# Experimental Study on Local Scour Depth around Monopile Foundation in Combined Waves and Current

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{b}) are: flow velocity (v), water depth (h) and median particle size (d

_{50}) of soil on seabed or riverbed. Furthermore, the dimensionless depth h

_{b}/D (D is the diameter of column) may be expressed as the function of three dimensionless quantities of v/v

_{0}, h/D and D/d

_{50}; see Equation (1):

_{0}is the critical initial velocity of silty sand. In case of combined waves and currents, the relative flow velocity U

_{cw}and KC number (Keulegan–Carpenter) [15] are the two important factors that influence the scour depth surrounding the piles. The U

_{cw}value may be obtained through Equation (2):

_{c}means the flow velocity at the point 1.0 D below the bed surface under single action of water flow and U

_{w}is the maximum horizontal velocity of wave water particles near the bottom. When U

_{cw}is close to 1, it can be deemed that there is pure action of currents; when U

_{cw}is close to 0, it can be deemed that there is pure action of waves; where U

_{cw}is greater than 0.5, the scour is mainly dominated by currents; when U

_{cw}is greater than 0.7, the maximum scour depth is closer to the pure action of currents. KC number is a main parameter that controls the scour process of movable bed in case of pure action of wave. It is defined as the three main factors that influence the local scour depth surrounding the columns under single action of waves; the relationship among the maximum horizontal velocity U

_{wm}of wave water particles near the bottom, the wave period Tw and the column diameter D is shown in Equation (3):

## 2. Existing Design Methods for Local Scour Depth

## 3. Experimental Verification

#### 3.1. Experiments Arrangement

_{50}was 0.22 mm; unevenness coefficient C

_{u}= d

_{60}/d

_{10}= 1.67; the soil saturation density ρ = 1370 kg/m

^{3}; and dry density ρ

_{0}= 1096 kg/m

^{3}. The grain distribution curve of the soil samples is shown in Figure 5.

#### 3.2. Experimental Results and Analysis

#### 3.2.1. Verification of Main Influencing Factors

#### 3.2.2. Verification of Local Scour Depth

## 4. Prediction Equation in Combined Waves and Current

#### 4.1. Dimensional Analyses

_{50}, flow velocity v, water depth h, wave height H

_{w}and wave length L

_{w}. The relationship can be stated as following (Equation (4)):

_{0}, a

_{1}, a

_{2}, a

_{3}and a

_{4}are undetermined parameters. Through fitting of experimental data, the parameters with scour depth predication formula are 1.318, 0.624, −0.282, −0.288 and −0.757, respectively. Therefore, the formula for local scour depth under combined waves and current is finally organized as:

#### 4.2. Verification of New Predication Formula

#### 4.3. Discussions

## 5. Conclusions

- (1)
- For the prediction of the local scour depth of bridge piers, Formula 65-2, 65-1 (modified formula) and HEC-18 equation have similar computed results, and the Formula 65-2 is the most stable and reliable.
- (2)
- The local scour depth around monopile foundation in combined waves and current is important in the field of coastal and offshore engineering, but it has not been sufficiently studied. The design methods above cannot assess the maximum scour depth accurately in all instances. The Han Haiqian formula focuses on estimating the maximum local scour depth at foundation of sea/bay-crossing bridges in tidal currents. The Wang Rukai formula takes waves into account, but this equation requires more parameters than other methods, which means it may be not convenient when used at the design stage. The Sumer method has a simple calculation process, but it may underestimate the scour depth due to waves combined with strong currents. The mean relative errors of Formula 65-2, 65-1 (modified formula), HEC-18, Han Haiqian Formula, Wang Rukai Formula and Sumer method proposed herein are 74.7%, 82.5%, 966.5%, 490.1%, 76.8% and 425.9%, respectively.
- (3)
- Considering to the principle of dimensional analysis, experimental phenomena, and the main influencing factors of the local scour depth of a monopile, a new equation for predicting the equilibrium scour depth of a monopile under the action of combined waves and current is proposed. The mean relative error between the predicted value of the formula and the measured value in this paper is 49.1%, which is significantly smaller than other formulas.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Collapsed Sichuan Panjiang Bridge [2].

