Prepared for:
Rijkswaterstaat, RIKZ
Dune erosion
February, 2007
Contents
List of Tables List of Figures List of Appendices 1 Introduction...1 1.1 General...11.2 Objective of this part of the study...4
1.3 Approach of this study...4
1.4 Reader’s guide ...4
2 Model concepts for dune erosion ...7
2.1 Introduction...7
2.2 Types of models ...7
2.3 Deterministic model...8
2.3.1 Original 1984-model...8
2.3.2 Modified model for larger wave periods ...9
2.3.3 Additional sensitivity elaborations ...10
2.4 Probabilistic model ...11
2.4.1 Reliability functions...11
2.4.2 Computation of failure probabilities...12
2.4.3 Available probabilistic methods...13
2.4.4 Applying design points ...14
2.5 Guideline model (1984-version)...15
2.5.1 Introduction...15
2.5.3 Additional requirements... 17
3 Summary of required input data ... 19
3.1 Introduction ... 19
3.2 Summary of input parameters ... 19
3.3 The initial cross-shore profile... 20
3.3.1 Introduction ... 20
3.3.2 Standard profile or reference profile ... 21
3.3.3 Uncertainty in volume content ... 21
3.3.4 Other cross-shore profiles along the Holland Coast... 21
3.3.5 Additional profiles beyond the Holland Coast ... 22
3.4 Grain diameter of the dune material... 23
3.4.1 Introduction ... 23
3.4.2 Standard case... 23
3.4.3 Other locations along the Holland Coast... 23
3.4.4 Other locations beyond the Holland Coast... 24
3.5 Hydraulic conditions ... 24
3.5.1 Introduction ... 24
3.5.2 Maximum surge level... 25
3.5.3 Wave height as a function of storm surge level... 26
3.5.4 Wave period as a function of wave height... 28
3.6 The duration of the maximum surge ... 29
3.6.1 Introduction ... 29
3.6.2 Additional DUROSTA-simulations ... 29
3.6.3 Conclusions ... 30
3.7 Gust surges and gust oscillations... 30
3.7.2 Results of further analysis ...30
3.7.3 Results of additional simulations...31
3.7.4 Conclusions ...31
3.8 Inaccuracy of the deterministic model...31
3.8.1 Introduction...31
3.8.2 Modified model ...32
3.9 Summary of relevant parameters ...32
4 Set-up of the probabilistic model...33
4.1 Introduction...33
4.2 The definition of the 1984-model ...33
4.2.1 Introduction...33
4.2.2 Procedure ...34
4.2.3 Distribution functions ...34
4.3 Reproduction of the base case ...35
4.3.1 Introduction...35
4.3.2 Deterministic results ...35
4.3.3 Probabilistic results...36
4.3.4 Design point analysis...36
4.3.5 Effect of the perturbation value ...37
4.3.6 Reduction of the number of parameters...38
4.3.7 Additional comparisons ...38
4.3.8 Conclusions ...39
4.4 The definition of the new probabilistic model...39
4.5 Comparison with the 1984-method...40
4.5.1 Introduction...40
4.5.3 Conclusions ... 41
5 Application of the probabilistic model ... 43
5.1 Introduction ... 43
5.2 Basic results for selected prototype profiles... 43
5.2.1 Introduction ... 43
5.2.2 Summary of results in the design point ... 44
5.2.3 Results for the water level... 45
5.2.4 Results for the wave conditions ... 46
5.2.5 Results for the sediment diameter ... 46
5.2.6 Results for the uncertainty in duration and model ... 47
5.3 Results for fixed hydraulic combinations... 47
5.3.1 Introduction ... 47
5.3.2 Summary of results in the design point ... 48
5.3.3 Results for the hydraulic conditions... 49
5.3.4 Results for the sediment diameter ... 49
5.3.5 Results for the uncertainty in duration and model ... 49
5.4 Additional results for Wadden Coast... 50
5.4.1 Introduction ... 50
5.4.2 Summary of results in the design point ... 51
6 Formulation, calibration and validation of the guideline model... 53
6.1 Introduction ... 53
6.2 Definition of an initial formulation ... 54
6.2.1 Further elaboration ... 54
6.2.2 Initial formulation ... 55
6.3 Calibration of the model... 56
6.4.1 Introduction...57
6.4.2 Basic set with local profiles...57
6.4.3 Validation for results with reference profile ...59
6.5 Application for higher probabilities...60
7 Definition and application of the guideline model ...63
7.1 Definition of the updated guideline model ...63
7.1.1 Introduction...63
7.1.2 Governing hydraulic conditions...63
7.1.3 Characteristics of the dune material...64
7.1.4 Shape of the erosion profile...64
7.1.5 Basic erosion volume A* ...65
7.1.6 Surcharge erosion volumes...66
7.1.7 Final erosion point ...66
7.2 Comparison with the previous guideline models...66
7.2.1 Introduction...66
7.2.2 Results for the original 1984-model ...67
7.2.3 Results for the ‘crash-model’ (2003) ...68
7.2.4 Results for the new model (2006)...68
7.2.5 Comparison of results of the three models ...69
7.2.6 Analysis of the difference with the old model ...70
7.3 Comparison with the 2001-situation...71
8 Additional elements of the guideline model...73
8.1 Introduction...73
8.2 Effect of profile variations and nourishments...73
8.2.1 Introduction...73
8.2.3 Results of additional probabilistic computations ... 74
8.2.4 Modified approach ... 75
8.2.5 Effect of nourishments ... 75
8.2.6 Probabilistic elaboration... 76
8.2.7 Conclusions ... 77
8.3 Effect of longshore transport gradients ... 77
8.3.1 Introduction ... 77
8.3.2 Basic formulation of longshore transport gradient... 77
8.3.3 Effect of the wave period ... 78
8.3.4 Conclusions and discussion... 78
8.4 The limit profile ... 79
8.4.1 Introduction ... 79
8.4.2 Basic dimensions... 79
8.4.3 Effect of the wave period ... 80
8.4.4 Applying lower limit profiles... 80
8.4.5 Conclusions and discussion... 81
9 Summary, conclusions and recommendations ... 83
9.1 Summary and conclusions... 83
9.2 Recommendations ... 84
References Figures Appendices
List of Tables
Tables in text:2.1 Relative effect on erosion parameters of an increased wave period (18 instead of 12 s) for different parameters
3.1 Overview of selected cross-shore profiles for the Holland Coast 3.2 Overview of additional cross-shore profiles for the Wadden Coast
3.3 Overview of sediment characteristics for selected cross-shore profiles at the Holland Coast
3.4 Overview of sediment characteristics for additional cross-shore profiles at the Wadden Coast
3.5 Hydraulic conditions applied for the preliminary application
3.6 Parameter values in Weibull distribution for maximum surge level for the Dutch Coast
3.7 Parameter values in Weibull distribution for significant wave height for the Dutch Coast
3.8 Parameter values for the relation between mean wave height and maximum water level
3.9 Marginal statistics of wave height and wave period for relevant stations
3.10 Parameter values in linear relation for conditional peak wave period relation for the Holland Coast
3.11 Summary of input parameters
4.1 Summary of input parameters applied for the 1984-elaborations 4.2 Overview of input for selected deterministic computations
4.3 Comparison between the deterministic results of the current studies and the 1984- elaboration
4.4 Comparison between the probabilistic results of the current studies and the 1984- elaboration
4.5 Comparison of values of random variables in the design point 4.6 Comparison of relative contribution of stochasts in the design point
4.7 Comparison of absolute deviation from the average value in the design point 4.8 Effect of perturbation value on water level in the design point
4.9 Relative influence of each stochast in the design point for increasing number of ‘active’ parameters
4.10 Effect of number of stochasts on the water level and retreat distance
4.11 Comparison between the additional results of the current studies and the 1984- elaboration
4.12 Summary of input parameters applied for the new elaborations 4.13 Computed retreat distances for defined cases
4.14 Design points for the dune erosion with frequency of exceedance of 10-5 per year 5.1 Probability of exceedance as a function of the retreat distance RD for Holland Coast locations
5.3 Overview of design points for dune erosion with a probability of exceedance of 10-5 per year
5.4 Difference in the water level with respect to the exact estimate of the computational water level
5.5 Difference in the water level with respect to the computational water level according to the HR2006
5.6 Difference in the wave height with respect to the value at the water level in the design point
5.7 Difference in the wave period with respect to the value at the water level in the design point
5.8 Difference in the sediment diameter with respect to the mean value 5.9 Results with respect to the surcharges in the design point
5.10 Local hydraulic conditions according to the HR2006
