Coastal Engineering xxx (2008) xxx-xxx. Contents lists available at ScienceDirect. Coastal Engineering

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1 CENG-02240; No of Pages 12 ARTICLE IN PRESS Coastal Engineering xxx (2008) xxx-xxx Contents lists available at ScienceDirect Coastal Engineering journal homepage: Prototype measurements and small-scale model tests of wave overtopping at shallow rubble-mound breakwaters: the Ostia-Rome yacht harbour case Leopoldo Franco a, Jimmy Geeraerts b, Riccardo Briganti a,d,, Marc Willems c, Giorgio Bellotti a, Julien De Rouck b a Department of Civil Engineering, University of Roma Tre, Via V. Volterra, Roma, Italy b University of Gent, Department of Civil Engineering, Technologiepark Zwijnaarde, Belgium c Flanders Hydraulics Research, Berchemlei 115, 2140 Borgerhout, Belgium d School of Civil Engineering, University of Nottingham, Nottingham, NG7 2RD, United Kingdom ARTICLE INFO ABSTRACT Available online xxxx Keywords: Wave overtopping Laboratory tests Field measurements Rubble-mound breakwaters The paper presents the comparison between the results of small-scale model tests and prototype measurements of wave overtopping at a rubble-mound breakwater. The specific structure investigated is the west breakwater of the yacht harbour of Rome at Ostia (Italy) and is characterized by a gentle seaward slope (1/4) and by a long, shallow foreshore. The laboratory tests firstly aimed at carefully reproducing two measured storms in which overtopping occurred and was measured. The tests have been carried out in two independent laboratories, in a wave flume and in a wave basin, hence using a two-dimensional (2-D) and a three-dimensional (3-D) setup. In the 2-D laboratory tests no overtopping occurred during the storm reproductions; in the 3-D case discharges five to ten times smaller than those observed in prototype have been measured. This indicates the existence of model and scale effects. These effects have been discussed on the basis of the results of several parametric tests, which have been carried out in both laboratories, in addition to the storm reproductions, varying wave and water level characteristics. Final comparison of all the performed tests with 86 prototype measurements still suggests the existence of scale and model effects that induce strong underestimation of overtopping discharge at small scale. The scale reproduction of wave breaking on the foreshore, together with the 3-D features of the prototype conditions and the absence of wind stress in the laboratory measurements, have been individuated as the main sources of scale and model effects. The paper also provides a comparison between the data and a largely used formula for wave overtopping discharges in the presence of structures similar to the one at hand. The suitable value of a roughness factor that appears in that formula is investigated and good agreement is found with other recent researches on rubble-mound breakwaters Elsevier B.V. All rights reserved. 1. Introduction Corresponding author. School of Civil Engineering, University of Nottingham, Nottingham, NG7 2RD, United Kingdom. addresses: briganti@uniroma3.it, Riccardo.Briganti@nottingham.ac.uk (R. Briganti). The complexity of the processes involved in wave run-up and overtopping on a breakwater induced researchers to investigate these phenomena using laboratory tests. Most of the design tools used in practice, such as empirical formulae, have been derived using these tests; the accuracy of the predictions of these tools, with respect to the real working conditions of the breakwater, has been investigated extensively within the EU funded research project CLASH (Crest Level Assessment of coastal Structures by full scale monitoring, neural network prediction and Hazard analysis of permissible wave overtopping, EVK3-CT ), by comparing prototype measurements of overtopping and small-scale laboratory test results. The starting point of these analyses is the outcome of the previous European project OPTICREST. The research carried out in that framework pointed out the evidence of the underestimation of run-up on a rubble-mound breakwater in small scale with respect to run-up in full scale (De Rouck et al., 2001), suggesting that scale and/or model effects in the small-scale reproduction of the phenomena can affect the results. One of the specific aims pursued during CLASH has been the quantification of this underestimation on wave overtopping and the identification of those situations in which the suspected scale and model effects were more relevant. To accomplish this objective, field measurements of wave overtopping have been carried out at three locations in Europe. The three prototype sites have been each modelled in two different laboratories. Laboratory results are compared to field measurements with the aim of developing new guidance on how to take into account scale and model effects when using empirical formulae based on small-scale laboratory tests. The three locations /$ see front matter 2008 Elsevier B.V. All rights reserved. doi: /j.coastaleng

2 2 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx Fig. 1. Location map and layout of Rome yacht harbour at Ostia (adapted from Briganti et al., 2005). have been selected in order to be each one representative of a typical layout in terms of sea bottom configuration and structural type. Among them, the newly built rock-armoured mound breakwater at the Rome yacht harbour at Ostia (Italy) has been chosen for its gentle seaward slope and because it is located on a shallow sandy foreshore in a micro-tidal sea. Due to the mild slope of the foreshore and to the limited water depth at the toe (4.0 m MSL), almost all the overtopping storm waves are breaking or broken. Moreover, the gentle slope of the breakwater enhances the importance of the infiltration of run-up water into the porous armour layer. All these aspects suggest a large sensitivity of overtopping to scale effects. Furthermore, the presence of head-on or slightly oblique wave attacks makes it possible to investigate the potential model effects in two-dimensional (2-D) conditions, i.e. in suitable wave flumes. The wave overtopping measurement station at Ostia (Rome) has been fully built ex-novo within the CLASH project: it has been operational since late 2002 and it has been able to measure seven different storms with overtopping events during the winter season for a total of 86 h (indeed the largest existing set of overtopping field measurements). The results of this field campaign have been described in Briganti et al. (2005), while the present paper focuses on the comparison between the prototype measurements and Fig. 2. Upper panel: Design cross-section of the west breakwater at the overtopping wave tank (from Briganti et al., 2005). Lower Panel: model setup for the 2-D tests.

