TomtatLA(TA): Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.

Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.Nghiên cứu ảnh hưởng của sóng phản xạ đến dòng phản hồi và xói chân đê biển mái nghiêng khu vực Bắc Bộ.MINISTRY OF EDUCATION AND TRAINING MINISTRY OF AGRICULTURE AND RURAL DEVELOPMENT THUYLOI UNIVERSITY NGUYEN THI PHUONG THAO INFLUENCES OF REFLECTED WAVE ON THE UNDERTOW AND SLOPPING SEA DIKE TOE SCOUR.

MINISTRY OF EDUCATION

AND TRAINING

MINISTRY OF AGRICULTURE AND RURAL DEVELOPMENT

THUYLOI UNIVERSITY

NGUYEN THI PHUONG THAO

INFLUENCES OF REFLECTED WAVE ON THE

UNDERTOW AND SLOPPING SEA-DIKE TOE SCOUR

IN THE NORTHERN COASTAL AREA OF VIETNAM

Major: Coastal Engineering

Code No.: 9580203

SUMMARY OF DOCTORAL DISSERTATION

HA NOI, 2022

This scientific work has been accomplished at Thuyloi University

Scientific supervisor: Prof Dr Thieu Quang Tuan

Reviewer No.1: Assoc.Prof Dr Dinh Quang Cuong - Ha Noi University of Civil Engineering

Reviewer No.2: Assoc.Prof Dr Phung Dang Hieu - Vietnam Institute of Seas and Island

Reviewer No.3: Assoc.Prof Dr Nguyen Viet Thanh - University of Transport and Communications

This Doctoral Dissertation will be defended at the meeting of the University Doctoral Committee in ThuyLoi university, 175 Tay Son, Dong Da, Ha Noi

At on 2023

The dissertation can be found at:

- The National Library of Vietnam;

- The Library of Thuyloi University

INTRODUCTION

1 Rationale of the study

Storm waves have an important effect on sea dike safety Depending on the interaction between hydrodynamic factors, bathymetry and dike structure, the different degree of scour and beach erosion in front of sea dike can be took place under wave energy and currents Previous researchs and reality conditions show that each type of structures have affected on different dimensions of the scour and beach erosion due to the present of different wave reflections The influence

of typical sloping revetment structure and the crest configurations such as the crown wall on the return flow and consequently on the toe scour depth through stormy reflected wave are not clarified yet The research on this problem has scientific and practical meaning and support for designer and manager in forcasting the impacts of stormy wave and choosing suitable sollutions for dike savety Therefore, the subject of “Influences of reflected wave on the undertow and slopping sea-dike toe scour in the northern coastal area of Vietnam” is selected to investigate

3 Subject and scope of the study

Undertow and toe scour under the interaction between stormy waves with sloping seadike structures through reflected waves in the north of Vietnam

4 Research contents

Study on the influence of sloping dike structure on reflected wave and undertow

by setting up fix bed model in wave flume; Study on the influence of sloping dike structure on toe scour by setting up mobile bed model in wave flume; Update

numerical model to simulate undertow and seadike’s toe scour in which the influence of sloping dike structure is taken into consideration through reflection coefficients and this model is calibrated and validated by data series from physical models Application of research results to simulate seadike’s toe scour

in Nam Dinh province

5 Approach and research methodology

In order to attain the above-mentioned objectives, literature reviews in order to summarize, analyse and synthesize the knowledge from previous studies in over the world as well as in Vietnam, then apply suitable methodologies to study deep inside, clarify and quantify the research’s subjects

The dissertation has used the following research methodologies: statistical methods; physical model experiments in wave flume; numerical models, and expert consultancy

6 Scientific and practical meaning

The dissertation has scientific meaning in quantitative assessment of the influence of the sloping seadike structure on the distribution of reflected waves and undertow, cross-shore erosion due to storm waves; Updating useful tool for forecasting, analysing hydrodynamic and seadike’s toe scour, beach erosion due

to storm wave; Application of research results for reality problems could give a more accurate assessment and quantification of the amount of cross-shore sediment transport and seadike’s toe erosion driven by return currents during storm That would be the scientific basis for the design and building the most appropriate solutions to protect the shoreline and toe of marine works; This dissertation is the foundation for further applied researches on coastal sediment transport

+ Deriving an empirical formula in order to compute the cross-shore distribution

of reflection coefficient in surf zone in front of sloping dike;

