Michiel Vanhalewyn, Arno Soetaert overtopping: 2D model tests Update on the use of parapets at storm walls for wave Academic year 2015-2016 Faculty of Engineering and Architecture Chair: Prof. dr. ir. Peter Troch Department of Civil Engineering Master of Science in Civil Engineering Master's dissertation submitted in order to obtain the academic degree of Counsellors: Maximilian Streicher, David Gallach Sanchez Supervisor: Prof. dr. ir. Andreas Kortenhaus
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Michiel Vanhalewyn, Arno Soetaert
overtopping: 2D model testsUpdate on the use of parapets at storm walls for wave
Academic year 2015-2016Faculty of Engineering and ArchitectureChair: Prof. dr. ir. Peter TrochDepartment of Civil Engineering
Master of Science in Civil EngineeringMaster's dissertation submitted in order to obtain the academic degree of
Counsellors: Maximilian Streicher, David Gallach SanchezSupervisor: Prof. dr. ir. Andreas Kortenhaus
Michiel Vanhalewyn, Arno Soetaert
overtopping: 2D model testsUpdate on the use of parapets at storm walls for wave
Academic year 2015-2016Faculty of Engineering and ArchitectureChair: Prof. dr. ir. Peter TrochDepartment of Civil Engineering
Master of Science in Civil EngineeringMaster's dissertation submitted in order to obtain the academic degree of
Counsellors: Maximilian Streicher, David Gallach SanchezSupervisor: Prof. dr. ir. Andreas Kortenhaus
i
PREFACE
As finalization of 5 years academic career as student Civil Engineering, major Dredging and
Offshore Engineering at Ghent University, we present our master’s dissertation. Over the last
six months we have intensively researched wave overtopping at storm walls and the effect of
parapets in further reducing this wave overtopping. We hope we brought up some new
knowledge about this topic and that the thesis can form a basis for further research.
In the process of making this master’s dissertation we relied upon the knowledge of the
members of Civil Engineering, unit Coastal Engineering, Bridges and Roads. Therefore our
sincere thanks go to the people who made this dissertation possible and helped us creating our
work.
First of all we want to thank our supervisor Prof. dr. ir. Andreas Kortenhaus who introduced
us in the interesting domain of wave overtopping and the coastal measure techniques present
to mitigate it. Also we’d like to thank him for the organizing several meetings, being
accessible for all our questions and his expertise in wave overtopping. In the same line we
would like to thank our counsellors Maximilian Streicher and David Gallach Sanchez to guide
us through the execution of the model tests itself and their guidance in respectively wave
forces and wave overtopping expertise. For all our technical questions and the preparation of
our experiments in the wave flume, we would like to thank the technical staff; Herman, Sam,
Dave and Tom.
Last thanking words go to our family, friends to support us through our academic career and
especially during the preparation of our dissertation.
Deze pagina is niet beschikbaar omdat ze persoonsgegevens bevat.Universiteitsbibliotheek Gent, 2021.
This page is not available because it contains personal information.Ghent University, Library, 2021.
v
ABSTRACT
Update on the use of parapets at storm walls for wave overtopping: 2D
model tests
By Arno Soetaert and Michiel Vanhalewyn
Master’s dissertation submitted in order to obtain the academic degree of Master of Science in
Civil Engineering
Supervisor: Prof. dr. ir. Andreas Kortenhaus
Counsellors: Maximilian Streicher, David Gallach Sanchez
Academic year 2015-2016
University Ghent – Faculty of Engineering and Architecture
Department of Civil Engineering
Chairman: Prof. dr. ir. Peter Troch
The average overtopping has been tested and analysed for many different kinds of
configurations, but many of those studies only included one single reduction factor. By
performing hydraulic models tests in the large wave flume of Ghent University, the effect of
combined measures is tested. In these tests a slope is combined with a berm and a wall or a
parapet. When performing the tests also the individual amounts of overtopping are measured
as well as the forces acting on the storm wall. By analysing the data, the current prediction
formula for the average overtopping is updated with new reduction factors for a wall, a
parapet and a berm. For the individual overtopping and wave forces, new prediction formulas
are drafted and an introduction to their relationship is given.
notated as Q. The formula takes the form of a Weibull
distribution. The factors a, b are dependent on the
angle α of the slope. The formula is valid for all
relative freeboards Rc/Hm0.
B. Probability of overtopping Pow
The probability of overtopping Pow is defined as the
ratio of the number of overtopping waves Now and the
total amount of waves Nw reaching the construction.
Eq.(5)
In literature [1], Pow is mostly predicted by a
Rayleigh type prediction formula in function of the
relative freeboard Rc/Hm0. (Eq.(6))
Eq.(6)
is a factor dependent on the structure.
C. Individual overtopping characteristics Vmax and
V1/250
Besides average overtopping quantities, also the
individual overtopping volumes are of importance.
Vmax [kg/m] is the maximum volume encountered
during a certain time frame, V1/250 [kg/m] the average
of 0.4% largest volumes of the same time frame.
III. HYDRAULIC MODEL TESTS
A. Geometrical configurations
Six different configurations, modifying the
reference case, will be tested. The reference case is a
simple slope with slope 1:2 (V:H). The six
configurations can be divided into two main groups:
configurations without berm and configurations with a
berm.
For the configurations without berm either a
vertical wall or parapet is installed on the top of the
slope. Two heights for the walls and parapets are
used: 5 and 10 cm.
For the configurations with a berm, two berm
lengths are used: 20 and 40 cm. At the end of the
berm either a vertical wall or parapet is installed.
Again two heights for the walls and parapets are used:
5 and 10 cm.
B. Test conditions
The hydraulic model tests were performed in the
Large Wave Flume of the Coastal Engineering
Section of the Civil Engineering Department at Ghent
University. All tests were carried out with irregular
waves (JONSWAP3.3 spectrum). A summary of the
significant wave heights Hs, wave steepnesses sp and
water depths d at the wave paddle used for the tests
can be found in Table 1:
Table 1: Wave conditions for the hydraulic model tests
Wave height Hs [cm] 5, 10 and 15
Wave steepness sp [-] 0.02 and 0.05
Water depth d [cm] 68, 70, 73 and 76
Not all water depths were used for each geometrical
configuration. In total 166 tests were performed (150
unique and useful tests and 16 repetition tests).
IV. RESULTS OVERTOPPING
A. Reference case: simple slope
The reference case is drawn in Fig. 1. The slope has
a height of 53 cm and rest in reality on a 20 cm thick
return channel.
Fig. 1: Reference case, simple slope
1) Average overtopping q
The average overtopping q for the 12 tests
performed was made dimensionless. The existing
prediction formula Eq.(1) with the correct coefficients
(cotα = 2) is given in Eq.(7) and plotted against the
data.
Eq.(7)
A good fitting of the dimensionless overtopping Q
was found for the test results, such that Eq.(7) will be
used as the reference equation for a simple slope.
Eq.(7) will be named the ‘updated vdM formula’.
2) Probability of overtopping Pow
By fitting Eq.(6) against the 12 test results, a
corresponding χ-factor can be determined. A χ-factor
of 0.917 is found. In literature already equations are
present for the determination of χ. One of them is
proposed by Victor [3] and given in Eq.(8).
Eq.(8)
With cotα = 2 a value for χ equal to 1.25 is found.
As Eq.(8) is based on much more test results the χ-
factor corresponding with Eq.(8) will be used for
comparison with other equations.
3) Vmax and V1/250
To investigate Vmax and V1/250 these quantities are
made dimensionless. In Eq.(9) and Eq.(10) the
dimensionless quantities considered are given. Due to
a lack of number of tests, no prediction formulas are
created for the configuration of a simple slope.
Eq.(9)
Eq.(10)
B. No berm and vertical wall
The configuration without berm and a vertical wall
(5 or 10 cm) on top of the slope is represented in Fig.
2.
Fig. 2: No berm with wall on top of slope
1) Average overtopping q
The average overtopping q is made dimensionless
and plotted against the relative freeboard Rc/Hm0.
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5
Q [-]
0,0001
0,001
0,01
0,1
no berm walltest results wallupdated vdM
Fig. 3: Data points no berm wall and the pred. form.
The data points are compared with the updated vdM
formula for a simple slope in Fig. 3. The data points
lie clearly below the updated vdM formula. The
updated vdM formula needs to be modified such that
it can be applied for the configuration with a wall on
top of the slope. A reduction factor is used to take
into account the influence of the wall. The adapted
equation is given in Eq.(11).
Eq.(11)
The -factors are determined by rewriting Eq.(11)
to and to fill in all the required quantities of the
considered test results. The resulting equation is given
in Eq.(12).
Eq.(12)
The values resulting out of Eq.(12) are plotted
against Rc/Hm0 (Fig. 4). For these values a prediction
formula is created, only function of Rc/Hm0. This
prediction formula is given in Eq.(13).
Rc/H
m0 [-]
0 1 2 3 4
v [-]
0,0
0,2
0,4
0,6
0,8
1,0
1,2
reduced data set
prediction formula v
v = 0.1441x + 0.5692
R² = 0.5876
Fig. 4: Reduction factor in function of Rc/Hm0
Eq.(13)
Eq.(13) is really valid for Rc/Hm0 in [0.3;2.2]. An
extrapolation is made for Rc/Hm0 > 2.2. Remarkable
for Eq.(13) is that for Rc/Hm0 > 2.99, the values for
is 1. This means that no extra reduction will be found
in comparison with a simple slope. The prediction
formulas for the dimensionless overtopping Q for the
configuration of a wall on top of the slope (Eq.(11)) is
plotted in Fig. 3. Eq.(11) is also strictly valid for
Rc/Hm0 in [0.3; 2.2].
