Influence of Wave Directionality on Stability of Breakwater Heads

Transcription

1 CHAPTER 101 Influence f Wave Directinality n Stability f Breakwater Heads Y. Matsumi \ E.P.D. Mansard 2 and J. Rutledge 3 Abstract An experimental investigatin was undertaken t investigate the stability f breakwater heads under uni and multidirectinal wave attacks. Waves f nrmal and blique incidence were used in the investigatins and the stability results were assessed alng with relevant measurements f wave surface elevatin, measured in the prximity f breakwater heads. INTRODUCTION In spite f the grwing number f multidirectinal wave facilities arund the wrld, breakwater designs are still evaluated using unidirectinal regular r irregular waves, because it is widely believed that testing under unidirectinal wave prvides cnservative results (i.e. verdesigned breakwaters). This may be true fr the trunk sectin f the breakwater where the directinal spread assciated with the multidirectinal seas tends t reduce the wave lads imparted n the structure. Fr the breakwater heads, this assumptin is perhaps nt valid. Because f the directinal characteristics in multidirectinal waves (i.e. 3D waves), sme sectins f breakwater heads may be expsed t larger wave heights than nrmally encuntered under unidirectinal waves (i.e. 2D waves) Assciate Prfessr, Dept. f Scial Systems Engineering, Tttri University, Tttri, Japan. Senir Research Officer, Institute fr Marine Dynamics, Natinal Research Cuncil f Canada, Ottawa, Canada. Prt & Marine Dept., Sandwell Inc., Vancuver, Canada. 1397

2 1398 COASTAL ENGINEERING 1994 Generally, under unidirectinal waves f nrmal r blique incidence, the head sectins f breakwaters are mre susceptible t damage than their trunk sectins wing t the large wave heights and velcities that result frm prcesses such as refractin, diffractin and shaling n and arund the head sectins. Because f this, researchers such as Jensen (1984) and Vidal et al. (1991) suggest that the weight f stnes fr the heads shuld be abut 1.5 t 4 times the weight f armur stnes in the trunk sectin. Under multidirectinal waves, the wave heights that a breakwater head sectin encunters thrugh the varius prcesses described abve, are pssibly made even larger due t waves directly attacking the breakwater frm ther directins. Therefre mre wave lads are expected n the heads, resulting thereby in lwer stability. EXPERIMENTAL SETUP Layut f the basin The physical mdel tests were carried ut, at the Natinal Research Cuncil f Canada, in the multidirectinal basin f the Castal Engineering Labratry f the Institute fr Marine Dynamics. The basin used fr this purpse has a length f nearly 20m and a width f 30m. Figure 1 shws a plan view f the experimental set-up. A sixty-segment wave generatr is lcated alng ne f the 30m sides f the basin. Perfrated expanded sheet absrbers, capable f limiting wave SEGMENTED WAVE MACHINE,St-2 /St-7 ^St-8 -St-9 -St-10 * St-11 I 6 m j -St-12 m SHfe Wave gauge Figure 1. Plan view f the experimental set-up

