toe and bed scour lectures lecture note.pdf

scour

1. 1
Estimating Scour
CIVE 510
October 21
st
, 2008

2. 2
Causes of
Scour

3. 3
Site Stability

4. 4
Mass Failure
• Downward movement of large and intact
masses of soil and rock
• Occurs when weight on slope exceeds the
shear strength of bank material
• Typically a result of water saturating a
slide-prone slope
– Rapid draw down
– Flood stage manipulation
– Tidal effects
– Seepage

5. 5
Mass Failure
• Rotational Slide
– Concave failure plane, typically on slopes
ranging from 20-40 degrees

6. 6
Mass Failure
• Translational Slide
– Shallower slide, typically along well-defined
plane

7. 7
Site Stability

8. 8
Toe Erosion
• Occurs when particles are removed
from the bed/bank whereby
undermining the channel toe
• Results in gravity collapse or sliding
of layers
• Typically a result of:
– Reduced vegetative bank structure
– Smoothed channels, i.e., roughness
removed
– Flow through a bend

9. 9
Toe Erosion

10. 10
Toe Erosion

11. 11
Site Stability

12. 12
Avulsion and Chute Cutoffs
• Abrupt change in channel alignment
resulting in a new channel within the
floodplain
• Typically caused by:
– Concentrated overland flow
– Headcuttingand/or scouring within
floodplain
– Manmade disturbances
• Chute cutoff –smaller scale than
avulsion

13. 13
Avulsion and Chute Cutoffs

14. 14
Site Stability

15. 15
Subsurface Entrainment
• Piping –occurs when subsurface flow
transports soil particles resulting in
the development of a tunnel.
• Tunnels reduce soil cohesion causing
slippage and ultimately streambank
erosion.
• Typically caused by:
– Groundwater seepage
– Water level changes

16. 16
Subsurface Entrainment

17. Normal ( Normal (baseflow baseflow) conditions ) conditions
Seepage Seepage
flow flow
Normal water level Normal water level
Groundwater Groundwater
table table

18. Seepage Seepage
flow flow
Flood water level Flood water level
During flood peak During flood peak

19. After flood recession After flood recession
Seepage Seepage
flow flow
Normal water level Normal water level
Area of high seepage Area of high seepage
gradients and uplift pressure gradients and uplift pressure

20. 20
Site Stability

21. 21
Scour
“Erosion at a specific location that is
greater than erosion found at other
nearby locations of the stream bed or
bank.”
Simons and Sentruk (1992)

22. 22
Scour
• Scour depths needed for:
– Revetment design
– Drop structures
– Highway structures
– Foundation design
– Anchoring systems
– Habitat enhancement

23. 23
Scour Equations
• All empirical relationships
• Specific to scour type
• Designed for and with sand-bed systems
• May distinguish between live-bed and
clear-water conditions
• Modifications for gravel-bed systems

24. 24
Calculating Scour
• Identify type(s) of expected scour
• Calculate depth for each type
• Account for cumulative effect
• Compare to any know conditions

25. 25
5 Types of Scour
• Bend scour
• Constriction scour
• Drop/weir scour
• Jet scour
•Local scour

26. 26
Bend Scour

27. 27
Bend Scour
• Caused by secondary currents
• Material removed from toe
• Field observations can be helpful in
assessing magnitude
• Conservative first estimate:
– Equal to the flow depth upstream of
bend
• Three empirical relationships

28. 28
Bend Scour
• Three methods
– Thorne (1997)
• Flume and river experiments
•D
50
bed from 0.3 to 63 mm
• Applicable to gravel bed systems
– Maynord (1996)
• Used for sand-bed channels
• Provides conservative estimate for gravel-bed
systems
– Wattanabe(Maynord1996)
• Ditto

29. 29
Thorne Equation
•Where
– d = maximum depth of scour (L)
–y
1
= average flow depth directly upstream of the bend (L)
– W = width of flow (L)
–R
c
= radius of curvature (L)
1
1.07 log 2
c
dR
yW
⎞ ⎛
=
−−
⎜⎟
⎝⎠
222
c
R
W
<
<

