Overexploitation of the land, enhanced by the constant rise of population density in coastal regions is a major global concern [1
]. A very large floating structure (VLFS) is an environmentally sensitive alternative for the creation of artificial land at sea [4
]. Offering broad space and high stability, it can be utilized for the accommodation of land-based operations out at sea. Thus, it may provide a much-needed relief and enable a more sustainable development in coastal regions.
VLFS types are traditionally categorized by their hull configurations into the pontoon or the semisubmersible types [8
]. The Delta-type VLFS [10
] is a newly developed concept. It is designed to operate at intermediate open sea condition and to withstand severe weather conditions with minimal downtime. The unique delta shape (see Figures 1 and 3) is designated to provide high hydrodynamic efficiency and a broad operational area. The innovative hull design maintains acceptable loads and motions and minimizes the structural complexity. A unique and important feature of the Delta concept is the integrated sheltered basin. Protected from the incoming waves by the frontal delta and the side hulls, the sheltered basin provides a year-round access to and from the facility. The basin’s ability to host a wide range of cargo handling operations with minimal downtime directly influences the operability and the utilization range of the Delta. Drimer and Gafter [10
] introduced the Delta VLFS, elaborated on the design considerations, studied the hydrodynamic attributes, and showed the favorable performance of the structure. Focusing on the structural design aspects of the Delta, [11
] presented a primary strength assessment tool, developed for the Delta. This study focuses on the sheltered basin and examines its operability as a service port and, as an expansion to the mentioned hydrodynamic study, we constructed an analysis procedure so it may be utilized as a design evaluation tool. The study aims to assess by practical engineering methods the performance of the sheltered basin serving the VLFS. While the same practice is common to the development of harbors, by means of numerical or physical agitation models, we here applied it to assess an innovative concept of VLFS, to extend the use of the open sea.
For the mooring design [10
], as well as for the structural design of the VLFS [11
], we applied extreme storms. However, for the operability aspects, as the downtime is in the order of few percent, we indicated the limit storms that will disturb the operability, which are storms that statistically appear every year. This is a common practice for harbors design, where the stability of the breakwaters is tested for extreme storms (stability models), while the operability is tested for storms that statistically appear every year (agitation models) [12
]. We followed this practice for the VLFS. For the storms that statistically dominate the downtime, the representation of a real sea by a spectrum of nonbreaking waves is practical and valid.
The hydrodynamic performances of the Delta are fundamental to the operability and feasibility of the concept. While the motion attributes of the hull were fairly examined in previous work, as presented by [10
], under severe wave conditions, the motion response of the structure was extremely low. The results of the application of the comfort evaluation criteria, presented in [10
], clearly demonstrated that low motion response. In addition, the time-domain analysis of the moored structure, presented in [10
], showed that under severe oblique waves, the structure maintained its preferable position, oscillating within acute angle while facing nearly head-on to the incoming waves. Presented in [10
] as well, the operability of the sheltered basin was studied in terms of wave agitation parameters alone. This work expands the operability research of the sheltered basin by conducting a hydrodynamic study of a typical ship moored to the Delta under severe sea conditions. As a significant part of the methodology, developed for the advancement of the Delta concept, the preliminary design of the mooring system aims to provide an initial frame of reference for basic evaluation and qualitative measure. The behavior of the system (the interacting Delta VLFS and moored ship) was simulated in the time domain, enabling the modeling of the mooring system with realistic nonlinear response characteristics. Such a simulation fairly represents the actual motion of the berthed ship and allow the evaluation of the sheltered basin in terms of its operability as the service port of the Delta. While, at this stage, we implemented the mooring analysis for the evaluation of the design that was hydrodynamically optimized in early stages, on later design stages (as more specific requirements emerge), the procedure may be readily used for other geometrical configurations as well.
Following the introduction, Section 2
presents the theoretical background, the analysis methods, the analysis tools, and provides the system’s description, evaluation criteria, and the load cases. Section 3
details the results and, finally, Section 4
presents a discussion and conclusions.
Typical to all load cases, the Delta’s position in load case c2, under the incoming waves is presented in Figure 7
. As expected, in all load cases, the structure oscillates within an acute angle to the incoming waves. Due to the asymmetry of the system, caused by the ship berthed to one side of the Delta, the point of equilibrium of the motion is not along the symmetry axis of the Delta.
The wave frequency position of the berthed ship along the 10,000-s simulations of the c2 and s2 load cases, are presented in Figure 8
and Figure 9
, respectively. The surge and sway motion are relative to the motions of the delta and the heave and rotational motions are absolute. However, in such conditions, the heave and rotational motions of the Delta are minimal and, therefore, negligible. The frequency position of the ship in all load cases are presented in Appendix A
presents the maximal motions (for a relatively high sea state duration of 10,000 s) of the moored ship in each load case. Table 8
presents the maximal tension in the mooring lines and the maximal compression in the fenders for each load case.
