Staticstability of rubble mound breakwaters

Stabits _Tetrapods

·~.·

Static stability

of

rubble mound breakwaters

Do fosse

(1) Armour units tested.

The test mdbod

Cover layers were built on a smooth under-layer at a predetermined slope (2). Strings were attached to several units in the pack and the steady force required to remove a unit was measured. This force was applied at right angles to the slope on the basis that wave action will 'll'eed to move a block in this direction in order to bring about its removal from the pack. This will not always be the case but it is the simple concept behind the tests (3).

If this force (F) can be assumed to be

some measure of the block's stability in wave action then the method can be used to study the variations in 'stability' depending on the attitude of the unit in the pack (ie whether it is more or less interlocked), the effect of sJope, position of blocks on the slope, block density etc. Most of the tests were done with Dolosse but some were done with stone, Tetrapods and Stabits.

A breakwater subject to wave action and

beyond the point of no damage is made up of units whose stabilities between certain limits are random. This means that to get a statistically significant result from even one series of tests, hundreds of tests would have to be carried out. Time did not allow this and neither was it felt necessary to do any more than 110 runs in each case. The idea was to obtain a qualitative appreciation of the problem by studying a number of variables. This could then be followed by exhaustive testing to provide quantitative answers if the method proved to be useful.

The slopes were rebuilt each time to ensure that the removal of a block did not affect the disposition of other units in the pack. To consolidate the slope to an even consistency before each test vibrators were

Lime stone

used. This technique was carried a stage further. Even in moderate seas armour units like Dolosse are on the move and this means that their stability is varying in space and time. Zwamborne demonstrated this in an excellent time-lapse film shown at the J6th International Coastal Engineering Confer-ence in Hamburg. Such movements can be imitated in the laboratory by using vibrators. Whether these movements are analogues to those produced by wave action is open to question but nevertheless their study might give a clue to the behaviour of complex blocks.

Test 1 Spread of stabitity and effect of compaction

'With units like Dolosse that interlock how does their stability vary with their

posi-tion in the pack?' A double layer Dolosse

slope was hand laid in a small tray at a slope of 1 : 2 (2). The units at the centre of the

square tray (30 ems x 30 ems) had strings

attached which enabled a force to be applied at right angles to the slope to the centre unit. The force to remove the block was noted. The slope was relaid and the test carried out 10 times for each layer. Only

one block was removed each time. It was

an easy matter to determine wihether a

Dolos was in the top or bottom layer. A

random series of forces were recorded which have been plotted in order of magnitude on (4).

The forces were not recorded in this order but were plotted this way to make compari-s·ons easier to appreciate. Before comment-ing on the results the second series of tests will be described.

THE DOCK & HARBOUR AUTHORITY

By W Alan Price

UK Hydraulics Research Station

It is not possible to design rubble mound structures employing complex blocks entirely

from first principles. Each type of armour

unit exploits properties like weight, inter-locking, inter-block friction etc, in varying degrees to achieve stability. This is one of the reasons that the empirical formulae often used are inadequate and why most designs have to be tested in the laboratory. This will continue to be the case until the basic prin-ciples are understood. The purpose of this article is to report the results of a series of simple tests on slope stability using Dolosse, Tetrapods, Stabits and stone (1). Essentially the tests consisted of measuring the forces required to remove units from the pack. The significance of the results will not be fully understood until they are correlated with stability tests under wave action. They do, however, give a clue as to how a slooe built of unitsl of complex shape behaves and are presented to create discussion along rather different lines than hitherto. All tests were done on smooth slopes.

It is well known that during the early life of a breakwater the units compact in moder-ate wave climmoder-ates to form a stronger assembly. In the laboratory slopes which are to be the subject of stability tests under wave action are usually compacted by running 2 000 or so waves of a height sufficient to bed the slope down without causing damage.