30. 30
MaynordEquation
•Where
–D
mb
= maximum water depth in bend (L)
–D
u
= mean channel depth at upstream crossing (L)
– W = width of flow at upstream end of bend (L)
–R
c
= radius of curvature (L)
1.8 0.051 0.0084
mb c
uu
DRW
DWD
⎞ ⎛ ⎞ ⎛
=− +⎟ ⎜ ⎜⎟
⎝⎠⎝⎠
1.5 10
c
R
W
<<
1.5 10
u
W
D
<<

31. 31
MaynordEquation
•Notes:
– Developed from measured data on 215 sand bed
channels
– Flow events between 1 and 5 year return intervals
– Not valid for overbank flows that exceed 20 percent of
channel depth
– Equation is a “best fit”, not an envelope – NO FOS
– Factor of safety of 1.08 is recommended
– English or metric units
– Width is that of “active flow”
1.8 0.051 0.0084
mb c
uu
DRW
DWD
⎞ ⎛ ⎞ ⎛
=− +⎟ ⎜ ⎜⎟
⎝⎠⎝⎠

32. 32
WattanabeEquation
•Where
–d
s
= scour depth below maximum
depth in bend (L)
–W = channel top width (L)
–R
c
= radius of curvature (L)
– D = mean channel depth (L)
– S = bed slope (L/L)
–
f
= Darcy friction factor
s
c
dW
DR
αβ
⎞ ⎛
=+⎟ ⎜
⎝⎠
2
0.361 0.0224 0.0394 XX
α
=−−
0.2
10
log
WS
X
D
⎞ ⎛
=⎟ ⎜
⎝⎠
1.584x
f
β
π
2
=
⎧⎫
⎡
⎤ ⎞ ⎛1 ⎪⎪
1.226 −
⎢
⎥ ⎟ ⎜ ⎨⎬
⎜⎟
⎢
⎥ ⎝ ⎪⎪⎠
⎣
⎦ ⎩⎭
1
1.1
1.5 1.42 sin cos
x
f
f
σ
σ
=
⎡⎤⎧⎫⎞ ⎛⎪⎪
−+ ⎢⎥⎟ ⎜⎨⎬
⎜⎟
⎢⎥⎪⎪⎝⎠ ⎩⎭ ⎣⎦
1
1.1
tan 1.5 1.42 f
f
σ
−
⎡
⎤
⎧
⎫ ⎞ ⎛
⎪
⎪
=−
⎢
⎥ ⎟ ⎜
⎨
⎬
⎜⎟
⎢
⎥
⎪
⎪ ⎝⎠ ⎩⎭
⎣
⎦

33. 33
WattanabeEquation
•Notes:
– Results correlated will with Mississippi River data
– Limits of application are unknown
– FOS of 1.2 is recommended
– English or metric units may be used
s
c
dW
DR
αβ
⎞ ⎛
=+⎟ ⎜
⎝⎠

34. 34
5 Types of Scour
• Bend scour
• Constriction scour
• Drop/weir scour
• Jet scour
•Local scour

35. 35
Constriction Scour

36. 36
Constriction Scour
• Occurs when channel features created a
narrowing of the channel
• Typically, constriction is “harder”than the
channel banks or bed
• Caused from natural and/or engineered
features
– Large woody debris
– Bridge crossings
– Bedrock
– Flow training structures
– Tree roots/established vegetation

37. 37
Constriction Scour
• Scour equations
– Developed from flume tests of bridge
abutments
– Equations can be applied for natural or
other induced constrictions
– Most accepted methods:
• Laursenlive-bed equation (1980)
• Laursenclear-water equation (1980)

38. 38
Constriction Scour
• Live-bed conditions
– Coarse sediments may armor the bed
• Compare with clear-water depth and use lower
value
• Requires good judgment!
– Equation developed for sand-bed streams
– Application to gravel bed:
• Provides conservative estimate of scour depth

