Final report on laboratory measurements on the Ostia case

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List of tables

Table 1: Material characteristics in prototype and in the 2D model... 30

Table 2: Material characteristics in prototype and in the 3D model... 36

Table 3: Overview of storms with overtopping measured at the Ostia field site... 40

Table 4: Overview of storm conditions used for reproductions in the laboratories... 40

Table 5: Overview of accurate parameters (prototype measurements) of reproduced storms... 41

Table 6: Test matrix of parametric tests in the 2D model (all values in prototype dimensions)... 44

Table 7: Test matrix of additional parametric tests in the 3D model (all values in prototype dimensions). ... 45

Table 8: Repeatability tests: spreading on wave parameters. ... 49

Table 9: Evolution of Hm0 along the foreshore (3D model and prototype)... 50

Table 10: Repeatability tests: spreading on overtopping discharges. ... 52

Table 11: Reduction coefficients due to crest berm and roughness... 58

Table 12: Wave characteristics for investigation of influence of spectral shape... 58

Table 13: Incident wave heights at the toe of the structure. ... 71

List of figures

Figure 1: Model section with glass wall of the UGent wave flume... 9

Figure 2: Wave paddle of the Ghent University wave flume. ... 10

Figure 3: Array of wave gauges in the wave flume for determination of wave parameters. 11 Figure 4: Detail of tray to capture overtopping volumes... 12

Figure 5: Digital display of the balance... 12

Figure 6: Typical time signal of the balance, showing periods of pumping... 13

Figure 7: Calibration of pump... 13

Figure 8: Overtopping volume as a function of time... 14

Figure 9: Calculated Qin as a function of time. ... 14

Figure 10: Wave basin at Flanders Hydraulics. ... 15

Figure 11: Wave generator in the wave basin... 16

Figure 12: Array of 3 wave gauges and 1 pressure transducer in the wave basin. ... 17

Figure 13: Overtopping tank behind the crest wall... 18

Figure 14: Typical examples of analysed overtopping signals... 19

Figure 15: Location of Ostia yacht harbour along the Italian Mediterranean coast. ... 20

Figure 16: Plan of Ostia yacht harbour. ... 20

Figure 17: Detailed plan view of the prototype measurement station. ... 21

Figure 18: Plan view of the harbour indicating the modelled area for the 3D tests. ... 21

Figure 19: Design cross-section A of the breakwater (at rear side tout-venant with concrete pavement where the control tower has been built). ... 23

Figure 20: Design cross-section B of the breakwater (caisson element at rear side). ... 24

Figure 21: Design cross-section C of the breakwater at the location of the overtopping tank (rear side with armour layer, near the head)... 25

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Figure 22: Distribution of stone weights in the armour layer (based on calculations). ... 26

Figure 23: Sieve curve for the armour layer seaside based on both design values (3 – 7t) and values resulting from field measurements (model scale 1:20). ... 26

Figure 24: Overtopping tank at the Ostia breakwater... 27

Figure 25: Examples of registrated overtopping events at the Ostia field site. ... 28

Figure 26: Cross-section of the complete model set-up in the wave flume (values in cm model)... 29

Figure 27: Cross-section of the breakwater in the wave flume (values in mm model; elevations in m prototype)... 30

Figure 28: View at the model after construction of core + filter. ... 31

Figure 29: View at the model after construction of the armour layer front... 31

Figure 30: View at the model after construction of the armour layer back ... 31

Figure 31: Shape of the stones in the armour layer (2D model - prototype) characterised by ratio L/H. ... 32

Figure 32: Position and orientation of the Ostia breakwater in the wave basin. ... 35

Figure 33: Cross-section with the overtopping tank in the wave basin (values in m model). 35 Figure 34: View at the isolines of the seabed. ... 36

Figure 35: View at the crest element of cross-section C and the head of the breakwater. ... 36

Figure 36: View at the core and the armour layer at the seaside of the breakwater. ... 37

Figure 37: View at the breakwater (left: cross-section C with armour layer at rear side ; right: cross-section B with caisson element)... 37

Figure 38: Side view at the 3D model ... 37

Figure 39: Overview at the model in the wave basin... 37

Figure 40: Shape of the stones in the armour layer (3D model - prototype) characterised by ratio L/H. ... 38

Figure 41: Comparison between target pressure spectrum and measured spectrum in the flume (2 iterations). ... 42

Figure 42: Comparison between target pressure spectrum and measured spectrum in the basin (4 iterations). ... 43

Figure 43: Evolution of Hm0 along the foreshore (3D model). ... 50

Figure 44: Dimensionless plot for parametric tests on the Ostia breakwater – Breaking waves. ... 54

Figure 45: Dimensionless plot for parametric tests on the Ostia breakwater – Non-breaking waves. ... 55

Figure 46: Breaking waves - Comparison smooth structure to Ostia breakwater. ... 56

Figure 47: Non-breaking waves – Comparison smooth structure to Ostia breakwater. ... 57

Figure 48: Influence of the spectral shape on the overtopping discharge... 59

Figure 49: Incident wave spectrum – Example 1... 60

Figure 52: Influence of low cut off frequency – Breaking waves. ... 62

Figure 53: Influence of low cut off frequency – Non-breaking waves... 62

Figure 54: Influence of closing connection between seaside and “landside” (CC)... 65

Figure 55: 2D breakwater model with adjusted model slope (AMS). ... 65

Figure 56: Comparison between original data points and data points with adjusted model slope (AMS). ... 66

Figure 57: Comparison between datapoints with – without longer foreshore – Breaking waves (LF)... 67 Figure 58: Comparison between datapoints with – without longer foreshore –

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Non-Figure 59: Comparison between data points with – without impermeable core – Breaking

waves (IMP). ... 68

Figure 60: Comparison between data points with – without impermeable core – Non-breaking waves (IMP). ... 69

Figure 61: Dimensionless plot for storm reproductions on the Ostia breakwater – Non-breaking waves. ... 71

Figure 62: Influence of wave parameters (3D tests) – Non-breaking waves. Upper part: orientation CL4 of the wave paddle / Lower part: orientation CL5... 73

Figure 63: Comparison of parametric tests in 2D and 3D – Non-breaking waves. ... 74

Figure 64: Influence of wave direction (3D) – Non-breaking waves. ... 75

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List of symbols

Ac = height of armour in front of crest element in relation to S.W.L. [m]

B = berm width, measured horizontally [m]

Cr = average reflection coefficient (= m0,r/ m0,i ) [%]

CF = complexity-factor of structure section = 1, 2, 3 or 4 [-] h = water depth just before the structure (before the structure toe) [m]

hdeep = water depth in deep water [m]

ht = water depth on the toe of the structure [m]

hb = berm depth in relation to S.W.L. (negative means berm is above S.W.L.) [m]

Dn50 = nominal diameter of rock [m]

Dn = nominal diameter of concrete armour unit [m]

D(f,θ) = directional spreading function, defined as: [°]

S(f, θ) = S(f). D(f,θ) met

∫

= 0 2π 0 θ)dθ D(f, f = frequency [Hz]

fp = spectral peak frequency

= frequency at which Sη(f) is a maximum [Hz]

fb = width of a roughness element (perpendicular to dike axis) [m]

fh = height of a roughness element [m]

fL = centre-to-centre distance between roughness elements [m]

g = acceleration due to gravity (= 9,81) [m/s²]

Gc = width of armour in front of crest element [m]

H = wave height [m]

