.= J

by

Krystian W. Pilarczyk

Ri jkswaterstaat

Dutch Ministry of Transport and Public Works

Road and Hydraulic Engineering Department april 1987

SEA DEPENCES

DUTCH GUIDELINES ON DIKE PROTECTION

by

Krystian W. Pilarczyk

Report WB-NO-87110

- A review -

-.-iïiMiiii.v,. *.i--^-air^»^ïs-J'

-.'"o.oo

& • > ; •

Kon';K;r:A„v..: »

25?o A A 's-C'rsven'cs©

I

Ri j kswater staat Dutch Ministry of Transport and Public Works

Road and Hydraulic Engineering Department P.O. Box 5044, 2600 GA Delft, The Netherlands

April 1987

*

- 1 -

CONTENT

ABSTRACT

1. INTRODÜCTION

2. DESIGN PHILOSOPHY OP COASTAL DEPENCE STRUCTURES

3. SHAPE AND HEIGHT OF A DIKE 3.1 Loading zones 3.2 Dike shape 3.3 Dike height and run-up

4. STRENGTH OP REVETMENTS 4.1 General approach 4.2 Failure modes and determinant wave load 4.3 Wave loading and wave structure-interaction 4.4 Stability of loosely materials 4.5 Uplift forces. Block and impervious revetments 4.6 impact forces. Asphalt revetments 4.7 Revetments under ship's induced loads 4.8 Stability of grass-slopes 4.9 Example of probabilistic calculations of revetment

5. DESIGN CONSIDERATIONS 5.1 General requirements 5.2 Dimensioning 5.3 Choice of revetment 5.4 Composition of dike and revetment 5.5 Subsoil requirements

5.6 Joints and transitions

6. MANAGEMENT AND MONITORING

7. CONCLUSIONS

REFERENCES

APPENDICES:

I A. Bezuijen, M. Klein Breteler and K.J. Bakker, Design criteria for placed block revetments and granular filters

II J.K. Vrijling, Probabilistic design of waterretaining str uctures

2 -

- 3 -

DUTCH GUIDELINES ON DIKE PROTECTION

ABSTRACT

The increased demand on reliable design methods for protective structures nas resulted in the Netherlands in preparing a set of design guidelines for revetments of the sea-, and river-dikes, and for bank protection. These guidelines are intended for technicians and organizations directly involved in the design and management of protective structures. In this report a brief review on general design philosophy, different hydraulic and geotechnical aspects and design criteria for various types of revetments is given. The sta-bility criteria based on small and large scale tests are formulated for the following systems: rip-rap, concrete units, asphalt and grass-mats. Developments for some other systems are also briefly mentioned.

KEYWORDS; sea defences, dike protection, revetments, guidelines.

CATALOGUE ENTRY; Pilarczyk, K.W. (1987), Sea defences : Dutch guidelines on dike protection, Rijkswaterstaat, Road and Hydraulic Engineering Dpt., Report WB-NO-87110, April 1987, Delft, The Netherlands.

CORRESPONDENCE:

Rij kswaterstaat Road and Hydraulic Engineering Department

P.O. Box 5044 2600 GA Delft The Netherlands

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Dutch coast, arosionat areas

,~^,.., sandy beacMas and dunas TÏ5ZSÜ «rosion areas, 1 to 5 m par yaar

Fig. 1 DUTCH COAST, EROSIONAL AREAS

fore-shore

landwards

dune (secundary)

gro,ns or t«-proteHon o f ^

permeable groins sea-dike

toe -/bottom -protection

sea-wall

Fig. 2 EXAMPLES OF SEA-PROTECTION

- 5 -.

1. INTRODUCTION

A large part of the Netherlands lies below the mean sea level; it is protected by dikes, daros and dunes (fig. 1 en 2). The country is therefore dependent on good (safe) sea defences. Driven by the nec-cessity to withstand the water, during centuries the Outch engi-neers built up their knowledge on hydraulic engineering, and parti-cularly on constructing of dikes and protection measures (revetments) . However the design of dikes and their revetments was mostly based more on rather vague experience than on the general valid calculation methods. Due to the increasing demand on reliable design methode, i.e. as a result of more "hard" safety requirements, the Dutch Ministry of Transport and Public Works (Rijkswaterstaat) and the Technical Advisory Committee on Water Defences have initia-ted a long term research program on preparing the guidelines for the design of sea and river defence structures. Some of these guidelines have been reported recently (26 ) ,(27 ) ,(28) , ( 29) , ( 30) , ( 32) .

In the report aset of basic design guidelines for revetments of the sea dikes, based on the published and unpublished sources, will be given. This set of guidelines is intended for engineers and technicians directly associated with the design and management of dikes. Is is not intended as a scientific work dealing exhaustively with theoretical f undamentals. It has been endeavoured as far as possible to give the general practical design guidelines with some background information but without offering a solution for every conceivable problem. Por a treatment of these matters in greater depth the reader is referred to the original reports. For the revetment, i.e. the protective covering of a waterretaining structure (dike) requirements are formulated with reference to the purpose of the structure and the revetment, the technical features of constructing it, and possible special circumstances involved. The shape of the cross-sectional profile of the dike is of influen-ce on the type of revetment material suitable for revetment construction. The design of the shape and the height of a dike are thus also discussed.

Various types of revetment are distinquished with reference to the properties of the materials and/or the units, and of the base on which they are installed. The following types of revetments are treated: rip-rap and other loosely systems, concrete units, asphalt and grass.

As an interim result of long-term research being still in progress, some information concerning the stability of the different revetments (i.e. new stability criteria) is given. Requirements are ap-plied to the base layers of the revetment because these are important in maintaining its stability under wave action and in ensuring that the structure will continue to function permanently. In this connection a distinction is drawn between permeable and impermeable bases. It is stated what materials can suitable be used for a permeable- or impermeable-layer and what requirements they must satis-fy, more particularly with regard to the material properties and composition, compaction, penetration of material into the other layers and the manner of use, while the circumstances of the job may impose restrictions on applicability. In the experience of many dike managers, substantial damage is liable to occur at the transition from one type of revetment to an-other and in zones where the revetment ends. Although it is not practicable to give Standard solutions, outright mistakes can be highlighted. The toe construction, the upper boundary of the hard

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design ing execution management

problems

sandy coasts(incl.dunes)

• grass/day dikes

• rigid measures (groins)

• loose materialS rockfill.gravel,

• pitched stone/concrete SQnd

• asphalt

• mattresses/mats

alternative measures

blocks

in-site measurements

1 1

\ f

\ •

govermental/ research institutions

• models

• calculations

• experience

.solutions „

contractors manufacturers

consultants

COASTAL PROTECTION-INTEORATED APPROACH

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revetment and the transition to a different type of revetment are considered.

Because of the complexity of the subject there are as yet no simple-to-use mathematical models available for dealing with vari-ous kinds of revetment and subgrade. The actual progress in this direction is discussed. All the same, with the aid of the data yielded by theoretical/empirical research, and the available expe-rience, it is possible to determine approximately the necessary di-mensions of the given types of revetments.

Although the Dutch guidelines and other reports on the discussed subject are based on the research and experiences of the highly de-veloped country, the basic ingredients of this knowledge are of common value for the whole hydraulic engineering world including the developing countries.

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RESEARCH POLICY

O

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2. DESIGN PHILOSOPHY OF COASTAL DEFENCE STRÜCTURES

__ properly designed. Although all categories of events, that may cause the inundation of a polder, are equally important for the overall safety, the engi-neers responsibility is mainly limited to the technii neers responsibility is mainly limited to the technical and struc-tural aspects. In the case of the sea-dike the following main events can be distinguished (see also fig. 3): - overflow or overtopping of the dike

óvertopping

wave overtopping

slip circle inner stope

micro instability

"piping"

settlement

slip circle outer slope

liquefaction

drtfting ice

sliding

tilting

ship collision

erosion outer slope

erosion fore shore

1 EROSION OF CREST

2 EROSION OF INNER SLOPE

3 MICRO STABIUTY

4 SLIDING

5 INTERNAL EROSION

6 FLOW SLIOE (LIQUEFACTION)

7 WAVE IMPACT

8 TOE- AND B0TT0M-PROTECTION

9SC0UR

10 SETTLEMENT

" ^ T

za* -L I

~ ^ ^

A) DIKE B) DAM

F/g. 3 OVERVIEW OF THE FAILURE MECHANISMS

10

GENERALLY:

INUNOATION

HUMAN FAILURE

EXPLOSION |_ SABOTAGE

['ACTS OF GOD'"]—J

FAILURE DIKESECTION 1

FAILURE

| LQAD > STRENGTH

FAILURE DIKE SECTION 2

EROSION INNER SLOPE

i l M W M M ^

OVERFLOW

SLIOE PLANE

3: OVERTOPPING

FLOOD > DIKE LEVEL HEIGHT

WAVE RUN UP

DIKE HEIGHT

FAILURE DIKE SECTION N

EROSION OUTER SLOPE

1 REVETMENT

FAILURE

WAVE » REVETMENT ATTACK STRENGTH

INTERNAL EROSION

PIPING

ETC.

WATER SLOPE PRESSURE STABILITY

Fig. 4 SIMPUFiED FAULT TREE FOR A DIKE

DAMAGE

1

1 — ' — . J PROBABILITY '

r i OF FAILURE i 1 1 1 — 1 I

IPOTENTIAL ! MODEL ["RESISTANCE"!

LTHREAT j ' TEST ! " • J

r _ _ L _ OR , i — - , ; TRANSFER | r i c i n iTHEORETICAL; i FUNCTIONS i r , L L U I MODEL ! u___ J QA T A i > _ . j

i i

BOUNDARY CONDITIONS

MATERIALS GEOMETRY

Fig. 5 THE CONCEPT OF THE ULTIMATE LIMIT STATE OF FAILURE MECHANISM

11

For all these modes of failure, the situation where the forces ac-ting are just balanced by the strength of the construction is con-sidered (the ultimate limit-state). In the adapted concept of the ultimate limit-state (fig. 5 ) , the probability-density function of the "potential threat" (loads) and the "resistance" (dike strength) are combined. The category "potential threat" contains ba-s ie 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 (colission) . The resistance of the construction is derived from the basic variables by means of theoretical or physical models (e.g. theoretical of semi-empiri-cal stability-model of grains). The relations that are used to de-rive the potential threat from boundary conditions are called transfer functions (i.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 technigues. The safety margin between "potential threat" and "resistance" must guarantee a sufficiënt low probability of failure. The different philosophies are currently available in construction practice: 1. deterministic, 2. quasi-probabilistic and 3. probabilistic. For fully probabilistic approach more knowledge must still be acqu-ired concerning the complete problems associated with the use of theoretical models relating loads and strength; improved knowledge of the theoretical relation between wave attack (induced pressures) and the strength of the revetment, of the probability of slope (in-)stability related to the various soil parameters, and also of the theory of internal erosion is urgently needed. Studies on all these topics are still going on 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 (13) ,(31) , (35 ) .

The ultimate potential threat for the Dutch dikes is derived from extreme storm surge levels with a very low probability of exceedan-ce (1% per century for sea-dikes and 10% for rivet dikes) and equa-ted 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 detoriation of constructional resistance in time, without any imminent danger of failure (e.g. fatique of concrete and steel, creep or erosion of clay under the revetment, clogging or u.V. detoriation of geotex-tile, corrosion of cabling, un-equal settlements or deformations, etc.) . However , this detoriation of constructional resistance can cause an unexpected failure in extreme conditions. These are, so called, the serviceability- and fatique 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 available yet. To overcome this problem a scheme to simulate nearly all pos-sible 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). Of course, field data of boundary conditions, resistance parameters and damage are

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aUALITY ASSURANCE / CQNTROL

and

RELIABILITY ANALYSIS

THERE IS DIFFERENCE BETWEEN THE RISK FOR THE CLIENT AND THE RISK FOR THE CQNTRACTOR

THE RISK FOR THE CLIENT IS TO END UP WITH DELAYS, CLAIMS AND IN THE WORST CASE WITH AN INADEGLUATE PRODUCT.

THE RISK FOR THE CONTRACTOR IS TO LOSE MONEY ON THE PROJECT OR HIS GOOD NAME.

IT IS BECOMING MORE AND MORE COMMONPLACE TO ASK A CONTRACTOR IN ADVANCE HOW THE aUALITY OF THE RESULT WILL BE GUARANTEED AND CONTROLLED = aUALITY ASSURANCE / CONTROL

aUALITY ASSURANCE WILL GIVE INCREASED CONFIDENCE THAT THE FINAL JOB IS FIT FOR ITS PURPOSE AND WILL REMAIN SO FOR A STATED PERIOD OF TIME UNDER SPECIFIED CONDITIONS OF USE AND TIME.

FOR aUALITY ASSURANCE TO BE EFFECTIVE IT IS NECESSARY TO DEFINE THE PURPOSE OF THE SCHEME, CONDITIONS OF USE, THE EXPECTED LIFE AND SERVICEABILITY. A FORMAL PROCEDURE SHOULD BE SET UP TO MONITOR EACH STAGE OF THE PROJECT (OLUALITY CONTROL).

_ J

- 13 -

preferred as base for correlation, if they are available in sufficiënt amount.

It has to be also stressed that having quantified (even roughly) the fault tree, it is possible to pay extra attention to those mechanisms which contribute most to the overall probability of fai-lure. Thus, this approach is an important element in the attempt to the total quality control of the dike design and dike execution.Mo-reover, the probabilistic approach can be applied to some important parts of the total defence structure (e.g. revetments) where the necessary input is already available from the recent investigations in the Netherlands (9) , (12) , (31) .

The fully description of probabilistic approach for dike design lies to far beyond the scope of this report. However , the detailed information can be found in the Dutch reports and publications (1), (9), (31),(35). Taking knowledge of these recent developments can be rather profitable especially for estimation of possible risks involved in the realized projects and for finding the optimum be-tween the risks and the investment.

QUALITY COSTS

X

total quality x normal costs ' v situation

optimum! situation.

failure costs

\

appraisal costs

pr«v«ntion costs

o» > o c u 3

low •> high QUALITY LEVEL

- 14 -

design water levet oading

Fig.. 6 LOADING ZONES ON A DIKE

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3. SHAPE AND HEIGHT OF A DIKE

3.1 Loading zones (26)

The degree of wave attack on a dike or other defence structure during a storm surge depends on the orientation in relation to the direction 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 mostly a certain correlation between the water level (tide plus storm surge and wind set-up) and the height of the waves, because storm surge and waves are both caused by wind. Therefore, the joined fre-quency distribution of water levels and waves seems to be the most appropriate for the design purposed (also from the economical point of view) . For sea-walls in the tidal region, fronting deep water, the follo-wing approximate zones can be distinguished (fig. 6): I the zone permanently submerged (not present in the case of a

high level "foreshore")j 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 re-duces 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 sufficiënt 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 (fig. 7).

3.2 Dike shape (21)

The shape of the dike needs to be observed in cross-section as well as longitudinally.

Cross-section

The gradiënt of the bank may not be so steep that the whole slope or the revetment can lose stability (through sliding) . These criteria give, therefore, the maximum slope angle. More gentle (flatter) slope leads to a reduced wave-force on the revetment and less wave run-up; wave energy is dissipated over a greater length. By using the wave run-up approach for calculations of the crest height of a trapezoidal profile of a dike for different slope gradients, the minimum volume of the embankment can be obtained. However, this does not necessarily imply that minimum earth-volume coincides with minimum costs. An expensive part of the embankment comprises the revetment of the waterside slope and the slope surface (area) increases as the slope angle decreases. The optimum

16 -

BLOCK PAVEMENT 5.50 m +

2.50m + 015m . r ^ f f f P * ' ' ^ ' O.SOroCLAY

FIXTONE ^ \ \ £ l * ^ J3.40m +

- . ' .0 1 2 J l ^ K . COniCRETE SLAB

RIPI 600

T|0.20m\2 W.L 0.20m+ ' T T T *

wp 111 r 11 ini^tffB^ 1 kg/m* j ^ S Ö S B * * ^ 020mT

FASCINE / REED / GEOTEXTILE

\^JS^^ \ °-10m

^HfSANDASPHALT

KSff • L \ 0 2 0 m

\ PALE FENCE

N.A.P. - 0

• 4.00 r«v*tro«trt of concr«tt Mockl 050 xO.50 x 0.20

subtayar contlsts of clay 0.80 thick or mineitone 0.70 thick undar crushad stona 0.10 thick

dim«n»ion* in m ktvtlt r«iat«d to N.A.F»

F/g. 7 EXAMPLE OF DIKE PROTECTIONS

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cross-section (based on costs) can be determined when the costs of earth works per m3 and those of revetment per m2 are known. Careful attention is, however, needed because the revetment costs are not always independent of the slope angle, e.g. for steep slopes the heavy protection is necessary while for the mild slopes the (cheap-er) grass-mat can provide a sufficiënt protection. Another point of economie optimalisation can be the available space for dike con-stuction or improvement. The common Dutch practice is to apply the slope 1 on 3 on the inner slope and between 1 on 3 and 1 on 5 on the outer (seaward) slope. The minimum crest width is 2 m. The original (old) Dutch dikes were made of local clay and as steep as possible to minimize the quanti-ty of soil. The steep outer slopes were protected against wave at-tack by all kinds of materials like wood, stone, bricks, mattresses of willow twigs balasted with stones, grass, etc. The core of a modern dike is made of great quantities of sand, brought into place mostly as hydraulic fill. This sand is covered mostly with a clay layer of thickness up to 1 m. In some recent works the clay layer have been replaced by the layer of mine-stone. In both cases the dikes have been protected by a revetment of pitched stones (basalt) or placed concrete blocks. The need to repair great lengths of sea dikes in a short time after the 1953 flood-disaster in the Nether-lands, led to the introduction of asphalt revetments. This has ne-cessitated entirely new dike construction with asphalt revetments overlying directly the sand core. Depending on the type of asphalt mixture the special requirements and restrictions can be formulated on the steepness of the slopes and the zone of application (under water of dry), (27).

The water-side berm is a common element in the Dutch dike construction. It could in the past lead to a reduction in the expenditure on stone revetments (on a very gently sloping berm a good grass-mat can be maintained) and it produced an appreciable reduction in wave runup. Present practice in order to obtain a substantial reduction in wave run-up, is to place the outer berm at (or close to) water level of the design storm flood. If the berm lies too much below that level, the highest storm flood waves would not break beneath or on the berm and the run-up will be inadequately affected, and the grass-mat on the upper slope too heavily loaded by waves leading to possible erosion. For the storm flood berms at high design levels as in the Nether-lands (freq. 10"^) there are in general no problems with the growth of grass on the berm and the upper slope. However , there can be circumstances which require also the application of a hard revetment on the berm and even on a part of the upper slope i.e. when higher frequency of water level is applied leading to more frequent overwashing of the upper part by salt water due to the run-up or wave-spray (a comon grass-matt can survive only a few salty events a year). An important function of the berm can be its use as an ac-cess road for dike maintenance. In general care should be taken to prevent erosion of the grass-mat at the junction with the revetment. The abrupt change in roughness may lead to increase of bottom turbulence and more local erosion. It is advisable to create a transition zone by applying the cell-blocks, geogrids or other systems allowing vegetation.

