SBW Wave overtopping and grass cover strength

SBW Wave overtopping and grass cover strength Model developement

Gosse Jan Steendam Gijs Hoffmans Jan Bakker Jentsje van der Meer Joep Frissel Maurice Paulissen Henk Verheij

1206016-007

© Deltares, 2012

Title

SBW Wave overtopping and grass cover strength Project

Client

Pages

Rijkswaterstaat Waterdienst 1206016-007

146

Trefwoorden

Wave overtopping, erosion, grass, sod, wave run-up golfoverslag, golfoploop, erosie, grasbekleding, grastrekproef, graskwaliteit Samenvatting

Referenties

-

Versie Datum

jun. 2012

Auteur

Gosse Jan Steendam Gijs Hoffmans Jan Bakker Jentsje van der Meer Joep Frissel Maurice Paulissen Henk Verheij

Paraaf Review

Mark Klein Breteler

Paraaf Goedkeuring

Paraaf

Leo Voogt

André van Hoven

State

draft This is a draft report, intended for discussion purposes only. No part of this report may be relied upon by either principals or third parties.

17 August 2012, draft

Inhoud 1 Introduction

1

2 Analyses of measured overtopping parameters 2.1 Theory on flow velocity and flow thickness 2.2 Analysis of measurements 2.2.1 Objective of the measurements 2.2.2 Test set-up at Tholen 2.2.3 Measurements and data processing 2.2.4 Analysis at the crest 2.2.5 Analysis at the landward slope 2.2.6 Analysis at the landward slope of the Vechtdike 2.3 Validation of theory 2.3.1 Tholen 2.3.2 Vechtdike 2.3.3 Comparison friction factor with roughness coefficients 2.3.4 Conclusions

3 3 5 5 7 9 14 17 23 28 28 29 31 32

3 Analysis of measured run-up parameters 3.1 Set up of the measurements 3.2 Analyses of run-up measurements 3.3 Analysis of run-down measurements

35 35 38 47

4 The cumulative overload method applied to wave run-up

49

5 Improvement of wave run-up simulation 5.1 Introduction 5.2 Small scale evaluation 5.3 The wave impact simulator used for run-up simulation

59 59 60 61

6 Testing the grass quality: comparing the current prescribed methodology with a new method 65 6.1 Measurements prescribed for the third assessment round currently in force 65 6.1.1 Shoot cover (grid method) 66 6.1.2 Root density 66 6.2 Method proposed for the prolonged 3rd assessment round 66 6.2.1 Sod cover 66 6.2.2 Root density (spade method) 67 6.3 Results of comparing the methods 67 6.3.1 Sod cover 67 6.3.2 Root density 68 6.4 Discussion 73 6.4.1 Current versus new methodology 73 6.4.2 Discrepancy between estimated sod strength and outcomes wave overtopping tests 74 6.4.3 Where to take samples, and how many? 75 6.4.4 Suggestions for improvement of the new method and its description 76 6.5 Conclusion and recommendations 76

SBW Wave overtopping and grass cover strength

i


7 Direct measurement of critical tensile stress in a grass cover layer 7.1 Description of the problem 7.2 The model set up 7.3 The tests

79 79 79 82

8 Erosion around objects and on transitions 8.1 Introduction 8.2 Theoretical approach 8.2.1 Erosion near trees 8.2.2 Erosion at a transition of a slope to a horizontal berm 8.3 Determining M from test results

85 85 85 85 91 92

9 Conclusions

97

10 References

101

Bijlage(n) A Theory of steady state flow on a slope by Schüttrumpf (2001)

A-1

B Measured flow velocities and thicknesses for individual overtopping wave volumes; wave overtopping at Tholen. B-1 C Measured flow velocities and thicknesses for individual wave run-up and run-down at Tholen. C-1 D Photo’s grass quality tests

ii

D-1



1 Introduction 1.1

Framework and research approach Wave overtopping and grass cover strength is part of the project SBW Wave overtopping and revetment strength (SBW: Strength of and loads on water defenses), or ‘SBW Golfoverslag en Sterkte Bekledingen’ in Dutch. The project is one part of the SBW research program to develop the safety assessment tools for primary water defenses in The Netherlands. The program is funded by the Dutch ministry of Environment and Infrastructure, delegated to Rijkswaterstaat Waterdienst (Dutch) and, again, delegated to Deltares, the independent research institute on delta technology. At the start of the SBW program in 2007 a project group was formed to tackle the research questions concerning the grass cover strength in case of wave overtopping. The project group is still active and contains Deltares, Van der Meer Consulting, Infram and Alterra. In the past five years, 2007-2012, research was carried out to determine the grass cover strength in case of wave overtopping. The research resulted in a Technical Report (ENW 2012). Tests were carried out with the wave overtopping simulator (WOS) on several Dutch and Belgium dikes in the winter season. A closed grass sod proved to be very resilient against the erosive forces of massive wave overtopping volumes. On the other hand rough herbal growth and open patches in the sod can make it vulnerable to erosion. The research in the 2007-2012 period was not conclusive on the effect of objects and transitions in the slope geometry and transitions from a grass cover to other (hard) revetment types. Also the wave run-up zone was not yet covered. The report at hand starts a next research period which will take until 2017 and where the aim will be to incorporate the aspects noted above. The research questions concerning grass erosion are approached in a cyclic way (Figure 1.1 www.thesis.nl/kolb). The current report ‘Model development’ aims to describe the state of the art models and ways to enhance insight in the process of erosion of grass around objects and transitions. The next step will be to use the models and methods to make a prediction and perform an experiment (wave overtopping test). Evaluation of the prediction and experiment results will lead to better models and methods.

Model development

Evaluation

Prediction

Experiment Figure 1.1 Cyclic research approach

In the period until 2017 two cycles are foreseen, followed by an update of the Technical Report.


1 van 146


Foreign readers are welcomed to use the research results generated within the SBW program. This is the main reason to report in English. Interaction and feedback on the use of the results are appreciated. It must be noted that the prediction models and experiences picked up by testing with the wave overtopping simulator are based on the Dutch and (some) Belgium circumstances, grasses and substrates. Grasses and substrate can be very similar in the wider region, however, they can also differ.

1.2

Readers guidance The report at hand contains the ‘model development’ step in the cyclic research approach. The following aspects about erosion of grass are covered by the report:: •

•

• •

•

•

•

•

Flow velocity development along a slope, depending on slope length and angle (chapter 2). The maximum depth averaged flow velocity during a wave overtopping event is the main loading parameter in the grass erosion model. The velocity depends on the geometric parameters and friction coefficient. Analyses of hydraulic parameters in wave run-up zone (chapter 3). Measurements were performed on a dike in Tholen, using the wave overtopping simulator placed on the outer slope, directed upward, thus generating wave run-up )and down). Preliminary model set up for the prediction of erosion in the wave run-up zone, based on the same principles as the model for wave overtopping (chapter 4). Improvement analyses and development of a wave run-up simulator, to validate the prediction model for wave run-up/down (chapter 5). The first wave run-up tests were performed with the wave overtopping simulator placed with the water release chute facing slope-upward. Improvement of the simulator set up is necessary to improve the simulation of the water movement on the slope. The new proposed method to determine the grass quality (ENW 2012) was performed together with the old method and compared (chapter 6). The proposed new method was developed at the end of the research period 2007-2012 and wave overtopping test sites in this period were not yet investigated with the new method. To prevent the development of the grass sod between testing and 2012 becoming a source of differences, the old method was used as well. The grass sod pull out strength was determined directly by a developed pull out test device and some first tests were performed (chapter 7). The strength parameter in the erosion model is a critical flow velocity. A good function between the critical velocity and grass parameters was not yet established. Determining the pull out strength directly from the field and connecting the load parameter (flow velocity) to pressure gradients over the grass sod can lead to a better understanding of the critical velocity and to a better model. This approach also opens the way to model the effect of transitions and objects in the grass cover. A theoretical and practical approach to the amplification factor on the load parameter in the erosion model were explored (chapter 8). The amplification factor multiplies the depth averaged maximum velocity during a wave overtopping event, in the case of an object in the grass cover, or a geometric transition from slope to horizontal. Each of the chapters ends with conclusions, they are summarized in chapter 9.

2 van 146



2 Analyses of measured overtopping parameters 2.1

Theory on flow velocity and flow thickness The main parameter to describe wave overtopping is the mean overtopping discharge, q. Other parameters are overtopping volume related, like the flow velocity, u, and flow thickness, h. Both change along the crest and landward side and are location related. Often the maximum value during an overtopping wave is taken. In previous research focus was often on the 2%-value of both velocity and flow thickness. The design of the wave overtopping simulator was mainly based on the then (2006) existing relationship between overtopping volumes and flow velocities at the beginning of the crest of a dike. For each released volume the overtopping simulator simulates an overtopping wave with a specific flow velocity and flow thickness. This overtopping wave floats over the remaining crest and then down the landward slope of the dike. It depends on the geometry of the crest and landward slope how much the flow decreases or increases. For a gentle slope and small overtopping wave the velocity may decrease significantly along the landward slope. The opposite may be true for a larger wave rushing down a steep slope. At a few locations hydraulic measurements have been performed where overtopping flow velocities and flow thicknesses were measured. Not a lot of these kind of measurements at full scale exist with real grass and an "uneven" slope. Most research has been performed on smooth straight slopes in small scale physical experiments. The forces and resistance on the flow over a dike crest and along the landward slope are mainly acceleration of gravity and the friction of the grass. It is this friction factor of the grass that is the big unknown for the intermittent overtopping by waves. The theory on flow velocity and flow thickness includes the friction factor along the slope. First the theory will be given in this section. Then the analysis of the measurements will be described and finally the validation of the theory with the measurements. The theory will be based on steady state considerations. Schüttrumpf (2001) describes the development of the theory of flow over a down slope in full depth. A copy of that part of the report is given in Appendix A. The final equations to describe the flow down the landward slope of a dike become:

k1h kt tanh 1 f 2 fu0 kt 1 tanh 1 hk1 2

u0 u

(1)

with

k1

2 fg sin h


(2)

3 van 146


u2 g 2 sin 2

u0 g sin

t

h

2s g sin

(3)

u0 h0 u

(4)

The terminal velocity can be described by:

2hB g sin f

uB

(5)

In Equation (5) the term

2g is equal to the Chezy coefficient. f

Equation (1) is an implicit expression, but is fully controlled by the initial conditions at the start of the down slope with u0 and h0 and by the "slope" conditions as slope angle and friction f and by the location on the slope s. Measurements at Tholen along the crest and landward slope give for the conditions at the crest the following ranges: u0 = 3-7 m/s and h0 = 0.05-0.4 m. The landward slope was about 1:2.4. Figure 2.1 and Figure 2.2 give predicted velocities and flow thicknesses along the landward slope, depending on the friction coefficient f, which was varied between f = 0.01 and f = 0.10. The input values were u0 = 3.5 m/s with h0 = 0.04 m; u0 = 5.5 m/s with h0 = 0.2 m; and u0 = 7.5 m/s with h0 = 0.4 m. 12

10

Flow velocity (m/s)

f=0.01 f=0.02

8

f=0.05 f=0.10

6

f=0.01 f=0.02 f=0.10

4

f=0.01 f=0.02

2

f=0.05 f=0.10

0 0

2

4

6

8

10

12

14

Distance along the slope (m) Figure 2.1 Prediction of velocity along a 1:2.4 slope, depending of friction, f.

4 van 146



0.50 0.45

Flow thickness (m/s)

0.40

f=0.01 f=0.02

0.35

f=0.05

0.30

f=0.10

0.25

f=0.01

0.20

f=0.02 f=0.10

0.15

f=0.01 f=0.02

0.10

f=0.05

0.05

f=0.10

0.00 0

2

4

6

8

10

12

14

Distance along the slope (m) Figure 2.2 Prediction of thicknesses along a 1:2.4 slope, depending of friction, f.

The figures show clear trends. For a small friction factor of f=0.01 flow velocity increases rapidly while flow thickness reduces. The same is true, but to a lesser extent, for f = 0.02. The trend changes for f = 0.05, where due to the larger friction, for all initial velocities the velocity along the slope decreases while the flow thickness increases. This is most obvious for the lowest initial velocities. For a large friction factor of f=0.10 the velocities decrease significantly and the flow thicknesses increase. With these predictions and looking at the trend of measurements it must be fairly easy to make a first guess for the correct friction factor for the measurements. All trends show a continuous increase or decrease along the slope to their terminal velocity and connected flow thickness. There is no trend that velocity increases first, due to gravity, and that friction takes over and reducing the velocity again.

2.2 2.2.1

Analysis of measurements Objective of the measurements From the start of testing with the wave overtopping simulator (2007) attempts have been made to measure flow velocities and thicknesses in overtopping waves in reality. Existing instruments from laboratory situations appeared not to be able to measure large velocities with high air content and turbulence. It is for this reason that instruments have been developed over time with the idea that they had to be simple and robust. The "surfboard" has been developed to measure flow thickness. The slightly curved and light board floats easily on the overtopping water and flow thickness is measured by the rotation of the surfboard at the hinged point. One surfboard was deployed in 2009 (at the Afsluitdijk) and this was increased to five surfboards at the Vechtdike (2010). Flow velocities of the overtopping wave front have been measured with a high speed camera (2009). It gives only the wave front velocity over a certain distance along the slope. It does not give a record of the flow velocity in time and, moreover, data processing is quite time


5 van 146


consuming. In 2010 the idea of a "paddle wheel" was explored. Such paddle wheels are used to measure the velocity of a small ship and exists of a small paddle wheel in a frame. Every turn around of the wheel gives a pulse and is a measure of velocity. These paddle wheels were placed in the surfboard and could measure the surface velocity of the overtopping wave. It is also possible to place these paddle wheels upside down on a plate on the ground surface. The first measurements with these paddle wheels were most promising. It was also concluded that the boundary layer of the overtopping flow was just a few centimeters, which means that the depth averaged flow velocity can also be measured by placing the paddle wheel 3 cm above the ground surface.

After the tests in 2009 and 2010 it was concluded that it was indeed possible to perform good hydraulic measurements with surfboards, including paddle wheels, and with paddle wheels on the ground surface. It was for this reason that more paddle wheels (eight in total) were bought. The first measurements had as main objective to develop the instruments and if they worked well, to describe the measured process of overtopping waves. Now it has been proven that the instruments indeed worked well, the objective has been changed. Theory on (steady) flow over a down slope exists, see section 2.1, and some validation on non-steady flow like wave overtopping has been performed on small laboratory scale. The main difference with a laboratory situation is that the landward slope of a dike has real grass on it and the surface is never completely straight. How well does the theory of steady state overflow describe the intermittent process of wave overtopping on a landward slope of a dike and what is the friction factor to be applied? The new objective became: measure the process of overtopping waves at the crest and along the landward slope at many locations and then try to validate the existing theory. A limited data set was achieved at the Vechtdike (2010) on a fairly gentle slope (upper part 1:3.7 and lower part 1:5.2). The dike at Tholen, which was tested in 2011, had a fairly steep slope of 1:2.4. Therefore it was decided to perform hydraulic measurements at this steep slope. Another objective was to measure also on the horizontal part of the crest, directly after release of the water from the wave overtopping simulator. Due to the limited number of surfboards this had not been done earlier. Only at the "force measurements" in Belgium (2010) measurements had been made on a horizontal and flat area. During these tests the wave overtopping simulator was placed on a horizontal area and forces were measured on vertical plates, simulating the wave overtopping along a boulevard and against a wall. A conclusion from the Vechtdike measurements was that flow velocity and flow thickness did not vary much along the landward slope (based on a limited number of paddle wheels). The measurements led to the following equations for flow velocity and thickness as a function of the released volume of water from the overtopping simulator, regardless of the location on the slope: h = 0,133 V0,5

with h in m and V in m 3/m

(6)

u = 5,0 V0,34

with u in m/s and V in m 3/m

(7)

Note that the theoretical relationship of u = h0.5 is not achieved by equations 6 and 7. The reason to deviate from this relationship is that the equations were based on measurements of overtopping waves and the measurements do not show the expected relationship. A reason

6 van 146



might be that intermittent wave overtopping is not similar to steady state overtopping, where the theoretical relationship comes from. It might well be that the maxima of flow velocity as well as flow thickness in an overtopping wave simply do not follow the rules for steady state overtopping or overflow. The objective of the present report is: •

• •

2.2.2

To establish the V, u, h relationship of the overtopping simulator on the horizontal crest, before the gravitational acceleration and friction of the grass can change the flow velocity and thickness on the landward slope; To measure the flow velocity and thickness along the landward slope; To validate the theory described in section 2.1 with these measurements

Test set-up at Tholen The hydraulic measurements at the landward slope of the dike at Tholen were performed with the wave overtopping simulator placed partly on the seaward slope and on the crest. The end of the guiding slope of the simulator was placed at the crest, just where the crest became horizontal. Then five surfboards were placed, one on the crest and four along the landward slope, see Figure 2.3 and Figure 2.4. Each surfboard had a paddle wheel to measure velocities, except for the upper one which had two paddle wheels. One paddle wheel (number 7, see Figure 2.4) was placed upside down in a plate on the ground surface. The locations of surfboards and paddle wheels are given in Table 2.1. Distance from toe of surfboard to start simulator Level of axis above ground level (m) (m) Paddle wheel Surfboard 1 2.2 1 1 (high) 2 (low) Surfboard 2 5.01 0.9 3 Surfboard 3 7.81 0.8 4 Surfboard 4 10.6 0.8 5 Surfboard 5 13.41 0.8 6 Surface 13.41 0 7 Table 2.1

Locations of paddle wheels and surfboards at Tholen.


7 van 146


Figure 2.3 Picture of the hydraulic measurements at Tholen with 5 surfboards and 7 paddle wheels. 6

Height (m above toe of dike)

PW 1

5

PW 2

Slope of hydraulic measurements

SB 1

Paddle wheels PW

PW 3

4

SB 2 PW 4

3

SB 3 PW 5

2 SB 4

1

PW 6 en 7 SB 5

0 0

2

4

6

8

10

12

14

16

18

Horizontal distance from the simulator (m) Figure 2.4 Set-up of hydraulic measurements at Tholen.

The idea to place two paddle wheels in one surfboard was first explored at the "force measurements" in Belgium. The basic idea for two paddle wheels is to measure the real maximum velocity for each released overtopping volume. If one paddle wheel is used, it will be placed quite close to the toe of the surfboard, just above the ground surface. For small released volumes this is a good set-up. However, with large released volumes the flow thickness becomes quite large and the toe or end of the surfboard becomes quite elevated above the surface with the possibility that the paddle wheel is released from the water. This may just miss the maximum velocity. By placing a second paddle wheel higher up in the

8 van 146



surfboard the maximum velocities will be measured correctly. But then there is a possibility that for small flow depths the velocity at this paddlewheel is not measured at all. The lowest paddle wheel is located just 2 cm above ground level. The higher paddle wheel is at a position more or less in the middle of the surfboard and 8.5 cm above ground level. If the surfboard is elevated significantly, then the higher surfboard measures correctly. If the flow depth is low it will be the lowest paddle wheel that measures correctly and the highest paddle wheel may not measure at all. The assumption is that one of the paddle wheels always measured the correct maximum velocity and that this maximum velocity corresponds to the maximum of both paddle wheels.

