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7/24/2019 WAVE FORCES ON A COMPOSITE BREAKWATER WITH CIRCULAR CYLINDER CAISSONS.pdf
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Coastal Engineering Journal, Vol. 54, No. 4 (2012) 1250023 (20pages)
c World Scientific Publishing Company and Japan Society of Civil EngineersDOI:10.1142/S0578563412500234
WAVE FORCES ON A COMPOSITE BREAKWATER WITH
CIRCULAR CYLINDER CAISSONS
ALF TRUM, ANNETTE JAHR and IVIND ARNTSEN
Norwegian University of Science and Technology,
Department of Civil and Transport Engineering,
Hgskoleringen 7, 7491, Trondheim, [email protected]
[email protected]@ntnu.no
Received 17 November 2011Accepted 31 October 2012
Published 14 December 2012
There is limited information on wave forces on caisson breakwaters with circular caissons.In this paper we report from model tests on wave forces from regular waves on a compositebreakwater with circular caissons in 55 m water depth. The results are compared with theGoda formula for wave forces on plain vertical wall caissons. The measured forces areapproximately 20% lower than the results of the Goda formula for the ultimate limit statehigh waves (H= 16 m) and 25% for the accident limit state (H= 19.8 m). However, therehave been some discussions on the accuracy of the Goda formula, from no over-predictionto approximately 10% over-prediction. Taking an over-prediction of 10% into account ourresults still indicate a 10%15% force reduction for high waves by using vertical circularcaissons instead of plain wall vertical caissons.
Keywords: Breakwaters; circular caissons; wave forces; wave pressures.
1. Introduction
Most caisson type breakwaters are built with rectangular shaped caissons. In some
few cases circular caissons have been used, e.g. Hanstholm harbor in Denmark and
Corresponding author.Current address: Kvaerner Jacket Technology AS, P.O. Box 74, N-1326 Lysaker, Norway.
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http://dx.doi.org/10.1142/S0578563412500234mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1142/S05785634125002347/24/2019 WAVE FORCES ON A COMPOSITE BREAKWATER WITH CIRCULAR CYLINDER CAISSONS.pdf
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A. Trum, A. Jahr & . Arntsen
25 m
Fig. 1. Composite breakwater with circular caissons.
Brighton marina, UK, Juhl [1994]. In connection with a feasibility study of a major
breakwater, circular caissons were proposed, as indicated in Fig. 1, by the consult-
ing company Multiconsult, Norway. The design wave conditions and water depth
conditions for this breakwater were as shown in Table 1. There is also a tidal varia-
tion, but since model tests were carried out only for the mean sea level (MSL), only
parameters related to MSL are given.
Table 1. Design wave parameter, water depths etc.
Parameters Ultimate limit Accident limitstate ULS state ALS
Water depth, m 55 55
Total height of caisson, m 37.5 37.5
Height of caisson above still water line (SWL), m 12.5 12.5
Significant wave height, Hmo, m 8.4 10.4
Maximum wave height, Hmax= 1.9 Hmo, m 16.0 19.8
Peak period,Tp, s 15.8 17.3
Load safety factor, E 1.3 1.0
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Wave Forces on a Composite Breakwater with Circular Cylinder Caissons
Since this breakwater is a high risk breakwater, the maximum design wave height
is set toHmax = 1.9Hmo. Note also that the wave load safety factor is set toE= 1.3
for ULS, similar to what is to a large extent used by the oil industry, NPD [1998].
This conservative approach is the reason for the rather wide caisson, 40 m.
There are two rows of cylinders, each cylinder with a diameter of 20 m. Thisconcept is based on the experience from building concrete platforms for the oil
industry in the North Sea. Three to five rows of two cylinders will be built simul-
taneously on a concrete slab and all these 6 to 10 cylinders are interconnected and
connected to the slab by concrete reinforcement to make one unit to be towed to
the breakwater site. For this circular cylindrical form the stresses will mainly be
tangential. This has the advantage that no partition walls are needed and the wall
thicknesses may be kept lower than compared to straight wall caissons. It was con-
sidered more economical to build the cylinders by sliding forms from the bottom to
the top of the caisson without any chamfered upper part to possibly reduce wave
forces.
