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PAPER 10

STABILITY TESTS OF THE EUROPOORT BREAKWATER

H. BERGE and A. TR)ETTEBERG

River and Harbour Research Laboratory at the Technical University of Norway. Trondheim. Norway

Summary.

This paper deals with model tests conducted at the Delft Hydraulics Laboratory (DHL) and the River and Harbour Laboratory at the Technical University of Norway (RHL) for the design of the Europoort Breakwater.

A serles of tests with regular waves was conducted at the

DHL from which the design of the breakwater was decided. The

chosen design was tested with irregular waves ba~ed on ln situ

observations. Wave spectra, wave height distributions and the

joint distribution of wave height and period were specified. These tests were conducted at the RHL, and some tests were re-peated at the DHL.

It has been commonly assumed that the destructive effect of a train of regular waves on a breakwater in model is equal to the effect of irregular waves with a significant wave height corresponding to the height of the regular waves.

*

The tests showed that for this particular breakwater the

irregular waves represented a more severe wave attack than the regular waves.

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INTRODUCTION

This paper deals with stability tests in model of the Euro-poort Breakwater conducted at the Delft Hydraulics Laboratory (DHL) and the River and Harbour Laboratory at the Technical

Uni-versity of Norway (RHL). The tests were run both with regular

and irregular waves.

Fig. 1 shows the outer part of Europoort. An 8 km long

breakwater extending from the south will protect new industrial

areas with adjoining harbour basins. The dry land will be

sepa-rated from the breakwater with a channel. This permits a

con-siderable amount of overtopping, and the breakwater has been

designBd with a very low crest. Fig. 2 shows typical cross

sec-tions for the deeper and for the more shallow parts of the break-water.

The sea bed consists of sand with a low stability against

erosion and a low beari.ng capacity. The jetty is therefore

con-structed with a wipe fill with flat slopes. The jetty is

protec-ted with cubical blocks in two layers placed pell mell. The

design wave height is 8,5 metres.

~~ The model tests consisted of tests with regular waves in

order to determine the general design of the breakwater and the

necessary block weight. These tests were conducted at the DHL.

DHL had planned to check the results in a wave basin equipped with a new wave generator which could produce irregular waves, but it became apparent that the new equipment would not be in opera-tion early enough to finish the tests before the deadline for the investigation.

At RHL equipment for producing irregular waves has been in operation since 1964, and RHL was asked to conduct these final tests.

This paper mainly deals with the tests which offer a possi-bility for comparison of results obtained with the use of regular

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and irregular waves, respectively.

**

TEST WITH REGULAR vlAVES

The tests were performed in scale 1:60 with a cross section

as shown in Fig. 3. (All elevations given in this paper are

re-ferred to New Amsterdam Ordnance Datum (NAP). The stability was

investigated with cubes with different dimensions and specific

densities. For every particular cube dimension the average wave

period and water level were varied independently.

By way of example Fig. 4 shows the results of a series of

tests. The damage is described in qualitative terms according

*

to a system of certain standard criteria used at the DHL. The

system not only takes into account the number of blocks which are removed from the armour, but also from where in the armour the

blocks are removed. Thus the damage is rated higher if a number

of blocks are removed from a consentrated area on the breakwater than if they are removed from different places more evenly dis-tributed over the whole armour surface.

From each series of tests the test glvlng the mlnlmum stabili-ty, at a damage between "none" and "slight" was used to calculate

the stability number, K/f(a) from the formula

G

=

The computed maximum values of K/f(a) (minimum stability)

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G yb H Hdestr/Hd KIF (a) 3 d tons tim m 27,5 2,2 5,5 1,68 11,3'10- 2 21,5 2,2 5,4 1,82 9,4'10-2 23,0 2,6 6,9

-

9,7'10-2 20,3 2,7 6,8 1,73 10,4'10-2 20,3 2,7 6,8

-

10,4'10-2 13,0 2,8 5,8 1,72 12,0'10-2 8,0 2,8 5,5 1,59 9,0'10- 2 25,0 2,8 7,3 1,70 11,8'10-2

Average values: K/f(a)

=

10,5'10-2

t

11%

H +

destr/H

d

=

1,7 - 1,5%

According to these values the design block weight, G

=

43 tons

with a specific weight of 2,65 t/m3, was selected for the design

wave of 8,5 metres.

