A Novel Conceptual Telescopic Positioning Pile for VLFS Deployed in Shallow Water: Structure Design

A conceptual design of using novel telescopic piles to position a multi-modular very large floating structure (VLFS), which is supposed to be severed as a movable floating airport, is proposed. The telescopic piles can automatically plug in the soil to resist the environmental loads and pull out from the soil to evacuate or move on to the next operational sea. The feasibility demonstration of the conceptual design includes two parts: function verification and structure design. In the latter part of the conceptual design, a time-domain structural analysis is firstly conducted by using Abaqus software. The simulation results suggest that the preliminary structure scheme is not optimum due to the insufficient structure utilization, although both structure safety of the piles and positioning accuracy are guaranteed. To realize a cost reduction of construction and installation, a Genetic Algorithm-Finite Element Analysis (GA-FEA) method is employed to perform structural optimization. After optimization, 31 percent of the weight of each pile is reduced and higher structure utilization is maintained. The difference of the self-weight and allowable buoyancy of a single module (SMOD) of a semisubmersible-type VLFS is much larger than the weight of the piles. Combined with the function verification in our previous work, the conceptual design of using the novel telescopic pile to position VLFS is demonstrated to be feasible.


Introduction
Very Large Floating Structures (VLFSs) can be used as artificial floating landing spaces on the sea, relieving the land pressure of the well-developed coastal cities. Based on its appearance, VLFS can be classified into two types, the mat-like type and the semi-submersible type (Watanabe et al., 2004). The former type VLFS is similar to a huge box, while the latter type VLFS is like the semi-submersible platform comprised of a deck box, columns, braces and pontoons. By utilizing the flexible or rigid connectors, the relative motion between adjacent modules are constrained, thus forming a multi-modular VLFS system. Owing to the huge demand of resource exploitation and space utilization, applications of VLFS such as floating airports, storage facilities, floating bridges, etc. have attracted many researchers in the past several decades (Kyoung et al., 2005(Kyoung et al., , 2006Wang and Tay, 2011). Several projects including the conceptual design and construction of VLFS have been launched, for example, mobile offshore base (MOB) in America, floating bridge in Norway, and Mega-Float in Japan which is the only manufactured VLFS in the world.
Obviously, a VLFS should be positioned in operational seas by certain positioning devices since it may move randomly and freely due to the presence of wave, current and wind, leading to huge financial loss, fatality and pollution (Loukogeorgaki et al., 2017). For ocean engineering practices, one of the most common positioning measures is dynamic positioning (DP), with which high accuracy of positioning is maintained (Fay, 1990;Xu et al., 2016). However, dynamic positioning may not be proper for a VLFS because of the huge energy consumption and the high prices of DP systems. Another frequently-used positioning measure is the mooring system, whose cost is relatively moderate despite the complex anchorage and unmooring processes with the aid of auxiliary vessels. In this situation, most studies for VLFS positioning are focused on the design and safety assessment of the mooring system. Shimada and Shogo (2002) developed a nonlinear mooring simulation program and calculated the coupled responses of the VLFS mooring system. Fu (2005) proposed a combined method, analyzing the nonlinear hydro-elasticity of the VLFS and tension forces of the mooring lines, and validated the accuracy of this method by comparing with the experimental data. Wang et al. (2017) experimentally investigated the motion response of a single module VLFS with a tension-leg mooring system in the shallow water environment. Recently, Wang et al. (2018) further studied a catenary-taut-hybrid mooring system for VLFS over a multi-sloped seabed. The above studies suggest that mooring systems provide a reasonable solution for VLFS positioning and mitigate the oscillating motions as well. However, when serving as a floating airport, the motions of VLFS should be constrained strictly to meet the requirements for aircraft taking off and landing. In this situation, mooring system may not be a good choice because of its relatively low positioning accuracy.
Recently, inspired by the wind turbine installation vessel and the self-elevating platform, a novel telescopic positioning pile for VLFSs deployed in shallow water was proposed in our previous work (Ji et al., 2020). As suggested, telescopic piles are automatically plugged into the seabed so as to resist the external loads acting on VLFS, and they can also be automatically pulled out when necessary. By adjusting the ballast water, the difference between the self-weight and buoyancy of VLFS could be employed to carry out plugging and pulling processes of the piles. This is the distinctive characteristic of this telescopic positioning pile when compared with traditional positioning techniques, i.e. less operational hours, less cost and higher positioning accuracy.
In our work, this novel telescopic positioning pile can be automatically folded up and stretched out, requiring a nonhomogeneous section which is different from traditional piles adopted by the previous studies ( Danno and Kimura, 2009;Sun, 2016;Meng, 2017). An illustrative scheme of the telescopic pile is presented in Fig. 1. The outer diameter of each segment is smaller than the inner diameter of next segment so that these segments could be conveniently folded up. The installation process of the novel positioning pile in the operational sea is given in Fig. 2. Ten piles are deployed for positioning a single module (SMOD) of the VLFS and each pile is driven by an actuation device. The center axis of the pile coincides with that of the column so that the telescopic piles can be folded up into the SMOD. When the VLFS reaches the operational sea, the ballast water is increased to form a difference between the self-weight and the buoyancy of VLFS, thus complete the installation of the piles. While the uninstallation could be maintained through reducing the ballast water. The detailed plugging and pulling processes of the piles have been fully described in the previous work, hence omitted herein.  The feasibility demonstration of the conceptual telescopic pile includes two parts: function verification and structure design. The former part, involving in bearing capacity analysis, dynamic response analysis and plugging and pulling analysis, has been thoroughly investigated by Ji et al. (2020). This work is mainly concerned with the latter part. We would like to adopt two steps to complete the structure design. The first step addresses preliminary structure analysis which involves in structural stress responses of the piles in the survival condition. In the second step, structure optimization is dealt with according to the results of the first step.
This paper is logically constructed in four sections. The computational models in the preliminary structural analysis are given in Section 2, followed by structure optimization of the pile by use of a GA-FEA method in Section 3. Conclusion is finally drawn in the final section.
2 Preliminary structure analysis 2.1 Main parameters of the SMOD Several modules are deployed in a line to provide a long runway for aircraft taking off and landing, as shown in Fig.  3. The SMOD working in the shallow water is comprised of a box-shaped upper hull, 10 cylindrical columns, 5 hexahedral pontoons and 8 cylindrical braces. The main particularities of the SMOD are given in Table 1. The coordinate system is defined as shown in Fig. 4: the origin is located at the hull center at the baseline, positive x is along the centerline from aft to forward, positive y is in the transverse direction from starboard to port, and positive z points upward. The water depth of its operational sea is 50 m.  Note that the yield stress of the steel for the pile is 235 MPa, and the safety factor in the survival condition is 1.11, thus the allowable stress is 212 MPa.