5.11 Overview of design points for dune erosion with a probability of exceedance of 10-5 per year applying fixed hydraulic conditions
5.12 Difference in the hydraulic conditions with respect to the results for the free boundary conditions
5.13 Difference in the sediment diameter respect to the results for the free boundary conditions
5.14 Results with respect to the surcharges in the design point for fixed conditions
5.15 Difference in the relative surcharge volume with respect to the result for the free boundary conditions
5.16 Probability of exceedance as a function of the retreat distance RD for Wadden Coast locations
5.17 Retreat distances RD with a probability of exceedance of 10-5 per year for the Wadden Coast
5.18 Overview of design points for the Wadden Coast locations 6.1 Overview of relevant dune erosion determining parameters
6.2 Overview of relevant dune erosion determining factors in the new model 6.3 Overview of input parameters for the assessment of the basic erosion rate
6.4 Comparison of total erosion volume A according to the probabilistic model and the basic erosion A* for the modifiederosion profile
6.5 Overview of input parameters for guideline model
6.6 Comparison of retreat distance for new guideline model with the probabilistic model
6.7 Comparison of erosion volumes for new guideline model with probabilistic model 6.8 Comparison of retreat distance for new guideline model with the probabilistic
model using the reference profile
6.9 Hydraulic conditions for higher probabilities of erosion point
6.10 Comparison of retreat distance for new guideline model with the probabilistic model for 10-3 per year
6.11 Comparison of retreat distance for new guideline model with the probabilistic model for 10-4 per year
7.1 Overview of input parameters for the guideline model
7.4 Comparison of retreat distances for new guideline model with probabilistic model using the reference profile
7.5 Detailed results for the 1984-model
7.6 Applied crash-surcharge and detailed results for the ‘crash-model’ 7.7 Detailed results for the new model
7.8 Contributions in the mutation of the erosion volume
8.1 Effect of the uncertainty in the volume content on the 10-5 per year retreat distance 8.2 Overview of design point characteristics for nourishment computations
8.3 Effect of nourishment on erosion and dune retreat distance 8.4 Overview of coastal curvature classes
8.5 Overview of coastal sections with more extreme longshore gradients
List of Figures
Figures in Appendix ‘Figures’:2.1 Principle of the deterministic model for dune erosion according to the original 1984- method
2.2 Example of the updated erosion profile for a wave period of 12 and 18 s
2.3 Erosion as a function of the wave period for the base case and other cases; Relative erosion volume above the maximum surge level and relative dune retreat
2.4 Example of dune retreat distances as a function of water level and wave height 2.5 Principle of the guideline model according to the original 1984-method 3.1 Overview of applied cross-shore profiles for the Holland Coast
3.2 Detail of applied cross-shore profiles for the Holland Coast including landward shift of profile #10 (denoted as #10s)
3.3 Intercomparison of cross-shore profiles for the Holland Coast; Cross-shore position relative to RSP
3.4 Intercomparison of cross-shore profile shapes for the Holland Coast; Cross-shore position relative to NAP-contour
3.5 Characteristic cross-shore profile shapes for the Holland Coast including dune face retreat for Tp =12 and 18 s at design surge level
3.6 Overview of additional cross-shore profiles for the Wadden Coast
3.7 Characteristics of dune sand along the Holland Coast; Mean diameter and variance as a function of the distance to Den Helder
3.8 Maximum storm surge level as a function of the frequency of exceedance for Hoek van Holland (two relations) and Den Helder
3.9 Significant wave height as a function of the maximum surge level for Hoek van Holland, IJmuiden and Den Helder
3.10 Peak wave period as a function of the significant wave height for Hoek van Holland, IJmuiden and Den Helder
3.11 Model inaccuracy for old and new deterministic model; Datapoints according to Fig 4.6 and Table A.14 from Product 2 report
5.1 Probability of exceedance as a function of the retreat distance for the selected locations along the Holland Coast
5.2 Probability of exceedance as a function of the retreat distance for the selected locations along the Wadden Coast
6.1 Comparison between the mean sediment diameter, the computational diameter and the diameter according to the probabilistic computations (in design point); Results for all locations along the Holland Coast
6.2 Relative deviation from the mean diameter as a function of the relative value for the computational diameter; Results for all locations along the Holland Coast
6.3 Reduction in erosion volume as a function of the deviation in the sediment diameter in the design point from the computational diameter; Results for all locations along the Holland Coast
6.5 Comparison between total erosion rate probabilistic model and basic erosion A* according to new formulation; Including fitted trendline; Applying fixed HR2006- conditions
6.6 Comparison between basic erosion A* according to new formulation and total erosion rate probabilistic model; Including fitted trendline; Applying fixed HR2006- conditions
6.7 Comparison erosion rates between probabilistic results and results of new model; For locations along Holland Coast (fixed HR2006-conditions)
6.8 Comparison RD-values between probabilistic results and results of new model; For locations along Holland Coast and Wadden Coast
6.9 Comparison RD-values between probabilistic results and result of new model; For locations along Holland Coast and Wadden Coast; Applying the reference profile for all locations
6.10 Comparison RD-values between probabilistic results and result of new model; For locations along Holland Coast and Wadden Coast; All available results (local and reference profile)
6.11 Comparison RD-values between probabilistic results and result of new model for higher probabilities; Results for 10-5, 10-4 and 10-3 exceedance frequency
7.1 Overview of updated guideline model
7.2 RD-values for three different dune erosion models applying the new HR2006 boundary conditions for all computations; For locations along Holland Coast and Wadden Coast (northward sequence)
7.3 Change in RD-value relative to the old 1984-model applying the new HR2006 boundary conditions for all computations; For locations along Holland Coast and Wadden Coast (northward sequence)
7.4 Dune erosion volumes for three different dune erosion models applying the new HR2006 boundary conditions for all computations; For locations along Holland Coast and Wadden Coast (northward sequence)
7.5 Change erosion volume relative to the old 1984-model applying the new HR2006 boundary conditions for all computations; For locations along Holland Coast and Wadden Coast (northward sequence)
7.6 Change in erosion rate new model compared to old 1984-model; Contributions of modified erosion profile and surcharge volume
7.7 Contribution of modified erosion profile as a function of the wave period; Absolute changes
7.8 Contribution of modified erosion profile as a function of the wave period; Relative changes
7.9 Contribution of modified surcharge volume as a function of the basic erosion volume A*
7.10 RD-values according to the old 1984-model for both HR2001 and HR2006 conditions and the new model for applying the new HR2006 conditions; For
locations along Holland Coast and Wadden Coast (northward sequence)
7.11 Change in RD-value for new model with HR2006 compared with old 1984-model with HR2001-conditions; For locations along Holland Coast and Wadden Coast (northward sequence)
7.13 Erosion volumes according to the old 1984-model for HR2001 and HR2006 conditions and the new model for applying the new HR2006 conditions; For
locations along Holland Coast and Wadden Coast (northward sequence)
7.14 Change in erosion volume for new model with HR2006 compared with old 1984- model with HR2001-conditions; For locations along Holland Coast and Wadden Coast (northward sequence)
7.15 Contribution of changed wave height and water level versus change in wave period and dune erosion model; For locations along Holland Coast and Wadden Coast (northward sequence)
8.1 Overview of trends
Appendices
A Details of the dune erosion profiles for the new model applying the new HR2006 boundary conditions.