Also some tests with more shallow and less exposed parts of

the breakwater were carried out in regular waves. In Fig. 5 is

shown the respective average K/fCa) values for all cross sections

concerned. Along the shallow part of the breakwaterscour scour is

expected to occure in front of the breakwater. The graph shows the

results under the condition of the original horizontal sea bed

untouched and under the condition that scour has taken place. In

the case of scour the models were tested with a 1:4 sloping bottom

~ in front of the structure from the original level of -7 and -10

metres down to -10 and -14 metres respectively.

TESTS WITH IRREGULAR WAVES

Cross sections.

The breakwater cross sections in Fig. 2 are the ones selected on basis of the tests in regular waves, but for minor modifications as the result of the tests with irregular waves.

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At RHL a number of 4 cross sections were tested in irregular waves, cross sections at depths -20, -15.5, -12 and -10 metres. The shift from the deep water to the shallow water design will be

at depth -12 metres. At depths less than approximately -5 metres

the breakwater is constructed entirely with sand.

Tests at RHL.

Test equipment. The RHL wave channel is shown in Fig. 6.

The waves are generated by a paddle moved by two oil hydraulic

pistons. The paddle movement is controlled by a servo system

with a voltage reference input and position and velocity feedback. For generating irregular waves the input signal is synthesized on magnetic tape from a white noise generator connected to electronic

filters. With the known transfer function of the wave channel the

filters are adjusted to give a wanted wave spectrum in the channel.

The wa~e generator works within a range of wave periods of

0.5 - 5 sec. and can produce waves with a maximum height of

approxi-mately 0.5 metres.

The wave generating system also includes a fan capable of producing wind with a maximum velocity of 10 m/sec.

~~ Waves. At the site, waves have been recorded continously

a considerable period, and a well specified wave programme could

be put forward as a basis for the tests. These specifications

consisted of wave spectra, wave height distributions and joint dis-tributions of wave height and period.

Fig. 7 shows the two maln types of spectra used In the model tests, a Neumann spectrum and a narrower one.

The spectra were run with three different peak frequencies corresponding to wave periods of 10, 12 and 14 second in the prototype.

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In Fig. 8 the dimensionless wave height distributions of model and prototype are shown, while Fig. 9 shows a diagram which

expresses the joint distribution of wave height and period. The

H-T correlation is derived from a wave record by plotting the ratio of the mean apparent wave period, T., according to the zero

l

upcrossing convention, in intervals of

HIHE

=

0,5 and the mean

apparent period of all waves, T , against the wave height para-m

meter

HIH

E

.

The two curves envelope H-T correlations of waves

outside Europoort, and the plotted values are examples of H-T

correlations of the model waves. All wave data from the model

are obtained from records of 200 successive waves.

The prototype wave conditions were found to be reproduced satisfactorily in the model.

The models. The test arrangement is shown in Fig. 10. The

tests were run using a scale of 1:36.

The wave basin is constructed for a water depth of approxl-mately 1.0 metre, Bnd a model bottom was constructed consisting of a slope 1:30 up to the correct sea bed level, whereafter the bed was kept horizontal.

Two cross sections with widths 1.0 metre were tested

simul-taneously, each positioned adjacent to the glass panels. With the

different sea bed levels on each side of the basin the cross sec-tion became as symmetrical, but this did not have any significant

*

influence on the wave conditions.

Test. For the deep water sections at depth -20 and 15.5

metres the stability of the given design was to be investigated.

For the breakwater in shallow water special precautions have to be taken against erosion, and the breakwater will be founded

on a dredged bottom below the original sea bottom level. To keep

the cost of dredging at a minimum the berms are to be as high as

possible below the still water level. The criterion for the

sta-bility of the berm was that no rock be washed into the front

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ad-dition to the study of the armour layer of 39 ton blocks an objec-tive of the tests was to find the maximum crest elevation of the berms.

During a test the significant wave heights used were 4, 5, 6, 7, 8, 8.5, 9, 9.5 metres, each run for a period equal to 10 hours in prototype.

The tests were conducted with water levels of + 0.5 and

+ 1.5 metres.

Test at DHL.

Test equipement. The system for generating irregular waves In the DHL channel works approximately on the same principles as that of the RHL, i.e. the signal from a noise generator is filtered to give an input to a servo controlled wave paddle, which generates a wanted wave spectrum in the channel. The control system of the wave generator is also designed to accept a wave record as input signal.

Waves. In the tests three types of spectra were used, and each spectrum was run with peak frequencies corresponding to wave periods of 10, 12 and 14 seconds in prototype. The spectra are shown on normalized form in Fig. 11.

