Experimental ampaign on te overtopping of te eawall Maleòn Tradiional Lui Fermin Cordova Lopez Centro de Invetigaione Hydraulià (CiH) of te Intituto Superior Politènio Joe Antonio Eevarria La Havana, Cuba Daniela Salerno, Fabio Dentale Department of Civil Engineering, Univerity of Salerno Fiiano, Salerno, Italy Aleandro Capobiano, Mariano Buino Department of Civil, Aritetural and Environmental Engineering, Univerity of Naple Federio II Napoli, Italy ABSTRACT Ti paper diue preliminary reult of a wide experimental ampaign arried out in te frame of a ollaboration between te Government of te ile of Cuba and te CUGRI onortium, an Italian intitution wi join te Univeritie of Salerno and Napoli Federio II. Te tet were aimed to analyze te performane of different olution deigned to redue te overtopping of te Maleòn, a vertial fae eawall proteting te nortern waterfront of te ity of La Habana. Te allow foreore in front of te truture allowed aeing te role of wave etup and low freueny omponent of te inoming wave petrum on te predition of te mean overtopping rate. KEY WORDS: Wave overtopping; pyial model tet; vertial eawall. Hydraulià (CiH) of te Intituto Superior Politènio Joe Antonio Eevarria ave preented a dek tudy were a number of olution are onidered, inluding a weak inreae of te wall freeboard, urvature of te outer profile and plaement of protetive truture, u a berm and detaed low-reted breakwater. To ave a deeper inigt on te effet of ea olution, a wide pyial model tudy wa ommiioned to te Conorzio interuniveritario per la previione e prevenzione dei Grandi RIi (CUGRI), wi join te Univeritie of Napoli Federio II and Salerno (Italy) Ti paper deribe te experimental ampaign and diue preliminary reult of te tet. Given te allow foreore affeting te Maleòn, partiular attention a been drawn to te role of wave et up and long wave omponent of te inident wave petrum on te preditability of te mean overtopping diarge. INTRODUCTION La Habana, apital of te Republi of Cuba, extend on an area of 740 Km, wit a population of over million people. It a been delared UNESCO eritage in virtue of te peuliar aritetural tyle, reulting from te Spani domination lating 400 year. Te nortern part of te ity entre i proteted from te wave ation by a vertial eawall, te Maleòn (Figure ), tat i worldwide known a te balony of Caribe, beaue of te plendid view it offer to tourit and inabitant. Reently, owever, te limati ange a aued an inreae of bot te freueny and te magnitude of te mot evere meteorologial event, inluding tropial ylone, urriane and intene front of old air reaing te ile of Cuba during te winter. Ti a led te Maleòn to be often violently overtopped, jeopardizing uman live and itorial building. For ti reaon te Cuban Government a long been looking for a olution wi redue te rik of flooding and repet te enormou value of te ite. In partiular, at te beginning of 0, ientit and engineer of te Centro de Invetigaione Fig. View of te Maleòn. WAVE OVERTOPPING AT VERTICAL STRUCTURES Wave overtopping i one of te mot intenively reeared topi in te field of oatal engineering. Baed on a wide erie of random wave
experiment on aion breakwater, Frano and Frano (999) propoed a imple exponential form: gh R exp H () in wi i te mean overtopping diarge, g i te gravity aeleration, R i te ret freeboard and H i te inident petral ignifiant wave eigt at te toe of te breakwater. Te parameter and are funtion of a number of ydrauli and trutural variable, inluding wave obliuity, ort retedne and urvature of te outer profile of te aion rown wall. Over te oure of te lat deade, ubtantial advanement in te predition of wave overtopping ave ome from te EC reear projet CLASH (De Rouk et al., 009), a well a from everal national program. Te EurOtop Manual (007) take aount te new reult and provide a ueful guide for pratial appliation. For te ae of imple un-proteted vertial eawall, te expeted value of te mean overtopping rate an be etimated by ditinguiing between two ydrodynami ondition and namely pulating and impulive : te former our wen wave are bot little