SCOUR AROUND PILE GROUP OF SMALL BRIDGE › 2006_pdf › 13-2.pdfconsisting of a 3D flow model with...

Tenth International Water Technology Conference, IWTC10 2006, Alexandria, Egypt

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SCOUR AROUND PILE GROUP OF SMALL BRIDGE

M.M. Ezzeldin 1, S.H. Moharram 2, Th.E. Sarhan 2 and A.M.S. Elhamrawy 3

1 Professor, 2 Associate Professor, 3 Teaching Assistant

Irrigation and Hydraulics Dept., Faculty of Engineering, Mansoura University, El-Mansoura, Egypt

ABSTRACT The paper presents an experimental study on local scour around pile groups subject to current (clear water scour). Tests were performed for five arrangement pile models with three different diameters of circular piles (21, 26, 32 mm), cohesionless sediment diameter (0.52 mm) as bed material and a range of water depths and flow velocities. The main purpose was to derive simple predictive formulas for the geometric properties of the scour hole in terms of non-dimensional parameters describing the flow, sediment, and pile characteristics. Results showed that the computed scour depths were in agreement with the experimental scour depths. Also, an equation of the relative maximum scour depth was obtained. INTRODUCTION Pile groups are widely used in the field to support bridges and marine structures. Clearly scouring at the piling is of importance in connection with the stability of the structure since the extensive scour may reduce the stability of the structure and leads to its failure, Sumer (1992). If the foundations of bridge structures are meant to be supported by the alluvial material of a stream bed, their design require knowledge or prediction of the lowest deformation of the bed which will occur during the anticipated life of the structure near its supports. Most of the literature reviewed classified the scour investigations into local scour around bridge piers, abutment, and local scour around piles. Raudkivi and Ettema (1983) conducted experiments on cylindrical piers of different diameters and different mean particle diameter, d50. They studied the different shape factor, SF for sediments and concluded the maximum equilibrium depth of clear water local scour was a function of the relative depth y/Dp and the relative size Dp/d50. Also Raudkivi (1986) discussed the functional trends of the local scour depth at bridge piers in subcritical flow. Melville (1997) summarized many of the results from an extensive program of bridge scour research undertaken at the University of Auckland. Sumer and Fredsøe (1998) presented the results of an experimental investigation on scour around pile groups with different configurations exposed to waves. Also Sumer and Fredsøe (2001) presents


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the results of an experimental study on scour around a pile subject to combined waves and current. Salim and Jones (1999) studied the scour around exposed piles groups for different conditions including spacing, skew angle, and exposures of the pile cap in the flow field. Bayram et al. (2000) studied the scour around a group of piles in the field exposed to oscillatory waves. Yen et al. (2001) constructed a morphological model consisting of a 3D flow model with a scour model to simulate the bed scour evolution around a bridge pier. Sheppard et al. (2004) performed local clear-water scour tests with three different diameters circular piles, three different uniform cohesionless sediment diameters and a range of water depths and flow velocities. Their tests extend local scour data obtained in controlled experiments to prototype size piles and various ratios of pile diameter to sediment diameter. Sumer et al. (2005) presented the results of an experimental investigation on scour around pile groups with different configurations exposed to steady current. Therefore, within this paper, the local scour around both bridge pier and pile groups are introduced. The aim of this study is to investigate how the scour hole characteristics are affected in magnitude. Several parameters such as the Froude number, piles diameters, piles gaps, and pile group orientation are considered to describe the score phenomena. Dimensional analysis is developed to perform some relationships between the relative maximum scour depth against the other parameters involved in the phenomena. EXPERIMENTAL SETUP The experimental program was performed at the irrigation and Hydraulics Laboratory, Faculty of Engineering, Mansoura University. A recirculating flume of 10 m long, 0.45 m width and 0.4 m deep was used. The different models of piles were placed in the flume equidistant from the walls. Medium sand was used as bed material with depth equals 0.15 m. The flume is provided with centrifugal pump to recalculate the water from ground tank to feed the flume with the required flow discharge, a rectangular weir was installed at the upstream to measure the flow discharge. Figure (1) shows the layout of the flume.