2) Probability of overtopping Pow
Fitting Eq.(6) against the test results, the
corresponding χ-factor can be determined. A χ factor
of 1.083 is found.
3) Vmax and V1/250
The dimensionless quantities represented in Eq.(9)
and Eq.(10) are plotted in function of Rc/Hm0. An
exponential and power law relationship described best
the dependency on Rc/Hm0. For smaller relative
freeboards the power law relationship gave better
results and is used for the prediction formulas.
Eq.(14) and Eq.(15) give the found prediction
formulas. These are valid for Rc/Hm0 in the interval
[0.4; 3].
Eq.(14)
Eq.(15)
C. No berm parapet
The configuration without berm and parapet (5 or
10 cm) on top of the slope is represented in Fig. 5.
Fig. 5: No berm with parapet on top of slope
1) Average overtopping q
The data points are compared with the updated vdM
formula for a simple slope in Fig. 3. The data points
lie clearly below the updated vdM formula and also
the prediction formula for a wall on top of the slope.
Further, Q depends on the wave steepness sm-1,0.
Rc/Hm0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Q [-]
1e-7
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
1e+0
sm-1,0 = 0.03
sm-1,0 = 0.05
no berm par. sm-1,0 = 0.03
no berm par. sm-1,0 = 0.05
updated vdMno berm wall
Fig. 6: Data points no berm parapet and the pred. form.
The updated vdM formula needs to be modified
such that it can be applied for the configuration with a
parapet on top of the slope. A reduction factor is
used to take into account the reduction in Q due to the
presence of a parapet. The reduction is considered
relative to the reduction already present by placing a
wall. The adapted equation is given in Eq.(16).
Eq.(16)
A similar procedure as for the configuration with a
wall is followed to determine with the help of the
test results. Only the resulting fitted equation for is
given.
Eq.(17)
Eq.(17) is valid for Rc/Hm0 in [0.3;1.7]. The prediction
formula for the dimensionless overtopping Q for the
configuration of a parapet on top of the slope
(Eq.(17)) is plotted in Fig. 6. For the two target
steepnesses another formula is plotted. Eq.(17) is also
strictly valid for Rc/Hm0 in [0.3;1.7].
2) Probability of overtopping Pow
Fitting Eq.(6) against the test results, the
corresponding χ-factor can be determined. A χ-factor
of 0.724 is found.
3) Vmax and V1/250
The dimensionless quantities Vdim,max and Vdim,1/250
are described by a power law. Eq.(18) and Eq.(19)
give the respective equations.
Eq.(18)
Eq.(19)
The equations are valid for Rc/Hm0 in [0.3;1.7]. The
same equations are valid when a berm of 20 or 40 cm
is present in front of the parapet. Therefor it can be
said that the berm width has no influence on the
dimensionless quantities Vdim,max and Vdim,1/250.
D. 20 cm or 40 cm berm and vertical wall
The configuration with berm (20 or 40 cm) and a
vertical wall behind the berm is represented in Fig. 7.
Fig. 7: 20 or 40 cm berm with vertical wall behind berm
1) Average overtopping q
In Fig. 8 the data points of the tests with a 20 or 40
cm berm are plotted along with the prediction formula
for the average overtopping in case of a vertical wall
without berm (Eq.(11)). It can be seen that the
formula over predicts the average overtopping,
especially for larger relative freeboards. An adaption
to the formula will have to be made to include the
influence of the berm.
Rc/Hm0 [-]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Q [-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
Data points 20/40 cm berm wall no berm wall
Fig. 8: Data points berm wall and the pred. form.
The influence of the berm is included by adding a
reduction factor γb in the formula. The new prediction
formula is given in Eq.(20).
Eq.(20)
A similar procedure is followed to determine
with the help of the test results and only the equation
is given. The average overtopping with a berm and a
vertical wall was dependent on the steepness and
therefore this factor is included in the formula.
Eq.(21)
Eq.(21) is valid for Rc/Hm0 in the range of
[0.3;2.2]. The prediction formula for the average
overtopping in case of a berm and a vertical wall
(Eq.(20)) is plotted on Fig. 8.
2) Probability of overtopping Pow
Fitting Eq.(6) against the test results, the
corresponding χ-factors can be determined. A χ factor
of 0.972 and 0.810 are found for respectively a 20
and 40 cm berm.
3) Vmax and V1/250
The dimensionless quantities Vdim,max and Vdim,1/250
are described by a power law. Eq.(22), Eq.(23) and
Eq.(24), Eq.(25) give the equations for respectively
20 and 40 cm berm. The equations are valid for
Rc/Hm0 in [0.3; 1.9].
Eq.(22)
Eq.(23)
Eq.(24)
Eq.(25)
E. 20 cm or 40 cm berm and parapet
The configuration with berm (20 or 40 cm) and a
parapet behind the berm is represented in Fig. 9.
Fig. 9: 20 or 40 cm berm with parapet behind berm
1) Average overtopping q
Installing a 20 or 40 cm does not influence the
average overtopping when a parapet is present.
Therefore the prediction formula is the same as
without the berm (Eq.(16)).
2) Probability of overtopping Pow
Fitting Eq.(6) against the test results, the
corresponding χ-factors can be determined. A χ factor
of 0.712 and 0.797 are found for respectively a 20
and 40 cm berm.
3) Vmax and V1/250
The dimensionless quantities Vdim,max and Vdim,1/250
are described by a power law. Eq.(18) and Eq.(19)
give the respective equations.
V. RESULTS FORCES
For the analysis of the wave forces, only tests with a
vertical wall are considered. To verify the influence
of the wave height and the relative freeboard, F1/250 is
examined. F1/250 is the average force of the 0.4 %
highest wave impacts. It varies between 13.4 N/m and
330.0 N/m. This variation is the consequence of the
influence that the wave height and relative freeboard
have on F1/250. A larger wave height leads to a higher
wave force and an increasing relative freeboard leads
to a decreasing wave force. To check the influence of
the water depth, steepness and berm width and to
come up with a prediction formula, a dimensionless
force needs to be introduced. The dimensionless force
P is equal to:
Eq.(26)
In this formula F1/250 is the force as mentioned
before, ρ is the water density, g is the gravitational
acceleration and Rc is the freeboard. The
dimensionless force P of every test is plotted in
function of the relative freeboard. This plot is shown
in Fig. 10. On this plot, all data points are closely
gathered and therefore the influence of the water
depth, steepness and berm width can be assumed zero.
With the help of Excel, a prediction formula can be
determined. The only parameter that will have to be
included in this formula is the relative freeboard since
the other parameters do not influence the wave force.
The prediction formula is equal to:
Eq.(27)
On Fig. 10, this prediction formula is plotted
alongside the test results. The plot shows that the
prediction line follows the test data quite nicely and
the scatter is limited. The correlation coefficient R² is
equal to 0.91.
Rc/Hm0 [-]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
P [-]
0.01
0.1
1
10
100
Prediction formula
P = 10.7*exp(-1.67x)
R² = 0.91
Fig. 10: Prediction formula plotted along with the test
results
To compare the wave forces acting on a simple
vertical wall to the ones acting on a parapet, 18 tests
are selected. When comparing the dimensionless
wave forces, the analysis shows that the forces acting
on the parapet are about 22 % higher than the ones
acting on the vertical wall. The reason for this rise in
horizontal forces is probably due to the fact that the
vertical forces that act on the parapet nose cause a
bending of the wall and this bending causes an
additional horizontal force onto the load cell.
However the exact reason for this phenomenon cannot
be determined since only horizontal forces were
measured. No prediction formula for the forces acting
on a parapet is determined because not enough data
was used for the analysis.
As a last part of the analysis of the forces, the
relationship between the wave forces and overtopping
was examined. To investigate whether there is a
relationship between both, the first 100 seconds of
three tests are studied. The three selected tests have a
water depth of 70 cm because the impacts and
overtopping events can be seen more clearly in this
case. The berm width is either 0, 20 or 40 cm. For the
three tests, a quadratic relationship between the wave
forces and overtopping can be seen. On Fig. 11 the
result for the test with a 20 cm berm is displayed. It
can also be seen that there needs to be a minimum
wave force before overtopping events occur. This
threshold is dependent on the berm width. For the test
without a berm the minimum force is equal to 15.2
N/m, for the 20 cm berm the minimum force is 19.6
N/m and for the 40 cm berm, the minimum force is
25.6 N/m. The influence of the water depth and
steepness on this threshold have not been determined
and therefore no prediction formula has been drafted.
Wave force [N/m]
0 20 40 60 80 100 120 140 160
Wave
ove
rto
pp
ing
[kg
/m]
-2
0
2
4
6
8
10
12
14
16
18
Fig. 11: Relationship between wave force and wave
overtopping
REFERENCES
[1] Platteeuw, J. (2015). Analysis of individual wave
overtopping volumes for steep low crested coastal structures
in deep water conditions.
[2] van der Meer, J., & Bruce, T. (2014). New Physical Insights
and Design Formulas on Wave Overtopping at Sloping and
Vertical Structures.
