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1 MINISTRY OF EDUCATION AND TRAINING MINISTRY OF AGRICULTURE AND RURAL DEVELOPMENT THUYLOI UNIVERSITY PHAN DINH TUAN PROPOSING THE UPDATED CROSS SECTION AND WAVE OVERTOPPING CALCULATION FOR SEA DIKES[.]

MINISTRY OF EDUCATION

AND TRAINING

MINISTRY OF AGRICULTURE AND RURAL DEVELOPMENT

THUYLOI UNIVERSITY

PHAN DINH TUAN

PROPOSING THE UPDATED CROSS-SECTION AND WAVE OVERTOPPING CALCULATION FOR SEA DIKES WITH HOLLOW QUARTER-CYLINDRICAL STRUCTURE

This scientific work has been accomplished at Thuyloi University

Scientific supervisor: 1 Prof Tran Dinh Hoa

Reviewer No.1: Prof Dr Thieu Quang Tuan - Thuyloi University

Reviewer No.2: As.Prof Dr Phung Dang Hieu – Vietnam Institute of Seas and

Islands – Ministry of Natural Resources and Environment

Reviewer No.3: As.Prof Dr Pham Hien Hau -National University of Civil

Engineering

This Doctoral Dissertation will be defended at the meeting of the University Doctoral Committee at

at ……… on 8.30 Am, 24 December 2022

The dissertation can be found at:

- The National Library of Vietnam;

- The Library of Thuy loi University

INTRODUCTION

1 Rationale of the study

Vietnam has a very large sea dike system, stretching from North to South, making

an important contribution to protecting people's lives and property, and serving production and development of the country In recent years, climate change has become increasingly complicated and unpredictable, which has had a great impact on life and production The problem of coastal erosion has become more and more complicated, especially in the Mekong River Delta There have been many research projects proposing various solutions to enhance the stability of sea dikes In which, coastal protection works to reduce wave impacts and waves overtopping sea dikes have been widely studied and commonly applied

Under the soft geological conditions in the Mekong River Delta, the increase of crest elevation necessitate a compact cross section, low self-load to limit ground subsidence The current common solution is to adopt a crest wall, which initially shows the efficiency in reducing wave overtopping by means of increasing crest elevation and decreasing the embankment height instead of enlarging the entire dike cross section Still, there have been numerous limitations due to the low wall height resulting in a large cross section and also the subsequent ground subsidence Besides, the crest wall generates high wave reflection with the coefficient Kr=0.7÷1, resulting in direct high pressure on the structure, and simultaneous erosion and the instability of the wall foot

Based on the basis of analysis and assessment of the existing solutions and in order to meet the requirements of the safe crest level when allowing wave overtopping and reducing the cross-sectional load in the design of sea dikes, the author has proposed a new cross section for sea dikes with hollow structure (see Figure 1), overcoming the limitations of cross-sectional loads, wave reflection

In recent years, hollow structures have been widely used for coastal protection works, especially detached breakwaters Hollow structures come in many different shapes, but they all have a common characteristic, which is a perforated seaward surface with design void ratio and a hollow chamber in the middle The research results have shown significant advantages such as: prefabricated concrete blocks, which are convenient in construction; effectively reduce wave transmission and reflection This is a solution with a new structural layout, which

is suitable for coastal protection works in the Mekong River Delta

Figure 1: Sea dike cross section including hollow structures

When applying the hollow quarter-cylindrical structure to the sea dike section, there are difficulty in wave reduction mechanism At the same time, the formula to determine the dike height according to the crest freeboard to ensure the design wave overtopping is not completed Therefore, the research topic

cross-"Proposing an updated cross section and corresponding wave overtopping calculation for sea dikes with the hollow quarter-cylindrical structure on the crest" has been chosen for this dissertation

3 Subject and scope of the study

3.1 Subject of the study

Sea dike cross-section with the hollow quarter-cylindrical structure on the crest and the corresponding wave overtopping

3.2 Scope of the study

To propose the sea dike cross-section with the hollow quarter-cylindrical structure on the crest; to study the corresponding wave overtopping on the basis

of current natural conditions in Mekong River Delta

4 Research methodology

Analyzing and assessing the existing sea dike systems, thereby proposing an updated sea dike cross section with the hollow quarter-cylindrical structure on the crest, which is suitable for Mekong River Delta On the basis of theoretical research combined with physical modeling experiments, an empirical formula for calculating wave overtopping in case of sea dike cross section with the hollow quarter-cylindrical structure on the crest has been proposed The obtained results

were then applied to the design of an actual project

5 Scientific and practical meaning

5.1 Scientific meaning

The research has proposed an updated cross section for sea dikes and an empirical formula to determine the corresponding wave overtopping It has contributed to supplement and enrich the existing research results on sea dikes in general and wave overtopping in particular At the same time, it is the basis for the next studies on other unresolved issues for sea dikes