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14

32

5

6 10

11

12

13

7 8

1

4

9

c- Three piles

d- Three triangular piles 0.0 e- Three triangular piles 180

tandema-Single pile b- Tow piles

tandem

flow direction

directionflow

1)- Centrifugal pump 8)- Sand bed.

2)- First head tank. 9)- Sand trap.

3)- Second head tank. 10)- Tail gate

4)- Flow measuring weir. 11)- Collecting tank.

5)- Approach basin. 12)- Graduated tank.

6)- Inlet screen. 13)- Laboratory sump.

7)- Piles group model. 14)- Sidewalk.

Fig. (1) Experimental setup

Fig. (2) Definition sketches for the piles arrangements used in the experimental program

DIMENSIONAL ANALYSIS Dimensional analysis was applied to develop the relationship between the maximum scour hole depth and the other variables involved in the phenomena. In this study, the maximum scour depth, S, is the dependent variable and can be expressed as a function of other independent variables as follows. S = φ (DP, G, y, v, ρ, ν, g, d50) (1)

Where: Dp= pile diameter, G = gap between piles, y = depth of approach flow upstream of the piles, v = mean flow velocity, ρ = fluid density, ν = fluid


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kinematics viscosity, g = gravitational acceleration. d50 = mean diameter of the sediment. The equation could be rearranged to: S /y = φ ( G/Dp, Dp/d50, 1/F2) (2)

TEST PROCEDURE Five models of piles were considered to represent the required piles arrangements. These arrangements can be classified into single pile, two piles tandem, three piles tandem, three triangular piles with orientation 0.0° and 180.0° degree to the flow direction. Diameters of the piles models were taken 21 mm, 26 mm and 32 mm. The gap between piles was 1, 2, 3 and 4 times the pile diameter. A specific flow discharge was taken 10 lit/s, with different flow depths. Results of bed configuration were carried out at the end of each run after drying the sand bed. The procedure to conduct each test was as the following: 1- The leveling of the bed surface was made to insure that all points of the bed had the

same elevation. 2- A tail gate was kept temporarily closed until the flume was filled up in a very low

flow rate to avoid any disturbance for the bed elevation. 3- The required discharge was allowed to flow gradually until it reaches a constant

value. 4- The tail gate was lowered gradually until it reaches the required water depth, then

start time of run is recorded. 5- As soon as the run time was over, the flow discharge has been stopped then the

water was drained slowly in order to prevent sediment movement. After the channel was dried, the measurements can be conducted.

At the beginning of the experimental work, many tests were conducted to identify the suitable discharge rates, the water depths and the duration of each run. It was observed that after 120 minutes negligible movement of sediment particles in the scour hole was obtained. This means that that most of the scour depth has been obtained. EXPERIMENTAL RESULTS The shape of the scour hole around the pile groups remained almost unchanged with respect to time. This shape can be approximated by an inverted cone having a circular base. Deposition occurs downstream the pile groups, the area of deposition increases with increasing the time.


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Dp=21 mm G/ Dp=2

FLOW DIRECTIONF= 0.26

2-PILES TANDEM

3-PILES TANDEM Dp=21 mm G/ Dp=3F= 0.26FLOW DIRECTION

Dp=21 mm


SINGEL PILE

Figures ( 3 to 7 ) show samples of bed configuration for different cases of pile group models under consideration. It clear that the scour hole occur mainly about the pile and consequently decrease along the length of scour hole. It based on Froude Number, diameter of pile and different gap ratios.