H1/x = average of the highest 1/x th of the wave heights derived from time series [m]

Hx% = wave height exceeded by x% of all wave heights [m]

Hs = H1/3 = significant wave height [m]

Hm0 = estimate of significant wave height based on spectrum = 4 m₀ [m]

Hm0,deep= estimate of significant wave height at deep water [m]

Hm0,toe = estimate of significant wave height at the toe of the structure [m]

k = angular wave number (= 2π/L) [rad/m]

Lberm = horizontal length between two points on slope, 1.0 Hm0 above and 1.0 Hm0

below middle of the berm [m]

Lslope = horizontal length between two points on the slope, Ru2% above and 1.5 Hm0

below S.W.L. [m]

L = wave length measured in the direction of wave propagation [m]

L0p = peak wave length in deep water = gT²p/2π [m]

L0m = mean wave length in deep water = gT²m/2π [m]

L0 = deep water wave length based on Tm-1,0= gT²m-1,0/2π [m]

mn =

∫

= n 2 1 f f n_S(f)df

f th moment of spectral density [m²/sn]

lower integration limit = f1 = min(1/3.fp, 0.05 full scale)

upper integration limit = f2 = 3.fp

mn,x = nth moment of x spectral density [m²/sn]

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Now = number of overtopping waves [-]

Nw = number of incident waves [-]

P(x) = probability distribution function p(x) = probability density function

PV = P(V ≥ V) = probability of the overtopping volume V being larger or equal to V [-]

Pow = probability of overtopping per wave = Now/ Nw [-]

q = mean overtopping discharge per meter structure width [m3/m/s]

Rc = crest freeboard in relation to S.W.L. [m]

RF = reliability-factor of test = 1, 2, 3 or 4 [-]

Ru = run-up level, vertical measured with respect to the S.W.L. [m] Ru2% = run-up level exceeded by 2% of the incident waves [m]

s = wave steepness = H/L [-]

s0p = wave steepness with L0, based on Tp = Hm0/L0p = 2πHmo/(gT²p) [-]

s0m = wave steepness with L0, based on Tm = Hm0/L0m = 2πHmo/(gT²m) [-]

s0 = wave steepness with L0, based on Tm-1,0 = Hm0/L0 = 2πHmo/(gT²m-1,0) [-]

Sη,i(f) = incident spectral density [m²/Hz]

Sη,r(f) = reflected spectral density [m²/Hz]

S(f, θ) = directional spectral density [(m²/Hz)/°]

t = variable of time [s]

T = wave period = 1/f [s]

Tm = average wave period (time-domain) [s]

Tp = spectral peak wave period = 1/fp [s]

TH1/x = average of the periods of the highest 1/x th of wave heights [s]

Ts = TH1/3 = significant wave period [s]

Tmi,j = average period calculated from spectral moments, e.g.: [s]

Tm0,1 = average period defined by m0/m1 [s]

Tm0,2 = average period defined by m₀/m₂ [s]

Tm-1,0 = average period defined by m-1/m0 [s]

TR = record length [s]

V = volume of overtopping wave per unit crest width [m3/m]

α = slope angle [°]

αwall = angle that steep wall makes with horizontal [°]

αberm = angle that sloping berm makes with horizontal [°]

β = angle of wave attack with respect to the structure alignment

(0° is perpendicular to the structure axis) [°]

η(t) = surface elevation with respect to S.W.L. [m]

γb = correction factor for a berm [-]

γf = correction factor for the roughness of or on the slope [-]

γβ = correction factor for oblique wave attack [-]

γv = correction factor for a vertical wall on the slope [-]

ξo = breaker parameter (= tanα/so1/2) [-]

µ(x) = mean of measured parameter x with normal distribution [..]

σ(x) = standard deviation of measured parameter x with normal distribution [..]

θ = direction of wave propagation [°]

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1 Introduction

The international CLASH project of the European Union (Crest Level Assessment of coastal Structures by full scale monitoring, neural network prediction and Hazard analysis on permissible wave overtopping, www.clash-eu.org) under contract no. EVK3-CT-2001-00058 is focussing on wave overtopping for different structures in prototype and in laboratory (De Rouck et al. (2003)). The main scientific objectives of CLASH are (i) to solve the problem of possible scale effects for wave overtopping and (ii) to produce a generic prediction method for crest height design or assessment. Therefore, wave overtopping events are measured at three coastal sites in Europe, namely at (i) the Zeebrugge rubble mound breakwater (Belgium), (ii) a rubble mound breakwater protecting a marina in Ostia (Italy) and (iii) a seawall in Samphire Hoe (United Kingdom). Those measured storm events are then simulated by laboratory tests and by numerical modelling and will be compared with the actual measured events. This will eventually lead to conclusions on scale effects and how to deal with these effects. Workpackage 4 of CLASH is aiming at the performance of model tests of these breakwaters. Partners in WP4 will perform both reproduction tests from storms observed in prototype and parametric tests to support analysis of the former and to give additional data for the overtopping database of CLASH (WP2).

Within WP4.2 laboratory investigations for the Ostia rubble mound breakwater are performed in the wave flume of Ghent University (later UGent) and in the wave basin of Flanders Hydraulics (hereafter FCFH). In order to check any influence that is typical for laboratory measurements and to identify possible causes for differences in results, tests with same characteristics are carried out in the two laboratories (UGent and FCFH).

This report describes laboratory facilities at both UGent and FCFH and results of the physical model tests carried out in those facilities.

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2 Test facilities

2.1 Wave flume at UGent

2.1.1 Wave Flume

The UGent wave flume measures 30.0 m long, 1.0 m wide and 1.2 m high. The overall design water depth is 80 cm. The maximum wave height in the flume is about 0.35 m. The walls of the flume are mainly made of reinforced concrete. A fifteen meter long section of one side wall is made of glass (30 mm thick), supported by a steel frame (Fig. 1). The rear end of the flume is closed off with a steel door. Removing this door allows people to enter the wave flume for model construction. The wave flume has four compartments which can be separated from each other by bulkheads in order to dry-dock very quickly one of the compartments for model construction and/or model adjustments. Openings in the side walls of the wave flume allow connection with pumps for tide and current simulations. The flume is equipped with the 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. All software is developed in-house at the Department of Civil Engineering.

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2.1.2 Wave paddle

A piston type wave paddle (Fig. 2) has been installed. The paddle is fixed to a moving open framework and moves on linear bearings. All mechanical and electrical connections and devices are located above the walls of the flume. The maximum stroke length is 1.50 m. The paddle displacement is accomplished by using an electro servo motor in step mode. The step motor is connected with the paddle using a spindle.

An updated version of the Wave Generation System ‘GENESYS’, i.e. a PC-based application software package, is used for generation of regular and random paddle displacement signals and for simultaneous acquisition of data from multiple wave gauges. Wave generation and DAQ procedures have been implemented using LabViewTM software. The paddle

displacements are controlled using a network connection between the PC and the real time controller of the wave generator.

The AWASYS active wave absorption system enables the wavemaker to generate the desired incoming waves and to absorb reflected waves simultaneously.

Figure 2: Wave paddle of the Ghent University wave flume.

2.1.3 Water surface elevation

For the determination of wave heights and wave periods typical resistance type wave gauges are applied (Fig. 3). Arrays of three wave gauges are used for reflection analysis at different positions in the flume. These arrays are required for the analysis of incident and reflected waves with the least squares method (Mansard & Funke, 1980). Furthermore, wave gauges are applied to measure the wave transformation through the flume. The positions of wave gauges used through the different tests are given further in this report.