2.2.3

Measurements and data processing The test sequence of the hydraulic measurements was quite simple. Predefined overtopping volumes were released from the wave overtopping simulator in ascending order. Each released volume was repeated once. The smallest released volume was 0.4 m 3/m and the largest was 5.5 m 3/m. Measurements of flow velocity and thickness were performed in Volts. An overall view of the complete measurements in Volts is given in Figure 2.5. One can clearly observe the increasing velocities and flow thicknesss with increasing released overtopping volume. In total 26 overtopping volumes were released.

Figure 2.5 Overall view of the measured records in Volts for the measurements at Tholen.

As the recorded signals were in Volts, the first data processing was to change them to records in SI-units. The paddle wheels have a default calibration function of u = Volt * 8.57 (m/s). The surfboards have to be individually calibrated at each location. The calibration functions for the surfboards are: SB1 SB2 SB3 SB2 SB2

h = 0.385(Volt - 1.90)1.00 m h = 0.350(Volt - 1.30)1.15 m h = 0.300(Volt - 1.95)1.07 m h = 0.340(Volt - 1.87)1.15 m h = 0.410(Volt - 2.16)1.00 m

The first data processing of the measurements, after calibration to SI-units, is to plot the measurements in order to be able to visually analyze the behaviour of the records. Appendix 2 gives two graphs for each released volume with all the measured records. The upper graph shows the measured flow velocities and the lower graph the flow thicknesses.


9 van 146


For every record and every overtopping wave volume the maximum was found, resulting in umax and hmax for each record. It is assumed that these values occurred simultaneously. Table 2.2 gives all measured maxima of flow velocity and thickness. Volume 3 m /m 0.4 0.4 0.6 0.6 0.8 0.8 1.0 1.0 1.5 1.5 2.0 2.0 2.5 2.5 3.0 3.0 3.5 3.5 4.0 4.0 4.5 4.5 5.0 5.0 5.5 5.5

PW1 PW2 PW3 PW4 PW5 PW6 PW7 SB1 m/s m/s 3.65 3.46 4.10 4.09 4.43 4.27 4.56 4.72 2.02 4.97 1.71 5.11 4.07 5.74 3.84 5.63 4.66 5.86 3.95 5.93 6.10 6.08 5.95 6.10 6.41 6.33 6.45 6.39 7.01 6.48 7.21 6.69 7.05 6.81 7.38 6.96 7.76 6.82 7.63 7.07 7.97 7.23 7.77 7.04

Table 2.2

10 van 146

m/s 4.90 4.63 5.32 5.45 5.87 5.85 6.06 5.80 6.02 6.30 6.60 6.75 7.19 7.23 7.14 7.49 7.89 7.72 7.69 8.52 8.17 8.07 7.86 7.81 7.77 8.23

m/s 4.89 4.63 5.77 6.10 6.50 6.55 6.97 6.87 7.29 7.59 8.43 7.94 7.99 8.24 8.56 8.09 9.15 8.95 9.09 9.23 9.14 9.16 9.63 9.48 10.17 9.76

m/s 4.28 4.69 5.69 5.80 6.24 6.61 6.83 7.12 7.55 7.11 7.70 7.93 8.10 7.97 9.07 8.42 8.63 8.68 9.12 9.27 9.72 9.71 9.81 9.92 10.03 9.60

m/s 3.09 3.38 3.94 4.47 4.80 5.04 4.92 5.43 6.26 6.59 7.29 6.42 8.37 7.40 7.56 7.97 8.76 9.04 8.44 9.35 9.03 9.62 9.71 9.91 9.76 9.65

m/s 3.25 3.75 4.63 4.84 5.60 5.54 6.18 6.04 7.01 6.98 7.56 7.37 7.91 8.77 9.01 8.75 8.89 8.88 9.21 9.43 9.04 9.42 9.40 9.36 9.16 9.23

m 0.040 0.046 0.065 0.066 0.093 0.091 0.105 0.115 0.136 0.142 0.180 0.176 0.208 0.209 0.237 0.238 0.266 0.269 0.321 0.313 0.351 0.347 0.391 0.396 0.429 0.458

SB2

SB3

SB4

SB5

m 0.018 0.027 0.042 0.043 0.081 0.066 0.071 0.071 0.116 0.128 0.138 0.143 0.154 0.151 0.158 0.155 0.177 0.169 0.209 0.207 0.236 0.257 0.300 0.299 0.503 0.596

m 0.061 0.065 0.104 0.098 0.120 0.124 0.118 0.113 0.146 0.139 0.178 0.172 0.204 0.212 0.231 0.222 0.231 0.235 0.255 0.249 0.271 0.263 0.279 0.277 0.302 0.294

m 0.039 0.050 0.072 0.077 0.101 0.102 0.109 0.110 0.117 0.123 0.134 0.132 0.144 0.137 0.157 0.149 0.171 0.179 0.212 0.210 0.223 0.223 0.241 0.234 0.265 0.268

m 0.037 0.041 0.065 0.070 0.097 0.090 0.113 0.110 0.121 0.125 0.145 0.136 0.146 0.147 0.152 0.150 0.166 0.170 0.180 0.174 0.189 0.177 0.204 0.202 0.241 0.258

Maximum flow velocities and thicknesses for each overtopping event at Tholen



Figure 2.6 Flow thickness record with determination of overtopping duration.

Another interesting wave overtopping parameter is the overtopping duration. Velocity and thickness increase quickly and then decrease more or less linearly to zero. In reality there remains often a little water on the slope and the paddle wheels and surfboard measure these very small flow velocities and flow thicknesses. For determination of the flow duration this part of the records should not be considered, see Figure 2.6. The following rules were applied to find the overtopping duration by data processing. First, the recorded signal is plotted to roughly estimate the maximum gradient of the signal aest (reference is the signal when there is no wave) and the overtopping time Test of each wave. Second, the starting point, maximum point and ending points (positions and values) of each recorded wave are determined. A number of samples in a step is chosen, for example 50. It is noted that there are about 140 samples (recorded values) within 1 second. If the sample (i + 50) satisfies.

sample (i 50) sample(i) a where a is smaller than the estimated maximum value aest of the studied wave ( j ) , then the sample(i) is considered the starting point start ( j ) of the wave ( j ) . The ending point end ( j ) of this wave is the starting point of the next wave start ( j 1) . Third, the overtopping time is determined. Depending on the estimated overtopping time Test , a wave record is divided into 6 or 7 parts, each contains of a certain number of samples, at least 70 or 80. The first three or four parts (when the record rises) are the begining of the studied wave and are not taken into account here. Corresponding slope of the last parts are determined and compared. The steepest line is extended to cut the time axis t at the point

t cut j . The overtopping time of the wave ( j ) is T j t cut j start j


11 van 146


Table 2.3 gives the overtopping durations and the yellow marked cells were modified manually.

Volume l/m 400 400 600 600 800 800 1000 1000 1500 1500 2000 2000 2500 2500 3000 3000 3500 3500 4000 4000 4500 4500 5000 5000 5500 5500 Table 2.3

SB1 s 4.86 3.41 4.17 3.78 4.34 3.36 4.49 3.63 4.15 3.83 4.24 3.89 4.13 4.03 4.16 4.39 5.47 4.51 4.91 4.61 5.80 6.19 5.85 6.22 6.40 6.60

SB2 s 4.36 3.94 3.82 4.09 3.75 4.07 3.87 3.92 3.79 4.50 4.90 4.72 5.21 5.56 6.15 5.91 6.42 6.33 6.19 6.64 6.30 6.64 7.00 6.82 6.80 6.60

SB3 s 4.48 3.36 4.95 3.57 3.94 4.30 3.51 3.98 4.41 4.59 4.56 4.90 6.07 6.27 6.04 6.08 6.70 6.47 7.11 6.87 6.40 7.54 6.77 7.33 7.99 6.50

SB4 s 4.16 3.46 4.23 4.14 3.94 4.70 4.81 4.84 5.35 4.59 5.70 5.92 6.47 6.22 6.28 7.10 7.56 7.00 7.46 8.31 7.40 8.31 8.56 8.75 8.50 8.64

SB5 s 3.85 3.96 4.34 4.22 4.30 5.07 6.19 5.19 5.67 5.47 6.12 6.33 6.52 6.27 7.09 7.03 7.48 7.30 8.03 8.36 7.20 7.91 8.96 7.75 8.02 8.20

Overtopping durations for each overtopping event. Yellow cells are manually adjusted.

The focus in this chapter is on the measurements on the dike at Tholen. In order to be able to perform a complete analysis on measurements directly after release of the water from the wave overtopping simulater on a horizontal crest, also the measurements in Belgium are important. Here one surfboard with two paddle wheels were used to measure flow velocity and thickness on a flat area, see Figure 2.7.

12 van 146



Figure 2.7 Measurements on a horizontal surface in Belgium (force measurement tests).

In Belgium two series of tests were performed (tests 2 and 4). In test 4 the simulator was raised by 0.6 m in order to generate even larger wave forces on the vertical panels. Table 2.4 gives the measured maximum flow velocities and thicknesses for the released overtopping wave volumes. A first quick analysis I (Fase 4D Evaluatie Vechtdijk) revealed that due to the implementation of two paddle wheels the calibration of the surfboard was performed at the toe of the surfboard and not at the lowest point to the ground surface. The original calibration was modified and the correct values of the flow thickness are given in Table 2.4.


13 van 146


start time s 6.06 17.89 27.15 39.52 54.24 67.13 82.88 95.86 111.20 125.97 144.75 161.29 179.23 193.00 206.99 226.73 237.71 255.72 271.77 288.11 307.56 339.15 Table 2.4

2.2.4

volume max m max m/s max m/s l/m thickness h velocity u1 velocity u2 1000 0.137 3.65 3.64 1000 0.197 2.90 2.46 1500 0.164 3.68 4.44 1500 0.174 4.67 4.58 1500 0.173 4.76 4.86 2000 0.187 4.91 4.85 2000 0.189 5.02 5.07 2500 0.206 4.99 5.34 2500 0.214 5.35 5.43 3000 0.226 5.68 5.56 3000 0.218 5.32 5.22 3000 0.244 5.38 6.00 3500 0.234 5.06 5.94 3500 0.290 5.79 6.57 4000 0.269 6.37 6.63 4000 0.311 5.56 6.64 4500 0.286 6.37 6.84 4500 0.344 4.79 6.92 5000 0.330 5.73 6.87 5000 0.354 5.73 7.10 5500 0.333 4.81 7.04 5500 0.363 4.87 7.49

start time s 13.56 22.57 31.62 45.32 59.88 69.81 78.53 87.59 96.98 104.20 113.24 120.32 129.86 137.75 146.67 155.59 167.07 180.92 191.03 202.41 212.73 223.02 234.09 244.89 255.08 271.88 282.07 294.44 306.58 318.68 330.90 345.19

volume max m max m/s max m/s l/m thickness h velocity u1 velocity u2 500 0.107 4.04 4.59 500 0.114 3.52 4.15 500 0.120 3.37 3.69 1000 0.129 4.08 5.15 1000 0.129 4.53 5.21 1000 0.141 5.27 5.35 1500 0.144 5.10 5.78 1500 0.151 5.27 5.34 1500 0.151 5.01 5.50 2000 0.152 5.18 6.18 2000 0.160 5.48 5.59 2000 0.203 5.44 6.21 2500 0.196 5.58 6.24 2500 0.195 5.30 5.82 2500 0.234 5.19 6.39 3000 0.230 5.67 5.99 3000 0.211 5.63 6.16 3000 0.234 5.66 5.97 3500 0.256 5.68 6.15 3500 0.229 5.86 6.36 3500 0.258 5.89 6.57 4000 0.262 5.74 6.23 4000 0.258 4.78 6.21 4000 0.291 5.52 5.62 4500 0.263 3.69 4.52 4500 0.289 3.74 4.52 4500 0.335 3.44 3.77 5000 0.331 3.42 3.71 5000 0.303 3.15 3.77 5000 0.371 3.77 3.98 5500 0.330 3.61 3.95 5500 0.350 3.68 3.88

Maximum flow velocities and thicknesses for each overtopping event at Belgium.

Analysis at the crest The maximum flow velocities and thicknesses as measured in Belgium and given in Table 2.4 have been given in Figure 2.8, Figure 2.9 and Figure 2.10. Equations 6 and 7, determined on the Vechtdike measurements, have also been plotted in these figures.

14 van 146


9

0.45

8

0.40

7

0.35

6

0.30

5

0.25

4

0.20

3

0.15

Velocity u1 Velocity u2 Velocity from Vechtdike Flow thickness h Flow thickness from Vechtdike

2 1

0.10

Maximum flow thickness (m)

Maximum velocity (m/s)


0.05

0

0.00

0

1000

2000

3000

4000

5000

6000

Volume (l/m)

9

0.45

8

0.40

7

0.35

6

0.30

5

0.25

4

0.20

3

0.15 Velocity u1

2

0.10

Velocity u2 Velocity Vechtdike

1

Flow thickness h Flow thickness Vechtdike

0 0

1000

2000

3000

4000

5000



Figure 2.8 Flow velocities and thicknesses for horizontal platform, Belgium, test 2.

0.05 0.00

6000

Volume (l/m)

9

0.45

8

0.40

7

0.35

6

0.30

5

0.25

4

0.20 Maximum velocity test 4

3

Maximum velocity test 2 Velocity Vechtdike

2

Flow thickness test 4 Flow thickness test 2

1

0.15 0.10



Figure 2.9 Flow velocities and thicknesses for horizontal platform, Belgium, test 4.

0.05

Flow thickness Vechtdike

0

0.00

0

1000

2000

3000

4000

5000

6000

Volume (l/m)

Figure 2.10 Comparison maximum flow velocities and thicknesses for horizontal platform, Belgium, tests 2 and 4.


15 van 146


A few conclusions can be drawn from Figure 2.8, Figure 2.9 and Figure 2.10: • •

•

•

•

•

Measured velocities are a little lower than measured at the Vechtdike; Velocities u2 are in Figure 2.8 a little larger than velocities u1, for the largest overtopping volumes. This indicates that the paddle wheel u1 at the toe of the surfboard emerges from the water. Paddle wheel u2 gives then the correct maximum; Flow thicknesses increase extra for larger volumes. This has been checked by video analysis and it has been proven that the surfboard remains at the water surface at all times (it does not jump out of the water) and that the extra "bump", which creates the larger thickness, is due to the sudden release of the large volume. It might be expected that this small "bump" disappears further down the slope ; In Figure 2.9 velocities show a sharp decrease for the largest volumes. In the following test (test 5) it appeared that both velocity and flow thickness did not give any signal. Probably something has occurred at the end of test 4, which caused the strange decrease in values; Figure 2.10 gives a comparison between the two tests. It may be expected that test 4 would give a little larger velocities as the wave overtopping simulator was placed 0.6 m higher, giving a little more potential energy. It seems that this is indeed true, but only for the smaller overtopping volumes. Equation 7 gives in Figure 2.10 larger velocities than measured, certainly for the larger overtopping volumes. The flow thicknesses are quite close to Equation 6.

At Tholen the flow velocities and thicknesses were measured at the crest of the dike as well as at the landward slope. At the crest these were paddle wheels PW1 and PW2 and surfboard SB1. Measured values for the flow velocity are given in Table 2.2 and plotted in Figure 2.11, where the maximum of paddle wheels 1 and 2 was taken. Also the velocities from the Belgian tests have been included, which agree fairly well with the ones at Tholen. Equation 7 for the Vechtdike is given with a dashed line and gives larger velocities than measured at the crest or horizontal area. Possibly, even on a gentle slope like the Vechtdike, velocities increase a little when the overtopping water flows along the slope. 10 9


8 7 6 5 4 Maximum velocity Tholen

3

Maximum velocity Belgium Vecht

2

New fit

1 0 0

1000

2000

3000

4000

5000

6000

Volume (l/m) Figure 2.11 Measured flow velocities at the crest or horizontal area and a new fit.

16 van 146



A new fit can be made between released overtopping volume and the flow velocity directly behind the overtopping simulator on a horizontal crest or area: u = 4.5 V0.3

(with V in m 3/m and u in m/s)

(8)

0.50


0.45

Flow thickness Tholen Flow thickness Belgium

0.40

Vechtdike

0.35

Flow thickness Vechtdike New fit

0.30 0.25 0.20 0.15 0.10 0.05 0.00 0

1000

2000

3000

4000

5000

6000

Volume (l/m) Figure 2.12 Measured flow thicknesses at the crest or horizontal area. Data of Tholen, Belgium and Vechtdike.

A similar graph is given in Figure 2.12, but now for flow thickness instead of velocity. Other existing data of Belgium and Vechtdike have been added. The relation from the Vechtdike (Equation 6) is quite good for the middle range of volumes, but not for the whole range. Although there is significant scatter for small and large overtopping volumes, a fair trend for the flow thickness is given by: h = 0,1 V0,75

with h in m and V in m 3/m

(9)

Note that the relationship h = V0.5 from equation 6, and which is expected from dimensionless analysis, is not longer valid for equation 9. But Equations 8 and 9 give the best expression for maximum flow velocity and flow thickness as a function of the released volume of the wave overtopping simulator, just after release on a horizontal crest or platform.

2.2.5

Analysis at the landward slope Table 2.2 gives the measured values of maximum flow velocities and thicknesses along the landward slope of the dike at Tholen. Figure 2.13 gives the flow velocities as a function of the overtopping volume. It is clear that most velocities increase along the steep landward slope. Detailed analysis will be performed further on.


17 van 146


12


10

8

6 Max PW1 and PW2 PW3 PW4 PW5 PW6 PW7 ground Velocity at crest

4

2

0 0

1000

2000

3000

4000

5000

6000

Volume (l/m) Figure 2.13 Maximum flow velocities at the crest and along the slope.

Figure 2.14 gives the maximum flow thickness at the crest and along the slope. The general picture is that flow thickness decreases down the slope, which is logical as the velocity increases and u x h should be more or less constant (assuming no change in overtopping duration). Figure 2.14 has some peculiar points, however. From volumes of 3000 l/m the flow thickness at the crest (SB1) increases more than expected from the curve of the Vechtdike. From the records in Appendix B it is clear that the flow thickness indeed increases, but the shape of the overtopping record is more or less similar as before. Figure 2.15 shows the records of the five surfboards for an overtopping volume of 5,500 l/m. The shape of the record for SB1 is not much different from that of SB4 or SB5 much further down the slope. It must be concluded that the flow thicknesses measured at the crest are correct. It remains a question whether this effect of increasing flow thickness would also be present if the volumes would have been simulated by real waves overtopping a dike crest. It might be well possible that the unexpected increase of flow thickness is an effect of the quick release of a very large volume of water from the overtopping simulator, which was measured directly behind point of release. Other strange points are the sharply increasing flow thicknesses for SB2 for 5,500 l/m. Figure 2.15 shows a strange high second peak in the flow thickness record of SB2, which is not present for smaller overtopping volumes. The reason is not clear, but the points are not reliable.