Fig. (3) Bed configuration of scour hole around single pile, Dp=21mm, Fr=0.26

Fig. (4) Bed configuration of scour hole around two piles tandem, Dp=21mm, Fr=0.26, G/DP=2

Fig. (5) Bed configuration of scour hole around three piles tandem, Dp=21mm, Fr=0.26, G/DP=3


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3-TRIANGULAR PILES 0.00 DEGREE Dp=21 mm G/ Dp=4


FLOW DIRECTION

Dp=21 mm G/ Dp=23-TRIANGULAR PILES

F= 0.26

180.0 DEGREE

Fig. (6) Bed configuration of scour hole around three triangular piles 0.00°, Dp=21mm, Fr=0.26, G/DP=3

Fig. (7) Bed configuration of scour hole around three triangular piles 180.0°, Dp=21mm, Fr=0.26, G/DP=2

One can see that, figures from (3) to (7), represents samples of scour pattern in two dimensional views. These figures show that the scour hole and the deposition are approximately symmetrical around the x-axis. Figures (8) to (11) show the deformation caused by scour along the center line of the flume. All runs are represented in groups. Each group contains four runs. These four runs have the same diameter, the same arrangement and the same G/DP ratio. Each run of them has different Froude number. So, these figures show only the variation of scour profile with Froude number with respect to the original bed level.

Tenth International W

ater Technology C

onference, IWT

C10 2006, A

lexandria, Egypt

991

0 10 20 30 40 50 60 70

-3

-2

-1

0

1

2

X (cm)

Z (

cm)

F=0.22F=0.26F=0.31F=0.38

Dp

0 10 20 30 40 50 60 70 80 90 100

-4

-3

-2

-1

0

1

2

X (cm)

Z (

cm)

F=0.19F=0.25F=0.30F=0.32F=0.45

Dp DpG

Fig. (8) Longitudinal section through c.l. of single pile Dp=21mm.

Fig. (9) Longitudinal section through piles c.l, 2-piles tandem Dp=21mm, G/Dp=1.


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01

02

03

04

05

06

07

08

09

01

00

11

01

20

13

01

40

-7-6-5-4-3-2-10123

X (

cm)

Z (cm)

F=

0.2

2F

=0

.26

F=

0.3

1F

=0

.38

Dp

Dp

G

010

2030

4050

6070

8090

100

-5-4-3-2-10123

X (c

m)

Z (cm)

F=0.

22

F=0.

26

F

=0.3

1

F

=0.3

8

Dp

Dp

G

It is obvious that the increase of Froude number increases both the scour hole depth, volume, and the length of aggradation. These figures show the maximum scour hole depth, and the steepness of slope of scour hole. In these figures, it is clear that the scour phenomenon depend on the Froude number. The depth of scour hole and the length of scour upstream and downstream the piles increase with the Froude number. Moreover, it is obvious that the length of

Fig

. (10

) Lo

ngitu

dina

l sec

tion

thro

ugh

pile

s gr

oup

c.l,

3-p

iles,

rot

atio

n 0.

0 °,

Dp=

21m

m, G

/Dp=

1

Fig

. (11

) Lo

ngitu

dina

l sec

tion

thro

ugh

pile

s gr

oup

c.l,

3-p

iles,

rot

atio

n 0.

0 °,

Dp=

21m

m, G

/Dp=

4.


