PARAMETERS INFLUENCING WAVE RUN-UP ON A RUBBLE MOUND BREAKWATER

8/6/2019 PARAMETERS INFLUENCING WAVE RUN-UP ON A RUBBLE MOUND BREAKWATER

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PARAMETERS INFLUENCING WAVE RUN-UPON A RUBBLE MOUND BREAKWATER

Bjorn Van de Wal le ', Jul ien De Rouck', Luc Van Damme', Peter Frigaard', Marc Willems'

Abstract: Full scale wave run-up measurements have been performed on theZeebrugge rubble mound breakwater. Wave run-up also has been investigated onvarious small scale models of the Zeebrugge breakwater. A significant differencebetween the results has been noticed. Addi tional smal l scale model tes ting hasbeen carried out on a slightly modif ied scale model: a regular armour unit pat ternhas been applied in stead of an irregular pattern as in full scale. The a im of theaddit ional laboratory tests was to investigate the inf luence of the spectra l widthparameter & and the influence of the position of the wave run-up step gauge withrespect to the armour unit pattern and the water level.

INTRODUCTIONWave run- up is on e of the main physical p rocesses which play an impor tan t role in the

design of the crest level of a sloping coastal s tructure. The crest level design of coastalstructures is mainly based on physical scale model results. Full scale measurements can onlybe carried ou t on existing structures and are very scarce du e t o the high co st s involved andthe dependency on weather conditions. However, full scale measurements ar e indispensableto val idate small scale model tes t resul ts . The smaller the scale model, the more impor tan tbecome scale effects and model effects. Sometimes, as it is in this case, it is very hard to findthe parameter(s) which is (are) responsible for discrepancies in results.

I research assistant, Ohent University, Department of Civil Engineering, Technologiepark 904, B-9052 Zwijnaarde, [email protected] professor, Ghent University, Department of Civil Engineering, Technologiepark 9, B-9052Zwijnaarde, j ul ien [email protected] head of department, Ministry of the Flemish Community, Coastal Division, Vrijhavenstraat 3, B-8400 Oostende, [email protected] assistant professor, Aalborg University, Department of Civil Engineering, Sohngaardsholmsvej 57,DK-9000 Aalborg, i5pf@civi!.auc.dk'researcher, Ministry of the Flemish Community, Flanders Hydraulics, Berchemlei 115, B-2140Borgerhout, [email protected]

Van de Walle, De Rouck,Van Damme, Frigaard, Willems

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Firstly, the full scale measurements which have been performed on a conventional rubblemound breakwater are discussed shortly. Secondly, laboratory investigation is describedextensively. Emphasis is put on additional small scale model tests in which the influence of anumber of parameters on wave run-up is investigated. Finally, results are compared.

ZEEBRUGGE MEASURING SITEIn Zeebrugge (Belgium) full scale measurements have been carried out on the northern

part of the western rubble mound breakwater sheltering the outer harbour (Troch et al.(1998. Th e breakwater is armoured with 25 ton grooved cubes. The core of the breakwaterconsists of quarry run (2-300 kg) and 1-3 ton rock has been used to construct the filter layer.

A measuring jetty with a total length o f 60 m is constructed on the breakwater. The wavecharacteristics are measured by two wave rider buoys at a distance of 150 m, resp. 215 mfrom the breakwater axis. An infrared meter placed on the measuring jetty and a pressuresensor fixed to the pile supporting the jetty measure the still water level (SWL) at the toe ofthe breakwater. An anemometer provides information on wind direction and wind velocity.

Wave run-up is measured by two completely different measuring systems (figure I).Firstly, the so-called 'spiderweb system' (SP), i.e. a set of seven vertically placed stepgauges, is installed between the armour units and the measuring jelly. Secondly, a run-upgauge (RU) is mounted along the breakwater slope on top of the armour units. This run-upgauge consists of five step gauges. The distance between the 'spiderweb system' and the runup gauge is about 2 arnlOur units.

Figure I: Zeebrugge rubble mound breakwater with measuring jetty, 'spiderweb system'(SP) (in the middle) and the five part run-up gauge (RU) (at tl,e right).