3 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx 3 the model results, both in the 2-D and the three-dimensional (3-D) setups. The choice of this location revealed to be particularly successful as the results of this study generally confirm that the hydraulic and structural conditions existing in Ostia induce relevant scale/model effects. The analyses carried out in this paper shed a light on the implication of these effects in predicting wave overtopping at coastal structures. The paper is organized as follows: first a summary is given of the field measurements already fully described in Briganti et al. (2005), then the 2-D and 3-D laboratory test results are described in detail and compared with the prototype data to allow the final discussion and conclusions. 2. Field overtopping measurements The measurement station is located in the yacht harbour of Rome, built along the eroding sandy shores of Ostia, about 25 km from Rome in central Italy (see Fig. 1). The harbour is protected by two rubble-mound breakwaters (the west breakwater extending for some 600 m, the east one for 700 m), which converge to a central straight entrance to form an elliptic-shaped outer harbour with variable depths up to 5 m MSL.Fig.1 shows also the area of the harbour modelled in the 3-D basin. The design cross-section of the final part of the west breakwater at the overtopping tank is shown in Fig. 2 (upper panel). The crest level of the crown wall is set at +4.5 m MSL, the rock armour seaward design slope is 1:3.5. The design armour stones gradation is 3 7 t. Topographic and bathymetric surveys have been carried out periodically (see Fig. 3 in Briganti et al., 2005, for a general description of the bathymetry in the region); these frequent surveys pointed out some differences between the actual and the design values of some parameters. The actual seaward slope of the breakwater at the measurement section may be considered equal to 1:4 and the foreshore slope is about 1:65. The dimensions of the top layer armour stones at the overtopping station have been measured individually, in order to allow a realistic model reproduction. The station equipment includes a steel overtopping tank (Fig. 4), suitable for collecting individual overtopping volumes. Two pressure sensors are installed on the bottom of the tank in order to measure the water level. Overtopping events produce a sudden increase of the water level inside the tank; given the area of the collecting tank, it is possible to know the volume of each overtopping event. Wave conditions in proximity of the structure have been retrieved using a shallow-water wave and sea level recorder (Valeport 730-TW), installed 220 m seaward of the overtopping tank in a water depth of 6.5 m MSL. Wave characteristics and water levels were measured for a few minutes every hour. Sea level was obtained as the average value of a 60 s measurement (sampling rate of 1 Hz); the surface elevation for wave parameters has been sampled at a rate of 4 Hz for 512 s until October 2003 and at a rate of 2 Hz for 1024 s from November A tidal gauge was also operational inside the harbour. Wave conditions in deep water have been obtained using a directional wave recorder buoy located offshore Civitavecchia (60 Km NW, see Fig. 1). In case of failure of the shallow-water instrument, wave characteristics have been computed by propagating nearshore with the numerical model SWAN, the recorded deep water spectra. A full description of the procedure is given in Briganti et al. (2005). It has to be mentioned that all wave conditions used as input in the laboratory storm reproductions have been measured directly by the shallow-water wave recorder. 3. Laboratory tests D experimental setup 2-D laboratory experiments have been carried out at the Department of Civil Engineering of the University of Gent (Belgium). The wave flume used for the tests is 30.0 m long, 1.0 m wide and 1.2 m high. The overall design water depth is 0.80 m. The maximum significant wave height that can be generated in the flume is about 0.35 m. The flume side walls are mainly made of reinforced concrete. A 16 m long section of one side wall is of glass (30 mm thick), supported by a steel frame. The flume is equipped with state-of-the-art model testing technology including an advanced wave generator system for both regular and irregular waves, active wave absorption, data acquisition system and wave data analysis software. Waves are generated by a piston type paddle. The wave generation software has been developed by the Department of Civil Engineering of the University of Gent. The 2-D model of the breakwater has been built in a 1:20 Froude scale. The resulting model setup, including the location of the wave gauges arrays, is shown in Fig. 2 (lower panel). The bottom level at the paddle corresponds to m MSL in prototype. The tested breakwater section has been modelled in scale merging on site surveys and design information. Waves overtopping the structure's crest have been captured in a tray (Fig. 4). The width of this tray is 0.20 m, corresponding to the scaled width of the field tank. The tray leads the overtopped water to a container, positioned on a balance. The weighing procedure has been chosen following Kortenhaus et al. (2002) who have shown this technique to be the most reliable one for the purpose of these experiments. The water volumes expected to be captured influenced the container/balance design. The balance has to be accurate for small overtopping volumes and able to measure large volumes as well. This consideration led to a balance with a maximum weight of 100 kg. The water level decrease in the flume due to water reaching the tank (and thus leaving the flume) should be kept as small as possible. A maximum volume of about 35 l has been allowed to leave the flume before water is pumped back into the flume, behind the structure. This volume corresponds to a water level decrease of about 1.2 mm in the flume (corresponding to 2.4 cm in prototype). This very small decrease has been considered to be acceptable for the tests. The weight signal of the balance has been continuously registered and shown on a digital display. The water surface elevation has been measured using resistance wave gauges. The position of these instruments is shown in Fig. 2;two arrays of 3 gauges each have been used. Array 1 provides the wave characteristics at the position of the pressure sensor in prototype. Array 2, closer to the structure, provides wave characteristics at the toe of the breakwater. Wave gauge 2 (array 1) had a fixed position corresponding to the position of the pressure transducer, while the positions of the other two gauges