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deposition increases and its height decreases with the Froude number as the flow washes the sediments. ANALYSIS AND DISCUSSION Effect of Pile Diameter (Dp) on the Maximum Relative Scour Depth (S/y): It is believed that the scour around a solid pier is due to impingement of a down-flow jet along the stagnation line together with a horseshoe vortex created ahead of the pier, Raudkivi (1986). But, the velocity of down flow and the size and strength of a horseshoe vortex themselves, depend on the size of the scour hole. The horseshoe vortex interacts with the down flow, acts as a catalyst, increases its strength and brings it towards the pier Melville (1988). Also, the scour hole itself in turn depends on the diameter of the solid pier. Thus, there is a strong interaction between the size of the pier, the size of the scour hole and the strengths of down flow and the horseshoe vortex. Hence, one of the methods of scour reduction could be to divide the solid pier into smaller piers, as is done in the pile group, and thus reduce down flow and break up the horseshoe vortex. Figure (12) shows the relationship between the relative maximum scour depth, S/y, and 1/F2, with different pile diameters DP, for single pile, from this figure it observed that the relative maximum scour depth, S/y, increases with increasing of pile diameter DP but for small values of Froude number F there is no effect of the pile diameter on the relative maximum scour depth. For the two piles tandem, figure (13-a) clarifies the relation between the relative maximum scour depth, S/y, and 1/F2, with different pile diameters DP. This figure shows that the relative maximum scour depth, S/y, increases with increasing of pile diameter DP, but there is relatively convergence between the values of the relative maximum scour depth of the two big diameters 26 and 32 mm. Figure (13-b) shows the same relation, for three piles tandem, it is observed that the relative maximum scour depth, S/y, increases with increasing of pile diameter DP, the values of the relative maximum scour depth of diameter 26mm converges with that of diameter 32mm. For the case of three triangular piles 0.0° orientation, figure (13-c) shows that the relative maximum scour depth, S/y, decreases with increasing of pile diameter DP. Similarly figure (13-d) illustrates the same relation between the relative maximum scour depth, S/y, and 1/F2, with different pile diameters DP, for three triangular piles 180.0° orientation, this figure shows that the relative maximum scour depth, S/y, increases with increasing of pile diameter DP.


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Dp

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1/F2

S/y

D p=2 1 m m .

D p=2 6 m m .

D p=3 2 m m .

Dp

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1/F2

S/y

Dp =21mm.

Dp =26mm.

Dp =32mm.

DpG

Dp

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1/F2

S/y

Dp =21mm.

Dp =26mm.

Dp =32mm.

DpG DpG

Dp

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1.2

1/F2

S/y

Dp =21mm.

Dp =26mm.

Dp =32mm.

Dp

G

Dp

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1.2

1/F2

S/y

Dp =21mm.

Dp =26mm.

Dp =32mm.

Dp

G

Fig. (12) Effect of pile diameter Dp on maximum relative scour depth S/y, single

Fig. (13) Effect of pile diameter Dp on maximum relative scour depth S/y, pile groups

G/Dp =1

a)

G/Dp =1

b)

G/Dp =1

c)

G/Dp =1

d)


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Dp

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1/F2

S/y

G/Dp =1.

G/Dp =2.

G/Dp =3.G/Dp =4.

DpG

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1/F2

S/y

G/Dp =1.

G/Dp =2.

G/Dp =3.G/Dp =4.

Dp DpG DpG

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1.2

1/F2

S/y

G/Dp =1.

G/Dp =2.

G/Dp =3.G/Dp =4.

Dp

Dp

G

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1.2

1/F2

S/y

G/Dp =1.

G/Dp =2.

G/Dp =3.G/Dp =4.

Dp

Dp

G

Effect of Piles Gap Ratio (G/Dp) on the Relative Maximum Scour Depth (S/y): Figures (14-a to 14-c) represent the relationship between the relative maximum scour depth, S/y, and 1/F2, with different piles gap ratio G/Dp, for pile groups.

Fig. (14) Effect of G/Dp ratio on maximum relative scour depth S/y, Dp=21mm

a)

b)

c)

d)


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From these previous figures (14-a to 14-b) it is clear that the scour depth reduces, as the spacing between the piles increases due to less interference from the adjacent piles. The interference effect between the individual piles will be larger and larger, as the spacing between the piles becomes smaller and smaller, this is linked to the fact that, for such small gap ratio, the pile group act as a "single" large pile, on the other hand, the interference effect between the piles particularly disappears; thus each pile in the group act as a single pile. As the distance between the piles decreases, the scour process will be affected by two processes. First, the vortices created around the piles will interact with each other, and secondly, the flow accelerated due to contraction created by the adjacent pile (the "jet" effect). This obviously results in a very high sediment transport induced by the gap flow, and hence contributes substantially to the scour depth. Effect of Pile Group Orientation on the Relative Maximum Scour Depth (S/y): Figure (15) represents the relationship between the relative maximum scour depth, S/y, and 1/F2, with two orientations of the three triangular piles group. It is clear that the three piles with 0.00o orientation to the direction of approach flow was found to be the best orientation, resulting in maximum scour depth. The foregoing results seem justified because in the 180o orientation, the gap between the front two piles of the group is blocked by the rear one.


