# Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{eq}around USAF. At last, a parametric study was carried out to study the effects of the Froude number F

_{r}and Euler number E

_{u}for the S

_{eq.}The results indicate that the present numerical model is accurate and reasonable for depicting the scour morphology under random waves. The revised Raaijmakers’s model shows good agreement with the simulating results of the present study when KC

_{s,p}< 8. The predicting results of the revised stochastic model are the most favorable for n = 10 when KC

_{rms,a}< 4. The higher F

_{r}and E

_{u}both lead to the more intensive horseshoe vortex and larger S

_{eq}.

## 1. Introduction

_{cr}) or live bed scour (θ > θ

_{cr}). Due to the set of foundation, the adverse hydraulic pressure gradient exists at upstream foundation edges, resulting in the streamline separation between boundary layer flow and seabed. The separating boundary layer ascended at upstream anchor edges and developed into the horseshoe vortex. Then, the horseshoe vortex moved downstream gradually along the periphery of the anchor, and the vortex shed off continually at the lee-side of the anchor, i.e., wake vortex. The core of wake vortex is a negative pressure center, liking a vacuum cleaner. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortexes. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow when the turbulence energy could not support the survival of wake vortex. According to Tavouktsoglou et al. [25], the scale of pile wall boundary layer is proportional to 1/ln(R

_{d}) (R

_{d}is pile Reynolds), which means the turbulence intensity induced by the flow-structure interaction would decrease with R

_{d}increases, but the effects of R

_{d}can be neglected only if the flow around the foundation is fully turbulent [26]. According to previous studies [1,15,27,28,29,30,31,32], the scour development around pile foundation under waves was significantly influenced by Shields parameter θ and KC number simultaneously (calculated by Equation (1)). Sand ripples widely existed around pile under waves in the case of live bed scour, and the scour morphology is related with θ and KC. Compared with θ, KC has a greater influence on the scour morphology [21,27,28]. The influence mechanism of KC on the scour around the pile is reflected in two aspects: the horseshoe vortex at upstream and wake vortex shedding at downstream.

_{wm}is the maximum velocity of the undisturbed wave-induced oscillatory flow at the sea bottom above the wave boundary layer, T is wave period, and D is pile diameter.

_{wave}is correction factor considering wave action, K

_{hw}is correction factor considering water depth.

_{w}is water depth.

_{cr}is critical shields parameter.

_{c}is critical velocity corresponding the onset of sediment motion.

_{m}and peak wave period T

_{P}to calculate KC. Khalfin [35] recommended the RMS wave height H

_{rms}and peak wave period T

_{P}were used to calculate KC for Equation (6). References [37,38,39,40] developed a series of stochastic theoretical models to predict equilibrium scour depth around pile under random waves, nonlinear random waves plus currents respectively. The stochastic approach thought the 1/n’th highest wave were responsible for scour in vicinity of pile under random waves, and the KC was calculated in Equation (8) with U

_{m}and mean zero-crossing wave period T

_{z}. The results calculated by Equation (8) agree well with experimental values of Sumer and Fredsøe [16] if the 1/10′th highest wave was used. To author’s knowledge, the stochastic approach proposed by Myrhaug and Rue [37] is the only theoretical model to predict equilibrium scour depth around pile under random waves for the whole range of KC number in published documents. Other methods of predicting scour depth under random waves are mainly originated from the equation for regular waves-only, waves and currents combined, which are limited to the large KC number, such as KC > 6 for Equation (2) and KC > 4 for Equation (3) respectively. However, situations with relatively low KC number (KC < 4) often occur in reality, for example, monopile or suction anchor for OWT foundations in ocean environment. Moreover, local scour around OWT foundations under random waves has not yet been investigated fully. Therefore, further study are still needed in the aspect of scour around OWT foundations with low KC number under random waves. Given that, this study presents the scour sediment model around umbrella suction anchor foundation (USAF) under random waves. In this study, a comparison of equilibrium scour depth around USAF between this present numerical models and the previous theoretical models and experimental results was presented firstly. Then, this study gave a comprehensive analysis for the scour mechanisms around USAF. After that, two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] respectively to predict the equilibrium scour depth. Finally, a parametric study was conducted to study the effects of the Froude number (F

_{r}) and Euler number (E

_{u}) to equilibrium scour depth respectively.

