doris, Salomon K/Saipem, Bideaud C /Technip, Labbé JP /Acergy, Moysan AG /Total.

Copyright 2008, Offshore Technology Conference This paper was prepared for presentation at the 2008 Offshore Technology Conference held in Houston, Texas, U.S.A., 5–8 May 2008. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract The benefits of synthetic fiber ropes for deepwater station keeping are now well established and their use is expanding. Nearly all current applications use a single grade of polyester fiber, but for different supports and environments this may not be the optimal choice. Properties of polyester fibers can be modified by adjusting processing parameters and there are other fibers available such as PEN, which offer higher stiffness. This study examines the benefits of intermediate stiffness fibres, stiffer than standard polyester but less stiff than the high performance fibers. The results indicate that there is scope for improving mooring line performance and reducing line weight by careful evaluation of material options.

Introduction

Polyester fiber ropes are finding increasing applications in offshore mooring systems as production moves to deeper water. Following successful installations offshore Brazil in the late 1990’s [Pellegrin 1999] the first Gulf of Mexico mooring was for the Mad Dog spar [Bugg 2004] in 2004, which employed 1200 tons of polyester down to 1670 meters water depth. The recently installed Independence Hub platform also used polyester moorings, in 2440 meters water depth [Paganie 2007]. Different rope constructions have been used but these mooring lines were all composed of similar high tenacity polyester fibers. The Red Hawk spar [Haslum 2005], also installed in 2004, used a modified polyester fiber with a higher initial stiffness to facilitate installation, and this raised the question of whether a higher fiber stiffness might be beneficial for other supports and allow rope diameter to be reduced. Previous work within the French Mooring line project [Davies et al 2002] studied high performance fibres such as aramids and HMPE and concluded that their very high stiffness, while allowing much smaller rope diameter and weight, did not improve durability as it would result in high fatigue loading of the metallic components of the mooring line. However, there is an intermediate stiffness region, shown in Figure 1, situated between the currently used fibres, with initial tensile modulus around 10-15 GPa, and the high performance fibers (> 60 GPa) which has not been explored previously for deepwater mooring applications.

Fiber behavior

0

0,2

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0,8

1

1,2

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Elongation, %

Téna

city

, N/te

x

PEN

HMPE, Aramids, Vectran,

Polyester (PET)

INTERMEDIATE STIFFNESSRANGE

Figure 1. Available fiber properties and unexplored intermediate stiffness region

2 OTC 19315

The aim of the present study is to examine under what conditions intermediate stiffness fibers would be attractive for

deepwater moorings. In order to do this it was first necessary to examine how the properties of these intermediate stiffness fibers transfer to ropes. Samples were then manufactured in order to characterize the ropes under appropriate loading conditions, as few stiffness data were available when the study started. Based on these results mooring line analyses were performed for different supports and environmental conditions to determine the influence of the improved rope stiffness. Finally, a series of long term characterizations including creep and cyclic loading was performed, to check whether increased stiffness results in deterioration of long term properties.

Materials and samples Three fibers have been studied, a standard polyester (PET, polyethylene terephthalate) fiber, widely used today for offshore tethers, an improved polyester, and PEN (polyethylene naphthalate), chosen to represent the intermediate stiffness range (fibre modulus around 30 GPa). The difference between the PET and PEN polymers is the presence of a double aromatic ring in the PEN molecule, Figure 2. Figure 3 shows the tensile response of new yarns, the PEN shows an initial modulus roughly twice that of the standard polyester.

Ester group

Figure 2. Structures of polyester PET (polyethylene terephthalate) and PEN (polyethylene naphthalate) molecules

0

0,1

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0,3

0,4

0,5

0,6

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0,8

0 2 4 6 8 10 12 14% strain

N/te

x

Modifiedpolyester

Standard polyester

PEN

Figure 3. Tensile behavior of standard and modified PET, and PEN, tests on new yarns. Stiffness data for the standard fiber ropes are available from previous work e.g. [François 2000], so the present study concentrated on testing the two improved stiffness variants. Table 1 shows the samples studied.

Scale Dimensions

diameter/test length Nominal break load

Single Filament 20-30µm / 50mm 0.5 N Yarn 110 tex 0.4 mm / 1 meter 90 N Assembled yarn 4 mm / 1meter 5 kN Sub-rope 32 mm / 8 meters 330 kN Rope 132 mm / 12 meters 5000 kN

Table 1. Sample sizes tested

All materials were supplied by Performance Fibers, Longlaville, France, with marine finish. Rope yarns and 3-strand

twisted sub-ropes were produced by Bexco, Belgium with the same construction for both fibers. Full size modified polyester ropes, an Integra parallel 7-strand construction, were manfactured by Scanrope, Norway.

OTC 19315 3

Test procedures Various test machines were employed to measure the properties over the range from single fiber up to full size rope. The

single filaments were tested on a special machine, Figure 4a [Bunsell 1971]. Yarns and assembled yarns were tested on a 10 kN test frame, Figure 4b. 500 and 1000 kN test frames were used to test sub-ropes. Two digital cameras linked to an image analysis system were used to measure strains, together with more conventional extensometry. More details of tests can be found elsewhere [Davies 1999, Lechat 2007]. Some samples were in the new state, others were subjected to a bedding-in sequence of 5 load-unload cycles to 50% break load.

aa

cc

bb

Figure 4. Test machines a) Single filament testing, b) yarn tests, c) sub-rope test machine, d) full size rope test.

Single fiber and some assembled yarn tests were performed at the Ecole des Mines de Paris (ENSMP), yarn and

assembled yarn tests were also performed at Ifremer in Brest, tests on over 20 sub-rope samples were carried out at IFP in Lyon and at Ifremer, and full size ropes were tested at the LCPC civil engineering laboratory in Nantes.

Fiber to rope transfer

By testing the components of large ropes at the different steps of fabrication it is possible to evaluate the influence of the fiber properties on the rope behavior. This is important, as if the transfer is poor there may be little to be gained by improving fiber properties. Figure 5 shows mean results from tests at each scale, for the improved PET and PEN fibers.

a) Modified PET

0

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/tex)


b) PEN

0

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/tex)


Figure 5. Stress-strain results, tension loading to failure after bedding-in. (Note different strain scales).

4 OTC 19315

Figure 5 shows the similarities and differences between the two materials. The failure strains are significantly lower for PEN fibers but failure stresses are similar. There is a drop in stiffness of sub-ropes compared to rope yarns but the stiffness transfer coefficients are similar for both materials. The behavior of the PEN fiber is more linear than that of PET after bedding-in. A permanent strain after bedding-in of around 1% is noted for both materials, significantly lower than that measured on standard polyester fibers and ropes. The similar permanent strains for the three levels of construction indicates that this strain is mainly due to orientation of the polymer structure rather than alignment of the rope construction. Based on low level material properties and geometrical parameters rope mechanics equations can be used to predict the quasi-static behavior of sub-ropes quite accurately. This will be reported elsewhere.

Stiffness properties

Mooring line analysis requires stiffness values measured under appropriate loading conditions. These are available for standard polyester but not for modified PET nor PEN, so it was necessary to perform a complete stiffness characterization for these materials. Tests were performed on sub-ropes to measure these values under quasi-static and dynamic loading as specified in the recent ISO document [ISO 2007]. All samples were bedded in by 5 cycles to 50% break load followed by a one hour hold period before starting stiffness measurements. Figure 6 shows examples of both types of stiffness test for PEN.

(a) last 10 of 60 QS cycles

0

20

40

60

80

100

120

2 2,2 2,4 2,6 2,8 3 3,2 3,4

Strain, %

Forc

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(b) Dynamic stiffness, last 10 of 500 cycles

160

165

170

175

180

185

190

4,1 4,15 4,2 4,25 4,3

Strain, %

Forc

e, k

N

Figure 6. Stiffness tests, a) Quasi-static, b) Dynamic high load , PEN sub-ropes

Tests were also performed on a full size modified PET rope to examine whether these sub-rope values correspond to those

of full size ropes. Table 2 presents results, Kr is the normalized load/strain.

Material Quasi-static stiffness Kr Standard PET [François 2000] 15 Modified PET sub-rope 14 Modified PET full-size rope 14 PEN sub-rope 20

Table 2. Example of measured quasi-static stiffness values over the range 10-30% break load

Although the stiffness of the modified PET yarn is higher initially, ie before bedding-in, as shown in Figure 3, after

bedding-in values are very similar to that of the standard PET material. Part of the permanent re-orientation strain has been removed during processing but working properties are very similar to those of the standard material. This is not the case for the PEN ropes, which are significantly stiffer before and after bedding-in, so this material was used subsequently to examine how stiffness affects mooring line response. However, this example shows the importance of understanding the behavior of these materials, as the relationship between yarn properties and useful rope stiffness can be complex. An initial factor of two between standard PET and PEN is reduced to an increase of around 30% for quasi-static rope stiffness and around 15% for dynamic stiffness at 45% mean load. Dynamic stiffness is strongly dependent on mean load [Fernandes 1999, Davies et al 2002].

In addition to these standard stiffness measurements some additional tests were performed on the full size rope to examine the influence of stochastic loading. Various sequences were defined using mooring line analyses for different scenarios and Figure 7 shows one example, for a production platform in the Gulf of Mexico.

OTC 19315 5

(a)

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2000

2100

2200

2300

2400

4,8 4,85 4,9 4,95 5 5,05 5,1 5,15 5,2 5,25 5,3Strain, %

Forc

e, k

N

Figure 7. Stochastic loading of 500 ton modified PET rope, mean load 200 tons. a) Sequence applied, b) Measured response.

These results are discussed in more detail elsewhere [François, 2008] but suggest that in a stochastic sequence, the stiffness does not depend on the amplitude of individual cycles, nor on the period of underlying (low and wave frequency) components.

Mooring line analyses Once the necessary property data had been obtained a number of mooring line analyses were performed to examine how the increased stiffnesses of a rope such as PEN would affect mooring line dimensions. Different supports were considered by the engineering companies participating in the project, for a depth of 2500 meters in two locations, West Africa and the Gulf of Mexico. The Ariane™ software was used, together with fatigue analyses.

Material Quasi-static Dynamic (function of mean load (ML))

Standard PET 15 18.5 + 0.33 ML PEN 20 23 + 0.33 ML

Table 3. Values of Kr used in first mooring line analyses.

Then in a second series of analyses, designed to look for the optimal rope properties, parametric studies of the influence

of stiffness were performed. These studies generated a large amount of data. Three examples of of results are shown below, for a semi-submersible drilling rig and a production platform, both in the Gulf of Mexico, and for a production barge off West Africa. For analysis, two parameters must be specified, the safety factor Tmax/Break load, and the minimum allowable tension Tmin. The choice of values to be taken for a new material clearly has an impact on whether a particular solution is interesting compared to a standard polyester choice. For this test case higher safety factors were taken and a 5% minimum tension was used for PEN, rather than the 2% now usually applied for polyester, taking into account the lack of experience with this product and the uncertainties on load-elongation properties. For the semi-submersible drilling rig with 8 lines and and production rig (a 12 lines system), loop current and hurricane conditions were applied. Tables 4 and 5 show examples of results.

Material Criteria: SF Dyn Intact SF Dyn Damaged Tmin applied Sizing: Diameter Break load

Polyester

1.83 1.375 2%

130 mm 542 T

PEN

2 1.5 5%

144mm 601 T

Table 4. Case study 1, Semi-submersible production platform, GOM 2500 meters depth.

6 OTC 19315

In the first example, the improved behavior of the PEN is clearly occulted by more conservative safety factors and, above all, by the criterion of minimum tension that sets the level of pre-tension in the mooring lines, the level of maximum tensions, hence the size.

Material Criteria: SF Dyn Intact SF Dyn Damaged Tmin applied Sizing: Diameter Break load

Polyester

1.83 1.375 2%

246 mm 1778 T

PEN

2 1.5 5%

246 mm 1778 T

Table 5. Case study 2, Semi-submersible production platform, GOM 2500 meters depth.

It is clear for both examples that with these model parameters there is little to be gained by increasing the line stiffness.

The third example involves a large production barge moored using 16 lines in 2500 meters depth off West Africa. Here the environment is much less severe and the offset criterion is governing the design. Table 6 shows an example of results from this case. The minimum tension criterion was also varied : Figure 8 shows how this affects the rope diameter and weight gain.

Material Criteria: SF Dyn Intact SF Dyn Damaged Tmin applied Sizing: Diameter Break load Prétension

Polyester

1.83 1.375 2%

168mm 782 T 150 T

PEN

2 1.5

5% / 2%

152 / 144mm 648 / 590 T 160 / 120 T

Table 6. Case study 3, Production barge, West Africa 2500 meters depth.

a) Rope diameter, mm

130135140145150155160165170

PET 2% PEN 5% PEN 2%

b) Rope weight, tons

0

200

400

600

800

1000

1200

PET 2% PEN 5% PEN 2%

-16% -23%

Figure 8. Influence of minimum tension criterion on PEN rope diameter and weight gain. These results indicate that the use of a higher stiffness material can lead to significant savings, over 200 tons of material

here. This reduction may also result in associated savings on account of easier handling of a smaller diameter rope and reduced storage requirements during installation. A further gain is to be found in the line pre-tensions, these are somewhat lower in the PEN line and may allow the use of a smaller tensionning system. It should also be noted that these are all

OTC 19315 7

conservative estimates, based on higher safety factors for the higher stiffness material. In order to justify lowering these factors it would be necessary to provide evidence that the long term behavior of the higher stiffness material is at least as good as that of the currently-used polyester ropes.

Long term behavior

Two aspects of the long term behavior of the two materials were considered in this study. This was not intended to be an exhaustive study, clearly further qualification work would be essential if a PEN rope was to be considered for this type of application, but simply to give a first indication of differences compared to the currently-used fiber.

First, creep tests were performed. Several types of test were run; first, constant loads were applied to single filaments and rope yarns for short periods, then sub-ropes were subjected to 3-day creep-recovery cycles, and finally longer creep tests (hundreds of hours) were performed to measure creep rates. Figure 9 shows an example of results for filaments, which indicate no significant difference in creep rates for the two fibers. This suggests that the intrinsic creep mechanisms are similar at a material level.

Creep of filaments

0,0

0,1

0,2

0,3

0,4

0,5

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

Creep load, N/tex

Cre

ep ra

te, %

/dec

ade

PETPEN

Figure 9. Creep rates from tests on single filaments.

Then sub-ropes were subjected to short term creep/recovery cycles at different load levels, Figure 10, designed to produce the parameters for a creep model developed previously (Davies 2003, Chailleux 2005). This allowed a direct comparison of the strains to be expected for load levels of 10, 30 and 50% break load to be determined. The creep rates are again similar for the two materials, but more importantly the overall strains and the permanent strain after unloading of the PEN ropes are much smaller than those measured on the modified polyester. As the modified polyester has already a significantly lower permanent strain than the standard polyester this indicates that the PEN rope may offer further significant advantages during installation in crowded areas. Finally some longer creep tests were performed, up to 50 days, to check the creep response over a longer period, Figure 11.

a) 72h Creep-recovery cycle

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80

Time, h

Load

, kN

b) Sub-rope response

0

1

2

3

4

5

6

7

0 20 40 60 80

Time, h

Stra

in, %

PENPET mod.

Figure 10. Creep/recovery cycle results for new sub-ropes of modified PET and PEN

8 OTC 19315

a) PEN creep 18 days, 40% break load

0

1

2

3

0 2 4 6 8log(t (s))

Stra

in (%

)

(b) strain = m x log(time, h)

00,020,040,060,08

0,10,120,14

0 20 40 60

Creep load, % break load

Cre

ep ra

te, m

PETPEN

Figure 11. Long term creep on sub-ropes, a) example of plots for 40% break load, b) creep rates versus applied load

The creep of PEN is linear on a semi-log plot, Figure 11a, and creep rates are plotted on Figure 11b. It is apparent from these results and other data generated during the project that the creep rates are very similar for the two materials, and similar to previously-published results for standard PET [Del Vecchio 1992, Davies 2000, Grosjean 2005 ].

The other property of interest for mooring line applications is fatigue life. It has now been clearly demonstrated by extensive testing that the fatigue life of standard polyester tethers is more than satisfactory [Banfield 2005]. The aim of the present study was not to generate fatigue data, but in order to obtain a first indication of whether fatigue behavior of PEN is significantly different to that of PET fibers two types of test were performed, tensile fatigue on single filaments and yarn-on-yarn abrasion. First, single filament tensile fatigue tests were performed in air at ENSMP. Figure 12 shows an example of the results, which indicate that the intrinsic tensile fatigue behavior of the PEN is very similar to that of the polyester.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07Lifetime (cycles)

Max

imum

forc

e (N

/tex)

Filaments PET

Filaments PEN

Figure 12. Tensile fatigue S-N curves, zero minimum load, various maximum loads, 50 Hz.

Then yarn-on-yarn abrasion tests were performed in natural sea water at Ifremer according to the standard test procedure [Cordage Institute 2001]. Figure 13 shows results for the two materials compared to the response of a standard yarn. The modified PET behaves in a very similar way to the standard material, the PEN lifetimes are a little lower and close to the recommended values [ISO, 2007]. However, it should be emphasized that whereas the marine finish on the standard polyesters has been developed over many years, the finish for the PEN fibers was not specifically developed for this fiber. Improved yarn-on-yarn abrasion lifetimes could probably be obtained for the latter if further development was carried out.

OTC 19315 9

Yarn-on-Yarn abrasion tests, 110 texin natural seawater

0

1

2

3

4

5

6

0 10 20 30 40 50 60

Applied load, mN/tex

Log

cycl

es to

failu

re

PENStandard PETModified PETISO 18692

Figure 13. Yarn on yarn abrasion results

Qualification of higher stiffness polyester fiber ropes for mooring lines These results suggest that the PEN material behavior is similar to that of standard PET fibers, so that additional safety

margins, as were considered in the above analyses, could be removed, subject to adequate qualification of fibre and rope. The modified polyester fiber ropes studied here were tested and installed on the Red Hawk cell spar [Haslum 2005]. A standard API/ABS test program was performed including full scale break tests and a range of tests on scaled (1:4) ropes including 80000 cycles over a range of 15-45% break load. Those provide confidence in the modified polyester, but, as was shown above, the stiffness properties of the worked rope are very simlar to those of the standard material. For ropes with a new fibre such as PEN or other improved polyester fibre (see below), the process of qualification [Bureau Veritas, 2007] shall focus, besides standard tests, on the two following aspects, as discussed in [François 2005]: - careful identification of the load elongation properties, that could be made for example by tests on sub-ropes, in addition to standard tests on a full size rope, - within the qualification of fibre, which is a pre-requisite to rope qualification, assessment of “in-rope properties” of the fibres for long term endurance and capacity to withstand low minimum load under cyclic loading, by tests on small ropes, and a comparison with results for current polyester grades (see [Banfield 2005]) .

Other material options In the current work PEN was studied, as this is the only fiber in the intermediate range commercially available for rope applications at present. It should be emphasized that this fiber was initially developed for tyre applications and there are potentially a very large range of other PEN fiber properties which could be obtained by appropriate drawing and heat treatment cycles [Wu, 2000]. A lower cost alternative to PEN might be to produce stiffer polyester fibers by drawing and heat treatments, and again development work has shown that polyester yarns can also be produced with a wide range of stiffnesses, up to those of PEN [Parguez, 2004].

While stiffness can be tailored to a particular application the strength of these fibers does not increase with increasing stiffness. However, ongoing research work in Japan has shown that polyester fiber strength can also be significantly improved [Kikutani, 2007] and this may result in an even wider range of possibilities for optimization in the future.

10 OTC 19315

Conclusions

While the polyester fiber grade used extensively today for station keeping ropes has proved very satisfactory, it is only one of a very large family of materials which could be used for this application. In this study the influence of increasing rope stiffness has been examined, and PEN ropes have been used to illustrate how in some locations where offset is the critical design parameter a higher stiffness rope can provide improved performance through smaller diameter lines, weight gain and lower pre-tensions. When strength is the dimensioning factor higher fiber tenacity is required compared to the standard fiber, and the currently available intermediate stiffness fibers do not provide increased tenacity.

This paper has concentrated on the technical advantages of intermediate stiffness fiber ropes. For a particular application the economic benefits of smaller diameter, lower weight ropes, in terms of transport, handling and installation must be offset against the material cost penalty. The latter will depend on the manufacturing route, and in particular on whether the existing polyester route can be modified or if a fiber based on a different molecular structure such as PEN is necessary.

Acknowledgements

This work was performed within Phase 5 of the French Mooring line project. The project, which started in 1996 and was completed in December 2007, involved research institutes (Ifremer, IFP, ENSMP), engineering companies (Acergy, Doris, Principia, Saipem, Technip), the Bureau Veritas and Total. It was performed within the framework of the CLAROM group, the French Club for Research Activities on Offshore Structures.

The authors are grateful to Caroline Muller and René Soenen of Performance Fibers for supplying material samples. The expertise of technical staff at Ifremer (N. Lacotte, A. Deuff, B. Forest, D. Choqueuse and L. Riou) at IFP (J. Bonnaves, P. Hamdoun), at the ENSMP (Y. Favry, C. Teissedre) and at the LCPC (G. LeRoux, B. Philippot) is also gratefully acknowledged.

The views expressed here are those of the authors, and do not necessarily reflect those of their respective companies. References Banfield SJ, Casey NF, Nataraja R, (2005) Durability of polyester deepwater mooring rope, OTC 17510. Bugg DL, Vickers DT, Dorchak CJ, (2004) Mad Dog project: Regulatory approval process for the new technology of synthetic (polyester)

moorings in the Gulf of Mexico, OTC 16089. Bunsell AR Hearle JWS, Hunter RD, (1971) An apparatus for fatigue testing of fibres, Jnl Physics E, 4, 868-72. Bureau Veritas , (2007) Certification of fibre ropes for Deep water offshore services, NI432R01 Chailleux E, Davies P, (2005) A non-linear viscoelastic viscoplastic model for the behaviour of polyester fibres, Mechanics of Time

Dependent Materials, 9, pp147-160. Cordage Institute standard, Test method for yarn-on-yarn abrasion, CI 1503-00, August 2001. Davies P, Baizeau R, Grosjean F, François M, (1999) Testing of large polyester cables for mooring line applications, Proc ISOPE, Brest,

p360. Davies P, Huard G, Grosjean F, Francois M, (2000) Creep and Relaxation of Polyester Mooring Lines, OTC 12176 Davies P, Francois M, Grosjean F, Baron P, Salomon K, Trassoudaine D, Synthetic mooring lines down to 3000 meters depth, (2002) OTC

14246. Davies P, Chailleux E, Francois M, Grosjean F, Bunsell A, (2003), Prediction of the long term behavior of synthetic mooring lines OTC

15379 Del Vecchio CJM (1992), Light weight materials for deep water moorings, PhD thesis University of Reading De Pellegrin I, (1999), Manmade fiber ropes in Deepwater Mooring Applications, OTC 10907. Fernandes AC, Del Vecchio CJM, Castro GAV, Mechanical Properties of Polyester Mooring Cables, Int. J. Offshore & Polar Eng., 9, 3,

Sept. 1999, pp207-213. Francois M, Davies P (2000) Fibre rope mooring – a practical model for the analysis of polyester mooring systems, Rio Oil & Gas, 2000. Francois M, (2005) Fibre ropes for Station-keeping : Engineering properties and qualification procedures, OCEANS 2005 MTS/IEEE -

Washington Francois M, Davies P (2008) Characterization of polyester mooring lines, OMAE2008. Grosjean F, Davies P, Francois M, (2005) Synthetic Fiber Ropes mooring: technical status and stiffness prediction, Proc CMOO4. Haslum HA, Tule J, Huntley M, Jatar S, (2005) Red Hawk polyester mooring system design and verification, OTC 17247. ISO 18692 (2007) , Fibre ropes for offshore station keeping – Polyester. Kikutani T, (2007) Private communication Lechat C, Mechanical behaviour of polyester fibres and fibre assemblies for mooring offshore platforms, PhD thesis (in French), Ecole des

Mines de Paris, 2007. Lechat C, Bunsell AR, Davies P, Piant A, Mechanical behaviour of polyethylene terephthalate & polyethylene naphthalate fibres under

cyclic loading, Journal of Materials Science, Vol. 41, 2006, pp1745-1756 Paganie D, (2007) Independence Hub breaks records through collaboration, innovation, Offshore, volume 67, issue 12th December, Parguez O (2004), Private communication Wu G, Li Q, Cuculo JA, (2000) Fiber structure and properties of poly(ethylene-2,6-naphthalate) obtained by high-speed melt spinning,

Polymer, 41, 8139-8150.

IPTC-12546-PP

LESSONS LEARNT FROM 12 YEARS OPERATIONS OF A HUGE FLOATING PRODUCTION UNIT MADE OF PRE-STRESSED HIGH PERFORMANCE CONCRETE Bertrand LANQUETIN TOTAL S.A., Heidi DENDANI TOTAL S.A., Pascal COLLET TOTAL S.A. and Jose ESTEVE Bureau Veritas

Copyright 2008, International Petroleum Technology Conference This paper was prepared for presentation at the International Petroleum Technology Conference held in Kuala Lumpur, Malaysia, 3–5 December 2008. This paper was selected for presentation by an IPTC Programme Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the International Petroleum Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the International Petroleum Technology Conference, its officers, or members. Papers presented at IPTC are subject to publication review by Sponsor Society Committees of IPTC. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the International Petroleum Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, IPTC, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax +1-972-952-9435.

Abstract The last years have seen an impressive increase of Floating Production Storage and Offloading (FPSO) units deployed all over the world both in number and in variety of designs. But all of them in steel. This paper presents the lessons learned from the huge floating production unit made of pre-stressed high performance concrete in operation for TOTAL E&P Congo. They touch all aspects of the life of the unit, design, construction and maintenance on site. The paper will also present the main key issues for the floating concrete structures and some guidelines on how to avoid them, resting on some of the available existing codes. The unit is in production since 12 years on the N’KOSSA oil field in 170 m water depth. Main characteristics: L 220 m, B 46 m, D 16 m, displacement 107,000 t including 73,000 t for the hull and 34,000 t for the topsides. This concrete unit used for construction 27,000 m3 concrete, 2,350 t pre-stressed steel and 5,000 t passive steel. This paper focuses on the following aspects specific to this floating production unit: - Structural modeling techniques taking into account the non-linear characteristics of concrete and incorporating a description of passive and active steel. - Ageing processes of the concrete units and the general typology of the defects encountered. - Development of a tailor-made inspection program. Pre-stress concrete has many virtues and the fabrication process gets more and more industrialized, with better knowledge of the parameters and how controlling them. This makes it a potential material candidate that can allow new-builds outside traditional shipyards, providing new opportunities. However the paper is not intended to make a recommendation between steel and concrete because this entails many other considerations that are not only technical; the paper remains on the technical ground and shares valuable knowledge on the behavior of floating concrete units on the long term prospective of a field life time and on the integrity management techniques developed to minimize the risk of production shutdown and optimize maintenance and repair costs. Introduction It will now be twelve years since the concrete FPU (Floating Production Unit) NKP was installed offshore Congo. During that time it has undergone one technical stop for process maintenance as scheduled in the design, else has been on uninterrupted service. The unit was built in south of France in 1994-95 and installed one year later in the N’KOSSA oil field in 170 m water depth and some 60 km offshore the Congo Coast. To the authors knowledge it is the biggest floating production concrete unit ever built and in service. Its main dimensions are 220 m long, 46 m wide and 16 m deep. This concrete barge used in its construction 27,000 m3 of concrete, 2,350 t of pre-stressed steel and 5,000 t of passive steel, references [3], [4]. Its displacement (weight of the equivalent volume of water occupied by the submerged body of the vessel) is 107,000 t. Two thirds account for the hull and the remaining 34,000 t are the topsides weight. The production facilities and living quarters for 160 people are fitted on the 10,000 m² deck area which, for construction purposes, is subdivided into six modules: accommodation and central control, utilities, electric power generation, gas compression for re-injection, crude oil, and gas.

2 IPTC-12546-PP

Design production is 120,000 b/d of oil sent to the shore terminal and 1,300 metric tons/day of Liquefied Petroleum Gas sent to an 80,000 cu.m LPG FSO. The unit is hold in place, 70 meters away of the NKF2 platform, in a spread moored configuration by means of 12 mooring lines. Figure 1 shows the unit in place with the fixed platform vaguely seen behind.

Figure 1: FPU NKP

Asset Integrity Management In order to constantly analyze and monitor the condition of the units, a tailor-made methodology has been developed and

implemented since 2004 for the Integrity Management of Total Floating Units currently in operation. The aim of Floating Units Integrity Management is to ensure management and continuous follow up of Floating Units

from the safety, environmental, operational, maintenance and quality management viewpoints. It includes recommendations on inspection, maintenance and repairs. This calls for: 1. Structural and anchoring modeling and analysis (1st assessment and subsequent annual re-assessments). 2. Qualitative RBI implementation (Risk Based Inspection). 3. Yearly reviews of the IRM plan (Inspection, Repair and Maintenance). 4. Data management and storage (including reports). 5. Assistance for Emergency Response. 6. Gives the framework for exceptional analysis. A detailed description of the Floating Units Integrity Management program is given in references [1] and [2]. The program is divided into four complementary, interacting modules as shown on Fig. 2:

1. Structural non linear Finite Element Analysis (FEM) model and dynamic mooring model. (ABAQUS, HYDROSTAR and ARIANE Models).

2. IRM (Inspection Repair Maintenance): inspection plan and schedule incorporating class requirements (renewal of certificates, repairs…), and incorporating RBI (Risk Based Inspection).

3. Database (plans, results of models, inspection reports, class status, etc.), with information shared in a network system.

4. ERS (Emergency Response Service).

IPTC-12546-PP 3

Figure 2: Units Integrity Management Modules

FEA, Anchoring Models &

Management Tool

RBI Analysis & IRM Cycle

Data Management & Reporting

EmergencyResponse

= interaction

Periodical (re-)assessment

In alignment with the integrity management program the unit has been placed within a Classification scope. This holds an important part as the surveys and maintenance actions required by the Classification Society are introduced and accounted for within the system. As they are known in advance they can be arranged to minimize impact on production. The french class society also reviews the work carried out by the Third Party Assistance company who contributes to the content and deployment of the program. Falling within the Class scope of work are the mooring, hull and marine systems, accommodation quarters and helideck structures and topsides connection to deck. In some cases risers and subsea equipment are also included.

Pre-Stressed Concrete FPU presentation The unit is divided in 26 lateral capacities (B and T capacities) and 13 central capacities (C capacities). The lateral capacities can be used as “ballast tanks” but only the 4 tanks in the corners are used on site to maintain trim and pitch. The central capacities are void spaces. Running through the central void spaces as a spine is the “Technical gallery” that connects the aft and fore pump rooms (see dark grey color in figure 3) and provides access to the internal capacities. The “nose” that can be seen on the fore end is a concrete cantilever that supports the flare tower as far away as it can be from the accommodation quarters.

Figure 3: Capacity plan & starboard profile

4 IPTC-12546-PP

The shell is not a full watertight continuous skin. It is pierced in several locations in order to suck in water for different purposes; process plant cooling, ballast, fire extinction means, fresh water production…. The most important of all comes in through space T9 with a pipe (metallic outside and concrete inside) that penetrates the side shell and runs through two capacities before reaching the “piscine”, an enclosed basin within C10. Three pumps (two in service, one spare) then move the water from the “piscine” to the process plant for cooling purposes. As it can be seen from figure 3 the hull self supporting structure is made of longitudinal and transversal walls (called bulkheads) that also provide the internal subdivision. They are made of reinforced concrete through which longitudinal, vertical and transversal tendons (pre-stress cables) extend providing compression in the shell plane directions. Depending on the location their thickness varies from 40 to 80cm. Figure 4 illustrates the most common way naval architects represent the main structure of a vessel, through the midship section, which is a transversal cut done halfway along the length of the unit. On it the transverse main dimensions are given.

Figure 4: Midship section

Concrete pre-stressing Concrete structure prestressing consists in applying a compressive load in order to provide global enhanced properties. The main aim is to maintain the concrete always on compression under the design forecasted external loads. This pre-stress can be applied either internally through the concrete walls or externally. On NKP it’s the former that was applied by using tendons made of several ultra-high.tensile steel strands going through metallic ducts set within the concrete section. The path of these ducts is carefully defined at the design stage having to solve practical constraints (access holes, equipment foundations…) while maintaining the required compressive load. In order to protect the steel tendons and provide a solid concrete section the ducts are filled with injection grout. Quality control procedures are set in place to minimize the risk of having water or air gaps trapped within. Figure 5 shows the horizontal tendons stretching throughout the deck concrete slabs above one capacity to illustrate the grillage density set in place. Each yellow line is a horizontal pre-stress cable within the deck thickness. Highlighted in red are shown the position of the main members; bulkheads and shell. Figure 6 illustrates the transversal cables through one section.

Figure 5: Deck pre-stress grillage

IPTC-12546-PP 5

C6, C7, C8 cables

C5 cables

C1, C3 cables

C2, C3 cables

C2, C4 cables

Figure 6: Cables running through a typical transverse section

In particular the longitudinal tendons were arranged from design in order to provide an overall bending moment in opposition to the hogging (deck in tension) still water bending moment of normal operation. The distribution of the longitudinal cables across a typical section results in a pre-stressing tension barycenter above the section neutral axis. This is illustrated in figure 7.

Figure 7: position of pre-tension centre of application and hull girder neutral axis.

Tensions barycenter

The pre-stress is set in place by a pulling jack capable of tensioning cables up to 200m long. Figures 8 and 9 present the pulling jack and a bundle of pre-stressed tendons. On construction the pulling force is calculated to counteract the friction losses, plus the anticipated loss of tension that will come with time from the concrete shrinkage and creep, the steel relaxation and the cable anchorage penetration into the concrete.

Figure 8: Tensioning phase Figure 9 : Tendons anchored

Once the winch removed the cable distribution of tension will depend on its length and on its path. Figure 10 shows the theoretical variation along a side shell vertical cable that runs from the deck to centerline along the side shell (cables C2 or C3 of figure 6), with active anchorage at both ends (the cables were pulled from both ends before clamping them onto the concrete). As said before, the metallic ducts through which the cables are extended are filled with grout, poured before releasing the pulling jack. This grout (a sort of concrete) will help retain the cables by bondage even if it severed at one point. In such case instead of having a sudden release of the cables tension it will redistribute with a local loss at the point of rupture.

Neutral axis

6 IPTC-12546-PP

"Long L" Cables C2&C3

2.6

2.7

2.8

2.9

3

3.1

0 10 20 30 40 50

Cable length m

Tens

ion

MN

Original Prestress

Modelled prestress

Side shell Bottom Bilge

Theoretic prestress

Modelled prestress"Long L" Cables C2&C3

2.6

2.7

2.8

2.9

3

3.1

0 10 20 30 40 50

Cable length m

Tens

ion

MN

Original Prestress

Modelled prestress

Side shell Bottom Bilge

Theoretic prestress

Modelled prestress

Figure 10: Tension distribution along pre-stress cable

So pre-stressing is done in order to ensure that concrete has a background compression in all directions high enough to keep it in that state even under the maximum operational external loads. In order to ensure appropriate loads distribution and shear capacity the known passive reinforcement steel is embedded in the concrete. They are those bars typically seen protruding from concrete beams in any building site on any city. They are also shown in figure 11, which is a photo taken during construction of the NKP barge. The design of this concrete structure was done according national standards Ref. [7], [8], [9]. Considering the environmental context such procedures enabled to define the operational, ultimate and accident limits.

Figure 11: NKP under construction

Materials Reinforced concrete has three particular properties worth of mention. First, its thermal expansion coefficient is very close to that of steel. This avoids internal stresses from expansion or contraction differences. Secondly, concrete naturally changes state from a flowing material to a solid as the chemical reactions within it take place. When it is poured care is taken to ensure that it occupies all the space between reinforcing steel. As it hardens concrete conforms and bonds to the steel bars, that are usually roughened to increase bonding surface. This bondage avoids relative deflection between concrete and steel and allows considering reinforced concrete as a material on its own as long as it works within the elastic behaviour zone. Third, the alkaline chemical environment provided by calcium carbonate (lime) causes a passivating film to form on the surface of the steel, thus protecting it from corroding. A high performance concrete was used for construction due to its qualities such as flowing capacity for pouring; resistance and low porosity once dried out. Low porosity in particular is essential to reduce phenomena like carbonatation and chloride ingress. As could be expected the steel used for the pre-stressing cables is not the standard marine steel. It has a very high yield limit although very sensitive to corrosion, particularly once loaded.

IPTC-12546-PP 7

Materials used: • High Performance Concrete BHP 70:

• Minimum compressive yield stress : 70MPa • Additive: Silica Powder • Initial resistivity 55 KOhms/m • Permeability < 10-12 m/s

• Passive steel: HA Fe E 500 / Mild Steel 235 • Pre-stressing steel:

• Tensile strength 1860 MPa • Yield limit: 1653 MPa • Young Modulus: 190000 MPa • Protected by steel shaft filled with cement mixtures.

Finite Element Model Analysis A numerical model was built aiming at assessing actual and future conditions. ABAQUS was chosen in order to evaluate the particular behavior of reinforced pre-stressed concrete, mainly due to its non-linear analysis capacity. The dynamic loads (motions and sea pressures) were assessed using HydroSTAR (a 3D diffraction-radiation analysis software) and taking into account the latest site meteocean data. An interface between HydroSTAR and ABAQUS has been developed in order to transfer the hydrodynamic loads directly to the structural model. The model was built with the following particularities: • Reinforced concrete was considered as a homogeneous material with yield capacity values according to tests performed

at construction time and using 3D 20-node solid elements (see Fig.12). Young Modulus was taken from standard literature, see references [8], [9].

Figure 12: FE Model cross section with elements shrinked for better view.

• Pre-stress cables were explicitly modeled, as illustrated in figure 6 showing the cables branching on a transversal section and in figures 13 and 14 where the whole model longitudinal and transverse tendons are presented. The modeled cables tension accounted for the variation of the pre-stressing load along each cable due to friction and losses due to anchorage penetration. The comparison between the theoretical cable tension and the one obtained in the model was seen in figure 10.

Figure 13: FE model longitudinal cables Figure 14: FE model transversal cables

• Concrete creep and shrinkage properties were considered bias coefficients directly applied on the tendons loads, see references [8], [9], [10].

8 IPTC-12546-PP

• Topside loads were introduced as concentrated masses placed at each topside module Center of Gravity (CoG) and connected to its supporting stools at deck through rigid connections as shown in figure 16. The flare tower cantilever support was assessed individually and illustrated in figure 15.

Figure 16: Complete FE model with topside masses and flare.

Operational experience The present section is fed from the experience feedback of the last years during the set in place of the integrity management system. Several different surveys and numerical analyses were carried out in order to define the foundation for the future unit inspection and maintenance plan. Inspection and Maintanance plan Based on drawings review, survey reports and FE results an inspection campaign has been set up. It includes not only the Class requirements but also additional tasks in order to maximize the unit efficiency. The main objectives are: • Identify any defect and the deterioration process:

• Chemical attack. • Corrosion. • Crack. • Coating deterioration. • Accidents.

• Define the severity of damage. • Provide recommendations for repair. • Provide an image of the condition of the unit to be compared in future campaigns. Figure 15: Flare tower

Means of survey Depending on location and inspection time differents means of survey will need to be used. They can be classed as follows: • GVI: Global Visual Inspection or Overall survey. Intended to report on the overall condition of the hull structure and

determine the extent of additional close-up surveys. It should be able to detect meaningful cracks, spills, concrete surface spalling, rust coloring from passive steel corrosion emanating from cracks, material loss, coating deterioration and corrosion of steel structures.

• CVI: Close Visual Inspection or Close-up survey. When carrying out a CVI the details of structural components are within the close visual inspection range of the Surveyor, i.e. normally within reach of hand. Prior cleaning of the inspection area may be required.

• NDT: Non-Destructive Testing. Is a close inspection by electrical, electrochemical or other methods to detect hidden damage. The inspection method requires direct access to the inspected area. Prior cleaning of the inspection item is normally required. For steel elements such methods include MPI (Magnetic Particle Inspection), ultrasonic images and penetrating dyes. For reinforced concrete such methods include the Sclerometer, sonic measures, potential mapping and radiography.

• Sample taking: In some cases the NDT for concrete only provide information of the surface (less than 20mm) and if doubts exist of the actual level of chlorures penetration or carbonatation depth samples may need to be taken. Adequate filling of the space left behind is necessary and procedures and materials to be used have been defined. If the samples are good enough strength tests can be undertaken for confirmation of concrete young modulus and mechanical behaviour.

• IWS: In-Water Survey: Survey carried out underwater by divers and/or Remotely Operated Vehicle (ROV). It usually implies prior marine growth cleaning.

IPTC-12546-PP 9

Inspection Program Finally the inspection program was defined by division of the asset into different zones as shown on figure 17. • Submerged Zone: everything below the water surface at the service draft. • Splash Zone: area submitted to intermittent wetting due to waves. • Atmospheric Zone: comprises structure and equipment on and above the upper deck. • Internal Zone: includes all structure, spaces and reservoirs beneath the upper deck. Each zone is then divided in sub-areas, each of which envelopes structure and/or equipment with similar inspection scopes.

Atmospheric zone

Internal zone

SSppllaasshh zzoonnee

Underwater zone

Figure 17: Zones sub-division

The following two figures 18, 19 are an extract of the inspection schedule and defined tasks for the internal compartments of NKP. Although empty capacities need appropriate ventilation before man-entry and the outer spaces need prior ventilation of the central ones. This means that surveys are carried all along the year as the different capacities are opened, ventilated, inspected and closed.

Figure 19

One of the requirements of the Asset Integrity Management is to know at any time the status of the scheduled inspection campaigns. It is necessary in order for the Integrity Manager to follow the condition of the unit. If a programmed survey has not been carried out he will be informed and make sure it is done. In figure 20 is illustrated an extract of the web-based inspection calendar for NKP. Colour levels indicate the survey status; done, to be done or overdue.

Figure 18

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Figure 20: Extract of web-based inspection calendar

Return of Experience Unconsciously reinforced concrete is understood as a durable, hard material and structures made with it are automatically assumed to be built to last. And that is exactly the impression one has when entering the capacities of the NKP. In its majority the walls are smooth and unscathed and making abstraction one would think himself on the basement of a building and not on a floating structure above 170m of water 60 miles from the coast. The doubts arise with the first cracks and for those not used to work with pre-stressed concrete structures some look menacing. It is then that it has to be recalled that concrete is a continuous chemical reaction and natural cracking is expected (endogenous cracking) during cement hydration. Concrete solidifies and hardens after mixing with water and placement due to a chemical process known as hydration. The water reacts with the cement, which bonds the other components together, eventually creating a stone-like material. During construction as the concrete is poured in different phases, shrinkage from water consumption exists at different levels at adjacent pouring blocks. Cracks may then appear from restrained shrinkage in any of the pourings. Such fissures are usually extremely thin and will end up sealing themselves up if appropriate resin injection is done between pourings, but will still be visible. That’s why simply reporting cracks (except those clearly indicating a significant loss of prestress) is not enough to indicate a problem is occurring. Crack progression with time needs to be recorded. In order to evaluate the risks the FE model is used to try to find an explanation to the defect. The different surveys mentioned above were defined in order to detect typical concrete degradation process namely:

- Effect of sea water on cements (sulfate, chloride), - Lime leaching-carbonation, - Alkali aggregate reaction, - Reduction in cement content and strength, - Increase of permeability (permitting Chloride Ingress), - Fatigue.

