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Distorted polyester lines for model testing of offshore moored platforms
Ocean Engineering 32 (2005) 817–825 www.elsevier.com/locate/oceaneng
Distorted polyester lines for model testing of offshore moored platforms A.C. Fernandesa,*, R.R. Rossib a
COPPE/UFRJ, Federal University of Rio de Janeiro, Centro de Tecnologia, C203, Caixa Postal 68508, Rio de Janeiro, RJ 21941-972, Brazil b Research Center (CENPES), Oceanic Structures, Petrobras, Rio de Janeiro, Brazil Available online 15 December 2004
Abstract Model tests of floating offshore platforms replace the mooring lines by inextensible cables connected to steel springs with a linear restoring capability. With the help of fundamental investigation on the similarity laws, the present work shows that the use of very thin polyester lines in model scaling is feasible and may allow a better physical representation of the full-scale polyester lines. The proposal is to use polyester lines with length distortion in order to keep the similar restoring capability and therefore, the same non-linear behavior would also be present during the tests. The work describes the application of these ideas in a model test of an Floating Production Storage and Offloading (FPSO) submitted to regular and random waves. The tests include both the linear spring lines and the distorted equivalent polyester lines, holding the FPSO model, submitted transversally to the same waves. q 2004 Elsevier Ltd. All rights reserved. Keywords: Synthetic mooring; Polyester fiber ropes; Model test; Dimensional analysis; Deepwater
1. Introduction The practice of model testing of floating platform particularly for new conceptions has becoming essential in the offshore industry. The tests allow analysts to anticipate problems and increase the possibility of going to full-scale free of unexpected behaviors. These ones are likely to occur for a new system never tried before, even if ones perform extensively computer simulations, usually full of very strict hypothesis concerning, for instance, * Corresponding author. Fax: C55 21 25628715. E-mail address: [email protected] (A.C. Fernandes). 0029-8018/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2004.10.008
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hydrodynamic phenomena. Since the offshore industry is highly dynamic, new systems are showing up all the time and, therefore, the model testing practice is natural. Under this trend, the community faces the problem of the physical modeling of polyester mooring lines. This kind of line is becoming a concrete solution for mooring systems in deepwater all over the world, due to its convenient properties concerning costs, weight, tension, installation, etc. Offshore Brazil, polyester lines hold effectively platforms in place in deep water for more than 7 years (Rossi, 2002). The common practice in model testing of platforms moored with polyester lines is to use linear springs combined with inextensible cables to simulate the lines. The constant values of the stiffness are set up according to the subject in focus during the test. If the focus is the maximum tension in a line, a greater value for the stiffness is usually used. If the interest is more in the maximum offset, a lower value is used. This approach is somewhat time consuming since requires larger test matrix. Besides, perhaps more importantly, for a broad environment analysis it may not be very representative of the polyester behavior since the later is highly non-linear (Fernandes and Rossi, 2002). As shown next, under the light of dimensional analysis, however, the use of linear springs is not the only alternative and that one may bring the polyester behavior into the model testing. The concept is to use a distortion of the model length designed in a manner to take into account the non-linear characteristics of the polyester lines. The ideas are applied in an actual model testing of an Floating Production Storage and Offloading (FPSO) submitted to regular and random waves. Both, the linear springs and the distorted equivalent polyester line, in different comparative tests, holding the FPSO model submitted transversally to the same waves. As clarified during the work, the behavior comparing the two cases is very different showing that the use of linear springs may not be the better option. It seems that this opens a new field for polyester lines model testing with new ways to specify environment combinations. It is also important to say that authors have been suggesting a Joint Industry Project for comparing the measurements with full scale, but this is outside of the present work. Anyway, it seems likely that the linear spring practice, which has itself never been validated, may not be the best idea. The work is based on the master thesis of Rossi (2002). Fernandes and Rossi (2002, 2003) present also some considerations.