Longitudinal profile

Due to irregularities in the longitudinal profile of an embankment,

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S1

S ,-settlement

^ seo level changes. frnat crest heiqht __

, execution (evet V

v seiche/squall oscillation • gust ^

run up

dike after construction

final dike shape

-toe protection

Fig, 8 DETERMINAT/ON OF DIKE HEIGHT

construction

H s t Q 9 e H

settlement

i.e.30years LOG time •

primary

settlement

(execution stage)

secundary

settlement

Fig. 9 SETTLEMENT AS FUNCTION OF TIME

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in connection with the topography of the terrain in front or behind the bank, some reaches of the slopes could be subjected to more than normal wave or current attack. Not all revetments are equally suitable for use on a curved longitudinal profile, e.g. some (ree-tangular) block systems may leave gaping joints going around curved.Also, the mechanical methods for placing of blocks is in prac-tice limited mainly to straight lines or to large radius bends with sufficiently large areas.

3.3 Dike height and wave run-up

3.3.1 General consideration on the height of a dike (16), (21)

The height of a dike was for many centuries based on the highest known flood level that could be remembered. It is evident that in this way the real risk of damage or the probability of flooding we-re unknown. Little was known about the relation between the cost to prevent flooding and the cost of the damage that might result from flooding. In the 20th century it was found that the occurrence of extremely high water levels and wave heights could be described adequately in term of frequency in accordance with the laws of probability calculus. However the curves of extreme values, based on a relatively short period of obsevations, have to mostly be extrapo-lated into regions far beyond the field of observations with the risk for some uncertainties. After the 1953 disaster, the frequency of the risk of flooding was studied in the Netherlands in relation to the economie aspects. Fi-nally it was decided to base the design of all sea dikes fundamen-tally on a water level with a probability of exceedance of 10~4 per annum. In the Netherlands the storm-surge is mostly incorporated in the estimated water level. If it is not a case, the storm-surge should be calculated separately and added to design water level. Besides the design flood level several other elements also play a role in determining the design crest level of a dike (fig. 8 ) . - Wave run-up (2% of exceedance is applied in the Netherlands) de-

pending, on wave height and period, angle of approach, roughness and permeability of the slope, and profile shape (gradients, berm) .

- An extra margin to the dike height to take into account seiches (oscillations) and gust bumps (single waves resulting from a sud-den violent rush of wind); this margin in the Netherlands varies (depends on location) from 0 to 0.3 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 (assumed roughly 0.25 m ) .

- Settlement of the subsoil and the dike-body during its lifetime (at least 30 years),(see also fig. 9).

The combination of all these factors mentioned above defines the freeboard of the dike (called in Dutch as wake-height) . The recom-mended minimum freeboard is 0.5 m.

3.3.2 Wave run-up (15, (18)

The effective run-up (R) , on an inclined structure can be defined

as R = Rn-YR-YB-YB where Rn • run-up on smooth plane slopes, defined as the vertical

- 20 -

i Ru max/Hs

up

0^

down 1 -

Rd max^s

I 2-

3h

Ru2% Jsmooth slopes

l" VRumax/Hs=0.9gp

,2 ,4 ,6 ,8 1i0

^ ^ % ^ /-np-rap gp=tana/]/2TcHs/gTp

2

Rdmax/Hs=031gp-0.17

smooth slopes;

Rd2%/Hs=0.33gp

rip-rap: D 35/015= 2.25

D5o=20; 30;40mm IRREOULAR WAVES

Fig. 10 RUN-UP AND RUN-DOWN FOR SMOOTH AND RIP-RAP SLOPES

- 21 -

height above still water levelfYR5* reduction factor due to slope roughness and permeability, Y B * reduction factor due to berm and YR • reduction factor due to oblique wave attack and £ • breaker index. For random waves Rn can be expressed by

Rn , tana 1 .25 - a cn /ÜF 6p - 2.5 Cn ip where §p - . . « - ^ Tp tana < 2.5

where Cn a constant depending on the type of wave spectrum and ex-

ceedance percentage, Hg » significant wave height, Tp - top period and a - angle of slope. The values for Cn • C2% (run-up exceeded by 2% of waves) estimated from the measurements are roughly equal to: c2% • 0.55 a 0.60 - for a small spectrum and C2% a 0.70 - for a wide spectrum. üsing C2% » 0.70 and wave steepness of about 5% (typical. storm value for the North Sea Coast) one obtains the so called "Old Delft Formula" commonly used in the past for calculation of 2% run-up (R2%) o n t h e Dutch sea dikes, viz.

R2% • 8 Hg tana

which is valid for ctga = 3 and relatively smooth revetments.

As a safe approach it is recommended to use C2% • 0.70 for deter-mining the run-up due to the wind-waves (smooth slopes) . In this case 2*2.% =» 1.75 p or R2% => 0.7 Tp ]/ g Hs' tana for g p < 2 a 2.5 Hl and ^2.% - 3.5 or R2% - 3.5 Hg for ^ p S 2.5 H7 Some experimental results for smooth and rip-rap slopes are summa-r ized in fig . 10.

The reduction factors for surface roughness and permeability, YRcan be roughly estimated as follows:

Covering layer _IB asphalt, smooth concrete 1 concrete blocks, geotextile-mats, 1 0.95 open stone-asphalt, grass-mat ' pitched stone, basalton 0.90 rough, permeable block mats 0.80 gravel, gabions 0.70 rip-rap (min. thickness 2XD50) 0.60 In a case of slopes with a berm the run-up will be reduced by a factor B« T n e effect of a berm with a constant width (B) is maximum when the berm is situated approximately at the average water level (dB < 0.5 H, see definition scheme in fig. 11). It has furthermore been found that the run-up diminishes with in-creasing berm-width although the reduction rapidly falls off once a certain minimum width is exceeded, i.e. B • 0.25 L0 for non- and weak breaking waves, and B » 4H for strong breaking waves, H/L0 > 0.03. The reduction factors YB f o r tne berm width equal or larger than the minimum width mentioned above, may be roughly estimated as follows:

- 22 -

FIQ.ADEFINITIONS

-1.0 -0.8 -0.6 -0A -0.2 O 0.5 10 15 2.0 2.5

Ro

FIG. B REDUCTION OF WAVE RUN-UP DUE TO BERM

AS FUNCTION OF &j- AND -RS~

H

V

1.0

0.9

0.8

(3 o.7

t 0,6

0.5

0,4

0.3

0.2

0.1

n 10 20 30 40 50 60 70 80 o 90

YR s T^- s c o s P • ^ 2 - c o s 3 2 p "O «O

FIC f REDUCTION OF RUN-UP DUE TO OBLIÜUE WAVE APPROACH *

Fig. 11 REDUCTION OF WA VE RUN-UP

- 23 -

slope, ctga Y B (at dB < 0,5 H) 5 to 7 0.75 a 0.80 4 0.60 a 0.70 3 0.50 a 0.60 Oblique wave attack, under an angle (3 can be roughly taken into account by Yp:

Yp » cos (|3 - 10*), |5 = 65* For |3 > 65°, Rn = Hs (not less than Hst) (N.B. (3 is reduced by 10* on account of variation of P).

Note 1° : a recent investigation in Gerraany * on the oblique wave attack indicates that in the range 0<B<35*, instead of reduction, there is even a slight increase of the runup (see Fig. 11c). For this reason (at this moment), it seems better to assume no reduction of runup in this range or (more safely) to follow the Fig. 11 c.

Note 2* : depending on the wave spectrum, i.e, the anticipated maximum wave height and the type and permeability of revetment, type of subgrade, the run-up can vary reasonably and thus, the slope protection has to be more or less extended. For particular cases model investigation may give a proper answer.

The lower limit of slope area attack by waves (where a primary protection is necessary) can be roughly defined by

-1 (down) * (0,8g + 0.5) for %< 2.5 Hs

and Rd *•

- £ = 2 . 5 for £ i 2.5 Hs

Below this limit, if necessary, slope protection has to be designed on the base of occurring return flow (shipwaves) or on the base of longshore current or (orbital-) velocities of wind waves.

*) Tautenahin, E, Kohlhase, S. and Partenscky, H.W., Wave run-up at sea dikes under obligue wave approach. Proc. 18th Conf. on Coastal Engineering, 1982.

- 24 -

GRAVEL STATIC EQUIUBRIUM FILTER

TOPLAYER -STONES - THICKNESS / WEIGHT ?

BLOCKS GRANULAIR SYNTHETIC

DYNAMIC EQUIUBRIUM DESIGN CRITERIA

??? <Öfc %****

FLOW PATTERN

% £ SCOÜR MEASURES

CRITICAL SAND-PACKING ? q> FLOW SLIDE?

CHOICE PROTECT1VE STRUCTURE AND DESIGN PROCESS

- 25 -

a « farces die to down-rush

b - uplift pressures due to water in filter

c - uplift pressures due to approaching wave front

d - change in velocity field

Fig. 12 FAILURE MECHANISMS OF 5L0PE REVETMENT

- 26 -

circutar slides

GEOTECHNICAL FAILURE MOOES

suffosion

&'/tiWtWfW/ZL dtstruction toptaytr or local iliding due to wave impact piping under clay-laytr

«trosion pattern »*dirtction

groundwater flow

b) macro-mtchanismi

lifting up af prottctivt units cyclic compactian dut to wavi impact

dtformation _,- s prof ile

s-shape)

micro initability at tht surfact

y phreatic tin*

<Y„-Yw)

flow stidt

dtformation profilt

mtirnal filttr transport consolidation

a) micro -mtchanims

Fig. 13 REVIEW OF GEOTECHNICAL FAILURE MODES OF A DIKE

- 27 -

4. STRENGTH OP RBVETMENTS

4.1 General approach

Once the hydraulic design conditions have been established, actual design loads has to be formulated. Por a given structure many different modes of failure may be distinguished, each with a different critical loading condition. Schematically, this is shown in fig. 12 and fig . 13. 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.

A modern (good) engineering pratice requires that attention should be given to all possible modes of failure of the construction under design .

A brief overview of the failure mechanisms of dikes, dams or banks is given below (35): An overflow and/or wave overtopping at high water-levels is a well known mechanism, which leads to water entering the polder and to soaking of the dike. The dangerous consequences result from the soaking of the body of the dike and erosion of the inner slope.

Micro-instability of the soil material at the inner slope may result due to seepage and a high phreatic plane.

A slip circle at inner slope may be caused among other things by a high phreatic plane in a dike. This will be the case when the dura-tion of the high waterlevel is long or permanent.

A slip circle in the outer slope may occur when a low water follows an extreme high water (or sudden draw-down). The body of the dike is heavy with water and slides down.

A slip circle in the waterway bank may obstruct the fairway. This instability can be caused by a rapid draw-down of the water table in the waterway or the presence of weaker or impermeable layers in the subsoil.

A local shear failure (sliding of a revetment) parallel to the slope may also be the consequence of a rapid draw-down or hydraulic gradients perpendicular to the slope.

Erosion (removal of particles) of the dike/bank protection or the bed may be caused by wave or current induced shear forces sometimes assisted by hydraulic gradiënt forces.

Piping (internal erosion) may occur i.e. the gradual formation of a material entraining flow under an impermeable revetment or through a local concentration of permeable material in the dike body/foundation. When the "pipe" eventually reaches the high waterside the process of internal erosion will accelerate.

Migration indicates the transport of material behind the revetment. The transport may be parallel to the bank causing local slumping of the revetment or vertical resulting in an S-shaped pro-file. Material may also be lost through the revetment when filter requirements are not met.

- 28 -

waves water -level

structure

4 externpl geometry

external pressures

interna! geometry

internal pressures

resultant load

L

Fig. U SET UP OF BASIC RESEARCH AND STABIUTY COMPUTATION

- 29 -

A liquefaction may occur in loosely packed sands under influence of a shock or a sudden draw down. In this case the sudden increase of pore pressure reduces the shear strength pratically to zero and the soil behaves as a liquid.

Pumping is seen when the revetment bends under external pressure and thus generates a flow of water underneath. The flow entrains particles of the soil.

Settlements are due to consolidation, compression, migration, oxi-dation of organic material (i.e. peat layers).

Horizontal sliding or tilting is mostly unlikely for a dike or an earth dam, however , for rigid structures it is of paramount impor-tance. Ice may severely attack the revetment during wintertime.

Heave of the soil may be caused by the formation of ice crystals within the grain skeleton of the soil during the winter.

Ship collision against the dike/bank may cause considerable damage.

In the design process, one is most interested in the ultimate limit state (U.L.S.) of a failure mechanism. This state is reached when the acting extreme loads are just balanced by the strenght of the structure. If the ultimate limit state is exceeded, the structure will collapse or fail. The concept of the ultimate limit state is given in fig. 5.

The present section is restricted to the stability of the front slope, moreover only instability as a result of hydrodynamical pro-cesses is taken into account. The set-up of the studies and stability computation is shown sche-matically in fig. 14. Starting with the hydraulic input data (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 strenght is inadequate the revetment will deform and may ultimately fail.

In many cases, the various processes cannot be described as yet. Therefore a "black box" approach is foliowed in which the relation between critical strength parameters, structural characteristics and hydraulic parameters are obtained empirically.

The types of revetments which are presently being studied are shown in fig. 15. in this figure the critical mode of failure, the cor-responding determinant loads and the required strength are summari-zed qualitatively. Results obtained for rip-rap, placed block revetments, asphalt and grass are discussed in more detail in the following sections.

- 30 -

sand/gravel

i i i

clay/g rass

rip-rap

gabions/ (sand-,stone-, cement-) mattresses incl.geotextiles

placed blocks incl. block mats

asphalt

critical failure mode

• inition of mofion

• transport of material

• prof i Ie formation

• erosion • deformation

• inition of motion

• deformation

• inition of motion

• deformation • rock ing • abrasion /

corrosion of wires

• u.v.

• lifting • bending • deformation • sliding

• erosion • deformation • lifting

determinant wave loading

• velocity field in waves

• max. velocity • impact

4P*

• max. velocity • seepage

^ \

• max. velocity • wave impact • climate • vandalism

^ P ^ s ^

• overpressure • impact

• max. velocity • impact • overpressure

strength

• weight, friction

• dynamic 'stability'

• cohaesion • grass-roots • quality of

clay

• weight, friction

• permeability of sublayer/ core

• weight • block ing • wires • large unit • permeability

incl. sublayer

• thickness, friction, interlocking

• permeability incl. sublayer/ geotextile

• cabling/pins

• mechanical strength

• weight

Fig. 15 REVIEW OF SLOPE REVETMENTS WITH CRITICAL

MODES OF FAILURE

- 31 -

4.2 Failure modes and determinant wave load

Classical slope revetments may be divided in different categories (see fig. 15) 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 gra-vel/rip-rap, as they cause displacement of the material while up-lift pressures and impacts, however, are of more importance for pa-ved 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 waterlevel, 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 set-down. Due to the internal strength of the protection wave loads are distributed more evenly over a layer area, thus cau-sing a higher resistance against uplift, compared with loose block pavement.

4.3 Wave loading and wave structure - interaction

The interaction between waves and slopes is dependent on the local wave height and period, the external structure geometry (waterdepth 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 conveniently characterized by the so called breaker parameter defined as (see also fig. 16):

where H • incident wave height L0 = wave length at deep water

(= 1.56 Tz in metric units) T • wave period a • slope angle of the front face

For large values of the wave length or for large values of (X (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 for g values in the range of 1 + 3. This figure is common along the Dutch coasts with slope angles of 1 to 3 + I to 5, wave periods 6-8 s and wave heights of 3*5 metres.

tga

- 32 -

STABILITY

(STATIC EQUILIBRIUM)

AND

PROFILE DEVELOPMENT

(DYNAMIC EQUI LIBRIUM)

OF COARSE MATERIALS . . • • • • #

AND

THEIR APPLICATION

IN

COASTAL ENGINEERING

- 33 -

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 highers uprush and the lowest downrush point. Obviously this zone is vary-ing with the tide. The value of maximum up and downrush is shown in fig. 10, both for impervious and pervious slopes. If the uprush ex-ceeds the crest level, figures are no longer applicable.

No reliable formula are available to predict the maximum velocities during uprush and downrush. Por surging and spilling breaker, nume-rical solutions have been obtained, which are, however , not yet operational. A solution for the plunging breaker has not yet been obtained. Thus, the wave loading on grass/clay dikes and gravel (rip-rap protection) cannot yet be computed properly.

4.4 Stability of loosely materials

An extensive research program has been performed recently in the Netherlands on static and dynamic stability of rubble mound revet-ments, breakwaters and gravel beaches (12), (17), (18), (19). These type of protection were studied experimentally to determine the re-lationship between the critical strength parameter, Hs/Aön (H • wave height, Dn « nominal grain/stone diameter and A • specific den-sity ps - p w / p w ) , and the parameter \ describing the type of wave attack. Using Hs/ Dn parameter, the rough classification of protec-tive applications is given in figs. 17 and 18.

tpilling

Fig. 16 BREAKER TYPES

borm dynomically break- profil» stabi« watars S-shapa rock slopas groval baaches •and btacto»

1000 3000 5000

• * Hs'ADn50

Fig. 17 TYPE OF STRUCTURE AS FUNCTI0N OF Hs /ADn50

New stability formula have been determined for different applications. An example of the general stability criterion involving all design variables is presented for rubble mound revetments in fig. 19.

- 34 -

prof ec f ion layer

rubble-mound breakwaters

strengthened part

! "self adjusted" or berm prof i Ie

homogeneous rock-fitl

profile formation

homogeneous gravel

profile formation

10 20 H/ADn

static stability rock-fill

dynamic stability rock-fill

dynamic stability gravel

sandy

beaches

(nourishment)

40

Fig. 18 APPLICATION OF COARSE MATERIALS IN COASTAL ENGINEERING

- 35 -

S/]/N"

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

a impermeable core

. m permeable core Thompson (1975)

• permeable core

* homogeneous structure

S = A / D 2

SWL ^

' ^ l L 8 B 8 É

B j ^ W

. • • J l l P l ^ ^

B /

B "/

B / *

" 7 m« B k B B

B / • B

*§fc ' »ï<aïY a

H^5S • •

1.0 2.0 3.0 4.0 5.0

Hs-Dn50.l/iz". P#-0.18 6.0 7.0

S » A/D r D n ' 5 0 " ( W 5 0 / P S Wso=50% value of the mass distribution

ÏÏA'

N • number of waves Hs

a significant wave height

T2 a average wave petiod

!az< 3(breaking waves) P =» permeability

coëfficiënt

formula for plunging waves

Fig. 19A GENERAL STABIUTY FORMULA FOR RUBBLE MOUND REVETMENTS

A physical description foc S is the number of cubical stones with a side of 1 x Dn5o, eroded over a width of 1 x Dn5o. The "no damage" criterion is taken generally to be when S is between 1 and 3 stones eroded.

