Coastal Engineering 72 (2013) 69–79
Contents lists available at SciVerse ScienceDirect
Coastal Engineering
journal homepage: www.elsevier.com/locate/coastaleng
Large scale model test investigation on wave run-up in irregular waves at
slender piles
J. Ramirez a, P. Frigaard a, T. Lykke Andersen a,⁎, L. de Vos b
a
b
Department of Civil Engineering, Aalborg University, Sohngaardsholmsvej 57 DK - 9000 Aalborg, Denmark
Afdeling Geotechniek, Departement Mobiliteit en Openbare Werken Ghent, Belgium
a r t i c l e
i n f o
Article history:
Received 2 April 2012
Received in revised form 23 September 2012
Accepted 25 September 2012
Available online 7 November 2012
Keywords:
Wave run-up
Irregular waves
Cylinder
Offshore wind turbine
Large scale tests
Entrance platforms
a b s t r a c t
An experimental large scale study on wave run-up generated loads on entrance platforms for offshore wind turbines was performed. The experiments were performed at Grosser Wellenkanal (GWK), Forschungszentrum
Küste (FZK) in Hannover, Germany. The present paper deals with the run-up heights determined from high
speed video recordings. Based on the measured run-up heights different types of prediction formulae for run-up
in irregular waves were evaluated. In conclusion scale effects on run-up levels seem small except for differences
in spray. However, run-up of individual waves is difficult to predict due to high importance of wave form.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
Offshore wind turbines that are installed in many places across Europe
are often exposed to severe storm conditions, where severe wave run-up
can occur in breaking or nearly breaking waves. As a consequence damaged entrance platforms have been observed at for example the large
Danish wind farm, Horns Reef. It is the interaction between waves and
structures which causes water to run-up along the structure. The
run-up height is determined as the vertical distance from the still water
level to the maximum level of the run-up. This height can be considerably
larger than the wave crest height.
There are significant challenges in the analysis of breaking waves interaction with an offshore wind turbine foundation. For estimation of the
run-up height so far physical small scale model tests and CFD models
have been applied. However, in both cases the thin run-up layer and
spray might cause significant model or scale effects. Large scale model
tests are not available but might clarify the importance of these effects.
The first notable experimental work on wave run-up on cylinders was
undertaken by Hallermeier (1976). He studied different cylinder geometries; circular and finned, H-beams and flat plates and suggested that
the run-up height can be expressed by the velocity head, given by
Bernoulli's equation, u2/2g (u, being the horizontal water particle
velocity). The benchmark experiments of Kriebel (1990, 1992) have subsequently been compared with a number of wave run-up calculation procedures. These include the linear diffraction theory approach of McCamy
⁎ Corresponding author.
E-mail address: [email protected] (T.L. Andersen).
0378-3839/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.coastaleng.2012.09.004
and Fuchs (1954), the second order frequency domain calculation procedure presented by Kriebel (1990, 1992), Isaacson and Cheung (1994) and
Buchmann et al. (1998) and second order time domain calculation approach of both Buchmann et al. (1997), and Isaacson and Cheung
(1993). In general, these researchers demonstrated that first order wave
run-up predictions revealed an overall poor agreement when compared
to the measured results of Kriebel (1990). On the other hand, comparisons
with second order approaches, both frequency and time domain diffraction theory, for waves of small steepness were shown to be acceptable.
Other studies on wave run-up with random waves have been
made by Niedzwecki and Duggal (2004), who conducted experiments
and adjusted the velocity stagnation head theory to the data. A recent
experimental investigation in this field was done by Martin et al.
(2001). The experimental results were compared with different theories and they concluded that most theories underestimate the run-up
height. Morris-Thomas et al. (2007) presented results from the experimental investigation on wave run-up on a fixed vertical circular cylinder in progressive waves. They concluded that with long wave
theory, the wave run-up is well predicted; however, using diffraction
theory the wave run-up is not well predicted.
