Effect of the Concrete Density on the Stability of Xbloc Armour Units

MASTER OF SCIENCE THESIS

Effect of the concrete density on the stability of Xbloc armour units

B.N.M. van Zwicht September 2009

Delft University of Technology Faculty of Civil Engineering and Geosciences Delta Marine Consultants Section Hydraulic Engineering Department Coastal Engineering

Effect of the concrete density on the stability of Xbloc armour units

List of trademarks used in this report

− Accropode is a registered trademark of Sograh Consultants, France; − Core-Loc is a registered trademark of US Army Corps of Engineers, USA; − Delta Marine Consultants is a registered trade name of BAM Infraconsult bv, the Netherlands; − Xbloc is a registered trademark of Delta Marine Consultants, the Netherlands.

The use of trademarks in any publication of Delft University of Technology does not imply any endorsement or disapproval of this product by the University.

Effect of the concrete density on the stability of Xbloc armour units

Student B.N.M. van Zwicht Smitsteeg 6A 2611 BH Delft Tel: +31 (0)6 47802924 Mail: [email protected] Studnr: 1092642

MSc thesis Committee Prof. Dr. Ir. M.J.F. Stive Delft University of Technology. Prof. Dr. Ir. W.S.J. Uijttewaal Delft University of Technology. Ir. H.J. Verhagen Delft University of Technology. Ir. P.B. Bakker Delta Marine Consultants.

Delta Marine Consultants H. J. Nederhorststraat 1 P.O. Box 268 2800 AG Gouda The Netherlands

Delft University of Technology Faculty of Civil Engineering en Geosciences Section Hydraulic Engineering Stevinweg 1 P.O. Box 5048 2600 GA Delft The Netherlands

Minelco B.V. Vlasweg 19, Harbour M164 P.O. Box 16 4780 AA Moerdijk

The Netherlands

II MSc thesis

Preface

This is the final report of my Master of Science thesis which I performed to obtain the degree Master of Science in the field of Coastal Engineering at Delft University of Technology. For this thesis research have been done on the influence of the concrete specific weight on the hydraulic stability of Xbloc armour units.

The research has been carried out at the coastal department of Delta Marine Consultant (DMC) in Gouda. Physical model tests have been done at the hydraulic flume of Delta Marine Consultants in Utrecht. I would like to thank DMC for making it possible to fulfil my thesis. I also like to thank Minelco b.v. for their participation in the research by supplying the concrete Xbloc model blocks for the physical model tests.

During my thesis I received great support from a number of people whom I want to thank. First of all I would like to thank the members of my thesis committee for their contribution to my thesis, Professor Dr. Ir. M.J.F. Stive, Professor Dr. Ir. W.S.J. Uijttewaal and Ir. H.J. Verhagen from Delft University of Technology and Ir. P.B. Bakker from Delta Marine Consultants.

Secondly I would like to thank the members of the coastal department of DMC for their support and expertise on breakwater design. I specially would like to thank Erik ten Oever and Markus Muttray for their input in the discussions we had and their expertise on Xbloc-breakwater design with which they supported me greatly.

Finally I would like to thank my parents for their unconditional support throughout my entire study and my friends for their supports especially during the last few months of my thesis.

Bart van Zwicht Delft, September 2009

B.N.M. van Zwicht III

Effect of the concrete density on the stability of Xbloc armour units

IV MSc thesis

Summary

This thesis has been performed to obtain the degree Master of Science in the field of Coastal Engineering at Delft University of Technology. The influence of the specific weight of concrete on the hydraulic stability of Xbloc armour layers has been investigated.

Since 2001 Delta Marine Consultants has developed a new innovative interlocking single layer armour unit, the Xbloc armour unit. Xbloc has a high structural and hydraulic stability. Improvements over other single layer units were made by improving the fabrication and placement of the units and reducing the concrete demand while retaining the hydraulic and structural stability.

The hydraulic stability of the Xbloc armour unit as well as other complex interlocking shapes is expressed by the stability number (Ns).

Hs NKs == with Δ=ρaw/1ρ − ΔDn K is dimensionless and in general a function of the structural parameters like slope angle, porosity and breaker type as well as damage progression and storm duration. In the armour layer design with Xbloc armour units no damage is allowed, therefore a constant design value of K = 2.77 is prescribed as the current design criterion. To determine the hydraulic stability of Xbloc several model test have been performed. The stability number has however not been validated for the influence of the specific weight.

The stability number is based on the assumption of dominance of lift, drag and gravity forces. If other forces have significant influence on the stability, which is the case for complex interlocking armour units like the XBloc, the power of one for the relative density (Δ) in the stability number might change. The hydraulic stability of single layer interlocking armour units described with the stability number is therefore investigated. The research question for this thesis is:

What is the influence of the specific weight on the stability of single layer interlocking armour units and can the stability of single layer interlocking armour units be described as a function of the dimensionless stability parameter Ns ?

2-D Physical model tests have been done at the hydraulic flume of Delta Marine Consultants in Utrecht to determine the influence of the concrete specific weight on the hydraulic stability of Xbloc armour units. On the basis of the findings in the literature study it can be expected that the effect of the specific weight on the stability of Xbloc armour layer will be a function of the slope angle. The model tests were performed using concrete densities of 2102, 2465 and 2915 kg/m3 and slope angles of 3:4, 2:3 and 1:2. The size of the model block was held constant for all concrete densities to eliminate the influence of the according structural parameters on the hydraulic stability.

It is concluded from the model tests that the influence of the specific weight on the hydraulic stability of Xbloc armour layers is not correctly described by the stability number (Ns). The assumed dominance of lift and drag forces stabilised by the submerged weight on which the stability number is based, does not hold because other forces have significant influence the stability. With an increasing slope angle, the inertia, friction and interlocking force become more dominant. For Xbloc

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Effect of the concrete density on the stability of Xbloc armour units

interlocking is the dominant stability mechanism. Although interlocking is the most characterising stabilisation mechanism there is a partial contribution of gravity and friction to the stability as well. The amount of contribution of each mechanism to the total stability depends on the armour units shape, placement (contact points) and slope angle. All stability mechanisms (gravity, friction and interlocking) depend on the weight of the element and are a function of the slope. Therefore the influence of the specific weight is always a function of the slope angle and depends on the type of element. The influence of the specific weight in relation to stability number can be concluded from the model test:

− The stability number underestimates the effect of the specific weight for single layer interlocking armour units for a slope of 2:3 and steeper. The underestimation increases for

steeper slope angles. The expected start of damage (Hs ≥ 120% Hd) and failure (Hs ≥ 150%

Hd), with Hd is the design wave height, is underestimated for heavy concrete elements and overestimates for the light concrete elements.

− For a slope of 1:2 the stability number tends to overestimate the effect of the heavy concrete element, where as the normal and light concrete element are in close resemblance

with each other and the expected start of damage (Hs ≥ 120% Hd) and failure (Hs ≥ 150%

Hd) .

The power of one of the relative density (Δ) value in the stability formula determines the influence of the relative density on the stability and is a function of the slope angle. The hydraulic stability of Xbloc armour units can therefore be described as a function of the slope angle and relative density by:

H =⋅Kf(,)α Δ with: ff(,)ααΔ= () Δg()α Dn This results in a general formula for the hydraulic stability for Xbloc armour units:

H =⋅Kf()α Δg()α Dn Definitions for the functions of the slope angle have been found by fitting the general formula to the data found by the hydraulic model testing. This has result in the following stability formula for Xbloc armour layers:

H = 0.55⋅+ (0.8cot(α )2 2) 5.4(tanα )3.3 Dn Δ

An additional finding is that the damage of Xbloc armour layers develops gradually after initial damage has occurred. This is in contrast to what was found by Van der Meer for Accropode single layer interlocking armour units.

Finally the damage curves of the proposed Xbloc stability formula Ns;x are presented in the graph below. The figure shows that proposed Xbloc stability formula Ns;x describes the influence of the specific weight of concrete correctly because almost all damage curves lie within the 80% confidence band.

VI MSc thesis

Summary

NewNew stability stability criterion creterion Ns;x = 0.55 1,40

1,20

1,00

Damage progression 0,80 80% conf. band

Nod 80% conf. band 0,60

0,40

0,20

0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25)

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Effect of the concrete density on the stability of Xbloc armour units

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Contents

PREFACE...... III SUMMARY ...... V CONTENTS...... IX LIST OF SYMBOLS ...... XIII CHAPTER 1 INTRODUCTION...... 1

1.1 RUBBLE MOUND BREAKWATERS ...... 1 1.2 PROBLEM DESCRIPTION ...... 2 1.3 PROBLEM DEFINITION ...... 4 1.4 APPROACH ...... 5 CHAPTER 2 ARMOUR LAYER DESIGN ...... 7

2.1 DESIGN RUBBLE MOUND BREAKWATER ...... 7 2.1.1 Main dimensions ...... 7 2.1.2 Failure modes...... 8 2.2 WAVE - STRUCTURE INTERACTION ...... 9 2.2.1 Flow on armour layer ...... 9 2.2.2 Flow forces on armour layer elements...... 11 2.2.3 Stability mechanism ...... 13 2.3 HYDRAULIC STABILITY ARMOUR LAYER ...... 14

2.3.1 Stability Number Ns ...... 14 2.3.2 Stability design formula ...... 15

2.3.3 Validity Ns ...... 16 2.4 INFLUENCE SPECIFIC WEIGHT ON HYDRAULIC STABILITY...... 17 2.4.1 Study on rock stability...... 17 2.4.2 Study on concrete armour units ...... 19 2.4.3 Research single layer interlocking armour units ...... 20 CHAPTER 3 ARMOUR LAYER DESIGN WITH XBLOC...... 21

3.1 MAIN DIMENSIONS ...... 21 3.2 HYDRAULIC STABILITY...... 21 3.2.1 Slope angle...... 22 3.2.2 Armour layer placement...... 22 3.2.3 Surf similarity parameter ...... 24 3.2.4 Wave steepness...... 24 CHAPTER 4 EXPERIMENT SETUP...... 25

4.1 SCALING ...... 25 4.1.1 Prototype and model similitude...... 25 4.1.2 Froude scaling ...... 26 4.1.3 Reynolds scaling...... 26 4.1.4 Scale effects...... 26 4.2 TEST FACILITY ...... 28

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4.3 WAVE GENERATION ...... 29 4.3.1 Energy density spectrum...... 29 4.3.2 Wave Reflection Analyses ...... 29 4.4 TEST PROGRAMME...... 31 4.4.1 Structural test parameters ...... 31 4.4.2 Hydraulic test parameters ...... 32 4.5 MODEL LAYOUT ...... 34 4.5.1 Main dimensions...... 34 4.5.2 Armour layer...... 35 4.5.3 Core ...... 39 4.5.4 Under layer...... 40 4.6 DAMAGE DEFINITION AND RECORDING...... 41 4.6.1 Damage Definition...... 41 4.6.2 Damage recording...... 42 CHAPTER 5 OBSERVATIONS...... 43

5.1 DESIGN WAVE HEIGHT...... 43 5.2 GENERAL OBSERVATIONS...... 44 5.2.1 Placement density ...... 44 5.2.2 Settlements...... 45 5.2.3 Failure Mechanisms ...... 47 5.3 SLOPE 3:4...... 50 5.3.1 Wave structure interactions...... 50 5.3.2 Failure mechanisms...... 50 5.3.3 Xbloc displacement out of armour layer...... 51 5.4 SLOPE 2:3...... 52 5.4.1 Wave structure interactions...... 52 5.4.2 Failure mechanisms...... 52 5.4.3 Xbloc displacement out of armour layer...... 52 5.5 SLOPE 1:2...... 53 5.5.1 Wave structure interactions...... 53 5.5.2 Failure mechanisms...... 53 5.5.3 Xbloc displacement out of armour layer...... 54 5.6 DISCUSSION...... 57 5.6.1 Relative placement density and settlements...... 57 5.6.2 Hydraulic stability ...... 58 CHAPTER 6 ANALYSIS EXPERIMENT RESULTS...... 61

6.1 ANALYSIS TESTS SERIES ...... 61 6.1.1 Test series slope 3:4...... 61 6.1.2 Test series slope 2:3...... 64 6.1.3 Test series slope 1:2...... 66 6.2 INFLUENCE SLOPE ANGLE ...... 68 6.3 INFLUENCE SPECIFIC WEIGHT ...... 70 6.4 DISCUSSION TEST RESULTS...... 72 6.4.1 Summary of the test results ...... 72 6.4.2 Additional findings ...... 73 6.5 DESIGN FORMULA XBLOC ARMOUR UNITS ...... 74

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Contents

6.5.1 General Xbloc stability formula...... 74 6.5.2 Influence specific weight ...... 75 6.5.3 Influence slope angle...... 77 6.5.4 Formulation design equation Xbloc armour layers ...... 80 6.5.5 Damage curves with new Xbloc design formula ...... 80 6.5.6 Damage development...... 84 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS ...... 87

7.1 CONCLUSIONS...... 87 7.1.1 Main conclusions ...... 87 7.1.2 Additional conclusions:...... 88 7.2 RECOMMENDATIONS...... 90 REFERENCES...... 93 LIST OF FIGURES ...... 95 LIST OF TABLES ...... 98 APPENDIX A CONCRETE ARMOUR UNITS...... 99 APPENDIX B STRUCTURAL INTEGRITY ARMOUR UNITS ...... 101 APPENDIX C SETUP HYDRAULIC MODEL TESTS...... 103 APPENDIX D CONSTRUCTION GABIONS...... 104 APPENDIX E WEIGHT DISTRIBUTION XBLOC MODEL BLOCKS...... 105 APPENDIX F SPECIFIC WEIGHT XBLOC MODEL BLOCKS ...... 108 APPENDIX G START AND END PHOTOS...... 111 APPENDIX H RELATIVE PLACEMENT DENSITIES ...... 127 APPENDIX I SETTLEMENTS ...... 129 APPENDIX J TEST RESULTS ...... 132 APPENDIX K INFLUENCE SPECIFIC WEIGHT ON THE HYDRAULIC STABILITY OF XBLOC ARMOUR UNITS...... 141 APPENDIX L FAILURE MECHANISM ...... 143

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Effect of the concrete density on the stability of Xbloc armour units

XII MSc thesis

List of Symbols

Symbol Description Unit

A effective surface area armour unit [m2] B buoyancy of block in Iribarren formula [N]

CD empirical drag coefficient -

CI empirical inertia coefficient -

CL empirical lift coefficient - D armour unit height [m]

Dn nominal diameter of the armour unit [m]

Dn50 median nominal diameter [m] E variance density [m²/Hz] E(f) variance density spectrum [m²/Hz] f frequency [Hz] fpeak peak frequency [Hz]

FD drag force [N]

FF resultant flow force [N]

FG gravitational force

FI inertia force [N]

FL lift force [N]

Fr Froude number - g acceleration of gravity [m/s2] H wave height [m]

Hd design wave height [m]

Hs significant wave height [m]

Hm0 significant wave height from the spectrum analysis [m] K stability parameter -

Kd Hudson stability parameter - L characteristic length [m]

Lop deep water wave length of the peak period [m]

Lx average horizontal length [m]

Ly average vertical length [m] m0 zeroth-order moment of the variance density spectrum E(f) - N Iribarren stability parameter - N number of waves (Van der Meer formula (2.3)) -

Nd percentage of displaced units out of a reference area -

NL length scale ratio -

Ng gravitational scale ratio -

NU velocity scale ratio -

Nν kinematic scale ratio -

Ns Stability number (Hs/∆ Dn) -

Ns;x Xbloc stability number -

Nod number of displaced units out of the armour layer within a strip with the -

width of the nominal diameter (Dn)

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Effect of the concrete density on the stability of Xbloc armour units

Symbol Description Unit

Nx number of Xbloc in the x direction -

Ny number of Xbloc in the y direction - P permeability parameter - Re Reynolds number -

S damage level, average erosion area per Dn50 unit of breakwater length -

Sop fictitious wave steepness (Hs/Lop) - SWL Still Water Line - t time [s]

Tp peak period wave field [s] U flow velocity [m/s] v flow velocity [m/s] W weight of block [N]

W50 nominal weight [N] X distance between two wave gauges [m] α slope angle degrees α scaling parameter (Pierson-Moskowitz) - γ scaling parameter (JONSWAP peak-enhancement factor) -

∆ relative density (ρa/ ρw -1) - μ friction coefficient - ν kinematical viscosity [m2/s] ξ surf similarity parameter or Iribarren number - 3 ρa specific weight of a armour unit [kg/m ] 3 ρr specific weight of rock [kg/m ] 3 ρw specific weight of water [kg/m ] σ scaling parameter (JONSWAP peak-enhancement factor) -

XIV MSc thesis

Chapter 1 Introduction

Breakwaters are important elements in coastal systems. Their main function is to reduce the wave impact on the lee side of the structure by reflection of the waves back into the sea and by dissipation of the wave energy. In this way breakwaters provide sheltering of harbour basins and harbour entrances. Other applications are the prevention or reduction of siltation of navigation channels, protection of valuable habitats and the protection against beach erosion.

There are many different types of breakwaters which are commonly divided into categories according to their structural features. This thesis is about rubble mound breakwaters.

1.1 Rubble mound breakwaters

A rubble mound breakwater has a core of loose material, mostly quarry run, armoured by a layer of larger elements. Filter layers are applied to prevent the finer material being washed out. The armour layer of the breakwater can be constructed either with rock or with concrete elements depending on the local wave conditions and available construction material. The function of the units in the armour layer is twofold. They must maintain the integrity of the construction by preventing the material below the armour layer from washing away under severe wave attack and dissipate the wave energy in order to reduce wave run-up, reflection and overtopping. Dissipation of wave energy occurs due to wave breaking on the slope of the breakwater and by turbulent porous flow. To do so the armour units must remain hydraulically stable. Hydraulic stability is the resistance of the armour layer against the flow forces caused by the wave structure interaction. The armour units are designed to stay in place as built, with only minor displacements. This requires a robust but porous armour structure.

Armour layers can be constructed with both rock and concrete elements. The development of the concrete breakwater elements is closely related to the development of ports around the world. As the increasing size of the ships demanded deeper ports and channels the location of the ports shifted seaward. Accordingly breakwaters needed to be built in deeper water. This resulted in increased wave exposure. As increase in wave load requires the use of larger rock, which is limited in size and availability, concrete elements were used.

Over the years various shapes of concrete armour units have been developed which can be distinguished into two categories namely: − Randomly placed armour units − Uniformly placed armour units The main difference between the types of elements is the mechanism from which it gains hydraulic stability. On overview of the most common used armour units is given in Appendix A.

Uniformly placed armour units depend mainly on friction between the units to provide hydraulic stability. Examples of these uniform placed elements are the Cob, Shed and Seabee. The elements are placed close together and have a very high hydraulic stability. However, placement of these elements is very difficult under water. Therefore they are normally only applied when construction can be done above water.

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Effect of the concrete density on the stability of Xbloc armour units

Randomly placed armour units can be divided into elements which obtain their hydraulic stability by their own weight and by interlocking. Elements with hydraulic stability by its own weight as with rock are bulky elements like cubes and Antifer cubes. These elements are placed in double layers and are not very cost effective due to the large concrete demand. The second type of random placed armour units obtain their hydraulic stability not only due to their own weight but also by interlocking between adjoining units. The elements could have less weight because they gained their hydraulic stability mainly due to interlocking instead of their own weight, resulting in a low concrete demand. An additional advantage is that the slender shape of the element increased the porosity of the armour layer which is favourable for wave energy absorption and reduction of the wave run-up. Examples of these elements are the Tetrapod, Dolos and Akmon which are placement in double layers.

During the development of these elements the focus was on increasing the hydraulic stability by increasing the interlocking capacities. This resulted in slender shapes. However, no attention was paid to the structural integrity of the elements. The more slender the element shape, the more vulnerable to breakage. As a consequence several armour layers failed due to the breakage of these slender elements. Improvement of the structural integrity resulted in the Accropode and Core-Loc elements which are placed in single layers, resulting in even less demand on concrete.

Although elements are divided into categories by their most characterising stabilisation mechanism they all have a partial contribution of weight, interlocking and friction to the stability. The amount of contribution of each mechanism to the total stability depends on the armour units shape, placement (contact points) and slope angle. The gravitational force is always present. Furthermore, interlocking and friction are a function of the (submerged) weight of the elements. The friction force depends on the normal force between the elements and the contact surface area. In the case of interlocking the amount of weight of the surrounding block which rest on top of the element is of importance.

Independent of the stability mechanism the weight of the armour units used is of great importance to the total integrity of the structure as it determines the allowable wave load it can endure.

1.2 Problem Description

In order to design the armour layer effectively insight is required in the physical processes of the wave-structure interaction. The processes for coastal structures in general are given in the basic scheme in Figure 1-1. The loads on the armour units are based on the interaction of the environmental and structural parameters. The environmental parameters describe the water motion in front of the structure and are not influenced by the structure itself. The resistance against the load is called the strength and depends on all structural parameters.

2 MSc thesis

Chapter 1 Introduction

Figure 1-1 Basic scheme for coastal structures under wave attack

At this moment the complex processes involved in armour layer design are not fully understood. The flow on the structure due to the wave-structure interaction is highly non-stationary. All forces except gravitational forces vary in size and direction with time. This in combination with the complicated shape of the units, random placement and the very complex flow field makes a deterministic calculation of the instantaneous forces at this time impossible to perform. Armour layer design is therefore based on empirical relations from small scale model tests in combination with simple qualitative force ratio analysis.

The hydraulic stability of the armour units is of importance for the integrity of the entire structure. The armour layer should therefore be designed with great care. In order to be able to derive expressions for the armour stability some simplifications of the flow and assumptions on the load and stabilisation forces are made to describe the hydraulic stability of armour units. The flow is assumed quasi stationary and the only stabilisation force on the element is the gravitational force. This has resulted in the expression of the stability of armour units by the dimensionless stability number:

H s ≤⋅K ijK (1.1) 1 n ΔDn

Hs/∆Dn is called the stability parameter or number and is in most literature denoted as Ns. The load of the wave structure interaction is related to the characteristic wave height Hs. The strength is characterised by the size of the element presented by the nominal diameter Dn and its relative

ρr density, Δ= −1 . Kl…Kn represent the influence of the slope angle, wave period, damage level, ρw etc. on the hydraulic stability. As determined earlier the weight of the armour units is of great importance as it determines the allowable wave load it can endure. This research focuses on influence of the specific weight (ρr) of the concrete on the hydraulic stability of armour units.

The hydraulic stability of the Xbloc armour unit as other complex interlocking shapes is expressed by the stability number (Ns). Several model tests have been performed to investigate the influence of the foreshore, slope angle, placement pattern and wave steepness on the hydraulic stability. The stability number is based on the assumption of dominance of lift, drag and gravity forces. If other forces have significant influence on the stability, which is the case for complex interlocking armour units like the Xbloc, the power of one for the relative density (Δ) in (1.1) might change.

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Effect of the concrete density on the stability of Xbloc armour units

The influence of the specific weight on the hydraulic stability of single layer interlocking is described by the stability number Ns ; however the stability number has not been validated for these complex armour units.

Knowledge on the influence of the specific weight on the stability could be of interest during the design process and during the executing of the work. When assuming the validity of the stability number, the relation between the nominal diameter (Dn) and the relative density (∆) for the same stability is given by:

11 Dn ∝= (1.2) Δ−()ρρaw/1

This means that when higher specific weight is used the required volume and the weight of the armour unit reduce significantly while obtaining the same hydraulic stability. The reduction of the weight is favourable for production, handling and storage of the armour elements. However, due to the reduction in size the number of armour units which has to be placed increase. A disadvantage is that due to smaller required diameter the armour layer thickness decreases which increases the run- up and overtopping. On the other hand, the crest height does not change, resulting in a higher core which is favourable for construction. Knowledge on the influence of the specific weight could tell us if the stability can be guaranteed when during the preparations of the works it becomes clear that the actual concrete density is less than described. This can be the case if the local (quarry) material has a low specific weight because the specific weight on the concrete depends on the aggregates used.

Several studies on the influence of the specific weight of armour units have been performed for rock, cubes and some interlocking armour units. HELGASON et al. (2000) analysed the studies which already have been done on the influence of the rock density on the stability. They concluded that the influence of the rock density as presented in the stability formula of Hudson and Van der Meer seems not completely correct. The formulas tend to overestimate the positive influence of increasing the specific weight while underestimating the stability when lower densities are used. The same results were found by ZWAMBORN (1978) for Dolos, an interlocking armour unit. However HELGASON et al. (2000) also concluded that there was no unique conclusion on the influence of the specific weight on the amour stability. According to their research it depends on the type of armour and the slope angle. An extended overview of the performed research on the influence of the specific weight is presented in paragraph 2.4.

1.3 Problem definition

The discussion on the hydraulic stability in the previous paragraph has shown the importance of research on the influence of the specific weight on the stability of single layer armour units. The power of one for relative density (Δ) in the stability number (1.1) might change as other forces have significant influence on the stability than the assumed dominance of lift, drag and gravity forces. Research on influence of specific weight on other elements has shown that it depends on the type of armour and the slope angle. The hydraulic stability described with the stability number for single layer interlocking armour units is therefore questioned. The research question for this thesis is:

4 MSc thesis

Chapter 1 Introduction

1.4 Approach

To answer the research question, first a theoretical overview will be given of the current design methodology of the armour layer of rubble mound breakwaters. As the validity of the current design formulae is questioned for complex shaped armour units, research will be done against the background of the stability number and the current design formula. Therefore an inventory will be made of the processes involved and their influence on the hydraulic stability. Furthermore a literature study has been performed on the existing knowledge on the influence of the specific weight. All will be discussed in Chapter 2. Based on the findings in Chapter 2 on the important processes and forces in the design of single layer interlocking armour units, model test will be performed in the hydraulic flume of Delta Marine Consultant to investigate the influence of the specific weight on the hydraulic stability of single layer interlocking armour units. Special attention will be paid to the design of the armour layer with Xbloc armour units which will be discussed in Chapter 3. The model setup will be discussed in Chapter 4. Based on observations from the performed model tests the processes involved are analysed which is described in Chapter 5. Chapter 6 represents the results of the model tests on the influence of the specific weight. According to the model test results and observations feed back is given on the influence of the specific weight on single layer interlocking armour units and to the validity of the current design formula. The conclusions and recommendations are presented in Chapter 7.

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Effect of the concrete density on the stability of Xbloc armour units

6 MSc thesis

Chapter 2 Armour layer design

In this chapter the basics considerations on the structural design of rubble mound breakwaters are discussed. The main dimensions of the armour layer of a rubble mound breakwaters are based on empirical relations. In paragraph 2.2 the processes involved in armour layer stability are discussed in more detail. This results in paragraph 2.3 in the current armour layer design formula for the hydraulic stability. The influence of the specific weight of the armour unit on the hydraulic stability is discussed in paragraph 2.4. The hydraulic stability of the armour layer could be hampered if the integrity of a single unit is lost. However the structural integrity is outside the scope of this research, some considerations on the influence of the specific weight it are discussed in Appendix B.

2.1 Design rubble mound breakwater

As described in Chapter 1 the main function of the breakwater is to reduce the wave impact on the lee side of the structure. In the case of rubble mound breakwaters this is particularly to shelter the harbour basins and entrances from offshore wave action.

The main body of the breakwater comprises the core and consist of wide graded dredged or quarry material. The breakwater is armoured by a layer of larger elements which have to withstand the wave forces and dissipate the wave energy. Filter layers are applied to prevent the finer material being washed out. The armour layer of the breakwater can be constructed either with rock or with concrete elements. See Figure 2-1 for a schematization of the cross section of a rubble mound breakwater.

Figure 2-1 Conventional multi layer rubble mound breakwater [CEM 2006]

2.1.1 Main dimensions

The layout of the breakwaters depends on the boundary conditions as wave characteristics, water depth and bathymetry but also the available construction material, functional requirements and construction method. The main dimensions which have to be determined are the crest height the crest width and slope angle. The design of these dimensions is briefly discussed.

Crest height The elevation of the crest is generally dictated by the acceptable overtopping discharge or wave transmission based on the functional requirements that have been determined of the structure and its

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Effect of the concrete density on the stability of Xbloc armour units

facilities in its lee [ROCK MANUAL, 2007]. The wave run-up and therefore the overtopping is a function of the wave structure interaction and can be described as a function of the surf-similarity parameter, see paragraph 2.2, taken into account the wave characteristics at the toe of the structure as well as the tide and wave set-up. Furthermore, the run-up is influenced by slope roughness and permeability of the structure which depends on the type of armour. Rubble mound breakwaters are constructed of loose material. Depending on the permeability of the entire structure long waves are not entirely damped and this may lead to transition of the wave energy through the structure. The allowable wave overtopping and wave transmission depends on the functional requirements for the area behind the crest, the accessibility of the breakwater and the allowable down time of these functions. For example, a harbour basin where the wave height influences the activities or buildings and roads on or behind the breakwater. The construction method can also influence the crest height. Construction with marine equipment poses no real constrictions on the crest level in contrary to land-based equipment which need a freeboard of 1m to allow save access to the tip of the breakwater.

Crest width The width of the crest depends mainly on the functional requirement like access roads and the construction method. Again if land based equipment is used for construction the crest needs to be wider. The top of the core has to be as wide to allow two dump trucks or a crane and a dump truck on top. Independent of these requirements a minimal crest width of 3 concrete elements or 3 to 4 rocks should be applied to protect the crest from erosion by overtopping flow.

Slope angle The slope angle depends on geotechnical characteristics of the material and the hydraulic stability of the element used. Mild slopes have a positive effect on the wave run-up. The effect on the hydraulic stability depends on the type of element which will be discussed later on. For an economic design the slope angle must be as steep as possible to minimise the use of material.

2.1.2 Failure modes

When all main dimensions are determined the construction requires hydraulic, structural and geotechnical analyses. This should cover all failure mechanisms which are summarised in Figure 2-2. This thesis focuses on the hydraulic and structural stability of the armour layer. This means the stability of the armour units against erosion and breakage under wave action and does not include sliding of the armour layer due to erosion of the toe or slip failure of the entire slope.

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Chapter 2 Armour layer design

Figure 2-2 Failure modes rubble mound breakwater [CEM 2006]

2.2 Wave - Structure interaction

Waves on a sloping structure will cause the water surface to oscillate over a vertical range. The up and down rush flow due to the wave action exerts forces that can move the armour unit from its original position. The flow forces are counteracted by interlocking, gravity and friction forces. The processes involved are discussed in the following paragraphs.

2.2.1 Flow on armour layer

The flow up and down the slope determines the destabilization force on the elements in the armour layer and depends on the wave structure interaction. The wave structure interaction causes the wave to break on the slope. The type of wave breaking determines amongst other parameters the wave run-up and rundown and therefore the flow forces on the armour units.

Breaker types can be described by the surf-similarity parameter or Iribarren number ξ [CEM 2006]. The Iribarren parameter is a function of the slope angle and the wave steepness and is given by:

tanα ξop = (2.1) Sop

H s 2π H s With Sop == 2 (2.2) LgTop p

Sop is referred to as the fictitious wave steepness and is based on the local wave height and the theoretical deep-water wavelength using the peak wave period. The different breaker types are presented in Figure 2-3.

