Sea dikes breaching initiated by breaking wave impacts - State of the art

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Integrated Flood Risk Analysis

and Management Methodologies

Breaching of Sea Dikes Initiated by

Breaking Wave Impacts

STATE OF THE ART REPORT

Date 30-05-2008

Report Number

T06-09-03

Revision Number 1_0_Pn

Task Leader Partner

FLOODsite is co-funded by the European Community

Sixth Framework Programme for European Research and Technological Development (2002-2006) FLOODsite is an Integrated Project in the Global Change and Eco-systems Sub-Priority

Start date March 2004, duration 5 Years Document Dissemination Level

PU Public

PP Restricted to other programme participants (including the Commission Services) RE Restricted to a group specified by the consortium (including the Commission Services) CO Confidential, only for members of the consortium (including the Commission Services)

Co-ordinator: HR Wallingford, UK Project Contract No: GOCE-CT-2004-505420

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DOCUMENT INFORMATION

Title Breaching of sea dikes initiated from the seaside. State of the art report

Lead Author Grzegorz Stanczak

Contributors Hocine Oumeraci, Andreas Kortenhaus

Distribution [Click here and list Distribution]

Document Reference [Click here and enter Document Reference]

DOCUMENT HISTORY

Date Revision Prepared by Organisation Approved by Notes

30/05/08 1_0_Pn Stanczak

ACKNOWLEDGEMENT

The work described in this publication was supported by the European Community’s Sixth Framework Programme through the grant to the budget of the Integrated Project FLOODsite, Contract GOCE-CT-2004-505420.

DISCLAIMER

This document reflects only the authors’ views and not those of the European Community. This work may rely on data from sources external to the FLOODsite project Consortium. Members of the Consortium do not accept liability for loss or damage suffered by any third party as a result of errors or inaccuracies in such data. The information in this document is provided “as is” and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information at its sole risk and neither the European Community nor any member of the FLOODsite Consortium is liable for any use that may be made of the information.

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SUMMARY

Sea dikes are of crucial importance in the defence systems of low-lying coastal areas in countries such as Germany, The Netherlands or Denmark, etc. Breaches of sea dikes induced by storm surges are regarded as the main cause of coastal flood disasters. Therefore a reliable prediction of both initial conditions for the breach occurrence and the breach development is urgently needed.

Depending on the structure of the sea dike and on the hydraulic and morphological boundary conditions, one may distinguish several causes for the initiation and formation of a breach. The main failure mechanisms are (TAW,1999a):

• wave overtopping and overflow, which may lead to the erosion of the shoreward slope and finally to breach initiation from the landward side

• breaking wave impact including wave run-up and run-down processes which may lead to the erosion of seaward slope (Fig. 1) and finally to breaching from the seaward side

The knowledge of the processes of breach initiation and development is crucial for the prediction of the initial conditions at the defence line needed to model the flood wave propagation. For the prediction of a dike breach initiated by the wave overtopping, a PhD research was completed very recently (D'Eliso, 2007). However, as the processes associated with the dike breach initiation from the seaside as well as the breach growth itself are completely different from those related to overtopping, there is also an urgent need for a model to predict the breach growth initiated from the seaside by breaking wave impact on the outer slope.

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1. Introduction

Sea dikes are of crucial importance in the defence systems of low-lying coastal areas in countries such as Germany, The Netherlands or Denmark, etc. Breaches of sea dikes induced by storm surges are regarded as the main cause of coastal flood disasters. Therefore a reliable prediction of both initial conditions for the breach occurrence and the breach development is urgently needed.

1.1 Motivations and problem formulation

Depending on the structure of the sea dike and on the hydraulic and morphological boundary conditions, one may distinguish several causes for the initiation and formation of a breach. The main failure mechanisms are (TAW,1999a):

• wave overtopping and overflow, which may lead to the erosion of the shoreward slope and finally to breach initiation from the landward side

• breaking wave impact including wave run-up and run-down processes which may lead to the erosion of seaward slope (Fig. 1) and finally to breaching from the seaward side

The knowledge of the processes of breach initiation and development is crucial for the prediction of the initial conditions at the defence line needed to model the flood wave propagation. For the prediction of a dike breach initiated by the wave overtopping, a PhD research was completed very recently (D'Eliso, 2007). However, as the processes associated with the dike breach initiation from the seaside as well as the breach growth itself are completely different from those related to overtopping, there is also an urgent need for a model to predict the breach growth initiated from the seaside by breaking wave impact on the outer slope.

The European Community supports within the integrated project FLOODsite research efforts aiming a.o. to develop a risk-based approach for flood defence systems. This approach is based on the analysis of predicted and tolerable risk. The former consists of the predicted flooding probability obtained from the risk sources and pathways and of the estimated potential damages and losses. The latter one contains the tolerable damages and tolerable probability of the disastrous event occurrence (Oumeraci, 2004). The problem might be presented as a fault tree, which contains all possible failure modes and linkages between them, whereas the top event is the flooding probability. Three main contributions to the prediction of the flood risk are needed: (i) hydraulic, morphological and topographical boundary conditions, (ii) possible failure modes for the particular parts of the system as well as their interactions and (iii) the knowledge on the process of breaching and flood wave propagation (Oumeraci and Kortenhaus, 2002). The first two aspects have already been discussed, by Morris and Hassan (2002) for instance, but it is emphasised, that there is a necessity to focus on the last one. According to above-mentioned problems, it is urgently needed to develop a process-oriented sea-dike breaching model that will enable one to predict the initial conditions for the simulation of the flood wave propagation (Oumeraci, 2004). It is therefore urgently needed to develop a process-oriented model for the prediction of sea dike breach initiation, formation and development. This will allow to determine the initial conditions for the simulation of the flood wave propagation.

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1.2 Objectives and methodology

The technical requirements of the model to be developed may be summarised as follows:

• it simulates the processes of initiation, formation and development of the sea dike breach induced by breaking wave impact as well as by wave run-up and run-down processes from the seaside

• it predicts the final width and depth of breach, including the associated duration and the outflow hydrograph.