As expected from the use of high quality concrete, only a number of the above defects were found on board and are presented on pictures below. Figures 21 & 22 show external hull photos, whereas figures 23 & 24 are pictures taken from the inside:

IPTC-12546-PP 11

Figure 21: outer shell 1: The corner of the hull had been protected by fiber reinforced layer against abrasion from over hanging object like chains, ropes, etc. 2: All steel pipe penetrations are protected by coating 3: The concrete hull was left unpainted and doesn’t present any major defect 4: Metallic inserts or passive bars with lack of concrete cover present local and superficial corrosion 5: Marine growth as usual on offsshore unit 6: Metallic insert protectd by coating

Figure 22 : Manhole on deck 7: Manhole for construction phase creates local corrosion

Figure 23: bottom of internal capacity 8: Anchors of prestress cables 9: Capacity ullage gauge

12 IPTC-12546-PP

Figure 24: inner sufarce of outer shell 10: Pouring bloc joint 11: Typical shrinkage crack

Concrete damage from steel corrosion As seen in the pictures one of the most common detectable defects is steel corrosion. Reinforcing steel (passive steel and pre-stressed cables) in concrete is protected from corrosion due to the formation of a passive oxide film on the surface of the steel. The process of hydration of cement in freshly placed concrete develops a high alkalinity, which in the presence of oxygen stabilizes the film on the surface of embedded steel, ensuring continued protection as long as the alkalinity is retained. However even without mechanical degradation (impacts, abrasion…), there are two major situations in which corrosion of reinforcing steel can occur; carbonation and chloride ingress. Either way the removal of the passive film leads to the galvanic corrosion process. When this occurs the produced rust takes up a lot more space than the originating steel, straining the surrounding concrete. Since concrete is relatively weak in tension, cracks develop, exposing the steel to even more chlorides, oxygen and moisture – and the corrosion process accelerates.

1. Carbonatation: Carbonatation is a process in which carbon dioxide (CO2) from the atmosphere diffuses through the porous concrete and neutralizes the alkalinity of concrete. The carbonation process will reduce the alkakine pH to approximately 8 or 9 in which the passive film is no longer stable. With adequate supply of oxygen and moisture, corrosion will start. The penetration of concrete structures by carbonation is a slow process, the rate of which is determined by the porosity and permeability of the concrete. Carbonatation not only can induce embedded steel corrosion but it also alters the concrete properties. 2. Chloride ingress: Chloride ions can enter into the concrete from de-icing salts or from seawater in marine environments. If chlorides are present in sufficient quantity, they disrupt the passive film and subject the reinforcing steel to corrosion. The levels of chloride required to initiate corrosion are extremely low. Macro cell corrosion can develop from differences in chloride ion concentration in different parts of the concrete structure. Such variations of chloride ion concentration are found whenever concrete deteriorates.

Chlorides penetration and carbonation levels were measured at different locations on NKP. In all locations the values showed high quality concrete with weak depths of both phenomena. As Figure 25 presents, the chloride depth on the outer shell after 7 years on site is limited to the first 10mm.

However, there are places were the steel elements had a too thin concrete layer and steel has been reached as seen on the pictures 21 & 22. As it is a superficial defect (no more than 20mm in shells that are 500mm thick) the repairs are relatively easy to carry out with appropriate scaffolding were necessary. Figure 25: Chlorides penetration after 7 years on site at outer shell

IPTC-12546-PP 13

In addition, the following corrosion protective systems were set in place at building stage: - Structure cathodic protection: Cathodic protection is a technique to control the corrosion of (reinforcing) steel by making the steel the cathode of an electrochemical cell. CP is defined as the reduction or elimination of corrosion by making the metal a cathode by connecting it to a sacrificial or galvanic anode, or via an impressed direct current. Cathodic areas in an electrochemical cell do not corrode. If all the anode sites are forced to function as current-receiving cathodes, then the entire metallic structure would be a cathode and corrosion would be eliminated. Electrical Continuity of all passive steels and other structural metallic parts is necessary for obvious reasons. 183 anodes (the anodes on internal shell are located in the four capacities used as water ballast tank at the corners of the unit) provide a steel-reference electrode potential around -850 mV as recommended in reference [7] and are intended to protect the reinforcing steel. - Exposed steel structures painted: High quality coating will eventually fail with time as shown of pictures 21 & 22. It is then necessary to clean exposed steel and repaint in order to avoid loss of steel and concrete damage. One way to check if corrosion of embedded steel is occurring is by means of potential mapping. If corrosion exists the current flow in the concrete is accompanied by an electrical field which can be measured at the concrete surface, resulting in equipotential lines that allow the location of the most corroding zones at the most negative values. This is the basis of potential mapping, the principal electrochemical technique applied to the routine inspection of reinforced concrete structures. The use of the technique is described in Ref.[12]. On NKP all measured potentials correspond to a very low probability of corrosion (less than 10%). Apart of visual examination of anodes oxidation the working order of the cathodic protection can be carried out by measuring the steel potentials in concrete versus reference cells. On NKP anodes showed consumptions of around 10% and potential measurements between -950 and -1100mV that correspond well to literature to the Aluminum anodes used.

Figure 26 & 26: NKP at construction site showing anodes on side shell and location of these on a cross section.

Concrete cracking. Concrete cracks due to tensile stress induced by shrinkage or stresses occurring during setting or use. As mentioned earlier shrinkage cracks can occur when concrete members undergo restrained volumetric changes (shrinkage) as a result of its water consumption either from autogenous shrinkage or thermal effects (concrete dries faster than normal). Plastic-shrinkage cracks are immediately apparent, visible within 0 to 2 days of placement, while drying-shrinkage cracks develop over time. Althoug high-performance concrete can accept a minor degree of tension it is insignificant compared to its capacity to resist compressive loads. Therefore it is usually considered as having no capacity for tensile stress and if a member is under tension loads it is the steel reinforcements that are assumed solicited. On NKP nearly all the significant cracks detected have been declared as plastic-shrinkage. Exceptions are found on the fore end where, due to flare heating, superficial drying-shrinkage cracks have developed. On the flare tower cantilever support surface signs indicate the structure probably got close to operational limit during towing phase.

FE Model comparison with real life

The FE assessment has verified that the design construction keeps the overall structure in compression. However the structural analysis has highlighted some localized areas where lack of compression can be found. These localized areas coincide with the findings of the inspection showing superficial defects, mostly due to practical difficulty of concrete reinforcement in these areas. Examples are degradation of deck edges and flare tower support ends, the latter having pre-stress cables ending on them. All of those are easy to repair and don’t need a high-tech qualification to bring back to as-built situation. Flare tower cantilever surface cracks were explained by the FE model showing that the design was optimized for the site conditions. Particular surveys have been defined for this member as a result of the numerical calculations.

14 IPTC-12546-PP

Figures 26 and 27 show the areas with localized lack of compression.

Figures 27, 27: Highlighted areas with lack of compression. Fore end and whole model.

Main conclusions So far it has been concluded that an efficient cathodic protection was set in place and is actively protecting reinforcement steel.

The choice of high quality of concrete is proving adequate protection agains carbonation and chloride penetration as well as satisfying ageing.

After 10 years concrete hull maintenance and repairs basically consisted on restoring concrete surface cover lost from abrasion and impacts.

Design enhances capacity inspectability. Spaces are open without intermediate members blocking the view (in opposition to webframes and secondary stiffening on steel vessels). GVI is easily done with a number of fixed illumination sources although additional means of access for CVI of the upper parts are necessary.

The main background danger will always be steel corrosion.

A better comprehension of structure aging process could have been obtained if samples had been prepared during construction and left on board (in order to have same ambient conditions) for posterior strength and mechanic properties tests. Similarly pre-stressed samples for fatigue capacity re-assessment should have been performed prior construction and not just base design values on literature. Although concrete preparation is now a well-known science it is also true that there are never two alike as their final properties depend on the used local water and aggregates.

Construction quality control is a must to ensure durability. Once properly set up with competent personnel the building site can be placed nearly anywhere without need for an empty drydock slot.

The definition of the Floating Units Integrity Management program for NKP has allowed changing from a passive and corrective action frame into a proactive scheme. Main non-accidental degradation process and most exposed locations have been identified enabling to set in place an inspection program particular to NKP. It has also made apparent that the sooner such a system is set in place the better. If it can be kept in mind during design it would help on the definition of means of access and identify critical members that cannot be repaired/replaced on site and allocate appropriate safety margins, not only to external loads but also corrosion allowance.

The creation of a finite element model representing as close as possible the as-built and site conditions has helped understand survey outcome. It also means that in case of accident it could be used to evaluate the condition of the unit and help make the right decisions. References 1. Lanquetin B. TOTAL S.A.: “Floating Units Integrity Management and Life Cycle Enhancement”, Offshore Europe 2005 Conference,

Aberdeen 6-9 September 2005. 2. Lanquetin B. TOTAL S.A.: “Experience gained from Floating Units Integrity Management”, paper OTC 18146, OTC 2006, Houston 1-

4 May 2006. 3. Lanquetin B. TOTAL S.A., Collet P. Bureau Veritas, Esteve J. Bureau Veritas “Structural Integrity Management for a Large Pre-

Stressed Concrete Floating Production Unit” paper 29535, OMAE 2007, June 10-15 2007, Sandiego, California. 4. Crozat F. “NKossa barge”, VSL News, 1995, n.2 v.6. 5. Valenchon C. Bouygues Offshore “A Concrete Oil Production Barge, Congo”, Structural Engineering International, February 1996, n.1

v.6. 6. Colliat J-L. TotalFinaElf, Boisard P., Andersen K., and Schröder K.: "Caisson Foundations as Alternative Anchors for Permanent

Mooring of a Process Barge Offshore Congo", paper OTC 7797, OTC 1995, Houston.

IPTC-12546-PP 15

7. “Electrochemical corrosion protection – Cathodic protection of concrete reinforcement – Buried or immersed works”, Normalisation Francaise A 05-611 February 1992.

8. French National Pre-stressed Concrete Standard BPEL 91. 9. Norwegian Standard NS 3473.E3. 10. R. Chaussin, A. Fuentes, R. Lacroix, J. Perchat.: “La Précontrainte”, Presses de l’Ecole Nationale des Ponts et Chaussées. 11. Denys Breysse et Odile Abraham “Méthodologie d’évaluation non destructive de l’état d’altération des ouvrages en béton”, Presses de

l’Ecole Nationale des Ponts et Chaussées. 12. ASTM C876-80, Standard Test Method for Half Cell Potentials of Reinforcing Steel in Concrete.

RULES AND CLASSIFICATION

Building practical rules from theoretical knowledge and new tools requiresdeep evaluation. The papers in this section show how new understandingsin structural behaviour of containerships and deep water moorings can bebuilt into class rules. The papers also cover development of rules forsubmarines and the future of maritime regulation.



A COMPREHENSIVE AND PRACTICAL STRENGTH ASSESSMENT METHODOLOGY FOR CONTAINER SHIPS TAKING INTO ACCOUNT NON LINEAR AND HYDRO-ELASTIC LOADING G de Jong and M Huther, Bureau Veritas, France SUMMARY The drive for economy of scale effects has fuelled the strong growth in size and capacity of new container ships. The combination of relatively low hull girder stiffness and high speed (decreased natural frequency of hull girder vibrations and increased wave encounter frequency) may cause phenomena which are of second order for average size vessels to become of high importance for these large vessels. This is particularly the case for vibratory structural response and associated fatigue damage caused by whipping and springing. Making use of experience feedback with calculations and full scale measurements this paper presents a methodology to estimate the consequences of these phenomena during the design stage of the vessel. Practical application of the methodology has been made possible by further developing the Bureau Veritas in-house hydrodynamic suite HydroSTAR to take into account hydro-elasticity and non linear time domain simulations. The software has been validated against model tests, while a full-scale measurement campaign is ongoing. Application of the methodology to ultra large container ships confirms that stress levels are indeed increasing. As a consequence, a significant increase both hull girder loads and fatigue damage accumulation is found, which can no longer be ignored when analysing the ship structure. When considering future designs for even larger container ships of 400 m in length and beyond, the effects of whipping and springing will become even more important. 1. INTRODUCTION Over the past five years the maximum size of Post-Panamax container ships has increased dramatically to achieve economy of scale effects. Together with the rapid growth in trade volume and mileage between the emerging production economies in the Far East and the established economies (mainly Europe), as well as a firm belief that market share is the key for future success, an unprecedented surge in new orders for ultra large container ships (ULCS, 10 000+ TEU) has been created. According to data published by Clarkson, the world orderbook for this segment stood at 187 vessels at the end of the first quarter of 2008. The majority of these giant boxships are expected to be delivered in 2009 (17%), 2010 (29%) and 2011 (43%). Although the turmoil in the financial markets and uncertainty regarding economic growth (possible slowdown in China, fear for recession in the US, high oil price) have drastically reduced the amount of new orders in the first quarter of 2008, there is no reason to believe that the drive for increasing the vessel size will come to a halt at the present maximum of 13 300 TEU for a ship overall length of about 370 m1. Therefore, realizing that a new upheave in container ship ordering would probably produce designs of well over 400 m in length, it is of key importance to reflect on the technical challenges associated with scale enlargement of ultra large boxships.

1 The only exemption is the E-class series of Maersk, with an estimated capacity of 15 200 TEU and a length of 397 m according to data from AXS Alphaliner.

In fact, if the increase in size is achieved through extrapolation of existing ship dimensions and application of environmental loads estimated from dimensional analysis, it may be expected that phenomena which are of second order for average size vessels can become important for large vessels. This is particularly the case for vibratory structural response and associated fatigue. Experience feedback shows that two dynamic phenomena affecting the hull girder require specific attention when considering large container ships: whipping (transitory hull girder vibrations caused by hydrodynamic impact at the bow) and springing (excitation of the first natural modes of vibration of the hull girder). Indeed, increasing the size of ships with large deck openings will decrease the natural frequencies of hull girder vibrations, while an increase in service speed will result in a higher wave encounter frequency. Consequently the wave encounter frequency may be in the same range as the lowest hull girder natural frequencies, causing important dynamic amplification effects. As it is not fully clear to what extent these phenomena are covered by the implicit and explicit safety margins of classical rules and regulations, the effect of the dynamic behaviour of large container ships in a seaway is to be studied by direct calculations. In this paper the two phenomena and their impact on ship structures are analysed. In addition, the methodology recently developed by Bureau Veritas to assess whipping and springing effects in large container ship is presented, as well as the implementation into the in-house developed hydrodynamic simulation suite HydroSTAR.

2. WHIPPING Whipping can be characterised as transitory response of the hull girder in the first natural mode caused by hydrodynamic impact at the bow due to re-entry of the foreship into the water (slamming) or violent wave impact at the stem (slapping), see figure 1. Figure 1: Container ship experiencing slamming The first natural mode of the hull girder could be simulated by a system with one degree of freedom damped at the corresponding frequency. The associated forces are extremely high but of short time duration, similar to an impulse [1] and consequently infer transitory damped vibrations. 2.1 SHIP STRUCTURAL RESPONSE Slamming and slapping are known to occur in head seas when the vertical (relative) motions are highest. The deformations associated with the hull girder vibration caused by hydrodynamic impact are superimposed on the wave induced hull girder deformations, see figure 2. Figure 2: Full scale measurements of stresses in the deck of the vessel Marcel Bayard It has been known for several years that ships with large deck openings are prone to sustaining damages as a result of whipping. First of all, the design value of the vertical bending moment can be exceeded, causing permanent deformation of the hull girder. Secondly, high frequent stress cycles can be generated, causing premature fatigue cracks in structural details [2, 3]. The understanding and analysis of the phenomenon of exceeding the acceptable bending moment is relatively straightforward, while the prediction of the occurrence of fatigue cracks is much more difficult. However, the risk for fatigue damages has been clearly demonstrated on the vessel Marcel Bayard. In fact, the full scale measurement campaign [2] was initiated after the appearance of fatigue

cracks when the vessel was only three years in service. The study showed that, although the vessel length is only 110 m, the cracks could be explained by frequent occurrence of whipping as a result of particular operating conditions for this type of vessel and large deck openings causing high stress concentrations in the deck. Therefore, it is important to be able to estimate effects of whipping on the stresses in the deck during the design stage. This requires the combined simulation of the behaviour of the vessel under wave loading and hydrodynamic impact caused by slamming and slapping. 2.2 CALCULATION METHODS Direct calculations on a ship in a seaway in order to determine the extreme hull girder loads and the fatigue life of structural details have been common practice for some decades. The methods used are based on the fast spectral approach and are, after calibration, sufficiently accurate for the classical checks. As whipping is a non linear impulsive phenomenon, the (linear) spectral approach does not longer hold. Instead, time domain methods have been developed which can solve the coupling problem between the 3D hydrodynamic diffraction-radiation calculations and the dynamic deformation of the hull girder modelled as a Timoshenko beam or a 3D finite element model. For this modal approach the motions and deformations of the vessel are represented by a series of six rigid modes and five to ten dry structural modes [4]. It is to be noted that the linear hydrodynamic coefficients in the time step equations are obtained from the classical frequency domain calculations [5, 6]. There are two methods available for the determination of the slamming and slapping loads (dynamically exciting the hull girder), which are essentially 2-dimensional: the ‘Generalized Wagner Model’ and ‘Modified Logvinovich Model’. The determination of the structural response to whipping is possible by combined application of calculation tools for the rigid ship in the frequency domain and for the elastic ship in the time domain (non linear). This set of tools was successfully verified on vessels of 260 m and 360 m of length [7], see figures 3 and 4. Figure 3: Example of time history of non linear bending moment time including whipping

Cwp∆SwCwp∆Sw

=+

Figure 4: Zoom of figure 3 at the instant of hydrodynamic impact (response types: elastic non-

linear, rigid non linear and rigid linear) The calculations are performed according to the scheme shown in table 1. Table 1: Step-by-step procedure for estimating the

extreme hull girder loads


2


3 Determination of navigation conditions for which slamming could occur (wave incidence, ship speed, wave height)

4 Calculation of the non linear behaviour for navigation conditions with high risk of slamming

2.3 EXTREME HULL GIRDER LOADS Observation of the elastic response shows that whipping increases the extreme values of the vertical bending moment. Therefore, it is necessary to take this effect into account for checking the ultimate strength of the hull girder. The performed calculations [7] and full scale measurements [2] show that whipping occurs when the ship is in sagging condition. Therefore, for the most severe navigation conditions the extreme slamming loads and consequently the increase of the sagging wave bending moment are calculated. Full scale measurements show that the damping of the vibratory response is small (of the order of ξ=1.5%), which means that whipping is still important half a wave period later when the vessel is in hogging condition and that the ultimate strength check is also to be carried out for this condition 2. This check can be done in analogy with the class rules for the bending moment corrected for the whipping effect as described [8].

2 Especially since container ships normally operate in hogging condition, thus providing the extreme hull girder bending moment.

Application on a 250 m container ship shows that the increase of the total bending moment can reach 20 to 30% for severe navigation conditions, which is in agreement with full scale measurements [2]. The calculations performed for ultra large container ships show that a similar percentage of increase may be expected for these ships. 2.4 FATIGUE Observation of the whipping response (figures 3 and 4) reveals two effects regarding fatigue: • Increase of amplitude of the wave frequent hull girder

stresses • Creation of high frequent damped stress cycles at the

first natural frequency of hull girder bending For welded details it is considered that the residual stresses due to the heat input create a high level of tension in zones where cracks may be expected, resulting in a high R coefficient (minimum stress divided by maximum stress, R > 0.5). For these high R values variation of the average stress level has little influence on the fatigue lifetime. For details without welding there are no residual stresses and analysis becomes somewhat more delicate. In order to simplify matters, in first instance the same approach as for welded structures is applied. As this means that a high level of residual stress is presupposed, this is a conservative simplification. Application of Miner’s law, which is linear by nature, allows for separating the low frequency (wave) and high frequency (whipping) contributions and add both individual effects to obtain the total result, see figure 5. Figure 5: Separation of whipping effects for fatigue calculation Knowing the stress range of the first whipping cycle and the damping it is possible to determine the distribution of cycles and their associated stress ranges as depicted in figure 6. Figure 6: Distribution of high frequent, whipping induced, stress cycles

The associated equations are

( )⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

−−=∆

23j4

21expAjSwp π

ξ

ξ (1)

with j designating the nth whipping cycle

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−−

∆=

21exp

SwCwpA

2

π

ξ

ξ (2)

The short term distribution is obtained by noticing that for every single whipping response there is only one cycle at every level and that there will be a whipping response associated to every wave cycle, i.e., at each level the number of cycles is equal to the total number of waves, see figure 7. Figure 7: Short term distribution of whipping stresses for a given wave amplitude Miner’s sum can be computed by superimposing the short term distributions of the stress ranges. Every cycle can be considered as a response to a regular wave of constant amplitude, while non linear response calculations to regular waves can be utilised as well. For a given wave frequency in head seas (being the dominant wave condition for slamming to occur) it is possible to determine the response function for a wave height H and a threshold wave height Hth below which there is no risk of slamming:

( )HfSwCwp =∆ thHH > (3) An overview of the step-by-step calculation method is presented in table 2. A study performed for an ultra large container ship shows that whipping effectively causes amplification of the hull girder bending stresses, as well as a measurable contribution to the accumulation of fatigue damage. In short term head sea condition the correction of the low frequency stress range can yield a very significant increase of up to 100% for some navigation conditions. Considering that whipping disappears for non-severe sea states, which are far more numerous than severe sea states, and that there is no whipping for transverse and following seas, the total long term increase of the Miner sum due to whipping is estimated to be of the order of 3 to 5%.

Table 2: Step-by-step procedure for estimating the

whipping induced fatigue damage

1


2 Calculation of the transfer functions and associated short term response spectra without whipping

3

Determination of the whipping response in head seas as function of the wave height according to the wave frequencies of the considered sea states and taking into account the whipping threshold

4 Approximation of a linear rule giving the amplitude of the first whipping cycle as a function of the amplitude of the rigid body response

5 Approximation of the variation on the linear rule as a function of the wave incidence angle

6 Identification of the short term sea states for which whipping is likely to occur

7 Correction of the low frequent (wave) stress range distributions for the whipping effect

8 Calculation of the Miner sum for all short term low frequent distributions

9 Determination of the high frequent whipping responses and associated Miner sums for every short term distribution for which whipping occurs

10 Calculation of total Miner sum taking into account low frequency contributions corrected for whipping and high frequency contributions

Following the analysis it can be concluded that the Miner sum associated to the high frequent part has a relatively small contribution for the following reasons: • Whipping occurs only in a limited number of sea

states (head seas, wave height above threshold value) • The reduction of the stress amplitudes due to

damping puts the majority of the cycles under the changing point of the slope of the S-N curve used (due to the random character of the phenomenon a 2-slope S-N curve is used for calculating the Miner sum).

3. SPRINGING Springing can be described as enforced wave induced hull girder vibrations. The calculation of the natural frequency of the two node hull girder bending mode for vessels with a length up to 350 m shows values above the frequency of the shortest observed waves. For instance, North Atlantic wave tables give a lower period Tz=3.5 s (0.28 Hz), while the natural frequency including added mass of a 300,000 dwt tanker has been calculated at 0.5 Hz (T=2.0 s). Springing was identified in 1972 during a full scale study on board a 340 m tanker [9], see figure 8. The response of the first natural mode of hull girder vibration, in spite of the high frequency, can be explained by the fact that for a given wave period the energy is distributed over a broad bandwidth. Using a Pierson-Moskowitz spectrum, the energy associated to a wave

period of 3.5 s is distributed over a bandwidth of 0.12 to 0.65 Hz, while for a wave period of 8.5 s this is 0.05 to 1.7 Hz. In addition, for head seas the encounter frequency is increased by the ship speed as follows:

Vg

2H

Heω

ωω += (4)

Figure 8: Response spectrum deck longitudinal stresses on a tanker in head seas for rigid mode and including springing [9] For the referenced tanker, sailing at a speed of 15 kn (7.7 m/s), the energy for a wave period of 3.5 s will be distributed over a bandwidth of 0.19 to 2.73 Hz, while for a wave period of 8.5 s this bandwidth is 0.06 to 16 Hz. These data clearly show that it the natural mode at 0.5 Hz is effectively excited. On vessels ranging from 300 to 350 m in length, if springing is at all visible from the spectral analysis, the level will be very weak and without effect on the structural resistance. When the length of the vessel increases or when the deck contains large openings the structural rigidity and therefore the first natural frequency mode decrease. When the ship speed increases, the encounter frequency increases as well. In both cases the frequency band associated with springing moves towards the region where the spectral density of wave energy is higher, thus amplifying the springing response (the springing associated peak in figure 8 moves to the left). This effect was noticed when performing design analysis for tankers of 550,000 dwt (414 m in length) and later confirmed during a four year full scale measurement campaign [10, 11]. When considering the characteristics of a typical ultra large container ship, with a length of over 360 m, speed of about 25 kn and large open deck structure, it becomes clear that springing is a phenomenon to be considered during the design of the ship structure. 3.1 SHIP STRUCTURAL RESPONSE A typical time series of measured longitudinal stress in the deck is presented in figure 9, which shows a high frequent springing signal of nearly constant amplitude superimposed on the low frequent (wave) component.

Figure 9: Measurement of deck longitudinal stress with visible springing effect Studies and measurements performed on 550,000 dwt tankers show that springing is sensitive for sea states with short wave periods. For these periods the maximum wave height is generally low, see table 3. Table 3: Maximum significant wave heights for North Atlantic wave environment according to IACS

Tz (s) 3.5 4.5 5.5 6.5 7.5 8.5 Hs (m) 1.5 4.5 9.5 13.5 14.5 14.5

Due to the weak damping, ξ=1.5% obtained from full scale measurements [2, 11], the available energy for the whipping response is limited and the amplitude remains small compared to the wave frequent response. Therefore, the influence of springing on the extreme hull girder loads, corresponding to severe sea states (higher natural period and very high significant wave height), is not significant. On the other hand, the high frequency and character of the enforced vibration (a quasi permanent phenomenon in sea states with relatively small waves, which are the most frequent during the life of the vessel) yield a non negligible springing induced contribution to the accumulated fatigue damage. This is confirmed by experience feedback of the 550,000 dwt tankers [11]. 3.2 CALCULATION METHODS Taking into consideration that the springing induced deformations are much smaller than the rigid body motions of the hull girder, it can be assumed that the problem can be treated in a linear sense and that the total response can be obtained by summation of the separately calculated rigid and elastic contributions [10]. Therefore it is possible to apply the linear tools developed for hydrodynamic and structural response calculations [13]. First of all, a classical calculation can be performed to determine the linear hydrodynamic coefficients, in particular the added mass and the transfer functions of the rigid body responses (figure 10). Secondly, the natural frequencies for the elastic hull and the associated transfer functions for springing are calculated (figure 11).

= + = +

Figure 10: Calculation of rigid body transfer functions Figure 11: Calculation of transfer function for springing in torsional mode (elastic hull) In this way the transfer functions for the quasi static, springing and total response are obtained for the selected navigation conditions (figure 12). Figure 12: Transfer function of peak stress in hot spot (welded detail) in a container ship (springing, wave and total) The calculations are performed according to the scheme shown in table 4. Table 4: Step-by-step procedure for springing analysis


2


3 Determination of navigation conditions for which springing could occur (wave incidence, ship speed, wave height)

4 Calculation of the linear elastic behaviour for wave incidences where springing occurs

3.3 FATIGUE Observation of the springing response for a given sea state (figure 9) shows that, on top of the wave frequent response, a time series of stress cycles with nearly constant amplitude at the first natural frequency of the hull girder is generated. The calculation of the short term fatigue damage accumulation requires the determination of the distribution of the high frequent stress cycles. The exact method for achieving this would be Rainflow counting. In order to do that a time history needs to be available, which is impractical for the spectral approach. By considering the same hypothesis as for the whipping and the using the linearity of Miner’s rule, it is possible to separate both the high frequent and low frequent contributions as depicted in figure 13 superimpose them to obtain the total result. As shown for whipping, the range of the wave frequent stress cycles needs to be corrected for the springing effect as well. As only the navigation conditions with a risk for the occurrence of springing need to be considered, it is important to take into account speed reduction in case the wave height increases, because this can cancel the springing effect altogether. Figure 13: Separation of springing effects for fatigue

calculation For each of the contributions corresponding to a signal with narrow banded spectrum, the fatigue accumulation can be computed according the methodology for wave frequent fatigue assessment [12]. The short term distribution of the stress range ∆Si can be described by a Rayleigh distribution, where the coefficient m0 is determined by the area under the response spectrum:

( ) ⎥⎦

⎤⎢⎣

⎡ ∆−=∆>∆

0

2i

i m8S

expSSprob (5)

For a given structural detail with known S-N curve it is possible to calculate the Miner sums separately and add them, taking into account the probability of occurrence of each short term navigation condition (wave height and period, vessel speed and wave incidence angle):

springingcorrected,wavetotal DDD += (6) An overview of the step-by-step calculation method is presented in table 5.

Table 5: Step-by-step procedure for estimating the springing induced fatigue damage

1


2 Calculation of the transfer functions and associated short term response spectra without springing

3 Determination of the frequency bands with high energy density within the wave spectra for the considered navigation conditions

4 Calculation of the natural frequencies of the hull girder, taking into account the added mass

5 Identification of the short term sea states for which springing is likely to occur

6 Calculation of the transfer functions for springing and associated short term response spectra for the considered sea states

7 Calculation of total Miner sum taking into account low frequency contributions corrected for springing and high frequency contributions

The method has been checked at short term level against the considered exact method, i.e. the Rainflow counting of the stress time history. To do so, a time history has been generated from the short term 2-peak response (see figure 12) using specific software. Then a Rainflow counting according to the AFNOR standard procedure has been performed and the Miner sum calculated. Two typical cases have been identified. For sea states with Tz above 5 s the low frequent wave stress is dominant over the high frequent springing, while for smaller Tz the situation is reversed, see figure 14. Figure 14: Stress time histories for Tz = 6.5 s (above) and Tz = 3.5 s (below) (First modal period T1 = 2.15 s) The comparison between the methods confirms that the proposed procedure provides acceptable short term Miner sum values. However, the correction factor for the

low frequent wave stress range has to be adjusted to the typical cases to prevent underestimations. A study performed for an ultra large container ship shows that, due to the large deck openings, the first natural mode of the hull girder is a torsional mode, which is followed by a number of vertical bending and torsional modes, see table 6. Table 6: Wet natural hull girder modes and frequencies ultra large container carrier Hull girder vibration mode f (Hz) 1-node torsional 0.37 2-node vertical bending 0.47 2-node torsional 0.50 3-node vertical bending 0.90 An investigation of the navigation conditions with a risk for springing occurrence showed that the torsional modes are to be considered for wave incidence angles of 120 and 90 degrees, while the flexural modes are to be considered for wave incidence angles of 180 and 120 degrees (180 degrees corresponding to head seas). The fatigue lifetime of a structural detail in the deck experiencing high dynamic loading has been calculated according applying North Atlantic scatter diagram, see figure 15. Figure 15: Fatigue analysis of hatch corner detail of an

ultra large container ship The springing response has been calculated for all wave heights and periods of the wave data table until a significant wave height of 5 m. For greater wave heights it is assumed that the vessel speed will be reduced and, consequently, that the shifted encounter frequency will yield only irrelevant springing response. The calculation of the short term Miner sum including springing shows that, compared to the situation excluding high frequent springing part, an increase in fatigue damage of up to a factor 3 can be reached for small period sea states. However, as small period sea states represent only a limited part of the long term total Miner sum, and taking into account that springing does not occur for transverse and following seas, the total long term increase of the Miner sum due to springing is estimated to be of the order of 4 to 10%.

A sensitivity study shows that if the maximum significant wave height is increased from 5 to 6 m, the springing related Miner sum increases by 20%. However, the effect on the total Miner sum is of second order. 4. HYDROSTAR The described methodology to assess the effects of whipping and springing during the design stage of ultra large container ships has been made practically applicable within the Bureau Veritas in-house hydrodynamic simulation suite HydroSTAR, which has been developed and validated for more than 20 years to support new technological challenges. Originally started as a linear 3D diffraction-radiation scheme for floating offshore units, today HydroSTAR is a multi disciplinary hydrodynamic package widely used in the marine and offshore industry. Typical issues like irregular frequencies, forward speed effect, roll damping, automatic mesh transfer, second order wave loads and multi body interactions are accounted for. In order to simulate whipping and springing hydro-elastic and non linear effects are to be accounted for. Hydro-elastic effects are handled using the modal approach, for which the equation of motion can be written as [13]:

[ ] [ ]( ) [ ] [ ]( ) [ ] [ ]( ) DIFξCkbBAm =+++−+− ωω i2 (7) where [m] is the structural mass, [b] the structural damping, [k] the structural stiffness, [A] the hydrodynamic added mass, [B] the hydrodynamic damping, [C] the hydrodynamic restoring, ξ the modal amplitudes and FDI the modal hydrodynamic excitation. The hydro-elastic coupling is visualised in figure 16. Figure 16: Hydrodynamic mesh following the structural deformation of the hull (first modal period) The non linear time domain simulations make use of the procedure proposed by Cummins (1962), for which the equation of motion can be written as follows [13]: [ ] [ ]( ) ( ) [ ] [ ]( ) ( )

( )[ ] ( ) ( ) ( ) ttdtt

ttt

0

QFξK

ξCkξAm

+=−+

+++

∫

∞

ττ &

&&

(8)

where [A∞] is the infinite frequency added mass matrix and [K(t)] the matrix of impulse response functions, which can be calculated from the frequency dependent damping coefficients [5, 13]:

( ) ( ) ωωωπ

dtcosB2tK0

ijij ∫∞

= (9)

This method enables the introduction of non linear components in the excitation forces F(t) and Q(t) [13]. As an example, for the calculation of the extreme hull girder bending moment including whipping effect a (weakly) non linear Froude-Krylov model is applied, see figure 17. Figure 17: Non linear time domain simulation using Froude-Krylov approach (loads on finite element model) The resulting overall computation scheme of the software called HydroSTAR++ is depicted in figure 18. Figure 18: Computation scheme of HydroSTAR++ for

hydro-structural simulation of container ships 4.1 MODEL TESTING In order to validate and calibrate the methodology for the hydro-elastic and time domain simulations, several model tests have been carried out and compared to the calculation results. In figure 19 depicts the torsional response of an elastic barge, showing good agreement between measurements and calculation results [13]. Figure 19: Elastic barge in torsion (impression of test left,

RAO of torsional angle right): comparison between experiments and calculation results

In figure 20 the initial deformation and the time history of the vertical displacement after releasing it from the original position are depicted. Again, there is good agreement between calculations and experiments. Figure 20: Elastic decay test (initial position left, time

history right): comparison between experiments and calculation results

4.2 FULL SCALE MEASUREMENTS Within the scope of the Joint Industry Project Lashing@Sea full scale measurements are carried out on board the BV class 9,400 TEU container ship CMA-CGM Rigoletto. Motion and acceleration sensors have been distributed over the hull and two cross sections have been equipped with strain sensors to record the dynamic response in terms of accelerations and internal hull girder loads. In order to study the behaviour of stacked containers and lashing equipment a dedicated measurement container has been installed above the aft deck. An example of a time series of measured accelerations in the container is shown in figure 21. Figure 21: Time series of full scale measurement in

transverse accelerations in container (normalised)

The results of the measurement campaign can be used to study the ‘real life’ behaviour of large container ships and to further validate and calibrate the developed numerical tools. 5. CONCLUSIONS An increase in the size and speed of container ships importantly changes the behaviour in a seaway. Phenomena already known for smaller size vessels can be amplified to reach levels high enough to have an impact on the design of the hull. This is particularly true for the cases of whipping and springing. The springing phenomenon was first studied during the construction of the 550,000 dwt tankers in 1975, for which time domain calculations have been performed. At that time the whipping phenomenon was also known, specifically in relation to ships with large deck openings, but computer simulation was not yet feasible. Recent developments in computer computation power and

efficient algorithms allow performing non linear hydro-structural calculations in the time domain. A methodology has been proposed to estimate the effects of whipping and springing on the extreme hull girder loads and fatigue lifetime of structural details. In order to be able to study the fatigue related effects during the design stage of a vessel, it is assumed that the low frequent and high frequent contributions can be dealt with separately. This simplification importantly reduces the required amount of non linear time domain simulations. The application of the methodology has been made possible by further development of the Bureau Veritas in-house hydrodynamic simulation suite HydroSTAR to solve hydro-elastic and non linear time domain problems. Extensive validation has been done by model testing, while the ongoing full scale measurement campaign will provide additional valuable feedback. Application of the methodology to ultra large container ships confirms that the stress levels are indeed increasing. As a consequence, a significant increase both hull girder loads and fatigue damage accumulation is found, which can no longer be ignored when analysing the ship structure. Whipping effects can cause an increase of about 20% in total vertical bending moment, for which the hull girder ultimate strength is to be checked. For current container ship designs of about 350 m with extremely large open deck structure, whipping can cause an increase in short term fatigue damage accumulation by a factor of up to 100% for some head sea navigation conditions. The increasing effect on the long term whipping induced fatigue damage accumulation is estimated to be in the range of 3 to 5%. With regard to springing, as a consequence of the flexibility of the hull girder and high vessel speed, current designs of about 350 m in length show an increase in short term fatigue damage accumulation by a factor of up to 3 for small period sea states, which is superior to the referenced tankers of 414 m. The increasing effect on the long term springing induced fatigue damage accumulation is estimated to be in the range of 4 to 10%. It is expected that full scale measurements results will provide valuable insight into the real dynamic behaviour of large container ships, as well as the accuracy of the calculations. In addition, further development of the methodology and hydro-structural computation schemes are ongoing and are expected to further enhance prediction capabilities. When considering future designs for even larger container ships of 400 m in length and beyond, it is

certain that with similar hull structural design the increase of fatigue damage accumulation due to whipping and springing will become even more important. By realizing that springing is a forced vibration phenomenon with little damping and that the whipping response is of non linear character, the dynamic phenomena and associated consequences will have to be analysed with greater attention. 6. ACKNOWLEDGEMENTS The models and results presented in this paper require strong interaction of many technical competencies. Therefore, the authors would like to thank all the people involved in the research and application of the developed methodologies, in particular Š. Malenica, F. Mauduit, N. Germain, F. Bigot, F.X. Sireta, S. Maherault, E. Stumpf, V. Bouitillier, J. Henry and G. Parmentier. 7. REFERENCES 1. Huther M, Ket N, ‘Water impact risk estimation

during ship design’, Ship Behaviour at Sea, International Symposium on Ship Hydrodynamics and Energy Saving, ISSHES, Madrid, September 1983

2. Osouf J, ‘Etude expérimentale du comportement dynamique dur houle du navire câblier Marcel Bayard’, Revue NTM, 1973 (in French)

3. Drummen I, Moan T, Storhaug G, Moe E, ‘Experimental and full scale investigation of the importance of fatigue damage due to wave-induced vibration stress in a container vessel’, Design & Operation of Container Ships, RINA, London, November 2006

4. Malenica Š, Molin B, Remy F, Senjanovic I, ‘Hydroelastic response of a barge to impulsive wave loads’, 3rd International Conference on Hydroelasticity, Oxford, 2003

5. Cummins WE, ‘The impulsive response function and ship motions’, Schiffstechnik, 1962

6. Ogilvie TF, ‘Recent progress toward the understanding and prediction of ship motions’, 9th International Conference on Numerical Ship Hydrodynamics, Ann Arbor (USA), 2007

7. Tuitman J, Malenica Š, ‘Some aspects of whipping response of container ships’, 23rd IWWWFV, Jegu (Korea), 2008

8. Bureau Veritas, ‘Rules for the Classification of Steel Ships’, November 2007

9. Planeix JM, ‘Wave loads, A correlation between calculations and measurements’, Revue International Shipbuilding Progress, August 1972

10. d’Hautefeuille B, Huther M, Baudin M, Osouf J, Calcul de springing par équations intégrales’, Revue NTM, 1977

11. Huther M, Osouf J, ‘SEFACO, Four years of experience in ship hull girder stress monitoring’, MARINTEC, Shanghai, October 1983

12. Huther M, Beghin D, Mahérault S, ‘A fatigue strength guidance note for welded ship structure assessments’, IIW/IIS doc XIII-111742-98/XV-992-98, 1998

13. Malenica Š, ‘Hydro structure interaction in seakeeping, International Workshop on Coupled methods in numerical dynamics IUC, Dubrovnik, September 2007

8. AUTHORS’ BIOGRAPHIES Gijsbert de Jong holds the current position of product manager at Bureau Veritas. He is responsible for the international business development in the field of container ships. Gijsbert joined Bureau Veritas in 2001 after obtaining an MSc in Naval Architecture & Marine Engineering from Delft University of Technology. Before moving to the sales and marketing management team in Paris, he has worked as hull surveyor and department manager in the plan approval office in Rotterdam. Michel Huther is a graduate Mechanical Engineer (Ecole Centrale de Lyon, 1965) and Naval Architect & Marine Engineer (Ingénieur Civil du Génie Maritime, 1967). Michel joined Bureau Veritas in 1969 and has worked as research engineer and department head for the ship research and rule development department, with many contributions to European R&D projects. In 2000 he was promoted deputy to the director of the marine technical management. After his retirement in 2003 Michel is holding the position of technical advisor to the Bureau Veritas marine technical management. He is a member of SNAME, ATMA & SF2M and has published over 200 scientific and technical papers on ship structural behaviour and safety.

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DOT PERTH December 2008 p 1 / 18

Fibre rope deepwater moorings:

Complete and consistent

design and qualification procedures Franck Legerstee, Michel Francois, Cedric Brun

Bureau Veritas

ABSTRACT

Fibre ropes are today extensively used for station-keeping of permanent Floating Production

Systems and Mobile Offshore Drilling Units in deep waters, and constitute a key technology,

as the waters in which they operate go deeper and deeper. Since the very first installations,

back in the late 90’s by Petrobras pioneers, this technology of lightweight mooring has been

widely used in various regions, yet not stopping a sustained Research and Development effort

from the Industry, including operators, designers and product manufacturers. This continuous

R&D effort led to a better understanding of a number of issues, and coupled with the

feedback from design, manufacturing, operation and related certification activities, permitted

the development of up-to-date and optimised product qualification and Certification

procedures, with a stage of maturity confirmed by the issuance of International Standards and

Guidance Notes from Classification Societies. An overview of these procedures will be given

in a first part of this paper.

An important aspect of this effort was the understanding of the engineering properties of the

rope as a line component, particularly the load-elongation characteristics of fibre ropes, which

are needed for the evaluation of the response of the mooring system. The current practical

model involves a separation in several terms, following the time scale of actions (ranging

from seconds - a passing wave - to system lifetime), that need to be consistently defined

between measurement procedures and data for analysis.

These properties have been the subject of a recent research project, aiming at confirming

previously acquired knowledge on polyester ropes, the material principally used. This project

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also provided a more complete understanding on some aspects, particularly the quasi-static

stiffness of polyester ropes, (addressing the variations of the mean tension in the lines, at a

very slow rate, under changing weather conditions). Results of extensive tests performed

principally on polyester sub-rope samples were interpreted to provide practical data for

mooring analysis, in the form of a quasi-static load-elongation characteristic.

As regards the dynamic stiffness of polyester ropes, recent test data confirmed the current

practice for modelling dynamic stiffness in design.

This paper then summarises how these recent advances resulting from Research and

Development have been successfully implemented in software tools and corresponding

Classification Guidelines, thus achieving a complete and consistent approach for design and

product certification of fibre ropes mooring systems.

INTRODUCTION

Fibre ropes are today increasingly used for the station-keeping system of permanent Floating

Production Units in deep waters, where they offer an elegant and efficient lightweight

solution, and for MODU's, where they give an extended water depth capability to existing

units.

Following a development period, and ten years after the first installations of semi-submersible

FPU's in Brazil, this technology has reached a stage of maturity now addressed in

International Standards:

• the ISO station-keeping standard ISO 19901-7 includes provisions and design criteria for

fibre rope station-keeping systems [1],

• a standard for polyester ropes for station-keeping : ISO 18692. This document is a product

standard, defining qualification and testing requirements for ropes [2].

This situation is the result of accumulated knowledge on the engineering properties of the

ropes, through a number of R&D studies over the world, and of growing practical experience

in the Industry, for both Users and Manufacturers, from which product qualification and

Certification procedures were developed [3].

The present paper reviews these two aspects that are indeed closely interrelated:

RopDOT_2(ID70).doc 16/12/08 10:12


• qualification and acceptance procedures of the product, ensuring that the purchased rope

has the expected properties and adequate durability,

• engineering properties of the rope as a line component, i.e. the properties that are required

for the design of a station-keeping system, such as rope breaking strength, endurance

under cyclic loading (T-T fatigue), load-elongation properties, etc…

This review highlights the most important parameters for system design and rope

qualification, focusing on the prevailing materials, principally polyester, setting the way for a

complete and consistent methodology for fire ropes mooring systems.