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Effect of the concrete density on the stability of Xbloc armour units

Figure 2-3 Breaker types [ROCK MANUAL]

The breaker types can be divided in breaking (ξ<2.5-3) and non-breaking waves (ξ>2.5-3), the surging waves. In the transition zone (2.5<ξ<3) the breakers have a collapsing nature. Plunging breakers (ξ=1.5) have a jet like impact on the armour layer, resulting in an instant high velocity turbulent flow. As a consequence there are locally high pore pressures, especially with impermeable slopes. Although there is a high velocity splash, due turbulence the wave energy is dissipated quickly and the run-up and rundown velocities along the slope are relatively small. The physics of the turbulent flow of breaking waves are not understood yet but they have a great impact on the stability of the armour units. In general, the run-up increases with increasing surf-similarity parameter. Surging breakers are usually due to longer wave period. The flow has a more oscillating nature resulting in higher wave run-up as there is less energy dissipation because the wave does not break on the slope. Run down is found important in dislocating armour units in combination with high outward velocities. The maximum outflow velocities occur near the maximum rundown just below the SWL (BRUUN & JOHANNESBURG, 1976) as quoted in HATTORI (1999). Collapsing breakers are found to cause the most damage. This could be explained by the fact that both surface roller turbulence and plunging jet act directly on the slope [SCHIERECK 2004].

The flow velocities are maximal on smooth impermeable slopes for a given sea state. The flow field runs parallel to the slope with the highest velocities around the still water level (SWL). The largest destabilization forces occur during downrush except for slopes flatter than 1:3.5 [CEM 2006].

On permeable structures the flow field changes in direction as well as in magnitude. The flow no longer just runs along the slope but more through the structure, see Figure 2-4. The increase in permeability reduces the flow velocities as the flow path is longer and less concentrated. The reduction of the flow velocity reduces the destabilization forces on the armour units. The flow into the structure leads to an increase of the phreatic line inside the structure. The internal setup is due to a greater inflow surface area during wave run-up than the outflow surface area during rundown. The mean flow path for inflow is also shorter than that for outflow. The rise of the phreatic line will continue until the outflow balances the inflow [CEM 2006]. The increase of the phreatic line leads to an increase in the mean pore pressures and reduction of the stabilization forces. The lower the permeability is, the higher this internal setup.

Increase in structure porosity also reduces velocity. A larger part of wave can be stored in the pores which reduces the destabilization force on the armour units. The positive effect of this reservoir

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Chapter 2 Armour layer design

effect is reduced in case of a large internal setup. This is the case with a porous armour layer on core with a low permeability.

Figure 2-4 Illustration of runup and rundown permeable and impermeable slopes (Burcharth 1993) [CEM 2006]

The influence of the core permeability will be even of greater importance for single layer armour units as the dissipation of wave energy in single layer will be smaller than for double layers because of the reduction on armour layer thickness. This results in higher velocities in and over the armour layer and therefore higher destabilisation forces.

2.2.2 Flow forces on armour layer elements

From the discussion in paragraph 2.2.1 it becomes clear that forces due to oscillation flow over and through the armour varies in magnitude and direction with time and depends on structural parameters and the type of breaking. This paragraph identifies these forces and their impact on armour stability.

In order to do so first a traditional schematisation of the forces on the armour layer is presented in Figure 2-5. It is assumed that the flow is mainly parallel to the slope. Due to the oscillating flow over the slope there is lift force (FL), drag force (FD) and inertia force (FI) acting on the armour unit which tries to move the unit. The stabilization force presented in Figure 2-5 is the gravitational force. Forces acting at the contact points with the neighbouring units might be stabilizing or destabilizing depending on the position and direction of the force. When stabilizing, these forces are due to friction and interlocking. The stabilization mechanisms were already introduced in Chapter 1 and further discussed in the following paragraph.

Figure 2-5 Schematization forces on armour units under wave attack [Burcharth, 1993]

B.N.M. van Zwicht 11

Effect of the concrete density on the stability of Xbloc armour units

The flow forces on a unit can be presented by applying the Morison equations [BURCHARTH 1993]:

FDDw≈ CAvvρ

FLLw≈ CAvvρ (2.3) dv FCV≈ ρ IIwdt

Coefficient CD, CL and CI are time depend empirical coefficients which depend on the shape of the armour unit, the Reynolds number and the Keulegan-Carpenter number. A is the effective surface area of the element at right angles to the velocity and V is the volume of the armour unit.

Rubble mound breakwaters have mostly permeable structures. The presented schematisation does not take into account flow inward and outward the structure or more plunging breakers types. The outward flow will result in a drag force perpendicular to the slope. As said before the flow is highly non-stationary and there is not always a resultant force which tries to remove the element but also pushes it against the slope. So the time dependency of the destabilization force is important if it is able to remove the armour unit entirely from its position which is reflected in the inertia force. The importance wave-structure interaction have been shown, different breaker types result in different flows. The influence of turbulent flow is not taken into account in this quasi static approach. Furthermore, for flatter slopes the flow forces become more drag and lift dominated but for steep slopes the inertia force becomes more and more dominating [HELGASON AND BURCHARTH, 2005]. Another phenomenon which is not taken into account in this schematisation is the influence of the pore pressure. Due to the difference in pressure underneath and on top of the armour unit, the unit can be pushed out of the armour layer.

The destabilizing flow forces can result in different failure mechanism some of which are shown in Figure 2-6. These mechanisms are rocking, downward or upward rotation out of the armour layer and sliding of the entire armour layer.

Figure 2-6 Armour layer failure modes [Burcharth 1993]

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Chapter 2 Armour layer design

2.2.3 Stability mechanism

Armour units remain stable on breakwater slopes under wave attack due to three mechanisms which were already introduced in Chapter 1, namely: − Armour unit weight − Friction − Interlocking

The relative contribution of each mechanism to the total stability depends on the armour units shape, placement (contact points) and slope angle. Even so, all mechanisms are a function of the slope angle. The influence of weight as stabilization force reduces with increasing steepness of the slope. While friction and interlocking become more dominant with increasing slope angles. This can be explained with Figure 2-5.

The direction of the stabilization force FG in Figure 2-5 is always directed to the centre of the earth. The force can be resolved into a component perpendicular to the slope and a component parallel to the slope;

FF= cosα GG⊥ (2.4) FF= sinα GG The lift force is counteracted by the component of the gravitational force perpendicular to the slope. The perpendicular component is maximal and equal to the gravitational force on a horizontal bed becoming smaller with increasing slope angle reducing the influence of weight as stabilization force reduces with increasing steepness of the slope.

If the equilibrium of forces is considered acting on an element on a slope with the failure mode of a sliding armour unit. The unit is still stable if:

μFFGGcosαα≥ sin (2.5) with μ as the friction coefficient between the armour unit and the under layer. If the gravitational force parallel to the slope exceeds the friction force the element will slide down the slope and will rest on the element(s) lower on the slope. The friction force depends on the normal force between the elements and the contact surface area. With increasing slope angle the component parallel to the slope increases and therefore the normal force between the elements with;

FFNG sinα − μα F G cos (2.6) Interlocking also increases with increasing slope angle due to the increasing component of the gravitational force parallel to the slope. However the contribution of each mechanism can not be defined precisely. This is why current design formulae are for several cases inadequate because they are based on the weight principle only. PRICE (1979) tried to solve this. He measured the amount of force necessary to pull an element out of slope in relation to its own weight which he plotted against the slope angle By subtracting the influence of the weight perpendicular to the slope he found the contribution of friction and interlocking. The results are presented in Figure 2-7.

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Effect of the concrete density on the stability of Xbloc armour units

Figure 2-7 Influence of the slope angle on the stabilization mechanisms, interlocking, surface friction and gravity, on the stability [Price 1979]

Armour layers with rock are commonly designed on a slope of 1:2 or 26.6 degrees. Interlocking armour layers are constructed on slope of 1:1.5 or 3:4 which is 33.7 and 36.9 degrees. This is still on the left hand side of both figures. For interlocking armour units on steep slopes interlocking and friction are more dominant but there is still a considerable influence of the gravitational force.

2.3 Hydraulic stability armour layer

From the complex physical processes it is clear that a deterministic calculation of the instantaneous forces is at this time impossible to perform. Armour layer design is therefore based on empirical relations derived from small scale model tests in combination with simple qualitative force ratio analysis. However one should be aware that the design formula are only applicable for limited number of cases due to limited range or wave conditions and structural parameters for which the tests were performed.

Stability is the ratio between load and strength. In the case of a breakwater armour layer both are functions of the geometry, see figure Figure 1-1. Stability is also a function of the allowable damage. In general form:

load Stability== f(,) geometry damage strength

The stability of armour elements is expressed by the dimensionless stability number Ns. The following paragraphs present the derivation of the stability parameter and its application in the current design formula.

2.3.1 Stability Number Ns By simplification of the situation it becomes possible to derive expressions for the armour stability. The method described in BURCHARTH (1993) is presented here. The forces on armour units on a slope under wave attack are schematised as presented in paragraph 2.2.2, with the Morison equations for destabilization forces. To formulate expressions for the armour stability the flow is assumed quasi stationary and the shape of the armour unit is assumed 1/3 ⎛⎞M to be characterized by an equivalent cube length Dn = ⎜⎟, where M is the mass and ρ is the ⎝⎠ρ

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Chapter 2 Armour layer design

specific weight. For this simplified situation the inertia forces are neglected and stability is assumed only by the own weight of the elements. The stability ratio can be formulated as the drag and the lift force divided by the gravitational force.

FF+ ρ v2 DL≈ w K (2.7) FgGrwn()ρρ− D

K is dimensionless and a function of the structural parameters like slope angle, porosity and breaker type as well as damage progression and storm duration. The velocity can be characterised by vgH≈ ,by assuming that the velocity of a wave on a slope (broken and unbroken) is proportional to the celerity in shallow water taking the wave height as an representative measure of the water ρ depth. Together with the relative density, Δ =−r 1 , we obtain the dimensionless stability number: ρw

H ≤ K (2.8) ΔDn

K is again a dimensionless parameter containing the influence of several parameters which are determined from model test. For design purposes it is important to check the range of the model test parameters on which the fitted coefficient K is based.

2.3.2 Stability design formula

Based on the principle described in previous paragraph several formulas for armour layers were developed. The most important are presented here.

Stability formula of Iribarren

Iribarren (1938) [D’ANGREMOND 2001] was the first to try to develop a theoretical model for the stability of stone on a slope under wave attack. He considered the equilibrium of forces acting on a element on a slope with the failure mode of a sliding armour unit. This resulted in the following relation:

H s =±()μαcos sin αN −1/3 (2.9) ΔDn

The coefficient N acts like a dustbin for many unknown variables and irregularities in the model tests. The friction factor μ was determined by measuring the angle of internal friction of the blocks.

Stability formula of Hudson On the basis of many experiments performed at the Waterways Experiment Station in Vicksburg, USA, Hudson proposed in 1953 [D’ANGREMOND 2001] the following expression:

ρ gH3 H r ss3 WK≥=3 or d cotα (2.10) Δ Kd cotα ΔDn

The formula is applicable for slopes between 1:1 and 1:4. Recommended values for Kd for different types or armour units and various circumstances can de found in the Coastal Engineering Manual (CEM 2006).

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Effect of the concrete density on the stability of Xbloc armour units

Stability formula of Van der Meer There are some limitations on simple presentation of the Hudson formula. The most important parameters which are not included are the wave period, permeability, number of waves and damage level. Van der Meer performed many experiment to overcome these shortcomings. In the first place he used a clear definition of damage (S). Furthermore he assumed the effect of the wave period to be connected with the shape and intensity of breaking waves, see also paragraph 2.2.1. He therefore used the Iribarren parameter (ξm). Because he performed his test with irregular instead of regular waves as Iribarren and Hudson used, he found a clear influence of the storm duration. This is reflected in the stability formula via the number of waves (N). Van der Meer also found the effect of permeability of the structure on the stability. This is reflected by the permeability coefficient P. Van der Meer found the following stability formula for quarry stone:

0.2 H 0.18 = 6.2PSN() / 1/ ξm for plunging waves (2.11) ΔDn50

H 0.2 = 1.0PSN−0.13 / cotαξ P for surging waves (2.12) () m ΔDn50

VAN DER MEER [1988] also gives the stability formula for frequently used concrete armour units as cubes and Tetrapods, which are not presented here. Reference is made to the ROCK MANUAL (2007).

2.3.3 Validity Ns The stability formula of complex interlocking armour units is based on the same approach and their stability is presented as a function of the stability number. The stability number is based on lift and drag force dominance stabilised by the submerged mass. The inertial, interlocking and friction forces are not taken into account. Therefore the stability number for complex armour units is not complete for situation where other forces dominate influence the stability. The inertia force depends on the wave period and has the same order of magnitude as the drag force. The effects of interlocking and friction are however difficult to quantify. Furthermore, armour units are not necessarily fully submerged when the combination of drag and inertia reach a maximum, which would affect the relative density term in the equation (2.8). [ZWAMBORN, 1978].

One of the questions that arise is on the influence of the specific weight. Most common design formulas do not give a clear conclusion on the influence of the specific weight, which has great influence on the stability number. Still the stability numbers are valid for the tested parameters but if other forces besides drag, lift and gravitational forces have significant influence on the stability then the power of one for Δ in (1.1) might chance. In paragraph 2.2.3 it is already shown that for flatter slopes the weight of the block is more dominant for the stability while for steeper slopes friction and interlocking are becoming more dominant. Paragraph 2.4 will discuss the influence of the specific weight on the hydraulic stability.

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Chapter 2 Armour layer design

2.4 Influence specific weight on hydraulic stability

Several studies on the influence of the density on the stability have been performed. To analyse the different results the stability formula is given in a general form:

D3 n =⋅⋅⋅⋅⋅ΔKK K −x (2.13) H 3 12 n

3 in which Dn represents the volume of the unit, H is the characteristic wave height, K1···Kn are coefficients depending on the influence of the slope angle, wave period, damage level, etc. The value of x determines the influence of the relative density on the stability. In the stability formula of IRIBARREN (1938), HUDSON (1953) and VAN DER MEER (1988) the value of x = 3. The validity of the value is discussed in the following paragraphs. 2.4.1 Study on rock stability

HELGASON et al. (2000) performed a study on the influence of rock density on the stability of rubble mound breakwater. They analysed the studies which already have been performed on the influence of the rock density on the stability. An overview of the existing studies is given as presented in HELGASON et al. (2000). The paragraph concludes with the results of HELGASON et al. (2000) and HELGASON & BURCHARTH (2005).

The design formula of Iribarren, Hudson and Van der Meer are based on extensive model testing varying a range of parameters. Model test by IRIBARREN [1938] and HUDSON [1958] were performed 3 using densities in the range of ρr = 2.6 – 3.1 t/m and regular waves. The influence of the density was not investigated but was based on theoretical considerations. 3 VAN DER MEER [1988] tested with densities in the range of ρr = 1.94 – 3.05 t/m . Only a few tests were performed with high density rock. He found no clear trends. HOLTZHOUSEN AND ZWAMBORN (1992) stated that no clear trends could be found due to the difference in the shape and size of the rocks with different densities.

Comprehensive model tests were done by Kydland and Sodefejd, their results were presented by 3 BRANDTZAEG (1966). They tested rock with densities in the range of ρr = 1.83 – 4.54 t/m and fluids 3 in the range ρw = 1.0 – 1.13 t/m using only regular waves. Two series of tests were performed. In the first test blocks with three different densities were used. For each specific weight three different sizes were used. The blocks were broken manually to establish the same shape and size blocks for the different densities. The weight for each material had a spread of 90%-110% of the average weight. The variation of the block dimensions was kept below 2.5%. In the second test the weight of the blocks was about the same and the size differed due to the different density of the used material. Three different slopes were used, 1:1.25, 1:1.5 and 1:2. The model was build up of a wooden slab with two layers of secondary stone to eliminate variation in permeability.

ZWAMBORN (1978) reanalysed the results presented by BRANDZAEG (1966). He plotted the relative 33 density Δ against (/)cotDHn α in a log-log graph, see Figure 2-8. The function term 33 −x fDH((n / )cotα ) = KΔ has been fitted using a non-linear least square algorithm. This gave a value for x of 2.1 for 1% of damage and 2.28 for failure.

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Effect of the concrete density on the stability of Xbloc armour units

Figure 2-8 Results of Kydland (1966) plotted according to Zwamborn (1978) [HELGASON et al. 2000]

The results of Sodefjed plotted by ZWAMBORN (1978) show different values of x for the same damage but for different slope angels: − for 1:1.25; x = 2.08 − for 1:1.5; x = 2.4 − for 1:2; x = 2.87

3 HELGASON et al. (2000) performed tests with rock of ρr = 2.65 & 3.05 t/m and slope angles of 1:1.5, 1:2 and 1:2.25. Using the method of Zwamborn he found a value for x of 2.67. This is higher than the reanalysed data of Kydland. As an explanation is given that, Kydland used regular waves and Helgason irregular waves. Another explanation could be the influence of the slope angle. HELGASON et al (2000) makes no difference between the slope angles, while from the reanalysed data of Sodefjed there is a clear relation between the slope angle and the value of x. Overall it can be concluded than the influence of the rock density as presented in the present stability formula of Hudson and Van der Meer seems not completely correct. The formulas tend to overestimate the positive influence of increasing density. It would be better according to their studies to use a value of 2.67 for x instead of 3. Hudson ascribes the disagreement with his own formula to scale effects, because the stability number should be independent of the density [ZWAMBORN, 1978].

3 HELGASON & BURCHARTH (2005) performed study on rock stability using ρr = 2.65 - 3.30 t/m and slope angles of 1:1.5 and 1:2. The results are plotted with the data from the previous studies for cotα = 1.5 and cotα = 2 for no damage (Sd=2), see Figure 2-9. It appears that for cotα = 1.5, x = 2. As a consequence the theoretical assumption of lift and drag dominance giving x = 3 seems not to hold for natural rock on a slope of 1:1.5. For a slope of 1:2 there seems good coherence with the assumed value of 3.

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Chapter 2 Armour layer design

Figure 2-9 Results historic results influence relative density rock for cotα = 1.5 (on the left) and cotα =2

(on the right) for no damage (Sd=2) [HELGASON & BURCHARTH 2005].

From the results it can be concluded that the influence of specific weight depends on the slope angle. For slopes of 1:1.5 the theoretical assumption of lift and drag dominance does not hold, the inertia become mores dominating as is friction. The formula of Hudson and Van der Meer tend to overestimate the positive influence of increasing density. HELGASON & BURCHARTH (2005) conclude also that for a slope of 1:2 the effect of density is correct described by the Hudson and Van der Meer formula.

2.4.2 Study on concrete armour units

As with rock the use of high density concrete could lead to a significant reduction of the necessary unit size. A downside would be the increase of tensile stresses in the armour units [ZWAMBORN 1978]. This would mean less structural integrity. This could be of big influence particularly for large slender units. The structural integrity is outside the scope of this research but the influence of the specific weight it on the structural integrity is discussed in Appendix B.

Several tests have been done to investigate the density influence for Dolosses, Tetrapods and Cubes which will be briefly discussed.

Influence specific weight on Dolos armour units

ZWAMBORN (1978) investigated the effect of relative density of the stability of Dolos armour units.

He tested the stability of Dolosse with densities of ρa = 2.65, 2.41 and 2.57 under regular waves on a slope of 1:1.5. The stability increased with higher density but no real relation good be derived. A greater range of densities was necessary. Further research by SCHOLTZ et al (1982) with ρa = 1.81, 2.39 and 3.02 resulted in an average value for x of 2.3. This is in agreement with the result of Kydland (1966) for rock under regular waves.

HOLTZHOUSEN & ZWAMBORN (1992) stated (looking at results of Sodjefeld) that for slopes flatter than 1:2 the Hudson formula describes the influence of specific weight correctly and therefore also

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Effect of the concrete density on the stability of Xbloc armour units

the Van der Meer formula. For steeper slopes the influence of the specific weight on the hydraulic stability is less. It can be expected that the effect of density on stability of Dolosse will also be a function of the slope angle although somewhat less than for rock due to the interlocking.

Influence specific weight on Tetrapod armour units

ITO et al (1994) did research on the influence of ‘high-gravity concrete’ on the stability of Tetrapods. He used five different densities, but he also changed the size of the model blocks with the different densities according to the expected stability number. He found no clear trend for the relationship between the Kd values and the density. This can be explained by the use of different size of armour units with different densities. With the change of the armour size, the load on the elements also changes.

Influence specific weight on Cubes

TRIEMSTRA (2001) performed tests with high density cubes for his MSc thesis study at the Delft University of Technology. He tested two cube elements with different densities on a slope of 1:1.5 under irregular waves. In his research he did not take into account the earlier research on quarry rock and Dolos. Triemstra chose to investigate cubes because they have a simple shape while at the same time eliminating the influence of interlocking. At first he found no clear correlation which could be attributed to the difference in size of the units with different densities. After analysing the data he found that the ‘laying-roughness’ of the armour layer influences the stability. With the ‘laying- roughness’ was meant the percentage of cubes that lie rough (on their edge or corner) on the slope. Comparison of the different densities with the same ‘laying-roughness’ gave almost a linear relation between the relative density and Hs/Dn. Therefore was concluded that linear relation between the relative density and Hs/Dn as in the formula of Hudson and Van der Meer are valid for cubes as they are for rock. There are some problems with this conclusion. Firstly, earlier research has pointed out that the relation of Hudson and Van der Meer overestimates the influence of higher density for rock as for interlocking armour units for slopes of 1:1.5 and probably steeper. Secondly, the conclusion has no clear correlation between the relative density and Hs/Dn. The reason for not finding a clear relation could be attributed to use of different sizes of cubes with different densities.

2.4.3 Research single layer interlocking armour units

Based on the results presented by HELGASON AND BURCHARTH (2005) for rock and ZWAMBORN (1978) for Dolos armour units is can be concluded that the influence of the specific weight on the stability for interlocking armour units is dependent on the slope. The stability number is based on lift and drag force dominance stabilised by the submerged mass. With increasing slope angles inertia, friction and interlocking forces become more dominating. The inertial, interlocking and friction forces are not taken into account in the stability number. Therefore it is expected that the influence of the specific weight for slopes of 1:1.5 and steeper is not correctly reflected by the stability number.

To investigate the influence of the specific weight on the stability of single layer armour units model tests have been performed with Xbloc armour units. Test were performed with concrete densities of 3 ρa = 2.1 - 2.92 t/m and slope angles of 1:1.33, 1:1.5 and 1:2. During the test the size of the elements used and the geometry of the construction were not changed to eliminate the influence of the structural parameters on the load and strength of the armour layer. The experimental setup will be discussed in Chapter 4.

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Chapter 3 Armour layer design with Xbloc

The hydraulic stability of the Xbloc armour units are represented with the stability number Ns. During the development of the Xbloc armour unit extensive model test have been performed to determine the hydraulic stability. This chapter gives the design concepts of the Xbloc armour unit.

3.1 Main dimensions

The main dimensions of the Xbloc armour unit are shown in Figure 3-1. The block consists of a flat base with 4 indentations. On both side of the block two cubic noses are located. The block has only two faces and is characterised by its main dimension D. The volume of the block is equal to 1/3 of a corresponding cube volume (V = 1/3D3). The thickness of all members is D/3.

Figure 3-1 Geometry of the Xbloc

3.2 Hydraulic Stability

To determine the hydraulic stability, several model test have been performed at Deltares (Delft

Hydraulics). The stability is expressed by the dimensionless stability number Hs/∆Dn. The results show that with Xbloc the start of damage can be expected at Ns between 3.3 and 5.5. Failure occurred between Ns = 3.7 and 6.0. A design value for Xbloc armour layers of Ns = 2.77 has been concluded, see Figure 3-2. This corresponds with a Hudson stability factor of KD = 16. The stability number is valid for slopes of 3:4 and 1:1.5 with gentle foreshore slopes of 1:30 or less and concrete with a specific weight of 2400 kg/m3.

Figure 3-2 Hydraulic stability Xbloc

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Effect of the concrete density on the stability of Xbloc armour units

During the model tests a number of parameters were varied. They are summarised in Figure 3-1. The influence of the most important parameters on the hydraulic stability of Xbloc armour units are discussed in the following paragraphs.

Table 3-1 Main parameters varied in Model test Wave steepness 0.02 – 0.06 Foreshore slope 1:∞, 1:30, 1:15, 1:8 o o o Angle of wave incidence Perpendicular, 15 , 30 , 45 Slope angle structure 1:2 and 3:4 Placement pattern Xbloc Regular and random

Crest height Relative freeboard Rc/Hs between 1- 4 No of rows 32 to 50

The design of the under layer is based on the weight of the armour layer of regular concrete with a specific weight of 2400 kg/m3 where:

WW Wto= (3.1) u 15 7

The grading of the under layer should be conforming:

− W85 ≤ WXbloc/5

− W50 ≤ WXbloc/9

− W50 ≥ WXbloc/7

− W15 ≤ WXbloc/11

In addition of the under layer one or multiple filter layers may be applied to prevent erosion of the core.

3.2.1 Slope angle

The slope angle for an armour layer wit Xbloc armour units should be 3:4 or 2:3 to ensure complete usage of the interlocking capacities. In Chapter 2 it has become clear that the influence of interlocking reduces with decreasing slope angles. A slope angle of 1:2 may be applied for areas with seismic activities but the hydraulic stability of the concept design should be checked with physical model tests.

3.2.2 Armour layer placement

Interlocking single layer armour units like Xbloc are placed on a staggered grid. Accurate placement is required for good interlocking and a stable armour layer. The blocks are randomly placed in a single layer to a certain packing density without any specification on the orientation of the individual blocks. The quality of the placement is determined by packing density and interlocking. The packing density is measurable whereas the interlocking can only be assessed by visual inspection, TEN OEVER et al (2006).

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Chapter 3 Armour layer design with Xbloc

Research on the placement of Xbloc armour layer has showed that placement densities above 1.18/D2 lead to better hydraulic stability. For lower placement densities the hydraulic stability is constant. For lower placement densities it was found that the units settle and obtain a density close to the design density, see Figure 3-3. [BAKKER et al, 2005].

Figure 3-3 Influence placement density on hydraulic stability

For hydraulic model experiments with Xbloc armour units Delta Marine Consultants prescribes a packing density of 1.20/D2. This results in a condition for the distances between the Xblocs of dx = 1.30D and dy = 0.64D. Each Xbloc shall be secured by two other Xblocs in the row above and beneath and by contact with the under layer. To meet these requirements the Xblocs have to be placed in a staggered grid.

The placement density of armour layer is controlled by measuring the centrelines of the representative part of the armour layer horizontally and vertically. With the following formula the relative placing density (RPD) is determined (See also Appendix H)

(1)(1)NNdxdyD−− 2 RPD =×xy 100% (3.2) LLxy

In which: Nx = number of Xblox in the x direction Ny = number of Xblox in the y direction dx = 1.3 dy = 0.64 D = Xbloc unit height (not the same as Dn) Lx = average horizontal length Ly = average vertical length

The RPD gives the ratio between the real packing density and the prescribed packing density of 1.20/D2. An additional requirement is that the packing density on the slope shall be between 98% and 105% of the theoretical required packing density.

B.N.M. van Zwicht 23

Effect of the concrete density on the stability of Xbloc armour units

3.2.3 Surf similarity parameter

As with rock the lowest hydraulic stability is to be expected in the transition zone between surging and collapsing breakers. Reference is made to BAKKER et al (2005).

3.2.4 Wave steepness

The influence of the wave steepness has been investigated for a typical foreshore of 1:30 with So = 0.01 – 0.04. The results, as presented in BAKKER et al. (2005), show that higher wave steepness results in a higher hydraulic stability. The stability number increases from 3.3 till 3.7 for start of damage and from 3.7 till 4 for failure. However the scatter in the data points was significantly higher for the larger wave steepness. The design criterion gives no relation for the wave steepness on the hydraulic stability.

24 MSc thesis

Chapter 4 Experiment setup

To analyse the influence of the concrete specific weight on the stability of single layer interlocking armour units hydraulic model test have been carried out based on the design criteria for Xbloc armour unit as described in Chapter 3. In the following paragraphs the experiment setup will be discussed.

4.1 Scaling

In coastal engineering physical modelling is an important tool to examine phenomena which are beyond our present analytical skills. But in order to obtain reliable results from physical model tests it is important that the model behaves in the same way as it would at prototype scale. Dimensions and forces need to be scaled accordingly. In the following paragraphs the basic principles shall be explained.

4.1.1 Prototype and model similitude

The idea of physical modelling is that the model behaves in the same manner as the prototype. In order to achieve this, model and prototype should be in similitude with each other. To obtain complete similarity between model and prototype, all dimensionless parameters have to be maintained in the model. There are different types of similarity which are required to be met depending on the type of study. The three types of similitude are briefly discussed below.

Geometric similitude Geometric similitude exists if all the corresponding linear dimensions between prototype and the model have the same ratio. This relationship is independent of motion and involves only similarity in shape. Geometric similitude aids to visual recognition of the processes as they occur in the model, but as will be shown later on it is not always possible to fully fulfil this relationship.

Kinematical similitude Kinematical similitude exists if there is similarity of motion between prototype and model. This is achieved when the vectorial components of motion have the same ratio for all particles at all time.

Dynamic similitude Dynamic similitude exists for geometrical and kinematical similar systems if there is similarity in the force between prototype and model. The ratios of all the vectorial forces have to be equal. There is no fluid which can fulfil all force ratio requirements. It is therefore important to recognise the force ratio’s for the scale model design that need to be in similitude in between model and prototype.

For most of the coastal engineering problems the surface tension and elastic compression are relatively small and can be neglected. This leaves the gravitational and viscous forces as the dominant driving forces. The necessary condition for hydrodynamic similitude in the majority of the coastal model tests can therefore be fulfilled with the similitude of the Froude or Reynolds number in combination with geometric similarity [HUGHES ,1993].

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Effect of the concrete density on the stability of Xbloc armour units

4.1.2 Froude scaling

Froude number gives the relative importance of inertial forces acting on fluid particle to the weight of the particle. The Froude number is given by:

U Fr = (4.1) gL

The Froude model criterion should be applied when the inertial forces are primarily balanced by the gravitational forces. To fulfil this criterion the Froude number needs to be the same for model and prototype.

⎛⎞⎛⎞UU ⎜⎟⎜⎟= (4.2) ⎜⎟⎜⎟gLgL ⎝⎠⎝⎠pm

Which results in terms of scale ratio’s:

N U = 1 (4.3) NNgL

4.1.3 Reynolds scaling

Reynolds number gives the ratio between inertial forces to viscous forces, is important parameter when viscous forces dominate in a hydraulic flow. The Reynolds number is given by:

UL Re = (4.4) ν

Which results in terms of scale ratio’s:

NN UL= 1 (4.5) Nν

This criterion is impossible to fulfil for breakwater studies at reduced scale. But when the model is large enough such that the flow through the primary armour layer remains turbulent this criterion is well enough satisfied.

4.1.4 Scale effects

It is important when models are used that one understands that complete similitude does not exists. Scale effects may occur especially when surface tension and surface roughness become important, which may occur in small scale models. The best way to prevent scale effects is to construct the model as large as possible. But this is not always possible mainly due to the limitations on the laboratory facilities. In short wave hydrodynamic models it is assumed that the gravitational forces are dominant and the Froude scaling is applied. By doing so the viscosity, elasticity and surface tension forces are not scaled correctly. At small scale model test this may lead to unwanted scale effects. The scale effects which are of importance for this research are further discussed.

