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- Summary of doctoral dissertation: Wave Overtopping at sea dikes with crown-walls in the northern coastal delta of Vietnam
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- MINISTRY OF EDUCATION AND MINISTRY OF AGRICULTURE
TRAINING AND RURAL DEVELOPMENT
WATER RESOURCES UNIVERSITY
NGUYEN VAN THIN
WAVE OVERTOPPING AT SEA DIKES
WITH CROWNN-WALLS IN THE NORTHERN
COASTAL DELTA OF VIETNAM
Specialization: Hydraulic Engineering
Code No : 62-58-40-01
SUMMARY OF DOCTORAL DISSERTATION
HA NOI, 2014
- This scientific work has been accomplished at Water Resources University
Advisor 1: Assoc. Prof. Nguyen Ba Quy
Advisor 2: Prof. Ngo Tri Vieng
Reviewer No. 1 Prof. Dinh Van Uu
Reviewer No. 2 Prof. Tran Dinh Hoi
Reviewer No. 3 Prof. Tran Dinh Hoa
This Doctoral Thesis will be defended at the meeting of the University Doctoral
Committee in room No………… on …….
This dissertation is available at:
- The National Library
- The Library of Water Resources University
- INTRODUCTION
1. Rationale
Viet Nam is a nation that is seriously affected by climate change and sea level
raise. There are many centres of economy and culture along the coastline. In the
north, sea dikes are relatively low with narrow crests, steep seaward and
landward slopes; most dikes are directly exposed to wave attack. Historical
records show that wave overtopping often causes damage to dike crests and
landward slopes. One of the effective measures to reduce overtopping is the use
of (low) crown-walls, because heightening dikes or constructing outer berms are
costly and not feasible, especially dikes with narrow margins. Till now, studies
into the influence of low crown-walls and interaction between wave-wall and
overtopping are limited. A better understanding of the influence of crown-walls
and promenade on overtopping is necessary to improve the present dike design
guidelines in Viet Nam. These facts lend the foundation for this thesis that is to
investigate “Wave Overtopping at sea dikes with crown-walls in the northern
coastal delta of Vietnam”.
2. Research objectives
The thesis aims to investigate the influence of low crown-walls on overtopping
discharge and the behaviour of overtopping flow at sea dikes. By doing so, the
reliability of overtopping estimation is increased to improve the dike design
guidelines currently applied in Viet Nam.
3. Scope of the study
Investigation of wave overtopping at sea dikes with low crown-walls in the north
of Viet Nam.
1
- 4. Research contents
Review on overtopping on sea dikes with low crown-walls; Physical model to
investigate the effects of low crown-walls on wave overtopping at sea dikes;
Numerical and physical examination of the wave-wall interaction and
overtopping flow on sea dikes with low crown-walls; Case study-Overtopping at
Giao Thuy dike, Nam Dinh province
5. Approach and study methods
5.1. Approach
To obtain the objectives, the author carried out a literature study on wave
overtopping at sea dikes with low crown-walls to select an approach that is
inherent and also creative, suitable for Viet Nam.
5.2. Study approaches
Literature review; Physical and numerical modelling; Application.
6. Implications
Building low crown-walls on seadikes to heighten the crest level, reduce wave
overtopping is considered technically and economically viable in Viet Nam.
There exists limited research into overtopping at sea dikes with low crown-walls,
especially the interaction between wave and wall. Therefore, better
understanding of the wall influence on wave overtopping discharge and the
overtopping flow characteristics will help improve the reliability of design for
this type of sea-dikes in Vietnam.
2
- 7. New contributions
- Insights into the influence of low crown-walls on wave overtopping and
the merit of wall promenade through a detailed examination of the wave-
wall interaction;
- Empirical equations to determine the overall influence factor of low
crown-walls for regular waves (Figure 2-12);
- Relationship between splash height and wave parameters and wall
geometry (Figure 2.13);
- Proposal on the use of a new sea-dike cross-section with crown-walls and
promenade, appropriate for the northern coastal detla of Viet Nam (Figure
4.8).
