wave basin experiments on floating breakwaters with different layouts

Applied Ocean Research 30 (2008) 199–207

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Applied Ocean Research

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Wave basin experiments on floating breakwaters with different layoutsLuca Martinelli a,∗, Piero Ruol b, Barbara Zanuttigh aa DISTART Idraulica, University of Bologna, Bologna, Italyb IMAGE, University of Padova, Padova, Italy

a r t i c l e i n f o

Article history:Received 26 October 2007Received in revised form21 July 2008Accepted 8 September 2008Available online 28 October 2008

Keywords:Floating breakwaterIntermodule connector forcesMooring loadsOblique wavesExperiments

a b s t r a c t

The general aim of this paper is to examine the effect of floating breakwater layouts onwave transmission,loads along moorings and connectors, under oblique waves. The specific contribution of this work is toprovide novel and accurate experimental results for a configuration that is widely adopted in existingprototypes. Tests were carried out in thewave basin (3.8m×20.6m×0.8m) of theMaritime Laboratoryof the University of Padova, Italy. Two layouts, characterised by different degrees of complexity (I- andJ-shaped), and three obliquities (0◦, 30◦, 60◦)were examined.With increasedwave obliquity, the floating breakwater becomesmore efficient thanks to the decrease

of wave transmission and of the forces along moorings and connectors. Under perpendicular waves, withincreasing layout complexity, no significant effect on wave transmission is observed, whereas mooringand intermodule connector forces significantly change, particularly in the case of frequent overtopping.

© 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Floating Breakwaters (FBs) are typically assembled froma seriesof concrete self buoyant modules [12]. They are intended todissipate or reflect the incident wave energy in order to providea sheltered area of relatively calm water for the mooring of boatsor a more protected coastal area for recreational activities.Obviously, the choice of technology used to connect the

different modules, and thereby the stiffness of the connections,is paramount as it affects the global performance of the entirefloating structure [13].Adjacent floating modules can be connected at the top portion,

thus allowing the elements to pivot in relation to one another, ashappened in the case of Fezzano harbour (La Spezia, Italy). Suchpivotal movement may provide a less effective inertial barrier tothe wave action than when the interconnection is complete, as forBrissago (Maggiore Lake, Italy). In this case a monolithic behaviouris established, wave transmission is minimised but loads on theintermodule connectors may significantly increase.In the recent past, severe structural damage to FBs has been

observed:

- in 2003, in Cannobio (Maggiore lake, Italy), the FB protectingthe small craft harbour collapsed in the absence of loading. Thestructurewasmonolithic and post-tensioned. It is probable that

∗ Corresponding address: DISTART Idraulica, University of Bologna, 40136Bologna, Italy.E-mail address: [email protected] (L. Martinelli).

0141-1187/$ – see front matter© 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.apor.2008.09.002

forces along the structure were underestimated, thus causing aprogressive deterioration of buoyancy capacity;- in 1999, the monolithic and post-tensioned FB protecting theharbour on Lake Zug (Switzerlad), collapsed under a storminduced by the Lothar hurricane;- in 1999, Charleston Marina (Oregon, USA) suffered majordamage during Hurricane Floyd. The marina owner sued thefloating dock manufacturer alleging design deficiencies in theFB, floating dock and anchor system.

According to Isaacson [1], a suitable design should consider,among others, the following wave induced failure mechanisms:

- failure in connections between breakwater units;- failure of the piles restraining the breakwater;- failure of the mooring lines or mooring line connections;- the dragging of anchors.

Examples of such failures are documented in the PIANC report[2] or by the US Army Corps of Engineers [3]. In particular, Richeyconcludes that ‘‘connections are the Achille’s heel in floatingbreakwater design. . .. Experience has had to substitute for analysisin evaluating the loadings to be transferred between modules’’.To the authors’ knowledge, there is a lack of experimental

investigation of complex schemes in 3D conditions, apart fromspecific designs it is too difficult to generalize about, such asthe Port of Brownsville Marina in Washington State [4]. Designguidelines are not very helpful on this point: for instance, theBritish Standards Institution (BS 6349: Part 6: 1989) merely warnsthat ‘‘particular care should be taken in designing the connectionsbetween units’’.