3 WAVE DIRECTIONALITY INFLUENCE 1399 reflectins t 5% fr mst frequencies f interest, are installed alng the remaining three sides f the basin. A 5m lng gate and a clsure plate f similar length at the tw extremities f the wave generatr are generally used fr techniques that intentinally use crner reflectin fr increasing the size f the hmgeneus area (see Figure 1). Layut f wave gauges The water surface elevatins were measured at 17 different lcatins indicated by dts in Figure 1. Eight ffshre wave gauges were munted n tw frames as a three-gauge and a five-gauge arrays. The three gauge array was set up t analyze the reflectin f unidirectinal waves f nrmal incidence by the methdlgy f Mansard and Funke (1987). The five gauge array was used t analyze the directinal characteristics f nrmal and blique incidence multidirectinal waves with and withut the structure in psitin. The remaining nine wave gauges were placed in the prximity f the mdel at a distance f 0.5m away frm the te f the structure, at lcatins shwn in Figure 1. (Nte that St stands fr wave gauge statin). Layut f breakwater mdel The layut f the breakwater mdel had t be designed carefully in this study, fr the reasns indicated belw. Althugh sphisticated techniques have been develped t simulate the directinal characteristics f the natural sea states inside labratry envirnments, the area ver which the sea state can be hmgeneus in a wave basin is limited because f prcesses such as diffractin and reflectin (see Sand and Mynett, 1987). Therefre careful cnsideratin had t be given in rder t ensure similar sea state severities alng the entire breakwater sectin. Fr this purpse, use was made f the WAGEN mdel which culd predict the watersurface elevatin and kinematics f the sea states prevailing at different lcatins in the basin. This mdel, develped by Isaacsn (1992), is based n the bundary integral equatin and linear diffractin thery and can accunt fr partial reflectin frm structures such as breakwaters. A sample utput resulting frm this prgram is presented in Figure 2. It illustrates the spatial distributin f wave heights in the basin withut the breakwater mdel, under a multidirectinal sea state. The expected wave heights presented in this figure were nrmalized with respect t target wave heights. Nte that their maximum value is nly 0.9. This is due t diffractin prcesses and can be increased by applying an amplificatin factr. It can be seen frm this figure that the useful test area, ver which the sea state is hmgeneus, is limited by a triangular bundary. Accrding t this figure, the best lcatin fr the mdel wuld be clse t the paddle. Hwever, since this wave basin is nt yet equipped with active absrptin, an ptimum lcatin which wuld simultaneusly ensure an hmgeneus sea state

4 1400 COASTAL ENGINEERING 1994 and minimize re-reflectins frm the paddle had t be chsen. Since the mdel breakwater ccupied nly a prtin f the basin width, reflected waves were expected t dissipate thrugh diffractin prcesses befre they are re-reflected by the paddles. Furthermre, since the prpsed breakwater gemetry had a symmetrical layut, it was cnsidered justifiable t study nly ne f its head sectins. Based n these different criteria, the mdel was lcated, as shwn in Figure 1, at a distance f 9m frm the paddle, and it was als ffset by 2m frm the center line. 20 x (m) K- i^.uv»»j;*vj**i^ai illlijl i K-'g WAVE GENERATOR iilililiilg y(m) 10 Figure 2. Spatial distributin f wave heights in the basin withut the breakwater in place Characteristics f breakwater mdel Figure 3 shws bth plan and prfile views f the breakwater mdel. In rder t achieve a better insight int the individual perfrmance f the varius breakwater cmpnents, nine sectins f interest were separated frm the ttal structure by using a steel frame with different cmpnents. Figure 3 shws the six trunk and the three head sectins included in the study. The three head sectins, called Frnt Head (FH), Middle Head (MH) and Back Head (BH), cver an area enclsed by an angle f 60 as shwn in Figure 3. The remaining parts f the breakwater were cvered with a steel mesh having square penings f 1x1 cm in size, in rder t avid rebuilding the entire breakwater after every test. The breakwater was f cnventinal type, cmpsed f tw layers f armur, a filter layer and a relatively prus cre. Its height was 80cm and it perfrmed as a nn-vertpping structure in a water depth f 50cm. The