Wave loads
The proposed novel telescopic positioning piles aim at positioning the VLFS working in shallow water areas. To this end, the structural safety must be satisfied during its working life, including installation, uninstallation, in the operational and survival conditions, among which external loads in the survival condition are most critical for the pile structure. Therefore, the survival condition is selected as the basis for designing the piles. It is noted that wave, wind and current are often considered as the composed survival condition in safety assessment of marine structures. However, the wave loads are thought to be the most important factor in the conceptual design. Hence loads introduced by the wind and current are neglected here.
A Jonswap spectrum characterized by the significant wave height of 5 m and the spectral peak period of 9.66 s is selected to represent the survival wave condition with a return period of 10 years. A beam sea (the wave heading 90°) is assumed since the wave generally travels from the deep to the shallow sea and the transverse axis of the VLFS is designed to be perpendicular to the coastal line.
The wave loads are obtained from a 1:100 scaled model test carried out in the State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University. The SMOD model is fixed in the ocean basin by pile models each with a disc contacted with the bottom of the wave basin. The wave loads acted on the SMOD are measured by six degrees-offreedom (DOFs) force sensors mounted on the pile model. The wave loads encountered at the gravity center of the SMOD in the and directions are denoted as and , respectively, while the moment about axis is , as shown in Fig. 5. The rest forces and moments are equal to zero because of the beam sea and the structure symmetry of the SMOD. Statistical analysis results of the wave loads are given in Table 2.

