ON OFFSHORE SCOUR AND SCOUR PROTECTION with the Ekofisk site as an example

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FORSKNINGSRÀO

(ROYAl NORWEGIAN COUNCll FOR SCIENTIFIC AND INDUSTRIAL RESEARCH)

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RAPPORTENSTITTEL

ON OFFSHORE

SCOUR AND SCOUR

PROTECTION,

WITH THE EKOFISK SITE

AS AN EXAMPLE

DATO

11. Dec. 1973 ANTALL SIDER OG BILAG

29 sider 17 bilag SAKSBEHANDLER/FORFATTER C.G. Bringaker/H. Moshagen PROSJEKTLEDER T. Carstens A. TçSrum SEKSJON OPPDRAGSGIVER

NORGES TEKNISK

NATURVITENSKAPELIGE

FORSKNINGSRAD

OPPDRAGSGIVERSREF.

BA CI030.0221

EKSTRAKT

The physics of scour lS briefly examined both for

The feeble unidirectional currents and for waves.

experience from ocean structures is cited.

For the Ekofisk site estimates show bottom velocities

to grossly exceed existing stability criteria. If the

site is swept by a current with a persistent direction scour is likely to occur within a distance of one tank

\ radius from the tank.

3 STIKKORD SCOUR EKOFISK SITE SCOUR PROTECTION

ltA~ ...

T. CARSTENS Head of research

TABLE OF CONTENTS Page TABLE OF CONTENTS . I 1. INTRODUCTION 1 2 • GENERAL ON SCOUR 2.l. 2 .2. 2.3. 2.4. 2•5.

Current and waves .

Sediments in suspension .

Scour at ocean structures

1 1 5 6 6 8 Unidirectional flow Waves . . . .

3. THE EKOFISK SITE 10

3.1. Estimates of the bottom velocities in an

irregular wave field . . . 10 3.2. Transport of bed material . . . 14 3.3. The bottom velocity field around a

verti-cal, semisubmerged cylindrical tank in

regular waves . . . 16 3.4. The steady flow field near a cylinder. . 17

3.5. Pore pressure 19

3.6. Model tests on the DNV's EKOFISK storage

tank . . . 19 3.7. preliminary estimates of the size of the

stones in a stone blanket as scour

pro-tection . . . . .. 23

4 . CONCLUSIONS ₂₅

LIST OF REFERENCES ₂₇

One of the items that has to be considered when designing a sea structure resting on a sandy bottom is local scour and scour protection. Scour holes at a structure may affect the overall stability of the structure as well as the stresses ln the structure itself. It is, therefore, of importance to know if scour may occur and to take possible measures for scour protection.

The structures that one has in mind in the following are gravity structures, typical examples of which are shown in Fig. 1.

/

Fig. 1.

2. GENERAL ON SCOUR

2.1. Unidirectional flow

The following is a very short r-evi ew of some of the fundamental aspects of sand motion in flowing water. Emphasis is placed on initial motion and local scour.

Movement of sand particles in flowing water occurs when the flow velocity is above a certain critical velocity. On a plane sand bed there may be mot ion of the particles without

scour. In this case the amount of sand moved into an area is

the same as the amount of sand moved out of the area. The

sand bed lS said to be dynamically stabIe.

If we place a structure in a stabIe sand bed, the flow pattern

will be changed. If there was no sand motion before, or if

the bed was dynamically stabIe, increased water'velocities in

the vicinity of the structure may cause the sand to move more intensely 1n certain areas, thus causing scour hbles at the structure with depths determined by a new dynamically stabIe

configuration.

The concept of shear force from flowing water is demonstrated

in Fig. 2.

Fig. 2.

A two-dimensional uniform canal flow is assumed. The forces acting on the water element are the weight WI

=

y"d"dx, the integrated water pressure p, and the integrated shear force T at the bottom:

or

T

=

Y . d . Slna

Since a usually is small,

sina

=

tga

=

I,

the slope of the canal.

Lf we apply the Chezy formula forthe flow a,n the canal, we have

v

= Cid . 11 where C

=

Chezy's coefficient

V

=

average velocity. We get then v2 T = Y • C2

The expression V*

=

[i:

where p

=

water densi ty, is designated "shear velocity".

The flow velocity varies from the bottom and up as indicated a.n Fig. 3.

