DESIGN PHILOSOPHY AND METHODOLOGY

FOR DIKES AND REVETMENTS

Krystian W. Pilarczyk

CONTENTS

INTRODUCTION

DESIGN PHILOSOPHY AND METHODOLOGY

Design Philosophy

Design Methodology

BOUNDARY CONDITIONS AND INTERACTIONS

Boundary Conditions

Processes and Interactions

Effect of Dikes and Seawalls on the Beach

DESIGN OF DIKES AND SLOPING SEAWALLS

Structural Aspects and Design Checklist

Slope Protection (Revetments)

Examples

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DESIGN PHILOSOPHY AND METHODOLOGY FOR DIKES AND REVETMENTS

Introduction

The low-lying countries as the Netherlands are strongly dependent on good (safe) sea

defences (sea-dikes and/or dunes). In the past the design of dikes and revetments was mostly

based on rather vague experience than on the general valid calculation methods. The increased

demand for reliable design methods for protective structures has resulted in increased research

in this field and, as a result, in preparing a set of design guidelines for design and maintenance

of dikes, seawalls, revetments and other coastal structures.

Seadikes/Seawalls are only one option for coastal defence and must be considered in

conjunction with or as an alternative to beach management and other options. These structures

are built to protect upland areas (incl. land reclamation) when resources become endangered by

erosion or inundation due to storm surges, waves and wave overtopping. The proper (reliable)

design of these structures is of major importance. All coastal protection systems have advanta-

ges and disadvantages which should be recognized before the choice is made.

The Dutch general design/safety philosophy and the principles of functional and technical

design of these structures are discussed. Design methods concerning the geometrical design

(shape/height of dikes), as well as stability criteria for slope protection (various types of

revetments) and for protection against overtopping are included. The Dutch experience can be

of value for solving similar problems elsewhere.

For a treatment of these matters in greater depth the reader is referred to the original reports and

publications.

Design Philosophy and Methodology

Design philosophy

Natural/artificial dunes and dikes are functioning to protect upland (population and

economical values) against erosion or inundation due to storm surges. The main purposeof a

dike or seawall is to fix the land and sea boundary, and it is not intended to protect either the

beach fronting it or adjoining, unprotected beaches. Thus, seawalls neither promote accretion

nor reduce the regional trend of the coast to erode, but are constructed for protection of upland

under extreme conditions. Dikes are one of various forms of coastal protection which may be

used singularly or in combination with other methods.

There is still much misunderstanding on the use of dikes and seawalls and their possible

disadvantages related to the disturbance of the natural coastal processes and even acceleration of

beach erosion. However, it should be said that in many cases when the upland becomes

endangered by inundation (as in The Netherlands) or by high-rate erosion (possible increase of

sea-level rise) leading to high economical or ecological losses, whether one likes it or not, the

dike or seawall can even be a 'must' for survival. The proper coastal strategy to be followed

should always be based on the total balance of the possible effects of the counter measures for

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the coast considered, including the economical effects or possibilities. It is an 'engineering-art' to

minimize the negative effects of the solution chosen (Kraus and Pilkey, 1988).

Absolute safety against storm surges is nearly impossible to realize. Therefore, it is much

better to speak about the probability of failure of a certain defence system. To apply this

method, all possible causes of failure have to be analysed and consequences determined. This

method is actually under development in the Netherlands for dike and dune design. The "fault

tree" is a good tool for this aim (Fig. 1). In Figure 1 all possible modes of failure of elements can

eventually lead to the failure of a dike section and to inundation. They can also influence the

behavior of the revetment even if properly designed.

Although all categories of events, that may cause the inundation of a polder, are equally

important for the overall safety, the engineer's responsibility is mainly limited to the technical

and structural aspects. In the case of the sea-dike the following main events can be

distinguished (Figure 2):

- overflow or overtopping of the dike

- erosion of the outer slope or loss of stability of the revetment

- instability of the inner slope leading to progressive failure

- instability of the foundation and internal erosion (i.e. piping)

- instability of the whole dike

Figure 1 Simplified fault tree for a dike

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Figure 2 Failure modes/mechanisms (limit states) for a dike or dam

For all these modes of failure, the situation where the forces acting are just balanced by the

strength of the construction is considered (the ultimate limit-state). In the adapted concept of

the ultimate limit-state, the probability-density function of the "potential threat" (loads) and the

"resistance" (dike strength) are combined. The category "potential threat" contains basic

variables that can be defined as threatening boundary conditions for the construction e.g.

extreme wind velocity (or wave height and period), water levels, and a ship's impact (collision).

The resistance of the construction is derived from the basic variables by means of theoretical or

physical models. The relations that are used to derive the potential threat from boundary

conditions are called transfer functions (e.g. to transform waves or tides into forces on grains or

other structural elements). The probability of occurence of this situation (balance) for each

technical failure mechanism can be found by applying mathematical and statistical techniques.

The safety margin between "potential threat" and "resistance" must guarantee a sufficient low

probability of failure. The different philosophies are currently available in construction practice

CUR/TAW, 1990, CUR/CIRIA, 1991):

a) deterministic,

b) quasi-probabilistic, and

c) probabilistic.

For fully probabilistic approach more knowledge must still be acquired concerning the complete

problems associated with the use of theoretical models relating loads and strength. Studies on all

these topics are still underway in the Netherlands. The present Dutch guidelines for dike and

dune design follow a philosophy, that lies between the deterministic and the quasi- probabilistic

approach.

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The ultimate potential threat for the Dutch dikes is derived from extreme storm surge levels

with a very low probability of exceedance (I% per century for sea-dikes and 10% for river dikes)

and equated with the average resistance of the dike without any apparent safety margin. Besides

the ultimate limit-state, there are situations, where the ever continuing presence of a (frequent)

load causes a deterioration of constructional resistance in time, without any imminence of

failure (e.g. fatigue of concrete and steel, creep of erosion of clay under the revetment, clogging

or ultra violet deterioration of geotextile (U.V.), corrosion of cabling, unequal settlements of

deformations, etc.). However, this deterioration of constructional resistance can cause an

unexpected failure in extreme conditions. These are, so called, the serviceability- and fatigue

limit states which can also be considered as inspection and maintenance criteria.

As already mentioned, the fully probabilistic approach for dikes based on the limit-state

concept is rather cumbersome because a theoretical description for various failure modes is not

yet available. To overcome this problem a scheme to simulate nearly all possible combinations

of natural boundary conditions in a scale model of the construction and to correlate the damage

done to the boundary conditions can be developed (black box approach).

The ultimate potential threat for the Dutch sea defences is derived from extreme storm surge

levels with a very low probability of exceedance (1% per century for sea-dikes and dunes) and

equated with the average resistance of the dike (or dune). Under these ultimate load conditions,

probability of failure of the dike (seawall) should not exceed 10%.

The probabilistic approach to sea defences as developed in the Netherlands is treated ex-

tensively in CUR/TAW-report (1990).

Taking knowledge of these recent developments can be rather profitable for each country,

especially for estimation of possible risks involved in the realized projects and for finding the

optimum between the risks and the investment.

Design methodology

When designing coastal structures, the following aspects have to be considered:

* the function of the structure

* the physical environment

* the construction method

* operation and maintenance

The main stages which can be identified during the design process are shown in Figure 3.

The designer should be aware of the possible constructional and maintenance constrains

(Pilarczyk, 1990, 1998).

Based on the main functional objectives of the coastal structure a set of technical

requirements has to be assessed. When designing a dike/seawall, the following requirements to

be met can be formulated:

1. the structure should offer the required extent of protection against flooding at an acceptable

risk,

2. events at the dike/seawall should be interpreted with a regional perspective of the coast,

3. it must be possible to manage and maintain the structure,

4. requirements resulting from landscape, recreational and ecological viewpoints should also

be met when possible,

5. the construction cost should be minimized to an acceptable/responsible level,

6. legal restrictions

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Figure 3 Design methodology

Elaboration of these points depends on specific local circumstances as a type of upland

(low-land or not) and its development (economical value), availability of equipment, manpower

and materials, etc. The high dikes/seawalls are needed for protection of low-lands against

inundation while lower seawalls are often sufficient in other cases. The cost of construction and

maintenance is generally a controlling factor in determining the type of structure to be used. The

starting points for the design should be carefully examined in cooperation with the client or

future manager of the project.

In this Chapter it is further assumed that the decision based on the conceptual and

functional design is in favour of sloping dike.

Boundary Conditions and Interactions

Boundary Conditions

Assessment of the existing situation. A lot of relevant information for a seawall/dike design

can be drawn from files and existing maps. In addition to this, a field reconnaissance and a land

survey are indispensable, as well as photographic recording of the characteristic points in the

area. Special attention should be paid to the position of the beach and/or onshore profiles, and

the morphology of the area considered (eroding/ accreting coast). The composition of the

existing dike body and the geologic structure of the subsoil are also very important. When these

data are not available, the soil investigation should be considered (soundings, borings etc.). The

more detailed information on these subjects can be found in TAW/CUR (1990).