In order to obtain stability formula including the permeability of the structure (revetment), a permeability coëfficiënt P is introdu-ced. This permeability in the stability formula e .g. P • 0.1 for the impermeable core and P » 0.6 for the homogeneons (permeable) structure tested. In fig. 20 four structures are shown with different estimated values for p. For the time being it is left to the engineers judgement to choose the correct value for the structure to be designed. The final formula for plunging waves (breaker index

< 3) is

H,

°n50 • ]/ïT ~ 6-2 P°' 1 8 (S/]/N)0-2

with Sz

(TZ

(2Tt Hs/g Tz2)-0.5 tand average wave period)

- 36 -

,H.

Ï D , nSO H , /AD n 5 0 - 4 . 4 ( S 2 / v / ï T ) ° 2 2 $ Z " ° M

/ - » / . r-\ 1/6 _0.1 H, /ADn 5 0 -1 .25v 3 ( S 2 / y N ) £ , FORcotQ^3

H./ADnso- 1.25Vcota' ( S 2 / \ Z H ) V S $J"1 FORcota€3

—*- ^ j - taa /N /z i fH t /gT i

0.5 ae a7 o.e 0.9 1 S 6 7 8 9 10

Fig, 19B RIP-RAP STABIUTY FORMULAE FOR N=3000 WAVES AND AN IMPERMEABLE CORE

- 37 -

0* \$& Dn50A/Dn50F = 4.5

Dn50F/Dn50C = 4

. ^ B=oi

Dn50A/Dn50C=3.2 " <*** no filter no core

Dn50A = nominal diameter armour

DnSOF = nominal diameter filter

Dn50C = nominal diameter core

Structures on (a),@ and (d) have been fested.

The value of P for @ has been assumed.

Fig. 20 THE PERMEABILITY COËFFICIËNT "P"

The methods of improvement of stability of rip-rap protection and the conceptional transition from the rip-rap into the block revet-ments are illustrated in figure 21 (19),(25).

£uJLriLn.JL iL^3^.^ • I n son,e cases, especially regarding the toe and bottom protection in front of the structure, it can be necessary to control the stability of loosely materials against attack of the current. For this purpose the formula developed by pilarczyk (16) can be applied:

Dn50 n 2 5

VBl|/k gjcr g A h ' /

where: Dn5Q = grain diametre; ( W 5 Q / P S )1 / 3 > 1 mm, h = water

depth, ü c r = critical velocity, i[tcr = critical Shields parameter, Azrelative density k = slope reduction factor = ( 1-sin2a/sin2<J>) °.5, <t> » angle of internal friction of material, O, = slope angle Bi =» stability coëfficiënt. The values of | c r and Bi can be estimated from tables 1 and 2 below:

- 38 -

A. RIPRAP

tr(l5+2»

B STONE OVERUY (ONE TOP-LAYERI

C. BINDERS ARE PLACED PERPENOICULAR TO THE SLOPE

BINDERS

0. A U STONES ARE PLACED WITH THEIfl LONGEST SlDE PERPENOICLLAR TOTHE SLOPE

PLACEO STONES

FILTER (RIPRAP)

E. STONE PITCHING (BASALT) WITH OR WITHOUT GROUTING

G ROUTING

F. BASALTON

Fig. 21 RIPRAP DESIGN AND IMPROVING MEASURES

- 39 -

Table 1 Table 2

flow conditions

major turbulent flow incl. local disturbances and constrictions; also outer bends of rivers

normal turbulence of rivers and channels

minor turbulence; uniform flow smooth bed conditions

»1

5-6

7-8

8-10

state of particles

absolute rest

start of instability

movement

4>cr

0.03

0.04

0.06

It has to be stressed that, whatever method is adapted, the experi-eno? and sound engineering judgement play a large part in a proper design of protective structure.

4.5 üplift forces. Block- and impervious revetments

The uplift forces are of importance as well for the impervious (as-phalt, concrete) as for the pervious (block-) revetments. However the calculation methods of uplift are quite different for the both cases.

Blocjt r e v e ^ n ^ s ^ £arge_ .sca_lj5 u^ts jinder ra_ve att^cjc

The quality of concrete blocks was gradually improving in the last decades and the cost diminishing (a.o. due to mechanical placing) s that, at present concrete blocks of various sizes and shape are used satisfactorily in coastal (dike) protection under a variety of conditios (especially in countries with shortage of natural materi-als). Many different kinds of, often patented, revetment blocks have actually been used. The fact that design rules are still limited in guantity has stimulated investigations in this area.

In respect to the block revetments a distinction can be made be-tween: 1. Pree blocks of different design. 2. Flexible interlocked blocks, i.e. due to grouting, cabling, etc.

(i.e. Basalton blocks, Armorflex-mats). 3. "Rigid" interlocked blocks(i.e. ship-lap, tongue- and groove,

etc .) . The first two systems (see also figure 22) have been recently teste in the Delta Wave Plume at the Delft Hydraulics Laboratory (DHL) in co-operation with Delft Soil Mechanics Laboratory (DSML). The free placed blocks were tested for both, permeable as well as umpermeable (clay) sublayers. The large scale tests have shown that rectangular closed blocks placed directly on clay form a very strong revetment. When there was "good" quality clay (no erosion of the sublayer) it was impossible to. create damage conditions within the range of possibilities of the wave generator (Hs • 2.0 m, Hmax "

2* 6 m ' blocks D * 0.10 - 0.15 m thick). Besides the requirement of good and homogeneous clay a very important execution requirement is the smooting of the slope before the placing of the blocks. If the blocks are to perform properly, they must adhere to the clay without the presence of too many interstices and cavities. In the case of poor clay (sandy clay) or

- 40 -

PLACED STONES

(VILVOOROSE STONE)

STONE PITCHING (BASALT)

PLACED BLOCKS TYPE 'HARINGMAN'

f ^

GOBI BLOCK ^ c ^ > BUILDING F W ^ J BLOCKS

TONGUE-AND GROOVE TYP

STEPPED WAFFLE TYPE TYPE

interlocking blocks

MODIFIEC TONGUE AND GROOVE TYPE

SIBfiEi • • wiiwrgi wwuff» wwTEM

fijafc

ARMORFLEX BLOCK AND MAT

'A BLOCK'

BASALTON

BASALTON REVETMENT

Fig. 22A EXAMPLES OF BLOCKS TESTED ON LARGE SCALE

- 41 -

sand (properly compacted), it is prefereable to use blocks with multilayer geotextile inbetween and HS/AD values about 20% higher than these in the case of a permeable sublayer. The Basalton (hexa-gonal prisms, polygon connection) and the Armorflex-mats (connected by cabling) were tested only on a permeable sublayer. The Armor-flex-mats were tested without cabling to be able to detect the strength of this system without involving the additional strength by cabling. Por both systems when grouted (filling of surface interspaces by gravel), it was impossible to create an instability (damage) within the possibility of the wave generator (H S/AD S 8). More information hereabout can be found in (4,9,25,26).

Jjp3LijEt_f£r£e£ juid £t.abj :lj :ty_ £,f__b.i,0clk j^ev^jiinenj^s

Wave uprush will cause an increase in water table, when the per-vious protection is placed upon a granular filter. This increase in hydraulic head, together with the low external level during down-rush, will cause uplift presures, which are highest near the point of maximum downrush. The actual value of these uplift forces is dependent on the external pressure in the breakers wave and the internal pressures due to the ground water flow in the filter and in the dike body. For schematized geometries of block revetments and steady state conditions uplift pressures can be computad analytically (9) . If the specific weight of the fluid and the blocks are known, together with the thickness of the layerr the critical stability number H/AD can be obtained, for which critical uplift conditions are obtained. Where H « critical wave height, D • thickness of block, and A• relative density of block material.

Parallel to the experimental and analytical studies, the Delft Soil Mechanics Laboratory developed a numerical model, in which the internal flow field and related pressures can be computed, using any arbitrary description of the external pressure. With this model the time dependent flow field can be determined for any given point within the structure (even with a more complicated geometry) , (9).

For wave impact no numerical models are available, and empirical data have to be obtained as given in (9), (21), (23), (26),(27). An evaluation of all (large scale) empirical data on block revetments, obtained from the Dutch research and other studies abroad leads to the design criteria as shown in the table 3 (see also fig. 29).

- 42 -

6 f OROUTED, ~ t > 8

AD'

'GOOD' CLAY Jg > 7 •

AD i

B ARMORFLEX-MAT D-0.11m ctga«3 (B)-SPECTRUM

• GROUTED, ?*>10 I AD

m i BASALTON-PRISMS

D-0.1Bm ctga«3 (O-SPECTRUM « - F R E E PRISMS

l . l . l . l ,

SQUARE BLOCKS 0.25 x 0.25 m O» 0.15 m

SQUARE BLOCKS _ 0.25 x 0.25 m

OESTERDAM-PROFILE ±5=6

NAP+3£m ctga«4

(O-SPECTRUM

RIPRAP (OE.RJC.) etgo» 3+4 (REGULAR WAVES)

_ . _ a - 3

(SMAU^ SPECTRUM A-JONSIW»" • B-PIERSOrTMCHHO C- MAROLLEGAT (OESTER DAM)

« -tga

•\f2vtH

F/g. 22B STABIUTY NUMBERS FOR SOME BLOCK REVETMENTS

- 43 -

Table 3: Stability of concrete revetment3

H- cosa

AD V f&

V /F

for gz < 3 (breaking waves)

ctga > 2

category cover layer definitions

2 < ip < 3 rip-N i vp -tole

rap (2 layers) 3000 waves 3 denotes max. rable damage

II < ^ < 4

III < lp <

IV < 6

q> >6

Pitched stone Loose blocks Blocks connected by geotextile;

Blocks interlocked by friction Grouted blocks connected by geotextile Cabled blocks

Loose blocks directly on "good clay"

Grouted cabled blocks Mechanically interlocked blocks

ip » strength coëfficiënt defined at e- = 1 . n _

. lz =* tafia (2 Tt H g/gT z2)-°. 5

. D • thickness of the block

. Por rip-rap D - D S Q » (W50/pg) V3

. For long term loading effects the thickness D should be increased by 25% a= slope angle

. Filter requirements of the soil have to be met by the geotextile and/or granular sub-layer (9), (26)

. Blocks placed directly on geotextile and well compacted sand: max. Hs - 1.2 m

. "Good clay" =» according to requirements given in (26)

. Cat. V must be carefully designed and examined

Notes blocks/systems with a well defined interlock have got a very high stability (category V ) . The behaviour of the sub-layer/filter can be a restrictive factor however. The adequate design criteria on internal stability of sub-layers/filters related to the level of hydraulic loading are necessary. In all cases-, the experience and sound engineering judgement play an important role in applying these design rules.

Research is now being directed towards a better description of the time dependent external pressure during the passage of the waves. Once this has been determined, the resultant loads on the elements can be determined. The structural strength of the block forms the final stage of this study. More complicated reactions are being studying starting with a single block, where the weight of the block delivers the stabili-zing force. With these data a probabilistic design approach can be developed.

- 44 -

c w : pw . 9 l p t hcosa)

triangle-rule

schematization of the water pressure under a sealed revetment

V¥* E: - — v f e g ^

~ öxarctg(n)*~-

max «"Pv

n=1 2 3 6

(slopej

1.0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

V i N

• • I - - - - I

—

—

—

• -

- -

—-

.._

\

_.

-

_ -

- - • •

X

—

._..

\

-

..._

_..

^

- -

._..

! /

^

--

• • • -

1

/ r ' • / i

i ) •

j i

N f

1 ^ ... j ....

•- i

.... ---

- •

1 1 t

i

^

....

j i

\ v

•—

—

X

-\

-

^

-

E ^ V ^ 1

*4j X

•

—

C--

• - - - •

- -

- -

- .i,. - .

. \—

• - j - -

X X

\

-

-—

—

^

X

n 0 Z stationary flow

. 0 2 non-stationary

flow

ai= 1 - JL

triangle rule

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

H,

Fig, 23 SCHEMA TIZA TION OF THE WA TER PRESSURE UNDER AN IMPERMEABLE REVETMENT

U p l i f t fo rces for irope£,viojas r_£vetinent£ ( i« e « conc re t e or dense a s -"phTlt) "" • ~ '

Hydr wate ter sur e - Qu

la wh gr

- Dy wh me re di

The r eve Van elem tria

aulic uplift pressures develop under absolutely or relatively r-impermeable dike revetment as a result of differences in wa-level inside and outside the dike body. Hydraulic uplift pres-s can be caused by: asi-static conditions i.e. the groundwater level in the dike gs behind the ebb and flood of the tide or after a storm surge en the water level outside the dike body falls rapidly and the oundwater in the dike falls more slowly. namic conditions i.e. uplift pressure develops in the dike body en the water level outside is lowered locally, over a shore ti-period, by a passing ship (water depression) or uplift pressu-s develop when wind waves produce changes in water level on the keface . (quasi-)static potential difference, p, at the surface of the tment can be calculated by simplified analytical methods (i.e. de Veer-method (25,(27) an electrical analogue or a finite ent calculation. The first approximation can be obtained by the ngle-rule (fig. 2 3 ) :

max

'wo Jw

line above still water leis known). The real uplift water

CTwo, is defined by (fig. 2 3 ) : g (p + h cosa )

where 0 V is a position of the phreatic vel (assuming that this position pressure,

which indicated that when p = 0, the uplift pressure

wo Pw h. cosa

The dimensions of the revetment can be obtained using the following formulas (27):

1. Sliding criterion f • °wo

h > p a g (f cosa - sina )

P 2. Uplift criterion

C"wo h >

p a .g .cosa A cosa

where A Pa -Pw

Pw

To prevent the revetment as a whole against sliding, off the dike body (equilibrium criterion), the slope angle must be less than the angle of internal friction. Por relatively impermeable revetment, the slope angle in places where water is likely to occur behind the revetment, should be

3. Equilibrium criterion Pw

tg a s tg<t> (1 - H - ) Pn

- 46 -

OIKES AND BANKS PROTECTION

SLOPE PROTECTION OF DAMS

BOTTOM PROTECTION OF CLOSURE-STRUCTURES

W ^ W W ^ W T T T T I T J I i • 11 i'i iTTfi r ivw* i Fii-i'riy^PPP*

BOTTOM PROTECTION OF DISCHARGE SLUICES

SEAL FUNCTIONS

""•^• . • . -SÜWIM:**

RESERVOIRS/CANALS

'••••^"•:::S!S?!¥SW?OTW.O:U.V.'!^V.

BITUMINOUS SEAL OF DAMS

REDUCTION OF GROUNDWATER FLOW/HYDRAULIC GRAOIENTS

,SANDASPHALT H.W. JJÜL zSi&

^ '. Wl1 U 1 I 9 ^ S

^ y&mwmtmssr^^ f i i i i w i i i j l i ' i ' i i j i i I I i i"i«w i t i i - i ' W^>>„

DAM CONSTRUCTION

H.W. _L»L > < ^

SANDASPHALT

[.•. 11.'!".".. i ••« . . i . i 11 iwi^ri'wrrr-p^w 1111 in i'ri'i rrii'J"! 11 iPiiWTTPPf

FILTER FUNCTIONS

STONE

< OPEN STONEASPHALT

SANDASPHALT (FILTERLAYER)

BLOCK '. REVETMENT

SANDASPHALT [

(FILTERLAYER) ^///,

OPEN STONEASPHALT SANDASPHALT

SAND

Fig. 2k APPLICATION AND FUNCTIONS OF ASPHALT

47

h • revetment thickness (m) , £7wo • maximum uplift ), a_* slope of dike face, p a • concrete or asphalt

density

Symbols used: pressure (N/m2. _ . , _ bulk density (kg/m3), p w * density of water (kg/m3), p n of wet soil (kg/m3), g * acceleration due to gravity (m/s2), f • coëfficiënt of friction: f » tg 0 if c|) > 0, else f » tg9 , <t> • angle of internal friction of the subsoil and 0• angle of friction between the revetment and the subsoil. More information hereabout can be found in (27).

4.6 impact forces. Asphalt revetments

Waves breaking on the slope cause high forces of short duration, called impacts. Apart from the wave conditions and the structural geometry, wave impacts are also affected by the physical properties of the water and the revetment, in particular the compressibility. For water this figure is determined highly by its air content. Wave impacts cannot be computed, as yet. Although the basis equati-ons are available solutions cannot be obtained due to lack of mea-sured data for the material properties. Empirical data are used therefore, obtained from large scale model test performed in Holland and Germany. Results of these tests are summarized below, used data mentioned in the guidelines for the design of asphalt (27).

Impact forces are of primarily importance for the impervious revetments (i.e. dense asphalt) and to the less extend for the pervious revetments (i.e. block revetments).

A wave impact (P) is in fact regarded as a pressure over a certain width (b): P * p.b. The maximum pressure p given by p»pw.g.q.H in which : p w • acceleration due to gravity (m/s2), factor related to the slope e.g. q and q • 2 for slope 1:6. The acting b = 0,4 H.

(p) which acts V lil O A X Hl Udl ^ 1 C O O J T 6 P ( N / l i l ) X S

density of water (kg/m3), g a

H « wave height (m) and q - a • 2.7 for 1:3, q • .2.3 for 1:4 width is assumed equal to:

Plate thickness of an asphalt revetment can be determined using the calculation model developed in (27), The formula reads:

h * 0.75 27 1

(.* (1-V2) \<Jb )49 0.2

in which: h - thickness of revetment (m) , <7D = asphalt stress at failure (N/m2), P • wave impact (N/m1), S • stiffness modulus of the asphalt (N/m2), V = Poisson ratio for asphalt ( ~ 0.35), c -modulus of subgrade reaction (N/m3) and 0.75 • reduction factor. It is evident that the stability of asphalt revetment should also be controlled regarding the uplift and sliding criteria which can be found in (27) (see also paragraph 4.5).

Bitumuous mixtures are placed on a large under water as protective

breakwaters and closing-dams, fig. 24). The different mixtures are applied as shown

scale in dry as well as of Dutch sea-dikes,

banks of navigation channels (see elements

in fig . 25 .

- 48 -

r 1 0 . 6

i j 0.4 £

| 0 2

1 o 10 7

slope

. to*

1 : 3

Hs(ml

^ ^ 6 ^ - 5

4

- ^ t 109

0.8

0.6

0.4

0.2

0 10

slope 1

, 7 10"

: 2 / 1 : 4

\ H s l m l

^0^6 —-~J—s ^ = ?

109

0.6

0.6

0.4

0.2

0 107

slope

10«

1:6

Hs(m)

: = = * 109

F/O A Necessary layer thickness for a revetment of dense stone asphalt plotted against the "' modulus of subgrade reaction and for various significant wave heights and slopes

107 108 109 "lO7 10a

modulus of subgrade reaction (N/m3)

Fig, B Necessary layer thickness for a revetment of open stone asphalt plotted against the modulus of subgrade reaction and for various significant wave heights and slopes

10

i *

i .