[3] Victor, L. (2012). Probability distribution of individual
wave overtopping volumes for smooth impermeable steep
slopes with low crest freeboard. Coastal Eng., pp. 87-101.
xiii
TABLE OF CONTENTS
Preface .............................................................................................................................................................. i
Abstract ........................................................................................................................................................... v
Extended Abstract .......................................................................................................................................... vii
Table of contents .......................................................................................................................................... xiii
List of Figures ................................................................................................................................................ xvii
List of Tables .................................................................................................................................................. xxi
List of Symbols and Abbreviations ................................................................................................................ xxiii
Chapter 3 Hydraulic model tests .............................................................................................................. 19
3.1 The wave flume at Ghent University .................................................................................................. 19 3.2 Model geometry ................................................................................................................................. 20 3.3 Test matrix ......................................................................................................................................... 23
3.3.1 Time series and test names ...................................................................................................... 25 3.3.2 Repetition tests ........................................................................................................................ 26
Chapter 4 Data processing ....................................................................................................................... 35
4.1 Wave measurements ......................................................................................................................... 35 4.1.1 Difference in generated and theoretical wave characteristics ................................................. 38
Table of contents
xiv
4.2 Average overtopping measurements ................................................................................................. 40 4.2.1 Scatter on the average overtopping ......................................................................................... 43
4.3 Individual overtopping measurements............................................................................................... 44 4.3.1 Scatter on the individual overtopping measures ..................................................................... 45
4.4 Force measurements .......................................................................................................................... 46 4.4.1 Scatter on the force measurements ......................................................................................... 52 4.4.2 Influence of the installation of a cover ..................................................................................... 53
Chapter 5 Average overtopping analysis .................................................................................................. 55
5.1 Influence of the water depth .............................................................................................................. 56 5.1.1 No berm .................................................................................................................................... 56 5.1.2 With berm ................................................................................................................................ 57
5.2 Influence of the wave steepness ........................................................................................................ 59 5.2.1 Reference case: slope no protection ........................................................................................ 60 5.2.2 No berm .................................................................................................................................... 62 5.2.3 With berm ................................................................................................................................ 65
5.3 Influence vertical wall/parapet .......................................................................................................... 66 5.3.1 No berm .................................................................................................................................... 67 5.3.2 20 cm berm ............................................................................................................................... 69 5.3.3 40 cm berm ............................................................................................................................... 70
5.4 Influence of the berm width ............................................................................................................... 71 5.4.1 Vertical wall .............................................................................................................................. 71 5.4.2 Parapet ..................................................................................................................................... 73
5.5 Comparison with literature ................................................................................................................ 74 5.5.1 No berm .................................................................................................................................... 74 5.5.2 With berm ................................................................................................................................ 78
5.6 Reduction factors ............................................................................................................................... 80 5.6.1 No berm .................................................................................................................................... 80 5.6.2 With berm ................................................................................................................................ 88
6.1 Probability of overtopping ................................................................................................................. 95 6.1.1 Factor 𝝌 determining the probability of overtopping Pow ........................................................ 96
6.2 Dimensionless individual overtopping quantities ............................................................................... 99 6.3 Influence of the water depth ............................................................................................................ 100 6.4 Influence of the wave steepness ...................................................................................................... 101 6.5 Influence of the berm width ............................................................................................................. 103 6.6 Prediction formulas for the dimensionless parameters ................................................................... 104
Chapter 7 Force analysis ........................................................................................................................ 111
7.1 Influence of the wave height ............................................................................................................ 111 7.2 Influence of the relative freeboard ................................................................................................... 112 7.3 Dimensionless wave force ................................................................................................................ 112 7.4 Influence of the water depth, steepness and berm width ................................................................ 112 7.5 Prediction formula............................................................................................................................ 113 7.6 Wave force when a parapet is installed ........................................................................................... 114 7.7 Relationship between wave forces and individual overtopping ....................................................... 115
Annex D: Test Matrix .................................................................................................................................... 139
xvii
LIST OF FIGURES
Figure 1-1: Maximum average overtopping rates for different activities ................................................................ 1 Figure 2-1: Overtopping parameters displayed on geometrical configuration ........................................................ 7 Figure 2-2: Range of chamfered and overhanging wall geometries and water levels ............................................. 8 Figure 2-3: FSS in comparison to upright seawall ................................................................................................ 10 Figure 2-4: Small recurve (left) and medium and large recurve (right); dimensions in m at prototype scale ....... 10 Figure 2-5: Principle of the vertical wall built in the dike .................................................................................... 13 Figure 2-6:Smooth slope with parapet, right case increased walking space ......................................................... 14 Figure 2-7: Schematically representation of parameters β and λ .......................................................................... 14 Figure 2-8: Generalised cross section of SSP walls .............................................................................................. 16 Figure 3-1: Large Wave Flume at Ghent University ............................................................................................. 19 Figure 3-2: Wave paddle ....................................................................................................................................... 20 Figure 3-3: Drawing of the whole flume; all dimensions are in cm ...................................................................... 21 Figure 3-4: The reference case .............................................................................................................................. 21 Figure 3-5: No berm and a parapet of 10 cm ........................................................................................................ 22 Figure 3-6: 20 cm berm and a parapet of 10 cm.................................................................................................... 22 Figure 3-7: 40 cm berm and a parapet of 10 cm.................................................................................................... 22 Figure 3-8: Drawing of the used parapets ............................................................................................................. 23 Figure 3-9: Generation of a time series in LabVIEW ........................................................................................... 25 Figure 3-10: Comparison between tests with the same time series (0091A: blue, 0091B: green, 0091C: red) .... 27 Figure 3-11: Individual pumping curves ............................................................................................................... 28 Figure 3-12: Average pumping curve ................................................................................................................... 29 Figure 3-13: Calibration curve weigh cell ............................................................................................................. 30 Figure 3-14: Set of 3 wave gauges near the toe of the structure ........................................................................... 31 Figure 3-15: Three hammer blows to the load cell................................................................................................ 32 Figure 3-16: Resonance frequency of the 10 cm wall/parapet .............................................................................. 32 Figure 3-17: Resonance frequency of the 5 cm wall/parapet ................................................................................ 33 Figure 3-18: Load cell without cover (left) and with cover (right) ....................................................................... 33 Figure 4-1: Input required to perform the reflection analysis ............................................................................... 35 Figure 4-2: Example of the output in the frequency domain in table form ........................................................... 37 Figure 4-3: Example of the output in the time domain in table form .................................................................... 37 Figure 4-4: Wave spectrum test 0011A ................................................................................................................. 37 Figure 4-5: Wave height distribution test 0011A .................................................................................................. 38 Figure 4-6: Generated significant wave heights plotted against the target significant wave heights (at the toe) .. 38 Figure 4-7: Generated peak periods plotted against the target peak periods (at the toe) ....................................... 40 Figure 4-8: Pumped absolute mass as function of the time ................................................................................... 41 Figure 4-9: Absolute mass in the reservoir as function of the time ....................................................................... 42 Figure 4-10: Cumulative absolute mass in the reservoir ....................................................................................... 42 Figure 4-11: Comparison 𝑞-values calculated with average overtopping script and individual overtopping script
.............................................................................................................................................................................. 44 Figure 4-12: Comparison between 𝑉𝑚𝑎𝑥 and 𝑉1/250 ........................................................................................ 45 Figure 4-13: Comparison between the measured, removed and filtered signal (low pass filter of 40 Hz) ............ 47 Figure 4-14: Comparison between the measured (black), removed (red) and filtered (blue) signal (low pass
filter of 85 Hz)....................................................................................................................................................... 48 Figure 4-15: Wave impact corresponding to the smallest wave is around 0.12 N ................................................ 49 Figure 4-16: Multiple peaks for one wave impact................................................................................................. 49 Figure 4-17: L-Davis only selects the highest peak per impact by applying a time domain search equal to the
