Dune erosion
Product 1: Deterministic dune erosion prediction methods
January, 2006
Rijkswaterstaat, RIKZ
Prepared for:Prepared for:
Rijkswaterstaat, RIKZ
Dune erosion
Product 1: Deterministic dune erosion prediction methods
Report January, 2006
WL | delft hydraulics
CLIENT: Rijkswaterstaat, RIKZ
TITLE: Dune erosion
Product 1: Deterministic dune erosion prediction methods ABSTRACT:
The dune erosion prediction method presently used to assess the safety level of dunes along the Dutch coast was developed
for situations with wave periods up to Tp = 12 seconds, while 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 lead to more dune erosion. However, effects of the wave period are not quantified sufficiently yet.
To allow for the five yearly safety assessment of the Dutch primary water defences the current safety assessment method needs to be extended. With this new method it should be possible to calculate dune erosion under normative hydraulic conditions taking effects of the wave period into account. The present report describes the first phase of this development. The objective of this part of the study is to develop a deterministic dune erosion prediction method based on existing data and existing knowledge on effects of the wave period.
All methods in this report have the current method as a starting point. Therefore, they should be considered as an extension of the present set of equations; no entirely new concepts are developed. The new formulations are derived on the basis of a limited amount of data on the effect of the wave period, mainly obtained from small-scale model tests. The formulations should be calibrated by including the results of the large-scale dune erosion tests to be carried out in a later stage of this dune erosion project.
REFERENCES: WL | Delft Hydraulics’ proposal (ref: MCI-10835/H4357/MvG, dated May 20th, 2005.
Acceptance of proposal RIKZ/2005/05707, dated July 7th, 2005.
Reference to this report is advised to be: WL | Delft Hydraulics (2006), ‘Dune erosion, Deterministic dune erosion prediction methods’, Report H4357, January 2006, Delft.
VER AUTHORS DATE REMARKS REVIEW APPROVED BY
0 Project team September 2005 First draft L.C. van Rijn W.M.K. Tilmans
1 Project team October 2005 Second draft L.C. van Rijn W.M.K. Tilmans
2 Project team January 2006 Final L.C. van Rijn W.M.K. Tilmans
PROJECT NUMBER: H4357
KEYWORDS: Dunes, dune erosion, physical model tests, prediction methods
NUMBER OF PAGES:
CONFIDENTIAL: YES, until NO
Contents
List of Figures List of Tables List of Symbols Summary 1 Introduction...1 1.1 General...11.2 Objective of this study ...4
1.3 Approach of this study...4
1.4 Reader’s guide ...4
2 Data from physical model tests...7
2.1 Introduction...7
2.2 Data collection ...7
2.3 Scale relations...8
2.3.1 Theoretical derivations of scale relations ...9
2.3.2 Derivation of scale relations based on measurements ...11
2.3.3 Applied scale relations...13
2.4 Description of tests ...15 2.4.1 Large-scale tests...15 2.4.2 Small-scale tests...21 2.5 Testbank...24 2.5.1 Structure of testbank ...24 2.5.2 File formats...25
3 Deterministic prediction methods ...27
3.1 Introduction...27
3.3 New methods... 29
3.3.1 Categories of new methods ... 29
3.3.2 Category 1: Period-dependent erosion volumes... 29
3.3.3 Category 2: Period-dependent erosion profiles ... 36
3.4 Other concepts from literature... 42
3.4.1 Introduction ... 42
3.4.2 The equilibrium profile concept ... 43
3.4.3 The wave impact concept ... 43
3.4.4 Other existing concepts ... 44
3.4.5 Conclusion on other existing concepts... 45
4 Evaluation of prediction methods ... 47
4.1 Introduction ... 47
4.2 Confrontation of prediction methods with model data... 47
4.2.1 Data selection ... 47
4.2.2 Scaling from model to prototype values... 48
4.2.3 Calculated erosion profiles and volumes... 49
4.2.4 Relative erosion volumes ... 52
4.3 Comparison of prediction methods using reference profiles... 53
4.3.1 Calculated erosion profiles and volumes... 53
4.3.2 Calibration of prediction methods... 58
4.4 Summary of evaluation of prediction methods ... 59
5 Preliminary application of prediction methods ... 61
5.1 Introduction ... 61
5.2 Description of UCIT... 61
5.3.2 Hydraulic conditions...64
5.4 Results of dune erosion calculations with UCIT ...64
6 Summary and conclusions...69
References ...73
Appendices
A Figures
B Tables
C Note on Scheldt flume tests 2003
D Derivation of dune erosion profile for Option wl2a
E Transition between erosion profile and initial profile
F Numerical results of UCIT calculations
G Possible effects of scaling procedure in DUROSTA
List of Figures
Figures to be found in the text:
Figure 1.1 Reference profile ...5
Figure 2.1 Hydraulic conditions of Test 3 of research programme M1263-3 ...16
Figure 2.2 Hydraulic conditions of Test 4 of research programme M1263-3 ...17
Figure 2.3 Hydraulic conditions of the tests of research programme M1797 ...18
Figure 2.4 Hydraulic conditions of Test 1 of research programme M1811...19
Figure 2.5 Hydraulic conditions of Test T21 (same as in Tests T22 to T28) ...22
Figure 2.6 Hydraulic conditions of Tests 1 ...23
Figure 2.7 Overview of testbank structure ...25
Figure 2.8 Example of a <research programme><test>.inp file. HS = Hs; Tp = Tp; WL = water level; D50 = D50; WS = w; n_d = nd. Nb: comments are preceded by a ‘*’...26
Figure 2.9 Example of a part of a zt0000.tek file. Nb: comments are preceded by a ‘*’ ...26
Figure 3.1 Erosion profile, erosion volume A and erosion point Q...27
Figure 3.2 Additional percentage of dune erosion due to larger wave load...32
Figure 3.3 Absolute erosion volumes (prototype) after 32.9 hours as a function of the wave steepness...35
Figure 3.4 Relative erosion volumes as a function of the wave steepness...35
Figure 3.5 Relative erosion volumes as a function of the wave period (Hs = 7.6 m)....36
Figure 3.6 Qualitative effects of longer wave period on dune erosion after 6 hours test duration, based on results of tests from research programme H4265, see also Den Heijer (2005)...37
Figure 3.7 Erosion profile in Option wl2a with reference profile as initial profile...39
Figure 3.8 Erosion profiles in Option wl2b and reference profile as initial profile ...41
Figure 3.9 Shift in dune foot location for Option wl2c ...42
Figure 4.1 Calculated relative erosion volumes relative to DUROS calculations as a function of the wave steepness ...53
Figure 4.2 Erosion volumes calculated with different prediction methods for different wave periods ...55
Figure 4.3 Calculated erosion volumes for reference profile relative to DUROS calculations ...56
Figure 5.1 JARKUS-transect no. 308 with a steep foreshore in the cross-shore profile (left) and JARKUS-transect no. 8175 with a relatively low dune top (right) ...63
Figure 5.2 Calculated erosion volumes for the selected JARKUS transects with all prediction methods for hydraulic conditions with exceedance frequency of 1/10,000 per year... 66 Figure 5.3 Relative change in calculated erosion volumes for the selected JARKUS
transects with all prediction methods for hydraulic conditions with
exceedance frequency of 1/10,000 per year ... 66
