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Local scouring at bridge piers and Local scouring at bridge piers and abutmentsabutments

2

Introduction

Main features of the flow field around bridge piers and abutments

Time evolution of the scouring process (qualitative aspects)

Scouring factors

Riprap mattresses as a countermeasure against scour at bridge abutments, under clear-water flow conditions.

Contents of the presentationContents of the presentation

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IntroductionIntroduction

What is local scouring ? Erosion directly induced by changes of the flow field (mean velocity;

turbulence intensity; Reynolds stresses) due, in turn, to the presence of obstacles inserted in the flow.

At the proximity of the inserted obstacles.

What is the importance of scouring for civil engineering ? Scouring can induce the collapse (total or partial) of bridges. It can also induce the change of rivers’ regime (case of bed-sills).

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• Is scouring a frequent problem ? in USA: – 383 bridges have been destroyed or damaged between

1964 and 1972 (average cost per accident: 108 USD).

– 73 bridges were destroyed in Pennsylvania; Virginia; WestVirginia in 1985;

– 17 bridges were destroyed in NY and in N Eng. in 1987;

in Portugal: Penacova; Alva; Gafanha; … Entre-os-Rios (56 casualties).

• What are the issues open to research ? The predictions of the available methods (scour depth; protection)

are often not satisfactory; this is particularly true for abutments.

• Other aspects … Local scouring must be superimposed to river-bed degradation as

well as to contraction scouring (due to the increase of U) .

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6

7

Main features of flow field around bridge piers and Main features of flow field around bridge piers and abutmentsabutments

The presence of obstacles implies the flow stagnation close to the walls pressure increase (kinetic energy potential energy).

Pressure increases are bigger at the free surface than close to the bottom.

h

y

u

Descending

flow

y

h

p = (u2)/2

bow wave

8

The local change of the pressure field originates:

bow wave; descending flow (which triggers the scouring process); flow separation.

stagnation point

main vortex

bow wave

descending flow

9

The combined action of the deflected descending flow and the separated flow creates:

the horseshoe vortex (in the case of piers); the main vortex (in the case of abutments).

Separation also occurs at the lateral walls of obstacles, inducing wake vortices (rotating at successively alternate senses).

For bridge piers:

descending flow

scour hole

horseshoe vortex

bow wavepier

approaching flow

wake vortices

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The horseshoe vortex (or the main vortex) carries the bed material downstream as bed load.

Wake vortices pick up sand particles from the bottom; they transportthe particles downstream in suspension.

secondary vortex

main vortex

The flow structure around abutments is very similar to the flow structure around piers.

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Time evolution of the scouring process (qualitative aspects)Time evolution of the scouring process (Time evolution of the scouring process (qualitative aspectsqualitative aspects))

Scouring may occur for two different sediment transport conditions: clear-water flow ( < c or U < Uc); live-bed flow ( > c or U > Uc).

Scour holes reach equilibrium when the amount of sediment coming in (the hole) is equal to the amount of sediment going out.

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So as to qualitatively describe the time evolution of the erosive process, let us consider a flow with constant h and increasing U.

• In that case, for cylindrical piers:

when U is very small there is no scouring; the mobile bed behaves as if it was fix;

when U > ≈ 0,5Uc (Hanco 1971) scour occurs (even for U < Uc);

initially, the scour depth increases very quickly with time;

the time needed to reach equilibrium depends on the type of approach flow: clear-water or live-bed flow;

for clear-water, equilibrium is reached asymptotically; equilibrium is static.

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For live-bed flow conditions:

removal of grains of the original bed is simultaneous with the removal of grains “fed” from upstream;

after a certain (short) time, the quantity of material coming in is equal to the quantity of material going out;

equilibrium is reached quickly; equilibrium is dynamic.

t

dynamic equilibrium

live-bed

static equilibrium

clear-water

hs

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Independently of the approach flow type (clear water; live-bed), three phases of the scouring process can be identified:

Several formulations can be found in the literature on the quantification of the time evolution of scour depth. We will come to this latter.

t

hs

equilibrium phase

Principal phase

Initial phase

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Independent variables influencing the processApproach flow ......................……….. h, J, gFluid properties ...........……………… , ()Properties of the bed material ..……. D50, D, sCharacteristics of the obstacle……… L (or DP), , shape (Kf)Channel geometry……………………. B, i, cross-section (KG)Time……………………………………. t

