UNESCO-IHE
INSTITUTE FOR WATER EDUCATION
Concrete crest construction
B = 3.0 m
Seaside
Clay
Clay
1:
3
4
1:
Core
to
1:
4
Drain
Hydraulic Model Tests of Wave Overtopping on
An Innovative Crest Drainage Dike
D.M.D.T.B. Dassanayake
MSc Thesis WSE - HECEPD - 07.06
May 2007
Hydraulic Model Test of Wave Overtopping on Crest
Drainage Dike
Master of Science Thesis
By
D.M.D.T.B. Dassanayake
Supervisors
Dr. Randa M. Hassan, PhD (UNESCO-IHE)
Dr. Andreas Kortenhaus (LWI-TU Braunschweig)
Examination Committee
Prof. Dano Roelvink, PhD (UNESCO-IHE), Chairman
Dr. Randa M.Hassan, PhD (UNESCO-IHE)
Dr. Andreas Kortenhaus (LWI-TU Braunschweig)
This Research is done for the partially fulfillment of requirement for the Master of
Science Degree at the UNESCI-IHE, Institution for Water Education, Delft,
The Netherlands.
Delft
May, 2007
The findings, interpretations and conclusions expressed in this research study do
neither necessarily reflect the views of the UNESCI-IHE, Institution for Water
Education, nor of the individual members of the MSc committee, nor of their
respective employers.
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Abstract
The risk of dike failure along the coasts worldwide is continuing to increase due to the
effects of climatic changes such as sea level rise, severity of storms, etc. Hence, there
is an urgent need for more appropriate technical and managerial solutions to mitigate
this risk. Most research has focused on understanding the failure of the shoreward
slope which was mainly induced by heavy wave overtopping. Principal mitigation
measures undertaken up to now have led to increased dike heights. However, due to
space limitation and high costs, heightening is no more feasible for most of the sea
dikes along the North Sea.
With framework of the European ComCoast project a Dutch company, DHV (2005),
proposed a method to reduce wave overtopping without altering the cross section of
the dike. This innovative idea was called ‘Crest Drainage Dike’ (CDD). main idea of
this innovative crest design is to reduce the wave load and wave overtopping of a dike
by installing an ”Overtopping Buffer Basin” on top of the dike crest where parts of
the overtopping water is discharged to the shoreward side.
The Crest Drainage Dike (CDD) was theoretically analysed by Nieuwenhuis et al
(2005). However, the study was based on many assumptions taken from existing
knowledge about standard dike profiles. Existing theories for wave overtopping
parameter are not applicable to a crest drainage dike, since the crest basin changes the
behaviour of the overtopping water on the dike crest. Therefore, the CDD was
proposed to be tested in hydraulic model tests to improve the understanding of
processes linked to the CDD and to propose overtopping formula for the design of the
CDD.
2D hydraulic model tests were conducted at Leichtweiss Institute (LWI) of the
Technical University Brauschweig, Germany. The research mainly focused to find out
the feasibility of using the crest drainage dike concept to enhance the safety of the
existing dikes. More specifically, research focused on (i) optimising the overtopping
buffer basin for a 1:4 seaward slope, (ii) identifying the best drainage system,
(iii) identifying undesired flow condition on the landward slope, and (iv) developing
new overtopping formulae for the crest drainage dike.
During the experimental study, wave conditions in front of the structure, wave
overtopping volumes per wave, flow depths and the flow velocities at the seaward
slope, the crest and the landward slope of the dike, were performed. After analysing a
total of 275 tests a dimensionless coefficient, γ CDD was found to calculate the
reduction in overtopping discharge. γ CDD can be used as a reduction factor which
includes the overall effect of the crest basin on the mean overtopping discharge.
Furthermore, suitable dimensions of the crest basin were proposed to reduce the mean
wave overtopping discharge to the desired quantities. Apart from that, the influence of
the crest basin on overtopping layer thicknesses and overtopping flow velocities on
the landward side of the dike were assessed.
Keywords
Wave overtopping, dike, 2D physical model, crest drainage dike, crest basin
i
ii
Acknowledgements
Two dimensional experimental investigations have been carried out with funding
from ComCoast (COMbined functions in COASTal defense zones; a European
project funded by the European community initiative program interreg IIIB North Sea
region and project partners.) and UNESCO-IHE WaterMill project.
I would like to express my deep gratitude to Dr. Randa Hassan and Dr. Andreas
Kortenhaus who gave me this opportunity to work at LWI laboratory and gain
valuable experience. Also their valuable guidance and spending their precious time on
discussions and on correcting the thesis etc are highly appreciated.
I wish to acknowledge all IHE staffs and specially lecturers from HE-CEPD; Prof.
Dano Roelvink, Ronald de Heer, Mick van der Wegen, and Hendrik Bijnsdorp who
have broaden my knowledge on many aspects;
I am very much thankful to all LWI staffs for their assistance and friendship during
my laboratory works at Braunschweig, Germany. Also valuable advices from Prof.
Oumeraci, kind care from Gabriele Fournier, energetic support from Kevyn Bollinger,
L~DAVIS and guidance to data analysis from Matthias Kudella, Techinical assistance
from Rainer Kvapil, Hans-Jörg Lambrecht, Herwig Appeltauer and his staff at
werkstatt, friendship and assistance from Markus Brühl, Juan Recio, Steffen Koß,
Sandra Burg, Peter Geisenheiner, Genia Schäferhoff are highly appreciated.
I would like to thank Paul van Steeg from TU-Delft for valuable discussions
I would like to thank all CEPD Colleagues for having great time together in the last
18 months in Delft and their great deal of friendship, especially for Meidi and Yenung
for their help, courage, and motivation during the stay in Germany.
Finally I like to express my gratitude deeply form heart to my parents who have been
continuously supporting and encouraging during my studies, And specially to my wife
Dilani, for her patient, encouragement and support during my study period.
D.M.D.T.B. Dassanayake,
Delft, The Netherlands,
May, 2007
iii
iv
Table of Content
Abstract ............................................................................................................................ i
Acknowledgements........................................................................................................ iii
List of Symbols ............................................................................................................. vii
List of Figures ................................................................................................................ ix
List of Tables ................................................................................................................. xi
Keywords ........................................................................................................................ i
1. Introduction................................................................................................................1
1.1 Background & Motivation .................................................................................1
1.1.1
Problem Statement ...................................................................................1
1.1.2
ComCoast Project ....................................................................................2
1.1.3
Millennium Development Goal Project ...................................................3
1.1.4
Aim and Scope of the Study ....................................................................4
1.1.4.1 Objectives ................................................................................................4
1.1.4.2 Scope........................................................................................................5
1.2 Study Overview .................................................................................................5
2. Review of available knowledge .................................................................................7
2.1 Introduction........................................................................................................7
2.2 Current design practices...................................................................................10
2.3 Wave Breaking and Breaker Types .................................................................11
2.4 Wave Run-Up ..................................................................................................12
2.4.1
Wave run-up height................................................................................13
2.4.2
Wave run-up velocities ..........................................................................14
2.4.3
Wave run-up layer thickness..................................................................15
2.5 Wave Overtopping ...........................................................................................15
2.5.1
Mean overtopping rate ...........................................................................16
2.5.2
Overtopping velocities and layer thickness at the crest of the dike.......18
2.5.3
Overtopping velocities and layer thickness at the landward slope of the
dike.........................................................................................................22
2.5.4
Overtopping Volume per wave..............................................................23
2.6 Crest Drainage Dike.........................................................................................24
2.7 Scaling and Further Aspects ............................................................................27
2.7.1
Scaling law.............................................................................................27
2.7.2
Scale effects and Model effects .............................................................28
2.7.3 Interpretation of Results-Transfer results to prototype conditions ........30
2.8 Objectives and Methodology (Revised)...........................................................31
3. Experimental Investigations.....................................................................................33
3.1 Model set up, Measurement Techniques and Test Programme .......................33
3.1.1
Model Setup ...........................................................................................33
3.1.2
Measurement Techniques ......................................................................36
3.1.3
Test Programme and Procedure .............................................................42
3.2 Data analysis ....................................................................................................44
3.2.1
Calibration of Measuring Devices .........................................................48
4. Discussion of the Results .........................................................................................51
4.1 Incident wave parameters at the toe of the dike...............................................51
4.1.1
Definitions..............................................................................................51
4.1.2
Results from the wave analysis..............................................................51
4.1.3 Summary and evaluation of the results..................................................54
v
4.2 Mean overtopping discharge............................................................................55
4.2.1
Mean overtopping discharges for standard dike profile ........................55
4.2.2
Influence of the crest basin on mean overtopping discharge.................56
4.2.3
Influence of drainage pipes on mean overtopping discharge.................66
4.3 Overtopping volume per wave.........................................................................76
4.4 Overtopping layer thickness at the landward side of the dike .........................78
4.5 Overtopping flow velocity at the landward side of the dike............................81
5. Conclusions and Recommendations ........................................................................84
5.1 Conclusions,.....................................................................................................84
5.2 Recommendations............................................................................................88
References......................................................................................................................90
Annex.............................................................................................................................92
vi
List of Symbols
B
BC
= crest width
= width of crest basin
C0
= dimensionless coefficient
C1
= dimensionless coefficient
C 2*
= dimensionless coefficient
C Au *
= empirical coefficient
C Ah*
= empirical coefficient
CCu *
= empirical coefficient
CCh*
= empirical coefficient
[m]
[m]
CBu *
= empirical coefficient
CBh*
= empirical coefficient
cV *
d
dC
db
Hs
h A2%
h C2%
h B2%
hA
hB
hC
h0
= coefficient
[ −]
[ −]
[ −]
[ −]
[ −]
[ −]
[ −]
[ −]
[ −]
[ −]
[ −]
[ −]
[ −]
= water depth at toe of the dike
= water depth inside the crest basin
[m]
[m]
= breaker depth
[m]
= incident significant wave height at the toe of the dike
[m]
= layer thickness on the seaward side of the dike, exceeded by 2% of incoming waves
[m]
= layer thickness on the crest of the dike, exceeded by 2% of incoming waves
[m]
= layer thickness on the landward side of the dike, exceeded by 2% of incoming waves
[m]
=layer thickness at a point A on the seaward side of the dike
[m]
=layer thickness at a point B on the landward side of the dike
[m]
=layer thickness at a point C on the crest of the dike
[m]
CCDD ,1 = empirical coefficient
CCDD ,2 = empirical coefficient
CCDD ,3 = empirical coefficient
=layer thickness at the beginning of landward slope, h 0 = hB (sB=0)
[m]
q
= mean overtopping discharge (measured at landward edge of crest)
Q∗
= dimensionless overtopping rate
⎡⎣ m / s / m ⎤⎦
[ −]
Qdrain = overtopping water discharge through drainage pipes
Qseaward = discharge flows back to seaward side
Qtotal
= total overtopping discharge ( Qdrain +q+ Qseaward )
R*
= dimensionless freeboard
R u 2% = wave run-up height, exceeded by 2% of incoming waves
sB
=distance of point B from the beginning of landward slope
3
⎡⎣ m3 / s / m ⎤⎦
⎡⎣ m3 / s / m ⎤⎦
⎡⎣ m3 / s / m ⎤⎦
[ −]
[m]
[m]
vii
Tm
[ s]
[s]
[m / s]
= mean wave period
Tm −1,0 = wave period based on zero and first negative spectral moment(s)
u A 2%
= wave run-up velocity at a point A above the SWL,
exceeded by 2% of incoming waves
[m / s]
[m / s]
u C2%
= flow velocity at a point C on the dike crest, exceeded by 2% of incoming waves
u B2%
= flow velocity at a point B on the landward slope of the dike,
u0
=velocity at the beginning of landward slope,
V2%
= Overtopping volume per wave, exceeded by 2% of incoming waves
x*
= remaining run-up length ( x ∗ = x z − x A )
xZ
xA
zA
α
β
γb
= R u / tan α
[m]
= position on the seaward slope
[m]
= height from SWL to point A
[m]
= seaward slope angle
= slope angle of landward side
[degree]
[degree]
exceeded by 2% of incoming waves
u 0 = uB (sB=0)
= reduction factor for berm
γf
= reduction factor for roughness at the seaward slope
γ f −C
= reduction factor for roughness at the crest
γh
= reduction factor for shallow foreshore
γv
= influence factor for vertical or very steep wall on the slope of the dike
γβ
= reduction factor for angular wave attack
[m / s]
⎡⎣ m3 / m per wave ⎤⎦
[m]
[ −]
[ −]
[ −]
[ −]
[ −]
[ −]
viii
List of Figures
Figure 1.1: Conceptual design of crest drainage dike....................................................2
Figure
2.1:
Definitions
of
overtopping
for
crest
drainage
dike
(Schüttrumpf,2001,2003).......................................................................................8
Figure 2.2: Definitions sketch (Schuttrümpf,2001) .....................................................19
Figure 2.3: Conceptual sketch; Crest Drainage dike (Not Scaled), Source (DHV,2005)
..............................................................................................................................24
Figure 2.4: Detailed crest construction, including pit and connection to landward
discharge. Source: Nieuwenhuis et al 2005 .........................................................25
Figure 2.5: Overview of possible reasons for differences in prototype and laboratory
results (Kortenhause et al, 2005) .........................................................................29
Figure 3.1: View of twin wave flumes at LWI ............................................................33
Figure 3.2: Wave generation system in twin flumes at LWI .......................................34
Figure 3.3: Cross section of dike constructed at LWI .................................................34
Figure 3.4: Details of crest construction for each model Configurations, 1:4 slope in
prototype dimensions ...........................................................................................36
Figure 3.5: Multi-gauge array in front of the dike .......................................................37
Figure 3.6: Calibrated time series of a wave gauge (example)....................................37
Figure 3.7: Measurement devices for overtopping measurements ..............................38
Figure 3.8: Weighing system for overtopping tank in the LWI flume ........................38
Figure 3.9: Calibrated recording of wave overtopping including individual
overtopping events (example)..............................................................................39
Figure 3.10: Pressure cell used for model tests at LWI ...............................................39
Figure 3.11: Schematic sketch and photo of velocity propellers used at LWI ............40
Figure 3.12: Velocity propellers and layer thickness gauges on the crest and seaward
slope .....................................................................................................................40
Figure 3.13: Position of video cameras and observed areas during the tests...............41
Figure 3.14: Methodology of the Crest Drainage Dike study......................................47
Figure 3.15: Calibration of velocity propellers............................................................49
Figure 4.1: Definitions .................................................................................................51
Figure 4.2: measured wave height for the test with and without active absorption
system ..................................................................................................................52
Figure 4.3: Relationship between Tp and Tm-1,0 ...........................................................52
Figure 4.4: Relationship between Hm0 and H1/3 ...........................................................53
Figure 4.5: Relationship between Hm0 and Hmax ..........................................................54
Figure 4.6: mean overtopping discharges for Standard Dike under breaking waves ..55
Figure 4.7: mean overtopping discharges for Standard Dike under non-breaking
waves....................................................................................................................56
Figure 4.8: mean overtopping discharges for C4SS under breaking waves ................57
Figure 4.9: mean overtopping discharges for C4SS under non-breaking waves.........57
Figure 4.10: reduction in mean overtopping discharge for C4SS under all waves......58
Figure 4.11: mean overtopping discharges for C4SL under breaking waves ..............59
Figure 4.12: mean overtopping discharges for C4SL under non-breaking waves.......59
Figure 4.13: reduction in mean overtopping discharge for C4SL under all waves .....60
Figure 4.14: mean overtopping discharges for C4WS under breaking waves.............60
Figure 4.15: mean overtopping discharges for C4WS under non-breaking wave.......61
Figure 4.16: reduction in mean overtopping discharge for C4WS under all waves ....61
Figure 4.17: mean overtopping discharges for C4WL under breaking waves ............62
Figure 4.18: mean overtopping discharges for C4WL under non-breaking wave.......63
ix
Figure 4.19: reduction in mean overtopping discharge for C4WL under all waves....63
Figure 4.20: sketch of crest basin used for controlled drainage test to find max Q drain
..............................................................................................................................67
Figure 4.21: discharge balance of overtopping water at dike crest..............................68
Figure 4.22: overtopping discharge by pipes related to total overtopping discharge. .68
Figure 4.23: input parameter range for tests with different drainage pipes .................69
Figure 4.24: percentage of overtopping water discharged through drainage pipe
(C4SS)..................................................................................................................70
Figure 4.25. Reduction in mean overtopping discharge with different drainage pipe
(C4SS)..................................................................................................................71
Figure 4.26: model setup for tests without crest basin.................................................71
Figure 4.27: reduction in mean overtopping discharge (in model scale).....................72
Figure 4.28: reduction in dimensionless overtopping discharge .................................72
Figure 4.29: reduction in mean overtopping discharge (in model scale).....................73
Figure 4.30: reduction in dimensionless overtopping discharge .................................74
Figure 4.31 overtopping volume per wave, V0.1% (in model scale) .............................76
Figure 4.32: overtopping volume per wave for Std Dike ............................................77
Figure 4.33: Vmax,0.1%. for different model configurations ...........................................78
Figure 4.34: Overtopping layer thickness at the landward side of Std Dike ...............79
Figure 4.35: Overtopping layer thickness at the landward side of C4SS configuration
during a higher overtoppng event.. (in model scale) ...........................................79
Figure 3.36: overtopping layer thicknesses for Std Dike and C4SS with 25mm
drainage. (in model scale) ....................................................................................80
Figure 4.37: overtopping layer thicknesses for Std Dike and C4WL with 25mm
drainage. (in model scale) ....................................................................................81
Figure 4.38: location of velocity measurement at the landward side of the dike ........81
Figure 4.39: Comparison of velocity propeller readings .............................................82
(in model units) ............................................................................................................82
x
List of Tables
Table 2.1: Classification of the Breaker type (Schuttrumpf, 2001).............................11
Table 2.2: Wave run-up formulae for smooth, impermeable slopes............................13
Table 2.3: Coefficient CAu*for run-up velocities .........................................................14
Table 2.4: Coefficient CAh* for layer thickness on seaward slope ...............................15
Table 2.5: Mean overtopping formulae for smooth, straight, impermeable slopes
(Schüttrumpf (2001), Soliman (2003), FEMA (2005) and Wiyono (2006)) .......16
Table 2.6: Overtopping layer thickness on the dike crest............................................19
Table 2.7: Coefficient CCh* for layer thickness on crest ..............................................20
Table 2.8: Overtopping velocity on the dike crest.......................................................20
Table 2.9: Coefficient CCh*for overtopping velocities on crest ...................................21
Table 2.10: Overtopping discharges on dike crest.......................................................21
Table 2.11: Calculated drainage discharges for different fill level in the crest drainage
..............................................................................................................................26
Table 2.12: Scale relations for model laws after Froude .............................................28
Table 2.13: specific objectives of the model study......................................................31
Table 3.1: Different dike configurations tested in LWI laboratory .............................35
Table 3.3: Selected test conditions for physical model test .........................................41
(dimensions given in prototype scale) .........................................................................41
Table 3.4: Overview of test programme for random waves and all configurations with
1:4 slope ...............................................................................................................43
Table 4.1: wave condition used to test the active absorption system ..........................52
Table 4.2: Coefficient for the formula 4.6 ...................................................................64
Table 4.3: Coefficient for the formula 4.7 ...................................................................65
Table 4.4: Overtopping reduction factor, due to CDD ................................................65
Table 4.5: Selection of pipe diameter to model tests ...................................................66
Table 4.7: Reduction in maximum drainage discharge due to losses ..........................66
Table 4.10: maximum discharge due to maximum volume per wave for standard dike
..............................................................................................................................76
Table 4.11: percentage increment in buffer capacity for each model configuration ...77
xi
xii
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
1. Introduction
1.1
Background & Motivation
1.1.1
Problem Statement
The risk of dike failure along the coasts worldwide is continuing to increase due to the
effects of climatic changes such as sea level rise, severity of storms, etc. At the same
time land value increases and as a result activities behind dike increases Present day
economical value of the land next to dike is much higher than any other time. This
increases the risk of dike breach (Risk = Damage × Probability ) . Apart from the
increments in activities with higher economical values, Probability of flooding also
increases due to climate change effects. One of the main climatic change effects is
Sea level rise, which can be looked as lowering of the freeboard of the dike which
increases wave overtopping. Also climate changes can bring more severe storms than
the predicted in the past few years. Similarly calculated return periods of storms are
questionable due to the acceleration in hydrological cycle as a result of climate
change. Hence dikes are at risk of failure. Polders are in danger because of the
vulnerability of excessive overtopping. Dike can either be structurally damaged or
polders can be flooded with overtopped water. Both of events are considered as dike
failure (Failure to meets it’s purpose). Hence there is an urgent need for more
appropriate solutions to mitigate this risk.
Failure modes of the dike can be classified as; failure on the seaward slope, failure on
the dike crest, failure on the landward slope and dike breaching (partially or totally).
A dike failure on the seaward slope is often caused due to erosion of the turf due to
wave run-up and run-down. Then waves will take the large soil particles away from
the dike, which gradually leads to a dike breach. Similarly on landward side dike
failure starts with the erosion of the turf. Soil particles are washed out of the turf. Turf
is set off at the dike crest due to infiltration of water and slides down on the landward
slope as a liquid mass. In conclusion overtopping water starts the erosion process and
infiltration responsible for the set of the landward side. This is followed by core of the
dike slide down and washed out. Finally dike will collapse. (Schüttrumpf, 2004).
Most research has focused on how prevent the failure of the seaward slope and to
avoid the overtopping by raising the dike. However due to space limitation and high
cost, heightening is no more feasible in most of dikes in North Sea.
According to Van Gerven & Akkerman (2005) there are two possible approaches;
First Conventional methods like raising the dike etc. Second is to find more
innovative sustainable long term solutions. DHV (2005) proposed a method to reduce
the overtopping without altering the cross section of the dike. This innovative idea
called ‘Crest Drainage Dike (CDD)’ (Figure 1.1) which is a more local measure with
less negative effects. Main idea of this innovative crest design is to reduce the wave
load and wave overtopping of a dike by installing an ‘Overtopping Buffer Basin’ on
top of the dike crest. Initial proposal was done on request of CUR to develop possible
innovative concepts for overtopping dikes. Further, a similar concept has used in
Monaco (Bouchet et al, 1994). Hence it is possible to argue that similar concept can
be used for dikes too. However structural parameter of the dike and breakwater are
D.M.D.T.B. Dassanayake
1
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
much different to each other. So this concept is needed to be proved before going for
implementations.
ComCoast (COMbined functions in COASTal defense zones) is a European project
funded by the European community initiative program interreg IIIB North Sea region
and project partners. ComCoast identified crest drainage dike as one of the leading
concept to reduce the overtopping of see dike (see section 1.1.2).
This research is to study the hydraulic performance of the crest drainage dike through
2D physical model test. Hydraulic modelling works were done at Leichtweiss institute
(LWI), Brauschweig, Germany from December 2006 to April 2007. This research
study was funded by ComCoast (See 1.1.2) and a UNESCO-IHE WaterMill project
which is a part of the United Nations’ Millennium Development Goals project (see
section 1.1.3).
B = 3.0 m
Seaward side
Concrete crest construction
Clay
Clay
Landward
1:3 to 1:4
1:
Drain
Core
Figure 1.1: Conceptual design of crest drainage dike (not in scale)
1.1.2
ComCoast Project
ComCoast - COMbined functions in COASTal defense zones - is a European funded
project, which develops and demonstrates innovative solutions for flood protection in
coastal areas. Five North Sea countries; the Netherlands, Germany, UK, Belgium and
Denmark are involved in the project. Rijkswaterstaat, a part of the Dutch Ministry of
Public Works and Water Management, leads the project. In total, ten partners
constitute the project consortium. The partners share their knowledge and experience
and develop the best possible practices, which will benefit all coastal defenses
comprising embankments in Europe.
The ComCoast concept aims to create multifunctional flood management schemes
with a more gradual transition from sea to land, which benefits the wider coastal
community and environment whilst offering economically sound options. The concept
focuses on coastal areas comprising embankments, to provide economical and
sustainable alternatives to traditional approach of raising the crest level and to achieve
flood management over a wide coastal zone with multifunctional land use.
One of the work packages, WP3 of ComCoast project focuses on Civil Engineering
aspects in adapting the basic innovative idea for the concept of ComCoast, which is to
D.M.D.T.B. Dassanayake
2
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
increase the allowable amount of wave overtopping or overflow. The present coastal
defense structures are not able to withstand major overtopping and overflow. This will
only be feasible if crest and the landward slope are strengthen. This will be an
alternative to heightening of the dike to improve the safety of the structure. However
a wide variety of technical solutions are possible to increase the allowable wave
overtopping and overflow, such as, introduction of alternative protection materials,
improve the geometry of the dike etc.
In the process of finding an alternative method to improve the dike safety, WP3
started with collecting the state-of-the-art technical solutions from wave overtopping
resistant coastal defense system. This was followed by studying alternatives for
strengthening the embankments under the reports "Sandy cover", "Smart grass
reinforcement" & "Crest drainage dike". WP3 group of ComCoast accepted “Crest
Drainage Dike” as one of the two leading concepts to reduce the effect of overtopping
of sea dike (Other concept is to allow more flow over the landward slope by
strengthening the top layer). Under the ComCoast project, Nieuwenhuis et al (2005)
did an extensive theoretical analysis of Crest Drainage Dike.
