Keywords

1 Introduction

Research and investment in offshore wind turbines have been in progress since the last 40 years. Wind energy life cycle production process has low carbon effect and is sustainable [1]. For water depth of above 25 m the jacket substruction configuration comes as the best option [2]. The X-brace jacket configuration was chosen because previous studies confirmed it has good performance compared with other bracings configuration [3, 4].

The wind, wave and dead loads were the main ultimate limit state loads for the offshore wind turbine jacket substructure. The wind loads are the design driving force whiles the wave loads have secondary effect on the response of the structure under ultimate load condition [5]. The key variables for the design are the wind speed, wind intensity, wave height and wave period. These data are normally taking from actual site records for a period.

Engineering optimization is generally classified into topology, shape, and size optimization [6]. Element types are specific to the different types of the optimization. Sizing optimization is a common process used to improve the performance of engineering designs [7]. The common geometry variables in sizing optimizations are diameter, thickness, length, width, and height. Motlagh optimized the jacket structure by using the diameter and the thickness of the jacket pipes as the design variables. The mass was minimized by 15% under ultimate loading [8]. In a similar research, Sandal et al., optimized the jacket using the thickness and diameter as optimization variables. The mass reduced by 40% and with reduced performance of the maximum horizontal displacement, increasing by 80 mm. In general, for the jacket substructure, the variables influencing the optimization process are the base width, the jacket height, the member diameter and thickness [9]. Therefore, for this research the base width, the diameter and thickness were the main variables. After the optimization process the responses were checked against code limitations and were within code limits whiles minimizing the mass. Therefore, the performance of the jacket with respect strength have been maintained, whiles reducing the mass.

2 The Jacket Boundary Conditions and Finite Element Modeling

2.1 The Boundary Conditions

To model the support as realistic as possible, the soil structure interaction was considered in the foundation behaviour, therefore spring support was used. The ultimate load on top of the jacket structure applied at the reference point (RP) is made of estimated wind load, rotor nacelle assembly (RNA), and the tower. The unfactored loads from wind are Fx = Fy = 5071 kN, Mx = My = 423875 kNm, Mz = −33324 kNm, and RNA, and tower load Fz = −14972 kNm. The wave load calculation was base on the Morisons equations. The velocities and acceleration of the wave were estimated by Stokes 5th order calculation model. The wave loads were based on the significant wave height (Hs) of 13.98 m, peak period (Tp) of 18.06 s, and wave length (L) of 308.07. The ultimate load used for the design was based on load combination in Table 1, which is based on Chinese code GB 50009-2012 [10]. The jacket configuration is shown in Fig. 1.

Fig. 1.
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The jacket model with spring support (MSL- mean water level)

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Table 1. Load combination for design
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2.2 Finite Element Model

From Fig. 1, a total of 196 components were modeled and members having similar geometric properties classified into 26 groups. In the absence of the tranistion piece, the top was model with 50 mm thick 2-dimensional plate element and 4-top pipe elements of 1550 mm diameter and 220 mm thickness to give enougth stiffness for transmission of applied load. The high water level of (HWL) 66.39 m was used in the model. The coordinates of the jacket substruture were modeled with python-Abaqus-scripting. The yield strength of the steel is 355 MPa, and the tensile strength used is 560 MPa. The B31 CPS3 linear pipe element type was used.

3 Parameter Studies and Optimization

3.1 Parameter Studies

Six parameters were studied for the optimization; 1) pile length (PL) above the mudline, 2) the base width (BW), 3) brace diameter (BD), 4) brace thickness (BT), 5) leg diameter (LD), and 6) Leg thickness (LT). The responses with respect to maximum displacement, maximum stress, maximum rotation, mudline displacement, mudline rotation and mudline stress were analysed.

Increasing the PL (1400 mm to 5900 mm), has little effect on the maximum stress (+0.8 MPa), the maximum displacement increased by 9.4% (+7.69 mm), the mudline displacement increased by 10.3% (+1.74 mm), the maximum top rotation increased by 2.3% (+0.007°), the maximum pile rotation at the mudline increased by 34.3% (+0.037°).

Increasing the BW (22500 mm to 40000 mm), has significant effect on the maximum stress (−42.98 MPa), the maximum displacement reduced by 49.3% (−70.29 mm), the mudline displacement decreased by 5.7% (−1.06 mm), the maximum top rotation decreased by 8.4% (−0.028°), the maximum pile rotation at the mudline increased by 36.2% (+0.034°).

Increasing the BD (by + 100 mm @ + 20 mm for each model), has little effect on the maximum stress (−1.68 MPa), the maximum displacement reduced by 2.7% (−2.28 mm), the mudline displacement decreased by 4.4% (−0.81 mm), the maximum top rotation decreased by 4.7% (−0.015°), the maximum pile rotation at the mudline decreased by 17.1% (−0.024°).