+ Integrating the effect of reflected waves in a numerical model to simulate seadike’s toe scour and successfully modelling for actual cross-section in Nam

8 Outline of the dissertation

In addition to the introduction, conclusions and recommendations, the dissertation consists of 04 chapters as follows:

Chapter 1: Literature reviews on the undertow and ssea-dike toe erosions; Chapter 2: Scientific bases for the study on modelling of the undertow due to

storm wave and sea-dike toe scour;

Chapter 3: Results of the study on influences of reflected wave on the undertow

and slopping sea-dike toe scour;

Chapter 4: Application of the research results to simulate sea-dike toe scour in

Nam Dinh province

CHAPTER 1 LITERATURE REVIEWS ON THE UNDERTOW AND SSEA-DIKE TOE EROSIONS

General introduction

Undertow and cross-shore sediment transport processes

Undertow is the name used for the shore normal mean current which in a surf zone moves seaward below the wave trough level [1] Accoding to Stive and Wind (1996), Svendsen (1984), undertow is formed due to the local vertical imbalance between the depth varying momentum flux and the depth uniform hydrostatic pressure due to wave set-up Cross-shore sediment transport are determined based on profile distribution of both concentration and currents (Fig 1-) In stormy conditions, suspended sediment transport prevail in nearshore surf zone [2] [3] [4]

Fig 1-2 Current and sediment concentration profile in surf zone [18]

Sea dike toe scour

The scour depth is created by the local imbalance of sediment transport at the sea-dike toe position due to revetment prevent material from being carried away

by storm waves/currents When coming to outside of surf zone, undertow is smaller, sediment is deposited and form offshore bar

Overview of the undertow

There have been many studies on undertow such as Svendsen (1984), Battjes (1985) Okayasu (1989) Steetzel (1993) Nam (2013) …The undertow simulation models are derived from the fundamental equations including the mass balance equation (or continuity equation) and the momentum balance equation The difference between these undertow models is that the modeling technique is used

to account for aspects of the physical process when solving equations such as assumptions, selection of boundary conditions, viscosity characteristics, bottom boundary layer treatment, wave theory types Most of the model's results are calibrated and validated by laboratory measurements with a limited number of scenarios, not taking into account the interaction of waves with low-sloping dike structures with overtopping and especially sea dikes with crown walls

Overview of sediment transport and cross-shore erosion

Many studies have been focused on hydraulic regimes, sediment transport, shore erosion and developed simulation mathematical models from simple to complex The Bruun (1954) and Dean (1987, 1991) empirical models are simple models and more simple is the formula to calculate the scour depth at the dike

cross-toe position such as Xie (1981), Hughes and Fowler (1992), Mc Dougal (1996) More complex simulation models for sediment transport and morphological changes usually include four modules: (1) waves; (2) flow; (3) sediment transport and (4) morphology Due to many influent factors on sediment transport and morphological changes related to hydrodynamic characteristics, sediment characteristics and topographic characteristics, the selection and application of formulas to calculate give the different results

Overview of wave reflection

The wave reflection phenomenon is considered as factor having influence on the hydrodynamic characteristics and shoreline circulations, increasing the dike’s toe erosion The reflection coefficient Kr is used to characterize this phenomenon There are many empirical formulas to determine the reflection coefficient due to the presence of coastal structures such as breakwaters, walls, and sea embankments as studied by Seelig (1981), that depend on the Irribaren number

In study of Van de Meer (2005) also taken into account the influence of the freeboard/wave height ratio Zanuttigh (2008) also calculates the effect of the embankment roughness coefficient Sheremet (2002) considered the ratio of incoming and outgoing wave energy fluxes Klopman and van der Meer (1999) give the ratio of the total measured wave height to the incident wave height

H m0,x /H m0i,x as a function of the reflected wave in the vicinity in front of the structure Geometric parameters of dike structure have a strong influence on wave behavior in front of the dike

Overview of studies on the undertow and sea-dike toe erosion due to storm in Vietnam