Figures to be found in Appendix A:
Figure A.1 Measured and calculated erosion profiles; pt-H4265 Test T01 Figure A.2 Measured and calculated erosion profiles; pt-H4265 Test T02 Figure A.3 Measured and calculated erosion profiles; pt-H4265 Test T03 Figure A.4 Measured and calculated erosion profiles; pt-H4265 Test T11 Figure A.5 Measured and calculated erosion profiles; pt-H4265 Test T12 Figure A.6 Measured and calculated erosion profiles; pt-H4265 Test T13 Figure A.7 Measured and calculated erosion profiles; pt-M1263-3 Test 1 Figure A.8 Measured and calculated erosion profiles; pt-M1263-3 Test 2 Figure A.9 Measured and calculated erosion profiles; pt-M1263-3 Test 3 Figure A.10 Measured and calculated erosion profiles; pt-M1263-3 Test 4 Figure A.11 Measured and calculated erosion profiles; pt-M1263-3 Test 5 Figure A.12 Measured and calculated erosion profiles; pt-H0298 Test 5 Figure A.13 Measured and calculated erosion profiles; pt-M1819-1 Test T01 Figure A.14 Measured and calculated erosion profiles; pt-M1819-1 Test T04 Figure A.15 Measured and calculated erosion profiles; pt-M1819-1 Test T05 Figure A.16 Measured and calculated erosion profiles; pt-M1819-1 Test T06 Figure A.17 Measured and calculated erosion profiles; pt-M1819-1 Test T13 Figure A.18 Measured and calculated erosion profiles; pt-M1797 Test 1 Figure A.19 Measured and calculated erosion profiles; pt-GWK98 Test F1 Figure A.20 Measured and calculated erosion volumes; H4265
Figure A.21 Measured and calculated erosion volumes; M1263-3
Figure A.22 Measured and calculated erosion volumes; M1819-1, M1797 & GWK98 Figure A.23 Calculated erosion profiles; Method ude-01
Figure A.24 Calculated erosion profiles; Method duros-01 Figure A.25 Calculated erosion profiles; Method kos1d-01
Figure A.29 Calculated erosion profiles; Method wl1a-01
Figure A.30 Calculated erosion profiles for different calibration coefficients α; Tp = 15 s Figure A.31 Calculated erosion profiles for different calibration coefficients α; Tp = 18 s Figure A.32 JARKUS-transects numbers 308 to 3775
Figure A.33 JARKUS-transects numbers 6625 to 11825
Figure A.34 Dune erosion calculation with DUROS for JARKUS transect 6625 with hydraulic conditions with a frequency of exceedance of 1/10,000 per year Figure A.35 Dune erosion calculation with Option kos3 for JARKUS transect 6625 with
hydraulic conditions with a frequency of exceedance of 1/10,000 per year Figure A.36 Dune erosion calculation with Option kos1d for JARKUS transect 6625
with hydraulic conditions with a frequency of exceedance of 1/10,000 per year
Figure A.37 Dune erosion calculation with Option wl2a for JARKUS transect 6625 with hydraulic conditions with a frequency of exceedance of 1/10,000 per year Figure A.38 Dune erosion calculation with Option wl2b for JARKUS transect 6625 with
hydraulic conditions with a frequency of exceedance of 1/10,000 per year Figure A.39 Dune erosion calculation with Option wl1a for JARKUS transect 6625 with
hydraulic conditions with a frequency of exceedance of 1/10,000 per year Figure A.40 Dune erosion calculation with ‘beheerdersoordeel’ for JARKUS transect
6625 with hydraulic conditions with a frequency of exceedance of 1/10,000 per year
Figure A.41 Dune erosion calculation with Option wl1a for JARKUS transect 11825 with hydraulic conditions with a frequency of exceedance of 1/10,000 per year
Figures to be found in Appendix D:
Figure D.1 Erosion profiles beneath storm surge level translated to prototype with nl =
nd (WL | Delft Hydraulics, 1982d)
Figure D.2 Example of -2 m depth contour: horizontal distance depth contour as a function of the depth scale factor nd
Figure D.3 Derived prototype erosion profile underneath storm surge level (WL Delft Hydraulics, 1982d)
Figure D.4 Inclusion of data points from WL | Delft Hydraulics (2004), example -2 m contour
Figure D.5 Corrected (normalised) data points from WL | Delft Hydraulics (2004), example -2 m contour
Figure D.6 Derived prototype erosion profile underneath storm surge level for different wave periods
Figures to be found in Appendix E:
Figure E.1 Definition sketch
Figure E.2 Measured profiles after 6 hours, A-series Figure E.3 Measured profiles after 3 hours, B-series Figure E.4 Transition slope as function of Tp
Figures to be found in Appendix G:
Figure G.1 Comparison of various DUROSTA results on prototype scale for test T12 of research programme H4265 after 5 hours
Figure G.2 Development of measured and calculated (DUROSTA) prototype dune erosion volume in time (Test T04 of research programme M1819-1)
Figures to be found in Appendix H:
Figure H.1 Erosion volumes versus H2T and H2; Measurements
Figure H.2 Erosion volumes versus H2T and H2; Measurements and Option wl2a Figure H.3 Erosion volumes versus H2T and H2; Measurements and Option wl2b Figure H.4 Erosion volumes versus H2T and H2; Systematic computations reference
profile and Option wl2a
Figure H.5 Erosion volumes versus H2T and H2; Systematic computations reference profile and Option wl2b
List of Tables
Tables to be found in the text:
Table 2.1 Overview of research programmes ...8 Table 3.1 Summary of erosion volumes at prototype scale after 32.9 hours ...34 Table 4.1 Data selected for the analysis of the performance of prediction methods ...48 Table 4.2 Change in dune erosion volume relative to calculated volume for sop = 0.034 or Tp = 12 s...56 Table 4.3 Calculated dune erosion volumes for all prediction methods for different
dune heights (the relative change in dune erosion volume compared to the reference profile with a dune top at NAP + 15 m is indicated between brackets)...57 Table 4.4 Calculated dune face retreat for all prediction methods for different dune
heights (the relative change in retreat compared to the reference profile with a dune top at NAP + 15 m is indicated between brackets) ...57 Table 4.5 Relative change in calculated erosion volume (left) and dune face retreat
(right) for a change in wave period from Tp = 12 s to Tp = 18 s for different dune heights ...58 Table 5.1 Locations used in preliminary application (*This is the expected value of
the diameter based on the values in TAW, 1984) ...63 Table 5.2 Hydraulic conditions in preliminary application ...64
Tables to be found in Appendix B:
Table B.1 Overview of hydraulic conditions, sediment characteristics and scales of each test in the testbank (* PM = Pierson Moskowitz spectrum; J = Jonswap spectrum; TMA = TMA spectrum)
Table B.2 Overview of profile measurements in each test in the testbank (profile measurements not in testbank are indicated in bold characters)
Table B.3 Brier Skill Scores for dune erosion prediction methods and selected data
Tables to be found in Appendix E:
Table E.1 Locations of transition points for A-series Table E.2 Locations of transition points for B-series
Tables to be found in Appendix G:
Table G.1 Overview of DUROSTA calculations to investigate effects of scaling procedure
Tables to be found in Appendix H:
Table H.1 Conditions applied to investigate relationship between dune erosion volume and wave energy flux for Options wl2a and wl2b
List of Symbols
Symbol Unit Meaning