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FULL SCALE MEASUREMENTSThirteen storms have been observed and measured at the Belgian coast during the last 6

years (1995-2001). During these storms, the wave climate in front of the Zeebruggebreakwater was characterised by a mean wave period TOI of approximately 6.24 s, a peakwave period T p of 7.93 s on average, a significant wave height H mo varying between 2.40 mand 3.13 m, a wind force of at least 7 Beaufort and a wind blowing direction almostperpendicular to the breakwater. The tide is semidiurnal (MHWS Z + 4.61, MLWS Z + 0.27) .During a time span of approximately two hours around the point in time of high water, theSW L remains almost constant.

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ANALYSIS RESULTS OF FULL SCALE MEASUREMENTSThe analysis of the wave run-up measurements yields some remarkable results. First of

all, the average dimensionless wave run-up value characterised by RUm/H ." i.e. thedimension less wave run-up value which is exceeded by 2% of the wave run-up events,equals 1.76. The number of wave run-up events is taken equal to the number of total waves.To determine this value, RU data collected during 9 storms is used. The mean Iribarrennumber equals ~ m= 3.59. Hmo and H, are the significant wave height determined by analysisin frequency domain, resp. in time domain. When SP data of 13 storms is used, RU1,,/Hmoequals 1.75. So, two measuring devices with a completely different measuring principle yieldidentical results. The most seaward step gauge (o f the SP) is used to measure wave rundown. Th e dimensionless 2% wave run-down value Rd1%/Hmo equals -0.87. The obtainedwave run-up values are clearly higher than any other wave run-up values found in literatureand obtained by small scale model test ing of rubble mound breakwaters (see further on).Wave run-down agrees well with literature.

_ Ru,..)Hmo

- - 0 - Ru ,,,JH/fft1_ RU2'l6/Hmo

- - 0 - Ru M4lHmo-A - Ru,aJH mo~ Ru/H rro- - -+- Ru""'H mo

...

2

3 , - - - - - , - - - , - - - - - - - - , - - - , - - - - - - - . 1 - - - '

II

~ - i - : i - -)

Time

Figure 2: Dimensionless prototype wave run-up Ru", / H mo vs. time(IHlV = the point in time of high water - 9 storms - RU data (30 minutes time series.

Secondly, wave run-up is clearly dependent on the still water level (SWL). Dimensionlesswave run-up values increase when the SWL decreases (figure 2). The lower the exceedance

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probability x, the more difference between the Rux%/H mo values measured at high water andat low water. This phenomenon could be explained by the fact that a t lower water levelswave run-up takes place at a lower part of the slope. The lower porosity of the armour layerat lower levels (due to the settlement of the armour units during the lifetime of thebreakwater (built in 1983)) may cause higher wave run-up. During rising tide these valuesare slightly larger than during receding tide. The influence of currents and the asymmetrictide is suspected.

Finally, all full scale measurement data analyses have shown that wave run-up on theZeebrugge rubble mound breakwater is Rayleigh distributed.

An extensive description of the full scale measurement results is found in De Rouck et al.(2001a).

SMALL SCALE MODEL TESTSThe Zeebrugge breakwater has been modelled in three selected laboratories: two 2D

models (1 :30) have been built in Flanders Hydraulics (FH - Belgium) and in UniversidadPolitecnica de Valencia (UPV - Spain) and one 3D model (1 :40) has been built in AalborgUniversity (AAU - Denmark). Small scale model tests have been carried out as part of theEC funded OPTICREST project ('The optimisation of crest level design of coastal structuresthrough prototype monitoring and monitoring' (1998/2001) - MAS3-CT97-0116). Severalstorms measured in the field are reproduced in all laboratories. In the laboratories, wave runup has been measured with a digital run-up gauge designed at Ghent University. In table I,the RUm/Bmo values obtained by full scale measurements and by small scale model tests arementioned. In all laboratories, the same storm sessions have been reproduced. Differencesbetween full scale measurement results and small scale modelling results are noticed. Alsosignificant differences between the results obtained in different laboratories are seen: a cleardifference between prototype measurement results and the physical modelling results of FHand AAU is noticed. The small scale model test results of UPV have the same order ofmagnitude of the prototype values. No wind was generated in the laboratories. For moreinformation, reference is made to De Rouck et al. (200 Ia and 200 Ib).