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Hydraulic boundary conditions. In view of the function of (coastal) water defences the loads

will be mostly due to the actions of long and/or short waves. In broad outline the following

wave phenomena can be distinguished:

(a) low-frequency water level changes, such as flood waves, tidal waves, wind set-up gradients

and seiches (Fig. 4);

(b) wind waves and swell;

(c) ship's waves in navigable waterways.

These water level variations strongly influence the area which needs to be protected with

hard revetment. The flow diagram on determination of hydraulic boundary conditions is given

in Figure 8.

Water level variations on canals and water-storage channels are comparatively small;

probably only caused by lock-water, seepage, drainage and wind effects. Water levels on lakes

can vary as a result of wind set-up, inflow or outflow of water, and evaporation. Water levels in

a reservoir can change markedly due to filling or emptying, but rainfall and wind set-up can also

play a role.

Water levels on a river are determined by the river's discharge regime, and in addition for

the lower reaches (estuaries) by tides and also wind-set-up. For a coastal defence embankment

water levels are governed by tides and winds. The most complex situation occurs at coastal

shores, where water level fluctuations can assume many forms.

Figure 4 Flow diagram on hydraulic boundary conditions

A lot of relevant information for seawall design can be drawn from files and existing maps.

In addition to this, a field reconnaissance and a land survey are indispensable, as well as

photographic recording of the characteristic points in the area. Special attention should be paid

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to the position of the beach and/or onshore profiles, and the morphology of the area considered

(eroding/accreting coast?). The specification of environmental parameters are given in CIRIA

(1986). The prediction methods related to hydraulic boundary conditions can be found in SPM

(1984).

Geotechnical conditions. For major structures a good geological analysis, based on the overall

geological structures of the country, is of the utmost importance for an understanding of the

geophysical and geohydrological conditions. The most important geological aspects are:

- geological stratification, formation and history

- groundwater regime

- seismicity

The main questions which a geotechnical investigation has to answer are:

- what kind of soil is found and at what depth, i.e. soft soils such as sand, clay and peat or

hard soils such as limestone and calcareous sandstone, or very hard soils such as quartzite

and basalt,

- what are the mechanical properties of the various soils with respect to their strength and

deformation characteristics,

- is the soil fissured or weathered,

- will the soil degrade in (short) time.

The first step is to organize and design site investigations. The field program forming part of the

site investigation is complemented by laboratory testing and geotechnical calculations. The last

and perhaps most difficult step is the integration of the result of the investigations and structural

design, resulting in the final foundation design.

At the set-up and organization of the soil-investigation program the geotechnical engineers

is confronted with the following questions:

- which soil data have to be collected,

- at what locations (number and depths),

- which site-investigation techniques and laboratory test should be performed,

- when is the programme to be carried out and,

- who will take care of the contracting work in the field, the laboratory tests and the

interpretation of the results.

The answer of these questions will depend among others on:

- the boundary conditions stipulated by the client (time and money schedule);

- the knowledge, judgment and experience of the geotechnical engineer;

- the availability of existing data, for example topographical, geological and geotechnical

maps;

- the phase of the design: for a preliminary design only global information over a wide area is

needed to recognize the main geotechnical problems; in the final design phase or during the

construction period detailed information on engineering soil parameters is needed;

- the type of geotechnical failure mechanisms involved;

- the availability and restrictions (including the terrain accessibility) of the investigation tools

and the quality of the personnel to handle these tools.

A high quality investigation must be economically efficient in the sense that the cost of the

investigation must be money well spent. The investigator must be able to justify each and every

item in the site investigation in terms of the value of that item in building up the geotechnical

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model. The investigator should be able to show good and sufficient reason for undertaking each

part of the investigation.

It is emphasized that there is no standard form of site investigation for a particular engineering

work. Each site investigation should be regarded as a completely new venture. Several

standardized investigation techniques have, however, been developed, of which the geological

and geotechnical engineer can make use for obtaining the relevant data for his basic calculations

and design criteria. Four types of site investigation methods can be listed:

a) geophysical measurements from the soil surface,

b) penetration tests, such as cone penetration and standard penetration tests,

c) borings, including sampling and installation of observation wells, and

d) specific measurements, such as plate loading tests and nuclear density measurements.

Construction materials. A large number of materials may be used in various forms in the

construction of seawalls and dikes. These can be: sand, gravel, quarry rock, industrial

waste-products (slags, minestone, silex from cement industry), clay, timber, concrete, asphalt,

geotextile, etc. (see also Figure 7). All these materials have to fulfil some structural and

environmental specifications that mostly are regulated by the national standards. The useful

informations can be found in various handbooks and guidelines reports (TAW/CUR, 1984,

1990, TAW, 1998, CIRIA 1986, PIANC 1987a, CUR/CIRIA, 1991, CUR/TAW, 1995,

RWS/CUR, 1995).

Processes and Interactions

Loading zones. The degree of wave attack on a dike or other defence structure during a storm

surge depends on the angle of attack of the storm, the duration and strength of the wind, the

extent of the water surface fronting the sea-wall and the bottom topography of the area involved.

For coastal areas there is a correlation between the water level (tide plus wind set-up) and the

height of the waves, because wind set-up and waves are both caused by wind. Therefore, the

joined frequency distribution of water levels and waves seems to be the most appropriate for the

design purposes (also from the economical point of view). For sea-walls in the tidal region,

fronting deep water, the following approximate zones can be distinguished (Figure 5):

I the zone permanently submerged (not present in the case of a high level "foreshore");

II the zone between MLW and MHW; the ever-present wave-loading of low intensity is of

importance for the long-term behaviour of structure;

III the zone between MHW and the design level, this zone can be heavily attacked by waves

but the frequency of such attack reduces as one goes higher up the slope;

IV the zone above design level, where there should only be wave run- up.

A bank slope revetment in principle functions no differently under normal circumstances

than under extreme conditions. The accent is, however, more on the persistent character of the

wave-attack rather than on its size. The quality of the sea-ward slope can, prior to the occurrence

of the extreme situation, already be damaged during relatively normal conditions to such a

degree that its strength is no longer sufficient to provide protection during the extreme storm.

The division of the slope into loading zones has not only direct connection with the safety

against failure of the revetment and the dike as a whole, but also with different application of

materials and execution- and maintenance methods for each zone.

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.

Figure 5 Definition of dike components and loading zones on a dike

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Figure 6 Wave interaction with structure and breaker types on a slope

Figure 7 Example of dike protection (Oester dam, The Netherlands)

Alternatives have to be generated during the conceptual, preliminary and detailed design

phase in order to select a most suitable design. It is emphasized that for each design phase these

alternatives should be evaluated at a comparable level of detail. The same applies to the

construction alternatives, which may have a great influence on the total structure costs.

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Wave-structure interaction. The interaction between waves and slopes is dependent on the

local wave height and period, the external structure geometry (water depth at the toe), slope

with/without berm, the crest elevation and the internal structural geometry (types, size and

grading of revetments and secondary layers). The type of structure wave interaction is defined

by the surf similarity parameter (or breaker parameter) which is defined as (see also Figure 6):

s/ tan= opopαξ (1)

with:

ξop

= breaker parameter

α = slope angle

sop = = gT

H22

p

sπwave steepness

Tp = wave period, peak period of the wave spectrum

Hs = significant wave height, being the average value of the highest 1/3 part of

the wave heights. This Hs is the significant wave height at the toe of the struc-

ture.

The wave steepness is a fictitious or computation quantity, especially meant to describe the

influence of a wave period. This quantity is fictitious as the wave height at the location of the

toe is related to the wave length in deep water ( π2 / Tg 2p 1).

Several wave periods can be taken from a spectrum, among them the peak period Tp, the

mean period Tm (computed from the spectrum or the time signal) and the significant period

T1/3. Applicable here is that the ratio Tp/Tm mostly lies between 1.1 and 1.25 and that Tp and T1/3

are virtually equal.

With ξop

2 < 2 - 2.5 the waves break on the slope. This is mostly the case with slopes of 1:3

or milder. For larger values of ξop

3 the waves do not break on the slope any longer. In that case

the slopes are often steeper than 1:3 and/or the waves are characterized by a smaller wave

steepness (for example swell).