peak period ............................................................................................................................................................ 49 Figure 4-18: Number of impacts according to the water depth ............................................................................. 50 Figure 4-19: Number of impacts according to the configuration .......................................................................... 51 Figure 4-20: Comparison between Fmax and F1/250 ................................................................................................. 51 Figure 4-21: Comparison between Fmax and F1/10 .................................................................................................. 52 Figure 4-22: Scatter analysis for test number 119 ................................................................................................. 53 Figure 5-1: Dimensionless overtopping discharge Q versus relative freeboard Rc/Hm0 for all the tests ............... 55 Figure 5-2: Influence of the water depth when there’s no berm and a wall (wave steepness 0.05) ...................... 56 Figure 5-3: Influence of the water depth when there’s no berm and a parapet (wave steepness 0.05) ................. 57 Figure 5-4: Influence of water depth when there's a 40 cm berm and a vertical wall (steepness 0.05) ................. 58 Figure 5-5: Influence of water depth when there's a 40 cm berm and a parapet (steepness 0.05) ......................... 59
List of Figures
xviii
Figure 5-6: Influence of the wave steepness when there's a slope without protection .......................................... 60 Figure 5-7: 𝑘𝑠-factors when there’s a slope without protection ............................................................................ 62 Figure 5-8: Influence of the wave steepness when there's no berm and a wall ..................................................... 63 Figure 5-9: ks-factors when there’s no berm and a wall ........................................................................................ 63 Figure 5-10: Influence of the steepness when there’s no berm and a parapet ....................................................... 64 Figure 5-11: 𝑘𝑠-factors when there’s no berm and a parapet ................................................................................ 65 Figure 5-12: 𝑘𝑠-factors configurations with wall .................................................................................................. 65 Figure 5-13: 𝑘𝑠-factors configurations with parapet ............................................................................................. 66 Figure 5-14: Comparison between the overtopping of a wall (left) and a parapet (right) ..................................... 67 Figure 5-15: Influence of parapet when there’s no berm (steepness 0.03) ............................................................ 68 Figure 5-16: 𝑘𝑝-factors no berm (steepness 0.03) ................................................................................................ 68 Figure 5-17: Influence of parapet when there’s a 20 cm berm (steepness 0.03) ................................................... 69 Figure 5-18: 𝑘𝑝-factors when there’s a 20 cm berm (steepness 0.03) .................................................................. 69 Figure 5-19: Influence of parapet when there’s a 40 cm berm (steepness 0.03) ................................................... 70 Figure 5-20: 𝑘𝑝-factors when there’s a 40 cm berm (steepness 0.03 left and 0.05 right) ..................................... 71 Figure 5-21: Influence of the berm width when there’s a vertical wall (steepness 0.05) ...................................... 72 Figure 5-22: 𝑘𝑏- factors 20/40 cm berm (with a vertical wall and steepness 0.05) .............................................. 73 Figure 5-23: Influence of the berm width when there’s a parapet (steepness 0.05) .............................................. 73 Figure 5-24: Comparison of test results and EurOtop Manual in case there's a slope with no protection ............ 75 Figure 5-25: Comparison of test results and updated vdM formula in case there's a slope with no protection..... 76 Figure 5-26: Comparison of test results and updated vdM formula in case there's no berm and wall .................. 77 Figure 5-27: Comparison of test results and updated vdM formula in case there's no berm and a parapet........... 78 Figure 5-28: Comparison between prediction formula of van Doorslaer and test results ..................................... 79 Figure 5-29: 𝛾𝑣-factors split up in steepness. ....................................................................................................... 81 Figure 5-30: 𝛾𝑣-factors without the values above 1 and linear trendline .............................................................. 81 Figure 5-31: Prediction formula 𝛾𝑣 based on the reduced data set ....................................................................... 82 Figure 5-32: Relationship between the predicted γv and the γv based on the test results ..................................... 83 Figure 5-33: Prediction formula Q no berm wall plotted through the test results ................................................. 84 Figure 5-34: γp-factors split up in wave steepness .............................................................................................. 85 Figure 5-35: Reduced test results with their linear trendline................................................................................. 86 Figure 5-36: Relationship between the predicted γp and the γp based on the test results .................................... 87 Figure 5-37: Prediction formulas Q parapet and no berm plotted through the test results .................................... 87 Figure 5-38: Test results plotted against prediction formula Q for a wall without berm ..................................... 88 Figure 5-39: Reduction factors relative to berm width B ...................................................................................... 89 Figure 5-40: Determination of the prediction formula for γb with a simple vertical wall .................................... 90 Figure 5-41: γb real relative to γb predicted ........................................................................................................ 91 Figure 5-42: Comparison between prediction formulas Q for wall without berm and wall with berm ................. 91 Figure 5-43: γb factor relative to the actual berm width ...................................................................................... 92 Figure 5-44: Determination of prediction formula for γb with parapet ................................................................ 93 Figure 5-45: Comparison between predicted overtopping and test results ............................................................ 94 Figure 5-46: Flowchart prediction formulas Q ...................................................................................................... 94 Figure 6-1: Probability of overtopping in function of the relative freeboard for all the tests ................................ 96 Figure 6-2: Prediction formula Pow for configurations without a berm ............................................................... 97 Figure 6-3: Prediction formula Pow for configurations with a 20 cm berm ......................................................... 98 Figure 6-4: Prediction formula Pow for configurations with 40 cm berm ............................................................ 99 Figure 6-5: Maximal volume in function of the relative freeboard ....................................................................... 99 Figure 6-6: Influence of the water depth on the maximum volumes for the cases with a wall ........................... 100 Figure 6-7: Influence of the water depth on the maximum volumes for the cases with parapet ......................... 101 Figure 6-8: Influence of the steepness on the maximum volume for the cases with wall ................................... 102 Figure 6-9: Influence of the steepness on the maximum volume for the cases with parapet .............................. 102 Figure 6-10: Influence of the berm width on the maximum volume for the cases with wall .............................. 103 Figure 6-11: Influence of the berm width on the maximum volume for the cases with parapet ......................... 104 Figure 6-12: Dimensionless maximum volume in function of the relative freeboard ......................................... 105 Figure 6-13: Two different forms of prediction formulas for the dimensionless maximum volume .................. 105 Figure 6-14: Two different forms of prediction formulas for the dimensionless maximum volume (linear) ..... 106 Figure 6-15: Graphical summary of the prediction formulae used for the configurations with a wall ............... 107 Figure 6-16: Graphical summary of the prediction formulae used for the configurations with a parapet ........... 108 Figure 6-17: Comparison between pred. formulas wall and parapet ................................................................... 109 Figure 7-1: F1/250 plotted against Hm0................................................................................................................... 111 Figure 7-2: Wave force F1/250 plotted against the relative freeboard Rc/Hm0 ....................................................... 112
xix
Figure 7-3: Dimensionless wave force P in function of relative freeboard Rc/Hm0 ............................................. 113 Figure 7-4: Prediction formula plotted along with the test results ...................................................................... 114 Figure 7-5: Comparison between wave forces with a vertical wall and a parapet .............................................. 115 Figure 7-6: Relationship between wave force and wave overtopping ................................................................. 116 Figure A-1: Influence of water depth when there's no berm and a wall (steepness 0.03) ................................... 123 Figure A-2: Influence of the water depth when there’s no berm and a parapet (steepness 0.03) ........................ 123 Figure A-3: Influence of water depth when there's a 40 cm berm and a wall (steepness 0.03) ........................... 124 Figure A-4: Influence of water depth when there's a 40 cm berm and a parapet (steepness 0.03) ...................... 124 Figure A-5: Influence of the wave steepness when there’s a 20 cm berm and a wall ......................................... 125 Figure A-6: Influence of the wave steepness when there’s a 40 cm berm and wall ............................................ 125 Figure A-7: Influence of the wave steepness when there’s a 20 cm berm and parapet ....................................... 126 Figure A-8: Influence of the wave steepness when there’s a 40 cm berm and parapet ....................................... 126 Figure A-9: Influence of parapet when there’s no berm (steepness 0.05) ........................................................... 127 Figure A-10 : 𝑘𝑝-factors no berm (steepness 0.05) ............................................................................................. 127 Figure A-11: Influence of parapet when there’s a 20 cm berm (steepness 0.05) ................................................ 128 Figure A-12: 𝑘𝑝-factors 20 cm Berm (steepness 0.05) ....................................................................................... 128 Figure A-13: Influence of parapet when there’s a 40 cm berm (steepness 0.05) ................................................ 129 Figure A-14: 𝑘𝑝-factors 40 cm berm (steepness 0.05) ........................................................................................ 129 Figure A-15: Influence of the berm width when there’s a wall (steepness 0.03) ................................................ 130 Figure A-16: kb-factors when there’s a 20/40 cm berm and a wall (steepness 0.03) .......................................... 130 Figure A-17: Influence of the berm width when there’s a parapet (steepness 0.03) ........................................... 131 Figure A-18: γv-factors without the values above 1 and quadratic trendline ..................................................... 131 Figure A-19: γv-factors without the values above 1 and power trendline .......................................................... 132 Figure B-1: Influence of the water depth on the 0.4% volumes for the cases with wall ..................................... 133 Figure B-2: Influence of the water depth on the 0.4% volumes for the cases with parapet ................................ 133 Figure B-3: Influence of the wave steepness on the 0.4% volumes for the cases with wall ............................... 134 Figure B-4: Influence of the water depth on the 0.4% volumes for the cases with parapet ................................ 134 Figure B-5: Influence of the berm width on the 0.4% volumes for the cases with wall ...................................... 135 Figure B-6: Influence of the berm width on the 0.4% volumes for the cases with parapet ................................. 135 Figure B-7: Comparison between pred. formulas wall and parapet .................................................................... 136 Figure C-1: Influence of the water depth on the wave force ............................................................................... 137 Figure C-2: Influence of the steepness on the wave force ................................................................................... 137 Figure C-3: Influence of the berm width on the wave force ............................................................................... 138
xxi
LIST OF TABLES
Table 2-1: Overtopping for different configurations with a relative freeboard of 1.67 ........................................... 8 Table 3-1: Chosen peak periods Tp with their corresponding wave height Hs .................................................... 23 Table 3-2: Summary of the test matrix .................................................................................................................. 24 Table 3-3: average overtopping for test 0091A and its repetition tests 0091B, 0091C and 0091D ...................... 26 Table 4-1: summary of reduction in wave height at the toe .................................................................................. 39 Table 4-2: Modifications performed in the MATLAB -script to predict the average overtopping 𝑞 ................... 41 Table 4-3: Scatter present on the average overtopping ......................................................................................... 43 Table 4-4: Comparison of the individual volume characteristics repetition tests 0091A, 0091B, 0091C and
0091D .................................................................................................................................................................... 45 Table 4-5: Comparison of the force measurements between a covered and uncovered test ................................. 53 Table 5-1: Target wave steepnesses and the range of the experimental reached values ....................................... 60 Table 5-2: Summary of tests with water depth 68 cm at the wave paddle ............................................................ 61 Table 6-1: Factor 𝜒 and its 95% confidence intervals determined with SPSS ...................................................... 96 Table 6-2: Prediction formulas Vdim,1/250 and applicability range ........................................................................ 109 Table A-1: Different formulas for γp with their unknown parameters and coefficient of determination R² ...... 132 Table D-1: Test matrix of the conducted tests .................................................................................................... 139
xxiii
LIST OF SYMBOLS AND ABBREVIATIONS
Symbols
a [-] coefficient used in the new form (Weibull distribution) of prediction formula for Q
A [-] parameter used in SPSS to fit prediction formulas
B [m] berm width of the structure
b [-] specific factor describing the behaviour of wave overtopping for a certain structure
b [-] coefficient used in the new form (Weibull distribution) of prediction formula for Q
B [-] parameter used in SPSS to fit prediction formulas
𝐵𝑏 [m] berm width of the structure defined by Kortenhaus et al.