## 2. Numerical Method

#### 2.1. Governing Equations of Flow

_{F}is the volume fraction; u, v, and w are the velocity components in x, y, z direction respectively with Cartesian coordinates; A

_{i}is the area fraction; ρ

_{f}is the fluid density, f

_{i}is the viscous fluid acceleration, G

_{i}is the fluid body acceleration (i = x, y, z).

#### 2.2. Turbulent Model

_{T}is specific kinetic energy involved with turbulent velocity, G

_{T}is the turbulent energy generated by buoyancy; ε

_{T}is the turbulent energy dissipating rate, P

_{T}is the turbulent energy, Diff

_{ε}and Diff

_{kT}are diffusion terms associated with V

_{F}, A

_{i}; CDIS1, CDIS2 and CDIS3 are dimensionless parameters, and CDIS1, CDIS3 have default values of 1.42, 0.2 respectively. CDIS2 can be obtained from P

_{T}and k

_{T}.

#### 2.3. Sediment Scour Model

#### 2.3.1. Entrainment and Deposition

_{i}is the entrainment parameter,

**n**is the outward point perpendicular to the seabed, d

_{s}_{*}is the dimensionless diameter of sand particles, which was calculated by Equation (15), θ

_{cr}is the critical Shields parameter, g is the gravity acceleration, d

_{i}is the diameter of sand particles, ρ

_{i}is the density of seabed species.

_{f}is the fluid dynamic viscosity.

_{i}confirms the rate at which sediment erodes when the given shear stress is larger than the critical shear stress, and the recommended value 0.018 was adopted according to the experimental data of Mastbergen and Von den Berg [43].

**n**is the outward pointing normal to the seabed interface, and

_{s}**n**= (0,0,1) according to the Cartesian coordinates used in present numerical model.

_{s}_{f,m}is the maximum value of the near-bed friction velocity; d

_{50}is the median diameter of sand particles. The detailed calculation procedure of θ was available in Soulsby [44].

_{cr}was obtained from the Equation (17) [44]

_{f}is the fluid kinematic viscosity.

#### 2.3.2. Bed Load Transport

_{b,i}is the bed load transport rate, which was obtained from Equation (20), δ

_{i}is the bed load thickness, which was calculated by Equation (21), c

_{b,i}is the volume fraction of sand i in the multiple species, f

_{b}is the critical packing fraction of the seabed.

#### 2.3.3. Suspended Load Transport

_{s,i}is the suspended sand particles mass concentration of sand i in the multiple species,

**u**

_{s,i}is the sand particles velocity of sand i, D

_{f}is the diffusivity.

_{s,i}is the suspended sand particles volume concentration, which was computed from Equation (24).

## 3. Model Setup

_{50}= 0.041 cm. The USAF model includes upper steel tube with the length of 20 m, which was installed in the middle of seabed. The location of USAF is positioned at 140 m from the upstream inflow boundary and 70 m from the downstream outflow boundary. Two baffles were installed at two ends of seabed. In order to eliminate the wave reflection basically, the porous media was set at the outflow side on the seabed.

#### 3.1. Mesh Geometric Dimensions

#### 3.2. Boundary Conditions

#### 3.3. Wave Parameters

_{p}is wave spectrum peak frequency, which can be obtained from Equation (27). γ is wave spectrum peak enhancement factor, in this study γ = 3.3. σ is spectral width factor, σ equals 0.07 for ω ≤ ω

_{p}and 0.09 for ω > ω

_{p}respectively.

_{r}were acquired form Equations (28) and (29) respectively

_{s}is significant wave height, T

_{a}is average wave period, k is wave number, h

_{w}is water depth. The Shield parameter θ satisfies θ

_{>}θ

_{cr}for all simulations in current study, indicating the live bed scour prevails.