For large values of the wave length or for large values of α (steep slopes), the wave behaves

like a long wave, which reflects against the structure without breaking - a so called surging

wave. For shorter waves and medium slopes waves will short and break, causing plunging

breakers forξop

4values in the range of 1 to 2.5. This figure is common along the Dutch coast

with slope angles of 1 to 3 to 1 to 5, wave periods 6 to 8 s and wave heights of 3 to 5 m. For

mild slopes wave breaking becomes a more continuous process, resulting in a more gradual

dissipation of wave energy. This type of breaking is called "spilling". For the design of

structures, surging and plunging breaker are of main importance. The area which suffers from

wave-loading is bounded by the higher up- rush and the lowest downrush point. Obviously this

zone is varying with the tide.

No reliable formula are available to predict the maximum velocities during uprush and

downrush. For surging and spilling breaker, numerical solutions have been obtained, which are,

however, not yet operational. As first approximation, the maximum velocity, Umax, on a smooth

slope can be computed by the following formula:

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Umax = a √(gHs) ξbop (2)

where: Hs = significant wave height, g = gravity, a = coefficient equal to about 1 to 1.5 for

irregular waves and b = exponent equal roughly to 0.5.

Load-strength concept. Once the hydraulic design conditions have been established, actual

design loads have to be formulated. For a given structure many different modes of failure may

be distinguished, each with a different critical loading condition. Schematically, this is shown in

Figure 2. For the dike as a whole, instability may occur due to failure of subsoil, front or rear

slope. Each of these failure modes may be induced by geotechnical or hydrodynamical

phenomena. The present section is restricted to the stability of the front slope, moreover only

instability as a result of hydrodynamical processes is taken into account.

Starting with the hydraulic input (waves, water levels) and the description of the structure,

external pressures on the seaward slope are determined. Together with the internal

characteristics of the structure (porosity of revetment and secondary layers) these pressures

result in an internal flow field with corresponding internal pressures. The resultant load on the

revetment has to be compared with the structural strength, which can be mobilized to resist

these loads. If this strength is inadequate the revetment will deform and may ultimately fail

(Figure 8).

Figure 8 System approach. Transfer functions

The phenomena which may be relevant can be divided roughly according to the three

components of the system: water, soil and structure. The interaction between these components

can be described using three Transfer Functions (see Figure 8):

I. The Transfer Function from the overall hydraulic conditions, e.g. wave height H, mean

current velocity U, to the hydraulic conditions along the external surface, i.e. the boundary

between free water and the protection or soil, e.g. external pressure P.

II. The Transfer Function from the hydraulic conditions along the external surface to those along

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the internal surface, i.e. the boundary between protection and soil. The hydraulic conditions

along the internal surface can be described as the internal pressure P.

III. The structural response of the protection to the loads along both surfaces.

Information about these functions can be obtained by means of measurements in nature and

(scale) model tests. If quantitative knowledge of the physical phenomena involved is available,

or if there is enough to hand experience then mathematical models or empirical formulae

containing information are formulated and referred to as "models". All three Transfer Functions

can be described in one model, or individually in three separate models, depending on the type

of structure and the loading. The distinction between the three functions here mainly serves as a

framework to describe the different phenomena that are important for the modelling.

In many cases, the various processes cannot be described as yet. Therefore a "black box"

approach is followed in which the relation between critical strength parameters, structural

characteristics and hydraulic parameters are obtained empirically.

Effect of Dikes and Seawalls on the Beach

A seawall forms a peculiar protection solution. It prevents further erosion of

the coastline (it fixes the land-water line) but does not stop the physical processes which cause

the erosion (a gradient in the longshore transport and the offshore transport). Therefore, it does

not stop the erosion of the inshore zone, and probably even increases it through reflection of the

incoming waves. Very often the local solution by a seawall leads to the displacement and

expansion of the problem downcoast (Figure 9a). On an originally eroding coast, the erosion in

front of a seawall can even lead to undermining the seawall or dikes, and often additional

measures are needed (i.e. heavy toe protection and/or groins in front of a seawall) to prevent this

(Figure 9b). The maintenance cost of this protection can be, therefore, sometimes very high.

This stresses the need for proper studies before the decision to construct a seawall will be taken.

In general can be stated that the coasts protected by a seawall will only have a beach in front of

this wall if sufficient sand supply is available. This happens where no erosion takes place under

normal circumstances. The seawall or dike is constructed then, for protection under extreme

conditions. However, it is possible that even under these circumstances wave reflection causes

so much erosion in front of the seawall that the beach will not be restored. Therefore, seawalls

are generally not a very feasible solution, but under special circumstances, such as along

strongly curved and heavily eroding coasts, they can be the only possibility. By locating the

defence line sufficiently landward from the eroding coast the possibility can be created for

observing the natural developments and preparing additional measures if necessary. To

minimize the effect of extra scouring due to reflection of waves the slope of seawalls or dikes

should be not more than 1 on 3. That is one of the reasons that the Dutch dikes have mostly

slope 1 on 4 or even milder. Also wave energy absorbing revetments as, for example, rubble

structures, will diminish the reflection and thus, the scouring intensity.

As a result of common controversy on the use of seawalls for coastal protection, the Coastal

Sediments'87 conference had as a theme "The Effects of Seawalls on the Coast". The results of

this conference have been evaluated and presented in a separate issue (Kraus et al., 1988). The

final conclusions are summarized below.

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Figure 9(a) Plan view of potential impacts of seawalls (Kraus et al, 1988)

Figure 9(b) Profile view of potential impacts of seawalls (Kraus et al, 1988)

The majority of quantitative-type laboratory and field studies indicates that seawalls neither

accelerate nor enhance long-term erosion of beaches, and no systematic difference in post-storm

recovery of beaches with and without seawalls was found if there was ample sediment or a wide

surf zone existed. If beaches are deficient in sediment or if sea (or lake) level is rising at the site,

erosion is more likely to occur at armored beaches as compared to unarmored beaches. The

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magnitude of the change does not appear to be extremely greater than the variability of change

in the natural, unarmored beach system. However, the armoring can cause localized additional

storm scour, both in front of and at the ends of the armoring. More study is needed to refine and

quantify these conclusions, as well as determine their limit of applicability. In order to better

utilize seawalls as an important instrument for shore stabilization, it is recommended that an

effort be made to review historical data on shoreline position, beach profile, and littoral

processes in the vicinity of existing seawalls, and to initiate comprehensive monitoring

programs. Finally, the researcher should attempt to purge all preconceptions and biases in

dealing with this controversial subject with the goal of defining and interpreting processes and

responses at the study site within the context of that site.

It can be stated that the results of the evaluation of this conference agree firmly with the

conclusions drawn by Dean (1986). Dean's final conclusions are cited below:

"Uncertainties resulting from a lack of definitive information has led to considerable speculation

and claims regarding the adverse effects to coastal armoring on the adjacent shorelines.

Employing sound principles and laboratory and field data, an attempt is made to evaluate the

potential adverse effects of armoring. It is concluded that:

1. There are not factual data to support claims the armoring causes: profile steepening,

increased longshore transport, transport of sand to a substantial distance offshore, or

delayed post-storm recovery.

2. The interaction of an armored segment of shoreline with the littoral system is more of a

"geometric" or "kinematic" interaction as contrasted to a "dynamic" interaction. The

interaction depends on the amount of sand in the system vis-a-vis the equilibrium beach

profile for the prevailing tide and wave conditions.

3. Armoring can cause localized additional storm scour, both in front of and at the ends of the

armoring. A simple sediment supply-demand argument is proposed to explain the scour.

A methodology is presented to quantify the potential adverse effects of an armoring installation

and appropriate periodic sand additions proposed as a means of mitigation to elevate the

installation to one of neutral impact on the adjacent shoreline".

Design of dikes and sloping seawalls

Structural aspects and design checklist

The selection of the structural concept depends on the function, the local environmental

conditions and the constructional constraints. The governing criteria are the technical and

economic feasibility for the project under consideration.

The function of the seawall is mainly to protect the hinterland against the adverse effect of

high-water and waves. If high-water protection is required the structure should have a height

well above the maximum level of wave-uprush during storm surge. This normally calls for high

crest elevation (TAW, 1990). If, however, some overtopping is allowed in view of the character

of the hinterland, the design requirement is formulated in terms of the allowable amount of

overtopping. Obviously crest-elevation can be reduced considerably in this case. A basic input

to the effective planning and designing of any protection scheme is a reliable set of statistics

which describe the physical environment against which such protection is necessary. The

principal items under consideration are: bathymetry, climate, water levels, wind and wave

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climate, coastal processes (sediment transport), geotechnical data, construction constraints etc.

The geologic structure of the subsoil is also very important (settlement!). When these data are

not available the soil mechanical investigation should be considered (soundings, borings etc.).

Primarily the requirement is for long term data (water-levels, winds, waves etc.), much of which

is readily obtainable from various national data banks, international specialistic organisations

(i.e. World Meteorological Organisation), publications, and local authorities.