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200 L. Martinelli et al. / Applied Ocean Research 30 (2008) 199–207

Fig. 1. Plan view (top) and cross section (bottom) of the wave basin.

Fig. 2. I-shaped and J-shaped layouts with tested obliquities (0◦ , 30◦ and 60◦). Numbers identify the load cells measuring mooring (1–4) and connector (5–8) forces. Chainsconnected to the central monitored module are shown with solid lines, other chains are dashed lines.

Numerical models can cope with the problem of oblique wavestructure interaction, but mainly in the case of a single module.The effects of mean wave direction and directional homogeneityin 2D conditions were studied by Isaacson and Sinha [5] withthe linear diffraction theory, by Isaacson and Nwogu [6] with theGreen’s function, by Sannasiraj et al. [7] with a 2D finite elementmodel and by Gesrah [8] with an eigenfunction expansion. Few 3Dnumericalmodels exist, which can represent complex layoutswithsomeuncertainty. Briggs et al. [9] found somediscrepancies amongthe measured loads on a full-scale V-shaped breakwater and theexamination of two 3D models based on the boundary elementmethod.In short, a proper design should consider 3D effects, e.g. the

effect of layout and obliquity, which cause severe loads on theconnections between the breakwater units, yet few guidelines forthe designer are available.The aim of this contribution is to experimentally investigate

on FB effectiveness as well as on forces along moorings andconnectors, for different layouts and under oblique waves.The paper is composed of five main sections. The first describes

the facility, the tested configurations and wave attacks, andcharacteristics of the mooring systems.The second briefly presents the types of analyses that have been

carried out on the data collected during the tests and the methodsadopted for them.The third discusses the results in terms of wave transmission,

forces exchanged by the modules making up the FB and mooringforces. Effects due to layout, wave obliquity and wave period arehighlighted.The forth and the fifth describe the applicability of the results to

prototype cases and draw conclusions that can be useful for designpurposes.

2. The tests

2.1. Experimental set-up

The facility is 20.6 m long, 3.8 m wide and 0.8 m deep(Fig. 1). The basin is equipped with a piston type wave makerformed by a single paddle, capable of generating irregular wavesusing standard software (HR Wallingford) in the absence of activewave absorption. Two absorbing metallic nets 0.40 m wide and0.80 m high are placed along the sides of the basin to avoidspurious reflection. Water depth at the wavemaker is 0.50 m.The bed is flat for approximately 11 m. The absorbing rampopposite to the wavemaker consists of a 1:5 sloping, gravel beach(D50 approx. 3 cm).Two layoutswere designed and analysed: (1) a straight I-shaped

one and (2) a composite J-shaped one. In prototype, the specialelement necessary to obtain the J-shaped layout can be easilyobtained by inserting an additional formwork before casting theconcrete unit. The I-shaped layout (Fig. 2) is placed in differentdirections as regards the wavemaker, i.e. 0◦–30◦–60◦.The floating elements are 0.10 m high and 0.20 m wide (Fig. 3),

reproducing typical prototypes on a 1:20 geometrical scale. Theattached plates at the sides are used to improve efficiency, asshown for instance by Koutandos et al. [10]. The three straightelements (Fig. 4) are 0.98 m long, connected by tie rods, with oneof them having been previously tested in the 1.0 m wide wavechannel housed in the same laboratory [11]. One of the testedconfigurations is shown in Fig. 5.As in many prototypes, buoyancy is assured by the presence

of a polystyrene core. The skeleton is made of aluminium withthe exception of the two ends which are made of teflon, wherethe moorings interfere with the structure. Specific weights ofaluminium and teflon, equalling to 2.7 and 2.2 respectively, are

L. Martinelli et al. / Applied Ocean Research 30 (2008) 199–207 201

Fig. 3. Cross section of the tested structure, dimensions in mm.

Fig. 4. Longitudinal section of the breakwater, formed by three modules. 2 tie rods at mean sea level connecting each pair of modules, dimensions in m.