ROPE QUALIFICATION

Objectives of rope qualification

The process of implementing the station-keeping system of a floating structure is, from the

initial stage of concept selection to the final installation, a multi-stage process, that is run

under scrutiny of all parties involved, particularly the Classification Society, to ensure that the

final installed system has the specified performance (vessel offset, strength and endurance).

During the engineering phase, where the station-keeping system is designed, the type, size,

and dimensions (length) of line components are specified, based on the today well known

properties of the products, clearly defined in international standards as [2] and [3]: it is

therefore of paramount importance that these properties are well understood by the Designer.

At the purchasing stage, the manufactured line components must be verified to have these

properties. The necessary assurance is obtained through a qualification process, based on

testing of a ‘prototype’ rope identical to intended supply.

This rope qualification is thus an essential stage, indeed a corner stone, in the process of

designing, manufacturing and installing a fibre rope station-keeping system:

• to ensure, prior to starting production of this ropes, that the product proposed by the

Manufacturer has the required characteristics, in terms of strength , durability, and

engineering properties such as rope load-elongation properties,

• to provide a documented reference to ensure, during the next step of rope production, that

the ropes supplied are identical to the prototype, thus have the expected properties.

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On the other hand, the rope for a given project is not in itself a unique product, that the

Manufacturer will never have produced before (except possibly for size), but one size in the

proposed design, and he will have normally produced, tested, and qualified other (often

smaller) sizes. Besides evidence of the Manufacturer's capability, this is giving possibilities to

resolve the dilemma between the high level of assurance that this application demands and the

economical (time and cost) constraints of a project.

Whilst some essential tests (such as breaking strength) shall be performed on full size

prototypes, other tests may be omitted when test results are available from previously

qualified ropes of the same model having gone through the full process, including

certification by the Classification Society, rather than being made on a ‘scaled rope’.

Selection of tests required (or not) on the same size depends on both the nature of the

properties and their criticality. As discussed below, the latest documents are reflecting State of

the Art practice (much more was required a few years ago). Besides, being defined as a

standardised process, the qualification does not need to be repeated if the same rope is already

qualified.

What has to be ‘identical’ (except size) between production, prototype, and previous

prototype has been carefully defined, albeit in broad terms, and will be verified during rope

Certification.

Most salient aspects are outlined below. Further guidance and discussion may be found in [2]

and [3].

Breaking Strength

The rope Required Minimum Breaking Strength is the principal parameter by which the rope

size is defined, as a result of the design, with other parameters that are accounted for in the

design loop being defined as a function of rope MBS.

Safety factors are basically the same as for steel components. However, most Operators and

Classification guidelines [4] specify an additional margin for permanent systems. In practice,

a size will be selected in the Manufacturer's catalogue, implying an additional (small) margin.

For the selected size, breaking tests on full size samples are required to get an independent

verification of the Manufacturer's prediction (i.e. to verify the breaking strength of the rope

against the specified MBS, not to determine it). For rope qualification, having 3 samples

tested, with all 3 results above the specified MBS is required.

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When a rope is already qualified, one test is considered sufficient to validate production, on

top of QA/QC and Surveys activities.

For this test, a standard bedding-in sequence is defined, in order to get meaningful stable

results for the breaking strength. This also provides an opportunity to get a measurement of

the rope dynamic stiffness at the end of that sequence (see below).

Cyclic loading endurance (T-T fatigue)

The T-T fatigue endurance has now been quantified, for typical polyester ropes for station-

keeping, by the extensive cyclic loading tests (up to 40 million cycles endurance) performed

within the ‘Rope Durability’ project [5], and found to be far above that of a steel wire rope of

the same size. Tests also indicated that the prevailing mode of failure of a properly designed

and manufactured rope under such conditions is internal abrasion.

A consequence of the high endurance revealed by the above-mentioned tests is that testing to

failure large ropes, even sub-ropes, with a load range that is relevant for internal abrasion, is

not practically achievable.

However, there are other potential failure mechanisms and a cyclic loading test remains

necessary to show that the overall construction of a particular rope does not present risks of

premature failure due to inadequate design or manufacturing, so can be expected to have the

required endurance. The range of load amplitude and the related endurance, in [2] and [3] are

keeping test duration within reasonable limits, without unduly triggering creep failure.

Besides, although fatigue is not fully size-independent, but as it is expected not to be critical,

a range of validity is defined around the size of tested rope, within the scaling allowance

quoted before, so as to avoid unnecessary repeat of a costly test, or the testing of very large

sizes - currently not reasonably achievable.

For Polyester ropes, the abrasion resistance comes from using ‘marine grade’ fibres. A test

method of Yarn-on-Yarn abrasion is specified within fibre qualification requirements.

However, this test is rather qualitative and comparative, and there is no documented

correlation between the results of the rope fatigue-testing project and the level of acceptance

specified for the Y-o-Y abrasion tests.

Therefore, for polyester fibres other than those tested in that project, or other materials, a

direct demonstration of endurance, e.g. on small size scaled ropes (or sub-ropes) is expected

to be presented, before claiming for the high level of endurance now expected by designer.

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Compression fatigue is also a potential mode of failure for synthetic fibres, but has been

evidenced not to be an issue, for polyester and HMPE, down to 1% of MBS minimum loads.

For fibres in other materials, compression failure should be documented by appropriate tests,

and pertinent minimum tensions are needed.

Durability

Chaffing, cutting, and internal abrasion by ingress of foreign materials (soil, marine

organisms) are known threats to any fibre rope, and can happen, in the first place, during the

installation of the mooring system. Detailed guidance on rope handling care is now provided

in [2].

A braided cover is currently used as the primary barrier. Polyester is most often used but other

materials could offer better abrasion resistance. Soil (or other particle) ingress below the

cover can in turn exacerbate internal abrasion mechanisms under cyclic loading, leading to a

drastic reduction of rope endurance. Therefore, providing a secondary barrier to avoid particle

ingress is an elementary precaution. Non-woven material is typically used, and the rope

standard [2] defines minimum performances to be achieved. Consequently, laying of ropes

fitted with such qualified filters on the sea-bottom during installation, with due care, is now

considered as acceptable.

Load-Elongation properties

As further discussed in the next section, load-elongation properties are critical data for

designing a station keeping system, but are rather complex to evaluate and specify, in

comparison with the linear elastic behaviour of equivalent steel components.

However, sufficient data are now available, as needed for analysis, i.e. far in advance of any

rope purchasing.

Then, on the basis that the load-elongation properties of a given fibre and rope construction

are known or have been previously identified, the purpose of rope qualification is to verify

that the supplied rope achieves the expected performance, and only a limited amount of full

size testing is needed. Besides, tests have shown that the dynamic stiffness ‘Krebi’ at the end

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of the standard bedding-in sequence (of the breaking test) does provide a pertinent indication

of the degree of stiffness of a given rope. Therefore, such test repeats can now be avoided.

In the polyester rope standard [2], this verification is thus defined as a three-step process:

• verification testing on one size in a given series of ropes, for a limited number of

conditions,

• measurement of ‘Krebi’, the dynamic stiffness at the end of bedding-in, for each new rope

to be qualified, within the breaking test procedure.

• measurement, for each new rope to be qualified, of the linear density, for later derivation of

rope length.

The length of a finished rope is defined, rather than the manufacturing length (or the length on

storage reel), as a bedded-in length at a reference tension. Issues of length variation are

discussed later below.

Torsional properties of rope can also be important in some cases, and will be addressed by the

selection of rope type (torque-neutral or torque-matched) on one hand, and by testing on one

size of a given model, when relevant.

FIBRE ROPES LOAD-ELONGATION PROPERTIES AND MODEL

Issues

A proper knowledge of the load-elongation properties of ropes is critical in designing a fibre

rope station-keeping system and evaluating its integrity under the expected conditions.

However, these properties are rather complex to evaluate and specify, in comparison with the

linear elastic behaviour of equivalent steel components. Besides, the loading regimes of a

rope in an anchoring line are quite specific with respect to usual service conditions of fibre

ropes.

A considerable improvement in the knowledge on this subject has been achieved in the recent

years, following the first insight given in [6]. Within the French CLAROM fibre rope

projects, since 1997, extensive testing has been carried out, over a wide range of sizes and

materials. Tests have been performed at scales from single filament to full-size ropes,

including the intermediate yarn, assembled yarn and sub-rope levels, over a wide range of

loading conditions.

RopDOT_2(ID70).doc 16/12/08 10:12


In 2000, based on these tests and the data from qualification tests of ropes for Petrobras, a

practical (engineering) model for the load-elongation characteristics of polyester ropes, was

presented and documented in [7] and [8], and is currently in use within several State of the Art

mooring analysis and line dynamics software packages [11]. Tests performed since on other

materials have generally confirmed the applicability of this model.

Model

The load-elongation properties of fibres and fibre ropes exhibit a non-linear and time

dependent (visco-elasto-plastic) behaviour. As a result these properties cannot be reduced to a

load-elongation ‘characteristic’, even a non-linear one, and particularly, NOT to the load

elongation curve of a new sample under monotonic loading (as obtained from a standard

breaking test).

In the lines of a station-keeping system, once the system is deployed/installed and set under

tension, the rope will be maintained under a sustained tension for months, even years or

decades in the case of a deep-water permanent mooring, then subjected to the random loads

induced by the environment (wind, waves, current).

It is then appropriate for the evaluation of system response to separate the response into three

terms, related to the time scale of actions, also matching the typical steps of a mooring

analysis (be it frequency or time domain):

• Mean elongation (system pretension, permanent load),

• Visco-elastic response to slow variations of mean load under changing weather, modelled

by the quasi-static stiffness,

• Response to dynamic actions (both low frequency and wave frequency - a separation was

found unnecessary) modelled by a mean-load-dependent dynamic stiffness.

For polyester ropes, numerical values for the parameters in this model were proposed

following the observation that, in spite of different fibres (i.e. fibre suppliers) and rope

constructions, ropes targeted to this application had very similar properties, and normalisation

by the (full size) rope MBS could be made.

In the latest phase of the CLAROM project, extensive tests were carried out, with the

objective of getting data on rope behaviour under a wider range of load and elongation than in

standard tests, so as to cover the particular situations that may occur in some systems or

design conditions. These tests also confirmed a number of aspects in this practical model, and

RopDOT_2(ID70).doc 16/12/08 10:12


gave a better insight into the visco-elasto-plastic response of fibre ropes, further

complementing the knowledge gained from earlier phases in this project.

The tests were performed principally on polyester sub-rope samples. Some tests were also

performed on a full size parallel construction 800-ton MBS rope based on the same sub-ropes

and on another full size rope with a different fibre.

Detailed presentations of the testing protocols and discussion of results are given in [9] and

[10].

Mean elongation

A particularly important aspect, quite specific to fibre ropes, is the modification of the

properties of a rope during the first loading(s) and during the early stages of rope service. This

process, called “bedding in”, results in an essentially permanent - not recoverable - elongation

with respect to the rope initial length at the time of manufacturing. Being primarily due to

changes at a molecular level within fibres, it also results in a stabilisation of the rheological

properties of the rope.

To define the length of a finished rope as a bedded-in length at a reference tension (typically

20% of rope MBS), a loading sequence that is deemed representative of the typical

installation conditions of a stationkeeping system is specified in the ‘linear density test’ in [2]

and [3]. Then this purchase length may be deemed a lower-bound evaluation of the as-

installed length of line under pre-tension. The length under pre-tension will however increase

with time, and re-tensioning may be needed from time to time, e.g. after an important storm.

Results of the ‘extended quasi-static stiffness’ test described later below gave data on the rope

length at a mean tension of 20%, as a function of the principal parameter affecting this length:

the maximum load previously attained (see Figure 1). Some dependence on the loading

history is however clearly apparent.

On two samples to which the ‘linear density test’ sequence was applied, the elongation at a

20% load, at the end of the sequence gave the reference length L20 for rope purchasing,

according to the length measurement method in the standard [2]. The two other samples, for

which the standard bedding-in sequence of strength and stiffness measurements in [2] and [3]

was used as initial loading sequence, showed a stable mean elongation, about 1.6% higher

than L20, for all loads up to above 40%.

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For the samples with a milder bedding-in, the elongation increases quickly when the load

exceeds the maximum seen during first bedding-in: given the time frame of the test (within

48h of the very first loading of the rope, i.e. much less than the time required to install a

system and to have it actually operating) it is likely that most of the permanent elongation will

quickly accumulate in the early days of the installed system, if not during installation itself.

Thus, in analysis, it can be normally assumed that, at a given time, the pre-tensions have been

reset to their design values. If needed for some particular situations (such as sudden storms),

lower bound pretentions may be considered.

For higher maximum loads, further (delayed) permanent elongation is observed, increasing

almost linearly until 70% MBS. This delayed permanent elongation is indeed included in the

‘quasi-static characteristic’ defined in the following paragraphs.

20

30

40

50

60

70

80

90

0.0 0.5 1.0 1.5 2.0 2.5elongation (% ) above L20

Fmax

(% o

f BS) OL1 OL2

OL3 OL4

Figure 1 . Mean elongation at a 20% load as a function of (previous) maximum load - four

samples.

Quasi-Static stiffness

Following the concept proposed in [6] a ‘quasi-static stiffness’ was defined, ten years ago, in

order to model the visco-elastic response of ropes to slow variations of mean load, under the

effect of changing weather conditions, i.e. a time scale of several hours or days, where the

tension in the line, initially the line pre-tension, increases (in the windward lines) or decreases

(in the leeward lines), at a very slow rate.

In this test (see [2] and [3]), after a proper bedding-in, the rope is cycled between two tension

levels, with a constant load plateau at each level. Typically, 3 cycles of twice ½ hour each are

used (a practical time frame for the duration of the test). A secant stiffness can be obtained

RopDOT_2(ID70).doc 16/12/08 10:12


from the end points of the last ½ cycles but, in order to get a stiffness that is more

representative of the duration of load rise of the events intended to be modelled, cycles of

longer duration are simulated from the measurement of creep or recovery during load

plateau’s and fitting to a log function of time.

The two load levels are normally taken as 10% and 30% of MBS, and the duration of load rise

τ is normally taken as 12 h, providing values of the non-dimensional quasi-static stiffness Krs

for typical storm conditions. However different levels or durations could apply to some design

or metocean conditions (e.g. a damaged system, a loop current event).

Extended quasi-static stiffness test

In order to widen the scope of characterisation, an extended quasi-static stiffness test was

developed: as shown in Figure 2a, a series of load-unload cycles is applied, similar to those of

the standard test, all with the same 20% range but at different sets of load levels, starting and

ending with a set of cycles at 10-30%. Figure 2b shows an example of the resulting force-

strain plot during the extended quasi-static stiffness test (continuous record over 48 h).

0

100

200

300

400

500

600

0 5 10 15 20 25 30 35 40 45 50Time, h

Forc

e, k

N

Linear density

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7 8 9 10

Strain, %

Forc

e, k

N

Figure 2 . Extended quasi-static stiffness sequence - samples 3 and 4

a) Force versus time, b) Force versus elongation

From the elongations at the end of each cycling, a secant stiffness is obtained (without

extrapolation at this stage). A close match was found between the results of all four samples,

with a very limited effect of previous bedding-in.

From the fitting and extrapolation of creep and recovery plateaus, the elongations for different

levels and durations are obtained, and a stiffness between two levels could be calculated.

RopDOT_2(ID70).doc 16/12/08 10:12


Indeed, in a station-keeping system, the tension will gradually increase (or decrease) more or

less monotonically in most cases, and over the same period of time, from initial tension to a

maximum (or minimum) value which will be different in each line. Then, by considering the

relevant points, a practical characteristic for the specified loading time can be obtained, that is

shown in Figure 3.

A first observation is that, for the 12h (standard) loading time, this characteristic is almost

linear over a large range of loads, i.e. the standard quasi-static stiffness derived from tests

between 10 and 30 % remains valid from about 7 to above 70%. At higher loads, this is

inclusive of the above mentioned delayed permanent elongation. Besides, for the 7 days

loading time, the slope of the characteristic (dX/dT = 1/Kr ) is only marginally different from

that for 12h.

Besides, for tensions below 10%, there is a clear increase of compliance with decreasing load.

In a system working at low tensions in leeward lines, this will have a similar effect as the

catenary effect in weighty components of the line.

More details and corresponding equations can be found in [10].

Figure 3 . Q-S PRACTICAL characteristics and included Xp

Dynamic stiffness

The ‘Dynamic stiffness’ is modelling the near-elastic response of the rope to cyclic actions

(both low frequency and wave frequency) induced by the environment.

In tests (see [2] and [3]), after bedding-in, the rope is cycled around a preset mean tension,

with harmonic (constant amplitude, sinusoidal) loading. The ‘dynamic stiffness’ is taken as

0

10

20

30

40

50

60

70

80

90

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0elongation (% ) above L20

Tens

ion

(% o

f BS)

Xij 12h

Xij 7d

QS 12h

QS 7d

included Xp

RopDOT_2(ID70).doc 16/12/08 10:12


the mean slope over several cycles at the end of the sequence. Normalising loads by rope

MBS, the non-dimensional dynamic stiffness KrD is then obtained.

In order to complement the characterisation work performed earlier (see [7]), a number of

dynamic stiffness tests were performed, on the same sub-ropes and full size ropes as those

above, with systematic variations of mean-load level, load range, and cycling period, so that

the dependence of dynamic stiffness on testing parameters could be definitely clarified,

beyond its known dependence on mean load.

A series of tests confirmed that the effect of cycling period (from 12.5 s to 500 s) on dynamic

stiffness is negligibly small, in accordance with earlier findings.

During tests (with harmonic loading), the stiffness quickly increases in the first cycles, then

tends to stabilise (at least apparently). From different tests, it seems that the stabilisation of

the dynamic stiffness (toward the maximum stiffness for the applied mean load) and that of

mean elongation (towards a stable condition) are closely related.

A series of tests under harmonic loading, with different mean loads and ranges, highlighted a

dynamic stiffness clearly decreasing when range is increased. However, the real loading is not

harmonic. Further tests were thus performed on the full size ropes, using time series obtained

by mooring analysis (i.e. a realistic wide band signal, with low and wave frequency contents).

An example of applied time series and resulting load-elongation plot is shown in Figure 4. It

is noteworthy that the load-elongation is very close to a single overall linear relation, with

effects of neither the amplitude of individual cycles, nor the period of underlying (low and

wave frequency) components.

Further analyses of the signals, both in time and frequency domains (FFT of signals)

confirmed that stiffness is independent of frequency, and indicated that the scatter around

mean position is primarily due to a small shift in mean elongation and tension, along the test,

secondarily to an axial (material) damping in the low frequency response: this can generate

only a small contribution to the overall low frequency damping of the system in the order of

1% of the critical damping.

Besides, from different tests it is apparent that this stiffness is almost independent of the

overall (min to max) amplitude of the signal, and is slightly higher than the stiffness under

harmonic loading, indicating that a better stabilisation, i.e. closer to real conditions, was

RopDOT_2(ID70).doc 16/12/08 10:12


achieved by these sequences. Thus, there is no point in taking into account an effect of load

range in analysis.

1500

2000

2500

0 10 20 30 40 50 60time, minutes

Forc

e, k

N

1500

1750

2000

2250

2500

3 3.1 3.2 3.3 3.4

Strain, %

Forc

e, k

N

Figure 4 Example of stochastic loading (1h)

a) time trace; b) resulting load-elongation and linear regression

Mean load has been identified before as the dominant parameter affecting the dynamic

stiffness, and a linear relation is currently used. As an update of earlier work, Figure 5 shows

the variation of dynamic stiffness with mean loads, for 11 different ropes from 6 rope

manufacturers, including the results of recent tests.

Some scatter is observed that can be attributed to several reasons such as differences in

amplitudes, degree of stabilisation, etc... The principal reason is, however, the differences

between the ropes material and construction, which are reflected in the ‘dynamic-stiffness-at-

end-of-bedding-in’ Krebi (shown by bigger marks, at 20% mean load in Figure 5). All are in

the range of 18.5 to 23, i.e. the range of a ‘normally stiff’ rope according to A1-5.7 in [3].

As shown in Figure 5, all data points are lying within the envelope formed by the design

(upper-bound) stiffness and the minimum stiffness, as proposed in [3]:

KrD = 18.5 + 0.33 ML (design)

KrDm = 15 + 0.25 ML (lower bound), where ML is the mean load (in % of MBS).

Only a few points are marginally outside.

The envelope given above is thus adequate for the design of a mooring system, i.e. typically

some significant time in a project before a particular product is selected and manufactured.

This envelope covers the possible range of stiffness of a ‘normally stiff’ rope. Then the

RopDOT_2(ID70).doc 16/12/08 10:12


standard measurements during rope qualifications will confirm that the purchased product has

properties within the range used for design.

A more accurate relation could be likely defined for a particular rope. This will however

require that further measurements are made, e.g. using stochastic loading, and that due care is

taken in the derivation of engineering values, which cannot be simply taken as the raw results

of a few tests.

15

20

25

30

35

40

0 10 20 30 40 50 60Mean load ( % MBS )

KrD

Krebi

Figure 5 . Dynamic stiffness as a function of mean load : test data from [7] (blue and green),

recent (red and pink), and relations in ref [3]

Outline procedure

The latest tests of CLAROM fibre rope project confirmed the practical model and data for

analysis initially proposed in 2000 ([7], [8]), and expanded it to better account for:

• Permanent (non-recoverable) elongation,

• Quasi-static stiffness, addressing the variations of the mean tension in the lines, at a very

slow rate, under changing weather conditions,

• Dynamic stiffness, for stochastic loading

Data for permanent elongation are based on purchase length L20 defined in [2].

The Quasi-Static stiffness KrS10-30, defined in [3] is applicable:

• over a large range of tensions,

• for large amplitude loading towards low tension or with longer loading time,

RopDOT_2(ID70).doc 16/12/08 10:12


This is summarised by the ‘quasi-static’ characteristic, as defined in [3], which is scalable

with KrS10-30.

The latest tests have also confirmed that the dynamic stiffness is a function of mean load only.

The model proposed in this paper is valid for a range covering design needs (tensions or

offset) and a range of products (all, based on ISO standard [2]).

The extended model described above is implemented in BV software [11].

CONCLUSION

The rope qualification process, a corner stone in the process of designing, manufacturing and

installing a fibre rope station-keeping system, is based on testing of a ‘prototype’ rope

identical to the intended supply. The qualification process is however taking advantage of

previous qualifications of the same rope design in a different size, in order to optimize the

process whilst keeping the high level of assurance that this application demands.

Whilst essential tests shall be performed on full size prototypes, other tests need not be

repeated when results are available from previously qualified ropes, i.e. ropes having also

gone through the full qualification process, including certification by a Classification Society.

Within the French CLAROM fibre rope project, tests have been performed to confirm and

complement the currently used practical engineering model that was derived from earlier

work. This work focused principally on the response of ropes to slow variations of mean load,

under the effect of changing weather conditions, usually modelled by the ‘Quasi-static

stiffness’. In addition to the standard tests described in [2], extended test sequences were

defined. From these specific sequences, and the number of data points provided, an

interpretation can be given that overcomes the discrepancy between the time scale of tests

(one or two days), and the real world.

Tests reported in this paper were principally performed on sub-ropes. Some full size rope test

results are also reported. The scalability of results, an already known fact, was shown.

Based on the interpretation of test results, a practical Quasi-Static characteristic could be

defined, addressing monotonic changes of line mean load, from around the line pre-tension.

This characteristic is an extension of the current Quasi-Static stiffness KrS. Two

characteristics are proposed for the 12h (standard) loading time, and for 7 days, a loading time

RopDOT_2(ID70).doc 16/12/08 10:12


more appropriate for some other design conditions (e.g. the effect of a loop current). Both are

scalable by KrS.

As background to the above characteristic, further separation of the rope response is

presented, based on the derivation of a fully relaxed characteristic (the characteristic for

‘infinitely slow’ rate of loading), and two additional terms: a permanent (non recoverable)

elongation, and a (remaining) un-developed visco-elastic elongation, modelling the effect of

loading rate. Nevertheless, development of a true ‘time domain’ rheological model and a

definitive understanding of underlying mechanism will require further effort.

For the dynamic stiffness, the discussion of the dependence of dynamic stiffness on testing

parameters, based on recent data, highlighted mean load as the principal parameter under real

stochastic loading. This confirmed the adequacy of current practice in the analysis of a

system, of modelling the dynamic stiffness as a linear function of mean load only. Besides, for

a particular rope, it is important to note that load history and other effects will always affect

the test results, thus due care is to be taken in the derivation of engineering values that cannot

be simply taken as the raw results of a few tests. Using stochastic loading time series for the

testing appears an efficient method in this respect.

The requirements of the International rope standard [2] and Bureau Veritas Guidance Note [3]

form a complete and consistent procedure for fibre ropes mooring systems covering:

• Analysis, with practical (engineering) model and data taken from today in-depth

knowledge of rope properties, obtained through standardised testing, and successfully

implemented in State-of-the-Art Mooring analysis software [11].

• Product qualification and certification, for verification at time of purchase

• Service conditions (seabed contact, fatigue)

ACKNOWLEDGEMENTS

The authors wish to thank Bureau Veritas for permission to publish this paper.

The views expressed are those of the authors, and do not necessarily reflect those of Bureau

Veritas

RopDOT_2(ID70).doc 16/12/08 10:12


REFERENCES

[1] ISO 19901-7:2005, Stationkeeping systems for floating offshore structures and mobile

offshore units

[2] ISO 18692:2007, Fibre ropes for offshore station keeping - Polyester

[3] Bureau Veritas, (2007), Certification of fibre ropes for Deep water offshore services,

NI432R01

[4] Bureau Veritas, “Classification of mooring systems of permanent offshore units”,

NI 493, 2004

[5] Banfield S J, Casey N F, Nataraja R, "Durability of polyester deepwater mooring rope",

OTC 17510, 2005

[6] Del Vecchio CJM (1992), “Light weight materials for deep water moorings”, PhD thesis

University of Reading

[7] François M, Davies P, (2000), “Fibre rope deep water mooring : a practical model for

the analysis of polyester mooring systems” , IBP 247 00, Rio Offshore 2000

[8] François M, Giulivo R, (2000), “Practical procedures for fibre rope moorings”,

Continuous Advances in Mooring & Anchoring, Aberdeen

[9] Davies P, Lechat C, Bunsell A, Piant A, François M, Grosjean F, Baron P, Salomon K,

Bideaud C, Labbé JP, Moysan AG., (2008), “ Deepwater Moorings with High Stiffness

Polyester and PEN Fiber Ropes” OTC 19315

[10] François M. , Davies P. , Characterization of Polyester Mooring Lines, OMAE2008-

57136, Estoril, Portugal, 2008

[11] Bureau Veritas, Ariane 7, Theoretical Manual, 2008

- 1 -

BUREAU VERITAS RULES FOR THE CLASSIFICATION OF

TRADITIONAL NAVAL SUBMARINES Bureau Veritas will soon launch classification rules for naval submarines. These rules are presently published as tentative rules that will be made available to the navies and the building shipyards for comments and possible application in June 2008. They will be updated and formally published one year later when the first comments are taken into consideration. This paper aims at introducing these rules to the naval community. 1. Philosophy of the rules The rules for classification aim to protect the safety of the crew and of the environment by setting minimum safety standards that will be verified neither by the shipyard nor by the end user Navy but by an independent third party in charge of the submarine safety: the classification society. Classification rules for surface vessels benefit from more than 150 years of experience. We have adapted this experience to the underwater naval world. 1.1 Principles of classification Classification is the compliance with safety rules developed and published by the classification society. These rules are public, they belong to the classification society that is the only body empowered to interpret them. Classification rules include design requirements applicable at new construction stage and maintenance requirements that are checked all along the life of the submarine. 1.2 Classification process Classification is carried out within two major cycles:

- Initial verification at the newbuilding stage

- Maintenance of classification during the whole life of the submarine through a survey regime based on periodical inspections.

The Navies involved in the classification process have for a long time classed their vessels at the newbuilding stage. It is quite a recent policy to maintain the classification of the unit during its whole life. 1.3 Verification at the newbuilding stage The classification of submarines at the newbuilding stage results in the verification of their conformity to the appropriate rules of the classification society, in our case the rules for classification of naval traditional submarines. Classification is carried out within a three-step process:

- Design approval where the conformity of all the parts related to safety is verified versus the applicable rule requirements. This concerns: structure, production and distribution of energy, propulsion, fire safety including structural fire protection and fire-fighting

- 2 -

devices, escape routes and evacuation, atmosphere control, stability at surface and submerged.

- Materials and safety related equipment certification at maker’s works. The main

equipment concerned are: auxiliary engines, propulsion set, batteries, insulated bulkheads, fire-fighting equipment, fire detection, electrical cables-switchboards-connecting devices …

- Construction survey at yard including:

kick-off meeting, where the applicable rules and the working procedures are agreed, approval of internal shipyard fabrication and quality plan; that should provide Bureau

Veritas with the opportunity to carry out the verifications requested by the rules, approval of welders and of welding procedures, survey at the yard’s premises, where the surveyor will validate the different parts of

the submarine and will ask for modifications when deemed necessary, attendance to tests and to quay and sea trials, which are the ultimate validation of the

whole building process, issuance of classification certificates.

1.4 In service survey regime The survey regime is based on a term of classification of five years. During the term the submarine is to be inspected six times by the classification society:

- four annual surveys, - one intermediate survey, - one class renewal survey.

Annual surveys consist in deep visual inspections of all the safety related items without dismantling, the submarine being alongside. The intermediate survey focuses on the inspection of the capacities and on thickness measurements. The class renewal survey is the inspection of all parts of the vessel with dismantling of major equipment including the propeller shaft and the visit of the hull in a dry-dock. Example of the five year term survey regime.

Five year term survey regime

- 3 -

As an example of the verifications carried out, below is a description of the items inspected during the annual surveys.

General Examination of the naval submarine, logbooks, operational records. A visual inspection of the hull, equipment and machinery of the submarine and some

tests thereof, so far as necessary and practicable in order to verify that the submarine is in an acceptable general condition and is properly maintained.

A depression test to be carried out for pressure hull and means of closure including first and secondary ones.

A diving test. A schnorchel navigation test. The demonstration that the alarms and safety devices are functioning correctly.

Pressure resistant hull, structures and hull equipment

Pressure resistant hull and structures. Outer hull and exostructures above the waterline, and accessible parts of the rudder(s)

including blades and fines. Internal examination of accessible parts of exostructures. If retractable trimming devices are fitted, a functional test will be carried out. Hull openings, doors and hatch covers, their securing arrangements and sealing

arrangements are to be checked in satisfactory conditions. Hull penetrations with their sleeves, and weld connection to the hull. General external examination of mooring equipment. A functional test of hoistable or movable parts and of interlocks and safety devices is to

be carried out. Spaces including compartments and cofferdams with particular attention to bilges. Accessible resisting structures including torpedo tubes, capacities and collective rescue

platform. Strength and watertight bulkheads, batteries compartments, watertight doors, and

associated local and remote controls, and their watertight penetrations. Confirmation that watertight doors are not precluded from immediate closure. Fire divisions and fire doors. Hull and bulkhead cable penetrations. Confirmation that emergency escape routes are practicable and not blocked. Critical structural areas. Hull equipment. Hull valves and hull plugs. Scuppers, valves on discharge lines and their controls. Closing systems.

Machinery and systems

General examination of machinery spaces with particular attention to the fire and explosion hazards.

General examination of the machinery, hydraulic, pneumatic and other systems and their associated fittings, for confirmation of their proper maintenance.

General examination of the ventilation system, their ducts, valves and fans including spare fan(s) with a functional test of the different modes.

Visual examination of the condition of flexible hoses and expansion joints in sea water systems.

External examination of pressure vessels, high pressure piping, their appurtenances, including safety devices, foundations, controls, relieving gear, clamp fittings, insulation and gauges.

As far as practicable, external examination of heel, trim and regulating tanks, their water level indicators and gauges and their piping systems.

Control and monitoring of air inlet valve of fresh air cupola.

- 4 -

Functional test, control and monitoring of hull opening moving equipments including masts, air inlet valves and exhaust gas system.

External examination of leakage indicators, drains with associated cocks. External examination of ballast vent valve as far as practicable. External examination of sea water piping withstanding immersion pressure, their

accessories, including operation of the pumps and detection. Bilge wells. Examination and functional test of main and auxiliary steering arrangements, including

their associated equipment and control systems, and manoeuvring gear. When the submarine is equipped with a refrigerating plant:

− pressure vessels of the installation, − refrigerant piping, as far as practicable, − for spaces where refrigerating machinery are fitted:

− electrical equipment, confirming its proper maintenance, − gas detection system.

Functional test of masts lowering without hoisting energy source available. Communication

Underwater, surface, emergency and internal communication systems are to be function-tested. It will be checked that the means of communication dedicated to rescue teams are in place; they will be tested if applicable.

Test of means of communication and order transmission between the control station and the propulsion station.

Navigation

Confirmation that the calibration of navigating and locating equipments including depth is still valid. As a rule, calibration is not to have been performed for more than one year.

Confirmation that the rudders angle indicators on navigation control room and locally are in working order.

Confirmation that navigation radar and gyro compass are in satisfactory working condition.

Functional test of optical surveillance system. Confirmation that safety navigation equipments including navigation lights and sound

signalling equipments are in satisfactory working conditions. Functional test of echo sounding and speed loch systems.

Electrical machinery and equipment

General examination, visually and in operation, as feasible, of the electrical installations for power and lighting, in particular main and emergency sources of electrical power if fitted, electric motors, switchboards, converters, switchgears, cables, cable supports and circuit protective devices, indicators of electrical insulation and automatic starting, where provided, of emergency sources of power

Functional test of lighting fittings including main and emergency. Checking, as far as practicable, of the operation of emergency sources of power,

including the automatic mode, if any. Checking, as far as practicable, of the proper operation of safety and ultimate functions,

that their instrumentation and safety devices are operational and that their alarms are satisfactory

Batteries

Batteries log books are to be made available to the Surveyor for examination of the records since the last survey, and checking of any unusual record, breakdown or defective items.

The survey of batteries is to cover the following items: − General examination of battery compartments, piping and equipments fitted inside

including battery cells and trays. − Examination of battery cells shoring and connections.

- 5 -

− Examination and confirmation of the satisfactory operation of battery auxiliary systems, including:

• ventilation system, • electrolyte agitation system, • refrigeration system.

Checking that the hydrogen detection system is in working order and checking of calibration.

Function testing, as far as practicable, of detection, remote control and monitoring systems and alarms.

Fire protection, detection and extinction

Checking that relevant instructions are available. Examination and testing, as feasible, of the operation of fire doors, where fitted. Checking, as far as practicable, that the following are in working order: remote controls

for stopping fans and machinery, shutting off of fuel supplies in machinery spaces, remote controls for stopping fans from a control station, means of cutting off power to the galley.

Examination, as far as practicable, and testing, as feasible and at random, of the fire and/or smoke detection systems and fire dampers.

Fixed fire-fighting systems

Examination of the system including piping. Checking that fire hoses, nozzles, spanners and international shore connection, where

fitted, are in satisfactory working condition and situated at their respective locations

Fixed gas fire-extinguishing system − external examination of receivers of CO2 (or other gases) fixed fire-extinguishing

systems and their accessories, − examination of fixed fire-fighting system controls, piping, instructions and marking;

checking for evidence of proper maintenance and servicing, including date of last system tests,

− test of the alarm triggered before the CO2 is released.

Sprinkler system when fitted − examination of the system, including piping, valves, sprinklers and header tank, − test of the automatic starting of the pump activated by a pressure drop, − check of the alarm system while the above test is carried out.

Water-spraying system or water mist system

− examination of the system, including piping, nozzles, distribution valves and header tank,

− test of the automatic starting of the pump activated by a pressure drop (applicable only for machinery spaces)

Fixed foam systems (low or high expansion)

− examination of the foam system, − checking of the supplies of foam concentrate and receiving confirmation that it is

periodically tested (no later than three years after manufacture and annually thereafter) by the manufacturer.

Atmosphere control

Oxygen containers are to be surveyed. The air regeneration systems including soda-lime, oxygen candle or unit, their fittings,

valves and safety devices when applicable are to be examined and a functional test is to be carried out as far as applicable. Checking of their proper stowage, expiry date and appropriate quantities.

The survey is also to include:

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− examination and testing as appropriate of gas analysis equipment, − confirmation of the availability and suitability of the portable gas detection equipment

and instruments for measuring gas levels. − verification of calibration status of the measuring instruments. As a rule calibration is

not to have been performed for more than one year. − checking of proper stowage and expiry date of emergency oxygen candles and

chemical product for carbon dioxide elimination and their appropriate quantities for survival period.

− checking that emergency breathing air appliances are in sufficient number, in satisfactory condition and properly stowed onboard.

Flooding fighting

Detection systems and their alarms. Level detectors shall be tested at default and incident levels. Flow detectors as far as practicable

Flow detectors inhibition of automatic action as far as practicable Safety shut-off valves and their emergency system including hydraulic energy

accumulators Emergency and rescue installations

Verification of expiry date of the alert and localization items including batteries when applicable.

Verification of proper stowage and expiry date of the food and fresh water emergency stock and their appropriate quantities.

Verification of proper stowage and expiry date of the medical supplies in each refuge compartment.

General emergency alarm system

Functioning to be carried out

Stability Confirmation that the following documents are available on board:

− weighting, trim and stability booklet, − damage control documentation in the appropriate language.

Confirmation that periodical weighing and stability checks have been carried out in due time.

Confirmation that the scales of draughts are permanently marked at the bow and stern as far as visible.

One can see from this long list the extent of the annual survey. The same list applies to the class renewal survey but all major equipment is dismantled and internally inspected. 2. Area covered by the rules The rules for classification cover all parts participating in the safety of the submarine. These parts are presented in the rules under seven main chapters covering stability and weight control, resistance of the structure, propulsion and systems, human occupancy and fire safety, additional class notations and trials. The arm system itself is not covered by the rules except when it has a direct influence on the safety of the submarine, water tightness of the torpedo tubes for example.

2.1 Stability and weight control Intact stability, with requirement for a minimum module of stability of 0.2 meter in surface condition.

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Diving and resurfacing conditions, with stability module to remain positive, otherwise operational precautions to be taken. Damage stability with requirement that submerged module of stability remains greater than 75% of minimum module in surface Weight control with rule requirements about the capability of systems involved in weight and trim control to be able to restore weight-buoyancy at any time and to operate trim correction.

2.2 Structure The main concern about structure is the scantling of the pressure hull; particular attention is paid to the scantling loads, the qualification of hull material and corrosion. For a better calculation of the pressure hull the rule requirements introduce a correlation between safety coefficients to be taken into account for design appraisal and the admissible shape default acceptable during construction. Exostructures, non-resisting structures and hull outfitting, in particular diving and direction rudders are also covered by rule requirements. 2.3 Propulsion and energy Requirements related to propulsion are to some extent similar to those of surface vessels with special emphasis on the water tightness of the line shaft (at least two sealing glands). Design and testing of diesel engine shall take into account surface and snorkelling operations. Requirements related to energy concern batteries (two batteries and a recharging device are required). The batteries are to be located in non-contiguous compartments; the system is to be so designed that one battery remains operational in case of damage (including fire or flooding) of one battery compartment. The rules also include requirements concerning ventilation and monitoring of battery compartment. 2.4 Systems Diesel engines, pressure vessels, masts, piping systems, refrigerating systems, steering gear are covered by requirements taking into account the operation in depth:

Requirements exist for automatic actions (engine shut down, air tube and exhaust valves closing).

Specific requirements, in particular double closing devices, are developed for pipes likely to withstand immersion pressure.

Requirements for masts deal with water tightness of the mast itself and associated penetrations, and safety of mast in case of over-immersion.

Rules requirements also cover communication and navigations. Navigation radar, radio navigation system, depth indicator, acoustic sensors, UT system are requested. COLREG convention is applied for navigation lights and whistles. 2.5 Fire Safety and Human Occupancy Fire structural protection and fire fighting systems requirements take into consideration the specificities of potential fire hazards on board a submarine, i.e. little heat released but large smoke production.

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A15 insulation is the maximum standard for structural insulation. Requirements dealing with atmosphere control on normal operation and under survival period are cover:

Main gas monitoring systems (O2, CO2, CO, H2), Oxygen production, Dangerous gases elimination, Emergency breathing air systems.

2.6 Emergency and rescue Particular attention is paid to emergency situations:

Flooding fighting: detection of flooding and means designed in order to recover pressure hull integrity are covered by the following requirements: − Compartments where detectors are to be implemented are detailed; location of

detectors in compartment is to allow proper detection independently from trim and list,

− Two “levels” for signals: default level just indicates presence of water in compartment; incident level involves immediate actions against water leakage,

− Safety shut-off valve closing shall remain possible even in case of loss of hydraulic energy in order to recover pressure hull integrity.

Emergency blowing: this piping system is not to be used for another purpose than emergency blowing

Emergency lightening: this system, when present, must remain available even in case of loss of its energy source through a dedicated standby source

2.7 Additional Class Notations Additional class notations cover functions or specific equipment that are not strictly related to the safety of the vessel but indicate a greater level of equipment. The rule requirements related to these additional notations become compulsory only when the notation is selected by the client. The additional class notations applicable to submarines are:

Comf-noise Limit noise levels are defined per type of space, under 2 situations: transit and snorkelling. Conditions for the noise level measurements are defined in details: measuring instruments and locations, operating conditions (water depth, meteorological conditions), suggested format for recording the data.

Ref-store This notation provides optional requirements for frigorific installations of submarines such as equipment redundancy, arrangement of refrigerated chambers, design of refrigerating units. It also enables review of the frigorific function in itself.

HSE Granted when BV has been requested to check Health, Safety and Environmental regulations specified by the Naval Authority.

AIP Air Independent Propulsion is considered an additional means of propulsion, including: − Electric energy production system − Fuel & combustive storage systems

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− Discharge system of the residual products Specific safety study is to be performed, addressing potential hazards: Explosion, Fire, Toxicity, Collision, Overpressure, Failure of support systems, Leakages … Requirements are covering operation, installation, safety, certification and testing.

Anchoring This notation provides optional requirements for: design of anchor chain, design of anchor, design of windlass and chain stopper, arrangement of chain locker.

Refuge compartment Refuge compartment is to be able to resist at least 20 bar immersion pressure (unless other pressure explicitly required by the Naval Authority) when pressure hull integrity has been jeopardized. Refuge compartment is to include: − Rescue equipment mentioned in the Rules (oxygen supply,…) and a direct access to

an escape trunk, − An access door able to withstand design pressure of refuge compartment. Piping system entering in refuge compartment is to be designed in order to obtain water tightness of refuge compartment when used

2.8 Quay and sea trials Trials and in particular sea trials are the ultimate verification showing that all functions and systems of the submarine are working correctly together. For classification the success of sea trials is the confirmation that all the necessary controls have been carried out satisfactorily. It is the validation of all the work done at the design stage and during construction that enables the classification society to issue the certificates. Quay and sea trials are carried out, in line with the following sequence:

Tests at harbour are required to validate essential functions involved in safety, production and storage of energy.

Tests at sea are provided to validate submarine hull and systems ability to manoeuvre in depth. This capability is tested gradually in an increasing range of immersion.

3. Interests of classification The great interest of classification lies in the fact that a third independent party, recognised by more than 125 government and flag authorities in the merchant ship community, will certify the safety of the submarine. This third independent party is bound neither to the building shipyard nor to the Navy that will use the submarine, the classification society is solely dedicated to the safety of the unit. The other advantage of classification is the classification rules themselves. These rules are self supporting; they contain the exhaustive list of requirements related to safety and therefore are easy to use for building shipyards and design offices. The rules also benefit from the return of experience gained during classification of all types of vessels, surface and submarine; they are developed, maintained and updated regularly under the aegis of the naval ship committee of Bureau Veritas, the members of which belong to several European navies and naval shipyards. The maintenance carried out within the scope of submarine in-service survey regime is cost effective and all the items important for the safety of the submarine are verified by the classification society.

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Last but not least, the classification of the unit when granted at newbuilding stage and maintained through the submarine in-service survey regime is a guaranty for the Admiralty that the safety of its submarine is effective, the certification by an independent recognised body is likely to protect its legal liability in case of a casualty occurring during peace time operations.

