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Copyright 2005, Offshore Technology Conference This paper was prepared for presentation at the 2005 Offshore Technology Conference held in Houston, TX, U.S.A., 2–5 May 2005. This paper was selected for presentation by an OTC Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Papers presented at OTC are subject to publication review by Sponsor Society Committees of the Offshore Technology Conference. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, OTC, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract Following the unexpected rupture of chains in the chainhawse of the Girassol buoy after only half a year of service a new bending fatigue mechanism of failure has been identified for mooring systems with high pretensions. The premature rupture was caused by bending fatigue of the first free chain link inside the chainhawse. Although the mooring system had been designed according to offshore industry standards, it failed due to this bending fatigue mode. Since this failure, SBM has studied this bending phenomenon in its laboratory and redesigned both the top chain segment size and the hawse connection, which now includes a new Connecting Arm. The main changes brought about by the Girassol incident are: - Doubly articulated chain stopper, - Use of very low friction bushings in chain stoppers, - Increased lever arm length between articulation and first chain link, - Increased chain diameter. This paper summarizes the methodology developed to estimate the fatigue damage in the chain subjected to bending. The methodology is then applied to the design of the CCA of the Girassol buoy. Although the methodology accurately predicts the fatigue failures of Girassol, it tends to be overly conservative when applied to other systems. The source of this conservatism is still being investigated and is currently the subject of further testing in the SBM Laboratory. Introduction The Girassol Loading Buoy was installed in September 2001 on Block 17 of the “Girassol” oil field situated offshore Angola, in 1350 m, water depth at Buoy location. The Buoy allows the export, via 2 mid-water 16” Export Lines, of the stabilized crude oil processed onboard the nearby FPSO, moored 1 nautical mile away, south of the Buoy. TOTAL E&P Angola operates both Loading Buoy and FPSO systems. SONANGOL is concessionnaire of the field. Block 17 is developped by a Group of Partners involving TOTAL E&P ANGOLA, ESSO ANGOLA, BP, STATOIL and NORSK HYDRO. The Buoy is anchored to the seabed by means of 3 groups of 3 anchor legs. Before the incident, the anchor legs were composed of co-linear segments of 81 mm studded chains and 130 mm diameter polyester ropes. Within one group, the Legs are spread 5° apart, while each group is spread 120° apart (see Figure 1). The Legs are numbered B1, B2, and B3 for the West group, B4, B5, B6 for the North group and B7, B8, B9 for the East group. The chain segments are situated at the upper and lower ends of the anchor legs, i.e. respectively at the Buoy connection and at the Anchor Pile connection. In May 2002, i.e. 235 days after the buoy installation, the anchor legs B4, B5 and B6 broke almost simultaneously, followed one month later by the rupture of the anchor leg B1. The ruptures in B4, B6 and B1 occurred exactly at the same location, i.e. at the 5 th link of the Upper Chain Segment connected to the Buoy inside SBM standard-type “curved chainhawses”, while Leg B5 broke in the Upper Rope Segment. This later rupture was primarily caused by an early accidental cut of the Rope through 2/3 of its section. The total rupture of B5 followed the rupture of B4 and B6 and the consequent load transfer. However, the 5 th link of Leg B5 was found severely cracked, thus confirming the same failure mechanism for all 4 Legs. OTC 17238 Failure of Chains by Bending on Deepwater Mooring Systems P. Jean, Single Buoy Moorings Inc.; K. Goessens, TOTAL E&P ANGOLA; and D. L’Hostis, DV Offshore
12

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Mar 06, 2018

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Page 1: Failure of Chains by Bending on Deepwater Mooring Systemsoffshorelab.org/...of_Chains_by_Bending_on_Deepwater_Mooring_Syst… · Failure of Chains by Bending on Deepwater Mooring

Copyright 2005, Offshore Technology Conference This paper was prepared for presentation at the 2005 Offshore Technology Conference held in Houston, TX, U.S.A., 2–5 May 2005. This paper was selected for presentation by an OTC Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Papers presented at OTC are subject to publication review by Sponsor Society Committees of the Offshore Technology Conference. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, OTC, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract Following the unexpected rupture of chains in the chainhawse of the Girassol buoy after only half a year of service a new bending fatigue mechanism of failure has been identified for mooring systems with high pretensions. The premature rupture was caused by bending fatigue of the first free chain link inside the chainhawse. Although the mooring system had been designed according to offshore industry standards, it failed due to this bending fatigue mode. Since this failure, SBM has studied this bending phenomenon in its laboratory and redesigned both the top chain segment size and the hawse connection, which now includes a new Connecting Arm. The main changes brought about by the Girassol incident are:

- Doubly articulated chain stopper, - Use of very low friction bushings in chain stoppers, - Increased lever arm length between articulation and

first chain link, - Increased chain diameter.