To represent this phase orf bedding-in the

Dolosse slope was vibrated for two minutes. There is no significance to this figure except that it is doubtful whether further vibration would have caused any more compaction. The test procedure described earlier was

repeated. The results shown in ( 4) can be

summarised as follows :

1 The force to remove a block from

either layer varied markedly and its spread

is illustrated in the following table. The

dimensionless ratio F /W is intended to give

an idea of the variation in the unit's stability and is defined as follows :

F Force to remove one unit from the pack

W Weight of block

Table 1 Dimensionless forces to remove a unit

F/W

SURFACE LAYER BOrrJlOM LAYER

As laid Vibrated As laid Vibrated

1.0- 5.6 1.2- 6.2 4.4 -12.4 5.7 - 14.8

Perhaps the best way to illustrate this spread in the stability of units in the top and bottom lavers is to express it in terms of standard deviations.

•

Table 2 Standard deviations in F

/W

STANHARD DEVIATION IN F/W SURFA>CE LAYER BOTTOM LAYER

As laid 1.35 Vibrated 1.64 As laid 2.66 Vibrated 2.25 How can we interpret these results from the structural point of view? At any one time there are units on the slope exhibiting a spread of stabilities. A bridge designer would not be happy if the pattern exhibited in (4} represented say, the strength of the beams in a bridge or the deck support wires for a suspension bridge. He would have to assume that the ultimate strength of his structure was controlled by the strength of the weakest link. Clearly this concept of overall stability cannot be used in the case of a breakwater because it is normally designed to damage and it is obviously stronger than its weakest link (the weight of a single Dolos), but how much stronger? This is a question that is: easy to pose but difficult to answer. What one can say is that if a unit becomes dislocated it has a good chance of being removed from the slope and this means the structure damages and has a finite life; the structure progressively becomes weaker. This is not a new concept. Shuttler and Whillock working at HRS have held this view for years and shown it to be the case.

2 Vibration compacted the slope in terms of a reduction of area by about 5%. This compaction increased the force necessary to remove units from the pack quite markedly. On average the increase for the top layer was 36% and for the bottom layer 3,1 %. These increases are significant and demonstrate that if a Dolosse slope 'as laid' has not been bedded down by a favourable wave climate before it is caught by storm then it could be vulnerable. How long this compaction takes depends on the time/intensity of wave action and on the roughness of the under-layer which controls the ability of the Dolosse to slide down the slope and com-pact. All the tests reported in this note were done with the units laid on very smooth slopes. It would be interesting to repeat these tests on slopes of different roughnesses.

Attempting to quantify this result is diffi-cult but if one interprets it in terms of a

··--u-· ..

approach then a 25% reduction in

(2) (left) Test rig with small tray. (3) (right) Sketch showing method.

ultimate strength due to non-consolidation would mean that the slope would experience the same damage for a wave height 10% less than the design wave height. This is very much a back of the envelope calculation presented to illustrate an order of change.

It depends for its validity on many assump-tions but it shows that this consolidation phase is very important in enhancing the stability of the structure.

Test 2 Block movement

'When a Dolosse slope is subject to a wave climate of sufficient intensity to move the units what is the time history of the stability

of one unit?' By analogy vibration was

assumed to cause the same motions of the units as wave action. Each slope was hand built as in Test 1 but this time the vibrator was operated for 15, 30, 45, 60 seconds etc. At the end of each time interval the vibrator was stopped and a force was applied to the central surface unit until it was just on the point of moving; the unit was not pulled out. The results are presented in (5}.

Knowing the amount of interlocking pre-sent on one block it was impossible to predict the force required to move it after the next interval of vibration indicating that

inter-( 4) Effect of consolidation on force required to remove a unit from the pack.

u. I No. of test 10 16 Bottom layer 12

r

10 6 I 4 10 No. of test

1•• Slope laid by hand

.J

Slope vibrated

F = Force to remove one DoJos {Newtons) W= Weight of unit

3

locking and dislocation can occur in a random fashion and sometimes quite quickly. (This is also the experience when testing breakwaters in flumes. To predict which block will be removed from the slope by the wave action is difficult}. The results: show that the slope is alive with units changing their levels of stability continuously. (5) shows blocks exhibiting an even stability, others decreasing and increasing their stabili-ties and then dislocating; the stability of a unit is random in time.