1.1.3
Millennium Development Goal Project
Since research is partly funded by UNESCO-IHE watermill project, Study should
have some objectives which help to achieve Millennium Development Goals (MDG).
In year 2000 the member states of the United Nations adopted the Millennium
Declaration as a renewed commitment to human development. The Declaration
includes eight Millennium Development Goals (MDGs), each with quantified targets,
to motivate the international community and provide an accountability mechanism for
actions taken to enable millions of poor people to improve their livelihoods. Eight
goals of MDGs are to be achieved by 2015 that respond to the world's main
development challenges. The 8 MDGs break down into 18 quantifiable targets that are
measured by 48 indicators.
The UN Millennium Project was commissioned by the UN Secretary-General in 2002
as an independent advisory body charged with putting forward the best strategies for
meeting the MDGs. During year 2005, under the leadership of prof. Jeffrey D. Sachs,
“UN Millennium Project 2005. Preparing National Strategies to Achieve the
Millennium Development Goals: A Handbook” was published. In this report Climatic
change has identified as a threat to the environment when formulating the strategies to
achieve MDGs. Hence report recommends strategies to reduce risks and mitigate the
impact of extreme events should be given important priority for countries that are
vulnerable to natural disasters. Further environmental strategies should be specific to
each country.
Many countries in South and South East Asia have been involved in low land
developments using dikes. Land value increases and as a result, activities behind dike
have increased a lot. Also as mentioned above, due to sea level rise and due to
acceleration in hydrological cycle, more severe storms than the predictions could
happen. Therefore, risk of dike failure is continuing to increases. Hence it is
important to assess the safety of the dike in countries like Bangladesh, Vietnam, India,
Indonesia, China, Sri Lanka (River dikes) etc. Due to limited land area in these
countries, more and more people move towards the coastal areas. Therefore flood
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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protection is a main issue when addressing the sustainable development and also in
the process of achieving the targets of MDGs in these countries.
Since crest drainage dike concept is a cheap and more sustainable solution to improve
the safety of dike, finding of this research can be used to the benefit of developing
countries too. Then the infrastructure investments from MD project can be used to
achieve more sustainable development while securing the life of the people.
Importance of coastal flood prevention, towards achieving MDGs is summarised in
annex-A.
1.1.4
Aim and Scope of the Study
Crest drainage dike was theoretically analyzed by Nieuwenhuis et al (2005).
However, the study was done on many assumptions, which were based on existing
knowledge about standard dike profiles. Existing theories for wave overtopping
parameter might not be applicable to crest drainage dike, since crest basin changes the
behaviour of overtopping water on the dike crest. Therefore, this new design, Crest
Drainage Dike (CDD) should be experimentally tested to get an insight on behaviour
of CDD and to find the applicability of existing overtopping formula to new designs
with CDD.
1.1.4.1 Objectives
This research is a preliminary test to find out the hydraulic performance of the crest
drainage dike using a two dimensional (2D) physical model tests (flume test) and to
find out the feasibility of use of crest drainage dike concept to enhance the safety of
the existing dikes. More specifically research focuses;
1. On optimising layout of the crest construction (overtopping buffer basin) for
different seaward slopes (including crest width of the dike and the dimensions
and the shape of Overtopping Buffer Basin).
2. On identifying the unwanted flow conditions under the unfavourable storm
conditions
3. On identifying the best drainage system.
4. Develop guidelines for design of crest drainage dikes
D.M.D.T.B. Dassanayake
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1.1.4.2 Scope
Two dimensional physical model tests were undertaken selected to achieve above
mentioned objectives. at LWI. A flexible construction was built in the small-scale
wave flume (length: 90 m, width: 2 m, height: 1.2 m) at LWI which is principally
based on the ideas laid out in the report by Nieuwenhuis et al. (2005).
The study comprises the following limitations,
1.2
•
Seaward side of the dike was 1:4 sloped smooth surface. Therefore all the
results used for analysis is limited to this geometrical conditions. Therefore,
effects of different seaward slopes cannot be studied.
•
No berm / no friction slope
•
Since wave flume can generated only two dimensional waves (2D), wave
obliquity and short-crestedness cannot be model. This could be very important
since there will be spreading along the length of CD which gives more buffer
capacity.
•
Also, for this research only landward drainage option was considered. And,
only size of the pipes was changed to find the influence of pipe diameter in
reducing wave overtopping.
Study Overview
The following section gives an overview of the content of each chapter in this
research study.
Chapter 1 describes the background problems, motivation and objectives of the
research study. Also scopes of the model testing were addressed.
Chapter 2 provides details about findings from pervious studies and relevance of
those to this research. Available literature on wave run-up and wave overtopping were
reviewed and summarised. Also researches done on wave overtopping layer thickness
and the overtopping flow velocity were studies. Formulae to calculate layer thickness
and velocity are summarised in this section. Apart form that scaling laws and scale
and model effects were explained. Section 2.6 describes the fundamentals of crest
drainage dike and the expected behaviour during an overtopping event. After the
literature review objective and methodology were revised. Final part of this chapter 2
focused on revised objectives and methodology.
In Chapter 3 Model setup, Measurement techniques and test programme are
described. It includes the calibration of measuring devices and method of data
analysis. During the physical model study four different (wave parameters, layer
thickness, velocity, weight of overtopping water) measurements were taken. Chapter
3 describes the method to measure each of these parameters with an instruction about
the instruments. Then calibration methods of each measuring devise are explained.
D.M.D.T.B. Dassanayake
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Chapter 4 gives the important results from the model testing. Mainly the reductions
of mean overtopping discharges due to different configurations of crest drainage dike
are described. Then influence of crest drainage dike in reducing the overtopping
volume per wave is explained. Finally results form the tests with different drainage
options, and overtopping layer thickness and overtopping flow velocities of crest
drainage dike are given.
Chapter 5 contains the summary, conclusion, recommendations and areas needed to
be investigate further.
D.M.D.T.B. Dassanayake
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2. Review of available knowledge
2.1
Introduction
This chapter describes the findings from pervious studies and relevance of those to
current research. After the literature review objective and methodology are revised.
Last part of this chapter focuses on revised objectives and methodology.
Dikes protect low land areas in many countries world wide. These Dikes fails due to
high storm surges or high water levels. Consequences of dike failures are ranging
from economic and ecological losses to loss human life. Many dikes in North Sea
coast line failed and dike breached due to storm surge disasters. Most recent examples
are; about 139 km of dikes damaged in 1953 in the Netherlands (1850 fatalities),
about 600 km of dikes damaged in 1962 (200 fatalities) in Germany and several dike
breaches and dike failures along the German coastline in 1976 (Schüttrumpf &
Oumeraci, 2004).
After the disasters due to dike failures, many studies have been carried out to
understand the hydrodynamic processes at the dike slopes. Most of these researches
aimed to develop design guide lines for sea dikes. Some of the important findings and
formulae for dike design are given in following sections. Studies started with
determining wave run-up level on sea dikes. After that those studies were extended to
calculate mean overtopping discharge and even overtopping volume per wave
exceeded by certain percentage of incoming waves. Also many studies have been
carried out to find a method to decide the design water level for sea dike etc. However
due to random behaviour of nature and changes in weather pattern and sea level rise
as a result of global warming have made the prediction extremely difficult. Further
more due to space limitations, dike heightening is not possible any more as a measure
to avoid overtopping. Therefore dikes should be strengthened to withstand some
overtopping. In other words, “Overtopping Resistant Dikes” should be built.
When consider overtopping resistant dikes, protection of the dike crest and the
landward slope is very important. In the past no overtopping criteria was assumed
when designing landward except some recent studies and guidelines which describe
the types of grass on the landward side slope of the dikes. Then designers suggested
steeper landward slopes with thinner clay cover (usually thinner than the seaward
side). Even at present, there is no physically based design criterion for the designing
of landward slope of the dike. Hence hand landward slope is designed only based on
experience mainly considering the mean overtopping discharges. However stability of
the landward side depends on the instantaneous loads due to wave overtopping,
which can be described by layer thicknesses and overtopping velocities. (Schüttrumpf
& Van Gent,2003
The following sections of chapter 2 provide literature review on wave overtopping of
sea dikes. After that, the principal of crest drainage dike is explained. Finally revised
objectives of the research are given.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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Definitions
Some important definitions related to this research study are given below. Whenever
possible, definitions used by Schüttrumpf (2001,2003) and Van Gent (2003) were
used (see figure 2.1). New definitions were introduced to describe the crest basin.
wave run-up
wave run down
breaker zone
wave overtopping
wind
Ru
L0
H0
d
crest
basin
crest
seaward slope
hC (xC=0)
hB (SB=0)
uC (xC)
hA (zA=0)
uA (SA)
SWL
landward slope
1
Rc
dC
Ru
m
1
BC
n
B
Figure 2.1: Definitions of overtopping for crest drainage dike
(Schüttrumpf,2001,2003)
Foreshore
There is a level difference of 7cm between the toe of the dike and the wave maker
(Slope 0.001). However, the flume bottom in front of the dike can be assumed as
horizontal. Also from the multi-gauge array to the toe of the dike no wave breaking
assumed since the flume bottom was horizontal. Therefore, the wave parameters from
the reflection analysis represent the conditions at the toe of the structure (wave
heights and wave periods).
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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Wave Height
The wave height used in the wave run-up and overtopping formulae is the incident
significant wave height H m 0 at the toe of the structure (Spectral wave height). Since
deepwater conditions (no wave breaking until the toe of the dike) are assumed at the
toe of the dike H m 0 and the average wave height (highest one third of the waves on
one test), H1/3 , are almost the same. Therefore formulae which originally defined
significant wave height, H s as H1/3 can be used for calculation by substituting H1/3
by H m 0 .
Wave Period
Spectral period, Tm −1,0 (= m−1 / m0 ) was used for the calculation of wave run-up and
wave overtopping. Tm −1,0 is a good representation of a characteristic wave period of a
spectrum because, it gives more weight to the longer periods and is independent of the
type of spectrum (TAW, 2002). Conversion factor for the peak period, Tp , was taken
as Tp = 1.1Tm −1,0 since deepwater conditions are assumed and only single peaked
JONSWAP spectrum was used. The mean wave period, Tm calculated dividing the
selected time frame (selected test duration ) for analysis by the number of incoming
waves within that time frame.
Surf similarity parameter
Wave run-up and overtopping described by the surf similarity parameter
(Battjes,1974). Slope of the structure ( tan ϕ ), characteristic wave height and
characteristic time period determine the surf-similarity parameter.
2π H m0
ξs,−1 = tan α /
⋅
(2.1)
g Tm −1,0
Wave energy spectrum
The value of the parameters which describe the wave conditions depend on whether
they are based on the energy of entire wave spectrum or whether a filtering technique
is applied. By applying a filtering technique, certain range of the spectrum can be
neglected. (Van Gent 2002). In this research low-frequency waves, which are smaller
than 0.16Hz, are filtered. Since sometimes dimensionless coefficient suggested by
authors are based on whether the full spectrum is considered or not, in those cases
coefficient for short waves were used for calculation (Ex. Van Gent 2002).
Wave overtopping parameters
The crest level of sea dikes and other coastal structures is determined by the design
water level and the relevant wave run-up height. A Wave run-up height is given as
Ru2% which is exceeded by two percent of the incoming waves. When crest height is
not enough, then wave overtopping occurs. Wave overtopping on a clay dike could be
lead to dike failure or dike breach. However, Wave overtopping can not be avoided
due to uncertainties in the prediction of the design water level and the incoming wave
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
parameters. Therefore, wave overtopping is considered as an important input for the
design of coastal structures and flood defences.
Still most of the national and international design guidelines are based on mean
overtopping rate although the discharge over the crest is not constant over time.
Various types of formulae available to calculate the mean overtopping discharge q
(see Table 2.5). Apart from the mean overtopping discharge there are several
important parameter to understand the hydrodynamic process on the dike surface. To
characterise wave overtopping events and to compare the overtopping with and
without crest drainage four parameters are selected
•
•
2.2
Mean overtopping discharge, q ⎡⎣ m3 / s / m ⎤⎦
Flow velocity at the dike crest, u C2% [ m / s ]
•
Layer thickness at the seaward side of the dike, h A 2% [ m ]
•
Overtopping volume per wave, exceeded by 0.1% of incoming waves,
V2% ⎡⎣ m3 / m per wave ⎤⎦ (max. value per 1000 waves)
Current design practices
In the Netherlands concept of probability of flooding is replacing the probability of
exceedance (TAW 2000). Here dike ring as a whole determines the protection of and
area rather than a section of a dike. Also This concept takes equally account of the
different failure mechanisms. Further it takes uncertainties in to account in a
systematic and verifiable way. Each dike sectioned designed to withstand certain
water level called the design water level. Frequency of exceedance varies from 1/1250
to 1/10,000. But when determining the final height; wave run-up, the accessibility and
extra margin for uncertainties are included. This will result a higher and strong dike
than the minimum requirement. Technical books and handbooks are available for
design and construction of dike. However these guidelines do not guarantee that dike
will not fail for any water level lower than the design water level. Therefore even after
adding the safety margins there are uncertainties to be dealt with. In flooding
probability calculations, uncertainties due to natural phenomena (Occurrence of storm
surge, long term developments in nature etc), problems with prediction models (A
calculation model is never an exact reproduction of reality, just an approach) and
statistical uncertainties due to lack of measurements data are taken in to
account.(TAW2000). This approach looks better than the probability of exceedance.
This concept can be extended to calculate the probability of flooding as well as
consequences of flooding (possible damaged due flooding). Then week points can be
strengthen in order to improve the safety of the area. Although this concept tries to
address all the uncertainties still there are limitations in predicting the future. For an
example climatic change makes the long term prediction very difficult. Also failure
due to overtopping and overflow was the most common reason for dike failures.
Therefore still it is very important to design the dike to allow more overtopping and
overflow than ordinary dikes.
Different authors (Van der Meer and Janssen 1995, Schüttrumpf and Oumeraci 2005)
has pointed out that designers should give more attention to the overtopping volume
per wave. According to TAW 2002 maximum wave overtopping volume per wave
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
( Vmax ) is in the order of 100 times of average overtopping discharge ( q ) for high
average wave overtopping discharges. For small average wave overtopping
discharges, Vmax is in the order of 1000 times of q . Most of the time erosion of the
landward slope starts with this larger events. Despite the importance of this low
exceedance events, still design guidelines uses average overtopping discharges. TAW
2002 guidelines suggest following average discharges are indicative for erosion of the
landward slope;
•
•
•
0.1 l/s per m for sandy soil with a poor grass cover
1.0 l/s per m for clayey soil with a reasonable good grass cover
10.0 l/s per m for a clay covering and grass cover according to the
requirement for the seaward slope or for a armoured landward slope
However, these guidelines only qualitative and still there are research going on to find
better relationship between overtopping and the capacity of the landward slope.
Schüttrumpf (2001) and Van Gent (2002) further studied individual wave overtopping
events with low probability of expedience and tried to come up with formulae to
calculate the flow field on dike surface. Also Möller et al (2002) carried out research
to find the interaction between wave overtopping and soil parameter. But still these
results are not adopted in design guide lines.
However during the model tests carried out at LWI for crest drainage dike, both
overtopping layer thickness and the velocity at the seaward slope, at the dike crest and
at the land ward slope were measured. Existing formulae for overtopping layer
thickness and the velocity by Schüttrumpf (2001) and Van Gent (2002) as well as
mean overtopping discharge formulae suggested by TAW 2002 were modified to
include effect of crest drainage.
2.3
Wave Breaking and Breaker Types
Wave overtopping discharges are depending on wave breaking and breaker types.
Therefore different breaker types were studied and summarised in table 2.1. Formulae
to estimate the wave overtopping discharges changes with different breaker types.
Table 2.1: Classification of the Breaker type (Schuttrumpf, 2001)
Spilling breaker
Plunging breaker
Surging breaker
Diagram
Valid range*
Breaker
criteria*
Breaking point
Breaking point
ξd =
tan α
H s / L0
< 0.4
H s / d B = 0.8
Wave
overtopping**
q
gH 3m0
=
0.4 ≤ ξ d =
tan α
H s / L0
≤2
Breaking point
2 < ξd =
H s / d B = 0.8 to 1.2
⎡
⎤
R
0.067
1
γ b .ξ0 .exp ⎢ −4.3 c
⎥
H m0 ξ0 .γ b .γ f .γ β .γ v ⎥⎦
Tanα
⎢⎣
tan α
H s / L0
H s / d B = 1.2
q
gH 3m0
⎡
R
1 ⎤
= 0.2 exp ⎢ −2.3 c
⎥
H m0 γ f .γ β ⎥⎦
⎢⎣
(1974)
der Meer &. Janssen (1995)
* Battjes
** Van
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
2.4
Wave Run-Up
This section describes the importance of quantifying the wave run-up on dike slopes.
Then available different formulae for calculation of wave run-up height for smooth,
impermeable slopes are compared. Then formulae for Wave run-up velocities and
Wave run-up layer thickness are discussed.
Wave run-up is one of the important hydrodynamic phenomena on a dike slope,
which can be categorised by the breaker parameter or surf similarity parameter (see
section 2.1).
Oldest and simplest formula used in the Netherlands to calculate wave run-up height
is;
Ru 2% = 8H S tan α
(2.2)
This formula only applicable for an average wave steepness of Sop = 0.040 and
reduction factor of 1.0. Hence other formulae developed to calculate run-up for wider
range of wave steepness. At the same time following reduction factors are introduced
to obtain more accurate results for specific cases than a rough estimation. (de Wall &
Van der Meer, 1992 and Van der Meer & Janssen, 1994)
γb
γf
γh
γβ
= reduction factor for berm
= reduction factor for roughness at the seaward slope
= reduction factor for shallow foreshore
= reduction factor for angular wave attack
De Wall and Van der Meer (1992) introduced following wave run-up formulae which
can be used for most of the dike profiles.
Ru 2%
= 1.5γ hγ f γ β ξ p ,eq where ξ p ,eq = γ β ξ β
Hs
with maximum of;
Ru 2%
= 3.0γ hγ f γ β
Hs
(2.3)
After that formulae were fine tuned for different scenarios by various authors, but
structure of the modern formulae is similar.
Schüttrumpf (2001) and Van Gent (2002) developed formulae to calculate the flow
field on the dike slopes. Both used the remaining run-up length ( z = Ru 2% − Rc )
concepts to calculate the flow fields on the dike surface (Figure 2.1 and 2.2). But they
selected different definition of wave height and time period were used to calculate
wave run-up. Schüttrumpf (2001) has used Tm to calculate surf-similarity parameter at
the toe of the structure where as Van Gent (2002) used Tm −1,0 . However, both used H s
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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at the toe. But in this report, H m 0 is and Tm −1,0 used for calculation. Detail of these
formulae are given below
2.4.1
Wave run-up height
Several run-up formulae have been suggested by several authors. Some of the recent
wave run-up formulae applicable to smooth, impermeable surfaces are summarised as
follows. This research only considers short waves (low frequency waves; lower than
0.16Hz are filtered). Therefore relevant dimensionless coefficients are calculated (for
short waves and 2% exceeding limit) and used in formulae form Van Gent (1999b)
and Schüttrumpf (2001) (see annex B).
Table 2.2: Wave run-up formulae for smooth, impermeable slopes
Authors
Structure
Surf-similarity
Run-up model
parameter
Impermeable,
Ru 2%
Van
der
= 1.5ξ0 p
smooth, rough, ξ = tan α / 2π ⋅ H s
Hs
Meer
&
p
straight
&
g Tp
Stam (1992)
with maximum of 3.0
bermed
de Waal & Impermeable,
Ru 2%
2π H s
= 1.5γ hγ f γ β ξ p ,eq
⋅
Van
der smooth, rough, ξ p = tan α /
Hs
g Tp
&
Meer (1992) straight
with maximum of;
bermed
Ru 2%
= 3.0γ hγ f γ β
Hs
Van
der Impermeable,
Ru 2%
2π H s
= 1.6γ hγ f γ β γ bξ 0 p
⋅
Meer
& smooth, rough, ξop = tan α /
g Tp
H
s
Janssen
straight
&
(1994)
bermed
with maximum of;
Van Gent * Impermeable
2π H s
⋅
(1999b)
smooth with ξs,−1 = tan α /
g Tm −1,0
foreshore
slopes of 1:4
and 1:2.5
Schüttrumpf
(2001,
2003)
Impermeable
2π H s
⋅
smooth
1.3, ξd = tan α /
g Tm
1:4 and 1:6
slopes
D.M.D.T.B. Dassanayake
Ru 2%
= 3.2γ f γ f γ β
Hs
R u 2%
= 1.55γ f γ β ξs,−1
Hs
for ξs,−1 ≤ 1.742
R u 2% ⎛
4.703 ⎞
= ⎜ 5.4⎟⎟ γ f γ β
⎜
Hs
ξ
s, −1 ⎠
⎝
for ξs,−1 ≥ 1.742
R u 2%
= 1.5ξd for ξd < 2
Hs
R u 2%
= 3.0ξd for ξd ≥ 2
Hs
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Schüttrumpf Impermeable
2π H s
⋅
(2002)**
smooth
1.3, ξs,−1 = tan α /
g Tm −1,0
1:4 and 1:6
slopes
Van
Gen Impermeable
2π H s
⋅
(2002)**
smooth /rough ξs,−1 = tan α /
g Tm −1,0
1:4 slope
R u 2%
= 1.25ξs,−1 for ξs,−1 < 1.4
Hs
R u 2%
= 1.35 ⋅ ξs,−1
Hs
for ξs,−1 ≤ 1.481
R u 2% ⎛
2.963 ⎞
= ⎜ 4.0⎟
⎜
Hs
ξs,−1 ⎟⎠
⎝
for ξs,−1 ≥ 1.481
TAW
(2002)
Impermeable,
2π H s
⋅
smooth, rough, ξs,−1 = tan α /
g Tm −1,0
straight
&
bermed
Ru 2%
= 1.75γ bγ f γ β ξ0
H m0
with maximum of;
⎛
Ru 2%
1.6 ⎞
= γ f γ β ⎜ 4.3 −
⎟
ξ0 ⎠
H m0
⎝
* Formula from Van Gent (1999b) has not presented in this format. Steps to reach this format is given
in Annex B
** Source: Schüttrumpf & Van Gent (2003)
2.4.2
Wave run-up velocities
Wave run-up velocity depends on the incoming wave parameters (wave height and
time period) and the fictitious wave run-up height. For practical purposes, the
fictitious wave run-up height is replaced by R u 2% . The wave run-up velocities can be
determined by the simplified energy equation (Schüttrumpf & Van Gent, 2003)
u A2%
R u 2% − ZA
= CAu *
Hs
gH s
C Au *
= empirical coefficient
ZA
= height from SWL to point A [ m ]
(2.4)
R u 2% = wave run-up height, exceeded by 2% of incoming waves [ m ]
The empirical coefficient C Au * determined by the model tests.
Table 2.3: Coefficient CAu*for run-up velocities
Coefficient, C Au *
Authors
Structure
Schüttrumpf
(2001, Impermeable smooth slopes with
1.37
2002)
1:3-1:6 foreshore slopes
Impermeable smooth / rough slopes
1.30
Van Gent (2002)
with 1:4 foreshore slopes
Impermeable smooth slopes with 1:31.32
Schüttrumpf (2003)
1:6 foreshore slopes
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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2.4.3
Wave run-up layer thickness
Similar to wave run-up velocity, layer thickness also depends on the incoming wave
parameters (wave height and time period) and the fictitious wave run-up height. The
layer thickness can be determined by assuming a linear decrease of layer thickness
from SWL to R u 2% (see figure 2.2).
⎡R
− ZA ⎤
h A 2%
= CAh * ⎢ u 2%
⎥
Hs
Hs
⎣
⎦
(2.5)
h A 2%
= layer thickness on the seaward slope exceeded by 2% of the incoming waves
CAh *
=empirical coefficient
Table 2.4: Coefficient CAh* for layer thickness on seaward slope
Coefficient, CAh *
Authors
Structure
Schüttrumpf
(2001, Impermeable smooth slopes with
0.33
2002)
1:3-1:6 foreshore slopes
Impermeable smooth / rough
0.15
Van Gent (2002)
slopes with 1:4 foreshore slopes
Before the above formula, Schüttrumpf (2001, 2003) suggested
h A = c 2* x* tan α
(2.6)
with x * = x z − x A , x A = n ⋅ z A
x A = n ⋅ R u 2%
This formula is valid for different exceedance (2%, 50%, 100%) limits of incoming
waves. For 2% exceedance limit of incoming waves, the empirical coefficient is
C2∗ = 0.216 (Schüttrumpf, 2003)
x * = remaining run-up length ( x ∗ = x z − x A )
x Z = R u / tan α
x A = position on the seaward slope
ZA = height from SWL to point A
C2* = dimensionless coefficient
2.5
Wave Overtopping
Wave overtopping and the failure of landward slope was the cause for most sea dike
failures. Most of the design guidelines are based on mean overtopping quantities
although the discharge over the crest is not constant. Also average overtopping
quantity cannot account for the stress and other effects due to extreme individual
overtopping events. Further failures on landward slope were initiated by individual
overtopping events (Schüttrumpf and Oumeraci, 2005). Also Van der Meer and
Janssen (1995) have shown that the individual overtopping events are more relevant
D.M.D.T.B. Dassanayake
15
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
in designing dike than thee mean overtopping discharges. Also in TAW report, Van
der Meer mentioned that the largest overtopping event will give as much as 1000
times move wave overtopping in small average wave overtopping discharges and 100
times move wave overtopping in large average wave overtopping discharges than the
average wave overtopping discharge (q). (TAW 2002 Pg 36). This phenomenon was
not identified at the beginning and it was a surprise to see dike failure initiated by
landward slope although waves are hitting the seaward slope.
