# A Laboratory Scale of the Physical Model for Inclined and Porous Breakwaters on the Coastline of Soc Trang Province (Mekong Delta)

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## Abstract

**:**

## 1. Introduction

## 2. Breakwater Block Designs

#### 2.1. Water Level and Wave Condition

#### 2.2. Breakwater Parameters

#### 2.2.1. Submerged Breakwater

_{tp}is the sea water level, Z

_{tp}= Z

_{1%}= +1.53, H

_{s}= 0.81 m is the wave height at the expected construction area, and the planned subsidence height S = 0.5 m.

#### 2.2.2. Emerged Breakwater

## 3. Physical Models

#### 3.1. Modelling Scales

#### 3.2. Model Construction and Scenarios

- -
- Defining an optimal diameter of the pores in the breakwater surfaces; the pores could be on either the front or the back side or on both sides;
- -
- Defining the wave energy dissipation ability of the block with chosen pores (presented in Table 3 below).

- -
- On the back side, the diameter of the largest pore is 5.7 cm, whereas the diameter of the smallest pore is 4.1 cm.
- -
- On the front side, the diameter of the largest pore is 8.9 cm. It is 5.7 cm for the smallest pore.

## 4. Results and Discussion

#### 4.1. Wave Parameter Estimations

- ❖
- Wave height at zero moment ${H}_{m0}$

_{m}

_{0}can be defined using the zero moment of the wave variance density spectra (Nguyen Viet Tien et al., 2013) [17]:

- -
- $S\left(f\right)$ is the variance density of the spectrum corresponding to frequency f;$$S\left(f\right)=\frac{\beta {g}^{2}}{16{\pi}^{4}}{f}^{-5}\mathrm{exp}\left[-\frac{5}{4}{\left(\frac{f}{{f}_{m}}\right)}^{-4}\right]{\gamma}^{b}$$$\sigma =\left\{\begin{array}{cc}{\sigma}_{1}& ,f\le {f}_{m}\\ {\sigma}_{2}& ,f>{f}_{m}\end{array}\right.$${\sigma}_{1},{\sigma}_{2}$—Spectral width parameters.

- ❖
- Wave peak periods ${T}_{p}$ and ${T}_{m-\mathrm{1,0}}$

- ❖
- Wave transmission coefficient of the breakwater

_{c}> 0 for emerged breakwaters and R

_{c}< 0 for submerged breakwaters (Figure 7, Top).

- ❖
- Wave reflection coefficient

- ❖
- Wave dissipation coefficient

#### 4.2. Dependency of Wave Dissipation Capacity on Pore Diameters of Breakwater

#### 4.3. Wave-Reducing Effects

_{c}/H

_{m0}varying within (2.60~3.56).

_{t}values between the HTB, PRWB, and rubble-mound breakwaters reveals that the transmission efficiency is low when the breakwaters are working in the emerging state. However, when breakwaters are submerged, the transmission coefficient of the rubble mound has the lowest value, with K

_{t}< 0.2. Rubble-mound breakwaters almost completely prevent incoming waves. Porous breakwaters, like HTBs and PRBWs, still enable waves to pass through the layer to a certain degree, and the transmission coefficients are almost unchanged, K

_{t}= 0.3–0.4. The PTPBW results presented in this figure correspond to the selected pore diameter (TH6, front-side porosity is 17.6%, D = 5.7 cm, and the back-side porosity is 12%, D = 4.1 cm). We note that although we favour the penetration of sediment-laden waters, the proposed PTPBW structure gives values of wave transmission coefficients that are comparable with the other structures. When R

_{c}/H

_{mo,i}> 2, the wave transmission coefficients given by the PTPBWs are nearly identical to those of the HTBs and PRBWs. This ensures that the main purpose of the PTPBWs is to facilitate sediment transport along the structure and stimulate sedimentation behind it.

_{c}varies from +14 cm to +21 cm, equivalent to R

_{c}/H

_{m0}varying from (1.39~1.63) to (2.60~3.56), respectively) and a high water level (without wave overtopping, R

_{c}varies within +7–0 cm, i.e., R

_{c}/H

_{m0}varies from (0.60~1.12) to 0), the reflection coefficients are nearly identical. This means that the designed breakwater dissipates much reflection wave energy.