of the same array 1 have been adjusted in order to better fit the conditions suggested by Mansard and Funke (1980) for separation of incident and reflected waves. Within array 2, wave gauge 6 had a fixed position at 2.00 m from the toe of the breakwater (i.e. 40 m in prototype), the position of the other two gauges of the array was varied depending on the characteristics of each performed test D experimental setup The 3-D physical model of the Ostia breakwater has been built in the wave basin of the laboratories of Flanders Hydraulics in Borgerhout (Belgium). The basin is 18.4 m long,19.3 m wide and 1.0 m deep. The area available for building the physical model has been 10.6 m long, 12.0 m wide and 0.49 m deep. The Froude scaling law has been used to scale the Ostia breakwater down to a 1:40 model. The largest possible scale has been chosen, the limiting factors being the stroke of the wave generator, the length and the width of the model area. The wave basin has been equipped with a piston type wave generator for both regular and irregular waves. This is 12 m wide and made of one paddle only, hence only long-crested waves can be generated. It can be rotated in order to vary the incident wave direction over 44 (i.e. 22 to the left and 22 to the right with regard to the normal mid-position of

4 4 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx Fig. 3. Upper panel: Layout of the 3-D model and basin at Flanders hydraulics, dimension in prototype scale. Lower Panel: Cross-section of the complete model setup in the basin along the normal to the overtopping tank (values in m model). the paddle). For 3-D experiments it has been possible to simulate different wave angles. Given the orientation of the breakwater in the basin, prototype storms in the sector N could be reproduced. The orientation will always be referred with respect to the North, unless otherwise stated. No active wave absorption is available for this facility. Wave reflection at the basin boundaries has been reduced by applying absorbing material behind the breakwater and next to its roundhead. At the end of the model there is also a gap in the side wall to give some reflected wave energy the possibility of escaping from the area in front of the breakwater. The sea bottom of the modelled area is show in Fig. 3 (upper panel). Fig. 3 (lower panel) shows the cross-section of the model along the normal to the tank. The seaward slope of the breakwater has been modelled as it was suggested by surveys of the breakwater carried out after the storms. Resistance-type wave gauges in the 3-D model have been placed along the normal to the overtopping tank. Their position is shown in Fig. 3. Three arrays have been used. One array (not shown on the figure) has been placed in deep water, in front of the wave paddle. Array 1 (wave gauges 1, 2 and 3) is in proximity of the position of the pressure transducer used in the field. Wave gauge 1 has been placed exactly at the position of the pressure transducer in prototype (bottom level 6.50 m MSL). As far as array 2 is concerned (wave gauges 4, 5 and 6), wave gauge 6 has been located at 1 m from the toe. Within each array the distances has been optimized for T p =9.85 s (typical wave period of measured storms) and kept constant. These distances are also acceptable for the wave periods (range 9 11 s) used in other tests.

5 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx 5 the rocks have been measured. For the filter and core elements the design drawings have been used. Details on material characteristics are given in Table 1. For the armour stones the following relationship between qstone ffiffiffiffiffiffiffiffi weight (W x ) and sieve diameter (D x ) was found: 3 Wx D x ¼ 1: This relationship has been verified to be accurate for both models. Porosity of the seaward armour, core and filter layers has been measured using a simple weight procedure. Considering the packing density in the 2-D laboratory model, a porosity of 38.7% has been measured for core and filter. Other packing densities have been tested in order to determine the porosity range. This ranged from a porosity of 35% for the densest packing to 43% for the loosest. Using the same procedure, a porosity of 43.5% has been measured for the armour layer. The densest and loosest packing resulted in porosity of 40% and 45% respectively. Porosity of the 3-D model has been determined as for the 2-D model. The measured porosity is 47% for core and filter layers and 48% for the armour layer. In order to compare the characteristics of the armour stones of the two models with the prototype, a shape factor a/b is defined as the ratio of the maximum dimension a of each armour stone to the minimum dimension b. The distribution in prototype of this ratio compares quite well with that of the 2-D and 3-D models. The ratio a/b for the 2-D model appears to be closer to the prototype one than the one in the 3-D model. 4. Performed tests Three types of tests have been performed in the two laboratories. A first set of experiments was intended to compare directly laboratory results with field measurements. For this set some of the prototype storms with measured overtopping have been reproduced in both laboratories. A second set of experiments concerned parametric tests carried out in order to investigate the sensitivity of the results to the variation of the water level, wave height and peak period. A third set of tests was carried out only in 2-D varying the tested structure and the bathymetry Reproduction of measured storms Fig. 4. Upper panel, aerial view of the breakwater roundhead and the overtopping tank. Central panel: detail of the overtopping capture system during a 2-D test. Lower panel: aerial view of the 3-D capture mechanism and the modelled structure. Waves overtopping the breakwater crest have been captured by an overtopping tank with an opening of 8 cm by 4 cm in the model corresponding to the overtopping tank of 4.0 m by 2.0 m in prototype. A screen has been built on top of it to collect the overtopping water exactly as in the prototype catching device. This overtopping tank is located immediately behind the crest wall, so the inflow for each overtopping event can be measured. The inflow in the overtopping tank has been measured by a load cell of 20 kg. The overtopping tank was large enough to collect the overtopping water of a whole test without need of evacuation of water during a test. From the overtopping measurements both average discharges and individual volumes could be derived. The technique used in computing the overtopping volume and discharge is based on the same procedure as used for prototype measurements (Briganti