2.5.1
Mean overtopping rate
Different models available to calculate the mean overtopping rate, q (See Table 2.5).
Most dimensionless equations for calculations of mean overtopping rate, q uses an
exponential function.
Q∗ = a ⋅ exp(-b R* ) or
(2.7)
*
*
Q = a ⋅ (1- R )
Q∗
= dimensionless overtopping rate
*
R
= dimensionless freeboard
Since this research only focuses on short waves (low frequency waves; lower than
0.16Hz are filtered). Also dike model consisted of smooth, straight, impermeable
slopes. Therefore only relevant mean overtopping calculation models are summarised
in Table 2.5.
Table 2.5: Mean overtopping formulae for smooth, straight, impermeable slopes
(Schüttrumpf (2001), Soliman (2003), FEMA (2005) and Wiyono (2006))
Authors
Structure
Overtopping
Dimensionless
Dimensionless
*
Model
Overtopping
freeboard R
discharge
Q∗
Owen
Impermeable,
(1980)
smooth, rough,
Owen
straight
&
Rc
1
q
⋅
(1982)
bermed slopes Q∗ = a ⋅ exp(-b R* )
Tm 0 ⋅ g ⋅ H s γ
Tm 0 ⋅ g ⋅ H s
under offshore
random waves
De Waal
and
Van der
Meer
(1992)
Impermeable,
smooth,
rough, straight
and bermed
slope
D.M.D.T.B. Dassanayake
Q∗ = a ⋅ exp(b R* )
Ru ,2% − Rc
q
g ⋅ Hs
3
Hs
16
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Van der
Meer
and
Janssen
(1994,
1995,
and 1998)
Impermeable,
smooth,
rough, straight
and bermed
slope
For ξop < 2;
q
gH 3m0
Tanα R c 1 1
⋅
⋅
ξop
Hs ξop γ
⋅
Q∗ = a ⋅ exp(-b R* )
For ξop > 2
For ξop > 2
Rc 1
⋅
Hs γ
q
gH 3m0
Hedges
and
Reis
(1998)
Impermeable,
smooth,
rough, straight
and bermed
slope
(Data
from Owen
(1982))
Van Gent Impermeable
* (1999b) smooth slopes
with several
foreshore
slopes
Schüttrum Impermeable
pf (2001)
smooth 1:6
slope (for no
freeboard (Rc
=
0) and without
overtopping
(Rc
>
Ru,max))
TAW
Impermeable,
(2002)
smooth, rough,
straight
&
bermed
For ξop < 2;
For 0 < R < 1;
Q∗ = a ⋅ (1 − R* )b
For R ≥ 1;
Rc
R u,max
q
g ⋅ Ru ,max
3
Q∗ = 0
q
∗
Q = a ⋅ exp(-b R )
*
Q∗ = a ⋅ exp(-b R* )
Rc
γ ⋅ Hs (1 + cξs,−1 )
g ⋅ H s3
Rc
Hs ⋅ ξm
q
2 ⋅ g ⋅ Hs
3
For ξop <≈ 2;
q
gH 3m0
⋅
For ξop <≈ 2;
Tanα R c 1 1
⋅
⋅
H m0 ξop γ
ξop
Q∗ = a ⋅ exp(-b R* )
For ξop ≈> 2
q
gH
3
m0
For ξop ≈> 2
Rc 1
⋅
H m0 γ
As shown above different formulations for Q∗ and R* can be found in literature ( See
Schüttrumpf 2001), which are mostly valid for certain range of boundary conditions
(Schüttrumpf and Van Gent, 2003). Since ComCoast model tests were done with
smooth, straight, impermeable 1:4 slopes, overtopping formulae applicable to testing
conditions discussed in following section.
D.M.D.T.B. Dassanayake
17
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
TAW (2002) Report calculation of average overtopping discharge is given by;
q
gH 3m0
=
⎡
⎤
R
0.067
1
γ b .ξ0 .exp ⎢ −4.75 c
⎥
H m0 ξ0 .γ b .γ f .γ β .γ v ⎥⎦ (for ξ0 <2 )
Tanα
⎢⎣
maximum of (and for ξ 0 >2 )
q
gH 3m0
⎡
R
1 ⎤
= 0.2 exp ⎢ −2.6 c
⎥
H m0 γ f .γ β ⎥⎦
⎢⎣
(2.8)
TAW (2002) presents this formula without differentiate the breaking and non braking
waves. Instead report states the second part of the formula gives the maximum
possible overtopping discharge.
Where;
q
= average wave overtopping discharge
H m0 = significant wave height at the toe of the dike
ξ0
= breaker parameter = tan α / s0
S0
= wave steepness = 2.π.H m0 /(g.T 2 m −1.0 )
= reduction factor for berm
= reduction factor for roughness at the seaward slope
= reduction factor for shallow foreshore
= reduction factor for angular wave attack
γb
γf
γh
γβ
γv
= influence factor for vertical or very steep wall on the slope of the dike
Rc
= Free crest height above the still water line
Tanα = slope
2.5.2
Overtopping velocities and layer thickness at the crest of the dike
Schüttrumpf and Oumeraci (2005) pointed out that the overtopping flow velocities
and layer thicknesses due to an extreme event are more relevant for the prediction of
erosion, infiltration and slip failure. Therefore, in addition to average overtopping
rates, both overtopping flow velocity and the overtopping layer thickness are required
as hydraulic boundary conditions for the geotechnical stability analysis of sea dike.
Schüttrumpf (2001) has done extensive studies about the flow field on crest dike.
Further Schüttrumpf and Oumeraci (2003) gives a set of formulae for the prediction
of overtopping layer thicknesses and the overtopping flow velocities on the crest of
the dike. And those formulae validated by the hydraulic scale model tests.
Van Gent (2002) done further investigation of flow fields in the dike and he tried to
fine tune formulae of Schüttrumpf.(see Table 2.6 and 2.8)
D.M.D.T.B. Dassanayake
18
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
hC (xC=0)
hB (SB=0)
uC (xC)
hA (zA=0)
Ru
uA (SA)ZA
1
Rc
SB
m
SWL
XC
1
n
B
XA
XZ-XA
XZ
Figure 2.2: Definitions sketch (Schuttrümpf,2001)
Table 2.6: Overtopping layer thickness on the dike crest
Schüttrumpf (2001)
Van Gent (2002)
h A = c 2* x* tan α
Seaward
edge of the
Crest
xC = 0
x ∗ = ( R u 2% / tan α ) − ( R c / tan α )
⎡R
h A2%
− Rc ⎤
= CAh′′ ⎢ u 2%
⎥
Hs
Hs
⎣
⎦
h C2%
⎡R
h C2%
− Rc ⎤
= C h′ ⎢ u 2%
⎥
Hs
⎣ γ f Hs ⎦
CCh′ =0.15
CAh′′ =0.216
Crest
0 < xC < B
Landward
edge of the
crest
xC = B
h C (x C )
x ⎞
⎛
= exp ⎜ −0.75 C ⎟
h C (0)
B⎠
⎝
h C2%
CCh′′ =0.216
⎡ Ru − Rc ⎤
h C (x C = B)
= CCh′′ ⎢ 2%
⎥
Hs
Hs
⎣
⎦
h C2%
B⎞
⎛
CCh′′ = exp ⎜ −0.75 ⎟ × 0.216 = 0.102
B⎠
⎝
⎡R
− Rc ⎤
h C2%
= CCh′ ⎢ u 2%
⎥
Hs
⎣ γ f Hs ⎦
CCh′ =0.10
Where;
hC
=layer thickness at the dike crest
xC
=horizontal coordinates at the dike crest
CCh′
= dimensionless coefficient
CCh′′
B
=dimensionless coefficient
=width of the dike
Schüttrumpf (2001) derived general formulae for all the dike slopes. But Van Gent
(2002) formulae are valid only for one particular location. Distance is not a variable.
Therefore in table 2.6, Schüttrumpf’s (2001) formulae are rewritten with parameters
D.M.D.T.B. Dassanayake
19
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
on seaward edge of the crest and land ward edge of the crest, for the comparison with
Van Gent’s.
Then Schüttrumpf and Van Gent (2003) developed following formulae to calculate
the layer thickness on the dike crest. Due to differences in model setup and
instruments, empirical coefficients have small different (see Table 2.7).
h C2%
x ⎞
⎛
= exp ⎜ −CCh * ⋅ C ⎟
h A2% (R c )
B⎠
⎝
CCh*
(2.9)
= empirical coefficient
Table 2.7: Coefficient CCh* for layer thickness on crest
Coefficient, CCh *
Authors
Structure
Impermeable smooth slopes with 1:3Schüttrumpf (2001, 2002)
0.89
1:6 foreshore slopes
Impermeable smooth / rough slopes
Van Gent (2002)
0.40
with 1:4 foreshore slopes
Seaward
edge
of
the Crest
xC = 0
Table 2.8: Overtopping velocity on the dike crest
Schüttrumpf (2001)
Van Gent (2002)
0.5
u C2%
R u,2% − R c u C2%
u A2%
⎡ R u 2% − R c ⎤
′
= 1.32
= CCu ⎢
⎥
Hs
gH s
gH s
⎣ γ f Hs ⎦
CCu′ =1.30
Crest
0 < xC < B
u C2%
Landward
edge
of
the crest
xC = B
u C2%
⎛ x f⎞
u C (x C )
= exp ⎜ − C ⎟
u C (0)
⎝ 2h C ⎠
⎡
u C2%
− R c / γ f Hs ⎤
0.5 R
⎥
= CCu′ ( γ f −c ) ⎢ u 2%
gH s
⎢⎣ 1 + CCu′′ ( B / H s ) ⎥⎦
CCu′ =1.70 CCu′′ =0.1
Where;
uC
= velocity at the dike crest
u0
= velocity at the beginning of dike crest ( x C = 0 )
xC
f
hC
= coordinate along the dike crest
= friction coefficient ( f =0.0058)
= layer thickness at the x C
D.M.D.T.B. Dassanayake
20
0.5
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Then Schüttrumpf and Van Gent (2003) developed following formula to calculate the
overtopping velocity on the dike crest. Due to differences in model setup and
instruments, empirical coefficients have small different (see Table 2.8).
⎛
u C2%
x ⋅f ⎞
= exp ⎜ −CCu * C ⎟
u A 2% (R c )
h C2% ⎠
⎝
u C2%
waves
CCu *
h C2%
Rc
xC
f
(2.10)
= wave overtopping velocity on the dike crest exceeded by 2% of incoming
= empirical coefficient
= layer thickness on the crest exceeded by 2% of the incoming waves
= free board
= position on the dike crest respect to the beginning of the dike crest
= friction coefficient
Table 2.9: Coefficient CCh*for overtopping velocities on crest
Coefficient, CCu *
Authors
Structure
Schüttrumpf (2001, Impermeable smooth slopes with 1:3-1:6
0.50
2002)
foreshore slopes
Impermeable smooth / rough slopes with
Van Gent (2002)
0.50
1:4 foreshore slopes
Van Gent (2002) developed formulae for discharge at the seaward edge and landward
edge of the dike (see Table 2.10). These formulae obtained from multiplying the
signals of the thickness of water layer with the signal of velocities. Since no direct
measurements were done at the locations, that may cause deviations between
measured and calculated discharge.
Seaward edge
of the Crest
xC = 0
Table 2.10: Overtopping discharges on dike crest
Van Gent (2002)
1.5
qc 2%
⎡ R u 2% − R c ⎤
h 2%
= C q′ ⎢
⎥
gH s 3
⎣ γ f Hs ⎦
Cq′ =0.20 σ =0.0203
Crest
0 < xC < B
Landward
edge of the
crest
xC = B
qc 2%
qc 2%
D.M.D.T.B. Dassanayake
1.5
⎡
− R c ) / ( γ f Hs ) ⎤
q C2%
0.5 ( R
⎥
= Cq′ ( γ f −c ) ⎢ u 2%
gH s
⎢ 1 + Cq′′ ( B / H s ) ⎥
⎣
⎦
Cq′ =0.17 Cq′′ =0.1 σ =0.0117
21
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
2.5.3
Overtopping velocities and layer thickness at the landward slope of the
dike
The overtopping flow on the dike depends on the input parameter (layer thickness and
the overtopping velocity at the end of dike crest), the slope of the land ward side and
the surface roughness Schüttrumpf and Van Gent,2003). Schüttrumpf (2001,2003)
developed following formula to calculate both Overtopping velocities and layer
thickness at the landward slope of the dike.
k1 h B
⎛k t⎞
.tanh ⎜ 1 ⎟
f
⎝ 2 ⎠
uB =
f v (0)
⎛k t⎞
1+ B
.tanh ⎜ 1 ⎟
h B k1
⎝ 2 ⎠
With
u B (0) +
t=−
(2.11)
u B (0)
u 2 (0)
2s B
+ 2B 2 +
g sin β
g sin β g sin β
2fg sin β
h
u ⋅h
hB = 0 0
uB
h B =layer thickness at a point B on the landward side of the dike
k1 =
h 0 =layer thickness at the beginning of landward slope
v0 =velocity at the beginning of landward slope
β = slope angle of landward side
s B =distance of point B from the beginning of landward slope
2h B g sin β
f
v B = Ch h B sin β
vB =
Ch =Chezy coefficient
Hence this is an iteration process, calculation is complicated. Van Gent derives a
simple formula for overtopping velocity on landward slope;
k
u B2% = 2 + k 4 exp −3 ⋅ k 2 ⋅ k 32 ⋅ s B
(2.12)
k3
(
)
k 2 = 3 g sin ϕ
k3 =
3
1
f
2 h 02% ⋅ u 02%
k 4 = u 02% −
D.M.D.T.B. Dassanayake
k2
k3
22
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
This formula required no iterative solution and easier to use for practical purposes.
Both formulae gives same asymptote for S B → ∞ ;
uB 2% =
3
2 g ⋅ h B ⋅ uB ⋅ sin β
f
(Schüttrumpf and Van Gent,2003)
Overtopping layer thickness on the landward slope (Van Gent (2002)
As described at the beginning of this section, Schüttrumpf (2001, 2003) developed
one formula to calculate both velocity and the layer thickness on the landward side of
the dike. But Van Gent (2002) derived a formula to calculate layer thickness on the
land ward slope with out iterative solution.
h=
h0u0
⎡ k2
⎤
2
⎢ + k 4 ⋅ exp −3 ⋅ k 2 ⋅ k 3 ⋅ s B ⎥
⎣ k3
⎦
(
)
(2.13)
For this formula input parameter are the overtopping velocity and the layer thickness
at the end of the crest (landward edge); h 0 = h B2% (SB = 0) and u 0 = u B2% (SB = 0) .
Also f L = 0.005 for smooth dike.
2.5.4
Overtopping Volume per wave
TAW (2002) suggested the following formula for calculation of overtopping
quantities for largest overtopping event for certain number of waves.
Vmax = a.[ ln(N ov ) ]
(4 / 3)
N ov
Tm
q
Pov
Vmax
N
with a = 0.84.Tm .q / Pov
(2.14)
= Number of overtopping waves
= Average wave period (N Tm is duration of storm or examined period)
= average wave overtopping discharge
= N ov /N =Probability of overtopping per wave
= Maximum wave overtopping volume for per wave
= Number of incoming waves during the period of storm
Van Gent (2001-a) found the formula for the volume per overtopping wave, exceeded
by 2% of the incoming waves.
⎛
⎞
V 2%
*
0.5 Ru 2% − Rc
c
γ
(
)
=
(2.15)
⎜
V
f −C
⎜ γ f H s ⎟⎟
H s2
⎝
⎠
γ f −C = reduction factor for roughness at the crest
cV *
= coefficient
D.M.D.T.B. Dassanayake
23
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
2.6
Crest Drainage Dike
Figure 2.3 shows conceptual sketch of crest drainage dike. Main idea of this
innovative crest design is to reduce the wave load and wave overtopping of a dike by
installing a “Overtopping Buffer Basin” on top of the dike crest, which is a concrete
U-Profile.(DHV,2005) Most of overtopping water will be collected to this
construction and after that will water be drained through drainage pipes. According to
the figure 2.3, drainage pipes are in landward slope of the dike. However part of the
water can be drained to seaside depending on the capacity of salt water storage at the
landward side of the dike. This option could be preferable in extreme situations. But it
could complicate the structure (might need regulating valves etc). (DHV, 2005)
As mentioned above new installation will trap a significant part of overtopping water;
reducing the amount of water runs off over the landward slope. This will result less
load on landward slope than normal conditions. Apart from that even if the capacity
of the crest construction exceeds in an extreme event, the overtopping wave will lose
its energy while flowing over. According to Nieuwenhuis et al (2005), crest drainage
dike is technically and financially feasible. Firstly, the cost is competitive with other
possible alternatives and also significantly lower than traditional heightening of dike.
Secondly crest construction provides sufficient buffer capacity in overtopping events
and reduces the water flow over the landward slope of the dike. Both buffer capacity
and rate of drainage can be increased easily depending on design requirements. Apart
from the buffer capacity, water which is trapped inside crest drain can absorb the
energy in overtopping wave, even in the extreme wave overtopping events, crest
drainage will result smooth flow with lower velocity than in conventional dike.
Finally Crest drain dike offers recreational values on the dike like footpaths, cycling
path etc.
Figure 2.3: Conceptual sketch; Crest Drainage dike (Not Scaled), Source (DHV,2005)
For the preliminary design of the crest drainage dike the Hondsbossche Zeewering
was used as pilot location. Design requirements are as shown bellow (Nieuwenhuis et
al 2005).
ƒ
ƒ
ƒ
ƒ
ƒ
The dike must be able to resist an average overtopping of at least 15l/s/m
(with a maximum of 2300l/m)
Storm duration taken in to account as 3 hours
The concept must be applicable for an landward slope gradients of 1:3 to 1:4
Heightening and widening of the dike is not allowed, the concept must fit
within the present crest sectional profile.
Effects on mature, landscape and cultural values must be minimized
D.M.D.T.B. Dassanayake
24
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
ƒ
ƒ
ƒ
Minimum maintenance
Cost of construction and maintenance must be acceptable compared to the
cost of traditional heightening of dikes.
The concept must meet the current legal standards
Finally Nieuwenhuis et al (2005) came up with two preliminary design alternatives
for concrete crest constructions:
ƒ
ƒ
A concrete crest construction (Prefab or in-situ) with drainage pipes towards
landward side of the dike (figure 2.4)
A concrete crest construction (Prefab or in-situ) with drainage pipes towards
seaward side of the dike (Figure 2.4)
As mentioned above the second alternative (figure 2.4) could be preferable in extreme
events since it can drain more water than having landward drainage pipes (Figure
2.4). However seaward drainage system will be a relatively complicated since the
discharge should be adjustable and sometimes water can penetrate into the crest
construction through the drainage pipes when inside pressure is lesser which will
reduce the buffer capacity of the crest basin.
landward discharge
Seaward discharge
Figure 2.4: Detailed crest construction, including pit and connection to landward
discharge. Source: Nieuwenhuis et al 2005
According to Figure 2.4. crest width is selected as 3m. Inner dimensions of crest
construction are 2m in width and 0.8m in height.
Drainage discharges for th crest bsin given by the formula 2.16. Table 2.11 give the
calculated drainage discharges using the formula 2.16.
Where,
V = 2 gh
Q = Cdrain × A × v
(2.16)
Cdraina= Coefficient of discharge, for preliminary calculation Cdrain = 1.
D.M.D.T.B. Dassanayake
25
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Table 2.11: Calculated drainage discharges for different fill level in the crest drainage
values in model scale
values in prototype scale
Qdrain (m3 / s / m)
h ( m)
0.000
0.006
0.012
0.018
0.024
0.029
0.035
0.041
0.047
0.053
25mm
1.5E-04
1.7E-04
1.9E-04
2.1E-04
2.2E-04
2.4E-04
2.5E-04
2.7E-04
2.8E-04
2.9E-04
32mm
2.6E-04
3.0E-04
3.3E-04
3.5E-04
3.8E-04
4.0E-04
4.3E-04
4.5E-04
4.7E-04
4.9E-04
38mm
4.0E-04
4.4E-04
4.8E-04
5.2E-04
5.5E-04
5.9E-04
6.2E-04
6.5E-04
6.7E-04
7.0E-04
Qdrain (l / s / m)
h ( m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
400mm
10.4
11.9
13.3
14.5
15.7
16.7
17.7
18.7
19.6
20.4
500mm
18.5
20.9
22.9
24.9
26.6
28.3
29.9
31.4
32.8
34.2
600mm
27.8
30.9
33.8
36.4
38.8
41.1
43.2
45.3
47.3
49.2
However at the end Nieuwenhuis et al (2005) highly recommend to further research
on most important technical aspects which is the amount of overtopping water that is
trapped by the crest contrition in relation to remaining overtopping flow. Further,
Nieuwenhuis et al (2005) recommend to conduct physical modelling tests to obtain
more insight in to flow patterns. Apart from that physical model tests are needed to
verify different assumptions regarding the inflow and outflow of the crest
construction such as
ƒ
ƒ
ƒ
To check the overtopping rate over the landward sidewall of the crest
construction (Flow velocity, flow layer thickness)
To check whether the overtopping water will easily flow into the crest
construction (as sheet flow) under the expected flow conditions.
To check when the overtopping water will start flowing over the present water
layer in the crest construction. (Nieuwenhuis et al assumed as 80% of the crest
construction)
Based on the recommendations of Nieuwenhuis et al (2005) for the further
investigation, the objectives of this hydraulic model study were decided. Small scale
physical model can give better view of the prototype behaviours of the dike with
“Crest Drainage”. Further model result of this research can tell whether it is worth
investigating further or not in terms of hydraulic performance of the conceptual
design suggested by Nieuwenhuis et al (2005)
D.M.D.T.B. Dassanayake
26
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
2.7
Scaling and Further Aspects
This section describes the scaling law and the influences of surface tension, viscosity
and other scale effects on the model results. Then interpretation of results and method
to transfer the latter to prototype conditions are addressed.
2.7.1
Scaling law
The main concern when testing a model structure is to ensure correct representation of
wave-structure interaction while minimising the results being biased by scale effects.
This means that the scale of the model should be selected in such a way that it is
practical to construct it in the flume and at the same time it should achieve the design
conditions. It is important that the geometric model scale should always be
undistorted, i.e. the vertical and horizontal length scales should be the same. (distorted
models are used only in special cases )
The geometric scale of the model was determined to be 1:17. This scale has been
derived from typical North Sea conditions in Germany and The Netherlands.
Constraints for a larger scale are the dimensions of the wave flume, the maximum
possible water level, anticipated final crest level and the capacity of the wave
generator.
Furthermore, the waves generated in the flume needed to be checked for consistent
behaviour as in nature. This required detailed checks of depth-limited wave breaking
conditions in the flume and expected behaviour of waves at the structure. With the
scale selected here (1:17) behaviour of waves seems to be similar to prototype. Since
the gravity and inertia forces in the model are the same as in the prototype, it is
necessary to use the Froude scaling law for correct representation of the prototype.
Froude criterion can be express as;
inertial force
=
gravity force
ρ L2u
u
=
3
ρL g
gl
(2.17)
This is called Froude Number. According to Froude scaling criterion, Froude
number should be the same in the model as in the prototype.
⎛ u ⎞ ⎛ u ⎞
⎜⎜
⎟⎟ = ⎜⎜
⎟⎟
⎝ gL ⎠ p ⎝ gL ⎠ m
(2.18)
This leads to;
⎛ g p ⎞⎛ Lp ⎞
= ⎜
⎟⎜ ⎟
um
⎝ g m ⎠⎝ Lm ⎠
Table 2.12 summarises the scale relationship of different parameters according to
Froude criterion.
up
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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Table 2.12: Scale relations for model laws after Froude
Parameter
Equation
Froude
u
= constant
g⋅ L
Length
NL
Area
NA = NL2
Volume
NV = NL3
Time
Nt = NL
Velocity
Nu = NL
Acceleration
Na = 1
Mass
Nm = Nρ⋅ NL3
Pressure
Np = N ρ ⋅ NL
Force
NF = N ρ ⋅ NL
Force per m
N F/m = N ρ ⋅ N L
3
2
Note: N is defined as the scaling ratio of prototype and model measure, e.g. NL = Lp/Lm or NF = Fp/Fm
2.7.2
Scale effects and Model effects
Basic assumption in Froude scaling is, gravity dominate the physical force balancing
of the internal forces. This assumption results scale effects as it scales other physical
forces of viscosity, elasticity, surface tension etc incorrectly. For example;
hydrodynamic models which are geometrically scaled down to Froude criterion do not
simulate the viscous and friction effects. Reynolds number between model and
prototype is different. Hence internal friction and bottom boundary layer friction
arising from the water viscosity attenuate waves (Hughes, 1993).