teep and relatively mall in relation to te loal dept, te latter wen wave are larger enoug in relation to loal water dept to break often violently againt te wall. In order to proeed wit aement of wave overtopping, it i neeary firt to determine te dominant overtopping regime (impulive or non-impulive) for a given truture and ea tate. An impulivene parameter a to be defined:.5 H gt 0 were i te mean water dept at te toe of te wall and T -0 i mean petral period baed on te moment of order - and 0 of te inident power petrum. Non impulive ondition dominate wen > 0., and impulive ondition are oberved wen < 0.. For 0. 0., overtopping ould be predited for bot non impulive and impulive ondition, and te larger value aumed. For impulive ondition, wi are toe of interet for te preent tudy, te preditive euation are: g.50 4 R H. () () if R /H < 0.0 For R /H ranging between 0.0 and 0.0, te maximum between te two previou formulae ould be ued. EurOtop alo provide a deiion tree to ae te effet of te urvature of te outer fae of te wall; te redution ratio: urve vert. K (5) an be alulated a a funtion of te non dimenional ret freeboard R /H a well a on te main geometri feature of te onave truture. A furter deign tool wa propoed by Goda (009) wo propoed a et of formulae valid for bot vertial and inlined truture, baed on te funtional form: gh R exp A B H were for any inlination of te front fae of te truture, te parameter A and B are funtion of te foreore lope and of te wave eigt to dept ratio. LABORATORY STUDY Faility :0 pyial model tet ave been onduted at te RAndom wave TAnk (RATA) of te Dept. of Civil, Aritetural and Environmental Engineering (DICEA) of te Univerity of Naple Federio II. Te faility i 6m long, 8m wide,.m deep and i provided wit 6 independent piton type wavemaker, apable of imulating bot regular and irregular wave train wit different angle of propagation and (for random wave) diretional preading. Te bain a been partitioned to form a 8.7m x.54m annel wit onrete wall, were te experiment ave been arried out (Figure ). Furter wall ave been ontruted along te generation line to eparate te tank into a dry zone, needed for te obervation of te tet, and a wet zone, wi a been filled wit water. Te purpoe of ti area wa to reate a large additional volume of fluid to ompenate for te loe aoiated wit te overtopping proe and avoid any variation of water level in te annel. (6) if 0.0 < g R /H <, and:.7 0 4 R H.7 (4) Foreore A 0m long portion of foreore (7.67m in te model) a been reprodued in te flume (in onrete); it brougt te ea floor from a dept of 8.7m below te MWL to te toe of te Maleòn eawall, wi i nearly at.70m (Figure ). After a 5.98m long flat area (model ale), te batymetry enompae a mild tret wit a 4.% lope, followed by a tep inlined by : and an upper zone made up on part wit a lope of 8.6% and 6% repetively.
Two rie of te mean ea level ave been onidered; one orrepond to te enario of te Wilma urriane (ourred in 005), te oter i aoiated wit a 50 year return period torm (Table ). For ea value of te till water dept, 8 JONSWAP driven random ea tate ave been run, wit a duration of 000 wave. 4 value of te petral ignifiant wave eigt (H ) at te paddle ave been ued, namely.7m, 4.0m, 5.0m and 6.5m, wit two peak period (T p = 0 and ). Current layout of te Maleòn +.96m MWL Fig.. Partitioning of te RATA wave bain..70m wave-maker foreore loation of te Maleòn eawall Curved variant a) MWL 6.00 4.67 0.67.00..70m Fig.. View of te foreore. Wall and defene truture In it urrent layout, te Maleòn eawall i a imple vertial wall wit a ret freeboard, R, of +.96m relative to te MWL (Figure 4.a). Additionally, a urve layout a been onidered, a keted in Figure 4.b. Along wit.96m, two furter learane ave been teted and namely + 4.46m and +4.96m. Aordingly, 6 model of eawall ( urve and vertial) ave been employed. Along wit te variation of ret freeboard and outer profile, alo te effet of rubble mound berm and detaed low reted breakwater (LCB) on te amount of overtopping a been invetigated. At te end of ti paper, wi foue mainly on