et al., 2005). The individual overtopping events have been identified using both an automated procedure and by visual inspection Breakwater characteristics in 2-D and 3-D The armour elements of the breakwater in both models have been selected on the basis of a prototype survey in which the dimensions of The prototype measurements have been reproduced as accurately as possible in laboratory. As reported in Briganti et al. (2005), seven storms with wave overtopping were measured in prototype. The reader is referred to Tables 2 and 3 of the cited paper for an overview of the analysis of these storms. As well as in Briganti et al. (2005), hourly values of wave and overtopping parameters have been used for the present study. Based on the information available at the time of the laboratory testing, four time intervals of 1 h each have been selected for reproduction in the two selected laboratories. Table 2 shows the storm conditions used for the reproduction. These particular time intervals are the ones with the maximum overtopping discharges during each storm. Note that the mean wave direction of the storm which occurred on October 8th 2003 is almost perpendicular to the cross-section of the overtopping tank (229 N). Table 1 Material characteristics in prototype and in the two models Layer Prototype 2-D Model (1:20 scale) 3-D Model (1:40 scale) Weight D n50 Weight D 50 (sieve) Weight D 50 (sieve) [kg] [mm] [g] [mm] [g] [mm] Core+filter Armour , (seaward) Armour (landward)

6 6 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx Table 2 Overview of the hydraulic parameters measured in prototype for the reproduced storms Storms Overtopping Date Reproduced hour q [m 3 /s/m] V max [m 3 /m] Njumps [ ] 08/10/ : /10/ : /10/ : /11/ : Storms Water level Waves at 14 m MSL calculated with SWAN Waves at 6.5 m MSL calculated with SWAN (wave recorder measurements) Waves at the toe ( 4 m MSL) calculated with SWAN Period [m MSL] H m0 [m] T p [s] H m0 [m] T p [s] Dir [ N] H m0 [m] T p [s] 08/10/ : (3.48) 9.56 (8.53) /10/ : (3.36) (9.85) /10/ : (3.17) (9.85) /11/ : The storm reproductions are based on the wave conditions measured in prototype by the pressure transducer. Since overtopping waves were always breaking at the position of the instrument, no accurate correlation exists between measured pressures and water surface elevations. A pressure transducer has been therefore placed at the foreshore in both models at exactly the same position as in prototype and iterative procedures were applied in order to generate waves inducing pressure spectra as similar as possible to those of prototype. Several tentative iterations have been necessary for each test in order to generate the proper sea state. A further difficulty is related to the limited length of the recorded pressure time series in prototype. Due to the characteristics of the measuring device, only approximately 13 min of sea surface records have been available every hour. Three different approaches have been tried in both 2-D and 3-D: 13 min time series has been scaled down to model, resulting in very short time series; a longer time series has been generated by repeating the 13 min prototype time series, smoothing the edges of each segment; a longer time series has been synthetically generated from the spectrum computed using the 13 min time series. All the three approaches have been used in the 2-D tests, while, in the 3-D tests best results were obtained using the third approach. All selected storm periods were reproduced in 3-D with both orientations of the wave generator Parametric and modified model tests These tests have been carried out both in 2-D and 3-D in order to study the variability of the overtopping in the two cases; they also provided more data for the CLASH overtopping database (Verhaeghe et al., 2003). In both setups random waves have been generated and wave height, peak period, still water level and the spectral shape (by changing the peak enhancement factor γ only) have been varied. A first series of tests has been carried out using the 2-D setup; this involved a structure built with a seaward slope of 1/4. Table 3 summarises wave height, period and still water level characteristics for these tests. A total of 95 tests have been performed using the original structure slope. A second series of tests has been performed in 2-D with the aim of investigating model effects that could have affected significantly the overtopping modelling. These tests involved modifications of the original setup. In other words these changes reflect the uncertainty of the experimental modeller when reproducing a maritime structure. These modifications are here listed and explained in details in the following: Closing the connection (CC, 6 tests performed) between the rear side of the breakwater model and the foreshore in order to avoid possible effects on the mean water levels in front of the breakwater. Adjusting the model slope (AMS, 15 tests performed), based on more recent surveys after the storm pointing out the steepening of the submerged slope. Lengthening the foreshore (LF, 16 tests performed) in order to check if the wave breaking was better modelled in this way. Making the core of the breakwater impermeable (IMP, 16 tests performed). These modifications have been applied cumulatively in the order they're listed. This implies that a direct comparison is not possible between tests with impermeable core and the original tests performed before the modifications, since the longer foreshore was always present in the tests with impermeable core. The number of tests carried out with these configurations is smaller than the first batch of tests. The connection between the rear side and the offshore side of the breakwater, which is present underneath the model and the foreshore, has allowed the overtopping water to flow back gently to the seaside without disturbing the incoming wave field. This connection might have caused lower overtopping since the wave setup at the structure might be lower. To investigate this effect, tests with exactly the same time series were performed with this connection closed. Bathymetric surveys in Ostia, carried out after the storms recorded in 2003 suggested that the submerged slope of the breakwater is Table 3 Test matrix for the parametric tests in the 2-D model involving a seaward slope of 1/2 (all values in prototype dimensions) Still water level [m MSL] H m0 [m] T p [s] D 2-D a 2-D D b D b D a D 2-D D b 2-D b 2-D b 2-D D a D a D a D 2-D 2-D 2-D 2-D D D 2-D 2-D 2-D 2-D D D b D b 2-D 2-D b 2-D 2-D b 2-D D 2-D b 2-D 2-D a b Tests performed only with AMS configuration. Tests performed both with the original slope and AMS.