5.2 Practical meaning

The updated sea dike cross section with the hollow quarter-cylindrical structure

on the crest and the empirical formula to calculate the corresponding wave overtopping will make an important contribution to the analysis, selection and more effective design of sea dikes applied in practice

6 Outline of the dissertation

In addition to the introduction, conclusions and recommendations, the dissertation consists of 4 chapters as follows:

CHAPTER 1: Overview of studies on waves overtopping sea dikes;

CHAPTER 2: Theoretical bases and research data;

CHAPTER 3: Proposing an updated cross section of sea dike with the hollow quarter-cylindrical structure on the crest and deriving an emperical formula for calculating the corresponding wave overtopping;

CHAPTER 4: Applying the research results for Nha Mat sea dike in Bac Lieu province

CHAPTER 1 OVERVIEW OF STUDIES ON WAVE OVERTOPPING AND APPLICATION OF HOLLOW STRUCTURES TO COASTAL PROTECTION WORKS

1.1 Overview of studies on waves overtopping sea dikes

When carrying out the studies on sea dikes with inclined slopes, Saville (1955) was the first to lay the groundwork for the research on wave overtopping with a series of experiments for regular waves [2] Thereafter, Owen (1980) conducted the experiments on physical models with 500 scenarios for random waves, and proposed an empirical formula to determine the average overtopping discharge

in case of smooth dike slope as follows [4]

R q

where, Tm is the mean wave period (s), Hs is the significant wave height (m) and

Rc is crest freeboard (m) Owen (1980) mainly used a simple smooth sea dike model with seaward berm to conduct a few experiments The derived empirical coefficients a and b were determined for different slopes of the dike Owen (1980) also considered the influence of the slope surface roughness on wave overtopping by means of the reduction factor γr

Owen (1980) then based on the additional experiments to re-verify the mentioned coefficients for oblique incident waves De Waal and Van der Meer (1992) continued to study the waves overtopping smooth impermeable dikes, taking the deficiency of the crest freeboard (Ru2% - Rc)/HS into consideration when calculating the average overtopping discharges, where Ru2% is the height of the 2% wave run-up (corresponding to 2% of the waves exceeding this level on the non-overtopping dike slope)

aboved-It can be seen that the applicable range of the formulae proposed by De Waal and Van der Meer (1992) has numermous limitations, such as: not taking into account the influence of the slope surface roughness, the influence of the berm and especially wave overtopping discharges are calculated by means of wave run-up Ru2% Therefore, Van deer Meer (1993) later improved the above-mentioned formula by relating the overtopping discharges directly to the relative crest freeboard Rc/Hs and using the results of Owen’s studies (1980) In addition, Van

deer Meer (1993) added the influence the characteristic interaction between incoming waves and the structure to assess the wave overtopping

TAW (2002) and EurOtop (2007) presents a fairly complete set of formulae for calculating wave overtopping applied to sea dikes, with a wide applicable range for a variety of sea dike geometries and taking into account various influence factors on wave overtopping Currently, these formulae has been widely used For vertical walls, Doorslaer et al (2015) proposed the influence factor for the wall height, the front base and the wave-return structures on wave overtopping

in case of vertical walls with steep front face

Up to now, in the world, there have been a number of studies on the influence of crest walls on waves overtopping sea dike These studies mainly focus on the relationship between the wall height (W), the crest freeboard above the dike surface (or the freeboard above the wall top Rc) and the front base in front of the wall (S) and the influence factors γw, γs, γv On the other hand, the studies have not analyzed the simultaneous influence between factors such as the front base

of the wall and the wave-return structure

Based on the general formula, Franco et al (1994) determined the parameters a

= 0.2 and b = 4.3 for deep water, while Allsop et al (1995) proposed the coefficients a = 0.05 and b = 2.78 in shallow water conditions Both formulae have been applied and compared with the same data set from CLASS project; the results shown by the theoretical lines are consistent with the formulae in the study range Franco et al (1994) obtained the convergent results in deep water; in shallow water, the results are derived correctly by means of the method proposed

by Allsop et al (1995)