The sea dike system in Vietnam is considered to be relatively low dike, in stormy conditions, the water level rises creating conditions for large waves to approach the dike toe, causing overtopping waves, erosion beach and dike revetment There have been many studies on hydrodynamics, sediment transport and morphological changes or erosion along the coast by the application of mathematical modeling software such as Mike family, Delft3D Several

reseaches on the shape of the crown-wall structure in the coastal area of Vietnam

to the amount of wave overtopping has been carried out by setting fixed bed models such as Tuan (2010, 2016), Thin (2014), Dung (2017) Ha (2003), Lap (2019) have also established a physical model in flume to study the sea dike toe protection measures The research problem of dike toe erosion has also been studied by the projects of the sea dike program Cat (2008), Quy (2009), Quy (2012) However, in Vietnam, there has been no study on the influence of the sloping dike structure on the distribution of the undertow and cross-shore sediment transport through reflected waves in front of the sea dyke toe

Conclusions for chapter 1

The interaction between the reflected wave and the incident wave can reduce the undertow, but it will increase the turbulent motion leading to incease mixing sediment How the influence of reflected wave on the changes in the undertow structure distribution, sediment transport and seadike’toe scour should be clarified in this dissertation

MODELLING OF THE UNDERTOW DUE TO STORM WAVE AND SEA-DIKE TOE SCOUR

Influences of wave reflection from coastal structure on undertow and sediment transport

Formulae for the reflection coefficient and incident wave height variation in front of reflective structure

Based on the research from Sheremet (2002), reflection coefficient is determined

𝑆𝜂𝑢 is the  – u co-spectrum; d is water depth; f is frequency

The wave and cross-shore velocity spectral density,  – u cospectrum, shoreward and seaward fluxes and reflection coefficients were obtained from each collocated 𝜂(𝑥, 𝑡) and u(x,t) sensor pair at location (x) Those results will show

the change of reflection coefficients K r along the cross-shore profile (x)

Influence of reflection coefficients on the distribution of wave height in front of seadike’s toe are determined based on formula of Klopman and Van der Meer (1999) Ratio between measured and incident wave height at a certain relative

location x/L (L is local wavelength) in the vicinity of reflective structures depends

on the reflection coefficient Kr as following:

Influences of reflected wave on undertow

The incident and reflected wave heights are calculated with the relation of formula of Goda (1976):

𝐻𝑟𝑚𝑠 = 𝐻𝑟𝑚𝑠0

√1 + 𝐾𝑟2= 𝑓𝐾𝑟𝐻𝑟𝑚𝑠0 (2-1) The increase of the wave reflection near dike structure in the breaking wave area significantly reduces the wave flux transported towards the shore The return flow back to the sea, to rebalance, also declines

Influences of reflected wave on sedement concentration

The interaction of reflected waves and incident wave create more disturbance in

a certain distance in front of dike, that will impact on flow characteristics as well

as sediment transport in breaking zone The influence of reflected wave on sediment concentration is expressing in mixing sediment formula of Steetzel (1993): s(z) = 0 + z In which 0 is reference mixing coefficient at bottom: z = 0m;  is vertical gradient of s(z) distribution:

 = 𝐾𝛾𝑐  = H/d (2-12)

𝐾 = 8.5*10-3; c is wave celerity ;  is breaking parameter

The larger the reflected wave in front of the dike toe causes the higher value of mixing sediment coefficient, increasing the concentration of suspended sediment with depth (the cross section of sediment concentration distribution becomes more uniform with depth)

Physical model setup for the studies on undertow and sea dike toe scour

Determination of similitude criteria and model scale

The experiment models were carried out based on the laboratory conditions at Hydraulic laboratory of Thuy Loi University and the prototype conditions in the north of Vietnam The Froude scaling law and relative fall speed criteria are selected to satisfy in this type of undistorted short-wave models The dike model dimensions and testing hydraulic conditions are selected in accordance with the model length scale NL = 9.0 and the time and fall velocity scales NT = 𝐍= 3.0

Experiment design and equipment arrangement

Fix bed experimental model is setting up to study the reflected waves and

undertow structures as illustrated in fig 2-7 There are 3 types of geometrical dike models: (1) low dike with crown wall; (2) low dike without crown wall; (3) very high dike (no overtopping and no crown wall) Dike slope is 1/3 Overtopping discharges are collected by a tank at the lee side of dike Overtopped water was pumped back to the flume at the back side of wave generator The collocated wave (WG) sensors and current meters (CG) were positioned at 9 points in front

of seadike Waves are also measured at five-gauges array

Fig 2-7 Fixed bed experimental setup

Mobile bed experimental setup is illustrated in Fig 2-8, in which sandy beach

slope is 1/100, dike’s slope is 1/4 Another scenario of dike models is setting for beach slope of 1/40 and dike’s slope is 1/3