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4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1/F2

S/y

Dp

Dp

G

Dp

Dp

G

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1/F2

S/y

Dp

Dp

G

Dp

Dp

G

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1/F2

S/y

Dp

Dp

G

Dp

Dp

G

4 6 8 10 12 14 16 18 20 220

0.2

0.4

0.6

0.8

1

1.2

1/F2

S/y

Dp

Dp

G

Dp

Dp

G

Fig. (15) Effect of piles orientation on maximum relative scour depth S/y, Dp=21mm

a) G/Dp =1

b) G/Dp =2

c) G/Dp =3

d) G/Dp =4


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REGRESSION ANALYSIS Regression analysis was used to deal with the experimental results and to finally get equations and relations relating scour parameters to the flow parameters and the geometric properties of the piles. Development of Equations Several mathematical equations have been found to evaluate local scour parameters in the clear-water scour condition. These equations are given below. The values of relative scour depth (s/y) was compared with the measured data in Figures (16) for a single pile, (17-a,b) and (18-a,b) for the case of pile groups. - The general equations for the single pile.

( )a3

a2 C50

p

dD

Fr yS

=

(3)

Where: S = Maximum Depth of the Scour Hole at a single pile; Y = Flow Depth; Fr = Froude Number; = v/(g*y)0.5; Dp = Pile Diameter; d50 = Geometric Mean of Sediment Diameter. - The general equations for the pile groups.

( )a4

D

Ga3

d

D a2 Cp50

pFr yS

=

(4)

Where: S = Maximum Depth of the Scour Hole at a pile group; y = Flow Depth; Fr = Froude Number; =v/(g*y)0.5; Dp = Pile Diameter; G = Gap Width between Piles; d50 = Geometric Mean of Sediment Diameter. The regression coefficients of the previous equations for a single pile and pile groups are summarized in table (1).


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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Predicted data of (S/y).

Ob

serv

ed

dat

a o

f (S

/y).

Dp DpG

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Ob

serv

ed d

ata

of

(S/y

).

Dp DpG DpG

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


Ob

serv

ed d

ata

of

(S/y

).

Dp

Table (1) Regression coefficients of the relative maximum depth equations

Piles Model Regression coefficients for (S/y) Correlation Coefficient

c a2 a3 a4 R Single pile 0.261 1.615 0.6230 - 0.929 2-piles tandem 0.2916 1.664 0.6354 -0.0090 0.947 3-piles tandem 0.2250 1.761 0.7520 -0.0802 0.948 3-triangular piles 0.0 ° 1.2230 1.882 0.3960 -0.2045 0.926 3-triangular piles 180.0 ° 0.2370 1.724 0.7740 -0.1660 0.982

Fig. (16) Relationship between observed values of (S/y) and predicted ones for single pile

Fig. (17-a, b) Relationship between observed values of (S/y) and predicted ones for two and

three piles tandem

Line of Perfect Agreement.




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0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2


Ob

serv

ed

dat

a o

f (S

/y).

Dp

Dp

G

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2


Ob

serv

ed

dat

a o

f (S

/y).

Dp

Dp

G

Fig. (18-a, b) Relationship between observed values of (S/y) and predicted ones for three triangular piles groups

From these figures, it is clear that the model arrangements gave a good agreements for most cases whereas there are differences in some cases, see figures (16 and 17-a). These figures have some scatter. However, these comparisons are not true criteria of the precision of the different equations because of that the equations were generated depending on the same data base. In that sense, figures are likely to present the most favorable comparison. CONCLUSIONS A clear water scour experiments were conducted to investigate the characteristics of the scour hole around pile groups, the results of these experimental tests were analyzed and discussed and the following conclusions could be drawn from the present study:

- The shape of the scour hole around the pile groups may be approximated by an inverted cone having a circular base, the area of deposition downstream the pile groups increases with time.