De Vos et al. (2007) conducted experiments for both regular and
irregular waves. Based on these experiments, they made a run-up formulae for irregular waves. They found that the maximum run-up
height can be determined by
u2
Ru;max ¼ ηmax þ m max
ð1Þ
2g
where ηmax is the crest level of the highest wave, umax is the horizontal
particle velocity in the top of the crest for the same wave, g is the
70
J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
0.56 m
Wave gauge
WG1
WG2
WG3
WG4
WG5
WG6
WG7
WG8
WG9
WG10
WG11
WG12
X
Distance [m]
50
51.9
55.2
60
70
80
90
100
103.5
107
110
111.02
Y
50 m
WAVE MAKER
BEACH
5m
WAVE GAUGES
INCIDENT
WAVE
DIRECTION
VIDEO
CAMERA
111 m
309 m
Fig. 1. Wave flume configuration.
acceleration due to gravity and m is a coefficient used to adjust Eq. (1) to
the data. De Vos et al. (2007) formulae and corresponding m values are
based on second order Stoke's theory for regular waves for which they
found m=2.71 for a monopile, and m=4.45 for a cone foundation.
Myrhaug and Holmedal (2010) have used the data from De Vos et al.
(2007) and analysed, based on the velocity stagnation head theory and
second order irregular wave theory. However the model shows a significant underprediction of run-up heights and can thus not be applied for
design.
Lykke Andersen et al. (2010) performed experiments with depth
limited and close to depth limited waves and fitted Eq. (1) based
on stream function theory for regular waves on constant depth to calculate crest elevation and kinematics. This approach was chosen even
though theories exist also for irregular waves which though require a
surface elevation time series that is usually not available for the designers. Using stream function theory significantly reduced the scatter on the predicted run-up heights and was also in well agreement
with De Vos et al. (2007) data. Moreover, they concluded that the m
factor is highest for waves with low steepness:
1:4x4 for s0p ¼ 0:02
m¼
ð2Þ
1:4x3 for s0p ¼ 0:035
The factor 1.4 was included because of underestimation of the
run-up heights for breaking or nearly breaking waves when surface
elevation gauges are used for the measurements. The data of Lykke
Andersen et al. (2010) corresponds when water depth to pile diameter ratios (D/h) from 2 to 4 and significant wave height to water depth
ratios (Hm0/h) from 0.35 to 0.46 were tested. The experiments can be
considered in the scale 1:50 of prototype.
A formula, similar to Eq. (1) but based on the phase velocity instead of
the particle velocity was presented by Hansen (2008), showing good
agreement with maximum run-up levels in Lykke Andersen et al.
(2010) data. However, this is expected solely to be due to the largest
Table 1
Experimental conditions (model scale).
At the paddle
At the pile
Test
h [m]
Tp [s]
Hm0 [m]
s0p
h [m]
Tp
Hm0
Hmax
H2%
s0p
1
2
3
4
4
3
4.5
5.9
5.9
1.05
1.10
1.10
0.033
0.020
0.020
3
3
2
4.7
6.0
6.0
0.91
1.00
0.81
1.41
1.66
1.08
1.16
1.23
0.96
0.026
0.018
0.014
J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
Fig. 2. The test facility Grossen WellenKanal (GWK) with the pile installed.
Fig. 3. Side view of the wave run-up impacting on the cylinder for Test No. 1, Wave No. 18.
71
72
J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
waves being depth limited and breaking. In shallow water the phase velocity is only slightly dependent on both wave period and height and
does thus not reflect that very large run-ups are only caused by the
highest waves.
• Previous design formulae are based on measurements with surface
elevation gauges which have shown to underestimate run-up of
breaking waves.
3. Experimental set-up
2. Motivation
In the present study, wave run-up of irregular waves on a slender
circular cylinder is investigated by conducting large scale experiments. The tests focus on breaking wave conditions because they
are most critical and also because it is here that the previous small
scale tests are less reliable. The overall aim is to quantify scale effects
and to develop new formulae for the run-up height under breaking
wave conditions based on the new large scale results.
The motivation for the present analysis is:
• All previous investigations are based on small scale results and
might be subjected to scale effects due to wave impacts, thin layer
of uprushing water and spray formation.
Experiments were conducted at the large wave flume (GWK),
Forschungzentrum Küste (FZK), in Hannover, Germany. The flume has
an effective length of 309 m, a width of 5 m and a depth of 7 m. The
wave channel has a piston wave maker with a stroke of 4 m and it is possible to generate wave heights up to 2 m. Regular, irregular and freak
waves were used in the present tests but in the present paper only the irregular waves are considered. At the end of the flume, at the distance of
270 m from the wave maker, a 1:6 concrete slope reduced reflection.
The reflected waves were absorbed by the active absorption system of
the wave maker.