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Figure 3: Array of wave gauges in the wave flume for determination of wave parameters.

2.1.4 Wave overtopping

Measurement technique

Waves overtopping the structure’s crest are captured in a tray (Fout! Verwijzingsbron niet gevonden. 4) The width of this tray was 0.20 m, in this case. The tray leads the overtopping water to a container which is positioned on a balance. It was chosen to measure the overtopping volumes by weighing technique since Kortenhaus et al. (2002) have shown this technique to be the most reliable one.

Different aspects had to be taken into account to make the design of the container / balance combination as appropriate as possible for these tests. For the balance a compromise between accuracy for small overtopping volumes and possibility to measure large volumes was envisaged. The volumes to be captured consequently influenced the tank design. Moreover 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. Finally a balance with a maximum weight of 100 kg and an accuracy of 5 g was chosen. A maximum volume of app. 35 l was allowed to leave the flume before water was pumped back from the tank into the flume (behind the structure). This volume corresponds to a water level decrease of app. 1.2 mm (corresponding to 2.4 cm in prototype, taking into account the 1:20 scale) in the flume. This very small decrease was considered to be acceptable for the tests. The weight signal of the balance is continuously registered and shown on a digital display (Fig. 5). Every time the maximum value (corresponding to app. 35 l) is reached, a pump starts pumping for a fixed time of 5 s. This fixed duration has been calibrated to correspond to the volume of approximately 35 l. The water is pumped back into the flume behind the structure. This part of the flume “communicates” with the part “seaward” of the structure by means of channels underneath the

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structure and foreshore. In this way the water is brought back in the flume without disturbing the wave field.

Figure 4: Detail of tray to capture overtopping Figure 5: volumes.

Digital display of the balance.

Calculation of overtopping discharges

Based on the measured weight of the overtopping water (= volume), the mean overtopping discharge during a test is calculated. Furthermore, as the weight is measured continuously, the overtopping discharge time series during each test is calculated by differentiation.

When performing the differentiation, the signal from the balance (Fig. 6) showing fast decreases when pumping, is corrected in the following way. The pump was calibrated carefully by repeating the 5 s pumping duration 14 times. Each of these 14 times the weight signal was registered. Fig. 7 shows all 14 time signals from this calibration. It is seen that the signal only varies slightly between different tests. Consequently, it is justified to calculate an “average” signal for this specific test set-up.

This average pumping curve gives the decrease of volume / weight as a function of time during such pumping event and thus gives the amount of water pumped out at every timestep. Consequently the time signal of the balance during an overtopping test can be corrected with the adverse of this pumping curve during each pumping event. This way a monotonously increasing weight signal is obtained (Fig. 8). From this signal the average overtopping discharge can be calculated using measured volume between two boundaries in time and dividing this volume by the appropriate time frame. Moreover, by differentiation a continuous overtopping discharge time series can be obtained (Fig. 9). Though in spite of all efforts it is not possible to make a perfect correction, which means that the overtopping time series is not completely correct at the time of pumping. This can be seen from Fig. 9. It appears that the overtopping discharge is sometimes negative. Of course, negative discharges can not occur, but this effect results form the disturbances in the water level at the time of pumping.

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the order of 30 s, model scale) this will be correct, even if pumping occurs within this frame. For reasons of completeness, it has to be mentioned that both wave analysis and calculation of overtopping discharges is based on the same time window, i.e. for this case the complete times series shortened by detracting 200 s at the start and at the end.

0 10 20 30 40 50 60 70 80 0 200 400 600 800 1000 1200 1400 1600 1800 Time (s) W e ight ( k g) Balance Signal

Figure 6: Typical time signal of the balance, showing periods of pumping.

35 40 45 50 55 60 65 70 75 0 1 2 3 4 5 6 7 8 9 1 Time (s) W e ight (kg) 0 pomptest1 pomptest2 pomptest3 pomptest4 pomptest5 pomptest 6 pomptest 7 pomptest8 pomptest9 pomptest10 pomptest11 pomptest12 pomptest 13 pomptest14

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0 100 200 300 400 500 600 700 800 900 0 200 400 600 800 1000 1200 1400 1600 1800 time (s) V o lu m e (l)

Figure 8: Overtopping volume as a function of time.

-2 0 2 4 6 8 10 0 200 400 600 800 1000 1200 1400 1600 1800 time (s) Q in (l/(s m ))

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2.2 Wave basin at FCFH

2.2.1 Wave basin

The 3D physical model of the Ostia breakwater is built in the wave basin of Flanders Hydraulics (Fig. 10). This wave basin is 18.4 m long, 19.3 m wide and 1.0 m deep. The model area (= area available for building the physical model) in this wave basin is 10.6 m long, 12.0 m wide and 0.49 m deep.

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The wave basin is equipped with a wave generator, one pump (60 l/s) to fill and empty the basin and to simulate a tidal water level variation and two pumps (2 x 200 l/s) to circulate the water and to simulate a longshore current.

2.2.2 Wave generator

The wave basin is equipped with a piston type wave generator for generating both regular and irregular waves. Standard wave spectra as well as measured wave spectra can be defined. The wave generator is 12 m wide. There is only one paddle, it is not a multi-paddle wave generator. Only long-crested waves can be generated (Fig. 11).

It is possible to rotate the wave generator in the wave basin and to vary the incident wave direction over 44° (i.e. 22° to the left and 22° to the right with regard to the normal direction). In this way oblique waves can be generated.

Because the wave generator is one paddle of 12 m wide, no active wave absorption is implemented in the steering software. Behind the breakwater model and next to the breakwater head passive absorption material is used to absorb as much wave energy as possible. At the end of the model there is also a gap in the side wall to give some reflected wave energy the possibility to ‘escape’ from the area in front of the breakwater.

Figure 11: Wave generator in the wave basin.

2.2.3 Wave gauges

For measuring the water surface elevation resistance type wave gauges are used.

9 wave gauges are placed in 3 arrays of 3 gauges to separate the measured waves into incident and reflected waves with the least squares method (Mansard & Funke, 1980) (Fig. 12):

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in deeper water : in front of the wave generator, bottom level –12 mMSL ;

at the location of the pressure sensor in prototype, app. 230 m in front of the breakwater,

bottom level –6.3 mMSL ;

at the toe of the breakwater, app. 40 m in front of the breakwater (distance according to

the recommendations of Klopman and van der Meer (1999)), bottom level -4.7 mMSL.

Figure 12: Array of 3 wave gauges and 1 pressure transducer in the wave basin.

2.2.4 Pressure sensor

To reproduce the prototype storms in the model it is prescribed to generate the same wave spectrum as measured in prototype. But the calculated wave spectra in prototype, derived from measurements with a pressure transducer, have an unrealistic shape in the higher frequency part. This causes an unacceptable behaviour of the wave generator when using these spectra as input for the wave generation.

Because the unrealistic shape in the higher frequency part is caused by the transformation from pressure to surface elevation, an extra pressure sensor is installed in the model at the same position as the pressure transducer in prototype (see Fig. 12). To reproduce the prototype storms as accurate as possible, the pressure spectra measured in the model are compared to the corresponding prototype spectra.

2.2.5 Overtopping tank

Waves overtopping the breakwater crest are 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 (Fig. 13). As in prototype a screen is built on top of it to collect the overtopping water. This overtopping tank is located immediately behind the crest wall, so inflow per overtopping wave can be measured.