In the past only local usage and experience have determined the selection of the type and

dimensions of the coastal protection. Often designs were conservative and too costly or were

inadequate. The technical feasibility and dimensioning of coastal structures can be actually

determined on the more founded basis and supported by a better experience than in the past.

Often, however, the solution being considered should still to be tested in a scale model, since no

generally accepted design rules exist for all possible solutions and circumstances.

The most critical structural design elements are a stability of cover-layer inc. splash-area,

secure foundation to minimize settlement and toe protection to prevent undermining. All of

these have a potential of failure of coastal structures. The checklist of the usual steps needed to

develop an adequate structure design is given below:

a) Formulate functional requirements,

b) Prepare alternative solutions,

c) Select suitable solution,

d) Determine the water level range for the site,

e) Determine the wave heights and (eventual) currents,

f) Detect suitable structure configurations (geometry),

g) Review the possible failure mechanisms,

h) Select a suitable armor alternatives and armor units size,

i) Design the filter and underlayers,

j) Determine the potential run-up to set the crest elevation,

k) Determine the amount of overtopping expected for low structures,

l) Design the toe protection, transitions and crest protection,

m) Design under drainage features if they are required,

n) Provide for local surface run-off and overtopping run-off, and make any

required provisions for other drainage facilities such as culverts and ditches,

o) Consider end conditions to avoid failure due to flanking,

p) Provide for firm compaction of all fill and backfill materials. This requirements should be

included on the plans and in the specifications, and due allowance for compaction must be

made in the cost estimate,

q) Make final check of your design,

r) Develop cost estimate for each alternative,

s) Select the final design, and

t) Prepare specifications for materials and execution incl. quality control.

The existing design rules for some (selected) structural elements (shape, height, cover-layer

etc.) are being briefly reviewed in the subsequent sections. For detail engineering

(dimensioning) the "Coastal Protection" (Pilarczyk, 1990), PIANC (1992), The Manual on Rock

(CUR/CIRIA 1991), SPM (1984) and CUR/TAW (1995), can be of use.

17

The design of coastal protection is not a simple matter. In all cases, experience and sound

engineering judgment play an important role in applying these design rules, or else

mathematical or physical testing can provide an optimum solution.

Geometrical design of dikes

Selection of the structural concept depends on the function, the local environmental conditions

and the constructional constraints. The governing criteria are the technical and economic

feasibility for the project under consideration.

The function of the dike/seawall is mainly to protect the hinterland against the adverse effect

of high-water and waves. If high-water protection is required, the structure should have a height

well above the maximum level of wave-uprush during storm surges (Figure 10). This normally

calls for high crest elevation (TAW, 1990). If, however, some, overtopping is allowed in view

of the character of the hinterland, the design requirement is formulated in terms of the allowable

amount of overtopping. Obviously crest-elevation can be reduced considerably in this case.

The shape of the cross-sectional profile of a dike/seawall is an influence on the distribution of

wave forces, and thus, also influences the choice of material (type of protective units and their

dimensions) suitable for slope protection (revetment), and the height of structure. The gradient

of the slope must not be so steep that the whole slope of the revetment can lose stability

(through sliding). This criterion gives, therefore, the maximum slope angle. More gentle (flatter)

slopes lead to a reduced wave-force on the revetment and less wave run-up; wave energy is

dissipated over a greater length. A similar effect can be obtained by applying a berm (trapezoi-

dal profile). By using the wave run-up approach for calculation of the crest height of a

trapezoidal profile of a dike/seawall for different slope gradients, the minimum volume of the

embankment can be obtained (see Figure 11). However, this does not necessarily imply that

minimum earth-volume coincides with minimum costs. An expensive part of the embankment

comprises the revetment, and the slope area increases as the slope angle decreases. Careful at-

tention is needed however, because the revetment costs are not always independent of the slope

angle, e.g. for steep slopes heavy protection is needed while for mild slopes the (cheaper)

alternative solutions (i.e., sand-mattesses, grass-mats etc.) can often provide sufficient

protection.

Another point of economic optimization can be the available space for dike/seawall construction

of improvement. All these factors should be taken into account optimizing the structure slope.

The common Dutch practice is to apply a slope 1 on 3 on the inner slope and between 1 on 3

and 1 on 5 on the outer (seaward) slope. These mild slopes also minimize the scour at the toe of

a dike (lower reflection). The minimum crest width is 2 m.

Present practice for obtaining a substantial reduction in wave run-up is to place the outer berm

at (or close to) design water level. If the berm lies too much below that level, the highest storm

flood waves would not break beneath the berm, and the run-up will be inadequately affected,

thus providing relatively heavy wave loading on the upper slope. However, the optimum

distribution of wave forces is obtained when the (relatively small) berm is about 0.5 to 1 wave-

height below the design water level. In such a case, the whole slope can be protected with the

same (relatively small) units. When the berm is equal or somewhat higher than the design water

level, the waves will always break on a lower slope. In this case, the lower slope needs much

heavier protection (but along a shorter length) than the upper slope (very often a grass-mat is

sufficient). An important function of the berm can also be its use as an access road for

maintenance or even for permanent use (promenade etc.).

The above discussion indicates that the proper choice of the shape is a very important step in the

design of a dike/seawall. Mostly it is an iterative procedure.

18

Figure 10 Determination of crest height

It was decided in the Netherlands to base the design of all sea dikes fundamentally on a

water level with a probability of exceedance of 10-4

per annum. In the Netherlands the wind set-

up is mostly incorporated in the estimated storm-surge level. If this is not a case, the wind set-up

should be calculated separately and added to the design water level. Besides the design flood

level, several other elements also play a role in determining the design crest level of a dike

(Figure 10):

- Wave run-up (2% of exceedance is applied in the Netherlands) depending on wave height and

period, angle of approach, roughness and permeability of the slope, and profile shape,

- An extra margin to the dike height to take into account seiches (oscillations) and gust bumps

(single waves resulting from a sudden violent rush of wind); this margin in the Netherlands

varies (depends on location) from 0 to 3 m for the seiches and 0 to 0.5 m for the gust

bumps.

- A change in chart datum (NAP) or a rise in the mean sea level in the Netherlands: till now

assumed roughly 0.25 m per century, in the future ~0.6 m per century (see Rijkswaterstaat,

1990),

- Settlement of the subsoil and the dike-body during its life time.

The combination of all the factors mentioned above defines the free-board on the dike (called in

Dutch as wake-height). The recommended minimum freeboard is 0.5 m.

Wave Run-up

The effective run-up (Run), on a slope can be defined as:

- for ξop < 2 to 2.5 (breaking waves)

Ru2/Hs = (1.5 to 1.75)(γf γb γβ γh) ξop = ( 1.5 to 1.75) γ ξop (3)

- with a maximum for ξop > 2 to 2.5

19

Ru2/Hs = (3.0 to 3.5)

where:

Run = run-up level exceeded by n% of waves (a vertical height above SWL),

n = index of exceedance percentage; in this case n=2

γ = total reduction factor, and γf γb γβ γh= reduction factors due to slope roughness, berm,

oblique wave attack and for depth limited wave attack, respectively.

Note: for actual relationships/values of γ-factors look to the Guide on Wave Runup and

Overtopping (2002) on www.tawinfo.nl .

The lower numerical values (1.5 and 3.0) represents the average values while the higher values

(1.75 and 3.5) represent the upper envelope of actual spreading in test results. These lower

values can be used in probabilistic calculations. For practical (deterministic) applications the

values 1.6 and 3.2 are recommended.

The surf-similarity parameter (ξop) is defined by:

αα

ξ tanT )H(

1.25 =

)L/H(

tan = p

sps

p (4)

where:

Hs = significant wave height at the toe of the structure,

Tp = peak period, and α = angle of slope

An example of possible variation of a crest-height as a function of a dike- or a seawall-shape is

given in Figure 11.

Figure 11 Example of dike calculation (alternatives); Hs= 4.7 m(depth limited), Tp= 8.5 sec,

berm reduction γb= 0.7 for ctgα= 4 and B= 4 Hs

20

In the case of low-crest elevation (overtopping allowed) the design requirement is formulated

in terms of the allowable amount of overtopping and the necessary protection of the splash-

area (dimensions of units, length). The method of calculation of overtopping discharge can be

found in Pilarczyk (1990, 1998), SPM (1984), PIANC (1991/92), and other specialistic

literature. However, the most actual approach for wave overtopping at dikes (research

commissioned by the Rijkswaterstaat) is recently presented by Van der Meer (1993, 2002).

Slope Protection (Revetments)

General considerations. In the past only local usage and experience have determined the

selection of the type and dimensions of the coastal protection. Often designs were conservative

and too costly or were inadequate. The technical feasibility and dimensioning of coastal

structures can be actually determined on a more founded basis and supported by a better

experience than in the past. Often, however, the solution being considered should still be tested

in a scale model since no generally accepted design rules exist for all possible solutions and

circumstances.