A number of numerical models to calculate the flood wave propagation is available, but there is still a lack of knowledge on the initial conditions for the flood wave simulation. The main task of the model to be developed is to fill this gap, providing a reliable information on the breach initiation and formation time as well as on the outflow hydrograph at the defence line that are necessary to model the flood wave propagation. Although a number of dike breaching models is available, almost all of them refer to the failures of sand dikes. It is therefore expected, that the new model will investigate the behavior of the dikes with sand core, a clay cover and a grass revetment. As for the described structure that breaches due to the wave overtopping a PhD research has recently been completed (D'Eliso, 2007) and there does not exist any process-oriented model of the dike breaching that is initiated from the seaside, the focus is here on the failure of a dike that is initiated on the seaward slope by repeated breaking wave impact. The main task of the model to be developed is the ability of being applied as the tool that:

• describes the process of the breach initiation

• gives the overview on the processes of breach formation and development • calculates the final width and depth of breach

• provides the outflow hydrograph

As a consequence, the model should improve the prediction of warning time for coastal floods that is defined as the sum of: breach initiation time, breach formation time, breach development time and flood propagation time.

While the existing models refer only to homogenous sand dikes (Visser, 2000), the new model will apply for sea dikes with sand core and a clay revetment with a grass cover. The typical sea dike to which the model will apply is schematically drawn in Fig.2.

Figure 2: Simplified example of typical sea dike in Germany (Kortenhaus, 2002)

The causes of the breaching that will be considered in the model are (i) the impact pressures of the waves breaking on the seaward slope and (ii) shear stress due to the wave run-up and run-down. The reasons of this choice are as follows: the erosion holes induced by breaching wave impact are among the most common damages of the sea dikes (Oumeraci, 2004). Furthermore, the recent studies have pointed out, that breaking wave impact pressures are the most significant and important source of

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damage from the seaside. It is also important to emphasise that the model will be based on process-oriented description of the dike breach development.

The main steps to achieve a computational model describing the process of dike breach initiation and development may be described in simplified manner as follows:

• formulation of the problem and selection of appropriate approximations • computer implementation of the model

• identification and quantification of uncertainties

• validation and verification using laboratory data and field observations • performance of parameter studies and application to a case study

In the following chapters, the detailed study on the causes of dike failures will be performed, with special emphasis on breaking wave induced impact pressures and shear forces related to the wave run-up and run-down. The erosion processes and sediment transport model are also to be subject to a detailed investigation. Subsequently, the process of breach formation and growth will be analyzed and the detailed objectives and methodology may be presented. The analysis of the range of applicability of the model will also be performed.

Based on the results of a detailed literature study in the Chapter 2 the objectives and methodology which have been tentatively formulated above will be specified more precisely in Chapter 3 before embarking into the development of the model.

2. Review of Processes and Models Associated with Sea Dike

Breaching

2.1 Relevant hydrodynamic and morphological processes: a brief outline

Before setting-up the mathematical formulation of the problem, it is necessary to perform a detailed literature review on the associated breaching mechanisms and modelling. The entire breaching process, from the initial conditions up to the outflow from the breach, should be analyzed.

As the breaching process occurs as a result of a complex interaction between fluid and structure, two types of boundary conditions are needed. The morphological boundary conditions describe the structure itself. Geometrical parameters, as cross-sectional area and plane view are needed. The former is needed for the analysis of the hydraulic boundary conditions; the latter is relevant for the spatial analysis of the failure probability. Other design parameters of the flood defence structure (material characteristics for instance) are also to be included. Second, the hydraulic boundary conditions are to be reliably assessed. This particularly includes (i) the mean water level and its variation (ii) wave heights distribution and (iii) transformations of waves propagating over the shallow foreshore (Kortenhaus and Oumeraci, 2002). The storm surge duration is also to be considered as a boundary condition. The short overview on breaching process and involved parameters and sub-processes is shown in Fig.3.

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Figure 3: Breaching processes

2.2 Morphological boundary conditions 2.2.1 Geometrical parameters

Sea-dikes are manmade structures consisting of a sand core that is protected from the effects of wave action by clay cover, with or without vegetation. The clay layer is usually about 1.0-1.5m thick, the depth of roots penetration varies between 5 and 30cm. The main function of the dike, i.e. its water retaining capacity is supplied by the height and shape of the cross-section as well as the watertight capacity of the body. The most important design parameter that defines the dike is the construction

level of the dike crown which is defined as the sum of six contributions (Fig. 4) (TAW,1999a): • the water level with a probability of exceedence equal to the statutory standard: the normative high water level NHW_xxxx, where xxxx stands for the year of fixing; is usually revised every five years. As this value is determined by long-term statistics, it includes also tides and surges;

• the rise in high water over the plan period; this value includes also the possible changes in tidal regime due to local conditions;

• the excess value for storm oscillations, gust bumps and seiches; (local) gusts are only taken into account if they have not been processed in the water level statistics;

• the wave run-up height which corresponds to overtopping of 1 l/m/s ; • the settlement of the bottom (subsoil) expected locally over the plan period

• the expected sinking of the crown due to settling of the dike body and of the subsoil over the plan period after delivery.

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Figure 4: Contributors to the construction level of the crown (after TAW, 1999a)

The crown width of 2 meters is adequate if a maintenance/inspection road is situated on an inside berm, otherwise the crown should be at least 3 meters wide. In the case, when a public road is located on the dike, more space is needed. The outer slope crown is usually sloped 1:4 - 1:6, if there no hard revetments are used. When using good clay with grass cover slopes of 1:5 or less can be maintained, depending on the strength of the wave attack. The inner slope is 1:3 -1:5 steep.

The second group of geometrical parameters refers to the plan view of a dike route. Since the wave action on the dike slopes is influenced by the longitudinal plan of the flood defence system, the location of breach occurrence and the way of breach development may vary depending on the composition of particular elements of the structure. However, this aspect will not be addressed here because the calculations will be performed on a single section, which will be considered as straight and homogenous.

2.2.2 Material characteristics

As mentioned before, a typical sea-dike is built of two or more main parts, which are made- up of different materials. The type and characteristics of the applied material depends on the function to be fulfilled and consequently on the expected loadings. The common materials that are used for the construction of the dike are: sand for the dike core and clay with a grass cover for the revetment. The revetment may also be made of asphalt, concrete blocks, plate revetments or loose deposit materials, but only the clay revetment with a grass cover will be considered in the present study.