There is limited information on the wave forces on breakwaters with circular
cylindrical caissons. Hence it was decided to carry out some further investigations
on such forces in a separate study.
2. Previous Work
Several investigations have been carried out on the wave forces on vertical caissons
with plain or chamfered walls. The most well known formula to calculate wave
forces on a caisson with plain vertical walls is the Goda formula referenced manyplaces, e.g. Goda [2010]. The Goda formula has been modified by Takahashi et al.
[1994] to include wave impact forces. The Takahashi et al.[1994] approach may give
excessive assessment of the impulsive breaking wave pressures for breakwaters in
relatively deep water. Shimosako and Osaki [2005] have according to Goda [2010]
recommended to use an apparent smaller water depth in this case (see later).
The use of the Takahashi et al. [1994] modification of the Goda formula, includ-
ing the recommendations by Shimosako and Osaki [2005] indicated that wave impact
pressures on a breakwater similar to the one shown in Fig. 1, but with straight ver-
tical walls, will not occur. It was assumed that this holds true also for a breakwater
with circular cylinders also.Khaskhachikh and Vanchagov [1971] carried out investigations on wave induced
pressures on straight vertical wall caissons, a breakwater with circular cylinders and
a breakwater with circular cylinders with a chamfered superstructure, both with
no overtopping. The measurements were done at several elevations and for each
elevation wave pressures were measured at several points along the periphery of the
cylinder. No wave impact pressures were reported.
Based on their measurement results Khaskhachikh and Vanchagov [1971] estab-
lished the following pressure distribution at any depth and angle, Fig. 2, in relation
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A. Trum, A. Jahr & . Arntsen
Fig. 2. Pressure distribution sketch.
to the pressure on a straight wall:
p() =K1
1 +K2
42
2
p(z) K1(1 + 0.4
2K2)p(z) (1)
or
p() =()p(z) , (2)
where () =K1(1 + 0.42K2) and p(z) is the pressure on a plain vertical wall at
depth z below still water on a straight vertical wall.
Khaskhachikh and Vanchagov [1971] expressed the maximum water surface ele-vation as a function of():
max,cyl=()max,wall, (3)
where max,wall is the maximum crest elevation in front of a vertical wall. K1 and
K2 are empirical coefficients as listed in Table 2.
These results as obtained Khaskhachikh and Vanchagov [1971] for the breakwater
with vertical cylinders (without any chamfer and no wave overtopping) are shown
in Fig. 3 where the pressures along the periphery of the cylinder are compared with
the pressures on a plain vertical wall. According to Khaskhachikh and Vanchagov
[1971] this relation applies for all levels.
Table 2. Medium values ofK1 and K2.
Wave steepness, H/L
Coefficient 0.100 0.067 0.050 0.040 0.033 0.025
K1 0.77 0.81 0.84 0.87 0.91 0.95K2 0.50 0.38 0.30 0.25 0.20 0.15
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Wave Forces on a Composite Breakwater with Circular Cylinder Caissons
Fig. 3. Ratio between the wave pressure on the cylinder and the pressure on a vertical wall,pcylinder/pverticalwall, versus angle . = 0 at point where the wave hit the cylinder first and = 90 is in the corner between the cylinders. This ratio applies to all elevations. AfterKhaskhachikh and Vanchagov [1971].
With reference to Fig. 2 the horizontal force on a unit length [height] of the
cylinder is:
f=
+/2/2
p()r cos d , (4)
where r= radius of the cylinder.
Although the pressures in the corners between the cylinders are high, the
contribution to the horizontal force is limited since the component in the wave
direction is small (see later).
Van der Meer and Benassai [1984] investigated wave forces, including wave im-
pact forces, from irregular waves on caisson breakwaters with circular and square
caissons with chamfered upper part. They concluded that the horizontal forces onthe circular and the square caissons were almost the same.
