Time scale of two dimensional local scour

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275

INTERNATIONAL ASSOCIATION FOR HYDRAULIC RESEARCH

TIME SCALE OF TWO DIMENSIONAL LOCAL SCOUR

by H. N. C. Breusers

Research Engineer, Delft Hydraulics Laboratory

Delft, The Netherlands

Synopsis

The time scale of local scour is of importance in many model studies of

practical problems. The use of a time scale is justified by the similarity in

experimental scouring holes under different conditions. A time scale is derived

from experiments with a wide range of length scales, velocity scales and material

scales. The influence of velocity profile and turbulence intensity is demonstrated

with some experiments.

Resume

L'echelle de temps de l'erosion local a une importance dans beaucoup des

etudes sur modeles reduits des problemes pratiques. L'application d'une echelle

de temps est justifiee par la simulitude des configurations de l'erosion dans

des conditions experimentales tres differences. L'echelle de temps est derivee des experiments avec une grande variation des echelles de hauteur, velocite et des

materiaux de fond. L'influence du profil de vitesse et de l'intensite de la

turbulence est demonstree aves des experiments.

l

276

1, INTRODUCTION.

The construction of civil-engineering works in canals, rivers and

estu-aries causes disturbances of the uniform flow and consequently generates

conditions for the development of local scour. Prevention of any scour is

not economic and therefore some scouring must be accepted and predicted.

Despite of some systematical investigations e.g. Ref, 1 it is not

possible to determine the scouring downstream of a construction ey compu

-tation, For fine sand the equilibrium scouring depth is very large and in

many practioal cases the factor time is important. This mey be the case in

temporary situations (enclosure of a river or tidal channel) or if the

scouring time is limited (rivers with peak discharges of short duration).

The interpretation of model studies in these casee requires a knowledge of

the time scale of the scouring process.

2, DEFINITION OF TIME SCALE,

The time scale of the scouring process in non-cohesive sediments should

be estimated from considerations on the sediment transport and the flow

pattern in the scouring hole, The flow pattern however is very complicated

so that a prediction of velocities or bottom shear-stresses at any time and

place seems impossible with present knowledge, Also little is known on the

amount of sediment transport in highly turbulent conditions. Practical

re-lationsfor a time scale must be derived mainly from model experiments with

different scales,

For a suitable definition of the time scale of the scouring process it

is necessary that in scale tests with similar flow configuration the

follow-ing relationship is valid,

~

f (.L ~ )

h ~ t ' h

0 0 0

( 1 )

in which h • scouring depth

h • ₀ waterdepth at the end of the bottom protection

X • distance from the end of the bottom protection

t - time

t -0 a characteristic time of the scouring process

f - the same function in both tests.

1, W. Eggenberger R. Muller (1944) Experimentele und theoretisohe

Untersuchungen uber das Kolkproblem. Mitt. Versuchsanstalt fur Wasserbau

E.T.H, Zurich no.

5

.

C

32.2

ted "" the time ratio nt' is now defined C\Y The time scale, deno "'

on local scour behind dam• and horizontal

n From many experiments

n • t •

t o hat (_{1 )} was valid under a wide range of

bOttom protections it vas found t .

( f 2) ven if the velooit;r scale waa different from the

conditions see re• e

the treshold velocities of the bottom sediments,

it waa also found that the maximum scouring depth

scale of

From the experiments

varied exponentially with time (see fig, 1)

(2)

t

1• t a t which hmax • h0

It was also found that this relationship was nearly independent of the flov

configuration, Two tests mey be compared nov C\Y nt • nt

0 • nt1

3

•

TH:EPRETICAL CONSIDERATIONS,

in the Scouring process under different conditions is of

The conformity

it is possible nov to express the time scale ae a

and sediment transport, For this

corre-great value because

function of the initial conditions

lation existing sediment transport relations could be used.

d . tly in suspension is sa&ll

If the amount of material which goes ireo

t . of continuity of the

h be.,.,oad transport then the equa 10n

compared vith t e

=

bottom material:

(3)

gives the scale relationship:

local scour only geometrically undistorted

It is asBU111ed that for

A simple approximation of the existing

models are used, hence nx •

~-the parameters used in describing sediment transport,

lations between

~ •

T.

d

-1

~5(gA)

-

0,5

2 and 'f • ux f -, . (with L I • ~ )

fv

( 'i

'I

i

)4

is given C\Y• ~ • A If/ - If/ crit

)

.