The types of revetments which are presently being studied are shown in table 2. In this

figure the critical modes of failure, the corresponding determinant loads and the required

strength are summarized qualitatively.

Classical slope revetments may be divided in different categories e.g.:

- Natural material (sand, clay and grass)

- Protected by loose units (gravel, rip-rap)

- Protected by interlocking units (concrete blocks and mats)

- Protected by concrete and asphalt slabs.

In this order the resistance of the protection is derived from friction, cohesion, weight of the

units, friction between the units, interlocking and mechanical strength. As a result of the

difference of strength properties, critical loading conditions are also different. Maximum

velocities will be determined for clay/grass dikes and gravel/ rip-rap, as they cause displacement

of the material while uplift pressures and impacts, however, are of more importance for paved

revetments and slabs, as they tend to lift the protection. As these phenomena vary both in space

and in time, critical loading conditions vary both with respect to the position along the slope and

the time during the passage of a wave. Instability for grass/clay and gravel/rip-rap will occur

around the water level, where velocities are highest during up and down rush. Moreover, wave

impacts are more intense in the area just below the still water level.

Instability of paved revetments without too much interlock occurs at the pink of maximum

down rush, where uplift forces are higher, just before the arrival of the next wave front. If the

protection is pervious uplift forces are strongly reduced. Instability will have occurred due to the

combined effect of uplift- and impact forces, just after wave breaking. Concrete slabs and

asphalt will mainly respond to uplift forces at maximum loads are distributed more evenly over

a layer area, thus causing a higher resistance against uplift, compared with loose block

pavement.

Stability (or threshold conditions) for loose materials, from sand to rock, is investigated

rather extensively, and the proper design criteria are available. However, the stability of

randomly dumped quarried rock can often be substantially improved by taking special measures

21

(= composite systems, i.e., grouting, pitched stone, mattresses, etc.). On the other hand there are

a number of protective systems related to artificial materials such as concrete (i.e., block-mats)

and asphalt. Also grassmats serve as slope protection. For most of these systems it is possible to

give some rough, indicative stability criteria which allow the engineer to make a comparison

with a random placed rock, and thus, to make a proper choice of protection. The following

systems will be considered: riprap, placed and/or pitched blocks/stones, grouted (bound) stones,

bituminous systems, gabions/stone mattresses, fabric containers (bags, mats), and clay/ grass-

mats.

Because of the great variety of the possible composition of protective systems it is not

possible to present a generally valid stability formulation for all these systems. Therefore, only

some principles and examples will be given in a general sub-section on stability criteria for

wave attack

General overview on stability criteria for wave attack. The general empirical (approximate)

formula derived by Pilarczyk (1990) and supported by large scale tests is:

b

p

u

m

s

D

H

ξα

φψcos

⋅⋅≤⋅∆

(5)

or

5.0

50,

cos

p

u

nm

s

D

H

ξα

φψ ⋅⋅≤⋅∆

= F cosα/ξp0.5

ops op

= tan

H / Lξ

α

in which:

ψu = system-determined (empirical) stability upgrading factor (ψu = 1.0 for riprap as a

reference and ψu ≥ 1 for other revetment systems) [-],

φ = stability factor or stability function for incipient of motion, defined at ξp = 1 [-],

Hs = significant wave height [m],

Tp = peak wave period [s],

Lo = wave length [m]; Lo = π2/gT2

p5

D = specific size or thickness of protection unit [m],

α = slope angle [°],

∆m = relative density of a system-unit [-],

b = exponent related to the interaction process between waves and revetment type

(roughness, porosity/permeability etc.), 0.5 ≤ b ≤ 1. For rough and permeable

revetments as riprap, b = 0.5. For smooth and less permeable placed-block revetments it

can be closed to b = 1. The value b = 2/3 can be treated as a common representative

value for other systems (i.e. more open blocks and block-mats, mattresses of special

design etc.).

D and ∆m are defined for specific systems such as:

• rock ; D = Dn = (M50/ρs)1/3

and ∆m = ∆ = (ρs-ρw)/ρw

• blocks ; D = thickness of block and ∆m = ∆

• mattresses; D = d = average thickness of mattress and ∆m = (1-n)∆, where n = bulk-

porosity of fill material and ∆ = relative density of fill material. For common quarry stone (1-n)

22

∆ ≈ 1.

The formula is applicable till ξp = 3 (breaking waves); for ξp > 3, the sizes calculated at ξp = 3

can still be applied.

The wave attack on a slope can be roughly transformed into the maximum velocity

component on a slope during run-up and run-down, Umax, by using the following formula:

Umax = p √(g Hs ξp) (for irregular waves and smooth slopes p = 1.5)

Stability factor φ for loosely aggregates can be more generally defined using the Van der Meer’s

formula (1984), namely:

φ = 6.2 Pb0.18

(Sb2 /N)

0.1 (for ξ < 3, breaking waves

where: Pb = permeability of the core material (i.e. Pb = 0.5 for breakwaters and 0.1 for

revetments), Sb = damage number and N = number of waves.

In the case of relatively impermeable core (i.e., sand or clay, Pb = 0.1, and limited number of

waves (N ≈ 3000)) the following indicative φ-values for rock can be determined:

φ = 2.0 for rest of stones (lower stability limit),

φ = 2.25 average value for incipient motion (motion 1 to 3 stones over the width of slope

equal to Dn),

φ = 3.0 as a first approximation for maximum tolerable damage for 2-layer system on granular

filter (damage-depth less or equal to 2Dn); φ = 3 can also be applied for incipient

motion of rock placed on permeable core (rockfill core or thick granular filter).

The φ-value equal to 2.25 will be used as a reference value for the stability comparison with

other alternative systems. The difference with stability of rock due to the improving measures

will be expressed by the upgrading of the factor ψu.

Figure 12 Design elements of revetments

23

The important difference between the loose rock and the alternative systems concerns the

behaviour of the systems after the initiated movement (damage). Due to the self-healing effect

of the loose rock a certain displacement of rock units can be often accepted (up to φ ≤ 3). In the

case of alternative systems, i.e., block revetment, the initial damage (i.e. removing of one block)

can easily lead to a progressive damage; there is no reserve-stability.

24

Table 1 Indicative categories for protective systems

25

The comparison of stability of various systems (parameter ψu), the necessary parameters for

calculation purposes, and other structural requirements and design rules concerning revetments

are given by Pilarczyk (1990, 1998), and are summarized in Table 1 where, for comparison of

all these systems, the stability of dumped rock will serve as a reference.

Stability of placed block revetments (incl. geotechnical aspects) is treated more extensively

in a separate sub-section due to the fact that these systems were actualy investigated more in

depth in the Netherlands. Moreover, these informations are also of use for other revetment

systems.

Comment for users

* block revetments and block-mats

The use of ψu -values higher than 2.5 is not advised except when supported by mathematical

models and/or large-scale tests incorporating geotechnical stability. For older revetments some

increase of stability is often observed due to the increase of natural friction and/or interlocking.

However, permeability may decrease which acts adversely.

The edges of the adjacent block-mats, if not properly connected to each other, should be treated

as free blocks (ψu = 1.33 to 1.50). For slopes steeper than 1 on 3 the geotechnical (in-)stability

(i.e. sliding) can be a decisive factor and it should be examined properly. In the case of toplayer

placed directly on (compacted-)sandy subsoil and geotextile the impinging wave height should

not be more than 1.5 m because of danger of local profile deformation and/or liquefaction. It

should be noted that for practical reasons the minimum thickness of loose blocks is about 0.10

m and for blocks grouted with granular material and blockmats is 0.08 m. More sophisticated

approach to stability aspects of these systems can be found in the guidelines on dimensioning of

block revetments (CUR/TAW, 1994).

* grouted stone

Surface grouting is not advised in the case of high permeable sublayers. Creating of the

completely impermeable surface should be avoided because it may introduce extra lift forces

(blasting effect). In the case of pattern grouting about 50 to 70% of the total

surface is filled. The upgrading factor is very dependent on the execution and care must be taken

to ensure that the grout does not remain in the surface of the stone-layer only, or sags completely

through the layers. In the area of high wave impact, the grouted lumps themselves can be split

by dynamic actions, therefore this type of construction should be applied up to H = 3 m

(frequent loading) and H < 4 m (less frequent loading). In the later case, for safety reasons, it is

recommended to use of three layers of broken stone. If a lump of grouted stones is split and

washed away, the third layer will still protect the core since it is held by the overlying grouted

lumps.