#### 3.4. Mesh Sensitivity

_{*}is an important factor for influencing scour process [1,15], so U

_{*}at the position of (4,0,11.12) was evaluated under three mesh sizes. As the Figure 4 shown, the maximum error of shear velocity ∆U

_{*1,2}is about 39.8% between the mesh 1 and mesh 2, and 4.8% between the mesh 2 and mesh 3. According to the mesh sensitivity criterion adopted by Pang et al. [48], it’s reasonable to think the results are mesh size independent and converged with mesh 2. Additionally, the present model was built according to prototype size, and the mesh size used in present model is larger than the mesh size adopted by Higueira et al. [49] and Corvaro et al. [50]. If we choose the smallest cell size, it will take too much time. For example, the simulation with Mesh3 required about 260 h by using a computer with Intel Xeon Scalable Gold 4214 CPU @24 Cores, 2.2 GHz and 64.00 GB RAM. Therefore, in this case, considering calculation accuracy and computation efficiency, the mesh 2 was chosen for all the simulation in this study.

#### 3.5. Model Validation

## 4. Numerical Results and Discussions

#### 4.1. Scour Evolution

_{c}is time scale of scour process.

#### 4.2. Scour Mechanism under Random Waves

#### 4.3. Equilibrium Scour Depth

_{wm}and wave period T. For random waves, the U

_{wm}can be denoted by the root-mean-square (RMS) value of near-bed velocity amplitude U

_{wm,rms}or the significant value of near-bed velocity amplitude U

_{wm,s}. The U

_{wm,rms}and U

_{wm,s}for all simulating cases of the present study are listed in Table 3 and Table 4. The T can be denoted by the mean up zero-crossing wave period T

_{a}, peak wave period T

_{p}, significant wave period T

_{s}, the maximum wave period T

_{m}, 1/10′th highest wave period T

_{n = 1/10}and 1/5′th highest wave period T

_{n = 1/5}for random waves, so the different combinations of U

_{wm}and T will acquire different KC. The Table 3 and Table 4 list 12 types of KC, for example, the KC

_{rms,s}was calculated by U

_{wm,rms}and T

_{s}. Sumer and Fredsøe [16] conducted a series of wave flume experiments to investigate the scour depth around monopile under random waves, and found the equilibrium scour depth predicting equation (Equation (2)) for regular waves was applicable for random waves with KC

_{rms,p}. It should be noted that the Equation (2) is only suitable for KC > 6 under regular waves or KC

_{rms,p}> 6 under random waves.

_{eq}between the present study and Raaijmakers’s equation was conducted. The position where the scour depth S

_{eq}was evaluated is the location of the maximum scour depth, and it was depicted in Figure 14. The Figure 15 displays the comparison of S

_{eq}with different KC between the present study and Raaijmakers’s model.

_{eq}between the present study and Raaijmakers’s model, and Raaijmakers’s model underestimates the results generally. Although the error exists, the varying trend of S

_{eq}with KC obtained from Raaijmakers’s model is consistent with the present study basically. What’s more, the error is minimum and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves by using KC

_{s,p}. Based on this, a further revision was made to eliminate the error as much as possible, i.e., add the deviation value ∆S/D in the Raaijmakers’s model. The revised equilibrium scour depth predicting equation based on Raaijmakers’s model can be written as

_{s,p}> 4) under random waves, a validation between the revised model and the previous experimental results [21]. The experiment was conducted in a flume (50 m in length, 1.0 m in width and 1.3 m in height) with a slender vertical pile (D = 0.1 m) under random waves. The seabed is composed of 0.13 m deep layer of sand with d

_{50}= 0.6 mm and the water depth is 0.5 m for all tests. The significant wave height is 0.12~0.21 m and the KC

_{s,p}is 5.52~11.38. The comparison between the predicting results by Equation (31) and the experimental results of Corvaro et al. [21] is shown in Figure 17. From Figure 17, the experimental data evenly distributes around the predicted results and the prediction accuracy is favorable when KC

_{s,p}< 8. However, the gap between the predicting results and experimental data becomes large and the Equation (31) overestimates the equilibrium scour depth to some extent when KC

_{s,p}> 8.

_{rms,a}in the stochastic model. To verify the application of the stochastic model for predicting scour depth around USAF, a validation between the simulating results of present study and predicting results by the stochastic model with n = 2,3,5,10,20,500 was carried out respectively.

_{eq}with KC

_{rms,a}obtained from the stochastic model is consistent with the present study basically. What’s more, the gap between the predicting values by stochastic model and the simulating results decreases with the increase of n, but for large n, for example n = 500, the varying trend diverges between the predicting values and simulating results, meaning it’s not feasible only by increasing n in stochastic model to predict the equilibrium scour depth around USAF.

