van der meer_wave over topping at coastal structures

Infram publication no. 11

Wave overtopping at coastal structures: development of a database towards up-graded prediction methods

J. de Rouck 1 J.W. van der Meer 2

N.W.H. Allsop 3 L. Franco 4 and H. Verhaeghe 5

1 Professor, Ghent University, Dept. of Civil Engineering, Technologiepark 9, B-9052 Gent, Belgium, fax +32 9 264 58 37, [email protected] 2 Head Coastal Structures, Infram, PO Box 16, 8316 ZG Marknesse, the Netherlands,

fax +31 527241119, [email protected] 3 Technical Director, Maritime Structures, HR Wallingford, Prof. (ass.) Univ. Sheffield, UK, fax +44 1491825539, [email protected] 4 Professor, 3rd University of Rome, Principal Eng., Modimar s.r.l., via Montezebio 40,

00195 Roma, Italy, fax +39 0636000789, [email protected] 5 Ph.D.Student, Ghent University, Dept. of Civil Engineering, Technologiepark 9, B-9052 Gent, Belgium, fax +32 9 264 58 37, [email protected]

Paper presented at the 28th International Conference on Coastal Engineering, Cardiff, UK

1 De Rouck, Van der Meer, Allsop, Franco and Verhaeghe

WAVE OVERTOPPING AT COASTAL STRUCTURES: DEVELOPMENT OF A DATABASE TOWARDS UP-GRADED PREDICTION METHODS

J. de Rouck 1, J.W. van der Meer 2, N.W.H. Allsop 3, L. Franco 4 and H. Verhaeghe 5

Abstract: safe use of low lying and densely populated coastal regions depends critically on the performance of coastal structures in defending these areas against storm surges, wave attack, flooding and erosion. Continuing sea level rise and climate change (storms are becoming rougher) emphasise the need for reliable and robust predictions as higher storm surges and bigger storms may lead to flooding. Population pressures on land use in coastal regions have sometimes ignored age-old appreciation of coastal hazards. The CLASH research project EVK3-CT-2001-00058 is being funded by the EU to provide �Crest Level Assessment of coastal Structures by full scale monitoring, neural network prediction and Hazard analysis on permissible wave overtopping�. It is intended to produce generally applicable prediction methods based on permissible wave overtopping and hazard analysis. This paper describes the general approach of this major European project and more specific the development of a homogeneous overtopping database, which will be the basis for the general prediction methods.

INTRODUCTION

Assessment of the safety of coastal defence works requires reliable and well-validated prediction methods. Actually there is a lack of widely applicable and safe 1 Professor, Ghent University, Dept. of Civil Engineering, Technologiepark 9, B-9052 Gent, Belgium, fax +32 9 264 58 37, [email protected] 2 Head Coastal Structures, Infram, PO Box 16, 8316 ZG Marknesse, the Netherlands,

fax +31 527241119, [email protected] 3 Technical Director, Maritime Structures, HR Wallingford, Prof. (ass.) Univ. Sheffield, UK, fax +44 1491825539, [email protected] 4 Professor, 3rd University of Rome, Principal Eng., Modimar s.r.l., via Montezebio 40,

00195 Roma, Italy, fax +39 0636000789, [email protected] 5 Ph.D.Student, Ghent University, Dept. of Civil Engineering, Technologiepark 9, B-9052 Gent, Belgium, fax +32 9 264 58 37, [email protected]


prediction methods for structure design. However, there exist several overtopping formulae for coastal structures. They rely on empirical fitting of equations to overtopping data, which are available from model tests. These present methods are however applicable to a limited range of structure configurations and only give partial predictions, see Van der Meer et al. (1998) for dikes, Franco et al. (1994) for vertical walls and Besley et al. (1998) for shallow water conditions. So the available overtopping data for different structure types have not been integrated to give a single design method.