A m3/m1 Dune erosion volume per meter dune length above storm surge level
D m Grain size diameter
D10 m Grain size diameter such that 10 % of the grains by mass are smaller than D = D10
D50 m Grain size diameter such that 50 % of the grains by mass are smaller than D = D50
D90 m Grain size diameter such that 90 % of the grains by mass are smaller than D = D90
g m/s2 Gravitational acceleration
h m Water depth (to mean surface level)
H m Wave height
Hs m Significant wave height
H0s m Significant wave height at deep water
Hm0 m Significant wave height based on wave spectrum
Hs m Significant wave height
L m Wavelength
L0 m Wavelength at deep water (= 1.56Tp2)
m - Slope angle (1:m)
nA - Erosion area (or volume per meter length) scale factor
nc - Sediment concentration scale factor
nd - Depth scale factor
nD - Grain size scale factor
nH - Wave height scale factor
nH/(T·w) - Scale factor for dimensionless fall velocity parameter H / (T·w)
nl - Horizontal length scale factor
nL - Wavelength scale factor
ns0 - Beach slope scale factor
nSf-1 - Steepness factor (= S1)
nt - Time scale factor
nT - Wave period scale factor
nw - Fall velocity scale factor
Pextra - Factor that determines extra amount of dune erosion
Q m Erosion point Q (intersection of erosion profile and storm surge
level)
Symbol Unit Meaning
S0 - Profile steepness factor applied in the model
S1 - Desired profile steepness factor (= nSf-1)
sop - Wave steepness at deep water
T s Wave period
Tp s Peak wave period, defined as the period in an arbitrary wave spectrum with a global maximum of the spectral density
w m/s Fall velocity of sediment with grain size D = D50, in stagnant water
x m Horizontal distance
y m Vertical distance
Summary
The dune erosion prediction method presently used to assess the safety level of dunes along the Dutch coast was developed for situations with wave periods up to Tp = 12 seconds, while 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 lead to more dune erosion. However, effects of the wave period are not quantified sufficiently yet.
To allow for the five yearly safety assessment of the Dutch primary water defences the current safety assessment method needs to be extended. With this new method it should be possible to calculate dune erosion under normative hydraulic conditions taking effects of the wave period into account. The present report describes the first phase of this development. The objective of this part of the study is to develop a deterministic dune erosion prediction method based on existing data and existing knowledge on effects of the wave period.
In the following phase of the dune erosion project large-scale physical model tests will be performed to validate the deterministic dune erosion prediction methods. Based on this validation one of the prediction methods is chosen for further development towards a probabilistic method to assess the safety of the Dutch dunes.
For this study data obtained from physical scale model tests is collected and stored in a so-called testbank. Because the small-scale tests carried out in 2003 in the Scheldt flume of WL | Delft Hydraulics are especially relevant for the present study, additional analyses on these tests have been performed.
The current deterministic dune erosion prediction method (TAW, 1984) consists of a set of equations that describes the dune erosion profile and that contains the effect of the significant wave height and the sediment fall velocity. The wave period is not an input parameter. To incorporate effects of the wave period in the current method, existing methods are analysed and a few new methods are developed with the current method as a starting point:
• Option wl1a, in which the formulations of the erosion profile in the current method remain unchanged and effects of the wave period on dune erosion are taken into account by means of a horizontal translation of the erosion profile based on an additional volume of dune erosion. This volume is expressed as a function of the wave period (or wave steepness).
• Option wl2a, in which the formulation of the under water erosion profile is changed taking effects of the wave period into account. This was done by using profile measurements in small-scale dune erosion tests.
• Option wl2b, in which the formulation of the under water erosion profile is also changed by taking effects of the wave period into account. This was done by adding the wave period to the existing formulation of the erosion profile in a rather straightforward way, similar to effects of the wave height and the sand diameter.
A method, in which (also) the vertical level of the dune foot depends on the wave period, could not fully be developed, because the available small-scale data did not clearly show such a dependency. If this dependency is reflected in the results of the large-scale tests that will be performed in the following phase of the dune erosion project, this method might be worked out further.
Other recently developed methods (Koster, 2004a) are taken into consideration in this study as well:
• Option kos1d, which can be seen as a predecessor of Option wl1a. There are some small differences in the derivation of the expression of the volume as a function of the wave steepness in Options wl1a and kos1d, but the main difference is that Option wl1a also takes new data obtained from small-scale tests into account.
• Option kos3, in which the formulations of the erosion profile in the current method remain unchanged and effects of a larger wave period are compensated for by a smaller sediment fall velocity.
All methods have the current method as a starting point and are derived more or less empirically. Therefore, they should be considered as an extension of the present set of equations; no entirely new concepts are developed. The new formulations are derived on the basis of a limited amount of data on the effect of the wave period, mainly obtained from small-scale model tests. The formulations should be calibrated by including the results of the large-scale dune erosion tests to be carried out in the following phase of this dune erosion project.
With the use of the collected data the performance of the new deterministic dune erosion prediction methods is assessed. In summary, Options wl1a, wl2a and wl2b seem to perform slightly better than Option kos3 and Option kos1d, but the differences are small. Furthermore, the amount of data on which the methods are based is limited, as is the reliability of the data, because it concerns data obtained from (a small number) of small-scale tests. Therefore, it is not yet possible to select certain methods (and to reject others) for the use in the next phases of this dune erosion project and it is chosen to use all methods mentioned above. The newly developed methods have the same range of validity as the current method, but a wider range for the wave period. Because of the limited amount of data for smaller wave periods, it is recommended to use the newly developed methods only for wave periods of 12 s < Tp < 18 s, and to use the current method for wave periods smaller than Tp = 12 s.