_{eq}/D′ between the predicting values and simulating results with different KC

_{rms,a}and n. Then, fitted the relationship between the ∆S′and n under different KC

_{rms,a}, and the fitting curve can be written by Equation (32). The revised stochastic model (Equation (33)) can be acquired by adding ∆S

_{eq}/D′ to Equation (8).

_{eq}with KC

_{rms,a}obtained from the stochastic model is consistent with the present study basically. Compared with predicting results by the stochastic model, the results calculated by Equation (33) is favorable. Moreover, comparison with simulating results indicates that the predicting results are the most favorable for n = 10, which is consistent with the findings of Myrhaug and Rue [37] for equilibrium scour depth predicting around slender pile in case of random waves.

_{rms,a}> 4) under random waves, a validation was conducted between the Equation (33) and the previous experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. The details of experiments conducted by Corvaro et al. [21] were described in above section. Sumer and Fredsøe [16] investigated the local scour around pile under random waves. The experiments were conducted in a wave basin with a slender vertical pile (D = 0.032, 0.055 m). The seabed is composed of 0.14 m deep layer of sand with d

_{50}= 0.2 mm and the water depth was maintained at 0.5 m. The JONSWAP wave spectrum was used and the KC

_{rms,a}was 5.29~16.95. The comparison between the predicting results by Equation (33) and the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] are shown in Figure 21. From Figure 21, contrary to the case of low KC

_{rms,a}(KC

_{rms,a}< 4), the error between the predicting values and experimental results increases with decreasing of n for KC

_{rms,a}> 4. Therefore, the predicting results are the most favorable for n = 2 when KC

_{rms,a}> 4.

#### 4.4. Parametric Study

#### 4.4.1. Influence of Froude Number

_{r}is the key parameter to influence the scale and intensity of horseshoe vortex. The F

_{r}under waves can be calculated by the following formula [42]

_{w}is the mean water particle velocity during 1/4 cycle of wave oscillation, obtained from the following formula. Noteworthy is that the root-mean-square (RMS) value of near-bed velocity amplitude U

_{wm,rms}is used for calculating U

_{wm}.

_{r}and the vertical location of the stagnation y

_{eq}/D and F

_{r}of the present study. In order to compare with the simulating results, the experimental data of Corvaro et al. [21] was also depicted in Figure 23. As shown in Figure 23, the equilibrium scour depth appears a logarithmic increase as F

_{r}increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increase of F

_{r}, which is benefit for the wave boundary layer separating from seabed, resulting in the high-intensity horseshoe vortex, hence, causing intensive scour around USAF. Based on the previous study of Tavouktsoglou et al. [25] for scour around pile under currents, the high F

_{r}leads to the stagnation point is closer to the mean sea level for shallow water, causing the stronger downflow kinetic energy. As mentioned in previous section, the energy of downflow at upstream makes up the energy of the subsequent horseshoe vortex, so the stronger downflow kinetic energy results in the more intensive horseshoe vortex. Therefore, the higher F

_{r}leads to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably. Qi and Gao [19] carried out a series of flume tests to investigate the scour around pile under regular waves, and proposed the fitting formula between S

_{eq}/D and F

_{r}as following

_{eq}/D and F

_{r}in present study is consistent with Equation (37) basically, meaning the Equation (37) is applicable to express the relationship of S

_{eq}/D with F

_{r}around USAF under random waves.

#### 4.4.2. Influence of Euler Number

_{u}is the influencing factor for the hydrodynamic field around foundation. The E

_{u}under waves can be calculated by the following formula. The E

_{u}can be represented by the Equation (38) for uniform cylinders [25]. The root-mean-square (RMS) value of near-bed velocity amplitude U

_{m,rms}is used for calculating U

_{m}.

_{m}is depth-averaged flow velocity.

_{eq}/D and E

_{u}of the present study. In order to compare with the simulating results, the experimental data of Sumer and Fredsøe [16] and Corvaro et al. [21] were also plotted in Figure 25. As shown in Figure 25, similar with the varying trend of S

_{eq}/D and F

_{r}, the equilibrium scour depth appears a logarithmic increase as E

_{u}increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increasing of E

_{u}, which is benefit for the wave boundary layer separating from seabed, inducing the high-intensity horseshoe vortex, hence, causing intensive scour around USAF.