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Condition Assessment Scheme for Ship Hull Maintenance

Christian Cabos, GL, Hamburg/Germany, [email protected] David Jaramillo, GL, Hamburg/Germany, [email protected]

Gundula Stadie-Frohbös, GL, Hamburg/Germany, [email protected] Philippe Renard, BV, Paris/France, [email protected]

Manuel Ventura, IST, Lisbon/Portugal, [email protected] Bertrand Dumas, Cybernetix, Marseilles/France, [email protected]

Abstract The goals of the CAS Project (Condition Assessment of aging ships for real-time Structural maintenance decision), which is concluded in spring 2008, were to increase ship safety through improved hull condition monitoring. The first step, and also the particular focus of the project, was an increased efficiency and quality of the thickness measurement process. The main results from the project are a standard exchange format, called the Hull Condition Model (HCM), and a suite of prototype tools which use this HCM format. Commercial tools are being derived from CAS: although they use the same HCM format, they involve different implementation principles. Validation of the underlying concept has been achieved by a real demonstration, at the Lisnave shipyard, in Portugal. We are exploring ways towards HCM acceptance as a maritime standard. The use of a Robot in the thickness measurements process is considered. Risk Based Inspections “RBI” and associated predictive tools would be of a great added value for HCM based processes. 1. Introduction Inspection and maintenance of a ship’s hull structure are vital to ensure its integrity. Such inspections are performed by surveyors of classification societies, by crew or owner’s superintendents, by vetting inspectors and by thickness measurement companies. Hull inspections typically cover: the state of coating, the assessment of possible structural defects and, most prominently, the remaining thickness of plates and profiles. For many years, there have been clear procedures for measuring and assessing thickness values (IACS URZ). Nevertheless, despite the large number of measurements which have to be taken during class renewal for aging tankers or bulk carriers (see IMO MEPC.94(46) and Resolution A.744(18)), measurement preparation, reporting and assessment are all typically performed manually, or with minimal IT support (e.g. Excel tables). Although the lack of IT support for handling thickness measurements seems obvious, no previous successful attempt for an integrated electronic support for this process is known to the authors. A prerequisite for the electronic exchange and interpretation of thickness measurement data is a data model covering all required elements of hull structural inspections. Such a model would then also form the basis for the development of tools for preparation, recording, reporting and assessment of thickness measurements. The EU project CAS focussed on comprehensive IT support for hull inspection and maintenance in general – and the thickness measurement process in particular. In the project, major stake holders of the thickness measurement process cooperated to devise an enhanced process, design a data model for the exchange of measurement data and implement prototype tools to examine possible benefits of the new procedure. 2. Business context 2.1 Virtual company The CAS project was defined in the light of the “virtual company” concept, where several independent companies act together as a single company, sharing the same information and using standard exchange formats. It was also inspired from the industrial ISO STEP exchange standards. In this particular project, all along the condition assessment process, involved companies (Owner, Thickness measurement Company, Classification society, etc) behave indeed as a single “virtual company”.

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2.2 Client driven developments 2.2.1 Software differentiation The CAS project is now very close to its official end, so we have the resulting basic tools, which fit the specifications of the project. However those basic tools are already being transformed into commercial applications which are quite different because they cater with the needs of different types of clients. 2.2.2 Ship-owners For ship operators, it is of the utmost importance to reduce off-hire periods and to keep repair cost under control. In that respect, a clear view of the current status of the hull structure is required so that areas in need of further investigation could immediately be identified. Furthermore, decisions on necessary repairs must be taken without delay and be communicated unambiguously to repair yards. The electronic thickness measurement support devised in CAS largely supports these requirements, through reduction of manual copying of data, clear visual display of measurement results directly on a 3D model of the ship and fast generation of final reports. 2.2.3 Oil companies Floating Production Storage Offloading units (FPSOs) operators are showing interest for HCM type tools, as a means for the follow-up of their units. They especially do not want to miss any future degradation, which could potentially lead to the interruption of oil production. Prevention of production interruption, through timely repairs, is their main objective. Therefore, the history of all inspections on the FPSO (by the classification society and the owner’s people) should be recorded and updated in the tool, enabling at any time the drafting of an exhaustive specification of the due repairs. Predictive tools, extrapolating from the past inspections, would also help anticipate the need for repairs. 2.2.4 Charterers Charterers would like to protect themselves against bad surprises regarding the structural condition of the vessels they charter, which could lead to environmental disasters and long litigation procedures. Thus, as a condition for chartering a vessel, they may require an HCM file, providing a transparent view of the structure condition. 3. Goals and State of the Art 3.1 Goals The specific goals of the CAS Project were to increase ship safety, by providing a permanent easy and transparent access to all ships structural data. This was a means of protecting the coasts of Europe from oil spoilage disasters, as well as protecting crews of bulk carriers from sudden sinking. The CAS project was a three-years EC funded project, gathering partners involved in all aspects of the condition assessment process. A standard exchange format, called Hull Condition Model “HCM”, was to be developed in order to support the full condition assessment process. A standard exchange format is especially needed in this process, because Thickness measurement companies work with all Classification societies, and ships sometimes change their Classification societies.

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Fig.1: Condition assessment workflow

A by-product was the increase of the process efficiency, because measurement reports are made available at any time during the measurement campaign, and in particular they can be delivered after 2 or 3 weeks only, which means before the ship leaves dry-dock, easing the undertaking of repairs resulting from those measurements. Coherence of measurements between successive measurements campaigns can be ensured, because the measurements are in a structured electronic format. 3.2 State of the art The main results from the project are: the standard Hull Condition Model (HCM), a suite of prototype tools using the HCM format and supporting the condition assessment process in all its phases, including data interfaces to and from classification software. The following phases of the process are particularly supported:

- Creation of the ship’s 3D-model, - Entry of the measurements into the model, either by a robot or human operators, - Assessment of the structural condition.

HCM was written in XML language and is made publicly available on the project web file: http://www.shiphullmonitoring.eu Validation of the tools, concepts and methodologies developed in the project has been successfully achieved by a real demonstration in the Lisnave shipyard in Setúbal / Portugal. This demonstration has been documented by a video film that is shown at the end of this presentation. The ship chosen for thickness measurements tests was an oil tanker, 150 000 DWT, L = 274 m, 5 years old. A portion of the ship’s outside shell was measured by a robot. The inside of some water ballast tanks and cargo tanks was measured through rope access. Both groups of measurements were recorded together into the HCM model, and analysed through visualisation and condition assessment tools. After the end of the CAS research project, a Consortium is expected to take care of the updating of the HCM standard. The Consortium will initially consist of all partners of the project, but will be open to additional candidates. Therefore this paper is entitled to consider the potential developments and applications expected in the next years.

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4. IT Tools 4.1 Developing around the HCM standard Commercial tools are being derived from the CAS project. Although they use the same HCM format, they involve different implementation principles and have been used for different types of marine clients. 4.2 IST tool 4.2.1 Hull Modeling Software Tools In the scope of CAS, prototype software tools were implemented by Instituto Superior Técnico (IST) to produce in a short period of time a product data model in accordance to the HCM standard. The main concept of CAS, of a paperless data collection for a faster and more efficient processing, requires the existence of a 3D product data model, to assist planning of the measurement campaigns, to visualize the data collected and to provide support to its subsequent analysis. For the intended use, a set of requirements were specified. From the geometric point of view, the model does not need to have high accuracy because a simplified geometric description, based on linear approximations of both curves and surfaces was adopted on the HCM. From the structural point of view, all the plates and stiffeners to be inspected during a campaign must be present and identifiable on the model. In future business scenarios, 3D models of the ship hull may be available during the operational life of the ship, as a result from the engineering analysis carried out during the design process. However, currently and in the near future, a large majority of existing ships will not have such models. One of the issues of creating the hull models for existing ships is the eventual lack of information. Whenever the only data available are the drawings available onboard the ship, the model must be developed from a reduced set of data and also in a short period of time, due to the time constrains on the repair yards. So, for the required purpose it was assumed that the simplified model should be able to be developed from the information on the drawings commonly existing on board the ship, such as the general arrangement, body plan, docking plan, midship section, shell expansion, transverse and longitudinal bulkhead. Sometimes, in an existing ship, neither the body plan nor an offset table is available. In this case, a rough hull shape must be defined using the existing data. For instance, some aspects of the hull shape can be obtained from the available drawings, such as some cross-sections from the docking plan, the stern and bow contours from the general arrangement, the bilge radius, the rise-of-floor, and deck camber from the midship section drawing. For the purpose of creating a ship 3D product data model, compatible with the HCM, two new prototype software tools were developed and implemented in CAS, one for the generation of a simplified hull form and the other for the modeling of the ship hull structures. 4.2.2 Parametric Definition of the Hull Shape An approximated hull shape can be generated from the main dimensions, some form coefficients, and a set of main curves, each defined by a set of shape parameters. The parameters consist of a set of distances and angles that can easily be obtained from the general arrangement and structures drawings. The main curves used are the flat of bottom, the flat of side, the midship section, the stem and stern contours, Fig.2. The sectional area curve is also obtained parametrically and used to generate additional cross sections in the aft and fore bodies, in compliance with the required displacement and form coefficients.

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From these curves a set of surfaces is generated. The intersection of those surfaces with transverse planes produces the set of cross sections needed to define the hull in a way similar to the traditional body plan. The purpose of this tool is not to generate a fair hull form but only to provide an acceptable external boundary for the development of the structure generation tasks. In this context, by acceptable it is meant that the strakes of plates and the stiffeners existing on the ship can be entirely mapped into the 3D model.

Fig.2: Main hull curves

The application has a modular structure composed by two main modules, a NURBS kernel and a set of naval architecture functionalities. The NURBS kernel provides the basic functionalities for parametric curve and surface modeling, such as curve fitting and approximation, surface generation, curve/curve intersection, curve/plane intersection, surface/plane intersection and surface/surface intersection. The naval architecture module provides the specific functionalities for the parametric generation of curves, alteration of the section area curve, computation of areas. 4.2.3 Hull Structures Product Data Modeller The modeller system developed is not just a geometric modeller but a product data modeller. The system must be able to manage not only the geometry but also the data specified in the HCM model, which contains information such as as-built plate thicknesses and stiffener scantlings, the associated structural systems and compartments, as well as the acceptable diminutions in accordance to the structural safety criteria adopted by the classification society. The arrangement of the internal structures is kept separate from the hull form to allow a larger flexibility during the modeling activity: slightly different hull shapes can use the same internal structural arrangement or different internal arrangements can be evaluated for the same hull form. For modeling purposes, the hull structure is considered divided into two main groups, the external hull and the internal structural systems. The external hull can be composed of one or more shells and may have planar or curved regions that depend directly of the hull shape and the main deck. The internal structures are planar, and their boundaries can be partially obtained from the outer hull and main deck shapes. The structural systems considered are the bulkheads, the decks, the web frames, the bulkheads and the girders. For each of these systems, generating templates can be defined. These templates have two main parts, corresponding to the two stages of the modeling process: first the shape of the base molded surfaces is obtained and next, the geometric description of plates and stiffeners is determined.

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The first part defines the geometry identifying the external boundaries, a set of shape parameters and some form features specifications, such as openings, if any. The second part defines the associated stiffened panels. Each generating template defines a family of structural system members, with similar shape and scantlings. The scantlings are defined by one or more plate sets and stiffener sets, which describe sequences of adjacent groups of plates/stiffeners, identifying the quantities, dimensions, spacings, scantlings and materials. These generic definitions are designated by templates because they do define explicitly neither the shape nor the exact arrangement of the associated plates and stiffeners. Wherever the boundaries or the scantlings of the system change, a new template must be defined.

Input Main

Dimensions, FrameTable

Import Hull Form

Compute Local Geometry

Define Templates ofthe Main Structural

Systems

Define ActualInstances of the

Structural Systems

Generate Plates & Stiffenersand Store in Database

Ship Database

Fig.3: Structures Modeling Sequence

To obtain the actual system members, the templates must be instantiated to a precise location on the hull. Then, the plane or planes associated to the system are first trimmed by the outer hull (shell and main deck) and next by all the boundaries enumerated. The result of this process is the actual external shape of the member, defined by a closed polygonal line. Then, from the application of the specified plate sets to the member shape, a set of seam lines is obtained, defining the contours of the plates. From the application of the stiffeners sets, a set of trace lines is obtained. The typical modeling sequence is presented in Fig.3. The system has a modular structure and is composed by seven main component layers. The simplified geometry kernel provides the functionalities to process polygonal lines and surfaces, including some elementary modeling and intersection operations. The structural modeling functions provide the capability to process the input shape parameters to generate the 3D representations of the mentioned structural systems. The ship data storage is a relational database, implementing standard SQL language. The scripting engine is based on the Python language and a number of extensions were developed to allow the generation, storage and retrieval of data from the database. The XML processor provides capabilities to import and export data from measurement campaigns in accordance to the HCM data model. The graphical interface provides the 3D visualization of all the entities generated by the modeller.

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In compliance with the simplified geometry adopted, plates and stiffeners are represented only as surface meshes without thickness, Fig.4, Fig.5, although the product data stored in the database can provide the information for a solid model representation.

Fig.4: Web frames Fig.5: Simplified plate and stiffeners

The shell can also be displayed in a 2D expanded view. The user interface is based on dialog-boxes for data input and editing. 4.2.4 Validation and Testing To validate the methodology implemented, one cargo hold of an existing Suezmax oil tanker was modelled, based on a set of structural drawings. The system was able to produce a model on which, in spite of some irregularities on the distribution of the plates on the shell, all the plates and stiffeners were correctly mapped, Fig.6. An XML data file was exported in accordance to the HCM. The information was used by the surveyors to associate the measurements obtained during the campaign carried out on the ship, in a shipyard dock.

Fig.6: Suezmax cargo tank Finally the file with the campaign measurements was imported back into the system. The points were correctly assigned to the shell plates and able to be compared to the as-built thickness values.

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4.3 GL-Pegasus 4.3.1 Principles The concept of the CAS Project aimed at the development of methodologies, data formats and software prototypes to validate the developed ideas/solutions around Hull Condition Monitoring and Assessment. Due to the urgent necessity for adequate computer tools for data collection, visualisation and assessment of Thickness Measurements (TM) to be used operatively, for Germanischer Lloyd the exploitation of the results of the CAS project have been reflected in the development of a commercial tool – GL Pegasus – to support the whole TM Process. Within this context, GL Pegasus has been developed in parallel to the CAS project, providing additional input for the refinement of user requirements and for the development of the data model itself. GL Pegasus utilises HCM as its main data format. According to the new defined TM workflow, Fig.7, the initial HCM file is created in POSEIDON, GL's software system for ship structural design and scantling calculations. For this purpose and as part of the activities of the CAS project, the corresponding data interfaces from POSEIDON to HCM have been developed. However, as HCM has been developed as a neutral data format and with interoperability in mind, it should be possible to utilise any HCM file created with other Ship Structural CAD systems in a similar way. This has been demonstrated within the CAS Project by using GL Pegasus with 3D Models that have been generated from the FORAN system of SENER and from the CAS-Tool prototype of IST (see section 3.2).

Fig.7: TM Workflow with GL Pegasus

Once the initial HCM file is generated from POSEIDON, it is loaded into GL Pegasus and used for the different phases of the TM process:

• Campaign preparation • Data collection • Visualisation and Assessment • Reporting • Structural assessment

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4.3.2 Campaign Preparation Based on the requirement to display the 3D model in the traditional 2D representation for TM purposes, Jaramillo et al. (2006), GL Pegasus generates corresponding views (TM configurations) as typically shown in the sketches of the structural areas. Basically two different types of TM configurations are used for this purpose, which correspond to the IACS recommended procedures for reporting of Thickness Measurements:

a) Strake oriented: In this case the plate strakes of a single structural element are arranged in tabular form together with a corresponding sketch (e.g. a deck or shell expansion view)

b) Cross section oriented: for so called ring measurements, transverse sections of longitudinal structural parts at specific frame positions are considered. However, this type of view is also applicable for transverse structural parts at the corresponding frame position.

A TM configuration displays a tabular and a graphical view of the relevant structural parts. Both views are interconnected to each other as they show a different representation of the same data as contained in the HCM file. Fig.8 and Fig.11 show a cross section oriented and a strake oriented TM configuration, respectively.

Fig.8: Cross section oriented TM configuration

Depending on the scope of the measurement, the user creates the required TM configurations and positions the points manually or automatically on the corresponding structural components, either before or after the data collection. Furthermore, for a better organisation of the measurement campaign, GL Pegasus introduces the concept of measurement sequence. A measurement sequence is a set of numbered points arranged at a specific TM configuration that can be used to interface with an UTM Gauge. The definition of measurement sequences can be achieved prior or during the data collection. This provides additional flexibility and adaptability to different working procedures of TM operators. Measurement sequences play an important role for the interfacing mechanism with UTM gauges. Most data interfaces of UTM gauges are based on different types of arrangements of points (often called files) in form of lists and arrays. GL Pegasus communication with UTM gauges has been achieved by mapping between the proprietary file format defined by the UTM Gauge vendor and the measurement sequences. Fig.9 shows an example of a measurement sequence that has been transferred to a GEIT DMS-2 UTM Gauge. This is one of the most sophisticated UTM gauges on the market and is equipped with a large alpha-numeric display allowing for a tabular representation of the data. The bidirectional data transfer possibilities of such an UTM Gauge makes it possible to define complete measurement tasks, transfer them to the UTM Gauge, perform the measurement and send the results back to GL Pegasus.

Tabular View 2D Sketch

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Fig.9: Data Transfer with UTM Gauge using a measurement sequence

4.3.3 Data Collection Principally, the actual data collection procedure is not changed by GL Pegasus, as the TM operator must take the readings one by one ensuring that they are correctly assigned to the corresponding positions. However, GL Pegasus provides support in different ways. In particular, it is possible to establish an optimised combination of the sketches and the lists of points being measured. The corresponding print outs for use on board are generated from GL Pegasus prior to the measurement task. The entry of the data into the system can be achieved in different ways, adapting to the individual way of working of the TM companies and the equipment available. Basically, the following possibilities for data entry are supported by GL Pegasus:

• Manual entry: this reflects the conventional procedure and represents the support for simplest UTM devices that do not support any kind of data transfer with the computer.

• Semiautomatic entry: for UTM Gauges supporting a one-way data transfer to the computer. This a typical configuration for devices equipped with a simple data logger such as the GEIT DM4-DT. Measurement sequences are marked manually on the printed sketches and are later entered into GL Pegasus. The corresponding measurement values are then associated automatically during data transfer from gauge to PC.

• Automatic entry: For UTM Gauges supporting a bi-directional data transfer with the computer such as the GEIT DMS-2. This allows for an easy identification of measurement points on device and eliminates the creation of additional measurement configurations in the UTM Gauge.

• Direct connection: this requires two operators involved during measurement, which are wire connected. The measurement equipment and the computer running GL Pegasus remain on deck (e.g. within a container) and the operator inside the ship structure only has the probe in the hand sending the reading values. Coordination for correct assignment of the readings in GL Pegasus is ensured by voice/video communication. Fig. 10 depicts how data collection is performed using a direct data communication between UTM equipment and GL Pegasus. This procedure has been used by MME during the demonstration measurements in the CAS project.

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Fig.10: Data collection using a direct connection between UTM equipment and GL Pegasus

4.3.4 Visualisation and Assessment As soon as the measured values are entered into GL Pegasus by any of the options explained above, the results can be visualised in the tables, in 2D and in 3D. For this purpose, a colouring scheme has been defined reflecting the degree of corrosion with respect to the specified corrosion margins. The colouring schema is displayed in the tabular representation and in 2D as per measurement point. In 3D, the colouring schema applies additionally per plate/stiffener making it easier to identify hot spots and areas that require special attention.

Fig.11: Visualisation of results on a strake based TM configuration

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The visualisation in 3D makes it possible to obtain an overview of the TM results in a consistent way. Structural parts can be hidden or displayed as required, applying different mechanisms and criteria such as the type (plate/stiffener), the functionality, the resulting degree of corrosion, etc.

Fig.12: Overview of the TM results

Fig.13: Easy identification of hotspots

Standard functionality for 3D visualisation such as rotate, pan and zoom are available. It is also possible to limit the area being displayed by interactively applying a user defined clipping box as shown in Fig.14.

Fig.14: limitation of the 3D display by a clipping box

4.3.5 Report generation Addressing one of the highest prioritised user requirements concerning the reduction of the time needed for the elaboration of the final TM report, see CAS Report D-1-2-1, Jaramillo et al. (2006), GL Pegasus provides the functionality to automatically generate a TM report in compliance with IACS requirements. The time for availability of the final report is therefore reduced to a matter of minutes in contrast to days or even weeks as for large TM campaigns utilising conventional procedures. The generated report contains a cover page with information about the vessel and the corresponding measurement campaign, a list of contents and the documentation of the each measured area (TM configuration) including the tables and the corresponding sketches.

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Additionally, a summary of hotspots can be included in the report. For each individual item in the list of hot spots, a link to the corresponding section in the report is available for easy reference. The summary of hotspots is a valuable instrument for the TM assessment. The technical expert and surveyor can concentrate on the areas requiring special attention and reflecting the actual result of the measurements in terms of possibly required measures to be initiated.

Fig.15: Automatic generated TM Report

As the scope of documentation in the generated report can be adjusted by the user, the reporting functionality can also be used for the generation of partial reports (e.g. reports at the end of each campaign day). In Fig. 15 some sample pages of a TM report generated by GL Pegasus are shown. 4.3.6 Structural Assessment Depending on the resulting hull condition with respect to corrosion degradation it might be necessary to perform strength calculations to verify the integrity of structural components locally or globally and to eventually determine the required scope of repairs. For this purpose and within the scope of the CAS Project, corresponding data interfaces from HCM to POSEIDON have been developed. HCM files can be imported directly into POSEIDON. The measurement values are associated automatically to the respective plates and profiles of the POSEIDON model and the following longitudinal strength assessment refers to the actual measured values. 4.4 VeriSTAR HLC 4.4.1 From theory to practice A great deal of adaptations and ergonomic developments are required to move from the research projects prototype to any derived commercial tool. In particular a commercial tool must be appealing to operational people, typically to the ships’ superintendent or offshore oil fields operational people. Although it can be used for ordinary vessels, the tool developed by Bureau Veritas is currently oriented towards the offshore oil industry, because those clients have, in the first place, expressed their interest. Therefore, the tool was associated with an existing asset management tool (AIMS), which

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was designed for the planning and reporting of all inspection and maintenance tasks for a given unit, whether required by the classification society of the owner’s operational teams. The tool is understood as the first module of a new series of customer oriented tools, providing a initial 3D geometric model that will be used later on for finite element analysis, tonnage calculation, hydrodynamics, etc.

Fig.16: 3D View

4.4.2 Coarse modeling The tool includes a function that allows starting up with a coarse model of the ship and later on the addition of details, by super-imposition of smaller elements. For instance, only the area in way of one single cargo tank may be initially needed for the first renewal survey, so this area must be modelled in details, but the rest of the ship’s model may be fairly well represented with a good enough coarse modeling. At the next renewal survey, other areas of the ship will have to be modelled in details, which will be achieved by super-imposing smaller structural elements above the coarse structural elements.

Fig.17: Super-imposition of smaller elements

4.4.3 “2D” views for data input To ease the input of measurements into the 3D-model, the tool provides “2D” views, which are technically 3D views, but perpendicular to the structural elements to be measured. So the 2D views are

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automatically derived from the 3D model and there is no need for drawing additional 2D views for the purpose of data input.

Fig.18: “2D” view for measurements input

4.4.4 Visualisation means A set of visualisation means has been added, for instance:

- to erase selected structural elements, in order to get a better view of previously hidden structural elements, - to extend a selected structural element to all similar elements on board or to larger structural assemblies including this element.

Fig.19: Erasing elements

4.4.5 Google Earth All inspection data (thickness measurements, coating condition, cracks, inspection reports, pictures, video films), can be visualised on the 3D-model. Flags are displayed with a “look and feel” similar to “Google Earth” pictures. The user adjusts the level of details to be shown on the screen, and the type of information he wishes to see.

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Fig.20: Easy storage of inspection data

Fig.21: Google Earth look and feel

Fig.22: Repair preparation (what is wrong in the structure)

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4.4.6 Repairs preparation The superintendent is expected to check the tanks, one by one, inside the virtual ship, which is a convenient alternative to visiting the real ship, as a preparation of the repairs. But, it helps the superintendent very much to have access to a dedicated view, which focuses on what is wrong with the structure, for instance the plates to be repaired and the pictures and reports related to damages or degradation. 5. Outlook and further development 5.1 Level of detail The guideline for defining the proper level of detail of the 3D-model is expected to be clarified during the real-life implementations which are to be carried-out in the next future:

- for new-building ships and for offshore units which always stay with the same owner at a fixed location, a detailed model can be expected, - at the contrary, for many ships in service, changing owners frequently and sailing around the world, simpler models should be considered as an alternative.

5.2 Using a Robot The Robot used in the project was a Magnetic Hull Crawler, designed for inspection and maintenance of steel surfaces. A permanent magnet enables the Robot to crawl on a ship’s outer shell in dry-dock. This robot is able to operate both in air and underwater (50 m). It is Joystick or PC controlled. Dimensions are 610 x 460 x 400 mm and the weight is 60 kg.

Fig.23: Measurements Robot

In the air (as it was the case in the demonstration), the positioning of the Robot is done by 3 odometers (each odometer consisting of a steel cable rolled around its coding device) which transmit in real time the motion of the Robot as x, y, z coordinates to the Cybernetix software “Robolocalisator”. This software is searched by the “Hullmap” software which merges the values of the position and the steel thickness. The “Hullmap” software, from the position of the Robot in the 3D environment of the 3D-model, detects automatically the reference of the plate, using an invisible video camera, always perpendicular the plates. This reference is displayed on the “Hullmap” screen and is automatically added to measurements and positions in the HCM file.

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Fig.24: Robot scanning outer shell Fig.25: Robot crawling on outer shell The role of a Robot in the thickness measurements process is now clarified. The Robot is well adapted to flat surfaces, such as outer shell and flat cargo bulkheads. Surfaces should be in a clean condition. It is very good at scanning doubtful plates. Close-up survey, implying the physical proximity of the surveyor, is not required for the outside shell, so that the robot can be left alone. The robot could even be programmed to take, say, all bottom measurements alone and unattended. The Robot could also be useful for naval vessels at sea, because they have clean hulls and consequently ultrasonic gauging can be done without a prior cleaning of the hull. For FPSOs, which do not dry-dock, and therefore have underwater hull covered with fouling, the Robot could be used, if it could be found a way to remove the fouling (high pressure nozzles) or to take measurements through the layer of fouling. In the future, other types of robots might be developed:

- for underwater NDT inspection of hull of vessels at harbour (hull thickness measurement and cathodic protection inspection).

- to measure stiffened plates, for instance inside the ballast tanks. In narrow double skin ballast tanks, where human access is difficult, a swimming robot could perform the gauging. However, under current IACS rules, a close-up survey is required in this case, for instance for web frames in ballast tanks, so that the surveyor must also be present, close to the robot, at the time of measurements. Therefore, the advantage of the Robot is reduced, if anyway the presence of a human surveyor is required in those locations. 5.3 RBI developments Risk Based Inspections “RBI” and associated predictive tools would be of a great added value for HCM based processes. The use of degradation models and extrapolation from several measurement campaigns for planning of repairs is examined in this paper and can be combined with an evaluation of the severity of resulting damage, to finally provide RBI based inspection schemes. The main reasons for implementing a risk based approach in inspection planning are:

• to ensure that the “Base Line Risk” does not exceed the risk acceptance criteria, as set by the operator, at any time;

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• to focus the inspection effort on items where the safety, economic or environmental risks are identified as being high, whilst similarly reducing the effort applied to low-risk systems;

• to identify the optimum inspection or monitoring methods to match the identified degradation mechanisms.

A risk assessment has to consider all relevant failure modes and mechanisms, however, in a first approach the focus is on corrosion. Starting point for a risk based inspection strategy is

1. a screening of the current ship condition, to identify areas of high risk as well as medium and low risk level; followed by:

2. an estimation of a risk value on a consistent methodology and the development of a risk matrix;

3. the prioritisation of the different areas; 4. the development of an appropriate inspection program.

The screening of the ship to identify the areas of high risk starts with the segmentation of the ship structure. As not every part of the structure will have the same risk, segmentation is necessary. For each segment, the risk can be estimated by evaluating the probability of failure and the consequence of failure. The combination of both leads to the risk. The probability of failure can be estimated by using different methods, such as: qualitative methods (e.g. questionnaire, simple risk matrix), semi-quantitative methods (e.g. index procedure) and quantitative methods (fully probabilistic approach). Qualitative methods deal with few essential data and lead to a rough estimation of the failure probability. The semi-quantitative methods use more information and some calculations are carried out, which result into a more accurate failure probability. The quantitative methods consider fully probabilistic approaches and lead to an accurate estimation of the existing failure probability. The semi-quantitative approach presents a good medium, because the fully quantitative approach requires a lot of data which are normally not available for existing ships and the semi-quantitative approach gives a more detailed failure probability than the pure qualitative approach. A combination of index procedure, which leads to a general result for the probability of failure, and the remaining life, which is related directly to the corrosion, is appropriate for the assessment of the threats due to global thinning based on corrosion. The assessment of the consequence of failure for each segment considers the consequences for safety, the environment and the economical consequences. The combination of the failure probability and the corresponding consequence leads to the current risk of the ship segment regarded. The joining of all segments leads to a risk value for the ship. The merging of the local segment risk to a global risk is not considered, however this aspect should be covered in a further study. Several different approaches exist in the literature, e.g. reliability block diagram, fault tree analysis, reliability networks. After the estimation of the risk related to each segment, an appropriate inspection strategy should be developed. The inspection effort and interval should be determined taking into account the current and the future risk of the segment regarded. The possible risk based improvements of the existing inspection methods can be carried out in two ways:

• adjustment of the inspection effort, • adjustment of the inspection schedule.

Both possibilities and a mixture of both are conceivable. The aim of the adjustment is to investigate the vessel with the higher risk more intensively than the vessel with the lower risk. This could also lead to a modification of the date for the next class inspection. It is thinkable that for ships where the risk assessment was carried out and show a low risk level, the inspection intervals could be extended. On the other hand, for ships with a high risk level, the inspection intervals should be reduced in order to avoid unacceptable risks.

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Beside the modification of the inspection interval, the effort could also be modified. This is implicitly already covered in the specific codes, as the inspection effort increases with the age of the ship. Using the risk based approach would extend the current procedure to other effects than only regarding the age. Based on the risk assessment, it is possible to identify areas of the ship with higher and those with lower risk. The inspection amount taken at the higher risk areas should be larger than at the lower risk areas. The procedure given above could be a starting point for a development of a risk based inspection program. 5.4 IACS standard There is an on-going action versus IACS to add the HCM-based reporting of thickness measurements into the IACS Uniform Requirement UR Z10, as an alternative to the existing Excel-based reporting formats. It is believed that a few real-life implementations of HCM by ship-owners are a pre-requisite to having HCM accepted as an IACS standard.

Fig.26: Towards an IACS standard

5.5 Export of HCM from shipyard All big enough shipyards center their shipbuilding process around a very complete CAD model of the ships, which contains not only the ship’s detailed hull structure, but also mechanical systems, fluid systems, ventilation and electrical systems. These CAD models are very detailed, because they must provide enough information for the building of the real ship. They incorporate a lot of the shipyard’s experience and know-how and are generally, for that reason, not handed-out to the ship Owners after the delivery. The easiest way to have ships equipped with HCM files would be that the building shipyard generates the HCM file directly out of its CAD model. We can expect that this would be acceptable for shipyards, because HCM only covers hull structure and is so simplified that it cannot be used by a competitor to build a sister-ship.

Fig.27: HCM from shipyard

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5.6 Regional Waters Authority scheme 5.6.1 Definitions A “Regional Waters Authority” (RWA) can be defined as the Official Body having the law enforcement powers over an extent of sea waters (the “controlled” waters), surrounding a given region of the world. Regional Waters Authorities could typically be the EC Maritime Administration, the US, Canadian or Japan Coast Guards. 5.6.2 Technical approach We examine hereafter the new technical possibilities offered by the HCM technology to an RWA, however the legal aspects and the associated repartition of maritime actors’ responsibilities, would have to be analysed as well, if we had to draft a complete proposal for implementation. 5.6.3 Continuous follow-up versus status control The only way for the RWA, to make sure that the condition of a vessel, sailing in its controlled waters, is safe, is to have a direct access to the current structural condition status of the vessel, at the time of its entry into the controlled waters. Thus, the RWA does not need to examine the history of the vessel (past owners, flags, classification societies, damages, detentions, etc), which may include some missing or subjective aspects, but only needs to concentrate on the objective structural condition status of the vessel, at this precise point in time.

Fig.28: Regional Waters Authority scheme

5.6.4 RWA scheme major steps Therefore the following tentative scheme can be considered:

- all “risky” ships entering the controlled waters are required to have an updated HCM file. - at the entry into the controlled waters, those ships must send their HCM file to the RWA. In practice, this file would be complemented by a set of administrative and cargo-related information. - on the basis of the HCM file, the RWA will activate the proper response:

* continuous follow-up of the ship and communication to shore stations, * request of an inspection by the Port State Control authority at next port of call, * access refusal to the ship in the controlled waters.

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- in a bad weather period, the RWA would require all “risky” vessels trading inside the controlled waters to send their HCM to the RWA. Vessels deemed weak would be required to reach the nearest port of call, to wait safely for the improvement of weather conditions.

5.7 Extension of ship status file Following the same line of thoughts, in order to provide the RWA with a complete ship status, we could develop a complementary tool, to reflect the condition of the machinery equipments. Both structural and machinery status should indeed be taken into consideration, because:

- structural failures occur seldom, but usually cause serious consequences; - machinery equipments failures (steering gear, diesel generators or main engine) are frequent,

but usually cause relatively less serious consequences, in relation with collision or grounding.

By opposition to the structure, where the condition is easily and obviously reflected by the thickness of steel plates and stiffeners, some research is a pre-requisite to establish a list of the parameters describing the condition of the machinery equipments. References RENARD, P.; WEISS, P. (2006), Automation of the ship condition assessment process for accidents prevention, 5th Int. Conf. Computer Applications and Information Technology in the Maritime Industries (COMPIT), Oegstgeest, pp.403-408 JARAMILLO, D.; CABOS, C.; RENARD, P. (2005), Efficient data management for hull condition assessment, 12th Int. Conf. Computer Applications in Shipbuilding (ICCAS), Busan JARAMILLO, D. et al. (2006), CAS Deliverable D-1-2-1, Business Process Analysis and User Requirements, March 2006 JARAMILLO, D. et al (2007), CAS Deliverable D-1-3-1, Specification of HCM (Hull Condition Data Model), Oct. 2007 JARAMILLO, D.; CABOS, C. (2006), Computer support for hull condition monitoring with PEGASUS, 5th Int. Conf. Computer Applications and Information Technology in the Maritime Industries (COMPIT), Ooestgeest, pp.228-236 IACS URZ, Requirements concerning Survey and Classification, 2003

ATMA 2008

DEVELOPPEMENT, IMPLEMENTATION, MAINTENANCE ET FUTUR DES REGLEMENTS

STRUCTURAUX COMMUNS DE L'IACS POUR LES VRAQUIERS ET PETROLIERS A DOUBLE COQUE

Philippe BAUMANS Bureau Veritas, Département Développement, Paris-La-Défense (France)

SOMMAIRE

Ce document expose les défis rencontrés dans le développement effectué par l’IACS des Règlements Communs pour la Structure (Common Structural Rules, CSR) des vraquiers et des pétroliers, en ce qui concerne les techniques de modélisation utilisées et intégrées dans les hypothèses de chargement, les réponses structurales et les critères d’acceptation.

Il précise également comment l’IACS répond au besoin de cohérence pour l’application de ces Règlements et de leur maintien dans le futur.

Comme tout document contenant des prescriptions réglementaires, il est nécessaire de trouver un juste équilibre entre l’intégration de méthodes de pointe de haute technicité d’une part, et les besoins d’applications déterministes et pratiques d’autre part, sachant que l’Industrie souhaite de plus en plus utiliser des modèles de pointe au stade du projet tout en voulant, à la fois, un procédé lui fournissant aussi bien des ébauches rapides de conception que des cycles rapides de construction. Tout cela sans jamais perdre de vue l’objectif principal: le développement de Règlements allant dans le sens de la sécurité, de la solidité et de la durée dans le temps, ce que demande la société dans son ensemble.

Au cours du développement des critères des CSR, la nécessité de cet équilibre a conduit à incorporer des prescriptions de Règlements existants et des approches basées sur le risque pour identifier les dangers et leurs conséquences afin de concentrer, dans le développement des nouveaux règlements, l’attention sur les zones les plus critiques. Alors que les CSR ont tendance à reprendre des parties de Règlements de Sociétés de Classification ou des parties de Règles Unifiées (UR) de l’IACS, il faut savoir que de nombreuses parties ont été développées ou validées à l’aide de techniques plus avancées et d’une analyse des risques et de leurs conséquences.

Parallèlement à la rédaction des CSR, commençait, à l’Organisation Maritime Internationale (OMI), le développement de normes de construction des navires neufs en fonction d’objectifs (goal-based standards ou GBS) et destinées à fixer les normes de base utilisées pour la conception des navires. Les personnes en charge des CSR suivaient en permanence ces développements pour inclure dans les CSR les critères qui semblaient pertinents.

Ce document traite aussi des nouvelles relations qui se sont établies entre les Sociétés de Classification et l’Industrie grâce au processus de consultations mis en place durant la phase de développement. La rédaction des CSR par les dix membres de l’IACS représente une étape dans la manière de fonctionner de l’IACS et de satisfaire les règles d’administration de chacun de ces membres. Du fait de la rédaction des CSR, l’IACS se trouve devant une nouvelle nécessité : la maintenance des règlements des CSR. Des processus ont été mis en place pour garantir une maintenance efficace des CSR, avec consultation régulière de l’Industrie. Des interprétations et des retours d’information ou d’expérience ont été collectés auprès de toutes les sociétés de l’IACS et auprès de l’Industrie, et ce qui en a découlé a été accepté et adopté par tous les membres. Par ailleurs un programme visant à harmoniser les versions actuelles des CSR pour les pétroliers et les vraquiers a été établi dans l’éventualité d’une future extension à d’autres types de navires.

Tous droits de reproduction réservés - ATMA 2008

NOMENCLATURE

CSR Règlements Communs de l’IACS concernant la Structure. Applicables aux pétroliers à double-coque et aux vraquiers à simple ou double-coque.

GBS Normes de construction des navires neufs en fonction d’objectifs (Goal-Based Standards) développées par l’OMI.

IACS Association Internationale des Sociétés de Classification (International Association of Classification Societies).

1 INTRODUCTION Ce document retrace le travail commun de développement des règlements entrepris par les sociétés de classification de l’IACS afin de formuler de nouveaux Règlements pour la Structure (CSR) des vraquiers et des pétroliers. L’objectif étant de donner une idée générale des défis et difficultés rencontrés au cours du processus de développement et du travail important fourni par les membres de l’IACS en charge du projet. Il précise quelques-uns des aspects de modélisation des règlements communs et la façon dont ils ont été développés et calibrés pour les charges et les réponses structurales.

Les prescriptions réglementaires doivent être un compromis entre les besoins intégrant des méthodes de pointe de grande technicité et ceux d’une application déterministe pratique. L’industrie, globalement, réclame de plus en plus l’emploi de moyens de pointe au stade du projet pour l’application des règlements alors qu’elle attend aussi des règlements permettant d’établir rapidement la conception initiale d’un projet et la possibilité de satisfaire les exigences réglementaires dans des cycles rapides de conception et de construction. Tout cela ne faisant pas oublier à l’IACS que son objectif principal reste le développement de règles et règlements allant dans le sens de la sécurité, de la solidité et de la durée dans le temps, qui correspondent à l’attente de la société au sens large.

Au cours du développement des critères des CSR, ce même compromis a amené à incorporer des prescriptions de Règlements existants et des approches basées sur le risque pour identifier les dangers et leurs conséquences afin de concentrer,

dans le développement des nouveaux règlements, l’attention sur les zones les plus critiques. Alors que les CSR ont tendance à reprendre des parties de Règlements de Sociétés de Classification ou des parties de Règles Unifiées (UR) de l’IACS, il faut savoir que des parties ont été développées et validées à l’aide de techniques de pointe et d’analyses des risques et de leurs conséquences.

Alors que les CSR étaient en cours de rédaction commençait, à l’Organisation Maritime Internationale, le développement de normes de construction des navires neufs en fonction d’objectifs et destinées à fixer les normes de base utilisées pour la conception des navires. Les personnes en charge des CSR suivaient en permanence ces développements pour inclure dans les CSR les critères qui semblaient pertinents

Après la publication de la première édition des CSR et des données techniques ayant servi à son élaboration, des périodes d’examen étaient accordées à l’Industrie pour leur permettre de prendre connaissance du projet, d’en vérifier l’application et de transmettre leurs commentaires. Ces périodes étaient aussi un bon moyen de perfectionner et d’ajuster le projet en augmentant le nombre de tests dans les développements et les applications réglementaires. Les règlements et documents supports s’en trouvant, par la même occasion, affinés.

En plus des améliorations techniques apportées, la rédaction des règlements évoluait pour inclure les corrections et les clarifications jugées utiles à la suite des commentaires reçus.

2 OBJECTIFS DE DÉVELOPPEMENT INITIAUX

Les premières mesures dans le processus de développement des CRS consistent à fixer les objectifs du projet, en mettant en évidence les besoins toujours croissants de sécurité, de solidité et de longévité des navires. Le développement de ces objectifs sous-jacents et de leur cadre était essentiel pour garantir une compréhension et une orientation mutuelles du projet. Ces objectifs peuvent se résumer comme suit :

• Éliminer toute compétition entre les sociétés de classification pour tout ce qui touche aux exigences structurales et aux standards, situation qui, si elle n’était pas abandonnée,


pouvait aboutir au final à une évaluation et une vérification incompatibles de l'intégrité structurale de la coque et donc mettant en péril la sécurité du navire. L’idée consiste à placer la compétition ultérieure sur le plan les services apportés aux clients.

• Cerner par anticipation les intentions des exigences de l’OMI pour les normes de construction des navires neufs en fonction d’objectifs (GBS).

• Exploiter toute l’expérience des sociétés IACS pour développer un standard unique accepté, ou un jeu de règlements et procédures, et ainsi aboutir à des prescriptions structurales identiques quelle que soit la société qui classe le navire.

• Garantir à tout navire satisfaisant les nouveaux règlements d’être reconnu par l’Industrie comme présentant au moins la même sécurité, la même solidité et la même longévité qu’en application de n’importe quels autres règlements existants.

• Réduire le coût de l’utilisation de plusieurs règlements qui bien que similaires sont malgré tout différents.

• S’assurer que les règlements et procédures résultant sont rédigés de façon à conduire à des exigences identiques en matière d’échantillonnage.

Ces objectifs ont été développés, pour chaque jeu de règlements, par l’équipe constituée pour le projet et par le comité de pilotage, en réponse aux demandes des armateurs et des chantiers pour une standardisation déjà en place dans d’autres industries et aussi, en réponse aux propositions nationales de coordonner les prescriptions d’échantillonnage qui avaient été faites au sein de l’OMI.... A l’OMI, les exigences reposeront sur des normes d’objectifs de plus haut niveau.

La finalité des CSR est la création d’un standard unique reconnu permettant la vérification de la structure des pétroliers à double-coque de longueur supérieure ou égale à 150 m et développé par le groupe IACS responsable du Projet commun pour les pétroliers (JTP) d’une part, et des vraquiers à simple ou double-coque de longueur supérieure ou égale à 90 m et développé par le groupe IACS responsable du Projet commun pour les vraquiers (JBP) d’autre part, développement fait, dès le départ, en

collaboration étroite avec la communauté maritime.