8. Thesis contents
In addition to the Introduction, Conclusions and Recommendations, the thesis
consists of 04 chapters
Chapter 1: Literature study on overtopping on sea dikes with low crown-walls;
Chapter 2: Physical model to investigate the effects of low crown-walls on wave
overtopping at sea dikes;
Chapter 3: Wave-wall interaction and overtopping flow on sea dikes with low
crown-walls;
Chapter 4: Case study-Overtopping at Giao Thuy dike, Nam Dinh province.
CHAPTER 1 REVIEW ON OVERTOPPING ON SEA DIKES WITH
LOW CROWN-WALLS
1.1 Introduction to research into overtopping at sea dikes
Due to significant changes of climate and environment, the frequency and
intensity of natural hazards gradually increase especially storms, tide and sea
level rise. As a result, overtopping at sea dikes remains as a risk to countries with
3
- sea. There exists limited research on overtopping at sea dikes with low crown-
walls and no one is comprehensive yet. Therefore, studies on overtopping at sea
dikes are essential in Viet Nam and elsewhere
1.2 Causes, failure mechanisms of sea dikes and measures
1.2.1 Causes of damage to sea dikes
There are many failure mechanisms of sea dikes but historical records show that
wave overtopping mainly causes damage to the dike crest and landward slope
and dike breaching as a consequence.
1.2.2 Damage mechanism due to wave overtopping
There are many mechanisms leading to dike failure, from local damage to overall
collapse; the reasons, influence factors, consequences are very various. Analysis
indicates that dike failures due to wave overtopping are the most common.
1.2.3 Measures to reduce overtopping at sea dikes in the north
Nowadays, there are several ways to reduce overtopping at sea dikes, ‘hard’ and
‘soft’ solutions such as submerged breakwaters, concrete blocks, seaward berms,
high crests and mangrove … However, the conditions of construction space and
economy are limited low crest-walls are popular and effective in reducing
overtopping at sea dikes in Viet Nam.
1.3 Sea dikes with low crown-walls in the northern coastal delta
Sea dikes with low crown-walls (W/Hs ≤ 0.5) located near the seaward edge are
very popular in Viet Nam. This is considered as a simple and effective method
to increase the crest level, reduce overtopping in the present situation. Crown-
walls are applied where there is no more land to enlarge the dike cross-sections
or budget is constrained; or it is not allowed to heighten the crest level in order
to reserve residence and tourism areas.
4
- 1.4 Research into overtopping at sea dikes with low crown-walls
1.4.1 TAW 2002
In TAW (2002), the influence of crown-walls on overtopping discharge is not
clear because it is an unknown variable; crown-walls increases the equivalent
slope that the discharge becomes greater. However, the discharge is then
corrected by a factorv. This overall influence factor only takes into account the
seaward inclination but not the interaction between wave-wall, overtopping flow
and the wall dimensions.
1.4.2 Viet Nam
Till now, there is limited research into overtopping at sea dikes with low crown-
walls in Viet Nam. Recent works do not cover all aspects of overtopping at
Vietnamese dikes. Tuan et al. (2009) proposed a new method to assess the effect
of crow-walls on overtopping. However, the influence of promenade was not
discussed (S = 0). Tuan (2013) investigated the influence of crown-walls and
promenade on overtopping. Though, he did not consider the interaction between
wave-wall and the behaviour of overtopping flow when the wall exists.
Furthermore, reduction effect was not determined for regular waves.
