STABILITY OF UNDERWATER STRUCTURE UNDER WAVE ATTACK

C. Paotonan Engineering Faculty, Hasanuddin University, Makassar, INDONESIA

E-mail: [email protected]

D. B. P. Allo Civil Engineering Department, Cenderawasih University, Jayapura, INDONESIA

E-mail: [email protected]

ABSTRACT

Geotube is, among others, a type of coastal structure that is increasingly accepted for coastal

protection especially underwater breakwater. Besides its relatively low cost, it has other advantages

such as flexibility, ease of construction and the fact that it can be filled with local sand material.

Similar to all other coastal structures, it should also be stable under wave attack. A simple theoretical

approach based on linear wave was adopted to estimate the stability of such structure. The theoretical

solution was then compared with an experimental study. The experimental study was conducted at the

Hydraulics and Hydrology Laboratory of Universitas Gadjah Mada. However, instead of a real

geotube, PVC pipe was used where the weight of the PVC was varied by adjusting the volume of sand

in the pipe. The result indicated that the agreement between the theoretical solution and the

experiment was encouraging. The analytical solution may be utilized to predict underwater pipe

stability under wave attack with certain degree of accuracy. Keywords: Geotube, initial movement, submerged structure.

INTRODUCTION Geotube is a type of coastal structure which can be used as coastal protection. Basically geotube is a geosyntetic type of material which is stitched to form a tube when filled with sand or cement material.

Geotube can be used as groin, jetty, or even breakwater as long as the material is strong enough against debris or sunlight. The advantage of geotube is its flexibility size as normally the size of geotextile is almost unlimited when stitched to one another. It is also lightweight which makes transportation easy. There are other economic advantages that make the structure increasingly acceptable.

When used as a breakwater it has to be strong enough to withstand wave force and current (Pilarczyk, 1998, 2000). For this reason, the paper discusses the stability of geotube underwater breakwater. Researches related to geotube as a coastal structure have been carried out by many such as Shin E.C, and Oh Y.I. (2007) who studied the stability of Geotube based on two-dimensional physical model. Paotonan et al (2011) analyzed the geotube stability under sinusoidal wave attack. The use of geotube as coastal protection has been realized in many parts of Indonesia and other countries. El Dorado Royale Resor, Mexico is one of the examples. Geo Me in E det line Ind loc Tir The req fille the fill ass was TH The ine buo A.

The wri Wh per gra

 a u L C F

Where be and a is w tuting u in

is a l cient on cyli eid 1963). In wave is simp

(lift force) ac Figure 1. ft force was on e u is velocit nd C

The flow ed to follow ue to such di

t Force wave propa d be differen m of the geot m of geotube

L C F 



C F _L

Lift When should bottom bottom flow. assume 1). Du force ( The lif equatio Where m/s, an coeffic and Re linear w geotub Substit yields or where

(3) reads (4) is given by (5) B.

(2) ponsible for written as:

D in meter,

, and vely. If the

, V

H is wave h ²

u D C _L

h s

(Wilson ty under (7) oe of the uation 8

(6) ucture in ift force

(Figure vertical as in this

, using Equ be, there p to the ty at the ro or no may be

ean (1992) a p of the stru efficient. Li dy is 4.493 ( water, velocit epth at the to ude.

he geo tube

e the geotub from the top t, the velocit garded as zer geotube m wave theory ow, there is geotube.

/ h

is the de wave amplitu Equation 7 high. ^s

 s h g L

given by De ty at the top lift force co indrical bod n shallow w ply e h

Lift force on th

8 ²  agates above nt velocities tube. In fact e may be reg above the w the linear w ifferential flo cting on the g

C g /

 L D H

2 ²

D h ga C

ρ s

g is earth

g a

4 ² D

 g 

4 ² D

   

  _{R s} g

 

   ^{s s}

g _s

, m oss section is weight of g e buoyancy reduced we ernatively, fo e net force o uation 5.

is ge r meter len avitational ac are kg/m

ρ s

Gravitationa e weight of itten as: here

HEORETICA e forces act rtia force, oyancy force

otube can a exico to prot El Dorado R ached break e protected donesia, geo ations, for rtamaya reso e cross sect quired, thoug ed with sand geotube wil is not full umed to be s nearly roun

W _a ^a W W _R F _B ^B F

cro the The the alte The Equ

 ^{B s}

  also be fou tect the erod

is volume

otube, and The unit of m/s

V s

(1)

) may be

W a

West Java. e shaped as when fully he shape of en the sand eotube was nd the shape drag force, onal force, w.