2. Polyester Stiffness According to Del Vecchio (1992), the stiffness of the polyester depends on the mean tension level, the amplitude of the tension and the excitation period. Fernandes et al. (1999) suggests a nomenclature for Del Vecchio’s formula for the specific modulus E/r that is reproduced below E Z a C bLm K gLa K d logðtÞ r
(1)
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Fig. 1. Influence of the mean tension on the stiffness.
where Lm is the mean tension, La is the amplitude of tension, t is the excitation period and a, b, g and d are parameters of the expression that, of course, have different dimensions. For the same amplitude of tension and excitation period, if the mean tension increases, the stiffness increases, as shown in Fig. 1. For the same mean tension and excitation period, if the amplitude of tension increases, the stiffness decreases, as shown in Fig. 2.
Fig. 2. Influence of the amplitude of tension on the stiffness.
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Fig. 3. Influence of the excitation period on the stiffness.
For the same mean tension and amplitude of tension, if the excitation period increases, the stiffness decreases, but the change on stiffness is negligible, as shown in Fig. 3.
3. The distorted model Fernandes and Rossi (2002) (see also (Rossi, 2002)) have proposed the distorted length model, as described next. Consider the subscript ‘m’ referred to the model and the subscript ‘p’ referred to the prototype. The stiffness K is given by the ratio between the force F and the displacement x KZ
F x
(2)
Strictly speaking, the stiffness may not be constant due to the non-linear behavior. Therefore, the analysis should be understood dimensionally. Considering l the length scale and using the Froude scaling (Sarpkaya, 1981), the force scale will be l3. Therefore, the stiffness scale will be Kp Fp =xp Fp =Fm l3 Z Z Z Z l2 Km Fm =xm xp =xm l
(3)
The axial stiffness is the longitudinal elasticity modulus E multiplied by the area of transversal section A dividided by the rope length. KZ
EA l
(4)
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Multiplying the numerator and the denominator of the expression (4) by the specific mass of the material r and knowing that r multiplied by A yields the linear mass m of the rope EA r EðrAÞ m Z Z E=r (5) KZ l r rl l E/r is known as specific modulus of elasticity and it is commonly used by the textil industry to synthetic materials (see del Vecchio, 1992; Fernandes et al., 1999). Therefore, for the polyester Kp ðE=rÞp mp =mm Z Z l2 (6) Km ðE=rÞm Lp =Lm The fundamental step is to specify the use of the same material of the synthetic rope of the real scale, i.e. the use of the same specific modulus ðE=rÞp Z1 ðE=rÞm
(7)
Substituting (7) into (6), the ratio between the linear masses follows Lp mp Z l2 mm Lm
(8)
At this moment, it is convenient to introduce a distortion factor fd. This factor is the ratio between the distorted length lm and the length l 0 m and this is the one that obeies the scale between prototype and model, that is Lp Zl lm0 Lm Z 4d lm0
(9) (10)
Now with (9) and (10) into (8), the result is Lp mp l2 Lp l2 Z l2 Z Z l mm 4d lm0 4d lm0 4d Consequently fd is determined by the expression (12) as follows m 4d Z l3 m mp
(11)
(12)
After defining fd, the length of the polyester line yarn (lm) is determined to be used at the model test, using the expressions (9) and (10). The above procedure naturally brings the histeretic characteristics and the fading memory effects of the polyester ropes. These last cosiderations are discussed in Rossi (2002) but are outside the scope of the present work. However, it is important to recall that since Del Vechio (1992) and noticed by Fernandes et al. (1999) the diameter is not an important parameter for the specific modulus (1) determination, at least for the longitudinally assembled cables as the offshore ones. The work uses this fact specifically through Expression (7).
