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: Code No.: Coastal Engineering 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 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 Research objectives + To evaluate the effects of reflected wave from sea dike slope on undertow and scour; + To simulate the scour due to undertow with influence of reflected wave from sea dike slope and to apply to case study in Nam Dinh 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 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 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 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 New contributions + Evaluation of the influence of revetment and crest configurations on seadike’s toe scour through the effect of reflected wave on undertow and mixing coefficient of suspended sediment concentration profile; + 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 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 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, crossshore 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 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 Hm0,x/Hm0i,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 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 CHAPTER SCIENTIFIC BASES FOR THE STUDY ON 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 as following formula: K 2r = 𝑓𝑈 𝐹± = ∫ 𝑓𝐿 F − (x) F + (x) (2-6) 𝑑 √𝑔𝑑 [𝑆𝜂𝜂 (𝑓) ± (2√𝑑/𝑔)𝑆𝜂𝑢 (𝑓) + 𝑆𝑢𝑢 (𝑓)] 𝑑𝑓 𝑔 In which: F-, F+ are seaward and shoreward energy fluxes; 𝑆𝜂𝜂 𝑎𝑛𝑑 𝑆𝑢𝑢 are wave and cross-shore velocity spectral density respectively; 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 Kr 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: Hm0 (x) x 1/2 = [1 + K 2r + 2K r F( ) ] Hm0i (x) L (2-8) 𝑥 𝐿 - At x = (toe of structure) 𝐹( ) = and 𝐻𝑚0 (0) = (1 + 𝐾𝑟 )𝐻𝑚0𝑖 (𝑥) 𝑥 - Far away from structure 𝐹(𝐿 ) = and 𝐻𝑚0 (∞) = 𝐻𝑚0𝑖 (𝑥)√1 + 𝐾𝑟2 Influences of reflected wave on undertow The incident and reflected wave heights are calculated with the relation of formula of Goda (1976): 𝐻𝑟𝑚𝑠0 (2-1) 𝐻𝑟𝑚𝑠 = = 𝑓𝐾𝑟 𝐻𝑟𝑚𝑠0 √1 + 𝐾𝑟2 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: 𝑐 = 𝐾 𝛾 = 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 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 points in front of seadike Waves are also measured at five-gauges array Fig 2-7 Fixed bed experimental setup 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 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 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 11 asymptotic values at the boundaries of this Fx function are as following: Fx 1.0 Fx x/L0 x / L (3-2) It become: Kr ,x K r ,0 1 Fx ( x / L) K r ,0 0.5 (3-3) Fig 3-11 Local reflection coefficient profile Kr relative distance x/L in front of seadike Based on equation (3-3), with measured data from fixed bed tests, calculating Kr,x and reflection coefficient at the boundary Kr,0, the relationship Fx ~ x/L can be determined The results are shown in Fig 3-12 Regression analysis of the function Fx(x/L) with experimental data and considering the asymptotic values at the boundary gives the following distribution function results (R2 = 0,55): 𝑥 𝑥 (3-4) 𝐹𝑥 ( ) = exp(−6,65 ) 𝐿 𝐿 Fig 3-12 Analysis results of spatial autocorrelation function Fx (x/L) 12 Data analysis from mobile bed model 3.1.3.1 Measurement results of bed level change Dike toe erosion is a complex problem, which depends on many parameters including hydraulic factors, sediment, structures and the interaction between waves and dike structures The general trend for the simulation scenarios in the mobile bed experiment is to erode the dike toe and form a small offshore dune bar and follow a shallow scour hole and then to a stable section The highest bed changes area is about 2m from the diketoe 3.1.3.2 Evaluation of the factors that effect on scour depth Experimental observation results show that waves mainly break on the dike revetment and the analysis results in Fig 3-18 show that the relative maximum scour depth is proportional to the Iribarren number and this trend is also reasonable because it is related to the dike slope The beach slope also plays an important role, affecting the wave characteristics, especially creating breaking waves phenomenon at different locations leading to the different erosion