**1. Introduction**

Suction Bucket (SB) is a highly competitive foundation solution among the several types of foundations currently implemented to support offshore wind turbines (OWT) due to their quick and noise-free installation. They are also a more economical solution compared to other foundations, especially for a large-scale wind farm [1]. The main design factors of such a SB support structure are the horizontal bearing capacity and the stiffness of the foundation. Latini and Zania, 2017 [2] investigated the dynamic behavior of SB and concluded that the skirt length of a SB is an important parameter that determines the dynamic behavior, and the horizontal bearing capacity is greatly affected by the ratio of the bucket diameter and length. Foundation stiffness is strongly dependent on the relative density of sand and the bucket's geometry and has been investigated in a series of studies [3–5]. When existing SB support structures are installed in area where the geological structure is a shallow soft-layer soil on top of a hard-layer soil, there is a problem that the SB diameter must be abnormally large to fulfill the required bearing capacity. To solve this problem, a pentapod suction bucket (PSB) support structure was developed by Ngo et al. [6], and a seismic fragility analysis was performed on the developed support structure.

Scouring is recognized as a risk factor that weakens the bearing capacity around the turbine support structures. Accordingly, local scour around OWT foundations has been studied by many researchers [7–9], and most studies have used scale model tests and numerical simulations. A series of laboratory experiments were conducted by Hu et al. [10] to investigate the scour development around tripod foundation in combined waves and the current. The influence of installation angles, KC number, and the ratio of velocities Ucw on the scour depth were also examined. In another study, Hu and his colleagues proposed a method to predict the equilibrium scour depth around the umbrella suction anchor foundation [11]. In order to reduce the risk of scouring, a prevention method is

**Citation:** Kim, Y.-J.; Ngo, D.-V.; Lee, J.-H.; Kim, D.-H. Ultimate Limit State Scour Risk Assessment of a Pentapod Suction Bucket Support Structure for Offshore Wind Turbine. *Energies* **2022**, *15*, 2056. https:// doi.org/10.3390/en15062056

Academic Editor: Paweł Liz ˛ega

Received: 23 January 2022 Accepted: 7 March 2022 Published: 11 March 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

installed around the support structures [12]. Since the scouring protection method incurs costs, a reasonable risk assessment by scouring is necessary for the development of an economical power generation complex. Studies on the behavior of supporting structures by scouring have not been actively performed. A few studies have been recently reported. Yi et al., 2013 studied the effect of scour on dynamic instability of monopile offshore wind turbines [13]. In the study, the natural frequency change according to seabed scour depth (SD) was analyzed and possible resonance due to scour was discussed. Ma et al., 2018 [14] studied the effect of local scour around foundation on the dynamic behavior of the support structure. Both studies revealed that scour had little effect on frequencies but had some effect on dynamic behavior. Scour risk assessment around marine structures has also been performed in many studies. Yanmaz and Salamak [15] evaluated the risk of the scouring process at bridge piers. They established a probabilistic model for the scour depth predictions through empirical equations in the dimensional state. Khalid et al. [16] applied a non-linear regression-based technique to calculate the reliability of scour depth values at bridge piers installed in cohesive bed sediments. A study that evaluated a reliabilitybased probabilistic of the wave-induced scour depth around marine structure piles was performed by Homaei et al. [17]; they developed a probabilistic model by using an artificial intelligence method so as to predict the scour depth at pile groups under regular waves. However, these studies were conducted on monopiles, and the risk of scouring could not be evaluated quantitatively. Kim et al., 2020, proposed a scouring risk assessment method by combining the scouring hazard and fragility of the support structure [18]. They showed, for the first time, that scour risk can be evaluated by modifying the seismic risk assessment approach. Scour fragility of a tripod suction bucket (TSB) was found by defining a critical displacement at foundation. Ngo et al. recently reported a seismic fragility analysis of PSB support structure and showed that the seismic performance of the pentapod is superior to that of the TSB [6].

In this study, a scour risk analysis was performed to evaluate the stability of the newly developed PSB support structure at an ultimate limit state. For this, the hazard according to the scour depth was calculated. For the scour depth, an empirical formula defined as a function of marine environmental variables was used. As for the fragility, the bearing capacity limit state according to the ultimate load was used instead of the fragility function based on displacement [18]. The safety factor (SF) was applied to the reaction force of the PSB to determine how the scour risk was affected.