« •4-4-

i\ w \V. W ^

\

A \ ^

flxtont on IMttr Manktt I T . M l H C O T < 4.10 MC O T i S.12 MC

fixtont on wn« atpnaH » T i 3.03 MC • T • 4.10 MC • T . RW MC

A • 11 <o 1.15

H

'O

, « n - « ^ . „ a / v ^

Fig. C Fixtone®: damage-parameter versus breaker-parameter

Fig. 26 DIMENSIONING OF ASPHALT REVETMENTS AGAINST WAVE IMPACT - 49 -

a-UNMftFIUCO MIX t-INTERMEOMTE • - OVEMIUEO MIX FIUINO

I EITUMEN EZ3 MMEML AMMOATE Q v o * M

% . 25 Z?£ïï/?£f 0 f BITUMEN FILLING OF AGGREGA TE

In overfilled mixtures the visco-elastic properties of the bitumen dominate, in underfilled mixtures the properties of the mineral aggregates are dominant. The described overfilled mixtures are mastic asphalt and overfilled stone asphalt; asphalt concrete belongs to the category exactly filled mixtures, underfilled mixtures are very permeable to water. The large scale- and prototype-tests indicated that the open-stone asphalt, if properly designed, can resist the current attack up to 6 m/s and the wave attack up to H s • 3 m (6), (20,(25). It is also reasonable to expect that open-stone asphalt revetment on the thick bed of sand-asphalt can be designed even to unfrequent loading of waves of H, 5 m. However , in such extreme cases, special attention should be paid to the preparation of sand-body (compaction). The resistance of the sand-asphalt is limited to the velocity of 3 m/s and the wave height of 2 m.

As an example of the calculation method mentioned before (fig. 26) , for some asphalt revetments, with slope 1 on 3 and the bed constant c •' 108 N/m-3 (compaoted sand bed), the following layer thickness can be given as an indication: wave height asphalt open

*s (m)

2 3 4 5

concrete

0. 0. 0. 0.

10 20 30 40

stone asphalt

0.20 0.40 0.65 0.90

sand asphalt

0.40 0.80

The detailed information on design and execution methods for different applications of asphalt can be found in (20) and (27).

4.7. Revetments under snip1s induced load

Por design of bank protection of navigation channels and harbour entraces is not only the laod due to the wind-waves but also the load induced by ship movement (waves and currents) of major ii tance.

Lmpor-

The design criteria in respect to this aspect are still scarce. However, in respect to the inland vessels, the systematic modeland prototype researach on this subject is being carried out in the Netherlands. Reference should be made to Blaauw et al (1984) and Pilarczyk (1984) , (3) . The prototype measurements took place in the Hartel Canal (Rotterdam) j bottom width 75 m, depth 7 m. The following test embankments, equipped with geotextile filter, were purposely constructed on slope 1:4 for the measurements campaigns (see fig. 27):

- 50 -

HARTELCAHAL

m*«ting cabfn

potitfOMnf tyitwn

F/j.-4 Schematized set-up of prototype measurements

! saüing paraid te HM emtraliM . — «auo* i—»

•MrMvX iMUr • «atarvaloetty meter • f low dlractfon m»t«r m «cho soundvr

F/V7.3 Cross-profile at central measurement stage + 500 .

F/p. f Typical cross-section of prototype embankments

F/g. 27 PROTOTYPE TESTS HARTEL CANAL (ship's waves)

fflB Ptaced - btacks

Example of a Reno mattnns

ACZ-0«tta mat

Fiitons (o.15m)-

Sand-mattrass on gravel

-gaotaxtil*

Fixtone on sand-asphalt

Fig.0 Examples of constructions tested

on on on

on on

clay Clay sand

sand sand

1. rip-rap (5-40 kg) 2. blocks (0.15 m) 3. blocks on gravel, 4. blocks on sand 5. basalton (0.15 m) 6. rip-rap (5-40 kg) 7. coarse gravel (80-200 mm) on sand 8. fine gravel (30-80 mm) on sand 9. basalton (0.12 m) on silex/sand 10. fixton (0.15 m) on sand asphalt on sand 11. sand-mattresses (0.20 m) on gravel/sand 12. armorflex-mats (0.11 m) on gravel/sand 13. PVC-Reno matresses (0.17 m) on sand 14. ACZ Delta block-mats (0.16 m) on gravel/sand The test embankments (toplayer and subsoil) , testships and wet cross-section of the test location were equipped with various in-struments. The tests have been carried out with tugs (700 hp and 1120 hp) and with push-tows (pushing units 4500 hp and 5400 hp) . Both, four loaded and empty barges and six loaded barges in 3 x 2 and 2 x 3 formation have been used. These test ships sailed both along the central axis and close to the embankment of the canal at different speeds to study the relationship between the- ship-induced water motion and the forces exerted on the banks. The typical maximum values of watermotion-components were as follows: maximum velocity of maximum waterlevel depression, Z secundary waves, H * 0.85 m. The gravel embankments (30-80 mm and verify the model relations describing the beginning of movement and transport of loose materials under ship-induced water motions. It has been proved that, in general, calculation methods based on model results give a proper approximation of the prototype values. The following stability criteria have been established:

induced return

m 0.85 m and

8 0-2 00 mm)

by these flow, ür

maximum

testships • 2 ms" 1 , height of

were applied to

1° 050 =T * r 2

"2gS COS 0C 1 -

tan 2ct tan2(|>

-1

where: ü, velocity of return flow [ms"1) , angle of internal friction, R = slope factor

a • angle of slope, $ = and 0 » 1.1 to 1.4.

2* Zmax/AD50 =§ 2.3

where: Z m a x * waterlevel depression in front of transverse sternwave

. Hi (cos B ) 0 . 5

3' — ! S 1.8 to 2.3 AD 50

where: Hi * height of secundary waves, ö • angle of wave approach; ji s 55', D50 •" average sieve value diameter (50%) .

The hydraulic components of ship induced water motion (ür, Zmax> Hi) can be calculated accordingly to Blaauw, et al (1984),(3).

The behaviour of the other revetment types, used in the prototype tests, was rather satisfactory. With some exceptions, no instabili-ty was detected.

- 52 -

CUTTING OF THE SOOS FROM A DIKE

- 53 -

After the completion of the short-term measurements in the Hartel Canal it was decided to keep all these prototype embankments for further studies on long term behaviour in the coming years.

4.8 Stability of grass-slopes

Some of the existing dikes along the Wadden Sea (Northern part of the Netherlands) need still reinforcement as these do not yet meet the specific safety requirements. One of the options for reinforce-ment is a slope pcotection 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 Laborato-ry was commissioned to assess 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. Two investigations have been per-formed. 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 co-vered 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 re-inforced ten years ago). During the tests, the wave heights and pe-riods and water levels (tidal cyclus) were varied continuously ac-cording to predetermined boundary conditions during the design storm surge. The maximum Hs was equal to 1.85 m with Tp • 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 con-tinuous 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 con-siderably enlarged some of these holes, the residual strength of the dike was such that its collapse was far from imminent (7). The second investigation was carried out in a large (site) f1urne 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 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 (8).

Some additional information on resistance of unprotected clay-sur-face (slope 1 on 3.5) were obtained during the investigation carried out for the Eastern Scheldt dikes (10). 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 (Ha • 1.05 m, Tp • 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.

- 54 -

FULL-SCALE STABILITY TESTS OF A "GRASS DIKE"

- 55 -

After the sarae time, the erosion below S.W.L. was about 7 cm for a good clay, while for a lean qlay a local cavity of about 0.4 m depth was created at the impact point. This latest probably because of the local non-homogenity of clay. Also during this investigation a number of additional tests on the erosion of different sublayers (incl. clay) at locally damaged toplayers (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 guality of clay and the condition of grass and its rooting. The general design rules cannot be defined yet. However, these informations can be of a great value for the designing of grass dikes at the present time. Some additional information on this subject can be found in (5).

4.9 Example of semi-probabilistic calculation of revetment

The deterministic approach is the most traditional design method ( ). The designer selects values of load parameters that are assu-med to be adequately high and thus safe. The choice of load and strength parameters is often subjective, based on traditional prac-tice or the designer's personal experience. The design method is based on the assumption that the structure will not fail if the loads are less than the strength, provided a good (and verified) theoretical model is available. A factor of safety is used to cover uncertainties.

The probabilistic method is a systematic approach using statistical techniques. For constructional design the use of probabilistic cal-culations is preferred. A probabilistic procedure for revetments is currently under development, and a report will be presented by PIANC workinggroup no. 3 later in 1987. The reliability function z may be defined as Z • R (Xj) - s (Xi), where R * resistance function, S • load function and Xi * basic variables. The limit state of the considered component occurs at Z * 0; the failure state is re-lated to Z < 0. There are three internationally agreed levels on which the limit state equations may be solved (31),(35): Level I : jc[u£S_i j)rj3babil Sjtic £P£r£ac_h; present construction de-

sig"n"~ methods witlï relevant" partial safety factors. Level II: j^nü-proj3aj3rlist_£c a£p£oa_c£j approximation methods are

applied* in whTch normal probability distributions are assumed for both strength and laoding: 1. First order mean value approach. 2. First order design-point approach. 3. Approximate full-distribution approach.

Level III: Full-distribution approach; this method accounts for the exact joint probability distribution functions including the correlations among the parameters. It usually requi-res a considerable computational effort.

It goes beyond the scope of this report to deal with all the methods in detail, but the mean value approach will be discussed because of its simplicity and its illustrative value for studying the effect of the value of various strength and load parameters invol-ved. In this method the reliability function Z is linearized about the expected mean value of the parameters involved. Mutually independent normally distributed variables are assumed. The mean value \Xz and Standard deviation Cfz can be evaluated as:

- 56 -

ISITENOUGH?

- 57 -

|iz - z ( M- (XT ) V- (xn>)

and

0 5 ^z"

The reliability index |i = |iz/ G"z is the distance between Z • 0 and the mean value, measured in Standard deviation units and is as such a measure of the probability that Z will be less then zero. Assuming the normal distribution for Z: 4>N(Z -[1/(7), then for Z • °s0N(-|i). Now the probability of failure can be read from tabu-lated normal distribution. Thus the probability of failure is now: P(Z <0) = <3>N(-(3) . This method is less accurate then a more detailed elaboration and bet-ter approximations of the reliability function but is for becoming aware of portant parameters. The next example may

|3Z=HZ/C7

i l l u s t r a t i v e t h e most im- Flg. 28 RELIABILITY INDEX

illustrate this: stability of block ments, according to the Pilarczyk formula (for 2 s ip < 3 -valid for rip-rap on relatively impermeable sublayer):

revet-, also

ls cosa and

tana 1 .25 T p tana

^Hs/Lp' AD j/fÊ

where: Hs ° significant wave height, A • relative density of block-units; A= ( pg - p w)/p w,

a= angle of slope, length) , D »

-, « breaker index The limit state function:

* (top-)wave period (LT wave length), D • thickness of block,

p • breaker index and ip * stability factor.

HsVf£ Z • R - S * tp .A.D -

• ip .A.D -

cosa Hs 1 .25

Tp tana

5 T p tana

cosa

The derivative of Z according to each variable:

6z 3 .

9HS 8 cosa

dz , — • ip . D

3A

3z

3(c t g a)

Hs ^5 Tp/4 1 s i n a

2 c t g a i/ctga' c o s a ]/ctga" c o s 2 a ( 1 + c t g 2 a )

- 58 -

?

59 -

az H,

3Tp 2 cosa

— - AD 39

-vpA 3 D

5 tand.

4Tp /Hs*

The following steps are taken to calculate the mean value of Z (|iz) and the Standard of input variable Hs A ctga

Standard deviation variables

deviation G"z as a result of each stochastic are as follows:

of parameter

the weighed partial . The assumed values

D(assumed)

2.0 m 1 .4 3 (cos a =0.95 5 s 5 0,45 m

CT(Xi) 0.25 m 0.05 0. 25

s 0.50

or (0.10 n)

or (0.5 s)

0.0 1 m

<Si 1.47)

N.B. The deterrainistic calculation provides in this case D » 0.36 m with (per definition) 50% probability of failure (in this case the mean

|!z • 0, so i • M-z/ z a 0). When the uncer tainties value for Z is 0: regarding the Hs

2.25 m and ip =» 5 des D » 0.45 m.

« 2 + 0 . 2 5 = and ip are taken into account, e.g. H, - 0.5 = 4.5, the determinist ie calculation provi-

Assuming, as a first approximation, D = 0.45, the probability of failure will be calculated in the following way:

|iz - 5(1 .4)0.45 -2.0

0.95

1.25 5.1/3

yT 3.15- 2.555 0.595

x i

Hs A c t g a T P

D

e . 3X Ï

3 z / 3 H s - - 0 . 9 6 0 3 z / 3 A • ^ « D * 2 . 2 5 0 3 z / 3 < c t 9 ° 0 - 0 . 5 1 2 3 z / 3 T p * 0 . 2 5 6 3 z / 3 9 - A - D - 0 . 6 3 0 3 z / 3 D = q>.D * 7 . 0 0 0

<ÖCi

0 . 2 5 0 . 0 5 0 . 2 5 1 . 0 0 0 . 5 0 0 . 0 1

9z GV.

2 4 0 . 1 0 ~ 3

1 1 2 . 1 0 - 3

1 . 2 8 . 1 0 - 3 2 5 6 . 1 0 - 3 3 1 5 . 1 0 - 3

7 0 . 1 0 - 3

& N' 5 7 . 6 . 1 0 - 3 1 2 . 6 6 . 1 0 - 3 1 6 . 3 8 . 1 0 - 3 6 5 . 5 4 . 1 0 - 3 9 9 . 2 3 . 1 0 - 3

4 . 9 0 . 1 0 - 3

<TZ2 - 2 5 6 . 3 1 . 1 0 - 3

|iz p - - / ( 7 Z * 0 . 5 9 5 / 0 # 5 0 6 = 1 m 1 7 6 g z m 0 . 5 0 6

Ti, 22

5 6

26 39

2

100%

the of. .es

(Xi) on C7Z

- 60 -

3 * |

Ik (o) frcqucncy § •= £

of toading | *• * c *> o

•f

(b) r«spen*« function

(e) damag»

\

domogo S « fcs.f.T

intcnsity of tooding(P)

intensity of loading(P)

inttnsity of lood ing (P)

% <?* OUTUNES OF A PROBABIUSTIC DESIGN APPROACH

- 6 1 -

Further research for lowering the probability of failure may then focussed on the characteristics of these parameters. In this case the variability (or uncertaintly) about the actual wave conditions (wave height and wave period) is most important (assuming that the accuray of the formule, thus , can not be improved). Of course if one takes a larger thickness of block, a more safe situation and thus, a lower probability of failure can be expected.

Assuming that in this case the prediction of the actual wave conditions can be improved nl. G"Hg=i 0,1 m and G"Tp • 0,5 sec, the re-peating of this calculations provides p * 1.495 and the probability of failure equal to about 7%. The lay down of the criterion of acceptable probability of failure is mostly left to the responsible authorities. However, the best way is to calculate the probability of failure for various design alternatives in combination with some economical studies regarding the execution and maintance costs, and economical consequentes of failure. Such an approach can easily be used for decisional analy-sis, where the costs of each decision and its consequences are weighed by the probability of these events.

The general outlines of the probabilistic approach are shown in Fig. 29 One may relate this to the design of slope protection by loosely materials (i .e. r iprap) . First of all one shoul'd be able to "predict" the frequencies of occurence of hydraulic loads during the lifetime of construction (Fig.29a.) Secondly, the response function should be obtained from hydraulic model tests or by applying known "transport" relationships (Fig.-29b). The resultant damage (Sd) during the lifetime of the construction is obtained as shown in Fig 29c.

P Sa • I s.f.T.

where: T * lifetime of the construction, f • frequence of occurence of a given load intensity, s * damage per unit time and p » inten-sity of load. If more than one type of loading is acting, the summation of the damage should be computed by integration over the various load com-binations and their probabilities. The resulting total damage is a measure of the expected maintance of the slope protection works for a given size of the top layer and revetment composition. A process of economical optimalization, based on the costs of construction and maintance, can further be carried out, leading to the selection of the optimum size of the revetment. Besides this minimum integral cost criterion, one should als restrict the "expected total damage". The maximumn acceptable damage depends on:

the relationship between "expected total damage", which is an average over the total protection length and the "maximum possi-ble damage" that may take place at a certain location, the type of"construction and the vulnerability of the subsoil, the risk of progressive damage if repair in time is impossible for technical, organisational or financial reasons.

The actual state of the knowlegde allows to apply this approach on-ly for slope protection by loosely materials where the adequate transfer-functions (transport formulae) have been developed in the recent years. However in general, there is still a lack of data and insight in many of the above aspects. Therefore the research programmes in the Netherlands for the coming years are being systema-tically directed towards economically justified design criteria for different protective structures and different applications.

- 62 -

undesired top event collopse of embankment/ revetment

probability of faiture/damage

probabilistic calculations with density of events, or: events and effects guesses

single element

ac transitions

shear stress

pressure head

ship traffic

river ftow

surges

wind woves

s ship traffic

ground-water flow

filter charac-teristics

wind set-up

element weight

bank slope

— cohesion

— friction

L

toleronce in alignment

r4~i\

segments of structure

J T ^ L

J l_. I

F/g. A Example of simplified fault tree for a riverbank and dike revetment

«won auhrsloa

M >R

wavt ottack

X rtvthntnt

stitnglh

-rafi luit r#*thii#nt

tlip cirtlt

5*1

nLn ortock

fhickn*» rtvttmtnt

faitun sta dikt

Mttp wattri GCNERALLY:

|FAILURE[

w t r -topping

brtaeh LOAD > STRENGTH (S) IR)

inttrrwl troiion

«rosion inner slopt

*Tp'ptn«"

x m

liqut-fotrion

53E htod

, — I

ovtr-toppinq

M £ WQVt

OMtrtopping,

length grainsin

flood hraht

(ow t i l t

rabbi t-M M

WQVt run up

5zfc X dikthtight

slop*

5'"" bom hol»

_ — I l—' *—I

(lip crew

H rWlowl durarion

friction phrta plant

stttlcffltnt DonrtrucMor ntQnT

friction

guwtffy

X (ow tidt

tro*nn fort «hom

S>R

loost sent phrta, ptam

troswn fortthort

ë f ^ / v^ . ft^w faulMre» of o dike section

cumott pront non ttrtngtt)

F/g. 30 FAULT TREES FOR WATER DEFENCE STRUCTURES

- 63 -

5. DESIGN CONSIDERATIONS

5.1 General requirements for revetments

By definition, a revetment is a slope ptotection designed to pro-tect and stabilize a slope that may be subject to action by water currents and waves. To fulfil this function, the following aspects have to be taken under consideration in the design process: a) stability (toplayer, sublayer, subsoil, foundation). b) flexibility (e.g. following the settlement without influencing

the stability). c) durability (toplayer, asphalt, concrete, geotextile, cables,

etc.) . d) possibility of inspection of failure (monitoring of damage) . e) easy placement and repair (local damage). f) low cost (construction/maintenance). g) overall safety (primary or secondary defence, geometry of fore-

shore , etc .) . h) additional functional requirements, i.e. special measures for

reduction of run-up and/or roads for maintenance activities (berm requirements, etc,).

The best revetment is one which combines all these functions.