Soil is a complex material consisting of three main components - grains build the structure while water and air fill the pores between the solid particles. Besides the properties of the solid components, the proportion of water and air also has an influence on the properties of the soil. The most important ones are (TAW, 1999a):

• mean density: it determines the effective stress on a slip plane, determines whether uplift on the inside of the dike occurs, therefore indicates the type of stability analysis to be used. It also co-determines whether the piping can play a role;

• shear strength: determines the possibilities of deformations and therefore plays an important role in establishing whether a collapse may occur, it depends strictly on the effective stress;

• settlement properties: the settlement due to soil compressibility should be taken into account when constructing the dike, supplementary height allowance should be added;

• permeability: in case of sand, the permeability in water-bearing layer is important in the investigations of piping and thus the associated stability. The permeability of the clay shows its quality in terms of water retaining material. It influences also the macro-stability through determining the height of the phreatic line.

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Sand as the main material (dike body) may be characterised by the loose, non-cohesive grain structure with a high hydraulic permeability and a relatively high compaction. The percentage of fine particles should be lower than 5% and the compaction of the sand should be between 90% and 98% of maximum Proctor density. This high compaction level is the reason of good settlement and stability properties. However in some cases, the presence of loose or unprotected sand may cause the risk of soil liquefaction.

Clay is a natural soil consisting of erosion and breakdown products of natural rocks, that have been

brought together again by natural processes. As shown in Fig. 5, the composition of the clay is based on the mass percentages of :

• sand: equivalent grain diameter greater than or equal to 63µm and less than 2 mm, • silt: equivalent grain diameter greater than or equal to 2µm and less than 63µm, • lutum (argil) - equivalent grain diameter less than 2µm.

Figure 5: Composition of the clay

The fine fraction may also contain other minerals, such as quartz, iron and aluminium compounds or chalk. Clay usually contains organic materials in a form of remains of the plants and animals, fibres, bacteria or microscopic animal organisms. The good erosion resistance of the clay is caused by its two characteristic properties: cohesion and the ability of retaining the water. The former is due to large binding forces between the very fine soil particles. Water molecules bind to those particles, and form the links between them. In addition to the affinity of the solid particles for water, the cohesion in clay is also the result of connections of mineral compounds in the soil to each other. They may occur mainly in minerals and organic materials that are fixed chemically to the surface of more than one particle and therefore link the particles together like cement. This process causes very strong connections, by which the soil becomes hard. Those cementation bonds are not very flexible and are therefore broken in case of large deformations. The previously mentioned iron or aluminium compounds are an important category of those cementing materials and are the cause of the increase of the strength of clay that comes into contact with air. Clay retains water due to two main processes: surface tension and affinity for water. Surface tension is a consequence of the attraction between the water molecules and a solid surface, by which they are linked together. This mechanism retains water in fine pores and the small corners of larger pores. Affinity for water means that water molecules bind to the surface of the particles. The affinity is influenced by the surroundings and the composition of the surface of the solids and by the other compounds that are dissolved in the water. Such the compounds may also retain the water, and therefore improve the water retaining capabilities of the clay (TAW, 1996).

The erosion resistance of the clay can be evaluated using one of the following approaches: 1. Classification number N proposed by Weißmann (2003):

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n n B B B B N = ₁, ₂, ₃... (1) where: - B_n -

n

-th classification factor [-]

The following types of clay are distinguished (Tab. 2): Classification number N Quality of clay Applicability class 0.85 1.00≤ N ≤ Very good 1 0.75 0.85≤ N ≤ Good 2 0.65 0.75≤ N ≤ Moderate 3 0.50 0.65≤ N ≤ Weak 4 0.50 > N Bad 5

Table 2: Classification of soil according to the classification number N

The considered classification factors depend on the properties of the soil and are calculated as follows (Weißmann, 2003): -

B

₁ - infiltration rate k_f 20 4) log ( 0.7 = 1 + − kf B (2) -

B

₂ - decomposition time t_30% ) ( log 0.2 = _30% 2 t B ⋅ (3) - B₃ - shrinkage V_s 0.05) ( 1.25 1.0 = 3 − ⋅ Vs− B (4) -

B

₄ - plasticity index I_p =w_l −w_p ) ( 2 0.3 = 4 wl wp B + ⋅ − (5)

2. Approach used in The Netherlands to evaluate the erosion resistance of clay for dikes (TAW,1996). Tab. 3 shows the requirements that must be checked during evaluation of clay for use in dikes, within the following categories:

- Category 1. Erosion resistant;

- Category 2. Moderately erosion resistant; - Category 3. Little erosion resistance.

The distinction between the three categories is based on the Atterberg limits and the sand content. Category l w[-] I_p[-] Sand content S_p [%] 1 >0.45 _>0.73_⋅₍ l w -20) <40 2 <0.45 >0.18 <40 3 - <0.18 >40

Table 3: Classification of clay for dikes according to Dutch requirements (TAW,1996)

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The clay in sea dike cover is subject to the changes in water content that occur due to drying and wetting of a dike. Differences in suction pressure result in changes in the water content what leads to the changes of volume of the clay, the order of magnitude of those changes is of about half the change in water content (expressed in mass percentage). As a result, clay shrinks and expands and those processes in the unsaturated zone lead to the formation of two types of cracks (TAW,1996):

• pull-cracks appear when soil shrinks. Those cracks are different oriented according to their size - larger shrinkage cracks are almost always vertical, smaller are oriented in all directions;

• shear cracks: usually occur in shear areas that are caused by the swelling of clay. Those cracks may occure in all directions.

Crack formation produces a soil that consists of aggregates of various dimensions. The composition of the cracks and aggregates, together with pores and aggregates made by burrowing animals, is called the "soil structure" (TAW,1996). The formation of "soil structure" depends both on properties of the clay itself (interaction between soil particles and water, for instance), as well as on the external factors that determine changes in suction pressure. The biological activity in the soil should also be mentioned as the factor that influences development of "soil structure". Burrowing animals and grass roots cause the dynamic of "soil structure" - new aggregates are continually being formed and then collapse again. The development of "soil structure" can be more or less clear - the strongly developed one occurs when soil is subject to continuous expanding and shrinkage or in case of single but very strong shrinkage. This kind of development is characterized by the aggregates that are clearly individually recognizable and that show few connections with each other. The second type (i.e. fine structure) occurs due to rapid changes in water content, e.g., due to rainfall. In Fig. 6 a cross-section of a typical sea-dike cover made of clay with vegetation is shown - significant pull-cracks can be observed. According to information given by TAW (1996), in the uppermost decimeters under the grass cover the "soil structure" is usually strongly developed and consists of relatively small (i.e. millimeters to centimeters) aggregates that are often linked to each other by roots.