In addition, present prediction methods may be subject to scale or model effects. Scale effects refer to unwanted effects that appear as a result of the impossibility of correct scaling of a process, e.g. surface tension and kinematic viscosity. Model effects refer to unwanted effects that appear because of difficulties with correct modelling, e.g. the granulometry of the core of a rubble mound breakwater or wind effect on overtopping. The fact that present prediction methods may be subject to scale or model effects follows from a conclusion of the EU project OPTICREST (De Rouck et al., 2001). In this project it has been found that wave run-up Ru2% on rubble mound slopes, measured during full scale storms, was about 20% higher than modelled by selected hydraulic laboratories in small scale test facilities. This may lead to the tentative conclusion that scale or model effects may also be present for small scale testing on wave overtopping. Relatively few site measurements of overtopping have been made before. A single series of tests at large scale have been completed by the VOWS and Big-VOWS team (universities of Edinburgh, Sheffield and Manchester and HR Wallingford) to compare small and large scale tests to identify the occurrence and magnitude of possible scale effects. These results suggest that scale effects are not significant in mean overtopping for vertical walls, although these tests do not cover the model effect of not including wind (Bruce et al., 2002, and Pearson et al., 2002).

The CLASH research project (January 2002 - December 2004), funded by the European Community and consisting of 13 partners (see table1), is intended to deal with these problems and so improve knowledge about the overtopping phenomenon.

Table1. Partners of CLASH

PARTNER COUNTRY Ghent University (coordinator) Belgium

Flanders Community Coastal Division Belgium Flanders Hydraulics Belgium

Leichtweiss Institut für Wasserbau Germany Aalborg University Denmark

Universidad Politécnica de Valencia Spain Modimar Italy

Delft Hydraulics The NetherlandsInfram The Netherlands

Rijkswaterstaat The NetherlandsManchester Metropolitan University United Kingdom

University of Edinburgh United Kingdom Hydraulics Research Wallingford United Kingdom


The CLASH project has the following main objectives. A first objective is to solve the problem of the suspected scale/model effects. A second objective is to produce a generic prediction method for wave overtopping and so for crest height design or assessment. Also a description of allowable overtopping based on hazard analysis will be given. The prediction method will be realised by gathering all existing overtopping data in a homogeneous database, to screen it and supplement that database with the new full scale measurements and new scale model test results. Afterwards, a generally applicable design method will be developed with the use of neural network methods, including the conclusions on scale/model effects.

A neural network is a novel instrument which is an outstanding example of

recognising patterns in large data sets where there may be a large number of parameters and lack of physical understanding, see also Mase et al. (1995), Van Gent and Van den Bogaard (1999), and Medina (1999). OVERTOPPING MEASUREMENTS

Examination of possible scale/model effects requires a comparison of large scale overtopping results with small scale overtopping results. Because very little large scale overtopping measurements have been carried out in the past, full scale overtopping

Zeebrugge (Belgium) Ostia (Italy)

Petten (The Netherlands) Samphire Hoe (UK)

Figure 1. Measurement sites


measurements are crucial and will be established at 3 coastal overtopping sites in Europe (Belgium, Italy and UK). These prototype measurements will start at winter 2002/2003. The sites will be instrumented in such a way that both the incident wave field and overtopping discharges will be measured. At one additional measurement site (The Netherlands) the long wave phenomenon on very shallow water and breaking waves is investigated. The objective is here to understand the phenomenon of long waves (surf beat) and the effect on wave overtopping. The four sites are shown in figure 1.

The measured prototype storms will then be simulated in scale model tests

and/or by numerical modelling. Results of the modelling can then be compared with prototype results. This will lead to a firm conclusion on scale/model effects.

Another objective of the physical and numerical modelling is to generate more

data on overtopping to fill in gaps in the database. HOMOGENEOUS OVERTOPPING DATABASE First step: gather data

Large numbers of datasets on overtopping at several types of structures are available at research institutes and universities all over the world. Some of these datasets, which are based on generic tests or on tests of site specific locations, have already been assembled. However many other data have not been collected yet. Therefore the first task in creating a homogeneous database is to gather as much data as possible from all over the world. Not only the raw data (wave parameters, geometry and corresponding overtopping discharge) have to be gathered, but also details of measurement methods (such as wave measurements and overtopping measurements) and analysis methods are requested. This information is important for screening the data on reliability.

It has to be mentioned that also tests with no overtopping (discharge q = 0 m3/s/m) are assembled. These tests are necessary for the �training� of the neural network, in order to make predictions of zero discharge possible.

At present, a lot of data have been collected and re-analysed already. All kind of

structures are considered: dikes, rubble mound structures with rock or concrete armour, vertical structures, berm breakwaters and composite structures. Most tests are 2D but 3D tests are also included. As the tests concern overtopping measurements, only emerged structures are considered. Table 2 summarises the data that have been collected until now (September 2002).

More data are expected from several other institutions/countries such as CERC (USA), University of Kingston (Canada) and Japan and Europe.