!

y

rOT' tur-l.u Lcn t fLow with u fr-ee cur-facc, the velocity distri -bullon ;,.rithheight above the bottom is

v

=

1 In y_ + B

V. ~ ks S

whc re K = O.u (von Karman's constant).

The vari~tion of B_s vs.

-v-

(Reyno1ds nurnber) is shown III

Fig. 4. I

v~. 00";- -

--(1]

Thc start of sand motion is governcd by the grain size and the shear velocity. The critica1 shear Ve]ocity can roughly be found Ly use of Shie1ds diagram, Fig. 5:

To find the critical shear velocity from this diagram, a trial

and error procedure must be used. Enclosure No. 1 from [3J gives the critical shear velocity vs. grain size distribution.

2.2. Waves

If there is wave action, the particle velocity distribution is different from the distribution in flowing water. The water particle motions due to waves are as shown in Fig. 5.

Tl" -

---"c t.

zI

Decp water .1- < !!. < 1. 20 t. 2 !!.L > .t:l_ Fig. 5.

The water particles move in nearly closed orbits; but they have a slight forward motion (mass transport velocity).

It is to be expected that the shear stress due to waves is different from that due to unidirectional flow. The particle velocities close to the bed and shear velocities due to waves have not been as thoroughly investigated as for the case of unidirectional steady current. Riedel, Kamphuis and Brebner measured TO and estimated values for the friction factor used in the following expression for the shear stress due to waves:

TO

= ~

fw Ub2

f w

P

=

density of the water

Ub

=

water particle velocity at the bottom due to waves

From this expression it follows that the shear velocity 15

Enclosure No. 2 shows the results of Riedel et al.

[

4

J.

2.3. Current and waves

Bijker

[5J

has to some extent treated sediment transport due

to waves and currents. But the flow field close to the bottom

is not very well known and this case will not be considered

further at this time.

2.4. Sediments 1n suspens10n

It is known that when the water velocity is above a certain

value, some of the bottom material is thrown into suspension. It is of course difficult to state an exact value for the start

of the material being suspended. Engelund

[6J

gives this

criterion for the start of the suspension:

where W lS the settling velocity of the material. This veloc -ity is dependent on the specific weight of the sand, the diameter

of the grains, the "roundness" of the grains, and the kinematic

viscosity of the water. Fig. 6 from

[

1

]

gives the settling

velocity of spheres.

Bijker et al.

[3J

refers to Shinohara and Tsubaki

[7J

who state

in suspension is larger than the material moved as bed load

V

when

w*

> 1.7. A similar criteria for waves is not existing, but for the time being it is assumed that approximately the

same criteria applies.

fig. 6.

Chan, Baird and Round [l~ are concerned with the effect of

oscillatory liquid motion on a bed of dense particles. The

intention with their study was to investigate the transition between a stationary bed regime and a complet~ suspension of

particles in the liquid.

•

The transition from a dune-forming bed to a bed in which the surface particles were in motion through the oscillation cycle was found to occur when

1

aw2

₌

a

=

liquid particle amplitude D = bed material diameter w = angular frequency

The criteria for the transition of the material in total sus-pension seems somewhat unrealistic in relation to a prototype situation and is therefore not mentioned here.

2 .5 . Scour at ocean structures

The following is taken from the introduction of Reference [8]; "The purpose of the study, the results of which are summarized in this report, is to define:

"The occurrence and effects of scour and fill in the vicinity of ocean bottom structures and foundations. The study shall consist of a summary and an appraisal of available information within the present state of the art and a compilation of methods which may be usable for predicting the occurrence and effects of scour and fill in the vicinity of ocean bottom struc-tures and foundations".

liltmay be stated at the onset that no case of scour and depo-sition in the deep waters could be found in a special library of about 10.000 reports and papers on ocean engineering and oceanography which was sufficiently complete to permit a signi-ficant analYsis. There are instances in which a flow was ob-served, but not resulting in scour or deposition of sediment. In other cases the sediment pattern was described, but the flow that had caused it was unknown. One is therefore entirely de-pendent on experience obtained in the laboratory or under

non-ocean conditions in predicting the relationships between flows and the resulting scour and deposition of ocean sediment".

Numerous papers have been written on scour due to current at bridge piers etc. Reference

\)1

also describes some model results on.local scour due to waves and current, but none are directly relevant to a large volume ocean structure.

Reference [l~ gives some interesting results of prototype scour at a framed platform in about 13 m of water, where the bottom material is a mixture of fine sand and silt. Fig. 7 shows how the scour due to waves and current occurred.

