MINISTRY OF EDUCATION AND TRAINING
UNIVERSITY OF TRANSPORT AND COMMUNICATIONS

DO MINH DAT

RESEARCH ON WAVE-REDUCING EFFECTIVENESS
OF PILE-SUPPORTED INCLINED-PLATE DIKE FOR
COASTAL PROTECTION

Major: SPECIAL CONSTRUCTION ENGINEERING
Code
: 958.02.06

SUMMARY OF DOCTORAL THESIS

HA NOI – 2023


The Thesis was completed at the University of Transport and Communications.

Academic Supervisor 1: Assoc. Prof. Dr. Nguyen Viet Thanh
Academic Supervisor 2: Assoc. Prof.Dr. Phung Dang Hieu

Reviewer 1:
Reviewer 2:
Reviewer 3:

The Thesis will be defended in front of the University–Graded Committee of the Thesis
Evaluation according to Decision No. XXXXX/QĐ-ĐHGTVT dated 2023, signed by
the University of Transport and Communications.

The Thesis can be found at:
- National Library;
- Library of the University of Transport and Communications.


1
INTRODUCTION
1

Research background
Research and development of other breakwater types are increasingly encouraged to
optimize materials' use, providing environmental-friendly solutions for coastal engineering
problems. Studying and selecting structure types with high durability and economic efficiency
is necessary, especially for coastal protection works.
The pile-supported inclined-plate breakwaters have many outstanding advantages, such
as simple structure, little impact on the surrounding environment, increasing water exchange,
use of fewer materials, and are suitable for areas with soft soils, deep water, and
uncomplicated construction technology. This type of structure has great potential for
application in coastal and maritime protection works in Vietnam. The Thesis aims to
empirically study the interaction between waves and the inclined plate breakwater using the
physical model in the 2D wave flume. The results are a reliable basis for applying inclinedplate breakwater structures in constructing port and coastal protection works in Vietnam.
2 Research objective
A study of the interaction between the wave and the inclined-plate breakwater structure
is necessary to clarify the hydrodynamic characteristics when the waves act on the inclined
plate.
Based on the results, the study proposed the most effective type of pile-supported
inclined-plate breakwater, which can be applied for coastal protection, stabilization works,
and harbor basins.
3 Research object and research scope
3.1 Research object

This study's objective is the interaction between the wave and the pile-supported inclinedplate breakwater in the different experimental wave scenarios suitable for site conditions in
Vietnam.
3.2 Research Scope
The interaction between waves and structures is studied using physical model
experiments in a 2D wave flume. This study does not consider the structure's strength and the
pile foundation's influence on the inclined plate.
4 Scientific and practical significance
4.1 Scientific significance
Studying the interaction between wave and inclined plate breakwaters will contribute to
uncovering the mechanisms of wave transmission, wave reflection, and wave energy
dissipation of this type of structure.
4.2 Practical significance
The traditional inclined plate breakwater was improved by adding notches and holes to
improve wave energy dissipation and reduce the height of reflected waves in front of the
breakwater. This structural solution has an economic cross-section and a low environmental
impact.
5 The new contribution of the Thesis


2
- The influence of some basic input parameters such as water depth; slope of inclined
plate, wave period, and wave steepness on the change of hydrodynamic characteristics,
including wave transmission, wave reflection, and wave energy dissipation when the wave
interacts with the inclined plate breakwater was investigated. Some relationships were
established between wave steepness and wave transmittion, wave reflection, and wave energy
dissipation.
- The inclined plate breakwater structure with highly effective wave-absorbing notches
and holes was proposed in the coastal protection field. In addition, the technical characteristics
of inclined plate breakwater structures were applied in the coastal protection in Canh Duong
commune, Quang Trach district, Quang Binh province.

6 Thesis outline
In addition to the introduction, conclusion, and recommendations, the Thesis has four
chapters, including:
Chapter 1 Overview of domestic and international research on pile-supported inclined
plate breakwaters.
Chapter 2 of the Thesis focuses on setting up and installing a physical model by using
similarity parameters, discussing some methods measuring reflected waves, and analyzing
the basis of experimental wave selection, thereby suggesting a basis for developing the
research scenarios.
Chapter 3 of the Thesis presents the characteristics of wave transmission, wave reflection,
and wave energy dissipation of inclined plate breakwaters. In addition, the Thesis also
discusses the wave pressure distribution on the inclined plate and the maximum velocity
distribution caused by the waves at the gap between the breakwater and the sea bottom.
Chapter 4 of the Thesis applies the research results from Chapter 3 to propose two types
of inclined plate breakwater structures on pile foundations for coastal protection. The designs
are applied to coastal stabilization and protection projects in Canh Duong commune, Quang
Trach district, Quang Binh province.
CHAPTER 1. OVERVIEW OF STRUCTURE AND THE INTERACTION
BETWEEN WAVES AND BREAKWATER
1.1
Overview of breakwater research
Researching new technologies in coastal protection works in Vietnam conditions is an
urgent requirement with high practical significance. Solutions for sand prevention and wave
reduction often used in coastal protection works include (Figure 1.1): Mangrove forests;
Artificial beach nourishment, groin system; Near-shore wave attenuation barrier system
(submerged or immersed); Combination of many solutions.
Structure of coastal protection works
Coastal protection structures are classified as follows:
a.
a. Sloping structure

b.
b) Upright structure
c.
c. Semi-circular breakwater structure
d. Wave reduction breakwater using centrifuge wall
e. Wave reduction breakwater using Busadco blocks
f. Wave reduction breakwater using a hollow A-shaped structure with a pyramid.