Figure 6: Clay cover of a dike - cross-section and sketch. Soil structure and cracks clearly recognisable (TAW,1996)

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At depths greater than 50cm under the grass cover the aggregates are often less clearly recognisable. The aggregates in this region are sometimes larger than 10 cm and there is often still some cohesion present between the aggregates. The presence of the "soil structure" influences the hydraulic permeability of the clay layer. A top layer of clay, with clearly developed "soil structure" has a considerably greater permeability than measured on compacted clay samples. The same effect is induced by root penetration from growing vegetation on the dike (TAW,1996). At greater depths "soil structure" may occur as a result of worm tunnels that deeply penetrate into the dike. Consequently, the hydraulic permeability of the entire clay layer is affected - in Tab. 4 values for clay cover in different conditions are presented.

Conditions Hydraulic permeability [m/s] Directly after construction ₁₀−6

Fine "soil structure" ₁₀−5

Large cracks and worm tunnels ₁₀−4

Table 4: Hydraulic permeability of clay in different conditions

The formation of the "soil structure" considerably limits the homogeneity of a clay layer and a network of coarse pores will occur. The civil engineering properties of a clay package with the "soil structure" therefore differ strongly from those of individual aggregates. In a structured soil, surface water can infiltrate rapidly and a considerable amount of water can be drained off through the large cracks and tunnels. The soil structure formation is favorable and even essential for vegetation and other soil life, considering that aeration is greatly improved and roots can find an easier way into the soil (TAW,1996)

Grass cover

Although clay has quite good erosion resistance, it is generally reinforced by protective layers made of grass, asphalt or concrete blocks. Those layers improve also the recreational or natural properties of the dike. As shown in Fig.7 a grass cover is composed of clay layer and herbage being the grass rooted in soil.

Figure 7: Structure of a grass cover - principle sketch and a photo of a cross-section

The soil directly under the slope surface consists of small and larger aggregates, between which pores and roots are found. Those aggregates are formed due to changes in the ground level of the surface, ice formation, burrowing animals or grass roots penetration. Especially plant roots and chemical processes in their closest neighbourhood are important for the existence of these bonding materials. The very fine hair roots and symbiotic fungal threads due to connections with the finest particles bonds the soil particles, while the coarser plant roots keep large and smaller aggregates together in a sort of a

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network. This network of fine and coarse roots is the main reason, why the grass cover of a dike is a strong, springy and flexible layer that can deform without tearing. Both effects, i.e. keeping the soil together by the reinforcement made of roots and the structure of the soil between the roots, contribute to the good erosion resistance of the grass cover. The existing approach (Wu et al, 1979) enables one to calculate this reinforcement as the increase of the shear strength (so-called apparent root cohesion) of the soil due to bonding action of the root network (Fig. 8).

The apparent root cohesion can be calculated as (Wu et al, 1979):

) (

= cos

θ

tan

φ

sin

θ

V V T c r R r ⋅ + (6) where:

•

c

_r - apparent root cohesion [ / 2]

m

N

•

T

_R - root tensile strength [ / 2]

m

N

•

V

_r

/

V

- root volume ratio [−]

•

θ

- root angle of shear rotation [deg]

Figure 8: Flexible elastic perpendicular root reinforcement model (Wu et al, 1979)

The values in Eq. 6 may be briefly described as follows (see also Young, 2005): • Tensile strength (

T

_R)

Various authors ( Simon and Collison, 2001 or Cazzuffi and Crippa, 2005) state that root tensile strength has a negative exponential distribution with respect to root diameter. However it should be noticed, that none of the authors has presented root diameter distribution function. Instead of that, average root diameter from the range given for some grass species is used to obtain root tensile

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strength. The measured tensile strength of roots for different types of grass vary in range 1.3-56MPa (Young, 2005)

• Root Volume Ratio

V

_R

/

V

Root volume ratio gives information on the amount of roots in a soil body. Cazzuffi and Crippa (2005) state that although it is obvious that root volume ratio decreases with depth, there are no detailed investigations on the description of this decrease. The mentioned authors suggested that either a linear or exponential function might be used to describe this course. Sprangers (1999) has investigated the dependency of dry root mass densities on the depth under the surface for 24 dike grasslands in the Netherlands. Regression analysis was used to fit eighteen different functions. The one that is considered to fit the best is the exponential function presented in Fig.9.

Figure 9: Dike grassland - RVR as an exponential function of depth (Sprangers, 1999)

• Root angle of shear rotation

θ

Very little information is available on the values of

θ

. Wu et al. (1979) suggested a range of 450 to 700_{from field observations of conifers, however it is unknown if any similarity to dike grasses exists.}

The available literature (Young, 2005) suggests that for grassland

θ

should be very close to the upper limit of 700_.

It is necessary to put the emphasis on the fact, that although some laboratory experiments on the erosion resistance of grass cover have been conducted (Smith et al., 1994, Lautstrup et al, 1990), the latter provide only basic information on the processes that lead to damage of the revetment. The approach of Wu et al. (1979) to calculate the reinforcement of soil by the roots network has been never verified in tests on grass. Furthermore, no detailed information on the influence of root volume ratio on the progress of erosion due to impact pressures is available. In order to shed some light on those problems, experimental tests on the influence of vegetation on the erodibility of soil should be performed.

2.3 Hydraulic boundary conditions

For the reliable prediction of the dike breaching, the assessment of the hydraulic boundary conditions is necessary. The main hydraulic boundary conditions are (i) extreme water levels and (ii) wave action. Those two conditions are directly related - as the mean water level rises, larger waves occur and the dike is subject to stronger wave impact.

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2.3.1 Water levels

The water level is subject to several types of fluctuations that are classified according to their period as follows:

• short-term fluctuations - storm surges, tides, barometric surges, seiches etc.; • seasonal fluctuations - precipitations, evaporations;

• long-term fluctuations - eustatic sea level variations, isostatic land level emergence and subsidence, global climate changes

In the terms of the dike breaching simulation, only the short-term fluctuations are considered.