1.5 Conclusions of chapter 1
Overtopping is a danger to sea dikes. Damage due to overtopping is the most
important. Crown-walls are effective to heighten the crest level and reduce
overtopping. Studies on overtopping from TAW (2002) to Tuan (2013) are not
complete. In line with Tuan (2013), the author performed tests with physical
model to investigate the influence of crown-walls on regular waves, especially
the interaction between wave-wall and the flow behaviour at walls. The thesis
used numerical models from NLSW to RANS-VOF to consider the wall effects
with regard to the interaction between wave-wall and the flow behaviour at walls.
5
- The obtained results will provide insight into the characteristics of overtopping
at dikes with low crown-walls, partly improve the dike design in Viet Nam.
CHAPTER 2 PHYSICAL MODEL TO IVESTIGATE THE EFFECTS
OF LOW CROWN– WALLS ON WAVE OVERTOPPING AT SEA
DIKES.
2.1 Study objective
Consideration of the influence of low crown-walls on overtopping discharge, the
interaction between wave-wall and the behaviour of overtopping flow at sea
dikes with walls.
2.2 Model similitude
For the similarity between model and prototype, three criteria are required
geometry, kinematic and dynamic. For the similitude of wave, model has to be
geometric similarity; the scale has to follow the Froude criterion. In short wave
tests with geometrically undistorted models, the Froude criterion is automatically
satisfied.
2.3 Experiments with regular waves
2.3.1 Wave flume
The Holland wave flume is 45 m long, (effective length of 42 m), 1.2 m high,
and 1.0 m wide. The wave maker, which is equipped with an advanced automated
system of Active Reflection Compensation, is capable of generating regular and
irregular waves (JONSWAP) up to 0.3m in height and 3.0 s in peak period
(Figure 2.1).
6
- Figure 2.1 Overview of the wave flume.
Hình 2.1 Toàn cảnh máng sóng sử dụng thí nghiệm
2.3.2 Dike model and parameters
The dike model dimensions and testing parameters are selected according to a
model length scale of 1/10. The dike slopes were smooth and impermeable, 70
cm height with a seaward slope of 1/3. The low crown-walls were 4, 6 and 9 cm.
The walls were made detachable to allow varying wall height (W) and promenade
width (S) with regard to test scenarios. The wall could be moved back and force
to change the promenade from 0 to 10 and 20 cm. The foreshore was 24.5 m long
and 1/100 steep (Figure 2.5).
Figure 2.5 Test set-up for regular waves.
2.3.3 Test programme
A water depth of d = 0.60m was chosen for testing. A group of 3 wave gauges
was positioned at the dike toe and another gauge was 24.5 m away from the toe.
A camcorder with high resolution was mounted normal to the flume to capture
50 frames/second in order to observe the interaction between wave-wall and
overtopping flow. Each test consisted of 10 regular waves and stopped before
these got disturbed by reflected ones (Table 2.1).
7
- Table 2.1 Test programmes with regular waves
Number Wave parameter
Rc (m) W (cm) S (cm)
of tests H (m) T (s)
40 0.16- 0.24 1.5 – 2.5 0.10 0; 4; 6; 9 0; 10; 20
2.3.4 Test procedures and measurement parameters
Preparation time was from June to August 2012 and test duration lasted from
August till September 2012. Measurement parameters includes: wave height H,
wave period T, mean overtopping discharge q, splash height Hb, flow thickness
on wall crest Ht, crest freeboad Rc
2.4 Data analysis
2.4.1 Influence of crown-walls on wave overtopping discharge
The overall influence factor by crown-walls is the product of component factors
due to wall height and wall promenade, respectively.