B Dune erosion profiles for the old 1984-model (2001), ‘crash’- model (2003) and new model (2006) for HR2006 boundary conditions.
1
Introduction
1.1 General
Background information
In The Netherlands, the Law on Water Defences prescribes a five yearly safety assessment of the primary water defences by the administrators of those water defences. The Dutch government draws up the safety assessment regulation for this purpose (in Dutch: ‘Voorschrift Toetsen Veiligheid’ or VTV). In the current VTV (valid for the period 2001 till 2006) use is made of the Guideline on Dune Erosion for the safety assessment of dunes as water defences (in Dutch: ‘Leidraad Duinafslag’ by the Technical Advisory committee for Water defences, TAW, 1984).
In the Guideline on Dune Erosion, the under water dune erosion profile under severe hydraulic conditions is calculated using a parabolic profile. The significant wave height at an offshore location where the bed level is at NAP -20 m, and a characteristic diameter of the dune sand are used to calculate the shape of this erosion profile. However, the dune erosion profile is expected to depend on other variables such as the wave period also. The wave period in the current method is only used to determine the height of the necessary minimal limit profile (in Dutch: ‘grensprofiel’). The wave period is not used directly in the calculation of the erosion profile. The method to determine this erosion profile (TAW, 1984) is based on a peak wave period of Tp = 12 seconds at relatively deep water and does not
account for effects of other values of this wave period.
Some years ago, it became clear that the wave period with a frequency of exceedance of 1/10,000 per year is at many locations along the Dutch Coast significantly larger than the period of 12 seconds as applied in the present method to calculate dune erosion (see also Alkyon, 2002 and WL | Delft Hydraulics, 2003). Because the wave load on the coast increases with increasing wave period, it was expected that the volume of dune erosion would increase as well. To what extent the dune erosion volume might increase was not clear yet; this needed to be investigated further. However, based on a preliminary analysis, taking estimates of longer wave periods into account, a number of locations along the Dutch Coast were identified as weak sections in the primary water defence. Some of these weak sections concern dunes. Therefore, it is especially relevant to obtain knowledge on the influence of the wave period on dune erosion, and to account for the influence of the wave period in the method to calculate dune erosion.
Assignment
the VTV of the year 2006. With this new method it should be possible to calculate dune erosion under normative hydraulic conditions taking the effects of the wave period into account more explicitly. Dune erosion calculations are expected to be based on new hydraulic boundary conditions that will also be defined in the year 2006 (in Dutch: ‘Hydraulische Randvoorwaarden 2006’ or ‘HR2006’; see RWS/RIKZ 2006).
The ‘Directoraat-Generaal Rijkswaterstaat’, RWS/RIKZ, accepted (ref: RIKZ/2005/05707, dated 7 July 2005) WL | Delft Hydraulics’ proposal (ref: MCI-10835/H4357/MvG, dated 20 May 2005) to carry out the present project in which a new safety assessment method needs to be developed for dunes (VTV2006) in which effects of the wave period are incorporated.
Problem definition
The existing dune erosion prediction method in the Guideline on Dune Erosion was developed for situations with wave periods up to Tp = 12 seconds, while at the Dutch Coast
situations can be expected with wave periods larger than Tp = 12 seconds. Preliminary
analyses of the potential influence of longer wave periods on dune erosion indicate that larger wave periods may lead to more dune erosion (Alkyon, 2002; RWS/DWW, 2003; WL | Delft Hydraulics, 2004a). However, effects of the wave period are not quantified sufficiently yet. Nevertheless, this is necessary to improve the safety assessment method for dunes (VTV2006).
Objective
The objective of this project is to develop a new safety assessment method for dunes as part of the VTV2006. This new methodology should account for effects of the wave period on dune erosion as well be applicable for a nourished coast. This project is focussed on achieving this by improving the existing method (TAW, 1984), because of the following reasons:
• The VTV2006 has to agree with the HR2006. A time-dependent dune safety assessment is not taken into account in the development of the HR2006. For example no storm duration will be given. The influence of the storm duration needs attention in a following version of the VTV, for instance in the VTV2011. The HR2011 then also needs to contain detailed information on storm durations, etc. Furthermore, the HR2006 is expected to be limited to general boundary conditions like for instance design water levels, wave heights and wave periods with exceedance frequencies of 1/1,000 per year and 1/10,000 per year. No information on storm duration nor other types of information will be given in the HR2006.
• The available time to obtain a new assessment method for dunes is relatively short. Therefore, it is only feasible to improve the VTV2006 with effects of the wave period. • By making use of the existing methodology, a similar probabilistic approach can be used
and therefore it becomes feasible to obtain an extended method within the available time. • The acceptation by water defence administrators is simplified by proposing an
Attention is primarily focussed on quantifying effects of the wave period on dune erosion. Other effects, e.g. the effect of storm duration, are foreseen to be taken into account in the VTV2011, if the HR2011 also includes data on storm duration. Therefore, more knowledge has to be developed on other effects in the period between 2006 and 2011. It should be clear that the result of this project is aimed at an improvement of the existing methodology and not at a method that accounts for all relevant phenomena.
The new method that will be developed will be evaluated in order to give support to the users and to identify gaps in knowledge. The new method is expected to be robust enough to assess the safety of the dunes on a short term. However, the range of validity will still be limited. The identified knowledge gaps could be a reason for further research for the VTV2011. A part of the present study is to prepare a plan for the period between 2007 and 2011 to identify the knowledge gaps and the required research to achieve an appropriate safety assessment tool for dunes for the VTV2011.
Approach
The entire dune erosion project is originally divided into 5 products: Product 1) Deterministic dune erosion prediction method.