18 van 146



0.6 SB 1 SB 2 SB 3 SB 4 SB 5 Vechtdike

Maximum flow depth (m)

0.5

0.4

0.3

0.2

0.1

0.0 0

1000

2000

3000

4000

5000

6000

Volume (l/m) Figure 2.14 Maximum flow thicknesses at the crest and along the slope.

Figure 2.15 Flow thickness records for the five surfboards for an overtopping wave volume of 5,500 l/m, showing a correct signal for SB1, but an unexpected second peak for SB2.

In order to validate the theory described in section 2.1 it is better to show the change in flow velocity and thickness along the slope for given wave overtopping volumes. The change is caused by the slope (gravity) and by the friction along the grass slope. Figure 2.16 and Figure 2.17 give this dependency of flow velocity and thickness on location. At the second vertical axis the slope itself is given in order to relate directly the location of measurements to the location on the slope. The trend that larger overtopping wave volumes give larger velocities is also clear in Figure 2.16. But the figure also clearly shows the trend along the slope. In general the velocity increases on the upper half of the slope. Then the velocity decreases, probably due to friction. The decrease is most significant for small overtopping volumes and hardly present for the largest volumes, which is also what can be expected. Figure 2.17 shows that flow thickness increases with increasing released overtopping volume. The trend along the slope is a little more difficult to describe. The main point is that SB2, the second location from the crest at x = 4.8 m, gives consistently lower values than the two SBW Wave overtopping and grass cover strength

19 van 146


surrounding locations at the crest and at x = 7.6 m. In order to have a better look the records for an overtopping volume of 2000 l/m are studied more in depth in Figure 2.18. 12

6 400 600

5

800 1000 1500

8

4

2000 2500 3000

6

3

3500 4000

4

2

4500 5000 5500

2

Height on the slope (m)

Maximum flow velocity (m/s)

10

1

0

0 0

2

4

6

8

10

12

14

16

18

Horizontal distance from simulator (m) Figure 2.16 Flow velocities along the slope. 6

0.50


600

0.40

5

800 1000

0.35

4

1500

0.30

2000 2500

0.25

3

3000

0.20

3500 4000

0.15

2

4500 5000

0.10

1

5500

0.05 0.00


400

0.45

0 0

2

4

6

8

10

12

14

16

18

Horizontal distance from simulator (m) Figure 2.17 Flow thicknesses along the slope

20 van 146



Figure 2.18 Flow thickness records for the five surfboards for an overtopping wave volume of 2,000 l/m, showing two flat parts for SB2.

In this Figure 2.18 SB2 indeed shows lower values than for SB1 and SB3. The main observation, however, is that the signal has a completely flat peak, then drops quickly and has a second flat signal again. Also the sudden increase when the overtopping wave front hits the surfboard is a little less steep than for the other surfboards. It is from these observations that it must be concluded that in one way or the other the measurements of flow thickness for SB2 are not correct. The surfboard underestimates the maximum values. Although the maximum values are underestimated it might be well possible that overtopping durations are still measured correctly. Figure 2.16 and Figure 2.17 show all the measured data, which makes it difficult to distinguish for individual overtopping volumes. Therefore, Figure 2.19 and Figure 2.20 have been limited to only three or four overtopping volumes: the smallest (400 l/m), a middle one (2000 l/m) and the largest (5500 l/m). Also the two measurements for one overtopping volume have been averaged to one point only. In Figure 2.20 also an overtopping volume of 5000 l/m is given as surfboard SB 2had completely unreliable maxima (see before in this section). In Figure 2.19 (as well as Figure 2.16) the most right location at the toe of the slope has two points close to each other. In fact these are the paddlewheel in SB5 and the paddlewheel at the ground surface. They have exactly the same location on the slope, but the paddlewheel at the ground surface has artificially been shifted a little to the right, in order to make comparison between the two paddlewheels possible. In all cases the two paddle wheels give similar maximum values. Figure 2.19 clearly shows the earlier observation that flow velocity increases at the upper half of the slope, decreases then for the smaller volumes, but remains more or less the same for the largest overtopping wave volumes. The conclusion for Figure 2.20 is more difficult to draw. For the largest overtopping wave volumes it is clear that the flow thickness decreases along the slope. As SB2 gives unreliable (too low) values the only observation for smaller overtopping volumes is that it remains more or less the same along the slope. Given the observation for the flow velocities one would expect a decrease of flow thickness in the upper part of the slope and again an increase for the lower part. The trend for an overtopping wave volume of 2000 l/m looks close to this expectation, but this is less the case for 400 l/m.


21 van 146


12

6 400 2000

5

5500

8

4

6

3

4

2

2

1

0



10

0 0

2

4

6

8

10

12

14

16

18

Horizontal distance from simulator (m) Figure 2.19 Flow velocities along the slope for three overtopping wave volumes.

400 2000 5000 5500


0.45 0.40

5

0.35

4

0.30 3

0.25 0.20

2

0.15 0.10

1


6

0.50

0.05 0.00

0 0

2

4

6

8

10

12

14

16

18

Horizontal distance from simulator (m) Figure 2.20 Flow thicknesses along the slope for four overtopping wave volumes.

This may lead to the conclusion that not only flow velocity and thickness play a role, but also the overtopping duration. If the overtopping duration changes, the assumptions for steady state flow (section 2.1) are no longer valid. If the overtopping duration increases along the slope it is possible that flow velocity and thickness do not always give opposite trends. Figure 2.21 gives the overtopping durations as a function of released overtopping volume. In general there is a clear trend that overtopping durations are smallest at the crest and increase along the slope. This conclusion can also be drawn from Figure 2.22 where the trend is given along the slope for overtopping volumes of 800 l/m, 2000 l/m and 5000 l/m. Figure 2.19 and Figure 2.20 are a good test case for validation of the theory given in section 2.1, where also the influence of the trend in Figure 2.22 should be taken into account.

22 van 146



10 9

OVertopping duration (s)

8 7 6 SB1

5

SB2

4

SB3 SB4

3

SB5

2 1 0 0

1000

2000

3000

4000

5000

6000

Volume (l/m) Figure 2.21 Overtopping duration as a function of released volume. 6

10 800 2000

8

5

5000

7

4

6 3

5 4

2

3 2


Overtopping duration (s)

9

1

1 0

0 0

2

4

6

8

10

12

14

16

18

Horizontal distance from simulator (m) Figure 2.22 Overtopping duration along the slope for three released overtopping volumes.

2.2.6

Analysis at the landward slope of the Vechtdike In 2010 tests with the wave overtopping simulator have been performed at the Vechtdike near Zwolle, including hydraulic measurements. The measurements and analysis have been described in the SBW-report phase 4D on the Vechtdike and by Steendam et al. (2010) and will not be repeated here. But also these measurements are useful for validation with the theory in 2.1 as the landward slope was much gentler than for the dike at Tholen. The results will be summarized here in a way that they can be used for validation with theory.


23 van 146


The test consisted of three times repeated overtopping wave volumes, which increased in time from 200 l/m to 5,500 l/m (the maximum capacity of the Wave Overtopping Simulator). Five surf boards were placed along the slope, see Figure 2.23. Paddle wheels were used here for the first time. As this was a new development and results were not guaranteed, only three paddle wheels were bought and installed. Two were installed in surfboards and one upside down on a plate in the soil. This last one measured the flow directly at the bottom, the others at the top of the flow. Measurements were made from the inner crest line (at the transition to the landward slope) and 12 m along the slope. The slope was not completely straight, the upper part was 1:3.7 and the lower part 1:5.2. Surfboard 1 was located at the crest and surfboard 5 at the down slope.

Elevation (m)

1

2

4.0

3

3.5

Simulator

2m 2m

4

3.0 2.5

5

2.0

4m

4m

1:3.7

1:5.2

1.5 1.0 0

2

4

6

8

10

12

14

16

Distance (m) Figure 2.23 Set-up of measurements at the Vechtdike.

Figure 2.24 gives the (maximum) flow thickness, h, versus the released overtopping wave volumes and for all five surfboards along the slope. The flow thickness at the crest and also directly behind the crest is larger than further down the slope. It remains more or less the same from 8-12 m from the crest, which may be explained by the changing slope angle after surfboard 3, see also Figure 2.23. The flow thickness at the crest, mainly fitted on the larger overtopping wave volumes, was then developed as Equation 7, described earlier.

24 van 146



Flow thickness (m)

0.35 0.30

h = 0.133 V0.5

0.25 0.20 Board 1 crest

0.15

Board 2 2 m Board 3 4 m

0.10

Board 4 8 m Board 5 12 m

0.05

Trend line crest

0.00 0

1000

2000

3000

4000

Wave volume (l/m)

5000

6000

Figure 2.24 Measured flow thickness at the Vechtdike.

It should be noted, however, that the flow thicknesses for the large overtopping volumes, however, were manually modified. The original data gave an unexpected increase for large overtopping waves and at that time it was assumed that this was caused by the surfboard jumping out of the water. The tests in Belgium and at Tholen gave also this increase, see Figure 2.12, but it was validated that this was not due to a jumping surfboard. The flow thicknesses at the crest (surfboard 1) have already been changed back to the original data (Figure 2.13). It should also be done here for the other locations (Figure 2.25). In order to make a validation with theory easier the flow thicknesses have been given as a function of the location on the slope, see Figure 2.26. The general trend is that flow thickness decreases along the slope, except for the last and more gentle part, where it increases again a little. 0.50 Board 1; crest Board 2; 2 m Board 3; 4 m Board 4; 8 m Board 5; 12 m New fit crest

Flow thickness (m)

0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0

1000

2000

3000

4000

5000

6000

Wave volume (l/m) Figure 2.25 Flow thicknesses at Vechtdike with original data.


25 van 146


4.0

0.50 0.45

Flow thickness (m)

3.0

0.35

600

0.30

800

0.25

1000

2.5 2.0

2000

0.20

1.5

3000

0.15

4000

0.10

5000

1.0

5500

0.05

Slope eleavation (m)

3.5

0.40

0.5

Slope

0.00

0.0 0

2

4

6

8

10

12

14

16

18

Distance (m) Figure 2.26 Flow thicknesses at Vechtdike as function of location. 4.0

0.50 0.45

Flow thickness (m)

3.0

0.35

2.5

0.30

2.0

0.25 0.20

1.5

0.15

1000

0.10

5500

1.0

3000

0.5

Slope

0.05

Slope elevation (m)

3.5

0.40

0.00

0.0 0

2

4

6

8

10

12

14

16

18

Distance (m) Figure 2.27 Flow thicknesses along the slope at the Vechtdike for three overtopping wave volumes.

Just like for the tests at Tholen (Figure 2.19 and Figure 2.20) it is easier for the validation of theory if only a few volumes are taken and also with the average value for tests with similar overtopping volume. This has been done in Figure 2.27 and this graph shows again a decrease on the upper part of the slope and a slight increase at the lower part. The (maximum) flow velocities, u, are given in Figure 2.28. There were only a few paddle wheels, but it seems that the velocity along the slope did not change significantly. All measurements form together a nice line and can be given by Equation 6, described earlier. Note that velocities were not measured at the crest. As discussed earlier the velocity at the crest after being released from the wave overtopping simulator is a little lower than given by Equation 6. The new formula for the crest is given by Equation 8 and both equations are given in the graph.

26 van 146



Flow velocity (m/s)

10 9

u = 5.0 V0.34

8 7 6

Board 3 4 m

u = 4.5 V0.30

5

Board 4 8 m

4

Board 5 12 m

3

Trend line

2

New fit for crest

1 0 0

1000

2000

3000

4000

5000

6000

Wave volume (l/m) Figure 2.28 Measured velocities at the Vechtdike with old and new formulae.

Overtopping durations can be established from the flow thickness records. It was hard to determine the overtopping durations for small overtopping wave volumes as water is still flowing a little along the grassed slope when the actual wave has passed already. Also small overtopping wave volumes slowed down the slope and although they were visible at the crest, they were not observed 12 m further down the slope. Figure 2.29 gives the overtopping durations, Tovt, as they were established from the various flow thickness records. There is quite some scatter for overtopping volumes smaller than 1000 l/m, as explained above, but there is a nice trend for larger volumes. The data points show that there is hardly a change in overtopping duration for the first 8 m on the slope, but there is a slight increase between surfboard 4 and 5 along the more gentle slope. The overtopping duration at the crest can well be described by: Tovt = 4.4 V0.3

(Tovt in s; V in m 3/m)


(10)

27 van 146


10

Flow time (s)

9 8 7 6 5

Board 1 crest Board 2 2 m Board 3 4 m Board 4 8 m Board 5 12 m Trend line crest

4 3 2

Tovt = 4.4 V0.3

1 0 0

1000

2000

3000

4000

5000

6000

Wave volume (l/m) Figure 2.29 Measured overtopping durations at the Vechtdike.

Tholen The theory of steady state flow has been described in section 2.1 and the measurements on a dike crest and landward slope in section 2.2. The measurements at Tholen were performed on a fairly steep 1:2.4 slope. Measurements show that the velocity increases fairly rapidly from the crest, but slow down near the toe of the dike. This is of course a trend that cannot be calculated by steady state flow and is probably caused by the intermittent flow and the increase of the overtopping duration along the slope. Nevertheless it is worthwhile to compare the steady state theory with the overtopping measurements. 7

14 400 measured 2000 measured

12

6

5500 measured


2.3.1

Validation of theory


2.3

f=0.005

10

5

f=0.005 f=0.005

8

4

f=0.01 f=0.01 f=0.01

6

3

f=0.02 f=0.02

4

2

f=0.02 f=0.08 f=0.08

2

1

f=0.08

0

0 0

2

4

6

8

10

12

14

16

18

Horizontal distance from simulator (m) Figure 2.30 Validation of flow velocity at Tholen for various f-values.

28 van 146



7

0.45 400 measured 2000 measured

6

5000 measured

0.35



0.40

f=0.005

5

f=0.005

0.30

f=0.005

0.25

f=0.01

0.20

f=0.01

4

f=0.01

3

f=0.02

0.15

f=0.02

2

f=0.02

0.10

f=0.08 f=0.08

0.05

1

f=0.08

0

0.00 0

2

4

6

8

10

12

14

16

18

Horizontal distance from simulator (m) Figure 2.31 Validation of flow thickness at Tholen for various f-values.

Figure 2.30 and Figure 2.31 give the results for Tholen, for the flow velocity and flow thickness, respectively. The bold lines with solid symbols give the measurements. Various fvalues of f = 0.005, 0.01, 0.02 and 0.08 have been used to calculate the behaviour of flow velocity and flow thickness over the slope and are given by thin lines. The rapid increase of velocity after the crest is best described by f=0.01. At the toe of the dike (near x = 13 m) the calculated flow velocity is a little larger than the measured one, probably due to the slowing down of the overtopping process (increasing overtopping duration). The decrease in flow thickness is also well described by f=0.01. The graphs also show that a change of f by a factor 2 (f = 0.005 or f = 0.02) still has significant effect on flow velocity and thickness.

2.3.2

Vechtdike The landward slope at the Vechtdike was significantly gentler than at Tholen (1:3.7 for the first 5 m, then 1:5.2). The trend of the measurements was that from the crest onwards the flow velocity increased a little and then remained constant, where the flow thickness first reduced and also remained constant further on. Only a limited number of paddle wheels (flow velocities) were present.


29 van 146


4.0 3.5

f=0.005

10

f=0.005

3.0

f=0.005

8

f=0.01

2.5

f=0.01 f=0.01

6

2.0

f=0.02 f=0.02

4

1.5

f=0.02

1.0

f=0.08 f=0.08

2

0.5

f=0.08 Slope

0 0

2

4

6

8

10

12

14

16

Slope elevation (m)


12

0.0 18

Distance (m) Figure 2.32 Validation of flow velocity at the Vechtdike for various f-values. 4.0

0.45

3.5

1000 3000 5500 f=0.005 f=0.005 f=0.005 f=0.01 f=0.01 f=0.01 f=0.02 f=0.02 f=0.02 f=0.08 f=0.08 f=0.08 Slope

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0

2

4

6

8

10

12

14

16

3.0 2.5 2.0 1.5 1.0

Slope elevation (m)


0.50

0.5 0.0 18

Distance (m) Figure 2.33 Validation of flow Thickness at the Vechtdike for various f-values.

Figure 2.32 and Figure 2.33 show the calculations of flow velocity and thickness along the slope, with also the measurements for the flow thickness. Note that these figures have to be analyzed from right to left, just opposite to Figure 2.30 and Figure 2.31. The trend of increasing velocity and then remaining more or less constant is well given for f=0.01, but also quite good for f=0.02. A value of f=0.005 gives a too large increase of the flow velocity. The trend for flow thickness is well described for the smaller values of f. In Figure 2.33 even a value around f=0.005 should be used for the flow thickness to come close to the measurements. It means that flow velocity and flow thickness, Figure 2.32 and Figure 2.33, do not give similar values for f. Overall a value of f=0.01 is best, but there might be an effect of increasing overtopping duration along the slope, which is not in the theory of steady state flow.

30 van 146



2.3.3

Comparison friction factor with roughness coefficients In this section the friction factor f has been used defined as (Schüttrumpf, 2001):

u

2g / f hS

(11)

With S the slope gradient. A more common method is related to the Chézy coefficient:

u

C hS

(12)

In which C is the Chezy coefficient. Combining (11) and (12) gives a relationship between f and C:

C

2g / f

(13)

Substituting f = 0.0058 and 0.01 results in C = 60 and C = 45 respectively. The first value for f is recommended by Schüttrumpf and Oumeraci (2005). The value of 45 seems too low as for rivers with ripples and sand dunes values of 35 to 40 are applied. Note: in American literature also the Darcy-Weisbach friction factor f DW is in use, defined as:

u

8g / fDW hS or C

8g / fDW

(14)

Another option is to relate the friction factor f with the relative turbulence intensity r0 via the Chézy coefficient (Hoffmans, 2012):

r0

1.2 g / C

(15)

Combining (12) and (15) gives:

u

1.2 ghS / r0

(16)

Combining (11) and (16) subsequently results in:

r0

1.2 f / 2

(17)

Substituting f = 0.0058 and 0.01 results in r0 = 0.06 and r0 = 0.08 respectively. Both values seem too low, since normal turbulence is about 0.1. However, due to the smoothness of grass lower turbulence intensities might be possible. Nevertheless, based on measured flow velocities a higher value for r0 can be computed. For example, substituting a flow velocity of 6.5 m/s corresponding with an overtopping volume of 4000 m 3 and a water depth of about h = 0.25 m on a slope 1V:2.4H results with Equation 16 in: r0 = 0.18. With Equation 11 a value for f results of f = 0.045 which is considerable higher then the recommended values by Schüttrumpf and Oumeraci (2005).


31 van 146


Taking into account 30% air results in a modified equation 16:

r0

1.2 g h

With an air content of

a

a

S /u

(18)

= 0.3 the value r0 is r0 = 0.15 and f = 0.031.