_{r}and E

_{u}reflect the magnitude of adverse pressure gradient pressure at upstream. Given that, the Equation (37) also was used to fit the simulating results with A = 8.875, B = 0.078 and C = −9.601, and the results are shown in Figure 25. From Figure 25, the simulating results evenly distribute around the Equation (37) and the varying trend of S

_{eq}/D and E

_{u}in present study is consistent with Equation (37) basically, meaning the Equation (37) is also applicable to express the relationship of S

_{eq}/D with E

_{u}around USAF under random waves. Additionally, according to the above description of F

_{r}, it can be inferred that the higher F

_{r}and E

_{u}both lead to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably.

## 5. Conclusions

_{r}and Euler number E

_{u}to the equilibrium scour depth around USAF under random waves. The main conclusions can be described as follows.

- (1)
- The packed sediment scour model and the RNG k−ε turbulence model were used to simulate the sand particles transport processes and the flow field around UASF respectively. The scour evolution obtained by the present model agrees well with the experimental results of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22], which indicates that the present model is accurate and reasonable for depicting the scour morphology around UASF under random waves.
- (2)
- The vortex system at wave crest phase is mainly related to the scour process around USAF under random waves. The maximum scour depth appeared at the lee-side of the USAF at the initial stage (t < 1200 s). Subsequently, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.
- (3)
- The error is negligible and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves when KC is calculated by KC
_{s,p}. Given that, a further revision model (Equation (31)) was proposed according to Raaijmakers’s model to predict the equilibrium scour depth around USAF under random waves and it shows good agreement with the simulating results of the present study when KC_{s,p}< 8. - (4)
- Another further revision model (Equation (33)) was proposed according to the stochastic model established by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves, and the predicting results are the most favorable for n = 10 when KC
_{rms,a}< 4. However, contrary to the case of low KC_{rms,a}, the predicting results are the most favorable for n = 2 when KC_{rms,a}> 4 by the comparison with experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. - (5)
- The same formula (Equation (37)) is applicable to express the relationship of S
_{eq}/D with E_{u}or F_{r}, and it can be inferred that the higher F_{r}and E_{u}both lead to the more intensive horseshoe vortex and larger S_{eq.}

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) The sketch of seabed-USAF-wave three-dimensional model; (

**b**) boundary condation:Wv-wave boundary, S-symmetric boundary, O-outflow boundary; (

**c**) USAF model.

**Figure 6.**Comparison of surface elevation between the present study and Stahlmann [53].

**Figure 10.**Velocity profile around USAF: (

**a**) Flow runup and down stream at upstream anchor edges; (

**b**) Horseshoe vortex at upstream anchor edges; (

**c**) Flow reversal during wave through stage at lee side.

**Figure 12.**Turbulence intensity: (

**a**) Turbulence intensity of horseshoe vortex; (

**b**) Turbulence intensity of wake vortex; (

**c**) Turbulence intensity of accretion area.

**Figure 15.**Comparison of the equilibrium scour depth between the present model and the model of Raaijmakers and Rudolph [34]: (

**a**) KC

_{rms,s}, KC

_{rms,a}; (

**b**) KC

_{rms,p}, KC

_{rms,m}; (

**c**) KC

_{rms,n = 1/10}, KC

_{rms,n = 1/5}; (

**d**) KC

_{s,s}, KC

_{s,a}; (

**e**) KC

_{s,p}, KC

_{s,m}; (

**f**) KC

_{s,n = 1/10}, KC

_{s,n = 1/5}.

**Figure 16.**Comparison of S

_{eq}between the simulating results and the predicting values by Equation (31).

**Figure 17.**Comparison of S

_{eq}/D between the Experimental results of Corvaro et al. [21] and the predicting values by Equation (31).

**Figure 18.**Comparison of S

_{eq}between the simulating results and the predicting values by Equation (8).

**Figure 20.**Comparison of S

_{eq}between the simulating results and the predicting values by Equation (33).