So just beyond the point of no damage the slope is made up of units changing their stability in space and time in a random fashion and subject to seas which in them-selves are random. It is difficult to define in such a situation what level of strength or stability to ascribe to a breakwater, or whether the term 'strength' has any mean-ing in this context. Intuitively one feels that if Dolosse can interlock and dislocate quickly then the 'strength' of the slope might be improved by slowing doWill the process. This might be achieved by slightly amending the shape of the block. Block movement means wear and wear means rounding of edges. One would think that as a breakwater aged and the limbs of the units became rounded intedocking and dislocation would occur more easily.. Further testing will be done with worn units and the presence of broken units will be investigated.

T•mt 3 Effect of block position

'Do the armour units situated down the slope have greater stability than those above? How does this stability vary with the

position on the slope?' For these tests a

longer slope was built contained in a tray 90 cm x 30 cm (6). It was supported at a slope of 1 : 2, a two layer Dolosse slope was hand laid and then vibrated for two minutes. The force required to remove units from four positions in the surface layer and three in the bottom layer was measured. The test was done eight times, the slope being relaid and vibrated between each test. The average results for each position are shown in Table 3.

The results indicate that for the surface layer the average force required to remove a unit from the pack is the same for all points on the slope. For the bottom layer the force increases down the slope but not markedly.

4

1

1

-0 30 60 90 120 150 180 210 0 30 60 90 120 150 Vibration time {secs)

-Talble 3 Effoot of position on ,1Jhe slope

TOP LAYER BOTTOM LAYER

Distance Force to Djsfunce Force to from top remorve from top remove

of slope unit of slope unit

(ems) Nxi0-2 _{~ems) Nxl0-}2

Ji1.2 199 22.5 473 33.7 198 45.0 600 56.2 ,189 67.5 650 78.7 t186

Test 4 ~locking and effect of block density

'If by interlocking is meant the ability of a unit like Dolosse to enhance its stability by bringing into play the weight of other units then if we reduce the block's weight by

reducing its density, keeping its shape and

size the same, then the force required to remove units from the pack wifl be directly proportional to block density.'

Although this description of interlocking appears to be obvious there are reasons why it need not necessarily be true.

Within the present series of tests the easiest way of bringing about a considerable reduction of block density and effective weight was to carry out the experiments in

Test 11 under water and compare the results.

As before a double layer Dolosse slope was

hand laid in the smaller of the trays at a

slope of 1 :2. The force required to remove the centre block was measured: the slope was relaid each time. Tests were done for both layers after hand laying and with the slope vibrated as before. Only the results

(5) (left) Force to remove a unit in the surface. layer.

(6) (above) Test rig with large tray.

(7) (right) Effect of block density on _force required to remove a Dolos from a consohdated pack.

for the vibrated slopes are plotted on (7). The Specific Gravity of the units in air was 2.33.

If the definition of interlocking is as stated

above

then-Average force to remove Dol os in air

= 2.33 - - - =11.75 (2.33-1) Ex.perimental results , water

Top layer (hand laid) . .

Average force to remove Dol os m a1r

175

- = 1.92

~1

, water

Bottom layer (hand laia) ...

Average force to remove Dolos in air

-~---528

- = 1.88

280

, water

Top layer ( vibratecf)

Average force to remove Dolos in air

239

- = 1.87

128

,, water

Bottom layer ( vibrateil)

Average force to remove Dolos in air

692

-=2.04

339

, water =

The observed ratios which average out at 1.92 are slightly higher than the ratios of

block densities in air and water of 11.75. One

of the reasons for this might be that the water acts as a lubricant. This would

some-what reduce the forces observed in water. A

10

[

:

u..