* bituminous systems

In the case of open stone asphalt on sand asphalt filter, the thickness of the system may be

defined as the total thickness of both layers. For the edges of all bituminous systems the ψu = 2

should be applied. Because of possibility of liquefaction, the open stone asphalt on geotex- tile

and sand is recommended only up to H = 2 m. For H > 2 m the sandbitumen filter under the

toplayer of open stone-asphalt is recom- mended. Due to the limited resistance of open

stone-asphalt against surface erosion (max. velocity, u = 7 m/s) this system can be applied up to

26

H = 3 m, and, for a less frequent wave loading, up to H = 4 m. For practical reasons, the

minimum thickness of open stone asphalt is 0.08 m if prefabricated and 0.10 m if placed insitu.

However, the more common thickness are respectively 0.10 and 0.15 m. Bituminous

plate-systems (especially impermeable ones) should also be examined concerning the allowable

stresses and strains (bending mo- ments) and the uplift criterion. The calculation methods can be

found in (TAW, 1985). The example of thickness of various asphalt revetments related to the

allowable stresses is given below for compacted sandbed with slope 1 on 3:

Hs (m) asphalt concrete open stone asphalt sand asphalt

2 0.10 m 0.20 m 0.40 m

3 0.20 m 0.40 m 0.80 m

4 0.30 m 0.65 m

5 0.40 m

In general, the resistance of the sand-asphalt is limited to the velocity of 3 m/s and the wave

height of 1.5 m (or H < 2 for less frequent loading). Currents are not usually a determining load

in the design of asphalt concrete.

* gabion baskets and mattresses

The primarily requirement is that the gabion or mattress of thickness "d" will be stable as a

unit. The thickness of the mattress can be related to the stone size D . In most cases it is

sufficient to use two layers of stone in a mattress (d = 1.8 D ) and the upgrading factor can be

recommended in the range 2 < ψu < 3 (max). The secondary requirement is that the movement

of stones in the basket should not be too high because of the possible deformation of baskets

and the loading on the mesh-wires. To avoid the situation that the basket of a required thickness

"d" will be filled by too fine material, the second criterion, related to D , have been formulated.

The choice of ψu = 2 to 2.5 related to D means, that the level of loading of the individual

stones in the basket will be limited roughly to twice the loading at the incipient motion

conditions. Thus: D (dynamic stable) when ψu ≤ 2.5, and d (stable) when d ≥ 1.8 D .

In more than 2-layer systems it is preferably to use a finer stone below the toplayers (i.e. up

to 1/5 D ) to create a better filter function and to diminish the hydraulic gradients at the surface

of subsoil. The formulations for gabions and mattresses are only valid for waves with a height

up to H = 1.5 m, or for less frequent waves up to H = 2.0 m. In either case it is important that

both the subsoil and the stone infill are adequately compacted. When the current exceeds 3 m/s

or the wave height exceeds 1 m then a fine granular sublayer (about 0.2 m thick) should be

incorporated. In other cases it is satisfactory to place the mattress directly onto the geotextile and

compacted subsoil. For practical reasons, the minimum thickness of mattresses is 0.15 m.

* fabric and other containers

The stability criterion for fabric mattresses of thickness "d" filled with sand, sandcement or

other materials attacked by waves is derived from some (limited) tests and recent knowledge of

revetment principles. The value of upgrading factor (ψu) depends on the ratio of the

permeabilities of the mattress and the subsoil, P :

. for P < 1 : ψu = 1.0 (less permeable mattresses)

. for P = 1 : ψu = 1.5

. for P >> 1 (i.e. > 2): ψu = 1.75 ÷ 2 (permeable mattresses of special design).

27

The permeability of the mattress should be treated as an integrated permeability of all the

components i.e. geotextile container and fill-material together. For wave heights 1 m < H < 2 m

and a sandy subsoil special measures against sliding and/or liquefaction should be taken: extra

compaction, extra thickness (50 to 100%), eventually a fine granular sublayer 0.2 m thick (broad

graded) etc. In the case of permeable mattresses (i.e. gravel-fill) on sandy subsoil the underneath

part of the container should be preferably made of the sand-tight geotextile (filter function). For

slopes steeper than 1 on 3, to avoid sliding, special attention should be paid to the anchoring at

the top of the mattress and to the adequate toe support. Special measures should be taking

concerning the transitions (avoid exposed edges), scour protection at the toe and the protection

in the splash area due to the overtopping. Sand-mattresses, even properly compacted, are very

susceptible to deformation. Therefore, their permanent use should be limited to relatively mild

wave attack (H < 1.5 m). In general, the use of fabric containers of various (specific) design

exposed to wave height higher than 2 m and application of ψu-values different from above

mentioned is only responsible when supported by the large-scale or prototype tests, including

geotechnical stability. For practical reasons, the minimum thickness of fabric

containers/mattresses is 0.15 m. For promoting vegetation through the geotextile mattress the

sand and/ or fine gravel, mixed with cohesive additives and seed, are very suitable as fill

material.

More actual informations on design of various geotextile systems can be found in Pilarczyk

(2000).

* grassmats

Some of the existing dikes along the Wadden Sea (northern part of the Netherlands) still

need reinforcement as these do not yet meet the specific safety requirements. One of the options

for reinforcement is a slope protection of grass on a bed of clay, rather than stone, concrete or

asphaltic protection. This option is feasible because vast mud-flats (high foreshore) and

grasslands stretch away on the seaside of the existing dikes and are inundated only during storm

surges. Moreover, the wave action in the Wadden Sea is much reduced by a row of barrier

islands. Due to these factors the design wave height does not exceed 2 m. The Delft Hydraulic

Laboratory was commissioned to access the stability of such a grass dike by means of a full

scale model study which was an absolute requirement as grass cannot be scaled down (Seijffert

and Philipse, 1990). The investigations have been performed. In the Delta Flume, a five metre

wide section of the grass dike was reproduced on full scale. The model consisted of a sand core

covered with a clay layer on a slope 1 on 8. Sods of grass with the depth of the roots of

approximately 40 cm were laid on top of the clay layer (the grass was taken from an existing

dike that was reinforced ten years ago). During the tests, the wave heights and periods and water

levels (tidal cycles) were varied continuously according to predetermined boundary conditions

during the design storm surge. The maximum H was equal to 1.85 m with T = 5.6 sec.

(plunging breaker falling on a water cushion). The measured maximum velocity on the slope

(1:8) was about 2 m/s. After 30 hours of continuous random wave attack the condition of the

grass dike was still exceptional well. The surface erosion speed of clay protected by grass was

not more than 1 mm per hour. In a number of additional tests, the durability of the grass and the

enlargement of holes, previously dug in the grass, were studied. Although wave action

considerably enlarged some of these holes, the residual strength of the dike was such that its

collapse was for from imminence (Delft Hydraulics Laboratory, 1984). The second investigation

was carried out in a large (site) flume on slope 1 on 4. Special equipment was used to simulate

the run-up and run-down velocities on this slope. Two qualitatively different grass- mats on clay

were used. The grass-mats were tested with the average velocity of 2 m/s (average over 40 hours

28

of test) and the thickness of a water layer of about 0.6 m. The maximum velocity was about 4

m/s. Erosion speed of the clay surface was 1 to 2 mm per hour up to 20 hours depending on

quality of grass-mat. After 20 hours of loading the erosion speed started to grow much

progressively for a bad quality grass-mat. Similar process took place for a good quality

grass-mat but after 40 hours of loading. The detailed information on the results and grass-mat

specification can be found in (Delft Hydraulics Laboratory, 1984b).

Some additional information on resistance of unprotected clay-surface (slope 1 on 3.5) were

obtained during the investigation carried out for the Eastern Scheldt dikes. Also in this case two

qualitatively different clays were used (fat and lean clay). The surging- breaker conditions were

applied to eliminate the effect of wave impact (H = 1.05 m, T = 12 s, max. velocity 3 m/s). The

erosion on the upper part of slope was for both clay-types the same and equal to about 2 - 3 cm

after about 5 hours of loading. After the same time, the erosion below S.W.L. was about 7 cm

for a good clay, while for a lean clay a cavity of about 0.4 m depth was created. This latest

probably because of the local non-homogeneity of clay. Also during this investigation a number

of additional tests on the erosion of different sublayers (incl. clay) at locally damaged top layers

(some protective units were removed) were performed. All the tests mentioned above indicated

that the strength of the grass slopes is strongly affected by the quality of clay and the condition

of grass and its rooting.

Recently, new large scale tests on overtopping and erosion of grass dike with slope 1 on 4

were performed in the Delta-Flume of Delft Hydraulics (Meijer and Verheij, 1994, Smith et al,

1994). This investigation has resulted in preparing a new set of stability criteria for design of

grass-mats on dikes. Distinguish has been made between the stability due to direct impact of

breaking waves and the erosion-rate due to the run-up and overtopping. The final formulation of

both criteria is actually underway.