zones The general trend is that the steeper the slope, the more erosion or the smaller the relative water depth, the greater the relative maximum scour depth Fig 3-18 Variation in maximum scour depth with Iribarren number The presence of crownwall increases the reflected waves, increases the turbulence and thus increases the scour depth Fig 3-15 shows the dependence of the relative scour depth on the reflection coefficients of 60 tests The results of the fixed bed tests show that when the reflection increases, the undertow 13 decreases near the diketoe but increases the scour size significantly This will be demonstrated to clarify the results of the mathematical model study in the next section Fig 3-15 Influence of reflection coefficient on relative maximum scour depth Results of upgraded mathematical model to simulate undertow and sea dike toe scour The upgraded mathematical model Wadibe-TC Based on the research results, Wadibe-TC model is updated with the distribution relationship of the reflection coefficients according to equations (2-1) and (3-3), (3-4) in calculating the current and morphological changes Corresponding to each type of dike structures and boundary conditions, there will be a different offshore boundary reflection coefficient Kr0 The modules in the Wadibe_TC model simulating sea dike toe erosion are calibrated and validated with experimental data as performed in the previous section Results of wave module calibration and validation The comparison results between measured and simulated wave heights of a typical scenarios are presented in Fig 3-20 Model calibrated parameters include breaking parameter, energy dissipation coefficient, slope of the face of the wave and friction coefficient All simulation scenarios give quite suitable results with the measured wave height data for both high dike and low dike models, especially in the breaking wave area, the measured values are very close to simulated values 14 Fig 3-20 Calibrated and validated results of wave height – High dike scenario Results of current module calibration and validation 3.2.3.1 Simulated results of mean undertow Simulated results of mean undertow along the cross-section of per 12 scenarios corresponding to three types of dike’s structures compared with measured data are shown in Fig 3-23 When taking into account the effect of reflected waves, the simulated mean undertow results are better than those that not take into account the reflected waves The dike structures have an influence on the undertow magnitude and the simulation results here prove it The agreement between the simulated and measured results in the breaking wave area is better than at the dike toe area, because the area close to the dike toe is also affected by the backwash flow on revetment and overtopping which have not been calculated in the Wadibe-TC equation 15 Fig 3-23 Mean return flow – low dike with crownwall scenario 3.2.3.2 Simulated results of undertow distribution The simulated results of the undertow distribution with and without the reflected wave of the per 12 scenarios are shown in Fig 3-34 Fig 3-34 Calibrated results of undertows - scenario 16 With the effect of the reflected wave according to a definite function, the simulation results of the average velocity as well as the distribution of the undertow are much better, especially in the area of breaking waves where dissipate the most wave energy Results of morphological module calibration and validation After calibrating and analyzing the sensitivity of the parameters, simulations of dike toe erosion are conducted under the influence of reflected waves The results of the change of bottom topography before and after the wave impact, with and without taking into account the influence of reflected waves for 6/9 scenarios are presented in Fig 3-43 and fig 3-44 In general, when taking into account reflected waves, the scour depth is larger than not taking into account Although the undertow in front of the diketoe is smaller, the larger mixing coefficient lead to larger scour depth For dike scenarios with lower reflection, this difference is smaller than for scenarios with higher reflection Fig 3-2 Simulated results of seadike’s toe erosion– Low dike without crown-wall 17 The increases of reflection coefficient Kr cause the increases of scour size The