,_,, ( l.

I'

re-2, H,N.C, Breusers (1966). Conformity and time scale in two-dimensional

model and protot:Y~e conformity, Poona P 1-8.

From this it follows that: n • n T ( x x )4 u -u crit ao that n t . nh 2• n 1,5. n 0,5 o ~ d • n -1,5. n -0,5 A d n (u•-u• . )-4 crit

This relation will ba compared with the experimental results.

4.

EXPERIMENTAL INVESTIGATIONS.

(6)

The deter.mination of the ti.me scale for different conditions required

many experiments. A great pa.rt of these e:z:periments were done in three

flumes (width 0,5, 1.0 and 3.0 m, waterdepth 0.25, 0.5 and 1.5

m)

on the

scouring downstream of a long horizontal bottom protection oonaiatillg of

stones: dstone. (0.02 - o.04)h

0 •

Testa vith different mean velocities and sediment diameter (sand:

d • 0.1 - 2.6 mm) could be correlated ey (see fig. 1)

nt • n(U -U )- 4 (7)

ma:z: orit

in which Uma:z: • (1+3r)U and Uorit in the critical mean velooi1;;y computed

from the critical shear velooi1;;y as given ey Shields. Values of

u

vere used

instead of ux for practical reasons. r is the mean relative turbulence in

-tensi1;;y, measured with a small propellor-1,;ype current meter at the end of the

bottom protection. The factor (1+3r) was determined from the experiments. The

influence of the sediment diameter on the critical velocity was sufficient to

take into account the influence of the grain diameter on the time scale. (see

fig. 2)

By comparing teats with different h (0.25 - 1.5 m) it was found that on

th a 2 • 05 ( · ) o

e verage nt~ nL fig. 2 . The e:z:ponent was slightly- greater than 2 due

to the fact that with increasing h the ratio U/ux increases and that the

X 0

value of u is more appropriate for sediment transport.

The influence of the material density was studied with sand, bakelite and

polystyrene (t... 1.65, 0.35 and 0.050). lo' comparing the materials it was found that relationship (7) was valid and that nt varied with (nA) 1• 6 (see

fig. 3).

Other flow conditions e.g. scouring downstream of lov dams and long

bottom protections could be correlated equally- vell with

(7)

.

The velocity

profiles were reasonably similar to the profile at the end of a rough bottom.

In case of deviating velocity profiles e.g. flow over a smooth bottom pro

-tection or downstream of high dams a correotion f t had

duoed: ac or o(u to be

intro-(see fig. 4)

C32.4

The final result of all experiments was the relation:

2.05 1.6

n - ~ . n . n -4

t o A (uma:z: -U cri t)

(8)

The influence of A is in accordance with the factor 1.5 obtained

qy

as-suming a fourth power relation between~ en 'f' , the influence of the sediment

diameter was less than predicted. Other factors as cohesion ma,:, be very

im-portant in practical oases (Ref. 3).

The value of o< (1+3r) is not important for the determination of the time

u .

scale if

11J.

~

,

which is also the condition for reproduction of the

orit

equilibrium scouring depth. In other oases an estimate ofo<u(1+3r) or a

determination from two scouring teats with different velocities is necessary.

5

.

INFLUEN"CE OF FLOW CONDITIONS ON THE SCOURING PROCESS.

From the experiments it appeared. that the velocity profile and the

turbu-lence intensi1;;y were very important. The influence of the turbulence could be

represented in many cases

qy

the factor (1+3r) from which the strong influence

of peak velocities appears. This is shown in fig. 5 where the scouring

down-sream of a dam is given for different lengths of the bottomprotection. Even

with a relatively great length the scouring is more severe then in the case

without a dam due to the persistent character of the large scale turbulence.

Besides the turbulence, the form of the velocity profile is also of

im-portance. A blunt profile causes rapid spreading of the flow and a relatively

short and deep scouring bole with a small value of t₁• A profile with a large

velocit,y gradient also causes more scouring. This mey- be seen in fig. 6 where 5 velocit,y profiles are given from 5 tests with exactly the same scour-time relationship but with different mean velocities. The smooth bottom

(S 39 _ 2) and the large gradient (S 39 - 5) gave values for «u of 1.30 and

1.00 respectively.