1 1 1 𝑊 1 𝑆 1
= . = (1 + 𝑐1. . ) . (1 + 𝑐2. . ) (2-11)
𝛾𝑣 𝛾𝑤 𝛾𝑠 𝑅𝑐 𝜉 𝐻 𝜉
Determine the overall influence factor 𝛾v (measured) and 𝛾v (computed),
perform regression analysis to establish the relationship between these
parameters, derive two coefficients c1 =1.26, c2 = 1.44 (Figure 2.12)
1 𝑊 1 𝑆 1
= (1 + 1,26. . ) . (1 + 1,44. . ) (2-12)
𝛾𝑣 𝑅𝑐 𝜉 𝐻 𝜉
2.4.2 Wall influence on splash height
The splash height was estimated by image analysis with Matlab. The author
𝐻𝑏 𝑆.𝐻
established the relationship between and , which reads y = 1.544e-30.9x
𝐻 𝑔.𝑊.𝑇2
with R2= 0.624. Based on this curve, one may roughly predict splash height with
regard to wave and wall characteristics (Figure 2.13).
8
- Figure2.10 Overall influence factore of low walls v (measured - computed)
2.500
2.000
1.500 y = 1.544e-30.9x
R² = 0.624
Hb/H
1.000
.500
.000
.000 .005 .010 .015 .020 .025 .030 .035 .040
S.H/g.W.T 2
𝐻𝑏 𝑆.𝐻
Figure 2.13 Relationship between and
𝐻 𝑔.𝑊.𝑇 2
𝐻𝑏 𝑆.𝐻
Hình 2.13 Biểu đồ quan hệ 𝐻
với 𝑔.𝑊.𝑇 2
9
- 2.5 Conclusions of chapter 2
The thesis successfully established empirical formulas estimating the overall
influence factor by crown-walls on mean overtopping discharge for regular
waves (2-12) and functions of splash height with regard to wave and wall (Figure
2-13).
CHAPTER 3 INTERACTION BETWEEN WAVE – WALL AND
OVERTOPPING FLOW ON SEA DIKES WITH LOW CROWN-WALLS
3.1 Problem definition
At different levels of detail, the thesis modelled overtopping flow at sea dikes
with low crown-walls using several programmes including NLSW (Non-Linear
Shallow Water) and RANS-VOF (Reynolds Averaged Navier Stokes – Volume
Of Fluid).
NLSW modelling is simple and fast in calculation, e.g. 1000 waves can be
simulated in 5 to 10 minutes. This program can estimate relatively well mean
overtopping discharge at dikes with mild slope and have no crown-wall. It has
several shortcomings when applied to structures with complicated shape, e.g.
dikes with crown-walls. The thesis used NLSW (Tuan and Oumeraci, 2010) to
simulate and compute with regular waves. The obtained results were compared
to experiments in wave flume.
RANS–VOF modelling (COBRAS-UC, numerical wave flume) is able to
simulate the interaction between wave – wall and flow at structures of any shape
(vertical walls, hollow walls …), from wave generation at boundary to wave
propagation as in physical flumes. However, the calculation efficiency is low. It
takes many hours to simulate some seconds in real time when run on a normal
computer so that it is difficult to apply to regular waves.
Therefore, NLSW of Tuan and Oumeraci (2010) was used to validate the
estimated values of discharge. The computations were compared to
measurements with irregular waves. Both numerical and physical flumes were
10
- deployed to assess the interaction between wave – wall, i.e. overtopping flow
characteristics.
3.2 NLSW modelling (Tuan and Oumeraci, 2010)
3.2.1 Basic formulations
The model by Tuan and Oumeraci (2010) is based on the flux-conservative form
of the NLSW equations solved with a high order total variation diminishing
(TVD), Roe-type scheme:
U F ( x,U )
S ( x, U ) (3-1)
t x
where conserved vectors U , F ( x,U ) and source term vector S ( x,U ) are
defined as follows:
h
U ( x) (3-2)
uh
uh
F ( x, U ) 2 (3-3)
u h gh / 2
2
0
S ( x, U ) (3-4)
gh( Sbx S f Sr )
in which g is the gravitational acceleration, h is the flow depth, u is the horizontal
flow velocity, Sbx and Sf are bed slope and friction slope, respectively. Note that
Sr is the surface roller slope term, added by Tuan and Oumeraci (2010) to account
for the influence of wave breaking through the drastic motion of surface rollers
in the surfzone on the mean flow.