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4. The test and the results The tests were perfomed sending waves over the FPSO model in a 1:90 scale as shown in Fig. 4. The beam waves were used in the model testing with the intention of maximizing the drift and the slowly varying forces. The tests were performed with regular waves and an irregular sea state representing 1-year return period condition of Campos Basin, offshore Brazil. The FPSO hull is a former Very Large Crude Carrier (VLCC) which data are as follows: lengthZ320 m; breadthZ54.54 m; draftZ18,36 m; depthZ28.26 m; displacementZ2,543,972.8 kN; longitudinal position of the center of gravity (LCG)Z10.61 m; vertical position of the center of gravity from the keel (KG)Z14.57 m; transversal radius of gyrationZ18.86 m. Four horizontal lines were used to moor the VLCC in order to avoid other effects like mooring line damping. As a matter of comparison, two systems were tested: – with lines composed by polyester yarns representing the polyester rope in real scale (new alternative proposition); – with linear springs representing the stiffness used for line (usual procedure). In Fig. 4 below it is shown a sketch of the test using polyester yarns. An arrangement with linear springs is similar. Fig. 5 shows that, the tension in the Starboard side-Bow line (for a regular wave with 1 cm of amplitude) for the model using polyester yarn (SB) is lower than in the one using
Fig. 4. Model test using polyester yarn; similar arrangement with linear springs.
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Fig. 5. Tensions at Starboard side-Bow line (please note that there are two tests for the SB -polyester rope-case at 1.4 s).
linear spring (SB-S). The difference between them is greater near the roll natural frequency. Fig. 6 shows the time history of the wave amplitude for both systems: linear springs and polyester. For both cases, the excitation is the same.
Fig. 6. Wave amplitude time history.
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Fig. 7. Sway motion on both systems.
On the other hand, the sway motion is not the same probably due to the non-linearity of the polyester not present in the spring assembly (Fig. 7). Consequently, the line tensions will also be the different (Fig. 8). The comparison may go on and several different behaviors have been noticed. One very important behavior is that after a series of large waves, the response of the system with linear springs is different from the response of the system with polyester lines. The authors are under impression that this difference is not because of damping in the polyester line but
Fig. 8. Tension at the most tensioned line.
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due to change of natural period of the system. As shown in the Expression (1), the stiffness of the polyester decreases with the increasing of tension amplitude. Since the stiffness decreased, the natural period increased, as would be expected in full scale. Of course, this non-linear behavior has never occurred with the linear springs. It is important to mention that tests in regular waves and random sea showed an average dynamic tension reduction of 20% approximately. Finally one may consult Rossi (2002) about coping with very long lines (basically performing tests in long Ocean Basins or pulleys) and how to keep the hydrodynamic damping characteristics (essentially using dummy non-structural covers in the water). 5. Conclusions The work then recommends the use of the same material at model tests, in order to represent the non-linear characteristics of the polyester. The use of polyester yarns in model tests to represent the polyester ropes in real scale is feasible. The use of polyester yarns yielded lower dynamic tension than the spring lines. This fact is extremely important for fatigue analysis mainly if there are weaker materials, like Kenter links, in the mooring lines. Due to the use of the same full scale polyester material, this work is under the impression that with the proposed distortion procedure, it is possible now to bring the complete polyester behavior to the model scale. Acknowledgements The author thanks PETROBRAS for the support and the inclination of performing scientific and technological researches. The first author also thanks the support of CPNq, The Brazilian National Research Council.
References Del Vecchio, C.J.M, 1992. Light Weight Material for Deep Water Moorings, PhD Thesis, University of Reading. Fernandes, A.C., Del Vecchio, C.J.M., Castro, G.A.V., 1999. Mechanical properties of polyester mooring cables. International Journal of Offshore and Polar Engineering. 9 (3), 208–213. Fernandes, A.C., Rossi, R.R., 2002. On the model scaling of polyester mooring lines for offshore applications, 21st International Conference on Offshore Mechanics and Arctic Engineering, OMAE2002, June 8–13, Oslo, Norway 2002. Fernandes, A.C., Rossi, R.R., 2003. Distorted polyester lines for reduced model testing of offshore mooring lines, in: Zhang, J., Mercier, R.S. (Eds.), International Symposium on Deepwater Mooring Systems: Concepts, Design, Analysis and Materials, Houston, TX, USA. Rossi, R.R., 2002. Polyester Ropes for Mooring Oceanic Platforms in Ultra Deep Waters, COPPE/UFRJ, MSc, Thesis (in Portuguese). Sarpkaya, T., Isaacson, M., 1981. Mechanics of Wave Forces on Offshore Structures. Van Nostrand Reinhold Company.