An essential part of the design of revetments, which as a rule can only fully be applied quantatively at this design stage, is the fault tree. This is a scheme in which the events and their consequ-ences or the errors and causes, which contribute to the probability of failure, are arranged in a clear way (fig. 30). Por some events in the fault tree it is not yet possible to calculate with mathema-tical models or to measure -in physical models or actual practice-the probability of occurrence. Then, a best guess based on engineering judgement has to be made. Whatever the origin of the probabi-lities, there are always many uncertainties. Therefore the probabi-listic calcülations should also be made for both optimistic and pessimistic sets of assumptions. Only in this way does it become possible to investigate the contribution of the probability of a potential failure to the probability of the "undesired top event" . If this contribution is significant then it becomes relevant to put more effort into making a "better guess" either by means of more engineering expertise or further research, in order to rule out this uncertainty by changing the design. This means that this tech-nique also provides a guideline for the selection of (additional) necessary research and, finally, for the proper selection and design of the final protective structure.(Fig. 31)

5.2 Dimensioning

Por revetments it is essential to distinguish the nature of the at-tack and the duration of time; short loading times and loadings with a long cycle time. To the fir'st category belongs the wave at-tack from wind- and ships waves; to the second category belongs the variation of the waterlevel caused by tidal- and seasonal influen-ces, which can induce ground water flows. The first type of load (wave impact) is of importance for all types of revetments, while the second type of load (slow variation in ground water flow and in phreatic-line) is of primarily importance for impermeable revetments only. The variation of the pressure due to the variation of phreatic-line can be determined using an electric analogue or a finite element calculation. The uplift pressure due to wave attack has to be de-

- 64 -

boundarv conditions

technicQl optimal alternative

finat design

I

|alternafive design I

____r__i (see to fhe left)

execution

Fig. 31 DESIGN OEVELOPMENT

65 -

termined mostly by model (or prototype) tests for each revetment type under consideration. Por permeable revetments on permeable sublayer the mathematical model "Steenzet", as developed in the Netherlands, can be used (9) .

Por the dimensions of the revetments the following (genetal) design criteria can be set out ( 26, 27 en 28) : 1. Sliding criteria: the revetment should be designed so that it

does not slide under frequently occurring loading situations. 2. Equilibrium criteria: the revetment including sublayers and sub-

soils must be in equilibrium as a whole. 3. Uplift criteria: in loading situations which occur rarely, such

as storm surges, the component of the weight of the revetment, normal to the dike face should be greater than the uplift pres-sure caused by water.

4. Surface-resistance criteria: the surface partiele of revetment should have enough resistance against wave and current attack.

The models selected to establish the dimensions of a structure will have to prove itself in practive to ensure that this represents the primary behaviour of the prototype, as well as to ensure that the used safety factor is sufficiënt to cover the secondary effects and inaccuracies in the used data and boundary conditions.

5.3 Choice of revetment

From the classification of revetments (see fig. 15) it is obvious that there are very many possible combinations that can lead to a large number of possible constructions. This does not simplify the choice of a revetment. Besides, the choice of the main revetment construction has its own repercussions for the transitions and the other parts of the dike, and the execution and maintenance method. To make a choice out of various and in a certain situation possible alternatives, criteria for judging need to be formulated (functio-nal , technical and financial) with the help of the demands that are made. Even the best design may fail as a result of poor workmanship and bad management. Thus, the aspects which are concerned with construction and with management and maintenance should also be invol-ved in this stage. Because all the various criteria have not been defined equally well and do not play an equally prominent part in the definite choice, subjective experiences and/or prejudice can be decisive.

It seems to be wise to make the choice in a group so that the sub jective aspect can play the least possible part. Por the different aspects weighing factors can be made so that a more objective choice might be possible. This problem is actually treated by a special working group in the Netherlands. Som e possible aspects and solutions that can play a part in the choice of the construction of the revetment will be mentioned, in a more or less arbitrary way below.

5.4 Composition of dike and revetment

Composition of the construction (profile, yes/no berm, etc.) is an important condition for the design of a revetment. On one side this can influence the division of the wave forces on a dike. On the other side this can restrict the freedom of design concerning the revetment. The choice of a berm yes of no can be of a great influence to the choice of the upper part of the slope. The hollow shape of a slope can increase the clenching forces (and so stability) of

- 66 -

geotextïle

Fig. 32 DESIGN PRINÜPLES

- 67 -

block revetments and at the same time decrease the follow-up of foundation-transformations. A high or a low foreshore can be deci-sive for the level of extending the rip-rap and the sort of under-layer and/or toe construction. Conclusion: the design of a slope revetment must be seen as an in-tegral part of the total dike-design. The design also needs to be made (executed) and maintained. Both aspects must therefore already be taken along within the stadium of designing.

j?r,inc_ip_le_s_oJ[ oinpc^s^t^oii

a) Stability of top layers strongly depend on the sort/composition of sublayers and they must therefore be regarded as a whole. As an example, from the large scale tests (9), (26) it appears that a block revetment on a sublayer of "good clay" provides more stability than one on a permeable sublayer (see also table 3 on stability of concrete revetments) .

b) Instability (erosion) of sublayers and/or subsoil can lead to failure of a toplayer. The stability of toplayers and sublayers must therefore be designed steadily (with an equal opportunity of failure) .

c) A good tuning of the permeability of the top layer and sublayers (including geotextiles) is an essential condition for an equal design. The permeability (k) of the different parts of the construction must increase from toe to top:k ground < k sublayer/ filter < k top-layer. This principle is illustrated in figure 32 for block revetments.

The granular filters are mostly more expensive and difficult to re-alize (especially under water) within the requirement limits (fig. 33). A substitutional solution is a geotextile filter function) with a certain thickness of graded stone layer (with function to dump the internal hydraulic loads). A good and cheaper solution can also be realized by applying a thick layer of broadly graded waste products as minestone, slags, silex, etc. (range 0.5 m for high hydraulic loads, compacted, composition according to criteria of internal stability (9)). The extend review on geotextiles can be found in (23) and (32).

5.5. Subsoil requirements (26),(27)

Subsoils as dike or bank body play an important role in the stability of revetments and in the total stability of protective struc-ture. Thus, the type and state of subsoil or dike body can be deci-sive for the choice of the revetment type. In this respect the fol-lowing aspects are important: - the bearing capacity of the dike/bank body determines among other

the performance of a revetment under wave and current attack. If - the bearing capacity is large than the thickness of the revetment can bè reducéd (especially for asphalt revetments). Of importance are the properties of the soil such as the modulus of elasticity, the bedding constant and Poissons' ratio. They themselves are in-fluenced by the degree of compacting.

- A high degree of compaction can, among others, avert the lique-faction of a saturated or almost saturated soil by impact loads, for example wave attack. A relative proctor density degree of 95-100%, down to a depth of about 2 m, can in sand reduce the possibility of liquefaction, in general, to an acceptable minimum .

- 68

GRANULAR FILTERS

FILTER RULES

GEOTEXTILES

THIN TYPES

WOVEN

NON-WOVEN

MULTILAYER TYPES

FILTER- AND

THICKNESS FUNCTION

COMPDSED FILTERS

GRANULAR LAYER

THICKNESS-DAMPING

FUNCTION

GEOTEXTILE

FILTER FUNCTION

Fig, 33 CHOICE OF FILTER/SUBLAYER

- 69 -

- The permeability of the sand bed is important in connection with groundwater flow in the dike body and, therefore, the occurring of uplift pressures under a relatively watertight revetments and the softening of the sand body.

- The compaction by vibration in a loosely packed saturated sand-body can cause a liquefact ion. The dry placing of an open asphalt mix on a satucated sand bed through the influx of water will re-sult in the early development of stripping. Under impermeable mixes, as asphalt concrete, uplift pressures can develop while the asphalt is still soft when placed on hydraulically filled sand bed. To obtain a good compaction the sand-body can be built up in this layers using bulldozers for compacting and for profi-ling of the dike face. It is also possible to dump an excess of material, and then, after this has been compacted (for example by a vibration roller) to make the required profile.

- After construction the dike body will tend to settle. If it has not been well compacted or if there are clay of peat layers in the subsoil, the settlement can be large and irregular. If the bed is at the same time badly permeable then it is possible that the grain stress only recovers slowly and that the bearing capa-city of the bed temporarily appears to be insufficiënt. This effect must certainly be taken into account with clayey subsoils; good drainage in this case is essential. With very permeable ma-terials the situation does not develop.

- Por placement of block revetments on clay subsoil (or sublayer) besides the requirement of right composition and homogenity, the proper compaction and smooth surface (blocks placed as close as possible to the clay surface) are of primarily importance (26). in the case of "poor clay" (concerning composition or surface preparation) it should be recommended to protect the clay surface with a geotextile.

- The use of open top layers directly on sand body (with geotextile in between) is restricted to wave height of Hs • 1.2 m. The good compaction of sand is essential to avoid sliding or even lique-faction. Por loads higher than Hs • 1.2 m a well graded layer of stone on a geotextile is recommendable (e.g.alayer 0.2-0.3 m for 1.2 m <HS<2.5 m)

5.6 Joints and transitions (21), (26), (27)

In general, slope protection of dike or bank consists of a number of structural parts such as: toe protection, main protection in the area of heavy wave and current attack, upper slope protection (very often grass-mat) , berm for run-up reduction or as maintenance road. Different materials and different execution principles are mostly applied for these specific parts (see, as example, dike construction in figure 7). Very often a new slope protection has to be connected to an already existing protective construction which in-volves another protective system. To obtain a homogeneous strong protection, all parts of protective structure has to be taken under consideration. Erosion or damage often starts at joints and transitions. Therefore, an important aspect of revetment construction, which requires special attention, are the joints and the transitions; joints onto the same material and onto other revetment materials, and transitions onto other structures or revetment parts,A general design guideline is that transitions should be avoided as' much as possible. If they are inevitable the discontinuities intro-duced should be minimized. This holds for differences in elastic and plastic behaviour and in the permeability or the sand tight-

- 70 -

concrete blocks

gravel

minestone

asphalt-concrete

dumped stone

penetration

A Penetration of sand info the mine-waste stone geofexfile bet ween sand and minestone /gravel is necessary

separation basalt b o a r d

columns

concrete blocks

penetration

B Transition from basalt columns f o concrete blocks separation board too short

Fig. 54 ILLUSTRATION OF TRANSITION PROBLEMS

- 71 -

ness. Proper execütion is essential in order to obtain satisfactory joints and transitions. When these guidelines are not foliowed the joints or transitions may influence loads in terms of forces due to differences in stiff-ness or settlement, migration of subsoil from one part to another (erosion) , or strong pressure gradients due to a concentrated ground water flow. Examples to illustrate the problem of transitions are given in fi-gures 34 and 35.

BASALT (traditional/old Dutch solution)

dumped stone (rubble)

^ - clay

^ c l o s e pile-row

geotextile

brick layers

rubble

PLACED BLOCKS

sea bottom

77777* geotextile

5-10cm gravel 5-20mm (broken stone)

spaced piles and wooden plank (board)

blocks with penetration

asphalt

concrete

geotextile

sand

\ - wooden sheetpile

F/g. 35 EXAMPLES OF TOE-PROTECTION

- 72 -

technical the modical check-up as alarmbell

prevention is better than

cure

- 73 -

6. MANAGEMENT AND MONITORING

Coastal zone management involves management and decision-makig re-garding: • a coastal ptotection plan, that is a coherent set of measures,

specified in time and space, to achieve a certain extend of pro-tection against existing or anticipated damage;

• a monitoring and control system (inspection system, measure-ments).

Coastal zone mana Firstly, an integ because of the in tion measures and integral approach ques are involved potential solutio land use planning modelling techniq is required becau adjacent coastal

gement is ch ral approach ter relations the daily m is required in the anal

ns, for exam , environmen ues , etc. Th se of the po sections.

aracterized by its integ to the coastal problems

hip between land use, co anagement and control. S since various disciplin

ysis of the coastal prob ple, coastal engineering tal science, mathematica irdly, a certain spatial tential physical interac

ral nature. is required

astal protec-econdly, an es and techni-lems and their , economics, 1 and physical integrat ion

tions between

In generating and analysing a coastal protection plan, the follo-wing steps can be distinguished: 1. definition of coastal sections; 2. creation of basic alternatives; 3. identification of coastal protection measures; 4. screening of measures, by section; 5. creation of alternative coastal protection plans; 6. impact assessment (full specification of all relevant effects); 7. evaluation (by the decision-makers).

Inform coasta ment ( ted wi networ To red sign s agenci A gene monito consis 1. ide

2 3

ide det by

4. cal 5. exe

ation 1 str u Fig. 3 th mon ks and uce th hould es wit rally r ing n ts of ntifie ntifie ermina the ne culati cution

about the ctures is 6). Coast itoring a ,/or speci e, often yield an h suffici applicabl etworks b the five ation and ation of tion of t twork; on of the of a cos

actu indi

al ma ctivi fic f high, optim ent i e met eing main quan

the r he ef

cost t- ef

al s spen nage ties ield cos al s nf or hod actu step tif i elev fect

tate sabl ment and sur

ts o yste raati for ally s : cati ant iven

of the coastal area including e for optimal coastal manage-, is therefore intimately connec-the design of routine monitoring

veys. f the monitoring system, its dein which provides the responsible on at minimal costs. the design and optimalization of developed in the Netherlands

on of the objectives; proces dynamics; ess of the information provided

s of the monitoring network; fectiveness analysis.

Based on the results of analyse done in the second step, the neces-sary instruments for monitorig can be defined. It will lead very often to development of the new types of monitoring-instruments.

A new philosophy in coastal monitoring involves the combination of mathematical simulation models and measurements. in this approach, which is similar to that applied in the control of industrial pro-cesses, the results of measurements are compared with the forecast of the mathematical model.

74

AIM FUNCTION

Lhrg

CRITERIA ••CONSTRUCTION

(tolerante)

i-Ut ~/\-

DESIGN

SUPERVISION EXECUTON

iquality contrd

±_1

CRITERIA -HMAINTENANCE

MANAGEMENT

rp

CONSTRUCT»* AS BUILT

briginal state!

INSPECTION MONITORING

ACTUAL STATE OF

tONSTRUCTION]

RESPONSE

MODEL

3

PREDICTION FUTURE

CHANGES

HAINTENANCE SCENARIO

lL BOUNOARY CONOITIONS (LOAOS)

F/g. 36A MANAGEMENT MODEL

- 75 -

The main activities on the subjects mentioned above are carried out by the Rijkswaterstat and the Technical Advisory Comittee on Water Defences in co-operation with the Centre for Civil Egineering, Research, Codes and Specifications, the Delft Hydraulics and the Delft Geotechnics (laboratories) , and some other organization.

.o m X) o

'J5 1

*=inspection

observation limit

(warning)

\ (minimum) acceptable Standard

time

Fig. 36B INSPECTION CRAPH

- 76 -

SEA-DIKES, BOUNDARY CONDITIONS

EXTERNAL LOAD INTERNAL LOAD

u J t

x BANKS

EXTERNAL LOAD

DESK STUDIES U y

MODELS

•*—(SCALE EFFECTS>

NATURE LARQE FLUME(S)

LARGE MODEL (S) NATURE

SEMI BLACK-BOX

F

i r

APPLICATIONS

ANALYTICAL SOLUTION

i MATHEM. MODEL(S)

i :

SEMI BLACK-BOX =1

APPLICATIONS

FILTERS/ SUBSOIL

VERIFICATION MODIFICATION MATERIAL

PROPERTIES

LONG TERM EFFECTS

FUNCTIONAL REQUIREMENTS

/ DESIGN RULES

CONSTRUCT./COSTS MAINTENANCE

Fig. 37 SEA-DIKES AND BANK PROTECTION RESEARCH RESEARCH APPROACH

- 77 -

7. CONCLUSIONS

The limitation of this report does not allow to prepare a fully (detailed) evaluation of the available Dutch data on the dike pro-tection. The problem is too wide and too complicated for that. How-ever , this brief evaluation seems to be sufficiënt for the designers and institutions involved in this problem to find a way to the detailed informations. The guidelines presented will bring designers closer to the solution of the typical problem of the design of dikes and the proper choice of revetments in respect to design hydraulic load, ability of materials and skill, and desired func-tion of constructionThe local conditions in respect to availability and price of manpower, materials and equipment will be decisive for the final choice of construction.

It has to be stressed that, whatever calculation method and protec-tive system is adapted, the (local) experience and sound engineering judgement play an important part in a proper design of protec-tive structures.

The research on dikes construction (sea and river dikes and other sea-r and bank-defence systems) is still going on in the Nether-lands. Research is now being directed towards a better probabilis-tic description of the design, better understanding of the failure mechanisms, application of new or alternative materials (e.g. waste products of industry: minestone, slags, etc.) ,monitoring of damage, economical aspects of design and optimal choice of constructions applied incorporating future maintenance aspects. All these aspects are being treated in accordance with the terms of the current research on bank and dike revetments (fig. 37).

Because of the worldwide interest and the complexity of. the proper design and management of the water defence systems the international cooperation in this field should be stimulated. It will not on-ly safe money, but it will increase the reliability of the design and in this way it may guarantee more safety for the population and the economical values to be protected all over the world.

- 78 -

REFERENCES

1. Bakker, W.T. and J.K. Vrijling (1980), Probabilistic design of sea defences. In: Proceedings 17th Coastal Engineering Conference, Volume III, chapter 124, Sydney.

2. Bezuijen, A, Klein Breteler, M and Pilarczyk, K.W. (1985), Large Scale tests on a block revetment placed on sand with a geotexti-le as separation layer , 3rd Int. Conf. on Geotextiles, Vienna, Austr ia.

3. Blaauw, H.G., De Groot, M.T. , Van der Knaap, P.C.M, and Pilarczyk, K.W. (1984), Design of bank protection of inland na-vigation fairways. Pilarczyk, K.W. (1984); Prototype tests of slope protection systems. Int. Conf. on Fleixible Armoured Revetments Incorp. Geotextiles, London, 1984. Published by Thomas Telford Ltd., 1985.

4. Boer, K, Den, Kenter, C.K. and Pilarczyk, K.W. (1983), Large scale model tests on placed blocks revetments, Coastal Structu-res 1983, Washington.

5. Construction Industry Research and Information Association (CIRIA, 1985), Reinforcement of steep grassed waterways, techni-cal note 120, London.

6. Delft Hydraulics Laboratory, Delft Soil Mechanics Laboratory (1983) Bitumarin B.V., Fixtone: Stability under wave attack, report M1942.

7. Delft Hydraulics Laboratory (1984), Stability of the grass-dike during superstorm (in Dutch), Report M 1980.

8. Delft Hydraulics Laboratory (1984), Resistance of grass on clay slopes, Report M 1930 (in Dutch).

9. Delft Hydraulics Laboratory, Delft Soil Mechanics Laboratory (1984), Slope protection by placed blocks, summary of results 1980-1984, report M 1725/M 1881 (in Dutch) (the final report will be published in 1988).

10. Delft Hydraulics Laboratory (1985), Stability of the Eastern Scheldt dikes under wave attack at the fixed water level , report M 2036.

11. Delft Hydraulics Laboratory (1985), Hydraulic design criteria for rockfill closuce of tidal gaps. Evaluation report M 1741.

12. Delft Hydraulics Laboratory (1987), Slope protection by loosely materials. Static and dynamic stability under wave attack. Serie reports under M 1983- research (in Dutch).