te reult of te experiment onduted on un-proteted wall, preliminary outome relative to te effiieny of berm are diued. Converely, te performane of LCB are not preented ere. Tree berm geometrie ave been teted, all wit a front lope angle of :.5 (Figure 5). Te firt (Berm ) ad te freeboard (F) at +.8m above te MWL, werea te widt (B) eualed 5m; te eond (Berm ) wa at F = +.8m wit a B = 0m. Te tird (Berm ) ad F = +.7m and B = 0m. Ea berm a been teted wit a vertial wall wit R =.96m and wit a urved wall wit R = 4.46m. Te geometri arateriti of te berm ave been derived from te dek tudy preented by te Centro de Invetigaione Hydraulià of te Intituto Superior Politènio Joe Antonio Eevarria, onerning te poible protetive truture for te Maleòn. Water level and ea ondition Fig.4. a). Current layout of te Maleòn eawall. b) urved variant Fig.5. Berm proteted vertial eawall. Table. Conidered etup of te ea level. Senario Storm urge [m] Tide [m] Climati ange [m] Total [m] 50 year RP.06 0.40 0.7.7 Wilma Hurriane.5 0.48 0.7.8 Meaurement F Prior performing te overtopping tet, a :0 pending bea made of plywood a been mounted rear te foreore (Figure ); te inident wave ondition at te toe of te wall ave been ten meaured witout b) B
/((gh ) / ) te wall, via a twin-wire reitive wave probe ampled at 5Hz. Furter 4 probe were plaed on te flat bottom in front of te batymetry to eparate inident and refleted wave aording to te Zelt and Skjelbreia (99) metod. To meaure te mean overtopping diarge,, te pending bea a been removed and a m reervoir a been built leeward te eawall. Te water overpaing te truture wa olleted in te reervoir and ten onveyed bak to te wet zone (Figure ) by mean of ubmerible pump of te overall apaity of 800 l/min; Te pumped water paed troug an eletromagneti flowmeter, were te volume of fluid wa progreively omputed (Figure 6). Fig.7. Example of wave power petrum auired at te loation of te wall. Unproteted vertial wall Fig.6. View of te eletromagneti flow meter Te water volume in te reervoir at te beginning (V b ) and at te end (V e ) of ea tet wa ontrolled by a upplementary wave probe loated in te olleting tank and ampled at 5 Hz. Tu, te overtopping rate a been finally obtained a: V V V pumped e b (7) D t were D t i te duration of te tet. RESULTS Te inident wave petrum and related wave parameter Due to te allow foreore, inoming wave experiened ignifiant breaking before reaing te truture. Aordingly te power petrum reulted pretty broad-banded (Figure 7). In order to invetigate te effet on te mean overtopping diarge of te wave energy ditribution in te freueny domain, te petral funtion a been onventionally divided into te following omponent: Wave etup (or et-down), orreponding to te DC omponent of te wave petrum or te average of te wave oillation in te time domain (Longuet-Higgin and Stewart, 965; Calabree et al.,00). Long wave domain, inluding te petral omponent wit freueny larger tan 0 (wave et-up) and lower tan alf te offore peak freueny, f p ; Sort wave domain orreponding to freuenie inluded between 0.5 f p and te Nyuit freueny f N Ti etion aim to provide a deeper inigt on te influene of wave parameter (eigt, period and etup) on te uality of predition of te mean overtopping diarge. Te Figure 8 and 9 diplay te experimental data on te arateriti plane of te Frano and Frano (994) and EurOTOP euation. Here only te ort wave ave been onidered; aordingly te ret freeboard R i omputed from te till water level, leaving te wave etup out of onideration. Fig.8. Experimental data on te Frano and Frano (994) arateriti plane. Sort wave parameter ave been ued. In Figure 8, te experimental point plit into two loud, depending on te (till) water dept at te wall; onverely in Figure 9 tey ave an uniue trend, wi toug overwelm te EurOTOP predition (blak olid urve). Data an be onveniently fitted via te power form: 0. 0.0 0 0.5.5.5 R /H g Sea rie.8m R a H b Sea rie.7m vertial wall vertial wall+0.5m vertial wall+m (8)