Table 1Structure characteristics

Mass Inertia to roll(around gravity centre)

Freeboard Height of centre of gravity Height of centre of buoyancy Distance between metacentreand centre of buoyancy

7.25 kg 0.041 kg m2 34 mm +6 mm −19 mm 90 mm

Heights are referred to still water level.

Fig. 5. J-shaped layout. Test F4 in Table 2. Waves come from top right.

close to that of concrete. Structural characteristics are summarisedin Table 1.Two arrays of 3 and 5 resistive wave gauges (WGs) were used

to monitor the incident and reflected waves respectively inshoreand offshore from the structure. Fig. 6 shows the relative positionsof the WGs in the array. In some cases, but only if the structurewas perpendicular to the incomingwave directions, 4 alignedWGswere used instead of 5. A total of 8 load cells were installed, all inthe central floating module. The cell positions are shown in Fig. 2.Data were logged at 20 Hz.23 long-crested wave conditions were generated, with target

Jonswap spectrum (peak enhancement factor 3.3). The testsequence is given in Table 2, and comprises 8 wave heights in therange 1.5–8.0 cm, and 4 wave periods, with steepness lower than7%. Acquisition started 2 min before and ended 5 min after eachtest. The number of waves per test was approximately 600.

2.2. Mooring system characteristics

Chains, with length Lc equal to 1.18 m and submerged weightw equal to 78 g/m, were constrained at the bottom and at the

Table 2Generated waves

Test Hs (cm) Tp (s) Test Hs (cm) Tp (s)

A1 1.50 0.56 E3 5.50 0.78B1 2.50 0.56 F3 6.50 0.78C1 3.50 0.56 G3 7.50 0.78A2 1.50 0.67 A4 1.50 0.89B2 2.50 0.67 B4 2.50 0.89C2 3.50 0.67 C4 3.50 0.89D2 4.50 0.67 D4 4.50 0.89E2 5.50 0.67 E4 5.50 0.89A3 1.50 0.78 F4 6.50 0.89B3 2.50 0.78 G4 7.50 0.89C3 3.50 0.78 H4 8.00 0.89D3 4.50 0.78

Target values. Hs is significant wave height and Tp is peak period.

structure. Chains were initially slack (angle at the base≈0◦), beingthe initial horizontal load equal to wLc , and they were oriented∼=22.5◦ from the perpendicular to the FB as in typical prototypes.Along this direction, the horizontal and vertical projections of thechain were 94 and 47 cm.Maximum loads are usually due to dynamic impulses, possibly

snapping conditions. According to common practice and literature,snapping occurs when the chain is alternatively slack and tautduring motion of the structure, i.e. when the total mooring lineload (static and dynamic) becomes equal to zero during theloading cycle. In this case, there is a marked non-linearity due todiscontinuity in the line stiffness, with the load increasing sharplywhen the taut phase begins. Impulsive loads occur in the time scaleof a wave period, so that a 20 Hz logging frequency is sufficient todescribe the process.The theoretical response of the mooring system is analysed in

quasi-static conditions under the further assumption that the 4chains connecting each module are perpendicular to the structure.Fig. 7 shows the theoretical horizontal load applied to the FB

by the 4 chains, as a function of its horizontal movements. Thecurve is composed of two parts: the first is linear since the increaseof the load in the two front chains progressively tensioned isalmost compensated by the decrease of the tension in the rearchains [14]. The second is non-linear, and represents the case of2 taut chains and 2 almost slack ones. In order to fully extend the


Fig. 6. Plan view of the basin, with location of the 8 wave gauges used for reflection and transmission analysis.

