Artificial Surf Reef on Maasvlakte 2

Transcription

1 Artificial Surf Reef on Maasvlakte 2 Msc. Thesis M.P. Muilwijk Final Version June 2005

2 Delft University of Technology II

3 Artificial Surf Reef on Maasvlakte 2 Msc. Thesis M.P. Muilwijk Final Version June 2005 Delft University of Technology Faculty of Civil Engineering and Geosciences Section of Hydraulic Engineering Thesis Comity: Prof.dr. ir. M.J.F. Stive Ir. H.J. Verhagen Ir. T. Vellinga Ir. J.G. de Gijt Ir. M. Henriquez Delft University of Technology Delft University of Technology Havenbedrijf Rotterdam/ TU Delft Gemeentewerken Rotterdam/ TU Delft Delft University of Technology The use of trademarks in any publication of Delft University of Technology does not imply any endorsement or disapproval of this product by the University Terrafix soft rock is a trademark of Naue GmbH & Co. KG Delft University of Technology III

4 Delft University of Technology IV

5 Preface The report before you is the final result of my master thesis. This thesis is the final part of my study at the hydraulic Engineering section at the faculty of Civil Engineering and Geosciences of the Delft University of Technology. The study was carried out in corporation with Havenbedrijf Rotterdam and Gemeentewerken Rotterdam and is titled: Artificial surf reef on Maasvlakte 2 During this project I had a lot of help and suggestions from the people of the Maasvlakte 2 project from Havenbedrijf. These people gave me a push in the right direction and helped with the realization of this project. Furthermore I would like to thank my supervisors, prof. dr. ir. M.J.F. Stive, ir. H.J. Verhagen, ir. J.G. de Gijt, ir. T. Vellinga, and ir. M. Henriquez Michiel Muilwijk June 2005 Delft University of Technology V

6 Delft University of Technology VI

7 Abstract The growing need for space to offer the opportunities for growth and renewal of port related activities for the port of Rotterdam has lead to the project mainport development Rotterdam. Within the framework of this project, a land reclamation has been foreseen, Maasvlakte 2. For this land reclamation two different types of sea defences will be applied, on the northern boundary a hard flood defence and on the western boundary a soft flood defence. Between these two types of flood defences a transitional construction must be placed. In the design of Maasvlakte 2, the transition between the hard and the soft flood defence has not yet been sufficiently defined. Furthermore, the transition construction of Maasvlakte 2 may offer a unique opportunity to apply an artificial surf reef. In this thesis research a number of alternatives for the construction of a combination between the transition construction and an artificial surf reef will be presented, where the surfing conditions have been analysed for each of the alternatives. For the design of the construction hydraulic boundary conditions are required at different locations. With the aid of the model SWAN the hydraulic boundary conditions, as they are determined at several locations in the North Sea are translated to near shore conditions. The hydraulic conditions on the North Sea have been transferred from marginal probability to condition with combined statistics with the aid of physical relations that exist between the different hydraulic parameters. To determine the optimum working point for the design the functions of the construction have been divided into three basic functions: constraining of the sand profile, blocking of the longshore transport, and creation of surfable waves. The optimum dimensions of the construction for the first two functions are defined with an economical analysis. The result of this was a relatively long dam which costs slightly less than 40,000,000. The toe depth in this case is NAP m and the crest height is NAP m. The surfing optimum was found with a reef that starts at a water depth of 2 meter. The optimum dimensions for the surf reef were found to be to rather different for the toe depth and the crest height of the dam with respect to the morphological functions. For a better fulfilment of the functions it is advisable to split the functions into two different constructions. The design that provides the best fulfilment of the functions is the alternative with a separate reef (see figure). The stability calculations show that constructing the Westdam similar to the Noorderdam is a reasonable option. The calculations of the sand containers that will be used for the construction of the surf reef show that the elements need a nominal diameter, D n50 of 3.4 m. Due to the dynamic behaviour of the beach in the zone where the reef is placed, it is recommended to do additional research on the morphology around the reef on the beach. Delft University of Technology VII

8 Table of contents Preface... V Abstract... VII Table of contents...viii List of figures... XII List of tables...xiv 1 Introduction General Problem analyses Problem definition Objective Outline of the report Theoretical research Introduction The Dutch coast Flood defences Soft flood defence Hard flood defence Transition construction Maasvlakte Introduction Maasvlakte Maasvlakte Artificial surf reef Introduction Characteristics of surfing Characteristics of a Dutch surf ride Characteristics of a surfbreak Summary surf reef Program of requirements Introduction Requirements General Requirements Functional requirements Constructive requirements Recreational requirements Environmental requirements Safety level and design Lifetime Hydraulic boundary conditions and SWAN Introduction Setup swan Parameter reduction Conclusions parameter reduction Results SWAN...33 Delft University of Technology VIII

9 4 Modelling Introduction Morphological model Longshore transport Morphological model Confinement of the profile Economical optimalisation Conclusions morphological model Surfing model Surfing waves Offshore wave field Near shore wave field Conclusions surfing Design Functional design Westdam Transition construction Artificial surfing reef Alternatives Confine alternative Blocking alternative 1, series of reefs Blocking alternative 2, separate reef Discussion functional design Discussion of elements Discussion of alternatives Constructive design Westdam Transition construction (Westdam) Artificial surfing reef Discussion constructive design Westdam Transition construction Surf reef Conclusions and recommendations Conclusions Recommendations References Appendices...65 A Simulating WAves Nearshore...67 Introduction...67 Technical specifications...67 Numerical implementation...68 Boundary conditions...68 B Operating procedure...69 Introduction...69 Delft University of Technology IX

10 Control points...69 Adjustments...69 Significance...70 C SWAN Setup...73 Introduction...73 Flow...73 Grids...73 Time frame...73 Boundaries...74 Obstacles...74 Physical Parameters...74 Numerical Parameters...74 Output...75 MDW file for SWAN...76 D Grids and bathymetry...79 Bathymetry...79 Grids...79 Nesting...80 E Timeframe/ flow...81 Water level Influence of flow on waves...81 F Boundary conditions...85 Introduction...85 Boundary definition...85 Three boundaries...86 Boundary discussion...87 G Parameter reduction...89 Introduction...89 Wave height and wave period...90 Wave height and wind speed...91 Wind speed and wave period...92 Wind speed and wind set-up...93 Wave height and wind set-up...94 Wave period and wind set-up...96 Conclusions...97 H SWAN Results...99 Contour 20 m...99 Westdam contour Delft University of Technology X

11 Surfing conditions Spectra I Morphological model Toe depth Crest height J Financial/ Economical Analyses K Wave Parameter explanation L Peel angle M Program of Requirements General Requirements Functional requirements Constructive requirements Recreational requirements Environmental requirements Safety level and design Lifetime N Erosion profiles Delft University of Technology XI

12 List of figures FIGURE 1-1 AERIAL PHOTOGRAPH OF MAASVLAKTE FIGURE 2-1 LOCATION OF THE PRIMARY FLOOD DEFENCES IN THE NETHERLANDS...6 FIGURE 2-2 MORPHOLOGICAL ZONE OF THE SANDY COAST, TAW (1999)...7 FIGURE 2-3 DUNE EROSION PROFILE...8 FIGURE 2-4 ELEMENTS OF A DIKE, FROM TAW (1999)...10 FIGURE 2-5 TRANSITION SHAPES OF TRANSITION CONSTRUCTION...11 FIGURE 2-6 EROSION PROFILE UNDER NORMATIVE STORM CONDITIONS, FROM TAW (1999)...11 FIGURE 2-7 ROTTERDAM AND THE MAASVLAKTE...13 FIGURE 2-8 PICTURE TAKEN FROM THE SLUFTER, LOOKING AT THE BEACH...14 FIGURE 2-9 PICTURE TAKEN AT THE START OF THE BLOKKENDAM...14 FIGURE 2-10 LOOKING WEST OVER THE BLOKKENDAM...14 FIGURE 2-11 LOOKING NORTH, THE BLOKKENDAM AND THE DIKE COME TOGETHER...14 FIGURE 2-12 PROFILE OF THE SEA DIKE, LOOKING NORTH...14 FIGURE 2-13 PORT ENTRANCE AND HARBOUR DAMS...14 FIGURE 2-14 CONTOUR OF MAASVLAKTE FIGURE 2-15 INITIAL CONCEPT HARD FLOOD DEFENCE...16 FIGURE 2-16 INITIAL CONCEPT SOFT FLOOD DEFENCE...16 FIGURE 2-17 INITIAL CONCEPT OF THE EXTENDED NOORDERDAM...17 FIGURE 2-18 PEEL RATE, FROM DAVEY (2005)...20 FIGURE 2-19 SURFER SKILL AS A FUNCTION OF THE PEEL ANGLE AND THE WAVE HEIGHT (HUTT, BLACK AND MEAD, 2001)...21 FIGURE 2-20 SCHEMATIZED SURF REEF, FROM HENRIQUEZ (2004)...22 FIGURE 3-1 WIND AND WAVE DIRECTIONS ACCORDING TO THE NAUTICAL CONVENTION, VALUES IN 10 1 º...27 FIGURE 3-2 BATHYMETRY OF THE NORTH SEA (HYDROGRAFISCHE DIENST KONINKLIJKE MARINE)...28 FIGURE 3-3 POSITION OF THE EXTERIOR GRID ON THE NORTH SEA...29 FIGURE 3-4 NESTED GRIDS...29 FIGURE 3-5 SPATIAL DISTRIBUTION OF THE WATER LEVELS ALONG THE DUTCH COAST...30 FIGURE 3-6 WAVE FIELD 10,000 YEAR RETURN PERIOD, 330º, MAASVLAKTE 2 PHASE FIGURE 3-7 SWAN OUTPUT CONTOUR NAP FIGURE 3-8 WAVE HEIGHTS ALONG 20 DEPTH CONTOUR LINE...34 FIGURE 3-9 SWAN OUTPUT CONTOUR WESTDAM...35 FIGURE 3-10 WAVE PARAMETERS AT THE PROPOSED WESTDAM LOCATIONS...35 FIGURE 3-11 WAVE FIELD USED FOR DETERMINATION OF SURFABILITY...36 FIGURE 4-1 SIDE VIEW OF BEACH PROFILE...37 FIGURE 4-2 TRANSPORT IMAGE OF MAASVLAKTE2 FROM BOER AND ROEKEMA, FIGURE 4-3 DISTRIBUTION OF THE LONGSHORE TRANSPORT OVER THE SURFZONE...40 FIGURE 4-4 DISTRIBUTION OF THE TRANSPORT OVER THE VERTICAL...40 FIGURE 4-5 BEACH PROFILE MAASVLAKTE 2 FROM EXPERTISE CENTRUM PMR, FIGURE 4-6 SCHEMATIZED CROSS SECTION OF THE WESTDAM...42 FIGURE 4-7 ECONOMICAL ANALYSES FOR THE TOE DEPTH AND THE FREE BOARD...42 FIGURE 4-8 THREE-DIMENSIONAL VISUALIZATION OF ECONOMICAL OPTIMUM...43 FIGURE 4-9 SIMPLIFIED BOTTOM TOPOGRAPHY FOR DETERMINING PEEL ANGLE...45 FIGURE 4-10 WAVE ANGLES AT SHALLOW WATER DEPTH...45 FIGURE 4-11 PEEL ANGLE AS FUNCTION OF THE REEF TOE DEPTH...46 FIGURE 5-1 CROSS SECTION OF SANDY PROFILE WITH WESTDAM...48 FIGURE 5-2 PLAN VIEW OF THE WESTDAM AND TRANSITION CONSTRUCTION...49 FIGURE DIMENSIONAL VIEW OF SURF REEF...50 FIGURE 5-4 PLAN VIEW OF CONFINE ALTERNATIVE...51 FIGURE 5-5 PLAN VIEW OF BLOCKING ALTERNATIVE 1, SERIES OF REEFS...52 FIGURE 5-6 PLAN VIEW OF BLOCKING ALTERNATIVE 2, SEPARATE REEF...53 FIGURE 5-7 EROSION PROFILE FOR A NORMATIVE STORM...56 FIGURE 5-8 CLOSE-UP OF REEF TIP...57 FIGURE DIMENSIONAL VIEW OF THE ALTERNATIVE...59 FIGURE 8-1 LOCATION OF CONTROL POINTS...69 FIGURE 8-2 NUMERICAL PARAMETERS...75 FIGURE 8-3 POSITION OF THE EXTERIOR GRID ON THE NORTH SEA...79 FIGURE 8-4 LARGE GRIDS AND SMALL GRID...80 Delft University of Technology XII

13 FIGURE 8-5 SPATIAL DISTRIBUTION OF THE WATER LEVELS ALONG THE DUTCH COAST...81 FIGURE 8-6 EFFECT OF CURRENTS ON WAVES, WAVE DIRECTION 225º...82 FIGURE 8-7 EFFECT OF CURRENTS ON WAVES, WAVE DIRECTION 315º...83 FIGURE 8-8 INTERPOLATED BOUNDARIES...87 FIGURE 8-9 WAVE STEEPNESS DEPENDENT OF RELATIVE DEPTH...90 FIGURE 8-10 (LEFT) FETCH LENGTH OF 650 KM AND (RIGHT) STORM DURATION OF 26 HOURS, FEBRUARY 1953, LICHT EILAND GOEREE, DOTTED LINE...91 FIGURE 8-11 WAVE HEIGHT WIND SPEED RELATIONS ACCORDING TO DEMIRBILEK ET AL...92 FIGURE 8-12 WAVE PERIOD WIND SPEED RELATIONS ACCORDING TO DEMIRBILEK ET AL...93 FIGURE 8-13 WIND SPEED AND WIND SET-UP...94 FIGURE 8-14 RELATION BETWEEN THE WAVE HEIGHT AND THE WIND SET-UP...95 FIGURE 8-15 RELATION BETWEEN WAVE PERIOD AND WIND SET-UP...96 FIGURE 8-16 TRANSPORT AS A FUNCTION OF THE RELATIVE TOE DEPTH FIGURE 8-17 TRANSPORT AS A FUNCTION OF THE RELATIVE CREST HEIGHT FIGURE 8-18 COSTS AS A FUNCTION OF THE CREST HEIGHT OF THE WESTDAM FIGURE 8-19 COSTS AS A FUNCTION OF THE RELATIVE TOE DEPTH OF THE WESTDAM FIGURE 8-20 WATER SURFACE FLUCTUATIONS IN A FIXED POINT ON THE NORTH SEA FIGURE 8-21 PEEL ANGLES AS A FUNCTION OF THE WAVE HEIGHT Delft University of Technology XIII

14 List of tables TABLE 2-1 SOFT FLOOD DEFENCE PARAMETERS...9 TABLE 2-2 PARAMETERS CONCERNING THE TRANSITION CONSTRUCTION...12 TABLE 2-3 PROFILE ARTIFICIAL DUNE...17 TABLE 2-4 SAND CHARACTERISTICS SOFT SEA DEFENCE...17 TABLE 2-5 PROFILE SEA DIKE...17 TABLE 2-6 BREAKER TYPE TRANSITION VALUES...20 TABLE 2-7 SUMMARY SURF REEF...23 TABLE 3-1 SURF WAVE REQUIREMENTS...25 TABLE 3-2 GRIDS USED IN SWAN SIMULATIONS...30 TABLE 3-3 HYDRAULIC PARAMETERS WITH A RETURN PERIOD OF 10,000 YEAR...31 TABLE 3-4 HYDRAULIC CONDITIONS FOR THE 330º DIRECTION, EUROPLATFORM...32 TABLE 3-5 HYDRAULIC CONDITIONS FOR THE 330º DIRECTION, IJMUIDEN...32 TABLE 3-6 WATER LEVELS AND WIND SPEEDS AVERAGED BETWEEN EUR AND YM TABLE 3-7 WAVE PARAMETER MAXIMA AT NAP - 20 M DEPTH CONTOUR...34 TABLE 3-8 WAVE PARAMETERS AT THE PROPOSED WESTDAM LOCATIONS...36 TABLE 4-1 OFFSHORE CHARACTERISTICS OF SURFING WAVES...44 TABLE 4-2 CONCLUSIVE OPTIMUM DIMENSIONS FOR THE DIFFERENT FUNCTIONS...46 TABLE 5-1 OPTIMUM DIMENSIONS FOR FUNCTIONS...47 TABLE 5-2 DIAMETER OF ARMOUR LAYER FOR THE WESTDAM...55 TABLE 5-3 DUNE EROSION IN METERS REGRESSION PER RETURN FREQUENCY...56 TABLE 5-4 GEO CONTAINER DIMENSIONS FOR STABILITY UNDER WAVE ATTACK...58 TABLE 8-1 HYDRAULIC CONDITIONSUSED FOR THE SETTING UP OF THE MODEL...69 TABLE 8-2 TABLE OF ADJUSTMENTS...70 TABLE 8-3 MDW FILE, COMMAND FILE FOR SWAN COMPUTATIONS...76 TABLE 8-4 WATER LEVEL AT MAASVLAKTE TABLE 8-5 EXTREME VALUES FOR 10-4 EXCEEDANCE FREQUENCY AT EUROPLATFORM...86 TABLE 8-6 EXTREME VALUES FOR 10-4 EXCEEDANCE FREQUENCY AT IJMUIDEN AMMUNITION DUMP...86 TABLE 8-7 EXCEEDANCE LEVELS WITH A RETURN PERIOD OF 10,000 YEARS AT EUROPLATFORM, 330º...89 TABLE 8-8 HYDRAULIC CONDITIONS FOR THE 330º DIRECTION, EUROPLATFORM...97 TABLE 8-9 HYDRAULIC CONDITIONS FOR THE 330º DIRECTION, IJMUIDEN...97 TABLE 8-10 WATER LEVELS AND WIND SPEEDS AVERAGED BETWEEN EUR AND YM TABLE 8-11 WAVE PARAMETERS (WAVE HEIGHTS AND PERIODS) Delft University of Technology XIV

15 1 Introduction 1.1 General Within the framework of the Project Mainport Development Rotterdam (PMR) the subproject land reclamation has been developed in order to deal with the growing need for space to offer the opportunities for growth and renewal of the port related activities. "The focus of the sub-project land reclamation is to realise a maximum of 1000 ha of port and industrial site (net allocation) next to the current port area. This land reclamation will take place in the shape of Maasvlakte 2." The proposed shape and position of this Maasvlakte can be seen in Figure 1-1. Also clearly visible in this picture is the current Maasvlakte, with on the south side the Slufter, the dark spot on the bottom side of the peninsula. Bordering on this Slufter is the Slufter beach with its Northwest orientation, further to the north, barely visible is the start of the Blokkendam, orientated roughly towards the southwest, and running round the head of the Maasvlakte where it meets the sea defence and finally it runs back towards the land just below the Euro-Maasgeul. The new land reclamation Maasvlakte 2 is indicated in this picture with the bright colours. Well recognizable is the port entrance to Maasvlakte 2, which goes through the current Maasvlakte. Figure 1-1 Aerial photograph of Maasvlakte 2 The current Maasvlakte is a very popular spot for recreation, especially for surfing. Because of its unique orientation a very good rideable beach break occurs attracting surfers from all over the country. The most popular spots are the Southern part of the Slufter beach and the Northern part of the beach just below the "Blokkendam", the transition between the beach and the dike. With the construction of the Maasvlakte 2 the beach will be moved to the outer contour of Maasvlakte 2. Because the beach is placed deeper into the sea probably even better surfing conditions can occur. Moreover, the presence of breakwaters and other possible hard coastal protection elements can offer even better possibilities to enhance the surfing conditions. Delft University of Technology 1

16 1.2 Problem analyses The design of the flood defence of Maasvlakte 2 consists partly of a hard flood defence and partly of a soft flood defence; "hard" flood defences are mainly dikes, like they are found in Zeeland in the southwest of the Netherlands. "Soft" flood defences are beaches and dunes as the ones that can be found along almost the entire west coast of Holland. On the Northwest corner of Maasvlakte 2 these two different types of flood defence will make a connection and therefore a transition construction will have to be applied. In the current design for Maasvlakte 2 this transition construction is not yet entirely specified. The dimensions of this construction are unclear and also the length of the Westdam that will protrude slightly is unknown. The hard flood defence is also known as the Southern dam (Zuiderdam) and its tip, the part that acts as a transition construction is named the Westdam. The nature and basis outline of the transition construction offer a unique opportunity to design an artificial Surf Reef at the end of the Zuiderdam. Which form of surfing will be stimulated and for what level of surfer, will depend on the possibilities from the wave climate and the construction and of the quality of the present surfing conditions. Obviously the design for the transition construction has to comply with the demands for safety and functionality of Maasvlakte 2. The Maasvlakte itself is a unique area because of its large scale almost extreme operations. Also today some extreme sports are enjoyed on the Maasvlakte. And the sport of surfing is something that fits very well within the extreme experience and therefore the promotion of this sport is recommended by some in the policy for the development of Maasvlakte Problem definition The transition between hard and soft flood defence has not yet been sufficiently defined in the design of Maasvlakte 2. This design facilitates a protrusion of the Zuiderdam but the actual shape and details of the construction have not been worked out. Furthermore, the construction of Maasvlakte 2 will offer an in potency unique opportunity to apply an artificial surf reef. This functionality fits perfectly with the extreme experience that by some is sought in the design of Maasvlakte Objective The design of a number of alternatives for the transition constructions between the hard and the soft sea defence, taking the surfing conditions into account. The design needs to comply with the primary functions towards the safety and the functionality of Maasvlakte 2 and has to contribute to the improvement of the surfing conditions. Delft University of Technology 2

