WAVE TRANSMISSION THROUGH VERTICAL SLOTTED WALLS ABSTRACT

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1 CHAPTER 111 WAVE TRANSMISSION THROUGH VERTICAL SLOTTED WALLS by Jahim Grie an S6ren Khlhase 2 ABSTRACT This paper eals with the wave transmiss thrugh a vertial sltte wall. In an experimental stuy the transmiss effiient has been vestigate as a funt f the shape f the wall elements (retangular shape an H-beam shape), f the rati f sli wall t ttal wall lenght (wall-element rati) an f the wave apprah iret. The test results fr a wave iret perpeniular t the wall are mpare with previus vestigats an theretial erivats. Fr an blique wave apprah the test results are esribe by a semi-empirial frmula. This frmula, mbe with a theretial slut fr perpeniular wave apprah is use t esribe the transmiss effiient fr any angle f wave apprah. Dipl.-Ing. "Franzius-Institut fur Wasserbau un Kustengenieurwesen" 2 Dr.-Ing. Tehnial University f Hannver, Germany 1906

2 TRANSMISSION THROUGH WALLS 1907 INTRODUCTION Fr slvg erta astal engeerg prblems, sme times an artifiial nstrut is wante, whih shul be permeable with respet t urrents an seimentat prblems, n the ther han the same nstrut shul give a suffiient prtet agast wave at. Suh a nstrut ul be a vertial sltte wall. The general physial press, when a wave passes a vertial sltte wall, is shwn Fig. 1. The energy balane an be state as fllws: E I = E T + E R + E V where E = wave energy f the ient wave E = wave energy f the transmitte wave E_ «* wave energy f the reflete wave E = wave energy lss The wave ampg effet may be esribe nly by the transmitte wave energy mpare with the ient wave energy r (stea f wave energy) by the transmitte wave height mpare with the ient wave height. The purpse f the stuy esribe this paper, therefre was t bta the "wave transmiss harateristis" fr vertial sltte walls with respet t 1. the rati f the impermeable part f the wall t the ttal wall 2. the shape f the wall elements 3. the wave apprah iret

3 1908 ASTAL ENGINEERING DEFINITIONS AND NOTATIONS The transmiss effiient t is efe as the rati f the transmitte wave height H^, t the ient wave height H T : K f Hi The wave height after passg the sltte wall, als will be fluene by iffrat ue t the gemetry f the bas beh the wall. Therefre the transmitte wave height IL, must be efe iretly beh the wall as shwn Fig. 2 whih als shws sme pssible nfigurats f a sltte wall mbe with ajaent impermeable walls. The gaps exten ver the ttal water epth (Fig. 1). Therefre the "wall-element rati" W is given by (Fig.3):»-! where b is the with f eah wall element an e is the enterle spae f the elements. 100-W gives the relative wall-element rati %. The iret f wave apprah t the wall is efe by the angle B as shwn Fig. 4. EXPERIMENTAL EQUIPMENT AND PROCEDURE The experiments were nute a wave bas 0.5 m eep, 6.7m wie an 35 m lng (Fig. 5). The test area was 6.7 m wie an 25 m lng. The bas was equippe with a mbe flap- an pistn type wave generatr fr regular waves. The upper an lwer strkes ul be ajuste epenently t reprue the hrizntal partile velity istribut fr any esire wave peri an wave height as aurate as pssible.

4 TRANSMISSION THROUGH WALLS 1909 LU x X t LU x > < UJ X < a: a. a. < > < CC u. < LU CC < < s LU 1-1- _1 t/3 _1 z < O * t t/j h- t e ^* LU z: > (/) z < < a: X h- ID => LU > CC < X 3: 1- H Z LU < CC U- I- < O N"> CD

5 1910 ASTAL ENGINEERING?'- * ' e ' s 3 O 4) te <n us E 'H I* 09'2 IT) C n X j «> «, «- ^ 'UN ^WUUH. " <: '-"/.. / / i 0. * / i i i_ - ' i : <i» ble gui wall _ absrb > / a ( E 0Z9 q uiiii =. s > i GO OQ CJ3