Product 2) Large-scale model tests.
Product 3) Probabilistic dune erosion prediction method. Product 4) Technical guideline (for VTV2006).
Product 5) Evaluation of the method.
The present report describes the study for Product 3.
Project organisation
To carry out this project WL | Delft Hydraulics formed a so-called ‘Dune erosion alliance’ to make use of expertise at other organisations such as the Delft University of Technology, Alkyon Hydraulic Consultancy & Research, and Utrecht University. Also contacts with organisations abroad may contribute to the objectives of this study, in particular knowledge from the State University Oregon (USA) and the Technical University Braunschweig (Germany).
Project manager of this project is Dr. M.R.A. van Gent (WL | Delft Hydraulics). On behalf of the Delft University of Technology Dr. J. van de Graaff is involved. On behalf of Alkyon Hydraulic Consultancy & Research Dr. H.J. Steetzel participates in the project. Project coordinator on behalf of the client is Dr. M. Boers of Rijkswaterstaat, RWS/RIKZ.
Prof. Dr. M.J.F. Stive leads a committee to assist the client in the quality control of the products of this project.
quality control. Dr. H.J. Steetzel was in charge of this part of the study. Dr. F.L.M. Diermanse provided the results of the probabilistic computations.
1.2 Objective of this part of the study
The objective of the study for Product 3 is to develop a probabilistic method based on the deterministic model results of the previous phase of the project (Product 2). The result will be used for the definition of a new guideline for the assessment of the safety of dunes (Product 4).
It should be noted that the initial definition of the new guideline model was based on the HR2001-boundary conditions. The new HR2006-conditions have been used to re-evaluate this formulation and calibrate the final formulation. This report only summarizes the final results of this work. The intermediate results obtained for the old HR2001 conditions are not reported. The new model will have to be used in combination with the new HR2006 boundary conditions.
1.3 Approach of this study
The activities for the study for Product 3 are divided into three main groups, namely: • Phase A – Definition phase
In this phase of the project the definition of the required input data is elaborated, partly based on the results of Product 2 of this study.
• Phase B – Probabilistic model
In this second phase the actual probabilistic computations are performed and analysed. • Phase C – Dune erosion model
Based on the results of the previous phase a dune erosion model is defined which replaces the present 1984-method.
1.4 Reader’s guide
In Chapter 2 the general approach followed in this study is described. This includes the description of the various types of models, namely a deterministic model (which describes the amount of dune erosion as a function of a set of given parameters), a probabilistic model (which applies the aforementioned deterministic model and takes the density distributions of the relevant parameters into account) and a guideline model (which represents the results of the previous more complicated probabilistic approach in a relatively simple model to be used for practical applications).
Chapter 3 describes the required input of the model, including the hydraulic conditions according to the so-called HR2006.
In Chapter 5 the validated probabilistic model is applied for a series of locations and cross-shore profiles along the North Sea Coast.
Based on these results a new formulation for the guideline model has been defined. The calibration, and validation of this model is described in Chapter 6.
The derived guideline model is formulated in Chapter 7. In this chapter also a comparison with previous models is provided as well as the comparison for both the old 2001-situation and the new 2006-situation.
Chapter 8 provides some additional aspects of the new guideline model, including the effect of nourishments and longshore transport gradients.
2
Model concepts for dune erosion
2.1 Introduction
Dunes act as a primary sea defence and have the same function as common sea dikes as they prevent flooding and protect people against drowning. This report deals with the design method for these dunes. Since a large number of factors determining dune erosion are present, a so-called probabilistic design method has been used to assess the expected erosion. Such a probabilistic method is required because of the fact that, during a severe storm surge, the actual values of the determining factors are unknown.
2.2 Types of models
In the framework of this study, three types of models are used, namely:
• A deterministic model, which describes the amount of dune erosion as a function of a set of given parameters (e.g. surge level, wave conditions, sediment characteristics and initial cross-shore profile).
• A probabilistic model which applies the aforementioned deterministic model and takes the density distributions of the relevant parameters into account in order to assess the expected dune erosion.
• A guideline model, which represents the results of the previous more complicated probabilistic approach in a relatively simple model to be used for practical applications. These three types of models are elaborated in the given order also. The first step, the deterministic model (the result of Product 2 of this study) can be seen as the actual input of this part of the study. Given a set of well-defined density distributions for each of the dune erosion determining parameters, a probabilistic model is applied to gain insight into the relative importance of the parameters involved and to take the uncertainty into account. Based on the results of these probabilistic elaborations a simple guideline model will be defined which can be seen as the final result of this part of the study.
This stepwise approach was also followed for the initial definition of the present guideline (TAW, 1984). In order to take the effect of longer wave periods into account, a so-called crash-version of this model has been defined in 2003. In this model the latter effect was taken into account by applying an additional surcharge erosion volume. The objective of the present study is to develop a new guideline model that incorporates the latest knowledge on both the effect of the wave period on the erosion profile as well as the forcing parameters. This new model will replace the two earlier models.
Moreover, some of the density distributions have been redefined also, which will have consequences for the guideline model as well.
This study will result in new versions of the three models. In the following the most important aspects of these three model types are discussed.
The application of a probabilistic tool can be seen as the main activity of this study. For the probabilistic elaborations three types of methods are available. Usually these methods are discerned in three levels, namely:
• Level III Exact probabilistic methods taking into account the density functions of all parameters involved.
• Level II Approximate methods in which the problem is linearized around a carefully selected point (the so-called design point).
• Level I Design methods taking safety factors into account. Usually these methods are based on the results of level III or level II calculations.
In this study a Level II approach is applied. More information will be provided in Section 2.4.
2.3 Deterministic model
2.3.1 Original 1984-model
In Product 2 of this study the original deterministic model for the assessment of the amount of dune erosion is modified by adding the peak wave period Tp as an additional parameter in
the formulation of the erosion profile.
The original equation describing the erosion profile as formulated in (TAW, 1984) reads: (7.6 / Hs ) y = 0.4714 [ (7.6 / Hs )1.28 (w / 0.0268)0.56 x + 18 ] 0.5 - 2.0 (2.1)
where:
Hs the significant wave height in deep water (in m) w the fall velocity of dune sand in salt sea-water (in m/s) x the distance to the new dune foot (in m)
y the depth below the storm surge level (in m)
Landward of the dune foot at (x = 0, y = 0) a steep 1 : 1 slope is present.
The parabolic-shaped erosion profile according to Equation (2.1) is valid up to a seaward point with coordinates:
xmax = 250 (Hs / 7.6)1.28 (0.0268 / w)0.56 (2.2)
and
Seaward of this point, the profile continues as a straight line with a slope of 1 : 12.5 until it intersects the original bottom profile. This original deterministic model is shown in Figure 2.1 (TAW, 1984).
2.3.2 Modified model for larger wave periods
In the modified formulation, the effect of the peak wave period is included in the original equation by adding the (12/Tp)-ratio in the right-hand term of Equation (2.1).