The geotube is a typical the coastal 4 km. In in many g coast of

respectiv h diameter D that is resp water can be al geotube it n the water atan coast,

Royale Reso kwater. The by the st otubes wer example a ort area near tion of geotu gh it is most d. On the ot ll be close to l. In this pa fully filled w nd. AL APPROA ting on a ge lift force e that is desc al force f the structu eotube speci ngth of geo cceleration. m

ACH eotube are , gravitatio cribed below ure in air (W ific mass, V

Indramayu, ube may be tly rounded ther hand, th o ellipse wh aper, the ge with sand an

 und in Yuc ded beach. T ort, Mexico e length of tructure is re installed at Lombang

4 ² D

) eight in the w or cylindrica on geotube i ²

/m, and m s round with geotube is force (F

(8) (9) C. D The Wh from Keu Equ and For dist Fig On For The the Or D.

Wh wat mo des



H C g

(drag for is introduced r between th ion coefficie n steel) to as riment, the m he flume, w erefore, in th ed to find imental data 4, can be sim ce coincides is more lik ired to dest al parameter ^L

geotube is n buoyancy an the structure mbined forc

  

    

 f D



2 D fC 1    

 

  D h

  

   

fC f

2 ^L ^s



 

  

   

    C fC f _L ^s

4 ₂ ²

8 ²

C ^s _D

D / h ²

(15) (16) ft force, ur. The geotube

4 (loose placed at slightly he value rrelation eoretical

(14) on 14 as and the from as

when the is larger nd mode cal and ven by

s / h ²

2 ²

C /

D s h H

  

e. The secon ces of verti rce) as giv d in Equatio he geotube ent f ranges s high as 0.4 model was p which was his matter th out the cor a and the the mplified as: s with the lif kely to occ abilize the r form, Equa ^s

  

2 ²  not stable w nd lift force i

D L H C fC

2 ² 

h H C /

1 ^{L s}

  

 

C h D 

1 ^D ^s

  

 _s D h H g D g

F _D R W ^D F ^D F

H C g

C D g

istribution o ion, average ucture is loc 10 can be wr tial motion ect (geotube are two pos first is due quation 13. ² _L

mplification of v submerged g

 takes the fo drag force co roximately 2 penter (Dean drag force i ameter. of submerg an be simpli



2 ²

D ga C

 ^D

8 

 ^D

 ^s

  _{R s}  g  





u D C _D

Figure 2, di r simplificati erefore, stru n equation 1 Geotube init hen an obje ter, there a otion. The f scribed by Eq ²

Figure 2. Sim

m 1 to appr ulegan Carp uation 10, d d geotube dia r the case tribution ca gure 2.

C is d

Drag force e drag force here _D

4 ²  

D / h ² ^s D / h

Equation 14 the drag for cond mode height requi e written as: n-dimensiona written as:

 _D _s C f

In this exper ottom of th ded steel. Th will be varie en the exper

s case, the g orce due to b he weight of e to the com ntal forces on 14. oefficient f i ction factor m. The fricti s 0.0002 (on

 

 

  s f 

 

D H  H  ^s f 

   

 

(13) _s In this total fo than th is due horizon Equati The co the fri bottom little a sand). the bo corrod of f w betwee result. or Since t the sec wave h may be In non can be

rm of oefficient, w 2.2 and is a and Dalrym is function ged geotub ified and dr

(11) (12) rged in the s of initial al force as

considered. allow water

bution on n triangular.

e, velocity rawn as in

(10) which varies function of mple, 1986). of velocity

8 ² 

D h H g /

) is submer sible modes e to vertica _s

of velocity in e velocity is cated in sha ritten as:

velocity distrib geotube

(17) ation 15 (18) Therefore, the non-dimensional parameters relevant to the initial motion of the geotube are

 _{s s}

H/D,

 1 and Equation 16 will be used to  D calculate minimum wave height needed for the structure to start moving.