Further more the influence of surface tension on wave breaking as well as on wave
run-up, run-down and wave overtopping (especially for low layer thicknesses) cannot
be ignored. Schüttrumpf (2001) has estimated the influence of surface tension on
wave run-up velocities using the wave run-up velocity u A . Further more Schüttrumpf
(2001) estimated the influence of kinematics viscosity on wave run-up and wave
overtopping using the wave run-up velocity u A on smooth sea dike. Differences seem
to occur mainly for small overtopping rates and increase for longer and flatter slopes.
Wind is a very important factor for small overtopping rates. The observed differences
are very important for small overtopping discharges. Where scale model tests predict
zero overtopping where as prototype is not the case (Kortenhause et al, 2005 and De
Rouck et al, 2005).
According to Kortenhause et al (2005), it is difficult to quantify the scale effects with
reasonable accuracy. Consequently some simple rules for scale effect compensation
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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have to be extracted from the comparison of prototype and model data. Therefore, a
simple multiplication factor on small-scale model test’s overtopping/run-up data
should contain the following characteristics;
• Should increase with decreasing overtopping rate.
• Should be able to predict overtopping when in the model, incorrectly no overtopping
occurs due to scale effects.
• Should take into account if the core material grain size has been enlarged to avoid
porous flow Reynolds scale effects.
Apart from the scale effects, model effects also influence the results. One of the main
problems when generating waves in a flume is re-reflection of waves from the wave
maker. Although this effect can be minimised using an active absorption system
during wave generation, still there can be difference in laboratory results and
prototype measurements due to various other reasons. An overview of possible
reasons for differences in prototype and laboratory results are given in Figure 2.5.
Reasons for differences in prototype and laboratory results
accuracy of
measurements
scale effects
model effects
• differences in measuring
– waves (position, reflection
analysis)
– wave run-up
– wind / spray
• resolution of measuring
devices
• position of measuring
devices
– wave gauges
– wave run-up gauges
– layer thickness gauges
• quality of measurements
• influence of surface tension
on wave run-up and wave
overtopping
• influence of viscosity on
wave propagation
• influence of viscosity on
wave run-up and run-down
velocities
• influence of viscosity on
internal
flow
regime
(porosity
and
permeability)
• compressibility on wave /
wall
interaction
for
vertical structure.
• modelling of target spectra
(wave
generation
↔
nature)
• side wall effects on waves
• wind / spray effects
• currents
• reflection of waves / wave
absorption
• foreshore topography
• accurate modelling of
geometry
Figure 2.5: Overview of possible reasons for differences in prototype and laboratory
results (Kortenhause et al, 2005)
According to Oumeraci (1999a and 1999b) reliable results can only be expected by
fulfilling Froude’s and Reynold’s law, simultaneously. This is however not possible
so that scale effects cannot be avoided when performing scaled model tests. Also for
some model tests on sea dikes up to 25% higher wave run-ups were observed. But it is
still not clear whether this is due solely to scale effects (Kortenhause et al, 2005).
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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Since the researched on quantifying the scale and model effects are still under
discussion, influence factors are not used for interpretation of current research.
Although there are evidences for influence of wind on wave run-up on impermeable
slopes, wind effects is not taken into consideration. However results of this research
can be compared with other model tests since in most of the previous model tests
were performed without the wind effect.
2.7.3
Interpretation of Results-Transfer results to prototype conditions
This section describes the method of interpreting results in general and method to
transfer measured data in mode scale to prototype scale. This transferring is important
for comparison of the results with design guide lines and other studies.
Model verification
Correctly scaled hydrodynamic model does not require verification. Scaling
relationships (Froude’s, Reynold’s etc) has been thoroughly testes and proven correct.
As long as model has been carefully scaled and constructed, and it has been
determined that the scale and model effects are minimal, model is correctly
reproducing the hydrodynamic phenomenon (Hughes, 1993). For the current research
only a smooth dike slopes are used. Then most of the scaling effects are lesser
compared with the rough surfaces. Therefore, results can be can be scaled up to the
prototype scale and compare with the prototype scenarios.
Characteristic parameters
Characteristic parameter for the wave conditions for analyze the results were drawn
from both time-domain analysis and frequency-domain analysis.
For wave height for incidents waves, the significant wave height ( H s or H1/ 3 ), the
wave height exceeded by 2%; H 2% (Time domain analysis) and wave height H m 0
(Spectral analysis) are used.
Scaling up to prototype scale
Table 2.12 describes the important scale relationships. Since no verification is needed,
model results are scaled up using direct scale relationships.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
2.8
Objectives and Methodology (Revised)
After literature review objectives of the experimental study were revised and more
clear methodology was defined
Table 2.13: specific objectives of the model study
Objective
Revised objective
Remarks
1. Optimising layout of Optimise
the
crest 1:4 and 1:6 are the most
the crest construction for construction for 1:4 slope
common slopes. Therefore
different seaward slopes
model starts with 1:4 and
then results will be
extended to 1:6
2.
Identifying
the Identifying the unwanted Influence of crest drainage
unwanted flow conditions flow conditions at the will be on landward slope,
under the unfavourable landward slope under the hence only landward slope
storm conditions
unfavourable
storm is studied.
conditions
3. Identifying the best Identifying
the
drainage system
drainage system
best Only different diameter are
tested but with same
spacing
4. Develop guidelines for Develop guidelines for Only wave overtopping is
design of crest drainage estimate the overtopping analysed. Geotechnical and
dikes
and drainage of crest structural stability are not
drainage dike
studied
According to the literature overtopping volume per wave is much higher compared
the mean overtopping discharges. Therefore proposed crest basin might be too small.
Therefore 3 crest basins were selected for the testing. Buffer capacity of each crest
basin is given in table 4.9. Further overtopping flow velocities be reduced due the
damping effect of the crest basin. To damp the energy of overtopping flow, more
length across the dike is required. This reason also suggests a wider crest basin will be
more effective.
After referring the previous tests on overtopping layer thickness and overtopping flow
velocity it was found that comprehensive works on the seaward side has done. But
knowledge about the processes at the landward side is limited; Hence more attention
should put to collect more information on landward side of the dike.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
D.M.D.T.B. Dassanayake
32
Hydraulic Model Tests of Wave Overtopping
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3. Experimental Investigations
This chapter describe the model set-up and details about measuring techniques and
measuring equipments used during the current research. Final section of the chapter 3
describes the data analysis methodology and calibration of measuring equipments.
3.1
Model set up, Measurement Techniques and Test Programme
This section detailed description of the model setup and measurement techniques used
to during experiments to acquire required data. After that summary of the test
programme is given.
3.1.1
Model Setup
Wave flume at LWI
The model tests were performed in the small twin wave flume of LWI. The flumes are
about 90 m long, 1.25 m deep, and one has a width of 1.0 m, the other one being
2.0 m wide (Figure 3.1). All the model tests related to this research were done in 2m
wide flume.
2nd wav e f lume
1st wav e flume
wav e absorber
1.25 m
twin wav e generators
1.
00
windo w
m
00
2.
9. 10 m
m
c a.90 m
Figure 3.1: View of twin wave flumes at LWI
The side walls and the bottom of the flume are made of concrete. Three windows are
located at the model’s position in the 2m flume to observe and to video the cross
section, the breaking of the waves and other processes. The wave generators for both
wave flumes are from 2005 provided by HR Wallingford. They are both equipped
with an active wave absorption system and capable of generating solitary, regular and
random waves up to about 30 cm and wave periods between 1.5s and 6.0s in water
depth of 0.60 m to 0.80 m (Figure 3.1). Each test consists of 1000 waves and tests
conducted with active wave absorption system. This helps to carry out statistical
analysis of incident waves and wave overtopping.
D.M.D.T.B. Dassanayake
33
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
(a) General overview of twin-flume
depth = 1.25m
≈ 90m
b) Twin-Wave Paddle
2m
1m
Figure 3.2: Wave generation system in twin flumes at LWI
Construction
This section provides some constructional details of the model as used for all of the
configurations tested in the flume. Specific details of each of the configurations are
given in corresponding sections.
Details of overall construction
The outer slope is adjustable to 1:4 and 1:6 slopes. Whereas the inner slope is fixed to
1:3 slope. The inner slope was a separate construction as shown in Figure3.3 hence
the model could accommodate crest basins of different sizes.
Plywood
Crest Basin
SWL
Steel Beam
Concrete Block
Figure 3.3: Cross section of dike constructed at LWI
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Details of crest construction
First series of testing were done with the standard dike profile which is equivalent 3m
wide crest in prototype scale. For the first series of tests a crest basin was used with
the same dimensions (0.8 m deep and 2.0 m wide) as proposed by Nieuwenhuis et al.
(2005) (Configuration C4SS). After that, tests were repeated with different sizes of
the basins as shown in Fig 5. The basins have flexible depths which can be adjusted
depending on testing requirements. All the different crest basins were constructed
with flexibility to change drainage types (different pipe sizes from 0.225 m to 0.60 m
and different pipe intervals such as 10 m, 15 m, and 30 m etc in prototype).
In total seven pressure gauges were installed along the walls and the bottom of the
crest basin to measure the pressure variation in the basin. The pressure sensors at the
walls of the crest basin were at the same position for all the tests. The positions of the
pressure sensors at the bottom of the crest basin were changed for different basin
widths. Three wave gauges were installed inside the crest basin to identify the water
level inside the crest basin.
Test Configurations
Ten different configurations were tested including standard dike profiles for seaward
slopes of 1:4. Four basin sizes were tested for both slopes. Table 3.1 and figure 3.4
show the different configurations. Same landward slope; 1:3 was used for all the tests
configurations.
Table 3.1: Different dike configurations tested in LWI laboratory
Standard Dike Dimensions of Crest Basin: width (m) × depth (m)
Seaward
2.0 × 0.8
2.0 × 1.2
4.0 × 0.8
4.0 × 1.2
Slope
1:4
Std Dike
C4SS
C4SL
C4WS
C4WL
Tests were performed with random waves using a standard spectrum (JONSWAP).
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Standard Dike
Crest Basin
Drainage Pipe ( D = 400mm)
C4SS
C4SL
C4WS
C4WL
Figure 3.4: Details of crest construction for each model Configurations, 1:4 slope in
prototype dimensions
3.1.2
Measurement Techniques
Throughout the model tests a number of wave gauges, pressure cells and other
measurement devices were used. These devices are explained in more details in the
following subsections. Coordinates of the measuring devices are given in Annex L
Wave gauges
Resistance - type wave gauges were used to measure the water surface elevation. The
wave gauges used for the tests consist of two parallel electrodes of 60cm and 80 cm
respectively immersed into the flume water (see Figure. 3.5). Due to changes of the
water level the electrical resistance between these two wires change which also
changes the output signal given as voltage. Due to prior calibration tests, in which the
voltage for defined immersion depths is measured, a calibration factor for each wave
gauge is gained which allows the conversion of the recorded voltage signal in mV into
water surface elevation in meter. A typical signal of a wave gauge in the flume is
given in Figure 3.6.
D.M.D.T.B. Dassanayake
36
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Dike
80 cm
Figure 3.5: Multi-gauge array in front of the dike
Figure 3.6: Calibrated time series of a wave gauge (example)
With these resistance type wave gauges a scatter of ±5% with respect to the water
level can be expected. Wave multi-gauge arrays consisting of four wave gauges each
were used in the flume for later reflection analysis of the waves. At least three wave
gauges are required for the analysis of incident and reflected waves with the least
square method after Mansard & Funke (1980). Multi-gauge array in front of the
structure was placed according to the recommendations by Klopman and van der
Meer (1999). Both largest and smallest wave length were used to find the appropriate
distance form the structure.
D.M.D.T.B. Dassanayake
37
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Overtopping tank
An overtopping tank was installed behind the structure to measure the wave
overtopping discharge for some tests. The overtopping water was led into the tank by
means of a chute installed in the middle of the dike crest. The width of the chute was
23.1cm. The base area of the tank itself is 46 x 136 cm. By means of an electronic
weighing machine (Figure 3.8), on which the tank is placed, the weight of the
overtopping volume was acquired. Right next to the chute, a layer thickness gauge
was installed to identify the correlated single overtopping events.
measures in [cm],
drawin g not to scale
Bc
ov ertopping
tank
136
46
weighi ng
machine
Figure 3.7: Measurement devices for overtopping measurements
S ide v iew
1.35m
0.30m
ov ertopping container (0.186m³)
w eighing cell
w eighing cell
0.58m
mounting
Top v iew
1.35m
0.46m
w eighing cells
0.36m
0.58m
Figure 3.8: Weighing system for overtopping tank in the LWI flume
D.M.D.T.B. Dassanayake
38
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Typical records taken from these measurements are shown in Figure 3.9where the
mass of the water in the overtopping tank is plotted over the time.
0.15
Overtopping Volume [m3/m]
q = V/ttotal
ttotal
0.125
t7
t6
0.1
t4
0.075
t1
t2
V1
0.05
700
t3
t5
V7
V6
V5
V
800
900
V4 = Vmax
V2 V3
time [s]
Figure 3.9: Calibrated recording of wave overtopping including individual
overtopping events (example)
Pressure cells
Pressure cells with different capacities (from 0.075 bar to 0.7 bar) are available at
LWI Figure 3.10. The NATEC pressure cells have a natural frequency of 2kHz. They
are normally used to measure pressure on the surface of a structure or within the
structure. Pressure signals are amplified by pressure amplifiers and are usually not
filtered before being stored to hard disk. Seven pressure cells were installed inside the
crest basin to find the pressure fields around the crest basin.
Figure 3.10: Pressure cell used for model tests at LWI
D.M.D.T.B. Dassanayake
39
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Velocity propellers
Two types of velocity propellers were used to determine wave run-up and wave
overtopping velocities, micro propellers with a head diameter of 15 mm and mini
propellers with a head diameter of 22 mm (Figure 3.11). The SCHILDKNECHT
propellers can measure velocities up to 5 m/s or 10 m/s, respectively.
Figure 3.11: Schematic sketch and photo of velocity propellers used at LWI
Flow depth measurements
The flow depth on the slope was measured by conductivity gauges. These devices
were fixed at small height over the slope of the structure with two steel wires reaching
from the fixation point into the slope. Small holes in the wooden slope fixed the tips
of the gauges. The gauges were installed perpendicular to the slope. (Figure 3.12)
Layer thickness
gauge
Velocity propeller
Seaward edge of the crest
Figure 3.12: Velocity propellers and layer thickness gauges on the crest and seaward
slope
Camera positions and operation
During all model tests, video recordings were made showing the hydraulic processes
in front of, at and behind the dike. Special consideration and focus was laid upon the
processes in the crest basin. Two cameras were used at different positions
showing) the dike side view at the observation window in the side wall of the 2 m
flume, ii) the dike front viewed from a bridge stretching over both flumes and iii) the
rear slope in the 2 m flume from behind. These camera positions are shown in Figure
3.13 Since only two cameras are available positions ii) and iii) were used alternatively
depending on the configurations tested.
D.M.D.T.B. Dassanayake
40
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Wave absorber
Wave paddles
1m
2m
Wave gauges
bridge
window
Observed areas by means of video recording
Figure 3.13: Position of video cameras and observed areas during the tests
Preliminary calculations
Expected overtopping quantities for a normal sea dike for different test conditions
were calculated using the guidelines given in TAW (2002) (see equation 2.8). The
results of these calculations are given in Annex H. The results show that average
overtopping quantities are in a range of 0.1 l/m per second to 100 l/m per second. This
range reasonably covers the possible overtopping events under extreme conditions.
However, more attention was put to the range of 0.1 l/m per second to 15 l/m per
second, which is supposed to be the design range for the Crest Drainage Dike.
Taking these calculations into account and considering the general considerations in
section 3.1 the parameter variations as in Table 3.3 were selected.
Table 3.3: Selected test conditions for physical model test
(dimensions given in prototype scale)
Water
Depth
(m)
Rc (m)
Hs (m)
Tm0 (s)
Seaward
Slope
Basin
Dimension
(m)
Drainage Type**
(mm)
10.50
7.50
2.5
7.0
1:4
0.8 x 2.0
400 in 30m
intervals
11.25
6.75
2.9
8.9
0.8 x 4.0
500 in 30m
intervals
12.00
6.00
3.5
10.5
1.2 x 2.0
600 in 30m
intervals
12.75
5.25
3.8
12.6
1.2 x 4.0
14.7
no basin
** Drainage pipe diameter varied from 400 mm to 600 mm.
Combinations these of testing parameters resulted to about 275 tests in the flume.
D.M.D.T.B. Dassanayake
41
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
3.1.3
Test Programme and Procedure
The purpose of test variations was to analyse the influence of different parameters on
wave overtopping and related parameters (see Table 3.3). In Table 3.4 these
parameters have been combined so that a test matrix has been created which shows
the tests which were performed for a 1:4 slope.
Additionally, some of the tests were repeated, especially those performed for the
reference case in order to check for the repeatability of the test results. Some of the
tests were removed from the original plan for tests with larger crest basin. Because
larger crest basin trapped all most of the overtopping water and nothing expected on
the landward slope. Hence, those tests are unnecessary to be performed.
D.M.D.T.B. Dassanayake
42
Table 3.4: Overview of test programme for random waves and all configurations with 1:4 slope
Hs (m)
Tp(s)
d(m)
Dike
C4SS
C4SL
0.619
C4WS
C4WL
C4SS
C4SL
0.663
C4WS
C4WL
C4SS
C4SL
0.707
C4WS
C4WL
C4SS
C4SL
0.751
C4WS
C4WL
1.70
2.15
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
0.147
2.55
Figure: Standard dike model
3.05
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
3.60
1.70
2.15
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
0.171
2.55
3.05
3.60
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
1.70
2.15
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
0.206
2.55
3.05
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
3.60
1.70
2.15
0.224
2.55
3.05
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
Ratio
seaward slope, tan α
landward slope, tan β
freeboard Rc / H s
Nature*
1:3~1:8
1:3~1:5
1.0~2.5
Model
1:4
1:3
1.58~3.64
Hs / d
0.2~0.5
0.15~0.34
wave steepness, H s / L0
0.02~0.03
0.009~0.036
d / L0
0.1~0.18
0.042~0.168
breaker parameter, ξ0
0.75~1.50
3.60
1.25~2.45
*Schüttrumpf (2003)
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
3.2
Data analysis
Method of Data Analysis
First descriptions of concepts for data analysis are described in this section. Then
methodology used to analyse mean overtopping discharge, maximum volume per
overtopping wave, overtopping layer thickness and velocities are described in
following chapters. Results for the data analysis and discussion of the results given if
chapter 4.
During the model experimental study following data were collected
• wave conditions infront of the structure
•
wave overtopping volume per wave
•
flow depth and the flow velocity at seaward slope, crest and landward slope of
the dike
•
video records of wave overtopping and dissipation of energy in the basin
•
Pressure measurements inside the crest basin
•
Rate of drainage from drainage pipe.
Most of the design guidelines used 2% exceeding limit as a design criteria. Hence,
same concept adopted for the data analysis of this research. Most of statistical
parameters are describes as which exceeds 2% of incoming waves. Figure 3.14 gives
a overall view of crest drainage dike study.
Data analysis tools
L ~ DAVIS, data analysis and visualisation software developed by LWI was the main
tool for data analysis. L ~ DAVIS can perform reflection analysis, setting time frame,
statistical analysis of generated waves in both time and frequency domain, signal
filtering etc.
Incident waves
Two wave gauge arrays were set-up in the flume. One was infront of the wave maker
and the second one is 4.0m away for the toe of the dike. Measurements from the 2nd
wave gauge array are used for the reflection analysis (see 4.1). Hm0 and Tm-1,0 are used
as the characteristic parameters. All the model tests consist of 1000 waves. This
enables to perform statistical analysis on wave parameters (see figure 4.4 and 4.5).
Wave overtopping
Wave overtopping is affected by many factors. A methodology incorporate the
influence of the main parameters on wave overtopping events are discussed in this
section.
Overtopping water collected by 23.1 cm wide chute and then discharged it to tank
with weighing machine. Signal form the weigh machine was analysed to get the mean
overtopping discharge and overtopping volume per wave. From this results
overtopping volume per wave and mean overtopping discharge per one meter length
is calculated.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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Mean overtopping discharge is the most common and widely used parameter. Also
many studies have done on this topic. Therefore mote emphasis was given to mean
overtopping discharges and reduction in men overtopping discharges due the effect of
crest basin. As describes earlier mean overtopping discharges depend on the wave
breaking and breaker type. Therefore overtopping result related to breaking and nonbreaking waves are separated. First plotting started with the parameters given in the
TAW(2002). Then plots were made with new parameter to find the influence of crest
basin.(section 4.2).
However for initiation of erosion on the landward slope etc. determines by the
extreme events. Therefore wave overtopping parameters exceeded by 2% of
incoming waves and maximum overtopping volume per wave. Overtopping volume
per wave exceeded 0.1% of incoming waves (largest volume per 1000 waves) was
used to assess the performance of crest basin (see section 4.3)
Drainage from the crest basin
Water trapped in the crest basin was drain using a drainage pipe. This water collected
in a separate tank. Rate of discharge was measured by using two water level gauges.
Only one pipe was provided for the whole width of the flume There for the result,
drainage per one meter length was calculated.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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D.M.D.T.B. Dassanayake
46
Hydraulic Model Tests of Wave Overtopping
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1
2
3
Determination of relevant overtopping parameters related to wave overtopping
Experimental investigations (Small scale tests)
Literature
Methodology
1 Design parameters at dike toe
-Water Depth (d )
-Wave parameters ( H , T )
2
Flow field on crest
- Layer thickness (hC )
- Overtopping velocity (uC )
- Drainage from crest basin (qCDD )
3 Flow field on landward slope
- Layer thickness (hB )
- Overtopping velocity (uB )
- Overtopping rate (q )
- Overtopping volume per wave
(V0.01% )
Set of equation to predict overtopping flow parameters for Crest Drainage Dike
Figure 3.14: Methodology of the Crest Drainage Dike study
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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3.2.1
Calibration of Measuring Devices
Calibrations of measuring equipments are described in this section. After the
preliminary calculation, range of expecting values were decides and the equipments
were selected accordingly. Also methods of data analysis were considered before the
calibration procedure to
Five different type of measuring devices were used during the model testing. They are
Wave Gauges, Layer thickness gauges, Pressure cells, velocity Propellers and
Weighing machine. All the devices are calibrated using the HR wave data software.
Using the nominal parameters of the model, wave heights, overtopping layer
thicknesses, velocity were calculated and results were used to fix the rage for all the
measuring devices. It is important to find the range of expected values because it
helps to find the correct instruments for measurements (eg. if range of pressure
measurements are known, then selection of instrument is easy. If not either
instruments can be damaged due to high pressure or reading might not be accurate due
to very small reading. If the reading is very small then it is needed to me amplified,
then noise in the signal will be high.) After setting the gain appropriately each device
was calibrated as follows.
Wave Gauges
Usually wave gauges are calibrated just before the testing started. However when
same water is used for testing, no calibration is done until the nest filling (usually 34dats). When the flume is filled and water is calm, then gave known displacements
with 0.1m intervals. Altheas 5 readings were taken and then readings were fit to a
leaner relation ship to get the calibration factor.
Layer thickness gauges
Since layer thickness gauges are mounted in dry as well as all the gauges were
perpendicular to the dike slopes. Therefore external apparatus used to calibrate them.
However to achieve good accuracy, water form the flume is used. Depending on the
expected range of measurements each gauge is calibrated by giving known
displacements while recording the voltage reading. For smaller water layer gauges at
least 7 readings were taken and then those readings were fit to a line to obtain
calibration factor. All the time Goodness of fit (Gof) is checked and if the Gof is not
satisfactory (<0.99) then calibration is repeated. However during the calibration is
found that when the layer thickness is very small (<1mm) than gauges does not show
the linear relation ship. Therefore dike surface is drilled 1cm and wires were put
inside these hole. Before each test all the holes were filled with water to avoid any
possible errors. Layer thickness gauges are calibrated every time when flume is filled
with new water for testing (usually calibrations were done once in 3-4 days.
Pressure cells
Pressure cells were calibrated using the special instrument which can give known
pressures. Each pressure cell was fixed to this equipment and at least five readings
were taken covering the possible measuring range. Then as mentioned above, reading
the corresponding pressure values are plotted and a leaner relation was obtained.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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Propellers
LWI has a facility to calibrate velocity propeller. Apparatus consists of pipe rig and a
propeller. Speed (frequency of rotation ) of the propeller in the apparatus can be
controlled. This apparatus was calibrated and corresponding velocity for each
frequency of rotation is give. Therefore it is possible to set the velocity of the water in
side the ring pipes to a constant level and then values were taken using HR wave data
software and relation ship was found. For propellers at least 10 reading were taken
while increasing the flow velocity and decreasing the flow velocity. Figure 3.15
shows position of propeller during the calibrating and the devices to control the flow
speed in side apparatus.
Propellers were calibrated at the beginning of the test. Since outputs form the
propellers do not depend on the water quality, calibrations were checked once is every
4-6 weeks. However all the propellers we checked everyday for fine heirs and plastic
pieces which can disturb the movements of the propellers.