26 MSc thesis

Chapter 4 Experiment setup

Viscous scale effects If flow velocities and size of the units are small, viscous forces may be greater in the model resulting in scale effects. Mostly this is no problem in the primarily and secondary armour layer. Here the velocities are relative high because of the high permeability of these layers resulting in large Reynolds numbers. Turbulent flow is ensured in these layers. This is not the case for the core of the model structure. Due to the lower permeability there is a possibility of laminar flow in the core. Geometric scaling can lead to a too low permeability resulting in higher downrush pressures resulting in lower stability. Research has been done by several investigators on the minimal allowable Reynolds number at which the viscous scale effects can be neglected. The velocity in the

Reynolds number for the armour layer is represented as UgH= s

The results found for the required Reynolds number in the armour layer are summarized by HUGHES (1993) and presented in Table 4-1. For the core a turbulent flow has to be assured. After scaling the Reynolds number is calculated. When the Reynolds number in the core is higher than 2*10³ the flow in the structure is turbulent, conform to prototype situation, and the viscous scale effects are negligible [HUGHES ,1993].

Table 4-1 Reynolds numbers at which no viscous scale effects occur. (HUGHES [1993]) Researcher Reynolds number Dai and kamel (1969) 3*104 Jensen and Klinting (1983) 6*103 Oumeraci (1984) 3*104 Shimada et el (1986) 4*105 Van der Meer (1988) 4*104 Jensen (1989) core 5*103 Jensen (1989) armour layer 4*104

Friction scale effects In small physical model tests the friction forces between units may not be in similitude with the prototype. Although few studies have been reported it is common to reduce the surface roughness of the model blocks by painting the armour units. Scale effects due to no similarity in surface roughness are not considered to have any significant influence on the results of the experiment.

Aeration effects

Experiments conducted by Hall (1990) [HUGHES,1993] showed that air bubbles in breaking waves on a rubble mound breakwater are not in similitude in small scale models. The bubbles are relatively large in the model. This can be explained by the lack of similarity of the Weber number between model and prototype. The Weber number gives the ratio between the inertia forces and the surface tension. As a result the energy dissipation will be relative larger at model scale affecting the wave run-up.

B.N.M. van Zwicht 27

Effect of the concrete density on the stability of Xbloc armour units

4.2 Test facility

The hydraulic tests have been carried out in the wave flume of Delta Marine Consultants in Utrecht. The flume consists of a long rectangular glass tank with a wave generator on one side, see Figure 4-1. The flume has a length of 25 m, a width of 0.6 m and a height of 1.0 m. The maximal permissible water depth is 0.7 m with a maximal wave height of 0.3 m.

Figure 4-1 Top and side view wave flume Delta Marine Consultants

The flume is equipped with the Edinburgh Designs piston wave generator (see Figure 4-2), which can generate regular and irregular waves. The Edinburgh Designs piston wave generator is able correct the paddle motion to absorb the reflected wave. The wave paddle is force driven by a stepping motor. A stepping motor is a hydraulic motor which follows the commands of a stepped input signal to achieve positional accuracy. To produce the set wave height the wave height is transferred into a force, depending on the assigned water dept, with which the stepping motor has to move the paddle to produce the assigned wave. The incoming wave pushes with a certain force against the paddle. This force is absorbed such that the resulting force produces the right wave back into the flume. In this way the resultant wave is totally predictable.

Figure 4-2 Wave flume DMC in Utrecht.

The signal send out by the wave paddle is generated using the sea generator. The sea generator is used to load the predefined sea states, in this case the JONSWAP spectrum. The cycle time of the signal is defined in seconds. The cycle time is the length of the wave signal which is produced and depends on the frequency of the wave maker according to:

28 MSc thesis

Chapter 4 Experiment setup

2number cycle time = [s] wavemaker_frequency

The default frequency of the wave maker is 32 Hz. For example a cycle time of (11) = 64 seconds and (15) = 1024 second. The signal will continuously repeat itself. Use of the same file will results in the same signal.

4.3 Wave generation

4.3.1 Energy density spectrum

The tests are performed with irregular waves. The generation of the irregular wave field occurs according to the JONSWAP spectrum to simulate a young sea state. The JONSWAP energy density spectrum is given by:

2 ⎡ ⎛⎞ff/1− ⎤ −4 ⎢ 1 peak ⎥ ⎡⎤exp − ⎜⎟ 5 ⎛⎞f ⎢ 2⎝⎠σ ⎥ Efgf()=−απ245(2 )−− exp⎢⎥⎜⎟ γ⎣ ⎦ (4.6) JONSWAP ⎢⎥4 ⎜⎟f ⎣⎦⎝⎠peak with: E variance density (m²/Hz) f frequency (Hz)

fpeak peak frequency (Hz) g gravitational acceleration (m/s²) α scaling parameter (Pierson-Moskowitz) (-) γ scaling parameter (Jonswap peak-enhancement factor) (-) σ scaling parameter (Jonswap peak-enhancement factor) (-)

σ = σa for f ≤ fpeak and σ = σb for f > fpeak

For the standard JONSWAP spectrum the following holds:

σa = 0.07

σb = 0.09 γ = 3.3

The wave spectrum, generated in the experiments, is expected to be similar with the theoretical

JONSWAP wave spectrum. For narrow banded spectra in deep water Hm0 is approximately equal to significant wave height (H1/3) and is often referred to as the significant wave height. From the spectrum the significant wave height can be retrieved by:

H m00= 4 m (4.7)

+∞ With mEfdf= () 0 ∫ 0 4.3.2 Wave Reflection Analyses

Waves in coastal physical models are reflected by the structure. The reflected wave interacts with the incident waved and contributes to the characteristics of the wave field and flow field beneath the

B.N.M. van Zwicht 29

Effect of the concrete density on the stability of Xbloc armour units

waves. In many laboratory studies it is desirable to separate the measured wave train into its incident and reflected wave components so that model response can be related to parameters of the incident wave train. Therefore the surface elevation is measured with wave gauges.

The signal from the wave gauges was analysed with the program WAVELAB which is developed at the University of Aalburg. The program uses the method of MANSARD AND FUNKE (1980) for the reflection analysis of irregular waves. The method requires a simultaneous measurement of the waves at three positions in the flume in reasonable proximity to each other and on a line parallel to the wave propagation. For the spacing between the gauges the following is recommended:

X=1-2 L/10 p (4.8)

Lp /6 < X 1-3 < L p /3 and X 1-3≠≠ L p /5 and X 1-3 3L p /10

Laboratory tests by Mansard and Funke showed good agreement between incident wave spectra calculated by the least-square method and the corresponding spectra measured [HUGHES, 1993].

For these tests two sets of wave gauges are placed to measure the surface elevation. An array of three gauges has been placed 1m before the toe of the construction, measured form the last gauge in the array. The signal will give the actual wave height in front of the structure. A second array consists also of three gauges and is placed one wavelength from the construction, measured at SWL. Figure 4-3 shows the setup of one of the model tests.

Figure 4-3 Setup test facility

The second array is used as back-up if the results from the first array can not be used due to turbulent flow and reflection interactions from the model. The interactions become negligible beyond a distance of one wavelength from the structure corresponding to the peak period. The distance of 5,4 m corresponds with the wave length belonging to the largest peak period which will occur during testing. For the distance between the wave gauges there was according to equation (4.8) no single value recommended as the peak wave length for each run was different. In consultation with Ing. S. de Vree from the fluid mechanics laboratory of the faculty of Civil Engineering at the Delft University of Technology has been chosen to use a spacing 0.3 m between the first and second gauge and 0.7 m between the first and third gauge. A sampling rate of 32 Hz was applied during testing.

From the results of the reflection analysis in WAVELAB the significant wave height Hm0, the peak period TP and the reflection coefficient are used for analysis of the experiment. The results are shows in Appendix J.

30 MSc thesis

Chapter 4 Experiment setup

4.4 Test programme

On the basis of the findings in the literature study in Chapter 2 can be expected that the effect of the concrete specific weight on stability of Xbloc armour layer will be a function of the slope angle. Therefore we will try to eliminate the influence of all other parameters which determine the stability by keeping them constant throughout the test series. Which resulted in the test programme as presented in Table 4-2.

Table 4-2 Test programme Specific weight 1 Specific weight 2 Specific weight 3 Slope 3:4 Series A Series B Series C Slope 2:3 Series D Series E Series F Slope 1:2 Series G Series H Series K

Each series has been repeated several times to take into account the variance in the test data typical for Xbloc because the inherent difference in packing and subsequent interlocking. The repetition number in the report is indicated by roman numerals followed by a figure which indicates the run of the test series. For example code ‘A-I-1' is test series ‘A’, repetition I and run one. The specifications of each test performed can be found in Appendix J.

4.4.1 Structural test parameters

Specific weight There has been chosen to analyse the behaviour of three different specific weights, creating hereby three data points. This should give a good indication on the influence of the concrete specific weight. For the different specific weights a normal specific weight of about 2400 kg/m3, a light specific weight of about 2000 kg/m3 and a heavy specific weight of about 2800 kg/m3 is chosen. Minelco, a Swedisch supplier of minerals, has found willing to participate and produce the Xbloc elements for the model tests with a specific weight of about 2000, 2400 and 2800 kg/m3.

Slope angle Interlocking armour units in contrast with an armour layer of rock are less stable for flatter slopes. A flatter slope result in less interlocking and the stability of the armour unit will be more relying on its own weight. This is why interlocking armour layers are designed for a slope of 3:4 to 2:3. When the breakwater is constructed in an area subjected to earthquakes, the designed slope may be 1:2. In the last case the standard design criterion can not be applied and the design should be tested by physical model tests before construction. An Xbloc armour layer is generally used with slopes of an upper limit of 3:4 and a lower limit of 1:2. Therefore the influence of specific weight is investigated on these slopes.

B.N.M. van Zwicht 31

Effect of the concrete density on the stability of Xbloc armour units

4.4.2 Hydraulic test parameters

Wave steepness

Throughout the entire test series the fictitious steepness (Sop) is held constant. Typical wave steepness for wind generated wave lie between 0.02 and 0.04. For this research a wave steepness of 0.02 is used. The fictitious wave steepness is given by equation (2.2). By keeping the fictitious wave steepness constant throughout the test series, change in wave height will mean a change in the peak period. Thus increasing wave height results in longer waves. By doing so the Iribarren parameter (2.1) remains constant throughout the test series for a given slope angle. The idea is to have the same type of breaking on the slope throughout the test series. However, the Iribarren parameter will differ from slope to slope resulting in shift from complete surging breakers for the steepest slope to more collapsing breakers for the flattest slope. The Iribarren parameters for the different slopes are given in the table below. For additional information on the different breaker types reference is made to paragraph 2.2.1.

Slope ξop 3:4 5.3 2:3 4.7 1:2 3.5

Wave height and period The wave height is determined using the design formula for Xbloc armour unit presented in Chapter 3. Xbloc has a design value of the stability number of 2.77. For the model test a model block with a D of 2.9 cm is used. This results in the design wave height as presented in Table 4-3.

Table 4-3 Design wave height used in model test Relative Density Density [kg/m3] Wave height [cm] [kg/m3] Concrete Density 1 2000 1 5.57 Concrete Density 2 2400 1.4 7.80 Concrete Density 3 2800 1.8 10.03

Each test series consist of several runs with increasing wave height. The wave height is increased with each run, starting at 60 percent of the design wave height increasing till 180% of the design wave height. The period follows from the criterion of constant wave steepness (Sop). The wave height and period are presented for each specific weight in Table 4-4.

Water depth

The minimal required water depth should be at least 3 times the significant wave height (Hm0) of the in order to generate this wave height. Which result for this test programme in a water depth of 60 cm.

Number of waves The number of waves in a design storm which attack the breakwater construction depends on the duration of the storm. Hydraulic model tests are generally performed with 1000 waves. In prototype, 1000 waves represent a storm of 3 hours with a mean wave period of 10 seconds. For interlocking armour units is assumed that most of the damage has occurred after 1000 waves.

32 MSc thesis

Chapter 4 Experiment setup

Table 4-4 Wave characteristics model tests

% of Design

Variable wave height Hm0 [cm] Tp [s] Slope angle 3:4 / 1:1.5 / 1:2 60 3.34 1.03 density 2000 kg/m3 80 4.46 1.19 Sop 0.02 100 5.57 1.34 gamma 3.30 120 6.68 1.46 140 7.80 1.58 160 8.91 1.69 180 10.03 1.79

% of Design

Variable wave height Hm0 [cm] Tp [s] Slope angle 3:4 / 1:1.5 / 1:2 60 4.68 1.22 density 2400 kg/m3 80 6.24 1.41 Sop 0.02 100 7.80 1.58 gamma 3.30 120 9.36 1.73 140 10.92 1.87 160 12.48 2.00 180 14.04 2.12

% of Design

Variable wave height Hm0 [cm] Tp [s] Slope angle 3:4 / 1:1.5 / 1:2 60 6.02 1.39 density 2800 kg/m3 80 8.02 1.60 Sop 0.02 100 10.03 1.79 gamma 3.30 120 12.03 1.96 140 14.04 2.12 160 16.04 2.27 180 18.05 2.40

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Effect of the concrete density on the stability of Xbloc armour units

4.5 Model layout

The setup of the hydraulic model tests has already been shown in Figure 4-3. The setup of the three constructions is presented in Appendix C. In this paragraph the layout of the construction will be presented starting with the main dimensions after which the individual components will be discussed.

4.5.1 Main dimensions

The main dimensions of the 3 hydraulic models which are going to be tested are shown schematically in Figure 4-4. The crest height of the constructions is determined on the consideration that for the design wave height of the heavy concrete only minor overtopping takes place. Therefore a crest freeboard of two times the largest significant wave height has been chosen.

Figure 4-4 Main dimensions breakwater model

In order to minimise the amount of rows the lower part of the construction had to be fixated. It is of great importance to maintain the permeability, because it influences the flow field and therefore the load on the armour units. After consideration of a few options a gabion construction was chosen. Figure 4-5 show the placed gabion mattresses on the 1:2 sloped construction. The construction of the gabion is visually represented in Appendix D.

The toe, constructed of large stones, will support the gabion mattresses on which the armour layer is build. The size of rock used for the toe construction lies between 22.4 and 31.5 mm. The length of the armour layer is based on the damage expectation for Xbloc armour units. The area were damage can be expected lies between SWL +0.5 Hd and -1.5 Hd [DE ROVER, 2007]. The armour layer will be situated untill SWL -17.5 cm. This has been reduced to SWL -15 cm for the construction with the 1:2 slope angles due to the limited amount of available model blocks.

On the crest a concrete crest wall has been placed to prevent erosion and support the overtopping gully. On the inner slope gabion mattresses are placed to prevent the erosion of the inner slope due to the overtopping.

34 MSc thesis

Chapter 4 Experiment setup

Figure 4-5 Gabions placed on 1:2 slope

4.5.2 Armour layer

The armour layer is constructed with Xbloc armour unit with a unit height of 2.9 cm. This small size was chosen as it was expected that the waves generated in the flume could just cause damage to the heavy concrete units. It is the minimal size for which there is still turbulent flow through the armour layer. The size of the model block was held constant for all concrete densities to eliminate the influence of structural parameter on the hydraulic stability of the armour layer.

As said before Minelco has produced the models blocks. To determine the specific weight of the delivered model blocks several samples were taken of each series and the specific weight determined with a pycnometer.

This resulted in the following real densities which are used to further analyse the results. − Low concrete specific weight of 2102 kg/m3 − Normal concrete specific weight of 2465 kg/m3 − High concrete specific weight of 2915 kg/m3

Furthermore, the weight distributions of the samples of the different density series were quite wide. Therefore all model block have been weighed in dry and wet condition. There was no difference found between the results. The results for the weight distribution are shown in Figure 4-6.

The calculated weight of the model blocks should be, according to the design formula: − For 2000 kg/m3 the weight of a model block is 16.3 gram − For 2400 kg/m3 the weight of a model block is 19.5 gram − For 2800 kg/m3 the weight of a model block is 22.3 gram

The test program and model setup was based on these weights. The actual specific weights which were used should have a theoretical weight of: − For 2102 kg/m3 the weight of a model block is 17.1 gram − For 2465 kg/m3 the weight of a model block is 20.0 gram − For 2915 kg/m3 the weight of a model block is 23.7 gram

B.N.M. van Zwicht 35

Effect of the concrete density on the stability of Xbloc armour units

Light concrete block light concrete weight distribution

Density 2102 Kg/m3 70 1,4 Average 16.25 gr 60 1,2 Min 15.2 gr 50 1 40 0,8 Max 17.5 gr 30 0,6

Av. Deviatie 0.271435 units of No 20 0,4

Stand deviatie 0.335751 10 0,2 Probability Density 0 0 2 4 0 2 8 4 5, 5, 6, 6, 6,6 6, 7,2 7, 1 1 15,6 15,8 1 1 16,4 1 1 17,0 1 1 Weight [gr]

Normal concrete block Normal concrete weight distribution

Density 2465 Kg/m3 70 1,4 Average 18.85 gr 60 1,2 Min 17.9 gr 50 1 Max 19.7 gr 40 0,8 Av. Deviatie 0.2493 30 0,6 No of units No of Stand deviatie 0.31824 20 0,4 10 0,2 Probability Density

0 0

7 ,3 8,5 ,1 ,5 17,9 18,1 18 1 18, 18,9 19 19,3 19 19,7 Weight [gr]

Heavy concrete block Heavy concrete weight distribution

Density 2915 Kg/m3 70 0,9 60 0,8 Average 23.03 gr 0,7 50 Min 21.8 gr 0,6 40 0,5 Max 24 gr 30 0,4 0,3 No of units No of 20 Av. Deviatie 0.39533 0,2

Stand deviatie 0.482741 10 0,1 Probability Density 0 0

0 2 0 2 , , , , 4,0 21,8 22 22 22,4 22,6 22,8 23 23 23,4 23,6 23,8 2 Weight [gr]

Figure 4-6 Tables weight distribution Xbloc model blocks

36 MSc thesis

Chapter 4 Experiment setup

The variation in weight can have two reasons. When the specific weight is assumed uniform the variation in weight is due to variation in volume. This has been proven by measuring the dimensions of a sample of each specific weight. The second reason is due to non uniformity in the concrete mixture. Especially for light and heavy aggregates it could be a problem to get a good mixture as discussed in appendix B. The graphs of the light and heavy concrete weight distribution show two peaks which indicated two different mixtures with different specific weights. The difference in shape and use of mixtures with different specific weight has both a substantial influence on the weight distribution.

The Xbloc armour units are placed on a staggered grid with a dx of 1.30D and a dy of 0.64D. The model blocks were placed one by one by hand. The first layer was placed with the help of a mould. The following layers are placed by placing the Xbloc’s between the blocks of the previous layer in such a way that there is block makes contact with the slope and two element of the previous layer. Important is that the placement is random, adjacent armour units shall have different attitude and that each armour unit is keyed into two armour units of the row below. See Figure 4-7.

Figure 4-7 Xbloc armour layer placement

B.N.M. van Zwicht 37

Effect of the concrete density on the stability of Xbloc armour units

38 MSc thesis

Chapter 4 Experiment setup

4.5.3 Core

If flow velocities and size of the units are small, viscous forces may be greater in the model resulting in scale effects. The permeability of the core influences the armour layer stability, wave run-up and overtopping. Geometric scaling can lead to a too low permeability resulting in higher downrush pressures resulting in lower stability. Therefore is the core not scaled geometrically. The method described in BURCHARTH et al. (1999) is used to determine the core material. The method result in a diameter for the core material in the model such that the Froude scaling as described in 4.1.2 holds for a characteristic pore velocity. The pore velocity is chosen as the average velocity of a most critical area in the core with respect to the pore velocity.

First the pore velocity is calculated for the prototype scale. A fictitious scale length factor (NL) of 50 was chosen to transfer the model dimensions to prototype scale. The environmental parameters were scaled using Froude scaling.

For the pressure gradient in the prototype the average of 6 locations in the core at 6 moments in time was taken according to BURCHARTH et al. (1999) using the following equation:

π H ' ⎡⎤⎛⎞⎛⎞22ππ 22 ππ I =−s extxt−δπ2/xL⎢⎥δ cos⎜⎟⎜⎟ + + sin + (4.9) x '''⎜⎟⎜⎟TT LLL⎣⎦⎢⎥⎝⎠⎝⎠pp

With pressure gradient known the pore velocity in the core can be calculated using the Forchheimer equation given in BURCHARTH & ANDERSEN (1995):

22 ⎛⎞111−−nUnUν ⎛⎞ I =+αβ (4.10) x ⎜⎟2 ⎜⎟ ⎝⎠nnngdngd50 50 ⎝⎠

In which: nL0.5 2 δ Damping coefficient δ = 0.0141 p Hsb Hs Significant wave height n porosity b Core width Tp Wave Period L’ Wave length in the core L '= L / D valid for h/L<0.5 L Wave length (incident) α & β coefficients dependent on the Reynolds number and the grain shape and grading. See Burchart et al. (1995) for the values of α & β

According to the Froude scaling the velocity in the model should be:

UUmp= / NL (4.11)

With equation (4.9) and (4.10) the average velocity in the core of the model can be calculated. The diameter of the core should be chosen such that it fulfils (4.11). This resulted in a required D50 of 9 mm.

Use has been made of the available materials. A sieve curve has been made of the used materials which gave a slightly smaller D50 and higher grading then was accounted for. The D50 of the used

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Effect of the concrete density on the stability of Xbloc armour units

material is 7 mm with a grading of 1.63. This is accepted because the experiments are process- orientated .

100

% Weight 40

0 0 5 10 15 20 Dn [mm]

Figure 4-8 Sieve curve core material

4.5.4 Under layer

Design of the Xbloc under layer totally depends on the size of the above laying Xbloc unit. For the design of the under layer the normal configuration is used as described in Chapter 3. The under layer with the Xbloc of 2465 kg/m3 has been used applied to all constructions as the under layer design criteria are based on size and not weight. This results in a W50 of 2.4 gr and a Dn50 of 9.7 mm with a grade of 1.29. However, for execution purposes it was decided to use the same material for the under layer as used for the construction of the core.

40 MSc thesis

Chapter 4 Experiment setup

4.6 Damage definition and recording

4.6.1 Damage Definition

The definition of damage is subjective to different interpretations. What can be called damage and when is the amount of damage so great that can be said that the structure can no longer fulfil its function and has failed? Several failure modes have been presented in paragraph 2.1.2. The area of interest for this thesis is limited to the stability of the armour layer.

For single units in concrete armour layers of rubble mound breakwaters two types of failure can be distinguished; movement of one or more armour units and the breakage of a armour unit. A broken unit may loose his function due to reduction of the gravitational force and possible interlocking effect. The broken parts can cause further breakage of other units, because they are thrown around by the waves. Movement according to BURCHARTH (1993) can be divided in: 1. no movement 2. rocking a. Incidental movement b. regular movement c. continues movement 3. displacement single unit less than between 0.5 D- 1,0 D 4. Displacement > 1,0D. Unit is said to be removed out of the armour layer 5. Sliding of multiple units; Settlement entire or part of the armour layer.

According DE ROVER (2007) start of damage is defined as displacement of 1 or more Xbloc units (in the order of 4 units) from the armour layer and failure is defined as displacement of several units from the armour layer (in the order of 25 units) leading to exposure of the first under layer and displacements of stones out of the first under-layer. DE ROVER (2007) concluded that breakage of single layer armour units has a significant negative effect on start of damage of the armour layer. However breakage of single layer armour units has no significant effect on failure of the armour layer. Furthermore, the majority of the broken parts showed little to no movement during his research. It is therefore unlikely that rapid damage progression occurs due to broken parts damaging other units.

For this research the displaced of one element from the armour layer is defined as start of damage. Armour layers constructed with interlocking elements in a single layer are highly self repairing of nature. Elements will settle surrounding the location of the dislocated element resulting in improving interlocking and no further damage may occur. The same reason why breakage of single layer armour units has no significant effect on failure of the armour layer. However when multiple elements are removed from the same area the coherence is lost and damage development occurs more rapidly. From the observation during the model test it was found that this occurred when 4 or more element were displaced from the same location. This resulted as well in the beginning of the erosion of the under layer. Overall the total displacement was in the order of 10 units when this occurred. This is why for this research failure of the armour layer is defined as the displacement of 10 elements.

B.N.M. van Zwicht 41

Effect of the concrete density on the stability of Xbloc armour units

4.6.2 Damage recording

General there are two ways to present damage of random placed armour units, by the damage number Nd and Nod. Nd presents the number of displaced units out of the armour layer as a percentage of the total number of units within a reference area. Van der Meer uses a different definition of damage which is divined with Nod. He defined the damage number as the number of displaced units out of the armour layer within a strip with the width of the nominal diameter (Dn). For this research the method of Van der Meer is applied.

number of displaced units Nod = (4.12) width armour layer / Dn

According to the ROCK MANUAL (2007) the damage area for single layer armour units is SWL +/-

1.5 Hd (design wave height). For Xbloc armour units the area were damage can be expected lies between SWL +0.5 Hd and -1,5 Hd [DE ROVER, 2007].

42 MSc thesis

Chapter 5 Observations

This chapter discusses the observations made during the model testing. The placement density is an important parameter on the hydraulic stability of Xbloc armour layers which is already discussed in Chapter 3. It appeared difficult to control the placement density due the small size of the model blocks. The low weight of the light model blocks made it even more difficult to control the placement. The influence of the placement density on the damage development will be discussed as well as the variation in the settlement that has been observed. When damage occurred different failure mechanisms were observed. These are described in paragraph 5.2.3. First the observations on placement density, settlement and failure mechanisms will be discussed in general after which the observations are discussed in more detail for each slope.

5.1 Design wave height

The design wave used as an input parameter for the model tests is calculated according to three specific which were chosen preceding the start of the hydraulic model tests namely: 2000, 2400 and 2800 kg/m3. The actual specific weights of the model blocks used were 2102, 2465, and 2915 kg/m3. The wave height is calculated with the stability number (2.8). For Xbloc a stability number of 2.77 is determined. The design wave heights for the different specific weight are presented in Table 5-1 and Table 5-2. The definition of the design wave height used in this chapter corresponds with the values given in Table 5-1 and differs some from the actual design wave height as presented in Table 5-2. The difference has no influence on the final results as the damage is presented in relation to the dimensionless stability number.

Table 5-1 Design wave height used in model tests Density Relative Density Wave height [kg/m3] [kg/m3] [cm] Concrete Density 1 2000 1 5.57 Concrete Density 2 2400 1.4 7.80 Concrete Density 3 2800 1.8 10.03

Table 5-2 Actual design wave height Density Relative Density Wave height [kg/m3] [kg/m3] [cm] Concrete Density 1 2102 1.102 6.14 Concrete Density 2 2465 1.465 8.15 Concrete Density 3 2915 1.915 10.67

B.N.M. van Zwicht 43

Effect of the concrete density on the stability of Xbloc armour units

5.2 General observations

5.2.1 Placement density

The placement of the armour layer is essential for single layer armour units as it affects the hydraulic stability of single blocks. The quality of the placement is determined by packing density and interlocking. The packing density is measurable whereas the interlocking can only be assessed by visual inspection, TEN OEVER et al (2006). As discussed in Chapter 3 it has been found that placement densities above 1.18/D2 lead to better hydraulic stability. For lower placement densities the hydraulic stability is constant and it was found that the units settle and obtain a density close to the design density, [BAKKER et al, 2005]. DMC prescribes a placement density of 1.20/D2.

The Relative Placement Density (RPD) gives the ratio between the real packing density and the prescribed packing density of 1.20/D2 and is calculated according to formula (3.2). A requirement for construction is that the packing density on the slope shall be between 98% and 105% of the theoretical required packing density [MUTTRAY et al, 2003].

Placement of the armour layer took place as described in paragraph 4.5.2. The relative placement was determined after completion of the armour placement. The formula is highly sensitive for minor variation in the measurement of the distances and it was found difficult to determine in situ the lengths of the centreline trough the outer line of the armour layer. Therefore a RPD was taken by analysis of the start photos of each test series to overcome this problem. They showed the same trend but the values differ greatly from the in-situ measurement.

In order to see the results of the in-situ measurement and the photo analysis in more perspective a third value of the RPD is determined, the theoretical RPD. The theoretical RPD is the actual amount of rows divided by the amount of rows which should be on the slope theoretically according to a placement density of 1.20/D2. This value does not give the actual placement density as the armour layer might lie partly on the crest or just under the crest which is not visible on the photos taken. The three RPD’s are presented in Figure 5-1. The figure shows the same trend line for all tree methods. The average of the three RPD’s is a taken to give a good indication of the actual placement density, as presented in Appendix H. Two outline data points have been removed from the data set, the in- situ measurements of A-I and C-IV. The average RPD are presented in Table 5-3. The analysis on the influence of the relative placement density on the damage development is discussed in the next chapter.

Table 5-3 Relative placement densities per test series Test series RPD [%] Test series RPD [%] Test series RPD [%] Test series RPD [%] A-I 103.1 B-V 109.8 D-II 103.7 F-II 95.1 A-II 104.9 BL-I 102.5 D-III 99.9 F-III 98.3 A-III 102.5 BL-II 102.6 D-IV 96.1 G-I 102.5 A-IV 102.6 C-I 110.9 E-I 102.1 G-II 102,9 B-I 106.8 C-II 111.2 E-II 98.5 H-I 99.4 B-II 108.6 C-III 102.7 E-III 98.1 H-II 100.3 B-III 102.4 C-IV 106.9 E-IV 96.4 K-I 98.9 B-IV 107.8 D-I 105.1 F-I 97.7 K-II 100.0

44 MSc thesis

Chapter 5 Observations

For future model tests it is recommended that the placement density is determined according to photo analysis as this is the most accurate method. For this method the dimensions of the slope should be well indicated in the photograph as the dimensions are distorted by the angle from were the photo is taken. This can be accomplished by putting a sheet of paper on the slope. For the analysis of the photographs in this research we were not able to transfer the distorted scale in the photo completely back to the original dimensions because the scale was only known in two points in the photograph.

Relative placing densities

120,0

In situ 115,0 Foto theoretical 110,0

105,0

100,0 RPD [%]

95,0

90,0

85,0

80,0 A-I A-II A-III A-IV B-I B-II B-III B-IV B-V BL-I BL-II C-I C-II C-III C-IV D-I D-II D-III D-IV E-I E-II E-III E-IV F-I F-II F-III G-I G-II H-I H-II K-I K-II Test series

Figure 5-1 Relative placement densities

5.2.2 Settlements

In earlier tests on the placement of Xbloc armour layers it has been found that for packing densities of 1.15/D2 (or a RPD of 95 %) the armour unit above the waterline haven been displaced by 0.5D during the first test. This is in the order of 3% settlement. No further settlements have been observed in the following runs. For packing densities of 1.20/D2 and more, no settlements have been observed at all. The tests were performed on a relatively long armour layer slope with 28 rows. For this research the number of rows used was even higher; 34 rows for the 3:4 slope, 36 rows for the 2:3 slope and 40 rows for the 1:2 slope. Test series B-I till B-V and C-I and C-II were done on a shorter slope with 30 rows. (For a translation of the test series codes reference is made to paragraph 4.4). More settlement is to be expected due to higher number of rows used.