7 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx 7 steeper than the emerged slope. The submerged slope seemed closer to 1/2 rather than 1/4. The model cross-section has been adapted consequently to investigate the effects on overtopping. Several tests were repeated with this modified structure using exactly the same time series of paddle movements as before the adjustment. The reason for lengthening the foreshore has been to try to reproduce in a better way the wave breaking process occurring in prototype. Here waves start breaking at a distance from the breakwater and keep on breaking over the whole foreshore. For this purpose, the foreshore has been lengthened by 4.50 m (i.e. 90 m in prototype), the maximum for this facility. This has been achieved by shifting the transition slope (1/10) towards the paddle. One of the uncertainties of the field surveys on the structure has been the estimation of the core and filter permeability. Hence, it has not been possible to estimate the accuracy of the reproduction of that characteristic in the tests. The possibility of obtaining reduced overtopping due to a larger permeability suggested to perform a further test series using an impermeable core. This has been obtained by removing the armour layer and by placing an impermeable thin plastic sheet on top of the core. Afterwards the armour layer has been replaced. 70 parametric tests were carried out in the 3-D model. Table 4 and 5 show the wave heights and periods of these tests. It is worth remembering that the seaward slope of the submerged part of the structure used has been 1/2. These tests can be divided in two groups: Five of the parametric tests performed in the 2-D model (AMS tests, i.e. with submerged seaward slope of the structure of 1/2) were selected to be performed in the wave basin too (see Table 5). All 5 tests had a water level of m MSL (i.e. about 1 m higher than in prototype conditions). Some of the parameters of the reproduced prototype storms have been modified. Table 4 summarises the characteristics of these tests. Two orientations of the wave paddle have been used corresponding Table 4 Test matrix of parametric tests in the 3-D model Still water level [m MSL] H m0 T p [s] [m] a,b b b a,b +1.5 a,b a,b a,b a,b a,b a,b a,b a,b a,b a,b a,b a,b a,b a,b a a,b a,b a,b a a,b a a a a a a a a,b a a,b a,b a,b a,b a,b a,b a,b Italic: test classified as breaking waves. a Test performed in test series CL4 (direction 235 N). b Test performed in test series CL5 (direction 223 N). Fig. 5. Dimensionless plot comparing storms reproduction in 2-D and 3-D. R ¼ Rc H m0 and q ¼ p ffiffiffiffiffiffiffiffi q. to 235 N and 223 N. 28 of the tests in Table 4 have been performed with both orientations of the wave paddle. These variations have been performed with a Jonswap spectrum instead of the measured prototype spectrum. A Jonswap spectrum with γ=2 (typical of Mediterranean waves) has been used. 5. Results This section deals with the description and the analysis of the results obtained in the laboratory tests. One question to be addressed when overtopping tests are carried out in laboratory is the repeatability of these tests. For this purpose the variability of the overtopping discharges has been tested by repeating tests with the same wave height and peak period. The tests have been performed either reproducing exactly the same time series of paddle displacement either preserving only the generated wave spectrum, thus varying the wave time series. Overtopping discharges appeared to be very well repeatable when using exactly the same time series; differences between the overtopping rate averaged over all the considered experiments (q mean ) and the overtopping rate of each of these was of the order of 5%. When only the spectrum was preserved among the experiments, the variability of the discharge depended on the value of the discharge itself. In particular distinction is to be made between very small overtopping discharges (e.g. q mean = m 3 /s/m at prototype scale) for which differences between the experiments of the order of 30% were observed, and larger overtopping discharges (e.g. q mean = m 3 /s/m), with differences of about 8%. In the following we will refer always to the average wave overtopping discharge q mean measured in tests with the same hydraulic characteristics but the suffix will be dropped. The results of the performed tests will be plotted in dimensionless plots using the following variables: R ¼ gh 3 m0 R c H m0;toe ð1aþ q ¼ q 1=2 ð1bþ gd Hm0;toe 3 where R c is the crest freeboard of the structure, H m0,toe is the significant wave height at the toe of the structure, q is the overtopping discharge per unit length, ξ m 1,0,toe is the surf similarity parameter at the toe of the breakwater. This has been computed using T m 1,0 i.e. the mean spectral period defined by the relationship T m 1,0 =m 1 /m 0,wherem 1 and m 0 are spectral moments of order 1 and0respectively.