To identify and gain insight into possible effects of new deterministic dune erosion prediction methods for the Dutch coast, a preliminary application is performed using the software instrument UCIT. Ten locations were selected with a wide variety of cross-shore dune shapes and several deterministic hydraulic conditions. The preliminary application of the new deterministic dune erosion prediction methods with UCIT reveals that these methods can successfully be applied to a wide variety of dune configurations for several hydraulic conditions. Therefore, the new methods are assumed to be at least as robust in
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 (for the period from 2001 to 2006) use is made of the Guide on Dune Erosion for the safety assessment of dunes as water defences (in Dutch: ‘Leidraad Duinafslag’ by the Technical Advisory committee of Water defences, TAW, 1984).
In the Guide on Dune Erosion, the under water dune erosion profile under normative hydraulic conditions is calculated with a parabolic profile. The significant wave height at a 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 also on other variables such as the wave period. The wave period is only used to determine the height of the necessary minimal dune profile (in Dutch: ‘Grensprofiel’), but 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 variations 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 Tp = 12 seconds as applied in the present method to calculate dune erosion (see also Alkyon, 2002, Rijkswaterstaat, 1996 & 2002, TAW, 2002b, and WL | Delft Hydraulics, 2003). Because the wave load on the coast increases with increasing wave period, it is expected that the volume of dune erosion will increase as well. To what extent the dune erosion volume may increase is not clear yet; this needs 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 defences. 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
To allow for the five yearly safety assessment of the Dutch primary water defences the ‘Directoraat-Generaal Water’ of the Ministry ‘Verkeer en Waterstaat’ has commissioned the ‘Directoraat-Generaal Rijkswaterstaat’ to develop a new dune safety assessment method for
the VTV of the year 2006. With this new method it should be possible to calculate dune erosion under normative hydraulic conditions taking effects of the wave period into account. 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’).
The ‘Directoraat-Generaal Rijkswaterstaat’, RIKZ, accepted (ref: RIKZ/2005/05707, dated July 7th, 2005) WL | Delft Hydraulics’ proposal (ref: MCI-10835/H4357/MvG, dated May 20th, 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 Guide 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; WL | Delft Hydraulics, 2004). 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. This project is focussed on achieving this by extending 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, thus no information on storm duration nor other types of information.
• The available time to obtain a new assessment method for dunes is very 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 improvement of the current method rather than proposing an entirely new method. For the latter approach more time is needed.
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 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 guide (for VTV2006).
• Product 5: Evaluation of the method.
In Product 2 the deterministic dune erosion prediction methods developed for Product 1 will be validated. Besides the 3 conditions that will be tested in Product 2, additional tests are foreseen to be carried out to study processes that are expected to be relevant for the development of the VTV2011.
The present report describes the study for Product 1. 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 Hydraulics Research & Consultancy, 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 Hydraulics Research & Consultancy Dr H.J. Steetzel participates in the project. Project coordinator on behalf of the client is Dr M. Boers of Rijkswaterstaat, RIKZ.
Prof. dr M.J.F. Stive leads a committee to assist the client in the quality control of the products of this project.
The project team for Product 1, as described in this report, consisted of Dr M.R.A. van Gent, E.M. Coeveld, J.H. de Vroeg, D.J. Walstra, Dr M. van Koningsveld (all WL | Delft Hydraulics), Dr J. van de Graaff and Dr H.J. Steetzel. Prof. dr L.C. van Rijn performed the internal quality control.
1.2 Objective of this study
The objective of the study for Product 1 is to develop deterministic dune erosion prediction methods based on existing data and existing knowledge on effects of the wave period, within the limitations described in the previous section.
1.3 Approach of this study
The activities for the study for Product 1 are divided into the following groups of activities: • Data collection
• Data obtained from physical scale model tests is collected and stored in a so-called testbank. Because the small-scale tests carried out in the Scheldt flume (WL | Delft Hydraulics, 2004) are especially relevant for the present study, additional analyses on these tests have been performed.
• Inventory and development of deterministic dune erosion prediction methods
• To incorporate effects of the wave period in existing dune erosion prediction methods, existing methods are analysed and a few new methods are developed. • Evaluation of deterministic dune erosion prediction methods
• To evaluate the various prediction methods, a procedure to quantify the performance of each dune erosion method is developed. Based on the evaluation of the various dune erosion prediction methods, a few methods are selected that will be validated with the results of the large-scale model tests of Product 2.
• Preliminary application
• To gain insight into the robustness and possible implications of the developed dune erosion prediction methods, in this early stage of the project the methods are already applied at a number of locations along the Dutch coast.
1.4 Reader’s guide
In Chapter 2 the data collected from physical model tests is described. Chapter 3 describes the inventory and development of deterministic dune erosion prediction methods. In Chapter 4 the selection of the dune erosion prediction methods is described. In Chapter 5 a preliminary application of selected dune erosion prediction methods is described for a number of locations along the Dutch coast. Chapter 6 summarises the main conclusions. The following definitions have been used in this report:
• The reference profile is a characteristic profile for the Dutch coast and has a dune top located at NAP +15 m. The slope of the dune face is 1:3 and ends at NAP +3 m. From thereon the slope is 1:20 to a level of NAP. From NAP to NAP -3 m the slope is 1:70. From that point on seaward the slope is 1:180, see Figure 1.1.
• The dune top is the highest point of the dune, see Figure 1.1. The dune face is the steep part seaward of the dune top. The dune foot is the lower end of the dune face.
−200 0 200 400 600 800 1000 1200 1400 −10 −5 0 5 10 15 Cross−shore distance (m) Level (m) w.r.t. NAP 1:180 1:70 1:20 1:3 dune top dune face dune foot Reference profile Water level
Figure 1.1 Reference profile
The reader should note that the methods presented in this report are purely deterministic and concern preliminary applications of methods that are still part of on-going research. The results of any calculation with any of these methods cannot be related to the safety of the Dutch dunes at any location along the coast.
2
Data from physical model tests
2.1 Introduction
In studies on dune erosion use is often made of physical scale model tests. This kind of research allows for a systematic investigation of various parameters and processes that are considered to be important for dune erosion. Because data from field measurements of dune erosion are scarce, especially during storm surges, and because the measurements often do not cover all relevant parameters, field data alone are not suitable for model development. Nevertheless, apart from data obtained from physical mode tests, field measurements (with relatively low water levels) were also used in the research of WL | Delft Hydraulics (1982d) to derive scale relations and to check the dune erosion prediction method presently used in the safety assessment of the Dutch dunes. It was concluded that both the dune erosion volume and the erosion profile measured in the field were reproduced well with the prediction method. No new reliable data from field measurements relevant for the verification of the current dune erosion prediction method could be obtained for this study. Therefore data is collected only from existing physical model tests from various sources, see for a brief overview Section 2.2. If data from field measurements become available, it is recommended to analyse these data with the purpose of verification of the current dune erosion prediction method or of newly developed models. It may also be an option to prepare a detailed field test at the Dutch coast for that purpose.