6 TRANSMISSION THROUGH WALLS 1911 At ne sie f the vertial sltte wall a wave absrber was plae whih separate a wave bas beh the wall. At the ther sie f the sltte wall the transmitte wave was separate frm the ient wave by a mvable impermeable guie wall. Fr the wave iret fl = 0 (perpeniular t the wall) these guie walls were situate n bth sies f the sltte wall t ensure a nstant with. The wave irets 6 lue 0 45, 67.5 an 90. The shapes an the imenss f the wall elements are liste the fllwg table: shape f the wail-element Dimenss [m] it retangular b:t = 1:0.1 _-i pr > jjt retangular b:t = 1:1.5 0> 2 retangular b:t = retangular b:t = 1:0.75 1:0.5 1:0.66 1:1.33 ^T2 H-beam b:t = 1:2 Tlr, \^ u w (H Qi Eah test series (with a nstant wave iret 6, a nstant wall-element rati W an a given shape f the wall-elements) mprise abut 12 runs, eah with a ifferent wave. The parameters f these waves were varie steps the range f: wave height H ; wave lenght L: wave peri T: 4 m t 14 m 80 m t 300 m 0.7 se t 1.7 se wave steepness = : "I 1 : 12 t 1 : 40 The water epht f 3 5 m was hel nstant fr all tests. The waves were measure with a mvable parallel-wire resistane type wave gauge. Bth the ient wave H the transmitte wave H T were measure an average rss-setal prfiles, the ient wave K T abut f frnt f the sltte wall, the transmitte wave H

7 1912 ASTAL ENGINEERING iretly beh the sltte wall (Fig. 2). The ient wave als was measure a lngitual set prfile, t separate the reflex effet. In the ase f wave iret B > 45 fr the alulat f transmitte wave height mean values,abut 0.5 m f the ttal wall lenght n the wave absrber sie has nt been nsiere t elimate sen rer effets ue t iffrat extensively. EXPERIMENTAL RESULTS In the first stane the transmiss effiient K m was pltte as a funt f the wave steepness =. As an illustrat Fig. 6 shws sme results f 4 test series fr a H-beam shape wall element with a nstant wallelement rati W = The satterg f the ata may be fluene aitally by the effet f re-reflet an sen rer effets ause by iffrat. A straight le has been fitte t the ata, whih then has been use fr ther mputats an plts. Fig. 6 als shws a slight erease f the transmiss effiient with reasg wave steepness. The fluene f the relative water epth /L is fun t be negligible fr these test nits, whih is als agreement with prevs vestigats [lj. 1. RESULTS FOR WAVE DIRECTION 6 = 0 Fig. 7 shws the effet f ifferent shapes f wall elements an wall-element ratis W. It an be seen, that the shape f the wall elements has nly a small fluene. Fig. 8 shws the effet f the thikness t f the wall. As expete, K ereases with reasg thik-

8 TRANSMISSION THROUGH WALLS T T- r _ O - - II - - e : - - _l_ _l _l _l_ i i vt O U3 LU r> E Ol :* Ol E Ol : ""vz r 1 T _ - _ - - I _l_ i I i 1 r I i - - _. O II _J I ' 1 1 i. -f" t - - L us E 0).a 4) a r. t/i 0l E _> I CD t

9 1914 ASTAL ENGINEERING 1.0 K T H T /L=1:20 [3 = 0 wall-element shape: 0.4 O ' retangular b:t = 1;1.5 retangular b:t = 1:1.3 b:tr 1: A*,, ' retangular b.t ^ H-beam b:t = 1:2 J L J I I w 1.0 FIG. 7 TRANSMISSION EFFICIENT K y VERSUS WALL-ELEMENT RATIO W

10 TRANSMISSION THROUGH WALLS K T 0.9 W= (3=0 f retangular shape wall-element b = nstant = 3 m A m t i b FIG, 8 TRANSMISSION EFFICIENT K T VERSUS WALL THICKNESS T

11 1916 ASTAL ENGINEERING ness. It shul be nte, that this effet is strengthene with reasg wall-element rati W. Hwever, the fluene f the thikness, whih is prprtal t the wall frit area,is small. 2. RESULTS FOR WAVE DIRECTION 0 < 0-90 Fr wave irets fl > 0 the fluene f the shape f the wall elements is mre imprtant than fr B = 0. Figs. 9 an 10 shw the results fr K as a funt f the wave iret fr ifferent ratis W an shapes f the wall elements. In all ases with wave iret B = 90 the transmiss effiient K has abut half the value f that fr B = 0. This an reaily be explae by the effets f iffrat ue t the presene f the ajaent sli wall n ne sie (wave absrber), whih an be seen as a semi-fite impermeable breakwater. Generally it must be nsiere, that the transmiss effiient K T fr B >> 0 (espeially fr B > 75 ) ntas a part f the iffrat effets. These iffrat effets epen n the relative wall lenght /L (wall lenght % mpare t wave lenght L), whih this stuy has been the range 1.0< 'L<3.75. The test results shwn Figs. 9 an 10 an be esribe by the fllwg semi-empirial frmula: < Tfi = 0.5 x T (l+s a B) were < ** transmiss effiient fr any wave iret B K- = transmiss effiient fr the wave iret B = 0 a = shape effiient f the wall element

12 / // TRANSMISSION THROUGH WALLS 1917 ~T~ ii <: III T T II / / / 4' #r J L -&^ ^ 9 e i ;: _ T r a «-' 75 Jl -a E a tt) 3 -' B "^^ % it CD O m t< In _> LU 5 LU > 3: =3 en LU <_> / / / / T 00 CD O II T T I J^gg*,0* f / / I / / i j i<ui i i i L ID O " u ' II I en O CD C/0 CD