Ii

/

'''''

'''

,

~",_

]

.

.

y'r...;.tII",II,"1\1<',0:

~

-

~

'

~

~

r

..

'-

'

ç=-

'.

~:

.

~:.?:~

.

~

;: ~ o so 100 ~~~'~'- ' , ~,":!"'I;Ikd o_{L___l} 10 7_'0_{__} 30 __J S..:.)"~111n-...~N'!:t

-l'HO,),O'ïYl;E i'AT'i'I-:n!~OF-r-ouu, !-'I,0;.: ;\11::\SlJlll·::\n::\TSlIl' lJIVi·:aS

Fig. 7

It is seen that it is not local scour around each pile that occurred in this case, but a saucer-like-depression under the whole structure. Without any special view point taken regard -ing the reason for this erosion, the following is quoted from

"The more common type of erosion which causes individual scour holes can be visualized as being due to the local increase ln velocity around the piers with consequent re-moval of the material under the constant surging of the induced current. In the new type of erosion, these local steady concentrations of current are too feeble to attack, but large transitory currents induced in the bed by the varying pressures under the great waves become big enough to throw bed material into suspension. Turbulence gene-rated by the piles prevents it from settling until af ter it has been carried away from the structure. For those to whom the existence of flows through the bed seem un-real, we would point out that flow in a porous medium respond to unsteady conditions with a velocity of the order of that of sound waves, in other words practically instantaneous" .

Data on scour of large ocean structures in deep water are understandably not available, since such structures are non-existing. The first problem is to estimate from general know-ledge if scour possibly will occur and where this is likely to happen.

3. THE EKOFISK SITE.

3.1. Estimates of the bottom velocities in an irregular wave field

The water particle velocities (maximum) at the bottom due to regular waves are glven by:

u

=

TIH 1 (1. order wave theory)

An estimate of the distribution of peak ve10cities ln irregu1ar

waves, design storm conditions, are made according to the fo1

-lowing concept, which is often used in dea1ing with random1y

varying signa1s.

Wave power spectrum SH <f)

Transfer function Ub

H

Velocity power spectrum

U 2

EU <f)

=

<~)

.

SH(f)

b H

The re1ation between the velocity power spectrum and the

ve10cities is approximate1y:

It is further assumed that the velocity peaks are distributed according to a Rayleigh distribution:

U 2 _È_)

U 2 b

=

1 - exp

(-A wave power spectrum which is assumed to be valid (approxi-mately Ekofisk design waves) is shown in Enclosure No. 4. The spectrum has a significant wave height H1/3 of 12 m. In the following a wave period of 15 sec. is assumed for the Ekofisk site.

The transfer function of the water wave particle velocity at 70 m depth is shown in Enclosure No. 5 and the corresponding power spectrum of the water wave particle velocity in EncLo+ sure No. 6. The spectrum has a significant particle velocity in Enclosure No. 6. The spectrum has a significant particle velocity of 1.54 m/sec. Enclosure No. 7 shows the estimated distribution of the particle velocity Ub in a free wave. The diagram shows also a distribution of the particle velocity Up where Up is the sum of the water wave particle velocity and a current of 0.40 m/sec. at the bottom.

In this connection it is also of interest to know the order of magnitude of the shear velocities due to waves (see chapter 2.2.):

v

_x

=

y!w "

Based on the results in

(4] ,

a friction factor (fw) of 3.4'10-3 was calculated for the Ekofisk bottom sand (D50

=

0.15 mm).

The transfer function of the shear velocities at a depth of 70 mand the corresponding power spectra are shown in Enclosure No. 8 and 9 respectively. The significant shear velocity was estimated to 6.06 cm/sec.

The distribution of V lS shown in Enclosure No. 7. The

x

critical shear velocity is given in the same diagram, indi

-cating motion of the bed material at a relatively low wave

particle velocity. The estimate of V critical is based on

x the diagram in Enclosure No. 1.

Diver experience from the Ekofisk area (personal comrnuni -cation, I. FOSS, DnV) suggests that motion does occur during

storms. Following a storm the bearing capacity of the top

sand layer is reduced so that the diver's feet sink in some

10 cm, while the normal imprint is insignificant.