In general settlements were observed especially in the first test runs up to 100% of the design wave height. With increasing wave height the settlements still occurred but were less severe. Series of higher waves in the beginning of a run caused the most settlements. Before and after this series of higher waves just minor settlements were noticeable unless damage had occurred. The settlements created a dividing line which marks the maximal wave run up. This boundary line moved in upward direction with increasing wave height until the run-up had reached the breakwater crest.

B.N.M. van Zwicht 45

Effect of the concrete density on the stability of Xbloc armour units

The actual settlements were measured by photo analysis. For each run in a test series the distance of the same 6 Xbloc was measured relative to the fixated toe construction. In this way the relative settlement in relation to the start situation could be determined. At each run the same row was taken situated around one design wave height above the SWL for the normal density Xbloc, see Figure 5-2. In this way the settlements over the entire test series could be compared as the settlements created a dividing line which marks the maximal wave run up where above no settlement have occurred. On a slope the same number of rows was taken for each specific weight. The results are presented in Appendix I. The results found on the development of settlement are now discussed for each slope.

Figure 5-2 Measurement Settlement

Slope 3:4 On a slope of 3:4 the initial settlements are in the order of 3 %. The settlement gently develops to proximately 7% and 10% for test series BL-I. Only when severe damage occurs, the settlement increases rapidly. Analysis of the starting photos of BL-I and BL-II shows remarkable looser placement under the SWL of BL-I which could explain the higher settlement rates.

Slope 2:3 On a slope of 2:3 the initial settlement differ greatly between test series with different specific weights. The initial settlements are in the order of − 1 % for light concrete − 5 to 6 % for normal concrete − 7 % for heavy concrete The RPD of the different specific weights are between − 97% and 105% for the light concrete − 96% and 102% for the normal concrete − 95% and 99% for the heavy concrete The settlement gently develops to a maximum value which is equal for each specific weight, unless severe damage occurs then the settlement increases rapidly.

46 MSc thesis

Chapter 5 Observations

For the steep slopes, 3:4 and 2:3, is found that the largest settlements occur for light concrete at the design wave height, for normal concrete at 80% of the design wave height and for heavy concrete of at 60% of the design wave height. The development of settlement seems to increase with lower placement densities and increase in weight of the armour units.

Slope 1:2 On a slope of 1:2 only minor settlements occurred till 140% of the design wave height or the start of damage. These settlements were not observed during testing. The magnitude of the settlements gradually increases with higher specific weights while the RPD slightly decreases with increasing specific weight.

5.2.3 Failure Mechanisms

During the test two main failure mechanisms were distinguished which results in the displacement of an armour unit out of the armour layer. All displacements were by rotation out of the armour layer up-slope or down-slope after the following mechanisms occurred: 1. An armour unit is lifted perpendicular to the armour layer from the under layer. 2. An armour unit which has freedom of movement due to settlement or rocking is turned out of the armour layer under up or down rush. In addition to these failure mechanisms a third potential failure mechanism was identified; the armour layer under the SWL was lifted by multiple rows at once during extreme downrush and the following turbulent uprush. Video recording from the side were extensively analysed to investigate the processes involved. The results are described below. The displacement of armour units out of the armour layer is illustrated by a series of figures presented in Figure 5-3. For a more detailed view reference is made to Appendix L.

Displacement of Xbloc out of armour layer The displacement of armour units out of the armour layer has two appearances; rolling of the unit out of the armour layer in upward direction or in downward direction. The most dominant process observed is the rotation of an element out of the armour layer under influence of highly turbulent uprush. Prior to the rotation under the turbulent uprush always the same series of events occurred. A higher wave or series of higher waves in the wave train resulted in high run-up level followed by a deep downrush. The flow during downrush is almost completely parallel to the slope. At the lowest point the flow is directed outward. The following wave is overtaking the crest of the previous wave at the lowest point of the downrush resulting in a turbulent breaker which hits the slope under the SWL, see figure (1) to (4) in Figure 5-3. The flow inside the structure is running behind the wave crest resulting in high pore pressures inside the structure. In combination with the absence of water mass, this resulted in a strong flow directed outward at the lowest point of the downrush in the area under the SWL, see figure (2) and (3) in Figure 5-3. The turbulent breaker in combination with the outward directed flow destabilises the unit. The run-up flow rotates the element eventually out of the armour layer. On slope of 3:4 the element turned out of armour layer is taken far upward; this is becoming less for flatter slopes. This is illustrated by figure (5) to (8) in Figure 5-3. The destabilisation forces which are of importance here are − drag forces perpendicular to the slope due to the outward directed flow − drag and lift forces due to the run-up flow − inertia forces of the turbulent breaker and the lagging outward directed velocities

B.N.M. van Zwicht 47

Effect of the concrete density on the stability of Xbloc armour units

The unit is not always completely removed from the armour layer by the processes described above and settles on it original positions just moments after the turbulent roller has past. However the element no longer interlocks with the surrounding element and is easily removed by the following downrush due to the drag and lift forces of the run-up or run-down flow of which the run-down is more dominant.

If interlocking is lost due to settlements, removal of surrounding elements or rocking, the element is more easily displaced out of the armour layer. No extreme downrush accompanied by a turbulent uprush is required. In this case the element is rotated out of the armour layer by the drag and lift forces of the run-down flow.

Armour layer lifted from under layer The lifting of multiple rows from the under layer the SWL is initiated again by a higher wave or series of higher waves in the wave train resulted in high run-up level followed by a deep downrush field. The sequence of events is equal to the displacement of armour units due to the turbulent breaker. The difference is that no single element is removed from the armour layer but that the entire row comes loose from the under layer at the point were the breaker interacts with the construction. The elements settle again after the breaker has past. The lifting of armour layer no longer occurs after the uprush has past the SWL. The explanation for this phenomenon is the same. The flow inside the structure is running behind the wave crest resulting in high pore pressures inside the structure. In combination with the absence of water mass, this resulted in a strong flow directed outward at the lowest point of the downrush in the area under the SWL. The turbulent breaker in combination with the outward directed flow destabilises the armour units. However in this case the interlocking of all elements is sufficient to prevent single units to dislocate from the slope.

Lifting of the armour layer can result in an increase in settlement due to loss of friction forces between the armour layer and the under layer. However the elements are kept in place by the drag force from the run-up. In general minor settlements are observed due to the lifting of the armour layer Settlements due to lift of armour layer under SWL can result in not complete resettlement of the units. This result in a pile up of elements which makes the armour layer more vulnerable because the elements are more exposed to the wave action and the reduced interlocking. A positive effect is arch development which increases the strength of the armour, but if one element is dislocated the entire coherence is lost and damage will develop rapidly.

Settlements Interlocking is extremely important for the armour layer to remain hydraulically stable. For single layer armour units therefore no movement is allowed and the prescribed placement density of 1.20/D2 should be met to make sure the elements are all well interlocked. Minor settlement can be expected which results overall in better interlocking. Settlements have no negative effect on the hydraulic stability if the placing density is correct and not too many rows are used. DMC prescribed a maximum of 20 rows.

Settlement of entire armour layer is initiated by reduced friction between armour layer and under layer due to high pore pressures inside the structure and high outflow velocities. At the same time the elements are pulled downward due to gravity and drag forces from the run-down over and through the structure.

48 MSc thesis

Chapter 5 Observations

Figure 5-3 Displacement of a unit out of the armour layer

B.N.M. van Zwicht 49

Effect of the concrete density on the stability of Xbloc armour units

5.3 Slope 3:4

5.3.1 Wave structure interactions

During the testing the wave steepness was held constant resulting in a change of peak period with higher waves. The breaker type observed during testing was constant in appearance throughout the test series and corresponds with the calculated surf similarity parameter which indicated surging waves.

The breaker type for a slope of 3:4 was surging with occasionally some turbulence at the wave crest. Due to energy dissipation inside the armour layer the flow velocities inside the armour layer were significantly lower then the flow over the armour layer by which the wave crest over the armour layer surface overtakes the flow in the armour layer. Series of higher waves result in collapsing breakers with turbulent rollers during uprush. Impact of the collapsing breaker is largely under SWL and hits the armour layer directly. No body of water is present between the breaking wave and armour layer due to the deep downrush.

5.3.2 Failure mechanisms

Failure mechanisms were as described in paragraph 5.2.3. For each specific weight the characteristics concerning these mechanisms are discussed briefly.

Light concrete: − From 80%-100% of the design wave height multiple rows below SWL are lifted from the under layer. − First test series (A-I) the armour layer is lifted from the under layer. This resulted in the sliding down of the armour layer above SWL which results in a pile up of elements below SWL. Due to the low interlocking the elements are easily displaced out of the armour layer by the waves. The observed failure had more the appearance of geotechnical failure then hydraulic failure. There was an indication of slip failure of under layer in stead of failure armour layer. This is why the series in not taken into account in the analysis of the results later on.

Normal concrete: − From 120% of the design wave height multiple rows below SWL are lifted from the under layer. However the lift is less than for light model blocks. − There is a pile up of armour units under the SWL noticeable. This might be due to the lifting of the armour layer from the under layer in combination of the settlement of rows above. − The first test series (B-I) the armour layer failed due to the failure of the toe construction. This series in not taken into account in the analysis of the results later on.

Heavy concrete: − Only gradual settlements were noticeable. Furthermore there is barely any movement and no armour units have been displaced out of the armour layer.

50 MSc thesis

Chapter 5 Observations

5.3.3 Xbloc displacement out of armour layer

Analysis has been done on the displacement of the Xbloc armour units. It has been determined by the DE ROVER (2007) that failure could be expected between SWL + 0.5 Hd and SWL – 1.5 Hd for slopes of 3:4. For each tests the location of a displaced armour units was marked on a transparent sheet. On the sheet also the reference line of 1.5 times the design wave height for each specific weight is indicated. All is presented in Figure 5-4.

The displacements of the light concrete elements are situated in the area between SWL and SWL –

1.5 Hd ‘2000’. The displacements of the normal concrete elements are clustered between SWL and

SWL – 1.5 Hd ‘2400’. This is in accordance wit the observations made by De Rover and can be explained by observation that the impact of the collapsing breaker is largely under SWL. This is the most critical situation as in the area under SWL the rundown velocities are the highest and there is flow directed outward. There are high pore pressures inside the structure in absence of water mass outside due to the deep run down.

Figure 5-4 Slope 3:4 Xbloc displacement out of armour layer Legend: Location where a low density Xbloc has been removed out of the armour layer Location where a normal density Xbloc has been removed out of the armour layer Location where a high density Xbloc has been removed out of the armour layer

B.N.M. van Zwicht 51

Effect of the concrete density on the stability of Xbloc armour units

5.4 Slope 2:3

5.4.1 Wave structure interactions

As for the slope angle of 3:4 the breaker type observed during testing was constant in appearance throughout the test series. The breaker type was predominantly surging with occasionally some collapsing breaker. Series of higher waves resulted in the more collapsing breakers with turbulent roller during uprush. Impact of the collapsing breaker is shifted to the SWL, the heaviest attack occurred still under the SWL. 5.4.2 Failure mechanisms

Failure mechanisms were as described in paragraph 5.2.3. For each specific weight the characteristics concerning these mechanisms are discussed briefly.

Light concrete: − At 80%-100% of the design wave height multiple rows below SWL are lifted from the under layer. With increase in wave height it occurs more often. − After lifting of multiple rows, settlement resulted in pile up of units under the SWL.

Normal concrete: − From 120% of the design wave height multiple rows below SWL are lifted from the under layer. For test E-III at 80% series of high wave also lift the bed after which some settlements occur. Later on no more lifting was observed.

− At 120% Hd there is a pile up of armour units under the SWL. − Development of the pile up continues at higher waves.

Heavy concrete:

− At 140% Hd there is a pile up of armour units under the SWL.

5.4.3 Xbloc displacement out of armour layer

Analysis of the displacement of Xbloc armour units have been done as described. The displacements of the light concrete elements are situated in the area between SWL + 1.5 Hd ‘2400’ and SWL – 1.5

Hd ‘2000’. The displacements of the normal concrete elements are situated between SWL +1.5 Hd

‘2000’ and SWL – 1.5 Hd ‘2400’. The location where a high density Xbloc has been removed out of the armour layer is situated between SWL +1.5 Hd ‘2800’ and SWL – 1.5 Hd ‘2000’. All is presented in Figure 5-5.

In Figure 5-5 some elements have been dislocated high above the SWL. The light concrete elements lost the interlocking with adjoined units because of high settlements which were initiated by displacement of armour units beneath the SWL. The other elements lost their interlocking as well, but the settlements were not due to dislocation of armour units. At very high waves these loose element are removed easily from the slope as they no longer interlock. The removal of these element is due settlement and not because of wave structure interaction. In practice the displacements of armour units high on the slope is not expected to occur as they were observed in the model tests,

52 MSc thesis

Chapter 5 Observations

because construction of armour layers with Xbloc is normally limited to 20 rows with minimised settlements.

In comparison with the 3:4 slope the greater part of the dislocated elements is shifted a bit to the SWL. Incidental elements are dislocated higher up the slope.

Figure 5-5 Slope 2:3 Xbloc displacement out of armour layer Legend: Location where a low density Xbloc has been removed out of the armour layer Location where a normal density Xbloc has been removed out of the armour layer Location where a high density Xbloc has been removed out of the armour layer

5.5 Slope 1:2

5.5.1 Wave structure interactions

As for the slope angle of 3:4 and 2:3 the breaker type observed during testing was constant in appearance throughout the test series. The breaker type was shifted from totally surging to more collapsing breakers. Still series of higher waves resulted in the collapsing breakers with turbulent roller during uprush which were of great importance in the destabilisation of the armour units. The impact of the breaker was situated around SWL with the major part of the impact predominantly above the SWL.

5.5.2 Failure mechanisms

Failure mechanisms were as described in paragraph 5.2.3. For each specific weight the characteristics concerning these mechanisms are discussed briefly.

B.N.M. van Zwicht 53

Effect of the concrete density on the stability of Xbloc armour units

In general it is the model blocks are less firmly placed, resulting is less interlocking. There is more freedom of movement without an increase of settlement. This does not result in more displacement out of the armour layer, but it does result in more movement (rocking).

Light concrete: − Settlements are mainly due to blocks which tumble over. − At 140% of the design wave height there is a gradually arose pile up of armour units under the SWL. − From 100% till 180% of the design wave height multiple rows below SWL come loose from the under layer. There is movement in several rows of armour units below and above SWL. − From 100% of the design wave height the armour layer seems to move along with the run up and run down around the SWL Armour. Movement increases with increasing wave height.

Normal concrete: − From 120% / 140% of the design wave height multiple rows below SWL are lifted from the under layer. There is movement in several rows of armour units around SWL. − Armour layer seems to move along with the run up and run down around the SWL Movement increases with increasing wave height from 120%-140% of the design wave height.

Heavy concrete: − From 120% of the design wave height there is an increase in movement throughout the armour layer. − From 160% of the design wave height multiple rows below SWL are lifted from the under layer. There is movement in several rows of armour units below and above SWL. Armour layer seems to move along with the run up and run down around the SWL.

5.5.3 Xbloc displacement out of armour layer

Analysis of the displacement of Xbloc armour units have been done as described. The displacements of the light concrete elements are situated in the area between SWL + 1.5 Hd ‘2000’ and SWL – 1.5

Hd ‘2000’. The displacements of the normal concrete elements are situated between SWL and SWL

– 1.5 Hd ‘2000’. The location where the heavy concrete Xbloc’s have been removed out of the armour layer is clustered between SWL and SWL+1.5 Hd ‘2000’. All is presented in Figure 5-6

The run down observed is significantly less than on the steeper slopes. This results in a body of water between the turbulent collapsing breaker and the slope. There is less impact on the lower part of the slope. The presents of the body of water under the SWL reduces the run down velocities and it counteracts the pore pressures inside the structure, resulting in a lower pressure difference and lower outward velocities.

It has been found that the light element are more easily removed perpendicular from the armour layer as the have less resistance against the flow forces due to a lower weight. This applies for all slope angles. Therefore the light elements are displaced from the armour layer under the SWL where

54 MSc thesis

Chapter 5 Observations

these outflow velocities are the highest as well as above the SWL were the impact is of the collapsing breakers. The heavier elements are only displaced by the collapsing breakers which turn the elements out of the armour layer. The wave load and outflow velocities might be lower on a slope of 3:4 or 2:3 but the elements are also looser packed, resulting in a lower strength of the armour layer. The lower packing, which is not the same as the placement density, makes it also possible for the run up and run down velocities to displace the units out of the armour layer. This mainly occurs above the SWL. The lower packing is due to the reduced slope angle. As explained in paragraph 2.2.3 a flatter slope reduces the interlocking capacities, the greater part of the element is resting on the slope in stead of on the surrounding elements.

Figure 5-6 Slope 1:2 Xbloc displacement out of armour layer Legend: Location where a low density Xbloc has been removed out of the armour layer Location where a normal density Xbloc has been removed out of the armour layer Location where a high density Xbloc has been removed out of the armour layer

B.N.M. van Zwicht 55

Effect of the concrete density on the stability of Xbloc armour units

56 MSc thesis

Chapter 5 Observations

5.6 Discussion

In this paragraph the observation made during the model tests on the relative placement density, settlements and hydraulic stability as describes in the previous paragraphs will be further discussed. 5.6.1 Relative placement density and settlements

Observations made duration testing shows the importance of placement density as it influences the hydraulic stability. Measurement on the quality of placement can be expressed with the relative placement density as introduced in Chapter 3. The observations gave no clear relation between the start of damage and the relative placement density for the different slope angles and specific weights. Nevertheless the placement density is expected to influence the hydraulic stability.

For the relative placement density in relation to the damage development it is found that start of damage occurs at the same wave height with high as well as with low placement densities. Damage development increases the most at the lowest placing densities for each slope. However these lowest placing densities differ significantly between the slopes. To get more insight in the influence of the relative two data sets are plotted. The stability number for start of damage and failure is set out against the relative placement density, see Figure 5-7.

Influence RPD on Stability

7,0

6,0

5,0

4,0

3,0 Ns = Hs/Delta*Dn Ns = Hs/Delta*Dn

2,0

1,0 Start of damage Nod=0.05 Failure Nod=0.55 0,0 94,0 96,0 98,0 100,0 102,0 104,0 106,0 108,0 110,0 112,0 RPD [%]

Figure 5-7 Influence placement density on hydraulic stability (dashed line - - - Ns = 2.77; the design value of Xbloc)

Start of damage or failure did not occur for every test series. Figure 5-7 shows a slight increase in the stability number for the start of damage with increasing relative placement density. Failure occurs at significant higher stability numbers with increasing relative placement densities. So for higher placement densities start of damage remains almost constant throughout the test series. However the damage development is significantly lower for high placement densities. This is consistent with the results presented in Figure 3-3.

B.N.M. van Zwicht 57

Effect of the concrete density on the stability of Xbloc armour units

Figure 5-7 shows four test series for which start of damage already occurs before the design value for Xbloc of Ns = 2.77 is reached. There is no relation found between the relative placement density and the early start of damage. The individual tests will be further discussed in following paragraph.

The placement density seems to have no influence on the initial settlements for a specific test series. The placement densities on the 3:4 slope were all above 103% of the prescribed placing density. For these tests there was also no difference observed between the initial settlements of the test series with different specific weights. For a slope of 2:3 there is also no influence on the initial settlements for a specific test series with an average placing density of about 100%. Only here the influence of the specific weight on development of the settlement is very clear. The heavier the model block the quicker the development occurred. The maximal settlements occur at lower wave heights, form 60%

HD for the heavy elements to 100%-120% Hd of the light elements. For gentle slopes, despite the sometimes low placement densities, no or minor settlements take place. This applies to all test series foe each specific weight. Due to the absence of initial settlements the interlocking is less and the armour layer around SWL moves along with the wave motion starting for the light elements at 100% Hd to 160 % Hd for the heavy elements. The movement increases with higher waves.

In general the settlements occur on such a relatively long slope with many rows that it results in the exposure of the crest despite the sometimes very high placement densities. With overtopping waves the elements high on the slope are easily removed. The lower the placement density the higher the settlement and a larger area of the crest will be exposed. If such long slopes will be constructed, the placement should be tighter or after a while additional blocks should be placed to fill the gaps formed. The settlements improve the hydraulic stability as interlocking between the elements is increased.

5.6.2 Hydraulic stability

Several processes are observed which could hamper the hydraulic stability. They are summarized below: − A higher wave or series of higher waves in the wave train resulted in a high run-up level followed by a deep downrush. The flow during downrush is almost completely parallel to the slope. At the lowest point the flow is directed outward. The following wave is overtaking the crest of the previous wave at the lowest point of the downrush resulting in a turbulent breaker which hits the slope under the SWL. The flow inside the structure is running behind the wave crest resulting in high pore pressures inside the structure. In combination with the absence of water mass, this resulted in a strong flow directed outward at the lowest point of the downrush in the area under the SWL. The turbulent breaker in combination with the outward directed flow destabilises the unit(s), resulting in: o Lifting of multiple rows at once under the SWL which can result in sliding of the armour layer. o Turning of an armour element out of the armour layer

− If interlocking is lost due to settlements, removal of surrounding elements or rocking, the element is more easily displaced out of the armour layer. No extreme downrush accompanied by a turbulent uprush is required. In this case the element is rotated out of the armour layer by the drag and lift forces of the run-down flow.

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Chapter 5 Observations

− Due to the absence of initial settlements the interlocking is less and the armour layer around SWL moves along with the wave motion for a slope of 1:2 which threaten the structural integrity of the armour units. − On slope of 3:4 the element turned out of armour layer is taken far upward; this is becoming less for flatter slopes. On a slope of 1:2 the element is even transferred up and down the slope a couple of times before it is completely removed from the armour layer. This could cause major damage to the armour units.

The dominance of the high downrush with the turbulent breaker as the important destabilization process becomes less from the steep slopes to the more gentle slopes, where besides this process also the up and downrush velocities are able to dislocate the elements. The impact of the turbulent breaker is shifted from under the SWL to the SWL as the downrush decreases with flatter slopes. This result in a transfer of clustered damage under the SWL for the 3:4 slope to damage spread between approximately 1 design wave height around the SWL for normal concrete elements for the 1:2 slope. This can be explained by the change of wave structure interaction from surging to more collapsing type which can be good describe with the fictitious surf similarity parameter.

The main observations are summarized in Table 5-4.

Table 5-4 Observations Spec. weight Major settlements Lift of armour Slope ξop 3 Remarks [kg/m ] [% Hd] [% Hd] 2102 100-120 > 80 - Turbulent breaker as dominant 3:4 5.3 2465 100-120 > 120 destabilization force 2915 100-120 - - high relative placement density (>103%) 2102 100-120 > 80 - Turbulent breaker as dominant 2:3 4.7 2465 80 > 120 destabilization force 2915 60 - - relative placement density between 96-105% 2102 > 140 > 100 - Turbulent breaker & up and downrusch 1:2 3.5 2465 > 140 > 120 velocities as destabilization force 2915 > 140 > 160 - relative placement density around 100%

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Effect of the concrete density on the stability of Xbloc armour units

60 MSc thesis

Chapter 6 Analysis Experiment Results

The observations as described in the previous chapter gave no relation on the influence of the specific weight on the hydraulic stability. From the theory in Chapter 2 is concluded that the influence of the specific weight on the hydraulic stability is influenced by the slope angle. Therefore the hydraulic stability of the Xbloc armour layer is analysed in respect to the specific weight as well as the slope angle. The results of the model tests are presented in graphs where the stability number

Ns is set out against the damage number Nod resulting in damage curves for the individual test series

First the behaviour of the individual test series is discussed in relation to the current design conditions as described in paragraph 6.1 after which the results are discussed per density (6.2) and per slope (6.3) to analyse their influence. This has resulted in a new stability formula for Xbloc armour layer which is presented in paragraph 6.5. A discussion on the test results is presented in paragraph 6.4.

6.1 Analysis tests series

The results are analysed by comparison of the damage number Nod with the corresponding stability number Ns for the individual test series. Xbloc start of damage can be expected for normal concrete on a slope of 3:4 at Ns between 3.3 and 5.5 and failure between Ns = 3.7 and 6.0. (See paragraph

3.2). Start of damage correspond with Nod = 0.05 and failure with Nod = 0.55. In terms of design wave heights for model tests Delta Marine Consultants states the following:

− Start of damage occurs at wave heights ≥ 120% of the design wave height

− Failure occurs at wave heights ≥ 150% of the design wave height These values are for model tests with normal concrete on a slope of 3:4. The results may differ for different configurations. However if the stability parameter is assumed valid for single layer interlocking armour unit the results should be in accordance with the definition of start of damage and failure for normal concrete elements as describe above.

6.1.1 Test series slope 3:4

The test series on the slope of 3:4 should be in accordance with the results on which the current armour layer design with Xbloc armour units is based (See Chapter 3), at least for the normal concrete elements. From the damage curves it becomes clear that this is not the case for the light concrete elements. Here damage occurred well before the design criterion of Ns = 2.77. The normal concrete elements are more stable than expected as start of damage start at 200% of the design wave. For the heavy element even no displacement of armour units out of the armour layer take place.

Light concrete elements The tests with the light concrete units are presented in Figure 6-1. In Chapter 5 the deviating test results of test A-I were already discussed. The test series shows a wide variance in start of damage even if test A-I is excluded from the series. In test A-IV no damage occurred while for test A-III start of damage occurred well before the design criterion of Ns = 2.77. Damage development for A- III continues far after the design criterion has been past. This early start of damage can be explained

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Effect of the concrete density on the stability of Xbloc armour units

by the failure of a single badly placed element. The hydraulic stability of the entire armour layer is not hampered. Further damage development is being withheld due to the tight packing. It seems that the hydraulic stability is less for lower specific weight than what is expected according to the design stability criterion, especially with relative placement densities all above 102.5 %.

Light concrete

1,40

1,20

1,00

0,80

Nod A-II 0,60 A-III

0,40 A-I 0,20

A-IV 0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-1 Stability curves test series A

Normal concrete elements Two series of tests were performed with concrete elements with the normal specific weight; a series with a short slope of about 30 rows and a series with a long slope of 34 rows, equal to other test series.

The series with the short slope are presented in Figure 6-2. The series show good resemblance with the expected damage developments. Start of damage occurs above 120% of the design wave height. Accept for test B-III, all placing densities are far above the 100%. For these tests there is only minor damage development. Test B-III fails after the initial start of damage with the next increase in wave height which is still in accordance to the expected damage progression.

The series with the long slope are presented in Figure 6-3. Start of damage occurs considerable later than for the short slope while the placement densities are in the same order as with test B-III. A longer slope results in a higher hydraulic stability as the interlocking is improved by the increased weight due to the number of rows. A disadvantage of a long slope is that the total settlement increases as well, resulting in more exposure of the crest. The results of the test series with short slopes are excluded from the analysis of the results to exclude the influence of the slope length.

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Chapter 6 Analysis Experiment Results

Normal concrete

1,40 B-III 1,20

1,00

0,80 Nod 0,60

0,40

B-II 0,20 B-IV 0,00 B-V 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-2 Stability curves test series B (short slope)

Normal concrete

1,40

1,20

1,00

0,80 Nod 0,60

0,40

BL-I 0,20

BL-II 0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-3 Stability curves test series BL (long slope)

Heavy concrete elements As with the normal concrete elements two series of tests were performed for the heavy concrete element, with a long and a short slope. In both cases no units were displaced out of the armour layer.

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Effect of the concrete density on the stability of Xbloc armour units

6.1.2 Test series slope 2:3

Light concrete elements The tests with the light concrete units are presented in Figure 6-4. Start of damage is in accordance with the light elements on the 3:4 slope. The hydraulic stability seems lower than the design criterion prescribes as start of damage of test series D-IV occurred well before the design criterion of

Ns = 2.77. Here the early start of damage can not be explained just by one badly placed single layer armour unit as the damage develops gradually with increasing wave heights. The damage development for all test series is considerable larger than for the slope of 3:4. This could be explained by the lower placement densities. Test series D-I and D-II have considerable higher RPD than D-III and D-IV. Damage development starts later and has a more brittle failure pattern for the higher placement densities; D-II even fails instantly.

Light concrete

1,40 D-II D-IV 1,20

1,00

0,80

Nod D-III 0,60

0,40 D-I

0,20

0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-4 Stability curves test series D

Normal concrete elements The tests with the normal concrete units are presented in Figure 6-5. At test E-III and E-IV damage occurred in expectance with the design criterion for Xbloc. For test E-I en E-II no damage occurred resulting in a large variance between the test series. Start of damage is considerable lower than for the normal concrete elements at the 3:4. The reason for this could be found in the lower placement densities. However the placement density is of importance, but it is not expected to have such a big impact on the stability. The lower hydraulic stability is more likely due to the influence of the slope angle on the relative density and the hydraulic stability because the interlocking decreases with decreasing slope angles. Reference is made to Chapter 2 where this principle is introduced. The variance in the test data can be addressed to the properties of the Xbloc armour unit because the inherent difference in packing and subsequent interlocking.

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Chapter 6 Analysis Experiment Results

Normal concrete

1,40

1,20

1,00

0,80 Nod 0,60

0,40 E- III

0,20 E- IV E- II E- I 0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-5 Stability curves test series E

Heavy concrete elements The tests with the heavy concrete units are presented in Figure 6-6. Start of damage of test F-I occurs already before the design criterion after which only minor damage develops in contrary to the light elements and in less extends to the normal elements. The start of damage of test F-I is most likely a single badly placed element with minor interlocking with the surrounding elements as no further damage development take place in the following runs. Start of damage can be said to occur at

Ns = 3.7. The lower hydraulic stability in comparison to the slope of 3:4, where even no armour were displaced out of the armour layer, is likely due to the influence of the slope angle on the relative density and the hydraulic stability.

Heavy concrete

1,40

1,20

1,00

0,80 Nod 0,60

0,40

0,20 F-I F-III F-II 0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-6 Stability curves test series F

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Effect of the concrete density on the stability of Xbloc armour units

6.1.3 Test series slope 1:2

Light concrete elements The tests with the light concrete units are presented in Figure 6-7. The two test series show good resemblance in start of damage and damage development. Start of damage is in accordance with the prescribed criterion for Xbloc armour layers. This is in contrast with the results of the light concrete model tests on a slope of 2:3 and 3:4 where the average start of damage occurs at significant lower stability numbers. This is also in contrary with the general accepted idea that the hydraulic stability decreases for single layer interlocking armour unit on decreasing slopes.

Light concrete

1,40

1,20

1,00

0,80

G-I Nod 0,60

G-II 0,40

0,20

0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-7 Stability curves test series G Normal concrete elements The tests with the normal concrete units are presented in Figure 6-8. The two test series show good resemblance in start of damage and damage development. Start of damage is in accordance with the prescribed criterion for Xbloc armour layers.

Normal concrete

1,40

1,20

1,00

0,80 Nod 0,60

0,40

H-I 0,20 H-II 0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-8 Stability curves test series H

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Chapter 6 Analysis Experiment Results

Heavy concrete elements The tests with the heavy concrete units are presented in Figure 6-9. The two test series show good resemblance in start of damage. The damage development after start of damage is significantly larger for test K-I in comparison with test K-II. Placement densities are almost identical. Start of damage is in accordance with the prescribed criterion as is the damage development as described in paragraph 6.1. The hydraulic stability of the heavy concrete elements decreases for decreasing slopes, which is corresponds with the expected behaviour of single layer interlocking armour units.