Distorted polyester lines for model testing of offshore moored platforms A.C. Fernandesa,*, R.R. Rossib a
COPPE/UFRJ, Federal University of Rio de Janeiro, Centro de Tecnologia, C203, Caixa Postal 68508, Rio de Janeiro, RJ 21941-972, Brazil b Research Center (CENPES), Oceanic Structures, Petrobras, Rio de Janeiro, Brazil Available online 15 December 2004
Abstract Model tests of floating offshore platforms replace the mooring lines by inextensible cables connected to steel springs with a linear restoring capability. With the help of fundamental investigation on the similarity laws, the present work shows that the use of very thin polyester lines in model scaling is feasible and may allow a better physical representation of the full-scale polyester lines. The proposal is to use polyester lines with length distortion in order to keep the similar restoring capability and therefore, the same non-linear behavior would also be present during the tests. The work describes the application of these ideas in a model test of an Floating Production Storage and Offloading (FPSO) submitted to regular and random waves. The tests include both the linear spring lines and the distorted equivalent polyester lines, holding the FPSO model, submitted transversally to the same waves. q 2004 Elsevier Ltd. All rights reserved. Keywords: Synthetic mooring; Polyester fiber ropes; Model test; Dimensional analysis; Deepwater
1. Introduction The practice of model testing of floating platform particularly for new conceptions has becoming essential in the offshore industry. The tests allow analysts to anticipate problems and increase the possibility of going to full-scale free of unexpected behaviors. These ones are likely to occur for a new system never tried before, even if ones perform extensively computer simulations, usually full of very strict hypothesis concerning, for instance, * Corresponding author. Fax: C55 21 25628715. E-mail address: [email protected] (A.C. Fernandes). 0029-8018/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2004.10.008
818
A.C. Fernandes, R.R. Rossi / Ocean Engineering 32 (2005) 817–825
hydrodynamic phenomena. Since the offshore industry is highly dynamic, new systems are showing up all the time and, therefore, the model testing practice is natural. Under this trend, the community faces the problem of the physical modeling of polyester mooring lines. This kind of line is becoming a concrete solution for mooring systems in deepwater all over the world, due to its convenient properties concerning costs, weight, tension, installation, etc. Offshore Brazil, polyester lines hold effectively platforms in place in deep water for more than 7 years (Rossi, 2002). The common practice in model testing of platforms moored with polyester lines is to use linear springs combined with inextensible cables to simulate the lines. The constant values of the stiffness are set up according to the subject in focus during the test. If the focus is the maximum tension in a line, a greater value for the stiffness is usually used. If the interest is more in the maximum offset, a lower value is used. This approach is somewhat time consuming since requires larger test matrix. Besides, perhaps more importantly, for a broad environment analysis it may not be very representative of the polyester behavior since the later is highly non-linear (Fernandes and Rossi, 2002). As shown next, under the light of dimensional analysis, however, the use of linear springs is not the only alternative and that one may bring the polyester behavior into the model testing. The concept is to use a distortion of the model length designed in a manner to take into account the non-linear characteristics of the polyester lines. The ideas are applied in an actual model testing of an Floating Production Storage and Offloading (FPSO) submitted to regular and random waves. Both, the linear springs and the distorted equivalent polyester line, in different comparative tests, holding the FPSO model submitted transversally to the same waves. As clarified during the work, the behavior comparing the two cases is very different showing that the use of linear springs may not be the better option. It seems that this opens a new field for polyester lines model testing with new ways to specify environment combinations. It is also important to say that authors have been suggesting a Joint Industry Project for comparing the measurements with full scale, but this is outside of the present work. Anyway, it seems likely that the linear spring practice, which has itself never been validated, may not be the best idea. The work is based on the master thesis of Rossi (2002). Fernandes and Rossi (2002, 2003) present also some considerations.