Since the caisson breakwater cross section shown in Fig. 1 is different than the
cross section tested by Van der Meer and Benassai [1984] and since it will be heavily
overtopped when the wave height is above 11 m (see later), which was not the con-
ditions during the tests by Khaskhachikh and Vanchagov [1971], it was decided to
carry out model tests on the wave forces on the breakwater shown in Fig. 1 to obtain
more information on the wave forces on circular cylinder caissons and compare the
results with wave forces on a plain wall according to the Goda formula, Jahr [2010].
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A. Trum, A. Jahr & . Arntsen
Fig. 4. The wave flume with the breakwater model position.
3. Model Tests
3.1. Test setup
The model tests were carried out on the breakwater shown in Fig. 1 in model scale
1:100 in a wave flume as shown in Fig. 4.
The wave flume is 26.8 m long; it has a total depth of 0.90 m and a width of 0.60 m.
Since there were no wave slamming forces expected (see later) and no significant
influence of viscous forces, there will be no significant scale effects present in this
case when applying the Froude model law with respect to the horizontal forces.
Possible scale effects on the uplift pressures are discussed at the end of this section
and at the end of Sec. 3.4.
The main dimensions of the breakwater are shown in Fig. 1. The cylinder dia-
meter is 20 m. The breakwater model was made of aluminum cylinders and Fig. 5
shows a photograph of the model in the wave flume. The cylinders were glued tight
to each other and there was no flow of water in between them. The top of the
cylinders were covered with a transparent plastic plate. Lead weights were placed
inside the cylinders to keep the breakwater model stable.
Fig. 5. Photograph of the breakwater model in the wave flume.
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Wave Forces on a Composite Breakwater with Circular Cylinder Caissons
Fig. 6. The cut-out part mounted on force meters,F1, F2 and F3.
Due to the complicated geometry it was difficult to measure the force on a single
cylinder. Hence a part of the middle cylinder was cut out and mounted on force
meters, F1, F2 and F3, Fig. 6. The height of the cut out part corresponded to
34.5 m. The chord length of the cut out part of the cylinder was 17.4 m and thus
covered a maximum angle, max 60.5, Fig. 2. This configuration was chosen from
a practical point of view. The cut-out segment was sealed off by a soft/elastic tape
to prevent water to enter the inside of the cylinders. This is a sealing-off technique
we have experience of using whenever similar sealing has been required. The sealsdo not affect the measured forces significantly.
Six pressure gauges were mounted in front of one of the cylinders, marked 16,
Fig. 7. A seventh pressure transducer was mounted somewhat more in the corner
between two cylinders, marked 10 in Fig. 7. Unfortunately this pressure gauge did
not function during the tests. In addition three pressure gauges were placed under
the foundation slab, marked 79 in Fig. 7, to measure the uplift pressures.
The use of the Takahashi et al. [1994] modification of the Goda formula, in-
cluding the recommendations by Shimosako and Osaki [2005] (see later) indicated
that impact pressures on a breakwater similar to the one shown in Fig. 1, but with
straight vertical walls, will not occur. It was assumed that this holds true also for abreakwater with circular cylinders also (confirmed by the tests, see later).
Since no wave impact pressures were expected, the sampling frequency was set
to 30 Hz for both the force and the pressure transducers and the wave gauges.
The model caissons were placed on a 2 cm thick gravel layer, corresponding to 2 m
prototype value. The same material was also used for the front and back protection
of the mound. Based on the calculations using the recommendations in ISO 21650
the commercial available so-called gravel fraction 811 mm was deemed sufficient
for this layer. The results of sieve analysis showed however a significant fraction of
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A. Trum, A. Jahr & . Arntsen
Fig. 7. Location of pressure transducers in front and on the underside of the foundation slab. Modelmeasures in mm.
the material larger than 11 mm. The fraction larger than 12.5 mm was sieved away
and the resulting D50 was approximately 9 mm. The size of the core material was
partly based on Burcharth et al.[1999]. Because the flow of water through the gravel
layer is small compared to what the flow would have been if there had been a free
opening under the caisson, the horizontal forces are not significantly affected by the
gravel layers.