Section 2.3 provides a comprehensive overview of the scale relations applied in the present research to translate the results from physical scale model tests to prototype values.
In Section 2.4 the tests are described. A distinction is made between large-scale model tests (scale factor < ~10) and small-scale model tests (scale factor > ~10). In general, the series of small-scale tests are more extensive. The large-scale tests are generally considered to be much more reliable due to expected scale effects. The scale of the tests performed in The Netherlands is based on characteristic conditions along the Dutch coast and the size of available research facilities.
The data set is made homogeneous by collecting comparable information and storing the data in a data bank for model validation (from hereon referred to as testbank) that can be used for further research on dune erosion, see Section 2.5.
2.2 Data collection
Data is obtained from various research programmes carried out in various countries. The majority of the collected tests originates from research programmes in The Netherlands.
Research programme Number of tests in testbank
Reference
M1263-3 5 WL | Delft Hydraulics (1984)
M1797 2 WL | Delft Hydraulics (1982b)
M1811 1 WL | Delft Hydraulics (1982a)
H0298 5 WL | Delft Hydraulics (1987)
GWK86 6 Dette and Ulicka (1986)
LIP 11D 1 WL | Delft Hydraulics (1995)
Larg
e-scal
e
GWK98 5 Dette et al. (1998a & 1998b)
M1263-2 12 WL | Delft Hydraulics (1981) M1819-1 23 WL | Delft Hydraulics (1982c) M1819-3 1 WL | Delft Hydraulics (1983) Smal l-scal e H4265 7 WL | Delft Hydraulics (2004)
Table 2.1 Overview of research programmes
Table 2.1 shows an overview of the tests used in this research. The official names of the research programmes may deviate from the names used in this table. From hereon the names in Table 2.1 will be used throughout this report. The tests will be described more into detail in the following section.
2.3 Scale relations
Understanding the methods to translate results obtained from physical scale model tests to prototype values plays a key role in the interpretation of the results from the model tests. Theoretical elaborations alone are insufficient to come up with a consistent set of scale relations, because the applied theories have a limited validity (e.g. linear wave theory is less reliable within the surf zone and important physical processes in dune erosion are not fully understood). Van de Graaff (1977) and Vellinga (1986) performed an extensive series of model tests to verify and extend the scale relations. This work resulted in a more robust set of scale relations for dune erosion conditions. In WL | Delft Hydraulics (1996) an extension of the work of Vellinga (1986) is described by focussing on the steepness of the profile for different scales. This section is mainly based on Vellinga (1986) and WL | Delft Hydraulics (1996) and is aimed at providing a comprehensive overview of the scale relations applied in the present research.
2.3.1 Theoretical derivations of scale relations Hydraulic conditions
Water motion due to waves is primarily determined by gravitational and inertial forces. These forces should be preserved in the model to maintain a dynamic similarity, the resulting scale relation is (also known as the scaling law of Froude):
( )
0.5 H d l T d n n n n n = = = 2.1where nT is the scale factor of the wave period (i.e. hydraulic scale factor), nH is the scale factor of the wave height, nd is the depth scale factor, and nl is the length scale factor.
Grain size
Assuming that the hydraulic conditions are scaled correctly, the entrainment and settling velocity of the sediment also requires scaling so that the relevant forces on the sediment particles are realistic. A number of dimensionless parameters can be used for this (Reynolds number, deterministic Froude number and the dimensionless fall velocity parameter). In Vellinga (1986) these dimensionless parameters did not result in a consistent scale relation for the sediment. For the power β in Equation 2.2 Vellinga (1986) derived values in the range of -0.5 < β < 1 depending on the applied dimensionless parameter.
( )
D d
n = n β 2.2
where nD is the scale factor of the sediment diameter.
Equation 2.2 determines the geometrical scale effects (i.e. steepness of equilibrium profiles). In WL | Delft Hydraulics (1996) a scale factor is derived for the beach slope, ns0:
0 D D s d n n n γ = 2.3
where γD is a constant which is in the range of 0.25 < γD < 0.28. The constant has been determined by analysing the results of computations with numerical models and has not (yet) been verified with data from physical model tests.
Because nD is usually smaller than nd, the resulting equilibrium profiles are steeper in model tests compared to prototype conditions. Another, more common way to identify geometrical scale effects is discussed below.
Equilibrium profiles
Providing that longshore effects can be ignored, the shape of the equilibrium profile (i.e. the profile after a storm event) is a function of the wave conditions and the sediment characteristics and not the initial profile (according to Vellinga, 1986). This implies that an accurate representation of the profile shape requires a relation between wave conditions, sediment characteristics and the shape of the equilibrium profile. Based on (more or less) theoretical and empirical considerations it was found that the beach slope is related to the dimensionless fall velocity parameter H/(T·w) (Wiegel, 1964; Dalrymple and Thompson, 1976; Gourlay, 1980).
Based on this parameter, it can be concluded that beach profiles in reality (undistorted: nl =
nd) are reproduced in a small-scale model with undistorted beach profiles if: 1 H T w n ⋅ = 2.4
where nH/(T·w) is the scale factor for the dimensionless fall velocity parameter. If nH/(T·w) >1 a distorted profile (nl ≠ nd) should be applied in the model so that the profile agrees with the hydraulic and sedimentologic conditions.
Sediment transport
A fundamental (and very complex) way to derive a scale relation is to analyse the sediment transport process. Vellinga (1986) gives a derivation of this scale relation by using an idealized cross-shore sediment transport model and finds the following scale relations for the model distortion and the sediment concentration:
0.25 0.5 1 2 l T d Sf d w w n n n n n n n − = = = 2.5 0.25 2 d c w n n n = 2.6
where nSf-1 is the steepness factor (a measure for the model distortion), nc is the scale factor of the sediment concentration, and nw is the scale factor of the sediment fall velocity.
Equations 2.5 and 2.6 show that the scale factor for the sediment concentration is equal to the model distortion. For undistorted (nl = nd) models the scale factor of the dimensionless fall velocity parameter nH/(T·w) equals 1. Combined with Equation 2.1:
1 d H H n n n n n n n = ⋅ = ⋅ = 2.7
However, it is reported in WL | Delft Hydraulics (1996), based on numerical simulations (WL | Delft Hydraulics, 1994), that the scale factor of the sediment concentration is:
( )
c d
n = n γ 2.8
where γ was estimated to be in the range of 0.7 < γ < 0.8 based on an analysis of an analytical transport formulation.
In WL | Delft Hydraulics (1994) also a morphological time scale factor, nt, is derived: T t c n n n = 2.9
Application of Equations 2.8 and 2.9 implies that the hydraulic time scale factor, nT, is larger than the morphological time scale factor, nt.