In the second chapter, theoretical background of scour risk assessment is explained. How to calculate scour hazard, fragility and risk are shown in detail. In the third chapter, why a PSB is developed and features of PSB are explained. After that, numerical analysis and conclusions are described in turn.

#### **2. Scour Risk**

#### *2.1. Probability of SD*

During the design process, the capacity of OWT substructure (SB foundation in this study) is designed against external loads such as wind, wave, and so on. The magnitude of these external loads is governed by wind speed, wave height or current velocity, etc. and their effects have also been verified through various design load cases (DLCs). Nevertheless, the initial OWT foundation's design capacity may be decreased due to several reasons, with local scouring around its foundation being the most common. In previous studies, maximum equilibrium SD was suggested as a keyword to evaluate the influence of scouring on the structure. This leads to unnecessary costs in the design and operation of an OWT, especially when the scale of the wind farm project is large. Therefore, it is necessary to consider scouring as a probabilistic parameter in risk analysis.

In this study, the empirical formula of Equation (1) proposed by Sumer and Fredsoe, 2001 [19] is used to obtain the probability distribution of SD. In Equation (1), the SD is a function of the Keulegan–Carpenter (KC) number and the parameter Ucw, in which KC was

defined by the peak spectrum period ( *Tp*), pile diameter ( D), and maximum value of the undisturbed orbital velocity at the sea bottom just above the wave boundary layer (U m).

$$\frac{\text{S}}{\text{D}} = \frac{\text{S}\_{\text{C}}}{\text{D}} [1 - \exp\{-\text{A}(\text{KC} - \text{B})\}], \text{ KC} \ge 4 \tag{1}$$

where: S: SD; SC: SD in the case of steady current alone; D: pile diameter; KC = U m Tp/D = 2πa/D; A = 0.03 + 0.75 U2.6 cw; B = 6 exp(−4.7Ucw); Ucw = Uc/(Uc + U m); UC: the undisturbed current velocity at the distance, y = D/2 from the bed; U m: maximum value of the undisturbed orbital velocity at the bed; Tp: peak spectrum period; a: the amplitude of the motion of water particles at the bed.

In Equation (1), the SD probability distribution can be obtained by considering the variability of KC parameter. The variability of KC is governed by the variability of height and period of the significant wave. The probability density function (PDF) of SD obtained here is a scour hazard for risk analysis and denoted by *fSD*(*x*).

## *2.2. Scour Fragility*

The fragility curve of structures under earthquakes has been proposed by Shinozuka et al., 2000 [20]. These fragility curves are represented by logarithmic normal distribution functions, and the two coefficients of the lognormal distribution function, median and logarithmic standard deviation, are obtained by the maximum likelihood estimation method. For the *k*-th damage among various damage stages, the fragility curve can be expressed as:

$$F\_k(\mathbf{x}) = \Phi \left| \frac{\ln\left(\frac{\mathbf{x}}{c\_k}\right)}{\mathcal{J}\_\mathbf{k}} \right| \tag{2}$$

where Φ is the standard normal cumulative distribution function, *ck* is the median, and *ζ*k is the logarithmic standard deviation.

When assessing structural fragility, a limit state should be determined first. There are various limit states such as serviceability limit state (SLS), fatigue limit state (FLS) and ultimate limit states (ULS). Kim et al. found fragility curves of TSB based on displacement [10]. Because the displacement of the bucket causes a serviceability problem rather than the destruction of the support structure, it is a fragility based on SLS. However, the purpose of this study is to evaluate bearing capacity of a newly designed PSB under ultimate load case. Therefore, an event in which the reaction force of the bucket exceeds the allowable bearing capacity was defined as the failure. Therefore, the fragility of this study can be called ULS based.

## *2.3. Scour Risk*

By combining the probability of SD (hazard) and the scour fragility curve of the structure, the scour risk can be calculated as in Equation (3).

$$P\_f = \int\_{x\_0}^{x\_{\text{max}}} f\_{SD}(\mathbf{x}) F\_k(\mathbf{x}) d\mathbf{x} \tag{3}$$

where *xmax* and *x*0 is the maximum possible SD and the lowest SD, respectively.

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