c [-] coefficient used in the new form (Weibull distribution) of prediction formula for Q
C [-] parameter used in SPSS to fit prediction formulas
𝐶𝑟𝑒𝑓𝑙 [-] reflection coefficient determined with WaveLab at the slope of the structure
d [m] water depth at the specified location of the structure
D [-] parameter used in SPSS to to fit prediction formulas
E [-] parameter used in SPSS to to fit prediction formulas
𝐹1/10 [N/m] average horizontal force of the 10% highest force impacts
𝐹1/250 [N/m] average horizontal force of the 0,4% highest force impacts
𝐹ℎ [N/m] horizontal force defined by Kortenhaus et al.
𝐹𝑚𝑎𝑥 [N/m] maximal horizontal force found on the load cell for each test
g [m/s²] acceleration due to gravity, taken equal to 9.81 m/s²
ℎ𝑏 [m] foreland height defined by Kortenhaus et al.
𝐻𝑖 [m] wave height individual waves
𝐻𝑚0 [m] significant wave height in the frequency domain
𝐻𝑚0,𝑡𝑎𝑟𝑔𝑒𝑡 [m] target significant wave height in the frequency domain at the toe of the structure
𝐻𝑚0,𝑡𝑜𝑒 [m] significant wave height in the frequency domain measured at the toe of the structure
ℎ𝑛 [m] height of the inclined part of the parapet
𝐻𝑠 [m] significant wave height in the time domain
ℎ𝑡 [m] total parapet height
ℎ𝑤𝑎𝑙𝑙 [m] height of the storm wall
k [-] Ratio of two wave overtopping quantities
𝑘𝑏 [-] ratio of two dimensionless overtopping quantities Q; with berm or no berm, but all the
other test conditions the same
List of Symbols and Abbreviations
xxiv
𝑘𝑝 [-] ratio of two dimensionless overtopping quantities Q; with wall or parapet, but all the
other test conditions the same
𝑘𝑠 [-] ratio of two dimensionless overtopping quantities Q; with different steepness, but all the
other test conditions the same
𝐿𝑝 [m] wave length determined with peak period 𝑇𝑝
𝐿𝑚−1,0 [m] wave length determined with spectral wave period 𝑇𝑚−1,0
𝐿𝑝𝑎𝑑𝑑𝑙𝑒 [m] wave length determined with the peak period 𝑇𝑝 at the wave paddle
𝑚0 [m²] zero moment of the incident wave spectrum
𝑚−1 [m²s] first negative moment of the incident wave spectrum
𝑀𝑐.𝑎𝑏𝑠.,𝑒𝑛𝑑 [kg] end mass of the cumulative absolute mass curve
𝑀𝑐.𝑎𝑏𝑠.,𝑠𝑡𝑎𝑟𝑡 [kg] start mass of the cumulative absolute mass curve
𝑁𝑜𝑤 [-] number of overtopping waves
𝑁𝑤 [-] number of waves
P [-] Dimensionless maximum force
𝑃𝑜𝑤 [-] probability of wave overtopping
Q [-] dimensionless overtopping quantity
q [m³/s/m] average overtopping discharge
𝑄0 [-] dimensionless overtopping quantity when the relative freeboard is zero
R² [-] Coefficient of determination: defined as 𝑅² = 1 −𝑟𝑟𝑒𝑠
𝑟𝑡𝑜𝑡 and 𝑟𝑟𝑒𝑠 the residual sum of
squares and 𝑟𝑡𝑜𝑡 the total sum of squares
𝑅𝑐 [m] crest freeboard
𝑅𝑐 𝐻𝑚0⁄ [-] relative crest freeboard defined with the significant wave height of the frequency
domain, also equal to R*
𝑅𝑐 𝐻𝑠⁄ [-] relative crest freeboard defined with the significant wave height of the time domain
𝑅𝑢2% [m] 2 % run-up height: On average 2% of the waves run-up to that specified height
𝑠𝑝 [-] wave steepness calculated with peak period 𝑇𝑝
𝑠𝑚−1,0 [-] wave steepness calculated with spectral period 𝑇𝑚−1,0
𝑠0 [-] fictitious wave steepness calculated with spectral period 𝑇𝑚−1,0
𝑡𝑒𝑛𝑑 [s] end time of a test, excluding the extra outrun time
𝑇𝑖 [s] wave period individual wave
𝑇𝑚 [s] average wave period
𝑇𝑚−1,0 [s] spectral wave period
𝑇𝑝 [s] peak wave period
xxv
𝑇𝑝,𝑡𝑎𝑟𝑔𝑒𝑡 [s] target peak wave period at the toe of the structure
𝑇𝑝,𝑡𝑜𝑒 [s] peak wave period measured at the toe of the structure
𝑡𝑠𝑡𝑎𝑟𝑡 [s] start time of a test, excluding the extra time at the start of the test
𝑉1/250 [kg/m] average volume of the 0.4% individual overtopping volumes 𝑉𝑖
𝑉𝑖 [kg/m] individual overtopping volumes per meter
𝑉𝑑𝑖𝑚,𝑚𝑎𝑥 [-] dimensionless maximum overtopping volume
Also no difference is made in berm width for the configurations with parapet, because again
these different formulas lie close together.
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Vdim
, m
ax [
-]
0,0001
0,001
0,01
0,1
1
10
100
1000
no berm wall20 cm berm wall40 cm berm wallall data parapetpred. formula no berm wallpred. formula 20 cm berm wallpred. formula 40 cm berm wallglob. pred. formula parapet
111
CHAPTER 7 FORCE ANALYSIS
The aim of this section is to come up with a prediction formula for the wave loads on the
storm wall. To do so first the influence of different parameters such as wave height (section
7.1), relative freeboard (section 7.2), water depth, steepness and berm width (section 7.4) is
checked. These influences are first checked with the absolute force values. To be able to make
a prediction formula, it’s better to work with a dimensionless force and finding the right
dimensionless force is the next step in the analysis. The last step of the analysis is then
combining al the parameters that have an influence on the force impact to one general
prediction formula (section 7.5). For the general analysis of the forces, only tests with a wall
are considered and in section 7.6 the influence of installing a parapet on the wave forces is
examined. In the final section of this chapter, an introduction to the relationship between
wave forces and individual overtopping is given.
7.1 Influence of the wave height
In Figure 7-1 the absolute wave force F1/250 is shown in function of the incident wave height
Hm0 at toe of the dike. It can immediately be seen that the incident wave height has a great
influence on the wave force, a larger incident wave height leads to a higher wave force.
Because in Figure 7-1 no distinction is made between tests with different configurations
(berm width, relative freeboard), a lot of scatter is present and therefore no trendline is added.
FIGURE 7-1: F1/250 PLOTTED AGAINST HM0
Hm0
[m]
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
F1
/25
0 [N
/m]
0
50
100
150
200
250
300
350
Chapter 7 Force analysis 7.2 Influence of the relative freeboard
112
7.2 Influence of the relative freeboard
On Figure 7-2 the relationship between the absolute wave force F1/250 and relative freeboard
Rc/Hm0 is shown. The relative freeboard is, just like with the overtopping, an important
parameter. It combines the water depth, wave height and the crest level. According to the plot,
the wave force increases with decreasing relative freeboard.
FIGURE 7-2: WAVE FORCE F1/250 PLOTTED AGAINST THE RELATIVE FREEBOARD RC/HM0
7.3 Dimensionless wave force
Up to now only absolute values of the wave force have been used. To be able to come up with
a general prediction formula, it is required to use a dimensionless wave force. To make the
force dimensionless, it is divided by the water density ρ, the gravitational acceleration g and
the square of the freeboard Rc.
𝑃 =
𝐹1/250
𝜌 ∙ 𝑔 ∙ 𝑅𝑐2 (60)
The chosen form of the dimensionless force P is based on the master thesis of (Hohls, 2015).
By introducing the dimensionless wave force it is easier to check the influence of the water
depth, wave steepness and berm width.