BRATTELAND and BRUUN (1973) observed movement at the Ekofisk

site of a fluorescent tracer with grain size distribution does

the actual distribution for the local sediments. Fig. 8 ;ho~s

the result of a sampling on May 3rd 1973 of a tracer released March 15th.

s

Fig. 8

~;i.llnplwcosrc taken at S and 10 ft distanccs from the tracer source. It may be noted that tracers have mainly moved

to-waras northwest and towards

south, the concentration de -creasing with distance from the

3.2. Transport of bed material.

If it is assumed that the sand grains are spherical, - the

settling velocity of the grains CD = 0.15 mm) is about 1.5 cm/s.

It is seen that even without the structure being present the

V

ratio

w-

will exceed 1.7 from a relatively low wave particle

velocity. The ratio of 1.7 was assumed as the ratio when the

suspended load is larger than the bed 10adD1.

The ratio between the wave particle excurSlon amplitude at a

depth of 70 mand the amplitude estimated by the criteria

glven on page 7 is:

aCd=70m)

a. .

crlterla

= 0.8

where ad=70 is the significant wave excarsion amplitude at· the bottom. This ratLo indicates a high motion .intensit y dl the bottom Cchapt. 2.4.).

Bottom shear stresses when the structure is present can not be

calculated according to the results of [4] because the flow

field is different from that during the tests described in (41

Z011e. I-I(~ Î1(iS

r:l(~als wi.th sedjment.motion heyond the br-cakcr

-d(>velopedthe foLlow i.rigTahlc:

TASLE

ru

Wa\'e H.ilht (metre~~t(l Produ(eJncipiU\t MO!;'on00 Flat B~

100 metrrs deQP with Sand 0.2 rnrn. dia. ond S='2.0

,\"thor EqlA3tion T" 125K. r, 14.' sec.

C.rstens j 5.7 ~.6 IN.··J.2) Betnold 6 5." 2.9 .\\anohar 3 8.2 "'.3 (", Cl7.4~ Vincent 4 465 2.45 ..

From the work of Silvester we take the following conclusion:

"The depth at which the ocean bed can be disturbed by

waves was thought to be very limited when computed on

the basis of mean shear stress. As replication of the

water particle mot ion has approached that of natural

conditions, this apparent re ach of the waves has

in-creased significantly. From the discussion presented

herein, it would appear that the whole Continental Shelf

is the stage for the sediment drama of oceanic swell".

The wave mot ion causes a back and forth oscillatory motion

of the material when it is in bedload. This may not cause

any significant scour, although the waves may cause a net

motion in one direct ion due to the mass transport velocity.

More serious may be the waves' apparent ability to throw

the sand material into suspension. The current and the mass

transport velocity of the waves may then move the suspended

material away from the structure and thus scour holes may

Qccur.

The ability to get the bed materials into suspension increases

when the turbulence activity increases. The perforated

wall-system of the EKOFISK TANK is designed to convert wave energy

into turbulence, but to what extent this local turbulence picks

up bed material is not known.

However, simply by perturbing the free flow field of the waves

and the current, the tank has an important impact on the nearby

3.3. The bottom velocity field around a vertical, semi-submerged cylindrical tank in regular waves.

By reflection and diffraction of the incident waves, the tank

will impose a new wave reglme on its surroundings. The supe r-position of incident and reflected waves in front of the tank, and of crossing wave trains in the rear, cause higher than

incident waves to occur several wavelengths from the structure.

To get an impression of the scourlng potentialof this new wave field, we have computed the new velocity field at the bottom.

The velocity potential around a vertial, cylindrical tank fixed to the bottom and extending through the surface due to a regular incident wave is, according to 1. order wave theory, given by

gl! cosh k(z+d) -icrt m cfJ 00 Em(i) cos(m8) = _{2crcosh kd e}

z

m=O [ i(~ - Ym) (1) - Jm(kr~ . e _{sinYm H (kr)} m

Here g is the acceleration of gravity, H is wave height, cris frequency, k is wave number, d is mean water depth, z is vertical coordinate, r is radial coordinate, 8 is angular coordinate measured antiüockwise from the positive x-axis and t is time. The parameter Em is 1 for m

=

0 else 2, and J (kr) and H(l) (kr) are Bessel and Hanke L

m m

functions respectively, of first kind and m-th order.

Based on this formula velocity amplitudes in radial and

TI

tangential direction are calculated for 8 = 0, Tand TI,

and r

=

1, 2, 3 and 4 radial distances from the center of the tank, in all cases for z

=

-d corresponding to points

the sense that the series expansion is terminated af ter

m = 8, and t is given 10 discrete values within a half -period, and the numerically largest value is chosen as the

amplitude value.