calculation of Kr in the sediment mixing formula gives better results, it can be distinguished clearly the influence of wave interaction and different type structures The maximum scour depth can be increased from 11 ÷ 20% compared to case that the effect of reflected waves is not taken into account Fig 3-44 Simulated results of seadike toe erosion – low dike with crownwall Conclusions for chapter Due to the effect of the reflected wave, the incident wave is reduced and leads to decrease in local mean current and return flow distribution becomes steeper Measured data in wave flume show that the influence of reflected waves from different types of dike structures causes difference in distribution of the crosssection reflected currents In case the seadike structure having crown-wall, the maximum undertow is closer to dike than high dike The mathematical model that taken into account the reflected wave gives a better agreement with the experimental data than the case is not taken reflected wave into account 18 CHAPTER APPLICATION OF THE RESEARCH RESULTS TO SIMULATE SEA-DIKE TOE SCOUR IN NAM DINH PROVINCE Overview of Nam Dinh coastal area Nam Dinh coastal area has a complex hydrodynamic regime in the North of Vietnam with much morphological changes during storm conditions There are many types of shore protection structures due to the long distance of Nam Dinh coastline suffer from erosion seriously According to Vu (2003), the beach topography in Nam Dinh area is quite gentle, the average slope ranges from 1/150 ÷ 1/300, the part close to the shore from the dike toe to about 300m has a steeper slope, 1/ 50 ÷1/100 The reanalysis wave data at 106.5E_20.0N, about 25km from the coast of Hai Hau, Nam Dinh shows that waves caused by monsoon have wave height of about 2m, period of 6-8s Storm waves usually have wave height of ÷ 4m, the main wave direction to the shoreline is Southeast and Northeast The Nam Dinh sea dike system has a length of about 91km, of which 45km is a sea dike directly facing to the sea It is regularly reinforced and upgraded, but problems still occur when storms lands, especially erosion problem Therefore, the groin system was built to protect dike and beach Mathematical model calibration for Nam Dinh coast Input data for storm Damray 2005 at Thinh Long beach are collected based on research from Cát (2008), Tuấn (2008) including: Bathymetry; wave height Hs = 6,5m, wave period Tp = 9s; water level +2,6m; d50 = 200m, d90 =250m, porosity 40%; offshore reflection coefficient is calculated according to formula Zanuttigh (2008) Kr0 = 0,37; Simulation duration is 6h The simulation results of Thinh Long seadike toe erosion are shown in Fig 4-5 It can be seen that the results are closer to reality when calculating the reflection coefficient The simulated seadike’s toe scour depth is 22cm larger than when not taking into account the influence of reflected waves The range of the scour hole in the mathematical model is wider than that in the actual measurement Because the actual scour pattern is quite complicated, influenced by many factors 19 and especially affected by two consecutive storms, as in this case the simulation becomes more and more complicated The certain difference between the calculation and measurement is acceptable and the quantification of the scour dimensions in the numerical model taking into account the effect of the reflected waves gives suitable results that can be used to simulate scenarios for different sea dike structures Fig 4-5 Calibrated results of seadike’s erosion at Thịnh Long – storm Damrey 9/2005 Scenario simulations Scenario setup The data for the scenarios include: dike’s slope are m = 3, m = 4, crown wall is 0.8m high, dike revetment is protected by concrete cylinder 2m high or concrete pile and stone aprons ÷ 6m wide, T groynes are from 35-70m long; The water level is selected from 2.0 ÷ 3m Wave characteristics at offshore boundaries are statistically collected at position 106.5E_20.0N: Hm0 = 2.0 ÷ 3m, period ÷12s; Sediment characteristics, topography as in section 4.2, the beach is extended offshore ward with slope of 1/200 to a position about 3km from the dike; Simulation duration is hours Simulated results of sea dike toe scour Influence of hydrodynamic factors on scour depth The simulation results in Table 4-3 show the influence