This paper summarizes the methodology developed to estimate the fatigue damage in the chain subjected to bending. The methodology is then applied to the design of the CCA of the Girassol buoy. Although the methodology accurately predicts the fatigue failures of Girassol, it tends to be overly conservative when applied to other systems. The source of this conservatism is still being investigated and is currently the subject of further testing in the SBM Laboratory.

Introduction The Girassol Loading Buoy was installed in September 2001 on Block 17 of the “Girassol” oil field situated offshore Angola, in 1350 m, water depth at Buoy location. The Buoy allows the export, via 2 mid-water 16” Export Lines, of the stabilized crude oil processed onboard the nearby FPSO, moored 1 nautical mile away, south of the Buoy. TOTAL E&P Angola operates both Loading Buoy and FPSO systems. SONANGOL is concessionnaire of the field. Block 17 is developped by a Group of Partners involving TOTAL E&P ANGOLA, ESSO ANGOLA, BP, STATOIL and NORSK HYDRO. The Buoy is anchored to the seabed by means of 3 groups of 3 anchor legs. Before the incident, the anchor legs were composed of co-linear segments of 81 mm studded chains and 130 mm diameter polyester ropes. Within one group, the Legs are spread 5° apart, while each group is spread 120° apart (see Figure 1). The Legs are numbered B1, B2, and B3 for the West group, B4, B5, B6 for the North group and B7, B8, B9 for the East group. The chain segments are situated at the upper and lower ends of the anchor legs, i.e. respectively at the Buoy connection and at the Anchor Pile connection. In May 2002, i.e. 235 days after the buoy installation, the anchor legs B4, B5 and B6 broke almost simultaneously, followed one month later by the rupture of the anchor leg B1. The ruptures in B4, B6 and B1 occurred exactly at the same location, i.e. at the 5th link of the Upper Chain Segment connected to the Buoy inside SBM standard-type “curved chainhawses”, while Leg B5 broke in the Upper Rope Segment. This later rupture was primarily caused by an early accidental cut of the Rope through 2/3 of its section. The total rupture of B5 followed the rupture of B4 and B6 and the consequent load transfer. However, the 5th link of Leg B5 was found severely cracked, thus confirming the same failure mechanism for all 4 Legs.

OTC 17238

Failure of Chains by Bending on Deepwater Mooring Systems P. Jean, Single Buoy Moorings Inc.; K. Goessens, TOTAL E&P ANGOLA; and D. L’Hostis, DV Offshore

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2 OTC-17238

Figure 1 - Girassol buoy anchoring system.

Further to these 4 failures, extensive investigations and studies were undertaken by SBM inc. in order to understand the root cause and to find remedial solutions. The root cause was identified as being the out-of-plane fatigue stress (OPB stress), combined with the tension variations, occurring mainly in the 5th link located inside the Chainhawses. This 5th link is indeed the first link to oscillate with respect to the 4th link fixed onto the internal curved shape of the Chainhawse (see sketch below).

Figure 2 - Girassol buoy elevation view, location of failed

link

In this paper we propose:

An explanation for the failure mechanism of the Girassol chains

A methodology to account for the bending stress in the chains located at the connection with the buoy.

Out of Plane Bending (OPB) failure mechanism In this part, we propose an explanation for the failure of link 5 on Girassol buoy. Unlike a rod, a chain can be piled or laid in any shape and thus we tend to think that a chain does not have a bending stiffness. In most cases the tension in a chain is so low that the links can roll or slide on each other to accommodate the rotations imposed at the ends of the chain by the floating body. Rolling mode As for any articulation, when the pretension in the chain increases it will become more and more difficult to obtain a rotation between successive links. If the surfaces of contact of the links were perfectly cylindrical, a rolling mechanism would still be possible even for high pretensions. Small bending stresses would be generated because of the displacement of the point of application of the tension away from the plane of symmetry of the link. These rolling stresses can be analytically calculated but they are too small to explain the fast failure of Girassol.