Table 2. Available data

Hydraulic Research Wallingford (UK) basic tests → 1133 tests 34 projects → 956 tests Delft Hydraulics (The Netherlands) basic tests → 1019 tests 16 projects → 334 tests

Universidad Politécnica de Valencia (Spain), OPTICREST-data → 64 tests

University of Edinburgh (UK), VOWS-data → 317 tests Sigurdarson, 1993. → 39 tests Lissev, 1993. → 22 tests Mühlestein, 1992. → 96 tests Ahrens et al, 1986. → 239 tests Goda, 1975. → 126 tests Franco & Cavani, 1999. → 36 tests Modimar (Italy) :

• Enel-Hydro project tests → 151 tests research tests → 93 tests • Estramed-laboratories > 40 tested sections • University of Florence project tests → 149 tests research tests → 312 tests • Hydraulic laboratory of Padua

Leichtweiss Institut für Wasserbau (Germany) small scale tests → 323 tests large scale tests → 117 tests Aalborg University. Helgason, 1999. → 93 tests Pedersen, 1996. → 198 tests Kofoed, 2000. → 37 tests 1 project → 55 tests TOTAL → > 5909 tests

Second step: Select �general� formulae for comparison with data sets

To have a first idea of the reliability of the collected datasets, they are all compared with existing empirical prediction formulae. A general form of these formulae is:

(1) with q the mean overtopping discharge (m3/s per m width), Hmo the significant wave height based on spectral analysis (m) and Rc the structure crest freeboard relative to SWL (m). A and B are parameters of which the value depends on the considered

−=

m0

c

3m0

HR

.1.Bexp.AgH

qγ


formula. The parameter γ is a correction factor for the roughness and angle of wave attack (in case of dikes) or the geometry (in case of caissons).

The first form of the formula is the one that is prescribed by TAW (1999) for smooth dikes and non-breaking waves (Van der Meer et al., 1998). The value of the parameters A and B are here 0,2 and 2,6 respectively. The value of the parameter γ is 1 in this case (no reduction because smooth slope). The formula predicts relative large overtopping discharges and is considered therefore as an upper limit for all data. The second form of the formula is the one of Franco et al. (1994) for vertical structures. Here A = 0,2 and B = 4,3. The value of the parameter γ is 1 (vertical structure). The discharge is quite low compared to smooth slopes (and non-breaking waves) and it can be considered as a kind of lower limit. A prediction in between the two previous ones is that of Allsop et al. (1995) for vertical structures: A = 0,05 and B = 2,78. The value of the parameter γ is 1 (vertical structure). This prediction is considered as a mean value. The fourth formula is the one of TAW (1999) or Van der Meer et al. (1998) for dikes covered with rock or armour layers, for non-breaking waves. The formula is the same as the one for smooth dikes, except the value of the roughness factor γ is 0,5 instead of 1. This causes a lower prediction of overtopping discharge. Figure 2 gives an indication of the different formulae.

Figure 2. General formulae for dikes (non-breaking waves) and vertical structures

For breaking waves on dikes, the general form of an empirical formula is (TAW

2002):

(2)

−=

vβfb0m0

c

0b3

m0γ.γ.γ.γ.ξ

1.HR

. 4,75exp.0,067ξ.γ

tanα.gH

q

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4

Rc/Hm0

q/sqrt(gHmo3)

TAW 1999, dikes,non-breaking waves

Franco et al. 1994,vertical structures

Allsop et al. 1995,vertical structures

TAW 1999, dikes,non-breaking waves,j = 0,5

30/ mgHq

γf = 0.5


AcRc

hc

G c

B h

hb

α1

α2

ht

With: α the slope angle (°), ξo is the breaker parameter (-) based on the spectral period Tm-1,0 and γb, γf, γβ, γv correction factors for respectively berms, roughness of the slope, oblique wave attack and a vertical wall on the slope. Values for these correction factors can be found in TAW (1999, 2002) or Van der Meer et al. (1998). The value of the angle of wave attack β is zero for normal wave attack. Many other prediction formulae for overtopping exist (Bruce et al., 2001), e.g. the empirical formula of Owen (1980). They are not further considered here, although all Owen�s data are part of the available dataset. Third step: find a method to characterize all structures

The main aim of the database is to provide simplified data as input for a neural network. This means that all kind of structures (dikes, rubble mound structures with rock or concrete armour, vertical structures, berm breakwaters and composite breakwaters) have to be parameterised by means of a restricted number of parameters. The difficulty is to find parameters for all structure types that describe as much information as possible and still keep the number of parameters limited. A lot of information has to be described: armour type, porosity/permeability, crest width, crest wall, toe , berm, etc.