3.2.2 Wave overtopping of irregular waves
NLSW cannot model a vertical wall because the shallow water limit is violated,
a pragmatic manipulation of the wall geometry is necessary. The author used two
11
- pragmatic approaches: equivalent wall and equivalent freeboard (Figure 3.1 and
3.2).
Mean water levels were used in combination with wave signal recorded by
gauges, which were positioned in front of the model dike toe (the closer these
gauges to the toe, the higher accuracy the results of NLSW).
Figure 3.1 Conversion of crown-walls into slope (TAW-2002)
Figure 3.2 Conversion of crown-walls into equivalent freeboard method
On the landward side, the outflow boundary used a water level constant and very
low with regard to crest level (in order to prevent any influence on overtopping).
The simulation time was the same as the physical model experiments (1000.Tp
~ 10 minutes PC). In general, the computed results agree reasonably well with
the experimental data, R2= 0.88 and 0.87 for the first and second approaches,
respectively. The mean prediction error is 39.8% with a standard deviation of
56.2%. However, discrepancies still exist for some particular cases of very low
overtopping rates at high walls and walls without promenades. This is because
12
- the strong interaction between wave-wall could not completely be resolved in
NLSW by using pragmatic wall schematizations.
Figure 3.3 Wave overtopping computation with wall schematization
according to (TAW 2002): measured versus computed
Figure 3.4 Wave overtopping computation with equivalent freeboard
approach: measured versus computed
13
- 3.3 RANS-VOF modelling (COBRAS-UC, numerical simulation)
3.3.1 Numerical wave flume
Numerical wave flumes are capable of modelling the wave-structure interaction
that is very comparable to physical flumes. They are applicable for almost any
complex geometric and structural configurations. They have been validated
against experimental data giving reliable result.
3.3.2 Basic formulations
In the model, the mean turbulent flow is based on 2DV RANS equations
ui
0 (3-12)
xi
ui ui 1 p 1 ui
uj gi uiu j (3-13)
t x j xi x j x j
and the turbulence closure is the (k-) transport equations, which relate the
fluctuating components of the flow to the turbulence kinetic energy k and the
dissipation rate of turbulence
k k k ui
uj t uiu j (3-14)
t x j x j k x j x j
t ui 2 (3-15)
uj C1 uiu j C2
t x j x j x j k x j k
where ui is mean velocity in the i- the direction (i, j =1, 2 for a two dimensional
flow), p is mean pressure, is fluid density, gi is gravitational acceleration in
the i-th direction, uiuj is Reynolds stresses modelled according to the
nonlinear eddy viscosity. The empirical coefficients are k = 1.0, =1.3, C1 =
1.44, C1 = 1.92;= / and t = Cdk2/ (Cd = 0.99) are kinematic and eddy
viscosity, respectively.COBRAS-UC resolves the flow on a non-uniform
rectangular grid. The arbitrary free surface is tracked using the Volume of Fluid
(VOF) method.
14
- 3.3.3 Overtopping discharges of irregular waves
Each train consists of at least 1000 waves (1000.Tp = 2200s) which can be
simulated in 75hours on a 3.1GHz processor - 4GB RAM PC. Because of this
low efficiency, only 14 scenarios were considered. These are combinations of a
wave condition at the generator (Hm0 = 0.10 m, Tp = 2.2 s and water depth of 0.55
m) and several seaward slopes and crown-walls (height of W= 6 and 9cm; with
and withour promenade).
Figure 3.7 Wave overtopping of irregular waves: COBRAS-UC vs. NLSW
model
The study compares values of mean overtopping discharge obtained from
measurements with physical models and computation with COBRAS-UC,
NLSW (two ways of varying equivalent walls). Apparently, COBRAS-UC
works more properly than NLSW with mean errors of 60.1% (a standard
deviation of 63.2%) and 129.4% ( 100.6%) for PA1 and PA2, respectively.
