Numerical modeling of wave reflection and transmission in I-Shaped Floating Breakwater Series

The effectiveness of floating breakwaters in reducing waves can be achieved by adjusting the placement of structures according to conditions in the field. The effect of floating breakwater layout will affect the transmission and reflection waves. This study numerically modeled a floating breakwater with 0° porosity using Flow-3D to determine the reflection and transmission waves. The layout under study is a connection of three single-model floating breakwaters (I-shaped), connected by connectors made of coated wire rope in three variations of placement for wave incident angles (0°, 30°, and 60°). The study results show that the greater the angle of inclination of the structure causes an increase in the transmission coefficient and the lower the reflection coefficient. Floating breakwater layouts with tilt angles of 0°, 30°, and 60° have transmission coefficient values that differ not too significantly, where the tilt angle of 60° is more effective at damping waves compared to other tilt angles.


Introduction
The main problem in coastal areas is the presence of sediment, erosion, or abrasion, which impacts coastal damage [1][2][3][4][5][6].Coastal damage can occur due to human activities or occur naturally.Many efforts to protect against coastal damage can be made, namely by reducing wave energy with mangroves [7][8][9], bamboo [10], or artificial structures, such as fixed breakwaters [11][12][13][14][15] or floating breakwaters [16][17][18][19][20][21][22][23][24][25][26].Generally, The structures are fixed breakwater types consisting of conventional or rubble mound breakwaters, monolithic breakwaters, and composite breakwaters [27].Even though it is commonly used, fixed breakwater has certain limitations, especially regarding the economy.The deeper the water the structure will be built in, the greater the costs must be incurred.Generally, fixed breakwaters are used in shallow and sloping waters to reduce construction costs.These limitations encourage the development of a type of fixed breakwater into a floating breakwater (FB).
Many studies have been conducted dedicated to the development of FB structures.This structure began to be developed when World War II occurred for military purposes as a protector of small ships from the waves.However, over time this structure has been used commercially.FBs are usually used to dampen waves with a height not exceeding 1.2 m and a period not exceeding 4 seconds.This structure is said to be ineffective in a marine environment with heights up to 6 m and periods of up to 18 seconds, which can occur during storm conditions [28].
Research on FB layouts has previously been carried out [29].The layouts studied were I-shaped and J-shaped FB with variations in the placement of the slope of the structure and the incoming waves perpendicular to the shoreline.This research was conducted experimentally to determine the effectiveness and strength of FB along berths and connectors between modules in various layouts as well as variations in the angle of inclination of the structure.In each FB layout, the top between the modules can be connected by a connector to allow the structures to rotate together.This connector is a significant weakness in FB design because it indirectly acts as a load transfer between modules [30].Another study has also been conducted by [31].His research reported that an effective FB design must have a structure width of one-quarter to one-third of the incident wavelength.The structure is intended to be rigid and massive so that it does not cause wave generation.Research development of arc-shaped FB layouts has been carried out using the computational fluid dynamics (CFD) method [32].
FB is easy to install quickly, transport, and move in several locations with different wave conditions, and they are practical and economical, especially in deep waters.FB is a floating structure whose function is the same as other general breakwater types.However, what makes this structure different is the construction which was not built with an above-ground foundation system but using a mooring system.This study proves that the cost per meter required to construct FB is lower than that of a fixed breakwater, especially if the water is more than 30 meters [27].
Apart from that, other advantages of FB are that their effectiveness does not depend on the tides and ebbs of seawater, and the structure can be installed in waters with unsupportive ground surfaces [17].Although FB has been extensively studied theoretically and experimentally, their application in actual conditions is minimal.Because there is still a dynamic response to the waves that have been transmitted, FB needs to be designed as well as possible so that it can work effectively.One aspect that determines the performance of the structure is the transmission and reflection coefficient [33].
In this research, we will examine the ability of FB I-shape series to reduce and reflect waves in various layouts with CFD so that it can be determined the effectiveness of FB in producing optimum performance.

FB Model Data
The dimensions of the pontoon FB and the hydrostatic parameters used are based on research [21] [22].The model is made with a scale of 1:20, with a length of 0.1 m, a width of 0.15 m, a height of 0.15 m, and a draft of 0.1 m.Models 3 and 4 are designed to be porous with a proportion of 5% and 10%.This model operates with a wave height and period of 0.05-0.125m and 1.1-2 s, respectively (Fig. 1), and at a water depth of 0.75 m.Four single-model FBs were analyzed with Ansys static structural to determine their draft and displacement.The accuracy of these parameters needs to be validated by theoretical and numerical calculations (Table 1).