13. Graaff, van de (1983, Probabilistic design of dunes. In: Proceedings Coastal Structures 1983, Arlington, Virginia.

14. Hijum, E. van and Pilarczyk, K.W. (1982), Gravel beached: equi-librium profile and logshore transport of coarse material under regular and irregular wave attack, Delft Hydraulics Laboratory, Publ. no. 274.

15. Kaa, E.J;, v.d., De Groot, M.T., Hijum, E, van, Pilarczyk, K.W,, Stuip, J. and Verhey, H.J. (1985), Erosion control of navigation embankments, XXVI PIANC Congress, Brussels.

16. Mature, P.C. (1982), The development of the Dutch polder dikes, Keynots International Symposium "Polders of the World", Lelystad, the Netherlands.

17. Meer, J.W. van der, and Pilarczyk, K.W. (1984), Stability of rubble mound slopes under random wave attack, 19th International Conference on Coastal Engineering, Houston, D.H.L. Publ. no. 332 (see also Breakwaters 1985 Conference, October 1985, London), and D.H.L. Publ.no. 378, Febr. 1987).

18. Meer, J.W. van der, and Pilarczyk, K.W. (1986). Dynamic stability of breakwaters, rock slopes and gravel beaches, 20th International Conference on Coastal Engineering, Taipei.(Also, Delft Hydraulics Laboratory, Publ.no. 379, March 1987).

- 79 -

Pilarczyk, K.W. and Boer, K. den, (1983), Stability and profile development of coarse materials and their application in coastal engineering. International Conference on Coastal and Port Engineering in Developing Countries, Sri Lanka, D.H.L. public, no. 293 (see also "Gravel beaches: D.H.L. publ. no. 274, 1982). Pilarczyk, K.W. (1985), Stability of revetments under wave and current attack, 21st International Association for Hydraulic Research Congress (IAHR), Helbourne. Pilarczyk, K.W. (1986), Design aspects of block revetments. Post-graduate course on bank and dike protection. Delft Univer-sity of Technology, Civil Engineering Department (PATO), Delft, the Netherlands. Pilarczyk, K.W., Misdorp, R. , Lewis, R.J. and Visser, J (1986), Strategy to erosion control of Dutch estuaries, 3rd Int. Symposium on River Sedimentation, Jackson, Mississippi. Permanent International Association of Navigation Congresses (PIANC, 1986), Guidelines for the design and construction of flexible revetments incorporated geotextiles for inland water-ways. Report of a working group of the Permanent Technical Com-mittee 1 (be published in 1987).

(1984), Flexible armoured revetments incorporated geotextiles. Proceedings of the International Conference organised by the Institution of Civil Engineers, London, March 1984 (published by Thomas Telford Ltd., London 1985).

(1984), The Closure of Tidal Basins, Delft University Press, the Netherlands.

(1984), Guide to concrete dike revetments, Netherlands Committee for Research, Codes and Specifications for concrete and Technical Advisory Committee on water defences. Report 119, 1984 (in Dutch; English translation available).

(1985), The use of asphalt in hydraulic engineering. Technical advisory Committee on water defences/Rijkswa-terstaat. Rijkswaterstaat Communications, no. 37, 1985, The Hague.

(1985), Guide for design of river dikes. Part I: Opperriver-reaches. Technical Advisory Committee on water defences, The Hague, 1985, Governmental Publication Office (in Dutch).

(1984), Guide to the judgement of the safety of dunes as a sea defence system. Technical Advisory Committee on water defences (TAW), Staatsuitgeverij, The Hague, the Netherlands (in Dutch).

(1986), Manual on Artificial Beach Nourish-ment, Rijkswaterstaat, Centre for Civil Engineering Research, Codes and Specifications, Delft Hydraulics Laboratory, the Netherlands.

(1985), Probabilistic design of sea defences, Technical Advisory Committee on water defences. Internal report TAW 10 (in Dutch), the Netherlands. Veldhuijzen van Zanten, R, Editor (1986), Geotextiles and Geo-membranes in Civil Engineering (Handbook). A.A. Balkema, Rotterdam/Boston . Vellinga, P (1983), Predictive computational model for beach and dune erosion during storm surges. In: Proceedings Coastal Struc-tures 1983, Arlington, Virginia. Vellinga, P (1986), Beach and dune erosion during storm surges, Doctor thesis, Delft university of Techn., Civil Eng. Department, Delft, the Netherlands.(Also DHL Publ.no.372 Dec. 1986). Vrijling, J.K. (1985), Probabilistic Design of Waterretaining Structures, in the Proceedings of the NATO Advanced Study Institute: Conference on the Engineering Reliability and Risk in Water Resources, Tucson, Arizona, U.S.A.

- 80 -

APPENDIX I

DESIGN CRITERIA FOR

PLACED BLOCK REVETMENTS AND

GRANULAR FILTERS

by

A. Bezuijen , Delft Geotechnics M. Klein Breteler, Delft Hydraulics K.J. Bakker , Rijkswaterstaat, Hydraulic Eng. Div

DESIGN CRITERIA FOR PLACED BLOCK REVETMEMTS AND GRANULAR FILTERS

by

A. Bezuijen, Delft Geotechnics, The Netherlands M. Klein Breteler, Delft Hydraulica, The Netherlands K.J. Bakker, Public Works Department (Rijkswaterstaat), The Netherlands

ABSTRACT

Design criteria for the coverlayer and filter layer of a placed block revetment are presented. These design criteria were derived on the basis of large scale model tests on revetments and tests on granular filters. It is shown that the hydraulic loading in the filter layer can be described with equations of quasi-stationary flow. General filter criteria are developed on the basis of the similarity between flow in channels and flow in the pores of a filter.

1 . INTRODUCTION

In several areas of the world the land has to be protected against the sea by dikes. These dikes themselves must be protected against wave action by a revetment. The design of the revetment was formerly based on tradition and experience. For the Deltaplan, however, the Dutch Department of Public Works (Rijkswaterstaat) has the task of guaranteeing safety of dikes in conditions that are outside our experience. Therefore fundamental knowledge of revetment failure mechanisms is essential. To acquire the knowledge necessary for the design of placed block revetments the Dutch Department of Public Works commissioned Delft Hydraulics and Delft Geotechnics to carry out a research project on the stability of this type of revetments. Large scale model tests and detailed tests have been performed in this research project, the latter to investigate individual failure measurements in detail. In addition to these tests analytical and numerical models have been developed to determine the pore pressure response under the coverlayer when it is subjected to waves. This research programme has increased the qualitative and quantitative knowledge about possible failure mechanisms in a placed block revetment. The results will be used to assess the safety of existing revetments in the Netherlands and also for the design of new revetments. The results will be especially useful when a revetment has to be built with local materials for which there is llttle experience. This paper describes the theoretically based steps in the design procedure for placed block revetments: the calculation of the uplift pressures below the coverlayer and the hydraulic gradients in the sublayers and subsoil. The uplift pressures are compared wi-th the strength of the coverlayer against lifting and the hydraulic gradients with the strength of the subsoil against filter erosion. These steps are not the only steps in revetment design. The geotechnical stability of the structure is also important and there must be no possibility that the sublayer can be washed out through the coverlayer. These geotechnical steps have been studied in the research programme [1, 2], but are not discussed in this paper. The design steps are closely inter-related. The hydraulic loads on the coverlayer, the filter layer (the granular sublayer directly below the coverlayer) and subsoil are described in Chapter 2. The loads on the coverlayer are used to evaluate its stability. This is discussed in Chapter 3. Information about the hydraulic loads in filter layers and the subsoil can be used to design a filter which is not sand tight according to geometrie rules, but which will be stable for the hydraulic loads

- 1 -

expected. In order to design such a filter, using less stringent filter rules, it was necessary to obtain more detailed information on the strength of non-geometrical granular filters. How this knowledge was gained, is dealt with in Chapter 4.

2. HYDRAULIC LOADS

2.1 Loads which can contribute to failure

Wave attack on a revetment is a complicated process. In this paper we focus on a type of block revetment frequently used in the Netherlands, see Figure 1. This type of revetment comprises blocks placed on a filter layer of gravel or minestone laid on the subsoil. There are only small joints between the blocks.

phreatic line

Figure 1: Placed block revetment with granular filter layer

This type of revetment may be subjected to the following types of hydraulic loads: - shear forces on the coverlayer caused by wave run-up and run-down on the

revetment surface - dynamic pressure forces caused by wave impact - quasi-stationary pressure forces on the coverlayer caused by the difference between the pore pressures in the filter layer and the wave pressures on the revetment

- shear forces on the grains of the subsoil due to water movement in the filter layer.

The shear forces on the coverlayer are a dominant type of hydraulic loading on breakwaters. For placed block revetments, however, this type of loading can be neglected. This is because of the great strength of the coverlayer parallel to the slope. The loading forces in this direction are unimportant. In fact, the forces perpendicular to the revetment surface are decisive for coverlayer stability.

Although the wave impact is the most visually impressive loading, it is not necessarily the most dangerous. The duration of wave impact loading is generally less than a second (0.1 to 0.4 s) and to move a block more than just a few millimeters out of the revetment in such a short period would require enormous acceleration forces. In addition the force caused by the wave impact is transferred inside the revetment and only the considerably damped reaction forces, generated by the impact and transferred in the opposite direction can damage the revetment.

- 2 -

The two hydraulic loads last mentioned are of major importance when analysing the stability of the revetment: - quasi-stationary pressure differences which result In uplift pressures that

can exist long enough to lift blocks out of the revetment, and - shear forces on the grains of the subsoil due to water flow in the filter

layer which can cause filter erosion.

The knowledge that quasi-stationary phenomena are dominant simplifies the description of the hydraulic loads on a revetment due to wave attack considerably. The pore pressure distribution in the filter layer, necessary for the calculation of uplift pressures and the water velocities in the filter layer, can be described with a quasi-stationary flow model which is governed by the equation:

V'kV$ = 0 (1)

where: <J> : the potential piezometric head k : the permeability

Cm] [m/s]

For the type of revetment shown in Figure 1, the permeability of the filter layer is often much larger than the permeability of the subsoil which can therefore be neglected. In most structures the pore pressure distribution will be dominated by the flow in the filter layer which is parallel to the slope. In this situation the mean potential (<j>) can be derived using:

<(> - l/b <j> dx (2)

with: b : the thickness of the filter layer Cm]

Equation (1) then simplifies to;

d20 4>-<j),

dzz

where: z the vertical axis the potential on the surface of the revetment the mean potential in the filter layer the leakage factor

Cm] Cm] Cm] Cm]

(3)

The leakage factor is defined as:

\ - sina /(bDk/k') (4)

where: et

b D k' k

the slope of the revetment the thickness of the filter layer the thickness of the coverlayer the permeability of the coverlayer the permeability of the filter layer

C-] Cm] Cm] Cm/s] Cm/s]

Solutions for Equation (3) are presented in the following sections. A numerical solution is presented in Section 2.2, the results of which are confirmed by comparison with results of large scale model tests. An analytical solution is presented in Section 2.3, which can be usefully applied in the design of a revetment.

- 3 -

2.2 Numerical calculations

Equation (3) can be solved using discretisation (see Figure 2).

a rather simple finite difference

Figure 2: Finite difference discretisation used in the STEENZET/1 program

Near a joint in the coverlayer the flow to the joint raust be equal to the flow from the joint plus the flow through the joint. This leads to the following equation:

<J>. 1 • k b D

, ^ kbD 1 + 2FÏ7 <ïïïï7K-i+*i + i)

+ * t , i> (5)

where: <>. : the potential in the filter layer near joint i <j> . : the potential on the revetment near joint i L ' : the length of the blocks

For the other parameters, See Equations (2) and (H)

Cm] Em] Cm]

With some modifications for the highest and lowest joint in the revetment and at any phreatic surface, Equation (5) can be used for every joint in the revetment. In the computer programme STEENZET/1 this set of equations is solved iteratively in order to take into account turbulent flow. A turbulent flow description is used for the joints of the revetment, whereas a linear description is used for the filter layer. If turbulent flow is expected in the filter layer, the permeability at mean hydraulic gradiënt is used. In order to solve the pressure distribution, or potential, in the filter layer with STEENZET/1, it is necessary to know the permeabilities of the coverlayer and the filter layer and the pressure distribution generated by wave attack on the surface of the coverlayer. In the research programme mentioned above permeability experiments have been performed to determine the permeability of coverlayer and filter layer. These experiments have led to permeability formulas described in [8]. To date an adequate description of the time-dependent pressure distribution on the coverlayer (the wave pressures) has not been made. Data recorded in model tests have been used, in the numerical calculations. These model tests were performed at scales of 1:1 or 1:2 in the Delta Flume of Delft Hydraulics and made it possible to test the validity of the numerical model. The pore pressure response calculated, using the wave pressures and permeabilities measured in the model, has been compared with the pore pressure measured in the model. A result of such a pore pressure response simulation is presented in Figure 3.

i

_ H -

A best fit calculation is also presented in addition to a calculation with measured values of the permeabilities. The best fit result gives an indication of the uncertainty in the determination of the permeabilities and of the accuracy of the numerical model for describing the measured phenomena. From Figure 3 it can be concluded that this accuracy is good for this type of revetment. In a structure without a filter layer a different model has to be used [33. Such a model, STEENZET/2, has been developed and is described in [4].

1-1

0

-1

-2 pressure [kN/m2]

— measured ---calculated k' = 0.01 m/s

best fit k' = 0.02 m/s

Hj = 0.3m K =0,1 m/s 5 =2.41

7800 78 45 78.90 7 9 3 5 7^80 8 0 2 5 8070 8115 81.60 Q 2 0 5 82 50

time [si

Figure 3: Measured and calculated pore pressure response f indicates the point where measured and calculated pressures are compared

008

0.04-

- 0.04- -

-0.08-:

Figure kt Calculated hydraulic gradiënt at maximum uplift pressures on the revetment

- 5 -

From the pore pressure distribution in the filter layer it is easy to calculate the hydraulic gradiënt and the local filter velocity. The result of such a calculation, the hydraulic gradiënt in the filter layer at the time of maximum uplift pressure, is presented in Figure H together with the uplift pressures over the coverlayer at that moment.

2.3 Analytical oaloulations

Although the numerical calculations showed the validity of the calculation model, the model can be too complicated to apply in the early stages of the design. As an alternative analytical solutions are also possible if a linear relationship between filter velocity and hydraulic gradiënt is assumed and if wave pressures on the revetment are schematized. In this type of solution the leakage factor U ) is an important parameter. The solution derived by Wolsink [5] gives a good indication of the maximum uplift pressure that can be expected on a coverlayer loaded by wind waves. Using the schematisation shown in Figure 5 and some simplifications in the description of the pore pressures near the hydraulic surface the following formula for the maximum difference in potential ($_ ) has been derived:

max

A<t> max

where:

X H

2tana tanB (1 - exp(-tana tanB -y).)+ ~] [ 1 - exp(-2z,/A)] :6)

Hb a 6

the position of the phreatic surface wave height the slope of the revetment the angle of the wave (see Figure 5)

Cm] Cm] [°]

A graphical presentation of Equation (6) is also shown in Figure 5 for Zj - Hv

ï ï l i 6 i è » 10 Hb/X

Figure 5:- Results obtained with the 'Wolsink' solution and the schematization used

A long leakage factor X and a small value 'of 6 will result in high uplift pressures. In [6] it is shown that the schematization of the wave pressures, as presented in Figure 5 is relatively accurate at the moment of maximum run down when the maximum uplift pressures are expected. Values of between 20 and 60 degrees were found for the angle B.

- 6 -

The maximum negative hydraulic gradiënt in the filter layer is reached if there is no pressure building up under the coverlayer. In this situation the potential in the filter layer in each pöint is equal to the position of that point. The maximum negative hydraulic gradiënt is therefore determined by the slopeof the revetment. It can never be less than the value -sinci. Normally the slope of a revetment varies between 1:2 and 1:7 and the maximum negative hydraulic gradiënt possible between 0.4H and 0.14. The hydraulic gradiënt present in the filter layer is often even less, see Figure 4. This means that in most cases the maximum negative hydraulic gradiënt is so small that it is not necessary to apply geometrie filter criteria. Less stringent hydraulic criteria, which can be used, are presented in Chapter H.

3. DESIGN CRITERIA FOR THE COVERLAYER

After the uplift pressures have been calculated the stability of the coverlayer can be calculated provided that a strength criterion for it is known. In an early stage of our research project a simple stability criterion was suggested: the uplift pressure should never exceed the underwater weight of the blocks per square metre. With such a criterion Equation (6) becomes very useful. Analysis of the stability of various revetments built in the Netherlands indicates that these do not in fact meet this stability criterion for storm conditions which frequently occur. In spite of this the stability of these revetments has been quite satisfactory in these conditions. This stability has probably been due to friction and clamping forces. Friction and clamping forces between the blocks lead to increased coverlayer strength; the clamping forces especially, however, can rarely be quantified and it is always possible that they do not occur between all blocks. Occasionally a block is not clamped between its neighbours, but simply lies in the revetment. When analysing the stability of a coverlayer the clamped blocks are unimportant since the stability is determined by the incidental presence of loose blocks.

The stability of a loose block is determined by its weight, the friction force, but also by the duration of the pressure difference and probably also by the fact that water has to flow out of the filter layer to 'push' the block out of the revetment. More experimental evidence is needed, about the latter aspect. To date the stability of a loose block in a block revetment has been analysed analytically using Equation (3) and stability factors which depend on the mass of the block, the friction force etc, [93. A more detailed numerical analysis is, however, possible with special versions of STEENZET/1 which includes the calculation of the block movement and acceleration forces if uplift pressures exceed the pressure corresponding to the weight of the block [7]. A result of such a stability calculation, in which a maximum block movement of 1.5 cm was allowed is presented in Figure 6 and compared with the results of a large scale model test. The stability is presented as a dimensionless parameter H/AD against 5, the surf similarity parameter. Where H is the incoming wave height, A the relative density of the blocks ((p -p)/p) and D the thickness of the blocks. From Figure 6 it is clear that the measured stability is higher than the calculated value. This higher measured value is due to the difference between the failure criterion used in the model and that used in the calculations and the fact that there is clamping between the blocks in the model tests. It should be noted that the scatter in the calculated values of H/AD is much larger for the shorter leakage factor. In. this situation the stability is determined by the local steepness of the measured wave pressures at run down which varies more than the general wave pressure distribution on the revetment, a factor which is decisive for the stability of a revetment with a long leakage factor. The drawn Unes give the minimum stability calculated. This minimum is important in the design of a revetment.

- 7 -

4 -

3 -

2-JH_ AD *©.

x calculQted X = 0.19m

• cülculated X = 0 32 m

© measured X estimated O 3m

©

-+•

10 15 20 25 30 35 40

Figure 6: Stability calculations for a loose block in a block revetraent

U. DESIGN CRITERIA FOR GRANULAR FILTERS

4.1 Theoretlcal background

Instability of a placed block revetment can be caused by several failure mechanisms, such as uplift of the coverlayer, dealt with in Chapter 3, or unacceptable erosion of the base material under the filter layer. The latter causes deformation of the coverlayer, leading to the loss of the regular pattern of the blocks which decreases the stability enormously. For this reason investigations on filter stability have been included in our research program on placed block revetments. Granular filters have a much wider field of application than placed block revetments. They are used in bed protection, offshore structures, rubble mound breakwaters, in front of seawalls, etc. The results, presented in this chapter, refer specially to granular filters between a block revetraent coverlayer and the core (sand) of a dike or bank protection, but are applicable to any granular filter.