Fig. 7. Simulated horizontal load applied to the FB as function of its horizontalmovements. The grey line corresponds to the ideal conditions of pure FB translation,having an asymptotic behaviour represented by the dash-dotted vertical grey line.The black line accounts for the vertical translation and rotation induced by themooring force under static conditions.

chain, an infinite force is needed. This condition is represented bya simple vertical asymptote in the ideal case of pure horizontal FBtranslation. In practice, the vertical FB displacement and rotationdue to vertical forces applied by the chains have to be accountedfor, so that the asymptotic condition is different and correspondsto larger displacements. In dynamic conditions, the chain inertiaand damping further complicates the mooring response [15].Fig. 8 presents the quasi-static reaction force applied to the FB

by a single chain, as a function of the FB horizontal movements,together with the threshold value selected to identify impulsiveor snapping conditions. Snapping is considered to occur when thetotal load exceeds twice the initial load, which is equal to the chainweight (wLc ≈ 1 N, where Lc is the chain length). If the forcedynamic oscillations are symmetrical as regards the initial staticvalue, this threshold (2wLc ≈ 2 N) identifies conditions for whichthe load drops to zero during the wave cycle (coherent with thedefinition of snapping given above).For greater accuracy in the evaluation of the chain response, the

system rigidity was measured by displacing the I-shaped structureof a known quantity. It resulted negligible for roll and heave,whereas for sway (subscript 1) it was found that:

K11 ≈ 60 N/m for a displacement of 6 cm. (1)

The stiffness of the system in the vertical direction and rotationis mainly given by buoyancy (subscript 2 refers to rotation,

Fig. 8. Load applied to the FB by a single chain (black line), as function of theFB horizontal movements, with indication of the snapping limit (grey line). As inFigure 7, for the black line case, the vertical translation and rotation induced by themooring force under static conditions are accounted for.

subscript 3 to the vertical direction):

K22 ≈ MghM = 12.5 N m/rad (2)K33 ≈ ρgLB = 2.4 kN/m (3)

whereM is the structure mass, g is acceleration due to gravity, hMis the height of metacentre, L and B are the structure length andwidth.Natural modes of oscillations in 3D have been assessed in the

laboratory by releasing the structure from several non equilibratedpositions (heave is shown in Fig. 9). From forces measured alongthemoorings, displacements could be retrieved (by using a relationsimilar to the one presented in Fig. 7) and were separately fitted toa sinusoidal curve of the type:

η = A sin(ωt)e−ζ t . (4)

The different values ofω are representative of the 3 natural periodsof oscillations, which, for the I-shaped configuration, are given inTable 3. The system has several degrees of freedom and for the J-shaped configuration it became impossible to excite all the modesseparately, so that few modes could be identified with a greatdegree of uncertainty (Table 4).

3. Analysis

Incident and transmitted waves are obtained by using the Zeltand Skielbreja [16] method on the aligned WGs and the Bayesian


Fig. 9. At the left hand-side, a sketch of the oscillation modes; at the right hand-side, measured heave natural oscillations (solid grey line) and sinusoidal fitting (dashedblack line) based on Eq. (4).

Table 3Natural period of oscillations (Tn) and damping coefficient (ζ ) for the I-Shapedconfiguration

Heave Tn = 0.85 s ζ = 0.20Roll Tn = 0.87 s ζ = 0.02Sway Tn = 4.8 s ζ = 0.08Other (surge-like) Tn = 4.0 s ζ = 0.15Other (pitch-like) Tn = 4.6 s ζ = 0.10Other (yaw-like) Tn = 3.7 s ζ = 0.10

Table 4Natural period of oscillations (Tn) and damping coefficient (ζ ) for the J-Shapedconfiguration

Heave Tn = 0.85 s ζ = 0.2Roll Tn = 2.1 s ζ = 1Other Tn = 5.1 s ζ = 0.02

Directional Method on the array of WGs. Time domain analysis isthen carried out to define the incident and transmitted significantwaves, Hsi and Hst. Spectral analysis provides the peak period Tpand alternative value of Hmo, which is consistent with Hs.Loads are analysed in the time domain. After evaluating the

average load, the signal is high pass filtered to eliminate longperiod spurious oscillations (this operation also removes theaverage). Amplitudes of the loads due to each wave are identifiedby means of a zero-down crossing analysis and are fitted to astatistical distribution. The 1/250 and other characteristic valuesare extracted and summed to the average load. Within the sametest, the maximum among the 4 measured mooring forces andamong the 4 connector forces are selected.