The modified formulation for Tp > 12 s but Tp < 20 s reads:
(7.6 / Hs ) y = 0.4714 [ (7.6 / Hs )1.28 (12 / Tp )0.45 (w / 0.0268)0.56 x + 18 ]0.5 - 2.0 (2.4)
where:
Tp the peak wave period (s)
For Tp > 12 s, the erosion profile is less steep than the (original) erosion profile holding for Tp = 12 s. For Tp > 20 s, the relation for Tp = 20 s should be applied.
As a result, the most seaward point of the erosion profile is positioned at a reduced depth, namely:
ymax = [ 0.4714 ( 250 ( 12 / Tp )0.45 + 18 )0.5 - 2.0] (Hs / 7.6) (2.5)
For Tp = 12 s, the original formulation of Equation (2.3) with ymax ≅ 0.75 Hsis found.
For Tp > 20 s, the ymax obtained for Tp = 20 s should be applied.
The applied power of 0.45 in both Equation (2.4) and (2.5) is the result of the validation of the updated model (see Product 2 for more details).
The length of the erosion profile (denoted by xmax) remains unchanged, so Equation (2.2) is
still valid for Tp > 12 s.
It should be remarked that both Equation (2.4) and (2.5) are only valid for Tp ≥ 12 s
providing an increase in the amount of dune erosion for these more extreme wave conditions. Any reduction of the amount of erosion for Tp < 12 s is not taken into account. As a result,
the original Equation (2.1), remains valid for smaller wave periods.
Figure 2.2 shows the erosion profile for the so-called standard cross-shore profile for a surge level of NAP+5 m and the reference conditions (Hs = 7.6 m and w = 0.0268 m/s and thus D50
≅ 240 µm) yielding an erosion profile length of 250 m by definition (see Equation (2.2)). In the figure, both the computed erosion profiles for Tp = 12 s and Tp =18 s are presented. As
can be observed, the erosion profile for the larger wave period is less steep and yields consequently more dune erosion.
57.9 m for Tp = 18 s, yielding an increase of about 12%. The amount of erosion above the
surge level denoted as A* increases from 340 to 404 m3/m1, an increase of about 19%. It should be noted that aforementioned relative increase measures are only valid for a rather extreme increase of the wave period (namely 18 s instead of 12 s). If a characteristic wave period of Tp = 15 s was considered, the relative increase of the dune retreat distance and
erosion volume would be 7 and 11% respectively.
Figure 2.3 shows the relative amount of dune erosion as a function of the wave period for the interval Tp = 10 s to 20 s. The increase in the retreat distance is provided in the lower panel
using the bold line. In both cases the results remain unchanged for Tp < 12 s.
2.3.3 Additional sensitivity elaborations
Since the effect of the wave period is included in the formulation of the shape of the erosion profile, the relative effect on both the erosion volume A* and the retreat distance RD depend on the actual dune profile, the actual sediment diameter and the actual hydraulic conditions (both storm surge level and wave height) as well. In the base case (dune height NAP+15 m, 240 µm for the sediment diameter, yielding w = 0.0268 m/s, NAP+5 m for the surge level and 7.6 m for the significant wave height), the increase in erosion volume and retreat distance amounts to 19.0 and 12.5% respectively (see previous section).
Table 2.1 provides an overview of the results for other combinations of these parameters. For the four governing parameters the relative result for both a lower and a higher value is elaborated.
The effect of the cross-shore profile is investigated by computing the erosion parameters A* and RD for a low dune level of NAP+12 m and a high dune level of NAP+18 m. Compared to the base case, the erosion volume for the lower dune is less (293 and 348 m3/m1 for Tp= 12 s and 18 s respectively instead of 340 and 404 m3/m1 for the base case) whereas the
Parameter Erosion parameter
Dune level Diameter Surge level Wave height Volume A* Distance RD Remark
[m wrt NAP] [µm] [m wrt NAP] [m] [-] [-]
15 240 5 7.6 19.0 % 12.5 % Base case
12 240 5 7.6 18.6 % 14.4 % Effect dune height
15 240 5 7.6 19.0 % 12.5 %
18 240 5 7.6 19.4 % 10.8 %
15 190 5 7.6 16.3 % 11.8 % Effect sediment
15 240 5 7.6 19.0 % 12.5 %
15 290 5 7.6 22.0 % 13.2 %
15 240 4 7.6 29.0 % 15.9 % Effect surge level
15 240 5 7.6 19.0 % 12.5 %
15 240 6 7.6 14.4 % 10.5 %
15 240 5 6.5 16.8 % 10.6 % Effect wave height
15 240 5 7.6 19.0 % 12.5 %
15 240 5 9.5 24.9 % 17.2 %
Table 2.1 Relative effect on erosion parameters of an increased wave period (18 instead of 12 s) for different
parameters
The effect of the sediment diameter is such that (although coarse material provides less erosion), an increasing sediment diameter yields an increasing effect of an increased wave period (18 instead of 12 s) for both the erosion volume A* as the retreat distance RD. The absolute differences from the base case are limited.
An increasing surge level yields a decrease of the effect of both the erosion volume as the retreat distance. Compared to the base case, the application of lower surge levels results in a significant increase of the effect of the wave period.
The opposite effect is found for an increase of the wave height. Larger wave yield a significant increase of the effect of the wave period.
Above described results are added to Figure 2.3 showing the range in the relative erosion results.
It can thus be concluded that the effect of a larger wave period is more significant for especially lower surge levels and higher waves. A small increase is found for a lower dune and a coarser material.
2.4 Probabilistic model
2.4.1 Reliability functions
There are various mechanisms that can lead to failure of a flood defence structure. In this report only the mechanism of “dune erosion” is considered. Failure mechanisms are mathematically described by so-called reliability functions Z in which the resilience R is compared with the hydraulic load S.
The formulation is:
This means the structure fails if S > R and thus Z < 0. The criterion of failure for dunes is a certain critical dune retreat distance RDcrit. This means that if the retreat distance RD due to a
specific storm event exceeds RDcrit the dune has failed.
In formula, this means the reliability function equals:
Z = RDcrit – RD (2.7)
Instead of the actual failure of a (small) dune, this procedure can also be applied for a wide dune area. In this case other considerations can be used to define the critical position and failure resemblances the situation in which the erosion exceeds the critical position.
The principle of the reliability function is illustrated in Figure 2.4 with the (simplified) example. In this example the contour lines show the amount of dune erosion as a function of water level and wave height. For the sake of clarity, the effects of other relevant variables like wave period or sediment diameter are ignored in this example. Each point in the figure, i.e. each combination of water level and wave height, can be considered as the (maximum) dune retreat distance during a (synthetic) storm event. For a number of combinations the expected dune retreat distance is computed with the deterministic model as discussed in the previous section. The contour lines in the figure are based on the outcome of these computations.
Suppose the critical dune retreat RDcrit is equal to 50 m. The solid red line in Figure 2.4
represents this critical condition. The area to the upper right of this red line consists of all combinations of water level and wave height for which the resulting erosion exceeds 50 m and therefore will lead to failure of the dune. This area is referred to as the so-called failure domain. The red contour line itself is called the limit state, i.e. the threshold between failure and non-failure.