/( (g ) / ) /( (g ) / ) /( (g ) / ) wit a = 0.04 and b = -.6 (daed red urve). Te formula a a orreted R tatiti eual to 0.8. 00 0 vertial wall vertial wall+0.5m vertial wall+m EurOtop Bet fit 00 0 vertial wall vertial wall+0.5m vertial wall+m EurOtop bet fit 0. Fig.9. Experimental data on te EurOTOP arateriti plane. Sort wave parameter ave been ued. Wave etup a not been onidered It i wort notiing tat te appliation of E.(8) reuire in fat te knowledge of te petral ditribution funtion in te ort wave domain, wi i neeary for te mean period T -0 to be alulated. In ae only te amount of ort wave energy (H ) were available, along wit it peak freueny, te uality of te etimate would be ome poorer; after alulating te uantity via te offore peak period and refitting te data, an R = 0.77 wa aieved. A expeted te variation i not dramatially ignifiant, a T -0 i arely influened by te ig freueny omponent of te power petrum. Te inluion of te wave etup at te loation of te eawall (meaured in abene of truture) proved rater benefiial; in Figure 0 data appear le attered tan in Figure 9, altoug te EurOTOP formula till lie below te experimental value; te bet fit power form i now: 0. 0.0 0 0.05 0. 0.5 0. 0.5 R /H g R 0.06 H.6 in wi te value of wave et-up a been inluded eiter in R or in or in and te T -0 of te ort wave petrum a been ued. Te R tatiti i 0.90, indiating a good predition power. It i nie to oberve tat wen te offore wave period i ubtituted to T -0, te determination oeffiient ligtly inreae, reaing 0.9. Wen te entire power petrum i employed, inluding long wave, te data atter furter redue and te EurOTOP urve now provide reaonable etimate (Figure ). Te power form of E.(8) an be till effetively fitted to te data wit a = 0.00886 and b = -.058. Te R tatiti i 0.97, meaning tat almot all te variane of data i explained. Wen te offore peak period i ued intead of T -0, te performane of E.(9) remain ligtly woren, wit R dropping to 0.9. Table provide a ummary of te performed regreion analye. Lat olumn give te tandard deviation of te differene between meaured and predited flow rate (at prototype ale). (9) 0.0 0 0.05 0. 0.5 0. 0.5 0. R /H Fig.0. Experimental data on te EurOTOP arateriti plane. Sort wave parameter ave been ued. Wave etup inluded 0000 000 00 0 0. 0.0 0 0.0 0.04 0.06 0.08 0. R /H Fig.. Experimental data on te EurOTOP arateriti plane. Te entire petrum. Wave etup inluded. Table. Performane of te E.(). Wave parameter a b R Reidual t. dev. Sort- no et up [m //m] 0.04 -.60 0.8 0.07 wit T p 0.05 -.69 0.767 0. Sort + et up 0.06 -.66 0.899 0.079 wit T p 0.055 -.550 0.906 0.0760 Entire + etup 0.009 -.05 0.97 0.046 wit T p 0.040 -.69 0.9 0.066 Effet of urvature vertial wall vertial wall+0.5m vertial wall+m EurOtop bet fit Similarly to wat oberved for te mean overtopping diarge, alo te predition of te effet of te eawall urvature wa found to be ignifiantly dependent on te wave parameter employed and, aordingly, on te information available at te deign tage. If neiter long wave energy nor wave etup are known, te EurOTOP proedure give redution oeffiient K rater lower tan te meaured one (Figure ).
Redution rate. K 0.8 example i given in Figure 4, wi refer to te vertial eawall at te urrent eigt, wit te offore peak period T p = under te Wilma enario. Te grap diplay te rate of redution of te mean diarge (alulated a te ratio between te differene of te mean diarge witout and wit te berm, and te mean diarge in abene of berm) v. te offore wave eigt. 0.6 0.4 0. LINE OF PERFECT AGREEMENT urrent eigt +0.5m + 00% 80% 60% Vertial wall Senario Wilma Tp = 85.5% 7.5% 58.9% 56.4% Berm Berm Berm 0 0 0. 0.6 0.9. K ETop Fig.. Meaured redution oeffiient v. EurOTOP predition. Sort wave parameter ave been ued, exluding wave etup. On te oter and, if te full energy band i ued, and te wave etup i inluded in te alulation of te ret freeboard, bot te amount of overetimate and te atter of data around te predition line are oberved to redue (Figure ). K.0.00 0.80 0.60 0.40 0.0 0.00 0 0. 