1.2 Overview of hollow structures applied to coastal protection works

The idea of hollow structures was proposed by Jarlan in 1961 Since 1969 in Japan, a number of coastal protection works have been built with the application

of this structure In addition to the dissipation of wave energy, the absorbing chambers (BTS) in front of the caissons are also effectively used for fish farming and power plants taking advantage of wave energy

wave-In recent years, hollow structures with surface voids and wave-absorbing chambers have been increasingly studied and applied in offshore wave reduction

works in Mekong River Delta In 2017, Institute for Hydraulic Construction, affiliated to Vietnam Academy for Water Resources, applied a hollow semi-cylindrical structure, 5 rows of holes, each row of 4 holes in contact with incident waves, 2 rows of holes, each row of 4 holes, the hollow cylindrical side facing landwards The diameter of each hole is 30 cm, with capacity of reducing waves, environmentally-friendly effects, and resulting in considerable accretion Current studies have been focusing on the solution of offshore hollow structures, which allow wave overtopping and are evaluated by wave transmission and reflection parameters Therefore, the current research results help to show the effective reduction of the wave reflection and recommend the surface void ratios

as well as confirm the limitation and the necessity of studies on wave overtopping calculation for hollow structures

Dhinakaran et al studied the detached wave dissipating hollow structures from

2009 to 2012 by means of physical models in wave flume The analysis results shown that the optimal value of void ratio in terms of wave reflection and transmission is 11% Taking the influence of foreshore water depth into consideration, Dhinakaran et al recommended that the model height should be 1.25 times higher than the water depth, the rubble mound layer should be 0.29 times as high as the physical model

Some judgment on the magnitude of the effects can be obtained from one of the few studies (see Franco and Franco, 1999) for caisson breakwaters under non-impulsive wave conditions Studies have been carried out for structures with round or rectangular holes with surface void ratio of 20% The effect of air venting was also taken into consideration

Nguyen Trung Anh (2007) conducted experiments and studies on the caisson structure with wave-absorbing chambers and surface voids, and thereby evaluated the ability to reduce wave reflection with 3 types of surface void (horizontal slit, vertical slit and round hole) and 3 void ratios of 15%, 20%, 30% Structures with wave-absorbing chambers (BTS) have the best efficiency if B/L

is in the range of 0.1÷0.27 for all 3 types of surface voids The value B/L = 0.1 was recommended when designing the structure width The void ratios of 20% and 30% are better than that of 15%, but no recommendation was made for the selection of the design value In terms of surface voids, the results shown that

round holes are better than horizontal and vertical slits

1.3 Current status of existing sea dike systems in Mekong River Delta

Currently, two types of sea dike cross-sections have been being applied in Mekong River Delta: plain sloping dikes and sloping dikes with crest walls Both cross sections have advantages in reducing wave overtopping and partly meet the task of the structure However, there are still some problems as follows: with the sloping sea dike used to be built in the past construction of the dike crest elevation is relatively low Up to now, under the impact of climate change and the subsequent rise of sea level, the crest elevation has no longer met the task In addition, it will be difficult to increase the crest level by means of supplementary embankment due to weak subsoil

For the sloping dike cross section with crest walls, the greatest disadvantage is the wave reflection The reflected wave at the foreshore of the dike will cause erosion of the seaward slopes and toes In addition, when the sea dike has a low crest wall, the overtopping waves interact with the dike slope due to the large wave runup energy, so when the waves hit the crest wall, high wave splashes will

be generated, accompanied by storm winds from the sea with relatively high velocity; the water mass from splashing waves will directly hit the dike surface with a large kinetic energy, damaging the dike surface and leading to dike failure

Figure 1.25: Flood tides in combination with high waves, strong winds resulted

in waves overtopping the West Sea dike system on August 3, 2019

1.4 Conclusions for Chapter 1

In Chapter 1, the overview of the issues related to the field of research on “waves overtopping sea dikes cross-section with hollow structures” is presented Thereby, the author has generalized and made certain conclusions on the research field as follows:

1 The current studies of waves overtopping sea dikes are usually divided into two main types, which are sloping dikes and sea walls The studies on sea dike cross section including hollow structures at the crest are still limited and not mentioned in the world and in Vietnam

2 Hollow structures are usually large precast concrete blocks and commonly applied to detached wave-dissipating works with large overtopping Studies on wave overtopping in case of hollow structures included in the cross-sections of sea dikes and sea walls are still very limited

3 Analyzing the disadvantages and limitations of various cross sections and structures of current sea dikes and the governing wave parameters mainly related

to dike failure such as wave overtopping, wave reflection, etc Thereby, a suitable cross section of sea dike and governing parameters were proposed for the next steps of the research;