The

A-

and B spectra corresponds to the spectra used at the RHL, and in addition a very wide spectrum (C) was used.

Tests. The tests were run In scale 1:60 with two cross sections at depth -20.0 and -15.5 metres. The tests were run at water levels + 0.5 and + 1.5 metres.

TEST RESULTS

The results of the tests conducted at DHL and RHL are shown In Fig. 12-18. The line in the graphs, illustrating the effect of regular waves, is drawn on basis of the average values of K/f(a) and Hdestr/Hd from the tests in regular waves which gave the lowest stability.

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As the structure was supposed to be stable up to the design

~*wave height the damage was limited In all cases, and i t is diffi· cult to draw conclusions of a general nature about the influence of spectral shape, w&ve period etc. on the damage.

**

Also, the conclusions about the stability are of course limited to the particular breakwater design and under the parti-cular bottom conditions tested. However, at present very few tests on breakwaters have been conducted, In which the effect of regular and irregular waves can be compared, and i t might be of some interest to discuss the results in some detail.

The typical development in the 43 ton armour layer during a test was as follows: Already at a wave height of 4-5 metres the blocks began to rock In the highest wave, resulting in a slow set-tling in the armour and core. This process continued for increased wave attack, and the thickness of the armour on the crest decreased. In most tests just a few blocks were removed from the armour layer, and after the completed test the breakwater seemed impaired only to a small degree.

As a result of the tests with irregular waves i t was decided to compensate for settling in the core by increasing the initial crest elevation.

By comparing the tests which have been run both at DHL and RHL i t seems that no systematic difference can be traced in tests performed in the scales 1:60 and 1:36.

~ It has been commonly assumed that the destructive effect of a train of regular waves on a breakwater in model is equal to the effect of irregular waves with a significant wave height corre-sponding to the height of the regular waves.

~~ By comparing the results of tests run with regular and irre-gular waves i t can be seen that in this case the damage appeared in the armour layer at a lower significant wave height than the height of the regular waves. This is apparently due to the few high waves present also for lower significant wave heights.

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The difference in stability is somewhat greater than indi-cated by the average minimum curve as this curve is based on the results from the tests in regular waves giving the lowest

stabi-~ lity. To illustrate this all results obtained in regular waves

have been evaluated for the condition G

=

43 t and Y

b

=

2,65 t/m

3

and plotted in Fig. 19. In addition to the average minimum curve,

the curve corresponding to the average of all results is drawn. In Fig. 20 all results obtained in irregular waves for the cross sections at depth -20 and -15,5 metres respectively, have been plotted for comparlson with the average stability obtained in regular waves.

Also the stabllity of the berms seemed to be somewhat lower than observed in regular waves.

The increase of damage was, however, not considered to neces-sitate any change In the breakwater design.

In Fig. 21 is shown a diagram of damage vs. wave height for

different wave spectra. The damage is expressed by the number of

blocks which had to be placed on the model in order to restore

the original shape. The number of blocks used for construction

was approximately 250. In test of breakwater stability scatter

is inherent, and the shaded area between results from two tests run under identical conditions illustrate the scatter in the test

series. In view of the scatter, it is not possible to draw any

conclusions on the effect of spectrum sL~pe and peak frequencies

on the stability.

FINAL COMMENTS

The tests described in this article were not meant to give results beyond those necessary to draw conclusions about this

~~ particular breakwater for a given range of wave dimensions. For

this particular case, within the observed range of damage, ir-regular waves seemed to represent a more severe wave attack than regular waves with heights equal to the significant wave heights of the irregular waves.

(10)

In stability tests conducted at the RHL previously (Ref. 1, 2) relationships between damage and types of spectra have been

indicateJ. It was shown that irregular waves, depending on the

spectrum width, can be more or less dangerous than regular waves. Under certain conditions regular waves have been shown to be

considerable more destructive.

On the basis of the sum of experience made so far, the con-clusion seems to be that the factors which influence the stability of a breakwater are many and complex and vary within wide ranges

from project to project. The best basis for breakwater design is

(11)

HOEK •. HOLLAND

~\

Fig. 1. Plan Europoort.

DEEP WATER DE<;IGN

f~O ---~.-=~---~ ARMOUR. 43t -110 , \ , ~ \ .", ~ . , .. , " \ \ \ 1-6 t • SEA GRAVEL ! . . .