4. Results and discussion

4.1. FB effectiveness

FB effectiveness is mainly related to wave transmission. Fig. 10presents the transmission coefficient kt = Hst/Hsi as a functionof the ratio between the measured peak period of the incidentwave Tp and the heave natural period (Tn = 0.85 s for all cases).The figure also presents an additional dataset, which consists oftests performed in the wave flume (33 × 1.0 × 1.3 m) of thesame facility [11] and characterised by the same wave conditions,structure geometry and water depth. Transmission in the waveflume appears greater than in the basin in the case with 0◦obliquity, possibly due to 3D effects or to a slight difference on themooring position (chains diverge for an angle of 22.5◦ in the basin,whereas they are perpendicular to the structure in the channel).

Fig. 10. Measured wave transmission as a function of the peak wave period, non-dimentionalised with the natural period of heave oscillations (0.85 s).

If we still focus on the casewith 0◦ obliquity, we can see that theJ-shaped configuration presents a wave transmission coefficientsimilar to the I-shaped one.With increasing obliquities, kt decreases. This behaviour can

be easily explained in presence of infinitely rigid moorings, sinceonly the power component perpendicular to the axis is transmittedunder the structure. For real moorings, the relevance of waveobliquity is also related to the FB dynamics: sway, heave and rolldecrease as the incident wave angle increases for most of the waveranges [6], smaller movements induce lower radiation, and thisoften results in a further reduction of wave transmission.As shown in Fig. 10, kt is strongly related to Tp. If the data

points in Fig. 10 are fitted to a curve of the form kt(Tp/Tn) for eachtested structure, each curve can be characterised by a few valuesof kt for given Tp/Tn ratios (in the range 0.7–1.0). For the I-shapedconfiguration such values are plotted in Fig. 11, showing that ktalmost linearly decreaseswithwave obliquity. Obviously, the slopeof the fitting lines depend on the breakwater to wavelength ratio.

4.2. Loads

Fig. 12 shows the obtained maxima of the connector (greypoints, load cells 5–8 in Fig. 2) and mooring forces (black points,cells 1–4) per each test. The former are much greater than thelatter, mainly because the initial tension is approximately 20 Nin the connectors and 1 N in the moorings. Moreover, connector


Fig. 11. I-Shaped configuration. Transmission as a function of wave obliquity, forTp = Tn .

Fig. 12. Measured connector and mooring forces.

forces increase with Hsi slightly more rapidly than the mooringones.It can be also noticed that mooring forces for 60◦ obliquity do

not increase with increasing Hsi: for this very oblique case, thecomponent of the mooring force due to waves appears negligible.Whereas perpendicular waves apply a load which is in phase

along every section of the FB, obliquewaves apply a load that variesalong the structure.In the former case, the maximum pressure (which coincides

with thewave crest) is simultaneously applied to all the sections ofthe structure. In the latter case the maximum pressure is appliedonly on a certain number of sections, the adjacent ones being lessloaded. As a consequence, the maximum length-averaged force islower under oblique waves than under perpendicular ones.The effect of obliquity on mooring forces is an important issue

in designing a harbour layout, because the orientation of the FBscan be optimized with respect to the local wave climate.Mooring forces are investigated for design reasons. Focus is thus

given to the maximum load, which is the sum of the initial load(i.e. the load at rest), the drift force (the average within the wavecycle) and the load associated to the reaction during themaximumdisplacement of the floating body.Drift forces are evaluated by projecting the average load on

the perpendicular to the FB axis. They resulted to be in the range25%–40% of 1/16 ρg (H2rms,i + H

2rms,r − H

2rms,t ), that represents the

net radiation stress over the control volume inclusive of the FB. The

Fig. 13. Non-dimensional mooring forces vs. degree of overtopping.