Figure 3 gives an indication of the parameters that will be used to describe a

rubble mound section.

SWL

Figure 3. Parameters to characterize a rubble mound section With:

γf : a correction factor for the roughness of the slope (-) cotα : the average slope angle (-) Rc : the crest freeboard in relation to SWL (m) B : the berm width, measured horizontally (m) hb : the berm depth in relation to SWL (m) Ac : the height of armour in front of the crest element (m) Gc : the width of armour in front of the crest element (m) h : water depth in front of the structure (m) ht : water depth above the toe of the structure (m) hc : total height of the structure (m)


An important parameter for overtopping is the roughness/permeability of or on the slope. This can be expressed by the correction factor γf. For a smooth dike γf =1. Values of γf for different kind of dikes and rubble mound structures are prescribed in TAW (2002).

To determine the average slope of the structure, one considers the points on the

slope 1,5*Hs above SWL and 1,5*Hs below SWL. The horizontal distance between these two points is Lslope. The average slope angle cot(α) is then obtained by dividing Lslope by 3*Hs. This is only valid if there is no berm between the two considered points on the slope. If there is a berm, the average slope angle is obtained by dividing (Lslope-B) by 3*Hs. Notify that the berm width is not considered when determining the average slope angle. This is the method used in TAW (1999) for dikes. Another approach could be to include the berm in the average slope angle, still keeping B and hb as berm parameters. If 1,5*Hs is larger than Ac, logically Ac is considered instead of 1,5*Hs. In this case the average slope angle is obtained by dividing (Lslope-B) by (1,5*Hs + Ac). The determination of the berm width B in case of a sloping berm, is as follows: the sloping berm is replaced by a shorter, horizontal berm with width B, by extending the upper and lower slope attached to the berm. The depth of the berm is expressed by the parameter hb and is measured at the middle of the berm. More detailed information about the characterisation of the slope and berm of a structure can be found in TAW (2002). Fourth step: reliability and complexity

There are still two difficulties one has to deal with before one can generate a homogeneous database. The first one encloses the fact that data are available for a lot of structures with many different sections while it is not possible to describe every detail of a complex section and therefore in case of a complex section, information may be lost. Therefore a complexity-index is assigned to each section. The complexity-index has the value 1 (very simple section), 2, 3 or 4 (very complex section). The sections at which a complexity-index of 4 is assigned, will not be considered for the database because too much information will be lost in this case by simplification.

The second difficulty encloses the fact that sometimes not all information of

tests is available and an estimation or calculation is needed then (e.g. wave height at the toe of the structure), which causes less reliable information. This is mostly the case for the wave parameters. It was decided to use the wave height and period at the toe of the structure, because it is thought to be most relevant that there is a relation between incident waves and overtopping. The problem herewith is that in quite a lot of tests, only wave parameters at deep water are measured. This means that it is necessary to derive the incident wave parameters by means of a numerical wave model. It was decided to use SWAN (Simulating WAves Nearshore), a third generation model developed at TU Delft, see Booij et al. (1999). Another frequent problem is that the wave period Tm is available (mean period) instead of Tp (peak period). In those cases assumptions of Tm/Tp are made.


Depending on the quality of the data, a reliability-index is assigned to each

section. The reliability-index can have the value 1, 2, 3 or 4. A value 1 means very reliable information. This is the case when all relevant data for the tests are available, the measurement and analysis method are correct and no information is missing. A value of 4 means no reliable data. These data will also not be used in the database. The data with reliability-index 2, respectively 3, are reliable, but some respectively more parameters had to be calculated/assumed. Fifth step: Compare data with general formulae

Figures 4 and 5 are examples of tested cross-sections, where the measured overtopping discharge has been plotted together with the empirical prediction formulae, described above.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4

Rc/(Hmo*x0)

q/sqrt(gHmo3)

*sqrt(tana )/x0

TAW 1999, dikes,breaking wavesdata breaking waves

vβfb0m0

c

γ.γ.γ.γ.ξ1.