SHAllOW WATER DESIGN

39 t

-12

I

LROCK e\3-1t [APRON ROCK 1-6t CORE 1-6 t

(12)

-10 ROCK,l·U ROCK, 0,3-1 t -16 o 10 20 mel, . . I , 1 I i ' j , I • J

Fig. 3. Cross section. Tests with regular

I

ill

i i

II

i w

°1

N " ~ '" ! ~ 0

e! ..

'":

!--t

'" ~~

.

~IC>

~

E E E - " , or> '" -,... .,....~ o~

5 •

.

.

~-~~~~~~~~~~~~~~~~~~~~~ { W ) " H _

**

Fig. 4. Fig. 5.

Example of test results, regular waves.

DHL.

X WlTK ~ 10 -10 .. 15.10-'

x

11).10-2 ~_-!' _ _ _

+ ____

~_ -s -7 -10 -14 ORIGINAl. SI!A BEll LMl

Stability as a function of sea bed level.

(13)

WAvE GENERATOR WAVE FILTER SCALE OF METRES Fig. 6. 1.0 E!. Eo

**

Fig. 7. 90 80 '" :r 70 ;;-:. 60 :" 50 40 30 20 10 SECTION A- A

::

PLAN SECTION B-B Wave channel. " sec:-1 1.0 E, Eo· Wave spectra. GLASS PANELS GLASS PANELS ~ONTROl ~ ROOM

RHL.

RHL.

+ '0~---~---~---~---7---~---~

(14)

.'"

.

.

.,/

-"""'''''' 0 0 0 0 0 1

WAVES OF E\mf'OOIU

7

.

M

.

o MODEL

-

-

.

:IN' SPECTRUM

....

To" 12s4JC' j"

,.

. / 0_ lit" . /

/.

'~

/ L

Ti : MEAN PER\OO IN IN1ERVAlOF %E'(),5

~

Y ~: MEAN PERIOD OF All WAvES o o 0.1 1.0

..•

**

Fig. 9. Correlation between wave height and period.

WIND INTAKE o 1 2 3 4 5metres I Fig. 10. Fig. 11. Test arrangement.

RHL .

2 o 0 o o b I ')

I

.-SPECTRUM B.T 10,,"10,12 and 14 sec

-"PECTRUM A.Ttop.lo.l2 on

I I I

d 14 sec U;PECTRUM C.T'np"OJ2 an

\

d 14,..,< '\ \.

"'-

'

-U 1,lI 2!J model Ttop·U5_

0.08 0,12 0.16 protot.Ttop·l0 _

cwe 6h prolot.T'op.12 sec

cwe (),l2 protOl.Ttopl4 sec

- fREQUENCY

Wave spectra.

DHL.

(15)

MODERATE

I

LITTlE SLIGHT NONE 4 MOIlERATE lITTlE SLIGHT NONE 4

SEA BOTlOM LEVEL - 20 m

T---

r-Tf

----1

I I

)

I I i

V;

I I

~

er.(

i

I

.,

I

i 7 8 ~5 9 - H . ( m ) SPECTRUM: N

WATER LEVEL: + O,50m

MODERATE MItMl IIIIM. CUIW MT.IHWST lITTlE SliGHT NONE 4 -"" -~I

I

I

L~

I I

IA

~

~

..

I

!

III ee 7 8 '5 9 - H . ( m ) To sec 10 12 14 16 OHl 00 (t V Ii l III II

Fig. 12. Test results. Irregular waves.

SEA BOTlOM LEVEL - 20 m

I

I

I

I I

I I

MODERATE .... IIIOTTOIoI I.£'ftL -I 1:1 m

I I I ----"--"-I

!

I !

/

I i I "

t

Vi

7 6 LITTLE SlIGHl NONE I 4 5 fi 10 - H . ( m ) - H s C m ) SPECTRUM: B WATER LEVEL: + o.50m

Fig. 13. Test result s. Irregular waves.

MODERATE I SEA IOTTOI I 1.£YE~~""l5.m_

I I I I

+-

! I I I I

I

/

i I I I

I

!

/

!

171

I --" ... _""" ... I I

••

I i

..