Direction of Flow
Propeller
Propeller inside apparatus
Panel and display control
speed of rotation
Figure 3.15: Calibration of velocity propellers
Weighing machine
Overtopping tank has a capacity approximately 170l. During the calibration, 5l of
water put to the tank and corresponding reading was taken. This procedure continued
till the tank was fully filled. Then found that the voltage out put for the weighing
machine has linear relation ship with amount of water in the tank. Then the calibration
factor is drawn from this relationship.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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4. Discussion of the Results
This chapter describes the key results of the model tests. Result from the various dike
configurations are compared with the previous formulae. Whenever present results
deviate from the known formulae, new formulae are developed. Method of data
analysis described in section 3.3.
4.1
Incident wave parameters at the toe of the dike
4.1.1
Definitions
All the calculations were done based on the incident wave parameter at the toe of the
dike. Second wave gauge array (see Figure 4.1) was used to perform reflection
analysis and to find the incident wave height and time periods. Low frequency waves
were filleted. For the tests with time periods 1.7s, 2.15s and 2.55s, 0.16Hz was used
and for the tests with 3.05s, 0.13Hz was used as the high pass filter. Figure 4.1 shows
some important definitions and parameter related to data analysis.
4.0m
dike crest
1.060m
wave gauge array
freeboard, Rc
0.619~0.751m
0.000
Figure 4.1: Definitions
4.1.2
Results from the wave analysis
First standard dike profile was tested for 10 wave conditions (see table 4.1) without
active absorption system of the wave maker. Then same tests were repeated with the
absorption system and results were compared to check the effectiveness of the
absorption system. Results are given in figure 4.2 and figure 4.3. Without active wave
absorption system, input and output wave parameter showed considerable deviations
form the expected conditions. Wave heights were 10% to 30% lower than the nominal
values (see figure4.2). Tp is 10% higher than the Tm0,-1TAW (2002). Hence results are
compared with the this ralashinshp. According to figure 4.2 wave periods showed in
average 15% higher wave periods than than expected. However tests with absorption
system shows closer values to expected time periods (in average 10% higher than the
expected). When compare the shape of the wave spectrum there is no considerable
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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difference, however one conclusion drawn is, the absorption system reduces unwanted
long waves.
Table 4.1: wave condition used to test the active absorption system
Hs (m)
0.147
Tp(s)
1.70
2.15
2.55
0.171
3.05
3.60
1.70
2.15
2.55
3.05
3.60
0.22
with absoption
without absoption
0.2
Hm0 [m]
0.18
H m 0 = 1.15 ⋅ H nom
0.16
0.14
0.12
H m 0 = 0.7 ⋅ H nom
0.1
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
Hnom [m]
Figure 4.2: measured wave height for the test with and without active absorption
system
4
with absoption
10%
without absoption
Tm-1,0 [m]
3.5
10%
3
2.5
Tp = 1.1 ⋅ Tm −1,0
2
1.5
1.50
2.00
2.50
3.00
3.50
4.00
Tpnom [m]
Figure 4.3: Relationship between Tp and Tm-1,0
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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Wave heights used for all the calculations are the incident significant wave height
H m 0 (Spectral wave height) at the toe of the dike. Significant wave height also defines
as the average of the highest one third of the waves H1/ 3 . In deep water both
definitions produce almost the same value, but situations in shallow water can be lead
to a difference of 10-15% (TAW, 2002). Figure 4.4 shows the measured values during
the tests with standard dike profiles. According to the Figure 4.4, H m 0 and H1/ 3 have
only 3% differences. Since Hm0/d =0.17~0.37, depth is not shallow enough for wave
breaking. Hence wave conditions infront of the dike can be considered as intermediate
water conditions (no wave breaking due to limited depths).
0.24
0.22
0.20
H s = 1.03H m 0
Hs [m]
0.18
0.16
0.14
0.12
0.10
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
Hm0 [m]
Figure 4.4: Relationship between Hm0 and H1/3
Maximum wave height for 1000 waves which follows Rayleigh distribution, given by;
H max = 1.86 H m 0
(4.1)
However according to the reflection analysis results, H max = 1.65H m 0 (Figure 4.5).
only in few cases with the higher water levels gives H max around 1.86 H m 0 . Apart
from these few tests all the other tests give lower H max value. Specially for the lowest
water (d=0.619m) level, all the H max just reach the 1.65 line. In general H max is lower
than the predicted conditions for the 1000 waves. Since water depths from the wave
maker to the toe of the dike was intermediate conditions, Largest waves broke while
approaching the dike. This explains the results. (nominal H max / d = 0.364 ~ 0.619 )
However the breaking effect on Hm0 is negligible.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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0.50
depth at dike toe = 0.619
0.45
depth at dike toe = 0.663
depth at dike toe = 0.707
Hmax [m]
0.40
0.35
0.30
depth at dike toe = 0.751
H max = 1.86 H m 0
0.25
0.20
H max = 1.65 H m 0
0.15
0.10
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
Hm0 [m]
Figure 4.5: Relationship between Hm0 and Hmax
4.1.3
Summary and evaluation of the results
According to the figure 4.2 active absorption system of the wave generator gives
better results. It reduces the unwanted long waves and gives closer spectrum shape as
the input spectrum. Even though reflection analysis results shows lower Hmax values
than predicted, Figure 4.4 confirms water depths infront of the dike were sufficient to
avoid wave breaking before reach the dike.
Also most of the tests resulted lower Hm0 (50% of the tests shows 90% to 100% of
nominal Hs value) than the nominal Hs value. This could be as a result of losses in
wave generation system, model effects and friction in the flume etc (see section 3.1)
However, only incident wave parameters from the reflection analysis used during data
analysis and most of the results are presented in dimensionless form, which takes the
changed in wave height into account. So even if there is difference in incident wave
parameter, it will not affect the results.
Even though some changes in wave height were observed, wave periods were
reasonably closer to the expected conditions. ). In current research low-frequency
waves were filtered. When the nominal peak period id 3.05s, the frequencies lesser
than 0.13Hz filtered and for all the cases filtering frequency, 0.16Hz was used.
Hm0 and Tm-1,0 at the toe of the dike were used for the all analysis. According to the
figure 4.4, Hs1/3 and Hm0 has only 0.03% difference. Also, peak period, Tp showed
deviations in a range of 0% to 100% from the nominal peak period. (average of 20%).
Therefore it is not possible to use Tp for the analysis. Hence Hm0 and Tm-1,0 were used
for the analysis.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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4.2
Mean overtopping discharge
This section describes the influence of basin dimensions and drainage pipe systems on
the mean overtopping discharges. All the results are compared with the mean
overtopping discharges of standard dike model tests. Whenever possible, figures are
given in dimensionless form.
Overtopping water collected at the landward edge of the dike crest and discharges in a
tank. Tank was placed on a weighing machine which gives the time series of weight
of the tank. Mean overtopping volume and overtopping volume per wave calculated
basin this time series (see figure 3.7 and section 3.3)
4.2.1
Mean overtopping discharges for standard dike profile
dimensionless overtopping discharge . ⎛
q
⎜
⎜
3
⎝ gH m0
⎞
S0 ⎟
tan α ⎟
⎠
Mean overtopping discharges for standard dike (Std Dike) profile should follows the
formulae given in TAW (2002) report (see formula 2.8).. Figure 4.6 and Figure.4.7
show results from the model tests. Breaking (Breaker parameter, ξ0 < 2 ) waves shows
good agreement with the guidelines where as overtopping for non-breaking (Breaker
parameter, ξ0 > 2 ) waves show little higher values than the average line given in
TAW (2002) report. However all the overtopping values are within the 95% confident
limits (5% envelope).
1.E-01
1.E-02
1.E-03
1.E-04
Rc=0.314~0.446 4
1
1.E-05
0.176m
5%
3
1
5%
Van der Meer; Q*=0.067 exp(-4.75 R*)
Van der Meer; Q*=0.067 exp(-4.3 R*)
Std Dike 1:4 Slope
1.E-06
1.E-07
0
0.2
0.4
0.6
0.8
1
dimensionless freeboard
1.2
1.4
1.6
1.8
2
2.2
⎛ Rc S 0 ⎞
⎟
⎜
⎜ H m 0 tan α ⎟
⎠
⎝
Figure 4.6: mean overtopping discharges for Standard Dike under breaking waves
D.M.D.T.B. Dassanayake
55
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
1.E-01
1.E-02
dimensionless overtopping discharge
1.E-03
1.E-04
Rc=0.314~0.446 4
1
1.E-05
0.176m
3
1
Van der Meer; Q*=0.2 exp(-2.6 R*)
Van der Meer; Q*=0.2 exp(-2.3 R*)
Std Dike 1:4 Slope
1.E-06
1.E-07
0
0.5
1
1.5
dimensionless freeboard
2
2.5
⎛ Rc
⎜⎜
⎝ H m0
3
3.5
4
⎞
⎟⎟
⎠
Figure 4.7: mean overtopping discharges for Standard Dike under non-breaking
waves
4.2.2
Influence of the crest basin on mean overtopping discharge
Mean overtopping results of the model tests with all the model configurations are
given in following sections (4.2.2.1 to 4.2.2.4). Breaking and non-breaking waves are
plotted separately. At the end summary of all the results are given.
First overtopping results with crest basin were plotted on the same figure as 4.6 and
4.7 in order to find the difference. (see figure 4.8, 4.9; results for configuration C4SS).
Vertical dotted line marks the region of zero overtopping tests. Then the best fit line
was found for the deviated points from TAW formulae, which lead to a new
overtopping formula for crest drainage dike. No significant reduction observed for
non-breaking waves.(figures 4.9.4.12, 4.15, 4.18)
Since results of the first analysis were scatter, then new series of plots were made
considering reduction in overtopping discharges.(figures 4.10,4.13,4.16 and 4.19)
⎛q
⎞
−q
(4.2)
Reduction = ⎜ StdDike C 4 SS ⎟ × 100%
qStdDike
⎝
⎠
Where ;
qStdDike = mean overtopping discharge for standard dike
qC 4 SS = mean overtopping discharge for crest drain age dike
(in this case C4SS configuration)
Then formula for a new reduction coefficient ( γ CDD ) is given (4.5)
γ CDD = mean overtopping reduction factor due to crest drainage
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
⎛
q
dimensionless overtopping discharge⎜
⎜
3
⎝ gH m0
⎞
S0 ⎟
tan α ⎟
⎠
Model configuration-C4SS
1.E-01
1.E-02
1.E-03
1.E-04
0.176m
Rc=0.314~0.44 4
1
1.E-05
3
5%
1
Van der Meer; Q*=0.067 exp(-4.75 R*)
Van der Meer; Q*=0.067 exp(-4.3 R*)
Std Dike 1:4 Slope
C4SS-25mm drainage
1.4<R*<2.0; Q*=10 exp(-8.3 R*)
1.E-06
1.E-07
1.E-08
0
0.2
0.4
0.6
0.8
1
1.2
⎛ Rc
dimensionless freeboard ⎜
⎜ H m0
⎝
5%
Zero
overtopping
area for C4SS
1.4
1.6
1.8
2
2.2
S0 ⎞
⎟
tan α ⎟⎠
Figure 4.8: mean overtopping discharges for C4SS under breaking waves
A new curve can be defined as formula 4.3 (valid only to C4SS configuration).
⎛
S0 ⎞
S0
q
Rc
⋅
= 10 exp ⎜ −8.3
⋅
⎟
(4.3)
⎜
H m 0 tan α ⎟⎠
tan α
gH m 03
⎝
with the valid range = 1.4<R*<2.0 , after 2.0 Q*=0 similarly from figure 4.11,4.14
and 4.17 new formulae developed and summarised in formula 4.4 and table 4.2
1.E-01
1.E-02
dimensionless overtopping dis.charge
1.E-03
1.E-04
Rc=0.314~0.44 4
1
0.176m
3
1
1.E-05
Van der Meer; Q*=0.2 exp(-2.6 R*)
Van der Meer; Q*=0.2 exp(-2.3 R*)
Std Dike 1:4 Slopei
C4SS - 25mm drainage
1.E-06
1.E-07
0
0.5
1
1.5
2
2.5
3
3.5
4
⎛ Rc ⎞
⎟⎟
H
m
0
⎝
⎠
dimensionless freeboard ⎜⎜
Figure 4.9: mean overtopping discharges for C4SS under non-breaking waves
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Reductions in mean overtopping discharges were calculated and plotted in figures
4.10, 4.13,4.16 and 4.19). Crest basin can trap all the water for smaller overtopping
discharge. But when the discharge is higher, then only certain percentage trapped in
crest basin. (see figure 4.10). Shaded areas show the overtopping discharges
equivalent to prototype scale. As shown in figure 4.10, model configuration C4SS
(basin =0.8m*2.0m in prototype scale) and reduce 5l/s per m (when
Hm0=2.5m~3.8m) by more than 90% but 15l/s per m can reduced only up to 70%
(when Hm0=3.8m). Average overtopping reduction curve for Q*<2.5E-4 is showed in
red dash line. However some tests shows lower reduction than the average, therefore
reduction line for mean overtopping prediction is set as 90%.
100%
overtopping reduction (%).
90%
15l/s per m for
Hm0 = 2.5m~3.8m
80%
70%
Proposed curve with
safety margine
60%
Average overtopping
reducution curve
50%
5l/s per m for
Hm0 = 2.5m~3.8m
40%
30%
C4SS - 25mm draiange, breaking waves
20%
C4SS - 25mm draiange, non-Breaking waves
10%
Q*>2.5E-4; -0.2221 ln(Q*)-1.9444
Q*<2.5E-4; reduction=90%
0%
1.00E-06
1.00E-05
1.00E-04
1.00E-03
⎛
q
⎜
dimensionless overtopping discharge ⎜
3
⎝ gH m 0
1.00E-02
1.00E-01
⎞
⎟
⎟
⎠
Figure 4.10: reduction in mean overtopping discharge for C4SS under all waves
Best fit for the figure 4.10 was found as follows.
⎡
⎛
q
*
−4
For Q > 2.5 ×10 then qCDD = ⎢ −0.2221× ln ⎜
⎜ gH 3
⎢
m0
⎝
⎣
And Q* < 2.5 ×10−4 then qCDD = 0.1× q
⎤
⎞
⎟ − 1.9444 ⎥ × q
⎟
⎥
⎠
⎦
(4.5)
Where qCDD = mean overtopping discharge of crest drainage dike
Since the formula is valid up to a certain Q*, this bondary condition value defines as
Q*CDD=Maximum dimensionless overtopping discharge which show 90% reduction
when the crest basin is present
Similar type of equation can be developed for the configuration C4SL, C4WS and
C4WL. Results are summarised in formulae 4.5 ,table 4.3 and table 4.4
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
C4SL
⎛
q
⎜
dimensionless overtopping discharge…
⎜
3
⎝ gH m0
⎞
S0 ⎟
tan α ⎟
⎠
1.E-01
1.E-02
1.E-03
1.E-04
Rc=0.314~0.446 4
1
1.E-05
1.E-06
0.176m
3
1
Van der Meer; Q*=0.067 exp(-4.75 R*) zero overtopping
Van der Meer; Q*=0.067 exp(-4.3 R*) area for C4Sl
Std Dike 1:4 Slope
C4SL-25mm drainage
1.2<R*<1.8; Q*=1exp(-7.2 R*)
1.E-07
1.E-08
0
0.2
0.4
0.6
0.8
1
1.2
1.4
⎛ Rc
dimensionless freeboard ⎜⎜
⎝ H m0
1.6
1.8
2
2.2
S0 ⎞
⎟
tan α ⎟⎠
Figure 4.11: mean overtopping discharges for C4SL under breaking waves
1.E-01
1.E-02
dimensionless overtopping discharge
1.E-03
1.E-04
1.E-05
Van der Meer; Q*=0.2 exp(-2.6 R*)
Van der Meer; Q*=0.2 exp(-2.3 R*)
1.E-06
Std Dike 1:4 Slopei
C4SL - 25mm drainage
1.E-07
0
0.5
1
1.5
dimensionless freeboard
2
2.5
3
3.5
4
⎛ Rc ⎞
⎜⎜
⎟⎟
⎝ H m0 ⎠
Figure 4.12: mean overtopping discharges for C4SL under non-breaking waves
D.M.D.T.B. Dassanayake
59
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
100%
90%
80%
15l/s per m for
Hm0 = 2.5m~3.8m
Average overtopping
reduction curve
overtopping reduction (%).
70%
60%
50%
8l/s per m for
Hm0 = 2.5m~3.8m
40%
30%
C4SL - 25mm draiange Breaking
waves
``
20%
C4SL - 25mm draiange Non-Breaking waves
Q*>4.95E-4; -0.2755 ln(Q*)-1.1945
10%
Q*<4.95E-4; Reduction=90%
0%
1.00E-06
1.00E-05
1.00E-04
1.00E-03
dimensionless overtopping discharge
1.00E-02
⎛
q
⎜
3
⎜
⎝ gH m 0
1.00E-01
⎞
⎟
⎟
⎠
Figure 4.13: reduction in mean overtopping discharge for C4SL under all waves
⎛
q
⎜
dimensionless overtopping discharge…
⎜
3
⎝ gH m0
⎞
S0 ⎟
tan α ⎟
⎠
C4WS
1.E-01
1.E-02
1.E-03
1.E-04
1.E-05
Rc=0.314~0.446 4
1
0.294m
3
1
0.235m
Van der Meer; Q*=0.067 exp(-4.75 R*)
Van der Meer; Q*=0.067 exp(-4.3 R*) zero overtopping
Std Dike 1:4 Slope
area for C4Sl
1.E-06
1.E-07
C4WS-25mm drainage
1.1<R*<1.75; Q*=2.1 exp(-7.9 R*)
1.E-08
0
0.2
0.4
0.6
0.8
dimensionless freeboard
1
1.2
1.4
1.6
1.8
2
2.2
⎛ Rc S 0 ⎞
⎜
⎟
⎜ H m 0 tan α ⎟
⎝
⎠
Figure 4.14: mean overtopping discharges for C4WS under breaking waves
D.M.D.T.B. Dassanayake
60
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
1.E-01
1.E-02
dimensionless overtopping discharge…
1.E-03
1.E-04
1.E-05
Van der Meer; Q*=0.2 exp(-2.6 R*)
Van der Meer; Q*=0.2 exp(-2.3 R*)
Std Dike 1:4 Slopei
C4WS - 25mm drainage
1.E-06
1.E-07
0
0.5
1
1.5
dimensionless freeboard
2
2.5
3
3.5
4
⎛ Rc ⎞
⎜⎜
⎟⎟
⎝ H m0 ⎠
Figure 4.15: mean overtopping discharges for C4WS under non-breaking wave
100%
90%
Average overtopping
reduction curve
overtopping reduction (%)…
80%
15l/s per m for
Hm0 = 2.5m~3.8m
8l/s per m for
Hm0 = 2.5m~3.8m
70%
60%
50%
40%
30%
C4WS - 25mm draiange, Breaking waves
20%
C4WS - 25mm draiange, Non-Breaking waves
10%
0%
1.00E-06
``
Q*>4.4E-4; 0.2941 ln(Q*)-2.3773)
Q*<4.4E-4; Reduction=90%
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
⎛
⎞
q
⎜
⎟
dimensionless overtopping discharge ⎜
3 ⎟
⎝ gH m 0 ⎠
Figure 4.16: reduction in mean overtopping discharge for C4WS under all waves
D.M.D.T.B. Dassanayake
61
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
One of the important characteristics observed during the model tests with crest basin
is, model tests with same dimensionless freeboard gives different dimensionless
overtopping results ranging form 0 to 1×10−5 (see figure 4.17 vertical line at R*=1.6)
(according to the figure 4.18 full range is 0 to 1×10−2 ). Some of the reasons for this
observation are;
1. Two different test where one tests has a higher free board and a higher wave
height where as the second test with lower values, will lead to a same R* value
too. But combination of larger free board and the larger wave height will give
few but larger overtopping events which cannot be handled by the buffer
capacity of the crest basin. But when the combination of smaller parameters
will give a large number of smaller overtopping events and the buffer capacity
is enough for there smaller events. Then test with crest basin shows not
overtopping although standard dike test shows same overtopping for both
cases. (only applicable to non breaking waves)
2. when two tests with different R* values and different breaker parameters are
plotted with standard axis for breaking waves, can lead to same dimensionless
freeboard. For an example if smaller R* divided by smaller ξ0 and Larger R*
divided by larger ξ0 could result same figure. This could give same mean
overtopping discharges for Std Dike tests. But when the crest basin is
introduced, it works well with the smaller wave lengths but not with the
relatively longer waves. Then test results with crest basin will show different
mean overtopping discharges for these two cases.
C4WL
⎛
q
dimensionless overtopping discharge…
⎜
⎜
3
⎝ gH m0
⎞
S0 ⎟
tan α ⎟
⎠
1.E-01
1.E-02
Q* in a range of
0~10-4 for same R*
1.E-03
Rc=0.314~0.446 4
1
1.E-04
0.294m
3
1
0.235m
1.E-05
Van der Meer; Q*=0.067 exp(-4.75 R*)
1.E-06
Van der Meer; Q*=0.067 exp(-4.3 R*)
Std Dike 1:4 Slope
1.E-07
zero overtopping
area for C4Sl
C4WL-25mm drainage
1.2<R*<1.7; Q*=9 exp(-8.8 R*)
1.E-08
0
0.2
0.4
0.6
0.8
1
dimensionless freeboard
1.2
1.4
⎛ Rc
S0
⎜
⎜ H m 0 tan α
⎝
1.6
1.8
2
2.2
⎞
⎟
⎟
⎠
Figure 4.17: mean overtopping discharges for C4WL under breaking waves
D.M.D.T.B. Dassanayake
62
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
1.E-01
1.E-02
dimensionless overtopping discharge…
1.E-03
1.E-04
1.E-05
Van der Meer; Q*=0.2 exp(-2.6 R*)
Van der Meer; Q*=0.2 exp(-2.3 R*)
1.E-06
Std Dike 1:4 Slopei
C4WL - 25mm drainage
1.E-07
0
0.5
1
1.5
2
2.5
3
3.5
4
⎛ Rc ⎞
⎜⎜
⎟⎟
⎝ H m0 ⎠
dimensionless freeboard
Figure 4.18: mean overtopping discharges for C4WL under non-breaking wave
100%
15l/s per m for
Hm0 = 2.5m~3.8m
90%
overtopping reduction (%)…
80%
70%
Average overtopping
reduction curve
60%
50%
40%
30%
20%
10%
0%
1.00E-06
C4WL - 25mm draiange, breaking waves
C4WL - 25mm draiange, non-breaking waves
Q*>7.2E-4; 0.2436 ln(Q*)-1.8598
Q*<7.2E-4; Reduction=90%
1.00E-05
1.00E-04
1.00E-03
dimensionless overtopping discharge
⎛
q
⎜
3
⎜
⎝ gH m 0
1.00E-02
1.00E-01
⎞
⎟
⎟
⎠
Figure 4.19: reduction in mean overtopping discharge for C4WL under all waves
D.M.D.T.B. Dassanayake
63
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Summary and evaluation of the results
In the section 4.2, all the figures showed different best fit lines for each plot. But a
formula should be presented in more general form. Therefore this section summarised
the all the results shown in figure 4.8 to 4.19 and present in more general form.
Results of the mean overtopping plots
From figures 4.8, 4.11, 4.14, and 4.17, a formula can be found. This formula has can
be written as,
q
gH m 03
⋅
⎛
S0 ⎞
S0
Rc
= CCDD ,1 exp ⎜ −CCDD ,2
⋅
⎟
⎜
tan α
H m 0 tan α ⎟⎠
⎝
(4.6)
Formula 4.6 can be written in more simplified form as;
Q* ⋅
tan α
ξ0
⎛
R* ⎞
= CCDD ,1 exp ⎜ −CCDD ,2 ⋅ ⎟
ξ0 ⎠
⎝
Dimensionless coefficients for the formula 4.3 are given in table 4.3. if R* value is
smaller than the valid range then no reduction in mean overtopping is expected. If R*
value is larger than the valid range then at least 90% reduction in mean overtopping is
expected. This formula also valid only for 1:4 smooth dike profiles and only for the
tested crest basin configurations with 25mm diameter drainage pipes. (400mm
diameter in prototype dimensions)
Table 4.2: Coefficient for the formula 4.6
Configuration
Valid range
CCDD1
CCDD2
C4SS
10
8.3
2.0>R* >1.4
C4SL
1
7.2
1.8>R* >1.2
C4WS
2.1
7.9
1.75>R* >1.1
C4WL
9
8.8
1.2>R* >1.7
Results of the overtopping reduction plots
Based on above results new reduction factor, γ CDD can be introduced.
γ CDD = overtopping reduction factor due to crest drainage
mean overtopping discharge of crest drainage dike, qCDD is given by
⎡
⎤
⎛
⎞
q
⎟ − BCDD ⎥ × q
For Q* >Q*CDD ; qCDD = ⎢ ACDD × ln ⎜
(4.7)
⎜ gH 3 ⎟
⎢
⎥
m0 ⎠
⎝
⎣
⎦
*
*
And Q < Q CDD; qCDD = 0.1× q
Where;
qCDD = mean overtopping discharge for the crest drainage dike
Q*CDD = maximum dimensionless overtopping discharge which show 90% reduction
when the crest basin is present
D.M.D.T.B. Dassanayake
64
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
ACDD, and BCDD are dimensionless coefficients found experimentally and given in
table 4.3. These formulae valid only for 1:4 smooth dike slopes. Drainage pipes are
25mm diameter which is equivalent to 400mm diameter in prototype in 30m interval.