17 1.2.3 Outline of the report This report describes the design of the transition construction with all its inherent functions. In Chapter 2 the theoretical research concerning the different elements of the Westdam are explained. First the flood defence system of the Netherlands is described, after which the applications of the flood defences on Maasvlakte 1 and 2 are explained. The last paragraph deals with the design of artificial surf reefs. The results of the theoretical research are summarized and quantified in the program of requirements, Chapter 3. The hydraulic parameters that are required for the design are determined by means of SWAN simulations and described in section 3.3. The morphological processes occurring at the Westdam are described in Chapter 4. After describing the functions a model to estimate the morphological consequences of the length of the Westdam is described. With this model an economical analysis is made and an optimal morphological design will be defined. Finally the model is described that is used to determine the optimum location and dimension of the surf reef. In Chapter 5, three possible alternatives for the layout of the Westdam and the surf reef are given. The functional design describes the basic layout of the alternatives and the constructive design gives an estimation of the elements of the construction based on design rules for the stability. Finally in Chapter 6 the conclusions and recommendations are given Delft University of Technology 3

18 Delft University of Technology 4

19 2 Theoretical research 2.1 Introduction In this chapter the theoretical research that was conducted is explained. The research was done in order to obtain information and parameters concerning the different elements of the construction of the Westdam. First the flood defence system of the Netherlands is described, after which the two basic types of hard and soft flood defence are explained. These two systems are also present in the design in Maasvlakte 2, as will become apparent in section 2.4.3, and are joined by the Westdam. Design criteria for the two separate systems are critical for the transition construction, which is discussed in section Next the current Maasvlakte is described, where again the two flood defence systems can be identified. Finally, the current design by EC-PMR (2003) is discussed, followed by an explanation of the working and the design criteria of Surf reefs. 2.2 The Dutch coast The Dutch coast is the boundary between the North Sea and the Netherlands. Because large parts of the Netherlands are located below sea level protection from the sea is very important along this coast. The protection against inundation is taken care of by the flood defence; according to TAW (1999) a flood defence is defined as a dune, dike, or other construction with the function to prevent flooding. According to the sort of protection that is offered and the hinterland that is protected, a flood defence can be a part of the primary flood defences. The following definitions are given: a Primary flood defence is a flood defence that offers protection against flooding by either belonging to the system enclosing a dike ring area, with or without high grounds- or situated in front of a dike ring area." And a dike ring area is defined as: an area that must be safeguarded by a system of flood defences against flooding, in particular in the case of high storm tide. The locations of the primary flood defences in the Netherlands are shown in Figure 2-1. Also indicated in this picture are the parts of the Netherlands that are located above sea level. Those are the parts of the country located to the right (east) of the fat line. The entire North Sea coast, except for the Maasvlakte is part of the Primary flood defences. The sea defences of the Maasvlakte do not meet the requirements for primary flood defences, mainly because the area they protect, the Maasvlakte is constructed well above sea level. Along the North Sea coast the flood defences mainly consist of a combined system of bank, beach and dunes, in which a number of artificial protection forms are found on a small scale, such as dune foot protections, beachheads, bank structures and quay walls (boulevards). According to TAW (1999) the coast can be divided into four basic types based on the nature of the flood defence: Dune coast, approximately 254 km Sea dikes, 34 km Beach planes, 48 km Other 27 km. The dune coast takes up the largest part of the Dutch coast and is only interrupted by the sea dikes at the Hondsbossche seawall, the Pettemeer seawall, IJmuiden, Katwijk, Scheveningen, Stellendam, Flaauwe Werk, the Westkapelse sea dike and the Westzeeuwsvlaamse dikes. The dunes and the dikes have a water defense function. Because of the dynamic behaviour of the sandy coast and the nature of the material, sandy coastal defences are referred to as "soft" sea defences. Similarly the seadikes are called "hard" sea defences because of their typically static and robust nature. These two Delft University of Technology 5

20 types of sea defences behave in completely different ways and are constructed using different design strategies. Although different in nature for both flood defences the term strength plays an important role. The strength implies that the flood defence must still be able to function (for the dune coast this means: no break trough, and for the dike it means: wave overtopping within bounds) for the circumstances according to the design conditions. The basic elements and the design strategies for both the hard and the soft sea defences are described in the following sections. Primary flood defences Figure 2-1 Location of the primary flood defences in the Netherlands Delft University of Technology 6

21 2.3 Flood defences Since a hard and a soft flood defence are connected at Maasvlakte 2, some background knowledge of the flood defences will be helpful. In this section the soft flood defence will be described, with at the end a table showing the parameters needed to evaluate the design. In section the same is done for the hard flood defence, and in section the transition construction as a whole is discussed Soft flood defence In TAW (1995) the sandy coast is defined as follows: The sandy coast covers the stretch of coast where the dunes (sometimes supported by hard defence elements, such as beach heads and dune foot protection), together with the beach and the foreshore, form the boundary area between land and sea. An important feature of a sandy flood defence is its ability to adapt to the situation. When during a storm surge the flood prevention of the dune is claimed the dune will deform. This deforming will be accompanied by dune erosion and gives (in contrast to a dike) the flexible character of a dune in flood prevention. When the normal conditions have established again the profile recovers. Elements and Morphological zones On the sandy coast a number of elements can be distinguished. The terminology is universal and will be used throughout this section and the next. Because each of the elements has its own effect on the coastal development, the sandy coast is often divided into four morphological zones. The four zones can be found in Figure The sea bottom. The sea bottom has a very gentle slope, typically 1:1000, and starts at a depth of NAP -20 m because it is generally assumed that the processes seaward of this depth do not have a direct morphological influence; 2. Foreshore. The beginning of the foreshore is identified by a change in slope. Here the relatively flat sea bottom with a slope of 1:1000 transitions into the more steep foreshore with a typical slope of 1:100 to 1:200; 3. The beach. The beach is the zone between the foreshore and the dunes. The seaward boundary is the average low water tide line and the landward boundary is the dune foot, this is where the flat beach turns into the steep dune. The beach can be divided into the wet beach, which is located between the average low water tide line (GLW) and the average high water tide line (MHW), and the dry beach, which is located between GHW and the dune foot; 4. The dunes are the elements of the coastal profile that offer the actual protection against flooding. Important features are the dune width and the height of the crest of the dune. The dunes start at the dune foot on the seaside and end on the inside edge, on the landside. Figure 2-2 Morphological zone of the sandy coast, TAW (1999) Delft University of Technology 7

22 Strength and load The strength of a dune flood defence depends mainly of the total amount of sand in the profile. The amount can be found both in the height and the width of the profile. When a dune flood defence contains more sand during design conditions than the amount that can be eroded and still have a minimum profile according to the limit profile the flood defence is considered safe. The minimum profile as determined in TAW (1995) will be explained at the end of this paragraph. On the sandy coast two important morphological processes occur that can have a large effect on the stability of the coast. These two processes are dune erosion and structural erosion. The dune erosion process is a relatively fast cross-shore transport process that takes place during heavy wave attack in combination with high water level. When no seaward or lateral losses occur, the sand balance is sound in the cross-shore direction. The eroded material ends up on the foreshore that starts to act as a breakwater, preventing further erosion. During quiet periods the material is transported back towards the flood line. Structural erosion occurs when gradients exist in the long shore transport (the term longshore transport will be explained in section 0). In this case the profile does not recover itself and material can be lost from the dune area. In narrow dune areas structural erosion, could in time cause the safety of the flood defence to fail the safety norms defined in the Flood defence act (WWK, 1996). In other words, the flood defence is no longer safe and can collapse under design condition. Erosion profile As a result of dune erosion under normative conditions the normative erosion profile occurs, this profile can be calculated according to the following formula (TAW, 1995): w y = x H0s H0s In this formula H 0s is the significant wave height and w is the fall velocity of the sand grains. The x and the y- coordinate start at the level of MHW, or the SWL under normative storm conditions, and are positive in x-direction in a seaward direction. Landward of the zero point, the dune foot starts with a slope of 1:1 and the erosion profile ends at: x = 250 ( H 0s / 7.6) ( / w) y = H / 7.6 ( ) 0s 0.5 Figure 2-3 Dune erosion profile Beyond this point the profile continues at a slope of 1 : 12.5 until it intersects with the original bottom profile. In Figure 2-3, this profile is illustrated. The amount of erosion (A) can be found by calculating the area between the erosion profile and the equilibrium Delft University of Technology 8

23 profile, where the erosion profile leis below the equilibrium profile, indicated in the figure. The area where the equilibrium profile lies below the erosion profile is the area where the eroded material will be deposed. When the amount of erosion (A) is calculated, three surcharges will be added as follows: A surcharge of 0.10 A m 3 /m 1 for the uncertainty of the duration of high water level; A surcharge of 0.05 A m 3 /m 1 for the effect of showers and shower oscillations; A surcharge of 0.10 A m 3 /m 1 for the inaccuracies of the model used to calculate the dune erosion. In total these surcharges amount to 0.25 A m 3 /m 1. This surcharge will be translated into a horizontal shift of the dune foot during normative storm conditions. Critical profile Under normative storm conditions the safety of the hinterland must be guaranteed by a critical limit profile, which must still be present after the normative erosion. The dimensions of the critical profile are defined as: minimum crest width (B kr ) of 3 m and the interior slope should be 1 : 2 or gentler. The Minimum crest height can be calculated according to the following formula. h0 = RP + Hkr = RP Tˆ H0s NAP + m (whereh0 RP + 2.5) RP = still water level under design conditions [m + NAP] T P = ˆT, Peak period of the wave spectrum [s] H S = H 0s Significant wave height [m] H kr = Crest height of the limit profile with respect to the RP [m] RP is called in Dutch "Rekenpeil" and stands for the still water level under design conditions. The RP can be calculated by adding the design level + 2/3*decimation height. The decimation height is the difference in water level between the design level and the water level with a return period that is a factor 10 longer. Summary Soft sea defence The stability of the soft sea defence must be guaranteed by a critical limit profile that should be present under normative storm conditions. This limit profile can be calculated using the parameters given in Table 2-1. To check whether this limit profile is in place in the design, the normative erosion profile should be calculated using the parameters from Table 2-1. When after the normative erosion there still exists a limit profile equal to, or larger than, the limit profile the coast is stable. From the difference between the equilibrium profile and the erosion profile the amount of dune erosion (A) can be calculated. Table 2-1 Soft flood defence parameters Soft flood defence parameters Erosion Significant wave height profile Fall velocity sand grains Limit profile H 0s [m] w [m/s] Still water level under storm conditions RP [NAP + m] Peak period Significant wave height T P [s] H 0s [m] Hard flood defence Hard measures signify the use of solid materials. Along the Dutch coast these hard coastal defence measures have been frequently applied with dikes, as is the case with Maasvlakte 2. With dikes the sandy profile is almost completely replaced by a hard construction, which fixes in most cases the profile in such a way that the water defence is no longer flexible. Delft University of Technology 9

24 In (TAW, 1999) a distinction is made between the different dikes of the Netherlands according to the area they protect. Since this report describes the flood defence of Maasvlakte 2 that will be located in the North Sea, the emphasis will be on sea dikes. Sea dikes (Figure 2-4) are found in the Northern provinces on the Wadden Sea, Eems and Dollard, and in the head of Noord-Holland, and in the southern province of Zeeland. Elements In Figure 2-4 a typical cross-section of a Dutch sea dike is presented, with the names of the elements. The outside slope is divided into two by the outside berm. These berms are mainly to reduce wave run-up and wave overtopping, but also perform as access roads for maintenance work. The highest part of the dike is called the crown or the crest. The inside slope is steeper than the outside slope because a gentler slope is more expensive and the inside slope plays no role in preventing or reducing wave run-up and overtopping. Figure 2-4 Elements of a dike, from TAW (1999) Strength and load The probability that the permissible overtopping discharge that is fixed for the relevant dike section is exceeded ( overload is the consequence) must be less than the standard given in the Flood Defences Act (WWK, 1996). The permissible overtopping discharge follows from the characteristics of the dike section and the area behind it. Summary hard flood defence Contrary to the soft flood defence, the hard flood defence is not dynamic, but static. There exists no erosion profile, and damage is usually avoided at all costs. For this reason it is considered that the hard flood defence is not influenced by the transition construction, and therefore the stability of the hard flood defence is not considered in the rest of the research. The effect of the hard construction on the sandy profile however, as will be explained in the next section, is taken into account Transition construction Between the completely hard and completely soft structures several intermediate shapes are encountered. Part of the dune profile can be protected by a dune foot protection or a quay wall. Even parts of the foreshore can be protected with revetments, making the profile more and more static, or stable under wave attack. A type of construction that deals with the transition between different types of sea defence is the transition construction. According to TAW (1999) a transition construction is defined as follows. A transition structure serves to connect water-retaining structures of different types. This concerns the connection between a dike as a whole and a structure, dunes or high grounds. The different form or shape of transition structures means that turbulence, retention and/or reflection of wave energy may lead to locally higher loads. There are multiple possibilities of the types of construction that are connected by a connection construction but in the case of Maasvlakte 2 the emphasis is clearly on the transition of a soft water retaining structure (a dune) to a hard water retaining structure Delft University of Technology 10

25 (a dike). With respect to the morphological effects during dune erosion the transitions can be distinguished as shown in Figure 2-5 Figure 2-5 Transition shapes of transition construction The operation of a hard construction in the erosion profile is illustrated in Figure 2-6. The transition from a dune to a dike must be designed in such a way that it will not collapse during normative storm surge. In this context the transition structure must be able to offer sufficient resistance to wave overtopping and wave attack. Figure 2-6 Erosion profile under normative storm conditions, from TAW (1999) Important in the design method for the transition structure is the morphological behaviour of the unprotected dune during a normative storm. When the whole structure would be a soft construction the erosion profile would assume a certain position during the storm, indicated in Figure 2-6 with the solid line. When a part of the profile is protected with hard elements, this part will not erode and hence not act in the formation of an erosion profile. Because this part of the profile does not erode a sand deficit occurs that will be solved by increased erosion in the other parts. This increased erosion (T e ) can be translated to an erosion profile that is shifted more towards the landside, increasing the threat to the critical profile. This is influence is at a maximum at a dike-like structure. At a Delft University of Technology 11

26 toe protection or hidden water retaining structure the influence is less strong. The additional recession can be calculated as follows: Additional recession 1 T = + e Aont h A h0 h 0 A ont = Area of erosion in cross-section [m 2 ] h A = height of erosion zone [m] h 0 = height of erosion zone until intersection with hard construction [m] Summary transition construction The transition constructed must be designed in such a way that the safety of both the hard sea defence and the soft sea defence is guaranteed. The most critical element for the design is the ending. When the transition construction is designed with an open ending, during normative storm conditions material will be lost from behind the structure, directly undermining the hard sea defence. This leads to two demands, the sandy profile should be such that under normative storm constructions at least a critical profile remains, and the hard flood defence should be stable during this normative erosion. In Table 2-2 an overview is given of the parameters necessary to determine the stability of the transition construction Table 2-2 Parameters concerning the transition construction Transition construction parameters Additional Area of erosion A ont [m 2 ] recession Height of erosion h A [m] Height of erosion until intersection with hard construction h 0 [m] Delft University of Technology 12

27 2.4 Maasvlakte Introduction To give insight in the possible solutions, in paragraph a description of the Maasvlakte is given showing with the aid of pictures what the flood defences look like. After the current Maasvlakte, in paragraph the design for Maasvlakte 2 is discussed Maasvlakte 1 The present land reclamation is located at the West coast of Holland (Figure 2-7) and was constructed in the early nineteen seventies. The flood defences are realized in two ways. A dike with granite blocks protects the Northern part of the Maasvlakte and the Western and Southern parts consist of a sandy dune coast. The transition between the two types of flood protection is realised by introducing an attached breakwater from large concrete blocks at some distance from the beach creating a perched beach. This breakwater meets with the shore again further to the North, and this is where the dike starts. From here a heavy dike runs along the coast of the Maasvlakte towards the entrance channel. Figure 2-7 Rotterdam and the Maasvlakte The flood defences of the first Maasvlakte will be described on the hand of a number of pictures. The start will be on the Southside near the sand hook, where the flood defences are soft, and will go northward towards the part where the defences are completely hard. Figure 2-8 is taken from the Slufter. In the middle of the picture the dunes and some vegetation can be distinguished. Behind the dunes the actual beach begins. In this picture the dune crossing is visible through which the beach can be accessed. In Figure 2-9 the start of the blokkendam is shown. This blokkendam, starting on the left side of the picture is an emerged breakwater lying at a certain distance from the water line. At high water the dam is just above the water level and the wave that would otherwise attack the beach are broken by the blocks. Between the blocks and the dunes is a small beach. The profile of the beach is contained by the blokkendam. Figure 2-10 is taken looking west over the blokkendam. On the right hand side the beach can be seen that is protected by the dam. Left of the dam is the sea. The blocks are placed on the sea bottom, which is about 16 meters deep just outside of the dam. The blocks are made of concrete and have a weight of 30 tons. Figure 2-11 was taken looking in a northern direction. Here the blokkendam and the dunes come together again. The dune has been fortified with a revetment and when the two join, just round the bend, they continue their course as a sea dike Figure 2-12 was taken standing on the outside berm of the sea dike looking towards the North. Just visible in the background of the picture is the post that marks the end of the entrance dam of the Euro-Maasgeul. On the foreground is the quarry stone revetment of the lower slope, with at the waterfront the concrete blocks from the blokkendam. Above the berm the upper slope of the profile is protected by asphalt and the upper part by grass. The entrance to the Port of Rotterdam is flanked by the Maasvlakte on the one side and the Noorderdam on the other. In Figure 2-13 a view from the Maasvlakte towards the port entrance can be seen. Barely visible in the background (left) of the picture is the Delft University of Technology 13

28 Noorderdam. The current Noorderdam has a crest height of NAP meter, and has a double layer of concrete cubes with a size of 2.50 meter as armour layer. The core is made out of concrete cubes of 0.80*0.80*1.25 m 3 and quarry stones of 1-6 tons. Figure 2-8 Picture taken from the Slufter, looking at the beach Figure 2-9 Picture taken at the start of the blokkendam Figure 2-10 Looking west over the blokkendam Figure 2-11 Looking North, the blokkendam and the dike come together Figure 2-12 Profile of the sea dike, looking north Figure 2-13 Port entrance and harbour dams Maasvlakte 2 General description Delft University of Technology 14

29 Maasvlakte 2 belongs to the project land reclamation that strives for the strengthening of the position of the mainport Rotterdam and the improvement of the quality of the living environment in the Rijnmond area. Developing of this project has started in 1997 and construction is supposed to start within a couple of years. The design of Maasvlakte 2 is shown in Figure 2-14 by the coloured area. The concept shown in this picture has been frequently named the Doorsteek Alternative after the entrance channel towards the new port area, which runs through the current Maasvlakte (in Dutch doorsteken). The rough configuration of the wet harbour area is also indicated in this picture. Maasvlakte 2 has been divided into 3 construction elements, the so-called building stones. In the following section the building stones will be briefly discussed and the designs made by EC-PMR (2003) are shown. The building stones are: Terrain, Flood defence, and Harbour dams Figure 2-14 Contour of Maasvlakte 2 Terrain The dry part of the port area is referred to as the terrain. The terrain will be constructed at a certain level with respect to NAP in order to ensure that no inundations can occur under normative storm conditions. The design height of the terrain will be NAP m, and the construction height, assuming settling of 0.30 meter, will be NAP meter. This terrain will be constructed out of sand, and to prevent erosion of the terrain the area will have to be protected with flood defences. Flood defences Maasvlakte 2 has been characterized as an area that is located at the outside of the dike and situated on high grounds. Therefore the flood defences do not form a part of the primary flood defences, although they are designed in a similar way. The flood defence will be split up in a soft part and a hard part, see Figure 2-14 where the hard flood defence can be identified at the northwest side of Maasvlakte 2 The hard flood defence is made up by a sea dike with a crest height of NAP meter. The dike Delft University of Technology 15