Heavy concrete

1,40 K-I

1,20

1,00

0,80 Nod 0,60

0,40

K-II 0,20

0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-9 Stability curves test series K

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Effect of the concrete density on the stability of Xbloc armour units

6.2 Influence slope angle

The test series are divided per density to analyse the influence of the slope on the hydraulic stability of the different specific weights. Their damage curves are presented in Figure 6-10, Figure 6-11 and Figure 6-12. From these figures the following analysis are made:

− for units with a low specific weight (ρ=2102 kg/m3) start of damage is for slopes of 3:4 and 2:3 in accordance with each other. The damage develops more rapidly for the slope of 2:3 which could only partly be explained by the lower placement densities. A slope of 1:2 seems to be considerable more stable for light concrete elements.

− for units with a normal specific weight (ρ=2465 kg/m3) the average start of damage is for slopes of 2:3 and 1:2 in accordance as is the damage development. A slope of 3:4 seems to be relatively more hydraulically stable for the normal concrete elements. If the average damage curve is taken, a steeper slope results in a higher hydraulic stability which is in accordance with the expected behaviour of Xbloc armour units.

− for units with a heavy specific weight (ρ=2915 kg/m3) the hydraulic stability increases with increasing slope angles. For a 3:4 slope no damage occurred but the damage curve is expected to lie to the right of test series BL and so for even more to the right of the test series F and K. As mentioned the start of damage of test F-I is most likely a single badly placed as no further damage development take place in the following runs. Start of damage

can be said to occur at Ns = 3.7.

It is to be expected that for interlocking armour units the hydraulic stability increases with increasing slope angles, because the increasing contribution of interlocking and friction on steeper slopes. See Figure 2-7. The friction force depends on the normal force between the elements and the contact surface area. With increasing slope angle the component parallel to the slope increases and therefore the normal force between the elements. Interlocking also increases with increasing slope angle due to the increasing component of the gravitational force parallel to the slope.

The results from the model tests confirm this for the normal and heavy concrete elements. The light concrete elements seems however more stable on a slope of 1:2 which contradicts with the theory. For low concrete specific weight the effect of interlocking and friction is less and the elements behave more like bulky type of armour units where the increasing contribution of interlocking and friction on steeper slopes is dominated by the reduction of the influence of the gravitational force on the hydraulic stability. It can therefore be concluded that the hydraulic stability of Xbloc armour units is both a function of the slope as well as the specific weight.

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Chapter 6 Analysis Experiment Results

ρ =2102 kg/m3

1,40

1,20 Slope 2:3

1,00

0,80 Nod 0,60 Slope 3:4

Slope 1:2 0,40

0,20

0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-10 Stability curves test series A, D & G

ρ=2465 kg/m3

1,40

1,20

1,00

0,80 Nod 0,60

0,40 Slope 2:3 Slope 1:2 0,20 Slope 3:4 0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-11 Stability curves test series BL, E & H

ρ=2915 kg/m3

1,40

Slope 1:2 1,20

1,00

0,80 Nod 0,60

0,40

0,20 Slope 2:3

Slope 3:4 0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-12 Stability curves test series C, F & K

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Effect of the concrete density on the stability of Xbloc armour units

6.3 Influence specific weight

The test series are divided per slope angle to analyse the influence of the specific weight on the hydraulic stability of the different specific weights. If the stability parameter is valid for single layer interlocking armour units the damage curves of the different specific weights should lie between the same upper and lower limits. The damage curves are presented in Figure 6-13, Figure 6-14 and Figure 6-15. From these figure the following conclusions are drawn:

− For a slope of 3:4 the hydraulic stability increases with increasing specific weight. It indicates that the stability number underestimates the influence of the specific weight on the stability. Heavy concrete is significant more stable than would be expected according to the stability design criterion number. Light concrete is however relatively less stable than would be expected according to the stability design criterion number.

− For a slope of 2:3 the same relation is found as for the 3:4 slope; the relative hydraulic stability increases with increased specific weight with the remark that the spreading of the damage curves for the different specific weights is less wide and the results more closely resemblance the relation of the stability number as the results lie closer together.

− For a slope of 1:2 the high specific weight is relative less stable than the light and normal concrete elements which are in good resemblance with each other and with the prescribed criterion design criterion. The reduction of the interlocking and friction on more gentle slopes is more severe for heavier concrete specific weight. Therefore the relative density in the stability number Ns underestimates the hydraulic stability of concrete with a high specific weight

Overall it can be concluded that the influence of the concrete specific weight is a function of the slope angle.

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Chapter 6 Analysis Experiment Results

Slope 3:4

1,40

1,20

1,00

0,80

Nod ρ=2102 0,60

0,40

0,20 ρ=2465 ρ=2915 0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn Figure 6-13 Stability curves test series A, BL & C

Slope 2:3

1,40

1,20

1,00 ρ=2102 0,80 Nod 0,60

0,40 ρ=2465

0,20 ρ=2915

0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn Figure 6-14 Stability curves test series D, E & F Slope 1:2

1,40

ρ=2915 1,20

1,00

0,80

Nod ρ=2102 0,60

0,40

0,20 ρ=2465

0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn Figure 6-15 Stability curves test series G, H & K

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Effect of the concrete density on the stability of Xbloc armour units

6.4 Discussion test results

6.4.1 Summary of the test results

The objective of the physical model tests was to determine the influence of the specific weight on the hydraulic stability of the Xbloc armour units. Three different slopes were tested as it was expected from previous research that the influence of the specific weight differed for different slopes.

In general it is to be expected that for interlocking armour units the hydraulic stability increases with increasing slope angles. From the graphs as presented in this chapter this seems to be the case for the normal and heavy concrete elements. The light concrete elements seem however more stable on a slope of 1:2.

When concerning the influence of the specific weight on the different slopes is can be concluded from the presented results that:

− For a slope of 3:4 the hydraulic stability increases with increasing specific weight more than

is expected based on the stability number (Hs/ΔDn) and the expected start of damage and failure as described in paragraph 6.1

− For a slope of 2:3 the same relation is found as for the 3:4 slope; the relative hydraulic stability increases with increased specific weight with the remark that this effect is less which can be seen in Figure 6-14 where the damage curves for the different specific weights are more clustered.

− For a slope of 1:2 the high specific weight is relative less stable than the light and normal concrete elements which are in good resemblance with each other. All test series are is good resemblance with the expected start of damage and failure as described in paragraph 6.1

This indicates that the stability number as design criterion for single layer interlocking armour units does not hold. The formula tends to underestimate the influence of the specific weight for a slope of 3:4 resulting in heavy concrete elements which have more hydraulic stability than according to the stability number and light concrete elements which have less hydraulic stability than according to the stability number. The effect seems to be reduced for slope angle of 2:3 which means that the stability number describes the hydraulic stability more correctly on a slope of 2:3. Still the hydraulic stability increases with increasing specific weight. On a slope of 1:2 the damage curves are in close resemblance except for test K-I (heavy concrete). Because of this it seems that the heavy concrete has less hydraulic stability on a slope of 1:2.

From the model tests it can be concluded that the influence of the specific weight differs for different slope angles and that the relative density is therefore a function of the slope angle. Therefore hydraulic stability is not correctly described by the stability number for variations in the relative density (Δ). Furthermore, the hydraulic stability of single layer armour unit as a whole is also expected to be a function of the slope angle, because the interlocking increases with increasing slope angles. However this seems not to hold for light concrete elements. This could be again due to

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Chapter 6 Analysis Experiment Results

the varying influence of the relative density for different slope angles. This will be further discussed in paragraph 6.5.

6.4.2 Additional findings

Failure mechanisms In Chapter 5 a third potential failure mechanism was identified; lifting of multiple rows under the SWL. It has been found that the light element are relative more easily removed perpendicular from the armour layer as they have less resistance against the flow forces due to a lower weight. This applies for all slope angles. Reference is made to Table 5-4 for the wave height at which this phenomenon occurs.

Observations during model testing have shown that the armour layer on a slope of 1:2 moves along with the wave motion around SWL starting for the light elements at 100% Hd to 160 % Hd for the heavy elements. This is due to the absence of initial settlements and the gentle slope which both reduce the interlocking. The movement increases with higher waves. This movement is unwanted as it can cause significant damage to the elements. The use of light concrete is therefore not recommended as they are sensitive for these movements which already occur at the design wave height. The use of heavy concrete on a slope of 1:2 on the other hand should be used with great care as the current stability number overestimates the positive effect of the high specific weight and start of damage is not in accordance with the design criterion, see Figure 6-9.

Another phenomenon which is not reflected in the presented results is the movement of a dislocated element along the slope. On slope of 3:4 the element turned out of armour layer is taken far upward with the run-up flow; this is becoming less for flatter slopes as it takes longer to fully dislocate the elements out of the armour layer. This is can be explained by the reduction of the inertia forces with flatter slopes. On a slope of 3:4 the element is transferred almost immediately to the toe of the structure with the following downrush. On a slope of 1:2 the element is displaced up and down the slope a couple of times before it is completely removed from the armour layer. This could cause major damage to the armour units and hamper the hydraulic stability.

Validity model tests The result found by the hydraulic model test should be handled with care as the variance of the results is quite wide for most of the test series. A part of the variance in the test data can be attributed to the properties of the Xbloc armour unit because the inherent difference in packing and subsequent interlocking which will always be present to some extend. It is therefore important to minimise the variance in the other parameters. One of the important parameters is the placement density. If the placement density of 1.20/D2 is met, the chance on start of damage due to a badly placed element with minor interlocking can be minimised. In paragraph 5.6.1 was found that start of damage slightly increases with increasing RPD. Failure occurs at significantly later for higher placement densities.

For this research it was found difficult to fulfil the placement criterion of 1.20/D2 as it appeared difficult to control the placement density due the small size of the model blocks. The low weight of the light model blocks made it even more difficult to control the placement. Furthermore was there a wide scatter in the model block weight, partly to variation in the main dimensions but mainly due to non homogeneousness of the mixtures used, as discussed in paragraph 4.5.2. Both variations

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Effect of the concrete density on the stability of Xbloc armour units

could interfere with the test results especially when a lighter element is badly placed in an area were damage can be expected. This is why multiple repetitions were done for the different test series, to average these variations out. Therefore the results presented give a good indication on the influence of the specific weight on the stability of single layer interlocking armour units. However, additional testing could reduces the scatter and increase confidence in these findings.

6.5 Design formula Xbloc armour units

In this paragraph a new design formula for Xbloc armour units is presented which include the influence of the specific weight and slope angle on the hydraulic stability based on the results of the hydraulic model tests as described in the previous paragraphs.

6.5.1 General Xbloc stability formula

In the previous paragraphs the influence of the specific weight was described according to the damage curves with the stability number (6.1) as it is currently used to describe the hydraulic stability of Xbloc armour layers.

H s ≤ K (6.1) ΔDn

With K = 2.77 for Xbloc armour layers.

From this analysis it has been found that the influence of the specific weight is not described correctly by the stability number as presented. Furthermore, the influence of the specific weight differs for different slope angles and the influence of the slope angle on the hydraulic stability differs for the different specific weights.

To determine the influence of the specific weight first the current stability formula is given in its general form:

D3 n =⋅⋅⋅⋅⋅ΔKK K −x (6.2) H 3 12 n In the commonly used stability formula of Iribarren, Hudson and Van der Meer the value of x in (6.2) is 3. The stability number is based on lift and drag force dominance stabilised by the submerged mass. The value of x in the stability formula determines the influence of the relative density on the stability. As other forces have significant influence on the stability, which is the case for complex interlocking armour units like the Xbloc, the value of x as a power of the relative density (Δ) in (6.2) might change. It has been found that with increasing slope angles the inertia, friction and interlocking forces become more dominant.

Research on the influence of the specific weight on rock and Dolos interlocking armour units has already shown that the value of x differs for slopes steeper than 1:2. For slope angles of 1:2 there seems good coherence with the stability number. For rock and Dolos on a slope of 2:3 the stability number tends to overestimate the positive influence of increasing specific weight. For Xbloc armour units the model tests showed the opposite. The stability number tends to underestimate the influence of the specific weight for a slope of 2:3 and steeper. Still it has become clear that x as a power of the

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Chapter 6 Analysis Experiment Results

relative density (Δ) in (6.2) is a function of the slope angle which depend on the armour unit characteristics. The hydraulic stability of Xbloc armour units can therefore be described as a function of the slope angle and relative density by:

H s =⋅Kf(,)α Δ (6.3) Dn

The value of x in (6.2) is a function of the slope angle because the influence of specific weight differs for different slope angles. The function of the slope angle and relative density can be described by:

ff(,)ααΔ= () Δg()α (6.4)

Implementation of (6.4) in (6.3) gives the general formula for the hydraulic stability for Xbloc armour units:

H s =⋅Kf()α Δg()α (6.5) Dn

Equation (6.5) will be presented as the stability parameter for Xbloc armour units and will be denoted as Ns;x :

H NKfs =⋅()α (6.6) sx; = g()α DnΔ

Based on the measurements taken in the physical model tests a definition of the two functions of α will be presented in the following paragraphs.

6.5.2 Influence specific weight

To determine the function of x in equation (6.5) as a power of the relative density (∆) the method of

ZWAMBORN (1978) is used as presented in Chapter 2. First the stability numbers (Hs/∆Dn) are determined for start of damage (Nod =0.05), Nod =0.1 and failure (Nod =0.55) from the damage curves in paragraph 6.1. The stability numbers were used to plot the relative density Δ 33 against (/)cotDHn α in a log-log graph for each slope angle. The graphs are presented in Figure 33 −x 6-16 and Appendix K. The function term fDH((n / )cotα ) = KΔ has been fitted. This gives the value of x for each slope and damage number (Nod).

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Effect of the concrete density on the stability of Xbloc armour units

Figure 6-16 Influence relative density on hydraulic stability Xbloc armour units for cot α = 1.33, cot α = 1.5 and cot α = 2.

The values of x found by the Zwamborn approach are plotted against the slope angle in Figure 6-17. A power function has been fitted through the data points which give the power of Δ as a function of the slope angle:

xg/3== (αα ) 5.38(tan )3.25 (6.7)

The relation presented is only valid for slopes angles of 1:2 to 3:4 because when the slope angle goes to zero, x goes to zero. This indicates that for Xbloc armour units on a horizontal bed the hydraulic stability no longer is a function of the relative density and thus no longer dependent on the specific weight which is not true. The hydraulic stability of Xbloc on a horizontal bed is only determined by its own weight and therefore should the power of Δ be one for a horizontal bed. However the theory seems not in agreement with the relation found for Xbloc armour units on a slope 1:2 to 3:4.

76 MSc thesis

Chapter 6 Analysis Experiment Results

3,5

3 X = 5.3768tan α3.245 R2 = 0.9096 2,5

2 x/3 1,5

0,5

0 0 0,2 0,4 0,6 0,8 1 tan α

Figure 6-17 Relation of the power of Δ in the stability formula of Xbloc armour units

6.5.3 Influence slope angle

In the previous paragraph the influence of the slope angle on the contribution of the specific weight to the total stability has been presented. The slope angle in itself also influences the hydraulic stability as the influence of the weight of an armour unit decreases with increasing slope angles and the influence of interlocking and friction increases with increasing slope angles. The latter depends on the type of element. This has already been presented in Chapter 2. The figures presented by PRICE (1979) are presented again in Figure 6-18.

For single layer interlocking armour units like Xbloc the total stability increases due to the increasing contribution of interlocking and friction. This contribution depends on the characteristics of the armour element. For each element the contribution of the gravitational forces on the hydraulic stability decreases equally. The two mechanisms have an opposite effect on the hydraulic stability and depending on their contribution to the total, the hydraulic stability increases or decreases which depends on the type of element. Furthermore, interlocking and friction are also function of the (submerged) weight of the elements.

Figure 6-18 Influence of the slope angle on the stabilization mechanisms, interlocking, surface friction and gravity, on the stability [Price 1979]

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Effect of the concrete density on the stability of Xbloc armour units

The current design criterion of Xbloc is Ns = 2.77. No relation is presented for the influence of the slope angle as Xbloc armour layer are commonly designed for steep slope of 3:4 and 2:3 for which the model test were performed. Value of 2.77 is determined for a slope of 3:4 with concrete elements of 2400 kg/m3. This is the slope angle for which the interlocking concept of the Xbloc armour unit is maximised. If a different configuration is preferred the stability of the construction has to be checked with physical model testing.

Delta Marine Consultant gives a relation with the stability parameter of Hudson (Kd). In the stability formula of Hudson (6.8) the influence of the slope angle is presented as a function of cot α. This relation is presented in Figure 6-19. For increasing slope angles the hydraulic stability decreases. This is correct for were the contribution of interlocking and friction is low as is presented in the right figure in Figure 6-18. However the total hydraulic stability of single layer interlocking armour units like Xbloc in general increases with increasing slope angles. This has been observed in the model tests were the hydraulic stability for normal and heavy concrete elements increases with increasing slope angles. For light concrete elements the hydraulic stability decreases for increasing slope angles. The influence of the slope angle as described in the Hudson formula (6.8) is therefore not valid for single layer armour units.

H s 3 = Kd cotα (6.8) Dn

Influence slope angle on Hudson stability parameter 1,7 1,6 1,5 1,4 )^1/3

α 1,3

(cot 1,2 1,1 1 0,9 11,522,533,544,5 cot α

Figure 6-19 Influence of the slope angle by the Hudson stability parameter.

To derive a relation for the effect of the slope angle on the hydraulic stability the he stability numbers Ns;x were calculated according to (6.5) and (6.7) for the model test data. The calculated stability numbers were plotted against the slope angles, the graph is presented in Figure 6-20. A second order polynomial function has been plotted through the data points. The following relation has been found for the influence of the slope angle on the hydraulic stability:

2 Nsx; =++0.7671cot(αα ) 0.0886cot( ) 2 (6.9)

The second term in (6.9) can be neglected which simplifies the relation:

78 MSc thesis

Chapter 6 Analysis Experiment Results

2 Nsx; =+0.8cot(α ) 2 (6.10)

The relation as presented in formula (6.10) has no physical meaning for the relation of the slope angle and hydraulic stability of the interlocking armour units. Physically it is expected that the stability decreases with decreasing slope angles as the interlocking and friction component of the stability dominate the hydraulic stability for Xbloc. According to Figure 6-20 the hydraulic stability increases with decreasing slope angles (increasing cot α). This is because the effect of the slope angle is already taken into account in the power of Δ of the new stability criterion influence.

Furthermore the angle of tangent increases with increasing cot α. Physically it is expected that the stability decreases with decreasing slope angles as the interlocking and friction component of the stability dominate the hydraulic stability for Xbloc. Furthermore, Xbloc armour units on a horizontal bed have still some hydraulic stability. This should be reflected in Figure 6-20 by the reduction of the tangent angle to zero for cot α = ∞. Again this is because the effect of the slope angle is already taken into account in the power of Δ of the new stability criterion to describe the influence of the specific weight on the hydraulic stability.

8 ) α 7 y = 0,7671x2 + 0,0886x + 2 (tan (tan

f 2 ^ 6 R = 0,5194 Δ

3 Ns;x = (Hs/Dn)* Ns;x 2 Nod = 0.05 Nod = 0.1 1 Nod =0.55 0 0,7 0,9 1,1 1,3 1,5 1,7 1,9 2,1 2,3 2,5 cot α

Figure 6-20 Relation slope angle on hydraulic stability Xbloc armour units

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Effect of the concrete density on the stability of Xbloc armour units

6.5.4 Formulation design equation Xbloc armour layers

A general formula for the hydraulic stability for Xbloc armour units has been determined:

H s =⋅Kf()α Δg()α Dn

With the relations found for the power of Δ (6.7) and the influence of the slope angle (6.10) a new stability criterion for Xbloc armour layers is presented:

H 3.3 s =⋅K (0.8cot(α )2 +⋅Δ 2) 5.4(tanα ) (6.11) Dn

A design value of K has to be determined. The design value for Xbloc armour layers is Ns = 2.77 which has been concluded for the original stability number (Hs/∆Dn).

Hs Ns ==2.77 (6.12) ΔDn

The stability number is valid for a slope of 3:4 with gentle foreshore slopes of 1:30 or less and concrete with a specific weight of 2400 kg/m3. The proposed new design formula for Xbloc armour layers should be equal to the original design criterion for these conditions. Equation (6.11) is implemented in equation (6.12) with Δ = 1.4, tan α = 0.75 and cot α = 1.33. This result in a value of K of 0.55 and the proposed Xbloc design formula becomes:

H N ==⋅+s 0.55 (0.8cot(α )2 2) (6.13) sx; 5.4(tanα )3.3 Dn Δ

6.5.5 Damage curves with new Xbloc design formula

The proposed Xbloc design formula (6.13) is used to present the damage curves of the physical model test according to the new stability design formula for Xbloc armour units. Figure 6-21 to Figure 6-26 presents the damage curves with the new design formula. Compared with the original design criterion, as presented in Figure 6-10 to Figure 6-15, the damage curves show good resemblance with each other in the new situation. Only test F-I (slope 2:3, ρ = 2915 kg/m3) does not fit the data. Start of damage occurs before the (new) design criterion of Ns;x = 0.55. However the start of damage of test F-I is most likely a single badly placed element with minor interlocking with the surrounding elements in combination with a low placement density, because no further damage development took place in the following runs. Therefore the start of damage of test F-I is not taken into account. It can be concluded that the new stability parameter correctly represents the influence of the relative density and the slope angle because the damage curves for each specific weight and slope angle lie between the same boundaries. The scatter between the test series is significantly reduced. This is clearly visible in Figure 6-27 and Figure 6-28, where the damage curves of all test series are plotted. From these figures it can be concluded that the start of damage of the test series is in better accordance with the design criterion of the new stability parameter for Xbloc armour units Ns;x . For the stability parameter Ns start of damage of multiple tests already occurred before the design criterion of 2.77 was reached.

80 MSc thesis

Chapter 6 Analysis Experiment Results

ρ=2102 kg/m3 Ns;x = 0.55 1,40

1,20

Slope 2:3 1,00

0,80 Nod 0,60 Slope 1:2 Slope 3:4 0,40

0,20

0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25)

Figure 6-21 Stability curves test series A, D & G for the new stability number

ρ=2465 kg/m3 Ns;x = 0.55 1,40

1,20

1,00

0,80 Nod 0,60

0,40 Slope 2:3

Slope 3:4 0,20 Slope 1:2

0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25) Figure 6-22 Stability curves test series BL, E & H for the new stability number

ρ=2915 kg/m3 Ns;x = 0.55 1,40

1,20

1,00

0,80 Nod 0,60

0,40 Slope 1:2

Slope 2:3 0,20 Slope 3:4

0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25)

Figure 6-23 Stability curves test series C, F & K for the new stability number

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Effect of the concrete density on the stability of Xbloc armour units

Slope 3:4 Ns;x = 0.55 1,40

1,20

1,00

0,80 Nod 0,60 ρ=2102

0,40

ρ=2465 0,20 ρ=2915

0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25) Figure 6-24 Stability curves test series A, BL & C for the new stability number

Slope 2:3 Ns;x = 0.55 1,40

1,20 ρ=2102

1,00

0,80 Nod 0,60

0,40 ρ=2465 ρ=2915 0,20

0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25)

Figure 6-25 Stability curves test series D, E & F for the new stability number

Slope 1:2 Ns;x = 0.55 1,40

1,20 ρ=2102

1,00

0,80 Nod 0,60

ρ=2915 0,40

0,20 ρ=2465 0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25)

Figure 6-26 Stability curves test series G, H & K for the new stability number

82 MSc thesis

Chapter 6 Analysis Experiment Results

All test series

Ns;x = 0.55 1,40

1,20

1,00

0,80 Nod 0,60

0,40

0,20

0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25)

Figure 6-27 Stability curves test series for the new stability number

All test series Ns =2.77 1,40

1,20

1,00

0,80 Nod 0,60

0,40

0,20

0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 Ns = Hs/ΔDn

Figure 6-28 Stability curves test series for the original stability number

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Effect of the concrete density on the stability of Xbloc armour units

6.5.6 Damage development

The damage progression of the Accropode single layer interlocking armour unit has been presented by Van der Meer in PILARCZYK (1998). It is found that Accropode is completely stable up to a high wave height, but after start of damage the structure fails progressively. The performed model tests have shown a different damage progression for Xbloc armour units.

Damage progression Xbloc armour units The Xbloc armour layer remains it strength after initial damage has occurred. This can been seen in the damage curves of the individual test series as presented in paragraph 6.1, it takes an increase in the wave height to develop any further damage. Displacement of a single element has little effect on the stability of the entire armour layer because the surrounding elements settle and fill the gape left by the displaced until the elements have found a new more stable situation. The elements around the dislocated element gain new interlocking connections by these settlements. This self healing capacity is an important quality of the Xbloc armour unit. Only when multiple elements are removed from the same area the coherence is lost and damage development occurs more rapidly. From the observation during the model test it was found that this occurred when 4 or more element were displaced from the same location. This resulted as well in the beginning of the erosion of the under layer. Overall the total displacement was in the order of 10 units when this occurred. This is why for this research failure of the armour layer is defined as the displacement of 10 elements.

This more gradual development of damage has already been seen during the model tests which have been performed at Deltares (Delft Hydraulics) to determine the hydraulic stability. As presented in

Chapter 3 Xbloc start of damage can be expected for normal concrete on a slope of 3:4 at Ns between 3.3 and 5.5 and failure between Ns = 3.7 and 6.0. Start of damage correspond with Nod =

0.05 and failure with Nod = 0.55. In terms of design wave heights for model tests Delta Marine Consultants states the following:

− Start of damage occurs at wave heights ≥ 120% of the design wave height

− Failure occurs at wave heights ≥ 150% of the design wave height

Damage progression curves The stability numbers for the theoretical start of damage and failure as prescribed above have been calculates according to the stability number Ns (6.12). The damage progression line has been drawn through these points fitted to the test results as presented in Figure 6-29. In the figure the 80% confidence band are presented. The same has been done for the proposed Xbloc design formula Ns;x (6.13) which is presented in Figure 6-30.

From the Figures the following conclusions can be drawn:

− The damage progression curves describe the behaviour of the Xbloc armour layer correctly. Damage develops gradually after initial damage has occurred in contrast to what was found for Accropode single layer interlocking armour units.

84 MSc thesis

Chapter 6 Analysis Experiment Results

− The damage curves in Figure 6-29 do not fit the test series which confirm that the influence of the concrete specific weight is not correctly described by the stability number

Ns.

− The damage curves of the proposed Xbloc design formula Ns;x in Figure 6-30 describes the influence of the concrete specific weight correctly. Almost all damage curves lie within the 80% confidence band.

The damage progression curves for the stability number Ns and Ns;x are:

2 NNNod =+0.32ss - 2 3.15 (6.14)

2 NNNod =+5.14sx;; -8.06 sx 3.15 (6.15)

In the armour layer design with Xbloc armour units no damage is allowed. Therefore the proposed Xbloc design formula is no function of the damage progression and remains:

H N ==⋅+s 0.55 (0.8cot(α )2 2) sx; 5.4(tanα )3.3 Dn Δ

The damage progression curves show that Xbloc armour layers keep their strength after initial damage has occurred.

CurrentCurrent stability stability creterioncriterion Ns =2.77 1,40

1,20

1,00

0,80 Damage progression 80% conf. band Nod 0,60 80% conf. band

0,40

0,20

0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 Ns = Hs/ΔDn

Figure 6-29 Damage progression lines stability parameter Ns

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Effect of the concrete density on the stability of Xbloc armour units

NewNew stability stability criterion creterion Ns;x = 0.55 1,40

1,20

1,00

Damage progression 0,80 80% conf. band

Nod 80% conf. band 0,60

0,40

0,20

0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25)

Figure 6-30 Damage progression lines stability parameter Ns;x

86 MSc thesis

Chapter 7 Conclusions and Recommendations

In this chapter the conclusions and recommendation of the performed research are presented. Physical model tests have been done to investigate the influence of the concrete specific weight on the hydraulic stability of Xbloc armour units. One should be aware that the presented conclusions are based on the specific configurations for which the physical model test have been done and are only applicable for these cases. The research question for this MSc thesis is:

7.1 Conclusions

7.1.1 Main conclusions

Influence of the specific weight on the hydraulic stability In absolute sense the hydraulic stability increases with increasing concrete specific weight. When the influence of the specific weight on the different slopes is concerned it can be concluded from the hydraulic model tests that:

− For a slope of 3:4 the hydraulic stability increases with increasing specific weight more than

is expected based on the stability number (Hs/ΔDn) The expected start of damage (Hs ≥

120% Hd) and failure (Hs ≥ 150% Hd),with Hd is the design wave height, is underestimated for heavy concrete elements.

− For a slope of 2:3 the same relation is found as for the 3:4 slope; the relative hydraulic stability increases with increased specific weight with the remark that this effect is less, because the damage curves for the different specific weights are more clustered.

− For a slope of 1:2 the high specific weight is relatively less stable than the light and normal concrete elements which are in good resemblance with each other. All test series are in good

resemblance with the expected start of damage (Hs ≥ 120% Hd) and failure (Hs ≥ 150% Hd)

Stability as a function of the stability parameter Ns − It can be concluded from the model tests that the influence of the specific weight on the hydraulic stability of Xblox armour layers is not correctly described by the stability number

(NS) and that the influence of the specific weight depends on slope angle:

Hs Ns = ΔDn − The stability number underestimates the effect of the specific weight for single layer interlocking armour units for a slope of 2:3 and steeper. The underestimation increases for steeper slope angles.

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Effect of the concrete density on the stability of Xbloc armour units

− For a slope of 1:2 the stability number tends to overestimate the effect of the heavy concrete element, where as the normal and light concrete element are in close resemblance

with each other and the expected start of damage (Hs ≥ 120% Hd) and failure (Hs ≥ 150%

Hd)

− The power of one of the relative density (Δ) value in the stability formula determines the influence of the relative density on the stability. From the model tests it can be concluded that the influence of the specific weight differs for different slope angles and that the relative density is therefore a function of the slope angle. The hydraulic stability of Xbloc armour units can therefore be described as a function of the slope angle and relative density by:

H =⋅Kf(,)α Δ with: ff(,)ααΔ= () Δg()α Dn This results in a general formula for the hydraulic stability for Xbloc armour units:

H =⋅Kf()α Δg()α Dn − Definitions for the functions of the slope angle have been found by fitting the general formula to the data found by the hydraulic model testing. This has resulted in the following stability criterion for Xbloc armour layers:

H 3.3 =⋅0.55 (0.8cot(α )2 +⋅Δ 2) 5.4(tanα ) Dn

− The damage curves of the proposed Xbloc design formula Ns;x in Figure 7-1 describes the influence of the concrete specific weight correctly. Almost all damage curves lie within the 80% confidence band.

7.1.2 Additional conclusions:

Armour layer design in general − The assumed dominance of lift and drag forces stabilised by the submerged weight on which the stability number is based does not hold if other forces have significant influence on the stability. With increase slope angle the inertia, friction and interlocking force become more dominant. All stability mechanisms (gravity, friction and interlocking) depend on the weight of the element and are a function of the slope. Therefore the influence of the specific weight is always a function of the slope angle and depends on the type of element.

