10 th South African Conference on Computational and Applied Mechanics Potchefstroom 3 5 October 2016 MODELLING MOORING LINE BEHAVIOUR TO DETERMINE THE IMPACT FORCE ON SQUID EGG BEDS Vutlhari A Maluleke* 1, Graeme J Oliver 2, Michael J. Roberts 3 Organization(s): 1: Cape Peninsula University of Technology, South Africa; 2: Cape Peninsula University of Technology, South Africa; 3: Nelson Mandela Metropolitan University, South Africa 1 vutlharimabasa@gmail.com 2 oliverg@cput.ac.za 3 mike.roberts@nmmu.ac.za ABSTRACT In South Africa, squid fishing vessels need to find and then anchor above benthic squid egg beds to effect viable catches. However, waves acting on the vessel produce a dynamic response on the anchor line. These oscillatory motions produce impact forces of the chain striking the seabed. It is hypothesised that this causes damage to the squid egg bed beneath the vessels. Different mooring systems may cause more or less damage and this is what is investigated in this research. The commercial package ANSYS AQWA is used in the study to model the incoming wave and moored vessel motion and forces. The dynamic motion of the mooring line and its impact on the seabed is investigated beyond what is output from ANSYS AQWA using ABAQUS finite element analysis. Initial results for the motion of mooring line shows that there is contact force between the seabed and the mooring line. The impact pressure of the anchor chain is obtained by solving a contact problem in ABAQUS. The dynamic structural solution in ABAQUS is obtained utilising the tension on the cable from the vessel motion for a particular mooring and wave excitation. The impact pressure is found in contact so that we can determine what kind of damage would be done to the seabed with various mooring options under different ocean conditions. KEYWORDS Mooring line, seabed, contact pressure, ocean waves, vessel. 1. INTRODUCTION The South African chokka squid fishery is based in the Eastern Cape between Plettenberg Bay and Port Alfred, and is a major source of foreign revenue as the entire catch, on average some 8000 t, is exported to Europe. The fleet comprises 138 vessels ranging between 11 and 20 m in length, and cable of 3 weeks at sea (Figure 1a). Each vessel carries about 22 fishermen who land the squid using hand-held jigs on fishing line. This number excludes the number of crew who are not allowed to fish. Commercial squid fishing is only viable when the vessels are above spawning aggregations formed in the water column above egg beds on the seafloor (Figure 1b). Egg beds comprise hundreds of thousands of translucent, slim and slimy egg capsules about 15 cm in length that are glued to the bottom substrate forming massive mats often spanning tens of meters. Hatching occurs about 3 weeks from spawning. Traditionally, the fishing vessels position themselves above an egg bed using a single mooring system with the anchor dropped upwind of the egg bed. A significant part of the chain lies on the seafloor over eggs. Waves acting on the vessel set up dynamic behaviour in the mooring line which rapidly lifts the chain off the seabed, dropping it back with considerable force on the bottom (Sarkar & Taylor, 2001), and possibly damaging squid eggs. As sea and wind conditions change daily, vessels regularly pick up anchor and relay the anchor chain. In 2010, a new double anchor system was introduced and used by about 10 vessels. This V shaped anchor line configuration offers vessels greater position control over the egg beds but potentially doubles the impact of the chain on the eggs. In 2013, the chokka squid fishery crashed and has not recovered. Concern has been raised by both fisheries managers and boat owners that the chain impact especially from the double anchor system maybe causing excessive damage to the squid eggs reducing recruitment.