Preliminary structure scheme of the pile
In this work, the telescopic pile consists of three segments, namely Segment_1, Segment_2 and Segment_3, as shown in Fig. 6. Their lengths are 26, 23 and 44 m, respectively. The inner diameter of each segment is larger than the outer diameter of the former segment so that these segments could be conveniently folded up. The diameters of them are 4, 5 and 6 m, respectively. The lengths of conjunctions that connect Segment_1, Segment_2 and Segment_3 are both 2 m. The toe of the pile is 2 m long as well. Inner structures of each segment are similar, including inner cylindrical plates and stiffeners. In the preliminary structure scheme, thicknesses of all plates are set to be 50 mm.

FEM models of the piles and the soil
The FEM models of both the piles and the soil are created in Abaqus software, as shown in Fig. 7. Shell elements S4 and S3 are employed to construct the pile FEM model. While the soils are meshed by using solid elements C3D8 and C3D4. The meshes near the piles are finer than that in the region far away from the piles, as the stresses of the interfaces vary drastically in general and coarse meshes could not accurately estimate the true stress distribution. The interactions between the piles and the soil are simulated by surface-to-surface contact (Standard) in Abaqus. The normal behavior and the tangential behavior are set as "hard" contact and "penalty" with a friction coefficient of 0.25.
The impact of boundary conditions should be minimized in order to remove the influences of the finite extent of the FEM model which is not a realistic situation. To this end, the calculation domain is extended by 10 times the diameter of the pile in the horizontal direction and 40 m in the vertical direction.
The bottom boundary of the soil model is fixed and the side boundary of the soil model is allowed to move freely only in the vertical direction. Before applying the wave loads on the model, a geostatic equilibrium analysis is conducted to obtain stresses under the soil gravity without an obvious displacement.

−Kx
x K K To simulate the constraint among the ten piles and the SMOD, a reference point RP-1 located at the gravity center of the SMOD is created and linked to the connected components (marked in yellow in Fig. 7) of the ten piles by a "rigid body" type constraint. Obviously, the motion of the SMOD is represented by that of RP-1. Note that when the SMOD exhibits heave or roll or pitch motions, the hydrostatic restoring force can be excited by the sea water, which is represented by , where is the motion vector of the SMOD and the restoring matrix is denoted by . The detailed parameters in can be conveniently obtained by the hydrodynamic softwares such as Wamit® and Hydrostar®, hence are not discussed here.
The material of piles is steel with Young's Modulus 206 GPa and Poisson's ratio 0.3. The property of soil under seabed always varies with the increasing depth, thus different material properties are assigned to each layer. The parameters of all soil layers are from the field test in sea area near Qidong City, Jiangsu Province, China (Yang, 2015), as shown in Table 3, where is the depth range of the soil layer; is the dry mass density; is the Cohesion yield stress; is the friction angle; is the Young's modulus; is the Poisson's ratio.
Mohr-Coulomb model is selected to represent the soil. It is because that all processes including plugging and pulling    XU Sheng-wen et al. China Ocean Eng., 2020, Vol. 34, No. 4, P. 526-536 529 are operated under the undrained condition, with the permeability, the initial void ratio and the specific weight of wetting liquid being set as 1.0×10 −6 m/s, 1.0, and 10045 N/m 3 , respectively.