I

Vibrated No. of test Bottom layer

;··

'

---··

·--2 _ . . . No. of test

·-·--·

I

·--·

10 16 6

I

2

I

Test carried out in air

.I-

Test carried out in water F = Force to remove one Dolos (Newtons}

W= Weight of unit

Block density= 2.33 g/cm3

test will be done later to check this. To

provide the same lubrication with blocks

in the dry the blocks: will be sprayed with

water during the test.

It is reasonable to assume from the results that the force required to remove a block from the pack is approximately proportional to its density and that the simple concept of interlocking as stated earlier is· valid.

Test 5 The effect: of slope

'How are the stability of Dolosse affected by the angle of the slope? Can one separate the block's stability, even qualitatively, in terms of its weight and its ability to

inter-lock?' The Hudson equation describes the

stability of a breakwater in terms of slope as follows : Pr H3 _tan() W = -Kn ( Pr- 1) 3

Pw

H =Wave height

Pr = Specific weight of armouring

Pw = Specific weight of water

W = Weight of armour unit

() = Slope of breakwater faoe

Kn = Coefficient of stability

The slope dependence as expressed by this equation might be true for stone break-w;aters or even for Tetrapods· but it is un-likely to be true for complex blocks like Dolosse.

Stone brerakwaters

If it is assumed that the stability of a stone

can be described in terms of the force re-quired to move it at right angles to the slope then the forces acting on the stone are shown in (8).

MAY 1979

angles to slope

=

W cos ()

=

F. On this

argument stability improves with smaller slopes, a fact which has been weH proved for stone breakwaters.

Dolosse

A Dolos is an armour unit which relies on weight and heavily on interlocking for its

stability. Brebner in a very interesting paper

on Dolosse presented to the 16th Coastal

Engineering Conference (Ref 1) showed that

a certain slope is required before full inter-locking can be achieved. Thus interinter-locking

is a minimum when () =0°. He demonstrated

this fact by showing that the 'w.ipe out' velocity for stone and Dolosse laid on a horizontal bed was the same when the weights of a stone and a Dolos were equal.

The diagram (9) expresses the idea that

the interlocking will build up slowly at first but this tendency will then increase to a

maximum. If the stability of Dolosse can

be described partly in terms of its weight

then we must add to Curve (A) the weight

stability factor we have obtained .earlier which is a cos () relationship.

Note that the Curves (A) and (B)i show

that interlocking increases with slope whereas the stability due to weight decveases. Which means that there is an optimum slope which maximises the stability. This hypothesis is illustrated in Clil).

It is not possible to study or analyse the various parts of this hypothesis but it is possible to test whether the prediction that the force required to remove a unit from the pack reaches an optimum value.

As in previous tests a double layer of Dolosse were laid in the smaller of the two trays, the slope was vibrated and the force required to remove the middle block from the top layer was noted. Only one block was removed each time. The test was carried out ilO times for angles of slope between

oo

and 45°. The results were averaged and are shown in (12) ..

The results confirm that there is an opti-mum slope which lies in the region of 28 o (1 : 2}. The curve clearly exhibits a maximum in the force vequired to remove a unit from the pack but pel'haps this is not as

interest-J~

""

u 0

I

"ii " .5 _Interlock

/

.... 0 c

A

0

,_..,.I

..,

~ :g " c 0 u 0 20 40 60 80. slope-degrees

(8) (left) Forces on stone on a slope.

'(11) (right) Sketch of effects of interlocking and weight.

ing or surprising as the fact that these forces change markedly around the maximum for small changes in slope. Mr Pattern, who carried out the tests, reported that the feel of the slope each side of the maximum was noticeably different. The tests were dis-continued beyond a s'lope of 11 : 1 because the slopes were unstable and the results in practical terms meaningless. It was possible to consolidate the pack •up to a slope of 28 o

G1 :

2) but not for steeper slopes. Even well-made, hand laid slopes felt loose and this

was especially marked above 35 o. It

appeared that the natural angle of repose of Dolosse was being exceeded.

Only a limited number of Dolosse were available to check whether this was true. When these were tipped out on to a flat surface- their angle of repose was

approxi-mately 45 o. Other authors quote higher

.E 0"> ·a; ~

...