5 WAVE DIRECTIONALITY INFLUENCE 1401 frnt and rear slpes were 1:2. Similar stne weights were used bth in the trunk and head sectins intentinally, in rder t ensure high damage n the head sectin. One f the main reasns fr this is that an accurate assessment f the wave height that causes small degrees f damage is generally difficult because f the experimental variability assciated with effects such as interlcking (see Davies et al., 1994). Plan view f the mdel 13 cm 2 1 1*^-ARMOUR Prfile view f ttie mdel Figure 3. Plan and elevatin views f the breakwater mdel The characteristics f the cre, filter and armur stnes used in the experiments are presented in Table 1. The gradatins f the armur stne were meticulusly checked and the resulting D n85 /D n15 rati fr the armur was 1.3. In rder t differentiate the varius layers, each layer f armur stne and the filter layer were painted with a unique clr. With this clr scheme, the level f damage in each sectin culd be easily ascertained by visual bservatin and phtgraphs. Measurement techniques The prfiles f the trunk and head sectins f the breakwater were measured using the electr-mechanical prfiler described in Davies et al. (1994). The prfiles taken in the directin nrmal t the wave paddle, were generally spaced 10cm apart in the trunk and head sectins. The head sectin prfiles were then cnverted int plar crdinates t btain prfiles every 5. Since the head was subdivided int 3 sectins, each cvering an

6 1402 COASTAL ENGINEERING 1994 area enclsed by 60, an average f 11 prfiles was used t quantify the damage in these sectins. The erded area in the head and trunk sectins was cmputed after each test using average prfiles f riginal and final crss-sectins. The damage index, S, was then calculated by nrmalizing the erded area with the square f the armur stne's nminal diameter. Besides establishing damage values by prfile data, visual bservatins were als used t classify the degree f damage accrding t the fur classificatins suggested by Vidal et al. (1991): Initial damage, Iribarren's damage, start f destructin and destructin. T further assist the estimatin f damage, clr phtgraphs f each individual sectin were taken after each test. In additin, vide pictures were used t recrd the entire experiment. Table 1. Summary f the breakwater characteristics Wgg weight f armur (g) 118 WgQ weight f filter (g) 15 W 50 weight f cre (g) 2 D n50 nminal diameter f armur (cm) 3.54 prsity 0.45 length f trunk (cm) 600 diameter f head (cm) 333 crest breadth (cm) 13 height f breakwater (cm) 80 \1/3 D n6 = ( W 5 / P s ) > P s : unit weight f armur unit TEST SERIES Table 2 indicates the characteristics f the waves used in the experiments. The spectra were f the JONSWAP type with tw different peak perids (Tp - 1.4s and Tp = 1.7s). The peak enhancement factr y was chsen t be equal t 3.3. The multidirectinal waves were simulated using the well knwn Single Summatin Methd in rder t eliminate spatial variability f sea states. Since the bjective f this study was t assess the sensitivity f damage t spreading f the wave energy, the cmmnly used cs 2s mdel was chsen fr directinal distributin. Values f s=2 resulting in cs 4 and s= were applied t simulate multi and unidirectinal waves respectively. In rder t assess the influence f bliqueness, tw different mean angles f incidence 8=0 and -15 were used, ensuring at the same time hmgeneity f the sea state at all sectins f interest.

7 WAVE DIRECTIONALITY INFLUENCE 1403 In rder t minimize statistical variability assciated with shrt lengths f wave recrds, a recycling perid f 20 minutes (in mdel scale) was used in the synthesis by the Randm Phase Methd. This length crrespnded t abut 1000 waves when Tp=1.4s and 850 fr Tp=1.7s. The ratis f diameter f the head ver wave length and length f trunk ver wave length are indicated in Table 2. Eight test series were carried ut using different cmbinatins f spreading index and mean angle f incidence. In each series, the spectrumbased significant wave heights Hm were increased frm 5 t 15cm in steps f 2.5cm. Mst f these sea states were pre-calibrated in the basin withut the structure in psitin, while keeping all 17 gauges in place. Tests under each value f Hm were run until the stabilizatin f damage. This was achieved in abut 2000 t 5000 waves. Spectrum Table 2. Characteristics f waves in experiments T P (s) Y e (dg.) s TR (min.) N D/L Ti7L JONSWAP ,-15 2, JONSWAP ,-15 2, RE-REFLECTIONS IN THE TEST SET-UP The reflectin characteristics f the breakwater were estimated by the NRC algrithm, under unidirectinal waves f nrmal incidence. Figure 4, which summarizes these results, shws the reflectin cefficient, Cr, t be in the rder f 20 t 25%. Althugh the steepness parameter, Hm/L, used in the abscissa f the figure, incrprates the relevant wave length f the sea state, lnger perids result in higher reflectin cefficients. Table 3 prvides a summary f wave heights measured under different experimental cmbinatins fr ne particular severity f the sea state (i.e. Hm=12.5cm). The descriptin f the varius parameters presented in this table is given belw. Hm is the target significant wave height; Hm_n is the significant wave height measured withut the structure at the gauge 2. (This is the middle gauge in the 5 prbe array); HmCLwith is the significant wave height measured during the experiments by the gauge 2; and Hm,i is the incident wave height reslved by reflectin analysis.