3 TECHNIQUES DE MODÉLISATION

3.1 Concept d'épaisseur nette

Les formules des CSR sont exprimées en utilisant le concept d’ ‘épaisseur nette’. Le principe repose sur le fait que les éléments de structure se corroderont tous durant la durée de vie du navire, mais de façon plus ou moins importante. Cette approche en « épaisseur nette » permet de déterminer et de vérifier l’échantillonnage minimum de la structure à conserver tout au long de la vie du navire, et ce dès sa construction, pour satisfaire les prescriptions de résistance. La distinction est clairement faite entre l’épaisseur nette et la surépaisseur dépendant de la corrosion qui se produira au cours de la phase opérationnelle du navire.

Les concepts de base qui ont été couramment utilises aux navires en service pré-CSR ont été codifiés dans ces règlements CSR. Ceci consiste à appliquer une perte moyenne globale sur la poutre navire et les éléments primaires telle que la résistance globale de ces éléments soit assurée. La résistance de ces éléments est vérifiée en utilisant une marge de corrosion moyenne moindre. Cependant ces grands ensembles sont composés d’éléments locaux tels que mailles élémentaires locales et raidisseurs ordinaires dont la résistance est vérifiée en utilisant la totalité de la marge de corrosion locale. D’une manière générale, la résistance des éléments de structure est vérifiée en utilisant leur capacité structurale dans l’état corrodé, c.à.d. en épaisseur nette, tout en appliquant les charges extrêmes présumées. Ceci assurera au navire de posséder une résistance minimale alors qu’il pourra se trouver en conditions extrêmes vis-à-vis de la corrosion considérée. La fatigue étant un mode de défaillance cumulatif qui démarre dès le premier jour de mise en service, le navire étant neuf, jusqu’à son dernier jour d’exploitation où l’on peut supposer le navire dans son état de corrosion le plus avancé, l’épaisseur nette associée à la poutre navire et aux épaisseurs locales pour vérifier la résistance à la fatigue est moyennée et prise égale à la moitié des marges totales de corrosion.

La structure du navire est contrôlée en service en utilisant des références d’épaisseur similaires


à celles prises en compte lors de la vérification de la structure au niveau du projet. En effet les surépaisseurs de corrosion au neuvage sont définies dans chaque règlement (pour le règlement CSR/Pétrolier en Section 6/3 et les limites de corrosion en service en Section 12/1; pour le règlement CSR/Vraquier respectivement au Chap 3, Sec 3 et Chap 13, Sec 2) Pour la cohérence, les surépaisseurs de corrosion au neuvage et les limites de corrosion en service sont liées entre elles par une marge de réserve afin de couvrir la corrosion qui peut se produire dans l’intervalle de temps entre 2 visites successives. L’épaisseur nette est illustrée à la Figure 1

Figure 1 : Principe de l’épaisseur nette

Les valeurs de corrosion introduites dans les règlements ont été établies sur la base d’un travail approfondi du groupe de travail IACS sur la résistance (WP/S) qui a rassemblé une base de données de 600.000 mesures d’épaisseur [1]. Cette base de données couvre les mesures effectuées sur une large amplitude de corrosion de structures exposées à un environnement marin comme les cales de vrac, les citernes de pétrolier, les citernes de ballastage, soumises à différentes températures, etc. pour lesquelles les marges de corrosion s’appliquent. Le processus de propagation de la corrosion depuis son déclenchement initial a été étudié par le biais de la masse importante de données collectées sur ces mesures. Un modèle de corrosion a été développé sur la base d’une théorie probabiliste pour estimer la diminution des éléments structuraux. Une analyse statistique des données a été effectuée pour déterminer les marges de corrosion associées à une probabilité d’usure de 95% de la marge sur une période de 25 ans. Il est cependant noté que des éléments de structure sont peints de manière à combattre les effets de la corrosion. Bien qu’il soit admis que les peintures assurent cette fonction, les effets protectifs des peintures ne sont pas directement inclus dans l’application des surépaisseurs de corrosion utilisées pour la vérification de la

conception. En d’autres termes, les surépaisseurs de corrosion ne peuvent pas être réduites par la présence de peinture. La raison principale de cette décision repose sur le fait établi que les peintures se fissurent en fin de compte en certains points et qu’il n’est pas toujours possible de repeindre ces endroits lorsque le navire est en opération et exposé à des conditions environnementales difficiles. Par ailleurs, l’efficacité des peintures durant la vie du navire dépend des conditions d’application et de la politique de maintenance de l’armateur. Même en appliquant les normes de l’OMI pour le comportement des revêtements de protection des citernes spécialisées ballastées à l'eau de mer de tous les types de navires et des espaces de double muraille des vraquiers (PSPC), ces conditions ne peuvent pas être prise en compte pour l’évaluation des éléments de structure au neuvage.

La philosophie de l’approche en échantillonnage net et les valeurs de surépaisseurs de corrosion ont été adoptées dans les règlements IACS CSR pour les pétroliers et les vraquiers.

3.2 Charges

L’élément fondamental sur lequel les règlements reposent est constitué par les charges à appliquer. Ces charges à appliquer entraînent 2 autres éléments également fondamentaux dans le processus de vérification : la définition des formules de résistance et les critères de validation. Les charges sont décomposées en 2 parties majeures qui sont respectivement les composantes statique et dynamique. La composante statique, ou en eau calme, représente typiquement les charges associées aux conditions de chargement telles que le poids lège, la cargaison, les ballastes, la poussée hydrostatique de mer. La Figure 2 illustre des exemples de dispositions de chargement utilisés pour de grands pétroliers (VLCC) et vraquiers ayant des dispositions classiques de citernes/cales. La partie dynamique, ou induite par les vagues, représente les charges associées aux mouvements du navire et accélérations imposées au navire par la mer.

Les charges dynamiques sont basées sur les paramètres fondamentaux du navire de manière à calculer en premier lieu les mouvements et accélérations caractéristiques du navire et ensuite d’obtenir les composantes dynamiques des charges de pression extérieure, des moments

Epaisseur nette requise

Surépaisseur de Corrosion

Neuvage

Epaisseur de renouvel-lement requise

Corrosion limite en service

En Service

Mesures d’épaisseur

ll

Réserve de Corrosion supposée pour 2.5 ans

(0.5mm) (peinture or visite annuelle)


et efforts tranchants appliqués à la poutre navire et des charges internes. Les charges dynamiques associées aux phénomènes de ballotement (sloshing), d’impact local sur les fonds plats à l’avant et sur les parties avant de la muraille, les paquets de mer sur ponts,… sont également spécifiés. Beaucoup de ces charges sont basées sur des exigences unifiées de l’IACS (UR) développées dans le cadre de groupes de travail sur les données et charges de mer, disponibles sur le site web de l’IACS www.iacs.org.uk

Chargements Dispositions de chargement

Tirant d’eau

A1(3)

0.9 Tsc

A2(3)

Tsc

A3(4)

0.6 Tsc (4)

A4

0.6 Tsc

A5

0.6 Tsc

A6

0.6 Tsc

A7 (5)

TLC

A8(6)

TbalH

Les efforts dynamiques sont évalués pour différents scenarios de chargement afin de couvrir l’étendue des opérations associées aux exigences réglementaires. Pour la vérification de la résistance d’ensemble, les charges caractéristiques sont obtenues en utilisant les conditions météorologiques et états de mer extrêmes que le navire peut rencontrer, basés sur une probabilité de dépassement de 10-8.

Figure 2 : Exemples de cas de chargement

pour des pétroliers et des vraquiers

Ces charges représentent les efforts extrêmes rencontrés lors d’une exposition dans l’environnement de l’Atlantique Nord défini par la recommandation n°34 de l’IACS, pour une durée de vie de conception de 25 ans. Il a bien été noté lors du développement des règlements que de nombreux navires évoluent leur vie durant sans jamais transiter par l’Atlantique Nord ; cependant l’Atlantique Nord a été sélectionné comme l’environnement de référence pour la conception de façon à ne pas limiter une flexibilité future. De plus, l’Industrie et le public ont réclamé que soient incorporées dans les règlements une sécurité accrue, une plus grande robustesse et solidité ; l’utilisation d’un environnement marin plus sévère est une des pistes suivies pour atteindre ce principe. Les efforts dynamiques sont introduits par le biais d’une série de facteurs de combinaison de charge (LCF) pour prendre en compte la superposition des nombreuses composantes dynamiques des charges en un point donné au moment précis où la composante majeure considérée de la charge atteint son amplitude maximale. Les facteurs de combinaison sont appliqués en liaison avec les chargements statiques comme montré à la Figure 2.

Les règlements spécifient les conditions de chargement et les dispositions de chargement à considérer lors de la vérification de la résistance de la structure. Ces dispositions correspondent aux conditions opérationnelles les plus courantes que le type et la taille du navire doivent satisfaire. Ils constituent le niveau minimal en terme de chargement que les pétroliers ou les vraquiers doivent vérifier et viennent en complément des conditions de chargement spécifiées dans le manuel de chargement propre au navire.


http://www.iacs.org.uk/

Pour les vraquiers, les dispositions de chargement sont basées sur les exigences unifiées de l’IACS pour la résistance appelée UR S25. Cette exigence unifiée a été introduite en juin 2002 à la suite d’une discussion entre l’IACS et l’Industrie initiée par une lettre de l’Association des Armateurs de Hong Kong qui exprimait leurs inquiétudes relatives aux défauts de conception des vraquiers existants. Cette exigence UR S25 a été développée pour éviter la conception de navire basée uniquement sur des conditions de chargement spécifiques présentées dans le manuel de chargement du navire concerné et également la situation qui bien qu’approuvé, ne puisse donner à l’armateur l’utilisation de la totalité de son potentiel dans un grand nombre de cas.

Pour évaluer la résistance à la fatigue, des efforts caractéristiques sont utilisés pour représenter le grand nombre des amplitudes de charge modestes et cycliques, basés sur une probabilité de dépassement de 10-4. Sachant que les résultats de calculs en fatigue sont extrêmement sensibles aux charges et à l’application de l’amplitude de contraintes correspondante, les charges les plus représentatives sont appliquées de manière à éliminer au mieux les hypothèses les plus conservatives. Il faut remarquer que les méthodes de calculs en fatigue requièrent des marges de sécurité dans la méthode et dans les critères d’échantillonnage eux-mêmes, de sorte qu’il n’est pas nécessaire d’imposer des mesures plus sévères au stade de la détermination des efforts. Bien entendu comme indiqué ci-avant, l’environnement Atlantique Nord est utilisé.

Les efforts réglementaires dynamiques, déterminés pour le niveau extrême 10-8 ou pour le niveau représentatif de la fatigue à 10-4 ont été extensivement développés et vérifiés en utilisant des calculs directs hydrodynamiques.

L’introduction des facteurs de combinaison de charge pour les différents aspects, constitue la partie majeure du travail effectué dans les règlements. Les efforts sont combinés par cas de chargement en appliquant des paramètres spécifiques maximaux corrélés avec les autres composants correspondants du cas de chargement de manière à approcher la vague équivalente pour représenter des charges dynamiques réalistes. Les paramètres dynamiques de charge tels que moment de flexion d’ensemble, pression extérieure,

pression interne, etc. sont chacun maximisés pour imposer les efforts statiques et dynamiques sur les différents éléments de structure. Les règlements définissent des cas de chargement spécifiques à utiliser durant le processus d’examen de la structure.

3.3 Exigences structuralles

La portée générale des exigences structurales est similaire à celle des règlements actuels des Sociétés de Classification. Les prescriptions structurales couvrent la résistance de la poutre navire, des éléments primaires et des éléments locaux. Elles recourent à des principes de dimensionnement compréhensibles et transparents à travers le concept d’épaisseur nette et d’application des charges résumé précédemment en association avec les critères de validation. Ces critères sont définis en fonction des cas de chargement et du mode de rupture considérés.

En plus de l’objectif de transparence dans la définition et la description des critères de dimensionnement, la cohérence est également un objectif principal de sorte que des charges, des modes de rupture et des critères de dimensionnement similaires conduisent à des exigences réglementaires semblables.

3.3.1 Résistance d’ensemble

Les prescriptions pour la résistance d’ensemble de la poutre navire relatives à la documentation à bord et aux formulations des critères de résistance réglementaire sont en accord avec les exigences unifiées de l’IACS (UR S1, S7, S11 en général et S17 et S25 pour les vraquiers). Les prescriptions règlementaires couvrent les procédures détaillées pour l’examen de la structure soumise aux charges statiques et dynamiques de flexion et de cisaillement. L’évaluation de la résistance au flambement des tôles et raidisseurs ordinaires est également effectuée à ce stade pour les contraintes induites par la flexion et le cisaillement d’ensemble combinés.

3.3.2 Eléments primaires

Les exigences prescriptives relatives aux éléments primaires sont introduites dans le règlement CSR Pétrolier pour le double fond, la double coque, les porques de cloison longitudinale, les transversales de pont, les tirants et les serres de cloison. Les dispositions de chargement des citernes et les combinaisons


de charge pour ces éléments sont spécifiées de façon que les efforts résultants soient maximisés lors de la vérification des modes adéquats de rupture en utilisant des formules de dimensionnement basées sur les charges. Des exemples généraux de ces prescriptions sont donnés aux équations (1) et (2) pour respectivement la flexion et le cisaillement. Il est aisé de comprendre la combinaison entre les charges et les contraintes admissibles pour la flexion ou le cisaillement. Une configuration typique de l’anneau renforcé d’un VLCC est donnée à la Figure 3 pour illustrer quelques uns des paramètres des formules réglementaires.

La disposition structurale des vraquiers n’est pas propice à cette approche prescriptive pour les éléments primaires. Par exemple, la structure du double fond est constituée de varangues et de carlingues se soutenant mutuellement ; il est donc difficile de donner des formules simples pour pré-dimensionner ces éléments.

Pour les Règlements CSR, des critères additionnels de hauteur ou d’épaisseur minimale sont introduits pour limiter les déformations globales des panneaux raidis, donner une robustesse minimale et effectuer une première analyse sommaire vis-à-vis du flambement des panneaux ou de la stabilité des raidisseurs.

Les éléments primaires sont vérifiés par après par l’utilisation de méthodes de calculs directes en éléments finis. L’analyse par éléments finis est incomparablement plus performante pour déterminer l’interaction entre les éléments de structure tels qu’éléments participant à la flexion d’ensemble, effets de grillage, déformation de cisaillement d’ensemble, etc. qui ne peut pas toujours être complètement prise en compte dans une approche prescriptive. Les exigences prescriptives basées sur les charges sont donc typiquement plus conservatives que celles basées sur une analyse en éléments finis ; en conséquence, dans les zones où une analyse en éléments finis n’est pas pratiquée les exigences prescriptives demandent une résistance nécessaire.

Cependant, pour le règlement CSR / Pétrolier uniquement, dans les zones où l’analyse en éléments finis est effectuée, une réduction de 15% de l’échantillonnage par rapport aux exigences prescriptives est autorisée sous réserve que les résultats associés aux éléments finis satisfassent les critères relatifs ces calculs.

ydprsCMZσ−

=1000

cm3 (1)

Où:

M Moment de flexion de conception, en kNm

2vwbdglSPc −=

P Pression de conception pour le cas de chargement considéré, en kN/m2.

lbdg-vw Portée de flexion, en m.

S Espacement des porques, en m

Cs-pr Facteur de contrainte de flexion admissible

σyd Résistance élastique minimale spécifiée du matériau, en N/mm2

C Coefficient correspondant à la disposition structurale

ydprtshr C

QAτ−

=10

cm2 (2)

Où:

Q Effort tranchant de conception, en kN:

= ])([ uuluvwu PhPPlcS −+

Pu Pression de conception pour le cas de chargement considéré calculée à mi-hauteur du gousset supérieur de la porque, hu, situé à mi citerne, en kN/m2

Pl Pression de conception pour le cas de chargement considéré calculée à mi-hauteur du gousset inférieur de la porque, hl, situé à mi citerne, en kN/m2

lvw Longueur de la porque, en m

S Ecartement des porques, en m

hu Longueur effective de cisaillement du gousset supérieur de la porque, en m

hl Longueur effective de cisaillement du gousset inférieur de la porque, en m


cu Coefficient correspondant à la disposition structurale

Ct-pr Facteur de contrainte de cisaillement admissible donné en 2.6.2.2

τyd

3ydσ

= N/mm2

σyd Résistance élastique minimale spécifiée du matériau, en N/mm2

lt

ltlside

lbdg

CL

c.

l

hl

hu

hl

hu

CL

Figure 3 : Exemple de prescription pour les éléments primaires

3.3.3 Eléments de support locaux

Les prescriptions pour les éléments de support locaux sont exprimées pour la coque extérieure et la structure interne telle que double fond, double coque, pont, cloison longitudinale et transversale, etc. Les efforts utilisés pour la vérification de l’enveloppe externe des citernes/cales proviennent des chargements maximaux possibles pour des conditions correspondant à une capacité pleine d’un coté et vide de l’autre coté de l’élément considéré et inversement pour que tous les scénarios soient envisagés. Sur le même principe, la coque extérieure est examinée pour une charge externe maximale correspondant au tirant d’eau maximal sans contre pression interne et pour la situation opposée, une charge interne maximale (cale/citerne pleine) associée à une charge

externe minimale correspondant aux conditions de ballast. Les modes de défaillance utilisés dans les formules de dimensionnement sont ainsi développées pour les tôles et les raidisseurs ordinaires. Les prescriptions relatives aux raidisseurs ordinaires incorporent l’examen des détails en extrémité de portée avec la prise en compte ou non de la présence d’une mise ou d’un plat de raidissage dans le plan de son âme.

Les éléments locaux sont vérifiés dans une étape ultérieure pour les critères de contraintes dans le cadre des calculs par éléments finis. L’analyse en éléments finis est plus adéquate pour considérer l’interaction entre les éléments de structure et leur influence locale sur les éléments locaux comme les tôles de muraille, de double coque, de cloisons transversales et longitudinales, etc. qui ne peuvent pas toujours être pleinement prises en compte dans les exigences prescriptives. Cette vérification est établie par rapport à la limite élastique et la résistance au flambement ou résistance ultime.

Les éléments de support locaux incluent également les exigences pour la vérification de la raideur des cloisons ondulées et des tôles locales la constituant, ainsi que la structure des caissons de ces cloisons.

Des prescriptions supplémentaires concernant les épaisseurs minimales, les ratios pour l’âme ou la semelle des raidisseurs ou d’autres critères locaux sont appliquées pour s’assurer de la robustesse minimale et pour obtenir un premier examen des panneaux et de la stabilité des raidisseurs ordinaires.

3.3.4 Eléments structuraux des citernes avant et arrière

Les éléments de structure des citernes les plus en avant ou en arrière sont vérifiés dans le Règlement CSR/Pétrolier par utilisation de la même procédure que celle exigée pour les éléments participant à la résistance d’ensemble dans les zones de transition et également en utilisant les exigences requises pour la vérification locale. Une procédure générale est également introduite pour appliquer les résultats obtenus par l’analyse de la partie centrale par éléments finis aux citernes en dehors de la région des 0.4 L de part et d’autre du maître couple.


3.3.5 Eléments de structure à l’avant, dans la machine ou à l’arrière

Les éléments de structure à l’avant, dans la machine et à l’arrière du navire sont vérifiés par le biais des prescriptions détaillées introduites dans le règlement. La structure avant est vérifiée pour les impacts sur les fonds (slamming) et la muraille en considérant les différents tirants d’eau et remplissages des capacités utilisés pour l’opération du navire.

En plus des prescriptions mentionnés ci-dessus, des exigences générales vis-à-vis du soudage, des matériaux, des moyens de fermeture, des superstructures, des équipements de mouillage, etc. sont données dans les règlements CSR.

3.3.6 Conformité à la SOLAS XII/6.5.1 & 3 pour les Vraquiers

Le nouveau chapitre XII de la SOLAS qui est entré en vigueur le 1er juillet 2006 (date de pose de quille) a introduit une exigence supplémentaire pour les dommages des raidisseurs ordinaires installés à la périphérie de la cale à vrac. L’exigence exacte s’exprime en 6.5.3 comme suit : « La structure de la tranche de la cargaison doit être telle que la défaillance d'un quelconque élément structural de raidissement n'entraîne pas une défaillance immédiate d'autres éléments structuraux pouvant à son tour entraîner l'effondrement de l'ensemble des parois latérales renforcées. ».

Dans le cadre de l’IACS, l’exigence unifiée UR S12 rev 4 a été discutée depuis mi-2002 jusqu’au début de 2004. La conséquence de ces discussions a entrainé l’introduction dans le règlement CSR / Vraquier des résultats du groupe ISR ISWG ¼ et SOLAS XII/6.5.3. L’objectif à l’origine était d’accroitre la résistance de la structure de muraille (membrures mais également leurs goussets ainsi que les lisses les soutenant). Par la suite, la discussion a évolué sur la façon d’éviter un effet domino par déversement des membrures.

Les principes suivants ont été appliqués :

• Déformation locale de 20 mm imposée aux raidisseurs de la structure bordant la cale pour la vérification de la résistance ultime du panneau raidi soumis à 80% des charges de houle (moments de flexion et pression)

• Si le dommage est une cassure ou un problème de soudage, nécessité d’éviter une rupture fragile.

Les exigences sur la redondance structurale données en SOLAS XII/6.5.1 et 6.5.3 ont été introduites dans le règlement CSR / Vraquier au travers des prescriptions présentées par l’IACS et acceptées par l’OMI :

• 80% des charges dynamiques sont appliquées

• Facteur de sécurité de 1.15 requis pour les calculs de résistance ultime des panneaux raidis bordant les cales de cargaison (sauf le pont)

• Grade D/DH exigé pour les goussets inférieurs de membrures et la tôle de muraille située à la jonction avec la tôle du caisson inférieur de ballast latéral.

3.4 Analyse en éléments finis

Les règlements CSR/Pétroliers et Vraquiers exigent qu’une vérification de la structure soit effectuée par une analyse en éléments finis sur une modèle de 3 cales/citernes.

Comme mentionné ci-dessus, l’objectif de cette analyse structurale consiste à s’assurer que les niveaux de contraintes et la capacité de résistance au flambement des éléments primaires et de la structure de la coque soumis à des efforts statiques et dynamiques restent dans des limites acceptables. De plus, la résistance à la fatigue de détails de structure sélectionnés doit également être validée.

La vérification structurale repose sur un calcul en éléments finis en 3 dimensions (3D) décrit dans une procédure détaillée dans les règlements. Cette procédure couvre différents aspects comme les détails de modélisation, les chargements, les conditions aux limites à appliquer, et les critères de dimensionnement pour valider la disposition et l’échantillonnage des éléments. Les règlements détaillent aussi les analyses à mener sur des modèles fins et très fins à effectuer pour évaluer les zones à fortes concentrations de contraintes et les détails de structure dans ces zones.

La Figure 4 donne deux exemples de modèles globaux de 3 cales ou citernes. La Figure 5 montre des exemples de modèles très fins imbriqués dans des modèles fins.

L’étendue des modèles fins ou globaux, la densité de maillage associé, les épaisseurs nettes à prendre en compte, les critères de dimensionnement à appliquer à chaque type d’élément structural, les charges réglementaires


et le type d’analyse à utiliser sont spécifiés dans les règlements.

Figure 4 : Modèles globaux (3 cales/citernes)

Figure 5 : Modèles fins

3.5 Résistance ultime de la poutre navire

Les règlements CSR requièrent un examen simplifié de la résistance ultime de la poutre navire de manière à donner un niveau supplémentaire de vérification de la résistance d’ensemble par rapport à l’approche courante élastique provenant des exigences IACS UR S11, elles-mêmes reprises dans les règlements. Cet examen simplifié n’a pas pour objet de reproduire une vérification complète de la résistance ultime de la poutre navire dans laquelle toutes les charges et les courbes de capacité de tous les éléments participant à la résistance d’ensemble seraient développées par une approche typique non linéaire. En effet, une méthode a été développée pour vérifier la capacité en résistance ultime d’une section transversale de façon à exclure les navires dont la conception pour ce mode de défaillance pose problème.

Pour la section transversale considérée des pétroliers et des vraquiers, un niveau supplémentaire de sécurité est ainsi introduit pour les conditions de navigation en pleine mer dont le moment de flexion total correspond au moment de flexion admissible en eau calme et une houle de probabilité égale à 10-8. De plus pour les vraquiers, des conditions d’avarie sont également examinées ; elles correspondent au cas d’envahissement de n’importe quelle cale associées à un moment de houle réduit.

Il s’avère que les conditions en contre arc produisent la plus faible capacité en résistance ultime. Le règlement CSR / Pétrolier donne de ce fait uniquement des critères pour ces conditions de contre arc.

3.6 Fatigue

Le but général du contrôle en fatigue introduit dans les règlements consiste à s’assurer que la structure du navire soumise à des charges de fatigue c.à.d. des charges cycliques dynamiques a une durée de vie en fatigue adéquate par rapport à la durée de vie de conception du navire.

La procédure donne une approche orientée sur la conception et permet la vérification de la résistance en fatigue de certains détails structuraux par une méthode dite simplifiée au lieu de méthodes plus élaborées comme par exemple la méthode d’analyse spectrale. Le terme « approche simplifiée » est utilisé ici afin de distinguer cette approche de méthodes d’analyse plus élaborées.


Les critères introduits dans les règlements ont été développés et proviennent de sources diverses telles que le modèle de dommage linéaire de Palmgren Miner, les méthodologies des courbes SN, les données environnementales à long terme de l’océan Atlantique Nord (IACS Wave Data), etc. et supposent que la qualité de fabrication est acceptable pour les experts de la Société de Classification et reste dans les limites des standards établis. La capacité de la structure à résister à la fatigue est exprimée en dommage de fatigue pour assurer aux concepteurs la plus grande flexibilité possible.

La procédure de calcul est axée sur l’évaluation de la résistance en fatigue des détails de structure à leurs connexions soudées et est basée sur une méthode simplifiée. La vérification est applicable aux détails des extrémités de lisse en utilisant la théorie des poutres basée sur l’approche par contrainte nominale ; les autres détails tels que la connexion du double fond, de la tôle de caisson inférieur et de la carlingue latérale en abord se fait par la détermination du point chaud directement par un calcul en éléments finis.

Les principales hypothèses utilisées sont données ci-dessous :

• Modèle de dommage cumulatif linéaire (loi de Palmgren-Miner) utilisé en liaison avec les courbes SN correspondantes,

• Contraintes cycliques due aux charges utilisées et incluses dans les effets des contraintes moyennes,

• Durée de vie de conception égale à 25 ans,

• Données environnementales correspondant à l’Atlantique Nord,

• Les amplitudes des contraintes long terme d’un détail de structure peut être caractérisé par une loi de distribution statistique à un paramètre (ξ),

• Les détails de structure sont idéalisés, pour les pétrolier une classe de fatigue et pour les vraquiers par un facteur de concentration de contrainte, précisé dans les règlements,

• Pour les connexions en extrémité de lisses, la contrainte nominale obtenue par une la théorie des poutres utilisant les charges réglementaires est amplifiée par des formules empiriques basées sur des calculs en éléments finis pour une série de détails semblables pour déterminer le facteur de

concentration de contrainte applicable au détail considéré.

La classification des détails structuraux dans les règlements est basée sur une connexion géométrique soumise à des charges élémentaires. Des exemples de connexions typiques et leur classe de fatigue correspondante sont montrés à la Figure 6 pour les pétroliers et les facteurs de concentration de contrainte à la Figure 7 pour les vraquiers.

Lorsque la géométrie ou les chargements deviennent trop complexes pour entrer dans une classification par nature simplifiée, un calcul par éléments finis du détail doit être mené pour en déterminer la contrainte à prendre en compte. Des conseils sur l’analyse en éléments finis requise pour déterminer le point chaud du joint soudé sont donnés dans la procédure. Les détails devant être analysés par fatigue en éléments finis sont pour les 2 types de navire l’angle formé par le double fond et le caisson inférieur en abord et pour les vraquiers, indiqués à la Figure 8.

C ritica l L ocation s ID C on n ection typ e A B

1

A B

d

l e ff l eff

F2 F2

2

A B

d

l eff l eff

F2 F2 (see n o te iv)

3

A B

d

l eff l e ff

d /2

F F2

Figure 6 : Classification des joints en fatigue

Figure 7 : Facteurs de concentration de

contrainte


Figure 8 : Exemples des détails de structure de

vraquier à vérifier pour la fatigue

Les règlements permettent également l’utilisation optionnelle de méthodes spectrales plus détaillées pour la vérification en fatigue. Cependant ces analyses plus fines ne peuvent pas conduire à des réductions par rapport aux prescriptions réglementaires.

4 NORMES DE CONSTRUCTION DES NAVIRES NEUFS EN FONCTION D’OBJECTIFS

Au moment où les règlements CSR ont été développés, l’Organisation Maritime Internationale (OMI) démarrait les grandes lignes des normes de construction des navires neufs en fonction d’objectifs dont l’abréviation anglaise est connue sous le sigle GBS, ayant pour but de déterminer les normes de base qui seront utilisées pour établir les règlements des Sociétés de Classification. Le développement de ces GBS est toujours en cours à l’OMI. L’Organisation envisage 2 formats pour ces normes : une approche « prescriptive » et une approche par « niveau de sûreté ». Indépendamment du format, l’OMI est donc en train développer un « règlement pour les règlements » de sorte que les règlements des Sociétés de Classification devront satisfaire un niveau minimal de base de sûreté. Lors du développement des règlements communs, les évolutions en cours des GBS ont été suivies de façon à incorporer les critères pertinents dans les CSR. Ainsi la durée de vie de conception de 25 ans et la houle correspondant à l’Atlantique Nord ont été introduites dans les CSR.

Récemment, l’IACS a accepté de tester les règlements CSR dans le processus des GBS par le biais d’un projet pilote. Ce projet pilote sera utilisé pour améliorer les GBS et en parallèle d’identifier les zones d’amélioration des CSR.

5 IMPLEMENTATION DES REGLEMENTS COMMUNS DE L’IACS

En juin 2003, le Conseil de l’IACS réagit à des initiatives venant de l’OMI et de l’Industrie et décide de développer un jeu de règlements et de procédures communs pour la détermination des échantillons de structure des pétroliers et des vraquiers. Le 1er avril 2006, ces règlements entrent en vigueur. Ils incorporent les changements et améliorations antérieures et proposent une approche harmonisée pour la structure du navire et ce pour l’ensemble des Sociétés de Classification de l’IACS.

5.1 Maintenance des CSR

Au moment où les règlements communs entrent en application, l’IACS créent 2 équipes de projet sous la supervision du « Hull Panel » de l’IACS. Chaque équipe se voit confier la charge de la maintenance de l’un des 2 jeux de CSR. La Figure 9 montre l’organisation de l’IACS pour les CSR.

Chaque équipe est composée de 4 membres de l’IACS, 3 appartenant aux Sociétés de classification qui ont développé le règlement du type de navire concerné et un autre membre.

A ce jour, la maintenance des règlements est assurée comme suit :

• CSR / Pétroliers

− DNV,

− ABS,

− LRS,

− BV

• CSR / Vraquiers

− ClassNK,

− BV,

− GL,

− ABS

Une rotation des membres est prévue tous les 2 ans.

A la suite des demandes d’interprétation et des questions posées par les membres de l’IACS, les équipes de maintenance proposent des errata et des propositions de mise à jour réglementaires. Les errata concernent principalement les amendements éditoriaux des règlements alors


que les propositions de mise à jour réglementaires doivent recevoir l’aval des comités techniques de chaque membre de l’IACS avant son adoption définitive par le Conseil.

Figure 9 : Organisation de l’IACS

5.2 Interpretations des CSR

Les équipes impliquées dans la maintenance des CSR doivent également effectuer des interprétations des règlements. Ces interprétations peuvent constituer un moyen pour appliquer une exigence de la même façon par tous les membres de l’IACS. Elles établissent une étape possible vers une mise à jour réglementaire en proposant une solution temporaire aux membres et aux concepteurs de navires.

Ces interprétations sont enregistrées dans une base de données accessible aux membres de l’IACS. Lorsqu’elles sont jugées utiles pour l’Industrie, le secrétariat de l’IACS les rend disponibles sur le site internet de l’IACS.

Une fois par an, les équipes de maintenance passent en revue les interprétations pour proposer au « Hull Panel » une liste d’amendements réglementaires.

5.3 Harmonisation des CSR

Les règlements communs des pétroliers et vraquiers ont commencé à des moments différents et dès leur origine ont suivi des cheminements de développement également différents. Les membres de l’IACS se sont accordés pour harmoniser les 2 approches et un degré important d’harmonisation a été déjà atteint entre les 2 jeux de règlements. Les termes adoptés par chacune des sociétés par rapport aux

CSR sont identiques et un travail d’harmonisation plus ample continue.

Le processus a été divisé en 3 phases : un processus à court, moyen et long termes

La phase à court terme s’est concentrée sur :

• Les efforts tranchants verticaux de houle

• Les marges et surépaisseurs de corrosion

• La résistance ultime de la poutre navire

La phase à moyen terme sur :

• Les exigences prescriptives de flambement

− Flambement sous les efforts d’ensemble hors éléments finis

− Comparaison des analyses par calculs directs

• Analyse par calculs directs

− Elimination des problèmes majeurs entre les 2 procédures pour un échantillonnage commun

− Analyse comparative des structures de pétroliers et vraquiers par les équipes JTP (Projet Pétrolier) et JBP (Projet Vraquier)

Et la phase à long terme sur :

• Harmonisation des charges

• Fatigue

Les tâches des phases à court et moyen termes ont été menées à bien et leurs résultats incorporés aux textes réglementaires des CSR. Les projets à long terme ont d’abord été affectés au « Hull Panel ». Cette phase devait démarrer après une période d’implémentation afin de glaner un retour d’expérience dans son application.

Dès la fin 2007, le Conseil de l’IACS a créé un groupe de projet spécifique pour effectuer l’harmonisation des 2 règlements CSR, appelé Project Management Team (PMT). Ce groupe est codirigé par deux responsables, l’un venant du Bureau Veritas et l’autre du Det Norsk Veritas. Ce groupe répond au SG/CSR (Small Group/ CSR) mis en place par le Conseil pour l’aider directement sur les problèmes des CSR. L’organisation est décrite à la Figure 10.


IACS Council

SG/CSR(ABS, BV, LR, NK)

Hull Panel(10 members + 1 associated)

Project Management TeamCSR Harmonization

(BV, DNV)

CSR Secretariat

Project Teams(Including Cross Check Teams)

Project Teams(Including Development Projects)

Technical review

IACS Council

SG/CSR(ABS, BV, LR, NK)

Hull Panel(10 members + 1 associated)

Project Management TeamCSR Harmonization

(BV, DNV)

CSR Secretariat

Project Teams(Including Cross Check Teams)

Project Teams(Including Development Projects)

Technical review

Figure 10 : Organisation de l’IACS pour les

CSR

Le groupe PMT a proposé un plan de travail sur 4 ans pour produire un seul règlement harmonisé comportant une partie commune aux 2 types de navire et une partie spécifique à chacun des 2 types. Son objectif est de partir de l’existant et de faire converger les exigences qui sont parfois extrêmement proches et de proposer des solutions pour les méthodes qui le sont moins.

Les équipes de projets suivantes ont été créées en 2008 :

• Charge de mer

• Flambement

• Eléments finis

• Soudage

• Surépaisseurs de corrosion

De plus le PMT supervise 2 autres projets, l’un traitant de la mise à jour du règlement vraquier relative à la fatigue sous mer de trois-quarts et l’autre géré par le « Survey Panel » pour le suivi en service des navires.

Ce plan 2008 sera complété lors des années à venir par d’autres équipes de projet (fatigue, etc.…) pour atteindre l’objectif final.

5.4 Manifestation de la conformité aux CSR

Les pétroliers et vraquiers dont le contrat de construction est signé après le 1er avril 2006 et qui relèvent de l’application des règlements communs de l’IACS se voient attribuer une mention de service complémentaire CSR ajoutée à la mention de service pétrolier ou vraquier, signifiant que le navire satisfait aux exigences CSR ou Common Structural Rules. Cette procédure est appliquée par toutes les Sociétés de Classification de l’IACS.

6 CONCLUSIONS Le développement des CSR par l’IACS a été esquissé dans ce papier. Des exemples d’équilibre entre les méthodes de calculs techniquement développées et les besoins d’approches déterministes et pratiques ont été présentés. A l’époque où les règlements CSR furent développés, les normes de construction des navires neufs en fonction d’objectifs (GBS) de l’OMI étaient sous surveillance pour en incorporer les critères pertinents dans les CSR.

Les rapports nouveaux entre Sociétés de Classification et l’Industrie, conséquence directe des processus de consultation effectués durant les phases d’élaboration des règlements ont été décrits avec l’entrée en force et la maintenance des CSR par les 10 membres de l’IACS.

7 REFERENCES [1] Common Structural Rules for Bulk Carriers,

Jan 2006, NR522 DT R00 E

[2] Common Structural Rules for Double Hull Oil Tankers, Jan 2006, NR523 DT R00 E

Auteur

Philippe Baumans est responsable du Département Développement au sein de la Branche Marine au siège du Bureau Veritas, à Paris-la-Défense. Il est à ce titre responsable du développement des divers règlements du Bureau Veritas pour les navires et l’offshore ainsi que de celui des outils informatiques. Anciennement représentant du BV au « Hull Panel » de l’IACS, il a été nommé coresponsable du groupe PMT pour l’harmonisation des règlements communs.


RISK ENGINEERING

The papers in this section reflect a new focus by Bureau Veritas onergonomics and the man-machine interface. How to improve ship designby focussing on the risks of human-system interaction is the main topic.




Proceedings of the 27

th International Conference on Offshore Mechanics and Arctic Engineering

OMAE2008 June 15-20, 2008, Estoril, Portugal

OMAE2008- 57362

INCLUDING ERGONOMICS IN THE DESIGN PROCESS TO ADDRESS THE RISKS OF SLIPS, TRIPS AND FALLS: METHODOLOGY AND APPLICATION

Nicolas MERY BUREAU VERITAS

Marine Division Research Department

Risk, Sustainability and the Human Element section

Marc LASSAGNE Ecole Nationale Supérieure

d’Arts et Métiers GRID (research Group on Risk,

Information and Decision), ENSAM-ESTP-IAE de Paris

Jonathan McGregor BUREAU VERITAS

Marine Division Research Department

Risk, Sustainability and the Human Element section

ABSTRACT Much effort has been spent by the offshore and maritime

industries in order to improve the safety of the vessels and

installations. However, accidents such as Slips, Trips & Falls

(STFs) still need to be particularly addressed since their

likelihood and severity are often underestimated. According to a

study by Jensen et al. [1], they cause more than 40% of non-

fatal injuries onboard and a study by the American Club P&I [2]

asserts they are responsible for 23% of the cost of claims for

illness and injury. The best way to prevent personnel from

slipping, tripping and falling is to integrate safety early in the

design of the ships or offshore installations.

This paper describes the way a classification society has

developed guidelines based on ergonomic design principles in

order to improve the design of the means of access onboard

ships. The outcome of this exercise is to increase the safety of

surveyors, seafarers and sea-going personnel who inspect,

operate or work aboard the vessels. The methodology we used

featured a two step approach: a risk analysis based on feedback

from surveyors and other sources was performed; an

anthropometric analysis was then used to establish the

guidelines. Both exercises are detailed in the paper along with

the resulting guidance. We show how this work is a first step

towards a more general methodology for the inclusion of

ergonomic consideration in the design process.

1. INTRODUCTION Slips, Trips and Falls (STFs) are the accidents that occur the

most commonly at work. They can happen on an even level, on

ramps, on steps or stairs, or from a height. A wide range factors,

such as those identified by Haslam [3], namely health, age,

fatigue, medication, alcohol, environment (e.g. lighting and

floor surface) and activity (e.g. load carriage or performance of

a cognitive task) strongly influence the occurrence of STFs.

Because they feature numerous areas where STFs can occur,

ships and offshore installations should be seen as particularly

hazardous places, especially if maritime-specific contributing

factors, such as ship motion, weather conditions and work

organisation, are taken into consideration. This is reflected in

recent research. For instance Jensen et al in a 2005 paper [1]

present a study based on the statistical analysis of a

questionnaire filled in by 467 seafarers pointing out that STFs

would be responsible for more than 40% of non fatal-injuries

occurring onboard. Moreover, when analysing the seriousness

of the injuries (assessed by the number of days where the

seafarer is unfit for duty), this percentage increases to more than

60% for the most severe of them (involving more than 90 days

where the injured victim is unfit for duty).

The American P&I Club statistics [2], show that STFs

represented 23% of illness and injury claims costs for the 2001-

2003 period. This should be an incentive for the maritime

industry to not only focus on the prevention of ship losses but

also to save lives and money by trying to improve safety

onboard addressing STF accidents.

Bureau Veritas employs a significant number of surveyors who

have to face STFs related hazards during inspections of vessels

or installations. In addition to that, it has, as a classification

society, to be aware of and be involved in the ways to improve

safety at sea. It is consequently currently developing a guidance


note providing shipbuilders, shipyards and more generally the

maritime industry with requirements for a user-centred safe

design of the means of access onboard.

The areas of the ship most involved in the occurrence of STFs

are the Means of Access (MAs) i.e. walkways, ladders, stair

ladders, manholes, openings etc. The surveyors from the

classification societies have to carry out inspections using the

whole range of means of access and consequently, are very

likely to slip, trip or fall while onboard. Besides, classification

societies on behalf of IACS included in their rules unified

interpretations of the IMO Technical provisions for means of

access for inspections [4] which objective is to ensure the

surveyors can carry out inspections on board in safe conditions.

This paper presents the methodology employed to address STF

accidents and the way it has been applied for the development

of a guidance note for the ergonomic design of means of access

onboard ships.

2. METHODOLOGICAL DEVELOPMENT The maritime industry, notably under the influence of the

International Maritime Organisation (IMO) is increasingly

addressing the human element issues when dealing with the

improvement of safety at sea. Indeed, IMO [5] agreed in May

2006 that “significant reduction of accidents to seafarers and

human error can be obtained through the consideration of

ergonomics and their working environment onboard ship”.

People are the most valuable resource that any company holds

and consequently, the whole panel of issues linked to the ship

operation as well as the ship design has to be dealt with taking

this into account.

Concerning slips, trips and falls, two main questions arise:

• To what extent can the design of ships and offshore

installations prevent people from slipping, tripping and

falling?

• How is it possible to have people adopt safe practices

and not take unjustified risks once they are provided

with a safe working environment?

These questions cannot be answered independently but should

be seen as describing a dual problem. The way people are likely

to behave has to determine the design; and the policies,

procedures and organisational factors should be developed in

close relation to the design of the equipments. This led us to the

adoption of a human-centred design perspective. Human-

centred design is a concept derived from ergonomic science that

addresses the wide range of interactions between people and the

ship or installation they work on or, more generally, the

workplace.

For instance, the effects of ship motion on crew safety, the

effects of light, vibrations and noise on their endurance, the

suitability of the permanent means of access onboard are some

of the topics that can be focused on through user-centred

design. Thus, any part of the ship should be adapted to the

mental, cognitive and physical capabilities of the various

seafarers that will operate and maintain it.

2.1. General description The methodology that we have developed relies on the concept

that, in order to achieve the best results, the needs of end users

are of paramount importance and should be considered in the

earliest stages of the design process. Personnel operating, or

surveying, ships and installations should be invited to give

feedback to the engineers and designers on the usability of the

vessel or installation.

Moreover, it should be noted that the maritime industry does

not benefit from the advantages that can be derived from the

standardized production of vessels and offshore installations: as

each vessel is unique, even sister ships have differences, there is

almost no possibility to use prototypes and obtain expertise and

feedback from the users at this stage. Thus, feedback should be

collected from users who have a significant experience in the

operation of relevant vessels and installations.

Simulation is the second important means to integrate the

human element in the user-centred design process. Issues

arising from the ship’s operation that are not always observable

from trials and tests, but modelling can help to anticipate any

problems. Some emergency evacuation simulations, for

instance, are increasingly used for the design of stairs, escape

routes, and muster stations onboard vessels. For our purpose,

user-feedback can be used to describe the hazardous situations

that will then be modelled and assessed through simulation.

The methodology we developed has another important

characteristic in that it is explicitly risk-based. The

identification of hazardous situations or places where STF

accidents are most likely to occur is based on user feedback and

more specifically on the perception of the risks they face. Thus,

the users have the opportunity to give their own vision of the

STF hazards, i.e. their likelihood, their severity or the places

where they will most likely occur.