As occurs in an open channel, the base material will only be set into motion if the current near the interface is sufficiently large. This means that if the hydraulic gradiënt in the filter is sufficiently small, no erosion will take place, even if the pores in the filter are much bigger than the grains of the base material. However, if the pores are smaller than the grains of the base material then no erosion can ever ocour, even at an unrealistically high hydraulic gradiënt.

Conventional design criteria geometrical condition that the base material grains. This "geometrically sand tight" gran conventional design criterion filter material have to be used An advantage of the convent knowledge of the loading condit filter.

for granular filters rely completely on the pores of the filter have to be smaller than the criterion leads to what is referred to as a ular filter. An uneconomic consequence of this

is that in many applications several layers of to guarantee sand tightness. ional design criterion, however, is that no ion is necessary in order to design a granular

- 8 -

Since in many cases, such as block revetments, Information about the loading conditions is available, more economie design criteria can be applied which take into account this information. In Chapter 2 it is shown that the maximum gradiënt in the filter layer (directed downward along the slope) is never larger than sina. Model tests have been carried out on filters which in fact demonstrate that in this situation, conventional design criteria are too stringent, see for example [15] and C U ] , A filter which is not geonetrically sand tight can still perform satisfactorily up to a certain filter velocity (and accompanying pressure gradiënt in the filter). The basic assumption behind the design criteria proposed here is that the flow in the pores of a filter is similar to the flow in channels, even at the threshold of sediment transport. It is assumed that, given a granular filter with pores much wider than the grains in the base layer, the critical shear over the sand interface is equal to the critical shear in a channel with the same bed material. The threshold of sediment motion in open channels has been investigated very thoroughly by various scientists in the past. Shields [10] for example, found the following (empirical) formula for the critical shear:

er

with:

i|> Ag D

. er

b50

b50 v

critical shear Shields parameter relative density of sand grains (p -p)/p gravity grain size corresponding to 50% by weight of finer particles mass density of water mass density of sand

(7)

[N/ma] [-] (-) [m/s2]

Cm] [kg/m3] [kg/m3]

The Shields parameter \|> was determined empirically by Shields and depends, among other things, on thesgrain size and specific weight of the base material. i|> is plotted against D 5Q in Figure 7. The figure is derived6for a sand bed wfth relative density A » T?55 and for a water viscosity v - 10 m2/s.

By introducing the shear velocity, v, - /(x/p), Equation (7) can be rearranged as follows:

*cr /(*s A* W (8)

An equation for the critical filter velocity in a granular filter v„ can be derived from Equation (8), assuming a simple v„/v ratio:

v , • n v - n/e /(\D Ag DHt.n) f er per s ° b50

with: n e v per

porosity of filter coëfficiënt - v*/v

D

critical pore velocity

0.1

4>s

0.05

;0.03

z ^ _ ^ ^

0.15 0.3 0.5 1 2

Db50

5|mm]10

Figure 7: Shields parameter

(9)

[-]• [-] [m/s]

The coëfficiënt e takes into account the differences between granular filters and open channels, for example, the fact that the current distribution in the pores of the filter near the interface is different from that in an open channel. In case of a filter there is hardly any development of a boundary layer at the interface due to the irregular flow area between the grains. Consequently the shear velocity is bigger than at the bottom of an open

- 9 -

channel. The magnitude of the coëfficiënt e has been de.termined empirically. This is discussed in Section M.2.

Equation (9) is derived for stationary flow parallel to a horizontal interface. The influence of oscillatory flow can be estimated by considering an open channel. The threshold of sediment motion in an open channel is usually encountered at a smaller velocity amplitude with oscillatory flow than with stationary flow. This is because there is no time for a boundary layer or an ordinary velocity distribution to develop during each wave period, which causes a higher shear velocity. With filters however, since there is no development of a boundary layer or of an ordinary velocity distribution with either stationary or oscillatory flow, it is expected that the critical filter velocity amplitude with oscillatory flow will be equal to the critical filter velocity with stationary flow.

A formula describing the influence of a sloping interface and a perpendicular gradiënt component, can be derived as follows, assuming that* at threshold of sediment motion, there is an equilibrium of three forces [11], see Figure 8.

Fj_ : perpendicular force assumed to be induced by the perpendicular gradiënt component ij_ [N]

F : parallel force induced by the flow parallel P to the interface [N] F : gravitational force [N] o

Figure 8

F + F since P g

F cosa + Fi g x

tan<)>, the coëfficiënt of friction

with: <j> : natural angle of repose of single grains of the base material

a : slope angle C°3 [°-]

(10)

er

The influence of the sloping interface is represented by the force ratio (F /F ) relative to this force ratio at o. - 0 and ij_ - 0. It is assumed to be eqBal8to the critical shear stress T relative to the critical shear stress at a - 0 and ij_ - 0:

T F /F or p g

Since T - p vj, Equations (10) and (11) can be used to derive the following equation which describes the influence of the sloping interface and the perpendicular gradiënt component:

(11)

*cr rvT~!

*cr

A-sin(<J> - a)

sin<f>

F.

g

(12)

in which: [v* ] 0 - critical shear velocity at a - 0 and i - 0. *cr j_

A first order approximat'ion for the quotiënt Fj/F can be given by using Equation (13) which describes the critical vertical gradiënt for fluidization [12]:

Ml "b>

with: if = the critical vertical gradiënt for fluidization n£ = porosity of the base tnaterial

[-] [-3

(13)

- 10 -

For the situation with a horizontal interface the critical filter velocity is zero if if « ij_. With this fact, and Equations (8), (9) and (12) the following formula has been derived:

vfcr " n / e *^*g A g Db50(sln(<(> " a ) / s i n* " ly^d - nb))) (11)

This r'esult is compared with results of model investigations in Section 1.2.

1.2 Model investigations

Model investigations have been performed on various filters under different loading conditions to measure the critical hydraulic gradiënt and filter velocity. The critical filter velocity, v. , is the maximum velocity in the filter at which the sediment motion is such tnat the stability of the total structure is not yet in danger. This appears, in fact, to be comparable to the criterion used by Shields.

The investigations with stationary flow were performed in the Delft Hydraulics Filter-box. As an example, the test set-up with a sloping interface is shown schematically in Figure 9.

The hydraulic gradiënt was increased step by step until considerable erosion took place. A test was completed without interruption. During each step the hydraulic gradiënt was kept constant for at least half an hour, after which the transported sand was collected and dried. Sand transport of 0.2 gr/s/m of dry sand was considered to bè critical. The tests were performed using sand with steep sieve curves and which were well compacted, with an estimated porosity of approximately 10*.

Figure 9: Delft Hydraulics Filter-box test set-up

Some of the results of the model investigations using a horizontal interface and stationary flow are presented in Figure 10.

MEASUREO:

A Db50= -82mm

o Db50= .16mm

V 0550= .K)mm

CALCULATEO:

30 AO 50 70 90 —-'

stationary flow parallel to a horizontal

The values for the coëfficiënt e determined empirically from Figure 10, were

Figure 10: Filter-box tests interface.

- 11 -

if 0.1 < if 0.7 <

b50 b50

< 0.2 mm: < 1 mm:

e e

0.75 Re 0.22

•0.2' (15)

The Reynolds number Re is shown to be related to the filter grain size as follows:

Re vf Df15 / v

A dependency of the Reynolds-number Re for small values of Dh_n could be From measurements of Brauns expected from a theoretical point of view [13].

[14] it can be concluded that for 0.2 < D. calculated by a linear interpolation. b50 < 0.7 the value of e can be

Tests on sloping interfaces were performed to test Equation (1*1). Two tests were performed with fine base material (D.50 - 0.15 mm) with cota - 3 and -3. Both tests resulted in the same value for the natural angle of repose $, which confirms the validity of Equation (14) for 1_L * 0. The results are shown in Figure 11, together with the results of Fernandez-Lugue 4 v.Beek [11], who performed tests on a sand bottom in a pipe.

80

60

40

20

1

4>

>

[°]

Db50

•—- r T T " r " — • • ' 1 — 1 1 , ; • ' ; : i : ; i . , ,

1 j 1 , T H ! " " ^ -0-! !

i 1 ; i 1 1

Immjl -<

T

1 i

: j MEASURE0 i j ' 0 cot(a)= 3

1 j 1 i • co t (a )= -3

r * ) ! V [111 .2 .3 .4 .5 .7 1 1.5 2

Figure 11: Stat. flow along a sloping interface

The test results which show the influence of the vertical gradiënt component are presented in Fig. 12. The critical horizontal gradiënt component for l± * 0 is given relative to the critical horizontal gradiënt at ij_ - 0. Gradients are used here because filter velocities were not measured in most of the tests. The calculated values of the critical hydraulic gradiënt given in Fig. 12 have been calculated from v, using the permeability law of Forchheimer [14].

The coefficients of the permeability law were adjusted in such a way that the inaccuracy of these coefficients did not affect the aocuracy of i .

er 1.2

1.0

.8

.6

.4

.2

ST«*

f

1

ie r_

ro

! 0

0 |o O !

1 ^ ? ! 1 i 1 1

i 1 1 »x l -1

|

0 !

•

0

.

o > » MEASURED

E v E CALCULATED

o Df 15 = 1.5 mm 0b50= .15mm

• Df 15 = 3.3 mm

t>Dfl5=10.5mm Db50= 82mm

0 .2 .4 .6 .8 1.0

Figure 12: Stationary flow with vertical gradiënt component.

- 12 -

Frotn the figures it is clear that the calculated results are in good agreement with the measured values, except for the tests with a vertical gradiënt component. From the large variance in the measured values shown in Figure 12 one oan conclude that there are influences which are not yet completely understood. Nevertheless Equations (14) and (15) can be used for design purposes, since they give a safe approximation. The tests with cyclic flow and with a oombination of cyclic and stationary flow were performed in the Delft Hydraulics pulsating water tunnel. The test set-up and test results are shown in Figures 13 and 14.

TUNNEL ROOF 3

BALLAST LASER-DOPPLER VELOCITY METER

-PRESSURE CELL lm

to pulsating

piston

-TUNNEL BOTTOM

Figure 13: Vertical cross section of Pulsating water tunnel.

The tests were performed with a wave period of 2 sec, which is relatively small compared with wave periods experienced on dikes and bank protection. From the results of the measurements it is clear that the critical filter velocity amplitude for cyclic flow is equal to the critical filter velocity for stationary flow, even for this small wave period.

Finally the formulas have been verified successfully by model investigations carried out at a prototype scale in a wave flume.

50 Imm/s

O)

30

20 CYCLIC COMPONENT

10

vfcr i

\ ! \

"ö"Db50= .16,Dfi5 = 3.8mm

T ° b 5 0 = - 8 2 ; D f 1 5 = 20mm

oA MEASURED

— CALCULATED

vf

0 10 20 30 401mm/s] STATIONARY COMPONENT

Figure 14: Results from measurements with non-stationary flow

4.3 Discussion of results

From the previous sections it can be concluded that the calculated critical filter velocity agrees with the measured values. From the fact that the measured trends correspond very well with the trends calculated for the critical filter velocities, it can be concluded that the theory is correct. The coëfficiënt e is fitted to the measurements, which results in a useful formula. The present investigation was basically different from most previous work in this field, which was aimed directly at a description of the critical hydraulic gradiënt. Most of earlier work did not investigate the basic causes of erosion, which are the velocity and accompanying shear stress between the pores of the

- 13 -

filter near the interface. This led to the need to solve two problems at the same time: an equation for the critical filter velocity and a permeability equation. By aiming in the present investigation at the critical filter velocity only, it has been possible to compare the erosion in granular filters with the erosion in open channels, which simplified the investigation.

A design diagram for practical use is given in Figure 15. One can start in this diagram, for example, at a certain characteristic grain size of the filter (here 3.8 mm for a base material of 0.15 mm) and find the critical hydraulic gradiënt (here 0.2) via the filter porosity, 0.35, and slope angle, coto - 4, as is indicated by the broken line (example) or one can start at a desired critical gradiënt and find the necessary filter characteristics. The diagram is based on Equations (14) and (15) and the Forchheimer permeability law [11].

Figure 15: Design diagram

5. CONCLUSIONS

In this paper it has been shown, that in order to analyse the strength and stability of placed block revetments it is not sufficiënt to look at the external hydraulic loads alone. It is also necessary to analyse the internal water flow underneath the coverlayer of the revetment. This analysis can be made successfully using the model techniques employed when analysing groundwater flow. For placed block revetments on a granular filter especially it appears to be possible to derive simple analytical solutions for the potential distribution in the filter. Comparison with the results of the model tests and more detailed numerical solutions has shown that the method is accurate for calculating the maximum uplift pressures. Depending on the strength criterion against uplifting for a loose block, it is possible to evaluate the stability. Concerning the filter stability, it seems that for this type of structure the hydraulic gradients are relatively low, and so an approach based on geometrically sand tight filter criteria will be too strict. Using an approach in which the hydraulic load is taken into account gives a much less stringent criterion enabling perhaps local material to be used instead of other materials at high costs. The also presented hydrodynamic solution for filter stability, based on the analogy between filter flow near an interface and channel-flow, in which the slope angle and perpendicular gradiënt are taken into account leads to less stringent filter criteria.

- 14 -

REFERENCES

[I] Hoogeveen, R., Analytical solutions for judging the geotechnical stability of block

- revetments (in Dutch). Delft Geotechnics, Report CO-286010/4, 1986.

[2] Klein Breteler, M., Washing of filter grains through the coverlayer (in Dutch). Delft Hydraulios, Report M1881-16B, 1985.

[3] Bezuijen, A., Klein Breteler, M., Pilarczyk, K.W., Large scale model tests on a block revetment placed on sand with a geotextile as separation layer. Proc. Illrd Int. Conf. on Geotextiles, Vienna, 1986.

[4] Hjortnaes-Pedersen, A.G.I., Bezuijen, A., Best, H., Non-stationary flow using the Finite Element Method. Proc. 9th Int. Eur. Conf. on Geotechnics and Foundation Engineering, 1987.

[5] Placed block revetments, research 1980-198*1, Summary report (in Dutch). Delft Hydraulics/Delft Geotechnics, Report M1881/ XIV, CO-272500/7, 1984

[6] Duits, E. te, Sensitivity analysis (in Dutch). Delft Geotechnics Report CO-276920/5, 1986.

[7] Hoogeveen, R., Bezuijen, A., Design charts with STEENZET/1 (in Dutch). Delft Geotechnics Report CO-28570/7, 1987.

[8] Klein Breteler, M., Permeability of the coverlayer (in Dutch). Delft Hydraulics Report M1881/hl95.07, 1986.

[9] Klein Breteler, M., Coverlayer stability without clamping or interlocking. Delft Hydraulics Report M1881-04, 1986.

[10] Paintal, A.S., Concept of critical shear stress in loose boundary open channels. Journal of Hydraulic Research 9 (197D, No. 1.

[II] Fernandez Luque R., Beek, R. van, Erosion and transport of bed-load sediment. Journal of Hydraulic Research 14 (1976), No. 2.

[12] Graauw, A. de, Storm surge barrier Oosterschelde; Stability of granular filters for stationary gradients (in Dutch). Delft Hydraulics. Report M 1488, Volume 1, February 1982.

[13] Koenders, M.A., Hydraulic Criteria for filters, internal report. Estuary Physics, 1985.

[14] Brauns, J., Critical hydraulic gradiënt for filters with horizontal flow (in German). Wasserwirtschaft 10/85, October 1985.

[15] Graauw, A." de, Meulen, T. van der, Does de Bye, M. v.d., Design criteria for granular filters. Delft Hydraulics, Publication No. 287, January 1983.

- 15 -

APPENDIX II

PROBABILISTIC DESIGN OP

WATERRETAINING STRUCTURES

by

J.K. Vrijling Rijkswaterstaat, Locks and Weirs Division

ENGINEERING RBLIABILITY AND RISK

IN WATER RESOURCES

L. Ouckstein and E.J. Plate, Eds.

Martinus Nijhoff, Dordrecht,

The Netherlands

1986

- 1 -

PROBABILISTIC DESIGN OF WATBRRJ5TAINING STRÜCTORJBS

drs. ir. J.K. Vrijlinq

ABSTRACT

Water retaining structures are designed to keep the water in

the basin and out of habitated areas.

The rich tradition in the field of dikes in Holland as well

as the history of dam disasters shows that complete safety

is unattainable.

Realizing this, a method to assess the probability of

failure of a system of water retaining structures has to be

developed.

First all possible failure mechanisms of the structures and

all other possible causes (management, error, human error

etc.) have to be determined.

Then the relation between the failure mechanisms and the

other causes on one hand and the ultimate consequence a

flood or complete draw down has to be analyzed. The fault

tree is a very helpful tooi to solve this problem.

Thirdly the probability of failure of the various mechanisms

has to be calculated by means of probabilistic calculations

and the probability of occurence of the other causes has to

be estimated on the basis of historical data.

Now the probabilities of the base events (failure mechanisms

and other causes) may be combined in the fault tree to

derive the probability of the failure of the water retaining

system

And in the end the question arises if this probability is

acceptable from social economie point of view.

2

INTRODUCTION

In this paper the developments in the field of the

probabilistic design of water retaining atructures in

Holland, are outlined.

Although the theoretical methode were already known, the

practical application of probabiliatic methods was

stimulated by the design of the storm surge barrier

Oosterschelde. The good experience with these methods, that

enabled the designers to unify the design of structures,

mechanical eguipment and management in one approach, sparked

off developments in the field of dike design. At this stage

the methods are well known but the application is limited to

difficult cases. Thus the new dune design regulation is

based on probabilistic reaaoning. And a purap-storage scheme

with 50 m. high dams currently under design will be

evaluated along probabilistic linea.

SYSTEM DESCRIPTION

A probabilistic analysis aims at identifiing all possible

causes of failure of the water retaining system. Every case

may eventually lead to inundation of the hinterland or to

the loss of precious water. The depth of the analysis

depends on the description of the water retaining in detail.

A complete analysis is only possible if a very detailed des

cription (e.q. as built files and on site measurements) is

avaible. In the design stage the analysis is necessarily

siroplified.

In this paper we will confine ourselves to the very

schematic description of the flood defence system of

Holland. Holland is in principle lying at or below the low

tide level of the sea. It is protected from sea floods by a

system of defences that consists of dikes and dunes. The

dikes are partly shielded from severe wave attack by shoals

(see fig. 1).

- 3 -

HILLS

'seadike

/ 'XkT

/ / / shool /SYdune otd

<&>_ seodike H H, sluice

fig 1 Schematic sifuafion

- 4 -

The system is continued along the river. Here the dike

changes gradually from sea dike into a river levee as the

tidal movement dampens upstream. In the dike along the river

a sluice gives access to an old harbour. The sluice has to

be closed by hand at waterlevels exceeding mean high water.

The main harbours are situated outside the dikes at a high

level and are thus of no concern.for this study.