A steel pile with a diameter of 0.56 m was installed at a distance of
111 m from the wave paddle. A sand bed was installed in the flume
Fig. 4. Front view of the wave run-up impacting on the cylinder for Test No. 1, Wave No. 18.
J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
with roughly 1 m thickness at the pile. The sandy bed reshaped to be
in equilibrium with the generated waves. The water depth (h) was
varied between 2 m and 3 m at the pile. The setup in the flume is
shown in Fig. 1. The tests can be considered to be approximately
scale 1:10 of typical North Sea conditions.
The instrumentation of the flume consisted of 22 wave gauges
along the channel measuring the free surface elevation. In addition
seven surface elevation gauges were mounted on the pile for run-up
measurements. These run-up gauges have not been considered in
the present analysis as they were found to underestimate the run-up
significantly. The position of the wave gauges is shown in Fig. 1. All
time series were recorded with the sample rate 119.9 Hz and at
16 bit resolution. During all tests, videos were made to determine
the instances of the highest run-up events. In a repetition of the
same test, the highest run-up events were recorded by a high speed
73
video camera to detect run-up levels of individual waves. For the
Test No. 3, see Table 1, only normal video recordings were available
leading to higher uncertainty on the run-up levels than the other
tests. Marks were placed every 10 cm on the pile to qualify the
run-up levels from the high speed video images (Fig. 2).
4. Wave conditions
For the present paper three irregular sea states were generated
using a JONSWAP spectrum, with a peak enhancement factor γ = 3.3.
In a sample of 500 waves, most waves give a very small run-up, while
some waves give a very significant run-up. Only these significant
run-ups on the slender pile are considered for the present paper (24,
19 and 20 events respectively for the three considered tests).
Fig. 5. Proposed adjustment m factor plotted against deep water wave steepness. Wave kinematics are computed by stream function theory using Hmax for Ru,max, H2% for Ru,2% and
Tp in both cases.
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J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
Table 1 shows the sea states generated at the paddle and at the
pile for the three tests.
5. Data analysis
The incident wave trains at the pile are determined from the three
wave gauge at the side wall next to the pile (WG11, 12 and 13) using
the WaveLab software by Aalborg University (2010), which utilize the
Mansard and Funke (1980) method and inverse FFT to get the incident
surface elevation time series and the time domain wave characteristics.
In each test the waves giving significant run-up were determined.
For these waves, the run-up heights were determined, along with the
incident wave height and wave period, cf. Appendix A. For each of the
run-up events three run-up levels were determined:
• Level A: Level for green water run-up (thick layer), (Ru,A).
• Level B: Level for thin layer of water and air mixture, water layer
which is no longer attached to the surface of the pile or high
spray concentration, (Ru,B).
• Level C: Level for maximum spray, (Ru,C). When the spray went
higher than the maximum level which was marked on the pile,
this value was estimated as good as possible.
Figs. 3 and 4 show an example of a run-up events and the identification of the three levels.
To obtain the m factor in Eq. (1), stream function theory for regular waves was used to calculate the maximum wave crest and the particle velocity on the top of the crest (Brorsen, 2007). The number of
terms in the Fourier series was set to N = 30. In the calculations the
wave height and wave period H2% and Tp are used to calculate the
2% run-up (which is the wave run-up level exceeded by 2% of the
waves Ru,2%) and Hmax, Tp are used to calculate the maximum
run-up. The calculation method for the 2% and maximum run-up
heights is thus similar to that applied by Lykke Andersen et al. (2010).
Fig. 6. Comparison of the wave run-up predicted versus estimated, using Eqs. (3)–(5) for 2% and maximum run-up levels.
J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
75
Fig. 7. m factor plotted against deep water wave steepness for the individual waves.
6. Results Lykke Andersen et al. (2010) approach
In the following section the data has been analysed using the
methodology of Lykke Andersen et al. (2010). The m factor is deduced
by Eq. (1) for the 2% run-up and for the maximum run-up and plotted
against the peak deep water steepness s0p ¼ 2πH
. A linear interpolagT
m0
2
p
tion has been used when s0 is less than 3.5%, while m keeps a constant
value when s0 is higher than 3.5% for each level of wave run-up. For
level A the m values given by Lykke Andersen et al. (2010) are used
but without the factor 1.4 and for level B with factor 1.4, in Eq. (2).