The inflow in the overtopping tank is measured by a load cell of 20 kg. It was not possible to use the same measurement technique as in prototype (pressure cells in the overtopping tank) as this would give unreliable results in the small scale model.

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The overtopping tank is large enough to collect the overtopping water of a whole test without evacuation of water during a test. A first overtopping tank was designed based on the prototype measurements. After gaining the experience that the overtopping volumes in the model are smaller than in prototype, a second (smaller) overtopping tank was built, which was finally used.

Figure 13: Overtopping tank behind the crest wall.

From the overtopping measurements both average overtopping discharges and individual overtopping volumes can be derived.

Because of the small individual overtopping volumes it is difficult to identify automatically every small jump in the overtopping signal (continuous measurement of the weight of the overtopping tank). After processing the signal (identification of the larger jumps, if any), each signal is processed manually a second time. In between identified jumps (see Fig. 14) the weight sometimes increases very slowly caused by overtopping events that are too small to detect.

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CL5h06j20h30t99c -1.200 -1.100 -1.000 -0.900 -0.800 -0.700 -0.600 -0.500 -0.400 -0.300 0 200 400 600 800 1000 1200 1400 t [s] F_ ta nk [N] CL5h06j20h30t99c jumps F meas : 0.608 N_model Q : 0.13 l/s/m_proto Fmax indiv. : 155 l/m_proto Fmax indiv. : 0.095 N_model F indiv : 0.303 N_model number indiv. : 7 CL5h10j20h30t11c -1.000 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 0 200 400 600 800 1000 1200 1400 t [s] F_tank [N] CL5h10j20h30t11c jumps F meas : 8.246 N_model Q : 1.77 l/s/m_proto Fmax indiv. : 5870 l/m_proto Fmax indiv. : 3.599 N_model F indiv : 7.411 N_model

number indiv. : 21

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3 The Ostia breakwater models

3.1 Field site

3.1.1 Situation

The new private yacht harbour of Rome was designed by Modimar Srl. and built (1999-2000) along the eroding sandy shores of Ostia, about 25 km from Rome, just eastward of the main mouth of the river Tiber, at the Mediterranean coast (Fig. 15). The harbour is protected by two rubble mound breakwaters (the west breakwater extending for some 500 m, the east one for 650 m (Fig. 16)) which converge to a central straight entrance to form an elliptic-shaped outer harbour with variable (dredged) seabed elevations down to -5.0 m MSL.

Figure 15: Location of Ostia yacht harbour along the Italian Mediterranean coast.

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Near the head of the western breakwater, a fully instrumented overtopping measurement station was installed (Franco et al. (2003)). Fig. 17 shows a detail of the head of the western breakwater including the positions of the overtopping tank and the wave measurements. In the 2D model a section perpendicular to the breakwater, containing both the overtopping tank and the pressure sensor (i.e. wave recorder) is modelled.

The part of the breakwater modelled in the 3D model is indicated in Fig. 18. The grey parts are omitted. 2 different cross-sections are used. Cross-section A (at rear side tout-venant with concrete pavement where the control tower has been built) is replaced by cross-section C (rear side with armour layer). Cross-section B (caisson element at rear side) was built according to prototype.

Figure 17:

Figure 18:

Detailed plan view of the prototype measurement station.

B C

Plan view of the harbour indicating the modelled area for the 3D tests.

section B

_sectio

n C

B C B C

section B

_sectio

n C

section B

_sectio

n C

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3.1.2 Breakwater

Fig. 19 to Fig. 21 show design drawings of 3 different cross-sections of the breakwater. In the 3D model cross-sections B and C were used, while in the 2D model only cross-section C was relevant.

However field measurements of the rubble mound in front of the overtopping tank have shown clear deviations from the design drawing C (Modimar (2003)):

1) The seaward slope of the breakwater is rather 1/4 in stead of 1/3.5 and even 1/2 below the mean water level.

2) Weight distribution of core and filter layer are very similar.

3) Measurements of 111 stones of the armour layer in front of the overtopping tank were carried out. These measurements consisted of measuring three characteristic dimensions of each of these stones. Assuming a blockiness coefficient = 0.6, volumes of each of these stones were calculated as:

V =0.6*a*b*c

with:

a = horizontal projection of distance between the extremes of the rock along the major axis [m]

b = same distance along the minor axis [m]

c = same distance along the third axis perpendicular to the other 2 axes [m] The estimated value for the blockiness coefficient (0.6) seems rather high, but this is discussed further.

From the calculated volumes, stone weights were calculated using a stone density of 2650 kg/m³.

Fig. 22 shows the frequency distribution of the weight of all 111 measured stones. From this figure it is clear that the stones in the armour layer (seaside) correspond to a weight class which is considerably broader than the 3000 – 7000 kg class which is indicated in the design drawing.

Consequently this is a third modification to the design drawing taken into account for the design of the model. The influence of this third modification is shown in Fig. 23, where a logarithmic weight distribution (model scale 1:20) is drawn for the armour layer using both figures of the design drawing and figures based on the field measurements.

From the logarithmic diagram in Fig. 23 it is clear that the “new” distribution is considerably flatter than the theoretical one. Model stones are based on the distribution following from the one site measurements (blue line “linear” in Fig. 23).

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0.00 0.05 0.10 0.15 0.20 0.25 0.30 1400 2800 4200 5600 7000 8400 9800 11200 12600 >12600 Weight classes [Kg] Fr e que nc ie s

Figure 22: Distribution of stone weights in the armour layer (based on calculations).

0 10 20 30 40 50 60 70 80 90 100 10 100 D' [m m] m a s s p e rc e n ta ge pa s s t h ro ugh [% ] 3-7t 111 measured rocks linear

Figure 23: Sieve curve for the armour layer seaside based on both design values (3 – 7t) and values resulting from field measurements (model scale 1:20).

3.1.3 Overtopping tank

The overtopping tank is a steel tank with dimensions Length * Width * Height = 4.00 m * 2.00 m * 2.00 m. Its position on the western breakwater is indicated in Fig. 17. The water level in the tank is measured by continuous water pressure measurements. An Y-shaped weir allows progressive water outflow. A steel screen at the top catches the whole overtopping volume. Fig. 24 shows a picture of the tank at the field site.

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Figure 24: Overtopping tank at the Ostia breakwater.

3.1.4 Wave measurements

Waves in front of the structure are measured by a pressure transducer mounted near the seabed at a distance of about 200 m from the breakwater. Fig. 17 gives the exact position of this wave recorder. The wave recorder only measures during a limited time (ca. 13 min) every hour.

3.1.5 Bathymetry

The seabed in front of the breakwater was measured in a bathymetric survey in June 2002. The average slope from the breakwater’s toe to the position of the pressure transducer is about 1/65. However, the foreshore was modelled using exact distances between all depth lines in the modelled area.

3.1.6 Overtopping in prototype

Overtopping occurs several times a year at the Ostia breakwater. Fig. 25 gives two examples of registrated overtopping events.

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Figure 25: Examples of registrated overtopping events at the Ostia field site.

3.2 2D model at UGent

3.2.1 Model scale and flume set-up

The 2D model has been built to a 1:20 scale (Froude). This scale was the result of aiming at the largest possible scale and taking into account limitations of generating wave heights in a certain water depth.