2.3.2 Wave action

Sea dikes are subject mainly to wind induced waves. Although some ship-induced waves may occur in navigable areas they are negligibly small. For the conditions at the sea dike toe a double peaked wave energy spectrum reproduces the natural sea state, but in case when no recorded spectrum is available, the TMA spectrum is recommended (D'Eliso, 2005

2.4 Breach parameters

The process of dike breaching is described in space and time by four independent variables (x,y,z,t). Spatial parameters are defined in a 3D Cartesian space. As a consequence, all the parameters describing the breaching process are dependant on space and time.

Figure 10: Reference system

As shown in Fig.10 the following planes will be used in this work: • Plane XY (plan view) - breach enlargement and development • Plane XZ (longitudinal view) - breach progress from the seaside • Plane YZ (breach cross-section) - breach widening and deepening

2.4.1 Geometrical parameters of the breach

As the dike breaching is a natural process, the eroded area does not have any regular shape. During the mathematical modeling, the breach profile is approximated using the closest analytical and

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symmetrical geometry. Fig. 11 shows schematically three phases of a breach initiation and formation process induced by breaking wave impact on the outer slope of a dike. It is seen that after the initial breach (Fig. 11a) the breach continues to go further taking a form of a surf fillet (Fig. 11b). The abrasion plane is formed almost horizontally or as a beach profile. After the abrasion plane has reached a certain length, the waves are breaking before they have reached the cliff foot - as a result, the surf fillet disappears with the progress of the erosion process and a steep (sometimes even vertical) cliff is formed (Fig. 11c).

Figure 11: Progress of breach initiation and formation - principle sketch

The following parameters can be used to describe the geometrical shape of a breach (see also D'Eliso et al, 2005):

• Profile of breach cross-section - the shape of a breach initiated from the seaside is complex and depends both on the hydrodynamic and morphodynamic parameters. The breach profile is usually parabolical under the water surface due to surface erosion and vertical over the water level due to mass failure. Some models (INFRAM, 1999) represent the breach shape as an almost flat (1:10) bottom and steep (1:1) slopes. The shape analogical to a typical beach profile can also be observed.

• Breach centreline - is the axis of the breach channel described by the set of lowest points of each breach cross section

• Breach width - the distance between the breach edges along the direction that is orthogonal to the breach centreline. If the breach centreline is assumed straight along X, the breach width is the distance between the breach sides along Y. The values describing the width of the breach are:

- width at the breach top (

B

_T) - width at the water surface (B_W) - width at the breach bottom (

B

_B)

• Breach height - distance between a datum and a reference point in the breach along the Z

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- Height of the breach from the bottom to the water level, that is equal to the water depth at the breach centreline H_W

- Elevation of the breach bottom, that is equal to the bed elevation at the breach centreline

z

_B

- Breach height H =H_d −z_B

2.4.2 Temporal parameters of the breaching

The time of dike breaching can be considered as a sum of the following phases: • grass erosion (Fig. 12a);

• clay erosion, including the shear failure in water-filled cracks and clay undermining (Figs. 12b and 12c);

• erosion and washing-out of the sand core, including the mass instability (Figs. 12d, 12e and 12f).

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The total time of dike breaching can be given as a sum of the following phases (Fig. 13):

• Time of grass failure t_gf - time between the incipient erosion end the time of grass failure expressed in terms of erosion depth;

• Time of cover failure t_cf - time between the incipient erosion end the time when the revetment fails and the sand core becomes unprotected;

• Time of core failure t_sf - time between the incipient erosion end the time when the erosion reaches the inner slope and the erosion progress becomes irreversible;

• Total breaching time t_tb - time between the incipient erosion end the time when the water level on the landside becomes equal to the one on the seaside;

• Breach initiation time t_i - time between the incipient erosion and the initiation of the breach described in terms of erosion depth on the seaside;

• Breach formation time t_f - time between end of the breach initiation and the end of the breach formation;

• Breach development time t_d - time between the end of the breach formation and the start of the erosion of the inner slope;

• Core wash-out time t_c - time between the end of the breach development and the time when the water level on the landside becomes equal to the one on the seaside (final breach)

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2.5 Breach initiation

A dike breach induced from the seaside by breaking wave impact is mostly like to initiate at the location where simultaneously:

• the greatest loading, consisting of the impact pressures and flow of wave run-up and run down occurs;

• the soil structure is strongly developed and a numerous cracks are present or the dike revetment is partially damaged

2.5.1 Breaking wave impact

In the coastal areas the processes of wave breaking are of primary importance in the view of structural loadings and sediment transport processes. As the whole energy (Ekin+Epot) is converted into the heat,

the forces resulting from breaking waves are several times larger than those generated by non breaking waves. In this Section the process of wave breaking, including causes and forms of breaking as well as the analysis of generated forces will be presented.

Reasons of wave breaking

Wave breaking is caused by several mechanisms, but in the coastal engineering the most important are related to the influence of shallow water. In the frames of this work, the wave breaking due to wind action, or wave interaction are neglected. In principle, the wave breaks, when the orbital velocity at the surface (uob) is larger than the wave celerity (c), the wave reaches its terminal steepness and the angle

of the wave peak is smaller than 1200. Fig. 14 shows schematically the geometry of a breaking wave.

a) In the small LWI-flume b) principle sketch

Figure 14: Plunging breaker on a dike slope

Breaker type classification

One may distinguish three forms of wave breaking, depending on the nature of the bottom, and the characteristic of the wave. For very mild slopes, typical are spilling breakers within the surf zone (defined as that region, where the waves are breaking, extending from the dry beach to the seaward limit of the breaking). The spilling breakers break on a relatively long way, so the energy is released smoothly. Surging breakers occur on very steep slopes and are characterized by narrow or nonexistent surf zones and high reflection. Plunging breakers occur on steeper slopes and are characterized by the crest of the wave curling over forward and impinging onto part of the wave through. Those waves can be very spectacular when air, trapped inside the tube formed by the wave crest, escapes by bursting through the back of the wave or by blowing out at a non-breaking section of wave crest. Plunging breakers release their energy on very short way, so this process is very forceful. The type of wave breaking is estimated using the non-dimensional surf similarity parameter

ξ

(e.g. Battjes, 1974):

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ctra forwavespe 2 = with tan = 2 0 0

π

α

ξ

m s gT L L H waves forregular 2 = with tan = 2 0 0

π

α

ξ

L gT L H (7) where:

•

α

- outer dike slope [deg]