- It is clear that the scour phenomenon depends mainly on the Froude number. The relative maximum scour depth S/y, increase with increasing of Froude number, and it is obvious that the length of deposition increases and its height decreases with the Froude number as the flow washes the sediments.

- The scouring process is affected by the piles diameters, the relative maximum scour hole depth S/y, increases with increasing the pile diameter DP, but there is relatively convergence between the values of scour hole dimensions for larger diameters.

- It is found that the relative maximum scour hole depth S/y reduces, as the spacing between the piles increases due to less interference from the adjacent piles, this means that the effect of piles spacing ratio G/Dp on the scour hole dimensions is very important.




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- The scouring process is affected also by the pile groups orientation to the flow direction, it found that the three piles with 0.00o orientation to the direction of approach flow was found to be the best orientation, resulting in maximum scour depth S/y.

- An empirical equations were developed for stable scour hole in dimensionless form using regression analysis, which could help in predicting the relative maximum scour depth S/y.

SYMBOLS

Dp Pile Diameter; d50 Geometric Mean of Sediment Diameter; F Froude Number; = v/(g*y)0.5; G Gap Width Between Piles; g Gravitational Acceleration; S Maximum Scour Hole Depth; v Mean Velocity of Flow; X Coordinates of X axis; Y Coordinates of Y axis; y Upstream Flow Depth; Z Coordinates of Z axis; ρ Density of Water; ν Kinematic Viscosity of Water.

REFERENCES Bayram, A., and Larson, M.: "Analysis of Scour around a Group of Vertical Piles

in the Field", Journal of Waterway, Port, Coastal, and Ocean Engineering / July/August 2000, pp. 215-220.

Melville, B.W.: "Pier and Abutment Scour: Integrated Approach", Journal of Hydraulic Engineering, ASCE, Vol. 123, No. 2, February, 1997, pp. 125-136.

Melville, B.W., and Sutherland, A.J.: "Design Method for Local Scour at Bridge Piers", Journal of Hydraulic Engineering, ASCE, Vol. 114, No. 10, October, 1988, pp. 1210-1226.

Raudkivi, A.J., and Ettema, R.: "Clear Water Scour at Cylindrical Piers", Journal of Hydraulic Engineering, ASCE, Vol. 109, No. 3, March, 1983, pp. 338-350.

Raudkivi, A.J.: "Functional Trends of Scour at Bridge Piers", Journal of Hydraulic Engineering, ASCE, Vol. 112, No. 1, January, 1986, pp. 1-13.

Salim, M., and Jones, J.S.: "Scour around Exposed Pile Foundations", Proceedings of the ASCE, 1999, "North American Water and Environment Congress", Anaheim, CA.


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Sheppard, D.M., Odeh, M., and Glasser, T.: "Large Scale Clear-Water Local Pier Scour Experiments" Journal of hydraulic Engineering, ASCE (ISSN 0733-9429), Vol. 130, No. 10, October 1, 2004, pp. 957-963.

Sumer, B.M., and Fredsøe, J., and Bundgaard, K.: "Global and Local Scour at Pile Groups", International Journal of Offshore and Polar Engineering, ASCE (ISSN 1053-5381), Vol. 15, No. 3, September 2005, pp. 204-204.

Sumer, B.M., and Fredsøe, J., and Christiansen, N.: "Scour around Vertical Pile in Waves", Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE, Vol. 118, No. 1, January/February, 1992, pp. 15-31.

Sumer, B.M., and Fredsøe, J.: "Wave Scour around Group of Vertical Piles", Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE, Vol. 124, No. 5, September/October, 1998, pp. 248-256.

Sumer, M.B., and Fredsoe, J. (2001): "Scour around Pile in Combined Waves and Current." Journal of Hydraulic Engineering, ASCE, 127(5), pp. 403-411.

Yen, C.L., Lai, J.S., and Chang, W.Y.: "Modeling of 3D Flow and Scouring around Circular Piers", Proc. Natl. Sci. Counc. ROC(A) Vol. 25, No. 1, 2001, pp. 17-26.

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