3.2. Test program
Since one of the objectives of the tests was to compare the results with the Goda
formula, which is based on a single design wave height and period, it was decided to
carry out the tests with regular waves. This has also the advantage that one knows
then exactly the height of the incoming waves hitting the structure. The waves were
calibrated before the model breakwater was placed in the flume with little reflections
from the wave damping beach at the end of the flume. When running the wave force
tests all force recordings for analysis were taken before any waves reflected from the
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Wave Forces on a Composite Breakwater with Circular Cylinder Caissons
Fig. 8. Sample of measured wave surface elevation at the three wave gauges located in the middleof the flume.
wave generator came back to the breakwater model again. Figure 8 shows a sample
of wave recordings during the wave force testing. It is seen that after approximately
160 s (prototype) the re-reflected waves start to influence the wave recordings. Henceall wave force readings were taken, as mentioned, before any re-reflected waves came
back to the breakwater model. It is also seen that although the waves are regular
waves, they tend to vary slightly in height from wave to wave. This is often seen
when doing tests in wave flumes with regular waves.
Tests were carried out with wave periods T = 13, 14, 15, 16, 17 and 18 s with
wave heights in the range approximately 716.5 m. The generating capacities of the
wave generator set the upper limit of the wave heights. We were thus not able to
meet the maximum wave height for the accidental limit state conditions, Table 1.
3.3. Test results on wave forces
Figure 9 shows a sample of the recorded forces F1, F2 and F3, Fig. 6. Sometimes
the first wave gave a significantly higher force than the following waves. It is also
often seen then that the first wave in a train of regular waves is higher than the
following waves. Hence this first high force is omitted in the analysis.
Figure 10 shows time series ofF1,F2 andF3 and the total forceF =F1 + F2 +
F3 for a relatively low wave, H = 7.8 m and T= 13 s, while Fig. 11 shows similar
time series for a higher wave.
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A. Trum, A. Jahr & . Arntsen
Fig. 9. Time series of the measured wave forcesF1,F2 andF3, Fig. 6. Wave period T= 16 s, waveheightH= 15.6 m.
Fig. 10. Part of recorded time series ofF1, F2 and F3 and the total force F =F1 +F2 + F3 fora relatively low wave. H= 7.8 m,T= 13s.
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Wave Forces on a Composite Breakwater with Circular Cylinder Caissons
Fig. 11. Part of recorded time series ofF1, F2 and F3 and the total force F =F1 + F2 + F3 fora relatively high wave. H= 16.4 m,T= 13s.
It is seen, as expected, that higher order effects are very pronounced for the
highest wave, Fig. 11, compared to the forces for the lower wave, Fig. 10.
Figure 12 shows the maximum measured wave force for different wave periods
and wave heights.
Fig. 12. Maximum measured wave force on the cut-out part of the circular cylinder as a functionof the wave height and wave period.
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A. Trum, A. Jahr & . Arntsen
Fig. 13. Wave pressures measured at different elevations on the front of the cylinder, with numberingreferences as in Fig. 5. H= 16.4 m,T= 13 s. PC01 etc. refers to the pressure numbering, Fig. 7.
3.4. Test results of wave pressures
The tests results on wave pressures are not as thoroughly treated as the wave forces,
but some results will be shown.
Figure 13 shows time series of pressures measured at different location on thefront of the cylinder. The shown time sequence is the same as shown for the wave
forces shown in Fig. 11. It is seen, as expected, that there is some time delay of
the total force compared with the pressures in the front. This time delay is due to
the longer distance to travel for the waves into the corners compared to straight
vertical wall caissons, where the waves hit at the same time along the caisson front.
In Fig. 13 it is also seen that there may be a phase difference between the pressures
at different elevations.
Figure 14 shows the pressure distribution along the vertical of the cylinder at
different time points. Max value for PC03 is the pressures at the different elevation
at the time point when PO03 shows its maximum value. Theoretical-vertical isthe pressures obtained from the Goda formulations, while the pressures marked
theoretical-cylinder are the pressures obtained from the Goda formulation, but
adjusted with the findings of Khaskhachikh and Vanchagov [1971], Eq. (1).