The results are presented in Enclosures 10-17 for depths

ranging from 50 m to 200 m. All veloeities are calculated

relative to the velocity amplitude along the bottom in the

incident wave.

3.4. The steady flow field near a cylinder.

The increased oscillatory motion due to the perturbation of the wave field by the tank increases the suspension of bed partieles. Provided the steady current is not slowed down

by the tank, the transport of sediments out of the perturbed

area should increase. At the same time the transport of sediments into th is area has not changed, and so scour will result.

The steady potential flow field near a cylinder is glven by

a2

= u(r + --) cos e r

u - yelocity at r = 00

a - radius of cylinder r,e - polar coordinates

The velocity potential ~ glves the radial and tangential veloci-ties a2 ur = u(l - ~) cos e r a2 u

e

=-u(l + ~) sin e r

and a total velocity

2 4

=

u2Cl - 2a2 cos 2

e

+ a4)

r r

We want to find the area where the perturbed velocity ~

exceeds the velocity u without the cylinder. The limiting

condition

10/1

=

u

gives

cos 2

a

₌ 1

"2

At the cylinder r

=

a and

e

=

300 so reduced veloeities

are found in a rather wide pear - shaped area upstream

Cand for the potential field, downstream) of the obstruction.

CEnclosure No. 18).

The maximum velocity occurs at the side of the tank and is

about twice the undisturbed velocity for the steady current

and also for the longer waves.

Substantial velocity increases will prevail at considerable

3.5. Pore pressure

As described on page 9-10 the WdV~ action also induces an

upward pressure force on the bottom particles, due to the

pressure gradient set up within the soil.

We have estimated these gradients for North Sea conditions.

Enclosures No. 19 and 20 show pore water pressure profiles

for fine sand and silt, respectively, for a 15 second wave

of height 24 metres. These pressures are directly

propor-tional to the wave height, so a 12 m wave would give 50% of

the values for a 24 m wave.

The estimates are based on the assumption that the bed material

is nondeformable, and that on the other hand the water lS

com-pressible. This gives the following equation for the wave

pressure transmission

nv

Y

2.E.

kE . dX

Here x and y are horizontal and vertical coordinates resp.,

nv is relative po re volume, Y is spesific weight of water,

k is permeability of bed material and E is the modulus of

elasticity of water. The solution to this equation for a

bottom layer of thickness d when a regular pressure wave of

amplitude p, length Land period T has been acting on

o

the bottom surface for a sufficiently long time is given by

[ cosh l-1<y+d) p<x,y,t)

=

Re Po cosh l-1d x t -L--T)J i2rr e

with the vertical "wave number" l-1 glven by

[

. 4 n :y 2] 1/4

Arg(ll)

=

1 Arctg(~YY . L2 )

2 kE 2nT

The bed also is assumed to satisfy the condition of isotropie flow.

The pore pressure gradient is highest at the mud line. For a 24 m wave a maximum hydraulic gradient of about 0.3 is o b-tained for fine sand and about 10 times higher for silt.

Liquefaction is assumed to result when the pressure gradient exceeds unity.

In the vicinity of the tank the pore pressures must also be influenced by the oscillating wave load transmitted from the tank to the sea bed. While this effect is likely to be con-fined to the close proximity of the tank perimeter, it may yield high lift forces on the bed particles.

3.6. Model tests on the EKOFISK oil storage tank

During the tests on the EKOFISK storage tank at RHL an unsuc-cessful attempt was made to measure the wave pressures under the tank when the tank was resting on fine $and with DSO

=

0.076 (approximately). The scale of these tests was 1:100. It is of interest to look at the scour pattern at the tank

and to estimate to what extent the model tests can represent prototype conditions.

Fig. 9

Fig. 9 shows the bottom condition after approximately 1 hour

test run with waves of height H_m

=

24 cm (H_prot

=

24 m) and

periods T = 1.5 sec. (T = 15 sec.). Since these tests

m prot.

were not concerned with scour, no exact record was made of

bed movement s.

Shear velocity in the model. To determine the surface rou

gh-ness ks ENGELUND

[14]

suggests:

where Df is the fall-diameter.