Table 1: Laboratory results for Zeebrugge breakwater (a t high water).

length 01 RIU2,";,Hmo

l [-]"m [-J RU2";Hmo RU2";Hmo RU2";Hmo

time series u sc a e .,., [-J FH [-] UP v [-J AAUmeasurements

Aug. 28, 1995Jan. 19, 1998Jan. 20, 1998Feb. 7, 1999Nov. 6, 1999

Nov. 6-7, 1999

2h 15min2h 30 min

2h2h2h2h

1.66 3.76 1.42 1.911.73 3.70 1.53 1.76179 3.64 1.40 1.891.73 3.55 1.39 1.711.82 3.45 1.44 1.81 1.411.64 3.64 1 ~ 1 ro 1 ~

The additional small scale model tests have been performed on the model built inFlanders Hydraulics. The test matrix (table 2) has been run four times: four differentcombinations of armour unit pattern and position of the run-up gauge have been tested. Formost tests armour units have been placed in a regular pattern in order to avoid any influence

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of the pattern. Tests z2xx were test series with an irregular pattern of the armour units (yardplacing). Test series z3xx, z4xx and z5xx corresponded to a regular pattern of the armourunits (figure 4). The run-up gauge could be placed in three different positions relative to theregularly placed armour units (figure 3). The positions of the run-up gauge (z3, z4 and z5)correspond with the names of the test series (z3xx, resp. z4xx and z5xx in which the suffix'xx' indicates the test number within the concerning test series). When placed in position z5,there were no holes underneath the run-up gauge. In positions z3 and z4, armour units andholes between two neighbouring armour units alternate under the run-up gauge. Bothpositions were almost identical. When the water level increased over approximately oneblock height, position z3 became identical to position z4.

Table 2: Test Matrix of Additional Testing.SWL with Hmo [m] Tp [sI

Test n reference to Zr(full scale) [m] full scale scale model full scale scale model

) zx01 +0.00 3 3 3.00 0.10 7.6 1.39zx02 +0.00 3.3 3.00 0.10 9.8 1.79zx03 +0.00 3 3 3.00 0.10 11.6 2.12zx04 +2.00 3.3 3.00 0.10 7.6 1.39zx05 +2.00 3 3 3.00 010 9.8 1.79zx06 +2.00 3.3 3.00 0.10 11.6 2.12zx07 +4.00 3.3 3.00 0.10 7.6 1.39zx08 +4.00 3.3 3.00 0.10 9.8 1.79zx09 +4.00 3.3 3.00 0.10 11.6 2.12

x - test series (2, 3, 4 or 5)

The sample frequency in all tests is f, = 10.989 Hz (model scale). Each test lasted for1310 seconds (almost 22 minutes in model scale), which equals a testing period ofapproximately 2 hours at full scale. The ratio H.. oID,,5f) was equal or less than lA in all tests.

RESULTS OF ADDITIONAL SMALL SCALE MODEL TESTSFirst of all, dimension less wave run-up values exceeded by 2% of the waves R I I ~ H ,are

plotted against the spectral width parameter & (figure 5). The spectral width parameter &, asdefined by Cartwright and Longuet-Higgins (1956) has been used:

~

in which rn, = Jf 'S( / )dj and 0 S & S I.n

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z5 z3 z4

)

Figure 3: Different positions of the run-up gauge relative to the regular pattern of the armourunits in the outer annour layer.

Figure 4: Regular pattern of the armour units.

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In figure 5, a straight line has been fitted througb the test results using the least squaremethod. The 95% confidcnce boundaries have been calculated using a statistical I-test. An

influence of the spectral width parameter {; is noticed: a slight increase of {; implies a largeincrease in dimensionless wave run-up. Van Oorschot and d'Angremond (1968) came to thesame findings. Spectral width values vary within the interval [0.50, 0.601, whereasdimensionless wave run-up values RU2o/jH, vary within a much larger interval [1.5,2.01.

