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Wave Transmission on Submerged Rubble Mound Breakwater Using L-Blocks

Dayat Indri Yuliastuti

PhD Candidate, Department of Civil EngineeringUniversiti Teknologi PETRONAS, 31750 Tronoh

Perak, MALAYSIAEmail: dayat.indri@gmail.com

Ahmad Mustafa Hashim

Associate Professor, Department of Civil EngineeringUniversiti Teknologi PETRONAS, 31750 Tronoh

Perak, MALAYSIAEmail: mustafa_hashim@petronas.com.my

AbstractLaboratory tests on a permeable submerged rubblemound breakwater (SRMB) constructed using L-Blocksarmour unit with 40 tests for wave transmission were analyzedand the available empirical equations for wave transmissioncoefficient (Kt) were evaluated. The ranges of variation were

0.23< ds /d

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The value ofKt indicates the effectiveness of a SRMB toattenuate waves. It varies as 00.

Friebel et al , 1999 [16] suggested the followingequation:

0905.11359.0log0696.04257.00292.04969.0 +

+

+=

B

F

L

B

d

d

d

B

H

FK s

it

(7)

In the present paper, experimental data are comparedversus the above-mentioned empirical equations.

III. EXPERIMENTAL SETUP AND PROCEDURE

The selection of breakwater material was based on thenecessity of breakwater armor unit to withstand numerouswave conditions. A model breakwater was constructed in awave flume with 1.8 m depth, 23 m length and 2 m width inCoastal Laboratory of Civil Engineering Department inUniversiti Teknologi PETRONAS (UTP), Malaysia. The

armor units were L-Blocks artificial armor with the relativedensity of 2.3, average mass of 840 g, and Dnof 0.0629 m.Fig. 3 shows sections of the breakwater when submerged inthe flume. Fig. 4 presents views from the flume and theSRMB as built. Fig. 5 shows isometric view of the L-Blockand Fig. 6 shows characteristic dimension of L-Block unit.

Important parameters affecting the design and operationof SRMB varied systematically as listed in Table 1.Placement of the armor units followed the real life practice.The core was placed by shovel, trowelled and washed in

place to naturally compact. Each armor unit was placedindividually and properly by hand. An armor unit wasensured to be in contact with armor next to it without being

pushed into core layer material.

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Figure 3. SRMB Model

a. Core Layer . Armor Layer

c. Coastal Laboratory d. SRMB Model with d=0.65m

Figure 4. The Model Construction and Equipment Installation

Figure 5. Isometric view of the Modified L-Block

Figure 6. Characteristic dimensions of L-Block unit

All tests were performed with regular waves of variousheight and period. Wave heights at both sides of the

breakwater were measured using wave probes and the valueswere double checked by video clips played in pause mode orslow motion. Sixth wave probes were used, three at eachside placed at 1-m distance from each other, the first onenear the toe of the breakwater. The average of thetransmitted wave heights as captured by the first two probesdownstream of the breakwater was taken asHt.

Table 1. Breakwater Structure Configuration

SeriesCode

SubmergenceDepth, ds (m)

Crest Width,B (m)

Cot

A1 0.15 0.5 1.5B1 0.20 0.5 1.5C1 0.30 0.5 1.5

IV. RESULTS AND DISCUSSION

Fig. 7a shows the wave data with 650 mm water depth,wave height of 10 cm and T of 1.5 s. The following datafrom the figure are noteworthy:Hi,max=0.11 m,Hi,min=0.09 m,

Hi=0.10 m, Ht,max=0.10 m, Ht,min=0.08 m, and Ht=0.09 m.The incident and transmitted waves for 650 mm water depth,wave height of 11 cmand T of 2 s are shown in Fig. 7bfromwhich the following data are noted: H

i,max=0.12 m and

Hi,min=0.10 m, Hi=0.11 m and Ht,max=0.11 m, Ht,min=0.09 m,Ht=0.10 m. The pattern of the fluctuations is fairly regularshowing the data and measurement methods were reliable.