Increasing the BT (by + 25 mm @ + 5 mm for each model), has significant effect on the maximum stress (−85 MPa), the maximum displacement reduced by 10.4% (−9.61 mm), the mudline displacement decreased by 2.3% (−0.41 mm), the maximum top rotation decreased by 22.2% (−0.086°), the maximum pile rotation at the mudline decreased by 24.7% (−0.038°).

Increasing the LD (by + 100 mm @ + 20 mm for each model), has moderate effect on the maximum stress (−6.84 MPa), the maximum displacement reduced by 5.4% (−4.7 mm), the mudline displacement decreased by 3.4% (−0.62 mm), the maximum top rotation decreased by 2.8% (−0.009°), the maximum pile rotation at the mudline decreased by 0.8% (−0.001°).

Increasing the LT (by + 25 mm @ + 5 mm for each model), has significant effect on the maximum stress (−86.69 MPa), the maximum displacement reduced by 24.1% (−25.52 mm), the mudline displacement decreased by 4.8% (−0.87 mm), the maximum top rotation decreased by 4.1% (−0.013°), the maximum pile rotation at the mudline increased by 3.4% (+0.004°).

Based on the trends of the results achieved, the jacket was parametrically optimized. The PL and BW of the original model were maintained, so the response of the jacket with respect to the BW and PL has been retain to the original model. Increasing the BD has little effect on the maximum stress, and displacement, the some of the BD features were increased. to compensate for the increment in BD, BT parameters were decreased. Decreasing the BT, is expected to have significant effect on the maximum stress increment, moderate effect on the increment of the maximum displacement, significant effect on both the maximum top rotation and the rotation at the mudline level. To counteract the effect of the BT decrement, the LD parameter was moderately increased level 2 to level 4 members (original features maintained for level 1). Increment of LD, has moderate to little impact on all the responses studied. Finally, the LT was decreased to balance the reduction in stress by the increment of the LD.

3.2 Parametric Optimization

Based on the optimization philosophy developed from the above, the jacket model was parametrically optimized. The detail responses of the optimized solution are shown in Table 2, Figs. 2, 3, 4 and 5. Compared to the original design the optimized option (OPT1) mass reduced by 16%. The maximum stress reduced from 288.7 MPa to 274.91 MPa (Fig. 2). The Maximum displacement increased from 83.88 mm to 87.37 mm (Fig. 3), the maximum rotation reduced from 0.309° to 0.304° (Fig. 4) and rotation at the mudline increased from 0.1203° to 0.1384° (Fig. 5). From Fig. 2, the stress contour of the optimized model is well distributed compare to the stress contour of the original model.

Table 2. Results of optimized solution
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Fig. 2.
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Stress contours of optimized and original model

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Fig. 3.
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Displacement contours of optimized and original model

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Fig. 4.
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Rotation contours of optimized and original model

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Fig. 5.
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Mudline rotation contours of optimized and original models

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3.3 Comparing Results with Design Code Limits

The maximum stress response of the optimized structure is below the elastic limit of 355 MPa. The jacket has been parametrically optimized. The limiting value of the current design horizontal displacement based on the ASCE-7-16 is 175 mm. The maximum displacement from the parameter optimization is 87.37 mm. From Eurocode 7 [11], the relative maximum rotation acceptable for ultimate limit state is 1/150 rad (0.38°), the optimized solution satisfied the rotation condition under ultimate state. The optimized model has maximum top rotations of 0.3044°, and being lower than the original jacket maximum rotation of 0.3088°. The DNV code J101, limit the mudline rotation to 0.2500° under serviceability loading. The mudline rotations for the optimized solution under ultimate loading is 0.1384°, which is lower than the DNV codes limits but greater than the original model mudline rotation of 0.1203°.

4 Conclusions

The FEA models of the jacket substructure were built using GMSH module in python-scripting environment. The models were then converted to Abaqus-readable inp files. The foundation boundary conditions and the wave load were applied through Fortran subroutine using the UEL and Dload functions respectively. Parameter studies was conducted on the models of jacket substructure under extreme ultimate loading. Base on the parameter studies the jacket substructure was quickly optimized. The following are the summaries of the investigation:

Six different parameters of the jacket were studied for the parametric optimization.

From the results of the parameter studies, the maximum stress was mainly affected by the variation of BW, BT, and LT. The maximum displacement was mainly affected by the variation of BW and LT. The maximum rotation at the top was affected by the movement in BT only. The pile mudline rotation was affected by the movement in BW, PL, BD, and BT.

The parametrically optimized mass reduced 16%. The maximum stress reduced from 288.7 MPa to 274.9 MPa. The absolute value of the maximum rotation at top reduce from 0.309° to 0.304°. The maximum displacement increased to 87.37 mm from 83.88 mm. The mudline rotation increased by 14.2% (from 0.120° to 0.137°).

A quick optimized solution has been developed through the trend developed from the parameter studies. The works shows an efficient modelling of the jacket substructure for optimization. The work can be enhanced by developing mathematical models from the parameter studies for an efficient numerical optimization using a good optimization algorithm.