− For Xbloc it is found that the stability number underestimates the positive effect of increasing specific weight on a slope of 2:3 and steeper. This is the opposite of what was found for rock and Dolos armour units. For rock the stability number overestimate the positive influence of increasing specific weight on a slope of 2:3 and steeper, ZWAMBORN (1978). For a slope of 1:2 there seems good coherence with the assumed value of 3, HELGASON & BURCHARTH (2005).

88 MSc thesis

Chapter 7 Conclusions and Recommendations

For Dolos armour units it is found that the stability number also overestimates the positive influence of increasing specific weight on a slope of 2:3, although somewhat less than for rock due to the better interlocking capacities, ZWAMBORN (1978).

Xbloc armour layer design − Damage develops gradually after initial damage has occurred in contrast to what was found by Van der Meer for Accropode single layer interlocking armour units. The damage progression curves presented in Figure 7-1 describes the behaviour of the Xbloc armour layer correctly.

− The largest settlements for Xbloc armour layers occur for light concrete at the design wave height, for normal concrete at 80% of the design wave height and for heavy concrete of at 60% of the design wave height for steep slopes of 3:4 and 2:3. On a slope of 1:2 no initial settlements occur. For steep slopes the settlement depends on the specific weight of the element.

NewNew stability stability criterion creterion Ns;x = 0.55 1,40

1,20

1,00

Damage progression 0,80 80% conf. band

Nod 80% conf. band 0,60

0,40

0,20

0,00 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 Ns;x = Hs/(Dn*(2+0.8cotα^2)Δ^(5.38tanα^3.25)

Figure 7-1 Damage progression lines stability parameter Ns;x

− Start of damage remains almost constant for relative placement densities between 95% and 108%. The damage development is significantly lower for high placement densities. This is consistent with the results found in previous model testing.

− The dominance of the high downrush with the turbulent breaker as the important destabilization process becomes less from the steep slopes to more gentle slopes. Here the lift and drag forces due to the up and downrush velocities dislocate the elements as well. The impact of the turbulent breaker is shifted from under the SWL to the SWL as the downrush decreases with flatter slopes. This result in a transfer of clustered damage under the SWL for the 3:4 slope to damage spread between approximately 1 design wave height around the SWL for normal concrete elements for the 1:2 slope. This can be explained by the change of wave structure interaction from surging to more collapsing type which can be described well with the fictitious surf similarity parameter.

B.N.M. van Zwicht 89

Effect of the concrete density on the stability of Xbloc armour units

7.2 Recommendations

Xbloc armour layer design − It is recommended to use of the proposed Xbloc stability formula for future armour layer design with Xbloc armour units to take into account the effect of concrete specific weight and slope angle.

− The use of light concrete on a slope of 1:2 is highly not recommended, because the light elements are sensitive for extensive movements of the armour layer along with the wave motion around SWL which starts already at the design wave height.

− In general the settlements on a long slope with many rows results in the exposure of the crest despite the very high placement densities. With overtopping waves the elements high on the slope are easily removed. The lower the placement density the higher the settlement and a larger area of the crest will be exposed. If such long slopes will be constructed, the placement should be tighter or after a while additional blocks should be placed to fill the gaps formed.

Further research Research should be done on the physical processes of the wave structure interaction to be able to derive a deterministic approach for the design of a breakwater. The empirical approach is limited to the configurations for which it is derived. This could be done by numerical modelling of (turbulent) flow through a porous medium in combination with research on the turbulent flow of breaking waves. This has to be linked to research on the required force to remove an element out of the armour layer and hydraulic model testing. An indication of the required force to remove an element out of the armour layer can be measured by pulling test as described by PRICE (1979).

For future model tests with Xbloc it is recommended:

− That the relative placement density (RPD) is well controlled and equal to the prescribed packing density of 1.2/D2 because the RPD influences the hydraulic stability.

− The variation in the model block weight distribution is limited as it increases the scatter of the test results.

− That the placement density is determined according to photo analysis as this is more accurate than the in-situ measurement. Therefore the dimensions of the slope should be well indicated in the photograph as the dimensions are distorted by the angle from were the photo is taken. This can be accomplished by putting a sheet of paper on the slope.

90 MSc thesis

Chapter 7 Conclusions and Recommendations

B.N.M. van Zwicht 91

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TEN OEVER, E. (2006) Theoretical and Experimental Study on placement of Xbloc armour units. Proceedings of the 30th ICCE 2006, San Diego, California, USA

TRIEMSTRA, R. (2001) The use of high density concrete in the armourlayer of breakwaters, flume tests on high density concrete elements. MSc Thesis. Delft University of Technology.

ZWAMBORN, J.A. (1978) Dolos packing density and effect of relative Block density. Proceedings of the 16th ICCE 1978, Hamburg, Germany. pp 2285-2304

94 MSc thesis

List of Figures

Chapter 1

FIGURE 1-1 BASIC SCHEME FOR COASTAL STRUCTURES UNDER WAVE ATTACK...... 3 Chapter 2

FIGURE 2-1 CONVENTIONAL MULTI LAYER RUBBLE MOUND BREAKWATER [CEM 2006] ...... 7 FIGURE 2-2 FAILURE MODES RUBBLE MOUND BREAKWATER [CEM 2006] ...... 9 FIGURE 2-3 BREAKER TYPES [ROCK MANUAL]...... 10 FIGURE 2-4 ILLUSTRATION OF RUNUP AND RUNDOWN PERMEABLE AND IMPERMEABLE SLOPES (BURCHARTH 1993) [CEM 2006]...... 11 FIGURE 2-5 SCHEMATIZATION FORCES ON ARMOUR UNITS UNDER WAVE ATTACK [BURCHARTH, 1993] ...... 11 FIGURE 2-6 ARMOUR LAYER FAILURE MODES [BURCHARTH 1993] ...... 12 FIGURE 2-7 INFLUENCE OF THE SLOPE ANGLE ON THE STABILIZATION MECHANISMS, INTERLOCKING, SURFACE FRICTION AND GRAVITY, ON THE STABILITY [PRICE 1979] ...... 14 FIGURE 2-8 RESULTS OF KYDLAND (1966) PLOTTED ACCORDING TO ZWAMBORN (1978) [HELGASON ET AL. 2000]...... 18 FIGURE 2-9 RESULTS HISTORIC RESULTS INFLUENCE RELATIVE DENSITY ROCK FOR COTα = 1.5 (ON

THE LEFT) AND COTα =2 (ON THE RIGHT) FOR NO DAMAGE (SD=2) [HELGASON & BURCHARTH 2005]...... 19 Chapter 3

FIGURE 3-1 GEOMETRY OF THE XBLOC ...... 21 FIGURE 3-2 HYDRAULIC STABILITY XBLOC ...... 21 FIGURE 3-3 INFLUENCE PLACEMENT DENSITY ON HYDRAULIC STABILITY ...... 23 Chapter 4

FIGURE 4-1 TOP AND SIDE VIEW WAVE FLUME DELTA MARINE CONSULTANTS...... 28 FIGURE 4-2 WAVE FLUME DMC IN UTRECHT...... 28 FIGURE 4-3 SETUP TEST FACILITY...... 30 FIGURE 4-4 MAIN DIMENSIONS BREAKWATER MODEL ...... 34 FIGURE 4-5 GABIONS PLACED ON 1:2 SLOPE ...... 35 FIGURE 4-6 TABLES WEIGHT DISTRIBUTION XBLOC MODEL BLOCKS ...... 36 FIGURE 4-7 XBLOC ARMOUR LAYER PLACEMENT ...... 37 FIGURE 4-8 SIEVE CURVE CORE MATERIAL ...... 40 Chapter 5

FIGURE 5-1 RELATIVE PLACEMENT DENSITIES...... 45 FIGURE 5-2 MEASUREMENT SETTLEMENT ...... 46 FIGURE 5-3 DISPLACEMENT OF A UNIT OUT OF THE ARMOUR LAYER ...... 49 FIGURE 5-4 SLOPE 3:4 XBLOC DISPLACEMENT OUT OF ARMOUR LAYER ...... 51 FIGURE 5-5 SLOPE 2:3 XBLOC DISPLACEMENT OUT OF ARMOUR LAYER ...... 53 FIGURE 5-6 SLOPE 1:2 XBLOC DISPLACEMENT OUT OF ARMOUR LAYER ...... 55

FIGURE 5-7 INFLUENCE PLACEMENT DENSITY ON HYDRAULIC STABILITY (DASHED LINE - - - NS = 2.77; THE DESIGN VALUE OF XBLOC) ...... 57

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Effect of the concrete density on the stability of Xbloc armour units

Chapter 6

FIGURE 6-1 STABILITY CURVES TEST SERIES A...... 62 FIGURE 6-2 STABILITY CURVES TEST SERIES B (SHORT SLOPE) ...... 63 FIGURE 6-3 STABILITY CURVES TEST SERIES BL (LONG SLOPE)...... 63 FIGURE 6-4 STABILITY CURVES TEST SERIES D...... 64 FIGURE 6-5 STABILITY CURVES TEST SERIES E...... 65 FIGURE 6-6 STABILITY CURVES TEST SERIES F ...... 65 FIGURE 6-7 STABILITY CURVES TEST SERIES G...... 66 FIGURE 6-8 STABILITY CURVES TEST SERIES H...... 66 FIGURE 6-9 STABILITY CURVES TEST SERIES K...... 67 FIGURE 6-10 STABILITY CURVES TEST SERIES A, D & G ...... 69 FIGURE 6-11 STABILITY CURVES TEST SERIES BL, E & H...... 69 FIGURE 6-12 STABILITY CURVES TEST SERIES C, F & K ...... 69 FIGURE 6-13 STABILITY CURVES TEST SERIES A, BL & C ...... 71 FIGURE 6-14 STABILITY CURVES TEST SERIES D, E & F ...... 71 FIGURE 6-15 STABILITY CURVES TEST SERIES G, H & K ...... 71 FIGURE 6-16 INFLUENCE RELATIVE DENSITY ON HYDRAULIC STABILITY XBLOC ARMOUR UNITS FOR COT Α = 1.33, COT Α = 1.5 AND COT Α = 2...... 76 FIGURE 6-17 RELATION OF THE POWER OF Δ IN THE STABILITY FORMULA OF XBLOC ARMOUR UNITS77 FIGURE 6-18 INFLUENCE OF THE SLOPE ANGLE ON THE STABILIZATION MECHANISMS, INTERLOCKING, SURFACE FRICTION AND GRAVITY, ON THE STABILITY [PRICE 1979]...... 77 FIGURE 6-19 INFLUENCE OF THE SLOPE ANGLE BY THE HUDSON STABILITY PARAMETER...... 78 FIGURE 6-20 RELATION SLOPE ANGLE ON HYDRAULIC STABILITY XBLOC ARMOUR UNITS...... 79 FIGURE 6-21 STABILITY CURVES TEST SERIES A, D & G FOR THE NEW STABILITY NUMBER...... 81 FIGURE 6-22 STABILITY CURVES TEST SERIES BL, E & H FOR THE NEW STABILITY NUMBER ...... 81 FIGURE 6-23 STABILITY CURVES TEST SERIES C, F & K FOR THE NEW STABILITY NUMBER...... 81 FIGURE 6-24 STABILITY CURVES TEST SERIES A, BL & C FOR THE NEW STABILITY NUMBER...... 82 FIGURE 6-25 STABILITY CURVES TEST SERIES D, E & F FOR THE NEW STABILITY NUMBER...... 82 FIGURE 6-26 STABILITY CURVES TEST SERIES G, H & K FOR THE NEW STABILITY NUMBER...... 82 FIGURE 6-27 STABILITY CURVES TEST SERIES FOR THE NEW STABILITY NUMBER...... 83 FIGURE 6-28 STABILITY CURVES TEST SERIES FOR THE ORIGINAL STABILITY NUMBER...... 83

FIGURE 6-29 DAMAGE PROGRESSION LINES STABILITY PARAMETER NS ...... 85

FIGURE 6-30 DAMAGE PROGRESSION LINES STABILITY PARAMETER NS;X ...... 86 Chapter 7

FIGURE 7-1 DAMAGE PROGRESSION LINES STABILITY PARAMETER NS;X ...... 89

Appendixes

FIGURE A-1 CONCRETE ARMOUR UNITS ...... 99 FIGURE C-1 SETUP HYDRAULIC MODEL TESTS...... 103 FIGURE D-1 CONSTRUCTION GABION MATTRESSES ...... 104 FIGURE F-1 PYCNOMETER ...... 108 FIGURE G-1 TEST SERIES A-I START & END PHOTO ...... 111 FIGURE G-2 TEST SERIES A-II START & END PHOTO...... 112 FIGURE G-3 TEST SERIES A-III START & END PHOTO ...... 112 FIGURE G-4 TEST SERIES A-IV START & END PHOTO ...... 113 FIGURE G-5 TEST SERIES B-II START & END PHOTO ...... 113

96 MSc thesis

List of Figures

FIGURE G-6 TEST SERIES B-III START & END PHOTO ...... 114 FIGURE G-7 TEST SERIES B-IV START & END PHOTO ...... 114 FIGURE G-8 TEST SERIES B-V START & END PHOTO ...... 115 FIGURE G-9 TEST SERIES BL-I START & END PHOTO ...... 115 FIGURE G-10 TEST SERIES BL-II START & END PHOTO ...... 116 FIGURE G-11 TEST SERIES C-I START & END PHOTO...... 116 FIGURE G-12 TEST SERIES C-II START & END PHOTO ...... 117 FIGURE G-13 TEST SERIES C-III START & END PHOTO ...... 117 FIGURE G-14 TEST SERIES C-IV START & END PHOTO...... 118 FIGURE G-15 TEST SERIES D-I START & END PHOTO...... 118 FIGURE G-16 TEST SERIES D-II START & END PHOTO ...... 119 FIGURE G-17 TEST SERIES D-III START & END PHOTO...... 119 FIGURE G-18 TEST SERIES D-IV START & END PHOTO...... 120 FIGURE G-19 TEST SERIES E-I START & END PHOTO ...... 120 FIGURE G-20 TEST SERIES E-II START & END PHOTO...... 121 FIGURE G-21 TEST SERIES E-III START & END PHOTO ...... 121 FIGURE G-22 TEST SERIES E-IV START & END PHOTO ...... 122 FIGURE G-23 TEST SERIES F-I START & END PHOTO ...... 122 FIGURE G-24 TEST SERIES F-II START & END PHOTO ...... 123 FIGURE G-25 TEST SERIES F-III START & END PHOTO...... 123 FIGURE G-26 TEST SERIES G-I START & END PHOTO...... 124 FIGURE G-27 TEST SERIES G-II START & END PHOTO ...... 124 FIGURE G-28 TEST SERIES H-I START & END PHOTO...... 125 FIGURE G-29 TEST SERIES H-II START & END PHOTO ...... 125 FIGURE G-30 TEST SERIES K-I START & END PHOTO...... 126 FIGURE G-31 TEST SERIES K-II START & END PHOTO ...... 126 FIGURE H-1 MEASUREMENT CENTRELINES...... 127 FIGURE K-1 INFLUENCE RELATIVE DENSITY ON HYDRAULIC STABILITY XBLOC ARMOUR UNITS FOR COT Α = 1.33, COT Α = 1.5 AND COT Α = 2...... 142

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List of Tables

Main document

TABLE 3-1 MAIN PARAMETERS VARIED IN MODEL TEST ...... 22 TABLE 4-1 REYNOLDS NUMBERS AT WHICH NO VISCOUS SCALE EFFECTS OCCUR. (HUGHES [1993]) . 27 TABLE 4-2 TEST PROGRAMME ...... 31 TABLE 4-3 DESIGN WAVE HEIGHT USED IN MODEL TEST ...... 32 TABLE 4-4 WAVE CHARACTERISTICS MODEL TESTS ...... 33 TABLE 5-1 DESIGN WAVE HEIGHT USED IN MODEL TESTS...... 43 TABLE 5-2 ACTUAL DESIGN WAVE HEIGHT ...... 43 TABLE 5-3 RELATIVE PLACEMENT DENSITIES PER TEST SERIES ...... 44 TABLE 5-4 OBSERVATIONS...... 59

Appendixes

TABLE E-1 WEIGHT LIGHT CONCRETE MODEL BLOCKS [GR] ...... 105 TABLE E-2 WEIGHT NORMAL CONCRETE MODEL BLOCKS [GR] ...... 106 TABLE E-3 WEIGHT HEAVY CONCRETE MODEL BLOCKS [GR]...... 107 TABLE F-1 RESULTS PYCNOMETER TESTS ...... 109 TABLE G-1 TEST PROGRAMME ...... 111 TABLE H-1 RELATIVE PLACEMENT DENSITIES...... 128

98 MSc thesis

Appendixes

Appendix A Concrete Armour units

Over the years a large variety of concrete armour units have been developed. The armour units can be classified by their placement pattern and by their stability mechanism. Two placement patterns can be distinguished namely; uniform and random placements. Furthermore, the armour units remain hydraulically stable under wave attack by three main mechanisms: − Stabilization by their own weight; the gravitational force, − friction between adjoining elements, − and interlocking. Interlocking is the ability of an armour unit to bring into play the weight the surrounding armour units.

Armour units stability on own weight. Random placed in double layers, in some cases single layer placement is used.

Armour units stability on own weight and interlocking. Random placed in double layers.

Highly interlocking single layer random placed armour units.

Uniform placed concrete armour units. Stability based on friction

Figure A-1 Concrete armour units

Uniform placed elements like Seabee, Cob and Shed depend mainly on friction between the units to provide hydraulic stability. The elements are placed close together and have an open structure what results in high energy dissipation. These types of elements have a very high hydraulic stability. The multi-hole elements like Cob and Shed are armoured with fibre reinforcement while conventional the concrete armour units are made of unreinforced concrete. The elements demand very precise placement. Placement of these elements is therefore very difficult under water and they are normally only applied when construction can be done above water.

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Effect of the concrete density on the stability of Xbloc armour units

Randomly placed armour units can be divided into elements which obtain their hydraulic stability by their own weight and by interlocking. Elements with hydraulic stability by its own weight as with rock are bulky elements like cubes and Antifer cubes. The second type of random placed armour units obtain their hydraulic stability not only due to their own weight but also by interlocking between adjoining units. An advantage it that the slender shape of the element increased the porosity of the armour layer which is favourable for wave energy absorption and reduction of the wave run-up. Examples of these elements are the Tetrapod, Dolos and Akmon, which are placement in double layers.

To improve the interlocking of the element and thus the hydraulic stability, the elements became more and more slender. As units became more slender the structural integrity decreased. The units became more vulnerable for breakage especially when large units are required. This effect was not reflected in the model tests, which were performed to determine the hydraulic stability because the material properties are not easily scaled. The Dolos units applied at the Sines Breakwater in Portugal were so slender that they broke under wave action before the design wave height was reached. The broken Dolosse did no longer interlock with each other, resulting in the failure of the entire armour layer.

This resulted in the introduction of the Acropod unit. This was the first armour unit that could be placed in a single layer which resulted in significant cost savings in comparison with the double layered armour units as described above. Due to its compact shape and good interlocking it has a good hydraulic and structural stability. It has been a successful unit since its introduction. Later on CoreLoc and A-jack units were developed using the same philosophy. The latest development is the XBloc armour unit, developed by Delta Marine Consultants. Xbloc has a high structural and hydraulic stability. Improvements over other single layer units were made by improving the fabrication and placement of the units and reducing the concrete demand while retaining the hydraulic and structural stability.

The hydraulic efficiency of concrete armour units might be expressed in terms of the resistance against movements per volume of concrete required to armour a unit area of the slope. The hydraulic efficiency increases from massive units to slender units to multi-hole cubes, while the structural integrity decreases from massive units to slender units. Multi-hole cubes will experience very small solid impact loads provided they are placed correctly in patterns that exclude significant relative movements of the blocks. Due to the slender structural members with rather tiny cross sections, the limiting factors (excluding impacts) for long-term durability are material deterioration, abrasion on sandy coasts, and fatigue due to wave loads. [CEM 2006]

100 MSc thesis

Appendixes

Appendix B Structural integrity armour units

The hydraulic stability of the armour units is hampered if the armour unit breaks, because the reduction of the gravitational force and possible interlocking effect. Furthermore, the fragments thrown around by the wave action could cause the breakage of surrounding element. This is why it is necessary to guarantee the structural integrity of the armour units. However the structural integrity is outside the scope of this research the influence of the specific weight it is discussed here because its importance when applying concrete armour units.

Concrete armour units are usually made of unreinforced concrete. Reinforced elements are more vulnerable for breakage as the reinforcement will corrode under the influence of the seawater. Although the steel is covered with concrete, in time the steel will come in contact with seawater due to wear and small tensile cracks in the concrete.

Unreinforced concrete is brittle, has low tensile strength and a high compressive strength which is the reason why breakage is almost always due to load induced tensile stresses. Moreover the tensile strength reduces with repeated load due to fatigue effects. Over all are slender units more vulnerable for breakage because the small cross sections give rise to relatively large tensile stresses. Bulky elements are less vulnerable but here the temperature difference between the in and outside of the element during hardening could cause tensile stresses which exceed strength of young concrete. This type of failure is known as thermal stress cracking and reduces the strength of the element. It can 1 even result in breakage of the element. [BURCHARTH, 1993] . Good quality concrete is therefore required.

B.1 Concrete properties

Concrete is a composition of cement with stony aggregates. During the production of concrete the dry cement is mixed with the aggregates and water. The chemical reaction between the cement and water hardens the mixture en binds all the components. This chemical process is called hydratation. The strength of the concrete depends on the water-cement mixture, the type of cement and the grading and strength of the aggregates.

Water-cement mixture Cement is a hydraulic material which when mixed with water chemical reacts, resulting in a solid material; cement stone. The water-cement ratio is an important factor in the development of the strength of the cement stone. The higher the ratio the longer it takes for the cement stone is formed and the lower the final strength. The relative strength can be characterised by the third power of the water-cement ratio by complete hydratation. The hydration grade is also of importance for the development of the strength. A low water- cement factor is negative for permeability of the mixture, resulting in lower hydratation speeds and even incomplete hydratation.

1 BURHARTH, H.F. (1993) Structural integrity and hydraulic stability of dolos armour layers. Hydraulic & Coastal Engineering Laboratory, Department of Civil Engineering, Aalborg University, Denmark

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Effect of the concrete density on the stability of Xbloc armour units

Aggregates The aggregates have normally no influence on the chemical process, unless they contain containments. These contaminants could interfere in the chemical process and hamper the strength and structural integrity of the concrete. Some examples of containments are: − Opal and Chalcedon; they react with the cement making the concrete disintegrate. − Pyrites; they make the concrete swell, resulting in crack formation − Clay; hampers the binding of the cement with the aggregate, resulting in disintegration of the concrete.

The strength of the concrete also depends on the strength and grading of the aggregates used. The grading should be as such that the smaller elements fill the spaces between the larger elements, resulting in a very dense packing. However the processability of the mixture will have contradictory 2 requirements on the grading. [SOUWERBREN, 1986] .

B.2 Influence specific weight on structural stability

The concrete specific weight can be changed by adding different aggregates to the concrete mixture. The aggregates for normal concrete consist of sand and gravel or concrete rubble with a specific weight of 2650 kg/m3. This results in a concrete density between 2300 and 2400 kg/m3. By replacing the aggregates the specific weight of the concrete can be changed. Heavy concrete can be obtained by adding for instance magnetite, iron ore, barite or lead slag. This can result into a specific weight up to 4000 kg/m3

Change of aggregates should not have any influence on the strength if the properties are fulfilled on strength and grading and the aggregates contain no pollution which could chemically react with the cement. However the in the case of heavy aggregates it could be a problem to get a good mixture. The shape, strength and structure of the aggregates influence the mixture. Bad graded mixtures demand more water which increases the chance on segregation, resulting in lower concrete strength. The segregation is enhanced by the high specific weight of the aggregates. When assuming the design relation hydraulic stability correct as presented in paragraph 2.3 higher specific weight reduces the necessary nominal diameter of the element used. This reduces the weight of the block significantly, reducing tensile stress inside the unit.

Aggregates of light concrete are internal porous. It is common to use sand for a part of the grading supplement to the light aggregates. The combination increases the chance on segregation. The light aggregates have the tendency to float up resulting in a decreasing concrete quality. Due to the internal porosity of the light aggregates it could absorb water from the mixture which could have a positive effect on the water-cement factor resulting in stronger concrete. Therefore it is necessary to control the water content. When again assuming the design relation hydraulic stability correct as presented in paragraph 2.3, lower specific weight increases the necessary nominal diameter of the element used. This increases the weight of the block significantly, increasing tensile stress inside the unit. Furthermore the light aggregates have a lower strength reducing the compressive strength of the concrete.

2 For more information on concrete technology reference is made to SOUWERBREN (1986) .

2 SOUWERBREN, C. (1986) Betontechnologie, Vereniging Nederlandse Cementindustrie, ’s Hertogenbosch. 6e druk

102 MSc thesis

Appendixes

Appendix C Setup hydraulic model tests

Figure C-1 Setup hydraulic model tests

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Appendix D Construction gabions

Figure D-1 Construction gabion mattresses

104 MSc thesis

Appendixes

Appendix E Weight distribution Xbloc model blocks

The model blocks used for the hydraulic model test were delivered by Minelco a Swedish supplier of minerals. It appeared difficult to control the specific weight of the concrete mixtures used for the concrete model blocks especially for the non-conventional light and heavy concrete blocks. Therefore some spread in the weight distribution of the model blocks was expected. To visualize the scatter each block was weighted on a scale with the accuracy of a tenth of a gram. The results are presented for each specific weight in a bar diagram in which also the probability density function is given. Tables D-1, D-2 and D-3 give the weight of each model block used in the physical model tests.

Light model block light concrete weight distribution

Density 2102.8 Kg/m3 70 1,4 60 1,2 Average weight 16.25 gr 50 1 Min weight 15.2 gr 40 0,8 Max weight 17.5 gr 30 0,6 Av. deviation 0.271435 units No of 20 0,4

10 0,2 Density Probability Stand deviation 0.335751 0 0

4 2 8 4 5,2 5, 6,0 6, 6,6 6, 7,2 7, 1 1 15,6 15,8 1 1 16,4 1 1 17,0 1 1 Weight [gr]

Table E-1 Weight light concrete model blocks [gr] 15.8 16.4 16.4 16.4 16.6 16.5 16.5 17.5 16.5 16.2 16.6 16.4 16.5 15.4 16.5 16 16.3 16.1 16.4 16.2 15.6 16.4 16.3 15.9 16.5 16.6 16.3 16.5 16.5 15.3 15.4 16.5 16.2 15.8 16.1 16.9 16.6 16,3 15,6 16,3 16,5 16,2 16.3 15.9 15.3 16.3 16,3 16,6 16,2 16,3 16 16,3 16,6 16,5 16,3 15,9 16 16.5 16.1 16.4 16.1 16.5 15.7 16.1 15.8 16.5 16.1 15.7 16.4 16.6 16 15.3 16.3 16.3 16.5 16.5 15.6 16.4 16.7 16.7 16.7 15.5 16 16.2 16.3 16.3 15.6 16.3 16.1 16.3 16.4 16.3 16.2 16.3 16.4 16.6 16.7 16.1 15.4 15.9 16.3 16.2 16.7 16.6 16.3 16.3 15.9 15.9 16.5 16.3 15.9 15.9 15.7 16.3 16.4 16.6 16.5 16.6 15.9 16.4 16.4 16.2 16.6 16.4 16 16.5 16.5 16.2 15.5 15.8 16.6 15.9 15.7 16.3 16.6 16.8 16.3 16.4 16 16.1 16.3 16.1 16.5 15.6 16.3 16.5 16.4 16.2 16.5 16.6 15.9 16.3 16.6 16.3 16.1 16.4 15.9 16.2 16.4 15.9 16.5 16 16.6 15.8 16.6 15.7 16.5 16.4 16.1 16.3 16.4 16.4 16.2 16 16.5 16.5 15.8 16.6 15.8 16 16.3 15.9 16.4 16.3 15.8 16.2 16.5 16.4 15.7 16.4 16.1 15.8 16.5 16.3 16.2 16.3 15.9 16.3 16.4 16.4 16.2 15.9 15.8 16.3 16.8 16.7 16.6 15.8 16.5 16 16.4 16.4 16.6 16.2 16.4 16.5 15.9 16.6 16.3 16.4 16.1 16.5 16.6 16.6 16.4 16.5 16.3 16.6 16.3 16.4 15.6 16.7 16.7 16.5 16.6 16.6 16.7 16.5 15.8 16.5 15.9 16.6 15.6 16.7 16.6 16.8 16.3 15.7 16.4 16.3 16.4 16.2 16.6 16.3 16.5 16.2 16.3 16.3 16.5 16.6 15.5 16 16.6 16.7 16.5 16 16.4 15.8 16.5 16.2 16.5 16.5 15.9 16.6 16.6 16 15.8 16.4 16 15.6 16.6 15.5 16.4 16.6 16.2 16.1 16.4 16.2 16.6 16.8 16.2 16.4 15.6 16.4 16.2 16.6 16.4 15.8 15.9 16.3 16.6 16.4 16.5 16.3 16.4 15.2 16.3 16.3 16 16.1 15.7 16.5 16.1 16.5 16.6 16.5 15.5 16.5 15.6 16.4 15.9 16.6 16.2 16.5 15.8 16.3 16.5 16.5 16.6 16 16.4 15.8 16.2 16.4 16.5 16.4 16.6 15.9 16.5 16.4 16 16.3 16.5 16.6 16.3 16.5 15.9 16.4 16.3 15.9 16.6 16 16.6 16.5 15.8 16.4 15.8 15.9 16.4 16.5 16.8 16.4 16.5 16.3 16.3 16.2 16 16.7 16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5 16 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 16.3 16.3 16.3 16.3 16.3 16.3 16.3 16.3 16.3 16.3 16.3 16.3 15.6 16.2 16.2 16.2 16.2 16.2 16.2 16.2 16.2 16.2 16.2 16.2 16.2 16.4

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Effect of the concrete density on the stability of Xbloc armour units

Normal model block

Normal concrete weight distribution Density 2465.5 Kg/m3 70 1,4 Average weight 18.85 gr 60 1,2 Min weight 17.9 gr 50 1 Max weight 19.7 gr 40 0,8 Av. deviation 0.2493 30 0,6 No of units No of Stand deviation 0.31824 20 0,4 Probability Density 10 0,2 0 0 7 ,3 8,5 ,1 ,5 17,9 18,1 18 1 18, 18,9 19 19,3 19 19,7 Weight [gr]