Figure 3 -Chain links in rolling mode

Chainhawse

Chainhawse

Failed link

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OTC 17238 3

Equation 1 - Rolling

))1rr

r738.0(sin(TrM12

1total1rollingOPB +

−α=

21

12

1total

3

rollingOPBrollingOPB r

))rr

r738.01(sin(T2

16d

M

π−

+α=

π=σ

r1 is the link bar radius (0.5 * nominal chain diameter), r2 is the radius of curvature of the link at contact point. Formula is valid only for typical chain link geometry: r2 = 1.35 r1. Locking mode In the manufacturing process of a chain, a proof load (between 65% and 80% of breaking load) is applied on all links. Plastic elastic FEA (see Ref. [1]) of two links has shown that, under a tension equal to proof load, the surface of contact between the two links is permanently deformed, see Figure 6. The theoretical point of contact becomes a surface with an elliptical shape typically the size of a quarter of the chain diameter. The surface of contact has been observed on all chain links inspected (see Figure 4 and Figure 5).

Figure 4 - Surface of contact of 40mm lab test chain

Figure 5 - Surface of contact of Girassol 76 mm chain link

Figure 6 - FEA deformation of contact area under proof

load at 60% MBL, 124mm chain.

Once this surface is formed, the chain links cannot roll anymore, the links are locked. If a rotation is imposed on one chain link, the complete chain will have to bend just like a “rod”. FEA shows that most of the bending deformation occurs at the surface of contact between links. The stresses generated by this bending are large and can easily explain the fast failure of Girassol. Figure 7 shows how a bending moment (out of plane) is generated in the link when a rotation αtotal is imposed on the chain end and the link cannot roll on each other. Out of Plane Bending (OPB) refers here after to the bending of a chain link out of its “main plane” (the one containing the oval shape, see Figure 7). It is caused by the application of transverse forces and OPB moments which are resisted by reaction forces spread over the contact between links.

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4 OTC-17238

Figure 7 - Chain link in bending mode, links are locked at

surface of contact

T T

MA αtotal

Figure 8 - Chainhawse imposed rotations

Each wave is exciting the buoy in roll and pitch. These rotations are imposed on the top chain through the chainhawse. Because of the mechanism described above, bending stresses are generated for each wave cycle. It is the accumulation of these bending stresses that will cause the propagation of cracks in chain until failure. On Girassol, the combination of constant swell excitation with high pretension/MBL has led to a rapid failure. The hot spot for bending stresses can be identified by bending a link in FEA. Figure 9 shows that the highest bending stresses are located in the curved part of the link 45dg from the main plane of the link. The hot spots for pure tension are located in a different area, as shown on Figure 10. It is therefore possible to distinguish between a crack propagation generated by tension or bending.

Figure 9 - FEA location of hot spot stress in pure bending

Figure 10 - FEA location of hot spot stresses in pure tension

Area of max stress in Out of Plane Bending

MOPB

Area of max stress in Tension

Floating body imposes rotations at top chain end through the chainhawse

Locking area

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OTC 17238 5

Photographs of the failed links on Girassol, Figure 11, show that the fracture surfaces are consistent with bending.

Figure 11 - Girassol failed link No5, line B6

In order to calculate the fatigue life of chain undergoing bending cycles, we propose to:

Calculate the long term distribution of chain hawse angles (using scatter diagrams and buoy RAOs, not addressed in this paper)

Obtain long term distributions of bending stresses using bending stress vs chain hawse angle curve

Use an appropriate SN curve to calculate the fatigue damage

Combine tension and bending stresses or damages

Calculation of bending stress in chain In this part, we propose a methodology to calculate bending stress vs chain hawse angle curve. Simple analytical formula for a rod under tension undergoing large displacements.