3

Figure 0.1: Prevent sand and reduce wave breakwaters in shore protection works
Various coastal protection structures were built in Vietnam with positive initial results.
However, most have not yet experienced harsh weather conditions, so their long-term
effectiveness cannot be evaluated. On the other hand, soft soil conditions cause gravity
structure solutions to subside unevenly and tilt, inducing cracking of structures and difficulty
in coping with the marine environment. This result shows a few studies inclined plate
breakwater structures on pile foundations in Vietnam. Because the inclined plate structure is
placed on a pile foundation, the scope of application is widely applied to areas with soft soil
geology, such as the coastal areas of Vietnam. Therefore, the research direction of the topic
is highly practical.
1.2 Overview of research related to the direction of the study
Overview of international research
A total of 13 international researches on the interaction between waves and inclined-plate
breakwaters were summarized with the following results:
(i) Methods of the studies:
Numerical and physical modeling are two main research methods which numerous
researchers conduct.
(ii) Research conditions
- The research has only been carried out by experimental wave combinations without

studies on in-situ wave applications. These studies were not applied in practice to the site.


4
Unfortunately, the inclined plate breakwater structure has many advantages, such as
economical cross-section, simple construction, and effective wave reduction.
- Inclined plate breakwater: The authors conducted research under experimental
conditions with inclined plates with inclined angles from 0-90 degrees in both directions
forward and opposite the direction of the wave approach. According to some experimental
results, inclined plates with an angle of inclination of 45-60 degrees compared to the vertical
have the most effective reduction ability.
- Most studies have been performed with inclined plates with smooth, flat-sided
platforms. Only Shirlal's (2013) investigated the wave transmission of a submerged serrated
inclined plate breakwater with rectangular and square fixed in zigzag and parallel
configurations tested using monochromatic waves.
(iii) Practical application: Through an overview of research around the world, it can be
seen that the inclined plate breakwater structure (smooth-flat plate) was practically applied in
Japan, such as in Kimisu, Chiba, and Fujimori, Suruga Bay, Japan.
Overview of Vietnam research on the interaction between waves and structures
In Vietnam, no studies were conducted on pile-supported inclined plate breakwaters. The
Thesis reviewed studies on the interaction between waves and breakwater structures in our
country, as follows:
a) Studies related to sloping breakwaters
Studies on sloping breakwater using Rakuna IV blocks applied to Nghi Son breakwater
were conducted by Thieu Quang Tuan et al. (2014) [43], Le Thi Huong Giang (2016) and
Nguyen Quang Luong (2020) [7].
b) Numerical simulation research
In Vietnam, the numerical simulation research, including the model to determine the level
of wave reduction through mangrove forests, was conducted by Nghia et al. (2010) [1], the
2D model on VOF (volume of fluid) basis for simulating waves overtopping over a porous

breakwater structure (simulation results showed high correspondence with experimental data
of Hieu et al. (2012) [44]).
Hieu et al. studied the interaction between wind and waves at breakwaters with slopes of
m=4 using numerical wave simulation. The numerical wave simulation results are compared
with experimental data in the case of overtopping waves without the influence of wind [45].
Pham Van Lap (2019) applied a numerical wave simulation model and a physical wave
model to study the interaction between waves and sea embankments to determine the flow
velocity due to waves at the shallow base in the design of the stone embankment [8].
c) The research works on semi-circular breakwaters and 1/4 circular breakwaters.
Typical studies on semi-circular breakwaters for estuary regulation works were conducted
by Nguyen Viet Thanh (2014) [2, 3, 9] and Nguyen Viet Thanh et al. in 2017 [10, 11].
Regarding the studies of Tran Van Thai and Phan Dinh Tuan (2019) [12], Le Thanh
Chuong et al. [13], and Phan Dinh Tuan (2021) [14] about wave overtopping over semicircular breakwater structures were applied in the Mekong Delta and Nha Trang. However,
they were not exposed to extreme weather conditions, and the effectiveness of these structures
is still unclear.
d) Research works on submerged breakwaters
Nguyen Viet Tien's doctoral Thesis (2015) studied the wave reduction effectiveness of
submerged breakwaters [15].
e) Other breakwater research


5
Nguyen Van Thin (2014) [16] and Nguyen Van Dung (2017) [17] used a physical model
on a wave flume to study wave overtopping and wave pressure acting on the crest wall
structure of the embankment.
Regarding research on estuary and coastal management solutions, Truong Van Bon [18]
and Nguyen Thanh Hung [19] studied the effectiveness of preventing sand and wave
attenuation of coastal protection solutions Lo estuary - Cua Dai, Quang Ngai and Nhat Le
estuary, Quang Binh.
Vu Minh Tuan and colleagues (2022) studied the interaction between waves, box-shaped