30 will be constructed of quarry stone with an armour layer of 6 to 10 tons. An initial concept sketch of the cross-section of the sea dike can be seen in Figure Figure 2-15 Initial concept hard flood defence The soft part of the flood defence is indicated by the white broader line along the west and southwest coastline of Maasvlakte 2 in Figure Just below the Slufter the soft flood defence of Maasvlakte 2 will be connected to the defence of the old Maasvlakte. The soft flood defence will be an artificial dune, made of sand with a diameter (D 50 ) of 285 µm. The crest height will be at NAP m, with a width of 65m. The concept of the soft flood defence can be found in Figure Figure 2-16 Initial concept soft flood defence Harbour dams As a guideline for the ships entering and leaving the port of Rotterdam the entrance is bordered by harbour dams. These dams also create the necessary shelter in the entrance to make the harbour approach for the ships easier. For the Maasvlakte two dams had been contemplated, the Noorderdam and the Zuiderdam. The Zuiderdam, located south of the Euro-Maasgeul coincides for the current layout of Maasvlakte 2 with the sea dike. The new Noorderdam, to the North of the Euro-Maasgeul will be attached as an extension to the present Noorderdam. The crest of this dam will be at NAP m and the armour layer will be constructed of concrete cubes with a weight of 41 tons. The initial concept of this Noorderdam can be found in Figure The figures with the designs are shown more detailed in Appendix O Delft University of Technology 16

31 Figure 2-17 Initial concept of the extended Noorderdam Numerical abstract flood defences Maasvlakte 2 The main parameters in the design of the flood defences of Maasvlakte 2 are repeated as follows: Table 2-3 Profile Artificial Dune Profiel Artificial Dune Slope Dune Dune top (variable) until dune foot (NAP + 3m) 1:4 Beach Dune foot until dry beach (NAP + 1m) 1:25 Dry beach to wet beach (NAP - 1 m) 1 : 50 Foreshore Wet beach to NAP - 5 m 1 : 75 NAP - 5 m to NAP -10 m 1 : 100 NAP -10 m to original sea bottom 1 : 20 The artificial dune, Table 2-4, has a crest width of 65 m and a crest height of NAP m. The estimated nourishment amounts to 0.5 to 1.0 million m 3 per year for a stretch of coast of 4 km. The total construction time is 60 weeks. The sand that is used has the following characteristics (Table 2-4): Table 2-4 Sand characteristics soft sea defence Sand Characteristics Diameter D µm D µm D 50 (suspended part) 200 µm Specific weight ρ 2650 kg/m 3 Porosity n 40 % The Sea dike, Table 2-5, will have a top layer made of 3-6 tons quarry stones. The construction time will be 85 weeks. Table 2-5 Profile sea dike Profile Sea Dike Crest Height (design height) NAP m Width 5 m Slope Exterior 1 : 4 Interior 1 : 3 Berm 1 : 15 Berm Height NAP m Width 10 m Delft University of Technology 17

32 Delft University of Technology 18

33 2.5 Artificial surf reef Introduction Throughout the world only three known artificial surf reefs have been constructed and knowledge about designing such structures is limited although more and more research on the functioning of surf reefs is performed. And on a number of other locations construction of an artificial reef is considered. Some surf reefs are designed as erosion protection structure, where the secondary goal is to improve the surfing conditions. This results in a contradiction because the safety of the coast demands that the waves are as small as possible, while for surfing purposes a larger wave height is preferred. In the task description of a surf reef a common function definition is improvement of the surfing conditions. In order to define a good surf reef a better definition of the desired condition than improvement of the surfing conditions has to be defined. The functions of the reef will be described with the aid of measurable parameters in order to determine the quality of a surf spot. For a better understanding of these requirements first some basic principles of surfing are explained, after which the current status of surfing in the Netherlands is reviewed. Finally a thorough investigation of the surf reef itself and the possibilities with the current wave field is carried out Characteristics of surfing A surfable wave has been defined by Walker (1974) and Dally (1990) as one on which a surfer can maintain a mean speed equal to or greater than the peel rate. What this peel rate is, and what other aspects determine the ride is explained in this section. A wave ride will be induced by a special combination of the peel angle, the wave height and the breaker shape. When either one of these parameters is not present in the mix the ride does not work. The presence of currents is important since the quality of the ride is very sensitive to currents; high velocities can destroy the waves. Before the remaining three parameters are discussed a quick introduction into surfing is given. On a surfing day a surfer paddles into the water looking for a nice wave. When he has found his wave he turns his board around and starts paddling towards the coast. The wave catches up with the surfer and the surfer now paddles down the front slope of the wave crest. This is the point where the surfer has to catch the wave, the take off. After a successful take off, the surfer stands on his board and tries to stay on the wave in the area where the unbroken crest turns into the broken crest, the pocket. When finally the whole wave is broken the ride is over and the surfer has to start over. In this short description all the important parameters can be identified. The right conditions for the take off are induced by the breaker shape, the wave height and the peel angle. The three factors together determine the length of the ride. In the following section the three basic parameters are discussed and their most favourable value. The breaker shape Waves will only start to break when they reach a certain steepness. At deep water the steepness is a function of only the wave height and the period. When the water depth reduces, the waves start to shoal; the wave height will increase whereas the wave length will decrease until the waves become too steep and start to break. The breaker type depends on the way in which a wave breaks and is usually classified with the breaking types identified by Iribarren. The Iribarren number is defined as follows: Delft University of Technology 19

34 ξ = b s H L b 0 Where H b is the wave height at breakpoint, L 0 is the wavelength at deep water and s is the bottom slope. The breaker types with the corresponding Iribarren number are shown in Table 2-6. Table 2-6 Breaker type transition values Breaker type transition values Regime Range Surging/collapsing ξ b > 2.0 Plunging 0.4 > ξ b >2.0 Spilling ξ b <0.4 Waves that are considered surfable are in the spilling and plunging regime, but mostly a number of 1.0 is preferred. Breaking wave height The influence of the breaking wave height on the surf ride is more obvious. When the waves are very small, H s << 1, the wave front will also be very small and the wave does not contain enough energy. The wave height however is also one of the input parameters for the Iribarren number, defining the breaker shape. With increasing wave height the preferred wave type will move towards the spilling breaker (Iribarren < 0.4). Figure 2-18 Peel rate, from Davey (2005) Peel angle The peel angle is the angle that is enclosed by the wave crest and the breaker line or the peel rate V P and the downline velocity V S. When the waves come with an angle towards the bathymetry the depth along the wave crest will not be constant, making the waves break not all at once but peeling along the crest as the depth decreases. This principle can be seen in Figure Generally, breaking waves with peel angles between 30º (fast Delft University of Technology 20

35 ride) and 60º are considered to be surfable although Black, Andrews, Green, Gorman, Healy, Hume, Hutt, Mead, and Sayce(1997) noted that a peel angle less than 50º would be a difficult proposition for must surfers Characteristics of a Dutch surf ride A normal surf ride in the Netherlands does not include very spectacular waves like they can be found on Hawaii, but nevertheless surfing in Holland is a popular sport that is frequently practised by its fanatics. A typical Dutch ride can be characterized by the following specifications (expert opinion): Surfer skill 6 or lower A wave height H S = 1.0 meter Wave period T p = 8.0 seconds Breaker shape, spilling, ξ b= = 0.4 Hutt, Black and Mead (2001) presented design curves for surfer skill in relation to peel angle and breaker height, see Figure To determine the desirable peal angle for the Dutch surfers this figure is used. For a surfer skill of 6 or lower, a wave height of 1 meter means that the peel angle should be 45º or higher. With this desired peel angle the favoured toe depth of the reef can be estimated. Figure 2-19 Surfer skill as a function of the peel angle and the wave height (Hutt, Black and Mead, 2001) Characteristics of a surfbreak In the previous section the typical wave characteristics for a surf ride have been discussed and made clear that a natural or artificial reef can improve surf quality and the occurrence of surfable waves by: Increasing the wave height at the break point; increasing the breaker type; Promoting a progressively breaking rideable wave (peel angle). This section focuses on the geometry of the reef. The characteristics a bottom needs to contain in order to create those surfable waves are explained as well as the favourable dimensions of those features. Bathymetric features that produce surf breaks are: Beaches containing rip/bar morphology Headlands Submerged reefs Ebb tidal deltas at estuary/river inlets (Walker 1974) Delft University of Technology 21

36 In this research the focus will be on the submerged reefs. A reef can be schematized as is shown in Figure Important features are the depth of the reef toe, the reef slope, the reef angle, the submergence and the material used for the construction of the reef. Figure 2-20 Schematized surf reef, from Henriquez (2004) Reef toe depth The depth of the reef toe determines in a large way the peel angle of the breaking waves. A shallow reef toe affects the peel angle in a positive way, presuming the reef angle towards the incoming wave front is still at its optimum. Reef slope The influence of the reef slope is mainly on the breaker parameter. The slope of the reef can be found in the numerator of the equation for the Iribarren number, which means that an increase in reef slope, leads to a direct increase in the Iribarren number. Reef angle Along with the toe depth the reef angle is responsible for the peel angle. Research by Henriquez (2004) showed that the peel angle shows a maximum value for a reef angle of 66º towards the wave front. Submergence and material The submergence and the construction material are important for the safety of the surfer. When at the end of the ride his surfboard hits a hard emerged breakwater, the surfer might get injured. When the submergence of the reef can be very large the material that is used has no real effect on the safety of the surfer. However if the submergence of the reef is merely 1 meter, the surfers are bound to come in contact with the reef surface and a softer material is advisable. Delft University of Technology 22

37 The submergence of the reef also affects the Iribarren number, unfortunately there is a lack of studies to quantify this effect Summary surf reef The surf reef, should comply with the following figures, Table 2-7. In section 5.1, Functional design, these numbers are used in order to determine the dimensions of the surf reef. The surf reef will be constructed in very shallow water so the hydraulic conditions will be quite different to the ones used for, the dune erosion, or the Westdam itself. For the surf reef, the hydraulic conditions at shallow water during normal (everyday) conditions and during extreme storm events are desired. Table 2-7 Summary surf reef Summary surf reef Surf characteristics Reef characteristics Peel angle (deg) > 45º Wave height (H m0 ) 1 m Wave Period (T P ) 8 s Breaker shape ξ b (Iribarren) (Spilling) Reef angle 60-70º Delft University of Technology 23

38 Delft University of Technology 24

39 3 Program of requirements 3.1 Introduction In the program of requirements the results of the theoretical study are summarized and quantified. This chapter is divided into two; section 3.2 describes the requirements with respect to the design, and paragraph 3.3 describes the defining of the hydraulic parameters that are required for the design by means of SWAN simulations. 3.2 Requirements Most of the requirements given here were taken from EC-PMR (2002). This program of demand is a selection of the general program of requirements that can be found in Appendix M, supplied with requirements that followed from the literature study described in the previous sections. The shifting of the requirements was based on the relevance to the design of the transition construction and the surf reef. In the general program of requirements a lot of attention is given to the surrounding area and the wave conditions in the entrance channel. In this study these are neglected because these effects have already been minimized in the design of the contour of the land reclamation General Requirements The contours of the land reclamation will be assumed as they are shown in Figure 2-14; The functions that the construction should include are: the connection between the hard and the soft sea defence, blocking of longshore transport, enclosure of the sandy profile, and creating surfable waves; Functional requirements The stability of the flood defence should be guaranteed by the transition construction but is not part of this research; The design of the transition construction should not lead to failure of the hard or the soft flood defence; The Westdam is supposed to constrain (part of) the sandy profile and to block (part of) the longshore transport; The Westdam should provide surfable waves. Surfable waves are defined according to Table 3-1. Table 3-1 Surf wave requirements Surfable waves Peel angle (deg) > 45º Wave height (H m0 ) 1 m Wave Period (T P ) 8 s Breaker shape γ b (Iribarren) Constructive requirements The erosion profile as a result of the normative storm conditions can be calculated according to the formulas and the surcharges defined by TAW (1995) The critical profile that needs to be present after normative erosion is defined by TAW (1995) The effect of the hard construction on the soft flood defence can be calculated by an addition recession (TAW, 1999) The cross section of the hard flood defence is assumed as given in 2.4.3, the design height is NAP m Delft University of Technology 25

40 The cross-section of the soft flood defence is assumed as given in 2.4.3, the design height is NAP m For the hydraulic boundary conditions close to the land reclamation the reader is referred to section (These will be determined with SWAN computer simulations) The sand characteristics for Maasvlakte 2 are given in The diameter of the sand used for the soft flood defence will be fixed on a D 50 of 285 µm. To provide the waves determined in the functional requirements, the reef should have an angle of 60º - 70º towards the incoming waves. In the water level calculations a relative sea level rise of 60 cm will be taken into account, this correspond with the anticipating scenario as defined in EC-PMR (2003). Increases in wave height and wind speed are hereby neglected Recreational requirements Because of the probable loss of the beaches of the current Maasvlakte mitigating measures should be taken Environmental requirements From the viewpoint of designing in an environmental friendly way, the aim is at a minimal use of primary building materials. This implies that the necessary sand winning will be kept to a minimum and use of secondary building materials is stimulated Safety level and design Lifetime The safety level of the flood defences is fixed on 1/10,000 per year. The flood defence for Maasvlakte 2 will not be a part of the primary flood defences, but will, if possible, comply with the requirements associated with the primary water defences. Delft University of Technology 26

41 3.3 Hydraulic boundary conditions and SWAN Introduction In order to make a reliable design it is important to have wave information close to the shore. In the program of requirements for each of the parts of the construction the required wave parameters are given. For most cases where the construction forms a part of the primary water retaining construction this wave information is given in the Hydraulic boundary conditions (RWS, 2001). In the case of the sea defence of the Maasvlakte 2 this information is not available nor applicable, because this defence is not defined as a primary water retaining construction. A good way to obtain this close to shore wave information is to run simulations, giving a wave height, period and direction at chosen points close to the shore of Maasvlakte 2. A second reason to run these computations is that through these computations detailed information about the wave characteristics can be obtained that can be used in order to review the surfing conditions. For these kind of simulations Delft University of Technology developed two models. The second generation model HISWA and the third generation model SWAN. Because the SWAN model is the more modern of the two, the simulations in this research were carried out with SWAN. A description of the balance equation used by the SWAN model can be found in Appendix A. Wind and wave directions are defined according to the nautical convention. This means that the direction where wind and waves come from, calculated clockwise from the north (360º or 0º), is used. The results by Roskam, Hoekema and Seijffert (2000), also clearly show that there is a large "landwind sector" present, from 10º to 220º, where the water and wave parameters show very low values and the waves are in the offshore direction. This sector will be disregarded in the current research. Figure 3-1 Wind and wave directions according to the nautical convention, values in 10 1 º Accuracy During the calibration of the model, the differences between the cases were expressed in terms of percentages. If the output using a new model set-up only differed 0 to 5 %, the change was noted as insignificant. When the effects became more apparent, 10% or more, the changed parameter had a significant effect. These accuracy limits are coupled to the formulas that are used in the design phase. An increase of the significant wave height with 5 % leads to an equal increase in the calculated dimensions of the armour units for the construction. In this stage of the research, 10 % is taken as the upper limit. The results as a whole from the SWAN computations should be validated against near shore wave measurements, but because those measurements are rare the results are judged on the basis of common sense only. Delft University of Technology 27

42 3.3.2 Setup swan A SWAN simulation needs a number of input parameters and files; in Appendix B, C, D, E and F a complete overview of the model setup is given. The primary input files are the command file, bathymetry file and the bathymetry grids. The basic input parameters are given below and discussed briefly in this section. Bathymetry Grids Time Frame and Water Level Boundaries Output Bathymetry file The bathymetry file that was used is constructed from a very large file obtained from the Dutch Navy (Hydrografische Dienst van de Koninklijke Nederlandse Marine). They supplied a detailed digital map of part of the North Sea with measured depth every 20 meters. These sample points were interpolated to a grid, the bottom grid, were the sample points became depth points, describing in every point the local depth, in Figure 3-2 the bathymetry file is shown. Clearly visible in this picture is the protrusion of Maasvlakte 2. Also indicated in this picture by the rectangular box is the exterior calculation grid, to which also the bathymetry is interpolated. Figure 3-2 Bathymetry of the North Sea (hydrografische dienst Koninklijke marine) Grids The bathymetry grid file is the file that describes the grid on which the bathymetry is based, i.e. the starting point of the grid, the size and the number of elements and the orientation. It gives the coordinates of every point in this grid. The bathymetry depth file gives for each location the depth with respect to NAP. These files form the basis on which the computations are run. The computations can in their turn be carried out on the same grid or on a different grid. When the computational grid is the same as the bottom grid the computations are the most accurate because no accuracy is lost in interpolations between the grid points of both grids. Delft University of Technology 28

43 The size of the grid cells is limited both on the upper side as on the lower side. The upper limit for cell size is given by the bottom geometry; the cells should be small enough to describe any significant bottom changes properly. The lower limit is formed by the limited computational capacity. Smaller grid size leads to larger number of cells, which in turn leads to more computational time. To have enough detail close to the shore but still be able to cover a large area grids can be nested, in this case three grids nested in each other were used. Figure 3-3 Position of the exterior grid on the North sea As an outside limit for the exterior calculation grid the measuring points Euro platform and IJmuiden are chosen. The grid ends on the eastside just landward of the dunes on the northwest coast of Holland. The intermediate and detailed grids are chosen such that they cover the part of the Maasvlakte that is of interest in this research. The final grids that were used for the simulations are given in Table 3-2. In Figure 3-4 the nested grids are shown. Figure 3-4 Nested grids Delft University of Technology 29

44 Table 3-2 Grids used in SWAN simulations Grids Element Size Exterior 500m by 500m 100 km by 55 km Intermediate 100m by 100m 22 km by 15 km Detailed 40m by 40m 5.6 by 5.2 km Time Frame (water level and flow) Water level Since the water level under storm conditions varies along the Dutch coast a correction should be applied on the water. According to Van der Hout (1990) a water level reduction of 10 cm between Hook of Holland and Maasvlakte 2 is realistic, see Figure 3-5. Figure 3-5 Spatial distribution of the water levels along the Dutch coast Flow Current flow can have some effect on the waves, making them either higher or lower.in proceedings of the research executed by Jacobse and Groos (2002) and Vledder (2002), who investigated the influence of flow on waves. By running various SWAN computations he concluded that on the north-western corner of Maasvlakte 2 the relative influence from flow on waves is greatest (20%) with waves and wind from the direction 210ºN. However, the significant wave height and mean wave period are much greater with wind and waves from the direction 315ºN. (see Appendix E). Furthermore as the significant wave height, with wind and waves from 315ºN, is increasing with a maximum of 4% along the output points, the mean wave period is decreasing with 2.5%. So the wave load (H s *T m01 ) as shown at the bottom of Appendix E, due to flow increases with only 3.8%. Since these peak values are only true for less than half an hour, it is decided not to take the influence of flow in account in this stage. Boundaries The boundaries that can be imposed on the grid are very important for the calculations. Any inaccuracy on the boundaries proceeds into the area by the program and can lead to inaccuracies in the area of interest. It is therefore important to define these boundaries as accurate and detailed as possible. A simplification that was made was shifting the "real" values of the Euro platform and the IJmuiden station towards the ends of the boundaries; their actual locations are close to the corners. This simplification made the defining of the boundaries a lot easier and only leads to differences of the wave height of 2 to 3%, which is within the previously defined bounds of 5%. Output Delft University of Technology 30

45 A last input parameter in SWAN concerns the output. SWAN can show the results of the simulations graphically over a previously specified grid, this grid can be the same as the computational grid, but SWAN can also write the wave characteristics into a table for a number of user specified control points. In these points the effect of the change of one parameter can be compared numerically, giving a good insight into of the deviations in terms of percentages Parameter reduction When it is assumed that offshore significant wave heights, wave periods, wind speeds and near shore water levels exceed their design values simultaneously, very conservative conditions are taken. A reduction can be found by looking closely at physical relations between the parameters. More about the relations is explained in the sections below. It is stressed that the reductions found in this chapter will only be used for calculating wave parameters at the location of Maasvlakte 2. The crest height of the construction for example is calculated with a water level with a return period of 10,000 years with no reduction applied. The input parameters that determine the wave field are a) Wave height b) Wave period c) Wind speed d) Water level In Table 3-3 the values with a return period of 1 per 10,000 years can be found. These values were taken from Roskam et al. Table 3-3 Hydraulic parameters with a return period of 10,000 year Parameters with a return period of 10,000 year Wind speed 1 U [m/s] Wave height H m0 H s 8.15 [m] Wave period T p 13.0 [s] Water level W 4.77 [m+nap] Wave height For the wave height the marginal probability value was held fixed at the values determined by Roskam et al. The value for the wave height at Europlatform belonging to a return period of once in 10,000 years can be found in Table 3-3. Wave period There exists a very strong correlation between the wave height and the period. With the physical relation found for the Euro platform, the period corresponding with the wave height is slightly lower than found in Table 3-3. Wind speed The formulas by Demirbilek, Bratos and Thomson (1993) give a solution for duration limited wave growth as a function of either the wave height or the wave period. The discrepancy between the two is quite large, but both lead to an impressive reduction of the wind speed. Water level The water level under storm conditions can be considerably higher than under normal conditions. This water level (h) can be divided into two main components, the astronomical tide (a) and the wind set-up (s). In formula: h = a + s 1 The wind speed is derived from Verkaik, Smits and Ettema (2003) Delft University of Technology 31