Table E-2 Weight normal concrete model blocks [gr] 18 18.8 19 19.4 18.6 18.7 18.9 19.3 18.7 18.9 19.3 18.5 18.8 19 18.2 18.8 19 19.4 18.6 18.7 18.9 19.3 18.7 18.9 19.3 18.5 18.8 19 18.2 18.8 19 19.4 18.6 18.8 18.9 19.3 18.7 18.9 19.4 18.5 18.8 19 18.3 18.8 19 19.4 18.6 18.8 18.9 19.3 18.7 18.9 19.4 18.5 18.8 19 18.3 18.8 19 19.5 18.6 18.8 18.9 19.3 18.7 18.9 19.4 18.6 18.8 19.1 18.3 18.8 19 19.5 18.6 18.8 18.9 19.4 18.7 18.9 19.4 18.6 18.8 19.1 18.3 18.8 19 19.5 18.6 18.8 18.9 19.4 18.7 18.9 19.4 18.6 18.8 19.2 18.4 18.8 19 19.6 18.6 18.8 18.9 19.4 18.7 18.9 19.4 18.6 18.8 19.2 18.4 18.8 19 19.6 18.6 18.8 19 19.5 18.7 18.9 19.4 18.6 18.8 19.2 18.4 18.9 19 19.7 18.6 18.8 19 19.6 18.7 18.9 19.5 18.6 18.8 19.2 18.4 18.9 19.1 18.2 18.7 18.8 19 18.1 18.7 18.9 19.5 18.6 18.8 19.2 18.5 18.9 19.1 18.2 18.7 18.8 19 18.2 18.7 18.9 19.5 18.6 18.8 19.2 18.5 18.9 19.1 18.3 18.7 18.8 19 18.3 18.7 19 19.5 18.6 18.8 19.2 18.5 18.9 19.1 18.3 18.7 18.8 19 18.3 18.7 19 19.5 18.6 18.8 19.2 18.5 18.9 19.1 18.3 18.7 18.8 19 18.4 18.8 19 19.7 18.6 18.8 19.3 18.5 18.9 19.1 18.4 18.7 18.8 19.1 18.4 18.8 19 19.7 18.6 18.8 19.3 18.6 18.9 19.1 18.4 18.7 18.8 19.1 18.4 18.8 19 17.9 18.6 18.9 19.3 18.6 18.9 19.2 18.4 18.7 18.8 19.1 18.4 18.8 19 18.1 18.6 18.9 19.3 18.6 18.9 19.2 18.5 18.7 18.8 19.1 18.5 18.8 19 18.1 18.7 18.9 19.4 18.6 18.9 19.2 18.5 18.7 18.8 19.1 18.5 18.8 19 18.2 18.7 18.9 19.4 18.7 18.9 19.2 18.5 18.7 18.9 19.1 18.5 18.8 19 18.2 18.7 18.9 19.4 18.7 18.9 19.2 18.5 18.7 18.9 19.1 18.6 18.8 19.1 18.2 18.7 18.9 19.5 18.7 18.9 19.2 18.5 18.7 18.9 19.1 18.6 18.8 19.1 18.3 18.7 18.9 18.7 18.9 19.2 18.5 18.7 18.9 19.1 18.6 18.8 19.1 18.3 18.7 18.9 18.7 19 19.2 18.5 18.7 18.9 19.2 18.6 18.8 19.1 18.3 18.7 18.9 18.7 19 19.2 18.5 18.7 18.9 19.2 18.6 18.8 19.1 18.4 18.7 18.9 18.8 19 19.3 18.5 18.7 18.9 19.2 18.6 18.8 19.2 18.4 18.7 18.9 18.8 19 19.3 18.5 18.7 18.9 19.2 18.6 18.8 19.2 18.4 18.7 19 18.8 19 19.3 18.6 18.7 18.9 19.2 18.6 18.9 19.2 18.4 18.7 19 18.8 19 19.3 18.6 18.7 18.9 19.2 18.6 18.9 19.2 18.4 18.7 19 18.8 19 19.3 18.6 18.7 18.9 19.3 18.6 18.9 19.2 18.4 18.7 19

106 MSc thesis

Appendixes

Heavy model block Heavy concrete weight distribution

70 0,9 Density 2915 Kg/m3 60 0,8 Average 23.03 gr 0,7 50 0,6 Min 21.8 gr 40 0,5 30 0,4 Max 24 gr 0,3 No of units No of 20 Av. Deviatie 0.39533 0,2

10 0,1 Probability Density Stand deviatie 0.482741 0 0

0 2 0 2 , , , , 4,0 21,8 22 22 22,4 22,6 22,8 23 23 23,4 23,6 23,8 2 Weight [gr]

Table E-3 Weight heavy concrete model blocks [gr] 22.2 22.2 23 23.2 23.1 23.4 23.5 23.5 22.6 22.2 23.4 22 23.1 23.2 22.3 23.3 22.1 23.1 23.4 22.4 23.6 23.4 22.9 21.9 23.4 22.5 22.1 22.9 23.7 22.1 23.2 23.2 23 23.3 22.2 23.3 23.4 22.5 23.3 22.7 23.3 23.2 23.6 22.8 22.4 23.4 23.5 21.9 23.2 23.1 23.4 23.6 21.9 23.5 23 21.9 23.3 23.2 23.1 22.4 22.8 23.4 23.1 22.8 23.8 23.5 22.3 23.4 23.2 22.2 23.3 23.3 23.6 22.7 22.9 23.1 23.1 23.5 22.1 23.7 23.1 23.1 22.2 23.2 23.2 23.6 23 22.8 23.1 23.3 24 23.6 22.2 23.4 23.6 22.4 23.7 23 23.3 23.2 22.5 23.2 23.3 23.1 23.4 23.5 23.4 23.3 23.3 23.9 22.5 22.1 23 22.2 23 23.4 23.3 23.2 23 23.3 23.2 23.2 23.2 23.7 23.2 23.5 23.4 22.3 23.5 23.9 23.2 22.7 22.5 23.3 23.5 23.5 22.5 22.9 22.5 21.9 23.5 23.7 23.2 23.1 22.9 23 23.2 22 23.5 23.1 23.4 23.2 23.2 23.6 23.3 22.3 23.3 23.4 23.5 22.3 23.6 22.1 23.3 22.5 23 23.1 22.2 23.6 23.5 22.7 22.2 21.9 23.6 22.5 22.2 22.9 23.4 22.4 22.4 23.3 23.2 23.1 22.4 22.7 22.3 22.9 23.3 23.3 23.3 23.3 22.3 23.2 22.5 23.3 22.5 23.3 22.2 23.4 23.6 23 23.3 23.3 23.6 23.6 22.1 23.3 23 23.4 23.6 23.6 23.5 23.3 23.2 23.2 23.4 23.5 23.2 22.1 22.3 23.4 23.3 23.5 22.9 22.3 23.2 22.4 23.4 22.3 22.3 23.2 23.6 23.3 23.2 23.4 23.5 23.2 23.3 22.9 23 22.7 23.1 23.3 23.1 22.8 23.7 23.3 23.2 22.4 23.5 23.1 23.4 23.1 23.3 23.2 23.5 23.2 23.1 22.2 23.9 23.1 23.7 22 23.2 23.6 23.4 23.3 23.1 22.6 22.3 23.3 22.7 23.3 22.5 23.4 22.2 22.1 23.5 22.4 22.4 21.8 22.6 22.9 23.2 22.3 23.1 22.3 23 23.2 23.1 22.5 23.2 23.5 23.2 23 23.1 23.1 21.8 23.3 23.8 23.1 23.2 23.6 23.2 23.3 22 23 23.4 22.4 23.5 22.2 23.4 23 23.5 23.1 23.1 23.4 23.3 23.4 23.6 23.6 22.5 22.4 23.2 23.3 22.6 23.1 22.3 23.2 23.3 23.4 22.7 23.4 23.1 23.1 23.4 22.9 23.5 22.4 23.2 23.2 23.2 21.8 22.8 23.1 22.3 23.4 23.3 23.2 23.2 23.3 23 23.5 23.4 23.4 23.1 23.1 23.1 23.1 22.2 22.1 23.5 22.1 23.4 22.2 22.9 23.2 22.3 23.6 22.2 22.9 23.1 23.6 23.4 22.5 22.6 23 22.2 23 23.3 23.3 23.3 22.6 23.3 23 23 23.3 23.1 23.5 23.6 23.7 23.3 23.1 23 23.3 22.9 23.2 23.4 23.1 23.3 23.3 23.1 22.2 22.1 23.7 22.3 22.4 22.5 23.2 23.5 23.2 22.5 22.8 23.4 23.3 23.2 23.6 22.5 22.3 23.3 22.7 23.3 23.2 23.1 23 22.6 23.3 23.4 23.5 23.5 23.5 23.4 23.5

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Appendix F Specific weight Xbloc model blocks

To determine the specific weight of the delivered model blocks several samples were taken of each series and the specific weight determined with a pycnometer a presented in Figure F-1.

Figure F-1 pycnometer

The specific density of a sample was determined as follows: − The weight of the empty pycnometer was measured. − The sample of Xbloc armour units was put into the pycnometer and the weight was measured again. − Pure water was added till mark (4) in Figure F-1 and the pycnometer was put under a bell-glass were a vacuum was created to remove all the air. − After 20 min the bell-glass was removed and the pycnometer was filled till mark (1) in Figure F-1 after which the weight was measured. − The temperature of the water is measured to determine the density of the water.

Because the exact volume of the pycnometer is known it is possible to calculate the volume of the Xbloc model blocks from which the specific weight can be determined. The results are presented in Table F-1.

The average densities which are used to further analysis of the results are: − Light concrete specific weight of: 2102 kg/m3 − Normal concrete specific weight of: 2465 kg/m3 − Heavy concrete specific weight of: 2915 kg/m3

108 MSc thesis

Appendixes

Table F-1 Results pycnometer tests Pycnometer Weight Density Volume water Volume Xbloc Density Xbloc No Weigth with Xbloc with Xbloc & water Volume water Xbloc water Test series [-] [gr] [gr] [gr] [ml] [gr] [gr] [kg/m3] [ml] [ml] [kg/m3] 2000 [1] 3 699.9 1317 2330.8 1309.6 1013.8 617.1 997.7 1016.14 293.46 2102.8 2000 [2] 5 702.3 1285.5 2310.7 1304.7 1025.2 583.2 997.7 1027.56 277.14 2104.4 2000 [3] 6 712.5 1318.5 2343.7 1313.7 1025.2 606 997.7 1027.56 286.14 2117.9 2000 [4] 7 733.4 1364.6 2370.8 1305.6 1006.2 631.2 997.7 1008.52 297.08 2124.7

2800 [1] 11 733.3 1556.9 2580.3 1308.3 1023.4 823.6 997.7 1025.76 282.54 2915.0 2800 [2] 12 730.2 1580.9 2596.3 1309.9 1015.4 850.7 997.7 1017.74 292.16 2911.8 2800 [3] 13 699.8 1553.5 2564.5 1306.4 1011 853.7 997.7 1013.33 293.07 2913.0 2800 [4] 15 698.2 1571.8 2566 1296.8 994.2 873.6 997.7 996.49 300.31 2909.0

2400 [1] 11 733.3 1374.7 2422.6 1308.3 1047.9 641.4 998.2 1049.79 258.51 2481.1 2400 [2] 12 730.2 1354.2 2410.2 1309.9 1056 624 998.2 1057.90 252.00 2476.2 2400 [3] 3 699.9 1364.7 2399.6 1309.6 1034.9 664.8 997.7 1037.29 272.31 2441.3 2400 [4] 13 699.8 1310.1 2366.3 1306.4 1056.2 610.3 997.6 1058.74 247.66 2464.3

B.N.M. van Zwicht 109

Appendixes

Appendix G Start and End photos

Table G-1 Test programme Specific weight 1 Specific weight 2 Specific weight 3 Slope 3:4 Series A Series B Series C Slope 2:3 Series D Series E Series F Slope 1:2 Series G Series H Series K

Figure G-1 Test series A-I start & end photo

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Figure G-2 Test series A-II start & end photo

Figure G-3 Test series A-III start & end photo

112 MSc thesis

Appendixes

Figure G-4 Test series A-IV start & end photo

Figure G-5 Test series B-II start & end photo

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Figure G-6 Test series B-III start & end photo

Figure G-7 Test series B-IV start & end photo

114 MSc thesis

Appendixes

Figure G-8 Test series B-V start & end photo

Figure G-9 Test series BL-I start & end photo

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Figure G-10 Test series BL-II start & end photo

Figure G-11 Test series C-I start & end photo

116 MSc thesis

Appendixes

Figure G-12 Test series C-II start & end photo

Figure G-13 Test series C-III start & end photo

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Figure G-14 Test series C-IV start & end photo

Figure G-15 Test series D-I start & end photo

118 MSc thesis

Appendixes

Figure G-16 Test series D-II start & end photo

Figure G-17 Test series D-III start & end photo

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Figure G-18 Test series D-IV start & end photo

Figure G-19 Test series E-I start & end photo

120 MSc thesis

Appendixes

Figure G-20 Test series E-II start & end photo

Figure G-21 Test series E-III start & end photo

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Figure G-22 Test series E-IV start & end photo

Figure G-23 Test series F-I start & end photo

122 MSc thesis

Appendixes

Figure G-24 Test series F-II start & end photo

Figure G-25 Test series F-III start & end photo

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Figure G-26 Test series G-I start & end photo

Figure G-27 Test series G-II start & end photo

124 MSc thesis

Appendixes

Figure G-28 Test series H-I start & end photo

Figure G-29 Test series H-II start & end photo

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Figure G-30 Test series K-I start & end photo

Figure G-31 Test series K-II start & end photo

126 MSc thesis

Appendixes

Appendix H Relative placement densities

The placement density of armour layer is controlled by measuring the centrelines of the representative part of the armour layer horizontally and vertically as shown in Figure H-1 . With the following formula the relative placing density (RPD) is determined:

(1)(1)NNdxdyD−− 2 RPD =×xy 100% LLxy

In which: D = Xbloc unit height

Lx = average horizontal length Nx = number of Xblox in the x direction Ly = average vertical length Ny = number of Xblox in the y direction dx = 1.3 dy = 0.64

Figure H-1 Measurement centrelines

The relative placement was determined after completion of the armour placement. The formula is highly sensitive for minor variation in the measurement of the distances and it was found difficult to determine in situ the lengths of the centreline trough the outer line of the armour layer. Therefore a RPD was taken by analysis of the start photos of each test series to overcome this problem. They showed the same trend but the values differ greatly from the in-situ measurement.

B.N.M. van Zwicht 127

Effect of the concrete density on the stability of Xbloc armour units three RPD’s are presented Table H-1. The average of the three RPD is taken to represent the relative placing density. The two outline values of A-I and C-IV are not taken into account.

Table H-1 Relative placement densities Test RPD [%] RPD [%] Theoretical Average series In-situ Photo RPD [%] RPD [%] A-I 108.0 100.4 106 103.1 A-II 106.7 102.2 106 104.9 A-III 103.2 98.3 106 102.5 A-IV 103.2 98.8 106 102.6 B-I 108.0 102.0 110 106.8 B-II 108.7 103.8 113 108.6 B-III 103.7 97.7 106 102.4 B-IV 105.9 104.1 113 107.8 B-V 106.4 109.5 113 109.8 BL-I 100.4 101.4 106 102.5 BL-II 103.9 98.1 106 102.6 C-I 110.1 111.3 111 110.9 C-II 111.3 111 111.2 C-III 103.9 98.5 106 102.7 C-IV 118.7 108.0 106 106.9 D-I 105.2 104.1 106 105.1 D-II 102.7 99.5 109 103.7 D-III 100.2 96.1 103 99.9 D-IV 97.4 93.4 98 96.1 E-I 103.2 97.2 106 102.1 E-II 99.3 92.9 103 98.5 E-III 98.9 92.2 103 98.1 E-IV 96.3 92.7 100 96.4 F-I 97.7 97.7 98 97.7 F-II 95.4 91.8 98 65.1 F-III 98.5 98.8 98 98.3 G-I 103.5 100.6 103 102.5 G-II 103.8 101.5 103 102.9 H-I 101.3 98.4 99 99.4 H-II 101.0 101.3 99 100.3 K-I 99.7 98.4 99 98.9 K-II 101.2 100.3 99 100.0

128 MSc thesis

Appendixes

Settlement Settlement Appendix I Settlements Test Height % of Start % of prev Test Height % of Start % of prev A-IV-7 7.1 7.6 -0.6 B-V-3 5.5 2.5 -1.3 A-IV-8 7.0 9.2 -1.8 B-V-4 5.5 2.8 -0.3 Settlement B-V-5 5.4 3.9 -1.2 Test Height % of Start % of prev Start 5.8 0.0 0.0 B-V-6 5.4 4.5 -0.7 Start 7.4 0.0 0.0 B-II-1 5.8 0.2 -0.2 B-V-7 5.4 4.9 -0.4 A-I-1 7.4 0.0 0.0 B-II-2 5.8 0.9 -0.6 B-V-8 5.4 5.3 -0.4 A-I-2 7.2 2.7 -2.7 B-II-3 5.7 2.5 -1.6 A-I-3 6.9 6.3 -3.7 B-II-4 5.6 3.6 -1.1 Start 7.8 0.0 0.0 B-II-5 5.6 4.3 -0.8 BL-I-1 7.6 2.8 -2.8 Start 7.5 0.0 0.0 B-II-6 5.5 5.3 -1.0 BL-I-2 7.4 5.8 -3.0 A-II-1 7.5 0.8 -0.8 B-II-7 5.5 6.3 -1.0 BL-I-3 7.3 6.7 -1.0 A-II-2 7.3 2.5 -1.7 BL-I-4 7.2 7.7 -1.0 A-II-3 7.1 4.9 -2.5 Start 6.1 0.0 0.0 BL-I-5 7.2 8.3 -0.7 A-II-4 7.0 6.3 -1.4 B-III-1 6.0 1.4 -1.4 BL-I-6 7.1 9.6 -1.4 A-II-5 7.0 7.1 -0.9 B-III-2 5.9 3.8 -2.4 BL-I-7 7.0 10.0 -0.5 A-II-6 6.9 8.0 -1.0 B-III-3 5.9 3.8 0.0 BL-I-8 7.0 10.7 -0.7 B-III-4 5.7 6.8 -3.2 BL-I-9 6.9 11.5 -0.9 Start 7.6 0.0 0.0 B-III-5 5.6 7.6 -0.9 A-III-1 7.5 1.2 -1.2 B-III-6 5.3 12.2 -5.0 Start 7.1 0.0 0.0 A-III-2 7.4 2.9 -1.7 BL-II-1 7.0 1.8 -1.8 A-III-3 7.3 4.6 -1.8 Start 5.6 0.0 0.0 BL-II-2 6.9 2.7 -1.0 A-III-4 7.2 5.3 -0.7 B-IV-1 5.5 1.9 -1.9 BL-II-3 6.9 2.8 -0.1 A-III-5 7.2 5.7 -0.5 B-IV-2 5.5 2.5 -0.7 BL-II-4 6.8 4.2 -1.4 A-III-6 7.2 5.8 -0.1 B-IV-3 5.4 3.3 -0.8 BL-II-5 6.7 5.9 -1.7 A-III-7 7.1 6.8 -1.0 B-IV-4 5.4 4.3 -1.1 BL-II-6 6.6 7.0 -1.2 B-IV-5 5.3 5.8 -1.6 BL-II-7 6.6 7.4 -0.4 Start 7.7 0.0 0.0 B-IV-6 5.2 7.2 -1.5 BL-II-8 6.5 8.0 -0.6 A-IV-1 7.7 0.4 -0.4 B-IV-7 5.2 7.5 -0.3 A-IV-2 7.5 2.4 -2.0 B-IV-8 5.2 8.4 -1.0 A-IV-3 7.4 4.0 -1.7 A-IV-4 7.3 5.8 -1.9 Start 5.7 0.0 0.0 A-IV-5 7.2 6.8 -1.0 B-V-1 5.6 0.8 -0.8 A-IV-6 7.2 7.0 -0.2 B-V-2 5.6 1.3 -0.5

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Settlement Settlement Settlement Test Height % of Start % of prev Test Height % of Start % of prev Test Height % of Start % of prev Start 5.3 0.0 0.0 C-IV-2 7.6 3.0 -0.7 Start 9.2 0.0 0.0 C-I-1 5.3 0.6 -0.6 C-IV-3 7.5 3.3 -0.3 D-IV-1 9.2 0.2 -0.2 C-I-2 5.3 0.6 -0.1 C-IV-4 7.4 5.2 -2.0 D-IV-2 9.2 0.5 -0.4 C-I-3 5.2 1.9 -1.2 C-IV-5 7.3 6.0 -0.9 D-IV-3 8.6 6.5 -6.0 C-I-4 5.2 1.9 0.0 C-IV-6 7.2 7.3 -1.4 D-IV-4 8.3 9.5 -3.1 C-I-5 5.2 3.2 -1.4 C-IV-7 7.2 7.5 -0.2 D-IV-5 8.1 12.5 -3.4 C-I-6 5.2 3.2 0.0 D-IV-6 7.9 13.9 -1.7 C-I-7 5.1 4.7 -1.6 Start 8.6 0.0 0.0 D-IV-7 7.8 15.6 -1.9 C-I-8 5.0 5.5 -0.8 D-I-1 8.6 0.5 -0.5 D-I-2 8.5 1.0 -0.5 Start 8.7 0.0 0.0 Start 5.5 0.0 0.0 D-I-3 8.4 2.9 -1.9 E-I-1 8.5 2.1 -2.1 C-II-1 5.3 2.4 -2.4 D-I-4 8.2 5.0 -2.2 E-I-2 8.2 5.2 -3.2 C-II-2 5.3 3.3 -0.9 D-I-5 8.1 6.0 -1.0 E-I-3 8.2 5.2 0.0 C-II-3 5.2 4.5 -1.2 D-I-6 7.9 7.8 -1.9 E-I-4 8.2 5.8 -0.6 C-II-4 5.2 5.5 -1.1 D-I-7 7.7 10.7 -3.1 E-I-5 8.1 7.3 -1.6 C-II-5 5.1 5.8 -0.3 E-I-6 8.0 7.7 -0.4 C-II-6 5.1 6.0 -0.3 Start 8.4 0.0 0.0 E-I-7 8.0 8.2 -0.6 C-II-7 5.1 6.5 -0.5 D-II-1 8.4 0.4 -0.4 E-I-8 7.9 9.4 -1.3 C-II-8 5.1 6.9 -0.4 D-II-2 8.3 1.2 -0.8 E-I-9 7.8 10.2 -0.9 C-II-9 5.1 7.2 -0.3 D-II-3 8.1 3.8 -2.6 D-II-4 8.0 4.6 -0.8 Start 8.9 0.0 0.0 Start 7.6 0.0 0.0 D-II-5 8.0 4.8 -0.2 E-II-2 8.4 5.1 -5.1 C-III-1 7.4 3.1 -3.1 D-II-6 7.9 6.2 -1.5 E-II-3 8.3 6.8 -1.8 C-III-2 7.3 4.4 -1.4 D-II-7 7.8 7.6 -1.5 E-II-4 8.2 7.7 -1.0 C-III-3 7.2 5.6 -1.3 E-II-5 8.0 9.8 -2.2 C-III-4 7.1 6.5 -0.9 Start 8.8 0.0 0.0 E-II-6 8.0 10.0 -0.2 C-III-5 7.0 7.7 -1.3 D-III-1 8.7 1.0 -1.0 E-II-7 7.9 11.5 -1.7 C-III-6 6.9 8.6 -1.0 D-III-2 8.6 1.6 -0.6 E-II-8 7.8 11.9 -0.4 C-III-7 6.9 8.8 -0.2 D-III-3 8.4 4.5 -2.9 D-III-4 8.2 6.2 -1.8 Start 9.3 0.0 0.0 Start 7.8 0.0 0.0 D-III-5 8.2 6.4 -0.2 E-III-1 9.3 0.5 -0.5 C-IV-1 7.6 2.4 -2.4 D-III-6 8.1 8.1 -1.8 E-III-2 8.7 6.0 -5.5 D-III-7 7.9 9.8 -1.9 E-III-3 8.7 6.8 -0.8

130 MSc thesis

Appendixes

Settlement Settlement Settlement Test Height % of Start % of prev Test Height % of Start % of prev Test Height % of Start % of prev E-III-4 8.6 7.2 -0.4 Start 9.3 0.0 0.0 H-I-3 10.2 1.0 -0.3 E-III-5 8.5 8.6 -1.5 F-III-1 8.8 5.4 -5.4 H-I-4 10.1 2.1 -1.1 E-III-6 8.2 12.2 -3.9 F-III-2 8.7 6.6 -1.3 H-I-5 9.9 4.2 -2.2 E-III-7 7.9 14.9 -3.1 F-III-3 8.4 9.3 -2.9 H-I-6 9.5 8.0 -4.0 F-III-4 8.3 10.6 -1.4 H-I-7 9.2 10.5 -2.7 Start 9.2 0.0 0.0 F-III-5 8.2 11.9 -1.4 H-I-8 9.2 10.5 0.0 E-IV-1 9.1 1.7 -1.7 F-III-6 8.1 12.6 -0.8 E-IV-2 8.7 6.0 -4.4 F-III-7 8.0 13.3 -0.8 Start 10.1 0.0 0.0 E-IV-3 8.6 7.1 -1.2 F-III-8 7.9 14.6 -1.5 H-II-1 10.1 0.0 0.0 E-IV-4 8.5 7.9 -0.8 H-II-2 10.1 0.5 -0.5 E-IV-5 8.5 8.2 -0.4 Start 10.0 0.0 0.0 H-II-3 10.1 0.5 0.0 E-IV-6 8.2 11.3 -3.3 G-I-1 10.0 0.3 -0.3 H-II-4 10.0 1.3 -0.8 E-IV-7 8.1 12.0 -0.9 G-I-2 10.0 0.3 0.0 H-II-5 9.8 3.8 -2.5 G-I-3 10.0 0.5 -0.2 H-II-6 9.6 5.4 -1.7 Start 9.4 0.0 0.0 G-I-4 10.0 0.5 0.0 H-II-7 9.4 7.3 -2.0 F-I-1 8.7 7.4 -7.4 G-I-5 9.9 1.2 -0.7 F-I-2 8.6 8.3 -1.0 G-I-6 9.8 2.0 -0.8 Start 10.4 0.0 0.0 F-I-3 8.5 9.9 -1.7 G-I-7 9.6 4.5 -2.6 K-I-1 10.4 0.6 -0.6 F-I-4 8.3 11.1 -1.4 G-I-8 9.1 9.1 -4.9 K-I-2 10.3 0.8 -0.2 F-I-5 8.3 11.6 -0.6 K-I-3 10.3 1.6 -0.8 F-I-6 8.2 12.4 -0.8 Start 10.0 0.0 0.0 K-I-4 10.1 3.0 -1.5 F-I-7 8.1 13.4 -1.2 G-II-1 10.0 0.0 0.0 K-I-5 9.8 5.9 -3.0 G-II-2 10.0 0.3 -0.3 K-I-6 9.2 12.0 -6.5 Start 9.4 0.0 0.0 G-II-3 9.9 0.7 -0.3 F-II-1 9.0 4.8 -4.8 G-II-4 9.9 1.2 -0.5 Start 10.2 0.0 0.0 F-II-2 8.7 7.6 -3.0 G-II-5 9.7 3.0 -1.9 K-II-1 10.2 0.3 -0.3 F-II-3 8.6 8.9 -1.3 G-II-6 9.7 3.2 -0.2 K-II-2 10.1 1.0 -0.7 F-II-4 8.4 10.3 -1.6 G-II-7 9.5 5.3 -2.2 K-II-3 10.1 1.3 -0.3 F-II-5 8.4 11.2 -1.0 G-II-8 9.0 9.7 -4.6 K-II-4 9.9 2.6 -1.4 F-II-6 8.2 12.4 -1.4 K-II-5 9.7 4.6 -2.0 F-II-7 8.2 13.3 -1.0 Start 10.3 0.0 0.0 K-II-6 9.5 6.5 -2.1 H-I-1 10.3 0.2 -0.2 K-II-7 9.4 7.8 -1.4 H-I-2 10.2 0.7 -0.4

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Appendix J Test Results

Note: wave gauges positioned at X1-2=0.3 & X2-3=0.4 (unless mentioned differently)

Test density Slope Hd Hd Tp h Hm0 Tp Tm-1.0 RC N Ns Nod [-] [Kg/m3] [m/m] [%] [cm] [s] [m] [m] [s] [s] [-] [-] [-] [-]

(X1-2=0.16 & X2-3=0.24) A-I-1 2102 3:4 60 3.34 1.03 0.6 3.296 1.067 0.978 0.314 0 1.49 0.00 A-I-2 2102 3:4 80 4.46 1.19 0.6 4.38 1.164 1.102 0.3328 0 1.98 0.00 A-I-3 2102 3:4 100 5.57 1.34 0.6 5.488 1.306 1.223 0.3939 5 2.47 0.27 A-I-4 2102 3:4 120 6.68 1.46 0.6 0.00 A-I-5 2102 3:4 140 7.80 1.58 0.6 0.00 A-I-6 2102 3:4 160 8.91 1.69 0.6 7.734 1.778 1.534 0.3942 failure 3.49 0.53 A-I-7 2102 3:4 180 10.03 1.79 0.6 0.00

(X1-2=0.16 & X2-3=0.24) A-II-1 2102 3:4 60 3.34 1.03 0.6 3.305 1.067 0.980 0.3099 0 1.49 0.00 A-II-2 2102 3:4 80 4.46 1.19 0.6 4.462 1.255 1.103 0.3243 0 2.01 0.00 A-II-3 2102 3:4 100 5.57 1.34 0.6 5.583 1.306 1.224 0.3498 0 2.52 0.00 A-II-4 2102 3:4 120 6.68 1.46 0.6 6.701 1.455 1.331 0.3715 0 3.02 0.00 A-II-5 2102 3:4 140 7.80 1.58 0.6 7.754 1.561 1.430 0.3987 0 3.50 0.00 A-II-6 2102 3:4 160 8.91 1.69 0.6 8.88 1.73 1.531 0.4349 2 4.00 0.11 A-II-7 2102 3:4 180 10.03 1.79 0.6 10.02 1.73 1.618 0.4577 failure 4.52

(X1-2=0.16 & X2-3=0.24) A-III-1 2102 3:4 60 3.34 1.03 0.6 3.36 1.067 0.984 0.3178 0 1.52 0.00 A-III-2 2102 3:4 80 4.46 1.19 0.6 4.52 1.164 1.104 0.3352 0 2.04 0.00 A-III-3 2102 3:4 100 5.57 1.34 0.6 5.562 1.306 1.225 0.3577 1 2.51 0.05 A-III-4 2102 3:4 120 6.68 1.46 0.6 6.75 1.455 1.335 0.3812 0 3.04 0.05 A-III-5 2102 3:4 140 7.80 1.58 0.6 7.696 1.561 1.432 0.4073 0 3.47 0.05 A-III-6 2102 3:4 160 8.91 1.69 0.6 8.801 1.73 1.528 0.4369 0 3.97 0.05

132 MSc thesis

Appendixes

A-III-7 2102 3:4 180 10.03 1.79 0.6 9.816 1.829 1.644 0.4697 2 4.43 0.16 A-III-8 2102 3:4 216 12.03 1.96 0.6 11.54 1.939 1.786 0.5111 failure 5.20