Finally, also the Manning formula is often used:

u

h 2/3S1/ 2 / n or u

h1/ 6 / n

hS

(19)

Combining with (11) results in:

n

h1/ 6 f / 2g

(20)

Substituting f = 0.0058 and 0.01 for a water depth h = 0.25 m results in n = 0.014 and n = 0.018 respectively. This is considerably lower than the value mentioned in literature for grass in floodplains of n is about 0.03 (corresponding with a C value of 32). All results are summarized in the following table. f C r0 n

0.0058 60 0.06 0.014

0.01 45 0.08 0.018

0.02 32 0.12 0.03

0.045 21 0.18 0.054

On the basis of the above comparison between values for f < 0.01 recommended by Schüttrumpf and Oumeraci (2005) based on a theoretically derived equation for the flow velocity assuming steady state conditions but validated by large overtopping wave experiments, it should be concluded that the value of the friction factor f is too low given the corresponding values for r0 and n. However, measured flow velocities can be predicted well with a value of f = 0.01 (see sections 2.3.1 and 2.3.2). If we compute the values of r0 and f with measured flow velocities and water depths realistic values for r0 result with values of f in the range of f = 0.05. Thus, the conclusion should be that the value of f is somewhere in the range of 0.05 to 0.5 corresponding with values of r 0 in the range of 0.10 to 0.20.

2.3.4

Conclusions The objective of the present report is: •

• •


32 van 146



The conclusions that can be reached are: 1)

The theory of steady state flow is taken for validation. This theory assumes steady state over time, where wave overtopping is intermittent. Wave overtopping can be described by a more or less triangular record in time for flow velocity and flow thickness. The maximum values for these flow velocities and thickness are compared with the theory. The length of the record is described by the overtopping duration. Flow velocity and thickness are a function of slope angle, friction and initial conditions. As slope angle and initial conditions are given, the only variable is the friction factor f. The objective was to find a good fit for this correction factor and to judge whether found trends were indeed predicted well by theory. First predictions by various values of f show that small values (f < 0.05) give an increase of velocity along a steep slope and large values (f > 0.05) show a decrease. As measured velocities increased along the slope the correct friction factor should be well below f = 0.05.

2)

The wave overtopping simulator was used to simulate the overtopping waves over the crest and landward side of a dike. This simulator was designed to give a certain flow velocity on the crest for a given released (overtopping) volume. Each released volume gives a certain (maximum) flow velocity, flow thickness and overtopping duration, which is assumed to be similar to real overtopping waves. Due to the measurements at Tholen and in Belgium the relationships between released overtopping volume and flow velocity and thickness could be established a few meters behind the release of the water, on a horizontal crest. It is also apparent that for large overtopping volumes the flow thickness increases more than linearly, giving a kind of "bump" in the record. It might well be that for these large overtopping volumes flow velocity and thickness directly after release are not yet according to real overtopping waves.

3)

Flow velocities increase on the first part of a steep slope, but further down the slope these velocities reduce again. This cannot be predicted by steady state flow theory, where the velocity can only reach a certain equilibrium. The overtopping durations increased along the slope and that might well explain why velocities decreased at the lower part of the slope. Except for this effect all trends of flow velocity and thickness, for both the measurements at Tholen and at the Vechtdike, were fairly well calculated by a friction factor of f=0.01. This is the friction factor to be used for real grass on a slope in steady state flow calculations. This theory can quite well predict (maximum) flow velocities and thicknesses along a slope by wave overtopping, except for the lowest part on the slope where effects of increasing overtopping duration may play a role.


33 van 146


3 3.1

Analysis of measured run-up parameters Set up of the measurements Wave run-up tests on the seaward side of a dike have been performed at Tholen in 2011. Also hydraulic measurements have been performed on flow velocity and thickness in the runup as well as the run-down phase. The down slope is a conventional placed block revetment on a slope 1:4, then a 1:20 berm is present at a height of 4.2 m +NAP (NAP = Chart Datum). The lower part of the berm consists of an asphalt cycle path also used as maintenance road, the upper part is a grassed slope. The total width of the berm is about 4 m. Finally, an upper slope is present with a slope of 1:3 and a height of 6.8 m +NAP. The wave overtopping simulator was used to create up-rushing waves on the berm and upper part of the slope and the outflow point of the simulator was placed just on the asphalt berm with the actual simulator on the down slope. Figure 3.1 shows a set-up of the testing. Wave run-up was simulated over the berm (asphalt and grassed slope) and the upper grassed slope. With released volumes larger than 4000 l/m the up-rushing water reached the crest and overtopping was created.

Figure 3.1 -up of the wave run-up hydraulic measurements.

In order to be able to perform correct wave run-up tests the relationship between released volume and run-up height or level should be established. This was first performed at the steep inner slope (slope 1:2.4) at the Tholen dike and the found relationship was used to create the steering files for the run-up test. Figure 3.2 shows the set-up during this calibration of run-up levels, where the simulator outflow was directly placed against the slope (no horizontal transition). When the simulator was present on the seaward side for the testing on run-up similar calibration tests were performed to establish the relationship between released volume and run-up level, but now for the almost horizontal berm and more gentle upper slope. 35


The results of both calibrations are given in Figure 3.3. The largest run-up level on the steep 1:2.4 slope was about 3.5 m. The calibration on the 1:3 seaward slope terminates for 4000 l/m and larger as the crest is reached by the up-rushing wave and overtopping started. With similar released volumes the run-up was a little larger on the 1:3 slope with the berm in front. The actual slope was a little rounded, see Figure 3.4 and the calibration for this slope is given in Figure 3.3 as well.

Figure 3.2 Calibration of run-up levels on a steep slope 1:2.4. 4.0

Run-up level (m)

3.5 3.0 2.5 2.0 1.5 Calibration on slope 1:3

1.0

Calibration on slope 1:2.4 Calibration on actually measured slope

0.5 0.0 0

1000

2000

3000

4000

5000

6000

Released volume (l/m) Figure 3.3 Calibration results on run-up levels for different slopes.

36 van 146



7.5

Height (m NAP)

7.0

Slope for run-up tests Given profile OS1049

6.5 6.0 5.5 5.0 4.5 4.0 -14

-12

-10

-8

-6

-4

-2

0

2

4

Horizontal distance (m) Figure 3.4 Measured slope for run-up tests.

For the hydraulic measurements two surfboards have been used for measurement of flow thickness and eight paddle wheels for flow velocity. One surfboard was placed on the crest and could only measure overtopping waves (volumes of 4000 l/m and larger). After run-up the water runs down the slope what may hit the surfboard from the wrong side and damage it. For this reason a modified surfboard was developed, which is more rounded than the existing ones. Also a down rushing wave will then tilt the surfboard to float on the water surface. Figure 3.5 shows the set-up of the hydraulic measurements, including this modified surfboard. Paddle wheels were mounted in both surfboards. Another six paddle wheels were mounted in a plate on the ground surface, but measured the velocity 3 cm above this level (just outside the boundary layer). Paddle wheels can turn around in two directions, but only one direction is the correct one. For this reason two paddle wheels have to be used for measuring run-up as well as run-down. On two locations on the slope two paddle wheels were mounted next to each other, but measuring opposite directions, see also Figure 3.5. The other paddle wheels were placed in between the others. The precise locations of surfboards and paddle wheels is shown in Figure 3.6.

Figure 3.5 Set-up of hydraulic measurements on run-up with modified surfboard and velocity measurements up and down the slope

37


4, 5, 8

Simulator 2,2 m

1,5m 3

1

Instrument Location

2 New SB1 PW1 PW2 PW3 SB5 PW8 PW4 PW5 down PW6 PW7 down

6, 7 2,2 m

paddle wheels up and down paddle wheels up surfboard with paddle wheel new surfboard with paddle wheel

1.5 m on crest In SB1 0.5 m from crest 2.7 m from crest 4.9 m from crest in SB5 4.9 m from crest 4.9 m from crest 7.1 m from crest 7.1 m from crest

7.1 m = 0.90 m from berm/slope

Figure 3.6 Locations of surfboards and paddle wheels on the slope.

3.2

Analyses of run-up measurements The test on hydraulic measurements was similar to a test on wave overtopping. Fixed volumes were released from the simulator, starting with small volumes. The volumes were repeated and then increased to a larger volume. In total 24 volumes were released form 600 l/m up to 5,500 l/m. The records of all instruments and for each released volume are given in Appendix C. In order to describe the measured process of run-up as well as run-down the record of one overtopping wave will be analyzed in depth. Figure 3.7 shows the record for a released volume of 4000 l/m and from the time that run-up started till all released water had disappeared from the slope (by flowing underneath the simulator to the sea). Velocities have been given on the left vertical axis and flow thicknesses on the secondary right axis. Both run-up as well run-down velocities are present in the graph. The paddle wheels give a pulse every time they make a turn around. As pulses are always positive, the velocity is also always positive. It means that the direction of the flow has to be known as the paddle wheel does not give the direction (no negative values for run-down for example). This explains the shape of the velocity records: first a sharp peak to a maximum, then a decrease to zero and subsequently the start of run-down to a maximum, which terminates at zero again. Paddle wheel PW6 shows again two records around 225-228 s. This is a part of the water that reflects against simulator and then comes back onto the slope as a second wave. The conclusion is that in Figure 3.7 the run-up as well as the run-down are present and that it is better to divide the records in run-up and run-down only. Figure 3.8 gives the records of runup only. All run-up records show the same trend, a sharp increase at start and a more or less linear decrease to zero and start of run-down. These kind of records are similar to those found for overtopping. Figure 3.8 shows that at the location of paddle wheel PW6 the run-down has already started when the front of the up-rushing wave reaches the middle of the crest at surfboard PW1 and paddle wheel PW1. The released volume of 4000 l/m just runs over the crest of the dike. Another observation can be made on basis of Figure 3.8. The flow thickness of surfboard SB5 increases rapidly to a maximum value of around 0.3 m and after one and a half second 38 van 146



increases further to a thickness of almost 0.5 m. This is an unexpected result as a similar trend was expected as for the flow velocity. Analysis of video and pictures gave the explanation. Figure 3.9 shows the run-up and run-down process in pictures. The pictures show a nice run-up on to the crest, but then the water on the crest starts to run-down while there is still water released from the simulator and rushing up the slope. These two flows meet each other on the lowest part of the slope, creating a bump of water which finally runs down the slope. This is not the case for real wave run-up and is caused by the shape of the present simulator: it takes too much time to release the water on the slope. A more slender design could possible overcome this problem (which has been worked out separately). One can conclude that the horizontal part after the first increase of surfboard SB5 is the real flow thickness during run-up and not the later maximum. Therefore these maxima were used for maximum run-up flow thicknesses. The maximum values of flow velocity and thickness during run-up have been summarized in Table 3.1. If the run-up had not reached a specific instrument the cell was left blank. This is also the case if a specific instrument did not (properly) record. The record for surfboard SB5 gave after the first recorded volumes a negative value in between the released volumes, see Appendix 1. The "zero" had shifted, sometimes up to 0.04 m. Accidentally this occurs for the surfboards. As it is just a shift in zero and not a change in calibration steepness, the maximum run-up value was increased with the measured thickness before the next volume reached the surfboard.

39


0.7

7

5 4

Flow velocity (m/s)

0.6

PW1 PW2 PW3 PW4 PW5 down PW6 PW7 down PW8 SB1 SB2

3

0.5 0.4 0.3

2

0.2

1

0.1 0.0

0 216

218

220

222

224

226

228

Time (s) Figure 3.7 All records of flow velocity and thickness (run-up and run-down) for a released volume of 4000 l/m.

41

Flow thickness (m)

6


0.7

7 PW1 PW2 PW3 PW4 PW5 down PW6 PW7 down PW8 SB1 SB2

5

Flow velocity (m/s)

4

3

0.6 0.5 0.4

0.3

2

0.2

1

0.1

0.0

0 216

217

218

219

220

Time (s) Figure 3.8 Run-up records only of flow velocity and thickness for a released volume of 4000 l/m.

42 van 146


221

222

Flow thickness (m)

6


Figure 3.9 Simulated wave run-up and run-down. Volume 5500 l/m.

43


Volume l/m l/m 600 600 800 800 1000 1000 1500 1500 2000 2000 2500 2500 3000 3000 3500 3500 4000 4000 4500 4500 5000 5000 5500 5500

Table 3.1

PW1 m/s

PW2 m/s

PW3 m/s

PW4 m/s

PW5 m/s

PW6 m/s 1.24 0.96

PW7 m/s 0.78 0.98 0.89 1.62 1.26 1.76 1.82 2.69 2.80 2.53 2.91 2.88 2.48

2.02

1.91 1.20 3.09 3.05 3.78 3.65 4.06 3.72 4.25 4.81

1.49 1.50 2.25 2.08 3.12 3.10 4.00 3.46

1.80 1.75 2.48 2.65 3.72 3.30 4.32 4.30 4.26 4.67 4.94 4.96 5.32 5.77

2.54 2.36 3.25 3.44 3.89 3.93 4.01 4.45 4.32 4.42 4.49 4.39 4.85 5.36 4.82 5.13 5.20 5.36

0.80 1.88 1.41 2.35 2.70 2.73 2.58 2.73 3.26 3.14 3.23 4.04 3.53 3.58 3.56 3.88 3.75 3.38 3.88

PW8 m/s

5.25 5.42 5.97 5.65 5.93 5.09 5.07 4.02 5.78 5.90

2.401 2.647 3.081 2.715 3.426 3.724 3.918 4.111 4.216 4.012 4.117 3.960 4.049 3.604 4.661 3.970 3.405 4.661

4.32 3.50 2.98 3.69 4.22

SB1 m

SB5 m

0.029 0.021 0.054 0.057 0.110 0.096 0.147 0.152

0.065 0.046 0.104 0.146 0.183 0.160 0.196 0.199 0.238 0.237 0.307 0.307 0.363 0.385 0.368 0.404 0.455 0.478

Maximum flow velocities and thicknesses during run-up.

Figure 3.10 shows all measured maxima of the flow velocity. It is clear that flow velocity nicely increases with increasing released volume at least until volumes of around 4000 l/m. For larger volumes there is a slow down for some paddle wheels. The maximum depends of course on the location of the instrument on the slope. For a more in depth analysis it is better to look at specific groups of paddle wheels. 7 PW1 PW2

6

PW3 PW4

5

PW5 down

Flow velocity (m/s)

PW6

4

PW7 down PW8

3 2 1 0 0

1000

2000

3000

4000

5000

6000

Released volume (l/m)

Figure 3.10 Maximum run-up velocities for all paddle wheels.

Figure 3.11 gives the maxima for PW4 (on the ground surface, measuring in the run-up direction), for PW5 (on the ground surface, measuring in the run-down direction) and for PW8 (mounted in SB5 and measuring in the run-up direction). Only volumes of 1500 l/m or more 44 van 146



reach this location. It is expected that PW4 and PW8 give similar values as they both measure in the run-up direction. They are indeed quite similar except for released volumes larger than 4000 l/m, then PW8 in the paddle wheel gives lower values. This might be caused by the paddle wheel being released from the water surface if the flow thickness becomes too large. Another observation from Figure 3.11 is that PW5, which measured in the "wrong" direction for run-up, shows significant lower values than PW4. It must be concluded that paddle wheels indeed can only measure correctly in one direction. This conclusion is validated by the results in Figure 3.12 where PW6 (run-up direction) and PW7 (run-down direction) are compared. Although PW6 has not measured correctly over de full range, it is clear that PW7 is significantly lower than PW6. 7 PW4

6

PW5 down PW8

Flow velocity (m/s)

5 4 3 2 1 0 0

1000

2000

3000

4000

5000

6000


Figure 3.11 Three run-up velocity maxima at the same location on the slope. 7 PW6

6

PW7 down

Flow velocity (m/s)

5 4 3 2 1 0 0

1000

2000

3000

4000

5000

6000


Figure 3.12 Run-up velocity maxima for PW6 and PW7.

Figure 3.13 shows an overall view of all paddle wheels that measured run-up in the correct direction. Paddle wheels higher up the slope get only run-up if the released volume is large

45


enough and consequently the run-up comes high enough. Comparison of PW6 with PW4 and PW8 shows that they all give similar velocities, although PW 4 and PW8 are located higher on the slope. This agrees well with the analysis of real wave run-up, where it was concluded that the maximum velocity, or close to it, is present over a large part of the run-up area. Only in the last 15% of the run-up the velocity slows down (Van der Meer (2011)). Figure 3.14 validates this more or less, where flow velocities of 4000 l/m and more (which reach all instruments) are given against the location on the slope. This graph could be used for validation of theory (out of the scope of this work). 7 PW1

6

PW2 PW3

Flow velocity (m/s)

5

PW4 PW6

4

PW8

3 2 1 0 0

1000

2000

3000

4000

5000

6000


7.0

7.5

6.0

7.0

4000

5.0

6.5

4500

Height (m NAP)

Flow velocity (m/s)

Figure 3.13 All correctly measured run-up maxima at various locations.

5000 4.0

6.0

5500

5.5

3.0

2.0

5.0

slope

4.5

1.0

4.0

0.0 -12

-10

-8

-6

-4

-2

0

2

4

Horizontal distance (m) Figure 3.14 Trend of flow velocity along the slope.

46 van 146



0.6 SB1

Flow thickness (m)

0.5

SB5

0.4

0.3

0.2

0.1

0.0 0

1000

2000

3000

4000

5000

6000


Figure 3.15 Measured flow thickness during run-up.

Flow thicknesses have been measured by only two surf boards, one on the lower part of the slope (SB5) and one on the crest (SB1). The latter measures only flow thickness if the run-up exceeded the crest height, which was for released volumes of 4000 l/m and more. Figure 3.15 shows the increasing flow thickness with increasing released volume. Even on the crest a flow thickness of 0.15 m was reached for 5,500 l/m (with a flow velocity of 3.7 m/s).

3.3

Analysis of run-down measurements When the run-up has come to a stop the process of run-down will start. In reality most of the water starts to move down the slope at the same time. This is different for the wave overtopping simulator which has been used to simulate run-up. Figure 3.8 and Figure 3.9 clearly show that too much water is released from the simulator and that out flowing water meets the run-down half way the slope. In fact only the run-down above this "meeting point" is available for analysis. It has been concluded in section 3.2 that paddle wheels can indeed only measure correctly in one direction. There are only two paddle wheels that were mounted in a way to measure rundown: PW 5 and PW 7. Both are in or below the "meeting point" and therefore do not measure the real run-down. Flow thickness can be measured by the surfboards. But SB5 is in the area of the "meeting point", see Figure 3.9 and SB1 is on top of the crest. SB1 measures the flow that comes over the crest by wave overtopping (see Figure 3.15), but at the crest there is only overtopping, no run-down. The overall conclusion is that no correct measurements are available for run-down.