For level C the factor 1.4 is replaced by factor 3 in order to fit the present obtained spray levels. The spray level is thus significantly higher
than predicted by the m values given by Lykke Andersen et al.
(2010). Therefore, the following expressions are used:
• Level A
−66:667s0p þ 5:33 for s0p < 0:035
m¼
3
for s0p > 0:035
ð3Þ
• Level B
m¼
−93:333s0p þ 7:47 for s0p < 0:035
4:2
for s0p > 0:035
−200s0p þ 16 for s0p < 0:035
:
9
for s0p > 0:035
7. Results: individual waves
The methodology of Lykke Andersen et al. (2010) was used again
in this section, but here applied for each individual wave. This means
ηmax and u are again based on stream function theory but with wave
height and period for the individual waves. We apply the formulations for m given in Eqs. (3)–(5), but replacing s0p with the deep
water steepness of the individual waves calculated as s0 ¼ 2πH
. Fig. 7
gT
presents the obtained m values and are much more scattered than
those found in the previous section, this is reflected also in Fig. 8
where the prediction method is evaluated. The large scatter can be
explained by large run-up heights, which are only caused by breaking
or nearly breaking waves with steep fronts (see Appendix B for examples of the different run-up types observed). In these cases, the waves
can thus not solely be described by wave height and period. It is difficult
to establish a run-up model for individual waves except for the statistical model given by Lykke Andersen et al. (2010) and validated on the
2
ð4Þ
• Level C
m¼
al. (2010). Fig. 6 evaluates the prediction method and shows that the
scatter on m is less important for the overall prediction method as the
very high m values for level B are for cases with relative low velocity
head compared to ηmax. For the maximum events significant scatter
occur especially for one of the test (much larger than for 2% values).
This has also been found previously by Lykke Andersen et al.
(2010). The agreement with the formulae is thus very good for level
A and B, while level C is more scattered simply because in some
cases the spray formation is not significant. The results also indicate
that the scale effects on run-up levels are not significant as they are
well predicted by the procedure established by Lykke Andersen et
al. (2010) based on his small scale tests.
ð5Þ
Fig. 5 shows the results of m for the 2% and maximum run-up for
the three tests and is more scattered than found by Lykke Andersen et
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J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
Fig. 8. Comparison of the wave run-up predicted versus estimated for the individual waves.
model tests. A more detailed analysis of the wave shape, specially the
front steepness is needed if a model for the individual waves is needed.
Appendix A
Tables 2–4 show data for the individual waves giving significant
run-up in tests 1–3.
8. Concluding remarks
An experimental large scale study was carried out to improve the
knowledge of wave run-up on slender circular cylinders in an irregular
sea state. Run-up levels for green water run-up, thin layer of water air
mixture and maximum spray levels were determined for individual
waves.
The large scale measurements have been compared with the procedure by Lykke Andersen et al. (2010) based on small scale tests and
the agreement is excellent showing no significant scale effects on
run-up heights. Maximum spray levels are though significantly
higher than predicted by the Lykke Andersen et al. (2010) approach.
Analysis of the run-up of the individual waves show that extreme
run-up events only occur for breaking and nearly breaking waves with
a steep front. A procedure to calculate run-up of individual waves is
thus difficult to establish without taking the wave form into account.
Acknowledgements
The tests presented in the present paper were performed in the
large wave channel at Forschungszentrum Küste, Hannover, Germany.
This work has been supported by the European Community's Sixth
Framework Programme through the grant to the budget of the Integrated Infrastructure Initiative HYDRALAB III within the Transnational
Access Activities, contract 022441.
Table 2
Experimental details of the individual incident waves giving significant run-up in Test 1,
values in bold and italic show the Ru,max and Ru,2% respectively.
Wave no.