2.4.2 Computation of failure probabilities
The reliability function of the previous section describes for which (hydraulic) conditions the dune will fail. For the safety of the area that is protected by the dunes it is of course highly relevant to know the probability (or frequency) with which this will happen. Mathematically this means that the probability of occurrence of each combination of variables in the failure domain needs to be known. This means that a procedure is required that basically performs the following two tasks:
1. Find the failure domain. This involves exploration of the n-dimensional space of possible realisations, where n is the number of random variables involved.
2. Determine the cumulative probability of occurrence of all combinations in the failure domain.
The first task is done through application of the deterministic dune erosion model for various combinations of realisations of the n random variables. The required number of model computations strongly depends on the selected probabilistic method as will be discussed below.
their respective distribution functions can simply be multiplied. However, this will not work for the current example: for instance water level and wave height are not statistically independent. In that case a multivariate distribution function of water level and wave height that correctly describes their mutual dependency is required.
2.4.3 Available probabilistic methods
There are several methods that perform the aforementioned two tasks, such as: 1. Numerical integration
This method explores the n-dimensional space of possible realisations (where n equals the number of random variables) by dividing it into a number of discrete n-dimensional ‘cubicals’. Each cubical represents a combination of realizations of the n random variables. For each cubical the following is computed:
− The probability of occurrence.
− Whether or not the cubical is located in the failure domain (by using the deterministic dune erosion model).
− The probability of failure is equal to the sum of probabilities of all cubicles in the failure domain.
2. Crude Monte Carlo
With this method, N combinations of realisations of the n variables are randomly sampled from their respective distribution functions, where N is a user defined (very large) number. For each combination the deterministic dune erosion model is applied to find out if it leads to failure. The total number M of failures determines the estimated probability of failure: p = M/N.
3. Directional Sampling
This is one of many Monte Carlo techniques in which the samples are taken in a more ‘intelligent’ manner in order to reduce the required number of samples and, consequently, model computations. Other examples are: importance sampling, DARS, quasi Monte Carlo techniques and Latin Hypercube Sampling. All techniques have in common that compared to crude Monte Carlo a relatively large number of the samples are taken in and around the failure domain.
4. FORM
FORM is short for First Order Reliability Method. This method derives the so-called design point (see following section) with an iterative procedure. Subsequently, the limit state function (Z = 0) is linearized in order to estimate the probability of failure.
Directional sampling reduces the number of model computations in comparison with crude Monte Carlo, but also has its limitations. FORM has the advantage that it requires relatively little computation time. Furthermore, its output consists not only of the probability of failure, but also of the design point (see following section). The disadvantage of this method is that the iterative algorithm sometimes does not converge and results are not always reliable. This is especially the case if the relation between the input and output of the deterministic simulation model is highly non-linear.
Numerical integration and Monte Carlo techniques are called level-III methods because they fully consider the probability distributions and the domain of possible realizations of all random variables. FORM is called a level-II method because it uses a linearized approximation. Level-I methods are methods that use safety-coefficients for each random variable. The outcome (either failure or no failure of the construction) can be computed directly, without the use of any random variable.
In general, level-I methods are based on results of level-II methods. A good example is the guideline for dune erosion, which will be discussed in Section 2.5.
2.4.4 Applying design points
The hydraulic boundary conditions along the Dutch Coast consist of a combination of the water level and wave parameters (height, period and direction). These conditions serve as input for the test procedure of our flood defence system. This means that the dunes should be able to resist the hydraulic boundary conditions. A possible method to determine these boundary conditions is to derive the so-called design point. This method will be applied for dikes along the Dutch Coast to determine the boundary conditions for the period 2006-2011. For this purpose the probabilistic software package HYDRA-K is used.
The design point is defined as the combination of realisations of random variables that fulfils the following two features:
1. The design point belongs to the limit state (Z = 0). This means that the dune is just able to resist the conditions present in the design point.
2. Of all combinations that form the limit state, the design point has the highest probability of occurrence (or mathematically more correct: the highest probability density).
2.5 Guideline model (1984-version)
2.5.1 Introduction
For practical application a relatively simple test model for the assessment of the safety of a cross-section has been developed in such a way that the result corresponds with that of the more complicated probabilistic calculations discussed in the previous section.
The test method comprises of a number of computational rules for the determination of that degree of dune erosion with an exceedance frequency of 10-5 per year (for the Holland Coast) The values, to be used in the calculation, for the considered factors that determine the dune erosion are determined in such a way by probabilistic numerical techniques, that the thus calculated degree of dune erosion has a probability of exceedance equal to the required value.
2.5.2 Basic principle
A definition sketch of the guideline model is provided in Figure 2.5. In order to calculate the position of the erosion point R, two computational steps are required.
The first step is the application of the deterministic model for so-called computational values of the dune erosion factors, which are:
• The storm surge level h • The significant wave height Hs
• The grain diameter or fall velocity of the dune material D
When assessing the safety of a dune in view of its function as a primary sea defence, the computational value for the storm surge level h equals the design level plus a two third part of the decimation height. This level is called the computational level.
The design level has been defined as the (storm surge) level with (for Central Holland) a probability of exceedance of 10-4 per year. For the Delta region and the Wadden Islands higher probabilities are valid (2.5 10-4 and 5 10-4 per year respectively).
The decimation height is the difference in height between the water level with a probability of exceedance 10 times smaller than that of the design level, and the design level. Hence the frequency of exceedance of the computational level is 0.215 times the frequency of exceedance of the design level.
The mean value of the wave height Hs at the computational level has to be used as the
significant wave height. It should be noted that the value holds for deep-water conditions. The computational value of the grain diameter Dcomp must be computed from:
Dcomp = µD50 - 5 (σD50 )2/ µD50 (2.8)
µD50 the expected value of the D50 (in m)
σD50 the standard deviation of the D50 (in m)
For the standard deviation σD50 a minimum of 5% of µD50 is assumed.
The amount of dune erosion depends, according to Equation (2.1) on the particle diameter of the dune material via the fall velocity w. The fall velocity w in salt water of 5 °C can be approximated by:
10log (1 / w) = 0.476 (10log D)2 + 2.180 10log D + 3.226 (2.9)
where:
w the fall velocity of the dune sand in sea-water (m/s) D the diameter of the dune sand (m)
Using the three parameters (surge level, wave height and fall velocity), the location of the erosion profile can (for a given cross-shore profile) be assessed by applying the deterministic model described in Section 2.3.
This can be done as follows:
• The shape of the erosion profile is determined by the significant wave height and the grain diameter according to Equation (2.1).
• The position of the erosion profile in the vertical sense is determined by the storm surge level.
• The position in the horizontal sense is determined by positioning the erosion profile over the initial coastal profile in such a way that an erosion-sedimentation balance is obtained in the direction perpendicular to the coast.
The amount of dune erosion above the computational level is denoted as A* in Figure 2.5. In a second step the calculated amount of dune erosion above the storm surge level is increased with a surcharge T to take account of the influences of the inaccuracy of the deterministic model, the gust oscillations and gust surges, and the uncertainty about the time that the water level remains at about the maximum level. The effect of this surcharge is expressed in an additional recession of the steep dune front. As indicated in Figure 2.5, point P is the new intersection of this shifted dune front with the storm surge level.