The valve of «u varied from 1.0 to 1.4 in normal cases. For a

conserva-tive estimate of the time scale a measurement of the turbulence intensit,y is

sufficient if Cl(u is assumed to be 1,0.

A direct co~putation of the time scale is possible if the ratio U/Ucrit

is the same in model and prototype. The formula then reduces to:

2. 05 1. 6 -4 (9)

nt • nh na •

nu

0

3.J

.

Zeller, Versuche der VAWE uber die Erosion in koharenten Gerinnen.

Sobweizerische Bau~eitung 83 (1965) no. 42 P 733 - 738.

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0.2 0.4 0.6 0.8 1D _{2 4}

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6 8 1l ₂₀ h 40 so 80 1lO 200 (00

mox. AS A FUNCTION OF TIME.SCOURING DOWNSTREA - t In hours

M OF A ROUGH BOTTOM

SCOURING OOWNs!REAM CF A ROUGH BOTTOM PROTECTI~

SANO

'

•

6

'

•

0 V din mm 0.12 0.225 0.28 0.39 0.84 1.6 2.6 ~ "ait. 2.0

FOR ANV "mo.,- "ait. ' 11 :: h/°'

m/sec

r

1.0 OS

o.

1s;-

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,o

;t--

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~

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r---

7

so~

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,mk-

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!i00Jn

--~

1l00b

--::

2000

L

---

5000

j

fig.2 RELATION t₁ vs u _

max. ucrit. - t1(hours)

C 32.6

'lnax.-"cnt. 2.0

ffl/HtC

l

281

SCOURING DOWNSTREAM CF A ROUGH BOTTOM PROlcCT10N

•

0

•

5,\1,D BAKELITE BAJ<EUTE d.0.12·2.6mm d.0.6mm d.1.9 mm POI.YS!YR8E d. 1.5 mm RlR ANY "ma..-"crit.' "t1

10 20

n

_•

"

100 6. 1.65 600.35 6. 0.35 6.0.050 200 SOO 1lOO

fig. 3 INFLUENCE OF MATERIAL DENSITY

- t₁(hours)

u _max. - u _art. .

m/HC

r

SCOURING TESTS Wlnl l'OLYSTRYRENE 6-0.05 d-1.5mm

--

,

K

f-+

Iba

::-

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'

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v,

11 1.33 1.0 1.33

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0.03 1/, 20 1.60 1.0 1.60 + Q03 ½ 30 1.90 1.18 2.25 0 0 0 3.6 1.11 1.31 145 6 W M ) 0 5.0 1.15 1.16 1.33 V 0.08 0 8.0 1.2, 1.0 t24

.

.

0 0 2.7 1.08 1,82 1.97 1.0 •t SCOURING Dtlt£CTLY AFTER CONTRACTION L • 0 )

.

-·

_, ·'J\IC' TURIUlOIC INTENSITY

QS Q2

-....,_

~

~

,,-t, .. ( umax.- ucrit.

_

,

~ f f .

-..y.

~

..,___,

~ 0.1 1 10 20 50 200

fig. 4 INFLUENCE OF FLOW CONDITIONS

C32.1

hmax. ~

l

u. 20cm/sec t•0.05

~

l

,,

~

t • 0,3 .l.. _o<tot. 1+ lr

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_"'

1.24 132 1.00 X 44 1.45 1.46 2.8

•

20 ,.so 1.50 3.6 6 12 153 1.53 4.0 2.0 V 5 1.45 1.48 2.8 1.0 0.5 - t(hours)

fig. 5 INFLUENCE OF TURBULENCE

539 - 1 .... _____ 539 - 2

~

-

---<>

539 - 3 o - - -·--<> 539 -4

-

-

-

·

-

-<>

539 - 5 ----+ rt in cm Is~ u(crn/sec)

24 ROUGH HORIZttlTAL BOTTOM }

20.8 SMOOTH HORIZONTAL BOTTOM

18 539-1 WITH GRID TO PROOUCE EXTRA TURBULENCE ~~~~~ WITH

22.5 DAM D-0.3h,, BOTTOMPROTECTION L-8 Sh,,

20 DAM D• 0.Sh,, SLOPES 1 · 20

10 15 20 25 XJ 35 40 45 so

____. u in cm/sec

tig.6 INFLUENCE OF VELOCITY PROFILE