7.4 Influence of the water depth, steepness and berm width
To investigate the influence of the different parameters on to the dimensionless wave force P,
Figure 7-3 is shown. The data points shown in this Figure are closely gathered and the
Rc/H
m0 [-]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
F1
/25
0 [N
/m]
0
50
100
150
200
250
300
350
Chapter 7 Force analysis 7.5 Prediction formula
113
difference between them is smaller than the possible scatter that is present and therefore it can
be concluded that the water depth, steepness and berm width have no influence on the
determination of the wave force. In Annex C, the data points are split up according to water
depth, steepness and berm width and there it can be seen that all these parameters do not
influence the wave force.
The water depths play a role in the number of waves that hit the wall as was described in
section 4.4 but it has no influence on the wave force because the freeboard is present in both
axes. For the influence of the steepness and berm width, it has to be mentioned that this
conclusion is only valid for steepnesses between 3 and 5 % and for the berm widths presented
in this thesis. For other steepnesses and berm widths, no conclusion can be given.
FIGURE 7-3: DIMENSIONLESS WAVE FORCE P IN FUNCTION OF RELATIVE FREEBOARD RC/HM0
7.5 Prediction formula
Now that the parameters which influence the wave force are determined, an empirical
prediction formula can be developed with the use of Excel. This formula will be dependent on
the relative freeboard only since the other parameters have less influence on the wave force.
The prediction formula is plotted in Figure 7-4 along with the test results. The prediction
formula is shown in equation (61).
𝐹1/250
𝜌 ∙ 𝑔 ∙ 𝑅𝑐2= 10.7 ∙ exp (−1.67 ∙
𝑅𝑐𝐻𝑚0
) (61)
In this formula F1/250 is the average force of the highest 0.4 % impacts, ρ is the water density,
g is the gravitational acceleration, Rc is the freeboard and Hm0 is the incident wave height at
Rc/H
m0 [-]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
P [
-]
0.01
0.1
1
10
100
Chapter 7 Force analysis 7.6 Wave force when a parapet is installed
114
the toe of the structure. In Figure 7-4, it can be seen that the prediction formula follows the
test results quite nicely and this leads to a coefficient of determination equal to 0.91.
FIGURE 7-4: PREDICTION FORMULA PLOTTED ALONG WITH THE TEST RESULTS
7.6 Wave force when a parapet is installed
Up to now, only test configurations with a vertical wall were considered. In this paragraph a
comparison will be made between tests with a wall and a parapet but with every other
parameter the same. A selection of tests is made to compare the wave forces. The selection
contains nine tests in total with three different wave heights and three different berm widths.
The dimensionless force is used to compare the wave forces. In Figure 7-5 the dimensionless
wave force is plotted against the relative freeboard Rc/Hm0. The 18 data points (9 with a wall
and 9 with a parapet) are plotted alongside with the prediction formula presented in equation
(61). In Figure 7-5, the trendline of the data points of the tests with a vertical wall is fairly
close to the prediction formula. The trendline of the data points of the tests with parapet is
further off. Based upon this small selection of tests, it can be concluded that the wave forces
induced on a storm wall with a parapet are higher than the ones on a simple vertical storm
wall. The difference between both configurations is about 22 %. The reason for this rise in
horizontal forces is probably due to the fact that the vertical forces that act on the parapet
cause a bending of the wall and this bending causes an additional horizontal force onto the
load cell. However the exact reason for this phenomenon cannot be determined since only
horizontal forces were measured. To come up with a prediction formula for the wave forces
on a storm wall with a parapet, more tests should be used for the analysis.
Rc/H
m0 [-]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
P [-]
0.01
0.1
1
10
100
Prediction formula
P = 10.7*exp(-1.67x)
R² = 0.91
Chapter 7 Force analysis 7.7 Relationship between wave forces and individual overtopping
115
FIGURE 7-5: COMPARISON BETWEEN WAVE FORCES WITH A VERTICAL WALL AND A PARAPET
7.7 Relationship between wave forces and individual overtopping
During testing, the wave forces and overtopping have been measured. In literature not much
research has been done yet to the relationship between wave forces and individual
overtopping amounts. In this section a small introduction is given to this subject to see if there
is a clear relationship between them and if this is the case, further research might be useful.
To investigate whether there is a relationship, the first 100 seconds of three tests are looked at
more closely. The wave force and individual overtopping of each wave impact during this
time period are related to each other. The three selected tests are 0048A, 0073A and 00145A
(see Annex D). The chosen tests have a water depth of 70 cm and a berm width of 0 cm, 20
cm and 40 cm respectively. The chosen water depth is 70 cm because in this case, the
overtopping events are more limited and the wave impacts can be seen more clearly. To
correlate the wave impact to the right overtopping event, the videos are examined. In the
video analysis, every impact and potential overtopping can be seen. This impact can then be
correlated to the right wave force with the help of the excel files that were created in Chapter
4. When the impact lead to an overtopping event, the overtopping volume could be linked to
the impact with the help of the excel files created by the individual overtopping script. This
course of action was repeated for all the wave impacts in the first 100 seconds of the three
videos and so every overtopping event was linked to a certain wave force.
For test number 0073A the relationship between the wave force and overtopping is shown in
Figure 7-6. The lowest force for which an overtopping event occurs is 19.6 N/m and the
overtopping then is very limited (0.14 kg/m). Beyond this threshold the wave overtopping
Rc/H
m0 [-]
0.0 0.5 1.0 1.5 2.0 2.5
P [
-]
0.1
1
10
With parapet Trendline with parapetWithout parapetTrendline without parapetPrediction formula without parapet
Chapter 7 Force analysis 7.7 Relationship between wave forces and individual overtopping
116
shows a quadratic relationship compared to the wave force. The two other selected tests (test
number 0048A and 00145A) show a similar relationship. The only difference between the
three different tests is that the quadratic trendline is shifted to the left when there is no berm
or to the right with a 40 cm berm. The threshold for overtopping without a berm is 15.2 N/m
and for the 40 cm berm the threshold equals 25.6 N/m. This indicates that the berm width has
an influence on the relationship between the wave force and overtopping. The influences of
the other parameters (steepness and water depth) on this relationship were not determined
because not enough data was checked and therefore no formula based relationship was
established as well. However this small introduction into this domain shows that there might
be a fixed relationship between the wave force and overtopping and therefore further research
would be useful.
FIGURE 7-6: RELATIONSHIP BETWEEN WAVE FORCE AND WAVE OVERTOPPING
Wave force [N/m]
0 20 40 60 80 100 120 140 160
Wa
ve o
vert
op
pin
g [kg
/m]
-2
0
2
4
6
8
10
12
14
16
18
117
CHAPTER 8 CONCLUSION
8.1 Average overtopping
The analysis of the average overtopping happened in Chapter 5. To start the analysis, the
influence of different parameters on the overtopping was verified. For the verification of the
influences, the dimensionless overtopping Q was used. The water depth was the first
parameter to be checked and it was found that it has no influence on the dimensionless
overtopping because the freeboard, which is influenced by the water depth, is present in the x-
axis. Secondly the influence of steepness was examined. For the tests with a parapet, an
influence of the steepness was found whereas for the tests with a vertical wall, an influence of
the steepness was only present when there was a berm installed. When there was no berm and
a vertical wall, the steepness did not influence the overtopping. The third tested parameter
was the influence of a parapet in comparison to a simple vertical wall. It was found that
installing a parapet instead of a wall, greatly reduced the overtopping, especially for a larger
relative freeboard. The fourth and last investigated parameter was the berm width. For this
parameter it was found that it has an influence on the overtopping when a vertical wall was
installed. When a parapet was installed, the influence was much less and even negligible.
Once the influence of the different parameters was determined, the results were compared to
the existing literature. Here it was established that the updated van der Meer formula is the
most accurate prediction formula for the tests without any protection (wall or berm).
Therefore this formula was chosen as the basis for new prediction formulas. To adapt the
updated vdM formula, reduction factors were added when a wall, parapet or berm was
installed. These reductions are dependent on the previous discussed parameters (steepness and
berm width). In total three new prediction formulas, dependent on one or two reduction
factors, were drafted.
8.2 Individual overtopping
In the individual overtopping analysis (Chapter 6), different parameters were investigated that
characterize the individual overtopping behaviour of a structure. In a first part the probability
of overtopping Pow was investigated per structure. For each configuration separately,
prediction formulas of the Rayleigh type are used to predict Pow in function of the relative
freeboard Rc/Hm0. The factor χ determined the shape of the prediction formula.
In section 6.2 till 6.6, the characteristics Vmax and V1/250 were looked into. The different
parameters influencing Vmax and V1/250 were investigated. With the knowledge of the
influencing parameters (wave steepness), Vmax and V1/250 were made dimensionless. The
Chapter 8 Conclusion 8.3 Wave forces
118
reason for making those characteristics dimensionless is that the fitting procedure of
prediction formulas is facilitated. For the different geometrical configurations, prediction
formulas for Vdim,max and Vdim,1/250 were proposed. The prediction formulas follow a power
law and are again function of the dimensionless freeboard Rc/Hm0. In the last part, the
different formulas are compared to each other and some observations were explained.