Some additional information on this subject can be found in (CIRIA, 1976, 1987), TAW

(1990), and Pilarczyk (1998, 2000).

Stability Criteria for Current Attack.

Coastal morphology, scour process and, in some cases, stability of protective units (slope and/or

bottom protection) are or can be influenced not only by waves but also by currents and

combination of waves and currents. The currents can be of various origin, namely wave induced

currents, tidal currents, ship induced currents, natural currents (i.e. in the mouth of the rivers).

Information hereabout can be found in Pilarczyk (1990, 1998, 2000) and CUR/RWS (1995).

Optimization of slope stability

The wave forces on a plane (continuous) slope are distributed rather unequally (the high wave-

impact area near the water level, the intermediate uprush area and the low-attacked area beneath

the point of breaking). The wave action on relatively fine materials indicates that nature tries to

distribute the forces equally to provide equilibrium S-slopes. The same principle can be applied

in designing the shape of seawalls and dikes leading to application of smaller protective units

than in the case of a plane slope.

For practical reasons the 'optional' shape will be schematized to a trapezoidal profile. By

selection of a proper position of a berm below the design water level and a proper width of a

berm, the wave forces will be distributed in such a uniform way that the same material can be

29

used along the whole profile. In this case the increase of stability (50% or more) can be realized

by a berm with a width equal to 0.15 times wave length and situated (0.5 - 1.0) times wave

height below design water level. Based on the results of various studies, the indicative design

guidelines have been prepared for riprap bermed slopes and toe-protection (Pilarczyk, 1990 and

CUR/CIRIA, 1991).

Applying this concept stability of protection should also be verified at water levels lower

than the design one.

Final note: the approach to stability of revetments as discussed above is intended only as a first

(quick) estimation for comparison of various alternatives. The detailed design should take place

according to the design lines discussed in specific lectures of this course or based on the actual

technical documents.

References

1. Agema, J., 1982, "30 Years of development of the design criteria for flood protection and

water-control works", Proc. of Delta Barrier Symposium, Rotterdam.

2. Bakker, K.J. and Meijers, P., 1988, "Stability against sliding of flexible revetments", Int.

Symp. on Modelling Soil-Water-Structure Interactions, Delft, Publ. A. Balkema.

3. Barrett, M.G. et al., 1989, "Coastal Management", Proceedings Conference on Coastal

Management, 9-11 May 1989, Bournemouth, U.K.

4. Bezuijen, A., Klein Breteler, M., Burger, A.M., 1990, "Placed block revetments", Coastal

Protection (Chapter 8), Pilarczyk (ed.), Balkema, Rotterdam. ISBN 906191 1273.

5. Burger, A.M., M. Klein Breteler, L. Banach, A. Bezuyen and K.W. Pilarczyk, 1990,

"Analytical design formulas for relatively closed block revetments", Journal of Waterway,

Port, Coastal and Ocean Eng. ASCE, vol. 116 no. 5 Sept/Oct. 1990

6. CIRIA, 1976, "A guide to the use of grass in hydraulic engineering practice", Construction

Industry Research and Information Association (CIRIA), Report 71, London.

7. CIRIA, 1986a, "Sea Walls; A literature Review", Construction Industry Research and

Information Association (CIRIA) and Hydraulics Research Wallingford, London.

8. CIRIA, 1986b, "Sea Walls; Survey of performance and design practice", CIRIA, Technical

Note 125, London, England.

9. CIRIA, 1987a, "Design of reinforced grass waterways", Construction Industry Research

and Information Association (CIRIA), Report 116, London.

10. CIRIA, 1987b, "Reinforcement of steep grassed waterways", CIRIA, technical note 120.

11. CUR/RWS, 1987, "Manual on artificial beach nourishment", Centre for Civil Engineering

Research and Codes (CUR)/Rijkswaterstaat (RWS), Report 130, P.O.Box 420, 2800 AK

Gouda, The Netherlands.

12. CUR/TAW, 1989, "Guide to the assesment of the safety of dunes as a sea defence", Centre

for Civil Engineering Research and Codes/Technical Advisory Committee on Water

Defences (TAW), Report 140, Gouda, Netherlands.

13. CUR/TAW, 1989, "Guide to concrete dike revetments", CUR, Report 119, Gouda.

14. CUR, 1990, "Periodical judgement on the strength of dikes" (in Dutch), part 1 "methodolo-

gy" and parts 2 to 5 "case studies", CUR, Gouda, The Netherlands.

15. CUR/CIRIA, 1991, "Manual on use of rock in coastal engineering", Centre for Civil

Engineering Research and Codes (CUR), Gouda, The Netherlands.

16. CUR, 1992, "Artificial sand fills in water", CUR, Report 152, Gouda, Netherlands.

17. CUR, 1993, "Filters in Hydraulic Engineering", Report no. 161, Civil Engineering

Research and Codes (CUR), Gouda, The Netherlands.

18. CUR/TAW, 1994, "Design manual for pitched slope protection", Report no. 155, Centre

30

for Civil Engineering Research and Codes (CUR), P.O. Box 420, 2800 AK Gouda, NL.

19. CUR/RWS, 1995, Manual on use of rock in hydraulic engineering, CUR, Gouda.

20. Dean, R., 1986, "Coastal Armoring: effects, principles and mitigations", 20th Coastal

Engineering Conference, Taipei, Taiwan.

21. De Waal, J.P. and Van der Meer, J.W., 1992, "Wave runup and overtopping at coastal

structures", ASCE, Proc. 23rd ICCE, Venice, Italy.

22. Fakuda,N., Uno, T. and Irie, J., 1974, "Field observations of wave overtopping of wave

absorbing revetment", Coastal Engineering in Japan, Vol. 17; 117-128.

23. Führböter, A., Sparboom, U. and Witte, H.H., 1989, "Groβer Wellenkanal Hannover:

Versuchsergebnisse über den Wellenauflauf auf glatten und rauhen Deichböschungen met

der Neigung 1:6", Die Küβte. Archive for Research and Technology on the North Sea and

Baltic Coast.

24. Government of the Netherlands, 1989, "Law on Flood Control" (in Dutch), Draft 1989,

Dutch Ministry of Transport, Public Works and Water Management, The Hague, The

Netherlands.

25. Hales, L.Z. and J.R. Houston, 1983, "Erosion control of scour during construction",

Technical Report HL-80-3, Rep.4, U.S.Army, Vicksburg.

26. Hoekstra, A. and Pilarczyk, K.W., 1992, "Coastal Engineering Design Codes in The

Netherlands", Coastal Engineering Practice '92, ASCE Conference, Long Beach, CA,

USA.

27. Klein Breteler, M. and A. Bezuijen, 1991, "Simplified design method for block revet-

ments", Proceedings of Coastal Structures and Breakwaters Conference, London 1991,

Thomas Telford London.

28. Klein Breteler, M., G. Smith and K.W. Pilarczyk, 1994, "Performance of geotextiles on

clay, silt and fine sand in bed and bank protection structures", 5th Int. Conf. on Geotextiles,

Singapore.

29. Knauss, J. 1979, "Computation of maximum discharge at overflow rock-fill dams", 13th

Congr. des Grands Barrages, New Delhi, Q50, R.9.

30. Kraus, N.C. and O.H. Pilkey, eds., 1988, "The effect of seawalls on the beach", Journal of

Coastal Research, Special issue no. 4.

31. Meer, J.W. van der, 1990, "Static and dynamic stability of loose materials", in 'Coastal

Protection' (Pilarczyk, ed.), Balkema Publ., Rotterdam.

32. Meer, J.W. van der and J.P.F.M. Janssen, 1994, "Wave run-up and wave overtopping at

dikes and revetments", Delft Hydraulics Publications, no. 485, (comm. by Technical

Advisory Committee on Water Defences), Delft.

33. Meijer, D.G. and H. Verheij, 1994, "Grass dikes - analysis of measurements from large

scale tests", Delft Hydraulics, draft report Q1584 (in Dutch).

34. Owen, M.W., 1980, "Design of seawalls allowing for wave overtopping", Report No. EX

924, Hydraulics Research, Wallingford, UK.

35. PIANC 1992, "Guidelines for the design and construction of flexible revetments incorpor-

ating geotextiles in marine environment", PIANC, Suppl. to Bulletin 78/79, Brussels

36. Pilarczyk, K.W. et al, 1987, "Application of some waste materials in hydraulic engineer-

ing", 2nd European Conference on Environmental Technology, Amsterdam, The Nether-

lands.