47


4

The cumulative overload method applied to wave run-up Tests with the wave overtopping simulator have resulted in a method to predict the strength of a grass dike by wave overtopping. This method is called the cumulative overload method and can be described by: (u2 – uc2) = D

(1)

where: D = damage number (m 2/s2) u = maximum front velocity in overtopping wave (m/s) uc = critical (depth averaged) velocity representing the strength of grass on clay (m/s) = summation over all overtopping waves with u > uc For wave overtopping the maximum front velocity u has a direct relationship with the overtopping wave volume. The distribution of overtopping wave volumes gives directly the distribution of maximum front velocities. On the seaward side waves break and then run up and down along the upper part of the seaward slope. The run-up process is more or less similar to the overtopping process, although in this case the front velocity of the up-rushing wave decreases with run-up height, where for the wave overtopping the velocity is more or less constant along the whole slope. It has been observed that it is the front of the wave (overtopping or up-rushing) which causes damage to grass slopes. This implies that run-down does not give significant loading to the grass, as run-down does not have a wave front. For the time being wave run-down is not considered as a main load, only the wave run-up. As the wave run-up front velocity depends on the actual run-up height, a possible cumulative overload depends also on the location considered on the slope. A location near the crest of a dike will have a lower cumulative overload than a location close to the water level. If the impact zone of a dike has been protected (block revetment, asphalt, etc.), then the transition from protected area to the grass slope may give the largest cumulative overload. For this analysis the vertical distance from the still water level to the location considered is described by z1. In order to look at a specific case a wave condition (wave height, wave period) has to be chosen for a certain geometry of the dike, together with a given water level. Or a location on the dike slope could be defined to where the 2%-run-up value should come, giving then the associated water level. With the fixed water level the distribution of run-up levels on the slope is known. In Van der Meer (2011) the development of the wave run-up simulator has been described. This report also gives an analysis on run-up velocities along a dike slope. It has been concluded that the maximum front velocity in an up-rushing wave is almost constant in the area starting 15% from the water level to 75% of the actual run-up level. Beyond this level the front velocity will quickly reduce to zero at the maximum run-up level for that specific wave. The main area to be considered, therefore, is the area where the maximum velocity is more or less constant. Assuming that z1 is always higher than the minimum level of 15% of the maximum run-up level, then all run-up levels higher than z1/0.75 will contribute to a front 49


velocity u which should be considered for the method of cumulative overload. In case the location z1 would be very close to the water level it is proposed to take z1 at 0.15 Ru2%. The 2%-wave run-up level depends on wave conditions and dike geometry. Formulae and programs are available (TAW report (2002), EurOtop (2007) and pc-overtopping) to calculate this 2%-run-up level for all kinds of structures. The wave run-up distribution has often been observed as a Rayleigh distribution. By assuming such a distribution and by knowing the 2%run-up level Ru2%, the run-up distribution is given by: PRu = exp[{-(-ln(0.02))0.5] Rux/Ru2%

(1)

or: Rux = Ru2% (ln(PRu)/ln(0.02)0.5

(2)

where: PRu = probability that Rux is exceeded Ru2% = 2% run-up level Rux = run-up level at location x along the slope (measured vertically with respect to swl) Van der Meer (2011) gives the relationship between the individual maximum run-up level and the maximum front velocity during that run-up: umax = cu (gRux)0.5

with cu = 1.0 en (cu) = 0.25

(3)

The large standard deviation of (cu) = 0.25 shows that the relationship (3) is more a scatter plot around the mean than a fixed relationship. For the time being equation (3) is considered without taking into account the standard deviation. If it has been proven that the cumulative overload method can indeed by applied for wave run-up, then the large scatter should also be introduced in the application. Above procedure gives the distribution of maximum front velocities along the slope and also for a fixed point z1. By applying a critical velocity uc only the velocities above this level have to be applied to calculate the cumulative overload for that specific location. As example the tested situation at Tholen will be used. The cross-section consists of a 1:4 down slope with a block revetment, a berm at +4.2 m NAP (NAP = chart datum) of asphalt and a grassed 1:3 upper slope with a crest at +6.8 m NAP. Although the berm in reality had a slope of 1:20, for this example a horizontal berm is assumed. The transition from protected to unprotected (= grass) is at this level of +4.2 m NAP. For test conditions a wave height is assumed of Hs = 2 m and Tp = 5.7 s (wave steepness sop = 0.04). For simplicity a straight 1:4 slope is assumed and not the bermed section of Tholen. This gives a 2%-run-up level of Ru2% = 4.0 m. The storm duration is taken at 6 hours, giving 4547 up-rushing waves (with Tm = 4.75 s). A Rayleigh distribution is assumed for the run-up levels. This distribution is given with respect to the still water level. The distribution of run-up levels with respect to the slope depends then on the still water level applied. In this example the still water level is assumed at +1.8 m NAP, this is 2.4 m below the berm. Figure 4.1 shows the run-up levels on a Rayleigh scale, which gives a straight line in the graph. It also shows that only 25% of the up-rushing waves reach the berm.

50 van 146



The figure gives the still water level, the berm level, the crest level and the point z 1 at the berm level. Also the 2% level is given by a vertical line. The solid line gives the full distribution of run-up levels. Only run-up levels higher than z1/0.75, where z1 is the berm level at +4.2 m NAP, will be taken into account. These are run-up levels larger than 2.4/0.75 + 1.8 = +5.0 m NAP. Each run-up level is given by a triangle. In total about 8% of the up-rushing waves reach this level. In total 9 run-up levels will exceed the crest level of +6.8 m NAP, giving wave overtopping over the crest.

Run-up level (NAP m)

8

Crest

7

6

5

z1

Berm = z1

4

3

swl

2

Crest level Transition to upper slope Run-up distribution Ru > z1/0.75

1

0

100

90

70

50

30 20

10

5

2

1 0.5

0.1

0.01

Probability of exceedance(%) Figure 4.1 Wave run-up distribution on the cross-section at Tholen.

51



Crest

7

7 6

6 5

z1

Berm = z1

5 4

4 Crest level

3

swl

2

3

Transition to upper slope Run-up distribution

2

Velocity umax (m/s)

8

8

um ax distribution

1

1

0

0 100

90

70

50

30 20

10

5

2

1 0.5

0.1

0.01

Probability of exceedance(%) Figure 4.2 Velocity distribution on the cross-section at Tholen.

Maximum velocities can be calculated by Equation 3 and the velocity distribution can also be given, see Figure 4.2. This velocity distribution is present at point z1. Only (maximum) velocities larger than 5.5 m/s reach this point. The cumulative overload for the six hours period of storm duration can now be calculated, depending on the critical velocity assumed. For uc = 5 m/s the cumulative overload becomes (u2 – uc2) = 4346 m 2/s2 and for uc = 6 m/s it becomes (u2 – uc2) = 803 m 2/s2. The first value is already larger than the cumulative overload for failure due to wave overtopping ( (u2 – uc2) = 3500 m 2/s2). At Tholen damage was clearly observed, but not failure meaning "through the clay layer and sand core visible". The test condition described here was not the severest one. Three less severe conditions (lower water levels) and two more severe conditions were tested, each lasting for 6 hours. It must be realized, however, that the pilot test on run-up did not simulate the velocities as given by Equation 3. The pilot test was governed by the run-up levels to be simulated, not by the velocities. But it is possible to analyze this pilot test and to calculate the cumulative overload for each test condition. First of all the relationship between released volume from the wave run-up or wave overtopping simulator and the velocity directly behind the release should be established. This is the released velocity on a horizontal crest (or berm). In the Factual Report (2011) on the Tholen tests a first analysis has been performed on measured velocities. From that report Figure 4.3 is taken, showing the measured velocities on a horizontal part, directly after release of the water. The red line gives the curve that was established for the Vecht dike where velocities were only measured on the gentle inner slope, not on the horizontal crest. It was concluded that velocities increase after they have passed the crest and that for the velocities on a horizontal part the velocities should be smaller. It was proposed to make a new fit.

52 van 146



This fit is given in Figure 4.3 by the black line. The velocities released from the wave overtopping simulator on a horizontal part can be described by: umax = 4.5 V0.30

(4)

10 9 8

Velocity (m/s)

7 6 5 4 Maximum velocity Tholen

3

Maximum velocity Belgium Vecht

2

New fit

1 0 0

1000

2000

3000

4000

5000

6000

Volume (l/m) Figure 4.3 Maximum velocities on a horizontal part, directly after release from the wave overtopping simulator.

It are these velocities that have to be used for point z1, at the transition from the berm to the 1:3 upper slope. The execution of the pilot test on run-up started with a low water level and this water level was increased after every six hours of storm duration. In total five storms (water levels) were simulated, where the test with the final and highest water level was stopped after four hours. The run-up levels on the slope for each test condition are given in Figure 4.4. The difference between water level and the berm was called x, which here is indicated as z1. Values of x or z1 were respectively applied of x = z1 = 4.5; 4.0; 3.2; 2.4 and 1.6 m. Figure 5 shows the run-up levels by a straight line. The actually simulated run-up levels are given by the triangle symbols and are sometimes different.

53


8

Crest


7

6

5

Berm 4

Crest level Transition to upper slope

3

Simulation x=4.5 m Simulation x=4.0 m

2

Simulation x=3.2 m Simulation x=2.4 m

1

Simulation x=1.6 m 0

100

90

70

50

30 20

10

5

2

1 0.5

0.1

0.01

Probability of exceedance(%) Figure 4.4 Actually simulated run-up levels at Tholen.

It needs a certain time to fill the simulator to a requested volume and to open and close the valve. For this reason a minimum volume, and therefore a minimum run-up level, has been defined. A number of these minimum volumes/run-up levels were released which were supposed to be similar to the actual number of run-up levels below this minimum. The horizontal part at the lower end in Figure 4.4 gives these minimum run-up levels. For the maximum required run-up levels sometimes the volumes required to produce them where larger than the actual capacity of the simulator. Then a number of these maximum releases were simulated, resulting in the horizontal parts at the upper end of the lines in Figure 4.4. Equation 4 gives the relationship between the released volume and the maximum velocity directly behind release, which should be more or less equal to the velocity at the transition to the upper slope at point z1. Figure 6 gives Equation 3 with the average and 80%, 90% and 95% confidence bands. It gives also the realized velocities during the pilot test. The simulated velocities are well within the confidence bands, but the lowest simulations are below the average trend. It means that observed damage during the pilot tests could have been a little larger in reality. For each test condition the cumulative overload value can be calculated, as well as the total cumulative overload. The result is the following:

x = z1 m 4.5 4.0 3.2 2.4 1.6

uc = 5 m/s Cum. (u2 – uc2) (u2 – uc2) 2 2 m /s m2/s2 0 0 15 15 180 195 1140 1335 3439 4774

54 van 146

2

m /s 0 0 25 248 976

2

uc = 6 m/s (u2 – uc2) m2/s2 0 0 25 273 1249

Cum. (u2 – uc2)



10

Average, Eq. 3 80% 90% 95% x=4.5 m x=4.0 m x=3.2 m x=2.4 m x=1.6 m 75% van Ru

Maximale velocity umax (m/s)

9 8 7 6 5 4 3 2 1 0 0

1

2

3

4

5

6

Run-up level above swl (m) Figure 4.5 Realized velocities with respect to required velocities.

The total cumulative overload for a critical velocity of uc = 5 m/s amounts to (u2 – uc2) = 4774 m 2/s2 and for uc = 6 m/s this becomes (u2 – uc2) = 1249 m2/s2. The test results were as follows: • •

•

Only small surface erosion was noticed for tests with x = z1 = 4.5 m and 4.0 m. A first small erosion hole at the transition from berm to upper slope, about 7 cm deep, was noticed after 2 hours with x = z1 = 3.2 m. After the full test there were three small erosion holes each about 7 cm deep. This damage is close to the criterion of "several open spots". Damage increased during the next tests. The test was stopped after 4 hours with x = z1 = 1.6 m. A cliff had been formed at three holes at the transition from berm to upper slope with a height of about 0.5 m. The upper slope had not yet failed, see Figure 4.6, but the test had to be terminated as problems with the side boards (large hydraulic loads) led to unwanted effects.

55


Figure 4.6 Final damage after the pilot run-up test.

For a critical velocity of uc = 5 m/s as well as 6 m/s "start of damage" or "several open spots" was noticed well below the values of (u2 – uc2) = 500 m 2/s2 and 1000 m 2/s2, which were determined from overtopping tests. But for the wave overtopping tests it was also concluded that these values had very large deviations. Sometimes start of damage occurred very far before failure, sometimes start of damage and failure were very close. As the area around the transition had not much vegetation, but only a good quality clay, some superficial erosion could be expected for fairly low hydraulic loads. The slope did not fail, however, there was still quite a reserve capacity. With a total cumulative overload of 1249 m 2/s2 for a critical velocity of uc = 6 m/s it is well below the level for failure of (u2 – uc2) = 3500 m2/s2. Above analysis leads to the following conclusions: The cumulative overload method can be applied for wave run-up, but the main difference with wave overtopping is that a specific location on the slope should be chosen. The cumulative overload reduces for locations higher up the slope, where the loads on the inner slope of a dike by wave overtopping are fairly constant along the slope. The velocities simulated during the pilot run-up tests are equal or lower than the required velocities. For a good simulation of the run-up process larger velocities should be simulated, but also different velocities for more or less similar run-up levels. This might be achieved by a different (more slender) shape of the simulator and by steering the opening (rotation) of the valve. Start of damage and "several open spots" were observed for fairly low hydraulic overloads, mainly as superficial erosion of the clay with minor vegetation. These damage levels for wave overtopping have always been unpredictable. The best predictable measure is "failure" with (u2 – uc2) = 3500 m 2/s2. Using uc = 6 m/s gives a total cumulative overload for the whole test of (u2 – uc2) = 1249 m 2/s2. This is well below the value for failure, which was also the description of the final status of the slope after testing. It should be noted, however, that the main damage was observed at the transition from berm to upper slope, which can be considered as a main point for damage, comparable to the transition from a slope to horizontal (toe) at wave overtopping. This analysis shows that the method of cumulative overload can be applied to wave runup. There is, however, not enough validation to conclude that the same cumulative

56 van 146



damage values have to be used as for wave overtopping to describe the behaviour of the slope. More testing on run-up is required to come to final conclusions, especially for conditions where indeed a transition from berm to upper slope is present, but also where this transition is not present.

57


5 5.1

Improvement of wave run-up simulation Introduction In 2011 a pilot test was performed at a dike at Tholen on wave run-up simulation on the seaward slope. For this event the wave overtopping simulator was used and the machine was placed on the berm of the dike. The steering of the wave run-up was focussed on simulating the correct wave run-up distribution along the upper slope of the dike. This pilot test gave valuable insight in how such a test can be improved to simulate the wave run-up process as realistically as possible. The following conclusions can be made: •

•

All the released water rushing up the slope comes back by run-down. This water cannot be released immediately down the slope as the simulator was placed only 0.2 m above the berm. Water concentrates in front of the simulator and gives large forces to the side walls. Actually, the test had to be terminated as the stability of the side walls became insufficient as well as leaking underneath the side walls led to unwanted side effects (erosion). A necessary improvement is to stabilize the side walls close to the simulator and to seal the side walls in this area. The wave overtopping simulator was designed to give large overtopping volumes with the correct velocity and flow thickness at the crest of the dike. This led to the shape of the present simulator. By using it for run-up simulation it appeared that the wave run-up along the slope is quite fast (within a few seconds) and starts to run down when the remaining water in the simulator is still released. This gives a "bump" of water on the slope, see Figure 5.1. Actually there is too much water in the simulator, in combination with a limited valve opening. The main improvement would be to change the shape of the simulator to a much slender one, preferably with the same size as the valve opening.

Figure 5.1 Run-down meeting up-rushing water during the wave run-up simulation process.

It is the second conclusion that has been elaborated further in this chapter. First the idea of a slender shape of simulator was checked on small scale. Secondly, the development of the wave impact simulator led to the opportunity to test the idea at full scale.

59


5.2

Small scale evaluation A small scale version of the wave run-up simulator is available for demonstration purposes. The scale of the model is 1:12.5 and the simulator model is placed on a (aluminum) model of a dike. The valve can be opened manually. This scale model has been used to verify the idea that a slender simulator would be better for run-up simulation. First the present model of the simulator was placed at the toe of the scale dike, see Figure 5.2. Water was then released onto the slope. Figure 5.2 shows clearly the same effect as in Figure 5.1, where up-rushing and down-rushing water meet each other along the slope.

Figure 5.2 Run-down meeting up-rushing water during the wave run-up simulation process.

A slender box was constructed which fitted to the interior of the present scale simulator and which had the same dimension in width as the opening of the valve (0.6 m in reality, 0.05 m on scale). Figure 5.3 shows the set-up and the interior of the box. Figure 5.4 shows the runup measurements at the slopes at Tholen as well as the measurements with the scale model (present shape and slender box).

Figure 5.3 Set-up with slender box and the interior of the box.

60 van 146



5.0 4.5

Wave run-up level (m)

4.0 3.5 3.0 2.5 2.0 Tholen 1:3 slope

1.5

Tholen 1:2.4 slope

1.0

Present scale model 1:2.8 slope Slender shape scale model 1:2.8 slope

0.5 0.0 0

1000

2000

3000

4000

5000

6000

Volume in simulator (l/m) Figure 5.4 Wave run-up levels measured at Tholen and with the scale model, including a slender shape.

The conclusions on some trials to simulate run-up were that: • • •

larger run-up was reached with much smaller volumes of water; see Figure 5.4; the effect of run-down meeting run-up was much smaller; the whole process of run-up and run-down seemed to be closer to reality.

The overall conclusion was that a slender shape of wave run-up simulator would improve the simulation of run-up significantly.

5.3

The wave impact simulator used for run-up simulation In the SBW-project "Residual strength" Deltares has asked Van der Meer Consulting bv and Van der Meer Innovation to develop a wave impact simulator. A pilot test has been performed by Infram, under guidance of Deltares. The wave impact simulator has a slender shape. It is 0.4 m wide and 2 m long. The ultimate water column to be released was about 1.2 m. As the development of the impact simulator included different valves and different release/guiding structures, the whole system was constructed and developed using a modular system. Each separate unit could be attached to another unit. Initially a butterfly valve as well as a falling valve were tested. The final simulator has two small falling valves which are integrated in the guiding structure. The impact simulator is not able to simulate correct run-up as the water falls down onto the slope. To be able to validate the idea of a slender shape of wave run-up simulator a special guiding structure was made. This structure guides the falling water to a 1:3 upward outflow direction (directly parallel to the slope, see Figure 5.5, left). Both the construction of the guiding structure and a pilot test were made on own account. Various modules were combined to create a maximum water column of 3.3 m high, see Figure 5.5, right. The butterfly valve, developed initially, was used in the set-up. Paddle wheels and two surf boards were installed to measure velocities and flow thicknesses.

61


Figure 5.5 Butterfly valve with guidance structure (left) en full set-up (right).