• H - wave height at the dike toe [

m

] • H_s - significant wave height [

m

] • L₀ - deep water wave length [

m

] • T - wave period [

s

]

• T_m - mean wave period [

s

]

Table 5 gives the information on the wave breaking types and the criteria of their occurrence. Dike slope 1:n Plunging breaker Collapsing breaker Surging breaker 1:6

ξ

<2.1 2.1<

ξ

<2.8

ξ

>2.8 1:4

ξ

<2.4 2.4<

ξ

<3.1

ξ

>3.1 1:3

_ξ

_<_2.6 2.6<

ξ

<3.3

ξ

>3.3 mean

ξ

<2.3 2.3<

ξ

<3.0

ξ

>3.0

Table 5: Classificaton of breaking types on sea dikes (Schüttrumpf, 2001)

In the terms of sea dike breaching, the plunging breaker is the most dangerous form of the wave breaking. The wave energy is dissipated over a short distance and in a short time, which results in relatively small surfaces exposed for a very short period of time (0.01 to 0.1 s) to very high impact pressures (in the range up to 150 kPa). This impact load does not work sequentially, but intermittently in time intervals of at least one wave period (usually longer with predominant impact in the water layer that remains after the preceding wave), so that the actual loading time (0.1 to 0.01 s) is small in comparison with the time period between the loads (5-12s).

Impact pressures

Breaking wave generated impact pressures are considered to be the main reason of the breach initiation and formation. The impact pressures on the slope are subject to very large stochastic variations. Even in a regular wave train the impact pressures significantly differ for every single wave. Due to the complex characteristics of the problem, the researches were performed mostly experimentally, in the area of medium- and large scale models (TAW, 1990). Since the maximum impact pressure is a stochastic variable, a notation is used in the literature to indicate which maximum impact pressure is meant. To indicate the maximum pressure that is not exceeded in i % of the cases, the notation pmax,i is used. In practice, pmax,99 is considered as the highest measured maximum impact

pressure.

A large number of researches dealt with the breaking wave generated impact pressures, but all presented formulae base on the dependency of impact pressure on the incident wave height and steepness of the slope. The most recent, and commonly used approach was proposed by Führböter and Sparboom (1988) and reads:

α

ρ

tan = , const ⋅ ⋅g⋅H⋅ pmaxi i w (8) with:

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•

ρ

_w - density of the water [ / 3]

m

N

• const_i - coefficient taking the value of - const₅₀ =12

- const₉₀ =16 - const₉₉ =20 - const_99.9 =30

The decrease of the impact pressure on the flatter slopes is the result of the damping effect of the water layer that remains after the preceding wave. The thickness of this back-rush water layer increases with flatter slope so the maximum pressures decreases proportionally. This was reported by Bölke and Relotius (1974) and Führböter et al (1976), who presented time series of impact pressures based on simultaneous measurements during a storm surge in 1973. The conclusion states that the number of the waves generating impact pressures is much lower for a slope 1:6 than for a slope 1:4. The influence of the wave steepness on the maximum impact pressure is not taken into account by the presented approach. This serious disadvantage can be eliminated using instead of the constant value consti in

Eq.(8) an empirical function

κ

_i that depends on the wave steepness. This function can be derived using the experimental data. They are provided by Skladnev and Popov (1969) for instance, who gave a linear dependency of the maximal pressures on wave steepness, who stated that impact pressures reduces with increasing wave steepness. Similar results were obtained by Führböter and Sparboom (1988a) and Zhong (1985). In both cases the conclusion was given, that the normalized impact pressures decrease with increasing wave steepness parameter

ξ

. The empirical function based on the mentioned results reads:

mm T g H 2 11.2 289 = ₂ 50 + − ⋅ ⋅ −

κ

(9) and: •

κ

₉₀ =1.33⋅

κ

₅₀ •

κ

₉₉ =1.67⋅

κ

₅₀ •

κ

_99.9 =2.5⋅

κ

₅₀

In Fig.15 the comparison of measured results with Eq. 9 is shown.

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Location of the impact on the slope

The position of impact point is defined as the location where the highest impact pressure occurs per breaking wave event. In practice this position is determined by analysis of the pressure time history of a number of pressure transducers located along the dike slope. The determination of this location is performed in three steps:

1. per pressure transducer and per wave impact the time history of the pressure at each transducer is recorded,

2. for each time history the maximum impact pressure p_max is found

3. the location of the maximum impact is determined as the location of the pressure transducer (i) that measures the highest impact pressure pmax =max(pmax,i)

By applying statistical techniques the most likely position of maximum impact can be determined. The studies on this problem were performed by Grüne (1988) or Führböter and Sparboom (1988), for instance. The results of those studies show, that the area of the most probable maximum impact pressure lies below the mean water level, in a range about half the significant incident wave height. For regular waves the location of impact is more or less at a fixed position. For random waves, however, this position varies significantly.

Figure 16: Location of the impact on the slope (Schüttrumpf, 2001)

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Recently, Schüttrumpf (2001) gave considerably more precise formula, that shows the dependency of the impact point on the surf similarity parameter

ξ

2.1) ( 0.6 0.8 =MWL− + ⋅tanh

ξ

− H Z_impact (10) where Z_impact is defined as in Fig.16.

Distribution of pressures on the slope

For the computation of impact forces the knowledge on the size of the impact area and distribution of the impact pressures within this area is important. In the theoretical studies the shape of the impact area is described by a radius d or a hydraulic radius R. In case the impact area is assumed to be circular, the hydraulic radius is related to the radius d according to R= r/2. In practice however, the shape of the impact area will vary considerably per impact. The size of the impact area can be measured in two directions; in the direction of the wave slope and in horizontal direction, i.e. parallel to the dike. In most of the studies only the size in the direction of the slope was measured (referred to as the width of the impact area). Estimations of the size in horizontal direction are very scarce (referred to as the length of the impact area). Since wave flumes have a finite width, the waves will break over full width of the flume, more or less at the same time. Still, variations in the impact pressure are likely to occur, since the air content in the breaker varies in space. In field experiments the situation will be different; the impacting wave front will have a finite length and an irregular shape. The paper of Führböter and Sparboom (1988) presents graphically (see Fig. 17) the shape of impact area and distribution of pressures for p_max_,50 , p_max_,90 , p_max_,99 and p_max_,99.9 , but those results are based only on one set of parameters.