Item | Dimension/m |
---|---|

Main tube height | 11.2 |

Main tube diameter | 4 |

Main tube wall thickness | 0.02 |

Tube skirt height | 2 |

Tube skirt diameter | 8 |

Tube skirt wall thickness | 0.02 |

Anchor branch length | 4 |

Anchor branch thickness | 0.048 |

Case | Water Depth/m | Significant Wave Height H_{1/3}/m | Peak Period T_{p}/s | ε | U_{r} |
---|---|---|---|---|---|

1 | 8 | 3.0 | 8.79 | 0.029 | 0.658 |

2 | 8 | 3.5 | 9.53 | 0.029 | 0.928 |

3 | 8 | 4.0 | 10.37 | 0.028 | 1.282 |

4 | 8 | 4.5 | 10.76 | 0.029 | 1.567 |

5 | 8 | 5.0 | 11.19 | 0.030 | 1.898 |

6 | 9 | 5.0 | 11.19 | 0.030 | 1.480 |

7 | 10 | 5.0 | 11.19 | 0.030 | 1.184 |

8 | 11 | 5.0 | 11.19 | 0.030 | 0.965 |

9 | 12 | 5.0 | 11.19 | 0.030 | 0.800 |

Case | U_{wm,rms} | KC_{rms,a} | KC_{rms,p} | KC_{rms,s} | KC_{rms,m} | KC_{rms,n = 1/10} | KC_{rms,n = 1/5} |
---|---|---|---|---|---|---|---|

1 | 0.882 | 1.462 | 1.938 | 1.805 | 1.781 | 1.496 | 1.372 |

2 | 1.080 | 1.940 | 2.573 | 2.396 | 2.364 | 1.986 | 1.822 |

3 | 1.285 | 2.511 | 3.330 | 3.101 | 3.060 | 2.571 | 2.358 |

4 | 1.470 | 2.981 | 3.953 | 3.681 | 3.633 | 3.052 | 2.799 |

5 | 1.655 | 3.490 | 4.629 | 4.309 | 4.253 | 3.573 | 3.277 |

6 | 1.526 | 3.219 | 4.270 | 3.975 | 3.923 | 3.296 | 3.023 |

7 | 1.414 | 2.982 | 3.955 | 3.682 | 3.634 | 3.053 | 2.800 |

8 | 1.314 | 2.773 | 3.677 | 3.424 | 3.379 | 2.839 | 2.604 |

9 | 1.229 | 2.593 | 3.439 | 3.202 | 3.160 | 2.655 | 2.435 |

Case | U_{wm,s} | KC_{s,s} | KC_{s,p} | KC_{s,a} | KC_{s,m} | KC_{s,n = 1/10} | KC_{s,n = 1/5} |
---|---|---|---|---|---|---|---|

1 | 1.390 | 2.844 | 3.055 | 2.303 | 2.807 | 2.358 | 2.163 |

2 | 1.670 | 3.705 | 3.980 | 3.001 | 3.657 | 3.072 | 2.818 |

3 | 1.955 | 4.719 | 5.068 | 3.822 | 4.657 | 3.913 | 3.588 |

4 | 2.220 | 5.561 | 5.973 | 4.503 | 5.488 | 4.611 | 4.229 |

5 | 2.489 | 6.482 | 6.963 | 5.250 | 6.398 | 5.375 | 4.929 |

6 | 2.314 | 6.026 | 6.472 | 4.880 | 5.947 | 4.997 | 4.582 |

7 | 2.165 | 5.639 | 6.056 | 4.567 | 5.565 | 4.676 | 4.288 |

8 | 2.033 | 5.296 | 5.688 | 4.289 | 5.227 | 4.391 | 4.027 |

9 | 1.919 | 4.998 | 5.368 | 4.048 | 4.933 | 4.144 | 3.801 |

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**MDPI and ACS Style**

Hu, R.; Liu, H.; Leng, H.; Yu, P.; Wang, X.
Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. *J. Mar. Sci. Eng.* **2021**, *9*, 886.
https://doi.org/10.3390/jmse9080886

**AMA Style**

Hu R, Liu H, Leng H, Yu P, Wang X.
Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. *Journal of Marine Science and Engineering*. 2021; 9(8):886.
https://doi.org/10.3390/jmse9080886

**Chicago/Turabian Style**

Hu, Ruigeng, Hongjun Liu, Hao Leng, Peng Yu, and Xiuhai Wang.
2021. "Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves" *Journal of Marine Science and Engineering* 9, no. 8: 886.
https://doi.org/10.3390/jmse9080886