39. 39
LaursenLive-Bed Equation
•Where
– d = average depth of constriction scour (L)
–y
0
= average depth of flow in constricted reach without
scour (L)
–y
1
= average depth of flow in upstream main channel (L)
–y
2
= average depth of flow in constricted reach after
scour (L)
–Q
2
= flow in constricted section (L
3
/T)
–Q
1
= flow in upstream channel (L
3
/T)
–W
1
= bottom width in approach channel (L)
–W
2
= bottom width in constricted section (L)
– A = regression exponent
0.86
22 1
11 2
20
A
yQ W
yQ W
dyy
⎛⎞⎛⎞
=
⎜⎟⎜⎟
⎝⎠⎝⎠
=−

40. 40
LaursenLive-Bed Equation
ω= fall velocity of D50 bed material
(L/T)
U* = shear velocity (L/T)
= (gy
1
S
e
)
0.5
g = acceleration due to gravity (L/T
2
)
S
e
= EGL slope in main channel (L/L)
0.86
22 1
11 2
20
A
yQ W
yQ W
dyy
⎛⎞⎛⎞
=
⎜⎟⎜⎟
⎝⎠⎝⎠
=−
Suspended 0.69 >2.0
Suspended 0.64 0.5 to 2.0
Bed 0.59 < 0.5
Mode of bed
Transport
A U*/ω

41. 41
LaursenLive-Bed Equation

42. 42
LaursenLive-Bed Equation
•Notes:
– Assumes all flow passes through
constricted reach
– Coarse sediment may limit live-bed scour
– If bed is armored, compare with at clear-
water scour
– Both English and metric units can be used
0.86
22 1
11 2
20
A
yQ W
yQ W
dyy
⎛⎞⎛⎞
=
⎜⎟⎜⎟
⎝⎠⎝⎠
=−

43. 43
LaursenClear-Water Equation
•Where
– d = average depth of constriction scour (L)
–y
0
= average depth of flow in constricted reach without scour (L)
–y
2
= average depth of flow in constricted reach after scour (L)
–Q
2
= flow in constricted section (L
3
/T)
–D
m
= 1.25D50 = assumed diameter of smallest non-transportable
particle in bed material in constricted reach (L)
–W
2
= bottom width in constricted section (L)
– C = unit constant; 120 for English, 40 for metric
0.43
2
2
20.67 2
2
20
m
Q
y
CD W
dyy
⎛⎞
=
⎜⎟
⎝⎠
=−

44. 44
LaursenClear-Water Equation
• Notes:
– Only uses flow through constricted section
– If constriction has an overbank, separate computation made
for the channel and each overbank
– Can be used for gravel bed systems
– Armoring analysis or movement by size fraction
0.43
2
2
20.67 2
2
20
m
Q
y
CD W
dyy
⎞ ⎛
=⎟ ⎜
⎝⎠
=−

45. 45
5 Types of Scour
• Bend scour
• Constriction scour
• Drop/weir scour
• Jet scour
•Local scour
17 OCT – address mistake on equation two slides ago

46. 46
Drop/Weir Scour

47. 47
Drop/Weir Scour
• Result of roller formed by cascading
flow
•Caused from
– Perched culverts
– Culverts under pressure flow
– Spillway exits
– Natural drops in high-gradient mountain
streams

48. 48
Drop/Weir Scour
•Two methods
– U.S. Bureau of Reclamation Equation –
Vertical Drop Structure (1995)
• Used for scour estimation immediately
downstream of a vertical drop
• Provides conservative estimate for sloping
sills
– Laursenand Flick (1983)
• Sloping sills of rock or natural material

49. 49
USBR Vertical Drop Equation
•Where
–d
s
= scour depth immediately downstream of drop (m)
– q = unit discharge (m
3
/s/m)
–H
t
= total drop in head, measured from the upstream to downstream
energy grade line (m)
–d
m
= tailwater depth immediately downstream of scour hole (m)
– K = regression constant of 1.9
0.225 0.54
st m
dKHq d
=
−