_{r}and R

_{c}/H

_{m0}is shown in Figure 16. When R

_{c}/H

_{m0}= −1, i.e., in the emerging state, the wave reflection coefficients converge for all breakwaters with K

_{r}= 0.1–0.2. When the breakwaters work in an emerging state (R

_{c}> 0), the proposed PTPWB produced the smallest reflection wave coefficient of K

_{r}= 0.20–0.25. Next is the rubble mound with K

_{r}= 0.26–0.28; the HTB with K

_{r}= 0.35–0.47; and the PRBW with K

_{r}= 0.45–0.56; and the smooth breakwater yielded the largest reflected wave coefficient of K

_{r}= 0.54–0.72.

## 5. Conclusions

_{c}= 14 cm in the model), the structure reduces the wave by 50%, and the wave power is reduced tenfold after passing through the breakwater. The reflected wave in front of the structure has a wave height of 1/5 of the incident wave height.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Glossary

α—Angle of the incident wave; |

β—Spectral energy parameter; |

γ—Peak enhancement factor; |

D—Pore diameter; |

D_{o}—Outer diameter (of the rings composing the pore in the model block); |

D_{i}—Inner diameter (of the rings composing the pore in the model block); |

D_{s}—Back-side pore diameter; |

f_{m}— Value of pick frequency; |

H_{s}—Deep-water wave height; |

H_{m0}—Wave height at zero moment; |

H_{m0,i}—Incident wave height at zero moment in front of the structure at a distance of 1.5 m from the breakwater; |

H_{m0,r}—Reflected wave height in front of the structure at a distance of 1.5 m from the breakwater. |

K_{t}—Wave transmission coefficient; |

K_{D}—Wave dissipation coefficient; |

K_{r}—Wave reflection coefficient at the front of the breakwater; |

L_{m}—Wave length; |

m_{0}—Zero moment of the spectrum; |

m_{-1}—Zero moment of the spectrum; |

N_{L}—Length scale; |

N_{t}—Time scale; |

R_{c}—Crest freeboard; |

S—Planned subsidence height; |

S_{op} = H_{m0}/L_{m}—Wave steepness; |

T_{p}—Deep-water wave period; |

T_{m-}_{1,0}—Wave period; |

Z_{tp}—Sea water level; |

Z_{1%}—Sea water level at the probability 1%; |

Z_{s}—Crest level of the submerged breakwater; |

Z_{e}—Crest level for the emerged breakwater. |

## References

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**Figure 1.**Coastal zone satellite image processing of Soc Trang province from 1980 to 2018 (Google Earth).

**Figure 10.**Sizes of the rings composing the pore in the model block (D

_{o}—outer diameter; D

_{i}—inner diameter). 1—Outer and inner rings for pore emulation in the breakwater. 2—Rings are combined together to achive the necessary pore diameter. 3—Putting the combined rings to the breakwater phisical model.

**Figure 11.**Influence of the crest freeboard of the PTPBW on the coefficients K

_{r}, K

_{t}, and K

_{D}.

**Figure 14.**Variance spectrum of the reflected wave in different water depths. (

**a**) TH6-d26H10T15, Depth d = 26 cm, Variance density spectrum; (

**b**) TH6-d33H10T15, Depth d = 33 cm, Variance density spectrum; (

**c**) TH6-d40H10T15, Depth d = 40 cm, Variance density spectrum; (

**d**) TH6-d47H10T15, Depth d = 47 cm, Variance density spectrum.

**Figure 17.**Wave breakwaters with PTPBW structure, which was designed on the basis of the present research results.

Simulation Cases | Water Level (m) | Design Deep-Water Monsoon Wave: H_{s} = 3.03 m, T = 5.82 s | |
---|---|---|---|