When the Q* < Q*CDD then crest drainage dike can reduce more than 90% of
overtopping. 90% is a more conservative value, but this value is decided for designing
purposes. Also when the mean overtopping discharge is smaller then q → 0 .But this
is not included in formula 4.1 inorder to make is more simple. In reality even the
model scenarios with smaller input parameters can create higher random blues
depending on see conditions. Therefore there should be some margin for safety.
Configuration
C4SS
C4SL
C4WS
C4WL
Table 4.3: Coefficient for the formula 4.7
ACDD
BCDD
Q*CDD
Valid range
-0.2221
-0.2755
-0.2941
-0.2436
Q* > Q*CDD
Q* > Q*CDD
Q* > Q*CDD
Q* > Q*CDD
1.9444
1.1945
1.3773
1.8598
2.5E-04
4.95E-04
4.40E-04
7.20E-04
From the formula 4.1, reduction factor can be derived as shown in table 4.4
qCDD = γ CDD × q
(4.8)
Table 4.4: Overtopping reduction factor, due to CDD
Q* > Q*CDD
⎡
⎛
⎢
⎣
⎜ gH 3
m0
⎝
γ CDD = ⎢ ACDD × ln ⎜
q
Q* < Q*CDD
⎤
⎞
⎟ − BCDD ⎥
⎟
⎥
⎠
⎦
γ CDD = 0.1 **
⇒ γ CDD = ⎡⎣ ACDD × ln ( Q* ) − BCDD ⎤⎦
For the case of Q* < Q*CDD the reduction factor is given as a constant. This does not
mean that maximum overtopping reduction of crest drainage is only 90%. According
to the model results, crest drainage dike can reduce relatively low mean overtopping
discharges by 100%. However the buffer capacity of the crest drainage dike depends
on the amount filled by the previous overtopped wave too. Hence even in smaller
overtopping events there is an uncertainty if two larger waves are coming one after
the other. Then if the first wave fills the crest basin, the second wave can overtopped.
Therefore it is not safe to assume 100% even model test shows 100% reduction. (also
see scale effects). Therefore it is decided to use 90% as the maximum reduction due to
crest drainage dike.
D.M.D.T.B. Dassanayake
65
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
4.2.3
Influence of drainage pipes on mean overtopping discharge
This section compares the result with different drainage pipes sizes with previous
tests. Nominal wave parameter used for testing are Hs=0.206m and Tp=3.05s. Four
different freeboards are used and in total 32 testes were preformed with 32mm
(500mm in prototype scale) and 38mm (600mm in prototype scale) drainage pips
diameters. In addition results from the 25 other tests were used (20 from 400mm
drainage pipes tests and 6 from no basin testes).used for comparison. Results of the
analysis are described below.
During model test, single pipe was set at the centre of the crest basin (crest drainage)
to drain the water collected in the crest basin. Total width of the model is 2m, but
according to 1:17 scale, 30m c/c equivalent to 1.765m. Since drainage outlet was used
to model drainage pipe. Equivalent diameter for the drainage calculated as follows.
Additional amount of water to be pumped, if the normal discharge is q then new
discharge will be q’
q’ = 2m / 1.74m = 1.133 q
Table 4.5: Selection of pipe diameter to model tests
Prototype c/c
Diameter in
diameter in model Adjusted diameter
Distance
prototype (m)
1:17(m)
in model 1:17(m) *
30
0.400
0.024
0.025
30
0.500
0.029
0.032
30
0.600
0.035
0.038
*To discharge 1.133 time q, diameters increased accordingly;
Formula 2.16 is used for the calculations of drainage discharges for the crest basin.
Calculated drainage discharges for different fill levels are given in table 2.12. Further
the same formula used for the calculation of Qdrain in table 4.7. During the model
testing, drained water was collected and average rate of drainage was calculated.
Measured average drainage discharges for tests with different drainage pipe diameter
are given in table 4.7. Reduction percentage calculated using the formula 4.10.
⎛Q
− Qmeasured ⎞
(4.10)
* Reduction = ⎜ calculated
⎟ × 100%
Qcalculated
⎝
⎠
Q = Cdrain × A × v
and
v = 2 g (Δh)
(4.11)
Table 4.7: Reduction in maximum drainage discharge due to losses
configuration
pipe diameter
(mm)
calculated Q
3
measured Q
Reduction %*
3
Qdrain (m / s / m) Qdrain (m / s / m)
C4SS
25
32
38
2.79E-04
4.68E-04
6.74E-04
1.70E-04
2.74E-04
3.22E-04
39%
42%
52%
C4SL
25
32
38
3.26E-04
5.42E-04
7.77E-04
2.11E-04
2.64E-04
3.86E-04
35%
51%
50%
D.M.D.T.B. Dassanayake
66
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
By taking the average reduction from table 4.7, discharge coefficient for drainage
pipes can be found as, Cdrain =0.55. To provide the drainage CDD, new coefficient
should be used.
In order to find the maximum drainage capacity of the 25mm (400mm in prototype
scale) diameter pipe at 6mm put depth (top most edge of the entrance pipe is 6mm
lower than the bottom level of crest basin in model scale and in prototype scale
entrance pipe is 10cm lower than to bottom level of the crest basin) , two controlled
tests were carried out. (see figure 4.20) During the test crest basin was fully filled.
When both output files are plotted in L~DAVIS (the software used for the data
analysis and visualization) in same time scale, test with waves and fluctuating water
level shows higher gradient (see annex F) than the controlled test. This means
discharge is higher when the waves are presented and when basin is filled with the
overtopping water. Preliminary investigations show controlled test can drain only
42% of the calculated drain discharge rate in average where as measured discharge of
the model tests shows in average of 55% of the calculated drain discharge But it is
very difficult to draw a conclusion due to limitations in data. This problem is being
investigated.
0.294m
Seaward
side
1.06m
0.989m
Landward
side
0.071m
Drainage pipe
D=25mm
Figure 4.20: sketch of crest basin used for controlled drainage test to find max Q drain
When a wave overtopped the CDD, total amount of water flows in three different
direction. First, flowing back to the seaward side, second flowing over the landward
slope and flow through the drainage pipes (Figure 4.21). during the tests with wide
crest basin (C4WS and C4WL) it was observed that some amount of water flows back
to the seaward side. Then total overtopping discharge can be expressed n formula
4.12.
Qtotal = Qdrain + qCDD + Qreturn
(4.12)
Qtotal = total mean overtopping discharge
Qdrain = mean discharge rate of the drainage pipes in crest basin
qCDD = mean overtopping discharge over the landward side of the dike ( qCDD )
Qreturn = return flow to the seaward side due to reflection effect of the crest basin
D.M.D.T.B. Dassanayake
67
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
seaward side
landward side
Q1=Qreturn
Q2=qCDD
Qtotal
Q3=Qdrain
Figure 4.21: discharge balance of overtopping water at dike crest
However it is difficult to quantify the amount flows back to the seaward side. Hence
Figure 4.22 is plotted. According to Figure 4.22, Qreturn component is relatively lower
and can be neglected for the calculations of the narrow crest basins (2.0m wide in
prototype scale). Qreturn is less than 0%-15% for narrow crest basin where as 10% to
30% for wider (4.0m wide in prototype scale) crest basins. (see figures A1 and A2)
dimentionless [Qdrain+q] for CDD ...
1.E-02
C4SS, drainage; D=25mm
C4SS, drainage; D=32mm
C4SS, drainage; D=38mm
C4SL, drainage; D=25mm
C4SL, drainage; D=32mm
C4SL, drainage; D=38mm
C4WS,drainage; D=25mm
C4WS, drainage; D=32mm
C4WS, drainage; D=38mm
C4WL, drainage; D=25mm
C4WL, drainage; D=32mm
C4WL, drainage; D=38mm
15%
30%
15%
30%
30%
1.E-03
1.E-03
⎛
q
⎜
⎜
dimensionless overtopping discharge for Std Dike ⎝ gH m 0 3
1.E-02
⎞
⎟
⎟
⎠
Figure 4.22: overtopping discharge by pipes related to total overtopping discharge.
All the tests to find the influence of the drainage capacity were done with the nominal
wave height of 0.206m and nominal peak period of 3.05s. This conditions result non
breaking waves with dimensionless freeboard of 1.5~2.14 (red shaded area in Figure
1.23 ). According to the Figure. 4.23 dimensionless mean overtopping discharges
gives quite high scatter for values of this range. As a result tests with mean
D.M.D.T.B. Dassanayake
68
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
overtopping discharges with different diameters of drainage pipes gave scatter results.
Further if one test repeated several times there is a 20% scatter in overtopping results.
Therefore it is difficult to draw a relationship with few test results.
Range of dimensionless freeboards covered during model tests with Std Dike and
other configuration with 25mm diameter drainage pipe are shaded in green (R*
=1.5~3.0)
Rc
= 1.5 ~ 2.14
H m0
Rc
= 1.5 ~ 3.0
H m0
Figure 4.23: input parameter range for tests with different drainage pipes
[Source : TAW 2002]
Percentage of water discharged by the drainage pipes are plotted against
dimensionless overtopping discharge of Std Dike in Figure 4.24
.
Qdrain = qStdDike − qC 4 SS
Percentage discharge by pipes (percentage trapped in the crest basin)
Q
= drain ×100%
qStdDike
D.M.D.T.B. Dassanayake
(4.13)
(4.14)
69
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
100%
Proposed curve for max drainage
% discharged by pipes , C4SS..
90%
80%
70%
15l/s per m for
Hm0 =2.5m~3.8m
25mm drainage
32mm drainage
38mm drainage
max drainage
60%
50%
40%
30%
20%
10%
0%
1.E-11
0
y = -0.1225Ln(x) - 0.4494
y = -0.132Ln(x) - 0.5239
R2 = 0.9503
R2 = 0.9685
y = -0.1323Ln(x) - 0.5711
R2 = 0.9762
2.E-03
4.E-03
6.E-03
8.E-03
1.E-02
dimensionless overtopping discharge for Std Dike
Figure 4.24: percentage of overtopping water discharged through drainage pipe
(C4SS)
As shown in Figure 4.24 discharges from the drainage pipes are smaller percentages
(10%-40%) of the total overtopping volume. Therefore influence of the drainage
diameter cannot be seen clearly. However according to the Figure 4.23, larger
diameter drainage pipes resulted higher discharges through the drainage pipes, which
reduce the mean overtopping discharge on the landward slope if the total mean
overtopping discharge remains same during the test with Std Dike profile and C4SS..
The tests with larger mean overtopping discharges have lesser contribution from the
drainage where as tests with smaller mean overtopping discharges have more
contribution from the drainage to the Qtotal. Then if Qtotal increases due to the above
explained reason, reduction in overtopping discharge, q cannot be seen clearly (see
Figure 4.25). But test with smaller mean overtopping discharges shows a reduction in
dimensionless overtopping discharges. (see figure 4.25)
Curve corresponding to 38mm drainage is extended to meet the 100% drainage. Then
according to Figure 4.24, even the 38mm drainage pipe (In prototype scale 600mm)
can reduce 15l/s per m discharge by 7.5 to 9.0 l/s.
D.M.D.T.B. Dassanayake
70
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
100%
C4SS, drainage; D=25mm
% reduction in dimensionless me
overtopping discharge, C4SS
90%
C4SS, drainage; D=32mm
80%
C4SS, drainage; D=38mm
70%
60%
50%
40%
30%
20%
10%
0%
1.E-03
1.E-02
dimensionless overtopping discharge for Std Dike (q/(g*H3)1/2)
Figure 4.25. Reduction in mean overtopping discharge with different drainage pipe
(C4SS)
To find the boundary condition of drainage, some tests were done without any basin
(see Figure 4.26). In other words only a gap with same width as the crest basin was
left and tests with larger mean overtopping discharges were repeated. In Figure 4.24,
these results are shown as max discharge. Since only two tests were done with same
wave conditions it is difficult to predict a curve. However a proposed line for the
maximum drainage is given in Figure 4.25.
0.176m
0.118m
Seaward
side
1.06m
q
Qtotal
Landward
side
Qdrain
Water free fall
Figure 4.26: model setup for tests without crest basin
Percentage of overtopping water discharged through drainage pipe for other model
configurations also shows the same relationship as Figure 4.24 (see annex-D)
D.M.D.T.B. Dassanayake
71
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Mean overtopping discharges for different crest basins are plotted against the mean
overtopping discharge for Std Dike. Results of the tests with 25mm diameter drainage
pipes were used for better comparison. Tests with no basin (see Figure 4.27) give
boundary condition of maximum buffer capacity. This is the theoretical maximum
reduction for the narrower crest basin (2m wide in prototype scale).
1.E-02
C4SS-Breaking waves
C4SS-non-breaking waves
mean overtopping CDD [m3/s per m] .
1.E-03
15 l/s per
1.E-04
1 l/s per m
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
3
mean overtopping Std Dike [m /s per m]
Figure 4.27: reduction in mean overtopping discharge (in model scale)
1.E-02
Breaking waves
non breaking waves
1.E-03
no basin
15l/s per m
Hm0=2.5m~3.8m
dimensionless mean overtopping C4SS
1.E-04
1.E-05
1l/s per m
Hm0=2.5m~3.8m
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
⎛
q
⎜
dimensionless mean overtopping Std Dike ...
⎜ gH 3
m0
⎝
1.E-02
⎞
⎟
⎟
⎠
Figure 4.28: reduction in dimensionless overtopping discharge
D.M.D.T.B. Dassanayake
72
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
As shown in the Figures 4.27 and 4.28 mean overtopping of 15l/s per m (in prototype
scale) can only be reduced to 4.9l/s per by introducing crest basin with 2.0m wide and
0.8m deep and 400mm drainage in 30m interval (in prototype scale). Curve for the
maximum drainage is not reliable due to lack of data point. But according to
constructed curve 15l/s per m can be reduced to 1 l/s per meter by with theatrical
structure which has unlimited capacity and drainage but with width of 2m. As the
buffer capacity increases more overtopping can be reduced summary of all the curves
related to different crest basin configurations are given in Figure 29 and Figure 30.
All curves for different configuration are given in annex E..
1.E-02
mean overtopping C4SL
CDD [m3/s per m] .
1.E-03
1.E-04
C4SS
C4SL
C4WS
C4WL
no basin
15l/s per m
15l/s per m
1.E-05
1.E-06
Predicted line
for max
discharge for
4m basin
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
3
mean overtopping Std Dike [m /s per m]
Figure 4.29: reduction in mean overtopping discharge (in model scale)
Curves shown in Figures 4.27, 4.28, 4.29 and 4.30 are difficult to express in
mathematical terms. There is no simple mathematical function match with those
curves. Hence Figures 4.29 and 4.30 can be used for the prediction of mean
overtopping discharges.
At the end of the model tests programme 6 tests were conducted with out any crest
basin and leaving only a gap at the crest to find the maximum overtopping discharge
for 2m wide (in prototype scale. But no tests were done without the crest basin for 4m
wide (in prototype scale) basins. Hence curve for latter is predicted using the available
data. (see Figures 4.29 and 4.30)
D.M.D.T.B. Dassanayake
73
Hydraulic Model Tests of Wave Overtopping
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1.E-02
Q* CDD [m3/s per m] .
1.E-03
1.E-04
C4SS
C4SL
C4WS
C4WL
no basin
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
Q* Std Dike
Figure 4.30: reduction in dimensionless overtopping discharge
Summary and evaluation of results
Summary of the data analysis for section 4.1 (page 51) and section 4.2.1 and 4.2.2
(page 61-62) are given under each section. In this section results from section 4.2.3
are summarised.
Coefficient of discharge
First discharge coefficient for the drainage pipes (formula 4.11) is found as
Cdrain = 0.55
Reflection of overtopping water
Wider crest basin (4.0m wide in prototype scale) can reflect up to 30% of the mean
overtopping discharge back to the seaward side. But narrower crest basins (2.0m wide
in prototype scale)does not show significant reflection.
Influence of Drainage pipes
Selected conditions for the tests with different drainage diameter are limited to high
overtopping test with non-breaking waves. These high overtopping events has
significant scatter (see figure 4.23). Therefore it is difficult to draw a clear conclusion.
However by extrapolating the curves following results were found (Table 4.8). Since
these result obtained from extrapolation of the overtopping reduction curves,
verification is required. Therefore figure 29 and 30 developed comparing men
overtopping discharge and the dimensionless mean overtopping discharge. These
curves can be used to find overtopping discharges with crest basin. Table 4.9
indicated presents the expected overtopping discharges for different basin
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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configurations. Similar to table 4.8, table 4.9 also gives the resultant mean
overtopping discharges for 15l/s per m mean overtopping discharge for standard dike.
Table 4.8: mean overtopping reduction by 600mm drainage pipe in 30m intervals for
non breaking waves.
percentage
resultant mean
configuration
drainage pipe
reduction of 15l/s
overtopping
(width*depth)**
[mm]
per m case
discharge [l/s/m]
C4SS (2.0*0.8)
600
37%~46%
9.50~8.10
C4SL (2.0*1.2)
600
47%~56%
8.00~6.60
C4WS(4.0*0.8)
600
42%~50%
8.70~7.50
C4WL(4.0*1.2)
600
62%~76%
5.70~3.60
Note: all the dimensions are given in prototype scale [ H m 0 ≈ 3.4m and Tm-1,0 ≈ 12.5s ]
Then mean overtopping discharges for all the configurations with 25mm drainage
(400mm in prototype) were compared with maximum possible drainage in plots 4.274.30.According to figures, “no basin” tests can reduce 15l/s per m to 1l/s per m. non
of the other configuration can reach this target see (table 4.9). These values are valid
for both breaking and non breaking waves
Table 4.8: mean overtopping reduction by different model configurations-from figure
4.29 .
(with 400mm drainage pipe in 30m intervals)
Percentage
resultant mean
configuration
drainage pipe
reduction of 15l/s
overtopping
(width*depth)**
[mm]
per m case
discharge [l/s/m]
C4SS (2.0*0.8)
400
47%
8.00
C4SL (2.0*1.2)
400
70%
4.50
C4WS(4.0*0.8)
400
72%
4.25
C4WL(4.0*1.2)
400
80%
3.00
Note: all the dimensions are given in prototype scale
‘
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
4.3
Overtopping volume per wave
overtopping volume per wave, Std Dike[m3 per wave per m]
This section gives the results from maximum overtopping volume per wave analysis.
Since each test consists of 1000 waves, the maximum overtopping volume per wave
can be given as V0.1%. Figure 4.31 shows the maximum volume per 1000 incoming
waves. For smaller overtopping events, the volume per maximum event is closer to
1000 times of q (mean overtopping discharge) and for the larger events it is around
100 times q. Further the maximum volume per wave per 1000 waves gives the
maximum discharge for 1000 waves. Maximum volume per wave flows over a 2-3
second period depending on the wave length, giving the maximum discharge at the
landward slope of the dike. Therefore by dividing the maximum volume per wave
(V0.1%) by the relevant wave period (Tm-1,0), the maximum discharge during a 1000
wave period (1000 incoming waves) was found as 575 to 87 times of q depending on
wave period. (see table 4.10)
1.E+00
1.E-01
1.E-02
breaking waves
non-breaking waves
1.E-03
1.E-04
1.E-06
Vmax=1000q
Vmax=100q
1.E-05
1.E-04
1.E-03
1.E-02
[m33/s
m] per m]
overtopping discharge, Std Dike [m
perper
wave
Figure 4.31 overtopping volume per wave, V0.1% (in model scale)
Table 4.10: maximum discharge due to maximum volume per wave for standard dike
Model Scale
q
Vmax,0.1%
Vmax,0.1%
Vmax,0.1%
q
Tm −1,0
Prototype Scale
qmax due to
Vmax,0.1%
1.00E-06
[m3 per
wave]
1.E-03
977
454-575
4.55E-0~5.75E-04
1.00E-05
5.E-03
457
190-240
1.89E-03~2.40E-03
1.00E-04
2.E-02
186
87-110
8.66E-03~1.10E-02
[m3/s/m]
D.M.D.T.B. Dassanayake
[m3/s/m]
q
Vmax,0.1%
qmax / q
0.07
[m3 per
wave]
282.42
31-41
0.70
1320.98
150-190
7.01
5381.43
610-770
[m3/s/m]
76
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Overtopping volume per wave and the buffer capacity of the crest basin,
One of the main factor contribute to the performance of crest drainage dike is buffer
capacity of the crest basin. Argument here was when the buffer capacity if sufficient
to take the maximum volume of overtopping wave for 1000 incoming waves
(Vmax,0.1%.), then there will not be any overtopping. However model results show
different behaviours. In figure 4.32 overtopping volume per wave for the standard
dike (Std Dike) plotted against the mean overtopping discharge. Also buffer capacities
of all the configurations are showed. Then if the above argument is valid then there
will not be any overtopping for the test with lower Vmax,0.1%.
As figure 4.31 shows, there is a reduction in Vmax,0.1%. for the model tests with crest
basin compared with the Std Dike test results. But is not a significant reduction as
expected. Only during C4WL (in prototype scale 1.2m*4m)model configuration
where the buffer capacity increased by 200% (see table 4.11) considerable reduction
has observed. In conclusion above mentioned argument is only partially valid, but
there is not much reduction as expected. (DHV, (2005) expected to reduce 15l/s per m
in 1l/s per m).
Table 4.11: percentage increment in buffer capacity for each model configuration
Configuration
% increment in buffer capacity
C4SS
C4SL
C4WS
C4WL
overtopping volume per wave, Std Dike
1.E+00
50%
100%
200%
breaking waves
non-breaking waves
Vmax=1000q
Vmax=100q
buffer C4SS
buffer C4SL
buffer C4WS
buffer C4WL
1.E-01
1.E-02
1.E-03
1.E-04
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
mean overtopping discharge, Std Dike
Figure 4.32: overtopping volume per wave for Std Dike
(in model scale)
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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1.E+00
StdDike
C4SS
C4SL
C4WS
C4WL
buffer C4SS
buffer C4WL
1.E-01
overtopping volume per wave
1.E-02
1.E-03
1.E-04
1.E-05
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
overtopping discharge, Std Dike
Figure 4.33: Vmax,0.1%. for different model configurations
(in model scale)
4.4
Overtopping layer thickness at the landward side of the dike
This section describes the overtopping layer thickness at the landward side of the crest
drainage dike. All the figures are compared with the Standard dike results to find the
differences. Results from the layer thickness gauges (see figure 3.12, A18, A.19) are
used for the plotting. All the layer thickness gauges were perpendicular to the dike
slope. Therefore gauges measured direct layer thicknesses on the dike slopes (see
annex J) When the thickness of the water layer is smaller than 2mm, results are not
reliable. Therefore all the comparisons were done when larger layer thickness are
presented.
First overtopping profiles for standard dike and the crest drainage dike were
compared.
Figures 4.34 and 4.35 show the overtopping profiles at the landward side of the dike
during a higher overtopping event. According to figures, crest drainage dike makes
the profile much more complicated than the standard dike case. Hence previous
formulae for overtopping layer thickness at the crest and landward side cannot be
applied to the crest drainage dike.
Second, more detailed comparison was done by plotting results of the C4SS and
C4WL with standard dike test results. Previous literature previous literature used 2%
exceedance limit as the guideline and found the overtopping layer thickness for
standard dike follows an exponential relationship (see section 2.5.3). Hence figures
were done with h2% (layer thickness exceeded by 2% of incoming waves) as well as
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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h0.01%(layer thickness exceeded by 0.01% of incoming waves in other words
maximum thickness for 1000 waves).
1.20
layer gauges (LG)
1.15
max height during 788s to 789s
Y-coordinates of the model.
1.10
max height during 1620s to 1621s
1.05
1.00
0.95
0.90
0.85
0.80
Hs=0.206m
Tp=3.05s
Rc=0.441m
Test no: 16010701
0.75
0.70
81.00
81.50
82.00
82.50
X-coordinates of the model
Figure 4.34: Overtopping layer thickness at the landward side of Std Dike
(in model scale)
Y-coordinates of the model..
1.25
layer gauges (LG)
1.20
max height during 847s to 849s
1.15
max height during 2361s to 2361s
1.10
1.05
1.00
0.95
0.90
0.85
0.80
81.00
81.20
81.40
81.60
81.80
82.00
82.20
X-coordinates of the model
Figure 4.35: Overtopping layer thickness at the landward side of C4SS configuration
during a higher overtoppng event.. (in model scale)
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Figures 4.36 and 4.37 shows overtopping layer thicknesses for C4SS (crest
basin=0.8m*1.2m) and C4WL (crest basin=1.2mx4.0m) model configurations. There
was not single event which gives maximum layer thickness for all the measurement
devices. But highest 2% has 5-10 common events. Therefore results shown as 2%
credence are not the records of a single event.
Overtopping layer thickness for the 2% credence limit follows different shape (A “S”
profile) than the standard dike (see figure 3.36 and 3.37).