8 8 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx Fig. 8. Comparison of parametric tests in 3-D with the two different paddle orientations. Fig. 6. Ratio between prototype overtopping discharge and upscaled model overtopping discharge giving an indication about scale/model effects Reproduction of measured storms Reproduction of the measured storms in laboratory has provided overtopping discharges smaller than prototype ones. Experiments carried out in 2-D have resulted in no overtopping at all for these conditions, while in 3-D tests discharges about one order of magnitude smaller than prototype ones have been measured. Results are shown in the dimensionless plot of Fig. 5. The storm that occurred on November 27th 28th 2003 has been reproduced in the 2-D model using different water levels. Overtopping in the model only has started at a water level m MSL (prototype measure), but overtopping discharges comparable to those of prototype have been measured only at a water level m MSL. It has to be reminded that in prototype the measured wave setup during storms has always been of the order of m. Experiments in 3-D have been performed using two different orientations of the wave generator. Defining Δβ as the angle between the direction of the wave attack and the aforementioned normal, the different test series carried out in 3-D are referred as follows: test series CL4 (235 N): Δβ=+6 test series CL5 (223 N): Δβ= 6. Results of the two test series are very similar, as it can be seen in Fig. 5. The wave direction does not appear to have a strong influence on overtopping, at least for the values of Δβ considered here. As a first conclusion, the accurate process of reproducing in detail the measured conditions during two overtopping storms resulted in small-scale model overtopping rates smaller than those of prototype. When looking at Fig. 5 it can be seen that dimensionless crest freeboards are generally smaller in the model than in the prototype case. Upscaling the overtopping discharges obtained in laboratory tests (in the following indicated with qss regardless of the model layout) allows to make a direct comparison between the prototype overtopping discharges and their model reproductions. Results of this direct comparison are given in Fig. 6. This figure gives on the X-axis the overtopping discharge which would be obtained by simply upscaling the model value by Froude law (q ss, upscaled). As a function of this upscaled overtopping discharge (q prototype ), the Y-axis shows the ratio between the measured prototype overtopping discharge and the upscaled model discharge (q ss ). In this way an approximation of the influence of scale and model effects on the overtopping discharge for the given structure (and by extension for other similar rubble-mound breakwaters) can be made. The graph also shows a conservative curve giving the influence of the scale and model effects as a function of the upscaled overtopping discharge. The curve is governed by following equations: 8 24:0 for q ssb1d 10 5 m 3 =s:m >< 3 log q f ss 2 scale model¼ 1:0 þ 23d for q ssb1d 10 2 m 3 =s:m : 3 >: 1:0 for q ss z1d 10 2 m 3 =s:m ð2þ 5.2. Parametric tests and modified model tests Parametric tests have been carried out to investigate the dependency, for the considered breakwater, of the overtopping on wave and level characteristics. Some degree of uncertainty does indeed affect the wave and level conditions measured in prototype. Tests with the modified model try to understand the effects of the uncertainties on the reproduction of the structure. Table 5 Test matrix for the parametric tests involving a submerged slope of 1/2 in both 2-D and 3-D setups (all values in prototype dimensions) Fig. 7. Dimensionless plot for all the 2-D parametric tests on the Ostia breakwater. Still water level [m MSL] H m0 [m] T p [s] X 2.80 X 3.00 X 3.50 X X

9 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx 9 Fig. 9. Comparison of parametric and modified structure tests in 2-D, parametric tests in 3-D and prototype results. The results of the parametric tests and of tests with the modified structure are plotted in Fig. 7 for the 2-D layout; they refer to a total of 148 experiments. Since a dimensionless plot is used, the effect of varying each individual parameter can be hardly separated. However, the results show that increasing the water level plays a stronger influence than increasing the generated waves height. All parametric tests with significant overtopping have been carried out with a SWL at +0.7 m MSL or higher. The effect of modifying the structure and the experimental layout appears to be negligible or, at least, no clear tendency in the results (increased or decreased overtopping) was observed. Results of the 70 parametric tests carried out in 3-D are shown on the plot of Fig. 8. In this case the most important result is that the direction of the generated waves plays a negligible role on the overtopping. This can be justified by reminding that the two inshore wave directions, due to refraction induced by the sea bottom, tend to be closer to each other than offshore ones. The five tests described in Table 5 all pointed out that, in the same conditions, the experiments in 3-D produced a higher overtopping rate than those in 2-D, confirming the findings of the storms reproduction. It is interesting to note that the results of 2-D and 3-D tests show a very similar behaviour. Superimposing the two plots (see also Fig. 9) a very similar dependency of q on R can be observed. However, as one may expect, the cloud of points related to 2-D is much more disperse than that of 3-D experiments. In the former case both the structure, the waves and the level have been largely varied, while in the latter only waves and levels only have been changed in the parametric tests. Finally, all the performed laboratory tests (a total of 230 experiments) have been compared (see Fig. 8) to the full prototype measurement database, i.e. to 86 h of overtopping. Despite having varied several properties of the tested breakwater, it is possible to conclude that the variation of the non-dimensional overtopping rate q with the nondimensional freeboard R obtained in the two independent laboratories is different from that obtained by prototype measurements. As for the prototype storms, laboratory tests underestimate the overtopping rates measured in the field. It is worth to stress that prototype overtopping rates have been obtained only for R above When using similar values in the laboratory only very few tests resulted in (quite small) overtopping. 