Fig. 14. Maximum non-dimensional mooring forces vs. wave obliquity, fitted, forHsi/Fr = 2.5.

scatter is justified since drift forces are negligible compared withthe maxima.Fig. 13 shows the maxima of measured mooring forces

(occurring in chain no. 3 or 4 for the I-shaped configuration, andin chain no. 3 for the J-shaped one, see Fig. 2) non-dimensionalisedwithρgHsid, where d is the structure height (=10 cm), as a functionof Hsi non-dimensionalised with the crest freeboard, Fr (=3.5 cm).Note that ρgHsid is the order of magnitude of an impulsive force inthe presence of overtopping, i.e. when Hsi/Fr > 1.For all tested configurations, although more clearly for the J-

shaped one, in the case of severe loads, i.e when Hsi/Fr � 1,asymptotic (non-dimensional) values for the mooring forces seemto be reached.The J-shaped layout is associated with lower mooring forces

than the I-shaped one (under perpendicular waves). For the latterconfiguration, the non-dimensional maxima are fitted in order torepresent the same wave condition and plotted vs. wave obliquityin Fig. 14. It can be seen that the forces linearly decrease with theangle of wave attack, θ . The lower limit of the force cannot bezero, due to the non-zero initial load and some additional minoreffects. Such a lower limit is reasonable for the value obtained for60◦ obliquity, which, does not seem to depend on the wave action,as can be observed in Fig. 13.A similar analysis is carried out for the connector forces.

Loads are again non-dimensionalised with ρgHsid and plotted


Fig. 15. Non-dimensional maximum connector forces vs. degree of overtopping.The distance between the set of points and the curve of the initial load on the chains,i.e. the relative importance of the connector forces with respect to the pre-stress,increases with increasing wave height and tends to an asymptotic value for highovertopping rate.

Fig. 16. Non-dimensional maximum connector forces vs. degree of overtopping,with indication of the corresponding wave period.

vs. the degree of overtopping Hsi/Fr . Since in this case, theinitial load in the tie rods (≈20 N) is an essential contribution,Fig. 15 also presents the non-dimensional initial load (dashedline). The relative importance of the connector forces with respectto the pre-stress is given by the vertical distance between theset of points and the curve of the initial load on the tie rods.For high Hsi/Fr , and therefore low initial stress influence, thenon-dimensional connector forces tend to an asymptotic (non-dimensional) value, which is about 0.6 and 0.8 for the I-shaped andJ-shaped configurations, respectively.ForHsi/Fr < 1.5, i.e.when tested conditions include several low

and high wave periods, it can be can seen (Fig. 16) that connectorforces are close to the initial load when Tp < Tn and, on thecontrary, may differ quite significantly from the initial load whenTp > Tn. This is indeed expected, because in the latter case the FBmovements are larger.Connector forces show little variability with respect to the

average value (F1/250/Frms < 2) and a fatigue analysis, assumingfor instance F1/250 as the reference value, is recommended. Onthe contrary, mooring forces have a much higher variability(F1/250/Frms > 4). A statistical description is therefore needed inorder to accurately describe the maxima.Significant mooring forces have been analysed just for the I-

shaped configuration under perpendicular waves, which is clearly

Fig. 17. Example of fitting of mooring force values to a Weibull distribution.

Fig. 18. Mooring forces: frequency of exceedence of the threshold (snapping) valuevs. degree of overtopping.

the most critical condition. Values larger than twice the chainweight (2wLc) are selected, corresponding to the given definitionof impulsive or snapping conditions (see Fig. 8). These force valuesare fitted to aWeibull distribution (example in Fig. 17) with a fixedlocation parameter (equal to twice the chain weight):

P(f ≤ F) = 1− e−(a(F−2wLc )b). (5)

Fig. 18 shows the frequency of exceedence P(f ) of the selectedthreshold, which is evidently a function of wave height. Thenumber of snapping events is relevant for Hsi/Fr > 1.5, e.g. forHsi/Fr = 2 approximately 60% of the waves produce impulsiveor snapping conditions. Based on tests with P(f ) > 0.1, theparameters a and b of the Weibull distribution are plotted inFigs. 19 and 20, respectively. The shape parameter b is almostconstant and equal to 1, therefore the Weibull degenerates into aGumbel and a is the inverse of its scale parameter.Figs. 19 and 20 do not show any influence of Tp on mooring

force statistics, as also found for the other layouts. This lack ofcorrelation can be justified by considering that larger load eventsare due to dynamic impulses on the chains, which occur whenthese are (almost) fully extended. The chain impulsive reactioncauses the FB momentum (p) to drop suddenly to zero. Thereaction is proportional to the ratio between the FB velocity andthe impulse duration {F = ∆p/dt ∝ V/dt}, which, even if actually


Fig. 19. Statistics of mooring forces: ‘a’ parameter of Weibull distribution vs. thedegree of overtopping. Wave steepness shows no influence on the statistics.