46 The wind set-up (s) in this equation has a direct relation with the wind speed according to Weenink (1958) with the use of the two values for the wind speed found under earlier, two values for the water level are derived Conclusions parameter reduction Because the goal of this section is to find adjusted hydraulic boundary condition parameters for wave simulations using the SWAN model, it was thought that most reliable results are found keeping the wave height at a fixed level and reduce the other parameters accordingly. Because of the strong relation between wave height and wave period, a reliable reduction of the wave period (Tp) is found. More difficult is the reduction of the wind speed since it can be directly derived from the wave height or from the reduced wave period. It is chosen to use the average of both values. Since the wind set-up is a direct result of the wind speed, the wind set-up is derived from the wind speed. As for the wind speed, the two values found for the wind set-up are averaged By using physical relations instead of a pure statistic approach as used by De Haan (van Marle, 2000), a very good estimate of possible reductions is found. However errors are made because simplified formulas are used. Because the determination of the hydraulic parameters is only a small part of the total research, no further emphasis is put on the accuracy of the found reductions. A more detailed description of the parameter reductions can be found in Appendix F. The results of the reductions are shown in Table 3-4 for the Europlatform boundary, and Table 3-5 for the IJmuiden station. Table 3-4 Hydraulic conditions for the 330º direction, Europlatform EUR 330º 1/1 per year 1/10 per year 1/100 per year 1/1,000 per year 1/10,000 per year Hs (m) T P (s) Table 3-5 hydraulic conditions for the 330º direction, IJmuiden IJM6 1/1 per 1/10 per 1/100 per 1/1,000 1/10, º year year year per year per year H s (m) T P (s) Because the wind speed (U 10 ) and the normative high water level (MHW) are taken constant over the total simulation area in SWAN, the two different values of those parameters are averaged between Europlatform and IJmuiden. As a result the values will be taken as shown in Table 3-6. Table 3-6 Water levels and wind speeds averaged between EUR and YM6 Simulation area 330º 1/1 per year 1/10 per year 1/100 per year 1/1,000 per year 1/10,000 per year MHW (m+nap) U 10 (m/s) Delft University of Technology 32

47 3.3.5 Results SWAN In Figure 3-6 the wave field is shown for hydraulic conditions with a return period of 10,000 years. It can be seen that the refracted waves come in almost perpendicular to the construction. This plot is shown here as an example of the output that can be given by SWAN. Because it is very difficult to find a numeric value in this kind of plot, a different kind of presentation are chosen to evaluate the wave field. Figure 3-6 Wave field 10,000 year return period, 330º, MAASVLAKTE 2 phase 2 In Figure 3-7 the intermediate grid and the bathymetry are shown. In this figure a yellow line can be seen. This line indicates the location of the NAP - 20 m depth contour, which is used for the output of SWAN. Because the calculation of the erosion profile is done using wave parameters at a depth of 20 m, SWAN output is produced for this depth. Besides this deep water results, at the NAP -20 m contour, also results at shallower water were necessary for the stability of the surf reef and also for the functionality of the reef. First the results at the NAP 20 meter depth contour will be discussed, followed by the presentation of the shallow water results. Figure 3-7 SWAN output contour NAP - 20 Delft University of Technology 33

48 The results are given in Figure 3-8, where the wave heights are plotted along the NAP- 20 m depth contours, which is at a certain distance to the coastline of Maasvlakte 2. The plot begins at the most Northward point of the contour and runs south. 10 Significant wave height 10 Mean wave period Hs (m) 5 Tm01 (s) km 20 km Distance from begin point 2 10,000 years 1,000 years years 10 years 1 year km 20 km Distance from begin point Figure 3-8 Wave heights along 20 depth contour line Regarding the wave field no abnormalities are observed in the SWAN results. After refracting towards the Dutch coast, the waves refract towards Maasvlakte 2. The reason the waves do not come in perpendicular to the construction at all locations is the steep slope of the constructions. Both subplots of Figure 3-8 show a dent at two locations. This second and largest dent is the place where the contour crosses the Euro-Maasgeul, and the first dent, which is slightly smaller, also coincides with a sudden increase of depth in the bathymetry. Besides these two dents the wave parameters are fairly constant with a slight maximum at the location of the future Westdam. Expressed in numbers, those maxima have the following values, Table 3-7. Table 3-7 Wave parameter maxima at NAP - 20 m depth contour Depth 20 m 1/1 per 1/10 per 1/100 per 1/1,000 per 1/10,000 year year year year per year Hs (m) Tm01 (s) Delft University of Technology 34

49 The results on shallow water use a similar contour as the deeper water results, only now the contour is not parallel to the depth contour but perpendicular (Figure 3-9). The contour follows the Westdam and is shown in the figure by the yellow line, the result can be found in Figure Figure 3-9 SWAN output contour Westdam 10 Significant wave height 11 Mean wave period Hs (m) 5 Tm01 (s) Depth (m) 2 10,000 years 1,000 years years 10 years 1 year Depth (m) Figure 3-10 Wave parameters at the proposed Westdam locations The wave parameters in Figure 3-10 show a decrease for decreasing depth. Because the reef will be constructed at a shallow depth the lowest value for the wave heights will be taken. In Table 3-8 the numerical values for the parameters in shallow water are given. Delft University of Technology 35

50 Table 3-8 Wave parameters at the proposed Westdam locations 1/1 per 1/10 per 1/100 per 1/1,000 1/10,000 year year year per year per year Hs (m) T m01 (s) Since the functionability of the surf reef is not defined under normative storm conditions, but under everyday normal conditions (paragraph 4.3.2), different boundary conditions were used to define the functionability, than for the stability. The result of the simulation of these waves can be found in Figure Significant wave height 10 Mean wave period Hs (m) 1 Tm01 (s) Depth (m) 3 North 1m 6s North 2m 8s 2 West 0m 6s West 1m 8s West 2m 8s 1 South 1m 6s South 1m 8s South 2m 8s Depth (m) Figure 3-11 Wave field used for determination of surfability Delft University of Technology 36

51 4 Modelling 4.1 Introduction Originally the Westdam was designed to detain the sandy profile and to stop a part of the longshore transport. Because the sandy profile stretches from the waterline down to a depth of NAP 20 m, and the longshore transport (4.2.1) mainly takes place in the area between the waterline and NAP 8 m, these two functions lead to different dimensions for the Westdam. Moreover, to make the Westdam suitable for surfing again different dimensions and specifications are needed. Somewhere in between the optimum dimensions for each function separately is the optimum point for all the functions combined. In the following sections the occurring processes are described and the corresponding dimensions of the Westdam. The functions that are identified are: 1. Constraining of the sand profile (Figure 4-1) 2. Blocking of the longshore transport 3. Creation of surf waves These functions can be divided into two main functions, the morphological functions containing the longshore transport and the beach profile, which are described in 0, and the surfing function, which is described in paragraph 4.3. Further on a model to estimate the morphological consequences of the length of the Westdam is described. With this model an economical analysis is made and an optimal morphological design will be defined. Finally the model will be described that is used to determine the optimum location and dimension of the surf reef. Figure 4-1 Side view of beach profile Delft University of Technology 37

52 4.2 Morphological model Longshore transport The following definition is given: Longshore transport is the sediment transport caused by littoral drift, which is the flow of water along the coast by obliquely breaking waves, in the littoral zone. The Longshore transport rate is the rate of transport of sedimentary material parallel to the shore in the littoral zone, usually expressed in cubic meters per year. For the Maasvlakte 2 the longshore transport has been analyzed and roughly characterized by the following contributions (Boer and Roekema 2004), see Figure A large northbound tide driven sand transport on the foreshore on the Westside of Maasvlakte 2, located at the bend in the coastline. 2. A relatively small tide driven transport in front of the southwest coast of Maasvlakte 2 (outside the toe line of the coast profile) 3. A northbound wave driven surfzone transport along the northwest coast of Maasvlakte 2 (at the bend in the coastline and north of it). 4. A southbound surfzone transport along the southwest coast of Maasvlakte 2 (south of the bend). In Figure 4-2 the transports are presented by arrows. The white arrows represent the tidal driven transport, which is clearly larger around the bend of the coastline than to the north or the south. The dashed line perpendicular to the coast indicates the bend of the coastline. From the bend the surfzone transport heading in two directions can be distinguished; an increasing transport along the north-western part of the coast, and a more or less constant transport along the south-western part. Figure 4-2 Transport image of Maasvlakte2 from Boer and Roekema, 2004 The contour of Maasvlakte 2 is chosen such that the largest contraction of the streamlines takes place at the protruding bend (Boer et al) instead of the Westdam. This is because the largest protrusion of the land reclamation is at the bend, this is the part that extends farthest into sea, and here the streamlines are pushed farthest away from the original coastline. The benefit of this design is that a small change in the design of the Westdam does not directly influence the tidal current flowing around Maasvlakte 2. Delft University of Technology 38

53 The surf zone transport on the southwest coast is also insensitive to changes in the design of the Westdam, the Westdam (if very long) could create some sheltering for this area but this influence is neglected. The length of the dam however does have a direct influence on the surfzone transport on the northwest part of the coast, which will be (partly) blocked by the dam. In this research the surfzone transport on the northwest coast of Maasvlakte 2 is considered the only contribution of the transport that can be influenced and will hereafter be specified as the longshore transport. In the calculations by Boer et al., a Westdam was assumed that blocked the surfzone from the waterline unto a depth of NAP 5 m. The crest was above the water level and 70 % to 80 % of the transport is blocked. The amount of sand that still bypasses the Westdam amounts to 130,000 m 3 per year. The grain size used in these calculations is D 50 =285 µm. The so-called closure depth, the depth at the offshore limit of noticeable bathymetric change, is located at a depth of NAP - 8 m. Let us first consider the surfzone transport by assuming the crest height of the Westdam at the level of SWL (Still water level, the water level during storm conditions) or above. This implies that no sand can be transported over the dam; only transport around the dam can be possible. Tidal fluctuations in this analysis will be neglected for simplicity reasons. When the surfzone transport is blocked, accretion will occur. The sand in the water column will settle and the land will "grow". Due to these accretions the entire profile will shift slightly seaward pushing the end of the surfzone further offshore. When the surfzone is located far enough offshore the blocking will not be complete anymore and sand will start to flow around the dam. The distribution of the accretion is dependant on the angle of the waves when breaking and is very important for the time scale in which the sand will start to flow around the dam. On sandy beaches the profile is usually rather gentle making waves refract towards the coast before they break. These small angles at breaking make that the accretions are small and distributed over a large area, creating small accretions in the whole area. If the crest height of the Westdam is put below sea level sand transport is not only possible around the dam but also over it. Because the emergence or submergence of the crest will be directly influenced by the tide, tidal fluctuation can play a role in determining the amount of transport over the dam, but for simplicity reasons the tidal range is assumed to be more or less symmetrical and the net contributions will be negligible. To block the entire surfzone the Westdam should be constructed up to a depth of NAP - 8 m and have a crest height of at least NAP +1 m. The length of the dam will be 850 m, starting from the waterline and running perpendicular to the coast Morphological model The morphological analyses is conducted to find the optimum size of the Westdam in accordance with the morphological functions. The morphological function consists of a static contribution, the closure of the profile (the horizontal confinement), and a dynamic contribution, the longshore transport. The longshore transport is evaluated on in the horizontal and the vertical plane, to take the different effects of lowering the crest height and shortening the dam into account. In Appendix I the morphological model is discussed in more detail. Horizontal transport The horizontal plane is made up by the surfzone bounded by the waterline (NAP) on the landside and the closure depth, the NAP - 8 m depth line, on the seaside. The distribution of the transport is assumed to be according to Figure 4-3, with the assumption that the bottom has a constant slope between NAP and NAP - 8 m, and the sand concentration is constant over the surfzone. These assumptions make it possible to describe the processes with a Delft University of Technology 39

54 simple model. In the figure, the depth is presented on the horizontal axis (z) and the amount of transport on the vertical axis. The transport will be plotted for the relative toe depth, being the depth at which the dam begins, divided by the closure depth, NAP 8 m. A larger relative toe depth means that the toe is at a larger depth, which in turn signifies a longer dam. toe depth [m] Relative toe depth [-] = closuredepth [m] Ymax = 2/3 Yb S [m3/s] 76 % of total transport End of dam, Z =NAP -5 m 24 % Z [m] Figure 4-3 Distribution of the longshore transport over the surfzone In Boer et al. the outer edge of the surf zone, the so-called closure depth, is located at a depth of NAP - 8 m, some 700 m offshore. From van der Velde (1998) it follows that the velocity profile can be schematized into a triangle extending over a width equal to 1.6y b, where y b is the width of the actual surf zone. Its peak value occurs at y = 2/3 y b from the shore. This velocity profile appears to fit well with the parameters earlier defined by Boer et al. The total width is set at 700 m, where a depth of Nap - 8 m is assumed, leading to an averaged slope (m) of The maximum transport in the profile is found at m. This velocity profile leads to 76% of the transport in the area between the shoreline and the NAP - 5 m depth line and 24% beyond the NAP - 5 m line. Vertical transport The vertical plane looks at the distribution of the velocity and the concentration over the water column. The vertical transport profile is assumed to be the product of the velocity and the concentration, Figure 4-4. The amount of sand that is transported over the dam is estimated by calculating the crest height and the velocities and concentration in that part of the water column. The velocity is assumed to have a logarithmic profile over the vertical, and the concentration shows a Rousse-Einstein distribution (van der Velden, 1998). The two combined lead to the third graph in Figure 4-4, clearly showing that the largest part of the transport is located in the bottom half of the profile. z [m] Log(z) * (1-z/h) ll log(z)*(1-z/h) Vz [m/s] Cz [m3/m] Sz [m3/s] Figure 4-4 Distribution of the transport over the vertical The vertical transport will be plotted for the relative crest height, being the height of the water crest above the sandy profile, divided by the water depth. crest height [m] Relative crest height [-] = water depth [m] Delft University of Technology 40

55 4.2.3 Confinement of the profile The beach profile as it is described in section can be seen in Figure 4-5. When no construction is made at the side of the profile to prevent the sand from settling, it forms a natural gentle slope, which will take up a lot of sand. The Westdam in its current design is supposed to confine the sandy profile and depending on the length of this dam only a certain amount (or no sand at all) will flow around it. When the entire profile is protected the dam needs to have a length of 1050 meter from the waterline (NAP) perpendicular to the coast. It is assumed that the upper part of the profile, NAP and above, is protected by the hard sea defence that starts right after the end of the beach profile. So when the Westdam has a length of 0 m only the part of the profile below NAP will flow out. Since the water depth in this area is around NAP 20 m, the amount of sand lost to the flow out will still be considerable. Figure 4-5 Beach profile Maasvlakte 2 from Expertise centrum PMR, Economical optimalisation The economical analyses uses the models described above to compare the effect of the length of the Westdam on the morphological functions. The analysis was based on the designs and data from EC-PMR (2003). When the Westerdam is shortened basically three things happen. The dam is shorter and therefore less material is needed to construct it. The beach profile is bounded over a shorter length, so more sand will flow around it in order to create the necessary gentle slope. And last but not least, when the dam is shortened, a narrower part of the surf zone will be blocked for transport, so more sand will be transported around the tip. As a first estimate for the costs of the Westdam, a simplified version of the Noorderdam, the harbour dam, is taken. It is schematized to three layers. The first layer is the armour layer, which consists of two layers of 40-ton blocks. The second layer is the core material consisting of quarry stones of 300 to 1000 kg, this material are also used for the basis, the bottom section of the dam, where there is no more need for an expensive armour layer because it is located deeper under the water surface. The last layer is the armour toe protection, a relatively small amount of quarry stone placed at the toe of the armour layer to prevent the armour material from subsiding and sliding. The size of stones in this layer is 6 to 10 tons. In Figure 4-6 a picture of this schematized dam can be found. Delft University of Technology 41

56 Figure 4-6 Schematized cross section of the Westdam In Figure 4-7 the results of the economical analyses are shown for both the horizontal and the vertical optimum of the Westdam. This figure clearly shows that the contribution of the longshore transport on the optimum length is significantly smaller than the effect of the confining of the profile. The figure will be explained with an example. The costs used in the optimization for the construction of the dam and the sand nourishments are explained in Appendix P. Costs [million euro] Costs as a function of the toe depth Costs profile Costs construction dam Nourishments after 50 years Costs [million euro] Costs as a function of the crest height Costs construction dam Costs sand nourishment (50 year) Relative toe depth [-] Relative crest height [-] Figure 4-7 Economical analyses for the toe depth and the free board Example: in the current design of Maasvlakte 2, by EC-PMR (2003), the Westdam extends to depth of NAP 5 m, this means that the toe starts at a depth of NAP - 5 m. Since the closure depth is NAP 8 m, the relative toe depth is [-]. In the left hand plot the corresponding costs for the profile, the construction of the dam and the net present value of the nourishments during 50 years can be read. Because the crest is at SWL (or higher) there is no transport over the dam and only the left-hand plot should be used. When the crest of the dam is submerged, the right-hand plot can be used to determine the optimum crest height. The economical optimum can be found by adding all the costs and looking for the lowest occurring value for the costs. The toe depth corresponding with that value is the optimum toe depth. Because the dimensions of the dam are relatively small compared to the amounts of sand, a long dam with a small freeboard appears to be the optimum. In Figure 4-8 a 3- dimensional visualization is given of the optimum toe depth and freeboard of the Westdam. The optimum point will be found where the total costs are lowest. This is the case for a relatively high crest height and toe depth. Delft University of Technology 42

57 Figure 4-8 Three-Dimensional Visualization of Economical optimum Conclusions morphological model With the previously used example of the currently used design of the Westdam the total costs for this design can be found. The relative toe depth is [-] and the relative crest height is one (the crest of the dam is constructed on or above the SWL, so the crest height is equal to the depth). According to Figure 4-8 the total costs are around 50 million Euros (50,000,000 ). The economical optimum can be found through an increase in the relative toe depth and a slight decrease of the crest height. The costs will than be slightly lower than 40,000,000. The toe depth in this case is NAP m and the crest height is NAP m. The optimum can roughly be found on the front side of the graph where the plane crosses the lowest z- values (costs). Delft University of Technology 43

58 4.3 Surfing model Surfing waves A Dutch surfer goes surfing when the waves have an offshore wave height of preferably one meter or more and periods of 6 to 8 seconds. These wave conditions do not occur very often in the Netherlands but are vital for the creation of surfing waves close to the shore. When a reef slope of 1 : 10 is assumed the Iribarren number will be around 1, which is close to the 0.8 (which is preferred by most surfers). When the desired wave field is present the surf spot is further defined by the bathymetry and its orientation. The bathymetry of the surf spot and its orientation are important for the peel angle, one of the most important parameters of a surf wave. The surfing population in the Netherlands has a skill level of maximum 6, so the peel angle should be at least 45º. The peel angle is influenced by the angle that the reef makes towards the waves, the depth at which the waves start breaking, and the depth of the toe of the reef. Earlier research (Henriquez, 2004) showed that reef angles of 66º with respect to the incoming wave angle create the largest peel angles. The peel angle can be further improved by adjusting the starting depth of the reef until peel angles of more than 45º are reached Offshore wave field As was said before surfers need a certain offshore wave field in order to be able to surf. Waves with an offshore wave steepness of 0.01 to 0.02 are considered surfing. From the measurements available at the stations Europlatform and IJmuiden Munitieplatform (Ministerie van verkeer en waterstaat, 2002) the occurrence of these particular waves is known so an estimate of the probability of having surfing waves can be given. For the directions North, West and South three possible waves are chosen for the offshore wave field, based on the requirements described in paragraph 3.2.2, with wave heights and periods as shown in Table 4-1. For the northern direction the wave with a height of 1 meter and a period of 8 seconds had a probability of 0 %, therefore this wave characteristic is assumed to be non-existent. Table 4-1 Offshore characteristics of surfing waves Direction (wind) South West Wave height H m0 [m] Wave period T m02 [s] Percentage [%] Near shore wave field North The offshore waves will be entered into SWAN to simulate the characteristics of the waves closer to the shore and predict the breaking wave height as well as the peel angle as a function of the depth of the reef toe. The results of these SWAN simulations can be found in Appendix H and L. The waves are assumed perpendicular to the bottom profile, and the reef normal is at the optimum angle of 66º towards the bottom normal. When the waves encounter the reef they will start to refract until they reach the breaking depth. The peel angle can be found as the angle between the wave crest and the breaker line (Figure 4-9). Delft University of Technology 44