Assuming γ = 0.75 Equation 2.9 predicts significant differences between the hydraulic and morphological time scale factors (e.g. nd = 40 results in nt = 0.4 and nT = 6.3 or
nd = 5 results in nt = 0.7 and nT = 2.2). Using the scaling law of Froude according to Equation 2.1 to compare small-scale tests with large-scale tests, Equations 2.8 and 2.9 should result in a significant different temporal development of the erosion rates. This is not confirmed by the available experimental data and is (very) different from Vellinga (1986) where it is assumed that both time scales are identical. In the present study it is therefore assumed that the hydraulic and morphological time scale factors are identical.
2.3.2 Derivation of scale relations based on measurements
The theoretical analyses described in Vellinga (1986) provided a basic form of the scale relations: 1 2 l d Sf c d w t d n n n n n n n n α β − = = = = 2.10
Furthermore, the dimensionless fall velocity parameter:
H
Tw 2.11
appeared to be important to reproduce equal beach slopes (if the scale factor nH/(T·w) equals 1, undistorted beach profiles are reproduced in a small-scale model with undistorted profiles). In Vellinga (1986) the unknown parameters α and β were determined by using experimental data from a large series of small-scale tests. Furthermore, the dimensionless fall velocity parameter was verified.
Verification of the parameter H/(T·w)
Vellinga (1986) verified whether the shape of the under water profile is a function of the parameter H/(T·w). The verification was based on a comparison of the horizontal distance between the intersection of the erosion profile with the still water line and the depth contours 1 m, 2 m and 3 m as a function of the parameter H/(T·w) for 24 small-scale tests which had been scaled up to prototype (see for example Figure 46 in Vellinga (1986)). Although some scatter was observed, the overall conclusion was that for all considered depth contours there was a clear trend (with a correlation coefficient exceeding 0.9 for least square fits). Based on Figure 3.6 it can also be concluded that a change in the parameter
H/(T·w) leads to different shapes of the under water profile: a longer wave period (or a
smaller parameter H/(T·w)) leads to gentler slopes. Derivation of α and β constants
The distortion relation Equation 2.10 was verified and a value for α was derived using a similar approach as for the parameter H/(T·w). By using the prototype values (assuming
nd = nl), the profile steepness can be expressed in terms of the distance between the intersection of the still water line with the erosion profile and a depth contour. Fitting a function of the form shown in Equation 2.12 resulted in values for α in the range of 0.28 < α < 0.34:
1 d
l l n= −α 2.12
where l is the measured horizontal distance from the intersection of the still water line with the erosion profile to a depth contour for the model results scaled to prototype and l1 is a constant in the fitting function.
The value of β was derived by evaluating the erosion quantities as a function of the steepness of the initial profile for different moments in time. In case of a perfect scale relation all erosion quantities should lie on a single line (for all considered moments in time). The correlation coefficient for least square fits can be interpreted as an inverse measure of the scatter. For the small-scale experiments Vellinga (1986) found that least scatter was present for a value for α in the range of 0.20 < α < 0.28 and for β in the range of 0.0 < β < 0.5.
The method for determining α using Equation 2.12 can also be used to determine the value for β. Instead of using the profile steepness, the erosion rates (i.e. temporal development of erosion quantity) can be used to fit an equation of similar form:
1 d
t t n= −β 2.13
was decided to use this value also, because it is the same value as for the hydraulic time scale.
The presented derivations were initially based on small-scale tests. Verification with large-scale tests showed that there was a small time-dependency for the optimal values for α and
β. The dimensionless fall velocity parameter was verified by comparing erosion profiles in
large-scale and small-scale tests with approximately similar values for this parameter. Vellinga (1986) concluded on a visual comparison that similar values for the parameter
H/(T·w) resulted in a similar profile development.
In WL | Delft Hydraulics (1996) a re-analysis is carried out of the results of the tests used in Vellinga (1986). The conclusion is that the small-scale tests result in an under prediction of the erosion volumes compared to large-scale tests. Furthermore, the profile steepness at the waterline is steeper for small-scale tests, even if the parameter H/(T·w) was (approximately) the same. These aspects were confirmed by simulations with the numerical model DUROSTA (see Section 3.4.4 for a brief description of this model).
2.3.3 Applied scale relations
An important finding of Steetzel (1993) and WL | Delft Hydraulics (1994 and 1996) was that the experimental set-up of the large-scale tests (WL | Delft Hydraulics, 1984) as used by Vellinga (1986) overestimated the erosion volumes by about 30% due to the distorted profiles and an overestimation of the deepwater wave conditions. However, these findings are primarily based on simulations with DUROSTA and have to be treated with care. Hopefully this issue can (partly) be resolved by analysing the new large-scale tests that will be performed in the following phase of the dune erosion project in conjunction with recent small-scale tests (WL | Delft Hydraulics, 2004), since similar deepwater wave conditions are applied. If similar deepwater conditions are applied the main source of error in comparing small- and large-scale tests is due to different model distortions, which is expected to have only a limited effect: WL | Delft Hydraulics (1996) reports that a model distortion of 2 gives an additional volume of erosion of 5% to 10%.
Although the findings in WL | Delft Hydraulics (1996) suggest that the scale relations derived in Vellinga (1986) could be improved, no reliable updates of the scale relations can be made without additional experimental data. The findings of Vellinga (1986) are firmly based on a detailed analysis of applicable theories and a large number of data sets. Some of the conclusions in WL | Delft Hydraulics (1996) are related to a more detailed analysis of the erosion profiles, but could also be interpreted as scatter in the measurements used by Vellinga (1986). Based on the findings summarised in WL | Delft Hydraulics (1996) and scatter of the measurements analysed by Vellinga (1986), a preliminary conclusion is that the errors associated with the scaling to prototype are in the range of 5 % to 10 % for large-scale tests and 10 % to 20 % for small-large-scale tests. However, systematic errors (trend interruptions) might still exist in the extrapolation from model to prototype values. This can only be verified with reliable field data.
At this stage of the research it is decided to apply the scale relations described by Vellinga (1986) as summarised below:
0.28 1 2 0.5 l d Sf c d w t d n n n n n n n n − = = = = 2.14
Furthermore, the dimensionless fall velocity parameter (Equation 2.11) is assumed to govern the compatibility of the erosion profiles at different model scales. Assuming nw = 1 Equation 2.14 reduces to:
0.28 Sf d
n =n− 2.15
which implies that steeper equilibrium profiles will develop for small-scale tests compared to large-scale tests.