37. Pilarczyk, K.W. ed., 1990, "Coastal Protection", Balkema Publ., Rotterdam.

38. Pilarczyk, K.W., M. Klein Breteler and A. Bezuijen, 1995, "Wave forces and Structural

Response of Placed Block Revetments on Inclined Structures", in Wave Forces on Inclined

and Vertical Wall Structures (Demirbilek and Kobayashi eds.), ASCE, New York.

39. Pilarczyk, K.W. and R.B. Zeidler, 1996, Offshore breakwaters and shore evolution control,

31

A.A. Balkema (publisher), Rotterdam.

40. Pilarczyk, K.W., 1998, Dikes and Revetments, A.A. Balkema (publisher), Rotterdam.

41. Pilarczyk, K.W., 2000, Geosynthetics and Geosystems in Hydraulic and Coastal

Engineering, A.A. Balkema (publisher), Rotterdam.

42. Quelerij, L. de and Hijum, E. van, 1990, "Maintenance and monitoring of water retaining

structures", Coastal Protection (Pilarczyk, ed.), pp.369 - 401, 1990, Balkema, Rotterdam,

The Netherlands.

43. Quelerij, L. de, E. van Hijum and K. Pilarczyk, 1991, "Performance assessement and

maintenance of coastal defences", Proc. of Coastal structures and breakwaters'91,

Thomas Telford (Publ.), London.

44. RWS/TAW, 1985, "Guide on the use of asfalt in hydraulic engineering", Rijkswaterstaat

Communications, no. 37.

45. RWS (Rijkswaterstaat), 1987, "The Closure of Tidal Basins; closing of estuaries, tidal

inlets and dike breaches", published by the Delft University Press, Delft, The Netherlands.

46. RWS (Rijkswaterstaat), 1990, "A new coastal defence policy for The Netherlands",

Rijkswaterstaat, Tidal Water Division, The Hague.

47. RWS, 1994, "DESIGN PLAN OOSTERSCHELDE STORM-SURGE BARRIER: Overall

Design and Design Philosophy", Ministry of Transport, Public Works and Water Manage-

ment, Rijkswaterstaat (RWS), (A.A. Balkema, Publ.), the Netherlands.

48. Seijffert, J.W. and L. Philipse, 1990, " Resistance of Grassmat to Wave Attack", Proc. of

Inter. Conference on Coastal Engineering, Delft, NL.

49. Smith, G.M., J.W.W. Seijffert and J.W. van der Meer, 1994, "Erosion and Overtopping of

a Grass Dike Large Scale Model Tests", Proc. 24th Inter. Conference on Coastal

Engineering, Kobe, Japan.

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Defences in The Netherlands, Government Publishing Office, The Hague, The Nether-

lands.

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Water Defences (TAW), Published by the Centre for Civil Engineering Research and

Codes (CUR), Report 141, Gouda, Netherlands.

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Water Defences (TAW), Published by the Centre for Civil Engineering Research and

Codes (CUR), Gouda, The Netherlands.

54. TAW, 1995, "Guidelines on clay specifications'(in Dutch), Technical Advisory Committee

on Water Defences (TAW)/Rijkswaterstaat, Delft, the Netherlands.

55. Van Santvoort, G., 1994, "Geotextiles and Geomembranes in Civil Engineering", revised

edition, A.A. Balkema, Rotterdam.

NB. Actual publications can be found on the website: http://www.tawinfo.nl (English,

Publications downloads)

32

Calculation Examples

Short reminder of relationships for incipien of motion

33

Note: in stability calculations below, using Chinese version of Isbash formula, ‘C’ is a

stability coefficient (not Chezy !!)

34

Example current attack:

35

Wave and Current attack; calculation example Wave attack

ξ

25.2

50

=∆ n

s

D

H where

L

H s

αξ

tan=

Riprap on filter and geotextile on clay or sand Input data: Hs = 1.0 m (significant wave height) Tp = 4.0 s (top period of waves) Tm = 3.5 s (average wave period); (Tm » Tp/1.15 = 4/1.15 = 3.5) S = 2 (damage factor in formula Van der Meer; S=2 means nearly no damage for given wave conditions) golfcondities) N = 5000 (number of waves in formula Van der Meer)

ρs = 2600 kg/m3 (volumetric density of rock)

ρw = 1000 kg/m3 (volumetric density of water)

m = cotα = 2.5 (slope gradient) P = 0.10 (type of sublayer: thin filter layer with clay or sand beneth) H2%/Hs = 1.4 Stability of riprap protection can be calculated according to the simplified Pilarczyk’s formula as:

ξ

αψ

b

op

u

s =

D

H cosΦ

∆6

or, applying for riprap: b =0.5, ψu=1 and Φ=2.25,

=Φ∆

=αψ

ξ

cos50

u

ops

n

HD m

H ops42.0

93.06.125.2

21

cos25.2==

∆ α

ξ

where 2

25

15.2

1tan===

op

s

op

L

H

αξ

A riprap slope kan also be calculated using formula by Van der Meer or with his PC programma Breakwat. In the programma we choose "stability formula for rock" and after that "M50 required average mass of rock". On the monitor we get a screen for input data (wave conditions, slope, etc.). The result of the Van der Meer/Breakwat calculation is: M50 = 181 kg (mass of stones of which 50% is smaller) Dn50 = 0.41 m nominal diameter = cube size of stone (m); Dn50 = (M50/ρs)

1/3 Dn50 is the size of a cube with a mass of M50. The average stone diameter (from the sieve) is somewhat larger: D50 = Dn50/0.84 = 0.41/0.84 = 0.49 m.

36

Stone class 60 - 300 kg satisfies this requirement. The thickness of a two-layer system will be: 1.5 Dn50 (minimum)< t < 2 Dn50, say 0.75 to 1 m. Onder such coarse top layer a finer granular sublayer (filter layer) should be placed. This granular layer will protect the geotextile during dumping of stones, and also provides better (rough) contact (better stability against sliding), than in the case of top layer directly on geotextile. The filter layer must satisfy : Dn50F = Dn50A/4.5 thickness of layer: Dn50A/2 with: Dn50F = nominal diameter of filter stones (cube size with mass of M50f) Dn50A = nominal diameter of top layer (cube size with mass of M50) In this example, filter can be defined as: Dn50F = Dn50A/4.5 = 0.41/4.5 = 0.091 m (cube size)) Df50 = Dn50/0.84 = 0.091/0.84 = 0.11 m (average diameter from the sieve) layer thickness: Dn50A/2 = 0.41/2 = 0.2 m Subsoil and the choice of geotextile: 1) Subsoil consists of a stable clay with the following specifications: 45% is smaller than 2 mm Db40 < 60 µm

Db60 = 15 µm Db90 = 80 µm dry unit weight (or density): 13 kN/m3 wet unit weight (or density): 18 kN/m3 plasticity index: 53% cohesion: 7 kPa For a stable clay with Db40 < 60 mm and dynamic loading (waves) the requirement for a geotextile is: O90 < Db90 . Choose geotextile with opening: 50µm < O90 < 80µm. This choice is based on, so-called, geometrically closed approach. The recent model investigations with geotextile on clay have provided information on critical hydraulic gradients for clay protected by geotextile, namely:

55 = 050350

0340 =

Dn

0340 = i 2

f2cr .

..

..

15•

icr = 0.034/(n

2 Df15) =0.034/(0.352 0.05) = 5.5

where n is the porosity of the filter layer (assumed 35%) and Df15 is the grain size of the granular material on the geotextile (assumed 0.05m). This allowable critical gradient is very large. There is no exact method available for calculation of hydraulic gradient in a rock structure. However, one may imagine that the impact of waves with a height of about 1m on the rock surface of about 1m thick will be highly damped before it reaches the clay underlayer. At the surface, it is possible that high hydraulic gradients are present (i >> 3), but one may expect that this gradients will diminish at least to a level of 2 (or less) at the clay surface. But this magnitude of gradients is much lower than the critical value (=5.5). Therefore, one may conclude that even geometrically open geotextiles with O90 < 0.3 mm can be applied in this case (= can provide an adequate protection for clay sublayer).

37

That means that in the discussed case we may choose geotextile with opening between 0.1 and 0.2 mm. Such larger opening will provide better opportunity for dewatering of the (overpressured) saturated clay and minimize the danger of clogging.

2) Subsoil consists of sand with following specifications: Db10=0.095mm, Db50=0.15mm, Db60=0.16mm, Db90=0.25mm, Cu =D60/D10= 1.7, and permeability soil kb=10

-4m/s: Calculate: kg (geotextile)> 10 kb(soil), thus kg > 10

-3m/s O90 < Db90(soil), thus 0.15mm< O90 < 0.25mm Finally, one may choose, for example, geotextile F180 (Nicolon) with specification: O90 = 0.180 mm kg = 50 mm/s = 5 10-2m/s Tg(thickness)= 0.7 mm