Using this scale results in a model set-up as shown in Fig. 26. This figure shows a cross-section of the complete model set-up in the wave flume, indicating positions of wave gauges, position of foreshore, … The bottom level at the paddle corresponds to a level -14.00 m MSL in prototype.

Taking into account the 1:20 scale, the cross section of the breakwater shown in Fig. 27 has been built in the flume.

Additionally some modifications to the model have been made (see par. 6) to perform some extra tests.

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Figure 27: Cross-section of the breakwater in the wave flume (values in mm model; elevations in m prototype).

3.2.2 Construction of the model

Starting from the design drawing (Fig. 21), taking into account the modifications as mentioned in par. 3.1.2 and applying a Froude scale of 1:20, following material characteristics were obtained to use in the model (Table 1):

Table 1: Material characteristics in prototype and in the 2D model. Prototype Model (1:20 scale) Weight Dn50 Weight D50 (sieve)

Layer

[kg] [mm] [g] [mm] Core + filter 50 - 1000 439 3 - 330 27 Armour front 1000 - 13000 1290 241 - 2650 74 Armour back 2000 - 5000 1097 330- 950 63

For the armour layer at the rear side of the breakwater, only a weight range (2000 – 5000 kg) was given by Modimar. W50 has been determined, taking the mean value of 2000 and 5000

kg, i.e. 3500 kg. The relationship between weight and nominal diameter of the prototype rock is defined by 3 x x , n ₂₆₅₀ W = D .

For the model stones, the following relationship between stone weight and sieve diameter was

used : 3 x x ₂₆₅₀ W 15 . 1 =

D . The factor 1.15 in this equation has been verified (see par. 3.2.3).

Fig. 28, Fig. 29 and Fig. 30 show views of the model after construction of respectively the core + filter, the armour layer front and the armour layer back.

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Figure 28: View at the model after construction of core + filter.

Figure 29: View at the model after Figure 30: construction of the armour layer front.

View at the model after construction of the armour layer back

3.2.3 Characteristics of the model

Porosity

Porosity of both the armour layer front and the core + filter layer have been measured. This was done as follows:

- Weigh an empty large box: Wb [kg]

- Weigh the box completely filled with water: Wb+w [kg]

- Fill the empty box with stones and weigh it: Wb+s [kg]

- Add water to the box until it is full and weigh it: Wb+s+w [kg]

- Determine porosity: n = (Wb+s+w - Wb+s) / (Wb+w - Wb )

Stones were placed in the box in different packing densities.

For the core + filter layer a porosity of 38.7% was measured for a packing density as in the model. For the most dense packing tested a porosity of 35% was obtained while for the most loose packing tested a porosity of 43% was obtained.

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For the armour layer a porosity of 43.5% was measured. Most dense and most loose packings resulted in porosity of 40% and 45% respectively.

Characteristics of stones in the model armour layer

From the model armour layer on the seaside 102 stones (mostly taken from the part in front of the overtopping tank) were measured and weighed. The weight and three dimensions L, B and H were measured for each stone.

From the dimensions of each stone, the ratio L / H was calculated (i.e. ratio largest / smallest dimension). This value gives an idea about the shape of the stones: a ratio 1 means a cube or a sphere, the larger this ratio, the more elongated the stones are. The percentage of stones (number) exceeding certain values of L/H is plotted in Fig. 31. The percentages exceeding L/H = 2 and L/H = 3 are respectively 37% and 1%.

0 10 20 30 40 50 60 70 80 90 100 0.0 1.0 2.0 3.0 4.0 5.0 6.0 largest/smallest dimension L/H [-] P e rc e n ta g e l a rg e r [ % ] 2D model Prototype

Figure 31: Shape of the stones in the armour layer (2D model - prototype) characterised by ratio L/H.

Another parameter which gives an idea about the stones’ shape is the so-called blockiness coefficient. The latter is defined as the volume of the stone divided by its cubical dimensions:

[ ]

H • B • L V = B_k

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The mass density of all stones is 2650 kg/m³. The blockiness of all stones and the mean blockiness coefficient were calculated. Mean blockiness coefficient was found to be Bk = 0.456.

Relation stone weight – sieve diameter

As mentioned above following relationship (Shore Protection Manual (1984)) was used to determine the necessary stones to build up the Ostia breakwater model: 3

2650 W 15 . 1 = D . In

general this equation can be written as: 3 2650

W

. The factor K in this equation depends on the shape of the stones themselves. If this factor would deviate too much from the factor used in the calculations, the material should be adapted accordingly

K = D

.

Checking the factor K has been done as follows: for every fraction (core + filter, armour back and armour seaside) a representative number of stones has been randomly selected. For core + filter 200 stones were selected, while for both armour layer seaside and armour layer back 100 stones were selected. Each of these three “main fractions” was fineseaved. This means dividing the main fractions in as much “part fractions” as possible.

For each of the obtained part fractions were determined: − Gi: total weight of the part fraction [kg]

− Ni: number of stones in the part fraction [-]

− Gi / Ni: mean stone weight in a certain part fraction [kg]

− Dni = (Gi/(Ni *2650))1/3: mean nominal stone diameter in a certain fraction [m]

− Di: mean sieve diameter, i.e. mean of upper and lower sieve diameter used to obtain the

part fraction [m] − Ki = Di / Dni [-]

The K-factor of the used stones is the mean of all obtained Ki-factors. This way, a K-factor of

1.17 was found for all used materials. This value was judged to be sufficiently close to 1.15.

3.3 3D model at FCFH

3.3.1 Model scale

The Froude scaling law is used to scale the Ostia breakwater to a 3D model in a scale 1:40. The largest possible scale is chosen. The limiting factors are both the stroke of the wave generator and the length and the width of the model area.

Taking into account the depth of the wave basin, the bottom level of the basin is chosen at -12.0 m MSL. At the wave generator the relative water depth (h/L) is about 1/10, based on a peak period Tp of 11 s.

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3.3.2 Layout of the model

Preliminary information on the direction of overtopping waves restricted wave directions from the sector 200-250°N. As it is possible to rotate the wave generator and to vary the incident wave direction over 44° (i.e. 22° to the left and 22° to the right with regard to the normal direction), the normal direction in the wave basin is determined as 213°N. So the possible orientation of the wave generator is the sector 191-235°N (Fig. 32).

After building the model the storms measured in Ostia in the second winter season of the project showed a wave direction varying from 210°N to 234°N.

The orientation of the cross-section with the overtopping tank is approximately 229°N. So the possibility of generating perpendicular waves in this cross-section is included in the physical model. This is important for comparison with the 2D model. The layout of the cross-section with the overtopping tank is shown in Fig. 33.

The seabed was modelled up to app. 250 m in front of the structure (bottom level –5.5 to -7.0 m MSL and met a transition slope of 52 m (slope 1/8 to 1/10). The position of the wave recorder in prototype was included in the seabed model.

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229° N 235° N 234°N 223° N 21 0° N 213°N 19 1° N

Figure 32: Position and orientation of the Ostia breakwater in the wave basin.

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3.3.3 Construction of the model

Starting from the design drawings (Fig. 20 and Fig. 21), taking into account the modifications as mentioned in par. 3.1.2 and applying a Froude scale of 1:40, the material characteristics as found in Table 2 were used in the 3D model.