Figure 1. A chokka squid fishing vessel anchored above an active egg bed. These egg masses can extend over an area as large as 10 000 m 2 This study is the first part of an investigation into the impact of anchor chains on the seabed; it focuses on the mechanical chain system under various wave height scenarios. The second part of the investigation to be done after these results are available will then study the damage and consequences of the chain impact on the egg beds and hatching success. The numerical investigation of the behaviour of the mooring line and seabed interaction is performed here using ANSYS AQWA software to obtain structural motion and forces in the time domain, and by the ABAQUS finite element model to determine the impact force on the seabed. 2. MOORING SYSTEM DESCRIPTION Figure 2 presents a schematic of a single mooring system which is made up of three components the anchor, chain, and vessel (Vineesh et al., 2014). Figure 2. Mooring system The Klusman 100 150 kg anchor is mostly used by the chokka fishery with about 100 m of 20 mm link diameter steel chain. Chain weight, therefore, ranges between 9 and 10.8 kg/m. The chain controlled by a winch on the vessel s foredeck that feeds chain through the fairlead on the vessel s bow. There are two types of chain links namely studless and studded. The studded chain link is designed to prevent knot formation but is more susceptible to fatigue failure than the studless link (ABC Moorings, n.d.). In mechanics, the chain component is characterised by strong catenary stiffness (effect), low elasticity, high breaking strength and is relatively heavy. As shown, the mooring system is subjected to varying wind, waves and current, all of which introduce dynamic behaviour into the mooring line. The part of a mooring line that lies on the seabed is termed grounded chain while that suspended in the water column the catenary. The touchdown point is a position along the mooring where the chain begins lifting off the seabed. This point varies and is based on the sea conditions. Pellegrino and Ong, (2003) demonstrated that when the mooring chain is excited due to wave action loading, the chain dynamically interacts with the seabed; which creates a boundary condition that varies in time and in space. This is because of the significant change 2
in the chain s longitudinal profile resulting in a corresponding lifting off or touchdown action in the chain s Figure 3. Mooring line touchdown points resulting in time-varying boundary conditions (http://www-civ.eng.cam.ac.uk/dsl/ppao2/) touchdown position (Yu & Tan, 2006). This is illustrated in Figure 3 and can be modelled using a dynamic simulation which accounts for the application of loads on the system over time with consideration of wave inertia forces and structural damping. 3. MATHEMATICAL FORMULATION FOR ANALYSING THE MOORING SYSTEM 3.1. Structural dynamic equations The coupled dynamic deterministic model involves the formulation of a non-linear stiffness matrix which reflects mooring line tension fluctuations due to variable buoyancy and other non-linearities. The model requires that the selection and solution of wave theory to reasonably represent the water particle kinematics to estimate drag and inertia for all the six degrees of freedom. The statically coupled problem is solved iteratively using the Newton-Raphson method. The time domain is numerically integrated to solve the equations of motion and to obtain the response time histories (Jameel et al., 2011). The equation of motion describing the mooring system equilibrium between inertia, damping, restoring and exciting forces can be assembled as follows: Where, = Total mass matrix (Structural mass and added mass) t (1) = Damping matrix (simulated using Rayleigh Damping in Abaqus) = Total Stiffness matrix (consist of Elastic and Geometric stiffness matrix) {x}= 6 DOF structural displacements t = Excitation forces The added mass of the structure occurs due to the water surrounding the entire structure. The overall damping to the system is being offered by structural and hydrodynamic damping. The major damping is induced due to the hydrodynamic effects. This structural damping is simulated by Rayleigh damping (Jameel et al., 2011). Hydrodynamic damping is dominant in case of oscillating slender surrounded by water. 3