0

"'

.g

::1 ..c ·;::

...

"'

0

"

0

...,

~

I

.

,,

'\

\.. B Weight

"

\

20 40 60 80 slope-degrees

(10) Sketch of weight contdbution to stability.

figures than this. The true angle of friction

is less than the angle of repose and Dr T

Dunstan of University College, London, is to try and establish this in a shear box. The fact that the model Dolosse are large com-pared with the box in which they will be tested does not make it an easy experiment. However, it is likely that the divide between the two modes of behaviour might be con-trolled more by the friction on the interface between the cover and underlayers which in this case was smooth. If this. is so it empha-sises the importance of the underlayer in influencing the static behaviour and inci-dentally the dynamic behaviour of the cover layer when subject to wave action. Even in the absence of this data it is clear that the discontinuity on the curve separates two quite different modes of behaviour. For

slopes from

oo

to about 30°, below the angle

of friction, the slope can be consolidated by disturbing forces but above 30° the units remain 'loose'. This result might be taken to conflict with the results of Brebner. He tipped Dolosse slopes built in large trays up to beyond the vertical, but one suspects that even small forces applied to his steep slopes would have brought about collapse. In other words the steep slopes were very weak and

(9) (left) Sketch of build-up of interlocking. (12) (right) Effeot of slope on the force to remove a Dolos from the surface layer.

...

/

_'

'

~17'

_'\

0 0

i\

Interlock + Weight 15 .S A+B + .E 0> I -~ 20 40 60 BD slope-degrees

unstable but could remain intact in the

absence of disturbing forces (Ref 1).

The best trigonometrical functions to fit the two modes of behaviour illustrated in (12) are as follows : F - = 2.23

+

0.33 tan 3() W -between

oo

and 30° Eqn 1 F

- =

2.3'1

+

0.33 cot (3()-90°} W -between 30° and 50° Eqn 2

where F

=

Force to remove a Dolos from

the surface layer

W

=

Weight of block

() =

Angle of slope.

Note that Equation '1 is for practical

pur-poses a mirror image of Equation 2 about the axis ()

=

30°.

The implication of these results for Dolosse is that for practical purposes the discontinuity between the two modes of behaviour should be avoided. It should not be assumed, however, that the discontinuity

will take place at the same angle for rougher slopes. Tests are at present being done to investigate the effect of slope roughness and these will be reported in a future publication. As might be expected .the static stability of Stabits built in the 'brick wail' mode was quite different. The effect of slope is shown on ~13). Tests were discontinued at an angle

of 60° when the removal of one unit caused

the slope to collapse .. Up to 60° the curve is continuous and is very like the shape

pre-dicted in (111)., The simplest trigonometrical

function that fits this curve between

oo

and

50° is as follows : 4·0

H

r

Doloj~\

t

3·0

o/ ol. o'

!

/

o._o $: 0 - - 0

i

-;;: 2·0 ~--·

4

I .

Con.llidation Jck

7·0f

0~ 6·0 / 0

__.,..o

\

5·0° 0 4·0

\

Stab its 3·0 2·0 1·0 0 10° 20° 30° F - = 5.35 cos 8

+

1.7 sin 3.68

w

0 slope 60° Eqn 3 A better fit for the curve between

oo

and 25 o ie when interlocking is being generated

is: F

- =

5.35 cos 8

+

tan 38

w

Eqn 4

It is interesting that as for Dolosse the tan 38 term turns up once more. The first parts of Equations 3 and 4 represent the way in which the w,eight contribution to stabiliy decreases with s~ope and the second is a function describing interlocking and inter-block friction.