floating breakwater structures, and box-shaped floating breakwaters combined with a semicircular arch on top of the box [20].
e. Comment on domestic research results:
- Research works in Vietnam have mainly focused on the interaction between waves and
breakwater structures in the form of sloping breakwater or revetment, semi-circular, hollow
A-shaped blocks, hollow upright walls, two rows of piles combined with poured rock cores,
etc.
- No research was carried out on the contents related to problems mentioned in this Thesis.
Therefore, studying the interaction between waves and pile-supported inclined plate
breakwaters is a new direction that clarifies the hydrodynamic characteristics and is useful
for the practice in Vietnam.
1.3 Overview of study methods about the interaction between waves and
breakwater structures
According to general domestic and international studies, mathematical and physical
modeling methods mainly studied the interaction between waves and breakwater structures.
Mathematical models are popular in studying 1D and 2D problems, while physical models
are common in 3D problems. The use of mathematical or physical models depends on the
importance of the project and the research stage, as well as economic and technical
considerations. Solid physical model provide calibration data for a relatively accurate
mathematical model of the velocity field to calculate erosion and deposition characteristics to
present difficult and high-cost numerical models.
1.4 Existing problems need to be resolved by the study
Direction research of the Thesis:
- Research hydrodynamic characteristics when waves interact with pile-supported
inclined plate breakwaters with notches and holes to reduce waves.
- Applying the most effective type of pile-supported inclined plate breakwater structure
to protect and stabilize the coast of a given area.
1.5 Objectives and content of the study
Objectives of the study
The objective study considers the hydrodynamic interaction characteristics between
waves and pile-supported inclined plate breakwaters and proposes the most suitable pilesupported inclined plate breakwater structure for stabilizing and protecting the coast.

Specifically objectives as below:
- Overview of domestic and international research about the structural characteristics of
pile-supported inclined plate breakwaters.
- Setting up the physical model, selecting experimental wave parameters, and proposing
experimental scenarios.


6
- Clarify the hydrodynamic characteristics when waves interact with the breakwater.
- Propose solutions to protect and stabilize the coast and harbor basin.
Content of the study
- Overview of domestic and international research on breakwaters and pile-supported
inclined plate breakwaters.
- Scientific background of research on the interaction between waves and pile-supported
inclined plate breakwaters using physical models.
- Setting up, calibration, and verifying physical models.
- Research the characteristics of wave transmission, wave reflection, and wave energy
dissipation when waves interact with inclined plate breakwaters,
- Research the maximum velocity distribution in the gap between the breakwater and the
bottom caused by interaction between wave and breakwater.
- Propose pile-supported inclined plate breakwater structures for coastal stabilization and
protection works.
Expected results
- The inclined plate breakwater structure with notches and holes is a type of structure with
a simple cross-section. Using this structure can save materials and apply them for all types of
ground, piling construction, and fast-paced assembly of inclined plates. With these
advantages, clarifying the scientific background when waves interact with breakwaters is
necessary, thereby proposing a structure suitable for Vietnam's coastal conditions.
- The research results are a useful reference for a fairly new type of structure in Vietnam
that can help researchers, consulting companies, and managers have additional structural

options for comparison with traditional ones.
1.6 Methods of the study
Depending on the contents, the following methods were used:
- Information collection method: Collecting documents, conducting an overview of
studies on the interaction between waves and inclined plate breakwaters structures, and
techniques for exploiting information from the internet to update information related to the
topic.
- The methods of learning, summarizing experience, and absorbing advanced scientific
and technological results from previous research related to the topic.
- Based on some sample designs of inclined plate breakwater structural solutions,
improvement research was conducted to improve the structure's ability to reduce waves, save
materials, and ensure the ability to work stably under the effect of design waves. The physical
modeling method using wave flume was applied to consider the interaction between waves
and inclined plate breakwater structures on pile foundations.
1.7 Conclusion of Chapter 1
- Research on improving breakwater structures that are highly durable and have great
economic efficiency in coastal protection works is an attractive topic for many scientists
worldwide.
- Building wave attenuation works and breakwaters in Vietnam have achieved certain
effectiveness. However, they did not test with extreme weather conditions, so there are no
results to evaluate the lifespan of these types of structures. For soft soil areas, using gravity
structures will cause large settlements, making it difficult to ensure the long-term stability of
the works.


7
- There are two main research methods considering the interaction between waves and
breakwater, namely mathematical models and physical models. The mathematical model was
used to provide boundary conditions for the physical model to reduce unnecessary
experiments and investment costs.

- All studies on the interaction between waves and pile-supported inclined plate
breakwaters were performed using physical models. The research results described
hydrodynamic characteristics including wave transmission, wave reflection, and wave energy
dispersion. There were a few studies on velocity distribution at the base of the breakwater,
and no studies were conducted on the wave pressure distribution affecting inclined plate
breakwaters.
CHAPTER 2. SCIENTIFIC BACKGROUND FOR STUDYING THE
INTERACTION BETWEEN WAVES AND PILE-SUPPORTED INCLINED
PLATE BREAKWATERS
2.1 Research basis for interaction between waves and inclined plate breakwater
structures
The physical model needs to satisfy the following requirements to ensure it works as in
reality.
2.1.1 Similarity theory
The model theory is established based on similarity theory. When the similarity
conditions stipulated by the similarity theory are satisfied, the model (M) and the prototype
(N) are similar, and we can base on the results from the model to speculate the corresponding
results in the original form. For the model to be similar to the prototype, all similarity
conditions must be met, including geometric similarity, kinematic similarity, dynamic
similarity, similarity in flow state, similarity in wave motion, similarity in wave reflection,
and similarity in wave breaking.
2.2 Building, calibrating, and validating physical models
2.2.1 Selecting Model Scale
Based on available equipment in Vietnam, in-situ wave data along the coast, and
similarity requirements, the Thesis chose the scale of a physical model of 1:15.
2.2.2 Constructing inclined plate breakwater samples
Breakwater sample material: use organic glass with roughness equivalent to
0.0097÷0.012.
Dimensions of inclined plate breakwater prototype: 30m x 10m x 0.75m. Because of the
model scale 1:15, the inclined plate breakwater model has dimensions of 2m x 0.67m x 0.05m

(Figures 2.1 and 2.2).