3 , - - - - - - - - - - - - - - - - - - - - - - - - ,

)

2

~..

-- ... '}-. .: ~

~ ~

0.70.65.60.55.50

0 + - - - - - , - - - - - , - - - - - - . - - - - , - - - - - - 1

0.45

&[-]

Figure 5: Additional small scale model test results and 95% confidence boundaries.

The results of the additional scale model tests are compared to full scale measurementresults and scale model test results obtained during the OPTICREST project. Themeasurement results are shown in figure 6. The aim of the scale model tests performed in theOPTICREST project was to reproduce several storms measured at full scale and to comparewave run-up in order to detect eventual scale effects. Much attention has been paid to thecorrect reproduction of the wave spectrum. This was done by tuning the significant waveheight H mo and the spectral mean period of the laboratory tests to the full scale value.Therefore, a lot of tests have been performed, each time with a slightly modified wavespectrum, unti I a satistying agreement was found between the measured spectrum and thetarget spectrum. This was not an easy task as the spectrum measured by a wave rider close tothe breakwater had to be reproduced. At FH, the wave paddle and the location of the waverider were separated by a sand bar which transformed the wave spectrum. At AAU, in fourof the six reproduced storms, higher wave run-up was measurcd than in FH (table 1) due to ashift of the spectral peak to lower frequencies. Even though in most tests a good agreementwas seen between the frequency domain parameters H mo and TO!, the spectral widthparameter "d id not have necessarily the same value. The influence of the shape of thespectrum in general and the influence of the spectral width parameter" in particular is clear

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and may be (one of) the missing link(s) between full scale and small scale measurements toexplain why full scale measurements yield a much higher dimensionless wave run-up valueRlIlo/jH.


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However, the influence of the spectral width parameter is not overpowering. Therefore,the results of the additional tests are looked into detail. Figure 7 shows the results of testseries z5xx. Three different water levels are considered (2 + 0.00, 2 + 2.00 and 2 + 4.00).For every water level, three distinct target peak wave periods ( 1 ~ , 1= 7,6 s , Tp.2 = 9.8 sandTp ,3 = 11,6 s) and one target significant wave height (H, = 3 m) have been tested, All valuesare full size values, The equation of van der Mcer and Slam (1992) has also been displayed,This equation is valid for permeable structures protected with rip rap,

Quite a large spreading is seen on the rcsults, especially for tests with a high Iribarrcnnumber ';'rn. The increase of RU2,JH, with increasing lribarren numbers also has to do withthe influence of the peak wave period Tp , Dimensionless wave run-up also increases whenthe peak wave period Tp increases,

2.5 - . - - - - - - - - - - - - - - - - - - - - - - - ~)

2.0

...'.... 1.5~

:t:- -::>

1.00::

0.5 Z+O.OO Z+2.00... Z + 4.00- - van der Meerand Stam (1992)

60. 0 - I L - - - - ~ - - - ~ - - _ _ _ _ ' ; : = = = : : : ; : : : : = = = ; :

o)

Figure 7: The dimensionless wave run-up value RU2o/jH, [-] versus the lribarren number ~ o m[-1 for different water levels for test series z5 (regular armour unit pattern),

Measurement results also have been displayed in another format. In figure 8 the results ofthe tests with SWL 2 + 4,00 have been grouped per position of the run-up gauge, The onlytwo parameters that change between the four types of dots in each cloud in figure 8 are thespectral width parameter e and the position of the run-up gauge with respect to the armourunit pattern and the water depth, The maximum difference in spectral width LIe betwcen thedots in each cloud is indicated, The changes in spectral width parameter arc relatively small.On the other hand, the differences in RU2,JH, values are big! Relying on the linear trend ofthe best fitting curve in figure 5, the small increment in e cannot yield such a big difference(sometimes in negative !) in RU2o/jH, value, Another parameter must be responsiblc for thesc



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differences. In general, it can be concluded that the three related items ( l) SWL, (2) armourunit pattern and (3) relative position of the run-up gauge with respect to the armour unitshave a real influence on the fInal rclative wave run-up value. When performing scale modeltests, much attention must be paid to the location of the run-up gauge with respect to thearmour unit pattern.