1.20
1.15
1.10
h2% [m]
1.05
1.00
0.95
0.90
0.85
0.80
81.20
std dike profile
std dike Rc=0.441m
std dike Rc=0.397m
std dike Rc=0.353m
std dike Rc=0.309m
C4SS Rc=0.441m
C4SS Rc=0.397m
C4SS Rc=0.353m
C4SS Rc=0.309m
81.40
81.60
81.80
82.00
82.20
X-coordinate of the model [m]
Figure 3.36: overtopping layer thicknesses for Std Dike and C4SS with 25mm
drainage. (in model scale)
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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1.25
1.20
1.15
h 2% [m]
1.10
1.05
std dike profile
std dike Rc=0.441m
std dike Rc=0.397m
std dike Rc=0.353m
std dike Rc=0.309m
C4WL Rc=0.441m
C4Wl Rc=0.397m
C4WL Rc=0.353m
C4WL Rc=0.309m
1.00
0.95
0.90
0.85
0.80
81.20
81.40
81.60
81.80
82.00
82.20
X-coordinate of the model [m]
Figure 4.37: overtopping layer thicknesses for Std Dike and C4WL with 25mm
drainage. (in model scale)
Above is a qualitative description about the overtopping layer thicknesses. Hence
more analysis is required to get an in depth knowledge about the overtopping layer
thickness at the landward side of the crest drainage dike.
4.5
Overtopping flow velocity at the landward side of the dike.
One of the main argument in favour of crest drainage dike is, even if the crest basin
cannot hold the all the overtopping water, it can damp the energy of the overtopping
wave. This section describes the results of overtopping flow velocity analysis.
Following analysis was done only using results for the velocity meter set at the
landward side of the dike. (see figure 3.38)
10cm
Landward side
Seaward side
velocity propeller
(VP4)
Figure 4.38: location of velocity measurement at the landward side of the dike
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
This is a preliminary analysis to get a qualitative idea about the reduction in
overtopping for velocities. Even though use of propeller type velocity meter to find
the overtopping velocity is a not recommended practice, results for the propeller are
plotted below. To minimise the error due to insufficient flow depths to the propellers,
only high overtopping events with larger layer thickness are used. (see annex J)
Overtopping velocities with 2% exceedance limit used for the plotting and results
from C4SS and C4WL are compared with Standard Dike results. (see figure 3.39)
1.80
1.60
u2% [m/s]
1.40
1.20
1.00
0.80
0.60
0.40
0.30
Std Dike
C4SS 25mm drainage
C4SS 32mm drainage
C4SS 38mm drainage
C4WL 25mm drainage
C4WL 32mm drainage
C4WL 38mm drainage
0.40
0.50
Rc [m]
Figure 4.39: Comparison of velocity propeller readings
(in model units)
As shown in figure 4.39, for all the freeboard values, standard dike has recorded high
velocities where as C4WL (crest basin=1.2m*4.0m) showed lower velocities (about
15%).
Summary and evaluation of results
Following section summarised the result for the sections 4.3 , 4.4. and 4.5.
Overtopping volume per wave
Standard dike test results reasonably agree with the TAW (2002) guide lines. Then
reduction of overtopping volume per wave for each configuration were analysed.
Only C4WL (4.0m*1.2m) some reduction in overtopping volume per wave (figure
4.33) but results are scatter.
Even if buffer capacity is larger than the V0.1% , crest drainage could not trap all the
overtopping water. Therefore overtopping volume per wave is more important than
mean overtopping discharge in deciding required buffer capacity.
D.M.D.T.B. Dassanayake
82
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Overtopping Layer thickness
Overtopping layer profile shows major differences with the crest drainage. It makes
the profile more complicated. Hence more analysis is required to explain the layer
thickness at the landward side in mathematical terms. h2% does not show any
significant reduction. This means, extreme event which initiate the erosion at the
landward side are almost same for both standard dike case and crest drainage dike.
D.M.D.T.B. Dassanayake
83
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
5. Conclusions and Recommendations
5.1
Conclusions,
Climatic changes increase the risk of dike failure along the coasts worldwide (sea
level rise, severity of storms, etc.). Hence, there is an urgent need for more
appropriate technical and managerial solutions to mitigate this risk. Principal
mitigation measures undertaken up to now have led to increased dike heights.
However, due to space limitation and high costs, heightening is no more feasible
Innovative idea of crest drainage dike was developed by Nieuwhaus in 2005 as a
method to enhance the safety of a dike without altering its dimensions. Current
research mainly focuses on overtopping characteristic of crest drainage dike and to
find the optimum geometry of the crest basin. A two dimensional physical model
study was carried out to achieve the fore mentioned objective.
Physical model testing were done in small scale flume at Leichtweiss institute (LWI),
Technical University, Brauschweig, Germany. Total of 275 tests were preformed with
1:4 seaward slope and 1:3 landward slope. In order to deduce the effect of reducing
wave overtopping on dikes using crest drainage on dikes compared to standard crest
dikes, tests were carried out for both
cases. . Four different geometries of crest
drainage dike with four different freeboards were tested. Four incident wave
parameters ranging from 2.5m to 3.8m (in prototype scale) with five wave periods
ranging from 7.0s to 12.5s (in prototype scale) Each test consists of 1000 waves
generated by single peaked JOHNSWAP spectrum. Wave steepness is ranging from
0.009~0.036 and Breaker parameter is ranging form 1.25~2.45. Apart from the above
tests crest basins with three different drainage pipe sizes (400mm, 500mm and
600mm in prototype scale) were tested for selected wave conditions (1.5<R*<2.14).
Finally few testes were done without any basin to find the maximum possible
drainage for 2.0m wide crest basin.
A number of different aspects were studied during the research. Mainly the sensitivity
of different crest basin geometries to mean overtopping discharge was analysed. Both
width of the crest basin and depth of the crest basin were changed, while keeping
drainage conditions same (drainage pipe diameter; 400mm in prototype scale). Based
on the experimental results a method to estimate mean overtopping discharges of crest
drainage dike was developed. Apart form that, Influence of the drainage pipe
diameters on reducing the mean overtopping discharge were tested. Finally effect of
crest basin on reducing the overtopping volume per wave, the overtopping layer
thickness and overtopping flow velocity were studied.
Important findings of the research are described below including the mean
overtopping prediction method for crest drainage dike. However ranges of
applicability of these findings are limited to 1:4 smooth seaward slopes and 1:3
landwards slope. In addition, range of applicability limited by parameters described
above.
After analysing the test results for different crest basin geometries, it was found, that
wider crest basins (4.0m in prototype scale) are effective in two ways. First, it has
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
more buffer capacity to handle larger overtopping volumes per wave. Second, it can
reflect 10%-30% of overtopping water back to the seaward side( figure 4.22)
compared to 0%-10% in case of narrow crest basins This will reduce the required
storage capacity at the landward side of the dike. Crest basins with dimension 2.0m X
1.2m (C4SS-buffer capacity 2.4m2) and 4.0m X 0.8m (C4WS-buffer capacity 3.2m3)
showed mean overtopping reductions in same range (both configurations can reduce
mean overtopping discharge of 15l/s per m to a range of 4.25 l/s per m to 4.50l/s per
m) The first crest basin has more depth which increased the drainage discharge and
the second has more width and it reflects the water back to seaward side more
effectively than the first. Therefore when increase the buffer capacity of the crest
basin both, overtopping reduction due to reflection and overtopping reduction due
increment in drainage discharge should be considered. Average of 10% to 20%
increment in drainage discharge observed for different depths of crest basins.
Maximum overtopping volume per wave for all the crest drainage dike tests were
compared with maximum volume per overtopping wave for the corresponding
standard dike tests. It is concluded that there is no significant reduction in overtopping
volume per wave. Only for the case of crest drainage of dimensions 4.0mx1.2m
(C4WL) there is some reduction (maximum reduction is about 25%) in overtopping
volume per wave (figure 4.33) but results are scattered. Although the dimensions of
the crest basin increase, actual buffer capacities determined not only by the geometry
of the crest basin but also by the amount filled by the previous overtopped wave. In
some cases when two large waves come one after the other, the first wave fills the
crest basin. Then the second overtopping wave has a lesser buffer capacity.
Values of dimensionless overtopping discharges for various crest geometries were
plotted against the dimensionless overtopping discharges for standard dike. The plots
clearly show reduction in mean overtopping discharges due different crest basin
configurations.
However, it is difficult to find a simple mathematical expression for the plots (curves
in Figures 4.29 and 4.30).
Then mean overtopping reduction were plotted against the dimensionless mean
overtopping discharge of the standard dike. Based on these plots, a new formula has
been developed to calculate the reduction in mean overtopping discharges for crest
drainage dike. An overtopping reduction factor γ CDD is introduced to calculate the
mean overtopping discharges for crest drainage dike, when the mean overtopping
discharges for standard dike is known (section 4.2) .This formula is expressed as:
qCDD = γ CDD × q
For Q* > Q*CDD;
⎡
⎛
⎢
⎣
⎜ gH 3
m0
⎝
γ CDD = ⎢ ACDD × ln ⎜
For Q* < Q*CDD ;
In which,
q
⎤
⎞
⎟ − BCDD ⎥
⎟
⎥
⎠
⎦
γ CDD = 0.1
γ CDD = overtopping reduction factor
D.M.D.T.B. Dassanayake
85
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
ACDD = dimensionless coefficient with values ranging form -0.22~-0.30
BCDD =dimensionless coefficient with values ranging form 1.2~2.0
q =mean overtopping discharge for the standard dike
qCDD = mean overtopping discharge for Crest Drainage Dike
It has been concluded that for very small overtopping discharges (Eg. the model
configuration C4SS can reduce mean overtopping discharges less than 0.35 l/s per m
by 100% ), crest drainage can trap up to 100% of overtopping water. Due to the
uncertainties in waves, even smaller overtopping events can result insome
overtopping discharge. This phenomena can be seen in some of the model test results.
Therefore, for smaller overtopping invents overtopping reduction factor is taken as
γ CDD =0.1 . This value is included as a safety margin.
Effects of various sizes for drainage pipes were tested for selected wave conditions
(1.5<R*<2.14) with relatively high mean overtopping discharges. The results are
plotted on curves representing percentage of overtopped water drained by pipes
versus dimensionless mean overtopping discharges of standard dike ( annex D, figure
4.24) . These curves can be used to indicate the overtopping reduction for each size of
drainage pipe. By extrapolating, overtopping reduction for 15l/s per m cases were
found. Only C4WL configuration with 600mm drainage pipes showed 3.6 l/s per m to
5.7 l/s per m mean overtopping discharge. However, by increasing pipe diameter form
400mm to 600mm, drainage capacity can be increased by 10%~20%. While doing the
analysis, two occasions were found which can reduce the overtopping discharges form
15l/s per m to 1l/s per m and are given below.
First, with the case of the largest crest basin (4.0 wide and 1.2 deep and 400 mm
drainage pipes in 30m intervals ) it is possible to achieve such reduction for the case
of breaking waves ( ξ0 < 2 )
Second, with the case of ‘no basin’, where only a 2m wide gap was maintained at the
crest. In this case unlimited drainage and unlimited buffer capacity were tested. The
plot with these results shows, fore mentioned configuration can reduced the mean
overtopping discharged from 15l/s per m to 1l/s per m. This is not practical solution
but it gives some indication of limitations of the 2m wide crest drainage dike. Figure
4.29 compares the overtopping discharges of no basin case with other model
configurations.
This does not agree with the findings in the theoretical study from Nieuwenhuis et al
(2005) which indicated that crest drainage dike with dimensions of 2.0m X 0.8m can
reduce 15l/s per m to 1l/s per m. According to the model results, the crest basin with
the dimensions ( 2.0m × 0.8m )
can reduce overtopping discharges from 15l/s per m to 8 l/s per m with 400mm
drainage pipe.
Further discharges from the drainage pipes were measured with the time. Considering
the measured average drainage discharge and the calculated average discharges, a
discharge coefficient is calculated as Cdrain = 0.55 .
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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Overtopping layer thicknesses and overtopping flow velocities of same set of tests for
drainage crest dikes with various crest drainage dimensions and drainage pipes are
compared with the standard dike results. Based on the test results, it is concluded that
there is no significant reduction in overtopping layer thicknesses or overtopping flow
velocities. Overtopping flow profile at the crest of the dike and landward side of the
dike show different profiles compared with the standard dike. However, magnitudes
of overtopping layer thickness and velocities do not show significant reduction.
Apart from the conclusions drawn from the experimental results, some practical
aspects have been found form literature and discussions. The main problem in
heightening the dike is, that it will need widening of the entire dike to have it
geotechnically stable. This may be difficult to achieve because of space limitation.
Hence, it is necessary find out the solution to increase the safety of the dike without
heightening the dike. Crest drainage dike has been proposed as a solution to this
problem. However, crest drainage dike is a hard structure. This hard structure and
existing clay dike will not develop good connection. Therefore, joining between
concrete dike and the sand/clay of the dike is structurally a weak joint. Therefore this
system is not practicable for existing dikes with smaller crest width although this
concept gives some hydrodynamic performances. Space to construct filter between
sand core or clay and the concrete drainage is not available in the existing dikes. (if
width is only 3m~4m).
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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5.2
Recommendations
Recommendations for future model tests on crest drainage dike are first given.
Besides, other important aspects that need to be studied before implementing the crest
drainage dike are also included in the recommendations.
Influence of different drainage diameters
Limited range of wave conditions were tested for different drainage pipe diameters.
Only high overtopping tests ranging from 45l/s per m to 160l/s per m were conducted
for three different drainage pipe sizes (400mm, 500mm and 600mm in prototype
scale). Discharges for lower overtopping events were found by extrapolation. To
bridge this gap and to get more insight about the influence of drainage pipe sizes to
overtopping reduction, more tests should be carried out. These tests should cover a
wide range of wave conditions and overtopping discharges. Specially tests with lower
mean overtopping discharges (between 1l/s per m to 45l/s per m) should be conducted
to verify the extrapolated overtopping reduction curves.
Drainage coefficient is found Cdrain = 0.55 which make the drainage system
inefficient. Therefore more studies are required to make the drainage system more
efficient by changing the inlet and out let geometry etc.
Geometrical Changes
According to the test results even “no basin” tests recoded considerable overtopping
discharge. This indicates the limitation in improving the drainage system. Therefore,
some geometrical changes needed to be done for 2m wide crest basin in order to use
this concept to enhance the safety of existing dikes with 3m~4m wide crests. Instead
of collecting all the water for the overtopping wave it is recommended to use wave
reflecting wall. Then the amount to be drained to the landward side as well as the
buffer capacity requirement will be reduced.
Further drainage to landward side will create more problems. This water should be
pumped back to the sea again. Instead of landward side drainage, it may be a good
idea to put the drainage to seaward side as in MONACO caisson breakwater
Experimental investigations were done only for 1:4 slopes. Recently most of the dike
are constructed with 1:6 instead of 1:4 in most of the countries in North Sea. Hence
more testing is needed to find the applicability of developed formulae and use of crest
drainage dikes to the 1:6 slopes seaward slopes.
Seaward slope roughness, berm of the dike, shallow foreshore etc influence the
overtopping characteristics. Hence model testing should be extended to study the
influence of these parameters.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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3D Model Tests,
The current research investigated the efficiency of crest drainage dike in reducing
overtopping based on 2D model test. In these tests entire crest basin is overtopped at
once. In reality only a part of the crest basin will be overtopped due to the shortcrestedness of the waves. This gives crest basin a chance to spread extreme
overtopping rates in longitudinal direction. This means for same crest drainage will
have more buffer capacity in reality. Nieuwnhuis et al(2005) suggested length
spreading factor of 2. This needs to be further investigated based on 3D model test.
Structural and Geotechnical Aspects.
Not only the hydraulic aspects but also structural and geotechnical aspects should be
looked in. As indicated in the conclusions, crest drainage dike is a hard structure. This
hard structure and existing clay dike will not develop good connection. Hence joint
between concrete dike and the sand/clay of the dike needs more studies. Also, a need
method to construct a filter between sand core or clay and the concrete drainage need
o be further investigated since there is not enough space available in the existing
dikes.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
References
Burcharth, H.F., 1979. The Effect of Wave Grouping on on-shore structures, The 2nd Coastal
Engineering. Elsevier Scientific, The Netherlands, pp. 189-199.
De Waal, J.P., and Van der Meer, J.W., 1992. Wave run-up and overtopping at Coastal
Structures, Proceeding of the 23rd International Conference of Coastal Engineering
1992. ASCE, Venice, Italy, pp. 1758-1771.
DHV, 2005
Goda, Y., 1992. Transformation of wave crest pattern in shoaling water, Proceeding of the
23rd International Conference of Coastal Engineering 1992. ASCE, Venice, Italy, pp.
199-211.
Hedges, T., and Shareef, M., 2002. Predicting Seawall Overtopping by Bimodal Seas. In: J.M.
Smith (Editor), Proceeding of the 28th International Conference of Coastal
Engineering 2002. ASCE, Cardiff, Wales, pp. 2153-2164.
HR Wallingford, 1999. Wave Overtopping of Seawalls Design and Assessment Manual.
Report W178, Design and Assesment Manual, Hydraulic Research Wallingford Ltd,
Wallingford.
Hughes, S.A., 1993. Physical Models and Laboratory Techniques in Coastal Engineering,
Volume 7. Coastal Engineering Research Center, USA.
Kortenhaus,A., van der Meer,J., Burcharth,H.F., Geeraerts, J., Pullen, T., Ingram, D., Troch, P., 2005,
Quantification of Measurement Errors, Model and Scale Effects Related to Wave Overtopping,
Workpackage 7, CLASH programe
Lorenzo, A.B.M., Van der Meer, J.W., and Hawkes, P.J., 2000. Effects of bi-modal waves on
overtopping: application of UK and Dutch prediction methods. In: B.L. Edge
(Editor), Proceeding of the 27th International Conference of Coastal Engineering
2000. ASCE, Sidney, Australia, pp. 2114-2127.
Mansard, E.P.D., and Funke, E.R., 1980. The Measurement of Incident and Reflected Spectra
using a Least Squares Method, Proceeding of the 17th International Conference of
Coastal Engineering 1980. ASCE, Sidney, Australia, pp. 95-96.
Mansard, E.P.D., Miles, M.D., and Dalrymple, R.A., 1992. Numerical Validation of
Directional Wavemaker Theory with Sidewall Reflections, Proceeding of the 23rd
International Conference of Coastal Engineering 1992. ASCE, Venice, Italy, pp.
3468-3482.
Murhy, J., Schüttrumpf, H., and Lewis, T., 2001. Wave Run-up and Overtopping of Sea
Dikes: Results from new model studies. In: B.L. Edge, and Hemsley, J.M. (Editor),
Proceeding of the 4th International Symposium Waves 2001 ASCE, pp. 1575 -1584.
Nieuwenhuis,O,E, et al, 2005. Innovative concept of overtopping dike:Crest Drainage Dike Theoritical
study
Owen, M.W., 1980. Design of Seawall allowing for Wave Overtopping. Report EX924,
Hydraulic Research Wallingford Ltd, Wallingford.
Schüttrumpf, H., 2003. Wave Overtopping Flow on Seadikes - Experimental and Theoritical
Investigations - PIANC pp. 7-23.
Schüttrumpf, H., Möller, J., Oumeraci, H., Grüne, J., and Weissmann, R., 2001. Wave
Overtopping by Natural Sea States, Proceeding Waves 2001 Conference.
D.M.D.T.B. Dassanayake
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Schüttrumpf H., J. Möller, H. Oumeraci and J. Grüne R. Weissmann (2002), Effects of Natural Sea
States on Wave Overtopping of Sea dikes
Schüttrumpf, H., Murphy, J., 2000. 3D Model Tests on Wave Overtopping For 1:6 Dike. LWI
Report 857, LWI-HMRC, Braunschweig, Germany.
Schüttrumpf H. & H. Oumeraci, 2004 Learning from Dike Failures
Schüttrumpf H. & Van Gent, MR.A., 2003, wave overtopping at sea dikes , Coastal Engineering,2003,
TAW, 2002. Technical Report: Wave Run-up and Wave Overtopping at dikes, Technical
Advisory Committee on Flood Defence, Delft, the Netherlands.
Van der Meer, J.W., and Janssen, J.P.F.M., 1994. Wave run-up and wave overtopping at dikes
and revetments, WL | Delft Hydraulics.
Van Gent, M.R.A., 1999. Physical Model Investigations on Coastal Structures with Shallow
Foreshores; 2D model tests with single and double-peaked wave energy spectra.
Report H3608, WL | Delft Hydraulics, Delft, the Netherlands.
Van Gerven & Akkerman , 2005, State-of-the-art Inventor; ComCoast WP 3
Verhaeghe, H., Van der Meer, J.W., and Steendam, G.J., 2006. Database on wave
overtopping at coastal structures. EVK3-CT-2001-00058, CLASH Commission of
The European Communities.
Wiyono H.,2006, Effects of wave obliquity and short-crestedness on wave overtopping on sea dikes –
3d physical model tests, MSC THESIS WSE-HECEPD-06-04, UNESCO-IHE, Delft, the Netherlands.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Annex
Annex A: Importance of coastal flood prevention, towards achieving MDGs
Importance of coastal flood prevention, towards achieving MDGs can be summarized
in table A1
Table A1: MDGs targets and Importance of flood prevention
MDG
Target
Importance of Flood Prevention
Goal 1 :
Eradicate
extreme poverty
and hunger
Target 1: Reduce by half
the proportion of people
living on less than a dollar
a day
Target 2: Reduce by half
the proportion of people
who suffer from hunger
Damages to Income sources; fishery,
tourism, other industries related to
coastal zone, infrastructure damage etc
Goal 2: Achieve
universal
primary
education
Target 3: Ensure that all
boys and girls complete a
full course of primary
schooling
Goal 4: Reduce
child mortality
Target 5: Reduce by twothirds, between 1990 and
2015, the under-five
mortality rate
Target 6: Reduce by three
quarters the maternal
mortality ratio
Target 8: Have halted by
2015 and begun to reverse
the incidence of malaria
and other major diseases
Goal 5:
Improve
maternal health
Goal 6: Combat
HIV/AIDS,
malaria and
other diseases
Goal 7: Ensure
Environmental
Sustainability
Target 10: Halve, by
2015, the proportion of
people without sustainable
access to safe drinking
water and basic sanitation
Target 11: Have achieved
by 2020 a significant
improvement in the lives
of at least 100 million
slum dwellers
D.M.D.T.B. Dassanayake
Damages to Agricultural Lands due
coastal flooding have long-term effect
(due to salty water). Also damages to
irrigation infrastructure.
Damages to schools and to other
infrastructure related to education
system.
This is mainly addressing the health
sector but children are more likely to
die in flooding than elders
Damages to hospitals and to other
infrastructure related to health system.
Health problems are a common after
effect of Flooding
After coastal flooding ground water
cannot be used for long time. Also
Investments needs adequate protection
from flood damages
Most of the slumps located in coastal
areas. Proper dike system will protect
their lives. Before done any other
investment to improve their lives
standards, there life should be secured
from flooding
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ANNEX B: Wave run-up formulae
This section describes the method used to derive wave run-up formulae given in table
2.2 in section 2.4.1
Formula from Van Gent (1999b)
(A.1)
R u 2%
= C0 γ f γ β ξs,−1 for ξs,−1 ≤ P
Hs
R u 2% ⎛
C ⎞
= ⎜ C1 - 2 ⎟ γ f γ β for ξs,−1 ≥ P
⎜
Hs
ξs,−1 ⎟⎠
⎝
Hs
ξs,−1
= incident wave at the toe
2π H s
= tan α /
⋅
at the toe of the dike
g Tm −1,0
Tm −1,0 = wave period based on zero and first negative spectral moment(s)
α
γ
= sea ward slope angle
= γ f γβ
γf
γβ
=reduction factor for roughness at the seaward slope
=reduction factor for angular wave attack
γβ
= 1 − 0.0022 ⋅β where β ≤ 80D
C0 =1.55 , C1 =5.4 and C2 =
P=
0.25 × 5.42
= 4.703 (for short waves)
1.55
0.5C1 0.5 × 5.4
=
= 1.742
C0
1.55
when substituting above coefficients in general formula, a specific formula for smooth
impermeable straight slope with short waves will be;
R u 2%
= 1.55γ f γ β ξs,−1 for ξs,−1 ≤ 1.742
Hs
R u 2% ⎛
4.703 ⎞
= ⎜ 5.4⎟ γ f γ β for ξs,−1 ≥ 1.742
⎜
Hs
ξs,−1 ⎟⎠
⎝
Formula from Schüttrumpf (2002)
(A.2)
R u 2%
= C0 ξs,−1 for ξs,−1 ≤ P
Hs
C0 = 1.25
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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Calculation of value P;
Use coefficient from Van Gent to calculated P for the formula from Schüttrumpf
0.25 × 4.02
C0 =1.35 , C1 =4.0 and C2 =
= 2.963
1.35
0.5C1 0.5 × 4.0
P=
=
= 1.481
C0
1.35
Formula from Van Gent (2002)
(A.3)
R u 2%
= C0 ⋅ ξs,−1 for ξs,−1 ≤ P
Hs
R u 2% ⎛
C ⎞
= ⎜ C1 - 2 ⎟ for ξs,−1 ≥ P
⎜
ξs,−1 ⎟⎠
Hs
⎝
0.25 × 4.02
C0 =1.35 , C1 =4.0 and C2 =
= 2.963
1.35
0.5C1 0.5 × 4.0
P=
=
= 1.481
C0
1.35
Therefore above formulae can be rewritten as
R u 2%
= 1.35 ⋅ ξs,−1 for ξs,−1 ≤ 1.481
Hs
R u 2% ⎛
2.963 ⎞
= ⎜ 4.0⎟⎟ for ξs,−1 ≥ 1.481
⎜
Hs
ξ
s,
1
−
⎝
⎠
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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ANNEX-C: Reflection effect of the crest basin
dimentionless [Qdrain+q] for CDD
1.E-02
C4WS,drainage; D=25mm
C4WS, drainage; D=32mm
C4WS, drainage; D=38mm
C4WL, drainage; D=25mm
C4WL, drainage; D=32mm
C4WL, drainage; D=38mm
1.E-03
1.E-03
1.E-02
dimensionless overtopping discharge for Std Dike
Figure A1: overtopping discharges [Qdrain+q] fro tests with different drainage pipes
(4m wide crest basin in prototype scale)
dimentionless [Qdrain+q] for CDD
1.E-02
C4SS, drainage; D=25mm
C4SS, drainage; D=32mm
C4SS, drainage; D=38mm
C4SL, drainage; D=25mm
C4SL, drainage; D=32mm
C4SL, drainage; D=38mm
1.E-03
1.E-03
1.E-02
dimensionless overtopping discharge for Std Dike
Figure A2: overtopping discharges [Qdrain+q] fro tests with different drainage pipes
(2m wide crest basin in prototype scale)
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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ANNEX-D: percentage of overtopping water discharged through drainage pipe
100%
Proposed curve for max drainage
% discharged by pipes , C4SS..