Figure 2.1: Fabrication of inclined plate
breakwaters

Figure 2.2: Inclined plate breakwater cross section is
completed


8
The inclined plate model has truncated conical notches with a low bottom of 5 x 5cm, a
top-bottom of 3 x 3 cm, a height of 5.0 cm, and concave holes with a length of 5.0cm, Width
of 3.0cm, small bottom depth of 0.5 cm, large bottom depth of 1.0 cm.
2.2.3 Measuring equipment and arrangement on the experimental model
2.2.3.1 Wave flume
The experiment was carried out in a wave flume with a length of 37m, a width of 2m, and
a depth of 1.5m at the Key Laboratory of River and Coastal Engineering, Vietnam Academy
for Water Resources.
2.2.3.2 Wave generator
The wave generator can generate regular and random waves in a spectrum of Jonswap,
Jonswap Par, Moskowitz, Moskowitz Par, and Sin at a maximum water depth of 1.4m in front
of the wave generator. The maximum wave height generated in the flume is Hmax = 0.4m and
the period is from Tp = 0.5s ÷ 5.0s.
2.2.3.3 Wave probes:
Wave probe type 202 is manufactured by the Danish Hydraulic Institute (DHI).
2.2.3.4 The experimental model
(i) To measure wave height, four-wave probes are arranged as follows:
Probes G1, G2, and G3 are located in front of the breakwater and about 0.6L to 0.75L
away from the breakwater. They are moved during the experiment to correspond to
wavelength data and evaluate the reflection ability of the incident waves. Probe G4 is placed

behind the breakwater to measure the wave height behind the breakwater, about 1.5m as a
basis for evaluating the wave transmission efficiency of the breakwater.
(ii) To measure wave pressure, 6 wave pressure probes are arranged on the surface of the
inclined plate breakwater at designated positions about 0.135m apart.
(iii) the DCS 3900 probe (Doppler Current probe) is used to measure the flow velocity.
The measuring probe is placed in the middle of the gap between the inclined plate and the
bottom of the flume. During the experiment, the measuring probe are moved vertically to
measure the maximum flow velocity.

a. General layout of the experiment

b. Arrangement diagram of wave pressure

probes
Figure 2.3: Experiment general layout diagram and arrangement of measuring probes in the wave
flume

2.3 Calibration and validation of the model
Calibrating and verifying the experimental model ensure the accuracy of the wave
propagation process as in the original form according to the manufacturer's instructions.
2.4 Developing research scenarios
Based on the analysis mentioned above, the 45 scenarios were conducted in the Thesis


9
with the following input conditions:
- Experimental wave height includes four levels: 0,1; 0,12; 0,14 and 0,16 m;
- The experimental wave period includes four levels

: 1,2; 1,4; 1,8 and 2,2 s;


- The experimental water level includes three levels:
+ The water level is equal to the breakwater crest: WL1 = 0,67 m
+ The water level is lower than the breakwater crest 0,6Hs: WL2 = 0,59m
+ The water level is lower than the breakwater crest 0,78Hs: WL3 = 0,54m
- The slope of the inclined plate includes three types: m = 1; 1,33 và 1,5.
Basis for selecting input conditions:
- The experimental wave spectrum is selected based on monsoon waves and experimental
conditions of previous authors.
- The experimental water level selected includes the following cases: the water level is at
the level of the breakwater crest WL1, the water level is 0.6Hs lower than the breakwater
crest (WL2) and the water level is 0.78Hs lower than the breakwater crest (WL3),
corresponding to zero allow waves to overflow.
- Slope of inclined plate: Based on the research of previous authors, slopes of 1:1, 1:1.33,
and 1:1.5 are selected.
- Space below the plate surface: Because the plate length is constant, therefore, for each
case of the inclined plate (1:1, 1:1.33, and 1:1.5), the distance below the plate surface has
change.
- Experimental conditions were not considered within the scope of the Thesis: Influence
of the pile foundation on the inclined plate, thickness of the inclined plate, the influence of
flow and waves in the opposite direction on the bottom of the plate;
It can be seen that the experimental conditions generalize the wave height ranges and
wave periods typical of coastal areas in Vietnam. Total have 45 experiments. There are six
experiments to determine the wave pressure acting on the inclined plate breakwater and nine
experiments to evaluate the influence of the wave period on the hydrodynamic characteristics.
2.5 Experimental measurement and data processing methods
2.5.1 Method of Measuring Reflective Waves
The three-probe method of Mansard and Funke (1980) is used in the experiments.
2.5.2 Method of Calculating Reflective Waves
Wave reflection coefficient Kr is determined according to the formula:

Kr = Hr/Hs

(2-1)

2.5.3 Method of calculating wave energy dissipation coefficient
The wave energy dissipation is calculated according to Shih et al. (2015) as follows:
(2-2)
𝐾 = 1−𝐾 −𝐾
- Kr is the wave reflection coefficient, and Kt is the wave transmission

In which:
coefficient.
2.5.4 Method of Analyzing Received Wave Data


10
The WS Wave Analysis Tools (WSWAT) in MIKE 21 calculates the wave reflection
coefficient.
2.6 Conclusion for chapter 2
A physical model used to simulate the interaction between waves and the inclined plate
breakwater structure is designed and constructed with suitable similarity criteria to simulate
waves effectively.
Studying the hydrodynamic characteristics when waves interact with inclined plate
breakwaters on pile foundations based on wave transmission coefficients, wave reflection,
and wave energy dissipation.
In order to determine the reflected wave effectively, it is necessary to arrange the wavemeasuring probes according to the 3-probe method of Mansard and Funke (1980).
CHAPTER 3. RESEARCH ON HYDRODYNAMIC CHARACTERISTICS
WHEN WAVES INTERACT WITH INCLINED PLATE BREAKWATER
STRUCTURES
3.1 Wave transmission characteristics