2 . 5 , - - - - - - - - - - - - - - - - - - - - - - - - - - ,

LIe = 0.0200

2.0

""-1.5

J : : . ~-''":>1.0n:: )V,1,,= 0.0116

.....LIe = 0.0087

0.5 z2 (irregular pattern) z3 (regular pattern).. z4 (regular pattern) z5 (regular pattern)

6

0.0 + '===: : : : ;===: : : : ;== ' - - - - - - , - - - , . - - - , - - - - -1o

Figure 8: The dimensionless wave run-up value R1l2'YjFf, [-] versus the Iribarren number q"mI-I for SWL 2 + 4.00 for different positions of the run-up gauge relative to the armour layer.

)Remarkable as well is that all wave run-up distributions of tests performed at one

particular SWL (2 + 0.00, 2 + 2.00 or 2 + 4.00) show bumps and dents at exactly the sameRll levels. These indicate holes and gaps between armour units andlor armour units stickingout of or sunken down in the armour layer. It is concluded that the position of the blocks hasan important influence.

CONCLUSIONSFollowing conclusions are drawn from full scale measurement results:

the dimensionless wave run-up value R1l2'YjHmo measured with the run-up gauge equals1.76 (for !;"m= 3.59), which is higher than the values found in literature.

the dimensionless wave run-down value Rd 2YjHmo equals -0.87, i.e. in good agreementwith the values found in literature.

dimensionless wave run-up increases when water level is decreasing, probably due to thelower porosity at lower levels (settlement of armour layers).

the lower the exceedance probability x, the more variation in Rll x'YjHmo over a tide cycle. wave run-up is Rayleigh distributed.



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Small scale model tests gave more insight in the wave run-up phenomenon.Dimensionless wave run-up increases with increasing Iribarren numbers by influence of the

wave period. Results also showed that the spectral width parameterE

has a very importantinfluence on wave run-up: dimensionless wave fun-up RU2%/Hmo increases with increasingspectral width E. However, wave run-up measurements are influenced by the combinedaction of the water level, the pattern of the armour units and the position of the run-up gauge.Therefore, the position of the section in which wave run-up will be measured must be chosenvery carefully or wave run-up measurements have to be carried out in several sectionssimultaneously to eliminate the pattern parameter in small scale model tests on a rubblemound breakwater.

These two aforementioned model effects may explain why full scale measurement resultsand laboratory investigation results do not agree well.

ACKNOWLEDGEMENT

Results are obtained through the OPTICREST project ( 'The optimisation of crest leveldesign of sloping coastal structures through prototype monitoring and modelling' - MAS3CT97-0116). The financial contribution of the European Union and the Flemish Communityis very much acknowledged, as well as the efforts of the staff of Flanders Hydraulics toperform the additional tests.

REFERENCES

De Rouck J., Boone C., Van de Walle B., 2001a, Detailed scientific and technical report,MAS03/1 031, OPTICREST, http://awww.rug.ac.be/opticrest.

De Rouck J., Troch P., Van de Walle 8., van Gent M.R.A., Van Damme L., De Ronde J.,Frigaard P., Murphy J., 2001b, Wave run-up on sloping coastal structures; prototypemeasurements versus scale model tests, ICE Coastlines, Structures and Breakwaters,London.

CartwrightD.E., Longuet-Higgins M.S., 1956, The statistical distribution of the maxima ofarandom function. Proc. Roy. Soc. London, Ser. A, 237.

Troch P., De Rouck J., Van Damme L., 1998, Instrumentation and prototype measurementsat the Zeebrugge rubble mound breakwater, Coastal Engineering 35, pp. 141-166.

van der Meer J. W., Stam J.c., 1992, Wave run-up on smooth and rock slopes of coastalstructures, Journal of Waterway, Port, Coastal and Ocean Engineering, Vol. 188, No. 5, pp.534-550.

Van Oorschot J.H., d'Angremond K., 1968, The effect of wave energy spectra onwave run-up, Proceedings 11 th ICeE, London, pp. 888-900.

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PARAMETERS INFLUENCING WAVE RUN-UP ON A RUBBLE MOUND BREAKWATER

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