We decided to build several quantitative indexes based on the

users’ expertise: a probability or frequency score, a

consequence or severity score and with a combination of both, a

risk score that allows us to determine the level of significance of

the identified hazards. The rationale underlying the approach

we adopted is as follows: user-feedback is useful to make our

approach user-centred, but we could not hope to have found

accurate and reliable data about the probabilities of occurrence

of STFs or their severity depending on the situation or places.

Such maritime-specific databases do not exist or are not

complete enough to be used for our purpose. Furthermore, there

is no simple way to make analytical studies of STF accidents

depending on the ergonomics onboard.

That is why a simulation stage was necessary in the

methodology allowing for ergonomic-design concepts to be

introduced to address STFs.


The methodology that we developed is a two-stage-process

described in the figure below, which take into account the

points that we just presented.

Figure 1. Methodology for the development of

ergonomics-based design guidelines

2.2. First step: User feedback Feedback from the users constitutes the core of the method.

During this phase, we try to gather the maximum amount of

information from people operating the ships and offshore

installations in order to focus on the most relevant and practical

issues that arise onboard. This step is very important as it

provides significant qualitative and quantitative data that is

essential to carry out in each of the next steps of the process.

In order to get the most valuable and complete information from

the users as possible, we used three different tools: free and

semi-structured interviews, a visit on a vessel and

questionnaires. The first two tools provided only some

qualitative data whereas the questionnaires allowed a

quantitative analysis.

2.3. Second step: Risk Assessment The questionnaire we asked surveyors to complete is composed

of fourteen questions. Some of them are used for testing the

relevance of the answers. Another set of questions is focused on

the characteristics of the Slip, Trip and Fall accidents and the

way seafarers assess their likelihood and the injuries they cause.

This set will be helpful to evaluate the beliefs of the seafarers

about the STFs related risks; do they under or over-estimate the

risks? There is also a set of questions dedicated to the risk

analysis. Finally, some open questions allow us to have a

qualitative description of the issues with the Means of Access

(MAs) and the improvements they recommend to fix them.

Qualitative analysis of the questionnaire In order to interpret the qualitative data obtained with the

results of the questionnaire, we used Factorial Analysis (FA). FA

is a way to represent contingency tables i.e. tables such as those

we obtained with the results of the questionnaire. These tables

are two-way tables which variables are qualitative. An example

of contingency tables is shown below.

Table 1. A contingency table representing surveyors’ beliefs about STFs frequency of occurrence

Likelihood Slip Trip Fall

Never 7 12 23

Rarely 20 16 8

Sometimes 5 2 1

Often 0 2 0

The aim of FA is to allow the analyst to gather as much

information as possible on a very restricted number of graphs

called factorial plans formed by two factorial axes. The

different characters (slip, trip, fall, never, rarely, sometimes,

often) are analysed in terms of correspondences, i.e. only the

relative value between characters is important.

Each character is represented by a dot whose size depends on

the number of respondents and whose location determines its

relation with the other characters. The clouds of dots

representing the characters in line (never, rarely, sometimes,

often) and the clouds for the characters in column (slip, trip,

fall) are both centred on the origin of the space1. This space, in

which the clouds are centred and are represented on a common

scale, is composed of the factorial axes that are determined by

an eigen vectors calculus. The figures we analysed are

projections of the dots on factorial plans. Below is presented the

graph representing the previous contingency table:

1 The centres of the clouds are determined by the ‘centre of gravity’ of the

dots, each dot bringing its own inertia (depending on the number of respondent

associated to this character) to the cloud.

4) Development of ergonomic guidelines

• Design requirements definition

• Guidelines development

1st

stage

1) User feedback

2nd

stage

• Interviews

• Diffusion of questionnaires

• Field observations

2) Risk assessment

• Qualitative analysis of the feedbacks

• Quantitative analysis of the feedbacks

• Assessment of consequences

• Assessment of frequencies

• Risks ranking

3) Ergonomic /Anthropometric analysis

• Application of the ergonomic/human factors design principles

• Application of the anthropometric design process

• Simulations


Figure 2. Projection of surveyors’ beliefs about STFs

frequency of occurrence on a factorial plan

A graphical analysis can be carried out with this type of graphs;

quantitative indicators can also be derived from the data

analysis, in order to confirm the validity of the analysis, namely

the percentage of inertia explained by each of the factorial axes,

the quality of representation of the dots on the factorial axes,

the significance of each character regarding the factorial axes

and obviously the contingency tables (that after all contain the

whole information). Thus, the graphical analysis can be

rigorously performed. Sub-populations appear like more or less

concentrated groups of dots. In general, the proximity of two

dots reveals that their profiles tend to be similar.

Risk analysis We adopted a specific strategy to identify the hazards related to

Slip Trip and Falls. The hazards are characterized by their

location, their severity and their frequency. By constructing a

risk measure with severities and frequencies, we assessed the

STFs risks in the different areas of the ships and determined a

level of acceptance in order to focus on the areas that have to be

addressed in priority. We also assessed the severities associated

with each type of MA using the same method as for the

assessment of the frequencies.

It seemed more relevant to us to assess the frequencies of access

to the different places instead of the frequencies of occurrence

of STFs in these places. In fact, it is cognitively easier for a

surveyor to estimate frequencies concerning how often a given

location is accessed (by them or by seafarers) than estimate the

accidents frequencies, for the reasons that we previously stated.

To summarize, it is easier for the surveyors to give an estimate

on how often areas are accessed instead of how often a STF

occurs (whether or not the STF results in a injury).

Furthermore, this frequency is a good attribute for risk

assessment since more attention should be paid to the rooms

and compartments which are accessed more frequently.

Then, in order to provide a unique frequency score for each of

the areas onboard, we computed a weighted sum on the

percentages representing the different frequencies (several times

per year, several times per month, several times per week,

several times per day). The weights are directly proportional to

the frequencies i.e. the coefficient corresponding to the to the

frequency ‘several times per day’ is 365 times the coefficient for

the frequency ‘several times per year’ and so on. Finally,

assuming that the coefficient for ‘several times per year’ is 1,

the scores obtained are ranked on a 1 to 365 scale that can be

turned into (division by 365) a 0.03 to 1 scale. We show this

calculus for the lower hold on an example below:

Table 2. Access frequency for the lower hold

LOWER HOLD

Frequencies Percentages ip

Coefficients ik

several times / year 0.44 1.00

several times / month 0.11 12.00

several times / week 0.28 52.00

several times / day 0.17 365.00

We can calculate the score corresponding to the frequency of

access to the lower hold:

21.0365

36517.05228.01211.0144.0=

⋅+⋅+⋅+⋅=lowerholdF

Let us insist on the fact that F is a score and not a frequency;

here, F = 0.21 does not mean that the lower hold is accessed

every five days since 44% of people answered the lower hold

was accesses (only) several times per year.

We ranked each injury, ranging from a simple knock to a

fatality, into four groups based on their severity: ‘not dangerous

at all’, ‘not really dangerous’, ‘rather dangerous’, ‘very

dangerous’. As for the frequency score given to each of the

areas onboard, we calculated a score reflecting the severity

associated to each of them with a weighted sum. However,

when dealing with the severity of injuries, the coefficients

cannot be attributed according to a proportionality rule. In fact

the weights have to be defined according to the harm or

disutility each category of injury cause to the maritime industry.

Thus, the severity associated to ‘very dangerous’ is about 50

times the one associated to ‘not really dangerous’. In fact, as

shown on the figure below, we assumed that the disutility

function or negative utility function has an exponential shape.

365

∑ ⋅

=i

ii pk

F


Figure3. Exponential model of the disutility associated to

injuries

It was not possible to actually elicit this utility function. This

could be another perspective for future research. However, the

coefficients that we used for the negative utility function made

it possible to assess the severity of injuries associated to each of

the areas and rank them as we show for the lower hold on the

following table.

Table 3: Dangerousness of the lower hold LOWER HOLD

Severities Percentages ip

- Utility )( iu−

Not dangerous at all 0.33 0

Not really dangerous (knock

benign wound, sprain) 0.40 0.02

Rather dangerous (back

injury, serious wound,

fracture, eye injury)

0.13 0.14

Very dangerous (death risk,

disability) 0.13 1

We can calculate the score associated to the severity of the

injuries occurring in the lower hold:

16.0113.014.013.002.040.0033.0 =⋅+⋅+⋅+⋅=lowerholdS

At this point, we had scores for the frequencies and scores for

the severities for each of the areas onboard vessels. We needed

to define a risk ranking in order to assess each compartment in

terms of safety. Because of the relatively low accuracy induced

by the process employed for the computation of the scores, it

seemed to be useless to find a new scoring function combining

the two previous scores in order to rank the compartments by

risks. Thus, we adopted a risk matrix containing four levels of

risks and presented in the table below:

Table 4. Risk matrix for the assessment of the areas and means of access where STFs can occur

Severity < 0.2 Severity > 0.2

Frequency <

0.14

NO SIGNIFICANT RISK (no

action required)

SIGNIFICANT RISK

(immediate action required)

Frequency >

0.14

LOW RISK (non priority

action required) SAFETY CRITICAL

Through this matrix, we (legitimately) assume that the severity

of the injuries caused by STFs has a lower weight than the

frequency of access in the risk assessment. A high severity is

unacceptable whatever the frequency of access whereas a high

frequency of access associated to a low severity is considered a

low risk.

Surveyors’ beliefs The risk analysis we carried out results from thirty-two

feedbacks from surveyors. We have to consider its accuracy and

be aware of its limitations. In fact, biases may be introduced by

the way information is collected through questions. The most

significant biases come from the beliefs of the respondents

about the hazards linked to Slip, Trip and Falls (STFs) in

shipping. In fact, when they are asked to assess the frequencies

of occurrence of STFs or the severity of the injuries they cause,

the surveyors tend to underestimate the frequencies while they

overweight the consequences (severity of injuries). This seems

to be logical since people in general and even surveyors

consider STFs as common accidents and consequently do not

notice them when they occur except when they cause serious

injuries. The respondents also only keep in mind the most

serious STF accidents and forget to mention the various others

that occurred all along their career, in a fashion similar to what

Kahneman et al. describe as the availability bias [6].

Consequently, they are also often unaware of the STFs that

happened to their colleagues. That is the reason why we went in

field to attend a survey and interview the surveyors in their

working environments. Care was also taken to try to ask

questions in such a way that these biases are as minimised as

possible. Overall, the relevance and accuracy of the results we

worked on is good enough considering the type of analysis we

performed.

2.4. Third step: Ergonomic design of the Means of Access

Anthropometric design The following section explains the main concepts of

anthropometric design as defined by Pheasant [7].

Anthropometry is the branch of ergonomics dealing with the

measurements of body size, shape, strength, mobility and

flexibility. From the results of an anthropometric analysis we

Not dangerous at all Not really dangerous

Rather dangerous Very dangerous

)(severityfutility =−

)(∑ −⋅=

i

ii ukS


can extract many of the technical requirements for the user-

centred design. The objective of anthropometrics is to choose

the best compromise for the dimensions for equipment to be

employed by a large range of users. This compromise should

address the “four cardinal constraints of anthropometrics”:

• clearance,

• reach,

• posture and,

• strength.

The first constraint implies that the work environment should

provide adequate access and circulation space. Handles must

provide adequate apertures for the fingers or palm. These are all

clearance constraints. They are one-way constraints (i.e.

constraints defining semi-bounded dimensions) and usually

determine the minimum acceptable dimension in the object. The

second constraint defines the ability to grasp and operate

controls is an obvious example of a reach constraint, as is the

constraint mentioned above on the height of a seat or the ability

to see over a visual obstruction, etc. They are usually one-way

constraints but this time, are determined by a small member of

the population. A person’s working posture will be determined

(at least in part) by the relationship between the dimensions of

his or her body and those of the workstation. Postural problems

are commonly more complex than problems of clearance and

reach, since posture will almost certainly be affected by more

than one dimension of the workplace. Finally, the fourth

constraint concerns the application of force in the operation of

controls and in other physical tasks. Often, limitations of

strength impose a one-way constraint, and it is sufficient to

determine the level of force that is acceptable to a weak user.

There are cases, however, where this may have undesirable

consequences for the heavy-handed (or heavy-footed) user, or in

terms of the accidental operation of a control, etc. In these cases

a two-way constraint (i.e. constraints defining bounded

dimensions) may be applied.

Before starting the anthropometric analysis, three types of data

are required:

• The anthropometric characteristics of the user

population

• The ways in which these characteristics might impose

constraints upon design

• The criteria that define an effective match between the

product and the user

This information should be determined in accordance with the

requirements and suggestions obtained through the user

feedbacks.

Concerning the anthropometric characteristics of the

population, it is empirically true that most anthropometric

variables conform quite closely to the normal distribution (at

least with reasonably homogeneous populations). Thus,

population measurements are described with the percentiles of

the distribution. For instance, for the measurement of men’s

stature, if we consider the limiting user as the tallest of the 95th

percentile of the population, it implies that 5% of the population

will be taller than this user. Generally, for classic design

analyses designers often use the 5th %-ile of woman and the

95th-percentile of men as the limiting users. However, the body

measurements depend on the population studied and of the

criteria we choose.

Then three types of design solutions can be adopted depending

on the characteristics of the interactions between the user, the

product and the task:

• design for the limiting user,

• define an area of common fit and

• provide adjustments

Design of the means of access With the first stage of the process, we identified the most

significant hazards related to STFs so that we could focus on

the most important ones through an ergonomic analysis. The

objective of this analysis is to determine the ergonomic

requirements for the Means of Access (MAs) to be safe for

seafarers, surveyors and other persons using them.

Four types of requirements had to be taken into account:

requirements from the international regulations about crew

safety and access arrangements (IMO, IACS, ILO, etc.),

requirements from Bureau Veritas rules for steel ships,

requirement from the seafarers and surveyors’ feedback and

obviously the requirements derived from the four cardinal

constraints of ergonomics. We gathered and ranked all these

requirements in tables in order to have an overview of the

whole set of issues related to MAs, the seafarers and surveyors’

feedbacks, and the relevant regulations.

The environments on which we will focus are the locations

onboard vessels that we identified as the most risky. Moreover,

we had to take into account the marine environment since it also

determines the way MAs’ design should be addressed i.e. the

corrosive atmosphere that endanger the integrity of a certain

number of ladders and handles for instance and the weather

conditions that impact the vessels’ motions and consequently

the seafarers’ balance or alter their vision when using MAs on

the open decks.

Concerning the tasks carried out by surveyors and seafarers

while using the MAs, they are very simple, i.e. accessing rooms

or equipments and surveying.

The population that we targeted mainly comprised seafarers and

surveyors. As the ships can be operated by crews coming from

any region, the whole international population of seafarers and

surveyors had to be studied. However specific anthropometric

data about this population was not available. Data about the

whole international population was used. Assuming that there is


a majority of men among seafarers, we decided to use the

anthropometric data of the 5th %ile women Japanese population

for the ‘lower’ limiting users while we chose the 99th %ile of

the man American population for the ‘higher’ limiting users.

We also had to take into account the clothes and survey

equipments the members of the population are likely to have

since they increase the dimensions of their body. We assumed

that all of them wear protective boots, working clothes, gloves

and a protective helmet. Furthermore when this is required by

the situation analysed, the seafarers or surveyors were assumed

to wear specific survey equipment composed of oxygen

analyser or multi-gas detector, radiation meter, a camera,

gauges, a torch, a hammer and sometimes a self-breathing

apparatus for the study of emergency scenarios.

Each type of means of access implied scenarios depending on

the environmental conditions, the tasks to perform and the

seafarers physic characteristics (body measurements and

strength). Thus different design strategies had to be employed

for these different scenarios. Below are examples of design

strategies we adopted:

• For the ladders, stairways and inclined ladders

Design for the heaviest user to be able to

climb;

Design platforms for the largest user;

Design for the smallest and the largest users

to comfortable climb the rungs of a ladder;

The handles, treads, steps, guardrails and

other arrangements for safe access to ladders

should be sized for common fit.

Handrails, treads and guardrails should be

designed for common fit.

• For the openings, hatches and manholes

The vertical and horizontal openings should

be designed for access of the largest user.

People with dimensions higher than this

percentile must be advised of this. A person

wearing breathing apparatus should pass

through easily;

The handles, treads, steps, guardrails and

other arrangements for safe access to

openings and hatches should be sized for

common fit;

Markings of openings (especially horizontal

openings) should be clearly visible;

The openings should be large enough to allow

the evacuation of an injured crewmember.

• For the walkways, tunnel corridors

Obstructions should be clearly visible and

clearance around them should be sized for the

largest user;

Width of passageways should be designed for

the largest user;

Handrails, treads and guardrails should be

designed for common fit.

Walkways, tunnels and corridors should be

large enough to allow the evacuation of an

injured crewmember.

Simulations The simulation stage is the iterative phase of the process. The

objective is, considering the design strategies adopted and all

the constraints and requirements identified during the previous

steps, to find the best design trying to reproduce the real life

working situations on board. A CAD software was used in order

to model the interactions between the seafarers and the

environments they have to work in.

2.5. Step 4: Development of Ergonomic Guidelines From three previous steps of the methodology, we obtained

dimensional requirements for the design and arrangement of the

means of access onboard as well as some good practices. Thus,

the last step consisted in the development of a complete and

comprehensive technical document gathering all these

requirements and practices so that anyone interested in the

design of human-centred design of the means of access for

vessels and offshore installations can be provided with relevant

guidance.

3. APPLICATION AND RESULTS We applied our four-step methodology to the development of a

guidance note entitled “Guidelines for the design or Means of

Access onboard steel ships”, addressed to shipbuilders,

shipyards and every stakeholder intervening into the design

process of vessels. The main results that allowed us to develop

this note as well as the guidelines themselves are described in

the following sections.

3.1. The user feedback First, we interviewed one of the society’s ex-surveyors (whose

role is to carry out technical inspections onboard ships) in order

to collect background information concerning the main types of

issues encountered during a survey and to build the set of

questions that could be asked in the questionnaire. Furthermore,

this interview was very useful to prepare the further interviews

in terms of cultural background about the surveyors and the

relevant vocabulary and expressions to adopt when asking

questions.

Then we participated in a survey onboard a gas carrier (LNG)

led by an experienced surveyor who showed us the places and

means of access he has to use when inspecting a vessel. We

noted the good and bad practices in terms of safety and tried to

detect the STF hazards.


Figure 4. Visit onboard LNG – Entering the cofferdam

After the visit, we discussed with two other surveyors about

these points and analysed the potential design improvements

they would recommend for the prevention of STFs. We also

presented a first draft of the questionnaire that we adapted

according to the surveyors’ comments.

At this point, we had gathered a significant amount of

qualitative information required by the ergonomics-oriented

steps of our process and the questionnaire was in its final stage.

We consequently derived two versions of the questionnaire,

respectively addressed to seafarers and surveyors. The objective

was to obtain feedback from the largest possible number of

users in order to carry out quantitative analyses that would

reflect the largest range of users around the world. However,

none of the seafarers associations and unions or shipyards we

contacted accepted to disseminate the questionnaires to

seafarers and consequently we could not obtain a feedback from

them. This is an important first limit of our case study, one that

we plan to overcome in future research; nevertheless, we

believe that the results we obtained provide interesting insights.

Thirty-two questionnaires were answered by Bureau Veritas

surveyors: this can be considered sufficient all the more because

the returns were from a great majority of experienced surveyors

who have carried out inspections on a wide range of different

vessels as shown on figures 5 and 6 below.

21%61%

18%

< 5

5 _ 10

> 10

Figure 5. Work experience (number of years)

20%

20%

17%

11%

10%

8%

7%7%

Oil/Chemical

DCargo/Reefer

Bulk Carrier

Gas Carrier

Container S

Pax S/Cruise

Ro-Ro Ro-Pax

Supply

Figure 6. Type of vessels surveyed

3.2. The risk analysis Using the analysis of the causes involved in STFs and the

qualitative answers of the thirty-two respondents, we identified

on the one hand the root causes of Slip, Trip and Fall accidents

and on the other hand we developed a series of

recommendations to mitigate STFs and allow recovery.

First of all, we observed that (as expected) the seafarers tended

to minimise the likelihood with which STFs occur although they

seem to be aware of the severity of the injuries they may cause.

Seafarers seem to describe falls as the most ‘dangerous’ STFs

accidents but do not systematically take into account the fact

that slips and trips are very often the root causes for falling and

would be probably almost as dangerous as ‘direct’ falls. Maybe

a more precise definition of the STFs would have generated

more homogeneous answers.

Then, we identified the ballast tanks, the enclosed spaces, the

shaft tunnel and the pump room as the most risky areas

onboard. The fore and aft peaks, the steering gear and

machinery spaces appear to be very risky as well. These results

seem to be rather in accordance with the interviews and the visit

even though the peaks were said to be the most risky

compartments in vessels, followed by the ballast tanks.

Concerning the ‘dangerousness’ of the means of access,

according to the feedbacks from the questionnaires, almost all

of them (excepted stairways and corridors) have a high risk

score. This is in accordance with the information we got from

our previous interviews.

Finally, the main causes identified as the root of STFs are the

lack of handles for a safe use of the Means of Access, the

location of the openings, the poor signalisation of hazards, and

the lack of space. Clearance appeared as primordial to carry out

surveys safely (on platforms of around ladders for instance) as

well as to use the means of access with comfort and confidence.

In conclusion, the first stage of the process provided us with

precious information for carrying out the second stage that we

will now describe.

3.3. The ergonomic analysis We modelled four environments grouping the four main types

of Means of Access (MAs) that can be risky and cause Slip,

Trip and Fall accidents namely, vertical ladders, inclined


ladders and stairs, openings and walkways. The figure below

shows one of the environments modelled (walkways).

Figure 7. CAD model used for the anthropometric

analysis of walkways

Figure 8. CAD model used for the anthropometric

analysis of inclined ladders

Then we modelled the most risky working situations with

manikins and finally extract form the simulations the

dimensions and shapes the MAs would need to comply with in

order to fit the task and users requirements. Two examples

showing a simulation for the suitability of vertical ladders and

openings are presented in the figure below.

Figure 9. Pictures from the anthropometric analysis of the

vertical ladders and openings

3.4. The guidelines Developing the guidelines for Bureau Veritas was the last step

of the process we adopted for addressing the Slip, Trip and Fall

accidents (STFs). The guidelines had to provide the maximum

relevant information gathered during the previous steps about

the way to prevent STFs, especially by improving the Means of

Access on board. Thus, vessels complying with all the

requirements stated in the guidelines should be safer for the

personnel operating and surveying them. Most of the guidelines

are dimensional requirements for the MAs; however the last

section is about the safe design best practices dealing with

MAs’ texture, colour and marking, maintenance and use, or the

environment lighting.

A very short extract from these guidelines is presented below.

Dimension IMO-IACS

requirements Guidelines

Requirements

A Ladder width

≥ 350 mm in general

≥ 300 mm for access to hold

frames

≥ 400 mm 450 mm is

recommended

B Vertical distance between rungs

250 mm ≤…≤ 350mm

250 mm ≤…≤ 350mm

C

Lateral distance between two

adjacent sections of ladder (linking

platform)

At least the width

of the ladder ≥ 500 mm

D Gap length between wall and guardrail

- ≥ 850 mm

E Handles height

above floor - 1000 mm

F Lateral distance

between ladder and linking platform

- 200mm ≤…≤

350mm

G Rung dimensions

(square bars) ≥ 22×22 mm

22×22 mm ≤…≤35×35 mm 25×25 mm is

recommended

Figure 10. Extract of the ergonomics-based guidelines

developed for Bureau Veritas


4. CONCLUSION AND FURTHER WORK The maritime industry is increasingly aware of the necessity to

deal with the numerous issues raised around the human element

and has set to work its regulatory organs for sweeping along the

wide spectrum of stakeholders on these issues. Whereas much

effort is needed to increase safety through technology, there are

many gains to expect in terms of safety increase by addressing

the human element related issues. Consequently, this domain

was turned from a ‘second zone’ concern into a strategic one.

What we suggested through this paper is a way to introduce

both risk concepts and user feedback in the processes for

assessing safety through ergonomics.

Driven by an ergonomic risk-based process we adapted from

the wide spectrum of human factors and ergonomic methods we

managed to provide useful guidance for preventing and dealing

with Slip, Trip and Falls accidents, that would lead – if they

were followed – to lives and money savings for the shipyards

and to get a bit closer to the objectives established by the

International Maritime Organisation concerning the human

element.

The type of approach we adopted has to be seen a part of a

more global risk management framework such as the Formal

Safety Assessment (FSA) for instance. Actually, once the risks

have been assessed through the user feedbacks and the solutions

to improve the design adopted, an evaluation of the risk

reduction and the gains expected from the application of the

design improvements could be processed. Then tradeoffs

between the costs and the gains like in the Cost-Benefit

Analysis could be done as well.

In addition, in order to determine clearly the way safety should

be assessed and thus find a common measure for the assessment

of costs and losses attributed to each type of injury, we propose

as a further work to encode some utility functions (from the

shipyards, the flag states, IMO, etc…) describing the harm

caused by accidents and the gains obtained by addressing such

issues like human element issues that will help to set the criteria

for risk analyses. Determining precisely the way each of the

stakeholders perceives and manages risks at its own level would

clearly help the shipping industry to overstep management and

organisational issues surrounding the Human Element as well.

Finally, this way could be explored for addressing the whole

panel of human element issues, i.e. those dealing with the ship

design as well as those dealing with the ship operability.

REFERENCES [1] Jensen, O. C., Sorensen, J. F. L., Canals, M. L., Yunping Hu,

Nicolic, N., and Mozer, A. A. 2005. “Non-fatal Occupational

Injuries Related to Slips, Trips and Falls in Seafaring”,

American Journal of Industrial Medicine. 47, pp. 161-171

[2] American Club P&I Current newsletter, issue number 18,

May 2004, “Caring for the crew”

[3] Haslam, R., A., 2001, “Slip, Trip and Fall Accidents”. In

Karwowski, W., “International Encyclopedia of Ergonomics and

Human Factors.”

[4] IACS. March 2006. Unified Interpretations for the

application of amended SOLAS regulation II-1/3-6 (resolution

MSC.151(78)) and revised Technical provisions for means of

access for inspections (resolution MSC.158(78)). IACS UI SC

191

[5] IMO. 22 May 2006. Framework for consideration of

ergonomics and work environment. MSC-MEPC.7/Circ.3

[6] Kahneman, D., Slovic, P., and Tversky, A. 1982. Judgement

under uncertainty: Heuristics and biases. Cambridge:

Cambridge University Press. 163-200

[7] Pheasant, S., Haslegrave, C. 2006. Bodyspace:

Anthropometrics, “Ergonomics and the design of work” – Third

Edition. CRC Press, Taylor & Francis Group



OMAE2008-57734

PERFORMANCE ASSESSMENT OF DAVIT-LAUNCHED LIFEBOAT

Laurent Prat Bureau Veritas

Paris La Défense, France

Leo de Vries Alex W. Vredeveldt

TNO Delft, The Netherlands

Omar Khattab Ship Stability Research Centre

Glasgow, UK

Jean-Jacques Maisonneuve SIREHNA

Nantes, France

Thomas Boekholt Fassmer

Berne/Motzen, Germany

Ole Andersen Viking

Esbjerg, Denmark

David Cummings Carnival plc London, UK

Jan Block MARIN

Wageningen, The Netherlands

ABSTRACT In response to the recent changes to SOLAS, which further encourage the alternative design of life-saving appliances, the European Union has funded a Framework Programme 6 (FP6) project called SAFECRAFTS that was initiated by the Netherlands Research Organisation TNO. The aims of the project are two fold: to develop a methodology for assessing the performance of life saving systems (made up of life saving appliances or LSA); and to develop novel concepts. This paper focuses on the first objective and presents the results for conventional davit-launched lifeboats. The proposed performance indicator is the Success Rate of the evacuation process, which compares the final Human Health Status (the number of persons in good health, injured or deceased at the end of the process) with the initial Human Health Status (number of persons in good health onboard the mother ship). The Human Health Status calculation follows a step-by-step approach for both the human and the hardware as they progress along an obstacle course, which represents the evacuation sequence specific to the design. Associated to each obstacle is a transformation function that characterises the degradation of the Human Health Status. The determination of the transformation functions is based on first principle methods, risk analysis methods, and human factor methods some of which are inspired by the automotive industry. A scenario-based approach is applied to account for increasingly severe environmental and damaged ship conditions. In addition, the systems performance is represented along the evacuation and rescue route, so that it is possible to identify and quantify the contribution of individual obstacles to the overall degradation. This is essential to select the critical areas for improvement and support the development of innovative designs. Finally, the paper advocates that the set of scenarios and their associated Success Rates represent performance criteria for LSA which can be used for approving alternative designs and arrangements.

- 1 -

1. GENERAL

1.1. Context In December 2006, the Maritime Safety Committee of IMO adopted a new regulation of the SOLAS convention [1] which provides for “Alternative design and arrangements for life-saving appliances”. It allows operators and manufacturers to equip a ship with LSA that deviate from the prescribed requirements. This demands specific engineering studies and comprehensive evaluations to demonstrate their “equivalency” with prescribed designs. In view of the growing market for large cruise ships, the new regulation creates an opportunity for innovation in the field of survival crafts. This also paves the way for an in-depth investigation of the performance of current LSA.

1.2. Challenges and Objectives To demonstrate the equivalent performance of novel concepts with prescriptive designs, the methodology should include a quantitative assessment in line with IMO guidelines [3]. In particular, it is needed to apply the methodology to at least one existing conventional design in order to derive the baseline performance or the acceptance criteria against which alternative designs are to be assessed. In the case of LSA, novel concepts are not precisely novel features because the function (saving lives) is not changed. However, a novel concept or an alternative design may largely deviate from the prescriptive requirements, so that a global assessment is required to effectively address the principle of equivalence. Thus, the methodology aims to derive the global performance of LSA using a functional perspective that is not design specific. In addition, input calculation data are mostly supported by first-principle models. This paper presents the basics of the assessment methodology as well as the assessment results for a generic conventional davit-launched lifeboat.

Copyright © ASME 2008

2. METHODOLOGY This methodology was developed by Bureau Veritas and TNO in the course of the SAFECRAFTS project [2].

2.1. Conceptual Background Life-Saving System: An evacuation and rescue system is more than just one category of LSA. Two or more different types of LSA can be fitted on a ship. The capacity of each LSA unit, the location on the ship, and the means of transfer from the survival craft to the rescue ship are critical to characterise a Life Saving System (LSS). The proposed approach focuses on the system as a whole, because we deem it necessary to tackle the rescue of the entire population being evacuated. The global performance of a LSS is also the level of analysis that allows objective comparison between conventional systems and novel concepts. Rescue Route: It is the sequence of actions required to evacuate safely the entire population from the embarkation station to a safe haven. It involves the passengers, the crew and the hardware components of the LSS. Each LSS is associated with a specific rescue route. Conventional existing systems have similar rescue routes but novel concepts can differ radically in this respect. The rescue route elements (deployment, boarding, etc) that are identified for each LSA type can be grouped together within three generic phases: (1) Leaving the vessel; (2) Surviving at sea; (3) Being rescued from the survival craft. Obstacles: As the hardware systems and the humans proceed along the rescue route, they may face hazards and subsequent damages. Thus, the rescue route can also be considered the series of obstacles that the hardware and humans must overcome for the rescue to be completed. An obstacle is characterized by the hazard generated when the system meets with it. Some hazards directly affect the human body (like seasickness), whereas some primarily affect the hardware system (like mechanical failure). Human Health Status: It is a metric of the state of health of the population being evacuated: for each obstacle along the route a proportion of the population will succeed without any trauma whereas others will be injured, perhaps fatally. The Human Health Status (HHS) is therefore a variable representing the distribution of population (in %) in the following four categories: Good Health, Moderately Injured, Severely Injured and Dead (Table 1). The HSS of a particular population can be seen as a 4-dimensional vector that is transformed step-by-step. The comparison between the initial and final HHS characterises the HHS degradation (Figure 1). Design Casualty Scenarios: A set of assessment scenarios is defined that account for the increasingly precarious situation of the mother ship and severe weather conditions. This approach follows the IMO guidelines [3] that refer to Design Casualty Scenarios against which prescriptive and trial alternative designs must be assessed. In the SAFECRAFTS project, Design Casualty Scenarios represent the sequence of obstacles ranging the assessment scenarios (Figure 2).

- 2 -

HHS categories Description Related mobility

Good Health (GH)

Good physical and mental health Good mobility

Moderate Injury (MI)

Moderate bleeding No fracture, no trauma Mobility impaired

Severe Injury (SI) Fractures and/or trauma Mobility requiring

assistance

Deceased (D) Fatal injury No mobility

Table 1: Categories of Human Health Status (HHS)

Figure 1: Transformation of the Human Health Status

along the Rescue Route

Figure 2: Design Casualty Scenarios

2.2. Risk Model Assumptions and Limits: Firstly, we look at the HHS degradation along the rescue for one use corresponding to one evacuation and rescue process. The risk is therefore characterised by the expected degradation of the HHS, provided the conditional event “evacuation is required” is realised. Secondly, the model does not deal with timeline for the evacuation and rescue aspects. Only the period of survival at sea is set as a benchmark. Thirdly, we consider the sequence of obstacles is linear: they come one after the other. This assumption can be questioned if several obstacles act simultaneously, for instance during the phase of survival at sea. In this case, we compared the matrix products in different orders and found no significant difference in the results, so that we eventually chose the average sum of the different combination of matrix products. As we focused on design

Sc 1 Sc 2

Sc k

- - -

Ob.1 Ob.2

[Assessment scenarios of increasing severity]

Design casualty scenarios

Ob.N [Obstacles along the rescue route]

Rescue Route

Initial HHS

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

N

N

N

N

δχβα

Final HHS

Obs

tacl

e A

Obs

tacl

e B

Obs

tacl

e N

GH MI SI D

GH MI SI D ⎥

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

0

0

0

0

δχβα

10000 =+++ δχβα 1=+++ NNNN δχβα


Success Rate: Considering that the primary function of a

ed as the percentage of the

performance, first-principle methods were preferred. Thus maintenance and training were generally not considered. In some cases however, historical data were used that may incorporate some maintenance and training shortages.

Life-Saving System is to save lives, the comparison between the final and the initial HHS should be an adequate measure of the LSS performance. To ease the assessment, it is also useful to convert injuries into “equivalent fatalities” using the IMO index [4] reproduced in Table 2. Hence, the success rate is defininitial ship’s population in “equivalent Good Health” which is still in “equivalent Good Health” at the end of the rescue process. It reflects the global degradation of the HHS along the rescue route and therefore the global performance of the LSS. The formal expression of the success rate is given below in Eq. (1) with reference to one assessment scenario “k”.

Effects on human safety Equivalent fatalities Single or minor injuries 0.01

M ultiple or severe injuries 0.1 Single fatality 1

Table 2: Equivalent Fatalities

( )( )000 01.01.01

01.01.01βχδβχδ

++−++−

=kN

kN

kNkSR (1)

lobal Degradation Function: The overall HHS Gdegradation can be seen as a 4-dimensional function f: [0 ; 1]4 → [0 ; 1]4 that is applied to the initial HHS vector. The transformation can be written using matrix format in the standard basis ),,,( 4321 uuuuB rrrr

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

N

N

N

N

plhdokgcnjfbmiea

δχβα

δχβα

0

0

0

0

*

s the population cannot get healthier in the course of the

(2)

he global degradation function is a risk assessment tool

Aevacuation and rescue process, the global degradation function can be simplified in Eq. (2):

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

1000000

lhdkgc

fba

f⎪⎩

⎪⎨

⎧

=+=++

=+++

11

1

lkhgf

dcba

Tbecause the coefficients of the matrix are determined according to the expected degradation of the HHS through the sequence of obstacle and the likelihood of such degradation. Yet, the global degradation function can only be derived from the determination of the local degradation functions associated with individual obstacles.

- 3 -

ocal Degradation Functions: Local degradation

ractically, one characterises each obstacle to determine the

/ Hardware obstacles

Lfunctions account for the local degradation of the HHS when passing through one single obstacle and have identical structure as global degradation functions. Given the model’s assumptions, the global degradation is equivalent to the successive degradations caused by the local degradations – in mathematical terms, the matrix product of the local degradation functions. Pcoefficients of the matrix by means of engineering methods and models. As a result, the global degradation matrix is calculated as the product of the local degradation matrixes Eq. (3). There are two types of local degradation functions associated with two categories of obstacles: 1 refer to a failure or a hazard that

2/ an factor obstacles

directly affects the hardware components of the system, for instance a mechanical failure in the deployment system. The effect is binary with respect to the HHS of the people “inside” the hardware. If the hardware fails all occupants are deemed lost and furthermore the phenomenon does not depend of the HHS before the obstacle;

Hum are associated with a number of

phenomena that degrade HHS while the hardware part of the system remains operational. This includes impacts forces, accelerations, seasickness, and other mobility failures. Subsequently, the HSS before the obstacle is relevant because an injured person is more likely to “fail” the next obstacle than a healthy person.

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

⎥⎥⎦

⎤

⎢⎢⎣

⎡ABN ffff **...*

(3)

plemented Methodology: On Table 3 hereunder is the Imbasic scheme of the implemented methodology. It includes a phase of definition based on technical documentation and brainstorming, followed by a phase of analytical work to set up and perform the relevant analyses, and finally a phase of consolidation and exploitation of the results.

Main steps Description

Documentation System definition ving appliances, : ship, life-sapopulation, scenarios

Brainstorming cue route and stacles

Description of the Rescharacterisation of the sequence of ob

Analysis Selection of relevant methods and risk criteriafor each obstacle

Assessment al degradation matrixes

Determination of locthrough direct calculation, tests or simulations

Consolidation Calculation of Global degradation functions, final HHS and Success Rates

Exploitation proval of Identification of critical areas, apalternative design and arrangements

Table 3: I p mplemented method step by ste


3. PERFORMANCE ASSESSMENT OF DAVIT-LAUNCHED LIFEBOAT

3.1. System definition Abandoned Vessel: the mother ship model is a large cruise ship whose main features are given in Table 4.

Ship type Cruise liner Displacement 43,000 T

Passenger capacity 2,900 Crew members 900

LOA 294 m LDWL 265 m

Moulded Breadth B 32.2 m Moulded Draught T 7.8 m

KG 15.1 m LCG 123.3 m

Table 4: Features of the abandoned vessel Life-Saving System: The LSS that is assessed here is made up of three hardware components that are (1) the davit system, (2) the lifeboats, and (3) the pilot ladder that is used for disembarkation. In our model, only the lifeboat is specified in details because it is the most complex and important element among the three. Also, we do not model spare capacities, so that LSS capacity corresponds exactly to the population being evacuated. We then consider that the entire population to evacuate “P” is distributed in “N” lifeboats of full capacity “p”. Since all lifeboats are identical, the risk of fatality or injury expressed as a percentage of the total population is calculated as if the entire population was evacuating on one “big lifeboat”:

( )∑ ×=

Nfailure plifeboatTotalRisk )(Pr

PlifeboatplifeboatNTotalRisk failurefailure ×=××= )(Pr)(Pr

Survival Craft: Only one type of LSA is considered that is a standard 150pax partially enclosed davit-launched lifeboat, based on Fassmer’s SEL 8.8 design (Table 5 and Figure 3).

LWL (m) 8.69 BWL (m) 4.09 Draft T 1.05

Sinkage (m) 1.06 Trim (°) -1.35

Volume displacement (m^3) 17.58 Displacement (kg) 18 050

LCG (m) 4.16 VCG (m) 0.66 LCF (m) 4.25

Wetted surface area (m^2) 41.04

Table 5: Features of the lifeboat in fully loaded condition (150pax)

- 4 -

Figure 3: General view of the lifeboat design

Population Features: People’s age is an important aspect to consider because the elderly are generally more vulnerable to harsh conditions and unexpected physical stress. The population used for analysis is distributed as in Table 6 on the basis of internal data and IMO guidelines [5].

Age groups (years) Percentage of passengers (%) a ≤ 50 28%

50 ≤ a ≤ 75 58% 75 ≤ a 14% Total X + Y + Z = 100 %

Table 6: Age distribution among typical cruise population Initial Human Health Status: In realistic conditions, the typical population onboard cruise ship cannot be considered 100% in Good Health according to the model’s assumptions. In particular, people with impaired mobility are deemed more vulnerable to the physical stress and efforts required by the evacuation and rescue process. Based on IMO guidelines for evacuation analysis [5], it is estimated that about 55% of the population older than 50 years old has impaired mobility. With reference to Table 1, we then obtain the initial HHS as input for the calculation (Table 7):

Age groups (years) Initial HHS

a ≤ 50 ⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

00.000.000.000.1

50 ≤ a ≤ 75

75 ≤ a ⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

00.000.055.045.0

Table 7: Initial Human Health Status Assessment Scenarios: The selected scenarios have been derived from the damaged ship and environmental requirements that are currently in force with respect to the operability of LSA. The scenario parameters are independent from LSS design and arrangement and shall reflect the increasing difficulty of the evacuation and rescue process. The selection of relevant parameters may however depend on LSA specificities: for instance low temperature was identified as a relevant parameter for assessing the risk of hypothermia for life rafts, whereas it was not deemed relevant for lifeboats. Beam sea situation would correspond to the typical “dead ship” that has lost its manoeuvring capacity; sea states influence the motions of the abandoned ship and survival crafts; and the period of time at sea is 24 hours as a reference


to LSA Code requirements [6]. In order to limit the number of calculations, we have selected five assessment scenarios (Table 8). The environmental parameters are also described in Table 9; the ITTC spectrum with two parameters was used for seakeeping and ship motions calculation.

Abandoned ship

Scenario Sea state

Period at sea

Heading angle

List (°)

Trim (°)

Sc 1 0-1 ../. 0 0 Sc 2 3 Beam 0 0 Sc 3 5 Head 10 5 Sc 4 5 Beam 20 10 Sc 5 6

24 h

Beam 20 10

Table 8: Five Assessment Scenarios

Sea state

Beaufort scale

Mean wind speed

(knots)

Significant wave height

Hs (m)

Wave peak period Tp (s)

0-1 0 0.0 0.00 ../. 3 3 11.5 0.88 7.5 5 6 24.5 3.25 9.7 6 7 37.5 5.00 12.4 7 10 51.5 7.50 15.0

Table 9: Description of Sea States codes (source NATO)

3.2. Rescue Route For each LSA type, the rescue route in Table 10 was determined during brainstorming exercises through hazard identification and the contributions of experts from various backgrounds including classification, naval architects, LSA manufacturers, ship owners, shipyards and research institutes in both marine science and human health.

Phases Elements Obstacles Type Malfunction Hardware

Deployment Engine failure to start Hardware

Boarding Mobility failure Human factor Premature release Hardware Failure /impact hull Hardware Lowering Injuries / impact hull Human factor Fail to release Hardware

1

Release Injuries / Slamming Human factor

Clear ship Fail manoeuvring Hardware Capsizing Hardware Seasickness Human factor

2 At sea

Tossed around Human factor 3 Recovery Climbing pilot ladder Human factor

Table 10: Rescue Route for Davit-Launched Lifeboat

- 5 -

3.3. Obstacles and Degradation Functions Malfunction: From stowed to lowered position before disconnection, the failure probability is estimated based on historical data available within the project. Over two years and a half, a fleet of passenger ships has experienced 13,692 launches of lifeboats. Problem occurrences relevant to the deployment phase are reported and turned into a failure rate per launch of one lifeboat (Table 11). Due to the lack of details regarding the events actually reported, it is ensure that every occurrence actually prevented the use. Our approach is therefore conservative in this respect. We further consider that these basic events are independent one from each other, and that “Malfunction” can occur because of at least one of these causes. Using a simple fault tree model (Figure 4), we eventually obtain an estimate of the overall probability of failure associated with the obstacle “Malfunction” that is to say 3.2×10-03 per launch or about 1 malfunction every 300 launches. Since the event is independent from age groups and scenarios, there is only one degradation function to derive.