of a number of scenarios that combine of hydraulic factors including wave heights, water depths and wave periods on the scour depths The size of the dike toe scour hole depends a lot on 20 the incoming wave energy, so the same water depth d=1.8m, the higher the wave height, the larger the scour hole When the water depth is large, it allows larger waves to reach the dike toe, causing a greater shear stress, stirring up more sediment, and larger return currents can carry more sediment away, cause deeper scour hole However, depending on the characteristics of the incident waves, the scour depth may be higher or lower, and there may be existing water depth which create highest maximum scour depth corresponding to the combination of wave characteristics The change of wave period also seem does not affect the scour width, but only changes the scour depth Table 4-3 Influence of ydrodynamic conditions on maximum scour depth h(m) d(m) Hm0 (m) Tp(s) Hm0toe(m) Smax(m) Smax/Hm0toe Smax/Hm0 1,8 1,24 0,71 0,57 0,36 1,8 2,5 1,26 0,84 0,67 0,34 1,8 1,28 0,93 0,72 0,31 0,8 2,5 0,73 0,56 0,77 0,23 2,5 1,3 2,5 1,02 0,72 0,71 0,29 2,5 1,3 2,5 0,92 0,52 0,57 0,21 2,5 1,3 2,5 12 1,18 0,83 0,71 0,33 Influence of dike revetment and crest structures on scour depth Simulated results of the influence of sloping seadike structure on the maximum scour depth (Smax) with and without the reflection coefficients are presented in Table 4-4 The offshore wave reflection coefficient Kr0 is estimated according to the formula of Zanuttigh (2008), depending on the Irribaren number and the embankment roughness coefficient chosen by 0.9 In case of crown wall, the dike’s slope is calculated according to the TAW’s equivalent slope formula The coefficient Kr0 varies from 0.223 to 0.533 depending on the dike structure and wave conditions This result shows that the sea ike structure has a significant influence on the maximum scour depth The difference of Smax between taking into account the reflected wave (Kr0>0) and not taking into account the reflected 21 wave (Kr0 = 0) is from 0.08 to 0.45m, corresponding to an increase in scour depth of about 13-63% Table 4-4 Influence of seadike structure on maximum scour depth N0 10 11 12 13 14 15 16 Slope structure m = 4; CW=0 m = 4; CW=0.8 m = 3; CW=0 m = 3; CW=0.8 Hm0 (m) 3.5 3.0 3.5 3.0 3.5 3.0 3.5 3.0 3.5 3.0 3.5 3.0 3.5 3.0 3.5 3.0 T(s) Kr0 8 10 10 8 10 10 8 10 10 8 10 10 0.223 0.245 0.292 0.32 0.276 0.303 0.359 0.392 0.315 0.345 0.407 0.443 0.386 0.421 0.493 0.533 Smax(m) Kr0 = 0.64 0.61 0.75 0.71 0.64 0.61 0.75 0.71 0.64 0.61 0.75 0.71 0.64 0.61 0.75 0.71 Smax(m) Kr0 > 0.72 0.7 0.91 0.88 0.77 0.74 0.99 0.96 0.81 0.79 1.07 1.03 0.89 0.87 1.2 1.16 Changes Smax(m) 0.08 0.09 0.16 0.17 0.13 0.13 0.24 0.25 0.17 0.18 0.32 0.32 0.25 0.26 0.45 0.45 Fig 4-11 Simulated results of seadike’toe scour for in case groin length from 35-70m Influence of sea dike toe’ protection structures on the scour Two solutions to protect Nam Dinh seadike toe simulated in Wadibe-TC model include concrete cylinder embankment toe which is protected by a rock aprons with length of 3-6 times the wave height at structure toe and protected by T-groin (assuming the head of T groyne is long enough) With the first solution, the simulated results show that the depth of the scour hole does not seem to change, only moving according to the length of the rock aprons The second solution with 22 two scenarios of T groyne 35m and 70m long is presented in Fig 4-2 It can be seen that the scour depth is pushed away when increasing the width of the dike toe protection and increasing the size of the scour hole The reason for that difference is that at the groin head position, the wave height is larger and the water depth changes suddenly, leading to the breaking waves, which dissipates more energy here, creating a larger shear stress and mixing sediment coefficient than at the dike toe Conclusions for chapter The application of the Wadibe-TC model version updating the wave reflection coefficient for simulating sea dike toe erosion in Nam Dinh coast area gives more suitable results, especially it can be seec very clearly the influence of the dike revetment structure on the scour depth For the same offshore boundary conditions, dike structures with higher reflection coefficients gives results of larger scour