Locking mode Tensioned beam deformation differential equation taking into account the effect of large displacement:

Equation 2

( ) 0M)sL)(sin(T)s(y)L(y)cos(T)s(EIy TT" =−−α−−α+

The effect of beam mass has been neglected here, this is a good approximation as long as the pretension of the beam is high compared with its own mass and as we only concentrate on a very short length of chain. Solution for small angle of tension αT and small fairlead angle αO:

Equation 3

)kL(ch))sL(k(shEIT)(

)kL(ch)ks(chM)s(M OTB

−α−α+=

with EITk =

Figure 12 - Analytical model of a chain, bending under tension

Crack initiation at location of max stress in bending

αO

T

X

Y Beam: Modulus: E Inertia: I Length: L

αT

s=0

s=L

αtotal

MB

MA= -M(s=0)

END A END B

Positive rotations, moments

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6 OTC-17238

This equation simplifies if the chain when the chain length is bigger than the characteristic length 1/k and no moment is applied to the end B of the chain (MB=0). The maximum chain bending moment at connection with floating body becomes:

Equation 4

( ) totaloTA EIT)kL(thEITM α−≈α−α−=

Example: if the chain is 76mm diameter (3”), the tension 80tons and the Young modulus 201Gpa, the characteristic length 1/k is only 65cm. Therefore, even if we consider a length of 12 links i.e. 3.6m, th(kL)=0,99997≈1. The approximation is valid and we do not need to account for chain self weight as we only consider a very short length. Once the maximum bending moment is known, the maximum bending stress is obtained using the following formula (SCF derived from FEA):

Equation 5

16d

MSCF 3

AOPBOPBmax π

totalOPB2

OPBmax d90ETSCF απδ=σ

Units: σmax OPB : maximum bending stress in Pa δ constant T: tension in Newtons E: Young Modulus in Pa d: chain diameter in m αtotal : rotation at fairlead in dg SCFOPB: stress concentration factor in pure bending, 1.08 for standard chain geometry. To derive this formula, we have assumed that the chain is behaving like a continuous rod of equivalent diameter δ*d. The value of δ (close to 1) was found by comparison with experimental measurements of bending stresses for different chain diameters and tensions.

Sliding mode The locking mechanism between links is friction. Until sliding moment is reached the bending stresses in the chain increase with imposed rotation αtotal . Above the sliding moment, the link will slide on their surface of contact and the bending stress will remain constant and equal to the following simple value:

Equation 6

2dTM sliding µ=

the corresponding maximum stress at sliding is:

Equation 7

2OPBsliding dT8SCF

πµ=σ

Experiments have shown that the friction coefficient for chain µ is close to 0.3 in salt water and 0.5 in air dry.

Figure 13 - Summary of chain bending stress vs angle curve

σOPB (Pa)

Locking mode

Sliding mode

0 αsliding αinterlink

σsliding

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OTC 17238 7

Empirical formula based on lab tests results Description of tests

In order to validate the above theoretical approach a series of lab tests have been conducted in “SBM France” laboratory. The main purpose of the lab tests was to obtain a reliable relationship between the OPB stress and the interlink angle for different tensions and chain sizes. Figure 14 shows the test schematic. The chain tension is maintained constant by a hydraulic cylinder. The chain hawse is pushed down by another hydraulic cylinder to generate significant interlink angles and OPB stresses.

Figure 14 – Chain test schematic

The SBM Chain Test Facility is configured to simulate the relative motion between two adjacent links in a mooring chain. Depending on the chain size, a different length of chain links is arranged in the rig. Figure 14 depicts the arrangement for 81mm chain but the principle remains the same for all chain diameters tested. The chain is tensioned horizontally through a hydraulic cylinder before starting each test. The rig shoe is then forced into contact with the chain at link#T4 only (T is for Test). The chain hawse is pushed down by another hydraulic cylinder to generate significant interlink angles and OPB stresses. This action caused link #T5 to rotate relative to link #T4. The link surface of contact preventing rolling and the friction between links #T4 and #T5 induces out-of-plane bending in link #T5. The chain test rig allows the chain to run in dry conditions or submerged in water. Link #T5 is mounted with strain-gauges (see Figure 15 and Figure 16) to monitor bending stress variations when cycling the chain. Inclinometers are also used to measure the relative angle between links #T4 and #T5. All measurements are stored on a PC. Precision on measured strain is equivalent to a precision on stresses of +/-0.2MPa. Inclinometers have been clamped on the chain in the middle part. Precision of the angle measured is high. The system is calibrated against electronic inclinometers with a precision of 0.05dg. The tensioner is hydraulically controlled to maintain constant tension throughout the test. This is important to ensure that the stress variation is purely due to OPB moments.

It also simulates the behavior of a very long (and soft) deep water mooring line. The tension was monitored during each test so that it can be post-checked. Tension variations were in the order of +/- 3 tons during tests.