General equations

tKiBKDorLDgJhth GfpsDs ;;;;;);.(;;;;;;;;')( 50

GfpsDse KiBKDorLDgJhh ;;;;);.(;;;;;;;; 50

Scouring factorsScouring factors

a. General frameworka. General framework

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On the basis of Physics and by applying the theorem of Vaschy-Buckingham (L DP) (Simarro … & Cardoso 2007):

with hse = hse/L or hse = hse/Dp or hse = hse/h

Effects:U = Ic = U/Uc mean velocity of the approach flow;h = h/L approach flow depth;B = B/L contraction of the flow cross-section;D50 = D50/L size of the bed material; D gradation coefficient of the bed material;s = s/ specific density of the bed material;f shape of the obstacle;G cross section geometry; obstacle alignment.

;;;;;;;;50 GfDBhUh s

se

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For wide channels (no effect of B), uniform sand bed (no effect of ; s = const):

According to Melville 1992, the previous equation can be materialized as follows (equilibrium phase)

During the scouring process (effect of time), in general:

If we include the influence of bed material density

We will consider next the effects of U+D50, h+L, t, and s on hse.

KKKKKKh GfDUhse 50

;;;;;50 GfDUhhse

tGfDUhs KKKKKKKh 50

tsGfDUhs KKKKKKKKh 50

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b.b.Effect of the approach flow velocity and median size of the Effect of the approach flow velocity and median size of the bed material.bed material.

Let us consider: practically uniform bed material (D < 1.5; K = 1); sufficiently coarse bed material so as to avoid the development of

ripples (D50 > 0.6 mm).

In that case, for cylindrical piers: for U values such that U < ≈0.5Uc (Hanco 1971), scour holes do not

develop (U ≈ 0.5Uc condition of scour inception); for U values such that U > ≈0.5Uc, the variation of hse (t > te) with the

average velocity of the approach flow depicts the following characteristics:

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live bed

clear water

U/Uc0,5 1,0 2,0 4,0

hse

hse increases almost linearly with U until U = Uc, where it reaches a maximum.

The hypothesis of Hanco is very important for practical applications:protecting riprap should be designed to face a velocity equal to ≈ 2U (U= design approach flow velocity) at current, slender bridge piers.

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Melville & Coleman 2000 suggest that scour occurs as soon as there is flow: ≈0.5Uc 0.0Uc.

Scour inception recently studied for comparatively long abutments.The hypotheses of Hanco and Melville & Coleman were analyzed.

0.0

2.0

4.0

6.0

8.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

UU c

h se

h1 series - L/d = 2.332 series - L/d = 5.563 series - L/d = 9.234 series - L/d = 15.315 series - L/d = 20.546 series - L/d = 25.60

L/hL/hL/hL/hL/hL/h

There is a clear dependence of hse = 0 on L/h (Fael …& Cardoso2006).

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The value of Ic = (U/Uc)s above which scour at abutments occurs (scour inception) clearly depends on L/h, as follows (Fael … & Cardoso 2006).

This is very important in practice. It allows the definition of scour inception for a given abutment length.

0.0

0.5

1.0

0 5 10 15 20 25 30Lh

I c

Hager and Oliveto 2002

Eq. (4.29)

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hse

L Uniform sandD = 2,55

D = 4,11

2,0

1,0

0,00 1 2 3 4 5 U

Uc

For fine bed material (ripples) and for non-uniform bed material(pavement), the scouring process becomes much more complex.

These aspects will not be treated here.

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c. c. Effect of the approach flow depth and the obstacle Effect of the approach flow depth and the obstacle characteristic length.characteristic length.

Let us assume: that U/Uc = Cte; since the maximum value of hse is searched, let us

take U/Uc = 1 (KU = 1);

a wide – no contraction (KB = 1) – rectangular channel (KG = 1);

that the bed material is uniform (D < 1,5; K = 1) sand (s = Cte = 2,65; Ks = 1), non compatible with the development of ripples (D50

> 0.6 mm);

that D50= L/D50 is sufficiently high so that D50 does not influence

hse (KD50 = 1);

that the obstacle is a standard one (cylindrical pier or thin vertical wall Kf = 1 – normal to the flow direction, K = 1).