3.2. Cable motion equations in ANSYS AQWA Figure 4. Forces on a Chain Element (Adapted from ANSYS Aqwa, 2015) There are various forces that act on the mooring line; a single element of circular slender cable is shown in Figure 4, it shows the single element subjected to external hydrodynamic loadings and structural inertial loading (ANSYS Aqwa, 2015): The motion equation of this cable element is (2) is the structural mass per unit length is the distributed moment loading per unit length is the position vector of the first node of the cable element and are the length and diameter of the element respectively and are the element weight and external hydrodynamic loading vectors per unit length respectively is the tension force vector at the first node of the element is the bending moment vector at the first node of the element is the shear force vector at the first node of the element The dynamic response of the cable with bending governed by Equation 2 is solved numerically by employing the discrete Lump-Mass model in ANSYS AQWA. The entire mooring line is treated as a slender structure where nonlinear partial differential equations are used to compute the cable dynamics (Yu & Tan, 2006). 4
4. MOORING LINE SIMULATION METHODOLOGY In this study, the mooring line system is first modelled in ANSYS AQWA which models the incoming wave and moored vessel motion and forces in the time domain. The dynamic motion of the mooring line and its impact on the seabed is investigated beyond what is output from ANSYS AQWA using ABAQUS finite element analysis software. A two-dimensional finite element model is created in ABAQUS for the numerical analysis of the mooring line and seabed interaction. The model built in ANSYS AQWA accounts for the different directions of motion of the moored structure excited by different wave amplitudes. Figure 5 below shows the ANSYS AQWA model for the mooring system. Figure 5. ANSYS AQWA model of the mooring system in 2D and 3D model Figure 5 shows the mooring line system attached to a vessel. The clump weight of an insignificant mass is shown by the round yellow object in the figure above for tracking the actual chain displacement to be used for ABAQUS simulation. The vessel and the mooring line are both under the influence of wave forces. The mooring line is shown to be in contact with the seabed and has a catenary profile. Table 1 shows the dimensions of the vessel, the point mass which is the mass inertia matrix that is defined via the Radius of Gyration of the vessel. The K xx of the vessel is defined by K xx=0.34*width of the vessel, K yy = 0.25*Length, and K zz = 0.26*Length. The mass of the vessel is 127 364. Table 1. Vessel data Vessel Details Parameter Value Units Vessel dimensions 17 (Length) x 6 (width) x 3 (depth) K xx 2.04 K yy 4.25 K zz 4.42 Mass 127 364 Table 2 below shows the mooring line data. A studless chain link was used in this study. The test data obtained showed the mooring line weight per unit length to be 10 /. The maximum allowable tension of the mooring is 36. The mooring chain is solved as a catenary section with a circular diameter of 0.02 and a crosssectional area of 0.00031. The stiffness of the chain is defined by E which is the elastic modulus of the structure and the cross-sectional area. The Added Mass Coefficient and Longitudinal Drag Coefficient are the program s default values. The data in Table 1 and 2 is entered manually by either calculations or is obtained from literature who did similar work in similar conditions. 5
Table 2. Mooring line data Mooring Line Details Parameter Value Units Mooring Line Length 95 Mass/Unit Length 10 / Equivalent Cross-Sectional Area 0.006 Stiffness, EA 7 696 920.01 Maximum Tension 36 000 Added Mass Coefficient 1 - Transverse Drag Coefficient 1 - Equivalent Diameter 0.09 Longitudinal Drag Coefficient 0.025 - The above data is required to fully define the ANSYS AQWA model and is solved using a Time Response approach which calculates the dynamic forces and motion of the structure in time. 5. NUMERICAL SIMULATION The nature of the problem in this investigation suggests the use of coupled dynamic approach where the interaction of the mooring line and the vessel motion is modelled directly. ANSYS AQWA Time Response analysis offers this option. 5.1. Numerical simulation results in ANSYS AQWA When a 1 wave amplitude is applied for a period of 4.6 for a duration of 600, the dynamic simulation results in Figure 6 are obtained. The wave condition described on the latter best describes the actual chain motion in water. Figure 6. Horizontal motion of the vessel and vertical motion of the vessel As can be seen from Figure 6, the vessel s position is very unstable at the beginning of the simulation, the vessel starts to develop a more stable pattern after about 150. The vessel initial position is 29 m from its origin. The origin of the vessel is on it s on its stern while the mooring line is attached to the bow. The vessel then gradually moves closer to the origin where the mooring line takes the catenary profile which is typical for moored vessels. The catenary profile shows that the vessel is under tension because to the action of wave forces acting on it. A more stable pattern is developed after 150 seconds and the vessel oscillates between the range of 5 and 6 m. 6