Figure 15 - Rosettes

Figure 16 - Strain gauges

The test bench in principle is very similar to a classical SBM chain hawse. Nevertheless, the length of the chain is not infinite and therefore there is certainly an effect of the test bench on the test results. Several attempts have been made in order to correct the results for the effect of test bench, nevertheless, they were not fully consistent with all the tests results. For this reason, it has been decided not to plot directly a stress versus total rotation angle curve as the total chain angle may not be representative of a chain on a real mooring line. We have rather studied the stress versus interlink angle curve. The interlink angle being the relative angle between the link in contact with the chain hawse and the first free link (respectively link 4 and 5 in Figure 14 and definition of interlink angle in Figure 7).

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8 OTC-17238

Table 1 presents the list of chain bending tests conducted so far by SBM. Chain diameter [mm]

Chain type Tensions [tons]

41 Studlink Grade R4 30, 50 81 Studlink Grade R3S 20, 50, 75, 94 107 Studless Grade RQ3 60, 70, 80, 94 124 Studless Grade R4 60, 80, 85, 94 146 Studless Grade RQ4 60, 80, 85, 94

Table 1 – List of chain tests

The general test procedure for a given tension is as follows:

One calibration run to determine the interlink angle vs. chain hawse stroke relationship (10 cycles);

3 runs of 50 cycles to the maximum angle before sliding (noted αsliding, for sliding threshold) in order to check reproducibility;

1 run of 50 cycles to half the angle to half the sliding threshold to get more measures at small angles, which the area of interest for the design of chain connector and fatigue analysis;

1 run after the sliding threshold to check the value of OPB stress when sliding.

Tests results

Stress versus interlink angle curves

Figure 17 shows a typical test result obtained on 124mm studless chain. The variation of the maximum stress measured on the link is plotted against interlink angle. The interlink angle and stress have been arbitrarily set to zero for the lower sliding angle at the start of the ascending cycle. Only the stress variation is of interest as we are dealing with fatigue. One can clearly see the two different modes of stress variations depending on the interlink angle: locking and sliding.

Figure 17 - 124mm link OPB Stresses for 60tons pretension in water

Reproducibility and linearity with interlink angle Reproducibility was found to be very satisfactory throughout the series of identical tests (same tension), even though the chain was released between each set of 50 cycles. This point is very important, especially because the initial conditions slightly differ from one set to the other (not exactly the same areas in contact between links), when the chain is pulled in tension before starting the cycles. Figure 18 shows the 4 tests of 50 cycles performed at 94 tons (tests#29-3 a - b & c and 29-4, ascending cycles only). It appears that in the locking mode, OPB stress is almost linearly increasing with interlink angle.

94 tons - tests 29-3 & 4 - ascending cycles

0

50

100

150

200

250

0 0.5 1 1.5 2

rel angle (º)

stre

ss (M

Pa) 2

222

Figure 18 - 81mm link OPB stress, 4 different tests for 94tons pretension in water

Effect of tension

Figure 19 shows the results from all the tests at different tensions for the 81mm studlink chain.

Figure 19 – 81mm chain stress vs. interlink angle

relationship for different tensions

This clearly demonstrates that the higher is the tension, the steeper is the curve. OPB stress increases with pretension. A regression has been made on tests data of 81mm, 107mm and 124mm chains, see Figure 20. The following empirical formulas have been derived:

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OTC 17238 9

Using only the results of the tests on 81mm and 124mm chains:

Equation 8

erlinkint0.175.0

OPB daT α=σ −

with a constant T tension, in tons d chain diameter, in m αinterlink the interlink angle between the fixed and free link, in dg σOPB OPB stress in MPa. Using the results of the tests on 81mm, 107mm and 124mm chains:

Equation 9

erlinkint0.16.0

OPB dbT α=σ −

with the same units and: b constant

Reduced stress versus interlink angle

y = 1.298x

0.00

0.50

1.00

1.50

2.00

2.50

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00Interlink angle (dg)

Stre

ss/(T

^(0.