H_{s} (m) | T_{m}_{-1,0} (s) | ||

Tide level of Probability P = 1% | 1.53 | 0.81 | 4.83 |

Model Scale | Value |
---|---|

Length scale N_{L} | 7 |

Time scale N_{t} | 2.65 |

No | Experimental Model Pore Diameter | Prototype Pore Diameter |
---|---|---|

1 | D = 4.1 cm | D = 30 cm |

2 | D = 5.7 cm | D = 40 cm |

3 | D = 7.3 cm | D = 50 cm |

4 | D = 8.9 cm | D = 60 cm |

Test Cases | Front-Side and Back-Side Pore Diameter (cm) | Front-Side Pore Percentage (P_{1}) | Back-Side Pore Percentage (P_{2}) |
---|---|---|---|

TH2 | Di = 8.9 cm; D_{s} = 5.7 cm | 34.2% | 17.6% |

TH3 (without pore on front side) | Di = 0.0 cm; D_{s} = 5.7 cm | 0.0% | 17.6% |

TH4 | Di = 5.7 cm; D_{s} = 5.7 cm | 17.6% | 17.6% |

TH5 | Di = 7.3 cm; D_{s} = 5.7 cm | 25.0% | 17.6% |

TH6 | Di = 5.7 cm; D_{s} = 4.1 cm | 17.6% | 12.0% |

TH7 | Di = 7.3 cm; D_{s} = 4.1 cm | 25.0% | 12.0% |

Test Cases | Front-Side and Back-Side Pore Diameter (cm) | Water Depth d (cm) Crest Freeboard R _{c} (cm) | Wave Parameters |
---|---|---|---|

TH2 | Di = 8.9 cm; D_{s} = 5.7 cm | d = 47 cm (Rc = 0 cm) d = 33 cm (R _{c} = +14 cm) | H_{s} = 0.1 m; T_{p} = 1.5 sH _{s} = 0.1 m; T_{p} = 2.5 sH _{s} = 0.14 m; T_{p} = 1.5 sH _{s} = 0.14 m; T_{p} = 2.5 s |

TH3 | Di = 0.0 cm; D_{s} = 5.7 cm | ||

TH4 | Di = 5.7 cm; D_{s} = 5.7 cm | ||

TH5 | Di = 7.3 cm; D_{s} = 5.7 cm | ||

TH6 | Di = 5.7 cm; D_{s} = 4.1 cm | ||

TH7 | Di = 7.3 cm; D_{s} = 4.1 cm |

Test Cases | Water Depth d (cm) Crest Freeboard R _{c} (cm) | Wave Parameters |
---|---|---|

No structure | d = 47 cm (Rc = 0 cm) d = 40 cm (Rc = +7 cm) d = 33 cm (R _{c} = +14 cm)d = 26 cm (R _{c} = +21 cm) | H_{s} = 0.07 m; T_{p} = 1.2 sH _{s} = 0.10 m; T_{p} = 1.5 sH _{s} = 0.12 m; T_{p} = 1.6 sH _{s} = 0.14 m; T_{p} = 1.7 sH _{s} = 0.17 m; T_{p} = 1.8 s |

With structure |

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## Share and Cite

**MDPI and ACS Style**

Le, C.T.; Do, D.V.; Nguyen, D.B.; Wang, P.
A Laboratory Scale of the Physical Model for Inclined and Porous Breakwaters on the Coastline of Soc Trang Province (Mekong Delta). *Water* **2023**, *15*, 1366.
https://doi.org/10.3390/w15071366

**AMA Style**

Le CT, Do DV, Nguyen DB, Wang P.
A Laboratory Scale of the Physical Model for Inclined and Porous Breakwaters on the Coastline of Soc Trang Province (Mekong Delta). *Water*. 2023; 15(7):1366.
https://doi.org/10.3390/w15071366

**Chicago/Turabian Style**

Le, Chuong Thanh, Duong Van Do, Duong Binh Nguyen, and Ping Wang.
2023. "A Laboratory Scale of the Physical Model for Inclined and Porous Breakwaters on the Coastline of Soc Trang Province (Mekong Delta)" *Water* 15, no. 7: 1366.
https://doi.org/10.3390/w15071366