Whereas the heave (vertical) motion of the vessel oscillates between a range of about 0.95 and -0.77. The vertical oscillation of the vessel is directly proportional to 1 wave excitation. Figure 7 below show the chain motion tracked on the clump weight. This point was tracked in the x and y directions to obtain results shown in figure 6 below and the data is used in the ABAQUS model to excite the mooring line. Resultant motion (m) 3 2 1 0 17 m vessel resultant XY motion 0 10 20 30 40 50 60 Time (s) Figure 7. Chain motion in x and y directions Table 3 below shows the ocean environment condition selected for the analysis. Linear wave (Airy wave) was selected for regular ocean waves. This is considered as the simplest ocean wave and is based on the assumption of homogeneous, incompressible, inviscid fluid and irrotational flow. Table 3. Ocean environment data Ocean Environment Properties Parameter Value Units Water Density 1025 / Ocean Depth 30 Wave Type Airy wave theory/ Regular wave - Figure 8 below shows how pre-tension varies along the length of the chain. As expected, the ground part of the chain is assumed to have zero tension. This graph shows pre-tension force decrease along the line as the depth of the sea increases. The touchdown point is at about 60 away from the anchor point. Figure 8. Pre-tension Force along the mooring line The time response of the chain mooring line is shown in Figure 9 below which shows the time history of the tension force acting on the mooring line. The maximum tension force experienced by the mooring line is 22 and the minimum tension force is 650. The tension force is zero when the chain is slack. 7
Mooring Line Tension (N) 25 000,00 20 000,00 15 000,00 10 000,00 5 000,00 0,00-5 000,00 Mooring linetension time history 0 5 10 15 20 25 30 Time (s) Figure 9: Tension Force along the mooring line The mooring line force has been found to be of vital importance in this study. It has been found that the mooring line force increases as the wave amplitude increases. The horizontal forces on the vessel are greater than the vertical forces. This correlates with the purpose of mooring lines which is to limit the horizontal motion of a vessel. This observation was a result of applying a wave amplitude of 0.5 to 1.5. Wave height by definition is two times the wave amplitude. In general, the waves of 1 to 3 were evaluated in this study to be able to see the trend of the behaviour of the vessel at sea and the corresponding mooring forces. Figure 10 shows the mooring line forces when 1 wave amplitude excites the vessel. The maximum mooring line force in the horizontal direction is 15 692.83 while the minimum is -452.34 ; whereas the maximum vertical mooring line force is 389.75 while the minimum force -17 222.05. Table 4 shows the summary of the results obtained from ANSYS AQWA when the wave amplitude was varied. Figure 10: Mooring line horizontal forces and vertical forces with 1 m wave excitation Table 4. Mooring line forces with varying wave amplitude x x y y Wave amplitude (m) Max (N) Min (N) Max (N) Min (N) 0.5 902.64-20.40-220.78-3 683.13 1 15 692.83-452.34 389.75-17 222.05 1.5 33 041.95-1 278.40 807.90-26 046.50 8
5.2. Numerical simulation model in ABAQUS ABAQUS has a nonlinear option to solve dynamic problems. The model shows a section of the chain that was used for tracking using Tracker software; the model only analyses the length of the mooring up to the reference point which was used for tracking. The height of the reference point used for tracking is 15. The finite element model shown in figure 11 has been built for analysing the mooring line and seabed interaction. The properties of the data used to build the model are shown in Table 2. The wave amplitude for the simulation is 1 and wave period is 4.6. The computation lasts for 600. Hybrid beam elements with quadratic formulation were used to model the chain mooring because of their ability to handle very slender non-linear geometries, where the axial stiffness of the beam is very large compared to the bending stiffness (Abaqus Theory manual, 2012). This formulation has better convergence and is a good approximation of the chain mooring line. Dongsheng Qiao (2014) also used hybrid beam elements to simulate the mooring line (Qiao et al., 2014). Dashpots