Table 2: Material characteristics in prototype and in the 3D model. Prototype Model (1: 40 scale) Weight Dn50 Weight D50 (sieve)

Layer

[kg] [mm] [g] [mm] Core + filter 50 - 1000 439 1 – 16 13 Armour front 1000 - 13000 1290 16 – 203 37 Armour back 2000 - 5000 1097 31 – 78 31

For the armour layer at the rear side of the breakwater, only a weight range (2000 – 5000 kg) was given by Modimar. W50 has been determined, taking the mean value of 2000 and 5000

kg, i.e. 3500 kg. The relationship between weight and nominal diameter of the prototype rock is defined by 3 x x , n ₂₆₅₀ W = D .

For the model stones, the following relationship between stone weight and sieve diameter was

used: 3 x x ₂₆₅₀ W 15 . 1 =

D . Factor 1.15 in this equation has been verified for the 3D model (see par. 3.3.4).

Fig. 34 to 39 show pictures of the model during construction and after completion.

Figure 34: View at the isolines of the seabed. Figure 35: View at the crest element of cross-section C and the head of the breakwater.

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Figure 36: View at the core and the armour Figure 37: layer at the seaside of the breakwater.

View at the breakwater (left: cross-section C with armour layer at rear

side ;

right: cross-section B with caisson element).

Figure 38: Side view at the 3D model Figure 39: Overview at the model in the wave basin.

3.3.4 Characteristics of the model

Porosity

Porosity of the model was determined exactly as for the 2D model described in par. 3.2.2. The stones were placed in the box with the same packing density as in the model. The following porosity’s were measured:

- core + filter layer : n = 47% - armour layer : n = 48%

Characteristics of stones in the model armour layer

A figure analogue to Fig. 31 is made up for the 3D model (Fig. 40). The percentages exceeding L/H = 2 and L/H = 3 are respectively 56% and 13%.

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Comparing Fig. 31 to Fig. 40 learns that the stones used in the 2D model are more similar to the prototype situation. However, for the longer and flatter stones, there is a better similarity in the 3D model. 0 10 20 30 40 50 60 70 80 90 100 0.0 1.0 2.0 3.0 4.0 5.0 6.0 largest/smallest dimension L/H [-] P e rc e n ta g e l a rg e r [ % ] 3D model Prototype

Figure 40: Shape of the stones in the armour layer (3D model - prototype) characterised by ratio L/H.

Relation stone weight – sieve diameter

The same way as was done for the 2D model (see par. 3.2.2) the K-factor describing the relationship between the stone weight and the sieve diameter was verified. For the 3D model this was done for the 2 main fractions of the 7 fractions that are used to compose the armour layer at the seaside (22% of this layer (between 20 and 50 mm) consist of fraction 35/40 mm and 22% consist of fraction 40/45 mm).

The following K-factors were found : fraction 35/40 mm : K = 1.26 fraction 40/45 mm : K = 1.17

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4 Test programme

Three types of tests have been performed:

− reproduction of measured storms with emphasis on wave overtopping (in 2D + 3D). − parametric tests, varying water level, wave height and wave period among others

(in 2D + 3D).

− tests with regular waves to calibrate numerical models (in 2D).

These tests and some additional tests to check repeatability and influence of spectral shape are described below.

4.1 Reproduction of measured storms

One main objective of CLASH is to reproduce measured storms in laboratory focussing on wave overtopping to draw conclusions on model and scale effects.

4.1.1 Field measurements

Storms with wave overtopping were measured in prototype. Table 3 gives an overview of the latest and most accurate analysis of these storms. For each storm the storm period (1 hour period) with the largest overtopping discharge q [m³/s/m] is entered in the table (wave recorder measurements in italic). More information on overtopping measurements and wave conditions during the storms can be found in deliverable D32 (report on full scale measurements, Ostia site, 2nd full winter season).

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Table 3: Overview of storms with overtopping measured at the Ostia field site.

Storms Overtopping

Waves at –6.5m MSL

calculated with SWAN

(wave recorder measurements) Date Period q [m³/s/m] Vmax [m³/m] Njumps [-] Hm0 [m] Tp [s] Dir [°N]

05/10/2003 05/10/2003 18:30 3.06 ∗ 10 -5 _{3.83 ∗ 10}-2 ₆ 2.84 (2.86) 8.39 (7.53) 232 08/10/2003 08/10/2003 05:30 3.17 ∗ 10 -4 _{6.10 ∗ 10}-1 ₅ 3.09 (2.95) 10.90 (9.85) 223 23/10/2003 23/10/2003 22:30 1.31 ∗ 10 -5 _{2.03 ∗ 10}-2 _{3 2.58}_8.39₂₃₂ 30/10/2003 30/10/2003 14:30 2.05 ∗ 10 -4 _{2.93 ∗ 10}-1 _{14 ? ? ?} 27-28/11/2003 28/11/2003 13:30 2.93 ∗ 10 -4 _{1.69 ∗ 10}-1 _{19 3.00}_9.56₂₂₇ 14-15/01/2004 15/01/2004 13:30 9.29 ∗ 10 -5 _{8.52 ∗ 10}-2 _{8 2.82}_10.90₂₄₆ 23-24/02/2004 24/02/2004 09:30 3.65 ∗ 10 -4 _{5.95 ∗ 10}-1 _{13 3.02}_9.56₂₂₈

Based on the information available at the time of the laboratory testing, 4 one hour storm periods were selected for reproduction in the laboratories. Table 4 shows the available storm conditions used for the reproduction.

Table 4: Overview of storm conditions used for reproductions in the laboratories.

Storms

(wave recorder measurements)

Date Period WL [m MSL] Hm0 [m] Tp [s] 08/10/2003 08/10/2003 06:30 0.12 (3.48) (8.53) 08/10/2003 08/10/2003 07:30 0.16 (3.36) (9.85) 08/10/2003 08/10/2003 08:30 0.26 (3.17) (9.85) 27-28/11/2003 27/11/2003 23:30 0.28 3.01 9.56

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However, the latest and most accurate analysis of the storms measured at the Ostia field site (Table 5) resulted in slightly different parameters (overtopping and water level), these most recent data were only obtained after finalizing the model tests.

Table 5: Overview of accurate parameters (prototype measurements) of reproduced storms.

Storms Overtopping

Date Period q [m³/s/m] Vmax [m³/m] Njumps [-]

08/10/2003 08/10/2003 06:30 1.72 ∗ 10 -4 _{2.09 ∗ 10}-1 ₆ 08/10/2003 08/10/2003 07:30 2.45 ∗ 10 -4 _{3.40 ∗ 10}-1 ₄ 08/10/2003 08/10/2003 08:30 2.26 ∗ 10 -4 _{2.87 ∗ 10}-1 ₃ 27-28/11/2003 27/11/2003 23:30 1.45 ∗ 10 -4 _{1.37 ∗ 10}-1 ₉ Storms Water level Waves at –14m MSL

(wave recorder measurements)

Waves at the toe

Period [m MSL] Hm0 [m] Tp [s] Hm0 [m] Tp [s] Dir [°N] Hm0 [m] Tp [s] 08/10/2003 06:30 0.11 3.35 9.56 2.95 (3.48) 9.56 (8.53) 223 2.31 9.56 08/10/2003 07:30 0.12 3.76 10.90 3.07 (3.36) 10.90 (9.85) 223 2.39 10.90 08/10/2003 08:30 0.16 3.37 10.90 2.93 (3.17) 10.90 (9.85) 234 2.30 10.90 27/11/2003 23:30 0.29 3.65 9.56 3.01 9.56 210 2.32 9.56

This means that the input parameters for all model tests are based on Table 4 and that model results are compared with Table 5.