6. Discussion and conclusions The paper presents the comparison between field measurements and the results of two experimental investigations on wave overtopping over a rubble-mound breakwater in shallow water. A portion of the west breakwater of the yacht harbour of Rome at Ostia (Italy), where the measurement station was located, has been reproduced in two independent Belgian laboratories with two different setups and scales. The field measurements carried out on the breakwater and described in Briganti et al. (2005) have been used to reproduce prototype storm conditions in detail. The reproduction of the actual storms (4 hourly averaged rates) didn't result in noticeable overtopping in the 2-D (1:20 Froude scale) model, while the discharges measured in 3-D (1:40) are considerably smaller than the prototype. In order to study the hydraulic response of the considered breakwater several parametric tests have been carried out, varying waves and water levels. The results of these tests have also been compared to the results of 86 h of prototype measurements of overtopping. As for the reproduction of the storms the overtopping obtained in laboratory tests is smaller than that obtained in the field. It is also difficult to quantify this difference, because most of the experiments which were carried out using prototype average conditions (and not reproducing in details time series of waves as for the reproduction of the storms) do not show overtopping. These results clearly suggest the presence of model and/or scale effects. A further important conclusion which is discussed later is that, the increase of the water level had a stronger influence with respect of increasing the generated wave height. Some possible model effects have been evaluated by varying some properties of the model breakwater, in order to take into account the uncertainties of the prototype geometry. Hence, the variation of the structure parameters such as the seaward slope (from 1:4 to 1:2) of the submerged part of the breakwater, or the core impermeability did not induce relevant differences in the results. Other variations of the layout, such as closing any hydraulic connection between the rear part of the breakwater and the offshore side (i.e. simulating a perfectly confined area) did not increase significantly the wave setup and, in turn, no increase in overtopping was observed. Furthermore, increasing the length of the foreshore, in order to better reproduce the breaking wave process in front of the structure also had a negligible effect. The feeling of the authors is that the most important reasons of the discrepancy between overtopping measured in laboratory and the one measured in the field, found in this research, are related to the wave breaking process. Visual observations during storms at the Ostia breakwater have shown that waves started breaking at hundreds of meters offshore the structure. The actual wave characteristics (height, asymmetry etc.) at the toe of the structure are strongly influenced by this process which, as well known, may suffer of scale effects when reproduced at small scales. Turbulence and air entrapment which characterize the broken waves propagation are also intense during the run-up on the mild seaward slope of the breakwater, therefore a further relevant potential source of scale effects exists. A model effect is related to the onset of wave breaking. In the two models waves started breaking at the position of the pressure transducer, i.e. just behind the steep transition slope. This process might be influenced by the transition slope and the onset of the process is expected to be more intense than that occurring in the case of a mildly sloping foreshore, as in the prototype. As a consequence, waves propagating towards the breakwater may have experienced dissipations stronger than those in prototype, resulting in different wave breaking process and finally wave characteristics at the structure toe. The water level at the toe of the structure plays, as mentioned before, an important role in overtopping. The previous considerations on wave conditions suggest the presence of a saturated surf zone, hence the wave height is controlled by the water depth. Increasing the water level during the experiments induces higher waves at the toe of the breakwater. Increasing the offshore wave heights may only induce (small) increases of the inshore level due to the wave setup; however, waves would still break along the foreshore and the resulting wave height at the toe would vary only slightly. This may explain the different sensitivity of the reproduced overtopping to variations of the water level and of the wave height. A further model effect may be induced by the breakwater's curved planshape at the section where the overtopping tank was installed.

10 10 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx This layout may influence locally the wave propagation, in particular wave reflection, modifying the incoming waves' properties at the toe of the breakwater. As a result, the direction of the reflected waves in the 2-D model may be different from that of the 3-D model and prototype. However the influence of these separate effects is very difficult to quantify; a graph and a formula are provided to estimate the influence of scale and model effects for structure at hand and for comparable situations. We expect that less dramatic conclusions would apply for maritime structures characterized by less intense wave breaking processes, both on the foreshore and on the structure itself. This is for example expected at the Zeebrugge breakwater, which has a deeper foreshore and a steeper offshore slope (Troch et al., 2004) or for vertical walls such as the one at Samphire Hoe (Pullen et al., 2004), also studied in the framework of CLASH. It is worthwhile to stress that the experiments carried out didn't account for the role of the wind in the phenomenon. In Briganti et al. (2005) it has been shown that wind speed up to 15 m/s has been recorded during the field measurements. It has also been suggested that an increase of the wind speed by a factor of about 2 produces an increase of the overtopping rate by a factor of about 5. This relationship, however, is based on a limited number of data. It is possible to conclude that the absence of wind in the laboratory experiments introduces a further model effect, even though it is impossible to quantify it. Other investigations carried out during the project CLASH (González-Escrivá et al., 2004) analyze this aspect for the Zeebrugge field case. Finally, the parametric tests carried out in both models can provide some guidance on the use of the Van der Meer et al. (1998) formula, largely used in coastal structures design, for the cases similar to the Ostia one. As shown in the Appendix of this paper the 2-D tests qffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fig. A1. Dimensionless plot comparing parametric tests and tests for a smooth and impermeable structure on the Ostia breakwater. Upper panel: breaking waves q ¼ p qov ffiffiffiffiffiffiffiffi s0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi gh 3 tan a m0 and R ¼ Rc s0 H m0 tan. Lower panel: non-breaking waves; R ¼ Rc a H m0 and q ¼ p ffiffiffiffiffiffiffiffi q. The VDM equation for smooth slope is shown together with 95% confidence bands. gh 3 m0

