wave forces on a composite breakwater with circular cylinder caissons.pdf

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/S0578563412500234


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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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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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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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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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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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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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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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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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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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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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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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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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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

wave forces on a composite breakwater with circular cylinder caissons.pdf

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