59 Figure 4-9 Simplified bottom topography for determining peel angle This approach leads to a first estimate of the peel angle as a function of the toe depth and all the waves and directions combined lead to the best depth to start the reef. From the SWAN simulations a normative wave angle at shallow water (round the breaking point) can be determined. The reef should make an angle towards the normative wave angle of 66º. This Normative wave angle can be read from Figure 4-10, where the wave angles on shallow water from the SWAN runs are shown. From the eight different waves, four waves have an angle of 300º making this the normative wave angle. Wave angles at 0 shallow water Figure 4-10 Wave angles at shallow water depth In Appendix L, the results of the SWAN runs are given, showing the behaviour of the waves on shallow water depths as well as the relation between the peel angle and the water depth. In Figure 4-11 an example is shown of this relationship, in this case the offshore wave height was 1.0 m and the period was 8 seconds. When for surfing purposes a minimum peel angle of 45º is demanded the corresponding necessary reef toe depth can be read. In this graph the toe depth for an angle of 45º is less than 2 m. In Appendix L plots can be found showing the peel angle and the toe depth for the rest of the wave conditions Delft University of Technology 45

60 60 Starting depth of reef peel angle α [deg] water depth at reef toe [m] Figure 4-11 Peel angle as function of the reef toe depth When the angle of the reef is determined along with the depth and the slope of the toe of the reef, the surfability of the reef has to be determined. Three designs will be made consisting of combinations of reef and dam functions. Each of the three alternatives will be discussed on account of the surfability. Important results are the peel angle and the Iribarren number, necessary to determine the surf conditions Conclusions surfing The functions morphology and surfing lead to rather widely distributed values for the toe depth and the crest height of the dam. The surfing function demands low crest heights and shallow toe depths, whereas the morphological function is best fulfilled with a high crest and a deep toe depth. In the design it will be investigated if it is advisable to split the two functions into two different constructions, or that the functions can be combined into one multifunctional reef. Table 4-2 Conclusive optimum dimensions for the different functions Function Length of dam (m) Depth at toe (m) Crest height (m) Reef angle (º) Morphological 550 NAP - 7 NAP º Surfing 88 to 240 NAP -1.5 to NAP-3.5 to NAP 300º+/-66º Delft University of Technology 46

61 5 Design 5.1 Functional design In the previous sections the dimensions for the elements separately have been determined. Because these functions will have to be fulfilled within one construction a combination of the functions needs to be found. The functions are: 1. Constraining of the sand profile 2. Blocking of the longshore transport 3. Creation of surf waves The optimum dimensions for these three functions are quite different and would lead to different designs, if the construction were split into three parts. In Table 5-1 for the completeness an overview is given of the optimum toe depth and crown height for each of the functions Table 5-1 Optimum dimensions for functions Functions Constraining profile Blocking transport Creation of waves toe depth NAP - 7 m NAP - 7 m NAP - 2 m crest height (at toe) NAP - 6 m NAP - 1 m Because functions are impossible to combine in one construction, the solution will be sought in designing more than one construction, or developing three alternatives, each with a favoured function. In the first alternative, the constraining of the profile is considered to be the prime function and the construction is designed such that this function is optimally fulfilled. Also a possible utilisation of the other functions is investigated, off course no longer in their optimum point, but as close as possible. This approach leads to the following four alternatives: A. Confine alternative. This alternative is equipped with a submerged confinement dam, up to a depth of NAP 7 m. A separate reef will be made at a depth of NAP 2 m, working only in the southern direction. The confinement dam will be bend slightly to the north, and the reef will be placed at a distance from the dam. The reef will be connected to the coast with a beachhead like construction, blocking the sand transport from NAP - 2m. B. Blocking alternative 1. A series of reefs will be constructed separate from each other but with an overlap in shore longitudinal direction. These reefs will be placed directly on the foreshore and no confining of the profile will take place. The first reef will be at the optimum depth of NAP - 2 m, and the rest placed further offshore until a depth of NAP 7 m is reached. C. Open alternative. In this case no blocking of the transport or confinement of the profile will take place. The surf reef will be placed at the optimum depth (NAP 2 m), and work in two directions. This alternative is the most surfer friendly but nevertheless not very feasible, because the economical analyses already turned out that a dam length of 0 meter lead to the highest costs. D. Blocking alternative 2. Because of the impossibility of an open alternative a fourth alternative drawn up. It consists of a dam until NAP m blocking the transport and confining the profile. Because two mayor functions are already fulfilled, a simple surf reef working in two directions can be placed at a distance from the dam providing the desired surfing condition. Delft University of Technology 47

62 5.1.1 Westdam The dimensions for the Westdam have been determined in the economical optimization in paragraph The result of this analyses was a dam constructed until a depth of NAP m and a crest height at the toe of 6.2 m above the beach profile (Figure 5-1). The crosssection of the dam will be similar to the design of the Noorderdam. This dam has proved to be sufficiently sand tight, and the design is already optimized. The crest height for the Noorderdam however is lower than the Westdam, so in the constructive design (section 5.4.1), the influence of the lower crest height on the armour layer will be investigated. Figure 5-1 Cross section of sandy profile with Westdam Transition construction The design of transition construction that is best applicable at Maasvlakte 2 is the closed gradual transition. A closed transition (Figure 2-5) provides the best protection for the hard flood defence, when the line of the normative erosion profile lies before the landward boundary of the hard flood defence, no material losses from the sea dike will occur and the stability of the flood defence is guaranteed. The transition construction is closed by the Westdam, see Figure 5-2. This dam is extended so far landward that the end of the dam lies behind the erosion profile. In section 5.4.2, the erosion profile will be calculated to determine the length to which the dam should be extended. Delft University of Technology 48

63 Figure 5-2 Plan view of the Westdam and transition construction The transition between the Westdam and the sea dike is gradual. Because the sea dike has a higher crest than the dunes, some gradual lowering of the crest will have to occur and as the crest reaches a height of NAP m, the Westdam will start. From the intersection with the sea dike, the Westdam will proceed seaward, until at reaches the point, where the beach is at the level of NAP. Here the Westdam will also be at NAP. From here on the dam will have a length perpendicular to the coast of 670 m, and end with a crest height of NAP - 1 m. The actual length of the dam will be almost 1200 m Artificial surfing reef The optimum depth for the artificial surf reef is found to be at NAP - 2 m. Henriquez (2004) found the following dimensions for a surf reef in the conditions described in paragraph 4.3: Reef toe depth at NAP - 2m; Reef tip radius of 80 m; Reef tip slope 1 : 12; Reef side slope 1 : 10. To maintain a submerged reef the platform of the reef is set at a depth of NAP m. From the demand that the construction should occupy as little area as possible above the water surface, it is preferred to construct the reef at a level that it is always submerged. Because the depth at the reef toe for surfing condition must still be 2 m, the reef will be constructed such that the depth during low tide will be 2 m. When the reef is submerged during low tide, it will surely be submerged during high tide. A beneficial factor from defining the user function state during low tide is that in this stage the current velocities will be relatively low, and since they were not taken into account in the analyses of the surf reef, their neglectance is hereby justified. Delft University of Technology 49

64 In Figure 5-3 a 3-dimensional view of the surf reef are shown. The back slope will be made with a slope of 1 : 3. The toe depth will be NAP - 2 m minus the tidal range of 1.3 m; NAP m Figure dimensional view of surf reef When the waves encounter the reef the waves break gradually along the flank. The constructive design of the reef will be discussed in section Delft University of Technology 50

65 5.2 Alternatives In section 5.2 three possible alternatives for the layout of the Westdam, and the surf reef are given. In this section the alternatives are described in more detail and a plan view is shown Confine alternative In Figure 5-4, the plan view of the confine alternative is shown. The prime function of this alternative is the confinement of the profile and therefore the dam extends till a depth of NAP -7.2 m. This is the optimum length defined in paragraph The dam however will not be constructed until the optimum crest level, but the crest will be just above the level of the sandy profile. Because the dam is constructed relatively low a lot of sand will be lost due to longshore transport flowing over the crest of the dam. Still the level of the crest has been chosen at this rather low level in order to maintain a proper wave field for the surf reef. When the dam would have been constructed at the optimum crest height, the waves will break on the dam, and since the reef is in the sheltered area behind the dam, the reef would not function. At the landside of the surf reef it is attached to a beachhead, which together with the reef blocks the sand transport between the NAP m depth line and the beach. This beachhead will be made from the same material as the reef. The reef only works in one direction, producing a surfable break with a southwest orientation. The surfers surf away from the submerged dam and the entrance channel leading so a safe situation. Figure 5-4 Plan view of confine alternative Blocking alternative 1, series of reefs In Figure 5-5 a plan view of the first blocking alternative is shown. In this alternative there is no confining of the profile letting the beach flow out entirely. The blocking of the profile is taken as prime function and the profile is blocked until a depth of NAP -7.2 m, which is the optimum depth following from section Since the reefs will have a slightly lower crest height than is optimum for the blocking of the transport, this function will not be entirely optimal fulfilled. However due to the number of reefs, in almost every condition, with wave Delft University of Technology 51

66 height ranging from 1 to 5 meter, a surfable wave can be reproduced. And because they work in dual directions a very diverse surf field is the result The reefs will be positioned such that in cross section of the cross-shore profile the blocking will be continues. In other words the reefs will overlap each other in the cross-shore plane. Uncertainties remain about the way in which the longshore transport will flow between the gaps between the reefs, instead of being blocked, but this effect is outside of the scope of this study. However effects like the above and the fact that the entire profile is left free to flow out, make this probably the least cost friendly alternative. Because in this alternative there exists no true Westdam the transition construction will be slightly different than was described in section Now the closed transition will have to be formed by the sea dike itself. Instead of an armour layer only on the outside, the sea dike will have to have some protection at the backside for length as long as the regression due to the normative erosion. Figure 5-5 Plan view of blocking alternative 1, series of reefs Delft University of Technology 52

67 5.2.3 Blocking alternative 2, separate reef In Figure 5-6 the plan view of blocking alternative 2 is shown, clearly visible is the separation between the morphological functions and the surfing function. To fulfil the morphological function the optimized Westdam is applied, with a toe depth of NAP m and a crest height at the toe of NAP m. Because this dam will break the waves that are necessary for wave surfing the reef is placed outside of the sphere of influence. The reef is indicated with the red cirkel in the picture Since the dimensions of the Westdam are economically optimized, for the surf reef a completely separate construction is chosen, with a dual surfing direction. Because the reef has a dual direction more people can surf at the same time than in the case of a single direction. Figure 5-6 plan view of blocking alternative 2, separate reef Delft University of Technology 53

68 5.3 Discussion functional design In the functional design three alternatives are developed each favouring different fulfilment of the functions. In the previous paragraphs the alternatives were only presented, but in this paragraph they will be evaluated. First the elements separately will be discussed, after which the combinations presented in the alternatives will be discussed Discussion of elements The first element that will be discussed is the Westdam as a sand trapping construction, blocking the longshore transport and confining the profile. From the economical analyses followed the optimum dimensions for this dam, and when they are compared to the dimensions in the design by EC-PMR, they appear to be larger. The economical optimum as it is modelled in this report leads to a longer dam than the original design. The crest height however can be slightly lower. When the cross-section of the dam is optimized, making the dam itself cheaper, the economical optimum as it is presented in this report will shift further offshore. Lower construction costs for the Westdam mean that the length of the dam can be longer, and more sand can be detained. The transition construction that is designed in this report is difficult to compare, because in the designs for Maasvlakte 2 this part of the construction has not been worked out yet. Nevertheless the construction presented in this report seems on the safe side, because there will probably be some erosion reducing factors present in the profile. The first is the presence of the Westdam; this dam partly protects the profile just behind it from incoming waves, leading to lower wave attack on the coast and thus less dune erosion. The second factor is the expected accretion in the protected area just behind the Westdam. Because of the sand blocking characteristic of this dam sand will accumulate up drift of the dam shifting the sandy profile seaward, and thus creating more protection for the limit profile. The stability of the surf reef on the other hand is unsure. The surfing model turned out that the reef should start at water depths of 2 meter. Unfortunately this area of the sandy profile is morphologically very active. This means that the sand around the reef will probably erode, or the reef will be covered with sand because part of the longshore transport will be blocked. Which of these processes will occur is difficult to predict, but it is surely advisable to do a thorough study into the morphologic effect of the reef on the beach, and likewise of the beach on the reef Discussion of alternatives The design that provides the best fulfilment of all the functions is the third design, blocking alternative two, separate reef. In this design a Westdam is placed at the optimum dimensions and the reef is separate. The advantage of the separation of these two constructions is that they can both be constructed in their optimum dimensions. Furthermore, because they are separate, failure of one construction does not necessarily lead to failure of the other. In the other two designs one or more functions are fulfilled outside of their optimum or not at all. Using a surf reef to block the longshore transport does not seem like a good idea, since the stability of the construction placed on the ever changing sandy profile is not guaranteed. Furthermore, if the function containment of the profile is not fulfilled, the costs will be extremely high, where the extra costs for the construction of a separate reef will be rather low due to the size of the reef. Delft University of Technology 54

69 5.4 Constructive design In this section the dimensions of the elements of the construction will be given based on design rules for the stability. The design will be split into three sections, each designed with a different return frequency of the hydraulic parameters. The three sections are: 1. The stretched Westdam, with its morphological functions. Failure in this case does not lead to a direct danger to the land reclamation. Therefore a lower return frequency of once in 1000 years is used; 2. The transition construction, if this construction fails, damage can occur to the hard flood defence leading to serious damage to the land reclamation, hence a return frequency of once per 10,000 years is used; 3. The surf reef itself. This reef does not fulfil any key functions and damage is acceptable, a lower return period than 10,000 years can be applied Westdam The Westdam will go from the hard flood defence towards the sea. At the landside, it has the same height as the hard flood defence. In EC-PMR this the crest height is defined at NAP m, consisting of quarry stones up to a height of NAP + 10 m and of asphalt between this level and the crest. Because the function and appearance of the Westdam are so much similar to the Noorderdam, the design of the Westdam will be based on the design of the Noorderdam. This means that it will have an armour layer made out of concrete blocks and have several filter layers. Because the crest height of the Westdam will be lower than that of the Noorderdam, the stability of the armour layer will be checked. This will be done using the formula of van der Meer (1988) for concrete cubes, together with the hydraulic parameters found in the SWAN research. 0.4 H s N od 0.1 = s 0.3 om, where Dn N H s = wave height at the toe of the construction N = number of waves S om = wave steepness at deep water =(ρ c - ρ s )/ ρ s, ρ c = 2300 kg.m 3 (specific weight of concrete) In EC-PMR (2003) the requirements for the Noorderdam were, a design period of 100 years, and a damage level of N od = 2, for concrete cubes and a return period of 10,000 year and N od = 0.4 for a return period of 100 year. The results of the calculations can be found in Table 5-2. The gentler conditions following from the SWAN conditions lead to smaller cubes than in the report by EC-PMR (2003). The increased stability due to the lower crest height is not taken into account here, because the stability of the armour layer is only calculated here as an indication of the possible armour unit size. This research shows that when the Westdam is constructed using the same design as the Noorderdam, the construction is stable under wave attack, and a possible reduction of the armour layer can be contemplated. Only in the case of an exceedance frequency of 1/10,000 per year the calculated armour unit is larger than the one in the design by EC-PMR (2003), however in this case the water level is also very high submerging the crest of the dam several meters. Because of the submergence of the crest, less weight is needed for the armour unit stability and the 47 ton blocks will suffice. Table 5-2 diameter of armour layer for the Westdam 1/1 per year 1/10 per year 1/100 per year 1/1,000 per year 1/10,000 per year Hs (m) Nod (-) N (-) Delft University of Technology 55

70 som (-) Dn (m) Weight (ton) Transition construction (Westdam) For the dimensions of the transition construction the wave heights found at the 20-meter depth line will be used. The critical limit profile will be calculated, and the stability of the dune analysed. (if necessary a wider dune is advised). The extra regression due to the presence of the hard construction will also be calculated. The calculations will be done assuming a straight coast, with an abrupt closed transition between the hard and the soft construction. This assumptions leads to a probable over exaggeration of the erosion, which in turn leads to a design that is on the safe side. The erosion profile can be given according to the following formula: w y = x H0s H0s This profile starts at the point x = 0 m, and y = 0 m. This point is located at the foot of the dune and at the SWL during the storm condition. This can be seen in Figure 5-7. The still water level under storm conditions lies well above the normal water level (NAP), and the dune foot is shifted shoreward. 1 x = 0 y = 0 SWL (Storm level) Equilibrium f Erosion profile 2 NAP Figure 5-7 Erosion profile for a normative storm From the differences between the equilibrium profile and the erosion profile, the amount of erosion (A) can be calculated. The area between the erosion profile and the equilibrium is equal for area 1 and 2 (Figure 5-7). Area 1 is the actual amount of material that is eroded from the dune, and area 2 is the same material being deposited again. For the different return frequencies and the corresponding hydraulic characteristics the amount of dune erosion is calculated and in Table 5-3 they are shown as the retreat of the dunes in meters. In appendix N, the amount of erosion can be found expressed in square meters (A [m 3 /m 1 ]). Table 5-3 Dune erosion in meters regression per return frequency Regression Dune erosion A (m 2 ) 1/1 per year 1/10 per year 1/100 per year 1/1,000 per year 1/10,000 per year Delft University of Technology 56

71 Regression (A/h) Regression d (m) Additional regression T e (m) Total regression In section the surcharges are discussed that have to be added to the dune erosion, they can be seen in Table 5-3 expressed in an extra regression working on the erosion profile. Also in this table is the extra regression as a result of the presence of the hard flood defence, the sea dike, in the dune area. This extra regression can be calculated according to the following formula: (paragraph 2.3.3) 1 T = + e Aont h A h0 h 0 The parameter A ont is the amount of extra amount of erosion that takes place as a result of the presence of the hard construction. Depending on the position of the hard construction with respect to the soft profile, this extra erosion can be zero, or maximum equal to the normative dune erosion (TAW, 1999). In this research the maximum amount of erosion is assumed, making the design on the safe side. When the results of the dune erosion are compared with the results found in (EC-PMR (2003), and the stability of the dunes is investigated with the presence of the hard construction, it becomes apparent that the erosion found in this research is in the same order of magnitude as was found by EC-PMR, but that the regressions are much smaller. This is mainly due to the lower storm levels found in this research compared to the results by EC-PMR. The stability of the dunes is guaranteed by the current design of the soft flood defence by EC-PMR Artificial surfing reef Since the surf reef will be a separate construction it can also be made of a different material. Because the reef is very shallow and the possibilities of surfers getting injured as a result of a collision with the reef should be as small as possible, a soft material for the construction is preferred. A good option is presented by the Terrafix soft rock sand containers. According to Pilarczyk (2000), the stability of the geo containers can be calculating according to the following formulae H s = 1, where b is width of the sand container lying on the ground. b The sand containers will have to comply with the requirements of the dimensions of the reef. This means that they will have to be relatively flat (Figure 5-8) and it is rather difficult to estimate the stability of the bags. This is done using a nominal diameter. The nominal diameter is chosen such that a cube with a size equal to the nominal diameter has the same volume as the flat bags. The nominal diameter in relation to the wave height is assumed to be equal to the formula by Pilarczyk, where b is replaced by D n50 (nominal diameter) and the is taken equal to 1. Figure 5-8 Close-up of reef tip The dimensions of the geo-containers are shown in Table 5-4. The last term in the first column (L max ) is given to indicate w hat the largest length is that can be taken into account Delft University of Technology 57

72 when evaluating the stability of a geo-container placed parallel to the wave crest. In that case the maximum length for computations is three times the diameter. Table 5-4 Geo container dimensions for stability under wave attack 1/1 per 1/10 per 1/100 per 1/1,000 1/10,000 year year year per year per year Hs (m) d cr (m) D (m) L (m) L max (m) A (m) Delft University of Technology 58