8.3 Wave forces
In Chapter 7 an analysis of the horizontal wave forces was performed. For this analysis only
tests with a simple vertical wall were considered. To start the analysis the influence of
different parameters was checked. To verify the influence of the wave height, the average of
the 0.4 % highest wave forces was examined. It could be noticed that the wave force increases
for increasing wave height. The relative freeboard has on opposite effect on the absolute wave
force. The wave forces decreases with increasing relative freeboard. To verify the influence of
the water depth, steepness and berm width, a dimensionless wave force was created. With the
help of this dimensionless wave force it was found that none of the previous mentioned
parameters has an influence on the wave force. The only parameter that is taken up in the
prediction formula is therefore the relative freeboard Rc/Hm0. With this prediction formula all
the test data can be predicted quite well and this leads to a coefficient of determination of
0.91.
After the prediction formula was drafted, a comparison was made between the wave forces
acting on a storm wall and the ones acting on a parapet. To compare these two configurations,
a few tests were selected. Based upon the selected tests, it could be concluded that the forces
on a parapet are about 22 % higher than on a simple vertical wall. For the wave forces acting
on a parapet, no prediction formula was drafted because not enough data was examined to be
able to come up with an accurate formula. In the last part of Chapter 7, the relationship
between wave forces and individual overtopping was examined. Through the analysis of three
tests, a quadratic relationship was found. For every test, a certain threshold for overtopping
was found. Below a minimum force, there were no overtopping events. The analysis of the
three selected tests shows that there might be a fixed relationship between the wave force and
overtopping and therefore further research would be useful.
8.4 Further research
Regarding the overtopping there are still some influences that can be further examined. First
of all, the influence of a larger berm width needs to be verified. In this thesis it was often
found that the berm width does not have a clear influence but this is probably because the
tested berm widths are too small in comparison to the wave lengths of the used waves.
Chapter 8 Conclusion 8.4 Further research
119
Secondly, more tests with different steepnesses should be conducted to further understand the
effect that the steepness has on the overtopping. A third possibility for further research is the
influence of curved parapets. Coming up with reduction factors for different types of parapets
can be useful in the future. At last, the formulas created can be checked and possibly updated
with tests, performed with other relative freeboards or wave characteristics.
For the individual overtopping volumes also some further research can be performed. One
interesting research domain is to look into the distribution function of the individual
overtopping volumes Vi. Some literature is already present for the case of a simple slope. An
extension of this literature is to consider also the configurations described in the master thesis.
When looking at the forces, there are also still some things that can be investigated more
closely. The horizontal forces that act on a parapet are only briefly discussed in this thesis.
For these horizontal forces acting on a parapet, it can be investigated why they are larger in
comparison to the forces acting on a vertical wall and also a prediction formula can be
drafted. Besides horizontal forces also vertical forces will be present on the parapet.
Measuring and investigating these forces can be interesting. The relationship between wave
forces and individual overtopping has also been introduced in this thesis and here further
research can be conducted to be able to predict the overtopping when the forces are known or
vice versa.
121
REFERENCES
Altomare. (2014). Characterization of Wave Impacts on Curve Faced Storm Return Walls
within a Stilling Wave Basin Concept.
Cornett, A. (1999). Wave Overtopping at Chamfered and Overhanging Vertical Structures.
Daemrich, K. (2006). Overtopping at Vertical Walls and Parapets - Regular Wave Tests for
Irregular Simulation.
Goormachtigh, J., & Harchay, W. (2010). Experimentele studie van golfoploop en overslag
ter optimalisatie van golfenergieconvertoren gebaseerd op golfoverslag. Ghent,
Belgium.
Hohls, C. (2015). Wave-Induced Loading of a Storm Walls at the Belgian Coast.
Kamikubo, Y. (sd). Reduction of Wave Overtopping and Water Spray with Using Flaring
Shaped Seawall.
Kisacik, D. (2011). Description of Loading Conditions due to Violent Wave Impacts on a
Vertical Structure with an Overhanging Horizontal Cantilever Slab.
Kortenhaus et al. (2008). Storm Surge Protection Walls in Germany.
Kortenhaus et al. (2001). Design Aspects of Verticall Walls with Steep Foreland Slopes.
Kortenhaus, A. (2003). Influence of Parapets and Recurves on Wave Overtopping and Wave
Loading of Complex Vertical Walls.
Mansard and Funke. (1980). The Measurement of Incident and Reflected Spectra Using a
Least Squares Method.
Pearson. (2004). Effectiveness of Recurve Walls in Reducing Wave Overtopping.
Platteeuw, J. (2015). Analysis of individual wave overtopping volumes for steep low crested
coastal structures in deep water conditions.
Pullen et al. (2007). EurOtop.
Troch, P. (2000). Wave Flume Manuel.
van der Meer, J., & Bruce, T. (2014). New Physical Insights and Design Formulas on Wave
Overtopping at Sloping and Vertical Structures.
Van Doorslaer et al. (2015). Crest Modifications to Reduce Wave Overtopping of Non-
Breaking Waves over a Smooth Dike Slope.
References
122
Van Doorslaer, K. (2010). Reduction of Wave Overtopping on a smooth Dike by means of a
Parapet.
Van Doorslaer, K. (2010). The Influence of a Berm and a Vertical Wall above SWL on the
Reduction of Wave Overtopping.
Van Doorslaer, K. (2011). Measures to Control Wave Overtopping Inside the Harbor of
Oostende.
Van Doorslaer, K. (sd). Reduction of Wave Overtopping: from Research to Practice.
Victor, L. (2012). Probability Distribution of Individual Wave Overtopping Volumes for
Smooth Impermeable Steep Slopes with Low Crest Freeboard. Coastal Eng., pp. 87-
101.
Vroman and Pintelon, T. L. (2013). Experimental Study of the Overtopping Performance of
Steep Slopes with Small Freeboards in Shallow Water Conditions. Gent.
123
ANNEX A: AVERAGE OVERTOPPING ANALYSIS
Influence of water depth, wall/parapet and berm width
FIGURE A-1: INFLUENCE OF WATER DEPTH WHEN THERE'S NO BERM AND A WALL (STEEPNESS 0.03)
FIGURE A-2: INFLUENCE OF THE WATER DEPTH WHEN THERE’S NO BERM AND A PARAPET (STEEPNESS 0.03)
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5
Q [
-]
0,0001
0,001
0,01
0,1
depth 68 cm depth 70 cm depth 73 cm
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0
Q [
-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
depth 70 cm depth 73 cm
Annex A: Average overtopping analysis
124
FIGURE A-3: INFLUENCE OF WATER DEPTH WHEN THERE'S A 40 CM BERM AND A WALL (STEEPNESS 0.03)
FIGURE A-4: INFLUENCE OF WATER DEPTH WHEN THERE'S A 40 CM BERM AND A PARAPET (STEEPNESS 0.03)
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0
Q [
-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
depth 70/73 cm depth 76 cm
Rc/H
m0 [-]
0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8
Q [
-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
depth 70/73 cm depth 76 cm
Annex A: Average overtopping analysis
125
FIGURE A-5: INFLUENCE OF THE WAVE STEEPNESS WHEN THERE’S A 20 CM BERM AND A WALL
FIGURE A-6: INFLUENCE OF THE WAVE STEEPNESS WHEN THERE’S A 40 CM BERM AND WALL
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Q [
-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
sm-1,0 = 0.03
sm-1,0 = 0.05
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0