Fig. 20. Statistics of mooring forces: shape parameter (‘b’) of Weibull distributionvs. the degree of overtopping. Mean value is 1.04 with std 12%. Wave steepnessshows no influence on the statistics.

related to many different factors, can be reasonably assumed to beproportional to the wave period. The FB velocity is proportional tothe wave celerity, which in deep water is linearly dependent on Tp.As both the impulse duration and the FB velocity are proportionalto Tp, the maximum force in the chain is independent of Tp{F ∝V/dt = (αTp)/(βTp) = α/β}.The scale parameter a is inversely proportional to the average

force and increases with increasing Hsi. For Hsi/Fr > 1.5, i.e. whensnapping events are frequent, the parameter a linearly decreasesfollowing the relation: a = 0.5− 0.15(Hsi/Fr).

5. Discussion

The obtained graphs allow for the design of FBs that, comparedwith the 2D case (aligned modules, breakwater perpendicular towave attack) are more economical or more efficient.For typical wave conditions (Tp) and the desired transmission

coefficient (kt), the designer is guided by Fig. 10 to the choice ofstructure cross section (from a natural period of oscillation), layoutobliquity and shape. Connectors andmoorings can be dimensionedthrough Figs. 13–20 given the overall geometry and extremeincident wave height.

Sincemooring forces are highly variable, the designer is referredto Eq. (5) for a statistical evaluation of the load tuned to theaccepted failure probability.Unfortunately, it is implicit in the experimental approach

that the quantitative generalisation of the results is limited tostructures with similar configurations (cross section, structurelength, water level) and same mooring type as the tested ones.

6. Conclusions

Conclusions are drawn on the basis of 95 tests carried outin a 3.8 m × 26.0 m wave basin at the Maritime laboratory ofthe University of Padova. The tested FB model resembles typicalprototypes in scale 1:20. Two layouts were analysed, an I-shapedconfiguration and a J-shaped one. The I-shaped configuration wastested with 3 obliquities in the range 0◦–60◦ and compared withinvestigations performed in the wave flume of the same facility[11]. Waves were irregular and longcrested.For the I-shaped configuration, it is observed that:

- wave transmission and maximum mooring forces linearlydecrease with increasing wave obliquity. Transmission in thebasin is lower than in the flume possibly due to 3D effects anddifferences in the mooring geometry;- connector forces are much greater than mooring ones, mainlydue to the high initial stress necessary for constraining thestructure. The maximum connector force is lower than twicethe mean value, so that these tie rods should be designed forfatigue;- the maximum mooring force is associated to impulsiveevents. Mooring forces are highly variable and were described,for perpendicular wave attack, by a Weibull distributionwith shape parameter ≈1 and scale parameter inverselyproportional to incident wave height.

The increase of structure inertia to roll, obtained by varying thelayout (from I- to J-shape), has small effects on wave transmissionbut not negligible effects on loads, showing lower mooring andhigher connector forces.Wave transmission and connector forces are strongly related to

the incident wave period, whereas maximum mooring forces donot show any clear correlationwith Tp. For Tp � Tn, FBmovementsand transmission are small and both layout and obliquity have onlya limited influence on the maximum connector forces. For Tp �Tn, FB oscillations and transmission are significant, and maximumconnector forces considerably increase with higher wave obliquityand complexity of the layout.Both mooring and connector forces for high overtopping rates

appear to be upper limited.

Acknowledgements

The support of the Italian Ministry for Research throughPRIN2005 program ‘‘Tecnologie moderne per la riduzione dei costinelle opere di difesa portuali’’, Prot. 2005084953, is gratefullyacknowledged. The authors also wish to thank prof. AlbertoLamberti, University of Bologna, for our fruitful discussions, andINGEMAR S.r.l. for providing precious practical information on FBdesign.


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wave basin experiments on floating breakwaters with different layouts

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