Fig 2-8 Mobile bed experimental setup with beach slope of 1/100

Experiment scenario

The fixed-bed model has a total of 12 scenarios simulating waves and currents in front of the sea dike toe The simulation duration is selected based on the undertow stability tests The mobile-model has a total of 30 scenarios for the beach slope of 1/40 and 30 scenarios for the beach slope of 1/100

Mathematical model update to simulate undertow and sea dike toe scour

The research results obtained from the physical model on the effect of reflected waves on undertow, sediment transport and dike toe erosion will be updated in the Wadibe-TC model that developed by Prof Thieu Quang Tuan Two modules

in this model have been updated as following:

+ In hydrodynamic modul (wave, current), update reflection coefficient from dike structure (Kr0) and wave height that determined according to formular (2-6)

In which, coefficient fKr is obtained from fixed bed model results;

+ In morphological modul, mixing formula of Van Rjin (1993) is replaced by formula of Steetzel (1993): s(z) = 0 + z in which:  = 𝐾 𝑐

𝛾 ′ ; 𝛾′ = 𝑓𝐾𝑟 𝛾 The measured data from tests are used to calibrate and validate numerical models

Conclusions for chapter 2

The undertow structures, wave reflection coefficient Kr and reflected wave influent factor fKr are functions of relative position (x/L) where L is the local

wave length, based on the colocated wave and flow data series measured in the fixed-bed model The mobile-bed model is used to study the influent factors on dike toe erosion The dissertation additionally updates the research results of the effect of reflected waves on the undertow and seadike toe erosion through the reflection coefficient into the Wadibe_TC model to improve the quality of the simulation results

CHAPTER 3 RESULTS OF THE STUDY ON INFLUENCES OF REFLECTED WAVE ON THE UNDERTOW AND SLOPPING SEA- DIKE TOE SCOUR

Results analysis from physical model studies

Undertow structure study

The simulation duration for scenarios is 300Tp that is selected according to the actual simulation tests in flume in order to get the stable undertow values

3.1.1.1 Undertow distribution

Fig 3-1 is the results of measured undertow structure at locations corresponding

to different type of dike structures The distribution of undertow in the cross section in front of dike toe has a parabolic shape In general, the maximum magnitudes of undertow are about 0.5 ÷ 1m from the dike toe with crownwall structure, 1÷1.5 m for dikes without crownwall, and 1÷2 m for high dikes Dike with crownwall structure can create larger reflections, the flow is smaller than those with with lower reflective structures such as high dikes

Fig 3-1 Measured return flow profile of scenario D65H15T19

3.1.1.2 Influence of dike structure on averaged undertow

With the same hydraulic boundary conditions, beach and revetment slopes, the obtained results of the relative average undertow over the entire of cross-section for 3 types of dike scenarios are shown in Fig 3-5 The relative mean undertows are clearly affected by the dike roof structure and tends to increase gradually from shoreline to a position of about 0.5 ÷ 0.7 times the wave length, creating an average velocity gradient and leading to the transport of sediment from dike toe

to a position of about 1L offshore Then the flow becomes smaller and the sand will settle to form sandbar

Fig 3-5 Influence of dike structure on mean currents - scenario D65H15T19

Influence of reflected wave on undertow

From collocated wave height and velocity data at 9 positions, reflection coefficient Kr,x is determined by applying the Sheremet (2002) formula (2-6) for

11 tests The results show that the reflection coefficient Kr,x tends to decrease gradually off shore ward from the dike, especially from the waterline to the position of about x/L < 0.75 and asymptotic approach to constant value at a long sufficiently distance x/L (x/L >> 1.0) The reflection coefficient at this boundary (named Kr,0) is chosen as the reference value, the ratios between the local reflection coefficient Kr,x and Kr,0 (ratio Kr,x/Kr,0) can be calculated are shown in Fig 3-11 It can be seen that the variation trend of reflection coeffiecient in the vicinity of the dike toe is shown quite clearly Application of the Klopman and van der Meer (1999) formula (2-8) to calculate the variation of wave height ratio

Hm0,x/Hm0i,x in the vicinity in front of the dike structure and Fx(x/ L) is a function

of relative distance x/L that reflects the distribution of reflection coefficient The