In accordance with

[

14

J

Df lS estimated as a function of the

This gives: ks = 0.225 mm a = 6.27 cm ub = 26.3 cm/sec. a 280 k = 5 Re aUb 1.3'103 =

--

_v =

Enclosure 2 shows that fw 15 lying in the rough turbulent a

flow regime where fw only is dependent on the ratio k' 5 This functional relation is shown in Enclosure 3, with a

-3

friction factor fw of 0.07 which gives

Shear velocity v

=

4.9 cm/sec x

Critical shear

velocity v = 1.2 cm/sec ~cr

Shear velocity 1n the prototype. The following prototype data are used:

Wave height: H = 24 m Wave period: T ₌ 15 sec. Water depth: d ₌ 70 m Bed material: D = 0.15 mm

Calculation

a = 6.27 m ub

=

2.63 m/sec

~ > 6000 i.e. Smooth flow reg1me (Enclosure 2)

ks

fw = 2.7'10-3 Shear velocity V _{= 9.4 cm/}s x Critical shear velocity V _{= 1.3 cm/s} xcr

The conclusion which may be drawn is: When a prototype bed material is used in a model, it is not possible to estimate the prototype scour situation on the basis of the model data. This sort of model scour investigation is in general not

directly applicable for the prototype situation.

3.7. Preliminary estimates of the size of the stones in a stone blanket as scour protection

The best example known to us of a test of a material suitable

for scour protection in waves was reported in Hydraulic Research 1968 (Appendix 1). This material was a layer of shingle. The tests were made in an oscillating water tunnel.

It is seen that the diagram of Appendix 1 does not cover a depth of 70 m. However, since the water partiele velocity governs the size of the protection stones, the diagram may still be used.

The maXlmum water partiele mot ion due to a regular wave at

the bottom is given by 1TH

u

=

_Of 1

sinh 21Td

We now assume

Wave height: Wave period:

12 m

15 sec.

giving ub

=

1.3 mis. o

Near the tank we assume

+ u = 2'1.3+0.4

o

=

3.0 mis

where Uo is the steady current.

This gives: sinh 21Td

""""L

1531T'12 1 = 0.84 Fr-om tables 0.078 d

=

0.078·Lo

where Lo

=

g_ . T2 (deep water wave length) 21T

For T

=

15 sec., 10 ~ 346 m which glves

d

=

346 . 0.078 - 27 m

From the diagram in Appendix 1 it is seen that the required

It must be noted that the flow around a large volume ocean

structure is different from that of the tests on which the

diagram has been based.

The diagrams in Enclosure 10.to 14 indicate that the

tangen-tial velocity component decreases with the distance from the

tank.

Over a distance of about one "tank-radius" out from the tank

wall the tangential velocity component exceeds the undisturbed

bottom particle velocity. This means that the width of the

layer probably will have to be 40-50 m wide.

It is stressed that further consideration and testing are

needed before a final design of such a scour protection is

made.

4. CONCLUSIONS

Offshore scour is the result of a combined action of waves

and current. The waves provide the major destabilizing flow

forces on the bed particles, while the current carries them

away.

In the North Sea the wave action at the bottom is sufficient

to move loosely deposited sand everywhere except, perhaps,

ln the deepest parts (d > 250 m).

The presence of a structure agitates the wave action and in-cr~ases the bottom veloeities in the general vicinity of the

A cylindrical tank will slow down a steady current 1n

sector facing upstream, and accelerate it over the rema1nlng

upstream halfspace. The highest veloeities are.twice the un

-disturbed current speed and occur where the sides of the tank

are parallel to the undisturbed current.

A persistent current is likely to carve a scour pattern near

a structure, and the intensity of wave action is likely to

determine the depth of the scour holes.

However, if the current veers ~ufficiently, a redistribution

of the sediments will occur and the deepest holes will probably

be filled in.

The duration of a current from the same corner therefore seems

to be the governing parameter.

If complete scour protection lS desired for a cylindrical tank,

it is necessary to cover the bed to a distance of at least

one tank radius with a stone blanket. The required stone size

depends on the location and can only be very approximately

estimated at present.

Adequate protection may be provided by a narrower stone blanket,

limiting the scour to a shallow ring at a safe distance from

the tank. However, at present no method exists for predicting

such a partial scour protection.

LIS T

o

F R E F ERE N CES

1 YALIN, M.S.: Mechanics of Sediment Transport. Pergamon

Press, 1972.

2 VANONI, V.A.: Brooks N.H., Kennedy J.F. Lecture notes

OT! sediment trtinsportationand channel stability.

California Institute of Technology, Pasadena, Californii1~

Repor.t No. KH-R-l. January, 1961.