H[m]
T[s]
Ru,A[m]
Ru,B[m]
Ru,C[m]
s0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0.972
0.866
1.127
1.003
0.727
0.954
0.826
1.144
1.084
1.202
1.472
0.985
1.159
1.027
1.085
1.198
1.269
0.960
1.287
1.072
1.058
0.992
0.914
1.193
3.76
4.19
4.34
4.21
2.45
5.30
4.63
4.89
3.43
4.54
3.98
3.69
4.01
4.31
4.23
3.71
3.91
4.59
4.44
4.41
5.22
4.05
3.93
4.83
0.97
1.12
1.27
1.17
1.42
0.87
1.17
1.02
1.10
1.17
1.12
1.47
1.52
1.42
1.22
1.52
1.62
1.52
1.52
1.62
1.07
1.22
1.22
1.02
0.97
1.12
1.27
1.17
1.57
0.87
1.17
1.02
1.1
1.27
1.17
1.57
2.42
1.72
1.22
1.87
2.02
2.02
2.02
2.22
1.07
1.52
1.22
1.02
0.97
1.12
1.27
1.17
1.57
0.87
1.17
1.02
1.1
1.27
1.17
1.57
2.42
2.02
4.02
2.02
2.92
2.62
2.22
2.32
1.07
1.62
1.22
1.02
0.044
0.032
0.038
0.036
0.078
0.022
0.025
0.031
0.059
0.037
0.059
0.046
0.046
0.036
0.039
0.056
0.053
0.029
0.042
0.035
0.025
0.039
0.038
0.033
J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
Table 3
Experimental details of the individual incident waves giving significant run-up in Test 2,
values in bold and italic show the Ru,max and Ru,2% respectively.
77
Table 4
Experimental details of the individual incident waves giving significant run-up in Test
3, values in bold and italic show the Ru,max and Ru,2% respectively.
Wave no.
H[m]
T[s]
Ru,A[m]
Ru,B[m]
Ru,C[m]
s0
Wave no.
H[m]
T[s]
Ru,A[m]
Ru,B[m]
Ru,C[m]
s0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
1.221
1.527
1.138
1.255
1.608
1.217
1.242
1.296
1.205
1.333
1.145
1.277
1.26
1.337
1.058
1.321
1.162
1.729
1.188
4.33
5.92
6.15
4.06
5.05
6.76
5.79
5.21
5.49
4.69
5.91
5.54
5.51
6.29
5.91
6.09
8.08
5.41
6.19
1.22
1.82
1.27
1.67
2.12
1.37
1.52
1.52
1.52
1.52
1.42
1.87
1.92
1.52
1.12
1.77
1.22
1.72
1.72
1.22
2.82
1.27
2.22
3.02
1.47
1.72
2.02
1.62
2.02
1.82
2.02
2.92
1.52
1.32
2.62
1.32
2.72
2.42
1.22
4.52
1.27
2.22
4.32
1.47
2.02
2.32
1.72
2.87
2.52
2.02
4.52
1.52
1.42
4.12
1.32
2.82
3.52
0.042
0.028
0.019
0.049
0.040
0.017
0.024
0.031
0.026
0.039
0.021
0.027
0.027
0.022
0.019
0.023
0.011
0.038
0.019
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1.054
0.927
0.953
0.999
0.899
0.892
0.826
0.701
1.113
0.910
0.839
1.001
0.971
0.873
0.996
0.862
0.972
0.933
0.888
1.008
5.29
4.82
3.01
6.26
5.69
4.32
6.65
5.56
4.54
5.24
4.89
5.63
5.90
4.54
4.74
7.03
5.98
4.98
3.97
4.88
1.77
1.87
1.42
1.52
1.67
1.72
1.27
1.27
1.17
1.47
1.42
1.77
1.42
1.67
1.42
1.72
1.72
1.62
1.27
1.22
2.27
2.17
2.02
2.02
2.17
1.92
1.57
1.52
1.52
1.82
1.77
2.32
1.87
2.07
1.97
2.37
2.27
1.82
1.52
1.42
4.32
4.52
2.12
2.62
4.22
4.02
2.12
1.92
2.22
2.47
2.62
4.22
4.22
2.37
4.02
4.62
3.52
4.02
2.22
2.12
0.024
0.026
0.068
0.016
0.018
0.031
0.012
0.015
0.035
0.021
0.022
0.020
0.017
0.027
0.028
0.011
0.017
0.024
0.036
0.027
Appendix B
Figs. 9–11 show the different types of run-ups observed in the tests.
Fig. 9. Snapshot of the wave run-up, type A, i.e. thick run-up layer with low run-up velocity (Test 1, Wave 3).
78
J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
Fig. 10. Snapshot of the wave run-up, type B, i.e. thin run-up layer attached to pile with relative low run-up velocity.
J. Ramirez et al. / Coastal Engineering 72 (2013) 69–79
79
Fig. 11. Snapshot of the wave run-up, type C, i.e. very thin run-up layer, large spray formation for breaking or nearly breaking wave (Test 2, Wave 2).
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