HR

0b3

m0ξ.γ

tanα.gH

q

Figure 4. Example 1: simple dike with slope 1:6 The first example (Figure 4) concerns overtopping measurements over a simple

dike. The slope of the dike is 1:6 (seaside). The waves are breaking on the dike. A comparison can be made with the TAW 1999 formula for breaking waves on dikes. Although there is scatter, the figure shows a good agreement between de prediction formula and the performed tests. A reliability-factor of 1 is therefore assigned to the tests. The structure section is exactly characterised by cotα and Rc, so CF =1.

The second example concerns overtopping measurements over a battered wall

with a promenade. Figure 5 shows the tested section and the corresponding graph. As can be seen on this plot, measurements for normal wave attack as well as for oblique wave attack have been carried out. The results for the oblique wave attack show less overtopping than the tests for normal wave attack. The tests with the normal wave attack show an overtopping discharge lower than the discharge predicted by TAW (1999) for dikes, but higher than the discharge predicted by Allsop et al. (1995) for


vertical walls. Also here there is scatter on the data points, but one could say that the performed tests seem quite reliable at first sight, what makes the value of the reliability-index = 1 acceptable. It is not possible to describe the section of example 2 exactly with the parameters mentioned above. The best approximation of the section is the one that is obtained by using the parameters cotα, Rc and Gc. The approximation consists then of the battered wall followed by a horizontal crest with length Gc equal to the horizontal projection of the 1:30 slope. The fact that the crest is a slope is neglected here. That explains the choice of a complexity-index CF = 2.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4

Rc/Hm0

q/sqrt(gHmo3)

TAW 1999, dikes,non-breakingwavesFranco et al.1994, verticalstructuresAllsop et al. 1995,vertical structures

normal waveattack

oblique waveattack (45°)

30/ mgHq

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4

Rc/Hm0

q/sqrt(gHmo3)

TAW 1999, dikes,non-breakingwavesFranco et al.1994, verticalstructuresAllsop et al. 1995,vertical structures

normal waveattack

oblique waveattack (45°)

30/ mgHq

Figure 5. Example 2: battered wall with promenade


Sixth step All the data can be gathered in one database together with complexity- and

reliability-indexes. More than 5000 overtopping data have been gathered already at this moment (September 2002). For the neural network it is important that the database is complete, what means that overtopping data are needed in the whole parameter range, and this for all parameters. Probably there will be missing parameter ranges. These missing data, �white spots�, have to be filled with additional laboratory measurements. Probably these tests will contain tests on berm breakwaters. Also tests on roughness factors for various armour units like rock, cubes, tetrapods, dolosse, accropodes and core-locs will be performed. In this way, together with the measurements at site, a complete homogeneous data base will be established and will be input for the neural network.

Table 3 shows the parameters that will be used as input for the neural network.

Only the mean overtopping discharge is considered, so no percentages or individual overtopping volumes will be treated.

Table 3. Input parameters for the neural network

Hm0 toe (m) װ

Significant wave height measured at

the toe of the structure

Tp toe (s)

װ

Peak period

measured at the toe

of the structure

β (°) װ

angle of wave attack

h (m) װ

Water depth at

the toe of the

structure

Parameters to describe the

structure section:

γf (-), cot(α) (-), Rc (m), B (m), db (m), Ac (m)

and Gc (m)

Indexes:

Reliability-index RF

and Complexity-

index CF

q (m3/m/s) װ

Measured overtopping

discharge

There is still some discussion about the use of the wave parameters. Here it is proposed to use the wave conditions measured at the toe of the structure. Another method could be the method of Goda. In this method not the wave parameters at the toe of the structure, but the deep water wave conditions are used. It is necessary then to model the foreshore. Therefore Goda proposes to use the parameters Hm0 deep, Tp deep and m instead of Hmo toe and Tp toe. Here 1:m is the slope of the foreshore. Figure 6 explains the method of Goda. Deep water wave conditions: Hm0 deep, Tp deep

Figure 6. The method of GODA

Bathymetry

m

1 or 2 wave lengths

1


An advantage of the method of Goda is that one does not need to calculate the

wave conditions at the toe of the structure if they are not available. In case of a very irregular bathymetry, it is very difficult to describe the foreshore by a uniform slope. Probably both methods will be considered in the project.

CONCLUSIONS

A first completed homogeneous database will be ready at the end of 2002. A number between 7000 and 10000 data in the database is expected. This database will be anonymous without figures of cross-sections. With this completed database one can start for the neural network, which will lead to a first generic prediction method. During the second and the third year of CLASH, more data will be gathered (from institutions all over the world, from prototype measurements and from laboratory measurements). Halfway the third year (2004) a final database with a final prediction method will be available.