2. Polyester Stiffness According to Del Vecchio (1992), the stiffness of the polyester depends on the mean tension level, the amplitude of the tension and the excitation period. Fernandes et al. (1999) suggests a nomenclature for Del Vecchio’s formula for the specific modulus E/r that is reproduced below E Z a C bLm K gLa K d logðtÞ r
(1)
A.C. Fernandes, R.R. Rossi / Ocean Engineering 32 (2005) 817–825
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Fig. 1. Influence of the mean tension on the stiffness.
where Lm is the mean tension, La is the amplitude of tension, t is the excitation period and a, b, g and d are parameters of the expression that, of course, have different dimensions. For the same amplitude of tension and excitation period, if the mean tension increases, the stiffness increases, as shown in Fig. 1. For the same mean tension and excitation period, if the amplitude of tension increases, the stiffness decreases, as shown in Fig. 2.
Fig. 2. Influence of the amplitude of tension on the stiffness.
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Fig. 3. Influence of the excitation period on the stiffness.
For the same mean tension and amplitude of tension, if the excitation period increases, the stiffness decreases, but the change on stiffness is negligible, as shown in Fig. 3.
3. The distorted model Fernandes and Rossi (2002) (see also (Rossi, 2002)) have proposed the distorted length model, as described next. Consider the subscript ‘m’ referred to the model and the subscript ‘p’ referred to the prototype. The stiffness K is given by the ratio between the force F and the displacement x KZ
F x
(2)
Strictly speaking, the stiffness may not be constant due to the non-linear behavior. Therefore, the analysis should be understood dimensionally. Considering l the length scale and using the Froude scaling (Sarpkaya, 1981), the force scale will be l3. Therefore, the stiffness scale will be Kp Fp =xp Fp =Fm l3 Z Z Z Z l2 Km Fm =xm xp =xm l
(3)
The axial stiffness is the longitudinal elasticity modulus E multiplied by the area of transversal section A dividided by the rope length. KZ
EA l
(4)
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Multiplying the numerator and the denominator of the expression (4) by the specific mass of the material r and knowing that r multiplied by A yields the linear mass m of the rope EA r EðrAÞ m Z Z E=r (5) KZ l r rl l E/r is known as specific modulus of elasticity and it is commonly used by the textil industry to synthetic materials (see del Vecchio, 1992; Fernandes et al., 1999). Therefore, for the polyester Kp ðE=rÞp mp =mm Z Z l2 (6) Km ðE=rÞm Lp =Lm The fundamental step is to specify the use of the same material of the synthetic rope of the real scale, i.e. the use of the same specific modulus ðE=rÞp Z1 ðE=rÞm
(7)
Substituting (7) into (6), the ratio between the linear masses follows Lp mp Z l2 mm Lm
(8)
At this moment, it is convenient to introduce a distortion factor fd. This factor is the ratio between the distorted length lm and the length l 0 m and this is the one that obeies the scale between prototype and model, that is Lp Zl lm0 Lm Z 4d lm0
(9) (10)
Now with (9) and (10) into (8), the result is Lp mp l2 Lp l2 Z l2 Z Z l mm 4d lm0 4d lm0 4d Consequently fd is determined by the expression (12) as follows m 4d Z l3 m mp
(11)
(12)
After defining fd, the length of the polyester line yarn (lm) is determined to be used at the model test, using the expressions (9) and (10). The above procedure naturally brings the histeretic characteristics and the fading memory effects of the polyester ropes. These last cosiderations are discussed in Rossi (2002) but are outside the scope of the present work. However, it is important to recall that since Del Vechio (1992) and noticed by Fernandes et al. (1999) the diameter is not an important parameter for the specific modulus (1) determination, at least for the longitudinally assembled cables as the offshore ones. The work uses this fact specifically through Expression (7).
