EurOtop revisited. Part 2: Vertical Structures

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1 EurOtop revisited. Part 2: Vertial Strutures Tom Brue University of Edinburg, Edinburg, Sotland Jentsje van der Meer Van der Meer Consulting BV, Akkrum, Te Neterlands William Allsop Wallingford, Wallingford, UK Leopoldo Frano University of ome III, ome, Italy Andreas Kortenaus TU Braunsweig, Braunsweig, Germany Tim Pullen Wallingford, Wallingford, UK olger Süttrumpf WT Aaen University, Aaen, Germany Summary Te European Manual for te Assessment of Wave Overtopping ( EurOtop ) was issued free on te internet in 2007 and is now used worldwide. Te manual and te aompanying Neural Network give guidane on all aspets of wave overtopping. It was te result of syntesis of existing Dut, UK and German guidane and new resear findings arising out of projets su as te EC FP7 CLAS projet. During and sine writing, te manual team as identified gaps and areas in wi oter improvements and larifiations ould be made. Tis paper presents a summary of new analysis of existing data on vertial and very steep walls. A ompanion paper revisits sloping strutures (Van der Meer et al., 201). Speifially, two temes are explored. First, a reformulation of te proedures for overtopping analysis of vertial walls is presented offering a simpler and more pysially rational proedure. A distintion is made between overtopping at strutures witout influene of foresore and tose were te foresore plays a role in te ydrodynamis at te struture. Tis leads to an improved metod for iger freeboard situations. Seondly, omposite vertial strutures are revisited, and a proedure proposed tat integrates teir analysis wit tat of te updated proedure for plain walls. Introdution Te following topis were treated in te EurOtop Manual (2007), but were not explored as fully as would ave been desirable and are terefore key drivers for tis and te ompanion paper: Wave overtopping at low and zero freeboards for sloping strutures. Existing (old) teory and available data sets sow lower wave overtopping tan predited by te exponential type of formulae used in te EurOtop Manual. Tis topi is explored in te ompanion paper (Van der Meer et al., 201). Overtopping response at very steep slopes wit geometries lying between te fully-vertial and more familiar milder slopes, i.e. for slopes approximately in te range 5:1 (i.e. 5V:1) down to 1:1. Te ompanion paper also desribes te new analysis on tis topi. Pysial explanation of te relationsip between te formulae for vertial breakwaters and seawalls, for non-impulsive (or pulsating ) waves and for impulsive (breaking) wave overtopping, desribed by exponential and power-law formulae, respetively (EurOtop, 2007, Capter 7). Tis applies also to te analysis of omposite vertial breakwaters. Te first setion of tis paper deals wit tis topi. Explanation for te differene of mean overtopping rates between te formulae of Frano et al. (1994) and Allsop et al. (1995) for vertial strutures, by pysially rational reasoning and reanalysis of a part of te CLAS database. Tis is te seond fous of tis paper.