Note that the storm dd. October 8th 2003 is almost perpendicular to the cross-section with the overtopping tank (229°N).

4.1.2 Storm reproduction

For the first storm reproduction, the storm with highest measured overtopping discharge in prototype was chosen (at the time of the experiments: the storm dd. October 8th 2003).

Reproduction of storms is based on reproduction of measured pressure spectra. For this purpose a pressure transducer was placed at the foreshore in the models at exactly the same position as in prototype (see Fout! Verwijzingsbron niet gevonden.. 12 and Fig. 26).

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Since in prototype only approximately 13 minutes of wave records are available every hour, three different approaches were used:

− 13 min time series was scaled down resulting in very short time series.

− different 13 min time series were put one behind another (incl. some smoothing were they are put together).

− from the spectrum belonging to 13 min time series a longer time series was calculated.

However, since waves at the position of the pressure transducer were clearly breaking, there is no direct correlation between the wave heights at that location and the paddle movements. Consequently different iterations were necessary to obtain an optimized approximation of the wave pressure spectrum.

Fig. 41 and Fig. 42 illustrate the reproduction of storms by comparing a target pressure spectrum to the measured spectrum in the wave flume (after 2 iterations) and in the wave basin (after 4 iterations).

frequency f [Hz] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Spp (f ) [k Pa 2 s] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 target spectrum iteration 0 iteration 1

Figure 41: Comparison between target pressure spectrum and measured spectrum in the flume (2 iterations).

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CL2s081003_0630 0.000000 0.010000 0.020000 0.030000 0.040000 0.050000 0.060000 0.070000 0.080000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 f [Hz] pr essur e spect ru m : S [ k Pa² s ] 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 w a v e s p e c tru m : S [m²s ] pressure prototype pressure run a pressure run b pressure run c pressure run d wave spectrum Ostia wave spectrum run d

Figure 42: Comparison between target pressure spectrum and measured spectrum in the basin (4 iterations).

In the 3D model 2 orientations of the wave generator have been chosen according to the wave directions in prototype at the location of the pressure transducer (calculated with SWAN):

• test series “CL4” : 235°N • test series “CL5” : 223°N

All selected storm periods were reproduced with both orientations of the wave generator.

4.2 Parametric tests

2D model

The results of the parametric tests will supplement the overtopping database with additional information. Main parameters which have been varied during these parametric tests are:

− water level − wave period Tp

− wave height Hm0

− peak enhancement factor γ

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Table 6: Test matrix of parametric tests in the 2D model (all values in prototype dimensions). Tp [s] Still water level [m MSL] Hm0 [m] 6.0 7.0 8.0 8.3 9.0 10.0 11.0 12.0 +0.00 3.00 X X +0.26 3.88 X 2.00 XX 3.00 X XX +1.00 3.50 XX XX X X 2.00 X X X X X 2.20 X 2.50 X X X X X 2.60 X 2.80 X 3.00 X X X X X X +2.00 3.50 X X X X

X: parametric test carried out in the 2D model

XX: parametric test carried out in both 2D and 3D model

3D model

The 3D model focused on reproduction of prototype storms. Nevertheless some parameters of the storm conditions have been varied and these variations could be used as extra parametric tests.

2 orientations of the wave generator have been chosen (according to the wave directions in prototype):

• test series “CL4” : 235°N • test series “CL5” : 223°N

Table 7 shows the test matrix of the additional parametric tests in the 3D model with information about Hm0, Tp and SWL. These so-called ‘additional parametric tests’ (3D) were

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Table 7: Test matrix of additional parametric tests in the 3D model (all values in prototype dimensions).

Still Water Level [m MSL]

Hm0 Tp [s] [m] 8.53 9.00 9.56 9.85 10.00 11.00 2.00 +1.00 2.30 +0.90 2.60 +0.90 2.80 +1.0 +1.5 3.00 +0.26 +0.40 +0.50 +0.60 +0.70 +0.80 +0.90 +1.00 +1.00 3.20 +0.28 +0.26 3.40 +0.28 +0.16 +0.26 3.50 +0.12 +1.00 +1.00 3.60 +0.12 +0.28 +0.16 +0.26 3.80 +0.12 +0.16 +0.26 4.00 +0.12 +0.30 +0.40 +0.50 +0.60 +0.70 +0.80 +0.90 +1.00 +0.16 +0.26

28 of the tests in Table 7 were performed with both orientations of the wave generator.

Almost all tests were classified as tests with non-breaking waves. Only these tests are presented in the graphs.

4.3 Tests with regular waves

Tests with regular waves were carried out to supply WP5 “Numerical Modelling”. Results from these tests were given to the UGent and MMU team to calibrate and validate the numerical modelling.

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4.4 Repeatability

To check repeatability of both wave characteristics and overtopping discharges several tests with the same target spectrum were performed (with both same and different time series of paddle movements).

4.5 Influence of spectral shape

Influence of spectral shape is investigated by generating both a Pierson-Moskowitz and a Jonswap spectrum with same target wave characteristics. For the Jonswap spectra three different peak enhancement factors γ are used (γ = 2.0, 2.7 and 3.3 respectively).

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5 Test results - Waves

5.1 Analysis method

The position of the wave gauges in the 2D model is given in Fig. 26. Within different arrays of three gauges distances have been changed continuously dependent on the water depth and the wave period in order to fit better to the conditions suggested by Mansard & Funke (1980). However, within array 1, yielding wave characteristics at the position of the pressure transducer, wave gauge 2 had a fixed position corresponding to the position of the pressure transducer. This wave gauge was positioned in such way to be at the position where the prototype bottom level was at -6.30 m MSL. Within array 2, yielding wave characteristics at the toe, 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 wave gauges in the 3D model was given in Fig. 33. Wave gauge C01 of the array at the foreshore (gauges C01, C02 and C03) was placed according to the position of the pressure transducer in prototype (at bottom level -6.30 m MSL), wave gauge C06 of the array at the toe of the breakwater (gauges C04, C05 and C06) was placed at 1 m from the toe and a third array (gauges D01, D02 and D03) was placed in deeper water in front of the wave paddle. Within each array the distances were optimised for Tp = 9.85 s (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.

All wave measurements were analysed using the software “WaveLab” provided by Aalborg University. The analysis was performed in different steps:

− Determination of time window for the analysis: to avoid the period of building up the waves in the beginning and damping out at the end of a test, a time window was determined for every test. In the 2D model a time window starting at t = 200 s and ending at t = tend – 200 s wasselected for every test (duration of selected window about

1600 s). In the 3D model a fixed time window of 1200 s, by cutting off 100 s at the start and 30 s at the end of a test, was selected for the analysis.

− Bandpass filtering: in the general methodology of all laboratory tests in CLASH it was agreed to perform bandpass filtering with the following parameters :

fc,low = min( fp/3 , 0.05 Hzproto )

fc,high = max( 3*fp , 0.5 Hzproto )

− Reflection analysis: incident wave characteristics were determined using the method by Mansard & Funke (1980). This method requires three wave gauges at a certain distance from each other, dependent on the wave length.

− Time domain and frequency domain analysis for individual wave gauges: for all wave gauges in the tests both a time domain analysis and a frequency domain analysis for the

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individual wave gauges are performed. Results do not account for the reflecting waves and are not directly used for further analysis.