6)*D

^(-0

.8))

81mm studlink 106 mm studless rosettes in air 106mm studless SG in water124mm studless 1.298*(T (̂0.6)*D (̂-0.8)) Linear (1.298*(T (̂0.6)*D (̂-0.8)))

Figure 20 - Reduction of measured OPB stress data, 81mm, 107 and 124 mm chain tests for all tensions

Effect of friction

Figure 21 shows the stress variation vs. angle when the chain is in air (test #29-2-1 in pink) and submerged in water (test #29-3-1 in blue). Both tests were performed with uniaxial gauges, and the signals have been extracted from the same gauge J2. It clearly shows that the water does not significantly changes the contact regime between the 2 links, as the curve is not modified. Before the sliding threshold is reached the links contact surfaces are locked and the friction coefficient does not have an impact. The chain behaves as a single continuous elastic body (like a rod). The only effect of friction is to change the level of stress (or friction moment) for which sliding starts. This can be seen clearly in Figure 22.

stress vs. angle for different lubricating conditions

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

rel angle (º)

stre

ss (M

Pa)

29-3 129-2 1

Figure 21 - 81mm link OPB Stresses vs interlink angle, 94tons pretension, in air and in water

-50

0

50

100

150

200

250

300

0 1 2 3 4 5 6

relative angle (º)

Stre

ss V

aria

tion

(MPa

)Water Air

Figure 22 – 107mm chain, 94 tons pretension, effect of

water on sliding threshold

The two sliding limits up and down, correspond to the sliding when the links are forced to rotate in one direction or in the other. The double amplitude of OPB stress in sliding is

Equation 10

2OPBsliding dT8SCF*22

πµ=σ

This formula allows us to estimate the friction coefficients between chain links under tension. Considering the scatter in the measured sliding stresses, the following ranges of friction coefficients: In air: µ between 0.5 and 0.7, in water: µ between 0.3 and 0.5.

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10 OTC-17238

Going from interlink angle to total chain angle In order to calculate the stress in chain bending and derive the fatigue damage for a particular anchoring system, one need to know the relationship between bending stress and chain hawse angle as the interlink angle cannot be calculated. This is done by modeling the chain with finite elements. We derive the maximum chain bending moment MA at connection with floating body. To do so, a chain is composed of a series of simplified links connected at contact point. The global bending chain stiffness results of the combination of the local interlink bending stiffness between each link. Interlink local bending stiffness K(T,d) is represented by torsional springs connecting the beams composing the chain. Calculations have been performed on NASTRAN using large displacements. The interlink bending stiffness is derived from the test results regression formula:

Equation 11

16dM

)d,T(Kerlinkint

3erlinkint

erlinkint

OPB

απσ

=

αinterlink

MA

αinterlink

MA Figure 23 - Simple chain model for derivation of maximum

bending moment at connection with floating body.

Figure 24 - FEA model of chain under tension with

imposed end rotation

The moment MA at first free link was calculated as a function of the angle αtotal. In these calculations it was essential to use the large displacement module of NASTRAN otherwise the moment MA was increasing indefinitely with the length of chain. On the contrary, when the displacement of the chain under the loading is taken into consideration, the moment MA

converges rapidly after a certain length of chain is modeled. Here it was found that 12 links were enough to obtain convergence of MA and a small residual moment at last interlink contact at end B. Several tensions (500 to 1600kN) and chain diameters (81 to 152mm) have been used to derive an empirical formula:

Equation 12

604.1846.0

total

A

OT

A dTMM

)d,T(C κ=α

=α−α

= , without

107mm tests,

κ Constant C(T,d): Global stiffness in kN.m/rd MA: Total constraint Moment in kN.m αT: Tension angle in the global frame, in radian. αO: Angle imposed at fairlead in the global frame, in radian. T: Tension in kN. d: Chain diameter in m. αtotal = αT − αO Tension angle in the local fairlead reference axis, in radian And the formula for the bending stress:

Equation 13

16dMSCF 3

AOPBmaxOPB π

total396.1846.0

OPBmax dT αλ=σ −

with λ constant T tension, in tons d chain diameter, in m αtotal : rotation at fairlead in dg σmax OPB Maximum OPB stress in MPa. The formula is being updated following 107mm tests.

K(T,d)

K(T,d)

αtotal at the end of the chain

MA

A B

αT

T

T

αo=0 dg

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OTC 17238 11

Comparison theoretical vs experimental Using global chain stiffness empirical formula we have determined an empirical formula for bending stress versus total angle. The following curves (Figure 25) show a comparison between empirical curve and theoretical curve presented before. It appears that analytical formula is very close to lab tests results. Lab tests have confirmed an important finding of the analytical calculation: Before sliding:

OPB stress in chain is proportional to the square root of the pretension (T0.5)

OPB stress in chain is inversely proportional to the chain diameter (1/d)

OPB stress in chain is proportional to angle between chain hawse and mooring line (αtotal).