2 Basis of te EurOtop Manual EurOtop (2007), following from EA (1999), presents two metods for te predition of mean overtopping disarge () for vertial breakwaters or seawalls depending upon weter wave breaking and resulting impulsive or violent overtopping is present. A disriminating parameter, (Euation 1) is used to determine wi situation applies. 1. 2π 2 gt m 1,0 For > 0., wave breaking is expeted to be absent, and te familiar exponential relationsip between relative (non-dimensional) disarge and relative rest freeboard (Euation 2) works well. (1) a exp b (2) Early work by Frano et al. (1994) gave a 0.2 and b 4., wile Allsop et al. (1995) gave a 0.05 and b Wile te preditors are similar for lower freeboards, tey diverge signifiantly at iger /. Tis apparent problem is addressed in te new analysis later in tis paper. Overtopping at vertial and steep walls annot owever be desribed for all onditions simply by exponential-form euations like Euation 2. Goda s design arts (e.g. Goda, 2000) sow uite pronouned peaks for some sallower (relative) water depts. Goda (2009) notes tat loal water dept on a foresore is important. Pysial model studies in te 1990s under onditions were wave breaking on te struture was present gave rise to new empirial fits of te form wit a power law derease in overtopping disarge wit freeboard, rater tan an exponential one. Te impulsive overtopping euations (EurOtop, 2007, after Allsop et al., 1995) ave te form of a power law: 2 g a b () Te oeffiient a and exponent b in Euation ange depending on struture and wave onditions onsidered, taking values of a and b.1 for impulsive overtopping at plain vertial walls. Tis exponent is simply te result of fitting to data wit no basis in pysial reasoning. Tere is a strong evidene tat tese two, apparently distint metods work well. Te fat tat disarge and freeboard are non-dimensionalised in uite different ways for impulsive and non-impulsive onditions as prevented simple omparison of te formulae. Furter, tese differenes amper improved pysial rationalisation of te transition from one regime to te oter. elationsip between Non-impulsive and Impulsive Overtopping In order to establis a more unified, pysially rational framework of predition tools spanning a greater breadt of struture types and wave onditions, Brue & Van der Meer (2008) attempted to bring togeter te non-impulsive and impulsive formulations by fixing te exponent b in Euation at a (round) value of. Tis failitated algebrai manipulation, leading to an expression for impulsive overtopping tat uses te familiar non-dimensionalisation of te disarge (Euation 4). a 1 s m 1,0 (4) were s m-1,0 is te (fititious) wave steepness wit wave lengt based on T m-1,0. Euation 4 indiates tat te overtopping under impulsive onditions depends on a ombination of breaker index / and te wave steepness s m-1,0. Using tis formulation, Brue & Van der Meer (2008) plotted predition urves for impulsive onditions diretly alongside tose for non-impulsive onditions on te familiar dimensionless disarge versus dimensionless freeboard axes. ere, tis approa is developed. We re-examine te oie of oeffiient a and te strengt of te influenes of te steepness using existing data of te CLAS database.

3 eanalysis of Vertial Walls wit CLAS Data Te CLAS database ontains about 10,000 tests on overtopping, see Van der Meer et al. (2008). A part of tis database relates to tests wit a vertial or battered wall. In total 15 different data sets were used from te database tose sown in Table 1 as vertial seawall, arbour wall, or aisson. Also, tree furter datasets were used: two from te original dataset of Frano et al. (1994) and te dataset of vertial walls at te end of a 1:50 foresore of Allsop et al. (1995). In order to desribe te set-up of te dataset, information is given on te presene of a foresore slope, te type of struture investigated and weter a berm or toe struture was present. All datasets wit a foresore ad a straigt foresore wit a given, fixed slope. Of te 18 vertial wall data sets, 12 ad a orizontal foresore ( no foresore ) and 6 ad a sloping foresore. Two data sets wit a slope instead of a vertial wall were inluded as tey ontained rare data wit zero