Figure 17: Measured distribution of impact pressures (Führböter and Sparboom, 1988)

Stive (1983) proposed, after a series of full-scale experiments, a width of the impact area in the order of 0.1H. In this area impact pressures are expected with almost the same magnitude of the highest impact pressure pmax. The area where the impact pressure will be at least 0.8pmax and 0.5pmax

will have a width of about 0.4H and 0.8H, respectively. Those assumptions may be roughly described using the following formula (see also Fig. 18):

max impact i impact i i z z x x p H p =[−2.75⋅(( − )2+( − )2)+1]⋅ 2 (11)

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with:

• x_i and z_i - coordinates of the i-th point [m]

• x_impact and z_impact - coordinates of the impact point calculated as: - z_impact =MWL−Z_impact [m]

- x_impact = z_impact⋅cot

α

[m]

Figure 18: Distribution of impact pressures on the slope

Angle of incidence

Only one formula for the calculation of the incidence angle (Fig. 19) has been found. This theoretical approach proposed by Führböter (1966) gives the angle

α

_impact as the function of the seaward slope angle

α

and reads:

) ) ( cot ) ( cot 1 ( =

α

f f atan impact − ⋅ + (12) with

α

cot

1 cot

2

1 =

)

(

2

−

+

f

(13)

Figure 19: Angle of incidence

Time aspects of breaking wave induced impact pressures

In the first studies concerning the wave loads it was often assumed that the maximum pressure occurs simultaneously on the whole part of the structure exposed to breaking wave impacts. The spatial and temporal variation of wave impact pressure was not taken into account. Only recently it became possible to study the time dependant pressure behaviour more detailed, by the means of sensitive measurement equipment. Of this behaviour the rising time t_k (or compression time), i.e. the time needed to reach the maximum impact pressure after the breaking wave hits the slope, received the

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most attention. The definition of temporal parameters was given by Witte (1988), see Fig. 20, where

k

t is the compression time and t_e is the expansion time.

Figure 20: Definition of temporal parameters of impact pressure (after Witte, 1988)

It can be observed, that at the instant t=0 the pressure is at its minimum, and results from the possible presence of a water layer from a preceding wave, thus pmin >0. The time dependant pressure is

divided in a "quasi-static part" with maximum pressure

p

₁, and in an "impact" part with the maximum pressure

p

₂. Each single wave gives different values of

p

₁,

p

₂, t_k and t_e even for regular waves. Witte (1988) investigated also the relation between the maximum impact pressure and time needed to reach this maximum. It was found that the envelope of the rising time t_k is a function of the maximum impact pressure p_max. In terms of dimensionless variables the following expression was suggested:

0.28 14 = − ⋅ r max t p (14) where:

•

t

_r - dimensionless rising time defined as:

k r t H c t ⋅ /2 = (15)

The measured values of t_k are given in Tab. 6

Compression time t_k 10−3s

Minimum Mean Maximum Std. deviation

3 127 559 94

Table 6: Compression time values (Witte, 1988)

The values of total duration of an impact pressure of breaking wave were described only by Stive (1984) who reported an increasing impact duration with increasing wave steepness. Typical values for the dimensionless duration (t_k +

δ

_k)/T =0.01 for

ξ

=0.005 and (t_k +

δ

_k)/T =0.1 for

ξ

=0.01.

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2.5.2 Breaking wave induced flow of run-up and run-down

The second most important reason of the breach initiation and formation is related to the flow of wave run-up and run down. The following parameters are important to asses the loading:

• wave run-up height z₉₈ which is defined as the wave run-up height (measured vertically from the still water level) which is not exceeded by 98% of the number of incoming waves (van der Meer, 2002)

• wave run-down height z₋₉₈ which is defined as the highest point on the slope, that is covered with the water during the whole course of wave run-up and run-down (Schüttrumpf, 2001)

• wave run-up velocity v_run₋_up which is defined as directed upwards (positive) velocity related to the wave run-up that varies in time and space (Oumeraci and Schüttrumpf, 1999)

• wave run-down velocity v_run−_down which is defined as directed downwards (negative)

velocity related to the wave run-up that varies in time and space (Oumeraci and Schüttrumpf, 1999) • water layer thickness

h

_A that varies in time and space

Wave run-up height

After the tongue of breaking wave hits the dike slope, the flow of wave run-up occurs. The height of wave run-up can be generally calculated as (Hunt, 1959):

gr d d i i _c H z

ξ

≤ ⋅ for = 1, gr d gr i i c H z

ξ

for > = _1, ⋅ (16) where:

•

ξ

_gr - surf similarity parameter at the transition between plunging and surging breaker

The applicability of this equation has been verified in numerous investigations (Van der Meer and Janssen, 1995 for instance). Eq. 16 is not differentiable at the transition between plunging and surging breaker, what is a serious disadvantage. The problem has been solved by Schüttrumpf (2001) who proposed the following hyperbolic function

) ( tanh = * 1, 1,i i d i c c H z

ξ

⋅ ⋅ (17)

Table 7 summarizes the coefficients of Eqs. 16 and 17 calibrated based on a number of experimental tests.

Run-up height

_c

₁ *

1

c

ξ

gr Eq. Reference

z₉₈ 1.5 - 2.0 16 Van der Meer (1995)

z₉₈ 3.0 0.65 - 17 Schüttrumpf (2001) z₅₀ 2.25 0.5 - 17 Schüttrumpf (2001) z₅₀ 1.0 - 2.3 16 Hunt (1959) R

z

2.25 0.5 - 17 Schüttrumpf (2001) R

z

1.0 - 2.3 16 Hunt (1959)

Table 7: Empirical coefficients for wave run-up - regular waves

Figs 21 and 22 show the comparison between the values of run-up calculated using reported formulae with the measurements for wave spectra and regular waves, respectively.

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Figure 21: Wave run-up height for wave spectra (Schüttrumpf 2001)

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Wave run-down heights

The heights of wave run-down z₋₉₈ were profoundly investigated by Schüttrumpf (2001), who made the following observations:

• for the plunging breakers, the tongue of breaking wave hits in the water layer that remains after the preceding wave. During this process strong turbulences occur, which results in high energy dissipation and consequently in reduction of wave run-up. Therefore, in this area the the wave run-down levels higher than mean water level can be observed

• for the surging breakers, the run-down of the preceding wave is already finished, when the next wave hits the slope. In this case the energy dissipation is significantly smaller which results in higher levels of wave run-up and consequently lower heights of wave run-down For the calculation of the wave run-down height the following empirical formula can be used (Schüttrumpf, 2001): 2.1) ( tanh 0.7 0.7 = 98 ₊ _⋅ ₋ −

_ξ

s H z (18) In Fig. 23 the comparison of measurements with Eq. 18 is shown.

