*3.1. Background*

A ground survey was carried out on the coast of Gunsan, Southwest of Korea, prior to the design and installation of a 5.5 MW OWT. Figure 1a is the expected installation location, while Figure 1b and Table 1 show the ground investigation results. It is observed in Figure 1b that a bedrock layer appears at a depth of 7.5 m, and when an offshore wind turbine supported by suction bucket foundation is installed here, the length of the suction bucket skirt must be less than 7.5 m. Since the skirt length is limited, it is necessary to increase the bucket diameter to reinforce the overturning resistance and improve bearing capacity. However, various problems include the lack of manufacturing facilities for large-diameter suction buckets, transportation and installation equipment, etc. Moreover, increasing the diameter can make the spacing between the buckets too narrow, leading to overlap stress. Hence, developing a multi-pod suction bucket support structure that exhibits equivalent support is necessary.

**Figure 1.** Installation area: (**a**) map; (**b**) soil layer.

**Table 1.** Soil profile of survey site.


#### *3.2. Development of PSB Support Structure*

Figure 2 shows the top view and thrust direction of the PSB model. The spacing (R) between each bucket and the center of the tower is assumed to be the same. According to the thrust direction, as shown in Figure 2, the pull-out resistance (Vt) and compression resistance (Vc) are indicated by red and blue dots, respectively. Then, the resistance moment (MR) can be calculated as in Equations (4)–(7).

$$\mathbf{M}\_{\rm R} = \mathbf{V}\_{\rm t} \mathbf{b}\_{1} + 2\mathbf{V}\_{\rm t} \mathbf{b}\_{2} \tag{4}$$

$$\mathbf{b}\_{1} = \text{R} + \text{R}\cos(\text{\textdegree 36}^{\circ}) \;= 1.80 \text{\textdegree R} \tag{5}$$

$$\mathbf{b}\_2 = \mathrm{Rcos}(36^\circ) + \mathrm{Rcos}(72^\circ) = 1.118\mathrm{R} \tag{6}$$

$$\mathbf{M}\_{\rm R} = 1.809\mathbf{V}\_{\rm l}\mathbf{R} + 2.236\mathbf{V}\_{\rm l}\mathbf{R} = 4.045\mathbf{V}\_{\rm l}\mathbf{R} \tag{7}$$

When the number of buckets is 3 to 6, the moment of resistance (MR) can be calculated the same way, and the corresponding normalized resistance moments are shown in Figure 3 [6].

It can be seen from Figure 3 that the PSB has better pull-out and compression resistance than other multi-pod support structures. Therefore, a PSB support structure using five buckets was finally developed. Figure 4 shows the developed PSB support structure.

**Figure 2.** Top view of PSB [6].

**Figure 3.** Dimensionless resisting moment of buckets.

**Figure 4.** Pentapod support structure.

## **4. Numerical Example**

*4.1. Wind Turbine and Support Structure Model*

Figure 5 is a 5.5 MW OWT with PSB support structure modeled by Bladed [21]. The hub is located at the height of 110 from sea level and the water depth is 27.723 m. The total height of the offshore wind turbine is 137.723 m. Substructure is a pentapod with five single suction buckets. The geometric and material properties of the supporting tower structure are referred from a previous study [6]. The mechanical characteristics of the seabed connected to a substructure is represented by a soil stiffness matrix.

**Figure 5.** Analysis target.

## *4.2. Soil-Structure-Interaction Simulation*

In order to express the interaction behavior of the suction bucket and the contact ground, a three-dimensional displacement analysis of the bucket-ground model caused by an external force was performed. Then, a stiffness matrix from the analysis was applied to Bladed. The commercially available Finite Element (FE) software ABAQUS [22] was used. The finite element model was shown in Figure 6, the soil was modeled with C3D8R elements, and the bucket foundation modeled by shell element with a diameter (D) of 9 m and a skirt length (L) of 7 m. The center of the bucket top was set as the reference point to apply an external load. Displacements were obtained after sequentially applying external loads in the direction of 6 degrees of freedom (*Fx, Fy, Fz, Mx, My, Mz*) to the reference point. In order to consider the effect of ground nonlinearity, the load in each direction was divided into 10 steps and applied gradually. From the load-response relationship the following equation can be written

$$\left[\mathbf{d}\right] = \left[F\right]\left[p\right] \tag{8}$$

where [d] = Δ*x* Δ*y* Δ*z θx θy θz* T is the displacement vector; [*p*] =[*Fx Fy Fz Mx My Mz*]<sup>T</sup> the load vector; [*F*] the flexibility matrix from numerical analysis [23]. Then, the stiffness matrix for ground can be derived as

$$[p] = [\mathbb{K}][\mathbb{d}] \tag{9}$$

**Figure 6.** Stiffness matrix analysis model.

The stiffness matrix [*K*] is the inverse of [*F*] and obtained in this study for Bladed input as in Figure 7.