Up to a water column of 1.5 m the run-up was simulated quite well (reaching 4.5 m measured along the slope). Problems, however, occurred for larger water columns. Both the butterfly valve as well as the hydraulic cylinder to open and close the valve were designed for a water column of only 1.2 m. It appeared that de cylinder was not strong enough to open the valve fully in a few tenths of a second if the water column increased to 1.75 m or more. The opening process hampered, giving quickly release of the first water, but not release of all the water. In order to improve the situation a new and stronger cylinder was bought and installed. But also this cylinder, or at least the total system, was not able to improve the release of the water. Finally, it was decided to place the valve unit upside down. This would ease the work for the cylinder as it was asymmetrical designed. Also this system did not work as in this situation the valve could not fully be closed and the leaking was too much to give a sufficient water column. Actually, the system of butterfly valve and cylinder were not designed for the use with a much larger water column and for this reason it did not work. The test showed that a (very) quick release of the water is required to simulate a nice run-up process. Such a system should be water tight for large hydraulic pressures and should indeed open quickly. The initially developed fall valve is still available. This valve opens very quickly, but has a special system for closing and opening. It has to be closed by a hydraulic cylinder and should then be secured by a system of bolts. The hydraulic cylinder can then be released. The valve opens when the secured system is released. For the development of the impact simulator a 62 van 146



manually securing system (three bolts) has been developed. A manual system is not applicable for run-up simulation, but the system can fairly simple be improved by controlling the bolts hydraulically. This leads to the following recommendation: • • •

Strengthen the fall valve by ribs to cope with 3.5 m water pressure; Change the manually operated bolt system to a hydraulically operated system; Repeat the calibration test for wave run-up.

Although this simulator is only 2 m wide it might be a good alternative for simulation of wave run-up. If the systems proves to work properly, it is also possible to design a slender box to be placed inside the present wave run-up simulator (as in the scale model, see Figure 5.3).

63


6 Testing the grass quality: comparing the current prescribed methodology with a new method The method for the assessment of grass sod quality as prescribed in the Dutch Safety Assessment Regulation currently in force (V&W, 2007) is planned to be modified. The wave overtopping tests carried out on Dutch dikes in recent years have shown that dike grass sod quality as described by the method currently in force (V&W, 2007) does mostly not correlate well with the observed damage caused by wave overtopping (ENW 2012). A new method has been proposed in ENW 2012. The aim of the new method is that it is simple, robust and a better measure for the actual strength of a dike grassland than the current method as prescribed by the Dutch Safety Assessment Regulation currently in force (V&W, 2007). In the first half of April 2012, the field method prescribed for the third assessment round (V&W, 2007) was compared with the newly developed field method for the prolonged 3rd assessment round (Van der Meer et al., 2012). On four different locations (Figure 6.1), a total of seven plots immediately bordering wave overtopping test strips were sampled. The field tests were carried out in a paired setup, where both methods were applied to the same plots. Three locations (Tholen, Kattendijke and St Philipsland), with five plots in total, are located in the province of Zeeland. One location (Tielrode), with two plots sampled, is located in Belgium near Antwerp. Between 2008 and 2011, wave overtopping tests were carried out on the four locations. Photos of the fieldwork are presented in Appendix D.

Philipsland Tholen Kattendijk

Antwerpen Tielrode Figure 6.1 The four locations (light green dots) where the two field methods were compared.

6.1

Measurements prescribed for the third assessment round currently in force The method currently in force for the third assessment round is explained below. It is described in detail in appendix 8-1 ‘Quality of the grass sod’ of the Dutch Safety Assessment Regulation (V&W, 2007). For the study described here, it is important to mention that the Dutch Safety Assessment Regulation (V&W, 2007) does not prescribe to focus specifically on visually weak spots of dike grasslands. For the determination of the vegetation type (including estimation of the percentage cover), no specific directions are given for the selection of sampling sites. For the root density estimation as explained below, the Dutch Safety Assessment Regulation prescribes to take four samples with a gouge auger within a square of 5 x 5 m; further directions are not given.

65


6.1.1

Shoot cover (grid method) The Dutch Safety Assessment Regulation (V&W, 2007) mentions aboveground plant (shoot) cover as a quality indicator for dike grass sods (next to species composition, which is related to management type). A cover value of 70% is presented as a border value separating different quality classes. How shoot cover should be measured is not prescribed by the Dutch Safety Assessment Regulation. It may be estimated visually, but in order to ensure standardised measurements we used a grid in a 50 x 50 cm frame with 81 measuring points. Where necessary for easier measurement, the vegetation is cut back to a height of about 2 cm1. When estimating plant cover, no distinction is made between grasses and other herbaceous plants or forbs. However, mosses are not taken into account in the measurement as they have no proper roots and do not contribute to the strength of the sod. For every grid intersection (measuring point) a long needle is pricked perpendicularly into the sod, and it is determined whether there is 'plant contact' or 'ground contact'. The number of measuring points with 'plant contact', relative to the total number of measurement points, is a measure of the percentage sod cover1. In each sample plot, sod cover is measured on three spots within the sample plot. We carried out grid estimation measurements on three different heights (between crest and toe) of the dike slope; within each ‘slope height zone’, the grid frame is dropped on an arbitrary spot and the measurement is taken there. Afterwards, the percentage cover for the three separate measurements are averaged for the sample plot.

6.1.2

Root density Root density has to be estimated by the so-called ‘hand method’. A gouge auger is used to sample the top 20 cm of the grass sod, which is divided into eight layers of 2.5 cm thickness. In each layer, the number of root fragments of > 1 cm length is counted as a measure of root density. Based on this count, the quality of the sod root density is expressed in four categories: ‘very poor’, ‘poor’, ‘moderate’ and ‘good’ (see for example Figure 6.2). The Dutch Safety Assessment Regulation (V&W, 2007) prescribes to take four gouge auger samples within a square of 5 x 5 m. In this study, as in the root density tests at the time of the wave overtopping experiments, we took a sample near every corner of the 5 x 5 m square. This was done in a more or less arbitrary way, although we aimed to sample representative spots.

6.2

Method proposed for the prolonged 3rd assessment round Anticipating the prolonged 3rd assessment round, a new method for estimating grass sod quality is proposed in paragraph 6.4.2 of ENW 2012. The newly proposed method consists of a visual inspection of the sod openness, and an estimation of the sod strength (related to root density) by means of the so-called ‘spade method’. It is advised that the visual inspection be carried out in all instances. It is recommended that the spade method is carried out only in case of doubt about the sod quality as estimated by the visual inspection (ENW 2012).

6.2.1

Sod cover Based on visual inspection (ENW 2012) the grass sod can be divided into one of three categories: closed, open or fragmentary sod. The visual inspection has to be done within a 5 x 5 m square area. The new visual inspection method is different in that it explicitly demands to look for the presence of greater open spots and their potential presence has consequences for the quality verdict.

1

Cutting back of the shoots implies that the percentage shoot density rather than the percentage shoot cover is estimated by the grid method.

66 van 146



6.2.2

6.3 6.3.1

Root density (spade method) In case of doubt about the sod cover quality verdict as estimated by the visual inspection, a grass sod of 25 x 30 cm, with a thickness of about 7 cm, is to be cut loose using a spade. The sod strength (or root density) is divided into one of three categories: high root density, moderate root density or fragmentary root density (ENW 2012). According to the prescription, the spade method has to be done on a representative spot within a homogeneously looking part of the slope.

Results of comparing the methods Sod cover In Table 6.1, the sod cover is displayed as measured with the current and the new method. Sod cover as estimated in line with the method for the third assessment round (Dutch Safety Assessment Regulation currently in force) was higher than 70% for all locations and plots. This indicates adequate sod quality for the cover criterion. Application of the method proposed for the prolonged third assessment led to similar outcomes (highest sod quality class2) for all plots but one. In the case of this exception, it was difficult to assign the local situation to one of the three classes, so an intermediate score was given (‘open to closed’ sod). Interestingly, this plot did not have the lowest percentage cover as estimated with the grid frame. This will be further discussed in paragraph 6.4 below.

Sod

third

cover

estimation

Tholen

round

(grid rd

frame method)

Prolonged 3 round

% cover

(visual classification)

outer slope

91.8

closed

inner slope, no grazing

94.7

closed

inner slope, grazing

86.0

closed

Kattendijke

inner slope

93.0

open to closed

St Philipsland

inner slope

88.5

closed

Tielrode

outer slope ringdijk

86.4

closed

outer slope Durmedijk

95.5

closed

Table 6.1

Sod cover as estimated using the methods for the third and the prolonged third assessment round,

respectively.

Table 6.2 gives a more detailed view of the sod characteristics in the sampled locations. Neither the current nor the newly proposed method require recording of information about the sod on this detailed level. Still, we recorded this while in the field because it contributes to an impression of the actual management type and maintenance state of the dike grassland.

2

At Tholen outer slope, the horizontal grass stretch bordering the asphalt berm was visually of very poor (sparsely planted) quality and contained much stone debris in the root zone. However, this horizontal stretch has not been included in the current tests.

67


Detailed

third round

information

Location and plot

sod description

Tholen

outer slope

fairly short

95

85

30

5

10

-

10

inner slope, no

bumpy sod, connected

80

75

40

5

5

-

10

damaged due to trampling 95

70

25

3

1

artificial

9

hills /plot

# mole

used

fertilizer

litter

crop height

(non-moss)

round;

% other

sod

rd

% grasses

third and prolonged 3

% total

about grass

grazing inner slope, grazing

for wave overtopping tests Kattendijke

inner slope

open connected

85

70

60

10

10

-

25

St Philipsland

inner slope

bumpy, semi-open,

80

75

40

10

25

-

-

high moss cover Tielrode

outer slope ringdijk

bumpy sod

85

85

2

20

15

-

-

outer slope

closed

99

95

30

15

3

-

-

Durmedijk

Table 6.2

Details of the sod appearance as visually estimated in relation to the methods for the third and the

prolonged third assessment round, respectively.

6.3.2

Root density In the following figures, quality of the sod of the seven plots is shown according to the method for the third assessment round (Dutch Safety Assessment Regulation currently in force). To the right of the figures, the quality verdicts are displayed for both the current and the newly proposed spade method. The current method for the third assessment round only yielded the verdict ‘good’ for the three plots of the location Tholen. The Kattendijke plot yielded he verdict ‘moderate to good’, the Tielrode Durmedijk plot was scored as ‘moderate’, the St Philipsland site as ‘poor to moderate’ and the Tielrode ringdijk site as ‘poor’. Interestingly, the new spade method for the prolonged third assessment round led to a ‘high root density’ verdict for all seven plots.

68 van 146



third assessment round category root density: good

‘spade method’ prolonged third assessment round: ‘high’ root density

Figure 6.2 Tholen outer slope: sod quality as derived from the relation between depth and root density (n = 3 borings with gouge auger).



Figure 6.3 Tholen inner slope, no grazing: sod quality as derived from the relation between depth and root density (n = 3 borings with gouge auger).

69




Figure 6.4 Tholen inner slope, grazing: sod quality as derived from the relation between depth and root density (n = 3 borings with gouge auger).

third assessment round category root density: moderate to good


Figure 6.5 Kattendijke inner slope: sod quality as derived from the relation between depth and root density (n = 3 borings with gouge auger).

70 van 146



Photo 6.1

Grass sod at location Kattendijke as tested with the spade method; verdict ‘high root density’.

third assessment round category root density: poor to moderate


Figure 6.6 St Philipsland inner slope: sod quality as derived from the relation between depth and root density (n = 3 borings with gouge auger).

71


third assessment round category root density: poor


Figure 6.7 Tielrode outer slope ringdijk: sod quality as derived from the relation between depth and root density (n = 3 borings with gouge auger).

Photo 6.2

72 van 146

Grass sod at Tielrode ringdijk as tested with the spade method; verdict ‘high root density’.



third assessment category root density: moderate


Figure 6.8 Tielrode outer slope Durmedijk: sod quality as derived from the relation between depth and root density (n = 3 borings with gouge auger).

Photo 6.3

6.4 6.4.1

Grass sod at Tielrode Durmedijk as tested with the spade method; verdict ‘high root density’

Discussion Current versus new methodology In general, for the sod cover criterium the outcomes of the two methods corresponded very well. Only for one plot did the outcomes not match. The sod cover at Kattendijke obtained the score ‘good’ for the current third assessment method (grid frame) with a percentage cover of 93% (the third highest cover value measured). In contrast, the new visual method for the prolonged third assessment resulted only in the score ‘open to closed’. Visually, the sod cover near Kattendijke looked connected but open, and showed some larger open spots. Because these larger open spots are explicitly taken into account in the new method, this resulted in

73


the score ‘open to closed’ (see photos in Appendix D). With the grid frame method, three sampling sites are chosen in a more arbitrary way. In this case, none of the three sampling sites covered a larger open spot on the dike slope. This is why the sod cover score was relatively high for the current method (grid frame). Differences between the outcomes of the two methods were much more marked for the root density criterion. According to the new spade method for the prolonged third assessment round, all plots had a ‘closed’ sod, which was the best quality class. However, according to the current root density ‘hand method’ (gouge auger method, prescribed for the third assessment round), only three plots were classified as ‘good’. The discriminatory power of the current gouge auger method appeared to be larger and for the locations of St Philipsland and Tielrode, and this corresponds quite well with results of the wave overtopping test: these were relatively weak dikes. However, for the location of Tholen, another weak dike, the quality verdict was ‘good’ also when the gouge auger method was applied. The outcomes of the two methods might have been more similar, had all samples been taken consistently on the visually weakest spots.

6.4.2

Discrepancy between estimated sod strength and outcomes wave overtopping tests There was a discrepancy between the generally good sod quality indicated both by the current and in particular by the newly proposed methods, and the actual strength of the sampled locations as tested earlier during the wave overtopping experiments. Several explanations are possible. Depending on the location, the wave overtopping experiments had taken place 1 to almost 4 years before the measurements reported here were carried out. In the meantime, the grass sod may have been repaired or modified by adjusting the vegetation or management type. However, it is unlikely that this is the correct explanation for the observed outcomes. During the fieldwork in April 2012, the stretches of dike that had been newly sown after the wave overtopping tests were avoided (as far as any difference in vegetation type could be discerned). For that matter, one would expect a weaker sod in newly sown stretches. Also, the managers of the locations Tholen and Tielrode confirmed that no changes in vegetation type or management had taken place after the wave overtopping tests. On these locations, the discrepancy between strength estimated in April 2012 and the outcomes of the wave overtopping experiments was greatest, especially for the new method. Another possible explanation for the discrepancy found is the timing of the field measurements compared to the timing of the wave overtopping experiments. The fieldwork was done in the first half of April, while all wave overtopping tests took place in the winter halfyear. Based on a yearround research, Schaffers et al. (2010) advise not to measure sod strength after 1 March, since after that date the vegetation usually becomes active to such a degree that the strength of the sod increases significantly3. Thus, this seasonal effect may actually be an important cause for the observed discrepancy. If we subtract about 0.5 quality unit from every measurement, based on the seasonal difference observed by Schaffers et al. (2010), the verdict for most plots would be one quality class lower. At the time of the wave overtopping tests, sod strength estimations were carried out using the ‘hand method’ (gouge auger) prescribed by the Dutch Safety Assessment Regulation currently in force. At Tholen the verdict was moderate to poor. On the other hand, at Kattendijke and St Philipsland the verdict

3

Maximum difference on a year-round basis was 0.75 quality categories (cf. Figure 6.2); difference between six ‘summer months’ and six ‘winter months’ (a more robust measure of difference) average was 0.36 quality categories (Schaffers et al., 2010).

74 van 146



was ‘good’ at the time, which was in fact better than measured in April 2012. At Tielrode the ‘hand method’ was not applied, however, using the spade method just previous to the over topping tests lead to the sod description (translated from Dutch) ‘well rooted, however, loose and not maintaining its shape’ for the ‘Ringdijk’ and ‘very fixed shaped and not possible to tear by hand’ for the ‘Durmedijk’. Interestingly, as photos 26 and 27 in Appendix D show for the location of Tielrode ringdijk, testing the spade method on a site with stinging nettle (Urtica dioica, an unwanted rough growth species) yielded a rather fragmentary sod, even in the first half of April. A third possible cause of the observed discrepancy is that the estimated quality would have been less good had we focused sampling (for both methods) on the visually weakest spots. It is possible that this has contributed to observed discrepancy with the actual dike strength as indicated by the wave overtopping tests. Yet, this cannot explain the cases of discrepancy between the outcomes of both root density methods.

6.4.3

Where to take samples, and how many? We assume that exposure of dike grassland to wave overtopping can happen on any place along a given stretch of sea dike. Based on the observed results and what is known from the wave overtopping tests about the actual strength of the dike grasslands tested, we therefore advise to select the visually weakest spots for assessing the sod quality and root density. After all, one weak spot could cause a dike to fail during a wave overtopping event. Up to now, both at the time of the wave overtopping tests and during the present field work (April 2012), it has not been the rule to measure at the visually weakest spots. Rather, in line with the Dutch Safety Assessment Regulation currently in force, the assessments have tended to focus on the more ‘representative’ (or ‘average’) stretches of dike grassland. The newly proposed spade method has the advantage of representing a better measure for the actual strength of the top layer of a grass sod than the currently prescribed gouge auger ‘hand method’. One sample per test site (sample unit) could therefore be enough to estimate the strength of the grass sod, provided the test is carried out on a visually weak spot and that some time is invested in finding such a spot. For the rest, the Dutch Safety Assessment Regulation currently in force advises to divide stretches of dike into sufficiently small sample units to minimise the risk of overlooking discontinuities etc. (V&W, 2007). Again, visual observation is important not only within a test site (sample unit) but also in overlooking the whole dike stretch when selecting the individual sampling units.

75


Photo 6.4

6.4.4

Shoot distance Tholen, showing an open spot of approximately 15 cm across.

Suggestions for improvement of the new method and its description As the current investigation showed at the location Tielrode ringdijk (photos 26 and 27 of Appendix D), rough growth species are unwanted on dikes, as they usually cause sods to be relatively open, with little cohesion because of suboptimal root densities. This is in line with earlier observations on other dikes. We therefore propose to start the new methodology by rejecting dikes with either significant presence of rough growth species (e.g. thistles, Urtica dioica, Heracleum sphondylion, Fallopia spp., Anthriscus sylvestris) or high cover of moss species. The latter do not contribute to sod strength because they lack proper roots. Proper maintenance and management is important in this respect; for example, if significant amounts of plant litter remain present on the dike after mowing, this can cause open spots where thistles and nettles can establish easily. The newly proposed method mentions, for the visual estimation of the sod openness, an optimal shoot distance of < 0.1 m is suggested as a norm. Based on past observations on dikes, we still consider 0.1 m quite a large inter-shoot distance: even the shoots of a stinging nettle (Urtica dioica, an unwanted rough growth species) are often less than 0.1 m apart. When the current description of the new methodology (ENW 2012) going to be made available to managers of dikes for assessment purposes, it is important that the text is sufficiently readable and can readily be understood without ambiguities. Illustrations may then be helpful, e.g. (1) illustrating schematically what a sod belonging to each of the three quality classes (sod cover, visual method) could look like; or (2) illustrating how the spade method is to be applied. Also, using unit scales that fit optimally to the practical setting during testing (e.g. centimetres instead of metres) may make the description of the sod quality method just a bit quicker and easier to read.