3.1.1 Calculation results of the wave transmission coefficient
Experimental results corresponding to the slope m = 1 show that the wave transmission
coefficient Kt value ranges from 0.378 to 0.661. These values indicate that the inclined
breakwater structure on a pile foundation with notches combined with wave-absorbing holes
can reduce transmitted waves better than the similar inclined plate breakwater structure with
an inclination angle of 60 degrees to the vertical direction of Shirlal (2013) with Kt ranging
from 0,5 to 0,73. The influence of factors on the wave transmission process is studied below.
3.1.2 Effect of water level on wave transmission
Relationship between wave transmission coefficient Kt and wave height Hs corresponding
to different inclined slopes, corresponding WL1, WL2, and WL3, respectively in Figures 3.1,
3.2, and 3.3.

Figure 3.1: Relationship between
wave transmission coefficient Kt
and
wave
height
Hs
corresponding
to
different
inclined slopes, corresponding
WL1

Figure 3.2 Relationship between
wave transmission coefficient Kt
and
wave
height
Hs

corresponding
to
different
inclined slopes, corresponding
WL2

Hình 3.3: Relationship between
wave transmission coefficient Kt
and wave height Hs
corresponding to different
inclined slopes, corresponding
WL3


11
The results show that, with water levels lower than the breakwater crest WL2, the cases
with m=1 and m=1.33 have the same effectiveness in reducing transmitted waves. With m =
1.5, the transmitted wave is higher than the other two cases.
3.1.3 The influence of inclined slopes on transmitted waves
The influence of inclined slope on transmitted waves corresponds to WL1, WL2, and
WL3, respectively, shown in Figures 3.4 - 3.5. The summary results are as follows:
- With slope m=1: In this case, the water level at the breakwater crest increases linearly.
The remaining 02 cases initially decrease and then increase.
- With a slope of m=1.33, in the case of WL1, the effectiveness of reducing transmitted
waves is the highest compared to the other two slope cases.
- With a slope m=1.5, case WL1 also shows the highest effectiveness in reducing
transmitted waves compared to the other two slope cases.

Figure 3.4: The relationship
between wave height and wave

transmission coefficient
corresponding to water level
changes

Figure 3.5: The relationship
between Kt with different water
levels when the slope m=1.33

Figure 3.6: The relationship
between Kt with different water
levels when the slope m=1.5

3.1.4 effect of wave period
Nine experiments were conducted to study the effect of wave period, with a constant wave
height of Hs = 0,14m and three different water levels. The oscillation wave period is 1.2, 1.4,
and 2.2 seconds. Figure 3.7 shows the relationship between wave period and wave
transmission coefficient.
0,80

Kt

0,60
0,40
0,20
0

T=1,2 giây
1

T=1,4

2 giây

T=2,2
giây
3

4

Figure 0.7: Correlation between wave transmission coefficient Kt and wave period

3.1.5 The influence of wave steepness
3.1.5.1 General instructions
Correlation between Kt and the wave steepness (H0/gT2) for inclined plate breakwaters
were established by Shih et al. (2015) using a quadratic equation. Using a linear equation,


12
Acanal et al. (2013) indicated the relationship between Kt and wave steepness (H/L). In this
study, the Thesis also built the relationship between wave transmission coefficient and wave
steepness (H0/gT2) corresponding to different slopes through quadratic equation determined
through Matlab's Curve Fitting Tool. The SSE (Sum of Squares due to Error) and the RMSE
(Root Mean Square Error) were used to evaluate the reliability of the regression function. In
addition, the correlation coefficient R2 was also determined to evaluate the reliability of the
regression function.
3.1.5.2 Correlation between wave steepness and wave transmission coefficient when
slope m=1
Based on the measured data, the relationship between wave transmission coefficient and
wave steepness Ho/gT2 was built using a quadratic function (Figure 3.10). The results of
MatLab's Curve fitting regression calculation using the Trust-region algorithm give the
following regression equation:

𝐾 = 0,003897

.

×

− 0,0772

×

+ 0,91

(3-1)

With reliability assessment parameters including SSE = 0.0433, RMSE = 0.0627, and
R = 0,4307 as shown in Figure 3.10, equation (3-1) has acceptable reliability.
2

Figure 3.8: Correlation between Kt and wave steepness with slope m=1

3.1.5.3. Correlation between wave steepness and wave transmission coefficient when
slope m=1,33
The results of MatLab's Curve fitting regression calculation using the Trust-region
algorithm combined with the elimination of some outlier results give the following regression
equation form:
𝐾 = 0,03313

.

×


− 0,01648

×

+ 0,5611

(3-2)

Reliability assessment parameters, including SSE = 0.0148, RMSE = 0.0405, and R2 =
0,4743, show that equation (3-2) has acceptable reliability.
3.1.5.4 Correlation between wave steepness and wave transmission coefficient when
slope m=1,5
The results of MatLab's Curve fitting regression calculation using the Trust-region
algorithm combined with the elimination of some outlier results give the following regression
equation form:


13
𝐾 = 0,01609

.

×

− 0,08947

×

+ 0,6222


(3-3)

With reliability assessment parameters including SSE 0,0477, RMSE = 0,063 and R2
= 0,7686 as Figure 0.10, it shows that equation (3-3) has good acceptable reliability.