On behalf of establishing guidelines for crest level design for seawalls and

related sea defence structures, various levels of allowable overtopping discharge will be fixed. This will be done based on hazard analysis. The guidelines will be available at the end of the project (December 2004). ACKNOWLEDGEMENT

The CLASH project EVK3-CT-2001-00058 frames within the EESD programme of the Fifth Framework Programme of the EU. The financial contribution of the European Community is therefore very much acknowledged. The technical contributions of those who have provided data are also gratefully acknowledged. REFERENCES Allsop, N.W.H., Besley P. and Madurini L., 1995. Overtopping performance of vertical

and composite breakwaters, seawalls and low reflection alternatives. Paper 4.6 in Final Proceedings of MCS-project, MAS2-CT92-0047.

Aminti P., Franco L., 1988. Wave overtopping on rubble mound breakwaters. Proc. 21st Int. Conf. on Coast. Engrg., Vol.1, ASCE, New York, 770-781.

Besley P., Stewart T. and Allsop N.W.H., 1998. Overtopping of vertical structures: new prediction methods to account for shallow water conditions. Proc. Conf. Coastlines, Structures and Breakwaters, I.C.E., March 1998, publ. Thomas Telford, London.

Booij, N., L.H. Holthuijsen, and R.C. Ris, 1999: A Third-Generation Wave Model for Coastal Regions. 1, Model Description and Validation. J. Geophys. Res., Vol. 10, No. C, 7649-7666

Bruce T., Allsop N.W.H. & Pearson J., 2001. Violent overtopping of seawalls - extended prediction methods. Proc. Conf. on Shorelines, Structures & Breakwaters, September 2001, ICE, London.

Bruce T., Pearson, J. and Allsop, N.W.H., 2002. Hazards at Coast and Harbour Seawalls -Velocities and Trajectories of Violent Overtopping Jets. ASCE, Proc. ICCE 2002, Cardiff, UK.


De Rouck J., Boone C., Van de Walle B., 2001. OPTICREST, Final Report - Detailed scientific and technical report, MAS03/1031.

De Rouck J., Troch P., Van de Walle B., Van Gent M., Van Damme L., De Ronde J., Frigaard P., Murphy J., 2001. Wave run-up on sloping coastal structures: prototype measurements versus scale model tests. Coastlines, structures and breakwaters 2001, London.

Franco L., de Gerloni M. and Van der Meer J.W., 1994. Wave overtopping on vertical and composite breakwaters. ASCE, proc. 24th ICCE, Kobe, Japan, pp. 1030-1045.

Franco, L. and A. Cavani, 1999. Overtopping response of Core-Locs, Tetrapods and Antifer cubes. Proc. Conf. Coastal Structures '99, Vol. 1, pp. 383-388, AA-Balkema.

Mase H., Sakamoto M. and Sakai T., 1995. Neural network for stability analysis of rubble mound breakwaters. Journal of Waterway, Port, Coastal and Ocean Eng., Vol. 121, no. 6, ASCE.

Medina J.R., 1999. Neural network modelling of runup and overtopping. Proc. Conf. Coastal Structures '99, Vol. 1, pp. 421-429, AA-Balkema.

Owen M.W., 1980. Design of sea walls allowing for wave overtopping. Hydraulics Research Station, Wallingford. Report No. EX924.

Pearson J., Bruce T., Allsop W. & Gironella X, 2002. Violent wave overtopping - measurements at large and small scale. Proc. ICCE 2002, Cardiff, UK.

TAW, 1999. Technisch rapport golfoploop en golfoverslag bij dijken (Technical report on wave run-up and wave overtopping at dikes - in Dutch). Technical Advisory Committee on Water Defences.

TAW, 2002. Technical Report Wave run -up and overtopping at dikes, 2002. Technical Advisory Committee on Water Defences.

Van der Meer J.W., Tönjes P. and de Waal J.P., 1998. A code for dike height design and examination. Proc. Conf. Coastlines, Structures and Breakwaters, I.C.E., pp. 5-19. Ed. N.W.H. Allsop, Thomas Telford, London, UK.

Van Gent M.R.A., van den Bogaard H.F.P., 1998. Neural network modelling of forces on vertical structures. Proc. 26th ICCE, Copenhagen, pp. 2096-2109, ASCE.

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