freeboard. Table 1: CLAS datasets for vertial walls. Te table gives te dataset number and a referene if te dataset is in te publi domain. (CLAS) dataset eferene Foresore slope Type of struture Berm 006 Confidential 1:20 Battered 10:1 No 028 erbert (199) 1:10; 1:0; 1:100 Vertial seawall No 04 Pullen et al. (2004) 1:0 Composite Yes 044 Pullen et al. (2004) 1:0 Composite Yes 102 Süttrumpf and Oumerai (2005) No Slope 1:4 No 106 Oumerai et al. (2001) No Vertial seawall No 107 Smid et al. (2001) No Vertial seawall No 108 Smid et al. (2001) No Slope 1:1.5 No 11 Oumerai et al. (2001) No arbour wall Yes 224 De Waal (1994) 1:50 Vertial seawall No 225 De Waal (1994) 1:20 Vertial seawall No 228 Confidential No Caisson Yes 229 Confidential No Caisson Yes 15 Confidential No Caisson Yes 51 Confidential No Caisson Yes 80 Confidential No Caisson Yes 402 Confidential No Vertial seawall No 502 Brue et al. (2001) 1:10; 1:50 Vertial seawall No 50 Brue et al. (2001) 1:10 Battered 10:1 No 504 Brue et al. (2001) 1:10 Battered 5:1 No 505 Brue et al. (2001) 1:10; 1:50 Composite Yes 507 Pearson et al. (2002) 1:1 Battered 10:1 No 802 Goda et al. (1975) 1:10; 1:0 Vertial seawall No 914 Cornett et al. (1999) No Vertial seawall Yes Allsop et al. (1995) Allsop et al. (1995) 1:50 Vertial seawall No CEPYC Confidential No Caisson Yes ENEL CIS Confidential No Caisson Yes All datasets were ten plotted individually, wit four predition urves for omparison: Frano et al. (1994), Allsop et al. (1995), a steep smoot slope (Euation 2) and one speifi urve for impulsive waves (Euation 4 wit a wit / 0.9 and s m-1,0 0.0). Examples are sown in Figures 1 and 2. Figure 1 sows dataset 802 of Goda et al. (1975) and sows learly te inreased overtopping for seawalls at te end of a foresore slope, as all data points are along or above te urve for impulsive wave attak, wit few points around te Allsop or Frano urves. Figure 2 sows CLAS dataset 914 of Cornett et al. (1999) wit tests on a vertial wall wit deep water witout a foresore and wit a small and deep berm. Te overtopping is now signifiantly less tan in Figure 1 and is grouped well around te line of Frano et al. (1994). Individual analysis of all datasets led to te lear onlusion tat tere is a distint differene between overtopping responses of vertial strutures wit and witout a sloping foresore, wit a sloping foresore always giving larger overtopping. On te basis of tis, te datasets were split into two groups and ea group was ten analysed separately.

4 el. o'topping rate /( ) 1.E+00 1.E-0 Allsop(1995) Frano (1994) smoot slope E.4: s/s0.9; sop : : elative freeboard / Figure 1. Overtopping results of CLAS dataset 802, a sloping foresore wit a seawall (Goda et al., 1975). el. o'topping rate /( ) 1.E+00 1.E-0 Allsop(1995) Frano (1994) smoot slope E.4: s/s0.9; sop elative freeboard / Figure 2. Overtopping results of CLAS dataset 914, a vertial wall at deep water (Cornett et al., 1999). Vertial strutures witout foresore Figure sows all results for tests witout a sloping foresore. Tests of dataset 11 wit 0 ave been sifted artifiially a little to te rigt in order to distinguis tem from dataset 107 wit 0. For te lower freeboards / larger overtopping rates, te satter is small. Te satter beomes larger for / > 1. It turns out tat Frano et al. (1994) desribes tese smaller overtopping disarges very well. Figure sows tat Frano et al. (1994) will over-predit overtopping for lower freeboards. owever, te oter line, Allsop et al. (1995), overs tis area well. It means tat bot formulae are valid for vertial strutures witout a sloping foresore, but ea wit teir own range of appliation. elative overtopping rate /( ) 1.E-0 Allsop et al. (1995) Frano et al. (1994) CEPYC ENEL CIS % 5% elative freeboard / Figure. Vertial strutures on relatively deep water, no sloping foresore. Strutures in Figure an be desribed as aissons, vertial flood walls in arbours, and gates of loks in flood situations. Tey may ave a berm type struture relatively deep below water, wi does not affet overtopping. Te desription of wave overtopping is ten given by: For / < 0.91: Allsop et al. (1995): 0.05exp 2.78 (5)