6.5

Conclusion and recommendations The method proposed for the prolonged third assessment round to assess the sod quality (both the visual estimation of sod openness and the spade method to test sod strength) is a much faster method than the current method used for the third assessment round. With some modifications (explicitly prescribe focus on visually weakest spots for sampling; rejecting

76 van 146



dikes with significant presence of rough growth species or high moss cover) and practical textual streamlining, it appears to be a promising method that could be well applied by managers of Dutch dikes. It is however important that assessment of sod quality is done in the winter halfyear, also when applying the new method. Schaffers et al. (2010) found that the period 1 October until 1 March is suitable. Ideally, this field test should be repeated in the winter halfyear at least for the weak dike locations as established by the wave overtopping tests, in order to ensure that the discriminatory power is indeed great enough and not all sites end up in the class ‘closed sod’ when applying the visual sod openness estimation. The new method seems well suited for assessing the primary function of dike grassland: resistance against damage following load events. However, since it does not take floristic composition into account, it is less suited (in contrast to the current methodology) for assessing ecological value or the quality of the overall management and maintenance state of dike grasslands. It should be noted that the research reported here is valid only for the larger area in which the wave overtopping tests were carried out, e.g. the Netherlands and Belgium. The results cannot be translated to very different parts of the world, with different species or climatic conditions.

77


7

7.1

Direct measurement of critical tensile stress in a grass cover layer Description of the problem One of the parameters of importance for the strength of a grass covering under wave load (whether or not due to overtopping) is the force required to pull out a part of 0.15 / 0.15 m 2 of the grass covering. The size of 0,15 / 0,15 m 2 is based on observations in the field where it was found that the loose pollen were about that size. In the context of designing a numerical destruction model for a grass covering, it is necessary to know how great the force must be to pull out a sod of this size. The aim of the present research is double, namely: 1. The development of a model set up in order to establish necessary critical tensile stress. 2. Testing and optimizing the test set up on its suitability.

7.2

The model set up The “grass sod puller” consists of the following main components: 1. 2. 3. 4.

The portal in which the hydraulic cylinder is mounted. The cylinder with which the sod is brought under tension. The hydraulic hand pump to bring pressure into the cylinder, and The pin grab with which the force delivered by the cylinder is brought on the sod of 0,15/0,15 m 2.

The pressure in the cylinder is measured by means of a manometer. The model set up is illustrated in the photograph below.

79


Photo 7.1

Portal with cylinder and pin grab (behind the portal the cutting mole is visible)

The aluminium portal has a height of 0,70 m and has a surface of 0,70 x 0,50 m 2. The cylinder is connected to the portal in a hinged way. It is a double side pull cylinder with the following characteristics: Diameter of the bar is 2,4 cm, Diameter of the plunger 4 cm, Stroke 30 cm, Surface on the pulling side of the cylinder 7,66 cm 2. Next to the cylinder some space is available for a manometer. For the present setup three different manometers with different reaches were bought: one of 0-16 bar, one of 0-25 bar and one of 0-60 bar. In this way the most suitable read out can be obtained. A pin grab has been developed to transfer the cylinder force to the sod. This pin grab is connected to the cylinder in a hinged way. The developed and tested grab is of a type where the pins are pushed through the sod. If desired other grab types can also be connected to the portal. The pin grab consists of a structure in which 1 to 7 RVS pins (round 8 mm) can be used. The pin can be brought into the grass sod at a maximum depth of 8 cm. In the photograph below the pin grab is illustrated in detail.

80 van 146



Photo 7.2

The placed pin grab (with 4 pins)

Photo 7.3

The pin grab connected to the cylinder

To place the pin grab at least at two sides the soil has to be removed. For standardisation of the removal of the soil a cutting mole has been made with which up to a depth of 8 cm the soil at both sides can be cut of and removed. The distance between the cutting surfaces is 15 cm and the length of the cut is 18 cm which equals the length of the pin grab. The hart to hart distance of the two most outside pins is 15 cm. Photograph below shows the cutting mole.

81


Photo 7.4

The cutting mole

By means of an equalizer the two parts of the pin grab are connected to each other and to the pulling cylinder. One can choose whether the last mentioned connection is done in a hinged way or stiff. The necessary force was generated by a double, hand controlled, hydraulic pump with the following dimensions 0,60 x 0,23 x 0,32 m 3. The tubes have a length of 1,5 m lang.

7.3

The tests Two test series have been performed with the above described grass sod puller. The first test series have been performed on June 1, 2012 and was purely meant to get a first impression of its suitability. The test series have been performed on a not defined horizontal turf. For these preliminary tests the grab was connected to the cylinder hinged way. By enlarging the force the sod appeared to break through at its most weak side resulting in overturning of the grab. Resulting in a non-equal distribution of the force over the sod. This problem has been solved by connecting the grab stiffly tot the cylinder. Further it appeared during these preliminary test series that manometers with different reaches were needed. Resulting in the purchase of two additional manometers. These preliminary test series gave a first impression of the force necessary to pull out a sod that has been cut loose at two sides, the necessary force to do so was in the order of 0,7 kN. It also appeared that 4 pins were sufficient to perform the tests and that in case of a depth of 6 cm at which the pins were brought into the sod breaking surface was situated under the pins, see photograph below. On June 5 2012 the second test series have been performed. These tests were performed at the dike of the Waddenzee near the connection point with the Slachtedijk. This is the same location where in an earlier state the test with the wave impact generator have been performed. Here the test were performed on the slope of the dike where the quality of the 82 van 146



grass sod is well known from the test with the wave impact generator. A total of 5 tests have been performed.

Number of loose sides Number of pins Depth of pins Loading

Table 7.1

Test 1 4

Test 2 2

Test 3 2

Test 4 2

Test 5 2

4

4

1

4

4

4 cm

4 cm

5 cm

4 cm

4 cm

gradually ascending

gradually ascending

gradually ascending

fast ascending tractive force

In steps ascending tractive force

Characteristics of the tests

Some results: Test 1: Maximum force necessary to pull out the sod 0,85 kN Test 2: Maximum force necessary to pull out the sod 1,10 kN Test 3: At a tractive force of 0.73 kN the pin was pulled through the sod. Test 4: The resulting maximum force was the same as that of test 2 1,10 kN. Test 5: At a tractive force of 0,91 kN the sod started to get loose but the process of loosening stopped in order to proceed at a tractive force of 1,10 kN. On the basis of the experience gained during test preparation and operation the following conclusions can be drawn: 1. By means of the developed model setup the tests on direct measurement of critical tensile stress can be performed in a well-controlled way. 2. The ascending time for the load has hardly any influence on the final result. 3. The difference in the required tractive force in a compare between an on two sides loose sod and an on two sides loose sod is in the order of 0,25 kN (this is ca. 25 % of the eventually necessary tensile force). 4. In case of a “good” qualified sod on a clayey subsoil a depth of 4 cm to place the pins into the sod is sufficient to run the tests in proper way. 5. The time it took to perform one test was in the order of 15 minutes.

83


8 Erosion around objects and on transitions 8.1

Introduction Van der Meer et al. (2010) discussed the hypothesis of the cumulative overload method, which is a measure for the damage (or erosion) level on the inner slope of the dike. The damage number is determined by considering the number of waves and the flow velocity of the largest wave volumes and from observations after the hydraulic measurements. This chapter describes in outline the extension of this methodology for trees/piles on the inner dike slopes and transitions from the inner dike slope to the horizontal berm. The overload method is defined as: N

U 2 U c2

D

(1)

i 1

Where Uc is the critical depth-averaged flow velocity (m/s), U depth-averaged flow velocity (m/s), D damage parameter (m 2/s2) and N number of largest waves (-). Based on test results the following damage criteria are defined:

initial damage

D 500 m 2 /s 2

(2)

damage at various locations 500 m 2 /s 2

D 1500 m 2 /s 2

(3)

failure of dike slope

D 3500 m 2 /s 2

(4)

It should be noted that the value of D > 3500 for the failure of the dike slope is the most reliable one. The overload method is here extended by an amplification factor m: N M

U

2

U c2

D

(5)

i 1

The value of

m

will be estimated according to two approaches:

Theoretically using known methods that have an anology with the considered aspect (section 8.2) Empirically using observed results of overtopping tests (section 8.3). In section 8.4 some conclusions and recommendations will be presented.

8.2 8.2.1

Theoretical approach Erosion near trees The flow pattern (Figure 8.1) around a (bridge) pier can be divided into four characteristics features, namely the bow wave (or surface roller), the down flow, the horseshoe vortex and the wake zone with the shed vortices (or vortex street). The flow decelerates as it approaches

85


the pier coming to rest at the face of the pier. Near the surface, the deceleration is greatest, and decreases downwards. The down flow reaches a maximum just below the bed level. The development of the scour hole around the pier also gives rise to a lee eddy, known as the horseshoe vortex. The horseshoe vortex is effective in transporting particles and extends downstream, past sides of the pier. The flow separates at the sides of the pier leading to the development of shed vortices in the interface between the flow and the wake.

Figure 8.1 Characteristic flow zones around bridge pier

For trees, the following assumptions are made Prototype tests at Dutch dikes have shown that the erosion process of grass covers is negligible at slender trees (diameter is less than 15 cm); At relative thick trees whose trunk thickness varies from 0.15 m to 1 m (e.g. tree on the Vechtdijk) limited erosion was observed after a series of storms so these situations are further considered (Figure 8.2 and Figure 8.3); Erosion resistance of grass near trees and the erosion resistance of grass on the inner dike slope are assumed equal. In practice, due to shadow effects the grass strength near trees is less; For laminar flow conditions, the flow velocity alongside the object is two times as large as the upstream flow velocity (potential theories). When the flow is turbulent and supercritical M < 2 (Figure 8.4); Downstream of thick trees there will be no directly mixing of water, as practical tests have shown that there is no water flowed (Figure 8.5). Consequently, the load of the accelerated water along the tree is decisive with respect to the load of the downstream turbulence.

86 van 146



Figure 8.2 Limited erosion at tree; width of test section is 4 m

Figure 8.3 Restricted erosion at tree; width of test section is 4 m

To model the influence of trees on the erosion process an amplication factor is defined as the ratio between the flow velocity at the tree and the flow velocity upstream of the tree; The application of the force balance is effective only if equilibrium situations are considered. Because the erosion process close to the tree is not yet in equilibrium no analytical solution can be deduced due to acceleration terms in the balance of forces.

87


Figure 8.4 LEFT Sub-critical flow at pile, RIGHT Supercritical flow at pile

Figure 8.5 downstream of tree (there is no mixing downstream of the tree)

By using the continuity equation

U

M

U

b

(6)

Where M is the amplification factor (-), b width of trees/piers (m) and width of the test section (m). The amplification factor representing the increase of the flow velocity can be estimated by 88 van 146



M

(7)

b

A first approximation yields for tree) M

b

= 4 m (width of the test location) and b = 0.5 m (width of the

4 1.15 4 0.5

(8)

This value of M agrees with the experimental value for round piers as proposed by Melville (1975), see Figure 8.6: m

= Upier / U = 1.2

(9)

Where Upier is the depth-averaged flow velocity along the tree/pier (m/s).

Figure 8.6 Flow intensities at bridge pier (Melville 1975)

Since the amplification factor also depends on the shape of the pier a more general relation can be given (see also Hoffmans and Verheij 1997) M

1.2 K shape

(10)

Where Kshape is the shape factor of an obstacle (-). When m = 1.0 (no obstacle), then D 1000 m2/s2 (Eq. 3) at several locations erosion occurs which is acceptable since the residual strength is not yet applied. However, if m = 1.5 due to obstacles then D 3000 m 2/s2 (Table 8.1) and so significantly more erosion is expected. Assuming that m = 2 dike failure may occur (D 5500 m2/s2). It is concluded on the above approach that the amplification factor is in the range of 1.1 to 1.5.

m

for relatively large trees

89


V ( /m)

U (m/s)

200

2.89

0.40

2.83

5.42

11.11

17.47

200

2.89

0.40

2.83

5.42

11.11

17.47

M

=1

M

= 1.2

M

= 1.4

M

= 1.5

M

= 1.6

M

= 1.8

M

= 2.0

200

2.89

0.40

2.83

5.42

11.11

17.47

400

3.66

3.31

10.28

14.17

18.32

27.44

37.63

400

3.66

3.31

10.28

14.17

18.32

27.44

37.63

400

3.66

600

4.20

1.66

3.31

10.28

14.17

18.32

27.44

37.63

9.44

18.62

23.74

29.22

41.23

54.65

600

4.20

1.66

9.44

18.62

23.74

29.22

41.23

54.65

600

4.20

1.66

9.44

18.62

23.74

29.22

41.23

54.65

800

4.63

5.48

14.93

26.10

32.33

38.99

53.60

69.92

800

4.63

5.48

14.93

26.10

32.33

38.99

53.60

69.92

800

4.63

5.48

14.93

26.10

32.33

38.99

53.60

69.92

800

4.63

5.48

14.93

26.10

32.33

38.99

53.60

69.92

1000

5.00

9.00

20.00

33.00

40.25

48.00

65.00

84.00

1000

5.00

9.00

20.00

33,00

40.25

48.00

65.00

84.00

1000

5.00

9.00

20.00

33.00

40.25

48.00

65.00

84.00

200

2.89

0.40

2.83

5.42

11.11

17.47

1000

5.00

9.00

20.00

33.00

40.25

48.00

65.00

84.00

1000

5.00

9.00

20.00

33.00

40.25

48.00

65.00

84.00

1000

5.00

9.00

20.00

33.00

40.25

48.00

65.00

84.00

2000

6.33

24.05

41.68

62.50

74.12

86.54

113.77

144.21

2000

6.33

24.05

41.68

62.50

74.12

86.54

113.77

144.21

2000

6.33

24.05

41.68

62.50

74.12

86.54

113.77

144.21

3000

7.26

36.77

59.99

87.43

102.73

119.09

154.97

195.08

3000

7.26

36.77

59.99

87.43

102.73

119.09

154.97

195.08

3000

7.26

36.77

59.99

87.43

102.73

119.09

154.97

195.08

4000

8.01

48.17

76.41

109.78

128.39

148.28

191.91

240.69

4000

8.01

48.17

76.41

109.78

128.39

148.28

191.91

240.69

4000

8.01

48.17

76.41

109.78

128.39

148.28

191.91

240.69

5000

8.64

58.69

91.55

130.38

152.04

175.20

225.98

282.74

5000

8.64

58.69

91.55

130.38

152.04

175.20

225.98

282.74

5000

8.64

58.69

91.55

130.38

152.04

175.20

225.98

282.74

5500

8.93

63.69

98.75

140.19

163.30

188.00

242.19

302.75

5500

8.93

63.69

98.75

140.19

163.30

188.00

242.19

302.75

5500

8.93

63.69

98.75

140.19

163.30

188.00

242.19

302.75

1000

5.00

9.00

20.00

33.00

40.25

48.00

65.00

84.00

2000

6.33

24.05

41.68

62.50

74.12

86.54

113.77

144.21

3000

7.26

36.77

59.99

87.43

102.73

119.09

154.97

195.08

4000

8.01

48.17

76.41

109.78

128.39

148.28

191.91

240.69

5000

8.64

58.69

91.55

130.38

152,04

175.20

225.98

282.74

Damage number (m2/s2)

944

1609

2405

2855

3337

4393

5574

Table 8.1

Experimental values Vechtdijk V (wave volume ( /m), U and Uc = 4 m/s and computational results of the

overload method (

90 van 146

M

and D) (see also Eq. 5 in this section)



8.2.2

Erosion at a transition of a slope to a horizontal berm The situation at a transition can be compared with a jet that normally occur because of flow under, through or over hydraulic structures. In general, a jet lifts soil and transports it downstream of the impacted area. The jet impact area is transformed into an energy dissipater and a scour hole is formed (Figure 8.7). For 2D flow conditions, the equilibrium scour depth zm,e (m) owing to jets is proportional to (e.g. Hoffmans 2012): Zm,e = f(U0.5) As

m

(11)

is related to U (see also Eq. 9 in this section) the amplification factor can be given by

M

z2V z2 H

(12)

Where, z2H is the equilibrium scour depth related to 2D-H (m), and z2V equilibrium scour depth related to 2D-V (m). Also,

zm , e

z2V

c2V

qU sin g

(13)

zm , e

z2 H

c2 H

qU g

(14)

and

where is the angle of inner dike slope (o), q discharge (m 2/s), c2H strength parameter for two dimensional horizontal jet scour (-) and c2V strength parameter for two dimensional vertical jet scour (-). Hence, M

c2V c2 H

sin

(15)

If the range 0.1 mm < d50 < 1 mm is considered, where d50 is the mean particle diameter (m), then the mean values of c2H and c2V measure c2H = 2.5 and c2V = 5 (Hoffmans and Verheij 1997 and Hoffmans 2012). Substituting these values in Eq. 15 with = 30o yields

M

5 sin 30o 2.5

1.2

(16)

Hence, the best guess value of the amplification factor varies from 1 to 1.5. If the inner dike slope has no significant damage then more erosion could occur near the toe (see also Figure 8.7). Values for D for various values of m are shown in Table 1.

91


Figure 8.7 Scour hole at the toe of the dike; sub soil consists of gravel (Kattendijke)

8.3

Determining M from test results In order to apply the cumulative overload method for transitions and objects the formula has been extended with a factor M. N M

U

2

U c2

D

(17)

i 1

In fact this factor increases the actual velocity or load compared to the velocity over the slope without transition or object. Theoretical considerations have been described in section 8.1. Another way to try to establish the factor M is to look at the test results that have been gathered during recent years of investigation. If one can find comparable damage situations for a slope and also for an object or transition, then two damage values D are available for further analysis. This section describes this search and analysis. The Technical Report on Safety assessment of grass covers on Dikes (ENW, 2012) includes an appendix with all pictures of damages observed from testing with the Wave Overtopping Simulator from 2007 to 2012. It also gives a table with all damages, describing the cumulative overload D for various critical velocities uc, and describing grass and soil quality. It is this table that is used to find comparable damage situations for a slope and for a transition or object. The table has not been repeated here and one is referred to ENW, 2012. The first tests in 2007 at Delfzijl were only focussed on the slope and the toe (transition) was strengthened and was not part of the investigation. From these tests it became clear that small objects or initially made damages, smaller than 0.15 m by 0.15 m, did not increase the damage, where this was the case for larger initially made damages. For these tests there are no comparable situations for the slope compared to a transition or object. At the Boonweg four sections were tested. Two sections did not fail after full testing and two sections failed at the end of the test. Start of damage (first small hole) and failure were very

92 van 146



close. The two sections that did not fail also had no initial damage. For the two sections that failed also start of damage was recorded. Three of the four sections showed also initial damage to the toe (no failure) and one section did not show damage at all. In fact the behaviour of the slope with respect to initial damage is well comparable to the behaviour of the toe. The following cumulative overload values D were observed, using a critical velocity of uc = 6.3 m/s, which has been established as the correct critical velocity of this dike.

Section 1. Section 2. Section 3. Section 4.

Slope No damage D = 3426 m2/s2. No damage D = 3426 m2/s2. Initial damage D = 1598 m2/s2. Initial damage D = 3426 m2/s2.

Toe Initial damage D = 610 m2/s2. Initial damage D = 1963 m2/s2. Initial damage D = 1232 m2/s2. No damage D = 3426 m2/s2.