8 1404 COASTAL ENGINEERING 1994 This table shws that the estimatin f the incident wave heights is within an accuracy f 2.5%, while the build-up f wave heights due t re-reflectins is in the rder f 3.6%. (This small degree f re-reflectin was als cnfirmed by running sme regular wave tests and mnitring the build-up). Because the reflectin and the re-reflectin were small in this set-up, it was cnsidered justifiable t use the wave heights measured by gauge 2 with the structure in psitin, as the reference wave height in the stability analysis. " C r - h/l = h/l = Hm/L Figure 4. Reflectin characteristics f the breakwater Table 3. Cmparisn between different estimates f the significant wave heights when the target Hm=12.5cm Wave cnditin HmO (cm) Hm0_n (cm) Hm0_with (cm) HmO.i (cm) 2D nrmal waves D blique waves D nrmal waves D blique waves RESULTS OF BREAKWATER STABILITY The analysis f the results frm these eight test series, n the stability f the relatively large number f test sectins is still prceeding. This paper presents sme f the first findings n the stability f head sectins. A cmplete presentatin f the results will be given in Matsumi etal. (1995).

9 WAVE DIRECTIONALITY INFLUENCE 1405 Influence f wave perids Given the difference in wave lengths under the tw peak perids, substantially different patterns f wave diffractin were fund in the tw cases. In fact, alng the trunk sectin, the nn-unifrm pattern f damage reprted by Vidal et al. (1991) was als fund in this study under unidirectinal waves. (All results related t trunk sectins will be presented in Matsumi et al., 1995). Fr the head sectins, the difference in stability between uni and multidirectinal waves was relatively small when Tp was equal t 1.4s. Numerical simulatin f wave heights and kinematics is required t prvide a better insight f the influence f wave perid. Therefre in the next sectin, nly thse results that crrespnd t 1.7s will be discussed. Cmparisn between the damage under unidirectinal waves with nrmal and blique incidence In rder t facilitate the interpretatin f stability results, the significant wave heights measured at different lcatins in the prximity f the heads were cmputed and nrmalized with respect t the significant wave height measured at gauge 2. (The ratinale fr using the 2 nd gauge was discussed earlier). Figure 5 shws the results f the wave height ratis and the resulting stabilities fr unidirectinal waves under nrmal and blique incidence. Althugh the difference in the values f significant wave heights realized under nrmal and blique wave cnditins is small, the stability results shw mre damage under blique waves with 0=-15. In rder t achieve a better understanding f these results, the numerical mdel WAGEN, described earlier, was used. Assuming a partial reflectin f 30% frm the breakwater, the hrizntal velcity cmpnents in the x and y directins were cmputed using a regular wave f 1.7s. (Nte that x directin is nrmal t the wave machine, and y directin is parallel t it). Figures 6a and 6b shw the reslutins f the dminant directins f velcity cmpnents under nrmal and blique wave cnditins respectively. It can be seen that these are directed twards the FH sectin under blique waves, while under nrmal waves they wrap arund the sectin. This fcussing pattern is believed t be respnsible fr causing higher damage in FH sectin when =-15. In rder t explre the reasns fr similar increase in the damage f MH and BH sectins, a refractin analysis was carried ut using simple cases f regular waves. The intervals between wave rays were fund, in this analysis, t be narrwer under blique waves, implying mre cncentratin f energy and thus resulting in lwer stability. The higher damage n the frnt head under unidirectinal waves is hwever nt cmmn fr traditinal structures. Accrding t Jensen (1984)