Physical Model Simulation

Model

The experimental study was conducted in a regular wave flume of 30 cm wide. PVC pipes of different sizes that were closed at both ends were

Figure 4. Testing models in the wave flume

used as geotube models. In order to vary the weight of the model and hence its overall density, The models were run for all (three geotubes) the pipes were filled with water and sand of models. The results, together with the analytical different volumes. The diameter of the pipes was approach, were given in the next section. 13.02 cm (model I), 11.02 cm (model II) and 8.374 cm (Model III). The models are shown in

RESULTS AND DISCUSSION Figure 3. The results of the experimental work are given in Table 1 and Figure 5. It can be seen that the agreement between the theoretical and the experimental data is encouraging. However, the real friction coefficient has to be determined for better comparison. In this study, the friction coefficients was tried and the best fit was chosen.

Hence, with such value of f (the best fit) only a trend comparison between the experiment and the theoretical solution can be made. The final trial _{Model I Model II Model III} indicated that f = 0.00546 produced the best fit.

0.025 Experiment Data 0.020

) ry 0.015 o he

0.010 _{Model I Model II Model III} H (t 0.005 Figure 3. Model of geotubes 0.000

Each model was tested under sinusoidal waves

0.000 0.010 0.020 0.030

attack. The test was initiated using small wave amplitudes and was increased at small increment

H (experiment wave height, m)

to observe the initial motion of the geotube models that indicate instability. The wave heights

Figure 5. Theoretical vs Experimental wave height required

were measured using wave probes. The geotube for geotube models initial motion

( f = 0.00546; C = 2.200 and C = 4.489) _{D L} model during the test is shown in Figure 4.

Table 1. Experimental and theoretical minimum wave height for geotubes model stabilization

Model Specification m (kg)

0.05

causes the increasing value of H/D, which means that when the value of specific gravity of structure increases, the wave height required to stir the structure is greater. If the geotube specific gravity and the water depth are constant, the effect of water depth and geotube diameter ratio on H/D can be obtained. The influence of h

/ D on

H/D for a constant ρ s / ρ can be seen in Figure 7.

Figure 6. Relationship between ρ s /

ρ-1 and H/D

0.08

ρ s

0.11

0.14

0.17

0.20

0.23 0.200 0.700 1.200

ρs/ρ-1 Theorectical Experiment Data

/ ρ-1)

respectively at the initial movement of a submerged coastal structure. In terms of non dimensional parameter, the results of the experiment may be compared with the theoretical solution in Figure 6 and Figure 7. Figure 6 shows that increasing value of (

V (m ³ ) ρ s (kg/m ³ ) D

2.965 0.003 1.2600 0.110 0.250 0.0110 0.0110 2.965 0.003 1.2600 0.110 0.250 0.0100 0.0110 2.965 0.003 1.2600 0.110 0.250 0.0100 0.0110 75% of dry sand 3.481 0.003 1.3660 0.110 0.250 0.0130 0.0120

(m) h s (m) H

(experiment, m) H (theoretical, m) with f = 0.00546

(-)

I 100% of water 4.516 0.004 1.2600 0.130 0.250 0.0110 0.0110

4.516 0.004 1.2600 0.130 0.250 0.0110 0.0110 4.516 0.004 1.2600 0.130 0.250 0.0110 0.0110 4.516 0.004 1.2600 0.130 0.250 0.0110 0.0110

II 100% of water 2.965 0.003 1.2600 0.110 0.250 0.0110 0.0110

3.481 0.003 1.3660 0.110 0.250 0.0120 0.0120 3.481 0.003 1.3660 0.110 0.250 0.0120 0.0120 3.481 0.003 1.3660 0.110 0.250 0.0120 0.0120 100% of dry sand 4.627 0.003 1.8170 0.110 0.250 0.0180 0.0190

4.627 0.003 1.8170 0.110 0.250 0.0190 0.0190 4.627 0.003 1.8170 0.110 0.250 0.0180 0.0190 4.627 0.003 1.8170 0.110 0.250 0.0190 0.0190 100% of wet sand 5.605 0.003 2.2000 0.110 0.250 0.0220 0.0230

5.605 0.003 2.2000 0.110 0.250 0.0220 0.0230 5.605 0.003 2.2000 0.110 0.250 0.0220 0.0230 5.605 0.003 2.2000 0.110 0.250 0.0230 0.0230