were used to account for mooring line damping with a coefficient of 0.3. The model is solved using ABAQUS/Standard dynamic implicit analysis taking geometric non-linearities into account. Displacement/Rotation boundary condition was used at the mooring line fairlead point and the displacement was applied as tabular amplitudes. Figure 11. ABAQUS model with dashpots and with loads and boundary conditions 5.3. Contact problem The contact between the mooring line and seabed is an important consideration in both theory and practical applications. When contact is analysed in the ABAQUS model in the contact zone, the final state of offsets and tractions depends on the entire loading history. The problem has to be solved by applying the load incrementally. The contact algorithms in ABAQUS/Standard are designed to handle a large class of contact problems for which small-sliding contact formulation and master/slave algorithm can be used. The seabed is modelled as a master surface and the mooring line as a slave surface. The seabed is modelled as a fixed boundary across its entire length. The formulation assumes that the surfaces may undergo arbitrarily large rotations but that a slave node will interact with the same local area of the master surface throughout the analysis. A tangential behaviour option with friction formulation was used to describe the kind of contact between the mooring line and seabed. The friction coefficient of 0.74 recommended by Taylor and Valent which describes the roughness of seabed sand was used (Taylor & Valent, 1984). 9
5.4. Mooring line Tracker data analysis in ABAQUS This section presents results obtained by using a video motion analysis software Tracker for tracking the mooring line displacement under wave influence over time. The output from Tracker is shown in the Figure 12 below. These results are used as input for the ABAQUS model shown in Figure 13. The video analysis data showed the mooring line vertical displacement to be the most dominant compared to the horizontal motion. Furthermore, it was also noticed that part of the mooring line reached a maximum of about 2.5 vertical displacement under wave excitation; the chain then dropped back down to the seabed and lies for a certain amount of time and then lift up again. This behaviour is what is modelled in ABAQUS in order to determine the contact force with the seabed. Mooring line motion in x (m) Horizontal motion of the mooring line tracked at sea 1,5 1 0,5 0-0,5-1 0 5 10 Time (s) Mooring line motion in y (m) 3 2 1 0-1 Vertical motion of the mooring line tracked at sea 0 2 4 6 8 10 Time (s) Figure 12. Horizontal motion of the mooring line and vertical motion of the mooring line tracked at sea Figure 13 below shows the horizontal and vertical displacement of the mooring line when excited by the vertical motion obtained from Tracker. The vertical displacement reaches a maximum of 7.32 with the corresponding horizontal displacement of 1.5. Figure 13. Horizontal and vertical mooring line displacement in ABAQUS Figure 14 shows the maximum and minimum contact pressure on the seabed to be 68.30 and 9.45 respecticely. These result show that contact pressure on the seabed varies with time. The contact area of a single chain link varies depending on its orientation when in contact. When applying the pressure formula as follows: 10
The project contact area of a single chain link is 0.001 and the calculated surface area is 0.006. This means that the contact force on the seabed will vary depending on the single chain link orientation in contact. Figure 14. Maximum and minimum seabed contact pressure The ABAQUS model velocity showed to be in alignment with the measured velocity obtained Tracker. This shows that the ABAQUS model properly simulates the effect of the vertical motion of the mooring line contact with the seabed. Figure 15. Mooring line vertical velocity and vertical velocity tracked at sea 5.5. Mooring line ANSYS AQWA data analysis in ABAQUS Figure 16 below shows the data obtained from ANSYS AQWA model. This data helps on further analysis of the effects of the hydrodynamic environment on the boat and the mooring line. The tracked data of the mooring line at sea was used to calibrate the ANSYS AQWA model in order to evaluate other possible wave environment conditions effect on the mooring line behaviour. The ANSYS AQWA model mooring line displacements are in agreement with the tracked motion; the difference is the vertical motion which peaks to 3.5 in ANSYS AQWA. In Figure 16 shows the mooring line vertical displacement is dominant than the horizontal motion. This aligns well with the observation made from the data obtained by tracking the mooring line at sea as discussed in the previous section above. These results were obtained when a 1 wave height with a period of 4.6 for a duration of 600. 11