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4. The test and the results The tests were perfomed sending waves over the FPSO model in a 1:90 scale as shown in Fig. 4. The beam waves were used in the model testing with the intention of maximizing the drift and the slowly varying forces. The tests were performed with regular waves and an irregular sea state representing 1-year return period condition of Campos Basin, offshore Brazil. The FPSO hull is a former Very Large Crude Carrier (VLCC) which data are as follows: lengthZ320 m; breadthZ54.54 m; draftZ18,36 m; depthZ28.26 m; displacementZ2,543,972.8 kN; longitudinal position of the center of gravity (LCG)Z10.61 m; vertical position of the center of gravity from the keel (KG)Z14.57 m; transversal radius of gyrationZ18.86 m. Four horizontal lines were used to moor the VLCC in order to avoid other effects like mooring line damping. As a matter of comparison, two systems were tested: – with lines composed by polyester yarns representing the polyester rope in real scale (new alternative proposition); – with linear springs representing the stiffness used for line (usual procedure). In Fig. 4 below it is shown a sketch of the test using polyester yarns. An arrangement with linear springs is similar. Fig. 5 shows that, the tension in the Starboard side-Bow line (for a regular wave with 1 cm of amplitude) for the model using polyester yarn (SB) is lower than in the one using
Fig. 4. Model test using polyester yarn; similar arrangement with linear springs.
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Fig. 5. Tensions at Starboard side-Bow line (please note that there are two tests for the SB -polyester rope-case at 1.4 s).
linear spring (SB-S). The difference between them is greater near the roll natural frequency. Fig. 6 shows the time history of the wave amplitude for both systems: linear springs and polyester. For both cases, the excitation is the same.
Fig. 6. Wave amplitude time history.
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Fig. 7. Sway motion on both systems.
On the other hand, the sway motion is not the same probably due to the non-linearity of the polyester not present in the spring assembly (Fig. 7). Consequently, the line tensions will also be the different (Fig. 8). The comparison may go on and several different behaviors have been noticed. One very important behavior is that after a series of large waves, the response of the system with linear springs is different from the response of the system with polyester lines. The authors are under impression that this difference is not because of damping in the polyester line but
Fig. 8. Tension at the most tensioned line.
A.C. Fernandes, R.R. Rossi / Ocean Engineering 32 (2005) 817–825
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due to change of natural period of the system. As shown in the Expression (1), the stiffness of the polyester decreases with the increasing of tension amplitude. Since the stiffness decreased, the natural period increased, as would be expected in full scale. Of course, this non-linear behavior has never occurred with the linear springs. It is important to mention that tests in regular waves and random sea showed an average dynamic tension reduction of 20% approximately. Finally one may consult Rossi (2002) about coping with very long lines (basically performing tests in long Ocean Basins or pulleys) and how to keep the hydrodynamic damping characteristics (essentially using dummy non-structural covers in the water). 5. Conclusions The work then recommends the use of the same material at model tests, in order to represent the non-linear characteristics of the polyester. The use of polyester yarns in model tests to represent the polyester ropes in real scale is feasible. The use of polyester yarns yielded lower dynamic tension than the spring lines. This fact is extremely important for fatigue analysis mainly if there are weaker materials, like Kenter links, in the mooring lines. Due to the use of the same full scale polyester material, this work is under the impression that with the proposed distortion procedure, it is possible now to bring the complete polyester behavior to the model scale. Acknowledgements The author thanks PETROBRAS for the support and the inclination of performing scientific and technological researches. The first author also thanks the support of CPNq, The Brazilian National Research Council.
References Del Vecchio, C.J.M, 1992. Light Weight Material for Deep Water Moorings, PhD Thesis, University of Reading. Fernandes, A.C., Del Vecchio, C.J.M., Castro, G.A.V., 1999. Mechanical properties of polyester mooring cables. International Journal of Offshore and Polar Engineering. 9 (3), 208–213. Fernandes, A.C., Rossi, R.R., 2002. On the model scaling of polyester mooring lines for offshore applications, 21st International Conference on Offshore Mechanics and Arctic Engineering, OMAE2002, June 8–13, Oslo, Norway 2002. Fernandes, A.C., Rossi, R.R., 2003. Distorted polyester lines for reduced model testing of offshore mooring lines, in: Zhang, J., Mercier, R.S. (Eds.), International Symposium on Deepwater Mooring Systems: Concepts, Design, Analysis and Materials, Houston, TX, USA. Rossi, R.R., 2002. Polyester Ropes for Mooring Oceanic Platforms in Ultra Deep Waters, COPPE/UFRJ, MSc, Thesis (in Portuguese). Sarpkaya, T., Isaacson, M., 1981. Mechanics of Wave Forces on Offshore Structures. Van Nostrand Reinhold Company.