T'est 6 A comparison 1of Dolosse, Stabits,

Tetrapods ami stone

'How do the forces required to remove Dolosse, Stabits, Tetrapods and stone

com-pare?' Earlier results have shown the

con-siderable variation in the stability of units in a Dolosse pack. The present test was designed to compare the magnitude and the spread in the forces required to remove a block with slopes made of Dolosse, Stabits (Mark 2), Tetrapods and stone. The Stabits were laid in two ways called 'double layer' and 'brick wall' (14) and (15). The designer's brochure says 'the former being used for slopes flatter than 1 : 2 and the latter for slopes of 1 : 2 and steeper'. All tests were done on a slope of 1 : 2 and the forces re-quired to remove units from the pack were measured. As before only one unit was removed in each test and the test was done 10 times in each case. The results are shown in (16).

Even on visual inspection it is obvious that the spread of forces required to remove a unit is more for Dolosse than for Stabits, Tetrapods and stone. These spreads can be exoressed in terms of standard deviations as follows:

(13) (left) Effect of slope on the force to remove a Stabit from the surface layer.

Table 4 Sltandard deviations of non-dimensional force Unit

Stabits (Brick wall} Tetra pods

Stabits CDouble layer) Stone Dol os Standard deviation of F/W 0.46 0.51 0.6 0.9 1.64

One way of expressing the way in which a unit interlocks and uses its neighbours in the pack to enhance its own weight is to

compare the average values of

F /W:

Table 5 Av,erage values of non-dimensional

foroos

Stabits (Brick wall) Dol os

Stone

Stabits (Double layer) Tetra pods Average value

F/iW

6.28 3.62 2.!14 1.75 1.53

(14) Stabits laid in 'double layer' mode.

The results show that Stabits when laid on the 'brick wall' principle are very effective at interlocking but the F

/W

value drops to

1. 7 5 when randomly placed. The relative

high value for stone was a surprise and illustrates the effect of i:nterblock friction. The results demonstrate what has been said earlier that although they are good enough to illustrate a principle many more tests would have to be done to make them useful quantitatively.

The spread in the static stability of a unit (Table 4) must in some way affect the dynamic response of the slope to wave action. For example, it probably controls the time history of failure and the life of the struc-ture (Ref 2). Intuitively one feels that large spreads in stability are less desirable than smaller ones and this is the price one has to pay in taking advantage of the properties of interlocking. There will be blocks exhibit-ing stabilities as low as the block weight and others six to seven times more stable at any one time. One way of dealing with

THE DOCK & HARBOUR AUTHORITY

spread might be to include it as a Spread Factor in any equation that attempts to describe the stability of the units in wave action. As a suggestion it might be expressed in terms of the standard deviation in F /W.

It would make alloWiance for some of the

undesirable effects of interlocking and would reduce stability factors for complex units to reasonable working limits. Most designers of Dolosse breakwaters now seem to accept that a reasonable Kn value for this block is of the order of 14 rather than figures of 25 to 32 that are often quoted. Spread factors would operate to reduce Kn's in this way. It is interesting that the Hudson equation has been used successfully to describe the behaviour of stone, Tetrapods and Stabits. Could one of the reasons be that their spreads of stability are very alike? Dolosse exhibit quite different spreads and this too might partly explain why a Hudson approach is not likely to succeed in this case.

(16) demonstrates that when Stabits are used in 'brick wall' fashion they produce a slope which is statically very strong. Used in this way it is debatable whether they con-stitute a slope which can be called rubble mound in the accepted sense of these words. Nevertheless, when used in this mode the volume of the voids is less than if they were placed randomly and this could detract from their stability in wave action. The Kn's for the two methods of construction might be closer than anticipated from knowledge of the statics. The Kn values quoted for 'brick wall' and 'double layer', established bv model testing, are almost the same illustrating that static stability only contributes so much to dynamic stability, other factors like the per-meability of the slope, must be taken into account.

Note on units that in~rlock

Until we know more about the behaviour of complex armour units the implication of the results is that it would seem advisable to retain th~ property of interlock to the full especially at times of extreme wave activity because it contributes a major part of the block's stability. This means the units should not move.