A-IV-1 2102 3:4 60 3.34 1.03 0.6 3.372 1.067 0.980 0.3103 0 1.52 0.00 A-IV-2 2102 3:4 80 4.46 1.19 0.6 4.518 1.164 1.104 0.3231 0 2.04 0.00 A-IV-3 2102 3:4 100 5.57 1.34 0.6 5.619 1.306 1.225 0.3486 0 2.53 0.00 A-IV-4 2102 3:4 120 6.68 1.46 0.6 6.721 1.455 1.331 0.3738 0 3.03 0.00 A-IV-5 2102 3:4 140 7.80 1.58 0.6 7.768 1.561 1.431 0.4028 0 3.50 0.00 A-IV-6 2102 3:4 160 8.91 1.69 0.6 8.89 1.73 1.527 4358 0 4.01 0.00 A-IV-7 2102 3:4 180 10.03 1.79 0.6 9.953 1.829 1.642 0.47 0 4.49 0.00 A-IV-8 2102 3:4 216 12.03 1.96 0.6 12.29 2 1.793 0.5138 0 5.54 0.00

(X1-2=0.16 & X2-3=0.24) B-I-1 2465 3:4 60 4.68 1.22 0.6 4.921 1.255 1.123 0.352 0 1.67 0.00 B-I-2 2465 3:4 80 6.24 1.41 0.6 6.471 1.455 1.287 0.3838 0 2.20 0.00 B-I-3 2465 3:4 100 7.80 1.58 0.6 7.581 1.561 1.432 0.409 0 2.57 0.00 B-I-3.2 2465 3:4 100 7.80 1.58 0.6 7.573 1.561 1.435 0.4104 0 2.57 0.00 B-I-4 2465 3:4 120 9.36 1.73 0.6 9.22 1.73 1.567 0.4369 0 3.13 0.00 B-I-5 2465 3:4 140 10.92 1.87 0.6 10.65 1.882 1.712 0.4794 0 3.61 0.00 B-I-6 2465 3:4 160 12.48 2.00 0.6 12.32 2 1.827 0.5113 0 4.18 0.00 B-I-7 2465 3:4 180 14.04 2.12 0.6 13.4 2.133 1.937 0.4418 0 4.55 0.00

(X1-2=0.16 & X2-3=0.24) B-II-1 2465 3:4 60 4.68 1.22 0.6 4.834 1.255 1.119 0.3506 0 1.64 0.00 B-II-2 2465 3:4 80 6.24 1.41 0.6 6.277 1.455 1.283 0.387 0 2.13 0.00 B-II-3 2465 3:4 100 7.80 1.58 0.6 7.759 1.562 1.243 0.4183 0 2.63 0.00 B-II-4 2465 3:4 120 9.36 1.73 0.6 9.272 1.730 1.568 0.4474 0 3.15 0.00 B-II-5 2465 3:4 140 10.92 1.87 0.6 10.7 1.829 1.715 0.4892 3 3.63 0.13 B-II-6 2465 3:4 160 12.48 2.00 0.6 12.35 2.000 1.829 0.5376 2 4.19 0.22 B-II-7 2465 3:4 180 14.04 2.12 0.6 14.18 2.291 1.933 0.567 1 4.81 0.27

(X1-2=0.16 & X2-3=0.24) B-III-1 2465 3:4 60 4.68 1.22 0.6 4.757 1.255 1.122 0.3286 0 1.61 0.00 B-III-2 2465 3:4 80 6.24 1.41 0.6 6.233 1.455 1.287 0.3712 0 2.12 0.00

B.N.M. van Zwicht 133

Effect of the concrete density on the stability of Xbloc armour units

B-III-3 2465 3:4 100 7.80 1.58 0.6 7.745 1.561 1.432 0.406 0 2.63 0.00 B-III-4 2465 3:4 120 9.36 1.73 0.6 9.389 1.73 1.586 0.4389 0 3.19 0.00 B-III-5 2465 3:4 140 10.92 1.87 0.6 10.82 1.829 1.711 0.4862 1 3.67 0.04 B-III-6 2465 3:4 160 12.48 2.00 0.6 12.48 2 1.830 0.5362 28 4.24 1.29

(X1-2=0.16 & X2-3=0.24) B-IV-1 2465 3:4 60 4.68 1.22 0.6 4.748 1.255 1.127 0.3411 0 1.61 0.00 B-IV-2 2465 3:4 80 6.24 1.41 0.6 6.391 1.455 1.294 0.382 0 2.17 0.00 B-IV-3 2465 3:4 100 7.80 1.58 0.6 7.896 1.561 1.433 0.4084 0 2.68 0.00 B-IV-4 2465 3:4 120 9.36 1.73 0.6 9.704 1.73 1.569 0.4412 0 3.29 0.00 B-IV-5 2465 3:4 140 10.92 1.87 0.6 11.21 1.829 1.715 0.4895 0 3.80 0.00 B-IV-6 2465 3:4 160 12.48 2.00 0.6 13.04 2 1.833 0.5422 1 4.43 0.04 B-IV-7 2465 3:4 180 14.04 2.12 0.6 14.85 2.207 1.934 0.5708 0 5.04 0.04 B-IV-8 2465 3:4 206 16.04 2.27 0.6 15.76 2.207 2.072 0.5703 0 5.35 0.04

(X1-2=0.16 & X2-3=0.24) B-V-1 2465 3:4 60 4.68 1.22 0.6 4.717 1.255 1.124 0.3437 0 1.60 0.00 B-V-2 2465 3:4 80 6.24 1.41 0.6 6.174 1.455 1.289 0.3812 0 2.10 0.00 B-V-3 2465 3:4 100 7.80 1.58 0.6 7.669 1.561 1.433 0.4122 0 2.60 0.00 B-V-4 2465 3:4 120 9.36 1.73 0.6 9.161 1.73 1.568 0.4386 0 3.11 0.00 B-V-5 2465 3:4 140 10.92 1.87 0.6 10.56 1.829 1.710 0.4783 0 3.58 0.00 B-V-6 2465 3:4 160 12.48 2.00 0.6 12.14 2 1.830 0.5271 0 4.12 0.00 B-V-7 2465 3:4 180 14.04 2.12 0.6 13.77 2.207 1.933 0.5572 0 4.67 0.00 B-V-8 2465 3:4 206 16.04 2.27 0.6 15.66 2.286 2.071 0.5659 0 5.31 0.00

(X1-2=0.16 & X2-3=0.24) BL-I-1 2465 3:4 60 4.68 1.22 0.6 4.684 1.255 1.124 0.3098 0 1.59 0.00 BL-I-2 2465 3:4 80 6.24 1.41 0.6 6.17 1.455 1.287 0.3518 0 2.09 0.00 BL-I-3 2465 3:4 100 7.80 1.58 0.6 7.619 1.561 1.429 0.3924 0 2.59 0.00 BL-I-4 2465 3:4 120 9.36 1.58 0.6 9.217 1.73 1.567 0.439 0 3.13 0.00 BL-I-5 2465 3:4 140 10.92 1.73 0.6 10.6 1.829 1.690 0.4808 0 3.60 0.00 BL-I-6 2465 3:4 160 12.48 1.87 0.6 0 0.00 0.00 BL-I-7 2465 3:4 180 14.04 2.00 0.6 13.48 2.207 1.925 0.5514 0 4.57 0.00 BL-I-8 2465 3:4 206 16.04 2.27 0.6 15.27 2.207 2.097 0.5973 0 5.18 0.00

134 MSc thesis

Appendixes

BL-I-9 2465 3:4 231 18.05 2.40 0.6 17.04 2.462 2.202 0.6231 4 5.78 0.21

BL-II-1 2465 3:4 60 4.68 1.22 0.6 4.757 1.255 1.126 0.3382 0 1.61 0.00 BL-II-2 2465 3:4 80 6.24 1.41 0.6 6.361 1.455 1.289 0.3764 0 2.16 0.00 BL-II-3 2465 3:4 100 7.80 1.58 0.6 7.871 1.561 1.432 0.4149 0 2.67 0.00 BL-II-4 2465 3:4 120 7.80 1.58 0.6 9.544 1.73 1.562 0.4578 0 3.24 0.00 BL-II-5 2465 3:4 140 9.36 1.73 0.6 11.36 1.829 1.711 0.4991 0 3.86 0.00 BL-II-6 2465 3:4 160 10.92 1.87 0.6 13.05 2 1.829 0.5276 0 4.43 0.00 BL-II-7 2465 3:4 180 12.48 2.00 0.6 14.55 2.207 1.931 0.5465 0 4.94 0.00 BL-II-8 2465 3:4 206 16.04 2.27 0.6 16.19 2.207 2.050 0.5817 0 5.49 0.00

(X1-2=0.16 & X2-3=0.24) C-I-1 2915 3:4 60 6.02 1.39 0.6 5.935 1.455 1.267 0.3989 0 1.54 0.00 C-I-2 2915 3:4 80 8.02 1.60 0.6 7.952 1.561 1.454 0.431 0 2.07 0.00 C-I-3 2915 3:4 100 10.03 1.79 0.6 9.9 1.778 1.622 0.472 0 2.57 0.00 C-I-4 2915 3:4 120 12.03 1.96 0.6 11.88 2 1.798 0.5337 0 3.09 0.00 C-I-5 2915 3:4 140 14.04 2.12 0.6 14.14 2.207 1.932 0.5748 0 3.67 0.00 C-I-6 2915 3:4 160 16.04 2.27 0.6 16.2 2.207 2.071 0.5796 0 4.21 0.00 C-I-7 2915 3:4 180 18.05 2.40 0.6 18.31 2.462 2.169 0.5792 0 4.76 0.00 C-I-8 2915 3:4 200 20.05 2.07 0.6 18.83 2.065 1.920 0.5707 0 4.89 0.00

(X1-2=0.16 & X2-3=0.24) C-II-1 2915 3:4 60 6.02 1.39 0.6 5.944 1.455 1.261 0.3631 0 1.54 0.00 C-II-2 2915 3:4 80 8.02 1.60 0.6 7.955 1.561 1.447 0.4068 0 2.07 0.00 C-II-3 2915 3:4 100 10.03 1.79 0.6 9.931 1.829 1.627 0.46 0 2.58 0.00 C-II-4 2915 3:4 120 12.03 1.96 0.6 11.75 2 1.786 0.5025 0 3.05 0.00 C-II-5 2915 3:4 140 14.04 2.12 0.6 13.63 2.207 1.974 0.5533 0 3.54 0.00 C-II-6 2915 3:4 160 16.04 2.27 0.6 15.56 2.207 2.084 0.5875 0 4.04 0.00 C-II-7 2915 3:4 180 18.05 2.40 0.6 17.45 2.462 2.204 0.5999 0 4.53 0.00

(X1-2=0.16 & X2-3=0.24) C-III-1 2915 3:4 60 6.02 1.39 0.6 6.014 1.455 1.265 0.3511 0 1.56 0.00 C-III-2 2915 3:4 80 8.02 1.60 0.6 7.978 1.561 1.448 0.4016 0 2.07 0.00 C-III-3 2915 3:4 100 10.03 1.79 0.6 10.03 1.829 1.622 0.4604 0 2.60 0.00

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Effect of the concrete density on the stability of Xbloc armour units

C-III-4 2915 3:4 120 12.03 1.96 0.6 11.94 2 1.785 0.5123 0 3.10 0.00 C-III-5 2915 3:4 140 14.04 2.12 0.6 13.78 2.207 1.930 0.5539 0 3.58 0.00 C-III-6 2915 3:4 160 16.04 2.27 0.6 15.67 2.207 2.098 0.5996 0 4.07 0.00 C-III-7 2915 3:4 180 18.05 2.40 0.6 17.02 2.462 2.202 0.6251 0 4.42 0.00

C-IV-1 2915 3:4 60 6.02 1.39 0.6 6.25 1.455 1.268 0.3828 0 1.62 0.00 C-IV-2 2915 3:4 80 8.02 1.60 0.6 8.369 1.561 1.452 0.4343 0 2.17 0.00 C-IV-3 2915 3:4 100 10.03 1.79 0.6 10.51 1.829 1.620 0.4729 0 2.73 0.00 C-IV-4 2915 3:4 120 12.03 1.96 0.6 12.58 2 1.775 0.5226 0 3.27 0.00 C-IV-5 2915 3:4 140 14.04 2.12 0.6 14.66 2.207 1.948 0.5688 0 3.81 0.00 C-IV-6 2915 3:4 160 16.04 2.27 0.6 16.72 2.207 2.059 0.5834 0 4.34 0.00 C-IV-7 2915 3:4 180 18.05 2.40 0.6 18.79 2.462 2.158 0.5853 0 4.88 0.00

D-I-1 2102 2:3 60 3.34 1.03 0.6 3.377 1.067 0.981 0.2834 0 1.52 0.00 D-I-2 2102 2:3 80 4.46 1.19 0.6 4.475 1.255 1.103 0.2981 0 2.02 0.00 D-I-3 2102 2:3 100 5.57 1.34 0.6 5.571 1.306 1.226 0.3208 0 2.51 0.00 D-I-4 2102 2:3 120 6.68 1.46 0.6 6.686 1.455 1.333 0.3418 0 3.02 0.00 D-I-5 2102 2:3 140 7.80 1.58 0.6 7.784 1.561 1.435 0.3672 0 3.51 0.00 D-I-6 2102 2:3 160 8.91 1.69 0.6 8.918 1.73 1.419 0.394 0 4.02 0.00 D-I-7 2102 2:3 180 10.03 1.79 0.6 10.06 1.829 1.494 0.4224 5 4.54 0.27

D-II-1 2102 2:3 60 3.34 1.03 0.6 3.334 1.067 0.985 0.2821 0 1.50 0.00 D-II-2 2102 2:3 80 4.46 1.19 0.6 4.489 1.255 1.106 0.293 0 2.02 0.00 D-II-3 2102 2:3 100 5.57 1.34 0.6 5.537 1.306 1.226 0.3156 0 2.50 0.00 D-II-4 2102 2:3 120 6.68 1.46 0.6 6.671 1.455 1.333 0.3371 0 3.01 0.00 D-II-5 2102 2:3 140 7.80 1.58 0.6 7.728 1.561 1.433 0.3631 0 3.49 0.00 D-II-6 2102 2:3 160 8.91 1.69 0.6 8.855 1.73 1.529 0.3914 0 3.99 0.00 D-II-7 2102 2:3 180 10.03 1.79 0.6 10.01 1.829 1.621 0.4213 0 4.51 0.00 D-II-8 2102 2:3 224 12.48 2.00 0.6 12.1 2.133 1.822 0.476 5.46 0.00

D-III-1 2102 2:3 60 3.34 1.03 0.6 3.38 1.067 0.984 0.2771 0 1.52 0.00

136 MSc thesis

Appendixes

D-III-2 2102 2:3 80 4.46 1.19 0.6 4.493 1.255 1.105 0.2924 0 2.03 0.00 D-III-3 2102 2:3 100 5.57 1.34 0.6 5.617 1.306 1.226 0.3228 0 2.53 0.00 D-III-4 2102 2:3 120 6.68 1.46 0.6 6.739 1.455 1.332 0.3467 0 3.04 0.00 D-III-5 2102 2:3 140 7.80 1.58 0.6 7.827 1.561 1.432 0.3767 0 3.53 0.00 D-III-6 2102 2:3 160 8.91 1.69 0.6 8.986 1.73 1.528 0.3998 3 4.05 0.16 D-III-7 2102 2:3 180 10.03 1.79 0.6 10.05 1.829 1.618 0.4273 7 4.53 0.59

D-IV-1 2102 2:3 60 3.34 1.03 0.6 3.408 1.067 0.952 0.2899 0 1.54 0.00 D-IV-2 2102 2:3 80 4.46 1.19 0.6 4.537 1.164 1.104 0.2999 0 2.05 0.00 D-IV-3 2102 2:3 100 5.57 1.34 0.6 5.671 1.306 1.225 0.3178 1 2.56 0.05 D-IV-4 2102 2:3 120 6.68 1.46 0.6 6.706 1.455 1.332 0.3348 2 3.02 0.16 D-IV-5 2102 2:3 140 7.80 1.58 0.6 7.778 1.561 1.434 0.3601 2 3.51 0.27 D-IV-6 2102 2:3 160 8.91 1.69 0.6 8.956 1.73 1.528 0.3881 1 4.04 0.32 D-IV-7 2102 2:3 180 10.03 1.79 0.6 10.12 1.829 1.620 0.4194 16 4.56 1.17

E-I-1 2465 2:3 60 4.68 1.22 0.6 4.677 1.255 1.129 0.3047 0 1.59 0.00 E-I-2 2465 2:3 80 6.24 1.41 0.6 6.25 1.455 1.292 0.3408 0 2.12 0.00 E-I-3 2465 2:3 100 7.80 1.58 0.6 7.759 1.561 1.433 0.3748 0 2.63 0.00 E-I-4 2465 2:3 120 9.36 1.73 0.6 9.369 1.73 1.569 0.4159 0 3.18 0.00 E-I-5 2465 2:3 140 10.92 1.87 0.6 10.82 1.829 1.714 0.459 0 3.67 0.00 E-I-6 2465 2:3 160 12.48 2.00 0.6 12.4 2 1.830 0.4904 0 4.21 0.00 E-I-7 2465 2:3 180 14.04 2.12 0.6 14.15 2.207 1.930 0.5111 0 4.80 0.00 E-I-8 2465 2:3 206 16.04 2.27 0.6 15.87 2.286 2.052 0.5412 0 5.39 0.00 E-I-9 2465 2:3 231 18.05 2.40 0.6 17.52 2.462 2.173 0.5731 0 5.95 0.00

E-II-2 2465 2:3 80 4.68 1.41 0.6 6.061 1.455 1.287 0.3237 0 2.06 0.00 E-II-3 2465 2:3 100 7.80 1.58 0.6 7.577 1.561 1.432 0.3599 0 2.57 0.00 E-II-4 2465 2:3 120 9.36 1.73 0.6 9.159 1.73 1.567 0.4032 0 3.11 0.00 E-II-5 2465 2:3 140 10.92 1.87 0.6 10.57 1.829 1.710 0.4458 0 3.59 0.00 E-II-6 2465 2:3 160 12.48 2.00 0.6 12.18 2 1.829 0.4784 0 4.13 0.00 E-II-7 2465 2:3 180 14.04 2.12 0.6 14.22 2.207 1.931 0.5019 0 4.83 0.00

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E-II-8 2465 2:3 206 16.04 2.27 0.6 16.01 2.207 2.051 0.5332 0 5.43 0.00

E-III-1 2465 2:3 60 4.68 1.22 0.6 4.699 1.255 1.125 0.2957 0 1.59 0.00 E-III-2 2465 2:3 80 6.24 1.41 0.6 6.236 1.455 1.288 0.3299 0 2.12 0.00 E-III-3 2465 2:3 100 7.80 1.58 0.6 7.752 1.561 1.434 0.3631 0 2.63 0.00 E-III-4 2465 2:3 120 9.36 1.73 0.6 9.407 1.73 1.568 0.404 0 3.19 0.00 E-III-5 2465 2:3 140 10.92 1.87 0.6 11.2 1.829 1.713 0.4481 1 3.80 0.05 E-III-6 2465 2:3 160 12.48 2.00 0.6 12.87 2 1.830 0.4808 1 4.37 0.16 E-III-7 2465 2:3 180 14.04 2.12 0.6 14.62 2.207 1.933 0.503 3 4.96 0.37

E-IV-1 2465 2:3 60 4.68 1.22 0.6 4.713 1.255 1.126 0.3054 0 1.60 0.00 E-IV-2 2465 2:3 80 6.24 1.41 0.6 6.218 1.455 1.293 0.3393 0 2.11 0.00 E-IV-3 2465 2:3 100 7.80 1.58 0.6 7.739 1.561 1.434 0.3702 0 2.63 0.00 E-IV-4 2465 2:3 120 9.36 1.73 0.6 9.346 1.73 1.570 0.4104 0 3.17 0.00 E-IV-5 2465 2:3 140 10.92 1.87 0.6 11.08 1.829 1.712 0.4523 0 3.76 0.00 E-IV-6 2465 2:3 160 12.48 2.00 0.6 12.7 2 1.829 0.4823 0 4.31 0.00 E-IV-7 2465 2:3 180 14.04 2.12 0.6 14.39 2.207 2.000 0.5042 0 4.88 0.05

F-I-1 2915 2:3 60 6.02 1.39 0.6 6.129 1.455 1.266 0.3383 0 1.59 0.00 F-I-2 2915 2:3 80 8.02 1.60 0.6 8.237 1.561 1.454 0.3803 0 2.14 0.00 F-I-3 2915 2:3 100 10.03 1.79 0.6 10.28 1.829 1.622 0.4347 0 2.67 0.05 F-I-4 2915 2:3 120 12.03 1.96 0.6 12.18 2 1.801 0.4833 0 3.16 0.05 F-I-5 2915 2:3 140 14.04 2.12 0.6 14.37 2.207 1.935 0.5111 0 3.73 0.05 F-I-6 2915 2:3 160 16.04 2.27 0.6 16.11 2.207 2.055 0.5403 1 4.18 0.11 F-I-7 2915 2:3 180 18.05 2.40 0.6 17.68 2.462 2.180 0.5725 0 4.59 0.11

F-II-1 2915 2:3 60 6.02 1.39 0.6 6.028 1.455 1.270 0.3416 0 1.57 0.00 F-II-2 2915 2:3 80 8.02 1.60 0.6 8.013 1.561 1.452 0.3796 0 2.08 0.00 F-II-3 2915 2:3 100 10.03 1.79 0.6 10.02 1.829 1.640 0.4299 0 2.60 0.00 F-II-4 2915 2:3 120 12.03 1.96 0.6 11.94 2 1.800 0.4801 0 3.10 0.00 F-II-5 2915 2:3 140 14.04 2.12 0.6 14.05 2.207 1.933 0.5077 0 3.65 0.00

138 MSc thesis

Appendixes

F-II-6 2915 2:3 160 16.04 2.27 0.6 15.72 2.207 2.052 0.534 0 4.08 0.00 F-II-7 2915 2:3 180 18.05 2.40 0.6 17.8 2.462 2.180 0.5691 0 4.62 0.00

F-III-1 2915 2:3 60 6.02 1.39 0.6 6.165 1.455 1.269 0.3347 0 1.60 0.00 F-III-2 2915 2:3 80 8.02 1.60 0.6 8.226 1.561 1.454 0.3778 0 2.14 0.00 F-III-3 2915 2:3 100 10.03 1.79 0.6 10.32 1.829 1.621 0.4325 0 2.68 0.00 F-III-4 2915 2:3 120 12.03 1.96 0.6 12.3 2 1.799 0.4786 0 3.19 0.00 F-III-5 2915 2:3 140 14.04 2.12 0.6 14.47 2.207 1.930 0.5053 0 3.76 0.00 F-III-6 2915 2:3 160 16.04 2.27 0.6 16.18 2.207 2.051 0.5353 0 4.20 0.00 F-III-7 2915 2:3 180 18.05 2.40 0.6 17.8 2.462 2.175 0.5665 1 4.62 0.05 F-III-8 2915 2:3 200 20.05 2.07 0.6 18.84 2.783 2.431 0.6309 0 4.89 0.05

G-I-1 2102 1:2 60 3.34 1.03 0.6 3.329 1.067 0.984 0.2183 0 1.50 0.00 G-I-2 2102 1:2 80 4.46 1.19 0.6 4.49 1.255 1.057 0.2343 0 2.02 0.00 G-I-3 2102 1:2 100 5.57 1.34 0.6 5.659 1.306 1.162 0.2588 0 2.55 0.00 G-I-4 2102 1:2 120 6.68 1.46 0.6 6.837 1.455 1.255 0.2836 0 3.08 0.00 G-I-5 2102 1:2 140 7.80 1.58 0.6 7.955 1.561 1.342 0.3043 0 3.59 0.00 G-I-6 2102 1:2 160 8.91 1.69 0.6 9.155 1.73 1.436 0.3167 1 4.13 0.05 G-I-7 2102 1:2 180 10.03 1.79 0.6 10.33 1.829 1.532 0.3293 1 4.66 0.11 G-I-8 2102 1:2 215 12.03 1.96 0.6 12.71 2 1.624 0.3577 9 5.73 0.59

G-II-1 2102 1:2 60 3.34 1.03 0.6 3.34 1.067 0.983 0.2004 0 1.51 0.00 G-II-2 2102 1:2 80 4.46 1.19 0.6 4.518 1.255 1.106 0.2223 0 2.04 0.00 G-II-3 2102 1:2 100 5.57 1.34 0.6 5.619 1.306 1.226 0.2528 0 2.53 0.00 G-II-4 2102 1:2 120 6.68 1.46 0.6 6.721 1.455 1.334 0.2805 0 3.03 0.00 G-II-5 2102 1:2 140 7.80 1.58 0.6 7.814 1.561 1.434 0.3039 0 3.52 0.00 G-II-6 2102 1:2 160 8.91 1.69 0.6 8.972 1.73 1..534 0.3205 0 4.05 0.00 G-II-7 2102 1:2 180 10.03 1.79 0.6 10.03 1.778 1.619 0.3324 1 4.52 0.05 G-II-8 2102 1:2 215 12.03 1.96 0.6 12.31 2 1.779 0.3595 7 5.55 0.43

H-I-1 2465 1:2 60 4.68 1.22 0.6 4.694 1.255 1.127 0.2241 0 1.59 0.00

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H-I-2 2465 1:2 80 6.24 1.41 0.6 6.253 1.455 1.288 0.2668 0 2.12 0.00 H-I-3 2465 1:2 100 7.80 1.58 0.6 7.812 1.561 1.433 0.3008 0 2.65 0.00 H-I-4 2465 1:2 120 9.36 1.73 0.6 9.322 1.73 1.563 0.3235 0 3.16 0.00 H-I-5 2465 1:2 140 10.92 1.87 0.6 11.22 1.829 1.692 0.3457 0 3.81 0.00 H-I-6 2465 1:2 160 12.48 2.00 0.6 12.77 2 1.813 0.3696 0 4.33 0.00 H-I-7 2465 1:2 180 14.04 2.12 0.6 14.46 2.207 1.912 0.3935 3 4.91 0.16 H-I-8 2465 1:2 206 16.04 2.27 0.6 16.19 2.286 2.065 0.4183 1 5.49 0.21

H-II-1 2465 1:2 60 4.68 1.22 0.6 4.711 1.255 1.128 0.2382 0 1.60 0.00 H-II-2 2465 1:2 80 6.24 1.41 0.6 6.317 1.455 1.290 0.2779 0 2.14 0.00 H-II-3 2465 1:2 100 7.80 1.58 0.6 7.848 1.561 1.434 0.3062 0 2.66 0.00 H-II-4 2465 1:2 120 9.36 1.73 0.6 9.498 1.73 1.570 0.3256 0 3.22 0.00 H-II-5 2465 1:2 140 10.92 1.87 0.6 11.28 1.829 1.692 0.3443 0 3.83 0.00 H-II-6 2465 1:2 160 12.48 2.00 0.6 12.82 2 1.811 0.3679 1 4.35 0.05 H-II-7 2465 1:2 180 14.04 2.12 0.6 14.55 2.207 1.911 0.3927 1 4.94 0.11

K-I-1 2915 1:2 60 6.02 1.39 0.6 6.226 1.455 1.267 0.2697 0 1.62 0.00 K-I-2 2915 1:2 80 8.02 1.60 0.6 8.328 1.561 1.452 0.306 0 2.16 0.00 K-I-3 2915 1:2 100 10.03 1.79 0.6 10.36 1.829 1.624 0.3313 0 2.69 0.00 K-I-4 2915 1:2 120 12.03 1.96 0.6 12.29 2 1.779 0.3591 1 3.19 0.05 K-I-5 2915 1:2 140 14.04 2.12 0.6 14.32 2.207 1.910 0.3929 2 3.72 0.16 K-I-6 2915 1:2 160 16.04 2.27 0.6 16.01 2.286 2.064 0.4172 22 4.16 1.33

K-II-1 2915 1:2 60 6.02 1.39 0.6 6.185 1.455 1.269 0.2602 0 1.61 0.00 K-II-2 2915 1:2 80 8.02 1.60 0.6 8.307 1.561 1.455 0.2999 0 2.16 0.00 K-II-3 2915 1:2 100 10.03 1.79 0.6 10.31 1.829 1.624 0.3308 0 2.68 0.00 K-II-4 2915 1:2 120 12.03 1.96 0.6 12.24 2 1.779 0.362 0 3.18 0.00 K-II-5 2915 1:2 140 14.04 2.12 0.6 14.29 2.207 1.911 0.3941 1 3.71 0.05 K-II-6 2915 1:2 160 16.04 2.27 0.6 15.98 2.286 2.063 0.4203 1 4.15 0.11 K-II-7 2915 1:2 180 18.05 2.40 0.6 17.75 2.462 2.173 0.4367 3 4.61 0.27

140 MSc thesis

Appendixes

Appendix K Influence specific weight on the hydraulic stability of Xbloc armour units

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Figure K-1 Influence relative density on hydraulic stability Xbloc armour units for cot α = 1.33, cot α = 1.5 and cot α = 2.

142 MSc thesis

Appendixes

Appendix L Failure mechanism

During the test two main failure mechanisms were distinguished which results in the displacement of an armour unit out of the armour layer. All displacements were by rotation out of the armour layer up-slope or down-slope after the following mechanisms occurred: 3. An armour unit is lifted perpendicular to the armour layer from the under layer. 4. An armour unit who has freedom of movement due to settlement or rocking are turned out of the armour layer under up or down rush. In addition to these failure mechanisms a third potential failure mechanism was identified; the armour layer under the SWL was lifted by multiple rows at ones during extreme downrush and turbulent uprush. Video recording from the side were extensively analysed to investigate the processes involved

The most dominant process observed is the rotation of an element out of the armour layer under influence of highly turbulent uprush. The lift of the armour layer is due to the same process. For both mechanisms always the same series of events occurred. Therefore only the displacement of a light armour unit from a slope of 3:4 is presented in a series of photos to illustrate the events of both processes.

− A higher wave or series of higher waves in the wave train resulted in high run-up level followed by a deep downrush which can be seen in figure (1) to (5) − The flow during downrush is almost completely parallel to the slope (figure (4) and (5)). At the lowest point the flow is directed outward figure (6). − The following wave is overtaking the crest of the previous wave at the lowest point of the dowrush resulting in a turbulent breaker which hits the slope under the SWL, as shown in figure (7) to (9).

The flow inside the structure is running behind the wave crest resulting in high pore pressures inside the structure. In combination with the absent of water mass, this resulted in a strong flow directed outward at the lowest point of the downrush in the area under the SWL. The turbulent breaker in combination with the outward directed flow destabilises the unit. The run-up flow rotates the element eventually out of the armour layer. On slope of 3:4 the element turned out of armour layer is taken far upward; this is becoming less for flatter slopes

− Start of movement of the armour unit can be seen in figure (10). The start of movement is believed to be as the crest of the wave passes the armour unit (figure (9)). After the wave has passed the movement of the unit is observed, see figure (10). − After dislocation of the unit out of the armour layer the unit is transferred upward until the wave has reaches its maximum point on the slope. The element is removed from the slope with the following downrush. In this case the element remains stable for a while on the lower part of the armour layer. See figure (10) to (18).

The element is not always completely removed at ones from the armour layer. It can take several waves to dislocate a unit or the unit is not completely removed by the process described above. Another possibility is the instead reduction of interlocking due to settlements. In these situations the armour units is mostly displaced from the slope during downrush. But the main destabilisation process remains as described.

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1 2

3 4

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5 6

7 8

146 MSc thesis

Appendixes

9 10

11 12

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13 14

15 16

148 MSc thesis

Appendixes

17 18

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