I-Shaped Layouts
The single model of the four FB models (Figure .1) was arranged into an I-shaped layout (Figure .2), and transmission and reflection numerical simulations were carried out with Flow-3D.Between single FB models connected by flexible connectors [34] (Figure .3).In his research, the model parameters, especially the mass of FB used, have a ratio of 1:2 so that the characteristics of the connector used are adjusted first.The criteria and dimensions for the connector are Young's modulus 5100 Gpa, length 9 cm, outer length 3 cm, diameter 0.5 cm, and made of coated wire rope.There are two connectors installed at the ends of adjacent FB structures.Each end of the connector is placed inside the pontoon so that the connector allows the FB structure to rotate in the direction of the z and x axes.

Model Setups
The I-shape FB model was numerically simulated with Flow-3D in a domain measuring 610 cm x 346 cm x 105 cm.In this domain, eight wave probes are placed in different positions.The eight wave probes (wp) are divided into four groups based on the location of the y-axis with different distances between probes (s).The first group is at a position of 100 cm from the following structure called s1.As for the wave probe group that is at a position of 150 cm from the structure, it is called s2.In each group, the outputs wp1 and wp4 calculate the transmission coefficient (KT).In contrast, the wp2 and wp3 outputs are used to calculate the reflection coefficient (KR).

The effectiveness of the array model on I-shape FB
The parameter transmitted and the incident wave to calculate KT is the average wave height (H) from the elevation data recorded by wp1 and wp4.Where the results of the calculation of wave wp1 are incident waves, and wp4 are transmitted waves.The obtained KT is plotted in non-dimensional form as a parameter of wave steepness (H/gT²) (Figure . 5).
The graph shows that the resulting trendline between KT plotting and the wave steepness parameter for each floating breakwater array model appears to decrease slightly with the size of the wave parameters.In other words, FB structure is getting optimum when the wave parameter increases.This condition can happen because the wave parameters will get more significant when the wave period gets smaller.If the wave period is considerable, for example, when T=1.1 s and T= 2 s, the waves produced by T=1.1 s are more numerous, but the wavelengths are short.Whereas for T=2 s, the resulting wave will be longer so that it can significantly influence the motion of FB.As a result, KT will be greater than during the small wave period.
Trendline array model 1 shows a smaller KT value than other models.Array model 4 shows the highest trendline, FB with 10% porosity, followed by array model 3 with 5% porosity and array model 2 with 0% porosity.It can be concluded from the comparison of the trendlines in the graph that the most optimum array model for transmitting wave is the array model 1, namely the pontoon.At the same time, the most optimum porosity module is the array model 2 with a porosity of 0%-the greater the porosity of FB, the greater KT.A comparison of KT between the pontoon and the pivoting FB can be seen in Table 2.
In contrast to K T , K R is calculated using the Goda & Suzuki reflection equation [35].This method simultaneously separates the incoming and reflected waves recorded by wp2 and wp3.The results of plotting KR on the wave parameters are shown in Fig. 6.KR will increase along with increasing wave parameters (H/gT²).In contrast to KT, the larger the wave parameter, KR will also increase.In this study, the simulation was carried out by inputting several wave variations, namely H=0.05-0.125m.The greater the height of the incoming wave, the greater the wave parameter.If the wave parameter is large, it is ensured that KR is large.This condition can be explained because if the wave height is large, the area of the waves hitting the structure will widen so that the waves reflected will be even bigger.
Compared to KT, KR produced by each model set decreases.If the most optimum set of models for transmitting waves is model 1, which has the smallest KT, then KR is the other way around.FB will be said to be optimum if KR is high.It can be seen in Figure 6 that the trendline of model 1 is the largest, followed by models 2, 3, and 4 (Table 3).The most optimum series of models for reflecting waves is model 1 (pontoon).Because the pontoon's working area is perpendicular to the incoming wave, the reflected wave energy will be greater.Models 2, 3, and 4 have a slope to reduce wave energy.Of course, many aspects need to be considered in the design of FB.So that other aspects are reviewed and need ongoing research.The effect of porosity on the FB array model to determine optimum performance, KR difference between models 3 and 4, is calculated with model 1 (Table 3).
The analysis shows that model 4 reflects smaller waves because the 10% porosity effect is more significant than model 3 on 5% porosity.The greater the porosity, the greater the wave energy absorbed by the structure, and the wave reflection will decrease.Otherwise, the transmission will be more extraordinary.If we observe the non-porous shape (models 1 and 2), it turns out that the shape of the slope in front of the structure (model 2) can reduce wave energy, which can reduce wave reflection by 5.74%.A significant KR means that the structure can reflect many waves.If FB installation aims to protect the port, this could endanger fishing boats approaching when they sail near the FB structure.Based on the analysis of each incident wave direction (Figure .8 and 9), FB effectively transmits waves from 60°.The greater the wave incident angle, the smaller the resulting KT, meaning FB will be more optimum.This condition can happen because when a structure is placed perpendicular to the direction of the incoming waves, the structure will get a more significant force from the waves compared to when the structure is placed obliquely to the direction of the coming waves so that a structure that is placed perpendicular to the direction of the incoming waves will have a more significant motion response and cause a reduced ability of the structure to transmit the incoming waves.Martinelli et al [29] researched to examine the effect of the slope angle of the structure on KT of FB.
When the incident wave's incidence angle is 0° (Figure .10 and 11), KR at the 2 points where the wave probe (s) is placed coincides, indicating that KR at the two places is close to or the same.Likewise, the resulting trendline is almost the same when the wave incident angle is 30° and 60°.The most significant KR is produced when the wave incident angle is 0° or perpendicular to the FB structure at both wave probe points.For the wave angles of 30° and 60°, KR at the two wave probe points has a trendline that almost coincides but is more remarkable when exposed to waves from the 30° direction.
It can be seen in Table 4 that the most significant KR of 0.76 occurs when the structure is exposed to waves from 0°.KR in the two wave probes also has the same value.The same KR at both points can be caused because the surface area of the structure exposed to the incident waves has the same area, so the reflected wave is also of a similar value.The resulting KR is also almost similar for structures affected by waves from 30 deg, but there is a 0.15% difference at the two wave probe placement points.Meanwhile, when the waves come from 60 deg, the resulting KR at the two wave probe points has a difference of 0.74%.When the structure is hit by waves from a direction other than perpendicular to the structure, the surface of FB that is hit by incident waves is not as comprehensive as when it is hit by waves perpendicular to the structure.So the reflected wave is also not as perfect as when the wave's arrival direction is 0 deg.This fact explains that the greater the angle of incidence of the waves or the closer the incoming waves are parallel to the structure, the less effective FB is in reflecting the waves.