The three individual surcharges on the amount of dune erosion As (in m3/m1) above the
computational level, are respectively:
• A surcharge of 0.10 A* m3/m1 to take into account the uncertainty about the time which the water level remains at about the maximum level. This time span is the most determinative factor for the amount of dune erosion in the entire development of the water level during the storm surge.
• A surcharge of 0.05 A* m3/m1 to take into account the effect of gust surges and gust oscillations.
The sum of the surcharges on the amount of dune erosion As above the computational level
consequently amounts to 0.25 A* + 20 m3/m1. This surcharge A
s causes a landward shift of
the originally calculated erosion point. The final erosion point is denoted as R in Figure 2.5. For Central Holland, the probability of exceedance of this location amounts to 10-5 per year. The objective of this study is to update and modify the above-described guideline model. The elaboration of this task is presented in Chapter 5 whereas the final result is provided in Chapter 6.
2.5.3 Additional requirements
The basic description of the guideline model is not applicable for all circumstances. Both the amount of dune erosion and the related position of the dune face are subject to two other effects, namely:
• The effect of variations in the initial profile.
• The effect of positive (eroding) longshore transport gradients.
The first item refers to the influence of both the natural as nourishment-based fluctuation of the cross-shore profile on the amount of dune erosion. These fluctuations must be taken into account because of the fact that it is not exactly known which profile is present just before the (design) storm surge occurs.
3
Summary of required input data
3.1 Introduction
As already described in Section 2.5, the amount of dune erosion depends on a number of dune erosion determining parameters. In order to perform probabilistic computations, for every individual parameter the probability density function has to be defined. Since the wave period will also be taken into account in the new probabilistic model, this parameter is added to the original list of relevant parameters.
This chapter starts with a summary of the relevant input parameters in Section 3.2. Next, a more detailed elaboration of the basic data is provided in Section 3.3 through 3.8. Special attention is given to the hydraulic conditions as elaborated in Section 3.5 in which three sets of boundary conditions are being distinguished, namely the original conditions used for the 1984-elaboration, an ‘intermediate set’ as applied for the various elaborations and the new hydraulic conditions. The latter have been provided in the framework of the so-called HR2006. The initial development of the model has been based on the old hydraulic conditions. For the final definition the values according to the HR2006 have been used. Section 3.9 provides a summary of the data to be used as an input for the actual combinations, including a phasing of the subsequent steps.
3.2 Summary of input parameters
The amount of dune erosion and subsequently the so-called retreat distance RD, depends on a number of parameters and factors, namely:
• The shape of the initial cross-shore profile. • The diameter of the dune material.
• The maximum storm surge level. • The significant wave height. • The (peak) wave period.
• The duration of the maximum surge.
• The effect of gust surges and gust oscillations. • The accuracy of the deterministic model.
Due to the mass balancing procedure in calculating the volume of erosion, the shape of the initial profile, the profile as present just before the storm surge starts, is a determining factor for the amount of dune erosion. Since a profile measurement taken just before the storm surge will hardly ever be available, the uncertainty in the actual profile and thus the sediment content in the erosion-accretion zone is a relevant parameter also.
yields a relatively steeper and shorter erosion profile and thus a relative decrease in the amount of dune erosion. Also the uncertainty in this diameter should be considered.
Both the maximum surge level and the wave conditions, i.e. the significant wave height and the (peak) wave period, can be seen as the actual hydraulic load and thus play a very important role in the computation of the amount of dune erosion and the retreat distance. Not only the expected values of these hydraulic conditions are to be considered, but also the related standard deviations play a role.
Another important factor is the time that the water level remains at about the maximum surge level (denoted as ‘duration of the maximum surge’). This time span is the most determinative factor for the amount of dune erosion in the entire development of the water level during the storm surge and thus the uncertainty about this time interval should be explicitly taken into account. The actual effect of the time span is based on the results of series of physical model tests in which the evolution of the amount of dune erosion under constant hydraulic conditions was studied as a function of the duration of the wave attack.
Gust surges and gust oscillations will result in an additional fluctuation of the water level during the storm surge. This effect is not included in the deterministic model and should therefore be taken into account as a correction of the basic erosion volume.
The deterministic model, described in Section 2.3 and more extensively in the Product 2 report, is partly based on a series of small and large-scale model tests. The inaccuracy of the model plays an important role also.
In the following six sections, the individual factors are discussed more extensively.
3.3 The initial cross-shore profile
3.3.1 Introduction
Due to the mass balancing procedure in calculating the volume of erosion, the shape of the initial profile is a determining factor for the amount of dune erosion. In this study a number of cross-shore profiles is considered, namely a standard profile and a set of prototype profiles.
The objective of this elaboration is three-fold, namely:
• To investigate the effect of a different shape of the initial cross-shore profile.
• To validate the new formulated guideline model by comparing the results with the outcome of the probabilistic model.
3.3.2 Standard profile or reference profile
For the basic elaborations the so-called reference profile has been used. The crest of the dune in this profile is horizontal at a level of NAP+15 m (see also Figure 2.2). A more detailed description of this profile is presented in the previous product-reports.
3.3.3 Uncertainty in volume content
Since a profile measurement taken just before the storm surge will hardly ever be available, the uncertainty in the actual profile and the sediment content in the erosion accretion zone is a relevant parameter.
In the framework of the 1984-study, the volume content above a certain level between two vertical limits just land and seaward of the relevant part of the cross-shore profile was elaborated for a series of arbitrary profiles. From this elaboration it was found that the deviation of the actual volume content from the average content could be approximated by a normal distribution with a standard deviation σip of about 60 m3/m1 (where the subscript ip
denotes the initial profile).
The same situation will be used for the present elaborations, i.e. a standard deviation of 60 m3/m1 in the initial volume. In a ‘negative’ situation (a cross-shore profile with ‘less sand’ than the average profile), the position of the erosion profile in the horizontal sense must be such that a ‘positive deficit’ in the erosion-sedimentation balance is obtained in the direction perpendicular to the coast. In other words: the total erosion minus the total accretion should be equal to this ‘positive deficit’. In the computations the presence of a cross-section with ‘less sand’ is thus reproduced by applying a correction on the balance such that the erosion equals the sum of the sedimentation (for the original profile) and this deficit.
Since the magnitude of the standard deviation may vary along the coast, other values of the standard deviation have to be considered also, ranging from 0 and 30 (with less uncertainty) to 90 and 120 m3/m1 (with more uncertainty). The results of this elaboration are presented in Section 8.2.3. For the initial elaborations the base value of 60 m3/m1 will be applied.
3.3.4 Other cross-shore profiles along the Holland Coast
In the framework of the first product-report a number of locations along the Central Holland Coastline was selected to perform additional analyses. The cross-shore profiles for these 10 selected locations will be applied in this part of the study also.