**Figure 2.**ShengLi Well Workover Platform III overturning accident [3].

**Figure 6.**Pictures of scour holes and scour forms under steady current with flow velocity v = 0.25 m/s (Run A1).(

**a**) 0 s, (

**b**) After 15 s, (

**c**) After 1 min, (

**d**) After 15 min, (

**e**) After 1 h, (

**f**) After 2 h.

**Figure 7.**Pictures of scour holes and scour forms under combined waves and current (Run C1). (

**a**) After 15 min, (

**b**) After 3 h.

**Figure 9.**Comparison between computed and observed scour depth. (

**a**) Steady current, (

**b**) Combined waves and current.

Codes | Equations | Design Specifications | Notes |
---|---|---|---|

65-2 | ${h}_{b}=\{\begin{array}{ll}{K}_{\xi}{K}_{\eta 2}{D}^{0.6}{h}_{}^{0.15}\left(\frac{v-{v}_{0}^{\u2019}}{{v}_{0}}\right)& v\le {v}_{0}\\ {K}_{\xi}{K}_{\eta 2}{D}^{0.6}{h}_{}^{0.15}{\left(\frac{v-{v}_{0}^{\u2019}}{{v}_{0}}\right)}^{{\mathrm{n}}_{2}}& v>{v}_{0}\end{array}$ $\mathrm{where}\text{}{K}_{\eta 2}$$,\text{}{v}_{0}$$,\text{}{v}_{0}^{\u2019}$$\text{}\mathrm{and}\text{}{n}_{2}$ is given by ${K}_{\eta 2}=0.0023{\overline{d}}^{-2.2}+0.375{\overline{d}}^{0.24}$; ${v}_{0}=0.28{\left(\overline{d}+0.7\right)}^{0.5}$$;\text{}{v}_{0}^{\u2019}=0.12{\left(\overline{d}+0.5\right)}^{0.55}$$;\text{}{n}_{2}={\left(\frac{{v}_{0}}{v}\right)}^{0.23+0.19\mathrm{log}\overline{d}}$ | Hydrological Specifications for Survey and Design of Highway Engineering (JTG C30-2015) [26] | 1. Based on field and experiment data collected in China [29] 2. Performed well in the following decades 3. Dimensional disharmony 4. The expression is valid for both live-bed and clear water |

65-1 (modified formula) | ${h}_{b}=\{\begin{array}{ll}{K}_{\xi}{K}_{\eta}{}_{1}{D}^{0.6}\left(v-{v}_{0}^{\u2019}\right)& v\le {v}_{0}\\ {K}_{\xi}{K}_{\eta 1}{D}^{0.6}\left(v-{v}_{0}^{\u2019}\right){\left(\frac{v-{v}_{0}^{\u2019}}{{v}_{0}-{v}_{0}^{\u2019}}\right)}^{{\mathrm{n}}_{1}}& v>{v}_{0}\end{array}$$\mathrm{where}\text{}{K}_{\eta 1}$$,\text{}{v}_{0}$$,\text{}{v}_{0}^{\u2019}$$\text{}\mathrm{and}\text{}{n}_{1}$$\text{}\mathrm{is}\text{}\mathrm{given}\text{}\mathrm{by}$${K}_{\eta 1}\text{=}0.8\left(\frac{1}{{\overline{d}}^{0.45}}\text{+}\frac{1}{{\overline{d}}^{0.15}}\right)$$;\text{}{v}_{0}=0.0246{\left(\frac{{h}_{P}}{\overline{d}}\right)}^{0.14}\sqrt{332\overline{d}+\frac{10+h}{{\overline{d}}^{0.72}}}$$;\text{}\phantom{\rule{0ex}{0ex}}{v}_{0}^{\u2019}=0.462{\left(\frac{\overline{d}}{D}\right)}^{0.06}{v}_{0}$$;\text{}{n}_{1}={\left(\frac{{v}_{0}}{v}\right)}^{0.25{\overline{d}}^{0.19}}$ | Hydrological Specifications for Survey and Design of Highway Engineering (JTG C30-2015) [26] | 1. Based on field and experiment data collected in China 2. Performed well in the following decades 3. Dimensional disharmony [29] 4. The expression is valid for both live-bed and clear water 5. Makes up for the insufficiency of the large calculation value of the 65-2 type pair in predicting the local scour depth around the pier and the river bed in the foundations such as large boulders and pebbles |

HEC-18 | $\frac{{h}_{b}}{h}=2.0{K}_{1}{K}_{2}{K}_{3}{K}_{4}{\left(\frac{D}{h}\right)}^{0.65}{F}_{r}{}^{0.43}$ $\mathrm{where}\text{}{F}_{r}$ is given by ${F}_{r}=\frac{v}{\sqrt{gh}}$ | American Association of State Highway and Transportation Officials (AASHTO LRFD) [27] | 1. Based on field and experiment data collected in USA 2. Include the coefficients for the effect of bed forms, size of bed materials, and wide piers 3. Dimensionally consistent 4. The expression is valid for both live-bed and clear water |

Han Haiqian Formula | $\frac{{h}_{b}}{h}=17.4{k}_{1}{k}_{2}{\left(\frac{D}{h}\right)}^{0.326}{\left(\frac{{d}_{50}}{h}\right)}^{0.167}{F}_{r}{}^{0.628}$ $\mathrm{where}\text{}{F}_{r}$ is given by ${F}_{r}=\frac{v}{\sqrt{gh}}$ | Chinese Code for Design of Wind Turbine Foundations for Offshore Wind Power Projects (NB/T 10105-2018) [28] | 1. Based on field and experiment data collected in China under tidal current 2. Include the coefficients for the effect of arrangement form |