50. 50
USBR Vertical Drop Equation
•Notes:
– Calculated scour depth is independent of bed-material grain size
– If large material is present, it may take decades for scour to reach final
depth
– Must use metric units
0.225 0.54
st m
dKHq d
=
−

51. 51
Laursenand Flick Equation
•Where
–d
s
= scour depth immediately downstream of drop (L)
–y
c
= critical flow depth (L)
–D
50
= median grain size of bed material (L)
–R
50
= median grain size of sloping sill (L)
–d
m
= tailwater depth immediately downstream of scour hole (L)
0.2 0.1
50
50
43
c
scm
c
yR
dyd
Dy
⎧⎫⎡⎤
⎞⎞ ⎛⎛ ⎪⎪
=− −⎢⎥⎨⎬⎟⎟ ⎜⎜
⎢⎥⎝⎝⎠⎠ ⎪⎪⎣⎦⎩⎭

52. 52
Laursenand Flick Equation
•Notes
– Developed specifically for sloping sills constructed of rock
– Non-Conservative for other applications
– Can use English or metric units
0.2 0.1
50
50
43
c
scm
c
yR
dyd
Dy
⎧⎫⎡⎤
⎞⎞ ⎛⎛ ⎪⎪
=− −⎢⎥⎨⎬⎟⎟ ⎜⎜
⎢⎥⎝⎝⎠⎠ ⎪⎪⎣⎦⎩⎭

53. 53
5 Types of Scour
• Bend scour
• Constriction scour
• Drop/weir scour
• Jet scour
•Local scour

54. 54
Jet Scour

55. 55
Jet Scour
• Lateral bars
• Sub-channel
formation

56. 56
Jet Scour
• High energy side
channel or tributary
discharges

57. 57
Jet Scour
•Tight radius of
curvature

58. 58
Jet Scour
• Very difficult problem to solve
• Simons and Senturk(1992) provide
some guidance
• Good case for adding a substantial
FOS

59. 59
Jet Scour

60. 60
Jet Scour

61. 61
Jet Scour

62. 62
5 Types of Scour
• Bend scour
• Constriction scour
• Drop/weir scour
• Jet scour
•Local scour

63. 63
Local
Scour

64. 64
Local Scour
• Appears as tight scallops along a
bank-line
• Depressions in a channel bed
• Generated by flow patterns around an
object or obstruction
• Extent varies with obstruction
• Can be objective of design

65. 65
Local Scour
• Pier Scour Equations

66. 66
Local Scour
• Pier Scour Equations
– Developed for sand-bed rivers
– Provides conservative estimate for
gravel-bed systems
– Can be applied to other obstructions
– Assumes object extends above water
surface
– Colorado State University Equation

67. 67
Local Scour
• Colorado State University Equation
– Can be applied to both live-bed and
clear-water conditions
– Provides correction factor for bed
material > 6 cm –gravel beds
– Field verification shows equation to be
conservative

68. 68
CSU Pier Scour Equation
•Where
– d = maximum depth of scour, measured below bed elevation (m)
–y
1
= flow depth directly upstream of pier (m)
–b = pier width (m)
–F
r
= approach Froude number
–K
1
–K
4
= correction factors
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠

69. 69
CSU Pier Scour Equation
•K
1
= correction factor for pier nose shape
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠

70. 70
CSU Pier Scour Equation
•K
1
= correction factor for pier nose shape
– For angle of attach > 5
o
, K
1
= 1.0
– For angle of attach ‹5
o
• Square nose K
1
= 1.1
•Circular K
1
= 1.0
•Group of cylinders K
1
= 1.0
• Sharp nose K
1
= 0.9
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠

71. 71
CSU Pier Scour Equation
•K
2
= correction factor for angle of attach of flow
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠
0.65
2
L
KCos Sin
b
θθ
⎛⎞
=+
⎜⎟
⎝⎠
•Where
• L = length of pier (along flow line of angle of attach) (m)
• b = pier width (m)
•Θ= angle of attach (degrees)