73 5.5 Discussion constructive design Westdam The stability calculations show that constructing the Westdam similar to the Noorderdam is a reasonable option. Depending on the exceedance level that is required for the construction the weight of the armour layer can be between 5 and 51 tons. The cross section of the design of the Westdam can be optimized further leading to an economically even more attractive design. When the costs of the dam will be reduced significantly a longer dam can be contemplated, lowering the costs due to the sand losses even more Transition construction The dune erosion calculations have shown that the design for the soft sea defence made by EC-PMR is wide enough to provide the necessary protection for the transition construction. Due to the mitigating factor, already mentioned in paragraph the design of the transition construction is safe, and meets the requirements Surf reef The calculation of the geo containers that will be used for the construction of the surf reef show that the elements have to be quite large. Depending of the exceedance level chosen for the construction the bags will have a height of 1.3 until 2.8 m. The reef that has to be constructed with this material has rather specific dimensions. The front slope is 1 : 12 and the height is in the order of two meter. When the construction element itself has a height of 2.8 m it is impossible to obtain a reef with the desired dimensions. Furthermore when the geo-containers are placed directly on the beach erosion will occur directly around the reef, so probably some kind of bottom protection will have to be applied. Figure Dimensional view of the alternative Delft University of Technology 59

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75 6 Conclusions and recommendations 6.1 Conclusions For the SWAN wave simulations boundary parameters a set of hydraulic boundary conditions with a combined statistic is obtained. The combined statistics were obtained using the marginal exceedance frequencies and physical relations between the parameters The optimum dimensions for the Westdam are found using a morphologic model. The optimum point for the toe depth was found at a depth of NAP m, the crest height at the toe is NAP 1.0 m. The length of the dam will be around 1000 m; The optimum dimensions for the surf reef were found with a surfing model. The toe depth of the reef was set on NAP 3.3 m and the crest if the reef at NAP 0.75 m. The orientation of the reef is 300º, the flanks of the reef, where the actual surfing will take place will be at an angle of 66º towards the reef normal; The alternative that fulfilled the requirements best was the blocking alternative 2, separate reef. This alternative consists of a separate reef and Westdam construction. Constructive design calculations showed that the transition construction is stable for all the exceedance frequencies; Because the reef is rather small, the construction material needs to combine two contradicting properties, it should be heavy enough to be stable under wave attack, and small enough to fit within the dimension requirements for the reef. 6.2 Recommendations The morphologic behaviour of the beach around the reef should be investigated in order to be able to predict the effect of the reef on the beach profile and the effect of the beach profile in its turn on the beach; The values of the parameters that were reduced with the physical relations should be validated against the parameters that were reduced by means of the statistical approach. The statistical approach is previously used to obtain the set of combined exceedance frequencies and a comparison between the two methods gives more insight in the effects of combined statistics. The SWAN model should be calibrated with simultaneous measurements of the stations Europlatform and IJmuiden and somewhere close to Maasvlakte 2 in order to get an idea of the accuracy of the simulations. Delft University of Technology 61

76 Delft University of Technology 62

77 7 References ARGOSS (2002), kansverdeling van de waterstand van gegeven significante golfhoogten bij Europlatform, concept report, , ARGOSS Black, K.P., Andrews, C., Green, M., Gorman, R., Healy, T., Hume, T., Hutt, J. Mead, S. and Sayce, A. (1997), Wave dynamics and shoreline response on and around surfing reefs. Proc. 1 st International surfing reef symposium. Sydney, Australia. University of Sydney, 12 pp. Boer, S., & Roukema, D. (2004), Onderhoudsaspecten Doorsteekvariant definitief concept, INFRAM rapport, 041i00 versie 1.20, October 2004 Dally, W.R. (1990), Stochastic Modeling of Surfing climate. Proc. 22 nd International Conference on Coastal Engineering, Delft, The Netherlands. ASCE New York, pp Davey (2005), Sean Davey's Tasmania, Retrieved May 2005, from edited by Henriquez (2004) Demirbilek, Z., Bratos, S., and Thomson, E. (1993), Meteorology and Wave Climate. In: Vincent, L., and Demirbilek, Z. (editors), Coastal Engineering Manual, Part II, Hydrodynamics, Chapter II-2, Engineer Manual , U.S. Army Corps of Engineers, Washington, DC. Expertise centrum-pmr (2002)Publiek programma van eisen landaanwinning, PMR docs versie 4, 2002 Expertise centrum PMR (2003), Landaanwinning ontwerprapport, terrein, zeewering en Havendam, Versie definitief. Verkenning ontwerpruimte set 1 alternatieven, March 2003 Henriquez, M., Artificial Surf Reefs, Master thesis final version, Environmental Fluid Mechanics Section, Faculty of Civil Engineering, Delft University of Technology, Delft, November 2004 Holthuijsen, L.H., Booij, N. and Herbers, T.H.C. (1989), A prediction model for stationary, short-crested waves in shallow water with ambient currents, Coastal Engineering, 13, Holthuijsen, L.H., Booij, N. Ris, R.C., Haagsma, IJ.G. Kieftenburg, A.T.M.M., Kriezi, E.E., Zijlema, M., van der Westhuyzen, A.J. (2004), SWAN user manual, SWAN cycle III version Delft University of Technology, Faulty of Civil Engineering and Geosciences, Environmental Fluid Mechanics Section, 2004 Hutt, J.A. & Black, K.P.,& Mead, S.T. (2001) Classification of surf breaks in relation to Surfing skill. Journal of Coastal Research, Special Issue Jacobse, J.J. & Groos, J.G.C. (2002), Golfbelasting t.b.v. het voorontwerp van de uitbreiding van de Maasvlakte, Werkdocument RIKZ/AB x, Rijksinstituut voor Kust en Zee (RIKZ), May 2002 Van der Meer, J.W. 1988, Irragular waves, approach of van der Meer,Breakwaters and closure dams, chapter 7.2, D Angremond, k. And van Roode, F.C., 2001 Ministerie van Verkeer en Waterstaat (2002). Golfklimaat bestanden. Retrieved February 2005, from Pilarczyk, K.W. (2000). Geosynthetics and geosystems in hydraulic and coastal engineering, Rijkswaterstaat, Delft, 2000 P. Roelse (1993), Werkdocument GWWS x, "Eindconstructies van dijken en duinvoetverdedigingen in Zeeland" Rijkswaterstaat (2001), Hydraulische Randvoorwaarden 2001, voor het toetsen van primaire waterkeringen, Rijkswaterstaat, Dienst Weg- en Waterbouwkunde, Directoraat Generaal Rijkswaterstaat, Delft, April 2002 Rogers, W.E., Kaihatu, J.M., Petit, H.A. H., Booij, N., and Holthuijsen, L.H. (2002), Diffusion reduction in a arbitrary scale third generation wind wave model, Ocean Engineering., 29, Roskam, A.P. & Hoekema, J. & Seijffert, J.J.W. (2000), Richtingsafhankelijke extreme waarden voor HW-standen, golfhoogten en golfperioden, Rijksinstituut voor Kust en Zee, December 2000 Steijn, R.C. (1999), Zachte zeewering Maasvlakte 2, beoordeling van enkele varianten en suggesties voor verbeteringen, Rapport A395r1r1, ALkyon/WL/Arcadis, may 1999 Delft University of Technology 63

78 TAW (1995), Basisrapport Zandige Kust, behorende bij de Leidraad Zandige Kust, Technische Adviescommissie voor de waterkeringen, den Haag, Januari 1995 TAW (1999), Leidraad Zee- en Meerdijken + Basisboek, Technische Adviescommissie voor de Waterkeringen, Delft, December 1999 TAW (2004), De veiligheid van de primaire waterkeringen in Nederland, voorschrift toetsen op veiligheid voor de tweede toetsronde , Ministerie van verkeer en waterstaat, January 2004 TAW (1984) leidraad voor de beoordeling van de veiligheid van duinen als waterkering, leidraad duinafslag, 1984, onderdeel van Leidraad zandige kusten (TAW 1995) Valk, de, C.F. & Melger, F.J. (2002), Onderzoek onzekerheid extreme golfbelasting. Eerste statistische analyse reductie ontwerpwaarden, Eindrapport fase 1, ARGOSS rapport, RP_A258, July 2002 Van der Hout, G (1999), Hydraulische randvoorwaarden voor het ontwerp van Maasvlakte 2, Samenwerkingsverband Maasvlakte 2 varianten, Ingenieursbureau Gemeentewerken Rotterdam, 1999 van Marle, J.G.A. (2000) Meerdimensionale extreme waarden statistiek van belastingen en faalkansberekeningen. Rapport RIKZ , Rijswaterstaat, Rijksinstituut voor Kust en Zee, RIKZ, may 2000 van der Velden (1998), E.T.J.M., Coastal Engineering Vol 2, Morfologie van kusten en estuaria, Lecture notes CT5309, Delft University of Technology. Departement of Civil Engineering, Delft, january 1998 Verkaik, J.W. & Smits, A. & Ettema, J. (2003), Wind climate assessment of the Netherlands 2003, Extreme value analysis and spatial interpolation methods for the determination of extreme return levels of wind speed Royal Netherlands Meteorological Institute, 2003 Vledder, G.Ph. (2002), Onderzoek onzekerheid extreme golfbelasting. Effect stromingen op golven. Stappenplan toepassing SWAN model, Eindrapport fase 1, Alkyon rapport, A901, July 2002 Walker, J.R. (1974), Recreational surf parameters. Tech. rept. 30 University of Hawaii, James K.K. Look Laboratory of Oceanographic Engineering Weenink, M.P.H. (1958) A theory and method of calculation of wind effects on sea levels in a partly enclosed sea, with special application to the southern coast of the North sea Wet op de Waterkering (WWK, 1996) Staatsblad 1996, 8 SDU uitgeverij, Den Haag, 1996 Rijkswaterstaat, Dienst Weg- en Waterbouwkunde Wieringa, J. & Rijkoort P.J. (1983), Windklimaat van Nederland Koninklijk Nederlands Meteorologisch Instituut Delft University of Technology 64

79 8 Appendices Delft University of Technology 65

80 Delft University of Technology 66

81 A Simulating WAves Nearshore Introduction The model SWAN is a third-generation stand-alone 2 (phase-averaged) wave model for the simulation of waves in waters of deep, intermediate and finite depth. It is the successor of the stationary second-generation Hiswa model (Holthuijsen, Booij, & Herbers, 1989). Although SWAN is a non-stationary model, it can work in the stationary mode. In this research SWAN version 4.31 is used. The model description and basic equations were derived from the SWAN online manual (Holthuijsen, Booij, Haagsma, Kieftenburg, Kriezi, Zijlema, & van der Westhuyzen, 2004). The stationary assumption is considered acceptable for most coastal applications because the travel time of the waves from the seaward boundary to the coast is relatively small compared to the time scale of variations in incoming wave field, the wind or the tide. To avoid excessive computing time and to achieve a robust model in practical applications, fully implicit propagation schemes (in time and space) have been implemented. The SWAN model was developed at Delft University of Technology, Delft (the Netherlands). WL Delft Hydraulics has integrated the SWAN model in several models like Delft3D. Technical specifications The SWAN model is based on the discrete spectral action balance equation and is fully spectral (over the total range of wave frequencies and over the entire 360 ). The action density spectrum N (σ, θ) is used instead of the Energy density spectrum E (σ, θ), because under currents the action density is conserved, where the energy density is not. The E ( σ, θ) Action density with respect to the energy density is given in the equation N ( σ, θ) =, σ where σ = relative frequency (as observed in a frame of reference moving with current velocity) and θ = wave direction (normal to wave crest of each spectral component) The action density balance equation reads: δ δ δ δ δ S N + c XN + cyn + cσn + cθn = δt δx δy δσ δθ σ (basic equation) The first term on the left-hand side is the local rate of change of action density in time. The second and third terms are the propagation of action in geographical space, with propagation velocities c X and c Y. The fourth term represents the shifting of the relative frequency due to variations in the depth and currents. The last term on the left-hand side represents the depth and current induced refraction. The term on the right-hand side is a source term for generation, dissipation and nonlinear wave-wave interactions. Diffraction and reflections are not explicitly modelled in SWAN but diffraction effects can be simulated by applying directional spreading of the waves. 2 SWAN is also integrated under the numerical Delft3D model Delft University of Technology 67

82 Numerical implementation Since the nature of the basic equation is such that the state in a grid point is determined by the sate in the up wave grid point (hyperbolic property), the most robust and efficient scheme is the implicit upwind scheme (supplemented with central approximation in spectral space). For stationary large-scale applications SWAN uses the SORDUP scheme. SORDUP stands for Second-order upwind scheme with second order diffusion. For Other applications SWAN uses different numerical schemes, but since in this research all simulations are stationary, only the SORDUP scheme is relevant. For the SORDUP scheme, which is the default scheme for stationary computations, the two terms in the basis equation representing x- and y-derivatives are replaced by (Rogers, Kaihatu, Petit, Booij & Holthuijsen, 2002) it, n 1.5 c xn c xn 1 cxn i x ix ix 2 + x 1.5 c N 2 c N c N y y i y y iy 1 y iy 2 iy, iσ, iθ it, n ix, iσ, iθ Boundary conditions In SWAN both in geographical space and spectral space, the boundary conditions are fully absorbing SWAN simulates the following physical phenomena: Wave propagation in time and space Shoaling Refraction due to current and depth Frequency shifting due to currents and nonstationary depth Wave generation by wind Nonlinear wave-wave interactions (both quadruplets and triads) Whitecapping, Bottom friction Depth-induced breaking Blocking of waves by current Delft University of Technology 68

83 B Operating procedure Introduction For the setting up of the SWAN model in this research the following procedure was followed. First a series of grids was drawn up based on experience and insight. From this grid deviations started, first the grids were improved to make the calculations as fast and accurate as possible. With the final grids determined other parameters could be varied in order to gain insight on the effect on the outcome of the particular parameter. The outcomes were compared to a reference case Control points With respect to this reference case values for other parameters are tested and compared one at a time. Different values were tried for the wave height and the wave period, the effect of wind was evaluated with runs without any wind and runs with only wind and no waves. The effect on the computed wave characteristics is reviewed in a number of control points. In total eight control points were chosen and they are located close to the edge of Maasvlakte 2, Figure 8-1. The discussion of the effects of the changes in the parameters can be found in the next sections. Figure 8-1 Location of control points Adjustments All the adjustments and tests that were carried out to set the parameters to their optimum values are described in the following section. At the end of the section in Table 8-2 an overview is given of the different runs. The runs use several conditions each with a specific direction and originating from one of the measuring points. The four different conditions that are used are shown in Table 8-1. Table 8-1 Hydraulic conditions 3 used for the setting up of the model Condition Surge level Wave height Wave period (T P ) Direction North_EUR 3.81 m + NAP 7.55 m 12.5 s 0º North_YM m + NAP 8.14 m 14.6 s 0º South_EUR 0 m + NAP 7.2 m 11.5 s 210º West_EUR 0 m + NAP 8.1 m 12.3 s 300º Besides these directional conditions a few other conditions were used. For the first few runs with a Northern direction a condition similar to the West_EUR was used with a wave height of 8.2 m and a period of 13.6 with a direction of 0º, this condition will be named North_0m. In total eight different sets of runs were executed changing the following parameters. 1. The first runs were to check and improve the grids. The conditions that were used were South_EUR, West_EUR and the condition described in the above. 3 The objective was to use the marginal probability values from Roskam et al. (2000) for the wave parameters in the adjustments, but due to reading errors and communication failures some deviations from these values has occurred. Delft University of Technology 69

84 2. The second set was run to check the effect of the wind on the results. Wind conditions between 38 m/s and 0 m/s. The wave conditions were either West_EUR or zero. 3. In the third set the boundaries were investigated for sensitivity when described in sections. This was done using the North_EUR condition and shoaling the boundary sections. 4. A wind file was created describing in every point of the grid a wind velocity between 28 and 0 m/s. The wave conditions were North_EUR for the Northwest boundary and North_YM6 for the Northeast boundary. The results are not reliable because of some mistakes in the wind file but it is included in Table 8-2 for completeness. 5. In the previously used bottom files the sloping bathymetry just in front of the second Maasvlakte was not entered yet. Investigated was what the effect of this changed bathymetry was under both the South_EUR condition and the North_EUR condition. 6. A simple comparison was made using North_EUR on the Northwest and Northeast boundary and using North_YM6 also on the Northwest and Northeast boundary. 7. A further simplification on the boundary conditions can be achieved by shifting the EUR conditions and the YM6 conditions towards the ends of the Northwest boundary. This is done for both the South_EUR condition and the North_YM6 condition. 8. Finally the effect of scour holes in front of the Maasvlakte on the waves is investigated. To do this new control points had to be placed just behind the scour holes. These runs were done using the North_EUR and North_YM6 for the Northwest respectively the Northeast boundary and for a new case with waves coming from 330º. Wave height is 8.2 m, period is 13.0 s and the water level is 4.87 m above NAP. The results and the differences in the results that followed from these adjustments are given in Table 8-2. In this table there is a reference case defined for each of the 8 sets of test runs and the adjustments and deviations within this set is described. Significance During the study of the effects of some change in one of the parameters of the input, the difference between the cases was expressed in percentages. When a new parameter only differed a couple of percentages, 0 to 5 %, the change was noted as insignificant. When the effects became more apparent, 10% or more, the changed parameter had a significant effect. These boundaries for the accuracy are not theoretically grounded but will be coupled to the formulas that are going to be used in the next phase. In this stage of the research however, 10 % is taken as the upper limit. The results as a whole from the SWAN computations should be validated against nearshore wave measurements, but because those measurements are rare the results are judged on the basis of common sense only. Table 8-2 Table of adjustments Series name Grids Grids and Bathymetry GI100 GD40 Reference case Boundaries North_0m West_EUR South_EUR Wind 28 m/s 38m/s 28 m/s Runs Condition Changed Parameter Resulting difference in % Run_04 North_0m AI100 D40 2 % Det and Int klein 210 gr South_EUR AI100 D40 2 % DET and Int klein 300gr West_EUR AI100 e D40 3 % Series name Reference case (Run_05) Delft University of Technology 70

85 Grids and Bathymetry Boundaries Wind Wind&waves AI100 D40 West_EUR 38m/s Runs Condition Changed Parameter Resulting difference in % Run_06 Only wind 38 m/s -16 % Run_07 No wind - 36 % West_EUR Run_08 Medium wind 20 m/s - 21 % Reference case (Run_09) Series name Grids and Bathymetry Boundaries Wind Sections AI100 D40 NW&NE: North_EUR 28m/s Runs Condition Changed Parameter Resulting difference in % Run_10 NE in 10 sections < 1 % Run_11 NE in 2 sections < 1 % Run_12 North_EUR 12 % NE sections Counter (counterclockwise is clockwise the wrong direction) 1 op NWshoaled en 10 sections NW < 1 % NO 1 op North_EUR NWshoaled en NO new sections NW - 1 % Reference case (Run_09) Series name Grids and Bathymetry Boundaries Wind Windfile AI100 D40 NW: North_EUR NE: North_YM6 28m/s Runs Condition Changed Parameter Resulting difference in % windfile As reference windfile - 40 % Series name MV2 in bottom Grids and Bathymetry AI100 D40 Reference case (Run_09) Boundaries NW: North_EUR NE: North_YM6 Wind 28m/s Runs Condition Changed Parameter Resulting difference in % Run newmv2 360gr North_EUR MV2 in det grid 10 % Run_20 MV2 in det and int grid 10 % Run_19 MV2 in det grid 10 % Run newmv2 in South_EUR MV2 in det and int det and int grid 10 % Series name All EUR and All YM6 Grids and Bathymetry AI100 D40 Reference case (Run_09) Boundaries NW: North_EUR NE: North_YM6 Wind 28m/s Delft University of Technology 71

86 Runs Condition Changed Parameter Resulting difference in % Run_15 NE&NW all IJmuiden 6 % Run_17 Both bound in sections 5% Series name MV2 hoeken Grids and Bathymetry AI100 D40 Reference case (Run_09) Boundaries NW: North_EUR& NE: North_YM6 SW: South_EUR Runs Condition Changed Parameter RunMV2hoeken EUR&YMW 210gr RunMV2 Hoeken EUR&YMW 360gr Wind 28m/s 35 m/s Resulting difference in % Southwest NW 2sections No reference North_YM6 NW 2sections 5 % Scour Grids and Bathymetry AI100 D40 Reference case (Run_09) Boundaries NW: North_EUR& NE: North_YM gr NW Wind 28m/s 34 m/s Runs Condition Changed Parameter Resulting difference in % Scour 360gr As reference With Scour - 7 % tot + 2 % Scour 330gr gr NW 34 m/s With Scour - 4 % tot + 2 % Delft University of Technology 72