Figure 23: Wave run-down height(Schüttrumpf 2001)

Wave run-up velocity

The maximal wave run-up velocity plays a significant role in the analysis of the possible erosion processes, as it is necessary to calculate the shear stress on the dike surface. A large number of investigations on this topic has been performed (Tautenhain, 1981; van der Meer and Klein Breteler, 1990, for instance). The model of Schüttrumpf (2001) is however considered to be the state of the art. In this approach wave run-up velocity at a given point can be calculated for regular waves and wave spectra as, respectively:

T

H

z

n

v

R up run

⋅

−

⋅

−

π

ξ

(

)

0.75 =

(19)

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m s s R up run T H H z z n v − ⋅ ⋅ ⋅ − ⋅ ⋅

π

ξ

( ) 0.75 = ,98 ,50 (20)

In Fig. 24 the comparison of measurements with Eqs. 19 and 20 is shown.

Figure 24: Wave run-up velocity (after Schüttrumpf 2001)

Wave run-down velocity

The wave run-down is divided in two zones (Bruun and Johannesson, 1976) - see Fig. 25. The first zone is determined by velocities and accelerations parallel to the slope - in this area, lift forces may occur due to the high velocities parallel to the slope. High velocities and accelerations normal to the slope occur due to the breaking wave (second zone).

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According to Bruun and Johannesson (1976), the components of velocity parallel and normal to the slope at SWL can be calculated as, respectively:

t s h s t s v_p ∂ ∂ ⋅ ⋅ ⋅ + + ∂ ∂

γ

α

2 0 2 cos 1 tan = (21) t s v_n ∂ ∂ ⋅

γ

= (22)

with (see also Fig. 25):

•

s

- slope parallel coordinate with s=0 at SWL [m] • h₀ - layer thickness, if

α

=

γ

[m]

•

γ

- angle between slope and water surface of wave run-down [0]

•

α

- slope [0]

• t - time [s]

Another formula for the wave run-down velocity that is available bases on the ratio of the measured maximum velocities and theoretical, average wave run-up velocity v_HUNT calculated as (Hunt, 1959):

H

g

v

_HUNT

⋅

α

π

cos

1

2 =

(23)

The ratio of the measured maximum wave run-down velocities and average velocity v_HUNT for regular waves has been reported by Führböter and Witte (1989) - in Tab. 8 the summary of their results for slopes 1:6 and 1:12 is shown.

Slope Wave run-down velocity Smooth slope 1:6 HUNT v v− =(2.20⋅ )⋅ 0.40 98

ξ

1:12 HUNT v v− =(2.64⋅ )⋅ 0.40 98

ξ

Grass 1:6 HUNT v v− =(1.25⋅ )⋅ 0.40 98

ξ

1:12 HUNT v v− =(1.26⋅ )⋅ 0.40 98

ξ

Table 8: Empirical coefficients for wave run-down - regular waves

Water layer thickness

Very little information on the layer thickness in wave run-up and run-down is available. The knowledge on the water layer thickness on the slope is however important for the prediction of dike breach initiation, as it is needed to:

• calculate the infiltration, and consequently decrease in the shear strength of the cohesive soil that is used for the dike revetment

• estimate the damping effect of the water layer on the breaking wave induced impact pressures

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The experimental investigations on the layer thickness of wave run-up and run-down have been performed by Roos and Battjes (1976), Tautenhain (1981) and Waal (1996). All the authors reported the linear decrease of the mean layer thickness

h

_A

(

x

_A

)

from

SWL

(

x

_A

=

0)

up to maximal wave run-up height

z

_A and proposed the following formula for the calculation of layer thickness (see Fig. 26):

)

(

=

₂ _R _A A

c

n

z

x

h

⋅

−

(24) with: •

c

₂

=

0.041

- Tautenhain (1981) •

c

₂

=

0.088

- Roos and Battjes (1976) •

c

2

=

0.065

- Waal (1996)

Figure 26: Definitions of

h

_A and h_A in wave run-up (adopted from Schüttrumpf, 2001)

The layer thickness measured by Roos and Battjes (1976) is double of the layer thickness reported by the other authors. A reason might be the technology of measurement by Roos and Battjes (1976), who measured water on the slope even for high wave run-up levels over the whole wave period. Schüttrumpf (2001) made similar observations as above referred authors, but proposed a new formula, that takes also the breaker form into account:

* 2 2

(

)

=

c

x

c

x

h

_A

⋅

_z

−

_A

⋅

(25) with:

•

x

_* - residual run-up length [m]

•

x

_A - horizontal coordinate, with

x

A

=

0

at SWL [m]

•

x

_Z - horizontal projection of wave run-up height

h

_R [m] calculated as: - x_Z =c1 H⋅L for plunging breaker

- x_Z =c₁⋅

ξ

_gr⋅H/tan

α

for surging breaker

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Fig. 27 summarizes the values of

c

₂ for h_A_,50, h_A_,98 and h as well as the comparison of values calculated using Eq. 25 with the measurements for dikes with outer slope 1:4 and 1:6

Figure 27: Water layer thickness as the function of residual run-up length (Schüttrumpf, 2001)

Summation of loadings and influence of slope steepness on the breach initiation

The reports concerning the storm of February 1962 point out that the heaviest damages of the dike outer slopes were located generally within the range between 1m under the MWL up to the SWL (Träger,1962; Zitscher,1962). This is the area, where the points of impact of the plunging breakers of heights up to 2 m lie. It is also a location of highest wave run-up and run-down velocities. In Fig. 28 the schema of loading superposition is shown.

Figure 28: Summation of extreme forces due to flow and impact pressures

In the detailed analysis Zitscher (1962) examined the relationship between the location of the damage and the steepness of the slope above and below MWL. The results show, that the slope angle does not have any provable influence on the embankment damage above the MWL, while the angle of the slope within the range from the 1m under MWL up to MWL together with the entire cross section shape affects the severity of the embankment damage. The slope of the damaged clay revetments is generally