10 1406 COASTAL ENGINEERING 1994 B 4-. c-i b TO ffi H B a Z O b z S H /SH C (3 w r> P X5 ^ cu. <c tn * 3 i-, a^ 0) 3 W CO CO s I* * ~* p«*> O > ^J E- CJ >-a N IS O «J <U V) ID D< <u IX (ft E- a SB c u e '3 3 3 s z Figure 5. Cmparisn f significant wave heights arund the head, and f damage index, under unidirectinal nrmal and blique waves

11 WAVE DIRECTIONALITY INFLUENCE 1407 the mst susceptible sectin fr damage is at angle f abut 90 t 135 relative t the incident wave directin. Hwever fr berm breakwaters, which are generally cmpsed f smaller stnes than thse used in cnventinal structures, Jensen and S<j)rensen (1991) reprt damage t the frnt head sectins. It is therefre pssible that the reasn fr the higher damage in this study is the small gradatin f stnes used intentinally t cause larger degrees f damage. inn I I I I I I I ' ' ' I I I I I I ' I ' I \\\ll I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I \ I I (a) Nrmal Wave T p =1.7s (b) Oblique Wave T n =1.7s Figure 6. Dminant directins f velcity cmpnents under nrmal and blique waves (Regular wave T=1.7s) Cmparisn between damage under nrmal uni and multidirectinal waves Figure 7 shws a cmparisn f the significant wave heights arund the head fr nrmal uni and multidirectinal waves. It can be seen that the directinal spread under multidirectinal waves has increased the wave heights n the head sectins. This implies higher wave lading under these waves, and the stability results presented in this figure als cnfirm this fact. Hwever, the difference in damage between uni and multidirectinal waves is largest in the MH sectin when Hm was equal t 12.5cm. Under

12 1 ' 1408 COASTAL ENGINEERING 1994 i 0 : Nrmal Uni : Nrmal Multi 03 "a 3 P 3 a u 0 Z O 6 u z. C/3 V CM T- E m «IO? t "7 : C 3 (3 " ^ l c : d T3 a ie O a c\j z SH/SH >H i c 3 p cu a O. " < CO t * ^ r^ <u II 3 CO CO t a S a. rt ^1 h» II t* p. -^ O ^J E-. O -s N.*-> Z Z rf 0) t a) a, (U CU w H (0 1) a 5 2; 3- d S Figure 7. Cmparisn f significant wave heights arund the head, and f damage index, under uni and multidirectinal nrmal waves

13 WAVE DIRECTIONALITY INFLUENCE 1409 P#L "' "ill In if rum damagepp*?! >*- ~^ T «MNfiii vsk's'.^jkrisk *>isif> *> T*iSft " -IT VmL^C'-yf^. r(jfvt ^fysnlifc_a«<j ^,^*;^^^^:;V_; V Unifrm Damage Pattern in MH 1 under Unidirectinal Nrmal WaveMBcs!!^ Figure 8. Unifrm damage pattern in MH sectin under unidirectinal nrmal waves Nn - Unifrm Damage Pattern in MH under Multidirectinal Nrmal Waves, I Spt Damage in Bundary f MH and BHl Figure 9. Spt damage pattern in near bundary between MH and BH sectins under multidirectinal nrmal waves