The results from COBRAS-UC and measurements match relatively well with
a mean error 39.7% (a standard deviation of 24.5%). However, COBRAS-
15
- UC may produce an error up to 63% in the cases of small discharge (Figure
3.7).
3.3.4 Wave overtopping of regular waves (discharges and wave-wall
interaction)
3.3.4.1 Mean overtopping discharge
With 40 experiments performed on 10 dike models, regular wave trains were
generated to evaluate the mean overtopping discharge in for each test. The CPU
time for each test was around 6 hours on a standard PC (or about 1 hour CPU
time equals to 10 seconds of flow time). Discharges predicted by COBRAS-UC
were compared to the experimental data. Generally speaking, COBRAS-UC
appears to reliably estimate overtopping rates at low crown-walls of various
configurations (R2 = 0.95). The mean error is 23.4% with a standard deviation
of 30.2 %. Considerable discrepancy can be found for a few cases of high walls
(W=9cm, open triangles). In comparison with irregular waves, the overall
agreement is relatively good (Figure 3.8).
Figure 3.8 Wave overtopping of regular waves: measured vs computed by
COBRAS-UC
16
- 3.3.4.2 Interaction between wave – wall and flow
At first, the wave – wall interaction, which results in wave overtopping at sea
dike, is assessed using captured video images. A wave overtopping event can be
characterised through four successive phases: contact splash, fall-over, major
green overtopping and withdrawal. These phases are briefly described as follows.
The process of wave overtopping starts as the wave tongue collides with the wall
and results in a violent jet (splash) into the air (Figure 3.13).
In the second phase, the splash collapses as it reaches a certain height and falls
over the wall. At the end of this phase, a green flow over the wall is formed
(Figure 3.14).
If wave continues to thrust wave overtopping in the third phase simply follows
the earlier buffer flow in the form of green overtopping to obtain a maximum
depth above the wall crest (Figure 3.15).
Green wave overtopping continues until wave retreats on the seaward slope in
the last phase (Figure 3.16).
Snapshots of the flow computed by the model at all computed instances were
also reviewed to determine the corresponding maximum splash height for
comparison with the physical experiments. Numerically, COBRAS-UC is able
to capture a fragmented splash but not that with small individual drops (tiny
sprays) like in the physical models. Physically, the approximation of the free
surface tracking method (VOF), exclusion of the surface tension as well as
disregard of air entrainment an aeration processes are possible causal factors.
Practically, coarse grid resolution relative to the (extremely small) size of
individual drops employed in the numerical model may also play a role. These
issues require much more sophisticated studies as well as computer capacity to
be resolved. At present, this effect on wave overtopping with respect to the dike
design is neglected. The four-phase process of the wave-wall interaction for Case
REW6S20_4 is now examined in detail with COBRAS-UC. The model
considerably under-predicts the water surface profile in the splashing area around
the wall during the first two stages (Figures 3.13 and 3.14). In the mean time, the
surface profile in the last two stages, where mainly simply green overtopping
take places, is very well predicted by the model (Figures 3.15 and 3.16).
17
- Figure 3.13 Wave splash at wall t= 27.1s Figure 3.14 Overtopping flow on wall
( Measured) crest t=27.3s ( Measured)
Figure 3.15Overtopping flow Figure 3.16 Run-down t=27.8s
t = 27.5s ( Measured) ( Measured)
At a lower level of detail, Figures 3.17 and 3.18 respectively show the model
prediction of the maximum splash height (occur in phase , Figure 3.13) and the
maximum green flow depth above the wall (occur in phase 3, Figure 3.15)
compared with the experimental data. Under the same wave condition and wave
height, the maximum splash height decreases as the promenade width decreases
(Figure 3.17). Also, within the wall geometry and wave parameters considered
herein, a higher wall (relative to the wave height) would cause a higher splash
height.
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