III 100% of water 1.845 0.001 1.2600 0.0840 0.250 0.0090 0.0090

1.845 0.001 1.2600 0.0840 0.250 0.0090 0.0090 1.845 0.001 1.2600 0.0840 0.250 0.0090 0.0090 1.845 0.001 1.2600 0.0840 0.250 0.0090 0.0090

Figure 5 shows that the trend of the experimental wave heights that agree with the theoretical solution. Using regression technique a fitting curve as in Figure 5 indicates a slope of unity, showing the best fit of the f value and indicates the agreement of the experimental and theoretical data trend. The parameter for the best agreement was 0.00546; 2.200, and 4.493 for f, C

, and C

H/D

0.12 0.60 moving

0.11

0.50

0.10

0.40

0.09

0.30 D unmoving

D H/

0.08

0.20 H/ Theorectical

0.07

0.10 Experiment Data

0.06

0.00

1.50

2.00

2.50

3.00

3.50

0.00

5.00

10.00

15.00

20.00 h /D _s ((f( ρs/ρ-1)(hs/D)/(fCl+CD))0.5 Figure 7. Relationship between h /D and H/D _s Figure 9. Geotube Initial movement graph

Again, Figure 7 shows that the trend between the Using Figure 9, the initial movement of measurements in the laboratory and the submerged structure can be predicted. A situation theoretical calculation is similar. The increasing that is represented by a point located above of the value of h /D causes the increasing H/D value.

s curve of Figure 9 is unstable and vice versa.

Using Equation16 the combination of non Suppose a geotube under wave attack of ( /

ρ s ρ-

dimensional parameter that affects H/D is

1)(h /D) = 5.0 and H/D = 0.4 it indicates that the s

   h _{s s} structure is theoretically unstable while a geotube 1 where the correlation is indicated in

  of ( / /D) = 5.0 and H/D = 0.1 is

D ρ s ρ-1)(h s



  theoretically settled. Figure 8. The line and scatter point in the Figure are theoretical line and data experiment,

CONCLUSIONS respectively. Based on the explanation above, it can be concluded into some points below. Firstly, the

0.25

stability of a submerged structure is influenced by

0.20

wave parameters (height and water depth) and structure parameters; those are the specific

0.15 D

gravity and the diameter of structure, D.

Secondly, the wave height trend which is able to

0.10

move the structure obtained from experimental

Theoretical

0.05 data and calculation with Equation 15 are equal.

Experiment Data

Thirdly, as the value of structure specific gravity

0.00

increases, the wave height which is needed to

0.00

1.00

2.00

3.00

move the structure is increasing too. Or in other

( ρs/ρ-1)(hs/D)

words as the specific gravity of structure

Figure 8. The combinative effects of ρ / ρ-1 and h /D increases, the structure is more stable as well.

_{s s} on H/D Fourthly, if the value of water depth and structure diameter is getting greater, the effect on wave

Figure 8 shows the increasing value of ( /

ρ s ρ- height and structure diameter ratio is getting 1)(h /D) causes the increasing values of H/D. s greater and follows the logarithmic trend.

Theoretical value of H/D on Figures 5 to 8, were Combination of non-dimensional parameter calculated by assuming that

f, C , and C values

D L which influences the ratio of wave height value were 0.00546; 2.200 and 4.498 respectively.

and structure diameter is ( / /D). As the

s s ρ ρ-1)(h

Using Equation 17, H/D values as a function of value of ( / /D) increases, the value of H/D

s s ρ ρ-1)(h

geotube specific gravity and ratio of depth water increases too. The initial movement of geotube to geotube diameter can be calculated where the can be predicted by using Equation 17 or Figure result is presented in Figure 9.

9. ACKNOWLEDGMENTS The authors would like to thank Directorate General of Higher Education (DIKTI) and Hasanuddin University for financial support to do the research. Invaluable comments, suggestions and corrections by Prof. R. Triatmadja especially with respect to the stability of geotube of the original paper is highly appreciated. The authors also express their sincere gratitude to the Head of the Centre of Engineering Science Studies and the Head of Hydraulics and Hydrology Laboratory, Universitas Gadjah Mada, for the facilities to support this research.

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STABILITY OF UNDERWATER STRUCTURE UNDER WAVE ATTACK