3 DE BEST, A., BIJKER, E.W. and WICKERS, J.E.W.: Scouring

of a sand bed in front of a vertical breakwater.

Proceedings of First Conference on Port and Ocean

Engi-neerlng under Arctic Conditions, Trondheim, Norway, 1971.

4 RIEDEL, H.P., KAMPHUIS, J.W. and BREBNER: Measurement

of bed shear stress under waves. Paper submitted to

13th Conference on Coastal Engineering, Vancouver, 1972.

5 BIJKER, E.W.: Some considerations about sca1es for coastal

models with movable bed. Delft Hydrau1ic Laboratory,

Publication No. 50, 1967.

6 ENGELUND, F.: Turbulent energy and suspended load.

Coastal Engineering Laboratory, Hydraulic Laboratory,

Technical University of Denmark, Basic Research - Progress

Report No. 10, 1965.

7 SHINOHARA, K. and TSUBAKI, T.: Reports Res. Inst. of

App1. Mechanics Kyushi, Univ. Japan 7 (25) pp 15-45, 1959.

..

8 EIN_erosiSTEIN_on ,_{and depo}H.A., WIEGEL_{sition of s}, R.L.:_edimenA literature reVlew_{t near structures ln}on

the ocean. University of California, Berkeley, HEL 21-6,

9 BREUSERS, H.N.C.: Local scour near offshore structures.

Proseeding Symposium on Offshore Hydrodynamics,

Wageningen, The Netherlands, 1971.

10 POSEY, C.J.: Protection of offshore structures against

underscour. Proceedings of th e American Society of

Civil Engineers, Journalof the Hydraulic Division, HY 7,

July 1971.

11 POSEY, C.J. and SYBERT, J.H.: Erosion protection of

production structures. Proceeding of the Ninth Convention

of the International Association of Hydraulic Research, Dubrovnik, 1961.

12 SILVESTER, R. and AUST., F.I.E.: Sediment Movement beyond the Breaker Zone, Civi1 Engineering Transaction, April 1970.

13 CHAN, BAIRD and ROUND: Behaviour of beds of dense partieles in a horizonta11y osci11ating 1iquid. Proc. R. Soc. London A. 330, 537 - 559. (1972).

14 ENGELUND, F: A monograph on sediment transport 1n al1uvial

streams. Technica1 University of Denmark.

Hydr; Laboratory. Jan. 1967.

15 T~RUM, A.: Scour and grains protection at off-shore

current structures. Internal RHL note of'28. August 1973.

FROM HVDR

AU

LIC RESE

A

RCH

196

8.

HVDRAULIC RESEARCH STATION, WALLINGFORD, BERKSHIREI ENGLAND.

Thrcshold of movement of shingla subjeered to vveve action

Experimental studies of thc ihrcshold of movement of grnnular beds undcr wave action have in the 1'2$1,:.1.1

to bc limited to thc finer grain sizcs,The Pulsating Water Tunnel, described in Hydraulics Research 1966.j:'.S2,

bas now made it possiblc to dcicrmine the nccessary wave conditioris for thc initiatien of ni-vemen; of sl::"'~;~e sizes.

At the beginning of thc study it was thought to bc dcsirable to define the initiatien of movement in scrne

precise way ralher than to rely on a purcly visual assessmcnt. A method. analcgous to the zero transport approach, was carricd out for a number ortest runs byinitially marking aband across the bed and subseque.uly

noting thc number and position of particles which had movcd out of the markcd area. Tiiis type of rest was

carried out for various wave amplitudes, at set wave pcriods, for a cornrnon number of osciilations.

From the rcsulting distribution curves, the probability of a partiele moving from its initial pcsition to·a position within thc range x to (x+ öx) was determincd. The standard deviations elf the prob..bility C'..!~-"~:;

thus Iound wcrc plottcd against amplitude and the interccpt of the curve passing through ti~öC:points was

taken to he thc threshold condirion. Plouing thc numbcr of particles movcd, against amplitude, jie1è.5 an ill-conClitioned curve for thc dctcrmination of the point of intersectien.