Therefore, the study of the updated cross section of sea dikes including TSD structure and the corresponding wave overtopping is a new research orientation that needs to be carried out The research is conducted in order to propose a new structure for sea dike cross section, which is suitable for soft soil areas Simultaneously, theoretical studies and experiments were carried out by means

of physical models in wave flume to establish an emperical formula for calculating the corresponding wave overtopping

CHAPTER 2 THEORETICAL BASES AND RESEARCH DATA

2.1 Theoretical bases for the studies on wave overtopping

The process of wave overtopping sea dikes is divided into two main types, which are “overtopping” and “splashing” The main governing parameters of wave overtopping are:

Table 2.1: The main governing parameters of wave overtopping

Governing parameters Unit Symbol, definition Geometrical parameters of sea dikes

- Angle of seaward dike slope; equivalent

dike slope

o (-) α; tan α

- Crest freeboard (above design water level) m Rc

- Relative crest freeboard - Rc/Hs, d

+ Inclination of crest wall surface

+ Crest wall height

o

m

αw

dw

Wave parameters

- Significant wave height in deep water m Hs0 or Hm0,0

- Significant wave height at the dike toe m Hsd or Hm0, d

- Other wave periods s Tm-1,0, T1/3, Tm

- Incoming wave angle in deep water/at the

dike toe

o 0, d

- Wave length in deep water/at the dike toe m L0, L

- Length/shortness of wave crests - s

2.2 Method of calculating wave overtopping in case of characteristic cross sections

Based on the overview in Chapter 1, the sea dike cross sections and the corresponding wave overtopping calculation method were divided into 2 main categories as follows:

- Sea dike with composite slope (slope in combination with berm, dike crest wall with or without wave-return structure);

- Sea dike in the form of a composite vertical wall (sea wall with or without wave-return wall, with reinforced block, berm-typed toe protection structure)

2.2.1 Method of calculating wave overtopping in case of dike slope with crest wall

With dike slope of 1:2 to 1:4/3, the average overtopping discharge can be determined by the following formula:

1.3 c 3

m0 f β 0

R0.1035 exp 1.35

H γ γ

m

q gH

In case of sloping dike with crest wall, the average overtopping discharge can be determined by the following formula:

1.3

* 3

0 0

0.09 exp 1.5 c

m m

R q

 = − 

where, *is the influence factor for a crest wall; hwall is the wall height

2.2.2 Method of calculating wave overtopping in case of vertical wall

The average overtopping discharge in case of composite vertical wall with breaking waves (Van der Meer, JW, Bruce T, 2014) can be determined as follows:

0.5 3 0.5

0 3

1,0 0 0

0.5

0 3

where, q is the average overtopping discharge; Hm0 is the spectral wave height, d

is the submerging level at the wall toe; h is the water depth at the foreshore; Rc

is the crest freeboard above design water level; 2

m-1,0 H m0 1.56Tm1,0

s = − is the wave steepness

2.3 Theoretical bases for physical model experiments

2.3.1 Law of similitude and scale factor

To maintain the basic similarity of wave parameters, the model needs to be formalized; the model scale also needs to satisfy Froude's criterion F=V/(gL)0.5

(V is wave velocity; L is void diameter) The choice of NV = Nt = (NL)0.5 by means

of dimensional analysis and Buckingham's law  helps the model to ensure the Froude similarity index, by which Fm = Fn (m: model; n: prototype)

2.3.2 Dimensional analysis and determination of the general equations

By means of the equivalent transformations included in the PI-BUCKINGHAM method, the general equation of the average discharge overtopping the sea dike section with the hollow quarter-cylindrical structure on the crest can be determined as follows:

H h s m− and the surface void ratio ε

2.4 Bases for the selection of parameters and experimental scenarios

Based on the synthesis of current sea dike data, wave conditions, water level in the study area, the crest elevation for experiments was chosen as +3.5m, with the foreshore elevation ranges from -1.5 to 0m and design high water level from +0.7

to +2.6m, in combination with various water depths: 1.5 m, 2.5m, 3m, 3.5m and 4m The wave height ranges from 1 to 1.5m corresponding to the wave period determined by the formula proposed by Thieu Quang Tuan and Dang Thi Linh (2015) and SPM (1984) At the same time, taking the wave generation capacity

of the laboratory into consideration, the prototype wave periods were selected as 4.1s; 5.5s; and 6.6s

2.5 Model setup and experimental layout and scenarios

The model scale was determined as 1/10 according to Froude’s criterion,