13 1918 ASTAL ENGINEERING UJ UJ UJ i*i r - vf 5 'f _ ii 0 4^ <& ^ *^ /// III III III i MLJ 1 1 L 00 ID vies p If) " II en.n I r- if> CD C_) O CD

14 TRANSMISSION THROUGH WALLS 1919 The values fr the shape effiient were fun t be a =0.5 fr retangular shape b:t = 1:1.5 a =1.0 fr H - beam shape b:t = 1:2 V T element shapes espeially fr B = 67.5, prbably are generate by ey frmat beh the wall f the H-beam type. BRIEF REVIEW OF EALIER STUDIES AND MPARISON OF THE RESULTS Only fr a wave iret 6=0 previus wrk n wave transmiss thrughvertial sltte walls was publishe. Fr perpeniular wave apprah test results were btae by HARTMANN [l] fr retangular-set elements, HAYASHI [2] [3] et.al. an WIEGEL [4] fr irular-set elements, whih are a fair agreement with the authr's results as shwn Fig. 11. WIEGEL, HAYASHY et.al. an HARTMANN have als erive theretial equats fr the wave iret 6=0. WIEGEL [4] evelpe a frmula fr the transmiss effi- ient «K_ as a funkt f the wall-element rati W as fllws: K T = / 1 - W The values alulate frm this frmula are abut 25 % smaller than the measure values. HAYASHY et.al. [2] [3] stuie the transmiss effets fr the range W = 0.8 t 1.0. He evelpe the fllwg frmula [Y] : A i-,[- 3 e.^t^]

15 1920 ASTAL ENGINEERING where 2 e = (KIT) v b+s' / /1 " * - (tn~) v b+s' an = 0.9 t 1.0 This frmula an be transfrme t * T = 4 <a/l r. /T~^P^ "I H7?L e G + K E + 27L J where e = C (1-W) L-W) / A /I - (1-K) T" 1 The values alulate by this frmula fr the range W < 0.8 are mre epenent n the relative epht /L than is suggeste by the experiments. A mifiat f this erivat fr shallw water waves f small amplitue results the frmula \_3~\ T H, Uk- e _alm r_ e + Vfe 2 + t tanhj-: 1 i Q /L t a tanh k [ E re 27L Q2 k J,,,,, k. 2,,, sh 2 where a = 1.1 an a = ( r-t r-j) (1 + -^ k, sh k' 3 ) HARTMANN J_lJ erive a frmula by means f the energy transferability meth f GODA an IPPEN fr a wave issipatr mpse f wire mesh sreens. With apprpriate assumpts he btas K T = /l-vt This frmula is very g agreement with all experimental results (Fig.11).

16 TRANSMISSION THROUGH WALLS 1921 K T 1.0 HLI Hj/L 1: ^30 WO D B a HARTMANN [1] <0 4 HAYASHI [2] V HAYASHI [3] WIEGEL [4] O t> 9 AUTHORS ret. 1M.33A5 J I I w FIG, 11 MPARISON OF THE RESULTS FOR WAVE DIRECTION (3=0

17 1922 ASTAL ENGINEERING NCLUSION The experimental results an the mparisn with the results fr the wave iret 8 = 0 f ther authrs have shwn, that the transmiss effiient <_, epens nly slightly n the relative water epht /L an the wall-element thikness t. Mre imprtant fatrs are besies the wave steepness H/L an the shape f the wall elements maly the wall-element rati w an the wave iret B. Fr a wave iret fl > 0 it was fun, that the fluene f the wall-element shape is mre imprtant than fr a wave iret perpeniular t the wall (fl = 0 ). Fr the wave iret 0 < B 5 90 the fllwg frmula esribes the test results: K Tfi = 0.5 ie T (l+s a B) With that frmula,mbe with the equat fr fi = 0 erive by HARTMANN, the transmiss effiient < T fr any wave iret may be esribe by the fllwg frmula: K T = 0.5 V 1 - W 2 (l+s a B)

18 TRANSMISSION THROUGH WALLS 1923 REFERENCES [l] HARTMANN Das Stabgitter statiirer Strraungsbewegung Mitt, es Instituts fiir V T asserbau un Kasserwirtshaft TU Berl Heft 69, 1969 [2] HAYASHI et.al, [3] HAYASHI et.al. [4] WIEGEL Hyrauli Researh n the Clsely Spae Pile Breakwater Castal Engeerg Japan Vl. 9, Clsely Spae Pile Breakwater as a Prtet Struture agast Beah Ers Castal Engeerg Japan Vl. 11, 1968 Clsely Spae Piles as a Breakwater Dk an Harbur Authrity Sept. 1961

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