Failure type Occurrences Failure rate per use

Brake mechanism 8 5.84×10-04

Davit mechanism 12 8.76×10-04

Falls 7 5.11×10-04

Winch failure 17 1.24×10-03

Table 11: Failure rate per launch of davit-launched lifeboat

Figure 4: Fault Tree analysis of the obstacle "Malfunction"

0.9968 0.0000 0.0000 0.0000 0.0000 0.9968 0.0000 0.0000 0.0000 0.0000 0.9968 0.0000

“Malfunction”

All scenarios 0.0032 0.0032 0.0032 1.0000


Engine Failure to Start: Passenger ship disasters’ reports [7-9], suggest that lifeboat engine may fail to start, hence preventing the survival craft to clear the ship as required. The associated failure probability per use was derived from historical data available in the offshore industry [10]. The estimate is 0.01 per use which was considered reasonably applicable to passenger ships’ lifeboats. Since this failure is independent from age groups and scenarios, only one degradation function is derived.

0.9900 0.0000 0.0000 0.0000 0.0000 0.9900 0.0000 0.0000 0.0000 0.0000 0.9900 0.0000

“Engine failure”

All scenarios 0.0100 0.0100 0.0100 1.0000

Mobility Failure: Boarding lifeboat and move to final seat may be an obstacle for elderly people. However, if crew assistance is provided, the probability of falling is deemed negligible, so that the obstacle does not degrade HHS.

Premature Release: There are evidences that some on/off-load release hooks currently in use may be instable even with adequate maintenance [8, 11]. This concern in particular so-called “flat contact area cam” designs reproduced hereunder in Figure 5 and Figure 6, taken from [8]. Although many lifeboats are equipped with safer hook designs, we found it interesting to deal with this particular design in order to evaluate the contribution of this hazard to the overall performance of the system.

Figure 5: Mechanical description of flat contact area cam

hook design

- 6 -

Figure 6: Description of hook opening sequence

The contact surface between hook lever and cam is flat. The end of the hook lever pushes the cam open, which is prevented by the release cable attached to the cam lever. When the release cable is removed, the hook will open instantaneously. A simple mechanical model was developed to determine the relationship between the retaining moment in the cam and the cam angle. The following geometrical relations hold.

( ) ( )202 cossin)( ϕϕα vxvvx −++=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

)(sinarcsinαϕα

xv

)(αx Distance cam contact force from cam hinge

v Lever cam contact force related to hook hinge

ϕ Hook angle with respect to the “vertical”

0x Lever cam contact force related to hook hinge, at cam angle 0.0

α Cam angle with respect to the “vertical”

Considering equilibrium of moments about the swivel pin:

vFhF cpvh =

cpvcpc FF)cos(

1ϕα +

=


hF Hook load [N]

h Lever hook load related to hook hinge

cpvF Cam contact force perpendicular to lever v [N]

cpcF Cam contact force perpendicular to cam plane [N]

In line with other experiments [11], the graph in Figure 7 shows the retaining moment is always negative, meaning that the hook will open freely if, for whatever reasons, the retaining control cable is removed or disconnected. More importantly, if the cam is not properly reset, flat against the hook tail, the opening moment is big enough to make the mechanism open at any moment. Assuming a human error probability that the control release cable is improperly reset, the model goes on investigating the problem of premature release. If improperly reset, the control release cable will still apply a retaining force due to the frictional resistance of the cable in the mechanism. As the lifeboat is hoisted empty, back to its stowed position the model help calculate the probability that the frictional resistance of the control cable overcome the opening moment. Considering a 150 persons partially enclosed lifeboat, its typical total weight would be 17.70 tonnes. One hook would carry 8.85 tonnes. The associated cam retaining moment would be about 150 Nm. With a typical relative cam lever length of 0.085, the required retaining force in the mechanical operating cable (release cable) would be about 1760 N. A typical travel of the cable would be 100 mm. A suitable cable would then be a Heavy Duty cable with a travel of 5 inch and push/pull loads 1780/4450 N (400/1000 lbs). For this cable the manufacturer specifies an internal friction of , where cb stands for the total degrees of bend in the cable (in a boat often 180 degrees) and F

cableFcb0015.0

cable stands for the maximum control force. Therefore a typical internal friction would be 481 N (0.0015 × 180 × 1780) in the push mode. When a boat is retrieved after a launching exercise, the hooks will only have to carry the weigh of the empty boat and perhaps six crews. In case of a 150 persons life boat this will be about 6.18 tonnes. One hook has to carry 3.09 tonnes. The associated cam retaining moment is shown in Figure 8.

-500.00

-400.00

-300.00

-200.00

-100.00

0.00

100.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

CAM angle [deg]

CA

M M

omen

t [N

m]

Figure 7: Cam retaining moment against cam angle with

lifeboat fully loaded

- 7 -

-500.00

-400.00

-300.00

-200.00

-100.00

0.00

100.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

CAM angle [deg]

CA

M M

omen

t [N

m]

Figure 8: Cam retaining moment against cam angle with

lifeboat unloaded With a typical effective cam lever length of 0.085, the required retaining force would be as shown in the Figure 9. Up to a cam angle of 20 degrees the required cam retaining force is about 600 N. A probability of undue resetting can now be determined, assuming a normal distribution for the internal friction force, with a mean of 481 N and a deviation of 20%, as depicted in the Figure 10 below.

-7000

-6000

-5000

-4000

-3000

-2000

-1000

00.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00

CAM angle [deg]

Ret

aini

ng fo

rce

[N]

Figure 9: Retaining force required with lifeboat unloaded

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

200 300 400 500 600 700 800

friction force in morse cable [N]

prob

abili

ty d

ensi

ty []

Figure 10: Frictional resistance of the control cable


Undue hook reset is possible when there is sufficient friction in the control cable to provide for a required cam retaining force of 600 N. The cam angle would then be somewhere between 0 and 20 degrees. In this condition the weight of half the boat can be transferred into the release hook without immediate opening of the hook. Assuming the above density function valid, the probability of this being the case is 0.11. Subsequently, the probability of premature release is dramatically high: any additional load can disrupt the fragile equilibrium and trigger the release mechanism. In the worst case scenario, this will happen during a real emergency as people are starting to board the lifeboat. It is however true that this result depends heavily on the average friction force in the release cable and the deviation. The Table 12 below demonstrates this.

Deviation 10% 20% 30%

425 0.00 0.02 0.08 450 0.00 0.05 0.13 475 0.00 0.09 0.19 500 0.02 0.16 0.25 A

rithm

etic

m

ean

525 0.08 0.23 0.32

Table 12: Sensitivity analysis of the control cable frictional resistance model

Additionally we needed to determine the conditional probability that the control cable is improperly reset. This is a typical human error that can occur in the course of drill operations. On the basis of human errors probabilities that are quantified for generic tasks (Hunns & Daniels 1980) we estimated that the control cable is improperly reset once every 20 times (0.05). As a result, the overall failure rate associated with this obstacle is 0.0055.

0.9945 0.0000 0.0000 0.0000 0.0000 0.9945 0.0000 0.0000 0.0000 0.0000 0.9945 0.0000

“Premature release”

All scenarios

0.0055 0.0055 0.0055 1.0000

Structural Failure due to Impact against the Hull: As lifeboats are lowered from the embarkation deck to water level, their relative motions with the mother ship generate a pendulum effects so that lifeboats may impact the hull of the vessel. Apart from injuries induced by impact forces and accelerations, a lifeboat can undergo structural failures that put all occupants in danger irrespective of age or HHS. The aim was to analyse the structural response of a lifeboat during its lowering alongside the mother ship and with reference to the five assessment scenarios. The model has been implemented in Adams software which is dedicated to poly-articulated mechanical systems with large displacements and non-linearity. The mechanical system studied consists of two main parts: the vessel hull and the lifeboat. The davits are rigidly fixed to the hull. Shocks are detected and analysed to extract the velocity of impacts against the hull (Figure 11).

- 8 -

The mother ship’s hull is modelled by a parallelepiped rigid body (265m × 32m × 23m). The six degrees of freedom motions of the vessel are obtained with a 3D-linear seakeeping frequential code (AQUA+), and post-processed to take into account irregular waves (ALEA+). Motions are imposed at the vessel centre of gravity. The lifeboat’s geometry is inspired by Fassmer’s partially enclosed lifeboats SEL 8.8 type.

Figure 11: Setting-up of the lifeboat descent model

As risk criterion, we focused on the velocity of impacts against the hull, which is a relevant indicator with respect to the structural integrity of lifeboats. Indeed, one of the testing requirements for davit-launched lifeboats requires the lifeboat’s structure to withstand a minimum impact velocity of 3.5m/s against a fixed vertical rigid surface [12]. From a regulatory point of view, this requirement means that a lifeboat is approved to withstand impacts up to 3.5m/s. As a result, we deem the “regulatory lifeboat design” would not withstand higher impact velocity – even if a particular lifeboat could actually withstand beyond the regulatory level. This gives us a criterion to analyse the results of the simulations. We consider that a structural failure would occur for each recorded peak of impact velocity above 3.5m/s. The frequency analysis is based on simulated motions over 1700s for two lengths of the davit falls 7.5m (half way) and 12.5m (lifeboat at waterline). This provides an insight of the likelihoods of impacts against the hull. As the amplitude of the pendulum effect increases with the falls’ length, these two positions provides two reference values for estimating the risk of structural failure due to impacts during the descent. The results show that many impacts would occur in Beam Seas, even for medium weather conditions (sea state 3). Yet, most impacts would remain below the threshold of 3.5 m/s. When the ship is listing, there are two aspects: on the positive listing side, lifeboats would supposedly glide down along the ship’s hull; on the other side, the distance to the hull increases as the lifeboat is lowered, but impacts could occur with some of them above the threshold.


The only hazardous situation reported by the simulation is represented in Figure 12 with reference to Scenario 5. Over the time of the simulation (1700s), one dangerous impact is reported for cable length 7.5m whereas height impacts are reported for cable length 12.5m. At constant speed, for a typical descent time of 30 seconds, this would give a probability of respectively 0.017647 and 0.141176 of at least one dangerous impact. At this stage, we can make use of these reference values to approximate the overall probability of structural failure during a descent of 30 seconds. To do so, we have fitted an analytical function Eq. (4) thanks to the three points of reference: [0;0]; [7.5;0.017647] and [12.5;0.141176]. The function F represented in Figure 13 is a probability function associated to the event “at least one impact against the hull with velocity in excess of 3.5 m/s during the descent”.

Figure 12: Simulated impact velocity of the lifeboat against

the mother ship's hull

with (4) XbeXaXF ...)( =1

4

10137.310237.2

−

−

×≈

×≈

ba

0,141

0,018

0,0000,000

0,050

0,100

0,150

0,0 2,5 5,0 7,5 10,0 12,5Cable length (m)

Prob

. at l

east

one

impa

ct w

ith v

eloc

ity

> 3,

5 m

/s d

urin

g de

scen

t 30

s

Figure 13: Probability function associated with dangerous

impacts of the lifeboat against the mother ship's hull

At constant speed, we can calculate the expected value with a simple integration. The overall approximated probability that at least one dangerous impact occurs is 2.7×10-02 for a descent time of 30 s and with reference to Scenario 5.

25.12

0

107.2)(5.12

1 −×=∫ dXXF

- 9 -

The consequence analysis is that impacts against the hull can produce a failure in a lifeboat’s structure if the impact velocity exceeds the prescribed level. As we have explained earlier in the methodology, this kind of failure is considered as a “Hardware obstacle” which is binary in nature with respect to the human health status. In other words, when a structural failure occurs to a lifeboat due to impacts against the hull, all occupants are deemed lost. This is the worst case scenario, but the approach is for an approval process and it is designed to promote robust LSS. Age and HHS before the obstacle have no influence on the results. This is reflected in the simplified structure of the associated degradation function.

With reference to the scenarios defined in the methodology, the results indicate no risk of structural failure due to impacts against the hull for the first four scenarios. For Scenario 5, we have derived the failure rate for lifeboats launched on the negative listing side. On the positive listing side, it is assumed no impacts during the descent. Hence, the overall failure rate is half of 2.7×10-02, that is to say 0.0135.

1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000

“Impacts / structural failure”

Scenario 1 to 4

0.0000 0.0000 0.0000 1.0000 0.9865 0.0000 0.0000 0.0000 0.0000 0.9865 0.0000 0.0000 0.0000 0.0000 0.9865 0.0000

“Impacts / structural failure”

Scenario 5

0.0135 0.0135 0.0135 1.0000

Injuries due to impacts against the hull: Provided that no structural failures occur due to impacts against the hull, we then considered the problem of injuries for the lifeboat’s occupants. In short, lateral impact accelerations taken from the previous simulation were converted into biomechanical injuries in a way that is similar to a car crash accident using the Abbreviated Injury Scale (AIS) [13].

Injury is estimated on the basis of maximum acceleration that is scaled relative to a “tolerable acceleration limit” which is 5g for lateral impact. This value holds for cars where occupants have a sort of bucket seat. In a lifeboat with absolute flat benches and no armrests at all, we lowered the limit to 4g, and 3g for the oldest group of people. The conversion to AIS was based on a regression formula. Furthermore, a fatality was assumed for AIS 5 or beyond (“critical” or “fatal”); severe injury for AIS 2.5 to 4.99 (“serious” or “severe”); and moderate injury was assumed for AIS 1.0 to 2.5. Only Scenario 4 & 5 gave peak accelerations greater than 3g or 4g. Figure 14 below show the simulation results in scenario 5 conditions for the two cable lengths.


Figure 14: Simulated impact accelerations of the lifeboat

against the mother ship’s hull As with the previous obstacle, impacts and associated injuries are only considered on the negative listing side. Considering both sides, the overall degradation is as follows:

AGE ≤ 75

1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000

“Impacts / injuries”

Scenario 1 to 4

0.0000 0.0000 0.0000 1.0000 0.9445 0.0000 0.0000 0.0000 0.0472 0.9898 0.0000 0.0000 0.0083 0.0103 1.0000 0.0000


Scenario 5

0.0000 0.0000 0.0000 1.0000

75 ≤ AGE 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000


Scenarios 1 to 3

0.0000 0.0000 0.0000 1.0000 0.9584 0.0000 0.0000 0.0000 0.0417 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000


Scenario 4

0.0000 0.0000 0.0000 1.0000 0.8234 0.0000 0.0000 0.0000 0.1322 0.9479 0.0000 0.0000 0.0361 0.0419 0.9800 0.0000


Scenario 5

0.0084 0.0103 0.0201 1.0000

- 10 -

Fail to release: In addition to the risk of premature release, there exist a risk that the release system fails when it is required, hence preventing lifeboats to sail away from the touchdown area. There are certainly various causes that contribute to such event including poor maintenance. For the purpose of the assessment, we used historical data from within the project as well as from the offshore industry [8] (Table 13). For all age groups, the degradation functions are thus provided hereunder.

Environmental conditions Calm Moderate Severe Internal data 9.49×10-04 ./.. ./.. CMPT report 1999 0.000 0.015 0.140 SAFECRAFTS Data 0.001 0.01 0.1

Table 13: Release failure rate per use

0.9990 0.0000 0.0000 0.0000 0.0000 0.9990 0.0000 0.0000 0.0000 0.0000 0.9990 0.0000

“Fail to release”

Scenario 1 0.0010 0.0010 0.0010 1.0000 0.9900 0.0000 0.0000 0.0000 0.0000 0.9900 0.0000 0.0000 0.0000 0.0000 0.9900 0.0000


Scenario 2 0.0100 0.0100 0.0100 1.0000 0.9000 0.0000 0.0000 0.0000 0.0000 0.9000 0.0000 0.0000 0.0000 0.0000 0.9000 0.0000


Scenario 3, 4 & 5 0.1000 0.1000 0.1000 1.0000

Slamming: As the lifeboat is disconnected from the falls, it may drop in water due to the relative vertical motions with the surface of the sea. Slamming may then cause impact accelerations leading to injuries for the occupants. This aspect was investigated in the project but the results were not sufficiently reliable to use them in the overall assessment. As a result, we do not account for the degradation induced by the obstacle “Slamming”.


Fail Manoeuvring: This analysis was performed to derive the operational limits of a conventional lifeboat while clearing from the mother ship. Wind exposure may prevent lifeboats to sail away from the touchdown area close to the vessel’s hull. Lifeboats unable to clear are deemed lost because of the dangerous vicinity with the hull. The model ignores the influence of waves and does not account for several unsuccessful trials before successful clearing. Manoeuvring model of the lifeboat was generated from the main boat data (Table 14) using the manoeuvring suite SIMX [14].The lifeboat handling was done by the engine and rudder. The lifeboat is steered away from the ship by using a combination of engine and rudder setting. The handling criterion was set for a limit of two boat lengths along the side of the mother ship. Clearing from the bow or from the stern was considered for five different wind directions and height wind speeds ranging from 15 to 50 knots. If the trajectory was outside the defined lanes or the boat was pushed away by the environment in the direction of the mother ship, the manoeuvre was considered unsuccessful. The simulation results are reported in Table 15, whereas Figure 15 shows an example of graphical representation. Against the assessment scenarios, the results indicate that lifeboats in windward side should be able to clear in the first four scenarios. In Scenario 5, lifeboats in windward side could not sail away. This conclusion is dramatically conservative because some lifeboats could certainly withstand a few impacts while sailing alongside the hull to escape from aft or stern. However, it is very difficult to address such a complex situation, so that the degradation function was set in accordance with the simulation results. The authors believe the simulation is yet quite informative regarding the operational limits of conventional lifeboats.

Length Overall 8.80 Length between Perpendiculars 8.75 Beam (m) 4.26 Mean Draught (m) 0.85 Block Coefficient 0.5130 Position of LCB from Midship (m) 0.00 Trim (m) 0.00 Lateral Windage Area (m^2 23.76

Life

boat

dat

a

Transverse Windage Area (m^2) 18.90 Propeller Type FPP Number of Propellers 1 Propeller Diameter (m) 0.50 Propeller Pitch (m) 0.45 Propeller Shaft rev/s 14.10 Pr

opel

ler d

ata

Engine Delay Time 1.00 Number of Rudders 1 Rudder Area (m^2) 0.12 Rudder Height (m) 0.50 Rudder Aspect Ratio 1.67

Rud

der d

ata

Rudder Turning Rate (deg/sec) 2.25

Table 14: Input data for the lifeboat manoeuvring model

- 11 -

Wind direction (deg)

Head Quarter bow Beam Quarter

stern Stern

15 Stern or Bow Stern Bow Bow Stern or

Bow

20 Stern or Bow Stern Bow Bow Stern or

Bow

25 Stern or Bow

Stern or Bow Bow Bow Stern or

Bow

30 Stern or Bow Stern N Bow Stern

35 Stern or Bow N N N Stern

40 Stern or Bow N N N Stern

45 Stern or Bow N N N Bow

Win

d sp

eed

(kno

ts)

50 Stern or Bow N N N Bow

Lifeboat can clear away Lifeboat can clear away with difficulties Lifeboat can not clear away

Table 15: Lifeboat clearing manoeuvre simulation results

Figure 15: (Up) Successful manoeuvre by the stern (wind direction: Quarter bow / wind speed: 20 knots); (Down) Unsuccessful manoeuvre by the stern (wind direction:

beam / wind speed: 35 knots)

1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000

“Fail manoeuvring”

Scenario 1 to 4

0.0000 0.0000 0.0000 1.0000 0.5000 0.0000 0.0000 0.0000 0.0000 0.5000 0.0000 0.0000 0.0000 0.0000 0.5000 0.0000

“Fail manoeuvring”

Scenario 5

0.5000 0.5000 0.5000 1.0000


Capsizing: After disconnection, lifeboats have to sail until they can safely use a sea anchor and drift head-on. During this phase, dangerous wave incidences such as stern to beam waves will be encountered. The risk is higher in beam waves, and it is considered realistic that a lifeboat could be exposed for a maximum cumulated time of ten minutes. If capsized, a lifeboat is deemed lost with its occupants. Two main events are considered that contribute to capsizing the lifeboat: excessive roll motions and flooding – as the ship is partially enclosed. For excessive roll motions, risk criterion is roll angle in excess of 30.5° that corresponds to the maximum of the Gz curve. For flooding, risk criterion is vertical relative motion at mid-ship in excess of freeboard fully loaded: 0.78m. The assessment draws on seakeeping analysis for lifeboat afloat with minimum speed. Lifeboat motions and accelerations were calculated with AQUA+ and ALEA+ in the same way as for the mother ship. The simulation results reported on Figure 16 first indicate that the risk is negligible in moderate sea conditions. For sea state 5 and 6, the risk is substantially higher, in particular for flooding. In this respect, it is true that a canopy should protect the openings from water entry. However, in a real gale the canopy was deemed insufficient to prevent water entry, so that we considered the openings “opened”. In addition, we adapted the risk criterion by “adding” 20cm to the freeboard that means vertical relative motions should be as high as 0.98 to effectively cause flooding Eq. (5). Hence, for a period of ten minutes in Beam Sea, it is possible to derive the associated probability, assuming that it is proportional to the time of exposure. We then used a simple fault tree analysis to combine the two event using a “OR” gate as represented in Figure 17. The probabilities of capsizing (Table 16) for sea states 5 or 6 are quite closed, so that we rounded up to the upper value that is to say 0.0006. The corresponding degradation functions are then derived.

Figure 16: Seakeeping simulation results of free-floating

lifeboat

- 12 -

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−=

2/98.0exp)(

2

98.0RMSfloodingP (5)

Figure 17: Capsizing probability using fault tree analysis Sea states P (roll > 30.5°) P (flooding)0.98 P(capsizing)

3 4.43×10-33 6.01×10-31 Negligible 5 2.09×10-04 3.86×10-04 5.95×10-04

6 2.74×10-04 8.41×10-05 3.58×10-04

Table 16: Capsizing probability of lifeboat for 600s exposure in Beam Sea

0.9994 0.0000 0.0000 0.0000 0.0000 0.9994 0.0000 0.0000 0.0000 0.0000 0.9994 0.0000

“Capsizing”

Scenario 3, 4 & 5 0.0006 0.0006 0.0006 1.0000

Seasickness: In real emergency cases, lifeboat’s occupants may spend hours at sea before they can get rescued. Among the difficulties that an individual may face in such situation, seasickness is by far the most problematic. Seasickness would generally only create discomfort but it can also escalate to vomiting, headache, apathy, lack of appetite, etc. The most dangerous impacts on human health are dehydration and Loss Of Will To Survive (LOWTS). Especially for the elderly, additional dangers of continued vomiting are heart failure and suffocation in unexpelled vomit. Physically motion sickness occurs when sensed motions and accelerations differ strongly and continuously from what is expected or anticipated in the inner ear organ. Typical provocative motions include low-frequency1 linear and angular motions with special negative influence of vertical motions and accelerations.

Within the project, the analysis was conducted by specialists in motion sickness and human factors. The model is based on the core concept of Motion Sickness Incidence [15] that depends on the RMS of the vertical acceleration, the frequency, and the exposure duration (Figure 18). The model

1 Between 0.01 Hz and 1 Hz, with most sickness observed around 0.17 Hz (McCauley et al., 1976)


used in SAFECRAFTS is somewhat more sophisticated as it also accounts for lateral accelerations and variations related to people’s age. In this model, vomiting is taken as criterion of being seasick. The sickness incidence is then so-called Vomiting Incidence

As input data, we used lifeboat’s motions and accelerations simulated for lifeboats floating free with minimum speed for a constant incidence of waves on quarter bow (Table 17). The Vomiting Incidence was estimated for different age groups exposed for 24 hours (Table 18). The Vomiting Incidence values were further interpreted to derive the actual percentage in the HHS categories. The calculations do not include the effect of seasickness pills, which are available on board ships and LSA; however it is possible for these to be taken into account.

Figure 18: Illustration of the Motion Sickness Incidence

model

Input data at Centre of Gravity X acc Y acc Z acc Free

floating lifeboat

RMS (m/s2)

T2 (s)

RMS (m/s2)

T2 (s)

RMS (m/s2)

T2 (s)

Sea state 3 0.22 4.28 0.12 4.50 0.27 4.20 Sea state 5 0.57 4.72 0.32 4.96 0.71 4.59 Sea state 6 0.61 5.15 0.34 5.41 0.75 4.98

Table 17: Lifeboat motions input data for the calculation of seasickness

Exposure Age groups (years) Vomiting Incidence (%) SS3 SS5 SS6

a < 50 6 13.6 12.3 50 < a < 75 4.1 9.3 8.4 24h

75 < a 2.7 6.2 5.6

Table 18: Vomiting incidence for the three age groups for 24 hours at sea

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AGE ≤ 50 1.0000 0.0000 0.0000 0.0000 0.0000 0.9950 0.0000 0.0000 0.0000 0.0030 0.9968 0.0000

“Seasickness”

Scenario 2 0.0000 0.0020 0.0032 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.9895 0.0000 0.0000 0.0000 0.0070 0.9930 0.0000

“Seasickness”

Scenario 3 & 4 0.0000 0.0035 0.0070 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.9906 0.0000 0.0000 0.0000 0.0063 0.9938 0.0000

“Seasickness”

Scenario 5 0.0000 0.0031 0.0062 1.0000

50 ≤ AGE ≤ 75

0.9981 0.0000 0.0000 0.0000 0.0000 0.9953 0.0000 0.0000 0.0016 0.0032 0.9968 0.0000

“Seasickness”

Scenario 2 0.0003 0.0016 0.0032 1.0000 0.9958 0.0000 0.0000 0.0000 0.0000 0.9878 0.0000 0.0000 0.0035 0.0070 0.9930 0.0000

“Seasickness”

Scenario 3 & 4 0.0007 0.0052 0.0070 1.0000 0.9963 0.0000 0.0000 0.0000 0.0000 0.9906 0.0000 0.0000 0.0031 0.0063 0.9938 0.0000

“Seasickness”

Scenario 5 0.0006 0.0031 0.0062 1.0000

75 ≤ AGE

0.9953 0.0000 0.0000 0.0000 0.0000 0.9945 0.0000 0.0000 0.0032 0.0032 0.9953 0.0000

“Seasickness”

Scenario 2 0.0016 0.0024 0.0047 1.0000 0.9895 0.0000 0.0000 0.0000 0.0000 0.9878 0.0000 0.0000 0.0070 0.0070 0.9896 0.0000

“Seasickness”

Scenario 3 & 4 0.0035 0.0052 0.0104 1.0000 0.9906 0.0000 0.0000 0.0000 0.0000 0.9890 0.0000 0.0000 0.0063 0.0063 0.9907 0.0000

“Seasickness”

Scenario 5 0.0031 0.0047 0.0093 1.0000

Tossed around: In view of the relatively rough seating arrangement inside a lifeboat, people may glide or fall down due to motions that may cause injuries. However, no data was available on this issue to estimate the risk associated with this obstacle.


Climbing pilot ladder: Contrary to the evacuation phase that takes place on one specific vessel in some given environmental conditions, the final rescue may be more heterogeneous. Various means of rescue may be involved, and to some extent, it is possible to postpone the final operations if the weather conditions are too severe. In this assessment, we have only considered pilot ladder as final means of rescue because (1) it is likely to be the first means of rescue available, and (2) we wanted to put emphasis on its drawbacks. Full-scale experiments performed within the project showed that age and gender have little influence on the ability to climb if the volunteers are in good physical condition. Alternately, the relative motions between the survival craft and the rescue vessel were considered the most impairing factor. In this context, it is assumed that rescue operations with ships would only occur in calm or moderate sea conditions (Scenario 1 & 2). Thus, climbing a pilot ladder is possible and ship-to-ship impacts should be limited. Only healthy people at that stage of the process might be able to effectively climb the ladder. In severe weather conditions (Scenario 3, 4 & 5), it is assumed that no one would take the chance to climb a pilot ladder. At this stage of the analysis, we present two alternatives: 1/ “Case A”: pilot ladder is the only means of rescue available; therefore those unable to climb are deemed lost.

1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

“Climbing pilot ladder” Case A

Scenario 1 & 2 0.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

“Climbing pilot ladder” Case A

Scenario 3, 4 & 5 1.0000 1.0000 1.0000 1.0000

2/ “Case B”: the other people onboard the lifeboat wait for other means of rescue – helicopter for instance. To account for this drawback, we “assigned” these people at sea for another period of 24h, facing the risk of seasickness and capsizing.

AGE ≤ 50 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000

“Climbing pilot ladder” Case B

Scenario 1 0.0000 0.0000 0.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.9950 0.0000 0.0000 0.0000 0.0030 0.9968 0.0000


Scenario 2 0.0000 0.0020 0.0032 1.0000 0.9994 0.0000 0.0000 0.0000 0.0000 0.9889 0.0000 0.0000 0.0000 0.0070 0.9924 0.0000


Scenario 3 & 4 0.0006 0.0041 0.0076 1.0000

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0.9996 0.0000 0.0000 0.0000 0.0000 0.9902 0.0000 0.0000 0.0000 0.0063 0.9934 0.0000


Scenario 5 0.0004 0.0035 0.0066 1.0000

50 ≤ AGE ≤ 75

1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000


Scenario 1 0.0000 0.0000 0.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.9953 0.0000 0.0000 0.0000 0.0032 0.9968 0.0000


Scenario 2 0.0000 0.0016 0.0032 1.0000 0.9952 0.0000 0.0000 0.0000 0.0000 0.9872 0.0000 0.0000 0.0035 0.0070 0.9924 0.0000


Scenario 3 & 4 0.0013 0.0058 0.0076 1.0000 0.9959 0.0000 0.0000 0.0000 0.0000 0.9902 0.0000 0.0000 0.0031 0.0063 0.9934 0.0000


Scenario 5 0.0010 0.0035 0.0066 1.0000

75 ≤ AGE

1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000


Scenario 1 0.0000 0.0000 0.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.9945 0.0000 0.0000 0.0000 0.0032 0.9953 0.0000


Scenario 2 0.0000 0.0024 0.0047 1.0000 0.9889 0.0000 0.0000 0.0000 0.0000 0.9872 0.0000 0.0000 0.0070 0.0070 0.9890 0.0000


Scenario 3 & 4 0.0041 0.0058 0.0110 1.0000 0.9902 0.0000 0.0000 0.0000 0.0000 0.9886 0.0000 0.0000 0.0063 0.0063 0.9903 0.0000


Scenario 5 0.0035 0.0051 0.0097 1.0000


3.4. Success Rate and Identification of Critical Areas for Improvements

Success Rates: Once local degradation functions are determined, it is possible to calculate the global degradation functions for each scenario and each age category. Given the initial HHS presented in section 3.1, one obtains the corresponding final HHS that are required to derive the Success Rates for each scenario and each age category. Eventually, the overall results are obtained (Table 19) using a weighted sum of the three age categories (Table 6). The results for “Case A” show that scenarios 3, 4 & 5 are not practicable if only pilot ladders are used for the final rescue. Climbing the pilot ladder is clearly a showstopper. Even in drill conditions (Scenario 1), only 60% of the initial population is able to complete the process. The results for “Case B” show that the system performs rather well in the four first scenarios. Scenario 5 has a very low performance due to the obstacle “Fail manoeuvring” that accounts for 50% of the degradation. However, even when lifeboats are able to clear away from the wrecked vessel (Scenarios 1 to 4), many fatalities are predicted in this assessment. For instance, if 4,000 people would be considered in this evacuation and rescue process as modelled here, there would be around 80 fatalities in Scenario 1, and 480 fatalities in Scenario 3.

Success Rates Scenario Case A Case B

Scenario 1 59% 98% Scenario 2 59% 97% Scenario 3 0% 88% Scenario 4 0% 88% Scenario 5 0% 43%

Table 19: Estimated Success Rates for LSS using conventional lifeboats

Identification of critical areas: It is possible to calculate the Success Rate step-by-step and determine the actual contribution of individual obstacles to the overall degradation associated with the rescue route. Critical obstacles were selected if their contribution was higher than 1% of the total degradation of the Success Rate (Figure 19). For “Case A”, the obstacle “Climbing pilot ladder” is by far the most critical obstacle in the first two scenarios. More dedicated equipment should therefore be available on every merchant ship to effectively address this issue. For “Case B”, the contribution of the obstacle “Climbing pilot ladder” is significantly smaller due to the availability of other means of rescue. As a result, the relative contribution of the other obstacles is highlighted: hardware obstacles are the most contributing obstacles, whereas the two main human factor obstacles are “Seasickness” and “Climbing pilot ladder”. If we ignore “Fail start engine” and “Fail to release” that are based on historical data, “Premature release” is the main contributor. This confirms the feedback that the “flat contact area cam” hook design has been at the origin of numerous accidents. However, the vast majority of modern hook designs are radically different and this problem would not occur on brand new lifeboats using failsafe hook designs.

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2% 2% 1% 1% 0% 0% 0% 0% 0% 0% 0%

93%

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Figure 19: Selected critical areas for LSS using

conventional lifeboats


4. APPLICATION FOR APPROVAL OF

ALTERNATIVE DESIGN In SAFECRAFTS, the proposed methodology was developed with a view to (1) assess the performance of conventional systems, (2) identify critical areas for improvements, and (3) assess the performance of novel LSA concepts. This was achieved by focusing research on the functional performance of LSA, which was expressed as the Success Rate of the evacuation and rescue process in different scenarios. Hence, it is also possible to use it as an evaluation tool within a process of approval of alternative design and arrangements.

4.1. Dealing with a complete Life-Saving System As previously explained in the paper, a ship shall be equipped with a Life-Saving System (LSS) made-up of several LSA types. Hence, given the fact that the proposed methodology is linear in all aspects, it is possible to combine the performance of different LSA types in order to obtain the specific performance of the LSS considered. This provides a great flexibility in the application of the methodology and allows for a global comparison with novel LSS concepts.

4.2. Acceptance Criteria The process flowchart developed in the IMO guidelines for alternative LSA design [3] is reproduced hereunder in Figure 20. It is explicitly requested to “Evaluate performance of prescriptive vs. proposed” design in a quantitative fashion. The methodology presented in this paper provides effectively a conceptual approach to meet this requirement, where Success Rates calculated for the prescriptive design stand for acceptance criteria. When all relevant assessment scenarios are defined, the trial design should score a higher Success Rate than the prescriptive design for all scenarios (Table 20). Thus, the assessment results for a conventional design compliant with prescriptive rules provide a reference baseline for the approval process of alternative LSA designs. However, the results presented in this paper are essentially used to illustrate the methods and validate the identification of critical areas for design improvements. Moreover, if the methodology is generic, the implementation imposes many choices and assumptions in the modelling of the system, the rescue route and the scenario parameters that make every assessment tailor-maid for the purpose of the ship design project, for which alternative LSA design is envisaged.

Scenario #

Success Rate Prescriptive

design

Success Rate Alternative

design

Acceptance criteria

Sc 1 SR1(PD) SR1(AD) SR1(AD) ≥ SR1(PD)

Sc 2 SR2(PD) SR2(AD) SR2(AD) ≥ SR2(PD)

… … … …

Sc k SRk(PD) SRk(AD) SRk(AD) ≥ SRk(PD)

Table 20: Acceptance criteria concept for the approval of alternative LSA designs and novel concepts

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Figure 20: Process flowchart for Alternative design and

arrangement for LSA

5. CONCLUSION AND FUTURE WORK This paper demonstrates how one can practically implement a global assessment of life-saving appliances. The Success Rate of the evacuation and rescue process is recommended as the principal performance indicator of life-saving systems. It reflects the degradation of the Human Health Status as the hardware system and the population faces a sequence of obstacles along the rescue route. Different scenarios are defined to account for increasingly severe environmental and damaged ship conditions enabling the assessment of system robustness. Some obstacles were difficult to quantify such as slamming or being tossed around. Use of historical data also introduced a bias in the quantitative treatment, whereas the problem of premature release is specific to one designated hook design that is not representative of state-of-the-art designs. In the near future, the methodology will be applied on novel concepts developed within the SAFECRAFTS project. It is also intended to further streamline this approach with the IMO framework and contribute to defining a systematic approach for assessing existing and novel LSA concepts.


6. ACKNOWLEDGMENT A major part of this study presented herein, was financially supported by the European Commission under the FP6 Sustainable Surface Transport Programme. The support is given under the scheme of STREP, Contract No. FP6-PLT-506402. The European Community and the authors shall not in any way be liable or responsible for the use of any such knowledge, information or data, or of the consequences thereof.

7. REFERENCES [1] INTERNATIONAL MARITIME ORGANISATION,

SOLAS convention, Chapter III, Part C, Reg. 38, as amended in MSC 82, December 2006.

[2] McGREGOR J., PRAT L., CORRIGNAN P., BOER

L., “Risk-based approval of alternative designs and arrangements for life-saving appliances onboard passenger ships”, Proceedings of the 3rd Design For Safety conference, 2007, Berkeley, CA, USA.

[3] INTERNATIONAL MARITIME ORGANISATION,

MSC.1/Circ.1212, Guidelines on Alternative Design and Arrangements for chapters II-1 and III, December 2006.


MSC/Circ.1023, Formal Safety Assessment Guidelines, 2002.


MSC/Circ.1033, Annex 2, Interim Guidelines for the Advanced Evacuation Analysis of New and Existing Passenger Ships, 2002.


International Life-Saving Appliance Code, Edition 2003, section 4.4.6.8.

[7] BAHAMAS MARITIME AUTHORITY, Report of the

investigation into fire on and sinking of the passenger vessel “Sun Vista” on 20 and 21 May 1999 in the Malacca Straits, November 2000.

[8] LANG J. S. REAR ADMIRAL, “Review of Lifeboat

and Launching Systems’ Accidents, Maritime Accident Investigation Branch, 2001.

[9] PEACHEY J., POLLARD S., Burness Corlett-Three

Quays Ltd for the UK Maritime and Coastguard Agency, MCA Research Project 555: Development of Lifeboat Design, 2006.

[10] CMPT Centre for Marine and Petroleum Technology,

Guide to QRA for Offshore Installations, 1999 [11] INTERNATIONAL MARITIME ORGANISATION,

Measures to Prevent Accidents with Lifeboats (submitted by Canada), FP 50/INF.4, 20 October 2005.

[

[

[ [

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12] INTERNATIONAL MARITIME ORGANISATION, International Life-Saving Appliance Code, Edition 2003, section 4.4.1.7.

13] AIS (1998): Association for the Advancement of Automotive Medicine, The Abbreviated Injury Scale, updated of revision 1990, AAAM Des Plaines, IL-USA.

14] http://hydrosim.mysite.wanadoo-members.co.uk/

15] BOS, J.E., Scheepsbewegingen en “Motion Sickness Incidence” (MSI): Voorspellingen van het percentage bewegingszieken op basis van verticale bewegingen, TNO-TM 1995 A-71, November 1995 (in Dutch)


16ème Congrès de Maîtrise des Risques et de Sûreté de Fonctionnement - Avignon 6-10 octobre 2008 communication 7C-3 page 1/8

CONCEPTION ERGONOMIQUE ET ANALYSE DE RISQUE : METHODOLOGIE ET APPLICATION AUX MOYENS D’ACCES A BORD DES NAVIRES ERGONOMIC DESIGN AND RISK ANALYSIS: METHODOLOGY AND APPLICATION TO MEANS OF ACCESS ONBOARD SHIPS Nicolas Mery Marc Lassagne Bureau Veritas - Division Marine Arts et Métiers Paristech Tour Manhattan GRID, Maison de la recherche de l'ESTP 5/6 Place de L’Iris – La Défense 2 30 avenue du Président Wilson 92095 Paris La Défense Cedex 94230 Cachan

Résumé L’industrie maritime a mis en œuvre d’importants moyens dans le but d’améliorer la sécurité des navires. En effet, la navigation devient de plus en plus sûre, les navires sont mieux protégés contre les risques d’incendie et d’envahissement, de même que les structures sont de plus en plus fiables. Cependant, la majorité des accidents tels que les glissades, trébuchements et chutes (STFs), dont la gravité et la fréquence d’occurrence est très souvent sous-estimée, ne bénéficient pas encore d’une attention suffisante. Pourtant, il est non seulement possible mais il devient indispensable de prévenir les gens de mer de ces accidents et d’analyser les risques qu’ils représentent pour l’occupant. La maîtrise des risques passe en effet par la santé et la sécurité au travail, en particulier dans l’industrie maritime où les accidents sont fréquents, conduisent à des blessures graves et représentent un manque à gagner énorme d’une part pour les entreprises dont les employés doivent interrompre leur travail pour cause de blessure, d’autre part pour les assurances et les clubs de protection et d’indemnités (clubs Pet I) qui indemnisent ces dernières. Cet article décrit la méthode suivie par une société de classification pour développer des recommandations concernant la conception ergonomique des moyens d’accès à bord des navires commerciaux. Le but recherché est l’amélioration de la sécurité des marins, des experts, ainsi que de tous les gens de mer dont le rôle est d’inspecter ou de travailler à bord des navires. La méthodologie que nous avons mise en œuvre repose sur une approche en deux étapes : une analyse de risque basée sur le retour d’expérience provenant d’entretiens, d’une visite sur le terrain et de la diffusion d’un questionnaire aux experts à été menée; une analyse anthropométrique a par la suite été conduite pour établir des recommandations adressées aux chantiers navals et aux armateurs concernant la conception des moyens d’accès aux différentes parties des navires.

Summary The maritime industry engaged significant means for improving vessels’ safety. In fact, navigation is getting increasingly safer, ships are well-protected against fire and flooding risks, and in the same manner structures are getting increasingly reliable. However, the great majority of accidents such as slips, trips and falls, of which the severity and frequency of occurrence are very often under-estimated, are not sufficiently addressed. Yet, it is not only possible, but also indispensable to prevent seafarers from being the victims of these accidents and to analyse the related occupational risks. Risk management also involves health and safety at work, particularly in the maritime industry where accidents are frequent, lead to serious injuries and account for a very significant shortfall on one hand for the shipping companies which employees have to stop working because of their injuries and on the other hand for the insurance companies and the Protection and Indemnity Insurance clubs (P&I clubs) which have to compensate them. This paper describes the method followed by a classification society for developing recommendations about the ergonomic design of the means of access onboard commercial ships. The main objective is to improve safety of the seafarer and of the surveyor and of whoever has to inspect or work onboard vessels. The methodology we adopted is a two-stage approach: a risk analysis based on user feedback from interviews, a visit in the field and questionnaires have been sent to surveyors; an anthropometric analysis was then carried out in order to establish recommendations for the shipyards and shipping companies to be provided with guidelines for the ergonomic design of the means of access onboard.

Introduction

Selon une étude menée par Jensen et al. [1], les accidents de type glissade, trébuchement et chutes (Slips, Trips and Falls, ci-après STFs) seraient à l’origine de plus de 40% des blessures non mortelles se produisant à bord des navires commerciaux. Il est de même communément acquis dans la communauté maritime que cette proportion est identique en ce qui concerne les accidents mortels. De plus, une analyse menée par l’American club P&I (Protection & Indemnity) [2] les tient pour responsables de 23% des coûts associés aux plaintes pour maladies et blessures ; à ces coûts doivent aussi être ajoutés ceux associés au nombre de jours non travaillés pour cause de blessures sur le lieu de travail. Ces chiffres prêtent à penser que l’on peut obtenir des gains significatifs si l’on arrive à améliorer la sécurité des gens de mer. Pour ce faire, il est bien sûr très important de communiquer sur ces accidents de travail et d’insister sur les moyens de prévention simples tels que les bonnes pratiques de travail ou encore le port des équipements et l’utilisation des outils appropriés aux tâches d’opération, de maintenance et

d’inspection des navires. Cependant une des stratégies pour s’assurer que le personnel ne glisse, trébuche ou ne tombe pas, consiste à intégrer la notion de prévention le plus tôt possible, c’est-à-dire au moment même de la conception des navires [3]. Il est vrai que le type d’accidents mentionnés ci-dessus concerne tous les environnements de travail allant de la chaine de montage, au travail de bureau en passant par les cuisines de restaurants. Néanmoins, le caractère hautement accidentogéne de l’environnement maritime en fait un des plus propices à l’occurrence des STFs. En effet, la vie à bord des navires commerciaux est rythmée par des opérations de navigation, de veille, d’inspections et de maintenance qui doivent être assurées tout au long de la journée et de la nuit, et ce pendant parfois plusieurs semaines d’affilée. Le travail du marin repose donc sur une attention de tous les instants alors qu’il est particulièrement sujet au stress, à la fatigue et cela à cause des horaires, des conditions météorologiques, des pressions commerciales ou de son isolement. L’environnement dans lequel il évolue, lui, se veut fonctionnel et malgré la taille des navires commerciaux actuels, les contraintes structurelles et pratiques s’imposant à ce moyen de transport n’incitent pas particulièrement les concepteurs à tenir


compte des besoins qu’ont les marins pour accomplir en toute sécurité leur travail ; cet environnement est aussi son cadre de vie. S’ajoute encore à cela la pensée commune décrivant le marin comme une sorte de « cow-boy des mers » [4] qui sait s’adapter à son environnement de travail, quel qu’il soit même s’il doit prendre des risques inconsidérés pour y arriver. Pourtant, l’actualité semble montrer le contraire et il est important de garder à l’esprit que le métier de marin-pêcheur est l’un des plus dangereux au monde. Il est donc primordial pour améliorer la santé et la sécurité dans l’industrie maritime, de concevoir des navires moins dangereux pour le personnel qui les opère, et mieux adaptés à leurs tâches quotidiennes.