The erosion area (or erosion volume per meter dune) scale factor is: 0.28 2 2 d A l d d w n n n n n n = ⋅ = ⋅ 2.16
Often the desired steepness factor S1 (= nSf-1) deviates from the steepness factor S0 that was applied to the initial profile in the model. For example because application of the desired steepness factor S1 to the initial profile in the model led to a profile that was too long to fit in the flume. Thus, by multiplying the measured dune erosion area with nA (Equation 2.16) the prototype volume is obtained which applies for a prototype initial profile that is a factor S steeper than the reference profile:
0 1 S S S = 2.17
For example a large-scale test in the Delta flume of WL | Delft Hydraulics with a depth scale factor of nd = 5 and a fall velocity scale factor of nw = 1 has a desired profile steepness factor of S1 = 1.57. This means that the slopes in the profile of the dune in the model are a factor 1.57 steeper than the slopes in the reference profile: a prototype slope of 1:180 becomes a slope of 1:115 in the model. A profile with these slopes is still too long to fit in the Delta flume. Therefore, a steepness factor of S0 = 2 is applied: a prototype slope of 1:180 becomes a slope of 1:90 in the model. The profile applied in the model corresponds to a prototype profile that is a factor S = 1.27 steeper than the reference profile (see Section 1.4).
In summary, to translate model to prototype values use is made of Equations 2.1 and 2.14. The fall velocity scale factor in Equation 2.14 is obtained by dividing the prototype value of the fall velocity by the model value. For the prototype fall velocity a value of w = 0.0268 m/s is chosen, which was also used in earlier analyses (e.g. WL | Delft Hydraulics, 1984) and corresponds with a grain diameter of D50 = 225 µm which is considered characteristic
wave height are also obtained by multiplying the model values with the depth scale factor
nd. Prototype values for the wave period and the time at which profile measurements were carried out are obtained by multiplying the model values with the square root of the depth scale factor nd.
2.4 Description of tests
In this section a brief description is given of the physical model tests used in this research. For a more detailed description reference is made to the reports listed in Table 2.1. An overview of the hydraulic conditions, the sediment characteristics and scales used in each test in the testbank can be found in Table B.1 in Appendix B. Table B.2 shows at what time profile measurements were carried out in each test.
In the descriptions of the tests in the following subsections the scale factors and steepness factors explained in Section 2.3.3 are mentioned.
2.4.1 Large-scale tests M1263-3
The purpose of research programme M1263-3 was to verify the scale relations and the reliability of the deterministic dune erosion method according to Vellinga (1986). In total 5 tests were performed in the Delta flume of WL | Delft Hydraulics in the period of November 1980 till May 1981.
Test 1 and Test 2 were performed at a depth scale of nd = 5 and with a constant water level. In Test 1 the Dutch reference profile (see Figure 1.1) was used as initial profile with a steepness factor of S0 = 3, while in Test 2 a steepness factor of S0 = 2 was applied. Test 3 was performed at the same depth scale as Test 2 and with the same initial profile, but with a varying water level. In Test 4 the storm surge of 1953 in The Netherlands was reproduced at a depth scale of nd = 3.27. Test 5 can be considered as a full scale replica (nd = 1) of a moderate storm in nature; the reference profile was used with a steepness factor of S0 = 2.47.
0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 Time (h) Hs (m) or Tp (s) or h (m) M1263−3−Test−3 Wave height (Hs) Wave period (Tp) Water depth (h)
Figure 2.1 Hydraulic conditions of Test 3 of research programme M1263-3
At the time these tests were performed the wave board in the Delta flume was not yet equipped with active reflection compensation (ARC), nor with second-order wave steering. Whether the waves reflected from the dune were filtered out of the measured wave signal to determine the incoming wave signal is not described in the test report. Waves were measured at several locations in the flume, but not close to the wave board. According to Steetzel (1993) the wave heights near the wave board were Hs = 1.72 m and Hs = 1.70 m for Test 1 and Test 2 respectively. In Test 5 a wave height of Hs = 2 m was measured at a certain location in the flume which corresponded with a wave height of Hs = 2.86 m near the wave board according to Steetzel (1993). Although the latter wave height could not have been generated by the wave board, it is still chosen to incorporate that wave height in the testbank. Figure 2.1 shows the varying hydraulic conditions of Test 3 and Figure 2.2 those of Test 4.
0 2 4 6 8 10 12 14 16 0 1 2 3 4 5 6 Time (h) Hs (m) or Tp (s) or h (m) M1263−3−Test−4 Wave height (Hs) Wave period (Tp) Water depth (h)
Figure 2.2 Hydraulic conditions of Test 4 of research programme M1263-3
In all 5 tests sand was used with a diameter of D50 = 225 µm. The fall velocity was estimated at 0.0268 m/s. This diameter is considered to be a representative diameter for the Dutch coast.
The plots of the profile measurements of Test 1 and Test 2 in WL | Delft Hydraulics (1984) were digitised for this research. Only the measurements after 0 and 10 hours were digitally available. The digitising process may have led to some small differences in erosion profiles and erosion volumes between those in WL | Delft Hydraulics (1984) and in this report.
M1797
The main purpose of research programme M1797 was to determine the impact of an existing dune revetment at a coastal section of the Noorderstrand at Schouwen (The Netherlands) on the dune erosion volume during a specific design storm surge. In June 1981 2 tests were performed in the Delta flume: one without (Test 1) and one with revetment (Test 2).
The only difference between Test 1 and Test 2 is the presence of the revetment. The tests were performed at a depth scale of nd = 2 and with a steepness factor of S0 = 1.24.
At the time these tests were performed the capabilities of the Delta flume were the same as in the research programme M1263-3 described above. Figure 2.3 shows the varying hydraulic conditions of the tests.
0 5 10 15 0 1 2 3 4 5 6 Time (h) Hs (m) or Tp (s) or h (m) M1797−Test−1 Wave height (Hs) Wave period (Tp) Water depth (h)
Figure 2.3 Hydraulic conditions of the tests of research programme M1797
The grain diameter of the sand used in these tests was D50 = 225 µm. A fall velocity is not specified in WL | Delft Hydraulics (1982b). Given the execution dates of research programme M1797 and of programme M1263-3, the fall velocity is assumed to be the same as in the latter research.
M1811
The purpose of research programme M1811 was to gain insight into the effect of the presence of certain concrete structures on the dune erosion processes. Two concrete box-shaped structures were placed next to the wall of the flume in the dune top. The presence of these structures probably affects the dune erosion process and should be taken into account in the analysis of the results. One test was performed in the Delta flume in July 1981. At the time this test was performed the capabilities of the Delta flume were the same as in the research programme M1263-3. Figure 2.4 shows the varying hydraulic conditions of Test 1.
The grain diameter of the sand used in these tests was D50 = 225 µm. The fall velocity was estimated at 0.0267 m/s.
0 1 2 3 4 5 6 7 8 9 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (h) Hs (m) or h (m) M1811−Test−1 Wave height (H s) Water depth (h)
Figure 2.4 Hydraulic conditions of Test 1 of research programme M1811
H0298
The purpose of research programme H0298 was to gain insight into the relative effect of dune revetments on the development of the cross-shore profile. In the first 4 tests several configurations of dune revetments were applied and in the 5th test the same dune profile without revetment. The tests were carried out in the Delta flume in the period of October 1986 till December 1986.