Figure 0.9: Correlation between Kt and wave steepness with slope m=1,33

Figure 0.10: Correlation between Kt and wave steepness with slope m=1,5

b. 3.2. Wave reflection characteristics
3.2.1 Summary of experimental results
The experimental results were analyzed using the WSWAT tool of MIKE 21 software
for wave reflection coefficients Kr corresponding to experimental scenarios. Analysis of
factors affecting the wave reflection characteristics of inclined plate breakwaters on pile
foundations is carried out below.
3.2.2 Effect of water level on wave reflection
3.2.2.1 Corresponding to the water level at the breakwater crest WL1
The relationship between wave reflection coefficient and wave height is shown in
Figures 3.13 to 3.15. The experimental results indicated that:
- For different water levels, slope m=1 gives the highest wave reduction effect, and slope


14
m=1.5 gives the lowest wave reduction effect.
- With the same slope, the wave reflection coefficient does not significantly change
when changing the wave height. It shows that the notches and concave holes cause the
reflected wave to dissipate significant energy when it interacts with the inclined plate
breakwater.


Figure 0.11: Relationship
between Kr and wave height
with different plate slopes
corresponding to water level
WL1

Figure 0.12: Relationship
between Kr and wave height
with different plate slopes
corresponding to water level
WL2

Figure 0.13: Relationship
between Kr and wave height
with different plate slopes
corresponding to water level
WL3

3.2.3 Effect of inclined slope on wave reflection
The effect of inclined slope on wave reflection in Figures 3.16-3.18 shows that:
- With slope m=1: Water level WL1 has the lowest reflection coefficient, and water level
WL3 has the highest reflection coefficient because when the wave impacts the breakwater, a
part of it overflows the top, so the reflection is smaller.
- With slope m = 1.33, WL1 reflection initially tends to increase, then decreases with
increasing wave height; WL2 reflection coefficient increases with wave height, then Kr
decreases. The WL3 reflection coefficient is the lowest, and waves are mostly dispersed on
the surface of the breakwater, so the reflection is low.
- With a slope of m=1.5, WL1 slightly decreases reflectivity when the wave height
increases. With a gentle slope, waves were broken on the roof so the reflection coefficient
was is reduced.


Figure 0.14: Relationship
between Kr and wave height
corresponding to different
water levels when the inclined
slope m=1

Figure 0.15: Relationship
between Kr and wave height
corresponding to different
water levels when the inclined
slope m=1,33

Figure 0.16: Relationship
between Kr and wave height
corresponding to different
water levels when the inclined
slope m=1,5


15
3.2.4 Effect of wave period on wave reflection
The results in Figure 3.19 show that the reflection coefficient changes significantly with
a wave period of 1.2 seconds. It is quite stable with a period of 1.4 seconds, and changes
significantly with a period of 2.2 seconds.
Thus, it shows that the reflection coefficient is less variable for waves with medium
periods than for waves with short and long periods.

Figure 0.17: Relationship between Kr with the wave period Hs = 0,14m


3.2.5 Effect of wave slope on wave reflection
3.2.5.1 Correlation between wave steepness and wave reflection coefficient when slope
m=1
The results of MatLab's Curve fitting regression calculation using the Trust-region
algorithm have given the regression equation form:
𝐾 = 0,0023

.

×

− 0,0411

×

+ 0,5013

(3-4)

With reliability assessment parameters including SSE = 0.0336, RMSE = 0.0529 and R2
= 0,304 as above, it shows that equation (3-4) has acceptable reliability.
3.2.5.2 Correlation between wave steepness and wave reflection coefficient when slope
m=1.33
The results of MatLab's Curve fitting regression calculation using the Trust-region
algorithm have given the regression equation form:
𝐾 = 0,0022

.

×


− 0,0376

×

+ 0,6983

(3-5)

Reliability assessment parameters, including SSE = 0,0161, RMSE = 0,0366, and R2 =
0,4959, show that equation (3-5) has acceptable reliability.


16

Figure 0.18: Correlation between K r and wave steepness H/gT2 with slope m=1

Figure 0.19: Correlation between Kr and wave steepness H/gT2 with slope m=1,33

3.2.5.3 Correlation between wave steepness and wave reflection coefficient when slope
m=1,5
The results of MatLab's Curve fitting regression calculation using the Trust-region
algorithm have given the regression equation form:
𝐾 = 0,0027

.

×

+ 0,0563


×

+ 0,2092

(3-6)

With reliability assessment parameters including SSE = 0,019, RMSE = 0,0398, and R 2
= 0,4547, as shown in Figure 3, it shows that equation (3-6) has acceptable reliability.
The results of the Thesis show that the regression equations (3-4), (3-5), and (3-6) have
better reliability than the studies conducted by Shil et al. [52]


17

Figure 0.20: Correlation between Kr and wave steepness H/gT2 with slope m=1,5

c. 3.3 Characteristics of wave energy dissipation
3.3.1 effect of water level on wave energy dissipation
Figures 3.24 to 3.26 show the following two main characteristics:
- With the water level at the breakwater crest WL1, the slope m=1.0 has the best wave
dissipation ability.
- With the water level lower than the breakwater crest WL2 and WL3, the slope m=1,5
has the best wave dissipation ability.