Acknowledgment
Researchers would like to thank the Department of Ocean Engineering, DRPM-ITS, and Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia, for the financial support and facilities provided.

Figure 5 .
Figure 5. KT of each I-shape FB series.

Figure 6 .
Figure 6.KR of each model series on I-shape FB.

3. 2 .
Incoming wave effect on I-shape FBThe effect of the wave incident angle on transmission and reflection is studied to determine the most optimum I-shaped FB layout.The layout is simulated at three variations of wave incident angles, namely angles of 0 deg, 30 deg, and 60 deg (Figure.7).The analysis was carried out on wave parameters H=0.125 m and T=2 s, with a water depth of 0.85 m.In this layout, two groups of wave probes are placed differently along the y-axis towards the ends of the FB structure [5] (Figure.4).The complete effect of placing the wave probe is presented in Table4and Fig.8-11.

Figure 7 .
Figure 7. Variation of the wave incident angle.

Figure 8 .
Figure 8. KT at various angles of the incident wave.

Figure 9 .
Figure 9. KT at different wave probe locations.

Figure 10 .
Figure 10.KR at different wave probe locations.

Figure 11 .
Figure 11.KR at various angles of the incident wave.4.ConclusionIn this study, four array models were analyzed as objects of study.The results of the numerical model of KT and parameters are obtained by focusing.First, the poreless FB model is effective in reducing wave energy.The pontoon model can reflect waves well because it has a work area as a vertical wall.In model 2, without pores, adding a slope in front of the structure can effectively reduce KT to 0.75 and KR to 0.42.Second, when compared to the direction of the incident wave 0° at the position of the wave probe s1=100 cm, KT decreases by 4.63% and 7.37% at the wave direction of 30 deg and 60 deg.Meanwhile, at the position of the wave probe s2=150 cm, KT decreases by 7.23% and 7.67% in the direction of the incident wave at 30 deg and 60 deg.

[ 1 ]
Coastal Engineering Research Center (US) 1984 Shore protection manual.Department of the Army, Waterways Experiment Station, Corps of Engineers, Coastal Engineering Research Center [2] Sujantoko and Natakusuma D 2003 Model simulasi interaksi gelombang dan arus di perairan dangkal Jurnal Teknik Sipil 10(3) 99-108 [3] Sujantoko, Pratikto W A, Prastianto R W, Maulan M I and Vebriyanti A 2021 Study of changes in coastal morphology due to utilization of the Surabaya city coastal area International Journal of Marine Engineering Innovation and Research 7(1) 26-32 [4] Sujantoko, Mustain, M, Wahyudi and Ikhwani, H 2023 Hydrodynamic model due to reclamation in Lamong Bay IOP Conference Series: Earth and Environmental Science 1198 012004 [5] Mustain M and Sujantoko 2023 Spiral analysis of vertical currents in Lamong Bay IOP Conference Series: Earth and Environmental Science 1166 p 012024 [6] Mustain M and Sujantoko 2021 Simple Analysis of Determination of Tidal Types of Sea Water:

Table 1 .
Validate draft and displacement FB.

Table 2 .
KT on I-shape FB series.

Table 3 .
KR of model series on I-shape FB.

Table 4 .
KT and KR of various angles of incident waves.