1. Les STFs Les STFs (Slips, Trips & Falls) sont des accidents se produisant très souvent sur le lieu de travail. Ils peuvent arriver de plain-pied, sur des rampes, sur les marches d’un escalier, ou en hauteur. Il existe un grand nombre de facteurs susceptibles d’influencer fortement leur probabilité d’occurrence : la santé physique, l’âge, la fatigue, les médicaments, l’alcool, l’équipement (exemple : chaussures à semelles lisses), l’environnement (comme par exemple : l’éclairage et l’état de surface du sol), et l’activité pratiquée. La conception ergonomique de l’environnement de travail est donc bien évidemment de première importance lorsqu’il s’agit d’essayer de limiter l’occurrence des STFs. Les glissades se produisent lorsque il y a trop peu de frottements entre les pieds d’une personne et la surface sur laquelle il marche, ce qui se produit assez souvent dans l’industrie maritime, en raison de la présence fréquente à bord des navires de flaques d’eau, d’huile et autres substances glissantes. Il se peut aussi que le revêtement du sol soit inapproprié ou que l’individu en question ne porte pas des chaussures adaptées. Les trébuchements se produisent lorsque le pied d’une personne vient cogner un objet, causant une perte d’équilibre. Marletta [5] a suggéré que des irrégularités du sol de 7 mm sont suffisantes pour causer un trébuchement. Un faible éclairage peut aussi être la cause de ce type d’accidents. Des chercheurs en ergonomie ont montré par exemple que la probabilité que quelqu’un vienne buter sur une protubérance du sol lorsqu’il marche est fonction de la distance verticale entre l’objet et l’axe du champ de vision effectif de cette personne [6]. Les chutes quant à elles résultent non seulement des glissades et trébuchements mais peuvent également se produire pour des raisons telles que l’utilisation inappropriée d’une échelle ou d’un échafaudage. Il n’est pas rare que des chutes sur leur lieu de travail causent la mort de travailleurs. En ce qui concerne l’industrie maritime, la plupart des causes ‘classiques’ à l’origine des STFs sont réunies à bord des navires commerciaux comme le soulignent les divers auteurs des articles du numéro 17 de « HE Alert ! [7], une des revues professionnelles les plus lues pour les questions qui touchent à l’élément humain dans l’industrie maritime. Pour les glissades, la surface des ponts n’est pas systématiquement revêtue d’un matériau antidérapant alors que ceux-ci sont très souvent sujets aux intempéries d’une part et aux flaques d’huile et de graisse de l’autre. Les trébuchements, eux se produisent à cause notamment du grand nombre d’obstacles sur le chemin des marins dont la vue est souvent obstruée par les pièces d’équipement et autres charges qu’il doivent transporter manuellement d’un point à un autre du navire ou réduite à cause du manque d’éclairage de certaines zones du navire. Ces obstacles sont des câbles, des tuyaux, des panneaux d’éclairage, des boites de jonction, des conteneurs de stockage ou simplement des changements de niveaux du plancher non indiqués et des renfoncements. Pour ce qui est des chutes, deux facteurs spécifiques à la vie maritime sont très importants : l’atmosphère très corrosive due à l’air marin et les mouvements du navire qui doit affronter régulièrement une mer ‘démontée’. L’atmosphère corrosive cause le vieillissement prématuré des échelles et rambardes de sécurité qui deviennent alors vétustes et dangereuses d’utilisation. Les mouvements du navire, eux, jouent un rôle important lorsqu’il s’agit de maintenir son équilibre, particulièrement en cours d’opération. Cependant, les causes les plus profondes à l’origine

de ces accidents à l’occupant sont autant, voire plus importantes ; elles sont liées à la conception des navires ou plus précisément à la conception du lieu de travail des marins [3]. En effet, si il est important que les marins soient bien informés des risques qu’ils encourent lorsqu’ils exercent leur profession et des moyens de prévention des accidents dont ils disposent, c’est dès la conception du navire que doit se poser la question : « Comment assurer la sécurité des marins qui seront amenés à travailler à bord ? ». C’est au navire d’être conçu en fonction des capacités physiques et cognitives des marins et des tâches qu’ils ont à accomplir. En guise d’illustration nous avons retenu le récit d’un accident survenu récemment et mettant en cause la conception des moyens d’accès. Cet accident a été relaté dans le Maritime Accidents Reporting System

(MARS) qui est un système de

notification confidentiel géré par le Nautical Institute [8]. L’accident en question est survenu lors d’un exercice de lutte contre l’incendie. L’ingénieur en second, se rendant dans le compartiment de la pompe d’urgence contre l’incendie pour mettre en route cette dernière a dû emprunter une échelle verticale. Alors qu’il descendait à l’échelle en se tenant aux rails latéraux, il ne s’est par rendu compte qu’il y avait une coupure au niveau de ces rails (figure 1).

Figure 1 : Echelle à l’origine d’un accident du travail (MARS)

Il s’est alors retrouvé soudainement sans prise manuelle et a perdu l’équilibre pour tomber finalement d’une hauteur de trois mètres directement sur le sol de la salle des pompes. Il n’a heureusement souffert que de coupures et d’ecchymoses mais cet accident aurait pu lui causer des blessures beaucoup plus importantes ou lui être fatal. Pour que des pratiques de conception prenant en compte la sécurité des marins soient acceptées, adoptées et promues par les chantiers navals ainsi que par les armateurs, il semble nécessaire d’inclure ces pratiques au sein des réglementations maritimes. Il convient tout d’abord d’expliquer le double système de réglementation auquel doivent se conformer les navires. Les réglementations maritimes internationales concernant la sécurité des gens de mer, leur formation, la conception des navires, la sauvegarde de l’environnement maritime, etc. sont discutées et adoptées par une organisation des Nations Unies, l’Organisation Maritime Internationale (OMI). Ces règlementations sont par la suite adoptées et transposées dans les règlementations maritimes nationales par les états membres qui sont alors responsables de leur application. D’un autre côté, il existe des sociétés de classifications qui sont en charge de valider plus en détail la conception et l’état des navires suivant des critères (concernant uniquement l’intégrité structurelle du navire ainsi que la machinerie) issus de leurs propres règles. Ces règles remplissent néanmoins bien évidemment les exigences des réglementations internationales de l’OMI. Pour ce qui est des réglementations concernant la prévention des STFs, il n’existe pas pour l’instant de texte portant directement sur ces questions. Cependant, un groupe de travail de l’OMI, le Groupe de Travail sur l’Elément Humain a entre autre pour mission de développer les réglementations et recommandations concernant l’application de l’ergonomie à bord des navires dans le but d’assurer un environnement de travail sûr [9]. De plus, certaines réglementations internationales qui concernent la conception des moyens d’accès pour l’inspection des vraquiers et pétroliers ont pour objectif non seulement d’assurer un accès pour les inspections des zones critiques de ces navires, mais aussi


d’assurer la sécurité des inspecteurs en leur garantissant des moyens d’accès appropriés à leur travail. On peut citer à ce titre l’origine de la réglementation II-1/3-6 de la convention SOLAS (Safety Of Life At Sea) de l’OMI qui en 2004 a été amendée par des résolutions de l’OMI [10]. En réponse à ces amendements, l’Association Internationales des Sociétés de Classification (IACS) a publié des Interprétations Unifiées des recommandations techniques de l’OMI pour les moyens d’accès [11]. Ces interprétations fournissent aux chantiers navals et armateurs des spécifications techniques comprenant des recommandations dimensionnelles spécifiques garantissant la sécurité d’accès aux différents compartiments des vraquiers et pétroliers. Cependant, ces interprétations demeurent trop générales et ne prétendent pas couvrir l’ensemble des problèmes rencontrés avec les moyens d’accès ; on ne parle que d’inspection alors que les opérations pour le fonctionnement du navire et sa maintenance nécessitent aussi l’utilisation des moyens d’accès. De plus, elles ne considèrent que les vraquiers et pétroliers bien que les autres types de navires devraient eux aussi être dotés de moyens d’accès sûrs.

2. Démarche de prévention et gestion du risque des STFs

Nous nous sommes efforcés d’adopter une démarche structurée dans notre approche du risque de STF. Ainsi, nous nous sommes inspirés des grands principes de prévention, tels qu’ils sont utilisés par exemple en France par l’INRS. 2.1 De la mise en œuvre des principes de prévention Dans une logique de prévention, trois démarches complémentaires peuvent être employées. On distingue tout d’abord une approche par l’accident, qui s’appuie en général sur l’utilisation d’arbres des causes permettant de retracer les mécanismes ayant conduit à une situation dangereuse. Cette première approche, rétrospective, s’inscrit dans une logique d’analyse en vue de comprendre la nature et les causes du danger afin d’en tirer des enseignements. Dans cette optique, l’analyse par l’accident, loin d’être seulement un outil au service par exemple de l’enquête conduite à l’issue d’un accident, s’inscrit bel et bien dans une dimension d’apprentissage à l’échelle organisationnelle, au même titre que d’autres dispositifs de retour d’expérience et de capitalisation des connaissances [12]. Une deuxième approche, plus proactive, s’appuie sur l’analyse des risques associés à une situation donnée. Cette démarche fait appel à des techniques telles que les arbres de défaillances, les arbres d’événements [13]. Elle a pour finalité la détermination a priori de situations à risque, et l’élaboration subséquente de mesures de prévention ou de protection. Enfin, la dernière approche de réduction des risques du poste de travail s’appuie sur son analyse ergonomique : à partir de l’examen détaillé et in vivo des postures, des gestes, de la position de l’opérateur, il devient possible de prévenir les dommages physiques. Ces trois approches interagissent bien évidemment et se nourrissent les unes et autres. La conjonction des résultats obtenus dans chacune des démarches est ce qui va permettre l’élaboration d’une politique de santé et sécurité au travail.

Figure 2 : La prévention des risques au travail

2.2 La spécificité du milieu maritime en matière de prévention L’analyse des STFs en milieu maritime revêt donc comme nous l’avons vu une dimension particulière. En effet, le navire dans son ensemble constitue le poste de travail, ce qui induit une complexité importante, qui n’est certes pas complètement singulière (après tout, une usine prise dans son ensemble est aussi complexe), mais comporte quand même la particularité que de nombreux personnels, par la nature même des tâches qu’ils ont à accomplir (inspection, maintenance…) , vont être amenés à se déplacer dans des lieux dangereux, et non seulement y travailler à des postes spécifiques. Ce milieu est également particulièrement dangereux en raison des contraintes environnementales qui le caractérisent. Une caractéristique tend à rendre le milieu maritime spécifique : il est en effet en tension entre d’une part la volonté, en matière de prévention des STFs, d’être le plus générique possible afin de bénéficier d’effets d’échelle (si une étude spécifique pour une usine dans laquelle travaillent des dizaines de personnes peut se justifier, réaliser des études complètes pour des navires dont l’équipage comporte moins de 20 personnes n’est a priori pas économiquement viable), et d’autre part le fait que les navires sont fabriqués au mieux en très petite série de quelques unités. Ces considérations nous ont conduit à mettre en œuvre des techniques spécifiques pour notre analyse, au-delà des pratiques habituelles des préventeurs. Plus généralement, nous avons choisi de nous placer dans une approche avant tout ergonomique, qui a guidé le reste de notre travail. Adopter une telle approche n’est pas neutre dans le milieu maritime. En effet, nombre d’efforts à l’échelle internationale ont visé à essayer d’intégrer le « facteur humain » dans les analyses à l’aide de techniques quantitatives, par le biais d’analyses fiabilistes. Sans remettre en cause la valeur ou l’intérêt de telles approches, force est de constater qu’à l’heure actuelle, elles n’ont pas été très fructueuses, tant pour des raisons qui tiennent à la difficulté intrinsèque de l’exercice de modélisation qu’à, fréquemment, la faible qualité des données d’entrée [14] [15]. C’est donc aussi à un renversement de perspective par rapport aux pratiques habituelles de recherche en prévention dans l’industrie maritime que nous nous proposons de procéder, dans l’optique d’ailleurs défendue dans le plan stratégique de l’Organisation Maritime Internationale concernant l’élément humain [9]. 2.3 Analyse par l’accident et retour d’expérience Les techniques d’analyse par l’accident présentent ceci d’intéressant qu’elles sont fortement ancrées dans la réalité du terrain. Toutefois, elles souffrent d’un défaut majeur, en ce qu’elles ne permettent qu’une vision a posteriori des mécanismes accidentogènes à l’œuvre dans une situation de travail. En outre, si l’on considère que l’analyse de l’accident n’a pas seulement pour but que de proposer des solutions techniques à un incident mais est le premier pas d’un apprentissage, une difficulté supplémentaire peut se manifester : en effet, comme cela a été montré dans de nombreux travaux, des mécanismes de rationalisation de l’accident particulièrement puissants sont souvent à l’œuvre, qui peuvent gêner l’apprentissage visé [16]. Ces arguments plaident pour une approche plus proactive du retour d’expérience dont l’analyse des accidents est une composante, approche qui s’attache également à la prise en compte des quasi-accidents (near-misses), mais aussi à la détection des signaux faibles [17]. C’est dans cette optique que nous nous sommes situés. Nous nous sommes donc proposés de mener des entretiens auprès des utilisateurs les plus proches du danger, ce que certains ont qualifié d’utilisateurs « at the sharp end » [18]. Les entretiens permettent dans un premier temps de faire une évaluation qualitative des différents problèmes que les inspecteurs et les gens de mer sont susceptibles de rencontrer lorsqu’ils utilisent les moyens d’accès à bord. Nous avons pu ainsi faire un premier état des lieux des risques de glissades, trébuchements et chutes c’est-à-dire faire une première estimation des endroits à bord où ces accidents sont susceptibles de se produire, des moyens d’accès mis en question ainsi que de la gravité des blessures engendrées. L’observation participante est le dernier dispositif de recueil de données à ce stade qui permet d’opérer une triangulation et de s’assurer de la validité des éléments obtenus en entretien. Le résultat de cette démarche n’est donc pas seulement une analyse rétrospective d’accident (lors des entretiens sont apparus des récits de blessures), mais

Approche par

les risques Approche par les

accidents

Approche par le

poste de travail


365

∑ ⋅

=i

ii pk

F

aussi et surtout une vision plus générale et dynamique des mécanismes pouvant conduire à l’accident. L’ensemble des éléments recueillis a également pour but de permettre le développement d’un questionnaire plus spécifique, dont les résultats seront utilisés dans l’approche par les risques. 2.4 Approche par les risques Ces entretiens préliminaires ont aussi permis de développer un questionnaire dont nous détaillerons le contenu plus loin. Le questionnaire que nous avons demandé aux inspecteurs de compléter se compose de quatorze questions. Certaines d’entre elles sont utilisées pour tester la pertinence des réponses. Une autre série de questions est concentrée sur les caractéristiques des glissades, trébuchements et chutes et la manière qu’ont les gens de mer d’évaluer leur probabilité d’occurrence et des blessures qu’ils causent. Cette série sera utile pour évaluer les croyances des gens de mer concernant les risques liés aux STFs ; sous-estiment-ils les risques ? Il y a aussi une série de questions dédiées à l’analyse de risque. Finalement, certaines questions ouvertes nous permettent d’avoir une description qualitative des problèmes associés aux moyens d’accès et des améliorations qu’ils recommandent afin de résoudre ces derniers.

2.4.1 Analyse qualitative du questionnaire

Afin d’interpréter les données qualitatives obtenues grâce aux résultats du questionnaire, nous avons utilisé une analyse factorielle des correspondances (AFC). L’AFC est un moyen de représenter des tableaux de contingence i.e. les tableaux comme ceux que nous avons obtenus avec les résultats du questionnaire. Il s’agit de tableaux à deux entrées dont les variables sont qualitatives. Un exemple de tableaux de contingence est présenté ci-dessous :.

Fréquence Slip Trip Fall

Jamais 7 12 23

Rarement 20 16 8 Parfois 5 2 1

Souvent 0 2 0

Tableau 1 : Tableau de contingence représentant les croyances des inspecteurs en matière de fréquence d’occurrence des STFs

Le but de l’AFC est de permettre à l’analyste de rassembler autant d’informations que possible sur un nombre de graphes restreint appelés plans factoriels et formés pas deux axes factoriels. Les caractères différents (glissade, trébuchement, chute, jamais, rarement, parfois, souvent) sont analysés en terme de correspondances, i.e. seule la valeur relative entre les différents caractères est importante. Chaque caractère est représenté par un point dont la taille dépend du nombre de répondants et dont la position détermine sa relation avec les autres caractères. Les nuages de points représentant les caractères en ligne (jamais, rarement, parfois, souvent) et les nuages représentant les caractères en colonne (glissade, trébuchement, chute) sont tous deux centrés sur l’origine de l’espace. Cet espace, dans lequel les nuages sont centrés et sont représentés sur une échelle commune, est composé des axes factoriels qui sont déterminés par un calcul de vecteurs propres. Les figures que nous avons analysées sont des projections de points sur les plans factoriels. Ci-dessous est présenté un graphe représentant le tableau de contingence précédent :

Figure 3 : Représentation des croyances des inspecteurs en matière de fréquence d’occurrence des STFs

Une analyse graphique peut être menée avec ce type de graphes ; des indicateurs quantitatifs peuvent aussi découler de l’analyse de données, afin de confirmer la validité de l’analyse, soit le pourcentage d’inertie expliqué par chacun des axes factoriels, la significativité de chaque caractère au regard des axes factoriels et surtout les tableaux de contingence (qui après tout contiennent toute l’information). Ainsi, on peut mener à bien rigoureusement l’analyse graphique. Les sous-populations apparaissent comme des groupes de points plus ou moins concentrés. En général, la proximité de deux points révèle que leurs profils tendent à être similaires.

2.4.2 Analyse de Risques

Nous avons adopté une stratégie spécifique pour identifier les dangers liés aux glissades, trébuchements et chutes. Les dangers sont caractérisés par leur lieu, leur gravité et leur fréquence. En construisant une mesure de risque avec des gravités et des fréquences, nous avons évalué les risques associés aux STFs pour différentes zones du navire et déterminé un niveau d’acceptation afin de se concentrer sur les zones dont il faut s’occuper en priorité. Nous avons aussi évalué les gravités associées à chaque type de moyen d’accès en utilisant la même méthode que pour l’évaluation des fréquences. Il nous a semblé plus judicieux d’évaluer les fréquences d’accès aux différentes zones au lieu des fréquences d’occurrence des STFs dans ces lieux. En fait, il est cognitivement plus facile pour un inspecteur d’estimer les fréquences concernant l’accès à un endroit donné (par eux ou les gens de mer), plutôt qu’estimer les fréquences des accidents. Pour résumer, il est plus facile pour un inspecteur de donner une estimation de la fréquence d’accès plutôt que la fréquence d’occurrence des STFs (surtout lorsque les STFs n’ont pas de conséquences graves). De plus, cette fréquence est une bonne variable pour l’évaluation des risques puisque l’on devrait accorder une plus grande attention aux pièces et compartiments qui ont la plus grande fréquence d’accès. Par la suite, afin de donner un score de fréquence unique pour chacune des zones à bord nous avons effectué une somme pondérée des pourcentages représentant les différentes fréquences (plusieurs fois par an, plusieurs fois par mois, plusieurs fois par semaine, plusieurs fois par jour). Les coefficients de pondération sont directement proportionnels aux fréquences i.e. les coefficients correspondant à la fréquence ‘plusieurs fois par jour’ est 365 fois plus grand que le coefficient pour la fréquence ‘plusieurs fois par an’ et ainsi de suite. Finalement, en faisant l’hypothèse que le coefficient pour ‘plusieurs fois par an’ est 1, les scores obtenus sont rangés sur une échelle de 1 à 365 qui peut être transposée (division par 365) à une échelle de 0,03 à 1. Nous montrons ce calcul pour la cale sur l’exemple suivant :

CALE

Fréquence Pourcentages ip

Coefficients ik

Plusieurs fois/an 0.44 1.00

Plusieurs fois/ mois 0.11 12.00

Plusieurs fois / semaine

0.28 52.00

Plusieurs fois / jour 0.17 365.00

Tableau 2 : Fréquences d’accès de la cale

Nous pouvons calculer le score correspondant à la fréquence d’accès à la cale :

d’où

21.0365

36517.05228.01211.0144.0=

⋅+⋅+⋅+⋅=caleF [1]

Insistons sur le fait que F est un score et non une fréquence ; ici, F = 21 ne veut pas dire que l’on accède à la cale tous les cinq jours puisque 44% des personnes ont répondu que l’on accédait à la cale (que) plusieurs fois par an.


)(∑ −⋅=

i

ii ukS

Nous avons classé chaque blessure, allant de la simple bosse à la mort, en quatre groupes en se basant sur leur gravité : ‘pas dangereux du tout’, ‘pas vraiment dangereux’, ‘plutôt dangereux’, ‘très dangereux’. Comme pour le score de fréquence pour chaque zone à bord, nous avons calculé un score reflétant la gravité associée à chacune d’entre elle grâce à une somme pondérée. Cependant, lorsqu’il s’agit de la gravité des blessures, les coefficients ne peuvent pas être attribués en fonction d’une règle de proportionnalité. En fait les coefficients de pondération doivent être définis selon le mal ou la désutilité que chaque catégorie de blessure cause à l’industrie maritime. Ainsi, la gravité associée à ‘très dangereux’ est environ 50 fois plus grand que celle associée à ‘plutôt’ dangereux’. En fait, comme montré sur la figure ci-dessous, nous avons émis l’hypothèse que la fonction de désutilité ou d’utilité négative à une forme exponentielle.

Figure 4 : Modèle exponentiel de la désutilité associée aux

blessures

Nous n’avons pas eu la possibilité d’éliciter cette fonction d’utilité. Ce pourrait être une autre perspective pour des recherches futures. Cependant, les coefficients de pondération que nous avons utilisés pour la fonction d’utilité négative a permis d’évaluer la gravité des blessures associées à chacune des zones du navire et de les classer comme nous le montrons dans le tableau ci-dessous pour la cale.

CALE

Gravité Pourcentages

ip

- Utility

)(i

u−

Pas du tout dangereux 0.33 0

Pas vraiment dangereux (bosse, simple blessure, entorse)

0.40 0.02

Plutôt dangereux (blessure au dos, fracture, blessure à l’oeil)

0.13 0.14

Très dangereux (risqué de mort, handicap)

0.13 1

Tableau 3 : Dangerosité de la cale

Nous pouvons calculer le score associé à la gravité des blessures se produisant dans la cale :

d’où

16.0113.014.013.002.040.0033.0 =⋅+⋅+⋅+⋅=caleS [2]

Ceci nous a permis de disposer des scores de fréquence et des scores de gravité pour chacune des zones du navire. Nous avions alors besoin de définir une mesure de risque afin d’évaluer chaque compartiment en terme de sécurité. A cause du peu de précision du processus utilisé pour le calcul des scores, il ne nous a pas semblé nécessaire de trouver une nouvelle fonction de ‘scoring’ qui combinerait les deux précédents scores afin de classer les compartiments par risques. Ainsi, nous avons adopté une matrice de risques contenant quatre niveaux de risque et présentée dans le tableau ci-après :

Scores Gravité < 0,2 Gravité >0,2

Fréquence < 0,14 Risque non

significatif (aucune action nécessaire)

Risque significatif

(action immediate requise)

Fréquence > 0,14 Risque faible (Pas d’action prioritaire

requise) CRITIQUE

Tableau 4 : Matrice des risques

Au travers de cette matrice, nous avons (légitimement) considéré que la gravité des blessures causées par les STFs a un poids plus important que celui de la fréquence d’accès dans l’évaluation des risques. Une grande gravité est inacceptable quelques soit la fréquence d’accès tandis qu’une haute fréquence d’accès associée à une faible gravité est considérée comme un risque faible. 2.5 Les croyances des inspecteurs Les analyses de risque que nous avons conduites se basent sur le retour d’expérience de trente-deux inspecteurs. Nous devons considérer sa précision et être conscient de ses limites. En fait, il se peut que des biais soient introduits par la manière dont l’information est collectée à travers les questions. Les biais les plus significatifs viennent des croyances des interrogés en ce qui concerne les dangers liés aux STFs dans le maritime. En fait, lorsqu’on leur demande d’évaluer les fréquences d’accidents liés aux STFs ou la gravité des blessures qu’ils causent, les inspecteurs on tendance à sous-estimer les fréquences tandis qu’ils surestiment les conséquences (gravité des blessures). Ceci semble logique puisque les personnes en général et même les inspecteurs considèrent les STFs comme des accidents de la vie courante et par conséquent ne les remarquent généralement pas, à l’exception de ceux qui causent des blessures graves. Les répondants gardent aussi à l’esprit les accidents liés aux STFs les plus sérieux et occultent nombreux autres accidents survenus au long de leur carrière similairement à ce que Kahneman et al. décrivent comme le biais de disponibilité [19]. De la même façon, ils ne sont pas conscients des accidents mettant en cause leurs collègues. C’est la raison pour laquelle nous nous sommes rendus sur le terrain pour assister à une inspection et interroger des inspecteurs au sein de leur environnement de travail. Nous avons aussi porté une attention particulière à essayer de poser des questions de telle façon que ces biais soient minimisés. Quoi qu’il en soit, la pertinence et la précision des résultats à partir desquels nous avons travaillé sont assez bons pour l’analyse que nous avons menée. 2.6 La conception anthropométrique La section suivante explique les principaux concepts de la conception anthropométrique tels que définis par Pheasant [20]. L’anthropométrie est la branche de l’ergonomie qui traite de la mesure des dimensions, formes, force, mobilité et flexibilité du corps humain. A partir des résultats d’une analyse anthropométrique on peut extraire bon nombre de conditions techniques pour la conception anthropomorphique. L’objectif de l’anthropométrie est de choisir le meilleur compromis pour les dimensions afin que l’équipement soit employé par un large panel d’utilisateurs. Avant de commencer l’analyse anthropométrique proprement dite, on a besoin de trois types de données :

• Les caractéristiques anthropométriques de la population d’utilisateurs

• Les manières qu’ont ces caractéristiques d’imposer des contraintes sur la conception

• Les critères qui définissent une bonne correspondance entre le produit et l’utilisateur

Ces informations devraient être déterminées en fonction des spécifications et suggestions obtenues par les retours d’expérience des utilisateurs. En ce qui concerne les caractéristiques anthropométriques de la population, il est empiriquement vrai que la plupart des variables anthropométriques se conforment assez bien à une distribution normale (au moins pour une population raisonnablement homogène). Ainsi, les mesures de la population sont décrites par

Pas dangereux du tout

Pas vraiment dangereux Plutôt dangereux

Très dangereux

)(severityfutility =−


les centiles de la distribution. Par exemple, pour les mensurations de la stature d’un homme, si nous considérons l’utilisateur limitant comme le plus grand du 95

e centile de la population, cela implique

que 5% de la population sera plus grand que cet utilisateur (en termes de stature). Généralement, pour des analyses de conception classique, les concepteurs utilisent souvent le 5

e

centile de la population féminine et le 95e centile de la population

masculine comme utilisateurs limitant. Cependant, les mesures du corps dépendent de la population étudiée et des critères que l’on choisit. Par la suite trois types de solutions pour la conception peuvent être adoptés suivant les caractéristiques des interactions entre l’utilisateur, le produit et la tâche :

• la conception pour l’utilisateur limitant,

• la définition d’une zone commune à tous les utilisateurs et

• l’utilisation d’ajustements Lors de la première étape du processus, nous avons identifié les dangers relatifs aux STFs les plus significatifs de façon à ce que nous puissions nous concentrer sur les plus importants à travers une analyse ergonomique. L’objectif de cette analyse est de déterminer les contraintes ergonomiques pour que les gens de mer, les inspecteurs et les autres personnes amenées à travailler à bord des navires commerciaux, utilisent les moyens d’accès en toute sécurité. Il nous a fallu prendre en compte quatre types de contraintes : les contraintes venant des réglementations internationales concernant la sécurité de l’équipage et la disposition des accès (OMI, IACS, OIT, etc.), les contraintes venant des règles de classification pour les navires en acier de Bureau Veritas, les contraintes venant des retours d’expérience obtenus des gens de mers et inspecteurs et bien sûr, les contraintes cardinales issues de l’ergonomie. Nous avons rassemblé et classé toutes ces contraintes dans des tableaux afin d’avoir une vue d’ensemble des questions liées aux moyens d’accès, les retours d’expérience et les réglementations pertinentes. Les environnements sur lesquels nous nous sommes concentrés sont parmi les lieux que nous avons identifiés comme étant les plus risqués à bord. De plus, nous devions prendre en compte l’environnement marin puisqu’il détermine aussi la manière dont la conception des moyens d’accès doit être étudiée i.e. l’atmosphère corrosive qui met en danger l’intégrité d’un certain nombre d’échelles et de poignées par exemple et les conditions météorologiques qui influencent les mouvements des navires et par conséquent l’équilibre des gens de mer ou altèrent leur visibilité lorsqu’ils sont sur les ponts ouverts. Concernant les tâches menées à bien par les inspecteurs et les gens de mer pendant qu’ils utilisent les moyens d’accès, il s’agit des tâches liées à l’opération, la maintenance et l’inspection du navire. La population que nous avons étudiée comprend principalement les gens de mer et les inspecteurs. Comme les navires peuvent être opérés par des équipages venant de toutes les régions du monde ou presque, il fallait étudier la totalité de la population mondiale. Cependant les données anthropométriques spécifiques à cette population n’étaient pas disponibles. Les données relatives à l’ensemble de la population internationale ont donc été utilisées. En émettant l’hypothèse qu’il y a une majorité d’hommes parmi les gens de mer, nous avons décidé d’utiliser les données anthropométriques se rapportant au 5

e centile de la population

féminine japonaise pour l’utilisateur limitant le plus ‘petit’ tandis que nous avons choisi le 99

e centile de la population masculine

américaine pour l’utilisateur limitant le plus ‘grand’. Nous avons aussi du prendre en compte les vêtements et l’équipement d’inspection que les membres de la population sont susceptibles de porter. Nous avons considéré que chacun d’entre eux portait des chaussures de sécurité, un ‘bleu de travail’, des gants et un casque de protection. De plus, lorsque la situation étudiée le demandait, les gens de mer et inspecteurs, étaient considérés comme portant un équipement d’inspection spécifique composé d’un analyseur d’oxygène, d’un radiomètre, d’un appareil photo, de jauges d’une torche, d’un marteau et parfois

d’un masque et une bouteille d’oxygène pour les scénarii d’urgence. Chaque type de moyen d’accès impliquait des scénarii dépendant des conditions environnementales, des tâches à accomplir et des caractéristiques physiques des gens de mer. Ainsi il a fallu adopter différentes stratégies de conception pour ces différents scénarii : utilisation des échelles verticales, inclinées et des escaliers ; utilisation des ouvertures, écoutilles et trous d’homme ; utilisation des passerelles, tunnels et couloirs. 2.7 Les simulations L’étape de simulation est la partie itérative du processus. L’objectif est, en considérant les stratégies de conception adoptées et toutes les contraintes identifiées pendant les étapes précédentes, de trouver le meilleur moyen de reproduire les situations de travail réelles à bord. Un logiciel de CAO a été utilisé pour modéliser les interactions entre les gens de mer et les environnements dans lesquels ils doivent travailler. 2.8 Développement de recommandations ergonomiques A partir des trois précédentes étapes de la méthodologie, nous avons obtenu des spécifications dimensionnelles pour la conception et la disposition des moyens d’accès à bord ainsi que certaines bonnes pratiques utilisées dans le maritime. Ainsi, la dernière étape a consisté à développer un document technique complet et abouti rassemblant toutes les spécifications et bonnes pratiques de façon à ce que quiconque s’intéressant à la conception anthropomorphique des moyens d’accès pour les navires et installations offshore puissent se voir proposer les conseils pertinents à son problème.

3. Application et résultats Nous avons appliqué notre approche pour développer une note d’information intitulée « Guidelines for the design of the Means of Access for Inspection, Maintenance and Operation of Commercial Ships », adressée aux chantiers navals, aux armateurs ainsi qu’à tous les acteurs de l’industrie maritime intervenant dans la conception des navires. Les principaux résultats qui nous ont permis de développer cette note ainsi que les recommandations ou ‘guidelines’ elles-mêmes sont décrites dans les sections suivantes. 3.1 L’utilisation du retour d’expérience Tout d’abord, nous avons interrogé un des anciens inspecteurs de Bureau Veritas (dont le rôle est de conduire des inspections techniques à bord des navires) afin de collecter des informations de base concernant les principaux problèmes rencontrés pendant une inspection et élaborer une série de questions qui a été ensuite intégrée dans le questionnaire. Cet entretien fut très utile pour préparer les entretiens suivants en terme de ‘pré-requis culturel’ au sujet des inspections ainsi que le vocabulaire et les expressions justes à adopter pour poser des questions. Puis nous avons participé à une inspection à bord d’un gazier (GNL) sous l’égide d’un inspecteur expérimenté qui nous a montré les endroits où il se rend généralement et les moyens d’accès qu’il utilise lors de ses inspections. Nous avons noté les bonnes et mauvaises pratiques en terme de sécurité et avons essayé de détecter les dangers liés aux STFs. Après la visite, nous avons discuté avec deux autres inspecteurs au sujet des points soulevés précédemment et analysé les améliorations potentielles de la conception des moyens d’accès qu’ils recommanderaient pour la prévention des STFs. Nous leurs avons aussi présenté une première version du questionnaire que nous avions précédemment adapté. Nous avons ainsi finalisé deux questionnaires respectivement adressés aux marins et aux inspecteurs de Bureau Veritas. L’objectif était d’obtenir le retour d’expérience provenant du plus grand nombre possible d’utilisateurs afin de mener des analyses quantitatives qui reflèteraient le plus grand nombre d’utilisateurs à travers le monde. Cependant, aucune des associations et syndicats de marins ou des armateurs que nous avons contacté n’ont accepté de disséminer les questionnaires aux marins et par conséquent nous n’avons pas pu obtenir leur retour d’expérience. C’est une des premières limites de notre étude de cas, que nous projetons de franchir lors de nos études futures ; néanmoins, nous croyons que les résultats que nous avons obtenus constituent des éléments intéressants. Trente deux inspecteurs de Bureau Veritas


ont répondu au questionnaire, ce qui peut être considéré comme suffisant, surtout parce que les retours viennent d’une grande majorité d’inspecteurs expérimentés qui ont mené des inspections à bord d’un large panel de différents navires.

3.2 L’approche par les risques En utilisant l’analyse des causes conduisant aux STFs et les réponses qualitatives des trente-deux répondants, nous avons identifié d’une part les causes profondes des glissades, trébuchements et chutes et d’autre part nous avons développé une série de recommandations pour combattre les STFs ou du moins trouver des barrières pour les éviter. Tout d’abord, nous avons observé que, comme nous le pressentions, les inspecteurs avaient tendance à minimiser la fréquence avec laquelle les STFs se produisent bien qu’ils semblent conscients de la gravité des blessures qu’ils sont susceptibles de causer. Les inspecteurs semblent décrire les chutes comme le type d’accident le plus dangereux mais ne prennent pas systématiquement en compte le fait que les glissades et trébuchements sont souvent les principales causes à l’origine des chutes et seraient probablement presque aussi dangereux que les chutes ‘directes’. Peut-être qu’une définition plus précise des STFs aurait engendré des réponses plus homogènes.Ensuite, nous avons identifié les réservoirs de ballast, les espaces clos, le tunnel d’arbre et la salle des pompes comme les zones les plus dangereuses à bord. Les peaks avant et arrière, la gouverne et les espaces machines apparaissent aussi comme étant très risqués. Ces résultats semblent être plutôt en accord avec les entretiens et la visite même si les pics étaient censés être les compartiments les plus risqués des navires, suivis par les réservoirs de ballastage. Concernant la dangerosité des moyens d’accès, selon les retours d’expérience issus des questionnaires, presque tous (excepté les escaliers simples et les couloirs) ont un score de risque élevés. Ceci est aussi en accord avec les informations que nous avons obtenues des entretiens précédents. Finalement, les principales causes identifiées comme les causes profondes des STFs sont le manque de prises manuelles pour utiliser les moyens d’accès en toute sécurité, la localisation des ouvertures, la mauvaise signalisation des dangers, et le manque d’espace. En effet, un espace libre minimum est apparu comme primordial pour limiter les risques de glissade, trébuchement et chute lors des inspections (sur des plateformes étroites ou sur les échelles par exemples) mais aussi pour utiliser les moyens d’accès en toute confiance et avec un sentiment de confort. En conclusion, les précédentes étapes du processus nous ont fourni des informations précieuses pour conduire la troisième démarche que nous allons décrire dans les sections suivantes.

3.3 L’analyse ergonomique Nous avons modélisé quatre environnements regroupant les quatre principaux types de moyens d’accès qui peuvent être risqués et causer des glissades, trébuchements et chutes c’est-à-dire, les échelles verticales, les échelles inclinées, les escaliers, les ouvertures et les passerelles. Puis nous avons modélisé les situations de travail les plus risquées avec des mannequins virtuels et finalement extrait des simulations les dimensions et formes auxquels les moyens d’accès devraient se conformer afin de correspondre aux tâches et aux besoins des utilisateurs. Deux exemples montrant une simulation pour les échelles verticales et les ouvertures sont présentés sur la figure ci-après.

Figure 5 : Images issues de l’analyse anthropométrique

3.4 Les recommandations (guidelines) Développer les recommandations pour Bureau Veritas est la dernière étape du processus que nous avons adopté pour gérer les risques associés aux glissades, trébuchements et chutes. Les recommandations devaient fournir les informations les plus pertinentes possibles que nous avions rassemblées durant les étapes précédentes sur les moyens de prévention des STFs, particulièrement en améliorant les moyens d’accès à bord. Ainsi, les personnes qui utilisent les moyens d’accès pour opérer maintenir et inspecter un navire se conformant à toutes ces recommandations seront et se sentiront plus en sécurité.. La plupart des recommandations sont des spécifications dimensionnelles pour les moyens d’accès ; cependant, la dernière section concerne les meilleures pratiques rencontrées dans l’industrie maritime pour améliorer la sécurité par lors de la conception, en traitant de la texture, la couleur et la signalisation des moyens d’accès, leur maintenance et utilisation, ou l’éclairage de l’environnement.

Conclusion Les apports de cette recherche se situent à deux niveaux. Sur un plan méthodologique tout d’abord, nous pensons avoir contribué à la possibilité d’envisager les études de prévention de manière différente de celle pratiquée usuellement : les techniques que nous avons mobilisées, tant à l’échelle du retour d’expérience qu’à celle de l’analyse de risques ou de l’ergonomie n’ont en effet à notre connaissance jamais été utilisées conjointement jusqu’à présent. Sur un plan pratique maintenant, cette recherche a débouché, nous l’avons vu, sur des directives ayant vocation à améliorer les conditions de sécurité à bord des navires. Là aussi, si de nombreux travaux se sont attachés à cet objectif, rares sont ceux qui présentent une dimension directement opérationnelle à l’échelle de la conception. Les perspectives qui s’ouvrent à la suite de ce travail sont d’au moins deux ordres : d’une part, il pourrait s’agir d’approfondir, de compléter et de raffiner les techniques que nous avons utilisées. Par exemple, réaliser un encodage des préférences des individus pourrait permettre d’améliorer l’analyse de risques. L’autre perspective que nous envisageons concerne l’extension de ce travail à d’autres secteurs. D’ores et déjà, une analyse similaire à cette conduite sur les moyens d’accès à bord est en cours de réalisation pour ce qui est des salles des machines. D’autres industries pourraient toutefois sans doute également bénéficier de l’application des techniques que nous avons proposée à leur politique de prévention. Références [1] Jensen, O. C., Sorensen, J. F. L., Canals, M. L., Yunping Hu, Nicolic, N., and Mozer, A. A. 2005. “Non-fatal Occupational Injuries Related to Slips, Trips and Falls in Seafaring”, American Journal of Industrial Medicine. 47, pp. 161-171 [2] American Club P&I Current newsletter, issue number 18, May 2004, “Caring for the crew” [3] Fadier E. & De la Garza C., Safety design: Towards a new philosophy, Safety Science N°44, pp. 55-73, 2004. [4] Perrow, C. 1984. Normal Accidents – Living with High-Risk Technologies. Basic Books. [5] Marletta. 1991. Trip, slip and fall prevention. In Hansen, D., The Work Environment, Vol.1: Occupational Health Fundamentals. Michigan, Lewis Publishers, pp241-261 [6] Zohar, D. December 1978. Why do we bump into things while walking, Human Factors. [7] David Squire, 2008, HE Alert! bulletin n° 17“One hand for the ship … and one for yourself, pp. 4-5, [8] Nautical Institute, 2007, Fall in pump room. MARS report n° 200703 http://www.nautinst.org/mars/mars07/200703.htm [9] IMO. MEPC 56/17/3. 4 Avril 2007. Plan d’action relatif à l’élément humain mis à jour. [10] IMO Resolution MSC.158(78) (adopted on 20 May 2004) - Adoption of amendments to the technical provisions for means of access for inspections [11] IACS. March 2006. Unified Interpretations for the application of amended SOLAS regulation II-1/3-6 (resolution MSC.151(78))


and revised Technical provisions for means of access for inspections (resolution MSC.158(78)). IACS UI SC 191 [12] Bourdeaux, I. et Gilbert, C., 1999, Procédures de REX, d’apprentissage et de vigilance organisationnelles : approches croisées, Grenoble : Editions CNRS. [13] Henley, E.J. et H. Kumamoto, 1996, Probabilistic Risk Assessment and Management for Engineers and Scientists, New York : IEEE Press, 2e édition. [14] Kennedy, R, B. Kirwan, R. Summersgill, K. Rea, 2000, « Validation of HRA techniques – Déjà vu five years on? », in Cottam, M.P., D.W. Harvey, R.P. Pape et J. Tait (éd.), Foresight and Precaution: Proceedings of ESREL 2000, SARS and SRA-Europe Annual Conference (Edimbourg, UK, 15-17 Mai), Rotterdam : Balkema, pp. 359-368. [15] Kennedy, R, B. Kirwan, R. Summersgill, K. Rea, 2000, « Making HRA a More Consistent Science », in Cottam, M.P., D.W. Harvey, R.P. Pape et J. Tait (éd.), Foresight and Precaution – Proceedings of ESREL 2000, SARS and SRA-Europe Annual Conference (Edimbourg, UK, 15-17 Mai), Rotterdam : Balkema, pp. 341-349. [16] Roux-Dufort, C., 2000, « Why Organizations Don’t Learn from Crises : the Perverse Power of Normalization », Review of Business, vol. 21, n°3, pp. 25-30. [17] Gaillard, I., 2005. Etat des connaissances sur le retour d’expérience industriel et ses facteurs socio-culturels de réussite ou d’échec, Cahiers de l’Institut pour une Culture de Sécurité Industrielle, n°2005-2, Toulouse : ICSI. [18] Korte, J., Aven, T. et Rosness, R., 2002, On the Use of Risk Analysis in Different Decision Settings, ESREL 2002, Lyon. [19] Kahneman, D., Slovic, P., and Tversky, A. 1982. Judgement under uncertainty: Heuristics and biases. Cambridge: Cambridge University Press. 163-200 [20] Pheasant S. & Haslegrave C., Bodyspace : Anthropometrics – Ergonomics and the design of work – Third Edition, CRC Press ,2006.

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