It is somewhat interesting to see that the maximum pressures on the front are
larger than predicted as design pressures by the Goda formulae. At the time point
for the maximum force, approximately at 172.25 s, Fig. 11, or at approximately
0.75 s after the measured maximum pressure PC03, the pressure distribution to
some extent follows the Goda formulation below PC03, but is smaller above PC03.
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Wave Forces on a Composite Breakwater with Circular Cylinder Caissons
Fig. 14. Wave pressure distributions on the vertical front of the cylinder for different time pointsbefore and after the maximum value of PO03. H = 16.5m and T= 13 s. Max value for PC03are the pressures at the different elevation at the time point when PO03 shows its maximum value.Theoretical-vertical is the pressures obtained from the Goda formulations, while the pressuresmarked theoretical-cylinder are the presures obtained from the Goda formulation, but adjustedwith the findings of Khaskhachikh and Vanchagov [1971].
Figure 15 shows measured pressures under the bottom slab for the pressure
measurement points shown in Fig. 7. The theoretical distribution is the Goda
formulation adjusted with the findings of Khaskhachikh and Vanchagov [1971]. Note
that the front of the breakwater is to the right.
The uplift bottom pressures depend on the size and gradation of the foundation
material. But since we, to some extent, followed recommendations in Burcharth
et al. [1999] we believe that the uplift pressures can be applied for full scale use.
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A. Trum, A. Jahr & . Arntsen
Fig. 15. Pressures under the bottom slab. The theoretical distribution is the Goda formulationadjusted with the findings of Khaskhachikh and Vanchagov [1971]. Note that zero distance is atthe back of the cylinder caisson and that the front of the breakwater is to the right.
4. Review of the Goda Formula for Wave Forces on a
Plain Vertical Wall
The main objective of the tests was to compare the wave force test results with
the wave forces on a plain vertical wall. In this study there was no time to do
measurements on a plain vertical wall, so the comparison will be with the Goda
formula, Goda [2010], for wave forces on vertical caisson breakwaters. Figure 16
shows the wave pressure and uplift exerted on the vertical breakwater according
to Goda. We refer to Goda [2010] for his original formula and the calculation of
the different pressures p1, p3, p4 and pu and for later adjustments by others to hisformula.
The accuracy of the Goda formula has been discussed in several places, e.g.
Takayama and Ikeda [1992], van der Meer et al. [1994]. Goda [2010] refers to
Takayama and Ikeda [1992] who examined the reliability of the Goda formula by
using a set of 66 data from the original pressure measurement data of regular waves
by Goda and Fukumori [1972]. This examination gave a bias of 0.91 with a coeffi-
cient of variation of 0.19, e.g. the calculated wave forces were approximately 10%
higher than the mean force derived from pressure measurements. Van der Meer et al.
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Wave Forces on a Composite Breakwater with Circular Cylinder Caissons
p1
p4 *
hc
d h
h
pu
p3
Buoyancy
Fig. 16. Distribution of wave pressure and uplift exerted on the main body of breakwater accordingto Goda.
[1994] refer to tests on three different caisson cross sections with vertical, inclined
and curved superstructures in irregular waves. The results, F0.4%, have been com-
pared with the Goda formula. For the vertical case there is apparently no bias on the
Goda formula considering several cases, but there is a scatter. Van der Meer et al.
[1994] stated that the Goda formula is valid for caissons founded on a rubble mound
berm well above the sea bed. This is the case for the presently studied composite
breakwater.
There was no indication of measured slamming forces in our tests. This is also
in agreement with the Takahashi et al. [1994] modification of the Goda formula,
including the recommendations by Shimosako and Osaki [2005] as referenced by
Goda [2010].
5. Comparison of the Test Results with the Goda Formula
The first comparison will be of the wave forces on the cut-out part of the cylinder,
60.5, with a chord length of 17.4 m and a height of the cut-out part of 34.5 m,
Fig. 6. Figure 17 shows the vertical pressure diagram used for the cutout part. Thecalculations using the Goda formula are based on wave forces on a straight vertical
wall with a width of 17.4 m, the chord length, and on the pressure diagram of Fig. 17.
Then we will discuss the effect of the missing forces in the corners, 60.5