87 C SWAN Setup Introduction In the report only the most important setup parameters are discussed. In these appendices all the input parameters will be discussed after which the parameters that have already been singled out in the main report will be discussed more thoroughly each in a separate appendix. First however, the input will be discussed step by step followed at the end of this appendix by an example of an mdf-file, the command file used for the SWAN computations. A SWAN simulation needs a number of input parameters and files; the primary input files are the command file, bathymetry file and the bathymetry grids. The input sections are given below and discussed briefly in this section. Flow Grids Time Frame and Water Level Boundaries Obstacles Physical parameters Numerical parameters Output Flow SWAN offers the opportunity to enter flow velocities en water levels obtained from previous flow runs. These velocities and water levels can have some effect on the wave height and direction and are directly read from the output files of Delft 3-D Flow. In the section Time frame" a water level and velocity can also be defined but only under the flow option the water level and the velocities can vary in space. Further on in this paragraph will be explained why in this research the effects of currents on the waves is neglected. The Flow options were not used, Delft 3D flow computations were available but combining them with the current SWAN wave simulations was difficult. One of the complicating factors was the curvilinear grid that was used for the flow computations. A grid like that can be used with SWAN, but proved to be very difficult, so the flow data had to be interpolated to a rectangular grid. Because the effect of flow on the waves is considered negligible this elaborate action was avoided. Grids The bathymetry grid file is the file that describes the grid on which the bathymetry is based, i.e. the begin point of the grid, the size and the number of elements and the orientation. It gives the coordinates of every point in this grid. The bathymetry depth file gives for each location the depth with respect to NAP. These files form the basis on which the computations are run. The computations can in their turn be carried out on the same grid or on a different grid. When the computational grid is the same as the bottom grid the computations are the most accurate because no accuracy is lost in interpolations between the grid points of both grids. For a more detailed description of the grids that were used in the simulations, the reader is referred to Appendix D. Time frame The second important input is the Time Frame where the user can define at which point in time the calculations should be done, but in this case more important, the user can also enter hydrodynamic data in the form of: water level, X velocity and Y velocity. These parameters Delft University of Technology 73

88 will be assumed the same in every point of the grid. However since the effect on flow was considered negligible and already neglected for flow computations also here the flow velocity is set on 0 m/s. Boundaries The boundaries that can be imposed on the grid are very important for the calculations. Any inaccuracy on the boundaries proceeds into the area, as a result of the programs calculations, and can lead to inaccuracies in the area of interest. It is therefore important to define these boundaries as accurate and detailed as possible. Because the bathymetry can vary between points on a certain boundary, the wave conditions can vary also and it could be advisable to define the boundary in a number of sections. The data that will be used for the boundaries is explained in Appendix G. Obstacles Obstacles blocking partial or completely the wave transmission can be entered, but in this research this function has not been used. Physical Parameters In SWAN the physical parameters can be divided into constants, wind, processes and various. The process of wind growth in the area is rather important because in this case the area is quite large, the fetch can be up to 100 kilometer. The wind velocity and direction is the only physical parameter that is changed in this research. The other parameters were kept at constant values, which are as follows. Constants Gravity 9.81 m/s 2 Water density 1025 kg/m 3 Minimum Depth 0.05 m Forces: Wave energy dissipation rate Processes Formulation third generation Bottom friction JONSWAP (Coefficient 0.067) Depth induced breaking B&J model (α = 1, γ = 0.73) Non linear triad interactions LTA (α = 0.1, β = 2.2) Various Windgrowth, Whitecapping, Quadruplets, Refraction and Frequency shift activated Numerical Parameters The numerical parameters were kept at constant values like most of the physical parameters. The only exception is the number of iterations that was for most of the runs limited to five iterations to save time. A sensitivity analyses showed that the results converge when the number of iterations is set on 15. From now on this is the amount of iterations that will be used for the simulations. The settings of the rest of the numerical parameters are shown in Figure 8-2. Delft University of Technology 74

89 Figure 8-2 Numerical parameters Output A last input parameter in SWAN concerns the output. SWAN can show the results of the simulations graphically over a previously specified grid, this grid can be the same as the computational grid, but SWAN can also write the wave characteristics into a table for a number of user specified control points. In these points the effect of the change of one parameter can be compared numerically, giving a good idea of the deviations in terms of percentages. Also available for these points is the wave spectrum. Furthermore, so-called curves can be plotted, for a number of previously entered points SWAN makes an output file, not only containing the hydraulic parameters but also the distance form the output point to the first point. On the following pages, Table 8-3, an example is shown of the contents of one of the MDWfiles used by SWAN. The file shown here was used to simulate waves coming from 330º with a return period of 1 in 10,000 years. This file only shows the input for this direction, however the other directions and return periods were run over the same bathymetry, the only thing that changes is the boundary conditions, the water level and the wind characteristics. Delft University of Technology 75

90 MDW file for SWAN Delft3D WAVE GUI version '40.01' Table 8-3 MDW file, command file for SWAN computations Description * Project name 'fase2mv2' * number '0001' * Description 'reduced boundary conditions met wave setup en extra raaien(curves) 330 deg' Use bathmetry, use waterlevel, use current No, No, No Grids and bathymetry * Number of computational grids 3 * Filename comp. grid 'E500.grd' * Y/N Bathymetry is based on 1 comp. grid, * Filename bathymetry data 'E500.dep' * Directional space: type (1 = circle, 2 = sector), number of directions, start-direction, enddirection * Frequency space: lowest frequency, highest frequency, number of freq. bins, grid to nest in, Y/N write output for this grid * Filename comp. grid 'AI100.grd' * Y/N bathymetry is based on 1 comp. grid, * Filename bathymetry data 'AI100_MV2.dep' * Directional space: type (1 = circle, 2 = sector), number of directions, start-direction, enddirection) * Frequency space: lowest frequency, highest frequency, number of freq. bins, grid to nest in, Y/N write output for this grid * Filename comp. grid 'D40.grd' * Y/N bathymetry is based on 1 comp. grid, * Filename bathymetry data 'D40_MV2.dep' * Directional space: type (1 = circle, 2 = sector), number of directions, start-direction, enddirection) * Frequency space: lowest frequency, highest frequency, number of freq. bins, grid to nest in, Y/N write output for this grid e e e e e e e e e e e e Delft University of Technology 76

91 Time points * Number of tidal time points 1 * Time, h, u, v e e e e+000 * Water level correction e+000 Boundaries * Number of boundaries 2 * Boundary name, specifications:(1 'IJmuiden' = from-file, 2 = parametric), defined-by, conditions-alongboundary (1 = orientation, 2 = gridcoordinates, 3 = xy-coordinates), conditions-along-boundary (1 = constant, 2 = variable) * Orientation 8 (1 = N, 2 = NW, 3 = W, 4 = SW, 5 = S, 6 = SE, 7 = E, 8 = NE) * Shape (1 = Jonswap, 2 = Pierson Moskowitz, 3 = Gauss), period (1 = Peak, 2 = Mean), width-energy (1 = Power, 2 = Degrees), peak enhancement factor, spreading, * Significant wave height, peak e e+001 period, direction, energy distribution e e+000 * Boundary name (1 = from-file, 2 'EURO and YM6' = parametric), specifications, defined-by (1 = orientation, 2 = grid-coordinates, 3 = xycoordinates), conditions-alongboundary (1 = constant, 2 = variable) * Orientation 2 1 = N, 2 = NW, 3 = W, 4 = SW, 5 = S, 6 = SE, 7 = E, 8 = NE * Shape (1 = Jonswap, 2 = Pierson- Moskowitz, 3 = Gauss), period (1 = Peak, 2 = Mean), width-energy (1 = Power, 2 = Degrees), peak enhancement factor, spreading, * Number of sections, 2 1 Length along side is clockwise(=2) or counter(=1) clockwise * Distance from corner, significant wave height, Peak period, direction, energy-distribution e e e e e e e e e e+002 Obstacles * Number of obstacles 0 Delft University of Technology 77

92 Settings * Gravity, water density, north, e e+003 minimum depth e e-002 * convention: 1 = nautical, 2 = cartesian - setup: 0 = no setup, 1 = activated - forces: 1 = radiation stress, 2 = wave energy dissipation rate * Wind type (1 = constant, 2 = 1 variable) * Wind speed, -direction e e+002 * Type of formulations 0 = none, 1 3 = 1-st, 2 = 2-nd, 3 = 3-th generation * Depth induced breaking, alpha, e e-001 gamma - breaking: 0 = deactivated, 1 = B&J model * Bottom friction (0 = de-activated, e = Jonswap, 2 = Collins, 3 = Madsen et al), friction coefficient * Non-linear triad interactions (0 = e e+000 de-activated), 1 = LTA, alpha, beta * Y/N windgrowth, white-capping, quadruplets, refraction, freq. shift * Directional space, freq. space e e-001 * Hs-Tm01, Hs, Tm01, e e-006 perc. of wed grid points, e e max. number of iterations Output * Level of test output, debug level, Y/N compute waves * Y/N output to Flow grid; filename 0 of Flow grid * Y/N output to locations 1 * Output locations: 1 = from file, 2 1 = parametric * Filename for locations 'fase2pnts.loc' * Y/N table, 1-D spectra, 2Dspectra Delft University of Technology 78

93 D Grids and bathymetry The first case that was defined consisted of grids that had between and grid cells, see Figure 3-4, left hand side of the picture, leading to very slow computations and this was the basis from which the parameters were adjusted. Each time a parameter was adjusted and the newly acquired results correspond with the demand for accuracy the new parameter was adopted into the reference case and a new reference case came into being. In this section the original input for the grids will be described, the different wave parameters that will be used for the cases is described in the next sections. Bathymetry The bathymetry file that was used is constructed from a very large file obtained from the Dutch Navy (Hydrografische Dienst van de Koninklijke Nederlandse Marine). They supplied a detailed digital map of part of the North Sea with measured depth every 20 meters. These sample points were interpolated to a grid, the bottom grid, were the sample points became depth points, describing in every point the local depth. Grids The size of the grids was determined in such a way that the computations ran smoothly and took, preferably, not much over an hour. Because a grid can only have a limited number of grid cells, 800 by 800 cells, very large grids can only have cells that are in turn rather large. A bottom with a lot of spatial variations on small length scales is not well described by large cells, because these variations can be lost when translating to the relatively large cells. Another reason for small grid cells is when very detailed information in the area of interest is wanted. This is especially the case when the area of interest lies close the shore and the simulations start far offshore, as is the case with the second Maasvlakte. In this case the area of interest is located close to the future beach and dike that protects the area and the propagations start far offshore where detailed information is given by two offshore measuring installations. (See Figure 3-4) The distance between the two points is 100 kilometers, and distance between the points and the coast is about 50 kilometers. These points form part of the first grid but when this grid is extended to the coast to include the Maasvlakte it would become very large and the area of interest would not be sufficiently described. Figure 8-3 position of the exterior grid on the North Sea Delft University of Technology 79

94 Nesting To solve this problem a series of nested grids will be introduced, starting with a large Exterior grid covering the measuring locations and the Dutch North Sea shore (See Figure 8-4). The second grid, the intermediate grid, is nested in the Exterior grid and covers the entire area of the second Maasvlakte and an area of 10 kilometers on either side. The last grid is the detailed grid, and this grid covers only the part of the Maasvlakte where the wave characteristics are demanded. The exterior grid has cells of 500 by 500m, (Figure 3-4). On the Northwest boundary this grid includes the Euro platform, a measuring platform at a local depth of about 30 m, on the Northeast the IJmuiden ammunition dump (munitiestortplaats), located at a depth of 25 m. The landward boundary of this grid coincides with the position of the coastline and the Southwest boundary is chosen well away from the Maasvlakte 2. This exterior grid measures 100 by 55 kilometers and has 200 rows and 110 columns. Figure 8-4 Large grids and small grid The detailed grid needed a small grid size of about 20 to 50 meters wide. The step from the exterior grid, with elements of 500 m towards the small elements of the detailed grid has become too large to take in one grid, so an intermediate grid was put in between. The elements of this grid were chosen such that the step from exterior to intermediate grid was roughly the same size as the step from intermediate to the detailed grid. For the intermediate grid an element size of 100 by 100 m was chosen. New grid The final grids are: (see Figure 8-4, right hand side) Exterior grid, elements 500m by 500m, 100 by 55 kilometer Intermediate grid, elements 100m by 100m, 22 by 15 kilometer Detailed grid, elements 40 m by 40 m, 5.6 by 5.2 kilometer Delft University of Technology 80

95 E Timeframe/ flow Water level. Table 8-4 Water level at Maasvlakte 2 Directional sector Surge level (m +NAP) Maasvlakte 2 210º º º º º º 3.71 Omni directional 4.90 Since the water level under storm conditions (Basispeil in Dutch) varies along the Dutch coast a correction should be applied on the water levels from Table 8-5 and Table 8-6. According to Van der Hout (1999) a water level reduction of 10 cm between Hook of Holland and Maasvlakte 2 is realistic. In Figure 3-5 the distribution of the water levels along the Dutch coast is illustrated. Figure 8-5 Spatial distribution of the water levels along the Dutch coast Influence of flow on waves In proceedings of the research executed by Jacobse and Groos (2002), Vledder (2002) investigated the influence of flow on waves. By running various SWAN computations he concluded that on the northwestern corner of Maasvlakte 2 the relative influence from flow on waves is greatest (20%) with waves and wind from the direction 210ºN. However, the significant wave height and mean wave period are much greater with wind and waves from the direction 315ºN. (See Figure 8-6 and Figure 8-7). Furthermore as the significant wave height, with wind and waves from 315ºN, is increasing with a maximum of 4% along the output points, the mean wave period is decreasing with 2.5%. So the wave load (H s *T m01 ) as shown at the bottom of Figure 8-7, due to flow increases with only 3.8%. Since these peak values are only true for less than half an hour, it is decided not to take the influence of flow in account in this stage. Delft University of Technology 81

96 Figure 8-6 Effect of currents on waves, wave direction 225º Delft University of Technology 82

97 Figure 8-7 Effect of currents on waves, wave direction 315º Delft University of Technology 83

98 Delft University of Technology 84

99 F Boundary conditions Introduction The boundary conditions that were to be imposed on the model area can be defined by the wave height H S, the wave period T P, the wave direction in degrees and the width of the energy distribution. Three of these parameters, wave height period and direction, are given by the measuring stations at the two boundaries. The wave data from these stations can be obtained in a number of tables showing the exceedance frequencies for the direction dependent wave heights. These tables can be found in the results obtained by Roskam, Hoekema and Seijffert (2000). Boundary definition A proper definition of the boundary conditions is very important because the conditions on the boundaries are used to calculate the conditions on the rest of the grid. In this case the two of the boundaries are crossing the positions of measuring locations. In those locations the wave conditions and the still water level are known under both normal and storm conditions. But these locations are just points on boundaries stretching for 50 to 100 kilometers, passing over different water depths causing wave conditions to change along the boundary. The longest boundary has a length of 100 kilometer and runs over depths ranging from 25 meter up to 32 meter. The measuring point on this boundary, Euro platform, is located at a depth of 31 meter. With the aid of a shoaling coefficient the wave characteristics in this point can be translated into characteristics in a number of other points with different depth. In SWAN the number of section per boundary is limited to 10, so ten points on the boundary were selected and new wave conditions were calculated. The same was done for the northeast boundary where the wave data from IJmuiden was used. When the results from the simulations with this waveadapted boundary were compared with the results from simulations using a constant value along the boundary, the differences are in the order of 1 or 2 percent and are considered insignificant. Roskam et al calculated the extreme value distribution for small sectors of the wind direction using wind, water level and wave measurements over the period The summation of the exceedance frequencies of a certain parameter over all directions equals the omni directional extreme value for this parameter. The parameters used in this research are, storm surge level, significant wave height, peak period and mean spectral wave period. The storm surge results show that the distribution increases from the Southwest towards a maximum at West to Northwest. The wave heights show the largest extremes for all the measuring locations in the sector Northwest and the lowest at the sectors East to Southeast. The period distribution shows similar behavior as the wave height because of the strong connection that exists between the two parameters. Hence the normative directions are 330º and 360º (North). The results by Roskam et al, also clearly show that there is a large "landwind sector" present, from 10º to 220º, where the water and wave parameters show very low values. This sector will from now on be disregarded in the current research. According to the program of requirements wave conditions with return period of 10,000 years will be used. Depending on the width of the directional sector that is used the wave height is formulated by Roskam et al. In Table 8-5 the corresponding parameters are shown for the Europlatform and in Table 8-6 for the IJmuiden Ammunition dump station. The extreme values 4 are calculated for 10º sectors and for 30º sectors. In the tables, only the 30º sectors are shown since this is the most common sector width. 4 The accuracy of the wave height is in the order of 6 % and for the period in the order of 3 % (Roskam, Hoekema & Seijffert, 2000). Delft University of Technology 85

100 Table 8-5 Extreme values for 10-4 exceedance frequency at Europlatform Directional sector Surge level (m +NAP) Significant wave height (m) Mean spectral period (s) 210º º º º º º Omni directional Peak period (s) The storm surge levels shown in Table 8-5 and Table 8-6 are not measured at the stations Europlatform or IJmuiden ammunition dump, but at the Hook of Holland station, because this is the measuring station that is closest to the area of interest. More on storm surge levels can be found in Appendix 0. Table 8-6 Extreme values for 10-4 exceedance frequency at IJmuiden ammunition dump Directional sector Surge level (m +NAP) Significant wave height (m) Mean spectral period (s) 210º º º º º º Omni directional Peak period (s) Three boundaries The in the previous section defined exterior grid has three boundaries on the seaside and one boundary on the landside (Figure 3-4). For each of the sea boundaries different directions are important and different wave characteristics should be used. These boundaries, from now on to be named according to the direction in which they are facing will be discussed separately in the following section. Northeast boundary The Northeast boundary is placed on the Northern section of the grid running from the coastline towards the open sea. On this boundary the IJmuiden Ammunition dump measuring station can be found and data from this station is primarily used for the boundary conditions. From the Tables it becomes clear that the wave heights and periods from IJmuiden are structurally higher than those from Europlatform. Because one end of the boundary enters shallow water as it crosses the coast of Holland this part of the boundary plays no role in the simulations since all the waves in this area will be broken, or are refracted towards the coast before they reach the intermediate grid. Test including this part were compared with tests without conditions on this part of the boundary and differences were found to be around 2 %. Northwest boundary The northwest boundary is a true open sea boundary running over depths varying between 32 and 25 meters. The Europlatform measuring station is on this boundary and the extreme wave values from this station are used for the boundary conditions. Because the depths in this Delft University of Technology 86

101 area do not vary substantial, adjusting the wave height to the local water depth did not lead to significant differences in the outcome of the simulations. The depth adjusting was done using a shoaling coefficient (K S ). With this coefficient the wave characteristics in a known point can be translated into characteristics in a number of other points with different depth. In SWAN the number of section per boundary is limited to 10, so ten points on the boundary were selected and new wave conditions were calculated. Southwest boundary The Southwest boundary does not include any measuring points but it is close to the Europlatform so the extreme values from this station will also be used for the Southwest boundary. Because the normative waves in the area will come from the North and West this boundary will play a minor role in the simulations Boundary discussion Several different cases were tried in order to obtain a reasonable set of boundaries. it was found that when only one boundary is entered results are quite different from the reference case. Cases with only one boundary are therefore considered inaccurate. Other cases involved dividing the boundaries up into sections, and derive the wave height in each section through a shoaling factor (K S ). These cases showed that the effect of these "shoaled" boundaries was very small when compared to the reference cases. A simplification that was very convenient was shifting the "real" values of the Europlatform and the IJmuiden station towards the ends of the boundaries, as is shown in Figure 8-8. This simplification made the defining of the boundaries a lot easier and the deviation with the original case was only 2 to 3 %. Figure 8-8 Interpolated boundaries Delft University of Technology 87

102 Delft University of Technology 88

103 G Parameter reduction Introduction When it is assumed that offshore significant wave heights, wave periods, wind speeds and near shore water levels exceed their design values simultaneously, very conservative conditions are taken. A reduction can be found by looking closely at physical relations between the parameters. These relations will be explained in the sections below. It is stressed that the reductions found in this chapter will only be used for the SWAN computations, calculating wave parameters at the location of Maasvlakte 2. When working with other applications than the model, for instance to calculate the crest height of the construction with a certain water level the marginal probability without reductions is used. Roskam, Hoekema and Seijffert (2000) found the highest water levels, greatest wave heights and longest wave periods at Europlatform and IJmuiden with a storm from the 330º direction. Because the SWAN computations are not only executed for this direction, reduction calculations are also performed for parameters governing the 360º direction. First the method used to reduce the parameters is described at the hand of an example. As example case the 330º direction storm, with a return period of 10-4 year is chosen. At the end an overview will be given of the reduced parameters for the other directions and probabilities. The reductions will be determined keeping the wave height (H M0 5 ) at a fixed value and reducing the other hydraulic parameters one by one. Because some of the parameters have a direct relation and others only have an indirect relation, not every relation is treated with the same importance. An example of an indirect relation is the one between the wind set-up and the wave height. Both these parameters have a direct relation with the wind, but not towards each other. The relation between these two parameters is determined using the wind speed as a common cause factor. Table 8-7 Exceedance levels with a return period of 10,000 years at Europlatform, 330º Wind speed 6 U [m/s] Wave height H m0 H s 8.15 [m] Wave period T p 13.0 [s] Water level W 4.77 [m+nap] Initially the idea was to perform SWAN computations with each of the parameters kept alternately fixed and reducing the remaining three depending on the physical relation. From the output of these four SWAN simulations the design values should be extracted. During the research however it appeared that when instead of the wave height a different parameter was held fixed the physical relations led to higher values for the parameters instead of reductions. Since the values for the parameters became higher than the marginal probability this effect was found inaccurate, the method was dropped and only the wave height was held fixed. The reducing effect will be better understood when looking at the relations itself, which will be done in the following sections. 5 The return levels of the wave height in Roskam et al are given as the spectral wave height (Hm0) which is only 1 or 2 percent higher than the significant wave height (H s). Because the latter is used as input for the SWAN computations, the reductions found in this section are a bit conservative. However the differences between Hs and Hm0 are so small that both parameters will be used for the same wave height. 6 The wind speed is derived from Verkaik, Smits and Ettema (2003) Delft University of Technology 89