5 For / > 0.91: Frano et al. (1994): 0.2exp 4. (6) Te reliability of Euation 5 is given by σ(2.78) 0.17; tat of Euation 6 by σ(4.) 0.6. Vertial seawalls on sloping foresore All available CLAS datasets for vertial walls wit a foresore were ases wit a simple, singlegradient foresore slope. For all, te wave eigt was taken at te loation of te vertial wall. First 2 /( L m-1,0 ) 0.2 was used as a disriminator between defleting or non-impulsive and impulsive wave onditions. Note tat tis is approximately euivalent to 0., due to te fator 1. in Euation 1. Data wit 2 /( L m-1,0 ) < 0.2 are plotted in Figure 4. Note tat te non-dimensionalisation of used for te y-axis of Figure 4 is a generalised form of tat arising from te manipulation by Brue & Van der Meer (2008). /( ) /{( /) a /s m-1,0 b } 1.E : :0 28 1: : : : : : :0 Besley MAST 1: Exponential E Power urve E elative freeboard / Figure 4. All data of seawalls on sloping foresore for impulsive waves ( 2 /( L m-1,0 ) < 0.2) and wit optimum values of a and b-. Te fine dased lines indiate 5% under and upper exeedane limits. Te upper-left dotted line represents te extension of te power law (Euation 9) to freeboards below te appropriate range, wile te dotted line in te extreme lower-rigt sows te extension of te exponential (Euation 8) to freeboards iger tan te appropriate range. An optimum was sougt for te best value of 2 /( L m-1,0 ) as disriminator as well as te best parameter group on te vertial axis in Figure 4, by anging te exponents a and b in te expression in Euation 7: a b impulsive / non-impulsive disriminator / s m 1,0 (7) m 0 In Euation 4, te values are a and b Tis gives uite a large influene of te wave period on wave overtopping, were tere is little or no su influene observed on steep slopes and at vertial walls in deep water. By analysing te exponents a and b in Euation 7, te onlusion was drawn tat a and b - were good values, sowing least satter and a little less influene of te wave steepness. Tis gives on te vertial axis te parameter group {/( ) } / { /( s m-1,0 ) }. Analysis onfirmed tat 2 /( L m-1,0 ) 0.2 was indeed te optimum value to disriminate between nonimpulsive and impulsive waves, validating te earlier value of 0..

6 Te results for non-impulsive waves ( 2 /( L m-1,0 ) > 0.2) on vertial seawalls at te end of a sloping foresore sow tat Allsop et al. (1995) desribes te wave overtopping for tese kinds of strutures and for given wave onditions very well. Te remaining data for impulsive wave attak are given in Figure 4. Dataset 107 for deep water and zero freeboard were also given for omparison as no data were available for zero freeboard. Tere is uite some satter below te average trend of te data and almost all of tat data belong to dataset 28. But te oter data give a trend of a straigt line starting from zero freeboard to rater large relative freeboards ( / 1.5 2) and ten beomes a more orizontal trend for very large freeboards. Atually, su a more or less orizontal line goes on even beyond relative freeboards of / 5. In tis region, a power urve like Euation 4 fits well (Figure 4). From tat point of view, tere is no reason to abandon tese kind of formulae, wi originate from Allsop et al. (1995). It is owever lear tat a power funtion annot give te trend for small or zero freeboards as it will use te vertial axis as an asymptote. Tis is also learly sown in Figure 4 wit te dased line. It is for tis reason tat it was deided to keep te power funtion for larger freeboards and to introdue te ommon exponential funtion for zero and low freeboards. Te formulae are desribed by: exp 2. 2 sm 1,0 m s m m 1,0 for / < 1.5 and (8) for / > 1.5 (9) Te reliability of Euation 8 is given by σ(0.011) and tat of Euation 9 by σ(0.0014) Wave overtopping at vertial walls is tus now given by Euations 5 and 6 (relatively deep water, no sloping foresore); Euation 5 (sloping foresore, non-impulsive waves) and Euations 8 and 9 (sloping foresore wit impulsive waves). Composite Vertial Strutures For impulsive onditions at omposite vertial strutures, EurOtop (2007) gives: were d 2 gd d 2.9 (10) d 1. d 2π 2 gt m 1,0 (11) and d is te water dept above te berm. In te same way tat te parameter (Euation ) is used in te EurOtop (2007) metod as a disriminator between impulsive and non-impulsive onditions at a plain vertial wall, so d disriminates between two sets of formulae for omposite vertial strutures. As for vertial walls, it is not straigtforwardly possible to analyse in a generi way te differenes between impulsive and non-impulsive forms, and even arder to get a sense of te pysial transition. Brue and Van der Meer (2008) set te exponent in Euation 10 to and ten rearranged te relation to: d 0 1 m b a ( s 1,0 ) 0 0 m m m (12)