Figure 0.21: Relationship
between KL and Hs
correspondings to WL1

Figure 0.22: Relationship

between KL and Hs
correspondings to WL2

Figure 0.23: Relationship
between KL and Hs
correspondings to WL3

3.3.2 effect of inclined Slope on Wave Energy Dissipation
The relationship between the wave energy dissipation coefficient and the wave height
corresponding to the slope m=1, m=1.33, and m=1.5 shown in Figures 3.27 to 3.29 gives the
following summary results:
- The gentler the slope, the better the wave dissipation ability. It is obvious because the
gentle slope reduces the depth at the base of the breakwater, making it easier to generate
breaking waves and climbing waves on the inclined slope.
- With the water level at the breakwater crest WL1, the wave energy dissipation
coefficient is quite small and tends to increase but then decreases. This can be explained


18
because the higher the wave height, the higher the wave ability to overtop the breakwater,
thus reducing the level of wave energy dissipation.

Figure 0.24: Relationship
between KL and Hs
corresponding to m=1

Figure 0.25: Relationship
between KL and Hs
corresponding to m=1,33


Figure 0.26: Relationship
between KL and Hs
corresponding m=1,5

- The wave energy dissipation coefficient does not change much with water levels
lower than the breakwater crest WL2. This is because the notches and concave holes dissipate
wave energy quite evenly.
- The wave energy dissipation coefficient tends to increase when the water level
decreases (corresponding to WL3). This is the result of the waves mostly blocked by the
inclined plate breakwater, so the level of wave dissipation increases. When the water level
reduces, the ability to dissipate wave energy further.
- When the wave height is low, the possibility of waves breaking on the breakwater roof
is quite large, so the wave energy dissipation phenomenon is quite stable. When the wave
height increases, the wave density decreases because the wave overtopping the breakwater
crest is larger, leading to a decrease in the ability to dissipate of wave energy.
3.3.3 Effect of wave period on wave energy dissipation
- In both cases where the water level is lower than the breakwater crest WL2 and WL3,
the KL coefficient does not vary significantly. Especially with a gently inclined slope, the KL
tends to be stable
- These results show that the KL coefficient depends largely on water level but less on
wave height and period.
3.3.4. effect of wave slope on wave energy dissipation
3.3.4.1 Correlation between wave steepness and wave energy dissipation coefficient when
slope m=1
The results of MatLab's Curve fitting regression calculation using the Trust-region
algorithm have given the regression equation form:
𝐾 = −0,0244

.


×

+ 0,0275

×

+ 0,2588

(3-7)

With reliability assessment parameters including SSE = 0,1247, RMSE = 0,109 and R2 =
0,091 as shown in Figure 3.30, it shows that equation (3-7) has quite low reliability.
3.3.4.2 Correlation between wave steepness and wave energy dissipation coefficient when
slope m=1,33
With m=1,33, the results of MatLab's Curve fitting regression calculation using the Trustregion algorithm have given the regression equation form:


19
𝐾 = −0,0466

.

×

− 0,0117

×

+ 0,3217


(3-8)

With reliability assessment parameters including SSE = 0,2232, RMSE = 0,1364 and R2
= 0,1819, as shown in Figure 3.31 and the equation (3-8), it shows better results than the case
m = 1. However, it is quite small, so the reliability is quite low. This is also explained by the
fact that on the inclined plate breakwater surface, notches are combined with concave holes
to reduce waves. Therefore, when waves interact with the breakwater, the nonlinearity is so
large that it is difficult to give a general rule.

Figure 0.27: Relationship between KL and wave steepness with slope m=1

Figure 0.28: Relationship between KL and wave steepness with slope m=1,33

3.3.4.3 Correlation between wave steepness and wave energy dissipation coefficient when
slope m=1,5


20
With m=1,5, the results of MatLab's Curve fitting regression calculation using the
Trust-region algorithm have given the regression equation form:
𝐾 = −0,0007

.

×

+ 0,0285

×


+ 0,0891

(3-9)

Reliability assessment parameters include SSE = 0,1046, RMSE = 0,0933 and R2 =
5694. It shows that equation (3-9) has quite good reliability. Thus, it can be seen that the
gentler the slope, the clearer the relationship between KL and the wave steepness.

Figure 0.29: Relationship between KL and wave steepness with slope m=1,5

d. 3.4 Wave pressure distribution on the inclined plate
3.4.1 The issues
Determine the wave pressure distributed on the breakwater slope. The pressure value P
for each wave probe in each experiment was calculated and compared with the theory.
3.4.2 Wave pressure distribution on pile-supported inclined plate breakwater
Figure 3.33 shows the results of measuring and calculating theoretical wave pressure
from Appendix F - TCVN 9901:2014 and TCVN 12261:2018, drawing some comments
below:
- The wave pressure distribution acting on the inclined plate breakwater (m=1.33 and
m=1.5) has a similar trend to the wave pressure distribution on the sloping embankment. The
difference is that the maximum pressure is higher than the experimental results. At the same
time, the higher the depth, the larger the measured wave pressure distribution than the
calculated wave pressure of the sloping embankment.
- Wave pressure increases when wave height and wave period increase. The maximum
pressure value appears at the same position P2. The calculated maximum wave pressure is 56
to 97% greater than the experiment.
- The lowest wave pressure occurs at the bottom of the inclined plate (point P6). This
can be explained because part of the wave pressure passes through the gap between the
inclined slopes and the flume bottom. On the other hand, the higher the depth, the weaker
the wave interaction, so the wave pressure is significantly reduced. This result shows that,



21

in the absence of experiments on physical models to determine wave pressure, the Method
of calculating wave pressure on sloping embankments can be applied as instructed in
TCVN 12261:2018 and TCVN 9901:2014.