All tests were performed at a depth scale of nd = 5, a steepness factor of S0 = 2 and with the reference profile as initial profile. The resulting initial profile corresponds to the profile used in Test 2 of research programme M1263-3.
The wave board in the Delta flume was equipped with active reflection compensation (ARC) at the time these tests were performed. However, it is not clear whether this system was actually activated in these tests or not. There was no second order wave steering at that time.
GWK86
In the wave flume in Hanover (Grosse Wellen Kanal) 6 large-scale tests were performed in 1986 to investigate wave induced currents and sediment concentration in suspension across the surf zone.
These tests were not carried out with an initial profile similar to the Dutch reference profile, nor with hydraulic conditions characteristic for the Dutch coast. Scale factors or steepness factors can therefore not be determined in a similar way as in the research programmes in The Netherlands in the 1980’s. The initial profile in the model had a foreshore slope of
about 1:20 and the dune face had a slope of about 1:4. All 6 tests are incorporated in the testbank, although Test 2, 4 and 5 only show a very small volume of dune erosion.
The wave board of the flume was equipped with active reflection compensation (ARC), but had no second-order wave steering system. The exact location of wave measurements is not described in Dette and Ulicka (1986). It is assumed to be at a location where the bed level is still horizontal.
LIP 11D
The purpose of research programme LIP 11D was the generation of high quality and high resolution data on hydrodynamics and sediment transport dynamics on a natural 2DV beach under equilibrium, erosive and accretive conditions. In total 7 tests were performed in the Delta flume in the period of April 1993 till June 1993.
Two sets of tests were performed with different initial profiles. Because no dune was applied in the initial profile the first set of tests is not used in this study. In the second set of tests a dune was present in the initial profile. Test 2e is incorporated in the testbank, because the profiles and hydraulic conditions in this test correspond rather well to the Dutch situation. Since there is no direct agreement with the reference profile, scale factors or steepness factors cannot be determined in a similar way as in the research programmes in the 1980’s. The wave board in the Delta flume was equipped with active reflection compensation (ARC) at the time these tests were performed. Whether second order wave steering was used in these tests is not clearly described, but it is assumed that no second order wave steering was applied. Whether the waves reflected from the dune were filtered out from the measured wave signal to determine the incoming wave signal, is not clear. Waves were measured at a location 20 m from the wave board where the bed level was still horizontal.
The characteristics of the sediment used in this test are not extensively described in WL | Delft Hydraulics (1995). The sand had a diameter of D50 = 220 µm.
GWK98
The purpose of research programme GWK98 was to improve the methods of design and performance assessment of beach nourishments. In total 24 tests were performed in the wave flume in Hannover (Grosse Wellen Kanal) in the period of November 1996 till August 1997.
These tests were not carried out with an initial profile similar to the Dutch reference profile, nor with hydraulic conditions characteristic for the Dutch coast. Scale factors or steepness factors can therefore not be determined in a similar way as in the research programmes in The Netherlands in the 1980’s. In total 8 series of tests were performed with different initial profiles with and without supporting structures. In total 5 tests without structures are incorporated in the testbank, which have a dune-type cross-shore profile and hydraulic
It is not clear whether the wave board was equipped with ARC. The flume has no second order wave steering system.
In the tests sand was used with a diameter of D50 = 300 µm. The fall velocity was estimated at 0.042 m/s.
2.4.2 Small-scale tests M1263-2
The purpose of research programme M1263-2 was to gain insight into dune erosion processes during storm surges and to gather data to improve the computational methods of that time. In total 28 tests were performed in the Wind flume of WL | Delft Hydraulics in the period of September 1976 till March 1977.
The tests were performed at depth scales of nd = 26, nd = 47 and nd = 84 with the Dutch reference profile as initial profile with different steepness factors. Of this test programme the tests with a depth scale of nd = 26 are incorporated in the testbank and the tests in which sand was used with a diameter of D50 = 225 µm. The sediment characteristics varied in the tests, see Table B.1.
At the time these tests were performed the wave board in the Wind flume was not equipped with active reflection compensation (ARC), nor with second order wave steering.
The plots of the profile measurements after 0, 1 and 6 hours of the tests described in WL | Delft Hydraulics (1981) were digitised for this research. This was done based on the figures describing profile changes near the dune. The remaining part of the profile is schematised and is equal for all profile measurements. The digitising may have caused small differences in the erosion profiles and erosion volumes between those in WL | Delft Hydraulics (1981) and in this report.
M1819-1
The purpose of research programme M1819-1 was to determine the relative impact of all relevant parameters in the dune erosion process on the volume of dune erosion. In total 29 tests were performed in the Scheldt flume of WL | Delft Hydraulics in the period of August 1981 till January 1982.
All tests were performed at a depth scale of nd = 30. In Tests T01 to T14 and Test T29 a constant water level was applied. In these tests the Dutch reference profile was used as initial profile with a steepness factor of S0 = 1.68, except for Test T11 and Test T12 in which the dune height was different. In Tests T15 to T20 the reproducibility of the test results is checked by repeating Test T04 with slightly different model executions. These 6 tests are not used in this research. In Tests T21 to T28 the same varying hydraulic conditions were used, see Figure 2.5, and different initial profiles to check the influence of the shape of the initial profile on the volume of dune erosion during a super storm surge.
0 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (h) Hs (m) or h (m) M1819−1−Test−T21 Wave height (H s) Water depth (h)
Figure 2.5 Hydraulic conditions of Test T21 (same as in Tests T22 to T28)
At the time these tests were performed the wave board in the Scheldt flume was not yet equipped with active reflection compensation (ARC), nor with second order wave steering. Waves were measured at several locations in the flume, but not very near to the wave board. Table B.1 shows the wave heights near the wave board according to Steetzel (1993). Test T14 is assumed to have the same hydraulic conditions near the wave board as Test T04. In all tests sand was used with a diameter of D50 = 90 µm. Because the water temperature varied significantly during the tests, the estimated fall velocity varied as well, see Table B.1. The figures of the profile measurements after 1 hour of Test 1 to Test 14 and Test 29 WL | Delft Hydraulics (1982c) were digitised for this research. This was done based on the figures with the profile changes near-dune. Therefore, the seaward part was missing and was filled in with the initial profile measurement. Only the measurements after 0 and 6 hours were digitally available. The digitising may have caused small differences in the erosion profiles and erosion volumes between those in WL | Delft Hydraulics (1982c) and in this report.
M1819-3
The purpose of research program M1819-3 was to investigate the effectiveness of dune revetments during super storm conditions. In total 4 tests were performed in the Scheldt flume in November 1981 of which the first test was without a revetment.