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Under these conditions, for the equilibrium phase (Kt = 1):

hL

hL

se

h h h Lse se ;or

– According to Kandasamy (1989), the general form of the above equation is as follows:

C

zone 1

B

Ah

D

zone 2zone 3

L = h

hse

zone 4L

O

FG

L = a2hh = a1L

E

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According to Kandasamy (1989), for slender piers and short abutments (h/L > a1),

=============================

Lhse 3,2 pse Dh 3,2

Contributions of Melville e and Dongol 1994 for thin wall abutments:

For L/h ≈ 25, difference is ≈50%.

L/h

hse

0

2

4

6

8

12

10

20 40 60 80 100 1200

Dongol

Melville

hh

Lh

s e 20 5,

hh

Lh

s e 2 5 10 3

,,

hhs e 1 0h

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According to Fael … & Cardoso 2006:

This is a very important result since it reduces scour depth over-prediction frequently reported for long abutments.

0

2

4

6

8

10

0 25 50 75 100

Lh

h se

h

LiteratureFael et al. 2006

Melville 1992

Dongol 1994

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d. d. Effect of timeEffect of time

The previous discussion is valid for t te. For t < te, in the principal phase, and for the conditions leading to equation

one can expect that:

where t is any non-dimensional time parameter.

Most of the existing equations were established for cylindrical piersand can be written in the form:

hL

hL

se

t

s

Lh

Lth ;)(

ts

Lth

)(

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Some of the existing contributions are as follows (principal phase):

Ettema (1980):

where K1 and K2 are constant.

Franzetti et al. (1982):

a1 and a2 being constant.

Whitehouse (1997):

T = time scale; p = constant

21 log)( KKLth

ts 3

50

LtD

t

21exp1)( a

tse

s ah

th

LUt

t

pt

se

s

hth

exp1)(Tt

t

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Cardoso and Bettess (1999) generalized the previous contributions to bridge abutments by showing that K1, K2 e a1 depend on L = L/h.

0.0

0.1

0.2

0.3

0.4

0 5 10 15 20 25 30

Lh

k 10.99 < U/Uc < 1.120.90 < U/Uc < 0.920.75 < U/Uc < 0.810.57 < U/Uc < 0.65U/Uc = 0.40Literature: 0.90<U/Uc<1.06

Fael (2007) characterized the effect of the approach flow velocity (U/Uc).

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The question of time to equilibrium, te, i.e., the time needed to reach the equilibrium phase, is an open question, far from solved.

0.0

0.5

1.0

1.5

2.0

0 5 10 15 20 25 30

Lh

k 2 0.99 < U/Uc < 1.120.90 < U/Uc < 0.920.75 < U/Uc < 0.810.57 < U/Uc < 0.65U/Uc = 0.40Literature: 0.90<U/Uc<1.06

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e. e. Effect of obstacle alignmentEffect of obstacle alignment

Equilibrium scour depth depends on :

The effect of alignment is given by the coefficient

90º or given aor

fh

fhKse

se

flow

flow

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The variation of with is somewhat controversial. According to Melville 1997, this effect can be derived from

Comparatively recent studies (Kwan (1984) + Kandasamy (1989)), where equilibrium was reached, show that the highest value of K is obtained for = 90º.

0,70

0,80

0,90

1,00

1,10K

0 30 60 90 120 150 180

KwanKandasamy

AhmadLaursenSastryZaghloul

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According to Collel & Cardoso (1998), = 1 for > 90º.

1.10

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.300 30 60 90 120 150 180

K

Collel & Cardoso (1998)

Kwan (1984)

Kandasamy (1985)

K

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i. i. Effect of the bed material specific densityEffect of the bed material specific density

Until now, the bed material has been considered to be sand, i.e., the specific density has been assumed as 2.65.

In some physical models, the material used to simulate sand has a different specific density.

The effect of specific density can be of great importance.

A priori, it seems that:

- the scour rate increases with decreasing specific density;

- equilibrium scour depth should increase too;

No systematic study was known on the effect of specific density.

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Assuming U/Uc = cte. (> 0,5), KD50 = 1; Kf = cte.; K = cte.; KB = 1, KG = 1, Kt = 1, it can be postulated that the influence of s is schematically as follows:

L

L

h

hs1

s2

sn

hse

s1 > s2 > ..sn

Recent studies (Fael … & Cardoso 2006) have produced a surprising result.

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No reasonable explanation for the decrease of the equilibrium scour depth with decreasing specific density was found until now. Influence of viscosity?