The results for all tests are saved and key results (Hm0, Tp, Tm-1,0, Hs, …) are written to a

spreadsheet for further analysis. 5.2 Results

With regard to uncertainties related to wave analysis, distinction can be made between following sources of uncertainty tested in the wave flume:

− Reflection analysis vs. preconstruction tests: tests using exactly the same time series of paddle movements have been performed with and without the structure present in the wave flume. Despite the absorbent beach at the end of the flume reflection coefficients for tests without structure were up to 20 – 25%. This result suggests that wave analysis from tests without structure can not be used as incident wave characteristics for tests without the breakwater. However, reflection analysis for tests without structure results in the same wave characteristics as reflection analysis for tests with the structure in the flume.

− Generation of paddle movements: the movement of the paddle is among others dependent on the type of spectrum and a random phase. Assuming the same spectrum (same type, same Hm0 and Tp) the randomly chosen phase will result in a different time

series of paddle movements. Repeatability of wave parameters can be checked for different time series and for exactly the same time series (regenerating a previously saved file).

Table 8 gives coefficients of variation (i.e. standard variation divided by mean value) in percentage and proportional deviation from mean value for wave heights and wave periods at both the toe and at the position of the pressure transducer. All this is given for both using exactly the same time series as for using a different phase (seed).

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Table 8: Repeatability tests: spreading on wave parameters.

Variation of: Hm0,toe Tm-1,0,toe Hm0,pt Tm-1,0,pt

Coefficient of variation σ [%] < 0.30 < 0.39 < 0.21 < 0.08 Same time s eries mean mean x x x− [%] <1.20 < 1.60 < 0.70 < 0.30 Coefficient of variation σ [%] < 0.54 < 0.33 < 0.83 < 0.39 Differ

ent time ser

ies mean mean x x x− [%] < 1.89 < 0.92 < 2.27 < 0.90

pt= position pressure transducer

From Table 8 it is clear that wave characteristics are very well repeatable both when using exactly the same time series as when using a different phase. Overall, it can be stated that wave characteristics are repeatable with an accuracy of less than 3% compared to the mean values.

To check the evolution of the wave height and the wave breaking in the 3D model, the number of wave gauges in the cross-section of the overtopping tank was extended to 13. 3 wave gauges measured the waves generated by the wave maker, 10 wave gauges measured the waves along the foreshore built in.

Fig. 43 shows 5 different tests : 1 test (CL3s081003_0730b) with the same pressure spectrum at the pressure sensor (location indicated by a vertical line) and 4 tests with a Jonswap spectrum (γ = 2.0) and increasing wave height. It is clear that the wave height at the toe of the breakwater is depth-limited : higher generated waves do not result in higher waves at the toe.

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Hm0 in cross-section of overtopping tank -12.00 -10.00 -8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 -50.00 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 distance [m] bottom [m M S L] 0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00 4.40 4.80 Hm 0 [m _proto]

bathymetry water level

CL3s081003_0730b (total) CL3s081003_0730b (incident) CL3h02j20h34t99b (total) CL3h02j20h34t99b (incident) CL3h02j20h36t99b (total) CL3h02j20h38t99b (total) CL3h02j20h40t99b (total)

Figure 43: Evolution of Hm0 along the foreshore (3D model).

Also a different breaking process is observed in the wave basin. This is caused by the limited length of the foreshore that can be built in the wave basin. At the top of the transition slope (app. 1/10) all bigger waves are breaking and very few waves break closer to the structure, whereas in prototype wave breaking is continuously going on. This phenomena is clearly visible on video recordings of the model tests.

Table 9 summarises the parameters of the incoming waves (storm reproductions with measured spectra) to check whether this is also visible in the incoming wave characteristics. The model values are measured, the prototype values are calculated with SWAN.

Table 9: Evolution of Hm0 along the foreshore (3D model and prototype).

storm Deep (*) foreshore (-6.3mMSL) toe

period Hm0 Tp Hm0 Tp Hm0 Tp 08/10/2003 3.35 9.56 2.95 9.56 2.31 9.56 proto 06:30 3.23 10.79 2.93 10.79 2.40 11.26 model 08/10/2003 3.76 10.90 3.07 10.90 2.39 10.90 proto 07:30 3.44 10.36 3.08 10.79 2.49 9.96 model 08/10/2003 3.37 10.90 2.93 10.90 2.30 10.90 proto 08:30 3.42 8.93 3.11 8.93 2.52 9.60 model ( *) in proto: deep = -14mMSL in 3D model : deep = -12mMSL

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in prototype. This can be explained by the continuous breaking process in prototype that is not properly modelled.

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6 Test results - wave overtopping

6.1 Analysis method

The analysis method for wave overtopping has been described in detail in par. 2.1.4 and par. 2.2.5.

6.2 Results of the 2D model

6.2.1 Measurement uncertainties (repeatability)

Fout! Verwijzingsbron niet gevonden.10 gives coefficients of variation (i.e. standard variation divided by mean value) in percentage and proportional deviation from mean value for measured overtopping discharges. This is given for both using exactly the same time series as for using a different phase.

Table 10: Repeatability tests: spreading on overtopping discharges.

Variation of: q Coefficient of variation σ [%] < 1.5 / Same time s eries mean mean q q q− [%] < 5.5 / Variation of: q (q = 4.6E-06 m³/s/m) q (q = 9.6E-05 m³/s/m) Coefficient of variation σ [%] < 9.2 < 3 Differ

ent time ser

ies mean mean q q q− [%] < 30 < 8.3

From Table 10 it is clear that overtopping discharges are very well repeatable when using exactly the same time series. When using a different phase, distinction can be made between very small overtopping discharges (e.g. q = 4.6E-06 m³/s/m) and rather small overtopping

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spreading on the overtopping discharges depends clearly on the magnitude of the overtopping discharge. However, it can be stated that even for a rather small overtopping discharge (e.g. q = 9.6E-05 m³/s/m) overtopping discharges are rather well repeatable.

6.2.2 Presentation of overtopping results

Based on the wave characteristics at the toe of the breakwater, tests can be divided into on the one hand breaking waves and on the other non-breaking waves (van der Meer et al. (1998)). The overtopping measurements will be plotted in typical dimensionless graphs by using the following parameters (based on wave parameters at the toe of the breakwater):

• breaking waves

[ ]

toe , 0 , 1 m toe , 0 m c * c _H _• R = R ξ ( )

(

)

[ ]

toe , 0 , 1 m 2 1 3 toe , 0 m 2 1 * • H • g tan • q = q ξ α • non-breaking waves

[ ]

toe , 0 m c * c _H R = R

(

3

)

12

[ ]

toe , 0 m * H • g q = q 6.2.3 Storm reproductions

In the wave flume first the focus was put towards storm dd. October 8th_{2003, since this was}

the storm producing the highest overtopping discharge in prototype. All three approaches described in par. 4.1.2 were applied to reproduce this storm.

However, all three approaches resulted in zero overtopping in the 2D tests.

The storm dd. November 27th 2003, being the storm producing second most overtopping, was also reproduced. Also this reproduction resulted in zero overtopping.

Both storms were also reproduced with an adjusted model slope (see further, par. 6.3). But again these reproductions resulted in zero overtopping.

Final report on laboratory measurements on the Ostia case

Table of contents

List of tables

List of figures

List of symbols

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1 Introduction

2 Test facilities

3 The Ostia breakwater models

section B

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section B

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n C

section B

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n C

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4 Test programme

5 Test results - Waves

6 Test results - wave overtopping

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