14 1410 COASTAL ENGINEERING 1994 unidirectinal wave attack, the damage is fund t be unifrm near the waterline because f the high velcities generated by refractin, shaling and diffractin prcesses. In the case f multidirectinal waves, the cexistence f the abve prcesses added t the incidence f blique waves, has resulted in severe spt damage near the bundary between the MH and BH sectins (i.e. 90 t 135 ). Figures 8 and 9 present the phtgraphs crrespnding t these damages. Fr Hm=10cm, it is difficult t find any difference between the results f uni and multidirectinal waves. The reasns fr it are unclear, but are pssibly due t experimental variabilities fund under lw degrees f damage. T achieve a better insight int the reasns fr the increased damage, sme velcity measurements were made at St9 and St11, as a cntinuatin f the present study, by the principal authr at the Tttri University. The results indicate that the y-cmpnent velcities under 3D waves are larger by nearly 1-1/2 t 2 times the values measured under 2D waves. These findings supprt the stability results presented abve. Cmparisn between damage under blique uni and multidirectinal waves Under blique incidence, the multidirectinal waves result in large significant wave heights n the middle and back head sectins in cmparisn t the heights btained under 2D seas. The resulting damages d nt display a cnsistent trend except in the MH sectin where higher damage was bserved under 3D waves when Hm was equal t 12.5cm. Hwever, the velcity measurements described earlier clearly display larger y- cmpnent velcities under 3D waves. Fr the FH sectin, the damages under unidirectinal waves are larger than thse caused by multidirectinal waves (see Matsumi et al. 1995). CONCLUSIONS In this particular test prgram, sme crrespndence was fund between the wave heights measured in the prximity f the heads and the resulting damage. A clearer picture emerged when the x and y cmpnents f the velcity field were analyzed. The frnt head sectin f the breakwater suffered substantial damage under all cmbinatins f sea states wing t the small gradatin f stnes used in the tests. Fr waves f nrmal incidence, damage n FH sectin was larger under 3D waves due t directinal spreading. Hwever, with 0=-15, the trend was ppsite (i.e. unidirectinal waves induced mre damage). The MH sectin is mre prne t damage under 3D waves because f the c-existence f prcesses such as refractin, diffractin and shaling, alng with the pssibility f direct attack frm ther directins.

15 WAVE DIRECTIONALITY INFLUENCE 1411 Further analysis f wave kinematics at the Tttri University as a cntinuatin f this test prgram is expected t prvide a better insight int the damage pattern. ACKNOWLEDGMENTS The authrs are very grateful t the Institute fr Marine Dynamics f the Natinal Research Cuncil f Canadafr generusly prviding the facilities fr these experiments. REFERENCES Davies, M.H., Mansard, E.P.D. and Crnett, A.M. (1994), "Damage Analysis fr Rubble-Mund Breakwaters", Prc. 26th int. cnf. n Castal Engineering, Kbe, Japan. Isaacsn, M., (1992), "Diffractin Mdel fdirectinal Wave Generatin in a Basin with Partially Reflecting Bundaries", Reprt prepared fr Natinal Research Cuncil f Canada. Jensen, O.J., (1984), "A Mngraph n Rubble Mund Breakwaters", Danish Hydraulics Institute, Denmark Jensen, O.J. and S^rensen, T., (1992), "Hydraulic Perfrmance f Berm Breakwater Heads", J. f Hydraulic Research, IAHR, Vl.29, N.6. Mansard, E.P.D. and Funke, E.R., (1987), "On the Reflectin Analysis f Irregular Waves", Hydraulics Labratry Tech. Reprt TR-HY-017, Natinal Research Cuncil f Canada. Matsumi, Y. Mansard, E.P.D. and Rutledge, J. (1995), "Influence f Multidirectinal Waves n Breakwater Stability", Natinal Research Cuncil f Canada, Tech. Reprt (in preparatin). Sand, S.E. and Mynett, A.E. (1987), "Directinal Wave Generatin and Analysis", Prc. IAHR Seminar n Wave Analysis and Generatin in Labratry Basins, 22nd IAHR Cngress, Lausanne, Switzerland. Vidal, C, Lsada, M.A. and Medina, R., (1991), "Stability f Mund Breakwater's Head and Trunk", Jurnal f Waterway, Prt, Castal and Ocean Engineering, ASCE, Vl.117, N.6, Nv/Dec.