0

2

4

6

8

10

0 25 50 75 100

Lh

h se

h

SandPumiceLiterature-Sand

Melville 1992

Dongol 1994

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Riprap mattresses as countermeasure against scour at abutments, under clear-water flow conditions

Eve & Melville (2000) the failure mechanisms of riprap mats are essentially the same for bridge abutments as for piers

for clear water conditionsParola (1993)Chiew (1995)Lauchlan (1999)

identified 3 failure mechanisms

shear failurewinnowing failureedge failure

shear failure is related with the riprap stone size;winnowing failure is related with the thickness of mats (number of

layers) and with the gradation coefficient of the riprap stones;

edge failure is related with the shape and plan dimensions of mattresses.

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Design of riprap mattresses as a countermeasure against scouring near bridge abutments under clear water flow implies the knowledge of:

riprap stone size;

mattress plan dimensions.

mattress thickness.

3 sets of experiments have been carried out for vertical-wall abutments:

15 tests to evaluate the critical Dr50 of the riprap stones (critical flow velocity for scour inception).

1st set:

42 tests to address the thickness of the mattresses. 2nd set:

14 tests to address the plan dimensions of the mattresses. 3rd set:

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Experimental Set-up

Tests were carried out at UBI.

Reach where countermeasures were tested (recess box):Length = 3 mWidth = 4 mDepth = 0.6 m

Flume dimensions:Length = 30 mWidth = 4 mDepth = 1.0 m

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t = 3Dr50

Dr50 = 3.59 mm; Dr50 = 7.48 mm; Dr50 = 15.69 mm

Sand #1on a filter

• tests started with a low flow velocity.• the velocity was successively increased while the flow depth was

kept constant until riprap stones began to move close to the abutment.

1st set (on riprap stone size)

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• Critical value, Ic, of the approach flow intensity, Ic = (U/Uc)s, below which scour does not show up, for a given value of L/h:

Ic decreases with L/h.

It seems that Ic increases with h/Dr50.

An envelope curve was established that ensures the stability of riprap stones.

0.0

0.5

1.0

0 5 10 15 20 25 30

Lh

I c Sand Riprap #1Riprap #2 Riprap #3

Fael et al . 2006

Hager and Oliveto 2002

Envelope curve

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521

hLIc

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2nd set (on the minimum mattress thickness to face winnowing)

Velocities were kept equal to 90% of those inducing scour at the abutments, as defined in the first set of tests.

t = 1Dr50; 2Dr50 …. 20Dr50

Dr50 = 7.48 mm; Dr50 = 15.69 mm

sand #1 and sand #2

without filter

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• riprap matresses should preferably lay on filter clouth;• scour is practically negligeable for N > 6

riprap #3; sand #1

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10

Lh

h se

h N = 1N = 2N = 3

riprap #3; sand #2

0.0

0.2

0.4

0.6

0.8

0 5 10 15 20N

h se

h

L/h = 9.42L/h = 7.75

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3rd set (tests to evaluate the minimum plan dimensions of mats so as to avoid edge failure)

2.46 L/h 9.42

t = 2Dr50 = 31 mmriprap #3on cloth

U Uc of sand

w = ?

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Variation of w/h with L/h

w increases with L/h. The influence of h/Dr50 cannot be addressed since it was kept 120/15.69 7.65.

Richardson & Davis’s (1995) equation leads to safe predictions of w

0.0

1.0

2.0

3.0

0 2 4 6 8 10 12

Lh

wh

Richardson and Davis 1995

Failure

Non-failure

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END

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Conclusions

Local scour at bridge abutments

o The flow intensity for scour inception at the abutment nose decreases as the ratio L/h increases. A new equation is proposed.

o The results support the envelope curves for long abutmentscour depth as suggested by Dongol 1994.

o The generalized Ettema equation for time evolution, considering the effects of obstacle length, L/h, and U/Uc is suggested.

o The alignment factor can be taken as K = 1 for ≥ 90°.o The equilibrium scour depth is smaller for pumice than it is

for sand, all the remaining factors kept the same.

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Riprap mattresses design

o The concept of critical flow intensity, Ic, for scour inception applies to the design stone size.

o Scour due to winnowing did not develop when the riprap layer acted as a granular filter.

o Scour seems negligible when, in the absence of filters of any kind, the riprap thickness is such that N 6.

o Assuming edge failure to occur when stones are removed from the toe of the abutment, the lateral extent, w, of mattresses resisting to edge failure increases with L/d.