This thesis might seem to be in conflict with the well established design practice for stone breakwaters but there are reasons why the 'no movement' criteria need not

sarily be observed in this case. The greater part of the stone's stability comes from its weight which is not affected by movement. Hence it is quite reasonable to allow, move-ment and even damage to arrive at an economic design. Complex units employing interlocking operate in quite a different way; they lose a large part of their stability when they move just at the time they need all the stability they can muster.

What has been proposed is the very safe

approach. It does not imply that the 'no

movement' criterion is the right one to adopt for the most economic design but if move-ment is allowed the consequences should be fully understood. Further insight cannot come entirely from physical models -among others things they have scale prob-lems. Statistical mathematical models need to be built which rinteract the random cesses due to ,WJaves with the random pro-perties of the armour unit. There is already a move in this direction. The method pro-posed in this article might help to establish relationships which can be used in such models.

Conclusions

1 The force to remove a Dolos from the pack exhibits considerable spread and this is much higher for Dolosse than for Tetrapods, 'Stabits or Stones. It is sug-gested that a Spread Stability Factor be included in any equation that describes the stability of complex blocks. Work is being done on the best form this factor should take.

2 It is important that a slope made of

Dolosse should have time to bed down to generate its maximum stability. The tests illustrate the importance of corn-paction.

3 The simple definition of interlocking seems to have been confirmed in a test where it was shown that the force to remove a unit from the pack, top or bottom layer, is directly proportional to the effective density of the block.

4 Dolosse can interlock and dislocate very quickly so that just beyond the point of no damage the slope is made up of units changing their stability in a random fashion in space and time and subject to seasr which in themselves are random. 5 It would seem that the static stability of

Dolosse on a slope is about the same at all points. That is the stability of a unit does not increase with the weight of Dolosse above it.

6 The average force required to remove a Dolos from the slope reached a maximum at aJbout 28 o (1 : 2). It was not possible

to consolidate the slope properly for steeper slopes. The figure of 28o separ-ates two very different types of behaviour. The change from one mode to the other is quite dramatic. The true explanation is still being sought.

7 The significance of the results to the behaviour of rubble mound breakwaters is not completely understood but it is felt that this method, which 'looks at the statics, might be developed to give

further insight to slope stability. For example, other units' can be studied and factors like block wear investigated. It

is possible that by studying the problem in this way, empirical, and hopefully

fundamental, relationships could be

established which could be used to develop a better statistical approach to the problem bearing in mind that the behaviour of the units and the disturb-ing forces due to the waves are random. The development of such a statistical model would be a major contribution to the understanding of the underlying principles of design using complex units and will eventually replace the single-equation approach used at present.

_r-·~· --~·...r· 6 r·-__r--....r-·-Stabits (brickwall} : - - Dolosse

~

r·_j 1-'

r.J

I

4 ~

~

r---

Stone

~ _j ,. __ _! Stabits {double /ayerJ

u. 2 _j ..

J~

___

f __ _:---' ___ j ·· Tetrapods ,.. _ _! 10 No. of test

(16) The spread of forces to remove a unit from the surface layer for Dolosse, Stabits, Tetrapods and stone.

Acknowledgements

This article is published Wlith the per-mission of the Director of the Hydraulics Research Station.. I would like to thank Mr L E Pattern for the meticulous way he carried out the experimental work and to the many colleagues who put up with my enthusiasm for the project. Dr T Dunstan, University College, was· most helpful in dis-cussing the results.

Part way through the project I dis-covered that a colleague, Mr C L Abernethy, had done similar work with Tribars some years ago. These blocks mainly rely for their stability on interblock friction so it will be interesting to compare the results when they are published.

Note

Since this paper was written results from the box shear tests have been completed. These show that the angle of friction for Dolosse en masse is 60°. About 30 units were broken during this test and the way they broke was very consistent. More will be said

on this subject in a later publication.

Refe11enres

1 ·Brebner A: ,performance of Dolos blocks in an .open channel situation. 16th Intemational Coas•tal Engineel'ing Conference 1978. (In press).

2 ·Price W A: Some thoughts on rubble mound breakw:JJters. 161-h International Coastal Eng1ineering Conference 1978. (In press).