Number Km Name/location Remark
#00 Reference profile
#01 3.08 Den Helder Located landward of a tidal gully
#02 9.28 Botgat
#03 14.83 Zwanenwater
#04 19.55 Tweede Korftwater Showing a dune valley landward of the first dune row
#05 37.75 Egmond
#06 66.25 Zandvoort
#07 81.75 Noordwijk
#08 99.75 Scheveningen
#09 111.96 Monster
#10 118.25 Hoek van Holland Relatively small dune (not a primary defence)
Table 3.1 Overview of selected cross-shore profiles for the Holland Coast
Figure 3.1 provides an overview of the selected cross-shore profiles showing the bottom level as a function of the distance with respect to the so-called RSP-line (RijksStrandPaal). As can be observed, the profiles show a large variation in both dune crest level and profile shape. Furthermore, the first dune row of profile #10 near ‘Hoek van Holland’ is (due to the so-called ‘Van-Dixhoorn driehoek’) located relatively far seaward. A shifted version of the last profile (denoted as profile #10s) is provided in Figure 3.2. The positions of the intersections with the NAP-level are indicated in this plot also. A more functional comparison between the various profile shapes is presented in Figure 3.3 and 3.4, showing a more detailed version of the individual shapes.
Some preliminary insight in the erosion profiles as a result of the application of the modified deterministic model is provided in Figure 3.5 also (for the hydraulic conditions given in Table 3.5 and the sediment diameter given in Table 3.3). In addition to the erosion profile for Tp = 12 s, the position of the dune face for an erosion profile for Tp = 18 s is shown also.
As can be observed, the new dune face for profile #04 (Tweede Korftwater) is located on the landward side of the first dune row. This might yield a problem using the probabilistic model that may encounter a convergence problem for these types of dunes. Due to the relatively mild-sloping beach, the amount of dune erosion for profile #10 (Hoek van Holland) is only minor. Consequently, this profile seems less applicable for model testing also.
3.3.5 Additional profiles beyond the Holland Coast
In order to check the performance of both the probabilistic model and the new guideline model for other sections along the Dutch Coast, a set of additional locations has been defined. These additional profiles have been limited to the northern part of the Dutch Coast, viz. the Wadden Coast. Table 3.2 provides an overview of the selected locations. All locations are located more or less in the central section of the island. Figure 3.6 provides an overview of these five profiles.
Number Km Name/location Remark #11 18.53 Texel
#12 43.77 Vlieland Only seaward small dune row applied #13 17.00 Terschelling
#14 10.00 Ameland
#15 7.00 Schiermonnikoog
These profiles / locations have been used to check the initial formulation of the model based on the elaborations for the Holland Coast.
In the framework of this part of the study no computations have been performed for the Delta Coast, basically because of the fact that the peak wave period for this section is lower than the original 12 s. The application of the new guideline model for this part of the coast will be addressed in the framework of Product 4.
For the further elaborations a step-by-step approach is foreseen. In the first computations only the standard profile (profile #00) will be considered. Next the effect of other shapes of the cross-shore profile will be investigated. It should be remarked that the 1984-elaborations were limited to minor variations of the standard profile and thus no probabilistic experience is available for other, dissimilar profile shapes. Finally, the results obtained for the additional locations are used for validation of the model.
3.4 Grain diameter of the dune material
3.4.1 Introduction
As stated before, the diameter of the sediment of the dune is an important parameter since it affects the shape of the post-storm erosion profile. Not only the expected value of the D50,
the µD50, but also the uncertainty in this diameter, the standard deviation σD50, should be
taken into account.
3.4.2 Standard case
For the initial elaborations use will be made of the reference profile. For these elaborations the standard sediment diameter of D50 = 225 µm has been applied. For the standard deviation
a relative measure of 10% is used and thus σD50 = 0.10 µD50 = 22.5 µm.
Abovementioned values are comparable to the ones applied in the original 1984-elaborations.
3.4.3 Other locations along the Holland Coast
Number Km D50 (µm) σD (µm) Relative rate (-) #01 3.08 232 12 0.05 #02 9.28 259 16 0.06 #03 14.83 256 17 0.07 #04 19.55 241 14 0.06 #05 37.75 252 20 0.08 #06 66.25 184 11 0.06 #07 81.75 221 12 0.05 #08 99.75 217 18 0.08 #09 111.96 214 11 0.05 #10 118.25 255 15 0.06
Table 3.3 Overview of sediment characteristics for selected cross-shore profiles
Figure 3.7 shows the longshore distribution of both the mean sediment diameter and the standard deviation for the Central Holland Coast. In southerly direction, the average diameter reduces from about 250 µm near Den Helder to 200 µm near Hoek van Holland, whereas the standard deviation shows an opposite trend. The values for the selected locations are denoted by the large symbols in this figure.
3.4.4 Other locations beyond the Holland Coast
The representative values for the additional locations are summarized in Table 3.4. As can be observed, the average grain diameter decreases in easterly direction (from #11 at Texel towards #15 at Schiermonnikoog).
Number Km D50 (µm) σD (µm) Relative rate (-)
#11 18.53 194 10 0.05
#12 43.77 194 10 0.05
#13 17.00 188 9 0.05
#14 10.00 176 18 0.10
#15 7.00 164 8 0.05
Table 3.4 Overview of sediment characteristics for additional locations along Wadden Coast
3.5 Hydraulic conditions
3.5.1 Introduction
The hydraulic conditions during the storm surge determine, together with the fall velocity of the dune material, the shape of the erosion profile. In the modified version of the deterministic model (see Section 2.3 for more details) the wave peak period plays an important role also since it affects the steepness of its average slope for wave periods with Tp > 12 s.
Table 3.5 presents an overview of the so-called design level (surge level with frequency of exceedance of 10-4 per year) and the related significant wave height for the selected locations, both according to the statistics as applied in the initial phase of the project. These conditions have also been used to compute the erosion profile shown in Figure 3.5. In the framework of the HR2006, these values have been changed.
Number Km h ( m w.r.t. NAP) Hs (m) #01 3.08 4.47 8.98 #02 9.28 4.55 8.88 #03 14.83 4.62 8.79 #04 19.55 4.68 8.72 #05 37.75 4.92 8.45 #06 66.25 5.15 8.15 #07 81.75 5.15 8.08 #08 99.75 5.14 7.98 #09 111.96 5.08 7.86 #10 118.25 5.05 7.80
Table 3.5 Hydraulic conditions applied for the preliminary application (NOT according to HR2006)
As can be observed, the surge level increases in southerly direction (due to an increasing storm set-up in the southern part of the North Sea) whereas the wave height decreases in this direction (due to relatively smaller fetches).
3.5.2 Maximum surge level
The maximum surge to be reached during an arbitrary surge is the resultant of two stochastically independent phenomena, namely the astronomical tide and the wind set-up. Taking both phenomena into account, the resulting frequency of occurrence can be derived. In the 1984-elaborations the maximum surge level for Hoek van Holland was described using an exponential relation according to:
Pe (H > h) = α exp [ -β h ] (3.1) where:
Pe the probability of exceedance of the highest level h during a storm surge (in year-1) h the highest water level during a storm surge
α a parameter that depends on the location along the coast β a parameter that depends on the location along the coast
For Hoek van Holland the parameters α and β have been determined at 727.86 and 3.1 respectively (valid outside the breakwaters). According to this relation, the design level (10-4 per year) amounts to NAP+5.25 m.
This relation will be used to test the probabilistic model for the 1984-case (see Section 4.2 and 4.3).
Nowadays, a so-called conditional Weibull distribution function is applied to describe this relation (see amongst others (RWS/RIKZ, 2000) for more details).