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

0 1 2 3 4 5 6 7

Total chain hawse angle (dg)

Max

imum

ben

ding

str

ess

(Mpa

)

OPB stress analytical OPB stress empirical with 106mmBased on global chain stiffness without 106mm tests OPB stress analyticalBased on global chain stiffness without 106mm tests

Tension: 50 tons, Diameter: 81 mm

Tension: 100 tons, Diameter: 152 mm

Figure 25 - Comparison of empirical and analytical

formulas for OPB stress for a pretension of 50 tons and 100 tons

OPB fatigue damage Knowing the formula to derive OPB stress in chain from chain diameter, tension, and imposed fairlead angle long term distribution, it is possible to derive the OPB fatigue damage. By application of this methodology and comparison of failure times with Girassol failure durations, it was found that DNV B1 curve (for forged elements) is appropriate. The design shall therefore be based on B1-2stdv design curve with a safety factor of 10 as OPB is a new problem still requiring more investigations. Remedial solution: Rod Connecting Arms (RCA) On Girassol, in order to make sure that the top chains would not fail again the root causes of the failure have been tackled:

Reduce bending moment at chain hawse connection by having low friction bushings, double articulations and long lever arms between first chain link and articulation axes. Reducing bending moment directly reduces the bending stresses.

The RCA requires two articulations because the motions of the buoy result in bending in the mooring line plane and transverse to the mooring line plane.

Improve chain cathodic protection to prevent crack pit initiation and reduce fatigue crack growth rate.

Reduce pretension to reduce OPB stresses Increase top chain diameter in the first links subjected

to a significant OPB moment Using the formulas for OPB stress presented in this paper, SBM has designed a safe connection between the buoy and the chain. The RCA is presented below in Figure 26 and Figure 27. The chain and RCA are designed for 20 years accounting for combined tension/tension and OPB fatigue with a safety factor larger than 10.

Figure 26 - Girassol Rod Connecting Arm (RCA)

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12 OTC-17238

Figure 27 – Girassol Rod Connecting Arm mounting on

buoy

The curved chain stopper with only one articulation were replaced offshore with the new RCA in May 2004. Figure 28 shows the exchange performed by the Dynamic Installer.

Figure 28 - RCA load out for replacement of old stoppers

offshore

Conclusion and on going work In this paper, we have shown that vessel rotations applied on a chain under high pretension can lead high Out of Plane Bending (OPB) stresses in the first links close to the chain hawse (fairlead). These OPB stresses have led to failure of 4 chains on Girassol buoy. Lessons learnt from recovered failed links on Girassol buoy, SBM lab tests and analytical analysis are calling for a change of practice in the industry. New rules should include a design methodology to account for OPB stresses in chains. Sufficient data must be gathered to improve our understanding of stresses in chains under high pretensions. Comparison between SBM methodology and Chevron Texaco Finite element work is very encouraging. OPB stress vs interlink angle curves presented in the present paper are confirmed by FEA, see Ref [1]. A combination of FEA (plastic elastic with contact) and lab tests could be used to prepare guidelines for designers. Appropriate S-N curve are difficult to select. B1 - 2 stdv has been used for the purpose of the new deep water buoys designs in SBM. The selection of this curve is supported by the good consistency between the calculated and actual failure times of Girassol chain (4 failure points). Nevertheless, using this curve, we predict that OPB failure should occur on other systems such as Kuito buoy. Kuito chains have been inspected after 4 years of service and no fatigue cracks were found. SBM is currently doing chain failure tests on Girassol curved chainhawse and Kuito straight chain hawse designs. The purpose of these tests is to clarify if the curved chain hawse has enhanced the OPB problem. If this is confirmed by the tests, methodology will be refined to account for effect of curved chain hawse. Then, a less conservative S-N curve and/or stress vs angle curve for chain bending will be derived from the tests results Acknowledgments I would like to thank the management f SBM and TOTAL for giveing us the opportunity to present this paper. I would also like to thank Pedro Vargas from ETC Chevron Texaco for his help in the analyzis of the test data and in the elaboration of the OPB mechanism. References [1] Pedro M. Vargas, ETC, ChevronTexaco, Philippe Jean, SBM; “FEA of Out-of-Plane Fatigue Mechanism of Chain Links”; Proceedings of OMAE 2005.