104 Wave height and wave period There exists a very strong correlation between the wave height and the period, which can be shown by the depth related equations given in Roskam et al. For the Europlatform 7 the relation is given by the following set of equations. TM 02 = 3.14 HM 0 H M 0 P 0.14 = 1.33 d TT M 02 H T H = + d T d 0.14 M P 0.5 M M 02 When looking at his relations it becomes clear that for relatively low wave heights, or large depths, the steepness of the waves is given by a constant factor. However as the waves increase, or the depth reduces the depth starts to play an increasing role and the steepness of the waves is no longer constant; Slightly lower values for the wave period are obtained in the region of higher wave heights. 18 Reduction wave period (Tp) at Europlatform according to Roskam et al Wave period Tp [s] Tp = 12.4s 1.0E-4 EUR Hm0=8.2m, Tp=13.0 Hm0 = 8.2m Wave height Hm0 [m] Figure 8-9 Wave steepness dependent of relative depth Conclusion Because the steepness of wave seems to become slightly less in intermediate water depths lower periods can be assumed. From Figure 8-9 a new value for the wave period can be found at the point where the line representing the physical relation crosses the wave height of 8.15 m. At this point the period is 12.4 s. Clearly identifiable is that when the reduction is considered the other way around an increase of the parameter will be the result, higher than the marginal probability. This phenomenon was already mentioned in the introduction and follows directly from the relation between the parameters, if a certain wave height leads to a lower value for the period, the original period in its turn will lead to a higher wave height. 7 For the IJmuiden station the relation between the T m02 and the T P is assumed constant but for the relation between the H m0 and the T P a value of 3.24 instead of 3.14 was used. Delft University of Technology 90

105 Wave height and wind speed The wave growth by wind depends mainly on the fetch distance, the wind speed and the drag coefficient. The straight-line fetch distance for the 330º section is about 650 km (see Figure 8-10). Because of the great fetch distance, the storm duration becomes normative for the wave height (Demirbilek, Bratos and Thomson, 1993). On the right-hand side of Figure 8-10, the dotted line shows the wind speed at Licht Eiland Goeree during the storm in February A wind speed over 20 m/s (40 knots) endured for 26 hours. The length of this exceptional long storm is assumed to be normative. Figure 8-10 (left) Fetch length of 650 km and (right) storm duration of 26 hours, February 1953, Licht Eiland Goeree, dotted line The formulas by Demirbilek et al. give a solution for duration limited wave growth. Equations governing wave growth with wind duration can be obtained by converting the duration into an equivalent fetch given by: Delft University of Technology 91

106 In Figure 8-11 the relation between wind speed and wave height is plotted for a storm with a length of 26 hours. It can be seen that a wave height of 8.15 m corresponds with a wind speed of 21.5 m/s Reduction windspeed at Europlatform using wave height in Demirbilek relation storm duration 26 hours 1.0E m, 30.6m/s Windspeed U10 [m/s] U10 = 21.5 m/s Hm0 = 8.15 m Wave heigth Hs [m] Figure 8-11 Wave height wind speed relations according to Demirbilek et al. Conclusion Taking only the relation between wind speed and wave height into account one could conclude that the wind speed can be reduced to 21.5 m/s. Because of the number of parameters and their relations, the final reduction will be discussed in 0. Wind speed and wave period The relation between the wind speed and the wave period is found in the same way as for the wave height. For the formulas used, the reader is referred to 0. In Figure 8-12 the Demirbilek relation between wind speed and wave period is plotted for a 26-hour storm. The horizontal line in the top right corner indicates the reduction of the wave period that has been determined in 0. By using this wave period (12.4 s) and the Demirbilek relation the wind speed can be reduced from 30.6m/s to 27.8m/s. These relations confirm the previous statement about the marginal probability; also here the fixed wave height leads to a reduction in wind speed, where a fixed wind speed would have led to a considerable increase in wave height. Delft University of Technology 92

107 35 30 Reduction windspeed at Europlatform using peak period in Demirbilek relation U10 = 27.8 m/s 1.0E s, 30.6s Wind speed U10 [m/s] Tp = 12.4 s Wave period Tp [s] Figure 8-12 Wave period wind speed relations according to Demirbilek et al. Conclusion While using a fixed wave height of 8.15 m reduces the wind speed down to 21.5 m/s, a wave period of 12.4 seconds causes a wind speed reduction down to 27.8 m/s. This matter will be discussed further in 0. Wind speed and wind set-up The water level under storm conditions can be considerably higher than under normal conditions. This water level (h) can be divided into two main components, the astronomical tide (a) and the wind set-up (s). In formula: h = a + s The wind set-up (s) in this equation has a direct relation with the wind speed according to Weenink (1958) 2 u α s = g in which u = wind speed [m/s] α = dimensionless constant depending of the wind direction [-] 2 g = gravitational constant [m/s ] The value of the constant α is determined by calibrating the formula using storm measurements from storms coming from a 330º direction. These storm measurements where taken from Ministerie van Verkeer en Waterstaat (2002). For this calibration the measurements from Europlatform were used and the value found for the constant α is [-]. With this value the relation between the wind speed and the wind set-up can be represented as the solid line in Figure The blue point in Figure 8-13 represents the wind speed and the wave set-up with a return period of 10,000 years. The wind set-up equals the water level (NAP+4.77m) minus the spring tide level (NAP+1.40): NAP+3.37m. Delft University of Technology 93

108 Also in Figure 8-13 are the reduced wind speeds U 10 = 21.5 m/s (reduced in relation to the wave height), and U 10 = 27.8 m/s (reduced in relation to the wave period). The corresponding wind set-ups are 2.0 m for a wind speed of 21.5 m/s, and 3.4 m for a wind speed of 27.8 m/s. 6 Reduction wind setup (s) at North Sea according to Weenink 5 Wind set-up s [m] s = 2.0 m s = 3.4m U10 = 21.5m/s U10 = 27.8m/s 1.0 E m/s, 3.4m Wind speed U10 [m/s] Figure 8-13 Wind speed and wind set-up Conclusion The relation between the wind speed and the wind set-up shows that when the wind speed is not reduced, the wind set-up would become higher than the 10-4 condition. If however a reduction in the wind speed is taken into account a reduction in the wind set-up will be the result. The final values that will be used as SWAN boundary conditions are given in 0. This was the only relation that didn t show any initial decrease, hence would show an increase when the parameter reduction was started with the water level instead of the wave height. However, the wind speed has already been reduced as a result of previous physical relations and therefore again a reduction is found. When on the other hand the water level would have been taken as fixed value, a small reduction in wind speed would have been the result, but the relation between wind speed and wave height shows that an increase of wave height will be the result, cancelling out the positive effect of the relation between the wind speed and the water level. Wave height and wind set-up Finding a relation between the wave height and the wind set-up is a lot less trivial than was the case for the relations above. The wind set-up is not a direct effect of an increase in wave height and their relationship is difficult to determine. One way of getting an idea of the relation between the wave height and the wind set-up is by using the wind speed as a common cause factor Both the wave height and the wind set-up are a direct effect of the wind speed. For the wave height the previously explained relation of Demirbilek (1993) will be used. This formula calculates the wave height as a function of the wind speed. For the wind set-up the earlier used formula of Weenink (1958) is used. Like the formulas of Demirbilek (1993) with the wave height, the formula by Weenink (1958) calculates the wind set-up as a function of the wind speed. For the exact formulas the reader is referred to 0 and 0. The results are shown in Figure 8-14, where the solid line represents the relation between the wind set-up and the wave height. Also indicated in this figure is the point representing the once in 10,000 year conditions for both the wave height and the wind set-up. This point is shown in Figure 8-14 by the blue square. Delft University of Technology 94

109 5 Reduction wave height (Hm0) at Europlatform according to Demirbilek an Weenink Wind set-up (s) [m] s = 2.0 m 1.0 E-4 Hs = 8.15m, s = 3.4 m Hs = 8.15 m Wave height Hm0 [m] Figure 8-14 Relation between the wave height and the wind set-up Conclusion What this analysis clearly shows is the effect of the wind speed on the wind set-up. In an earlier section the wind speed was reduced according to the relation of Demirbilek et al (the relation between the wind speed and the wave height). This reduction can be found again in Figure 8-14, because this figure uses the same relation between the wind speed and the wave height. When the wave height is fixed at the 10-4 condition, the wind speed is automatically reduced to 21.5 m/s (instead of 30.6 m/s) and the wind set-up reduces to 2.0 m. (Blue dashed line) Delft University of Technology 95

110 Wave period and wind set-up For the wave period and water level more or less the same train of thought applies as for the wave height and the water level. In previous sections it has been shown that the wave height and the wave period have a direct relation. When similar to the previous section the wind speed is used as common cause factor and the formulas of Demirbilek (1993) and Weenink (1958) are used to relate the wind speed to respectively the wave period and the wind set-up, the following relation can be found (Figure 8-15) 5 Reduction wave period (Tp) at Europlatform according to Demirbilek and Weenink Wind set-up (s) [m] s = 3.4m Tp = 12.4s 1.0 E-4 Tp = 13.0s, s = 3.4m Wave period Tp [s] Figure 8-15 Relation between wave period and wind set-up In Figure 8-15 the relation between the wave period and the wind set-up is represented by the solid line. The blue square in the figure represents the 10-4 conditions for both the wave period and the wind set-up. Conclusion As was the case for the relation between the wave height and the wind set-up, the relation between the wave period and the wind set-up is a reflection of the effect of the wind speed on, in this case, the wave period. The slightly reduced wind speed that was found using the wave period leads to small decrease in the wind set-up, shown by the blue dashed line in Figure This is a direct result of the formulas used and the nature of the relation. Clearly the decrease in the wind set-up as a result of the relation to the wave period (3.4m) is a lot smaller than the decrease as a result of the relation with the wave height (2.0m). Delft University of Technology 96

111 Conclusions Because the goal of this section is to find adjusted hydraulic boundary condition parameters for wave simulations using the SWAN model, it was thought that most reliable results are found keeping the wave height at a fixed level, in the previous sections explained with a return period of 10,000 years (h s =8.15m). The results of the reductions with the physical relations underwrite the hypothesis that the most reliable results are obtained when the wave height is kept fixed. All the relations show that when the wave period, the wind speed or the water level was kept fixed, one or more parameters would obtain values that were higher than the marginal probability. Since this marginal probability is already an extreme, values higher than this are considered to be incorrect. Because of the strong relation between wave height and wave period, a reliable reduction of the wave period (Tp) is found. The adjusted peak period for Europlatform is 12.4 s. More difficult is the reduction of the wind speed since it can be directly derived from the wave height (U 10 =21.5 m/s) or from the reduced wave period (U 10 =27.8 m/s). It is chosen to use the average of both values, U 10 =24.7 m/s. Since the wind set-up is a direct result of the wind speed, the wind set-up is derived from the wind speed. As for the wind speed, the two values found for the wind set-up are averaged. A wind set-up of 2.7 m is derived. By adding the astronomical tide, a water level of NAP+4.1m is found. By using physical relations instead of a pure probabilistic approach as used by De Haan, van Marle (2000) a very good estimate of possible reductions is found. However errors are made because simplified formulas are used. Because the determination of the hydraulic parameters is only a small part of the total research, no further emphasis is put on the accuracy of the found reductions. The results of the reductions are shown in Table 3-4 for the Europlatform boundary, and Table 3-5 for the IJmuiden station. Table 8-8 Hydraulic conditions for the 330º direction, Europlatform EUR 330º 1/1 per year 1/10 per year 1/100 per year 1/1,000 per year 1/10,000 per year Hs (m) T P (s) Table 8-9 hydraulic conditions for the 330º direction, IJmuiden IJM6 1/1 per 1/10 per 1/100 per 1/1,000 1/10, º year year year per year per year H s (m) T P (s) Because the wind speed (U 10 ) and the normative high water level (MHW) are taken constant over the total simulation area in SWAN, the two different values of those parameters are averaged between Europlatform and IJmuiden. As a result the values will be taken as shown in Table 3-6. Table 8-10 Water levels and wind speeds averaged between EUR and YM6 Simulation area 330º 1/1 per year 1/10 per year 1/100 per year 1/1,000 per year 1/10,000 per year MHW (m+nap) U 10 (m/s) Delft University of Technology 97

112 Delft University of Technology 98

113 H SWAN Results Contour 20 m 10 Significant wave height 10 Mean wave period Hs (m) 5 Tm01 (s) km 20 km Distance from begin point 2 10,000 years 1,000 years years 10 years 1 year km 20 km Distance from begin point Delft University of Technology 99

114 Westdam contour 10 Significant wave height 11 Mean wave period Hs (m) 5 Tm01 (s) Depth (m) 2 10,000 years 1,000 years years 10 years 1 year Depth (m) Delft University of Technology 100

115 Surfing conditions 2 Significant wave height 10 Mean wave period Hs (m) 1 Tm01 (s) Depth (m) 3 North 1m 6s North 2m 8s 2 West 0m 6s West 1m 8s West 2m 8s 1 South 1m 6s South 1m 8s South 2m 8s Depth (m) Delft University of Technology 101

116 Spectra Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] x 105 Windspeed 10.0 m/s Absolute frequency [Hz] 2 x 105 Windspeed 12.5 m/s Absolute frequency [Hz] 2 x 105 Windspeed 15.0 m/s Absolute frequency [Hz] Wave spectra for 10e-00 conditions Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] x 105 Windspeed 12.0 m/s Absolute frequency [Hz] 2 x 105 Windspeed 13.0 m/s Absolute frequency [Hz] 2 x 105 Windspeed 17.5 m/s Absolute frequency [Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] 5 x Windspeed 12.5 m/s Absolute frequency [Hz] 5 x 105 Windspeed 16.0 m/s Absolute frequency [Hz] 5 x 105 Windspeed 17.5 m/s Absolute frequency [Hz] Wave spectra for 10e-01 conditions Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] 5 x Windspeed 15.0 m/s Absolute frequency [Hz] 5 x 105 Windspeed 17.0 m/s Absolute frequency [Hz] 5 x 105 Windspeed 20.0 m/s Absolute frequency [Hz] Delft University of Technology 102

117 Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] x 10 5 Windspeed 15.0 m/s Absolute frequency [Hz] x 10 5 Windspeed 18.0 m/s Absolute frequency [Hz] x 10 5 Windspeed 22.5 m/s Absolute frequency [Hz] Wave spectra for 10e-02 conditions Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] x 10 5 Windspeed 17.5 m/s Absolute frequency [Hz] x 10 5 Windspeed 20.0 m/s Absolute frequency [Hz] x 10 5 Windspeed 25.0 m/s Absolute frequency [Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] 10 x Windspeed 17.5 m/s Absolute frequency [Hz] 10 x 105 Windspeed 20.0 m/s Absolute frequency [Hz] 10 x 105 Windspeed 22.0 m/s Absolute frequency [Hz] Wave spectra for 10e-03 conditions Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] 10 x Windspeed 19.0 m/s Absolute frequency [Hz] 10 x 105 Windspeed 21.0 m/s Absolute frequency [Hz] 10 x 105 Windspeed 22.5 m/s Absolute frequency [Hz] Delft University of Technology 103

118 Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] 12 x Windspeed 16.0 m/s Absolute frequency [Hz] x 10 5 Windspeed 20.0 m/s Absolute frequency [Hz] x 10 5 Windspeed 25.7 m/s Absolute frequency [Hz] Wave spectra for 10e-04 conditions Energy density [J/m2]Hz] Energy density [J/m2]Hz] Energy density [J/m2]Hz] 12 x Windspeed 19.0 m/s Absolute frequency [Hz] x 10 5 Windspeed 22.0 m/s Absolute frequency [Hz] x 10 5 Windspeed 40.0 m/s Absolute frequency [Hz] Delft University of Technology 104

119 I Morphological model Toe depth The morphological model described in section 2.2 assumes a certain distribution of the transport over the surf zone and the water column. In Figure 8-16 the sand transport as a function of the toe depth is shown. For a very long Westdam, blocking the entire surf zone almost up to the closure depth, the toe will be constructed on relatively deep water, and the relative toe depth is high, 1 or slightly smaller. For this relative toe depth the transport is next to nothing to zero. If on the other hand the dam is not constructed at all, the toe starts theoretically at 0 meter depth in that case the relative toe depth is also zero and the amount of transport is at its maximum. The relatively flat slopes of the curves near the ends of the area indicate that the influence of the length of the dam is the most sensitive in the middle section, so around 4 meters of depth. When the dam is already very long or very short a further increase or decrease has very little effect compared to a dam with the toe at 4 meter of depth. 6 x 105 Sand transport as a function of the Toe depth 5 Sand transport around the dam [m3/year] Relative toe depth [-] Figure 8-16 Transport as a function of the relative toe depth 8.1 Crest height In Figure 8-17 the sand transport as a function of the relative crest height is shown. When the dam is constructed fully emerged, the crest height will be equal to the depth, and the relative crest height will be one. With this crest height the transport over the dam will be zero. A dam constructed with the crest height just above the beach profile level will have the opposite effect. The relative crest height will be high, in the order of 1 and the transport has reached a maximum. Also for the vertical transport distribution it can be noted that the transport is most sensitive to freeboard changes in the order of a relative freeboard of 0.5 or higher. Here the curve shows its steepest slope and this is where a change in crest level will be noted most effectively. The reader should keep in mind that the non-dimensional parameters relative crest toe depth and relative freeboard are opposite parameters. One Delft University of Technology 105

120 indicates the presence of the dam, where the other indicates the part not occupied by the dam. 6 x 105 Sand transport as a function of the crest height 5 Sand transport over dam [m3/year] Relative crest height [m] Figure 8-17 Transport as a function of the relative crest height Delft University of Technology 106

121 J Financial/ Economical Analyses The relation between the costs of the construction of the Westdam and the sand profile and the crest height is given in Figure The economical optimum can be clearly seen at a relative crest height of costs as function of the crest height Total costs [million euro] Relative crest height [m] Figure 8-18 costs as a function of the crest height of the Westdam Delft University of Technology 107

122 In Figure 8-19, the relation between the costs for the construction and the toe depth of the Westdam is shown. The optimum in this case is found at a relative toe depth of costs as function of toedepth Total costs [million euro] Relative toe depth [m] Figure 8-19 Costs as a function of the relative toe depth of the Westdam Delft University of Technology 108

123 K Wave Parameter explanation The water surface of the North Sea is subject to the influence of wind, with as result a highly irregular wave field, strongly varying in height and period, with a certain spreading coming from a main direction. Figure 8-20 gives an example of the vertical movement of the water surface in a fixed point on the North Sea. Figure 8-20 Water surface fluctuations in a fixed point on the North Sea The wave parameters, wave height and wave period can be defined in a number of different ways depending on the way the data is considered, in Table 8-11 a selection of the most used parameters for wave heights and wave periods is given. Table 8-11 Wave parameters (wave heights and periods) Wave parameters (wave height and period) H gem Average wave height Wave height H 1/3 Average of highest third part of the waves H max Highest measured wave H m0 Mean spectral wave height T gem Average of all the wave periods T 1/3 Average of longest third part of wave periods Period Average of wave periods of highest third part T H1/3 of the waves Mean spectral wave period T m01 The wave height H 1/3 is frequently referred to as the significant wave height, along with the wave height H m0, which is the equivalent of H 1/3 in the frequency domain. However these two wave heights are not entirely equal and show different characteristics, the difference between the two is usually only a few percentages. Likewise, the wave period T m02 is more or less equivalent to the average wave period T gem. Extremes for the wave height H m0 For the Dutch coastal area extreme values for the wave height H m0 are determined for five deep-water locations, based on wave height measurements in the period The presentation of these values is given in Roskam et al. Delft University of Technology 109