90%
15l/s per m for
Hm0=2.5m~3.8m
80%
70%
25mm drainage
32mm drainage
38mm drainage
max drainage
60%
50%
40%
y = -0.1225Ln(x) - 0.4494
y = -0.132Ln(x) - 0.5239
R2 = 0.9503
R2 = 0.9685
y = -0.1323Ln(x) - 0.5711
30%
20%
10%
R2 = 0.9762
0%
1.E-11
2.E-03
4.E-03
6.E-03
8.E-03
1.E-02
dimensionless overtopping discharge for Std Dike
Figure A.1: percentage of overtopping water discharged through drainage pipe
(C4SS)
100%
Proposed curve for max drainage
% discharged by pipes , C4SL…
90%
80%
15l/s per m for
Hm0=2.5m~3.8m
70%
25mm drainage
32mm drainage
38mm drainage
max drainage
60%
50%
y = -0.1517Ln(x) - 0.5527
40%
R2 = 0.8701
y = -0.1202Ln(x) - 0.4555
30%
R2 = 0.896
20%
y = -0.1363Ln(x) - 0.5693
10%
0%
1.E-11
R2 = 0.9844
2.E-03
4.E-03
6.E-03
8.E-03
1.E-02
dimensionless overtopping discharge for Std Dike
Figure A.2: percentage of overtopping water discharged through drainage pipe
(C4SL)
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
% discharged by pipes , C4WS…
100%
25mm
drainage
Proposed curve for
max drainage
32mm drainage
38mm drainage
max drainage
90%
80%
70%
15l/s per m for
Hm0=2.5m~3.8m
60%
50%
y = -0.1388Ln(x) - 0.5198
R2 = 0.9485
y = -0.1293Ln(x) - 0.5011
R2 = 0.8926
40%
30%
20%
10%
0%
1.E-11
y = -0.1267Ln(x) - 0.533
R2 = 0.9819
2.E-03
4.E-03
6.E-03
8.E-03
1.E-02
dimensionless overtopping discharge for Std Dike
Figure A.3: percentage of overtopping water discharged through drainage pipe
(C4WS)
100%
Proposed curve for max drainage
% discharged by pipes , C4WL…
90%
80%
70%
15l/s per m for
Hm0=2.5m~3.8m
25mm drainage
32mm drainage
38mm drainage
max drainage
60%
y = -0.23Ln(x) - 0.9325
50%
R 2 = 0.9322
40%
y = -0.2096Ln(x) - 0.8693
R 2 = 0.9913
30%
20%
10%
0%
1.E-11
y = -0.1405Ln(x) - 0.5853
R2 = 0.959
2.E-03
4.E-03
6.E-03
8.E-03
1.E-02
dimensionless overtopping discharge for Std Dike
Figure A.4: percentage of overtopping water discharged through drainage pipe
(C4WL)
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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ANNEX-E: comparison of mean overtopping discharges due to crest drainage dikes
with Std Dike results.
1.E-02
mean overtopping C4SL
CDD [m3/s per m] .
1.E-03
1.E-04
C4SS
C4SL
C4WS
C4WL
no basin
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
3
mean overtopping Std Dike [m /s per m]
Figure A.5: comparison of mean overtopping discharges of crest drainage dikes
(CDD) with Standard Dike (in model scale)
1.E-02
Q* C4SS
CDD [m3/s per m] .
1.E-03
1.E-04
C4SS
C4SL
C4WS
C4WL
no basin
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
Q* Std Dike
Figure A.6: comparison of dimensionless overtopping discharges of crest drainage
dikes (CDD) with Standard Dike.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
mean overtopping C4SS [m3/s per m] .
1.E-02
1.E-03
breaking waves
non breaking waves
no basin
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
3
mean overtopping Std Dike [m /s per m]
Figure A.7: comparison of mean overtopping discharges of C4SS with Std Dike (in
model scale)
1.E-02
1.E-03
Breaking waves
non breaking waves
no basin
Q* C4SS [m3/s per m] .
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
Q* Std Dike
Figure A.8: comparison of dimensionless overtopping discharges of C4SS with Std
Dike
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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1.E-02
mean overtopping C4SL [m3/s per m] .
breaking waves
1.E-03
non breaking
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
3
mean overtopping Std Dike [m /s per m]
Figure A.9: comparison of mean overtopping discharges due to C4SL with Std Dike
(in model scale)
1.E-02
Breaking waves
1.E-03
non breaking waves
Q* C4SL
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
Q* Std Dike
Figure A.10: comparison of dimensionless overtopping discharges due to C4SL with
Std Dike
.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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1.E-02
breaking waves
1.E-03
non breaking
mean overtopping C4WS [m3/s per m] .
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
3
mean overtopping Std Dike [m /s per m]
Figure A.11: comparison of mean overtopping discharges due to C4WS with Std
1.E-02
Breaking waves
1.E-03
non breaking waves
1.E-04
Q* C4WS
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
Q* Std Dike
Dike (in model scale)
Figure A.12: comparison of dimensionless overtopping discharges due to C4SL with
Std Dike.
D.M.D.T.B. Dassanayake
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Hydraulic Model Tests of Wave Overtopping
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1.E-02
Breaking waves
non breaking waves
1.E-03
Q* C4WL
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
Q* Std Dike
Figure A.13: comparison of mean overtopping discharges due to C4WL with Std
Dike (in model scale)
1.E-02
breaking waves
non breaking
mean overtopping C4WL [m3/s per m] .
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
3
mean overtopping Std Dike [m /s per m]
Figure A.14: comparison of dimensionless overtopping discharges due to C4SL with
Std Dike.
D.M.D.T.B. Dassanayake
102
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
ANNEX F: Drainage discharge measurements.
To find out the maximum drainage capacity, a controlled test was done. During the
test crest basin was fully filled. (see fig.1). When both out put files are plotted in
L~DAVIS in same time scale (see fig.2), test with waves and fluctuating water level
shows higher gradient than the controlled test. This means discharge is higher when
the waves are present and when basin is filled with the overtopping water.
0.294m
Seaward
side
1.06m
0.989m
Landward
side
0.071m
Drainage pipe
D=25mm
Figure A.15:sketch of crest basin used for drainage test
WL=0.751m, Hs=0.224, Tp=2.15s
Drainage test when crest basin in filled
Figure A.16: comparison of drainage discharges with 25mm pipe (plot from
L~DAVIS).
According to the fig.2, not only the filling but also empting takes long time. If the
same pump is used and if the same inflow to the talk is assumed then empting should
be much fasted than the test with higher drainage flow. This makes the test results
little suspicious. This could be as a result of wrong calibration factor.
D.M.D.T.B. Dassanayake
103
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Correction of data
rate of empting = Q pump − Qdrain
From the fist test (29030706);
Qdrain = 3.87 ×10−4 m3 / s
rate of empting = 4.005 × 10-4 m3 / s
Q pump = 7.875 ×10-4 m3 / s
Therefore
From the data of drainage test (30030702),
Qdrain = 2.7 × 10−4 m3 / s
rate of empting = 2.322 ×10-4 m3 / s
Q pump = 5.022 ×10-4 m3 / s
Therefore
Hence calculated discharges from the drainage tests should be multiply by factor of
1.568. Then discharge will be, Qdrain = 4.2336 ×10−4 m3 / s for the drainage tests.
Table 1 shows calculated discharge per meter length. When compare the calculated
and adjusted measured value, Qdrain ,calculated = 0.66 × Qdrain ,measured . Hence CD = 0.66 ,
which is a reasonable value for circular orifice.
Table A.2: Calculated drainage discharges, Qdrain in model and prototype scales
values in model scale
values in prototype scale
h (m)
25mm
Q (m^3/s/m)
32mm
38mm
h (m)
400mm
Q (l/s/m)
500mm
600mm
0.000
1.5E-04
2.6E-04
4.0E-04
0.0
10.4
18.5
27.8
0.006
1.7E-04
3.0E-04
4.4E-04
0.1
11.9
20.9
30.9
0.012
1.9E-04
3.3E-04
4.8E-04
0.2
13.3
22.9
33.8
0.018
2.1E-04
3.5E-04
5.2E-04
0.3
14.5
24.9
36.4
0.024
0.029
0.035
0.041
0.047
0.053
0.059
0.065
0.071
2.2E-04
2.4E-04
2.5E-04
2.7E-04
2.8E-04
2.9E-04
3.0E-04
3.1E-04
3.2E-04
3.8E-04
4.0E-04
4.3E-04
4.5E-04
4.7E-04
4.9E-04
5.1E-04
5.2E-04
5.4E-04
5.5E-04
5.9E-04
6.2E-04
6.5E-04
6.7E-04
7.0E-04
7.3E-04
7.5E-04
7.8E-04
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
15.7
16.7
17.7
18.7
19.6
20.4
21.2
22.0
22.7
26.6
28.3
29.9
31.4
32.8
34.2
35.5
36.8
38.0
38.8
41.1
43.2
45.3
47.3
49.2
51.0
52.7
54.4
Without this adjustment, measured value give 42% of the calculated value which is
quite unrealistic.
D.M.D.T.B. Dassanayake
104
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
ANNEX G; Different drainage options
Water Level
Water Level
h
h
L2
D
L1
D
X2
x1
D
(I)
D
(II)
Figure A.17: different drainage options to the model tests.
Q = CD × A × V
Q = C D × A × 2 h ( ΔH )
In figure (I),
QI = CD × A × 2h(h + L1 )
and in figure (II)
QII = CD × A × 2h(h + L2 )
since
L1 > L2
drainage setup in figure (I) give s higher overtopping.
Specially when water level h → 0 ; QII → 0 where QI still has a higher discharge.
However option (II) is more practical in implementation stage. Also it is more
conservative drainage option. Hence option (II) is used in the model testing at LWI.
D.M.D.T.B. Dassanayake
105
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
ANNEX H: Results from preliminary overtopping calculation
Table A.3 shows the preliminary overtopping calculations. These results were used to
in determining the model scale and capacities of measuring equipments.
Table A:3: Results from preliminary overtopping calculation
2.5 (0.167)
Overtopping
Rc (m) Tmo (s)
Prototype Prototype
7.5
7.0
8.9
10.5
12.6
14.7
2.9 (0.193)
Overtopping
6.75
7.0
8.9
10.5
12.6
14.7
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
0.17
1.92
2.56
2.56
2.56
417.60
2619.00
3465.68
3664.80
3896.78
1622.25
1945.35
1909.58
1930.05
0.46
3.72
7.96
7.96
7.96
937.13
3696.53
6413.85
6883.20
7408.58
1897.43
2745.90
2804.63
2715.08
1.16
8.25
24.34
29.40
29.40
1743.30
5686.43
11637.45
14980.50
16402.05
1435.05
2436.75
4054.50
5002.43
5357.25
1.74
11.56
32.71
49.15
49.15
2173.50
6844.73
13967.10
20561.40
22943.70
1522.58
2754.23
4677.98
6433.88
7073.55
2.9 (0.193)
Overtopping
6
7.0
8.9
10.5
12.6
14.7
5.25
7.0
8.9
10.5
12.6
14.7
3.8 (0.253)
Overtopping
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
0.52
4.01
5.05
5.05
5.05
970.43
3487.28
4487.63
4820.63
5190.30
1668.83
2009.25
2050.20
2130.53
1.05
7.32
14.47
14.47
14.47
1502.10
4844.48
8135.55
8888.40
9694.13
1179.45
2039.18
3008.93
3171.15
3373.20
2.56
15.40
41.31
48.16
48.16
2418.98
7388.33
15015.15
19066.50
21116.70
1390.28
2734.88
4767.53
5862.38
6383.93
3.72
20.91
54.32
77.44
77.44
2938.28
8874.90
17986.95
26053.43
29315.25
1524.83
3137.63
5542.88
7621.20
8478.00
2.9 (0.193)
Overtopping
3.5 (0.233 )
Overtopping
3.8 (0.253)
Overtopping
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
1.28
8.37
10.05
10.05
10.05
1505.03
4694.85
5911.65
6473.48
7069.95
1000.13
1848.83
2223.68
2349.23
2502.45
2.50
14.52
26.26
26.26
26.26
2138.18
6485.18
10584.45
11774.48
13011.75
1156.73
2336.63
3477.38
3768.53
4089.15
5.64
28.58
70.00
78.89
78.89
3300.53
9845.78
19836.68
24818.63
27784.58
1469.03
3236.85
5826.15
7116.30
75366.45
7.90
37.94
90.16
122.00
122.00
3975.75
11804.63
23692.50
33685.20
38196.23
1654.20
3753.23
6804.90
9303.08
10458.00
2.5 (0.167)
Overtopping
Rc (m) Tmo (s)
Prototype Prototype
3.5 (0.233 )
Overtopping
q (l/m/s)
2.5 (0.167)
Overtopping
Rc (m) Tmo (s)
Prototype Prototype
3.8 (0.253)
Overtopping
q (l/m/s)
2.5 (0.167)
Overtopping
Rc (m) Tmo (s)
Prototype Prototype
3.5 (0.233 )
Overtopping
2.9 (0.193)
Overtopping
3.5 (0.233 )
Overtopping
3.8 (0.253)
Overtopping
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
q (l/m/s)
Vmax (l/m
per wave)
V10% (l/m
per wave)
3.25
17.37
20.04
20.04
20.04
2174.18
6514.88
8038.58
8977.05
9946.13
1028.70
2205.90
2636.78
2872.58
3127.50
5.98
28.70
47.64
47.64
47.64
3019.05
8965.80
14204.48
16075.80
17986.50
1259.55
2854.80
4237.43
4707.23
5197.95
12.49
53.16
118.75
129.26
129.26
4603.50
13534.88
26890.65
33095.93
37416.60
1692.90
4039.88
7399.58
8948.70
10023.53
16.91
68.78
149.65
192.18
192.18
5529.38
16178.18
31974.75
44488.58
50800.73
1943.55
4715.10
8656.20
11701.80
13277.25
D.M.D.T.B. Dassanayake
106
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
D.M.D.T.B. Dassanayake
107
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
ANNEX I
Figure A.18: Overtopping layer gauges at the crest of the dike
Figure A.19: Overtopping layer gauges at the landward side of the dike
D.M.D.T.B. Dassanayake
108
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Figure A:20: Behaviour of crest basin during a high overtopping even I
Figure A.21:behavioud of crest basin during a high overtopping event
D.M.D.T.B. Dassanayake
109
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Figure A.22: Overtopping layer thickness gauges and the drainage gully of the crest
basin
D.M.D.T.B. Dassanayake
110
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
ANNEX J: Result Sheets: Overtopping layer thickness and velocity
Table A. : Measurement for Layer thickness gauges and Velocity propellers
Test No
Std Dike
16010701
25010706
25010705
24010702
C4SS
05020702
06020704
10020705
09020707
LG 24
LG 25
LG 26
LG 27
VP4
h0.1% h2% h0.1% h2% h0.1% h2% h0.1% h2% h0.1% V2%
0.036 0.023 0.034 0.016 0.023 0.015 0.016 0.010 1.904 1.549
0.049 0.027 0.040 0.016 0.042 0.017 0.057 0.008 0.985
0.060 0.032 0.071 0.021 0.042 0.023 0.028 0.014 0.919
0.057 0.031 0.060 0.023 0.041 0.021 0.039 0.013 1.958 1.615
0.028
0.035
0.050
0.053
0.019
0.024
0.024
0.034
0.044
0.036
0.052
0.052
0.020
0.024
0.031
0.036
0.021
0.021
0.040
0.045
0.008
0.011
0.017
0.024
0.028
0.025
0.026
0.042
0.113
0.016
0.013
0.020
1.924
2.263
1.840
-
1.440
1.534
1.571
-
27020705
28020701
04030702
04030701
0.028
0.033
0.044
0.056
0.016
0.022
0.027
0.033
0.032
0.039
0.059
0.059
0.017
0.024
0.030
0.037
0.034
0.032
0.019
0.042
0.010
0.015
0.011
0.022
0.024
0.028
0.019
0.026
0.008
0.012
0.011
0.014
1.718
1.731
1.941
1.761
1.358
1.403
1.513
1.477
27020704
07020703
07020702
07020701
C4WL
28030705
28030703
27030703
27030702
0.024
0.041
0.036
0.049
0.014
0.022
0.025
0.032
0.030
0.041
0.055
0.085
0.015
0.023
0.029
0.036
0.038
0.053
0.072
0.062
0.009
0.014
0.018
0.025
0.023
0.040
0.040
0.043
0.007
0.012
0.015
0.021
1.785
1.772
1.795
1.777
1.261
1.413
1.450
1.527
0.049
0.083
0.078
0.071
0.031
0.040
0.043
0.053
0.065
0.104
0.091
0.089
0.021
0.030
0.043
0.051
0.014
0.023
0.017
0.024
0.006
0.009
0.011
0.015
0.024
0.034
0.027
0.040
0.007
0.011
0.016
0.021
1.773
1.902
1.835
1.886
1.142
1.337
1.371
1.445
24030701
24030702
24030703
25030701
0.059
0.054
0.071
0.070
0.031
0.036
0.046
0.053
0.035
0.048
0.075
0.070
0.019
0.026
0.042
0.047
0.016
0.018
0.021
0.025
0.005
0.007
0.013
0.014
0.025
0.024
0.038
0.030
0.007
0.010
0.018
0.021
1.920
1.860
2.020
1.974
1.028
1.224
1.485
1.443
25030702
25030703
25030704
25030705
0.043
0.061
0.068
0.069
0.033
0.036
0.046
0.049
0.040
0.058
0.070
0.095
0.020
0.028
0.042
0.046
0.011
0.019
0.024
0.039
0.006
0.008
0.011
0.012
0.014
0.033
0.034
0.054
0.008
0.010
0.016
0.018
1.081
2.030
1.867
2.011
0.430
1.259
1.448
1.433
D.M.D.T.B. Dassanayake
111
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Annex K: Reduction in overtopping layer thickness due to the effect of CDD
⎛h
− h 2%, CDD ⎞
Reduction = ⎜ 2%, Std Dike
⎟⎟ ×100%
⎜
h
2%,
Std
Dike
⎝
⎠
150%
Reduction in h2 % [m]..
100%
50%
0%
81.20
81.40
81.60
81.80
82.00
82.20
-50%
std dike profile
C4SS Rc=0.441m
C4SS Rc=0.397m
C4SS Rc=0.353m
C4SS Rc=0.309m
-100%
-150%
X-coordinate of the model [m]
Figure A:23: Reduction in overtopping layer thickness (h2%) C4SS
150%
Reduction in h2 % [m]..
100%
50%
0%
81.20
-50%
-100%
-150%
81.40
81.60
81.80
82.00
82.20
std dike profile
C4WL Rc=0.441m
C4Wl Rc=0.397m
C4WL Rc=0.353m
C4WL Rc=0.309m
X-coordinate of the model [m]
Figure A:24: Reduction in overtopping layer thickness (h2%) C4WL
D.M.D.T.B. Dassanayake
112
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Annex L: Coordinates of measuring devices
Standard dike tests
Channel
Type
Name
Unit
x [m]
y [m]
1
Layer thickness gauge
LG 13 front
m
79.44
0.71
2
Layer thickness gauge
LG 14 front
m
80.25
0.91
3
Layer thickness gauge
LG 15 front
m
80.65
1.01
4
Layer thickness gauge
LG 16 front
m
81.06
1.11
5
Layer thickness gauge
LG 17 crest
m
81.16
1.14
6
Layer thickness gauge
LG 18 crest
m
81.25
1.14
7
Layer thickness gauge
LG 19 crest
m
81.34
1.14
8
Layer thickness gauge
LG 20 back
m
81.44
1.11
9
Layer thickness gauge
LG 21 back
m
81.84
0.97
10
Layer thickness gauge
LG 22 back
m
82.24
0.84
11
Layer thickness gauge
LG 23 back
m
82.64
0.71
12
Layer thickness gauge
LG 24 back
m
81.84
0.97
13
Velocity propeller
VP 1 front
m/s
80.85
1.06
14
Velocity propeller
VP 3 crest
m/s
81.25
1.14
15
Velocity propeller
VP 4 back
m/s
81.44
1.11
16
Weighing machine
Weighing machine
kg
41
Wave gauge
WG 1 1st array
m
5.02
0.00
42
Wave gauge
WG 2 1st array
m
5.74
0.00
43
Wave gauge
WG 3 1st array
m
6.21
0.00
44
Wave gauge
WG 4 1st array
m
6.89
0.00
45
Wave gauge
WG 5 2nd array
m
70.53
0.08
46
Wave gauge
WG 6 2nd array
m
71.21
0.08
47
Wave gauge
WG 7 2nd array
m
71.69
0.08
48
Wave gauge
WG 8 2nd array
m
72.42
0.08
49
Wave gauge
WG 9 slope
m
76.78
0.08
50
Wave gauge
WG 10 slope
m
77.44
0.21
51
Wave gauge
WG 11 slope
m
77.92
0.33
52
Wave gauge
WG 12 slope
m
78.42
0.46
D.M.D.T.B. Dassanayake
113
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Tests with crest basin
Channel
Type
Name
Unit
x [m]
y [m]
1
Layer thickness gauge
LG 13 front
m
79.44
0.71
2
Layer thickness gauge
LG 14 front
m
79.84
0.81
3
Layer thickness gauge
LG 15 front
m
80.25
0.91
4
Layer thickness gauge
LG 16 front
m
80.66
1.01
5
Layer thickness gauge
LG 17 front
m
81.06
1.12
6
Layer thickness gauge
LG 18 crest
m
81.11
1.14
7
Layer thickness gauge
LG 19 crest
m
81.14
1.14
8
Layer thickness gauge
LG 20 crest
m
81.20
1.03
9
Layer thickness gauge
LG 21 crest
m
81.28
1.03
10
Layer thickness gauge
LG 22 crest
m
81.35
1.03
11
Layer thickness gauge
LG 23 crest
m
81.38
1.14
12
Layer thickness gauge
LG 24 crest
m
81.41
1.14
13
Layer thickness gauge
LG 25 back
m/s
81.56
1.11
14
Layer thickness gauge
LG 26 back
m/s
82.76
0.69
15
Layer thickness gauge
LG 27 back
m/s
82.36
0.83
16
Weighing machine
Weighing machine
kg
0.00
0.00
17
Layer thickness gauge LG 28 crest glss bk
m
81.35
1.09
18
Layer thickness gauge LG 29 crest glss mt
m
81.28
1.09
19
Layer thickness gauge LG 30 crest glss bk
m
81.20
1.09
20
water level gauge
DT 1
m
0.00
0.00
21
water level gauge
DT 2
m
0.00
0.00
22
Layer thickness gauge
LG 31 back
m
81.96
0.96
25
Velocity propeller
VP 1 front
m/s
81.55
1.07
26
Velocity propeller
VP 3 crest
m/s
81.38
1.14
D.M.D.T.B. Dassanayake
114
Hydraulic Model Tests of Wave Overtopping
on An Innovative Crest Drainage Dike
Channel
Type
Name
Unit
x [m]
y [m]
27
Velocity propeller
VP 4 back
m/s
81.56
1.11
41
Wave gauge
WG 1 1st arry
m
5.02
0.00
42
Wave gauge
WG 2 1st arry
m
5.74
0.00
43
Wave gauge
WG 3 1st arry
m
6.21
0.00
44
Wave gauge
WG 4 1st arry
m
6.89
0.00
45
Wave gauge
WG 5 2nd arry
m
70.02
0.08
46
Wave gauge
WG 6 2nd arry
m
70.83
0.08
48
Wave gauge
WG 8 2nd arry
m
72.27
0.08
49
Wave gauge
WG 9 slope
m
76.78
0.08
50
Wave gauge
WG 10 slope
m
77.44
0.21
51
Wave gauge
WG 11 slope
m
77.92
0.33
53
Wave gauge
WG 12 slope
m
78.42
0.46
55
Wave gauge
WG 7 2nd arry
m
71.48
0.08
D.M.D.T.B. Dassanayake
115