The typical cross-section of a modern sea dike consists of a

body of sand covered with mattresses and asphalt

constructions in the zone attacked by waves and current.

The crest and the inside slope are covered by a layer of

clay with grass on top (see fig. 2).

A dune is a natuarally deposited mass of sand (see fig. 3),

which is in a state of dynamic equilibrium. During heavy

weather sand is lost to the sea in a reshaping process that

enables the dune to withstand wave attack. Ouring thesummer

the loss is regained by accretion. The wave transport sand

to the beach and the wind takes it further inland.

A typical cross-section of a river levee is given in fig. 4.

The dike stands mostly on a layer of alluvial clay and is

also covered with clay. On the clay grows grass.

PAILÜRB MBCHAMISMS

Good engineering practice requires that attention should be

given to all possible modes of failure of the construction

under design.

This is a conunon approach in the design of concrete or

steel structures.

In the design of waterretaining structures as dams, dikes

and dunes the approach is gaining ground especially in

combination with probabilistic reasoning. This is the result

of the influence of the design of the storm surge barrier in

the Oosterschelde.

A non exhaustive overview of the failure mechanisms of dikes

or dams is given below.

- 5 -

«torm f lood

cbb

fig. 2

aipholhc cone«tt

Seo dike

hv^"0*

storm

fig. 3 Oune

high

low w; ;; ;; ;/ // S; 7/ //

tig. 4 River levee

V # // 6

6 -

Overtopping ia a well known mechanism, which leads to

water entering the polder and to eoaking of the dike.

Wave overtopping ie also a mechanisn that gete a lot of

attention in dike design. In this case the aroount of

water entering the polder ie negligible, so the

dangeroue conaequencee, result frora the eoaking of the

body of the dike and eroeion of the inner slope.

A slip circle at inner slope may be caused amoung other

things by a high freatic plane in the dike*

This will be the case when the duration of the high

waterlevel is long or permanent.

Micro instability of the soil material at the inner

slope may result due to seepage and a high freatic

plane.

Erosion of the outer slope may be caused by wave

attack. The waves may be wind waves or displacement

wave8 from ships*

Erosion of the foreshore is caused by tidal or wave

induced currents.

Piping may occur i.e. the gradual formation of a

material entraining well. When the "pipe" eventually

reaches the high water side the process of internal

erosion will accelerate.

Sliding or tilt ing of the body of the dike may happen.

However this mechanism of failure is extremely unlikely

to occur for an earth dam. For rigid structures it is of

paramount importance.

Subsidence of the crest may occur due to settlement of

the dam and the subsoil.

Settlement may however also be caused by internal

erosion by oxidation of peat layers.

A slip circle in the outer slope may occur when a low

water follows an extreme high water (or sudden draw

down). The body of the dike is heavy with water and

slides down.

overtopping settlement

wave overtopping slip eire Ie outer slope

slip circle innerslope liquetaction

micro instability

.pipmg

drifting ice

ship collision

erosion outer slope

tilting erosion foreshore

fig 5 Overview of the tailure mechanisms of o dike

8 -

A liquefaction may occur in the same situation. Rere

however also the presence of a loosely packed sand and a

steep foreshore is neceaaary.

During winter time the dike may be severely damaged by

drifting ice especially on rivers.

The evergrowing traffic on the waters and the increase

in the displacement of ships makes a collision a non

negligible risk.

The failure mechanisms of a dune are fairly similar to the

already mentioned mechanisms for dikes. Erosion of the outer

slope is however essentially different. The body of the dune

contains enough material to take a special shape during

storm surges: "the storm profiIe". During this reshaping

process material of the dune is deposited on the near

foreshore to flatten the profile. No material is lost.

Due to accretion and erosion the position of the beach and

the foot of the dune is changing continually. Different

phenomena occur if in this erratical process the underlying

trend is accretion, erosion or dynamic equilibrium.

In the design process one is most interested in the ultimate

limit state (ü.L.S.) of a failure mechanism. This state

describes the situation wherein the acting extreme loads S

are just balanced by the strength R of the construction. If

the ultimate limit state is exceeded the construction will

collapse or fail. The concept of the ultimate limit state is

given in fig. 7.

Beside the ultimate state there are situations where the

ever continuing presence of a load causes a deterioration of

constructional resistance over time without imminent danger

of failure.

In the case of the dike the mechanisms "erosion of the

foreshore" and "settlement" are examples.

This deterioration of constructional resistance may cause

unexpected failure in etreme conditions. However the

service-ability of the structure is often hampered before

failure (excessive leakage due to piping). The service-

ability limit state (S.L.S.) is treated in the same way as

the ultimate limit state.

- 9 -

ef ö'S f óh"' óü'tèr* 'sïópë

wave overtopping

overtopping

y i

slip circle

„piping"

öynamic equilibrium

fig. 6 Failure mechanisms ot o dune

- 10 -

A point of great practical imnportance is that a service-

ability limit state, i.e. deterioration of constructional

resistance over time, can be improved in two ways:

1. increasing the resistance to guarantee sufficiënt

strenght during the service life;

2. the deterioration of the resistance can be controlled by

inspection and maintenance procedures.

The second solution, although often economically feasible,

introduces a certain risk because the constructional safety

now depends partly on the care of other people.

The application of limit state analysis presupposes in a

certain way, that the transfer functions to transform

boundary conditions into loads and the theoretical models

defining the resAance (see fig. 7) are mathematically known

and manageable.

In the field of dike and dune design this is not generall/

true.

Especially for erosion and scour processes neither the

transfer function to transform waves and current into forces

nor the theoretical models for the stability of grains are

exactly known.

Here the simulation of the limit state in a scale model may

bring a solution (see fig. 8).

A scale model of the structure is exposed to combinations of

the natural boundary conditions. The amount of damage done

to the model is correlated to the boundary conditions to

develop a limit state eguation.

However model tests require utmost care in the

interpretation of the results for a number of reasons. First

the scaling is done on the basis of the assumed physical

laws of the limit state. If the assumption is not correct,

the results will be unreliable.

Secondly the scaling is only correct for one mechanism.

E.g. in breakwater tests the armour units are far stronger

than in prototype. So in reality the breakwater collapsed as

a consequence of armour unit breakage.

- 11 -

P D. F.

LOAD

TRANSFER

FUNCTION

BOUNDARY CONDITIONS

NATURE

FAILURE

PROBABILITY

CONVOLUTION

P.D.F.

STRENQTH

THEORETICAL

MODEL

STRENGTH

PARAMETERS

fig.7 The concept of the ultimate limit state (U.L.SJ

1— 1

r...L... i i i

1 f- - — - . _ . _ - - .

1

1 BOUNDARY

CONDITIONS NATURE

FAILURE

PROBABILITY

1 r-J—: 1 J 1

L . . _ . , SCALE TEST 1 j

' OR L ! FIELD DATA j

1 i 1 1

L . . . . . . . . . . . . _ J

|

STRENGTH

PARAMETERS

tig.8 BLACK BOX APPROACH of a limit state

- 12 -

Thirdly limit state equations concentrate on equilibrium

bet ween load and resistance. In scale tests only daniage is

observable. Thus in the test, loads have to exceed

resistance by a margin.

In some cases, where the physical laws governing the

phenomena are not exactly known, field data of boundary

conditions, resistance parameters and damage are prefered as

a base for correlation.

Difficulties may however arise in extrapolating the limit

state equation to extreme loads (ü.S.L.) where field data

are missing. For the dune erosion the field data where extrepolated by

extensive scale model (Vellinga 1983).

RISK ANALYSIS OFTHE SYSTBM BY. MEANS OF THB FAOLT TREE

APPRCACH

The goal of designing a flood defence system is to provide'

a certain safe protection against inundation for the people

and their property.

In the foregoing paragraph the modes of failure of dikes and

dunes were listed. Now the total probability of inundation

of the polder (see fig. 1) has to be assessed taking into

account the mentioned mechanisms and the sluice.

Looking at the defense system it is clear that it is a

series-system. If during a storm surge one of the elements

fails, the seadike, the dune, the sluice or the dikes along

the river, then the polder will inundate. For this simple

case the main fault tree is given in fig. 9. The link

between failure of a dike section and the limit states of

the failure mechanisms is analysed in a more detailed tree

(see fig. 10). The same fault tree is also suited to

desprible the failure of a dune. The main difference is that

erosion of the outer slope immediately under wave attack as

a protecting revetment is generally not present.

- 13 -

FAILURE SEADIKE (deep water)

FAILURE SEAOIKE (shoal)

FAILURE DUNE

FAILURE SEAOIKE (river)

FAILURE SLUICE

FAILURE LEVEE

fig. 9 The mam faulttree of the f lood defence system

Further the actual position of the beach and the dune at the

moment of the storm surge is uncertairi due to the dynamic

equilibrium of accretion and erosion under normal

conditions. However if the beach and the dune recede too far

as a result of gradual erosion, the original profile will be

re-established by beach nourishment (maintenance; see fig.

The influence of human action is evident in the case of the

sluice. On one hand the sluice may fail due to technical

failure mechanism, such as loss of stability, collapse of

the doors, or piping or on the other hand due to human error

the sluice may stay open during a storm (see fig. 12).

It will be clear that the analysis of the sluice is very

schematic because no detailed description of the structure

is available.

- 14 -

failgr»

(»«tH»OHfl

ov»r-toppmg brroch

trosion out*r slop* i>»

ï int»rnol «rosion

WQV«

ottock r«v*tm»nt jtr*ngtti

foHur* r«v»tm»nt

I ..ptpirig '

s i * tifti*

WO»*

Ottock

liqu» fottion

es h*od

SMpflgt l*nght

g/oinin»

thickn»n nifolt slop» tov tidt

J.

trotion inntr tlop*

ov»r-foppmg

cETEn

rtvt ov*r topping

f lood l*v»l

dik* hught

-U&

E H ^

Hip cirtl»

wovt run up

roboit hol*i

bar» hol*»

2TB dik* htight,

tl op*

J^EL fleee t*v»l

durgtion fntficn

frtatir MQ

t*tti*m*nr constructen

htight

ars *»ttl»rti»nt

conttruihon g*cm»lry

frieten frtatit plan» o»oirntry

low tid» loet» isnd

frcotic pion» gtom»try

tronon 'or« snort

JU.

•rosion tor» thor»

• tg 10 Th» fautttr*» ol o dik» s»ction curr»nfs

prottction sfr*njtft

- 15 -

DUNE BREACH

U.L.S. TRANSFER FUNCTlON

THEORETICAL MODEL

storm surge waves

mathematical model based on scale tests and field data

gram si ze geometry

change ot geometry

S.L.S.

tide, wind waves,currenrs

stochastic model based on field data

groinsize geometry maintemonce

11 The process ot dun e erosion during storm surge modelled by two limit states

- 16

EVALOATION OP TBB PROBABILITY OP PAILORB

To evaluate the probability of inundation the probabilities

of failure of all the roechanisms must be known. Every

possible limit state contributes in principle to the total

probability of a disaster.

The probability of failure of a mechanism may be found along

two ways.

1. assessment of historical data

2. probabilistic calculations.

In the field of large dams a lot of work has been done

(Middlebrooks 1953) to derive average probabilities of

failure from historical failure cases. The table below gives

some results.

cause

overtopping

internal erosion

slipcircles

other

% of cases

30% 38% 15% 17%

Table I Causes of dam failure

The average probability of failure is 10~4 per dam per year.

These data are not useful in the design of dikes because

they do not reflect constructional improvements or simply

other circumstances. Por electrical and mechanical

components historical failure frequencies are very

important.

For constructional design the use of probabilistic

calculations is preferred. There are.three internationally

agreed levels on which the limit state eguations may be

solved.

- 17 -

The limit state equation is mostly written as

Z - R(Xi . ...X^) - S(Xn+1 Xm) « 0 1)

where R • resistance

S • load

Xi« basic variable

A level III calculation takes the probability density

function (p.d.f.) of all basic varibales into account and

calculates the exact probability of failure in case of

independent variables.

Pr ( Z ^ O ) - fff fXi(Xi) ... fXw(Xm),dxi d3L. 2)

Z < 0

where f (XJ[) • p.d.f. of Xj,

At level II the p.d.f.'s of the basic varibales are if

necessary approximated by a normal distribution in a more or

less refined manner.

Thereafter the expectation and Standard deviation of Z

are calculated by means of the equation

y~(z) -z (yi(xi) |^(xn)) 3) m

*M

*» »* 4)

and if Z is normally distributed

Pr (Z <: 0) - 1-$ | £~1~ 1 - $(f) 5)

where >( ) • Standard normal distribution

(3 « reliability index

- 18 -

Iterative computer programs are available that give good

approximations of the exact failure probability for

non-normal basic variables and non-linear Z-functions

(advanced first order second moment approach, approximate

full distribution approach).

The normal design calculations which use characteristic

values for the basic variables and partial safety

coefficients according to some format are indicated with

level I.

where Rkar» skar " characteristic strength, load

The analyses of dikes is performed on level II and III.

The joint probability density function of wave sprectra and

storm surge levels is evaluated at level III. A physical

model (see fig. 13) is used to extrapolate the historical

data set of storm surges to the mentioned j.p.d.f. (Vrijling

and Bruinsma 1980).

The distribution of the storm surge level HW is of the

Gumbel type

F (h) • e"e" ^

HW 7)

wtiere oi - 1.96 8)

£« 0.33

The conditional p.d.f. of significant wave heights is

modelled by

f (Hs) * N (>c, 0,692)

HS|HW

- 19 -

where - V 3.45 HW - 7.67 + 4.50

for HW > 2.50 m

The wave steepness is normally diatributed.

f(üf) - N(0.0375, 0.0062) 9) L

With this 8et of natural boundary conditons the limit state

of wave overtopping for the sea dike on deep water is

calculated as follows.

Z * hc - HW - Z 2 % - s - o - 1 10)

where hc * construction height HW » storm surge level

1 75 H Z2* * firjV 8 • t9«;wave runup

Hs * significant wave height s » settlement 0 * oscillation 1 » sea level rise

- 20

astro nomica tide

windfields

£ £

windset-up

£

1 wave-generation oeep woter

storm surgelevel

I £

. J

shools local windfields

dike

ri woves

locai wave-generation

north seo

eastern scheldt

fig. 13 Model to predict wave spectra in conjunction with storm surge levels

= l£

é HW

fig. H The conditional probability density function of wave energie on storm surge level

21

The result of the level II calculation is summarized in

Table II

*c

HW

H8

Hs/I*

8

b

1

j-c er

15 .8 0.10

Gumbel

0 0 .69

0.0375 0.006

0.50 0.10

0.40 0.10

0.10 0.03

*

Xi %

15.80 0 .00

3.14 0 .60

0.753 0 .20

0.031 0 .19

0.51 0.00

0 .41 0 .00

0.101 0 .00

P = 2.43 pf * 7.35 10_3Table II The result of the level II

calculation of the mechanism wave overtopping

The dune erosion may be calculated along the same lines. The fact that the erosion is only known as a computer program is no problem. Z - B - M * E (HW, Hs, o, 1, D 5 0, prof) 11)

where B * dune breadth (m) E( ) * erosion (computer program) (m) prof « beach level (m3)

D50 • grain size of the sand (ym) M •» model factor

- I*. -

The level II result is given in table III

b RW

Hs

0

1

D50 Prof

M

r 60.28

Gumbel

0

0.40

0.10

225 0.0 1.0

G

2.0

0.69

0.10

0.03

2 60

0.15

*

*i

59.72

4.51

0.32

0.42

0.10

200 -30 0.91

%

0.01

0.86

0.02

0.00

0.00

0.06

0.02

0.03

(i- 3.57 pf - 1.78 10"4

Table III The result of the level II calculation of the

mechanism dune erosion.

Por a typical river levee the probability of failure for the

relevant limit states may also be calculated on level II

(see Table IV).

mechanism

overtopping

slipcircle

piping

micro instability

"i

4.3 0.04

21.0

0.007

10-3

10-3

10-3

10-3

Table IV

An overview of the probabilities of failure of the

most important mechanisms of a river levee.

- 23 -

The total probability of failure of the levee aection lies

between the following boundaries

max j-l **3

4

Pf < ^ Pf sect j-l j 12)

21.0 • 10-3 ^ P f 4 25.3 . 10~3 secL

For practical purposes these boundaries are sufficiently

narrow. Zf the correlations between the mechanisme caused by

the storm surge Ievel HW are taken into account one finds a

total probability of failure that equals the upper boundary.

The problem of the length of the total system is not so

easily solved. The summing up of the probabilities of

failure of the dike stretches, the dune and the river levee

leads to an unacceptable high probability of failure.

Therefore at this moment sections are checked on their own.

ACCEPTABLE RISK LEVELS FRON SOCIO-BCONOMIC POINT OF VIEW

The last question, but not the least important,ist which probability of inundation is acceptable for society.

In Dutch dike design the Standard is a storm surge level

with a return period of 10.000 years, which must be fully

withstood by the sea defense system.

To accommodate the probabilistic calculations as shown in

this paper an acceptable probability of failure 10-times

smaller than the design frequency is advised (i.e. 10~5).

Studies are performed to find a more objective basis for the

acceptable probabilities of inundation. In these studies tw0 approaches are foliowed.

- 24

One approach translates all daroage done by the inundation in

monatary units. Then the total coat formed by the investment

in a safer dike and the present value of the risk is

minimised. The other approach looks only to the number of people that will drovm in the case of inundation. This number may be looked at from two points of view. The first is the point of view of the indivudual, who equates the probability to drown with the normal risk to die in an accident (10~4). An acceptable probability by inundation is from this viewpointi

Pf < B* . 10-4 Iacc^ — — (13) Pdlf

where 0.1 « B * « 10 « policy factor póiïf " probability to drown given

inundation

The second point of view is that of society. The assumption is that society finds a risk acceptable if the expected number of deaths is with some certainy below B*. 100 (for the Dutch situation; in general 10~5. population). Mathematically this is expressed as

E (Nd) • k. CT(Nd) « B* .100 (14)

where k * confidence limit (»3)

For one large polder this leads to: 2 2

Pf ^ B* .100 (15) ACC

k2Nd2

If B* • 0.1 and k * 3 the expression is

- 25 -

Although this last criterium is more strict for central

Holland than the already mentioned 10~5, the criteria

advised for environmental risks are generally far lower and

of the order

Pf <r 10-4 racc* —-Nd*

This would lead howeyer to somewhat unrealistic dike design

which underscores the difficulties in this field.

A lot more thought and discussion is needed before a clear

view of the acceptable risk level is reached.

REFERENCES

Vellinga, P. Predictive computational model for beach and

dune erosion during storm surges, Coastal Structures Conf.,

1983.

V.d. Graaff, J. Probabilistic design of dunes, Coastal

Structures Conf., 1983.

Bakker, W.T. and Vrijling, J.K. Probabilistic design of

seadefences, Coastal Engin. Conf., Sydney, 1980.

Middelbrooks, T.A. dam practice in the United States.

Transactions Am. Soc. of Civ. Engin., Centennial Volume,

1953, pp. 697-722.

Vrijling, J.K. and Bruinsma, J. Hydraulic Boundary

Conditions, Symp. on Hydraulic Aspects of Coastal Structures

Delft, 1980.