The acceptable load cases, in terms of motions, for each ship type and cargo handling equipment were:
The tension loads applied on the berths’ mooring lines in load case c2 are presented in Figure 10
. While the maximal load varies, the general trend is similar in all load cases. The highest load is applied on the breast lines, from which the stern line is the most loaded (line 27 in Figure 10
). From the spring lines, the highest load is applied on the line closer to the stern (line 26 in Figure 10
In terms of fender loading (compression), for significant wave heights of up to 2.5 m (load cases c1, c2 and s1, s2), the maximal reaction force does not reach the maximal nominal values of the fenders and, therefore, the maximal deflection is less than 35%.
For the assessment of the mooring line tension, we considered for each line 7 ropes for the compliant (“c”) system and 10 ropes for the stiff (“s”) system. As can be seen in Table 7
, the 50% MBL is reached for wave heights of over 2.5 m in the case of the compliant system and, in the case of the stiff system, the maximal tension is within acceptable limits for all load cases.
4. Discussion and Conclusions
The wave conditions considered in this study were selected to obtain the operability limits, in order to present the operability of the VLFS that forms a service basin at the selected design site. Indeed, the results are representative of the East Mediterranean Sea, while the method of assessment is general.
As investigated by [44
] and others, the analysis of the effects of important load mechanisms, such as wave breaking, slamming loads, and two-phase flow, directly influences the design of marine structure. While treating these subjects was out of the scope of this analysis they will be addressed in later stages of the design.
The modeling of the mooring system was simplified into the very basics: compression bearing fenders and tension bearing (linear) ropes. As such, unlike an actual mooring system, the simplified system offered no damping mechanisms (e.g., material damping, friction) that can reduce the risks of resonant effects and suppress loads and motions. For example, while the surge peaks at the 4000 s and 8000 s can be explained as a dynamic reaction to the Delta’s surge motion, that peaks approximately at those instances as well (see Figure 7
), still, the amplitude of the ship’s motion may well be affected by a resonance response. However, considering that such phenomena is directly related to the specific ship dimensions, its dimension-to-wavelength ratio [47
], and to the mooring system specification, it is an important matter to attend to at later stages of the more detailed design However, as it is, the study indicates that for most types of ships and cargo-handling equipment, the sheltered basin provides adequate protection and allow for safe berthing conditions for waves conditions of up to
m (operability during 95% of the year). In some cases, higher wave conditions are acceptable as well.
Providing additional assurance to the validity of the analysis, we conducted a sensitivity test in which we forced the incoming wave direction to a different, less acute, angle of about 15 degrees. As can be seen in Figure 11
, the applied tension on the mooring lines is even lower than in the more acute angle incoming direction presented in Figure 10
. Therefore, we are confident in the validity of our findings.
We expect that a detailed design and optimization of the mooring system may improve the operability of the sheltered basin. First, such design will include modeling the material damping of the fenders and the friction between the moored ship and the fenders, which will reduce the loads and motions as well as reduce resonant effects. Second, the design will include a more specific selection of the mooring equipment. Adjusting the mooring system specifically to each expected ship type, size, or cargo-handling operation, will improve its performance and assure the expected minimal downtime operability of the sheltered basin. In addition, if required, a structural optimization of the hull, oriented towards maximizing the basin’s performance will surely produce significant improvements as well.
The study clearly points towards a general trend in the mooring line tension. The results show that the highest loads are applied on the breast line and the loads applied on the spring lines are lower. However, as all loads are practically in the same order of magnitude, especially in the case of the bow and stern division, we cannot recommend optimization measures regarding the rope selection or division between the mooring lines.
As presented in the appendix figures, the compliant system’s surge increases with the wave height. Since the surge DOF of the moored ship is dominated by the second-order drift loads, the nonlinear growth of the surge amplitude with the increase of the wave height is expected. In addition, for wave heights of up to 3 m the surge motions are much lower with the compliant mooring, while the sway and yaw motions are lower with the stiff mooring. As, typically, the surge is the most critical, we conclude that the compliant mooring is more efficient.
As expected and practical, the vertical movements (heave, roll, pitch) are not considerably affected by the mooring stiffness.
As a design tool, especially in early, preliminary stages, the application of the time-domain simulation using AQWA-DRIFT is practical and efficient. The evaluated results of the mooring system’s loads and the ship’s motion provide comparable numerical measures to the basin’s operability and may be readily used as an integral part of the design methodology of the Delta concept.