Figure 0.30: Distribution of wave pressure on inclined plate breakwaters on pile foundations with
different slopes

3.5 Distribution of maximum wave velocity at the base of the inclined breakwater
3.5.1 Introduction
During the experiment, a velocity measuring probe was used to monitor the velocity
caused by the waves to evaluate the maximum velocity in front of the base of the pilesupported inclined breakwater. The results filtered out the maximum velocity value and the
corresponding velocity direction.
3.5.2 Maximum velocity distribution due to waves in the gap between the base of the
inclined plate breakwater and the bottom
Based on experimental data, it is possible to extract the maximum flow velocity and
direction corresponding to the original shape. The results shown in Figure 3.34 show that:
- The maximum flow velocity corresponding to the slope of the inclined plate m = 1 and
m = 1.33 tends to be similar and less than the theoretical maximum velocity.
- With a slope of m = 1.5, the measured maximum velocity tends to be larger than the
theoretical maximum velocity. It can be explained similarly to the study of Yagci et al.
because when the slope is gentle, the possibility of waves breaking on the inclined plate
appears, increasing the maximum velocity.
8,0

Vmax Tinh toán (m/s)
Vmax đo đạc (m/s)


7,0

V (m/s)

6,0
5,0

m=1

m=1,33

m=1,5

T thay đổi

4,0
3,0
2,0
1,0
0,0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Phương án thí nghiệm

Figure 0.31: Distribution of maximum velocity due to waves in the gap between the inclined plate
breakwater on the pile foundation and the flume bottom



22
- With the constant wave height and changing the wave period, the results show that the
maximum velocity appears corresponding to experimental plan PA44 with H=0.14m and
T=1.4 seconds corresponding to the original wave is Hnh = 2,1 and Tnh = 5,42 s with inclined
slope m = 1,5. This shows that it is difficult to determine the law of variation of the maximum
velocity caused by waves when impacting on inclined plate breakwaters on pile foundations.
- The maximum velocity caused by waves at the gap between the inclined plate and the
flume bottom with a large inclined slope is similar to the theoretical formula. However, the
wave-breaking phenomenon occurs when the slope is gently inclined, causing the maximum
velocity to increase significantly. The Thesis recommends that experiments be conducted on
physical models to determine the maximum velocity caused by waves.
3.6 Conclusion of Chapter 3
- The wave transmission coefficient can be determined through the relationship with the
wave steepness corresponding to each specific slope. The correlation equations (3-1), (3-2),
and (3-3) have been built with acceptable reliability. The Correlation becomes more obvious
when the slope of the inclined plate is gentler.
- Inclined plate breakwaters on pile foundations with notches combined with waveabsorbing concave holes have a wave reflection coefficient equivalent to inclined slope
breakwaters with covered blocks and can be determined through the relationship with the
wave steepness corresponding to each specific slope. The correlation equations (3-4), (3-5)
and (3-6) are built with acceptable reliability.
- The process of wave energy dissipation is a complex and highly nonlinear process.
Experimental results show that building a relationship between the wave energy dissipation
coefficient and the wave steepness is very difficult when the breakwater has a large slope.
When the slope is gentle, the nonlinearity is reduced, so the relationship according to equation
(3-9) can be used to determine the wave energy dissipation process through the wave
steepness.
- Experimental results show that wave pressure tends to concentrate near the water's edge
and is distributed similarly to theory according to TCVN 9901:2014.
- The maximum velocity induced by waves at the gap between the inclined plate and the
flume bottom with a large inclined slope is similar to the theoretical formula. However, the

wave breaking phenomenon occurs when the slope is gently inclined, causing the maximum
velocity to increase significantly.
CHAPTER 4. APPLYING RESEARCH RESULTS TO PROPOSE THE MOST
SUITABLE TYPE OF INCLINED PLATE BREAKWATERS ON PILE
FOUNDATIONS IN THE CONSTRUCTION OF COASTAL PROTECTION
WORKS IN VIETNAM
4.1 The cross-sectional solution of inclined breakwaters in protection coastal
works
For the goal of protecting the coast with erosion limitation and beach nourishment, it is
recommended to choose the solution of arranging an offshore breakwater or a T-shaped groin
or a fishtail-shaped groin in which the wing of the T-shaped or fishtail with an inclined plate
breakwater structure can be applied. Criteria for selecting shore protection structures include


23
(1) Criteria for route planning and (2) criteria for breakwater shape to ensure the best antierosion effectiveness.
4.2 Propose cross-section type of inclined breakwaters with coastal protection
works
Based on the research results, the Thesis proposes two types of cross-sections of inclined
plate breakwaters with notches combined with wave-reducing concave holes applied to build
coastal protection works as shown in Figures 4.1 and 4.2. The structural parameters are
selected as below.

1. Inclined plate; 2. Crest wall; 3. Stubby apex; 4. Concave; 5. Pile foundation; 6. Stone cushion;
7. Breakwater base strengthening block; 8. Selective stone riprap for breakwater reinforcement.

Figure 0.1: Scenario and ross-section of inclined plate breakwater on pile foundation with closed
bottom

Inclined plate

2. Crest wall
3. Stubby apex
4. Concave
5. Pile foundation
6. Stone cushion 7. Dike base strengthening block 8. Selective
stone 0.2:
riprap
for dike and
reinforcement
Figure
Scenario
ross-section of inclined plate breakwater on pile foundation with open

bottom

4.2.1.1 Breakwater Crest elevation
The crest of the breakwater is determined based on the following:
- For flooded breakwaters, the breakwater crest height is equal to the average water level;
- For submerged breakwaters, the breakwater crest elevation is lower than 0.3 times the
design wave height of the average water level (Hs);
4.2.1.2 Width and height of inclined plate breakwater:
- The Width of the inclined plate breakwater is selected to ensure stability during the
designed storm waves.