11 L. Franco et al. / Coastal Engineering xxx (2008) xxx-xxx 11 allowed the estimation of a best-fit value of γ f =0.35 of the roughness factor. Generally for all the parametric tests carried out both in 2-D and 3-D, a value of 0.4 gives acceptable results. This confirms the results of additional specific laboratory tests carried out within CLASH and described in Bruce et al. (2008-this issue). Appendix A Determination of the roughness factor for the Van der Meer et al. (1998) formula Aside from comparing the effects of different factors on overtopping, the performed parametric tests are useful to investigate the performances of existing formulae and eventually point out the differences between this dataset and the ones used for the formulae calibration. In this work the formula proposed by Van der Meer et al. (1998) has been taken into account and a further aim of the tests has been to determine the friction factor γ f used in this relationship. This investigation supports the findings of the more extensive laboratory tests investigation on the evaluation of γ f for different armour unit types carried out within CLASH and described by and Bruce et al. (2008-this issue). These tests have been carried out generally with steeper structures, however, the suggested γ f is comparable with the one suitable for Ostia case. Additional tests on an impermeable smooth structure have been carried out for comparison with the original structure. These tests have been also used to verify that results comparable to predictions from literature relationships were obtained using an impermeable smooth structure. This is a particularly important aspect since the original tests gave no overtopping when reproducing the measured storms. To obtain such characteristics without building a new structure, a smooth plate has been mounted directly on top of the existing rock breakwater model, resulting in a slightly higher crest level and a slightly flatter slope (1:4.4 instead of 1:4). Both aspects have been taken into account properly. Based on the wave characteristics at the toe of the breakwater, tests are plotted in a dimensionless graph using the following definitions: breaking waves R c R c ¼ H m0;toe d n m 1;0;toe ða1aþ q qd ð tan aþ 1=2 ¼ 1=2d ða1bþ gd Hm0;toe 3 nm 1;0;toe Non-breaking waves R ¼ R c H m0;toe ða2aþ q ¼ q 1=2 : ða2bþ gd Hm0;toe 3 This distinction is applied both for the original rubble slope and for the smooth one and the results are discussed separately. Breaking waves The dimensionless graph in Fig. A1 (upper panel) shows the theoretical prediction line for a smooth slope by Van der Meer et al. (1998), together with the 95% confidence interval (plotted in solid lines as well as the formula prediction). The diamond markers correspond to the new tests carried out on the smooth slope in the wave flume. The figure also reports the best-fit relationships found, together with the corresponding values of R 2, i.e. the coefficient of determination of the best fit. There is a strong correlation between these points as they fall just within the upper 95% confidence limit. Consequently, it can be concluded that for the standard case, the measured overtopping rates correspond rather well to the predicted values. However, all measured data points lay above the mean Van der Meer et al. (1998) prediction line. The roughness coefficient (γ f ) can be determined for the Ostia breakwater, starting from the measured data at the smooth slope as a reference case. To take into account the effect of roughness (and porosity) only, the effect of the permeable crest berm should be determined in advance. Once this is done, the roughness coefficient is physically meaningful and can be determined. To take into account the effect of the permeable crest berm, the methodology suggested by Besley (1999) has been applied to the data points. Besley introduced a correction factor (C r ) into the original Owen (1980) formula, however, C r may be used for the Van der Meer et al. (1998) relationship as well. C r is expressed in terms of the ratio between the permeable crest berm width (C w ) and the significant wave height, as given by the following relationship: C r ¼ 3:06exp 1:5 C w : ða3þ H m0 This factor has been determined by making use of Eq. (A3) and best fitting the data in the q R plane, as in Briganti et al. (2005), assuming C w =4 m (see Fig. 2). A reduction factor for the Van der Meer et al. (1998) formula C r =0.86 was obtained. This means that the overtopping discharges of the Ostia breakwater, in case the crest berm was not present, could be predicted by the dotted line in Fig. A1 (crest berm influence). The angle between the line related to the smooth dike and the dotted line has a physical meaning. It can be regarded as a measure of the roughness of the structure only (i.e. disregarding any crest berm). From the exponential part of both lines, the reduction factor due to only roughness is determined as γ f =0.35. Non-breaking waves The dimensionless graph in Fig. A1 (lower panel) shows the prediction line by Van der Meer et al. (1998) for non-breaking waves, together with the 95% confidence interval (also in solid lines). From this graph it is clear that the tests on the smooth structure all fall within this confidence interval. A good correlation between the data points is found as shown by the R 2. The same procedure used for breaking waves has been applied in order to determine the roughness factor. Again, the prediction line for the rough slope in case the permeable crest berm would not be present, is drawn in Fig. A1 (dotted line). This corresponds to a reduction factor C r =0.86, which is exactly the same value found for the breaking waves case. Calculation of the roughness coefficient starting from the best fit of the experimental data (thick dashed line) results in γ f =0.38, a value comparable to the breaking waves case. References Besley, P., Wave overtopping of seawalls. Design and assessment manual. Hydraulics Research Wallingford. R&D Technical Report W X. Briganti, R., Bellotti, G., Franco, L., De Rouck, J., Geeraerts, J., Field measurements of wave overtopping at the rubble mound breakwater of Rome-Ostia yacht harbour. Coastal Engineering 52 (12), Bruce, T., van der Meer, J.W., Franco, L., Pearson, J.M., 2008-this issue. Overtopping performance of different armor units for rubble mound breakwaters. Coastal Engineering. De Rouck, J., Troch, P., Van de Walle, B., van Gent, M., Van Damme, L., De Ronde, J., Frigaard, P., Murphy, J., Wave run-up on sloping coastal structures: prototype