III I LITTLE SliGHT NONE 4 5 fi 7 8 II.!I 9 10 - H . C m ) - H . C m ) SPECTRUM: C To sec

WATER LEVEL: • 0.50 m Olil

Vlil

(16)

LITTlE

SLIGHT

NONE

LITTLE

SLIGHT

su. 8OT1OM LEWEL - 20 III I ""-"--,-

r-I I , I I

t-l-h

I

v:

11\

;

fl

I I I , , I 5 1 SPECTRUM: N \tATER lEVEL: • 0.50111 LITTLE SliGHT NONE 4 5 To sec OHI. VHl 7 10 12 0

.0

8 l5 - H s ( m ) 14 16 4)

Fig. 15. Test results. Irregular waves.

5

I

I I I

su. IIOTlOM lEWEI.

-

20 III

"--."-""-~

I

!

I i

j

I I i

V

i

I

I

11\

I

1 ?

-H.

(III) SPECTRUM: N \tATER lEVEL:· \50111

Fig. 16. Test results.

SPECTRUM: .. \tATER I.EVEI.: • 11.50111

Fig. 17. Test result s.

- H S ( m ) To sec 10 12 14 16 OHl YHl 0

4) Irregular waves. - H . ( m ) To sec 10 12 14 16 OHI. VHI. 0

e • Irregular waves.

(17)

.

"---I

I

I

I

I I I I

~TE SEA IIOTlOM LEVEL - 20 m

I I 1i'" I I I I I

)

I I

V:

;

vI

LITTLE SLIGHT NONE

..

7 II ,,5 9 10 LITTLE SliGHT I I r

l-I I I

1

V.

I

fl

I

"

4 7 II "5 II 10 - H . C m ) - H s ( " ' ) SPECTRUM: .. To sec: 10 12 14 16 _TER LEVEL: + 1,50m DHL VHL 0 ee 411

Fig. 18. Test results. Irregular waves.

*

MODERATE

,

REGULAII . . lies

4\IEIIIAGE OF ALL RESULTS

~ " ~~---~----"--"--+---+---+~----~---r---1---o UI <!I 6 LITTLE

.

NONE 7 MODERATE B II

SEA BED LEVEL: - 20,0 m

REGU&'R WAIlES AVERAGE OF MINIMUM 11 12 RESULTS ~~--~----~---+----~~--.r----~----+­ ~ 6 SLIGHT NONE. 7 II 10 11 12

SEA BED LEVEL: -IS,S",

Fig. 19. Results from tests in regular

waves evaluated for conditions

3

= =

11.

(18)

9,5 I/) ~9 I -UJ ::E 8,5 1-"

e

8 iZi :x: UJ ~ 3: 7 I -Z « !::! 1..1.. 6 Z C) in 5 4 o

MOOERATE

.m ~----r1' 1+ •

'1"1

I

I

I I

._AV~EI-RA_GE_ ~_OF~=:::~_-'-+-.fiLoll""""-Ji'&'_~~:Atl" _~

:y""

I

_~ ~

---+--- ,

!

i LITTLE ~~IGHT 6 7 8

*

Fig. 20.

o

5 I , I

I

I

·1

I I

'1

I

I

·t

!

!. • I I

I

9 10 11 12 13 14 15 H mt'tres

Results lD irregular waves.

All test data.

-..

PEAK PERIOO To = 10 sec

N-SPECTRA III To ='2

..

To = 14 --1:)--- To = 10 B-SPECTRA ---0--- To = 12 10 ---.0.--- To =14

SEA BED LEVEl - 15.5 metres WATER LEVEL + 0,5 - ..

-15 20

NUMBER OF BLOCKS FOR REPAIR

(19)

References.

1. Svee, R., Tr~tteberg, A. and T¢rum, A.

"The Stability Properties of the Svee-block". XXI.st International Navigation Congress,

Stockholm 1963. Sect. II, Subj. 1, p. 133.

2.

Carstens, T., Tr~tteberg,

A.

and T¢rum,

A.

"The Stability of Rubble Mound Breakwaters against Irregular Waves".

Xth Conference on Coastal Engineering, Tokyo 1966.

(20)
(21)

DISCUSSION ON PAPER 10

J. H. van OORSCHOT

Delft Hydraulics Laboratory, The Netherlands

Berge and Treatteberg conclude, after having reviewed the results of experiments performed at the R.H.L.* and the D.H.L.~regarding the Europoort breakwaters, that "the factors which influence the stability of a breakwater are many and complex and vary within wide ranges from project to project. The best basis for breakwater design is still model

testing, preferably with irregular waves".

Additional tests performed at the D.H.L. with a somewhat different cross-section have once again positively underlined the significance of this conclusion. Moreover, some results of these additional experiments are so interesting that a short discussion seems justified.