Under water depth of 800 mm, the breakwater performedbetter with T=2.0 s compared to T=1.0 s asKt=0.73

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a.Wave Data, Hi =10cm, T=1.5s b.Wave Data, Hi =11cm, T=2s

Figure 7. Wave Data d=0.65m with different Hi and T

Figure 8. Variation ofKtwithHi /gT2

Figure 9. Variation ofKtwithHi/L

Variation of Kt versus Hi /(gT2) and Hi/L for different

values of relative submergence, ds/d,are shown in Fig. 8 and9, respectively. The horizontal axes are the indication of thewave steepness, the second being the actual wave steepness

and the first is a representative of the steepness. For example,in deepwater conditions, L=1.56T2. The plots show thatwhen submergence is greater than 40%, the breakwater doesnot attenuate the waves significantly. The performance withlow submergence is further improved as the wave steepnessincreases. For near zero submergence, a transmissioncoefficient ofKt=0.70 will result that is fairly independent ofthe wave steepness.

Figure 10. Influence of relative crest height on transmission(variable wave height, T=2 s)

Fig. 10 is a plot of transmission coefficient versus therelative submergence for five wave heights. As expected,the attenuation decreases with increase of submergence. Theinteresting observation is that the curves show a fairly linearvariation. Within the limits of the experimental data, thefollowing linear regression equation will result.

+=

d

dK

s

t 53.17.0 (8)

Figure 11. Effect of crest width on wave transmission

In a numerical prediction of performance of SRMB,

Rambabu and Mani [17] compared their numerical solutionwith the experimental data of Hall and Seabrook [13] in agraph showing the variation of Kt versus hs/d. The datarelate to a permeable SRMB with porosity of 0.3. The plotcontains 7 data points in the range of 0.25

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+=

d

dK

s

t 81.004.0 (10)

However, the present form (8) is comparable with theexperimental data presented by Abdul Khader and Rai [3] forimpermeable SRMB. The best fit line to their experimentaldata is

+=

d

dK

s

t 75.017.0 (11)

In the later stages of this ongoing investigation, thisequation will be improved to involve the effect of otherinfluencing parameters such as the breakwater top width B,

breakwater height hs, breakwater slope and permeability.Fig. 11 illustrates a plot of the transmission coefficient,

Ktagainst the dimensionless parameter B/d. As expected, astrong correlation cannot be observed because otherinfluencing properties such as submergence and wavecharacteristics are not captured in the variable B/d. Regular

patterns in the graphs presented by some authors (seeRambabu and Mani [17] or Sidek and Abdul Wahab [18])should be interpreted with care. In the former, Hi/(gT

2)involves the wave characteristics and the latter dealt onlywith a single submergence depth. However, within the rangeof the present data, the following linear fit can show theoverall pattern.

+=

d

BKt 5.082.0

(12)

A comparison was made between the present data andthose predicted by several design equations in the literature.They are those of DAngremond, Seabrook and Hall,Friebel-Harris, and Buccino. Fig. 12 is a graphicrepresentation of the comparison with four empiricalformulas. The formulas by Friebel-Harris and Buccino showa better performance.

Figure 12. Comparison between Measured Kt and Empirical Equation.

V. CONCLUSIONS

Laboratory experiments have been conducted in a waveflume to study the transmission of regular waves through

submerged rubble mound breakwater, SRMB. Four designparameters were varied systematically: wave height, waveperiod, water depth and submergence depth. The modelSRMB was 0.50 m high with top width of 0.5 m and sideslope of 1V:1.5H with L-Block armor of 0.0629 mDn. Thewaves were measured using both wave probes andvideographic method. Forty (40) tests were achieved and theresults were analyzed.1. The wave attenuation decreases fairly linearly with

increase of submergence. With submergence greaterthan 40%, the breakwater does not attenuate the wavessignificantly. The performance for low submergence isfurther improved as the wave steepness increases. Fornear zero submergence, a transmission coefficient of

Kt=0.70 will result that is fairly independent of the wavesteepness.

2. Within the range of the present experiments, Ktshows ameaningful correlation with the ratio of submergencedepth to the water depth. A fitted line was suggested.

3. In plotting the transmission coefficient versus the ratio oftop width to water depth (B/d), little correlation wasfound. This has to be expected because other influencing

properties such as submergence and wave characteristicsare not captured in B/d. However, within the range ofthe present data, a linear fit representing an overall

pattern was introduced.4. The measured transmission coefficients were compared

with those predicted by several empirical equations in

the literature. Formulas with better performance wereintroduced.

VI. ACKNOWLEDGMENT

The authors would like to thank Universiti TeknologiPETRONAS for providing the research facilities and grant toundertake the research.

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