7 wit a 1 and b Note tat tere is a typograpial error in Brue and Van der Meer (2008). Euation 12 is te orreted version of Euation 12 in tat paper. Te vertial wall re-analysis of te preeding setion found tat te influene of steepness was better represented by s m-1,0, i.e. by setting a in Euation 12. Te similarity of te pysial situation suggests tis adjustment be inluded for te omposite strutures too, giving a tentative predition euation (Euation 1). m 0 d 0 m b sm 1,0 Te apparently separate formulations for plain and omposite vertial strutures ave tus been redued to a single set, wit te differene between Euations 9 and 1 being te value of b and a fator of (d / ) wi beomes unity for plain vertial walls wit zero berm eigt ( d). Before an enaned predition seme an be proposed, a number of furter issues reuired exploration, based upon te CLAS database data. Composite strutures were identified by vertial upper slopes (ot α u 0), and by te presene of a toe or mound, i.e. were te water dept at te toe or berm is less tan tat offsore. Te onstant multiplier (b) in Euation 1 is not te same as tat for plain vertial walls (Euation 9), so for no berm (d/1), tese do not onverge as tey sould. Comparing new Euations 4 (for plain vertial) and 14 (omposite), it is apparent tat te two preditors oinide at a value of d/ 0.6, suggesting tat te mound s influene sould ease for d > 0.6, wi seems pysially sensible. Does te value of te disriminating parameter d 0. for transition between impulsive and nonimpulsive regimes remain optimal wen applied to te wider CLAS dataset? EurOtop (2007) gives te disriminator d < 0. for impulsive onditions. Tis riterion was applied to all CLAS database data for omposite strutures, wit separate plots being made for onditions predited to be impulsive or nonimpulsive. Te data identified as impulsive was well-predited. For data predited to be in te nonimpulsive regime, it was apparent, owever tat tere was a group of data at iger freeboards wi was signifiantly under-predited. Te under-predited data (Figure 5) belongs to set 505 for wi tere was a 1:10 foresore present. Before onsidering tis influene owever, te d 0. ross-over was tested. Moving from d 0. to 0.85 as te ritial value, te performane of te seme improves. Mean error goes from.15 to 0.87, and geometri error (measuring te standard deviation of te satter about te mean of te logaritm of te data) from 0.47 to 0.8, indiating average suess in te range / 2.4, improved from /.0 wit te previous, lower value of d. Data tat remains signifiantly over-predited inludes many data from sets 228 and 914, neiter of wi ad foresores. Does te presene or absene of a foresore influene overtopping at omposite strutures as was sown for vertial strutures in te earlier analysis? Adoption of adjusted forms of te new vertial wall proedures was ten explored. In addition to te advantage of onsisteny of approa, su a swit would also bring te pysially sensible beaviour at lowest freeboards to te analysis of overtopping of omposite walls. Te new vertial wall predition seme was ten applied, adjusted to omposite strutures by appliation of a orretion fator of 1. (d/) for all d/ < 0.6. Te multiplier of 1. allows omposite and vertial formulae to oinide at d/ 0.6 (Euations 14 and 15): d exp 2. 2 sm 1,0 m 0 d m 1,0 0 0 sm m m (1) for / < 1.5 (14) for / 1.5 (15) Te omposite wall data, exluding tose wit zero freeboard, are plotted wit Euations 14 and 15 in Figure 5. Te geometri error is 0.9. As noted above, te exponent of d/ was set at an influene of (d/) on te basis of te algebrai manipulation of te EurOtop formulation, after Allsop et al. s (1995) euation. Exploring alternative exponents demonstrated tat te value is optimal.