0.6 0.9. K ETop Fig.. Meaured redution oeffiient v. EurOTOP predition. Full petrum wave parameter ave been ued, inluding wave etup. Table report, for te different wave parameter, te mean and te tandard deviation of te differene between meaured and predited value of K. Te long wave energy appear now to play a leading role ompared to wave etup. Table. Quality of EurOTOP predition of te eawall urvature effet. Wave parameter mean St.dev. Sort- no et up 0.5 0.49 Sort + et up 0.5 0.48 Full + et up 0.055 0.08 Effet of berm LINE OF PERFECT AGREEMENT urrent eigt +0.5m Only preliminary analye on te berm effet ave been arried out o far. It indiate tat te degree of protetion offered by te rubble mound truture trongly dereae wit growing te wave eigt. An + 40% 0% 0% Fig.4. Relative rate of redution of te mean diarge a funtion of te berm geometry and te offore wave eigt. For te Berm, for example, te degree of protetion drop from 85.5% for te offore wave eigt.7m to.6% for 6.5m. CONCLUSIONS 4.% 9.4%.% 8.% 0.8% 9.8%.6% 5.%.7 4 5.4 6.5 H [m] In te frame of a leading projet for te protetion of te waterfront of te ity of La Habana (Cuba), a wide experimental tudy a been arried out at te DICEA Dept. of te Univerity of Naple Federio II. Pyial model tet ave been arried out to ae te average amount of water overtopping te itorial vertial fae eawall alled Maleòn Tradiional, a well a implement poible deign improvement, u a urvature of te outer profile, variation of freebord, plaement of protetive rubble mound truture (berm and low reted detaed breakwater). Ti paper diue preliminary outome of te experiment, wit a main fou on te effet of te allow water wave parameter (wave eigt, period and wave etup) on te predition of te mean overtopping rate at unproteted layout. It a been found tat a proper knowledge of te wole wave energy and etup at te wall (inluding low freuenie) lead te overtopping proe to be igly preditable (ee Table ); moreover, under ti ondition, te meaured value of te overtopping rate agree reaonably wit te predition of te EurOTOP formula (Figure ). However, wen only ig freueny petral parameter are available and/or a reliable etimate of te wave etup at te loation of te wall i not dipoable, te atter of data inreae dramatially and te EurOTOP formula may give ignifiant underpredition of te real flow rate. In tee ae, Table may upply engineer an order of magnitude preditor, along wit an etimate of te reidual atter. Figure and ugget tat te knowledge of te long wave energy at te wall alo influene te predition of te effet of a urved wall. Similarly to Table, Table ow tat a omplete knowledge of te wave limate pratially alve te atter of data. Tee finding are globally in agreement wit toe van Gent and Gianruo (00), wo ued toug only data from numerial model. Firt reult on te degree of protetion offered by berm indiate it i extremely redued for te mot energeti inoming torm (Figure 4).
REFERENCES Calabree, M., Viinanza, D. and Buino, M. (00). D wave etup beind low reted and ubmerged breakwater. Proeeding of te International Offore and Polar Engineering, ISOPE 00, 76-8. De Rouk, J., Veraege, H., and Geeraert, J.(009). Cret Level Aement of oatal Struture: general overview. Coatal Engineering, ELSEVIER, 56(), 99-07. EurOtop, (007). Wave overtopping of ea defene and related truture: Aement manual, T. Pullen, N. W. H. Allop, T. Brue, A. Kortenau, H. Süttrumpf, and J. W. van der Meer, ed., Environment Ageny, UK/ENW Expertie Netwerk Waterkeren, NL/KFKI Kuratorium für Forung im Küteningenieurween, Germany, ttp://www.overtopping-manual.om (Mar., 0). Frano, C. and Frano, L. (999) Overtopping formula for aion breakwater wit non-breaking D wave. J. Waterw. Port Coat. Oean Eng. ASCE, 5, 98 07. Goda, Y. (009). Derivation of unified wave overtopping formula for eawall wit moot, impermeable urfae baed on eleted CLASH dataet. Coatal Engineering., ELSEVIER, 56(4), 85 99. Longuet-Higgin, M.S., Stewart, R.W. (964). Radiation tree in water wave; a pyial diuion, wit appliation Deep-Sea Reear and Oeanograpi Abtrat, (4), pp. 59-56. Van Gent, M. R.A and Gianruo C.C. (00) Influene of low freueny wave on wave overtopping. CLASH Report and Delft Hydrauli Rep. H497.Delft Hydrauli, te Neterland.