Preliminary structure analysis results
In this section, to investigate whether the preliminary structure scheme is adequate in the survival condition, the FEM model in Fig. 7 is employed and a time-domain dynamic simulation is performed with wave loads in Fig. 5 applied at the reference point "RP-1".
It should be noted that some of the piles may be pulled out when the VLFS exhibits roll, pitch or heave. However, this problem could be solved by applying a reasonable vertical preloads on the piles, which could be realized by raising a corresponding amount of the ballast water. From the previous work (Ji et al., 2020), it is recommended that 10 percent of the displacement of SMOD is suitable for the vertical preload, and it could also mitigate most motions of the SMOD. It is the inherent superiority of this novel positioning measure since the motion requirements of a floating airports are quite strict. Therefore, 10 percent of the displacement of VLFS as the vertical preload is employed. The accelerations of the sway and heave directions of the SMOD in the survival condition are illustrated in Fig. 9, and the root-mean-squares of them are 0.1682 m/s 2 and 0.0656 m/s 2 , respectively. Since a lack of the motion requirements of floating airports, the rule about the acceptable degree of the ship motion discussed in the Nordic cooperation project "Ships' Seakeeping Performance" (NORDFORSK, 1987) are listed in Table 4. It is observed that all the items meet the requirements of "excursion steamer", indicating that the performances of this positioning system are quite excellent.
Figs. 10 and 11 demonstrate the equivalent stresses of global structure and each segment of the pile respectively. From the simulation results, it is found that the largest equivalent stress occurs in a leeward pile at 515 s corresponding to the largest value of roll and sway of the SMOD. Low stress regions are marked in blue colors, while red colors in-dicate high stresses. It can be seen that the maximum stress of the pile occurs at the connection with the SMOD and it has not yet reached the allowable stress.
In summary, the motion response of the VLFS is relat-  ively small and the structural safety of the pile is guaranteed in the survival condition, indicating the preliminary design of the pile could meet the positioning requirement. As a result, it is unnecessary for the SMOD to evacuate from the operational sea, which can extend the operating time and can also avoid the weakness on the piles' bearing capacity due to repeatedly plugging piles at the same spot. Therefore, the novel telescopic positioning pile can be employed for positioning the VLFS which requires high positioning accuracy as a floating airport. However, if we take a closer look at Figs. 10 and 11, most regions of Segment_1 and Segment_2 are in blue and yellow colors, indicating that there should be a scope to make a reduction in the thicknesses of corresponding plates. Moreover, it is noticed that these positioning piles are carried by VLFS itself to the operational sea and the weight of each pile is 1466 t. Consequently, the variable deck load of a single module for VLFS decreased by 14660 t. Therefore, it is of great significance to perform structural optimization of the pile, which can help realize reducing installation difficulty and a lower construction cost.

GA-FEA method
GA is based on the evolution of species in their natural environment. The underlying principles of GA are centered on evolution and the survival of the fittest concept. Huge amount of investigations with GA were conducted, and the results showed that GA was viable and efficient (Gauchia et al., 2010, Mohan et al., 2013and Khalkhali et al., 2014. In this connection, GA is used as an optimizer herein.
It is well noted that FEA is a numerical method to deal with complex structural problems and has become a standard method of structural analysis. The software used to perform FEA in this paper is ANSYS which is also a professional commercial code.
In this work, an optimization technique called GA-FEA that combines Genetic algorithms with FEA is proposed. The GA method developed in MATLAB and ANSYS is employed to calculate the stress responses of each generation of structure design generated by GA.
In GA-FEA, for the purpose of maintaining cost reduction while being in satisfaction with strength requirements, the objective function of the structural optimization is the weight of the whole structures.
where is the -th design variable and it represents the thickness of the -th plate. is the corresponding plate area.
is the number of all plates. It is noted that GA can search through all space states, but this is not appropriate because In the processes of structure design, structural safety is the most important factor. Thus, stress constraint was taken into account in the present optimizations. The element stresses should be smaller than the allowable stress according to the rule.
σ eqv σ allow where and are the element stress and allowable stress, respectively.
To ensure only feasible designs, the constraint in this optimization is handled by the penalty method. The penalty value is designated to designs that violates the constraints and takes the form where is taken as a coefficient of the penalty function. Thus, fitness function to be evaluated after achieving every single design is the sum of the objective function and the penalty value.
In this connection, we define a fitness function that not only takes into account the total weight of the pile but also the structural safety. Consequently, the goal of the structural optimization is equivalent to minimize the fitness function. GA's three operators (selection, crossover and mutation) are applied in GA-FEA as follows.
(1) After calculating all the fitness values of the current population, the selection is performed. The selective probability that individuals in the current population are copied and placed in the intermediate generation is set to be proportional to their fitness.
(2) Then, crossover would occur and could be viewed as creating the next population from the intermediate population. With a certain probability, new individuals are created by executing "crossover" with the intermediate population.
(3) After crossover, a mutation operator can be applied. A flowchart of GA-FEA illustrating the main processes is shown in Fig. 12. Once the new generation is created, the processes are repeated and the processes continue until some stopping criteria are satisfied. The number of generations is employed as the stopping criterion and the best individual corresponding to the minimum fitness is the final result of the GA-FEA optimization.
In the present GA optimization, the roulette wheel selection method is employed to facilitate the task and appropriate GA parameters are determined. Population size, crossover rate, mutation rate and penalty coefficient are listed in Table 5. 3.2 Sub-problem approximation method Sub-problem approximation method (SAM) by Fedorik et al. (2015) is an iterative method based on an approximated function. At first, the approximation of the dependent variables by least squares fitting is performed, and then the approximated objective function is minimized or maximized. Thus the aim of the process is to minimize or to maximize an approximated function instead of the true function. The general approximated objective function is defined in a fully quadratic form with cross terms as where represents the number of iterations; is the vector of design variables; , , and are coefficients determined by the weighted least square technique; represents the number of variables and is the quantity of performed loops. Like the aforementioned GA-FEA method, transformation is performed by the penalty function method which is applied to the objective function. Then, the minimizing or maximizing problem is expressed by X where is the penalty function used to denote the con- G F f 0 q j straints of design variables, is the penalty function which substitutes other constraints, is the unconstraint fitness function, is the reference objective function and is the penalty coefficient.