The cross-sections tested by R.H.L. and D.H.L. can be realized at those places where the original depth is about N.A.P. - 15 to - 20 m. However, parts of the Southern breakwater have to be constructed on a shallower bottom. After the construction is finished, the contraction of the tidal currents in combination with dredging work at the harbour entrance will cause a scouring in front of the bed protection of the br~akwater up to N.A.P. - 20 m or even N.A.P. - 25 m. The influence of this bottom configuration on the stability of the breakwater has been extensively tested by the D.H.L. Though the differences in the cross-sections compared with those described by Berge and Treatteberg are minor, the stability appeared to be entirely different. With a proposed length of the apron of 20 m, serious damage occurred under design-wave conditions, whereas, considering the former experiments, only slight damage was expected. Moreover, damage increased rapidly with increasing wave height. After having considered this result, it was decided to vary the apron length in the model. Four lengths were taken:

3,

12.5, 20 and

50

m.

± River and Harbour Research Laboratory, Tro~dheim. ~ Delft Hydraulics Laboratory.

(22)

The results show the smallest damage for the 3 and 50 m aprons and a maximum damage for the originally selected length of 20 m.

Visual observations of the model have created the impression that the character of the breaking wave

m

one of the causes of this phenorr.'lnon. Wave attack on the armour blocks got more the character of wave impact with increasing apron length up to 20 m, whereas at a length of 50 m a substantial amount of energy has already been dissipated by wave breaking in front of the breakwater.

One reference test applying regular waves showed hardly any damage at the design wave height of

8.5

m and an apron length of 20 m, ~lhereas in the case of irregular waves the structure was seri-ously damaged at the corresponding significant wave height and period. Though for some specific problems regular-wave experiments may yield useful information, this result once more focusses attention on the risk of this method.

The amount of influence of the apron length was not predicted, and was discovered only thanks to the fact that extensive model studies had been performed for the Europoort project. As apparently minor factors have an important influence on model results, the extrapolation of data to other problems, which may look similar in a first approximation, has to be applied with the utmost care. It is evident that the same holds good even more for the use of stability formulae.

(23)

+2.0

SEA BOTT

NORTHERN BREAKWATER

I

, _ _ ORIGINAL SEA BOTTOM

-SOUTHERN BREAKWATER

50m 20m 12.5m

___

:i3~~O

___

;:..i~-.;n.~~~~~~~~£;J

---

----

---I -20.0 _---~-

---:---I

- -

- ..-. -:::::::::::: -

(24)

Hs

10~--~--~----~---~---~---~ (m)

f

SOm ~ 12.Sm 9~-+~--~----~--~_-~,r'~---~---4

/'y"'3m

__

r ... _ _ - ! - -

t

,*/

//~.

""""5-

~_

S 20m

8

01" ..4"'- - - _ .~

:::::::.::;;;;.s--,'/

6~~--~--~---~---~---~----~ S~--~--~---4---~---~---~ ARMOUR BL OCKS : CUBES W=

43

TONS P=2650 kg

1m

3 4~--r---r---4---~---~---~

NONE SLIGHT LITTLE MODERATE MUCH SERIOUS DESTROYED

---I...

DAMAGE

DAMAGE ARMOUR-LAYER AS A FUNCTION OF WAVE HEIGHT

AND APRON LENGHT.

Hs 10

(m)

i :

7

6

5

4

..

la /""

/."p

IV" I

::.-I

i REGULAR WAVES T .. 10sec _ -APRON

LE~~ ~

__

~~=-_

..-"~ ~~- IRREGULAR WAVES ".. ~ -::;:::::::- :::::;;;- " ....-... T .. 10 sec.

~

APRON LENGTH 20m I I I

I

NONE SLIGHT LITTLE MODERATE MUCH SERIOUS DESTROYED

- - - I I ... DAMAGE

Cytaty

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With an elevation mask of 40 degrees, using satellites from one system does not allow for meaningful positioning solutions of more than 8 h within the test day, while mm-to-cm

We discuss the timing of changes in retreat, thinning, and acceleration across the ice sheet, quantify the sensitivity of ice discharge to retreat, and describe the roles of

In the Yellow Sea, cross-basin phase differences due to lateral depth differences as well as open boundary conditions favor the emergence of the “radial tidal current.” Further

A methodis presented for calculating the properties of com- pressible laminar boundary layers with heat transfer and arbitrary pressure gradients. The method is