Of course there is quite some scatter, but this can in a certain way be reduced by taking the average values: Initial damage for the slope starts at D = 2878 m 2/s2 and initial damage for the toe at D = 1808 m2/s2, which is at a 63% lower overload level. At St Philipsland both initial damage and failure were observed for the slope as well as for the toe. The critical velocity for this dike was established at uc = 5 m/s. The overload values D were as follows: Initial damage slope D = 1855 m2/s2. Initial damage toe D = 990 m 2/s2 (53%). Failure slope D = 5385 m2/s2. Failure toe D = 2965 m 2/s2 (55%). At Kattendijke there was very significant damage to the toe area (see Figure 8.11), but this area consisted of a loose gravel road which is completely different material than grass on clay. No comparison can be made from these tests. The Afsluitdijk was quite special as initial damage to the grass for slope as well as toe occurred very early and sometimes large areas of grass were ripped off. But the under lying clay with roots was very erosion resistant and both slope and toe did not fail. It is not possible to find comparable damages for these tests. At the Vechtdijk a dike transition was tested as well as a tree. The critical velocity for this dike was established at uc = 4 m/s. Several damages on the slope were observed for D = 847 m 2s2 and start of undermining of the grass-tiles on sand started at D = 1296 m 2s2, which is more or less similar (around D = 1000 m 2s2). The transition failed for D = 5926 m 2s2, which is significant more than the used value for a slope (D = 3500 m 2s2), but at that level the actual slope had not failed. Although it was quite close to it. The only conclusion that can be drawn is that for this dike with a critical velocity of uc = 4 m/s the transition of grass-tiles on a sandbed had more or less the same strength as the slope itself. Although the validation is limited, one could say that failure of a hard transition founded on sand might occur for D = 3500 m2s2, using a critical velocity of uc = 4 m/s. More validation would be welcome. Comparison of the observations for the test on the tree at the Vechtdijk gives the following overall view: Initial damage slope D = 997 m 2s2 Several open spots slope D = 2665 m 2s2 Non-failure slope D = 5926 m 2s2

Initial damage tree D = 997 m 2s2 Significant erosion roots D = 2665 m 2s2 Failure of the tree D = 5061 m 2s2

93


The damage development for the slope was quite similar as for the tree. The main difference is that the tree failed before the slope did, but due to this fact it was not possible to test the slope to failure. The overall conclusion is that the tree indeed failed (just?) before the slope, but the difference is not significant. At the other two sections of the Vechtdijk only the slope was tested, no transition or object. The Durmedijk at Tielrode showed no damage to slope and toe, but was also tested for limited conditions. The GOG-section (also known as Ringdijk) was not strong at all and one cannot not give a critical velocity to this section. The grass had hardly any strength, which makes it impossible to compare slope and toe transition. This was more or less similar for the tests at Tholen, where also a proper grass cover was lacking. The only exception might be section 4. Here the slope failed for D = 3299 m 2s2, using a critical velocity of uc = 4 m/s, and the toe failed earlier for D = 992 m 2s2. Above analysis of test results shows that there are no quantitative results for objects like a dike transition or a tree. The conclusion on the dike transition might be that for hard structures founded on a sand bed one should use a critical velocity of uc = 4 m/s and an overload value of D = 3500m 2s2 for failure. The area around a significant tree failed only marginally earlier than the slope itself. Quantitative results, however, were obtained for the Boonweg, St Philipsland and Tholen, where for comparable damages different overload values were found for slope and toe. These results have been analyzed further by using equation 17. For the given results everything is know, except the value of M. First the example of the Boonweg will be analyzed where initial damage for the slope started at D = 2878 m 2/s2 and initial damage for the toe at D = 1808 m 2/s2. The damage at the toe was observed after testing with 6 hours of 0.1; 1; 10; 30 and 50 l/s per m and 1.4 houres with 75 l/s per m overtopping (assuming Hs = 2 m and Tp = 5.7 s). The critical velocity of this dike was uc = 6.3 m/s. The question is now: what M is required to increase the overload damage for the same test duration and same number of overtopping waves to a value of D = 2878 m 2/s2 which is similar to initial damage of the slope. By trial and error a value of M = 1.05 was found, giving D = 2800 m 2/s2. So, only a M of 1.05 is required to increase the overload value by more than 50%. The case of St Philipsland with: failure slope D = 5385 m 2/s2 and failure toe D = 2965 m 2/s2 (55%), for a critical velocity of uc = 5 m/s led to M = 1.09. The case of Tholen with: failure slope for D = 3299 m 2s2, using a critical velocity of uc = 4 m/s, and toe failure for D = 992 m 2s2 (30%) led to M = 1.21. These values of M are quite close to 1. The effect of using M is not only that the hydraulic load increases for each wave considered, but also that significantly more overtopping waves are taken into account. An overtopping wave with a front velocity of u = 3.9 m/s is not taken into account with a critical velocity of uc = 4 m/s, but it is if M = 1.2 (1.2 x 3.9 > 4). It means that M = 1.1 doubles more or less the overload value of D, where a factor of M almost triples it.

94 van 146



The overall conclusion is that for a transition like a toe the factor M will be close to 1 and probably between M = 1.05 and 1.25. A "safe" value of M = 2 will completely under estimate the strength of a transition. ENW, 2012, gives tables of cumulative damage for all kind of hydraulic conditions and overtopping discharges. One hour overtopping with 50 l/s per m (Hs = 2 m) gives D = 156 m 2s2 for uc = 6.3 m/s and D = 605 m 2s2 for uc = 5 m/s. This is about a factor four difference in overload value. For an overtopping discharge of 75 l/s per m the values become respectively D = 366 m 2s2 and D = 1153 m 2s2, which is about a factor of three. Changing critical velocities for these overtopping discharges from uc = 5 m/s to uc = 4 m/s gives changes in overload values D of a factor of 2 or 3. Changing in critical velocity looks more or less similar to using a M-factor of 1.1 to 1.25. This example is only given to get some feeling for different M-factors and critical velocities. The theory assumes that the critical velocity does not change for a given slope, but that the hydraulic load increases.

95


9 Conclusions The objective of chapter 2 of present report is: •

• •


The conclusions that can be reached from this chapter are: 1

The theory of steady state flow is taken for validation. This theory assumes steady state over time, where wave overtopping is intermittent. Wave overtopping can be described by a more or less triangular record in time for flow velocity and flow thickness. The maximum values for these flow velocities and thickness are compared with the theory. The length of the record is described by the overtopping duration. Flow velocity and thickness are a function of slope angle, friction and initial conditions. As slope angle and initial conditions are given, the only variable is the friction factor f. The objective was to find a good fit for this correction factor and to judge whether found trends were indeed predicted well by theory. First predictions by various values of f show that small values (f < 0.05) give an increase of velocity along a steep slope and large values (f > 0.05) show a decrease. As measured velocities increased along the slope the correct friction factor should be well below f = 0.05.

2

The wave overtopping simulator was used to simulate the overtopping waves over the crest and landward side of a dike. This simulator was designed to give a certain flow velocity on the crest for a given released (overtopping) volume. Each released volume gives a certain (maximum) flow velocity, flow thickness and overtopping duration, which is assumed to be similar to real overtopping waves. Due to the measurements at Tholen and in Belgium the relationships between released overtopping volume and flow velocity and thickness could be established a few meters behind the release of the water, on a horizontal crest. It is also apparent that for large overtopping volumes the flow thickness increases more than linearly, giving a kind of "bump" in the record. It might well be that for these large overtopping volumes flow velocity and thickness directly after release are not yet according to real overtopping waves.

3

Flow velocities increase on the first part of a steep slope, but further down the slope these velocities reduce again. This cannot be predicted by steady state flow theory, where the velocity can only reach a certain equilibrium. The overtopping durations increased along the slope and that might well explain why velocities decreased at the lower part of the slope. Except for this effect all trends of flow velocity and thickness, for both the measurements at Tholen and at the Vechtdike, were fairly well calculated by a friction factor of f=0.01. This is the friction factor to be used for real grass on a slope in steady state flow calculations. This theory can quite well predict (maximum) flow velocities and thicknesses along a slope by wave overtopping, except for the lowest part on the slope where effects of increasing overtopping duration may play a role.

97


Chapter 3 described the analysis of measured run-up parameters. The following conclusions can be drawn: 4

The present wave overtopping simulator has been used for wave run-up simulation. It appeared that wave run-up levels up to 3.5 m (measured vertically) could be simulated. The relative crest freeboard during the wave run-up test was lower than this level and for the largest released volume the run-up created an overtopping wave at the crest with a thickness of 0.15 m and a maximum velocity of 4 m/s.

5

The present (bulky) shape of the simulator contains too much water to simulate the whole wave run-up process correctly. The down-rushing wave, after having reached its highest point on the slope, meets the still outflowing and up-rushing water, which creates a "bump" of water on the slope. It is also for this reason that correct wave rundown measurements were not achieved as all these measurement devices were in this "bump" area.

6

Paddle wheels were mounted to measure up-rush or down-rush. Comparison of measurements showed that these paddle wheels can indeed only measure velocity correctly in one direction.

Chapter 4 applied the cumulative overload method to wave run-up. The following conclusions were reached: 7

The cumulative overload method can be applied for wave run-up, but the main difference with wave overtopping is that a specific location on the slope should be chosen. The cumulative overload reduces for locations higher up the slope, where the loads on the inner slope of a dike by wave overtopping are fairly constant along the slope.

8

The velocities simulated during the pilot run-up tests are equal or lower than the required velocities. For a good simulation of the run-up process larger velocities should be simulated, but also different velocities for more or less similar run-up levels. This might be achieved by a different (more slender) shape of the simulator and by steering the opening (rotation) of the valve.

9

Start of damage and "several open spots" were observed for fairly low hydraulic overloads, mainly as superficial erosion of the clay with minor vegetation. These damage levels for wave overtopping have always been unpredictable.

10

The best predictable measure is "failure" with (u2 – uc2) = 3500 m 2/s2. Using uc = 6 m/s gives a total cumulative overload for the whole test of (u2 – uc2) = 1249 m 2/s2. This is well below the value for failure, which was also the description of the final status of the slope after testing. It should be noted, however, that the main damage was observed at the transition from berm to upper slope, which can be considered as a main point for damage, comparable to the transition from a slope to horizontal (toe) at wave overtopping.

11

This analysis shows that the method of cumulative overload can be applied to wave runup. There is, however, not enough validation to conclude that the same cumulative damage values have to be used as for wave overtopping to describe the behaviour of the slope. More testing on run-up is required to come to final conclusions, specially for

98 van 146



conditions where indeed a transition from berm to upper slope is present, but also where this transition is not present. Chapter 5 described the attempts to come to improvements of the wave run-up simulation. The following conclusions were drawn: 12

The main conclusion is that a slender shape of wave run-up simulator will improve the simulation of run-up significantly. This could, however, not yet be validated by a test with the newly developed wave impact simulator, which was modified to simulate run-up. The wave impact simulator was not designed for a water pressure of 3.5 m water column and showed too much leakage to create good up-rushing waves. The following recommendations were made: • • •

13

Strengthen the fall valve by ribs to cope with 3.5 m water pressure; Change the manually operated bolt system to a hydraulically operated system; Repeat the calibration test for wave run-up.

Although this impact simulator is only 2 m wide it might be a good alternative for simulation of wave run-up. If the systems proves to work properly, it is also possible to design a slender box to be placed inside the present wave run-up simulator (as in the scale model, see Figure 5.3).

Chapter 6 evaluates and compares the old and new method to describe the sod quality. The following conclusions were drawn: 14

The method proposed for the prolonged third assessment round to assess the sod quality (both the visual estimation of sod openness and the spade method to test sod strength) is a much faster method than the current method used for the third assessment round. With some modifications (explicitly prescribe focus on visually weakest spots for sampling; rejecting dikes with significant presence of rough growth species or high moss cover) and practical textual streamlining, it appears to be a promising method that could be well applied by managers of Dutch dikes.

15

It is however important that assessment of sod quality is done in the winter halfyear, also when applying the new method. Schaffers et al. (2010) found that the period 1 October until 1 March is suitable. Ideally, this field test should be repeated in the winter halfyear at least for the weak dike locations as established by the wave overtopping tests, in order to ensure that the discriminatory power is indeed great enough and not all sites end up in the class ‘closed sod’ when applying the visual sod openness estimation.

16

The new method seems well suited for assessing the primary function of dike grassland: resistance against damage following load events. However, since it does not take floristic composition into account, it is less suited (in contrast to the current methodology) for assessing ecological value or the quality of the overall management and maintenance state of dike grasslands.

17

It should be noted that the research reported here is valid only for the larger area in which the wave overtopping tests were carried out, e.g. the Netherlands and Belgium. The results cannot be translated to very different parts of the world, with different species or climatic conditions.

99


Chapter 7 describes the testing devise to determine the pull out strength of a piece or sod and the first test results. The following conclusions were drawn: 18 19 20

21 22

By means of the developed model setup the tests on direct measurement of critical tensile stress can be performed in a well-controlled way. The ascending time for the load has hardly any influence on the final result. The difference in the required tractive force in a compare between an on two sides loose sod and an on two sides loose sod is in the order of 0,25 kN (this is ca. 25 % of the eventually necessary tensile force). In case of a “good” qualified sod on a clayey subsoil a depth of 4 cm to place the pins into the sod is sufficient to run the tests in proper way. The time it took to perform one test was in the order of 15 minutes.

Chapter 8 considers the effects of objects and transitions on and in the slope. The effect is modeled by adding an amplification factor to the load parameter in the erosion model; the maximum depth averaged flow velocity during a wave overtopping event. The required amplification factor was estimated both in a theoretical way and a practical way. The following conclusions can be drawn: 23 •

•

24 •

•

Theoretical approach: The amplification factor m for relatively large trees is according to a theoretical approach about 1.2. Test results for a tree does not allow to give an estimate because the observed damage hardly differ from a regular slope. The area around a significant tree failed only marginally earlier than the slope itself. Based on all information, it is recommended to apply a value in the range of m = 1.1 to 1.5. For a transition the theoretical approach results in a value of 1.2. This is in accordance with the values derived of test results: M = 1.05 to 1.21. Probably the factor is in the range of 1.05 to 1.3. Practical approach: The M-factor can also be found from test results if comparable damages can be found for the slope as well as for the transition or object. This analysis of test results showed that there are no quantitative results for objects like a dike transition or a tree. The conclusion on the dike transition might be that for hard structures founded on a sand bed one should use a critical velocity of uc = 4 m/s and an overload value of D = 3500m 2s2 for failure. The area around a significant tree failed only marginally earlier than the slope itself. The overall conclusion for a transition like a toe (from slope to horizontal) is that the factor M will be close to 1 and probably between M = 1.05 and 1.25. Three examples give respectively values of M = 1.05; 1.09 and 1.21. A "safe" value of M = 2 will completely under estimate the strength of a transition.

100 van 146



10 References ENW, 2012. Technisch Rapport Toetsen Grasbekledingen op Dijken. ENW-report, version May 2012. Factual Report, 2011. Bakker, J.J., R.J.C. Mom, G.J. Steendam and J.W. van der Meer. Factual Report. Overslagproeven en oploopproef Tholen. Infram report 10i092. Van der Meer, J.W., 2011. The Wave Run-up Simulator. Idea, necessity, theoretical background and design. Report Van der Meer Consulting vdm11355, version 1.1. Available at www.vandermeerconsulting.nl Schüttrumpf, H. and H.Oumeraci (2005): Layer thicknesses and velocities of wave overtopping flow at seadike. Journal of Coastal Engineering 52 (2005) pp 473-495 Schaffers, A.P., Frissel, J.Y., Adrichem, M.H.C. van & Huiskes, H.P.J. 2010. Seizoensverloop in de doorworteling van dijkgrasland. VTV-toetsing buiten het winterseizoen nader bekeken. Alterra report 2014, URL: http://content.alterra.wur.nl/Webdocs/PDFFiles/Alterrarapporten/AlterraRapport2014.pdf

V&W, 2007. Voorschrift Toetsen op Veiligheid Primaire waterkeringen [Dutch Safety Assessment Regulation]. Ministerie van Verkeer en Waterstaat. URL: http://www.helpdeskwater.nl/publish/pages/27611/vtv2006.pdf Hoffmans, G. and H.J. Verheij (1997): Scour manual. Balkema Publishers

101


A

Theory of steady state flow on a slope by Schüttrumpf (2001)


A-1


B

Measured flow velocities and thicknesses for individual overtopping wave volumes; wave overtopping at Tholen.


B-1


B-2




B-3


B-4




B-5


B-6




B-7


B-8




B-9


B-10




B-11


B-12




B-13


C

Measured flow velocities and thicknesses for individual wave run-up and run-down at Tholen.


C-1


C-2




C-3


C-4




C-5


C-6




C-7


C-8




C-9


C-10




C-11


D

Photo’s grass quality tests Photo Attachment Tholen:

Photo 1: Tholeninside grazing, ‘closed’ sod cover with some open spots.

Photo 2: Tholen inside grazing, damaged by GOS. Sod cover on the GOS spot is ‘open’.


D-1


Photo 3: Tholen inside no grazing, ‘çlosed’ sod cover.

Photo 4: Tholen inside no grazing, bumpy sod.

D-2



Photo 5: Tholen, open spot with shoot in the middle.

Photo 6: Tholen, shoot distance to the next shoot?


D-3


Photo 7: Tholen, ‘closed’ sod cover

Photo 8: Tholen, open spot, shoot distance?

D-4



Kattendijke

Photo 9: Kattendijke, ‘closed’ sod cover

Photo 10: Kattendijke, sod cover with some open spots.


D-5


Photo 11: Kattendijke, grass sod, ‘high’ root density.

Photo 12: Kattendijke, grass sod, ‘high’ root density.

D-6



Photo 13: Kattendijke, grass sod back on its place.

Photo 14: Kattendijke, sod cover with open spot.


D-7


Photo 15: Kattendijke, sod cover ‘closed’

Photo 16: Kattendijke, grid method for sod cover.

D-8



Philipsland

Photo 17: Philipsland, grasssod

Photo 18: Philipsland, grass sod with ‘high’ root density.


D-9


Photo 19: Philipsland,‘closed’ sod cover

Photo 20: Philipsland, taking a grass sod.

D-10



Tielrode

Photo 21: Tielroderingdijk, bumpy sod cover

Photo 22: Tielroderingdijk, taking a grass sod.


D-11


Photo 23: Tielroderingdijk, grass sod with ‘high’ root density.

Photo 24: Tielroderingdijk, place where we took the grass sod.

D-12



Photo 25: Tielroderingdijk, grass sod.

Photo 26: Tielroderingdijk, grass sod taken on a place with stinging nettle; fragmentary root density.


D-13


Photo 27Tielroderingdijk, grass sod taken on a place with stinging nettle; fragmentary root density, the grass sod falls apart.

Photo 28: Tielrodedurmedijk, ‘closed’ sod cover

D-14



Photo 29: Tielrodedurmedijk, grass sod with ‘high’ root density.

Photo 30: Tielrodedurmedijk, grass sod with ‘high’ root density.


D-15