8 {/( ) }.(s /d).( s / ).s m-1,0 1.E-0 omposite, lower freeboards (E. 14) omposite, iger freeboards (E. 15) elative freeboard / Figure 5. Comparison of all CLAS database tests for omposite strutures wit foresore wit new seme for omposite strutures, based upon new vertial wall approa, adjusted d ut-off; applied for all d / s < 0.6. Te influene of te berm is indiated in Figure 6. From tis, it an be seen tat under onditions establised as impulsive, te berm s influene is to redue overtopping disarges. Te sale of te influene is not tat great, owever of te same orders of magnitude as te influene of wave steepness and relative dept on impulsive overtopping at plain vertial walls. elative overtopping rate /( ) 1.E+00 1.E-0 Es.14,15; d/0.45; / ; sm-1, Es.14,15; d/0.45; / ; sm-1, Es.8,9; plain vertial; / ; sm-1, Es.8,9; plain vertial; / ; sm-1, Allsop et al. (1995), E.1 Frano et al. (1994), E elative freeboard / Figure 6. Comparison of overtopping at omposite and plain vertial strutures, for nonimpulsive/defleting waves as well as for impulsive waves.

9 Te seme for omposite strutures is tus now aligned wit te improved vertial seme giving pysially rational beaviour at lowest freeboards (wi was not te ase for te previous, power-lawonly seme). In summary, overtopping at omposite strutures may be onsidered aording to te rigt side of te deision art (Figure 7). In ases were te mound is small (d/ > 0.6), te struture is treated as vertial. For d/ 0.6, in te absene of a foresore and possible breaking, te struture is again treated as plain vertial. In te ase of possible breaking, owever, te overtopping is predited aording to te metod for plain walls, but wit a fator of 1. (d/) inluded. vertial or omposite vertial? d/ > 0.6? yes (treat as vertial) no (treat as omposite) yes foresore? no foresore? no yes possible breaking? 2 /( L m-1,0 ) < 0.2? yes no possible breaking? d < 0.85? no yes lower or iger freeboard? / < 1.5? yes no lower or iger freeboard? / < 0.91? yes no lower or iger freeboard? / < 1.5? yes no exponential (En 8) power law (En 9) exponential Allsop et al., En 2 wit a0.05 b2.78 exponential Frano et al., En 2 wit a0.2 b4. exponential (En 14) power law (En 15) Figure 7. Deision art sowing new semes; vertial to left; omposite to rigt. Conlusions Vertial strutures sould be divided in strutures at relatively deep water witout a sloping foresore and seawalls at te end of su a sloping foresore. Te first type of struture desribes aissons, flood walls in arbours and gates in loks at ig water. Te Frano et al. (1994) formula, Euation 6, is valid in tis situation for larger freeboard, were te Allsop et al. (1995) formula, Euation 5, is valid from zero freeboard until te rossing wit te Frano formula. Te disriminator 2 /( L m-1,0 ) divides wave overtopping at a seawall on a sloping foresore in non-impulsive or defleting waves wit 2 /( L m-1,0 ) > 0.2, were te Allsop et al. (1995) gives te prediting formulae. For smaller values of te disriminator impulsive waves give larger wave overtopping and sometimes even signifiant wave overtopping for large freeboards, see Figure 9. Euations 8 and 9 desribe overtopping under impulsive wave onditions. Guidane ow to apply te orret formulae is given in Figure 7. Overtopping at omposite strutures an be analysed aording to a lose analogue of tis new seme for plain vertial strutures. Adjustments are applied for berms iger tan d/ s < 0.6. Te adjustment is simply a fator of 1. (d/ s ). A deision art summary of te proposed, unified seme for plain vertial and omposite strutures is presented (Figure 7). It is reommended tat an update of EurOtop (2007) be onsidered, to inlude te new insigts and design formulae found in tis paper for pratial use.

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