**Figure 7.** Bladed input for stiffness of foundation spring.

## *4.3. Wind Thrust*

Thrust force by wind is automatically calculated in Bladed. At first, a wind field was generated using the Kaimal model, and a total of 30 cases of thrust force set was calculated by changing the phase of the wind field. Figure 8 shows a time history of thrust force for 10 min calculated by Bladed.

**Figure 8.** Time history of thrust force.

#### *4.4. Calculation of Wave Load*

The Morrison Equation [24] was used to calculate the wave loading acting on the structure in Bladed. To evaluate the risk due to scouring, the most hazardous event caused by the environment during the life cycle was considered. Significant wave height (*Hs*) and wave period (*Ts*) are adopted from the HYPA model of the Korea Oceanic Research and Development Institute [25] from 1979 to 2003. Figure 9 shows the probability density function estimated using the Weibull distribution and it can be expressed as Equation (10) where *a* and *b* are 5.56 and 9.66, which mean scale and shape parameters, respectively. To obtain the ultimate limit state (ULS) wave load, the significant wave height corresponding to a 50-year return period, *Hs*50, was estimated to be 6.64 m from the PDF. It is the wave height at which an excess probability is 1/50. The significant period was estimated to be 12.9 s using Equation (11) [26].

**Figure 9.** PDF of annual maximum *Hs*.

$$f\_{\mathcal{X}}(\mathbf{x}) := \frac{b}{a} \left(\frac{\mathbf{x}}{a}\right)^{b-1} e^{-\left(\frac{\mathbf{x}}{a}\right)^b} \tag{10}$$

$$T\_s = 3.3 H\_s^{0.63} \tag{11}$$

To simulate the wave acting on the OWT substructure, Bretschneider's wave spectrum with significant wave height (*Hs*), period (*Ts*) and frequency (*f*) is adopted to generate the sea surface elevation time history, it was defined as

$$S(f) = 0.257 H\_s^2 T\_s^{-4} f^{-5} \exp\left[-1.03 \left(T\_s f\right)^{-4}\right] \tag{12}$$

Using the Bretschneider spectrum mentioned above, the surface wave elevation profile can be obtained and was shown as Figure 10.

**Figure 10.** Surface wave elevation.

#### *4.5. Probability Distribution of SD*

The probability distribution of SD can be obtained by giving random variability to the variable in Equation (1). The most important among them is the distribution of KC. From the Weibull distribution of Equation (10), the annual maximum significant wave, *Hs*, is generated and *Ts* is estimated from Equation (11). Then, peak period *Tp* corresponding to the *Hs* and *Ts* is calculated from the spectrum of Equation (12). Once *Tp* is calculated scour depth S can be obtained using Equation (1). With 50,000 times random sampling for *Hs*, KC distribution was developed as Figure 11.

**Figure 11.** Probability distribution of KC.

The distribution of current speed was collected from the National Oceanic and Atmospheric Research Institute [27]. The estimated distribution of current speed fits the normal distribution, and the mean and standard deviation are 1.34 and 0.19, respectively.

Since only values of KC greater than 4.0 are effective for scour generation, the depth of scour was calculated using the distribution of KC greater than 4.0 and the tidal flow distribution. As a result, the distribution of scour depth was obtained as shown in Figure 12. It was found that a log normal distribution fit well, as shown in Figure 12. Two parameters λ and ζ were 0.75 and 0.55, respectively.

**Figure 12.** Probability distribution of SD.

*4.6. Scouring Fragility Curve*

> To obtain the fragility curve, the limit state function of PSB is defined as the following equation.

$$\lg(X) = R\_{\mathfrak{a}}(SD) - R\_{\max} \tag{13}$$

where *Ra* is the allowable bearing capacity of a bucket; *Rmax* the maximum reaction force at each bucket. The *Ra* is a function of scour depth SD since the contact area of a bucket with ground is dependent on SD.