Obviously a grcat deal of v-ork was entailcd in thc dctcrminatiou of a single value of threshcld. However, obSCC'o'ationshowed three distinct piiases in bed movement. First, a broad band of conditions cxisred in w;_;ch particles rockcd to and fro without actually rnoviug position. This t':llse was followed by a fairly crit.cal

stago where one or two particles wcre dislodgcd and movcd a Icw I'~accsdownstream. Finally, with a srnall

Increase in velocity and accclcration, many particles movcd. lt was thc Inrermcdiate, crirical stage that was founc.ito equate with the dcduced limit of ihreshold. Aftcr a fcw tests the observer was able to deelde t:70n

the limiting eonditlens which wcrc eonsistcntly in agreement with thc calcclatcd values. Thus, having 'ca li-bratcd' thc obscrver, all subscquent detcrminatir rs were catried out visually.

Other possiblc rensons for inexactitude were an'icipatcd. ltwas t!:ought rhat the grading (Irnon-uniformity

in size of particles bcing testcd might influcnce the rcsult and give an unwanted scatter in lb.: ICSU)t~, All

materials tested ·...'ere thcrcfore sicvod between close limits. This in turn raised the

r"

obltm of partiele ~!.;;r-!.

Most naturally occurring gravcls have a distinct change inshape with change in par+cle size, Ar. .:x.:mir.::.:i·:·'1

of several matcrials showcd that limestone chips came closest to retaining the sarne shape over a wid! r::':-i~e of sizes. Initial experirnents wcre therefore concucted on various fractions of limestone chips, although tests on ether materials became ncccssary in order to extcnd thc range of conduions. As the tests proceeced it

became apparent th at shapc varintions 10 bcexpected in shingle would nothaveameasurable effecton~h;~~:-.,j·,d

values, for shapcs runging from cubcs to spheres had no apparent effect on thc results. Recent tests on a ~.dl

graded gravel from the North Seahave indicatcd ihat grading is relatively unimp"rtant and tl~'!'Dsosizeisthe

appropriatc dimertsion 10characterize it.

Within thc shin:;le range [i.c, m:1terial>2 mm diameter) the Reynolds Number was found to p!ay no i-".~ct

and a unified plot of the rcsults Ier matcrials ranging frorn Iimcstone chips nnd giass spheres te iigh!-w;_-:.;b.t

matenals such as coal and perspex cubes was obtained by plouicg the parameter a'g'T" against the parac.ecer

aID, a bcing thc semi-orbit lcngth at the bed, Dihe equivalent mean sphere diameter oithe particics. T :i~e

pcriod of ihe wave, and s' tb: e.Icc.ivc gra'. uy, equal to :; (r. -r);'p, whcrc ;\ =é,;,nsil)' of particles .ind

p=dcnsity of fluid.Thc parameter clD may bc considcrcd 10lol:the ratio of dC:l&forc:- d..i·..ided by::cce:'::-.i::·:n

force. a!g'Tz wou.d api'c.'r at t;r';t '.i:;hi to bc sirnply thc ratio ('Îacceler.uion force io gra\';~:'.t\on.:.1ict:».

Howcvcr, since accclcrauon f.·,Tces.I'C r,·Ll~i\-.;:I:r srnall this illLj.,c-talion secrus unlikcly. Rather than ::::,. ~(

Ol ecru-in finitc lcngtl: ot time befere particles cun bccorne displueed. etherwi-e rnercly rocking will occur.

This contrasis with tbc thrcshold condition in uni-dircctional Ilow where thc time dependcncy is purely

arbitrary. .

Frorn thc unified plot a werking diagram, Fig. 5, lias been prcpared, bascd (JO the assumption cf shin&l,: with as.g, of 2·65. This makes it possible todeterminc thc wave conditioris neccssary to move a partreular size

of shinglc "r. convcrsely, given a set of wave conditions 10detcrrnine the size of material that will not move,

Two cxi.mplcs are illustrarcd.

Exarnplc A shows that with an Ss wave, 3·5 m high in 20m depth of water fineshing'c with a median sizc

of (1,4 mm would be on the point of moving. In the case of examplc Bthe height of a 65wave in 4·5 m of water

n~::c:.s,u)'to move 35 mm diameter shingle would be 2 m,

-s 1,0 2 S 10 2

HE/GHT OF WAVE(mel,.s)

(ASS'Jmir:gspKific gravity of2·65J

Working dlagrams

E3d shear stress volocity v VAr~UD D fOT v~riouB ~~to~lals.

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PARTIClE VELOCITI~S. AT WAT~1LPEPTH OF 70 m -

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SHEAR VELOCITV AT WATER DEPTH 70 m.

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PRESSURE PROFILES IN SANO BOTTOM FOR REGULAR WAVE.

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20

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