First order method
Unlike SAM, first order method (FOM) (Fedorik et al., 2015) uses a derivation of functions to solve an optimization problem. The objective function and the penalty functions of the state variables are derived, which leads to the problem of searching a certain direction in the design space. For each iteration, a browsing of the direction by the steepest descent method and the conjugate gradient method is performed. This means that several sub-iterations are performed in each iteration computing both the direction and descent of the functions. The function which solves the optimization problem by FOM has the general form F X G f 0 q where is the unconstrained objective function. is the penalty function compensating constraints of design variables and is penalty functions of state variables. represents the reference objective function achieved in the current group of the design sets. The appropriate penalty parameter monitors how well the design constraints are being satisfied.

FEM model for structure optimization
The model of an initial pile is modeled in ANSYS. As shown in Fig. 13, a single pile is comprised of three segments, namely Segment_1, Segment_2 and Segment_3. Since structures of each segment are similar, the inner structure of Segment_3 is given in Fig. 14 and it can be divided to three substructures i.e. inner shell, vertical stiffener and cylindrical stiffener. Besides, the outer plates of a segment were named as side shell.  SHELL 181 element was used to discretize the plates of the pile. The entire model has 4893 nodes and 6976 elements, as can be seen in Fig. 13. Thicknesses of certain plates were selected as design variables and denoted as shown in Table 6. When referring to initial design, all the design variables were set to be 50 mm. For the sake of implementing optimization, we need to develop a design space by varying the variables. Lower limit and maximum limit of each design variable were set to be 15 mm and 50 mm, respectively.