The bearing capacity of a bucket can be calculated numerically in horizontal and vertical directions [28]. For the analysis, the suite of 30 cases were analyzed by changing the seed of the wind field. Based on the structural responses at the mudline location for each case (i.e., reaction force to tension, compression, and horizontal force), the scour fragility was obtained. Accordingly, the maximum reaction members at the mudline obtained by performing a dynamic analysis in the non-sour state were compared with the allowable bearing capacity by SD to determine to what extent SD is safe.

Figure 13a shows the allowable pull-out force of a bucket for each SD. From the figure, the allowable pull-out force rapidly decreases according to SD increase. The tension-bearing capacity of the SB is mainly provided by vertical friction between bucket wall and soil. Therefore, scour reduces bearing capacity in tension direction. Figure 13b compares the

allowable tension force at SD of 6.5 m, with the maximum pull out load corresponding to seed variation in wind field. The maximum pull out loads are smaller than the allowable tension capacity. Therefore, no failure is expected in tensional bearing capacity. Figure 14 shows the same results for compressive mode. While Figure 14a shows the allowable compressive force for each SD, Figure 14b compares the maximum compressive force calculated from the structural analysis results and the allowable compressive force at SD of 6.5 m. Both Figures 13 and 14 show that the tension and the compressive forces do not exceed the allowance one because the structural responses are far smaller than the allowable tension and compressive forces in all cases. Therefore, the fragility assessment of support structure in terms of tension and compression force here is not necessary.

**Figure 13.** Variation of pull-out reaction: (**a**) allowable reaction; (**b**) reaction at SD = 6.5 cm.

**Figure 14.** Variation of compressive reaction: (**a**) allowable reaction; (**b**) reaction at SD = 6.5 cm.

The results of horizontal force analysis are given in Figure 15. As shown in Figure 15a, the horizontal bearing capacity decreased as the SD increased. Figure 15b shows the result of comparing the maximum horizontal reaction force and the allowable horizontal force at SD of 4 m. It can be seen from Figure 15b that most of the horizontal reaction force exceeded the allowable horizontal force at the SD of 4.0 m. If more than 4.0 m scour occurs, the probability of failure will increase.

**Figure 15.** Variation of horizontal reaction: (**a**) allowable reaction; (**b**) reaction at at SD = 4 m.

To see how the safety margin affects the fragility, five cases of safety factors (SFs) were applied to the maximum horizontal reaction force. The fragility curves of the five safety factor cases are shown in Figure 16. The corresponding median and standard deviation values of the fragility curves are listed in Table 2. As can be seen from Figure 16 and Table 2, when the safety factor was not considered, the fragility was more than 50% at SD of around 3.93 m, and when the safety factor 2.0 was considered, the fragility was more than 50% at SD of approximately 2.43 m.

**Figure 16.** Scour fragility curve.

**Table 2.** Median and log-standard deviation.


The log-normal standard deviation is equal to 0.05 because, for each SD level, the analysis was carried out by considering only the load variability.

#### *4.7. Scour Risk Assessment*

Scour risk was evaluated by integrating the product of scour hazard (SD probability) and scour fragility as given in Equation (3). The scour hazard denoted by *fSD*(*x*) was found in Figure 12. It presents the probability density of SD. The fragility denoted by *Fk*(*x*)

was found in Figure 16 according to SF. SF of 1.0 is the most critical case. Multiplying the scour hazard with the fragility and then integrating them over possible scour depth results in scour risk. Scour risk is expressed as probability of failure, *Pf* . For convenience, the probability of failure is converted into a reliability index as follows.

$$\beta = -\Phi^{-1}\begin{pmatrix} P\_f \end{pmatrix} \tag{14}$$

Reliability indices are listed in Table 3 and plotted in Figure 17. The scour risk was 1.919 × 10−7~0.718 and the reliability index was 5.708~0.578, corresponding to the SF from 1.0 to 2.0. The level of target reliability index (*βt*) can be referred from some design standards. DNV GL [29] proposes target failure probability of <sup>10</sup>−4, corresponding to *βt* of 3.719, while IEC 61400-1 [30] proposes *βt* of 3.3. Since the DNV guideline is for offshore wind turbine design, the reliability index was set higher than the IEC standard for onshore wind turbines. Furthermore, compared with the design standards, the reliability index evaluated for the PSB in Gunsan test bed seems higher than those standards if SF is below 1.5.

**Table 3.** Scour risk and reliability index.


**Figure 17.** Result of scour risk and reliability index: (**a**) scour risk; (**b**) reliability index.