Mooring line motion in x (m) Horizontal motion of the mooring line from ANSYS AQWA 0,5 0,4 0,3 0,2 0,1 0 0 10 20 30 40 Time (s) Mooring line motion in y (m) Vertical motion of the mooring line from ANSYS AQWA 4 3 2 1 0 0 10 20 30 40 Time (s) Figure 16. Horizontal and vertical motion of the mooring line tracked using a clump weight marker When the vertical excitation of the mooring line from ANSYS AQWA analysis is used to determine the contact pressure on the seabed. The contact pressure in Figure 17 is obtained showing the maximum and the minimum contact pressure of 138.46 and 3.64. Figure 17. Maximum and minimum seabed contact pressure obtained using ANSYS AQWA data 6. CONCLUSION It is hypothesised that squid fishing vessels off the South African coast, destroy benthic squid egg beds as a result of mooring line movements. Given the large number of vessels in the fishery, this could influence recruitment and hence the squid stock biomass (and ultimately catches). The objective of this work has been to analyse the mooring line interaction with seabed under the influence of ocean waves. The motions and structural forces were first modelled in ANYS AQWA hydrodynamic software which accounts for the environmental loads. We have been able to develop a modelling system that allows us to study the mooring line contact with the seabed for different wave conditions as well as different chain types and single or two point moorings. The linked simulation procedures have enabled us to determine the effect of ocean conditions such as the wave amplitude on mooring line impact on the seabed. It is shown in this study that an increase in wave height leads to an increase in the forces acting on the mooring line in the horizontal direction. The mooring line motion showed to have greater vertical displacement than the horizontal displacement; whereas the horizontal forces of the mooring line were found to be significant and greater than the vertical forces. So the drag of the chain on the seabed is significant. The corresponding vertical mooring force also increases. The ABAQUS model has made it possible to quantify the amount of impact force. Frictional contact between the seabed and the mooring line has also been found to be a significant factor in this study. The tension along the mooring line decreases with the increase in depth. The mooring line forces significantly influences contact with seabed especially the horizontal component of the mooring force. Future work will focus on finding ways 12
to develop seabed soil models for deformable analyses. This will include finding different seabed surfaces and compositions in order to determine the actual chain mooring line impact on the seabed. This could also relate to the position of the boat relative to the mooring line touchdown point to minimise tension as the boat rides a wave. This will also be looked at for a two-point mooring system. REFERENCES 1 Abaqus Theory manual. 2012. Abaqus 6.1 2. 2 ABC Moorings. Mooring Lines. http://abc-moorings.weebly.com/mooring-lines.html 2 April 2015. 3 ANSYS Aqwa Theory Manual. 2015. Aqwa Theory Manual. 4 Chrolenko, M.O. 2013. Dynamic Analysis and Design of Mooring Lines. 5 Ebbesen, C. 2013. Analysis of Motions and Anchor Line Forces for Floating Production Units. Norwegian University of Science and Technology. 6 Jameel, M., Ahmad, S., Islam, A.S. & Jumaat, M.Z., 2013. Non-linear dynamic analysis of coupled spar platform. Journal of Civil Engineering and Management, 19(4), pp.476-491. 7 Pellegrino, S. & Ong, P.P.A. 2003. OMAE2003-37465. In Proceedings of OMAE 03 22nd International Conference on Offshore Mechanics and Arctic Engineering. 1 10. 8 Qiao, D., Yan, J. & Ou, J. 2014. Effects of mooring line with buoys system on the global responses of a semi-submersible platform. Brodogradnja, 65(1): 79 96. 9 Sarkar, A. & Taylor, R.E. 2001. Dynamics of Mooring Cables in Random Seas. Journal of Fluids and Structures, 16: 193 212. http://discovery.ucl.ac.uk/73002/. 10 Taylor R & Valent P, 1984. Design Guide for Drag Embedment Anchors, Naval Civil Engineering Laboratory (USA), TN No N-1688. 11 Vineesh, M. V, Sabu, N. V & Manju, P.M. 2014. Finite Element Analysis of Mooring Cable. International Journal of Engineering Research and Applications (IJERA) ISSN, (January): 13. 12 Yu, L. & Tan, J.H. 2006. Numerical investigation of seabed interaction in time domain analysis of mooring cables. Journal of Hydrodynamics, 18(4): 424 430. 13