depths Depending on the combination of hydraulic conditions and the structure’s dimensions, especially when the dike has crown-walls, the maximum scour depth taking into account reflected waves is different from 20 ÷ 60% in comparision with cases not taking into account the reflected waves CONCLUSIONS AND RECOMMENDATIONS Achievements of the dissertation The influence of the reflected wave from seadike structures on the incident waves, the undertow and the seadike’s toe erosion is considered in two aspects, the first is the influence range and the second is the degree of influence through the reflection coefficient Kr Research results on the fixed bed model with three types of sloping dike structures corresponding to different hydraulic boundaries show that the influence area of reflected waves is about 0.7 times the local wavelength from the waterline on revetment (Fig 3-4) The degree of influence of the reflected wave through the variation of reflection coefficient is determined by the equation of Klopman and Van Der Meer (2-2) and equation (3-3) 23 + The dissertation has quantified the different size of the scour hole when the waves are reflected from the different types of inclined seadike structures + Updating research results on the influence of reflected waves on incident waves, undertows and seadike’s toe erosion into Wadibe-TC software which the simulated results are more suitable with the measured data in mobile-bed model In addition, the results of applying this numerical model for simulation of seadike’s toe erosion for seadike cross-section in Nam Dinh are much better agreement with reality than before the update + Applying the numerical model Wadibe-TC version of updated reflected waves to simulate scenarios in Nam Dinh coastal area shows the obvious influence of the construction structure on the seadike toe erosion through the wave reflection coefficient This numerical models have higher reliability and higher practical applicability Limitations and Recommendations + This study has just considered the conditions with straight contour and parallel to the shore and normal incident waves Further studies can be done with different types of bathymetry to find out more general rules + The dissertation has only studied a type of straight crown-wall placed right at the top edge of the revetment Other types of sea dike structures are also needed for further study + Seadike’ toe scour due to interaction between coming waves and dike structures includes main causes: by breaking waves, by reflected waves and by backwash flow on the dike revetment The research has just only focused on reflected waves and the other causes need to be carried out more detail in the next studies + When applying mathematical model to simulate dike toe erosion for design study, it is necessary to pay attention to run many scenarios combinations of water level, dike sloping structures, and wave boundaries to find the most dangerous scenario for the project safety 24 PUBLICATIONS OF THE AUTHOR Nguyen Thi Phuong Thao (2022), Wave reflection from typical sloping dike in the north of Vietnam, The 4th International Conference on Sustainability in Civil Engineering - ICSCE 2022, University of Transport and Communications (UTC), pp 51 Nguyen Thi Phuong Thao (2021) Influences of crown-walls on the undertow in front of slopping sea-dike during storms, Journal of Water Resources and Environmental Engineering, Vol 6.2021, pp 32-38 Nguyen Thi Phuong Thao (2020) Study on the undertow in front of seadike by using physical models, Annual Science Conference, Thuyloi University, 11-2020, pp 549-551 Nguyen Thi Phuong Thao, Thieu Quang Tuan (2020) Influences of geometrical and structural configurations on beach and sea-dike toe scour during storms, Springer 2020, APAC 2019, Thuyloi University, pp 401-406 Nguyen Thi Phuong Thao (2019) Influences of beach’s slope on slopping sea dike toe scour in case of non-overtopping, Annual Science Conference 11-2019, Thuyloi University, pp 774-776 Nguyen Thi Phuong Thao (2018) Literature review on the modeling of processes related to sea dike toe erosion during storms, ISLT 2018, ThuyLoi university Nguyen Thi Phuong Thao (2018) Study on the slopping sea dike toe scour during storms by using physical models, Annual Science Conference 112018, Thuyloi University, pp 551-553