Structural optimization results of the pile
The most dangerous loads are selected with regard to the moment when the largest structural stress occurs, which is determined in the survival condition in Section 2. In the present problem, the loads acted on the pile are composed of pressures and frictional forces by the soil, inertia forces due to motions of the pile itself, as well as the displacements of top end and hydrostatic forces. In the former section, we can see that the acceleration of the pile is quite small in the survival condition. Accordingly, the structural stresses induced by its acceleration can be neglected in the structure optimization. The external forces and boundary conditions are shown in Fig. 15.
After the accomplishment of initial population, selection, crossover, mutation followed by evaluation of fitness value for each generation, the structural optimization is performed using GA-FEA. The evolution of the average weight is depicted in Fig. 16.
The best solution is obtained at the best fitness and the corresponding design variables are considered to be the optimal individual. In Table 7, the optimal design is presented. Considerable reduction is obtained for all the thicknesses, some of which are smaller than 50% of that in the preliminary design.
The equivalent stress of the optimized pile by GA-FEA  is demonstrated in Figs. 17 and 18 with the coloring of stress distribution of the whole model. More regions with red and yellow colors, which correspond to higher stress and higher utilization of materials, can be seen in the optimized design when compared with the preliminary design as shown in Figs. 10 and 11. Still, the optimized design satisfies the stress requirement, while the significant weight saving of about 461.5 t (31%) is reached on the whole pile structure. Differences of the weight, minimum stress and maximum stress of all the segments between the preliminary and optimized designs are listed in Tables 8 and 9. From Tables 8−9 and Figs. 17−18, the weight reduction and stress rising are observed in each optimized segment compared with the preliminary design. When referring to the first segment (denoted as Segment_1), there is weight saving of up to 60%, and the maximum stress experiences an increase of 63.6 MPa. And for Segment_2, the weight saving is 39% and the upper limit of stress has increased from 113 to 202 MPa. When it comes to the Segment_3, nearly 14% weight saving is obtained. The higher reduced percentage of Segment_1 and Segment_2 than that of Seg-ment_3 may mainly be because that the equivalent stresses of the former two segments were much smaller than the latter. Therefore, there is a considerable variation in the optimization degree in different segments. For comparison,Figs. 19a and 19b show the equivalent stress along the pile for the optimum design by SAM and FOM, respectively, and it is observed that stress distribution of the designs by these two methods is similar. When compared with the result by GA-FEA (see Fig. 17), the material utilization of Segment_1 by the former two methods is much less sufficient. Weight reductions of all the three methods are listed in Table 10. It is clear that the two mathematical optimization tools native to ANSYS, SAM and FOM, are not that effective in seeking the best solution of the current problem. It may be because that search procedures of these two methods are deterministic in nature. Therefore, it could be concluded that GA-FEA is proved to be an effective method when dealing with the structural optimization problem in this work.

Conclusions
A novel telescopic positioning pile for VLFS deployed in shallow water for airport use is proposed. Telescopic piles are employed to position a single module (SMOD) of VLFS and the installation can be accomplished by the SMOD itself by the difference of the self-weight and the buoyancy of the module. The feasibility demonstration of the novel conceptual telescopic positioning piles is divided into two parts: function verification and structure design. In this paper, the latter part is investigated for ten piles supported SMOD based on finite element method and the genetic algorithm.
A preliminary structure scheme of the pile is determined according to the function requirements verified in our previous work (Ji et al., 2020). Through conducting a direct time-domain structural analysis with Abaqus software, it is found that the piles are sufficiently strong to resist the ex-    ternal loads while providing an excellent positioning accuracy in the survival condition. However, the simulation results also suggest that the preliminary structure scheme is not optimum due to the insufficient structure utilization. To realize a cost reduction of construction and installation, a Genetic Algorithm-Finite Element Analysis (GA-FEA) method is employed to perform structural optimization. For comparison, two mathematical optimization tools native to ANSYS, SAM and FOM, are also adopted. More effective weight reduction is obtained by GA-FEA, indicating that it is a method suitable for structure optimization of the positioning pile. After optimization, 31 percent of the weight of each pile is reduced and higher structure utilization is maintained. The difference of the self-weight and allowable buoyancy of the SMOD is much larger than the weight of the piles. Therefore, the optimum structure scheme of the pile is finally obtained. Combined with our previous work, function verification, the conceptual design of using novel telescopic pile to position VLFS is demonstrated to be feasible. The novel telescopic positioning pile proposed in this paper is convenient and can provide quite high positioning accuracy, which deserves further research for physical application. To deploy the VLFS in different working sea, our future work focuses on establishing precise numerical models of VLFS-pile-seabed interaction. Also, the practical mechanical devices should be further investigated in the future since some of them may be beyond the present manufacturing capacity.