Q [
-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
sm-1,0 = 0.03
sm-1,0 = 0.05
Annex A: Average overtopping analysis
126
FIGURE A-7: INFLUENCE OF THE WAVE STEEPNESS WHEN THERE’S A 20 CM BERM AND PARAPET
FIGURE A-8: INFLUENCE OF THE WAVE STEEPNESS WHEN THERE’S A 40 CM BERM AND PARAPET
Rc/H
m0 [-]
0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8
Q [
-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
sm-1,0 = 0.03
sm-1,0 = 0.05
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Q [
-]
1e-7
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
sm-1,0 = 0.03
sm-1,0 = 0.05
Annex A: Average overtopping analysis
127
FIGURE A-9: INFLUENCE OF PARAPET WHEN THERE’S NO BERM (STEEPNESS 0.05)
FIGURE A-10 : 𝑘𝑝-FACTORS NO BERM (STEEPNESS 0.05)
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Q [-]
1e-7
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
wall sm-1,0 = 0.05
parapet sm-1,0 = 0.05
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5
kp [
-]
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
no berm sm-1,0 = 0.05
Annex A: Average overtopping analysis
128
FIGURE A-11: INFLUENCE OF PARAPET WHEN THERE’S A 20 CM BERM (STEEPNESS 0.05)
FIGURE A-12: 𝑘𝑝-FACTORS 20 CM BERM (STEEPNESS 0.05)
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Q [
-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
wall sm-1,0 = 0.05
parapet sm-1,0 = 0.05
Rc/H
m0 [-]
0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0
kp [-]
0,0
0,2
0,4
0,6
0,8
1,0
no berm sm-1,0 = 0.05
Annex A: Average overtopping analysis
129
FIGURE A-13: INFLUENCE OF PARAPET WHEN THERE’S A 40 CM BERM (STEEPNESS 0.05)
FIGURE A-14: 𝑘𝑝-FACTORS 40 CM BERM (STEEPNESS 0.05)
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Q [-]
1e-7
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
wall sm-1,0 = 0.05
parapet sm-1,0 = 0.05
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0
kp [-]
0,0
0,2
0,4
0,6
0,8
1,0
no berm sm-1,0 = 0.05
Annex A: Average overtopping analysis
130
FIGURE A-15: INFLUENCE OF THE BERM WIDTH WHEN THERE’S A WALL (STEEPNESS 0.03)
FIGURE A-16: kb-FACTORS WHEN THERE’S A 20/40 CM BERM AND A WALL (STEEPNESS 0.03)
Rc/H
m0
0,0 0,5 1,0 1,5 2,0 2,5 3,0
Q [
-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
1e+0
no berm20 cm berm 40 cm berm
Rc/H
m0 [-]
0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0
kb [
-]
0,0
0,2
0,4
0,6
0,8
1,0
1,2
20 cm berm 40 cm berm
Annex A: Average overtopping analysis
131
FIGURE A-17: INFLUENCE OF THE BERM WIDTH WHEN THERE’S A PARAPET (STEEPNESS 0.03)
Reduction factors
FIGURE A-18: γv-FACTORS WITHOUT THE VALUES ABOVE 1 AND QUADRATIC TRENDLINE
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0
Q [
-]
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
no berm 20 cm berm40 cm berm
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5
v [
-]
0,0
0,2
0,4
0,6
0,8
1,0
all dataquadr. trendline
v = 0.0061x² + 0.1301x+0.5757
R² = 0.5878
Annex A: Average overtopping analysis
132
FIGURE A-19: γv-FACTORS WITHOUT THE VALUES ABOVE 1 AND POWER TRENDLINE
TABLE A-1: DIFFERENT FORMULAS FOR γp WITH THEIR UNKNOWN PARAMETERS AND COEFFICIENT OF
DETERMINATION R²
Formula R² A B C D E
𝐴 ∙ (𝑠𝑚−1,0)𝐵∙ (𝑅𝑐𝐻𝑚0
)𝐶
0.813 0.078 -0.641 -0.337 - -
𝐴 ∙ (𝑠𝑚−1,0)𝐵∙ (𝑅𝑐𝐻𝑚0
)𝐶
+ 𝐷 0.838 -4.281 0.210 0.127 2.801 -
𝐴 ∙ (𝑠𝑚−1,0) + 𝐵 ∙ (𝑅𝑐𝐻𝑚0
) + 𝐶 0.866 -11.611 -0.324 1.446 - -
𝐴 ∙ (𝑠𝑚−1,0)𝐵+ 𝐶 ∙ (
𝑅𝑐𝐻𝑚0
)𝐷
0.836 -41.126 0.11 40.287 -0.006 -
𝐴 ∙ (𝑠𝑚−1,0)𝐵+ 𝐶 ∙ (
𝑅𝑐𝐻𝑚0
)𝐷
+ 𝐸 0.839 -50.725 1.62 971.309 0.000 -970.38
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5
v [
-]
0,0
0,2
0,4
0,6
0,8
1,0
all datapower trendline
v = 0.137x1.05
+ 0.576
R² = 0.588
133
ANNEX B: INDIVIDUAL OVERTOPPING
Analysis F1/250
FIGURE B-1: INFLUENCE OF THE WATER DEPTH ON THE 0.4% VOLUMES FOR THE CASES WITH WALL
FIGURE B-2: INFLUENCE OF THE WATER DEPTH ON THE 0.4% VOLUMES FOR THE CASES WITH PARAPET
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
V1
/25
0 [kg/m
]
0
20
40
60
80
100
120
140
water depth 70 cmwater depth 73 cmwater depth 76 cm
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
V1
/25
0 [kg/m
]
0
20
40
60
80
100
120
140
water depth 70 cmwater depth 73 cmwater depth 76 cm
Annex B: Individual overtopping
134
FIGURE B-3: INFLUENCE OF THE WAVE STEEPNESS ON THE 0.4% VOLUMES FOR THE CASES WITH WALL
FIGURE B-4: INFLUENCE OF THE WATER DEPTH ON THE 0.4% VOLUMES FOR THE CASES WITH PARAPET
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
V1/2
50 [
kg/m
]
0
20
40
60
80
100
120
140
sm-1,0 = 0.03
sm-1,0 = 0.05
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
V1/2
50 [
kg/m
]
0
20
40
60
80
100
120
140
sm-1,0 = 0.03
sm-1,0 = 0.05
Annex B: Individual overtopping
135
FIGURE B-5: INFLUENCE OF THE BERM WIDTH ON THE 0.4% VOLUMES FOR THE CASES WITH WALL
FIGURE B-6: INFLUENCE OF THE BERM WIDTH ON THE 0.4% VOLUMES FOR THE CASES WITH PARAPET
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
V1/2
50 [kg/m
]
0
20
40
60
80
100
120
140
no berm20 cm berm40 cm berm
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
V1
/25
0 [kg/m
]
0
20
40
60
80
100
120
140
no berm20 cm berm40 cm berm
Annex B: Individual overtopping
136
FIGURE B-7: COMPARISON BETWEEN PRED. FORMULAS WALL AND PARAPET
Rc/H
m0 [-]
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Vd
im ,
1/2
50 [-]
0,0001
0,001
0,01
0,1
1
10
100
no berm wall20 cm berm wall40 cm berm wallall data parapetpred. formula no berm wallpred. formula 20 cm berm wallpred. formula 40 cm berm wallglob. pred. formula parapet
137
ANNEX C: WAVE FORCES
FIGURE C-1: INFLUENCE OF THE WATER DEPTH ON THE WAVE FORCE
FIGURE C-2: INFLUENCE OF THE STEEPNESS ON THE WAVE FORCE
Rc/H
m0 [-]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
P [-]
0.01
0.1
1
10
100
water depth 70 cm
water depth 73 cm
water depth 76 cm
Rc/H
m0 [-]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
P [-]
0.01
0.1
1
10
100
sm-1,0=0.03
sm-1,0=0.05
Annex C: Wave forces
138
FIGURE C-3: INFLUENCE OF THE BERM WIDTH ON THE WAVE FORCE
Rc/H
m0 [-]
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
P [-]
0.01
0.1
1
10
100
no berm
20 cm berm
40 cm berm
139
ANNEX D: TEST MATRIX
TABLE D-1: TEST MATRIX OF THE CONDUCTED TESTS
Configuration RC
[m]
dpaddle
[m]
Hs
[m]
TP
[s]
Lpaddle
[m]
Ltoe
[m]
Spaddle
[-]
Stoe
[-]
XAWA1-2
[m]
XGHM6-toe
[m]
XGHM1-2
[m]
XGHM2-3
[m]
XGHM1-3
[m] Test # Timeseries
no wall, no promenade 0.05 0.68 0.05 1.2 2.16 2.03 0.02 0.02 3.38 3.0 0.22 0.28 0.50 001A 001A
no wall, no promenade 0.03 0.7 0.05 1.2 2.17 2.05 0.02 0.02 3.38 3.0 0.22 0.28 0.50 002A 002A
no wall, no promenade 0.03 0.7 0.05 0.8 1.00 1.00 0.05 0.05 3.38 3.0 0.16 0.16 0.32 003A 003A
no wall, no promenade 0.05 0.68 0.05 0.8 1.00 0.99 0.05 0.05 3.38 3.0 0.16 0.16 0.32 004A 004A
no wall, no promenade 0.05 0.68 0.1 1.8 3.99 3.52 0.03 0.03 3.38 3.0 0.50 0.40 0.90 005A 005A
no wall, no promenade 0.03 0.7 0.1 1.8 4.03 3.57 0.02 0.03 3.38 3.0 0.50 0.40 0.90 006A 006A
no wall, no promenade 0.03 0.7 0.15 2.2 5.20 4.53 0.03 0.03 3.50 3.0 0.51 0.39 0.90 007A 007A
no wall, no promenade 0.05 0.68 0.15 2.2 5.14 4.46 0.03 0.03 3.50 3.0 0.51 0.39 0.90 008A 008A
no wall, no promenade 0.05 0.68 0.15 1.4 2.79 2.54 0.05 0.06 3.38 3.0 0.28 0.32 0.60 009A 009A
no wall, no promenade 0.03 0.7 0.15 1.4 2.81 2.57 0.05 0.06 3.38 3.0 0.28 0.32 0.60 0010A 0010A
no wall, no promenade 0.03 0.7 0.1 1.1 1.86 1.78 0.05 0.06 3.38 3.0 0.19 0.41 0.60 0011A 0011A
no wall, no promenade 0.05 0.68 0.1 1.1 1.85 1.77 0.05 0.06 3.38 3.0 0.19 0.41 0.60 0012A 0012A
no wall, no promenade 0.03 0.7 0.05 0.8 1.00 1.00 0.05 0.05 3.38 3.0 0.16 0.16 0.32 003B 003A
no wall, no promenade 0.03 0.7 0.05 0.8 1.00 1.00 0.05 0.05 3.38 3.0 0.16 0.16 0.32 003C 003A
no wall, no promenade 0.03 0.7 0.05 0.8 1.00 1.00 0.05 0.05 3.38 3.0 0.16 0.16 0.32 003D 003B
no wall, no promenade 0.03 0.7 0.15 2.2 5.20 4.53 0.03 0.03 3.50 3.0 0.51 0.39 0.90 007B 007A
no wall, no promenade 0.03 0.7 0.15 2.2 5.20 4.53 0.03 0.03 3.50 3.0 0.51 0.39 0.90 007C 007A
no wall, no promenade 0.03 0.7 0.15 2.2 5.20 4.53 0.03 0.03 3.50 3.0 0.51 0.39 0.90 007D 007B