Wang Rukai Formula | $\mathrm{lg}\left(\frac{{h}_{b}}{h}\right)=-1.2935+0.1917\mathrm{lg}\beta $ where $\beta $ is given by $\beta =\frac{{H}_{w}{}^{2}{v}^{3}{L}_{w}D{\left[v+\left(\frac{1}{{T}_{w}}-\frac{v}{{L}_{w}}\right)\frac{{H}_{w}{L}_{w}}{2h}\right]}^{2}}{\left(\frac{{\rho}_{\mathrm{s}}-\rho}{\rho}\right)\upsilon {g}^{2}{h}^{4}{d}_{50}}$ | Chinese Code for Design of Wind Turbine Foundations for Offshore Wind Power Projects (NB/T 10105-2018) [28] | 1. Comprehensive considerations 2. Complicated calculation |

Sumer method | $\frac{S}{D}=\{\begin{array}{ll}1.3& KC<6\\ 1.3\left\{1-\mathrm{exp}\left[-0.03\left(KC-6\right)\right]\right\}& KC>6\end{array}$ | Chinese Code for Design of Wind Turbine Foundations for Offshore Wind Power Projects (NB/T 10105-2018) [28] & The DVN GL standard for Support structures for wind turbines (DNVGL-ST-0126-2018) [30] | 1. The expression is valid for live-bed conditions 2. For steady current, which implies KC→∞, it appears from this expression that S/D→1.3 3. For waves it appears that for KC < 6, no scour hole is formed. The physical explanation for this is that no horseshoe vortex develops for KC < 6 |

_{b}= the local scour depth (m); K

_{ξ}= type factor for piers; D = the diameter of column (m); h = the water depth (m); v

_{0}= sediment-moving incipient velocity (m/s); v

_{0′}= critical mean approach flow velocity for entrainment of sediment upstream of the pier (m/s); $\overline{d}$ = the average particle size of sediment bed (m); d

_{50}= median particle size of sediment bed (m); v = the flow velocity (m/s); ρ

_{s}= dry sand density (kg/m

^{3}); ρ = the water density (kg/m

^{3}); H

_{w}= the wave height (m); L

_{w}= the wave length (m); T

_{w}= the wave period (s); υ = the kinematic viscosity of water (m

^{2}/s).

Group | Hydraulic Condition | Model | Pile Diameter (m) | Water Depth (m) | Flow Velocity (m/s) | Wave Height (m) | Wave Period (s) |
---|---|---|---|---|---|---|---|

A1 | Steady current | Column | 0.04 | 0.3 | 0.25 | ||

A2 | Steady current | Column | 0.04 | 0.4 | 0.225 | ||

A3 | Steady current | Column | 0.04 | 0.4 | 0.25 | ||

C1 | Waves & current | Column | 0.04 | 0.4 | 0.225 | 0.06 | 1 |

C2 | Waves & current | Column | 0.04 | 0.4 | 0.225 | 0.08 | 1 |

C3 | Waves & current | Column | 0.04 | 0.3 | 0.225 | 0.06 | 1 |

Group | Measured Depth | 65-2 Formula | 65-1 Modified Formula | HEC-18 | Han Haiqian Formula | Wang Rukai Formula | Sumer Method |
---|---|---|---|---|---|---|---|

A1 | 4.1 | 2.29 | 3.42 | 56 | - | - | - |

A2 | 3.5 | 1.80 | 2.02 | 62 | - | - | - |

A3 | 3.7 | 2.19 | 3.95 | 70 | - | - | - |

C1 | 3.7 | 1.90 | 2.02 | 54 | 24 | 1.34 | 5.20 |

C2 | 4.0 | 1.80 | 2.02 | 62 | 24 | 1.54 | 5.20 |

C3 | 3.5 | 1.90 | 2.41 | 67 | 23 | 1.29 | 5.20 |

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**MDPI and ACS Style**

Li, J.; Zhang, B.; Shen, C.; Fu, X.; Li, W.
Experimental Study on Local Scour Depth around Monopile Foundation in Combined Waves and Current. *Sustainability* **2021**, *13*, 13614.
https://doi.org/10.3390/su132413614

**AMA Style**

Li J, Zhang B, Shen C, Fu X, Li W.
Experimental Study on Local Scour Depth around Monopile Foundation in Combined Waves and Current. *Sustainability*. 2021; 13(24):13614.
https://doi.org/10.3390/su132413614

**Chicago/Turabian Style**

Li, Junhan, Bin Zhang, Chao Shen, Xiaoli Fu, and Weichao Li.
2021. "Experimental Study on Local Scour Depth around Monopile Foundation in Combined Waves and Current" *Sustainability* 13, no. 24: 13614.
https://doi.org/10.3390/su132413614