72. 72
CSU Pier Scour Equation
•K
2
= correction factor for angle of attach of flow
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠
5.0 3.9 2.5 90
4.3 3.3 2.3 45
3.5 2.8 2.0 30
2.5 2.0 1.5 15
1.0 1.0 1.0 0
L/b = 12 L/b = 8 L/b = 4 Θ

73. 73
CSU Pier Scour Equation
•K
3
= correction factor for bed conditions
– Selected for type and size of dunes
– Use 1.1 for gravel-bed rivers
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠

74. 74
CSU Pier Scour Equation
•K
3
= correction factor for bed conditions
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠
1.3 >9 large dunes
1.2 3 to 9 medium dunes
1.1 0.6 to 3 small dunes
1.1 n/a plane bed/anti-dune
1.1 n/a clear water scourK
3
Dune Height
(m)
Bed Condition

75. 75
CSU Pier Scour Equation
•K
4
= correction factor for armoring of bed material
–K
4
varies between 0.7 and 1.0
–K
4
= 1.0 for D
50
< 60 mm, or for V
r
> 1.0
–K
4
= [1 – 0.89(1-V
r
)
2
]
0.5
, for D
50
> 60 mm
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠
(
)
()
90
i
r
ci
VV
V
VV
−
=
−
0.053
50
50
0.65
ic
D
VV
b
⎛⎞
=
⎜⎟
⎝⎠
1/6 1/3
1
6.19
cc
V
y
D =

76. 76
CSU Pier Scour Equation
•Where
– V = approach velocity (m/s)
–V
r
= velocity ratio
–V
i
= approach velocity when particles at pier begin to move (m/s)
–V
c90
= critical velocity for D
90
bed material size (m/s)
–V
c50
= critical velocity for D
50
bed material size (m/s)
–Y
1
= flow depth upstream of pier (m)
–D
c
= particle size selected to compute V
c
(m)
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠
(
)
()
90
i
r
ci
VV
V
VV
−
=
−
0.053
50
50
0.65
ic
D
VV
b
⎛⎞
=
⎜⎟
⎝⎠
1/6 1/3
1
6.19
cc
V
y
D =

77. 77
CSU Pier Scour Equation
•Where
– d = maximum depth of scour, measured below bed elevation (m)
–y
1
= flow depth directly upstream of pier (m)
–b = pier width (m)
–F
r
= approach Froude number
–K
1
–K
4
= correction factors
0.65
0.43
1234
11
2.0
r
db
K
KKK F
yy
⎛⎞
=
⎜⎟
⎝⎠

78. 78
Local Scour
• Abutment scour

79. 79
Local Scour
• Abutment scour
– Developed for sand-bed systems
– Provides conservative estimate for
gravel-bed systems
– Can be applied to other obstructions
– Results can be reduced based on
experience
– FroelichEquation

80. 80
Local Scour
• Froehlich Equation
– Predicts scour as a function of shape,
angle with respect to flow, length normal
to flow and approach flow conditions
– Provides conservative estimate for
gravel-bed systems
– Can be applied to other obstructions
– Assumes object extends above water
surface

81. 81
Froehlich Equation for Live-
Bed Scour at Abutments
•Where
– d = maximum depth of scour, measured below bed elevation (m)
– y = flow depth at abutment (m)
–F
r
= approach Froude number
– L’ = length of abutment projected normal to flow (m)
–K
1
–K
2
= correction factors
0.43
0.61
12
'
2.27 1.0
r
dL
KK F
yy
⎛⎞
=+
⎜⎟
⎝⎠

82. 82
Froehlich Equation for Live-
Bed Scour at Abutments
• L’ = length of abutment projected normal to flow (m)
θ
0.43
0.61
12
'
2.27 1.0
r
dL
KK F
yy
⎛⎞
=+
⎜⎟
⎝⎠

83. 83
Froehlich Equation
•K
1
= correction factor for abutment shape
–K
1
= 1.0 for vertical abutment
–K
1
= 0.82 for vertical abutment with wing walls
–K
1
= 0.55 for spill through abutments
0.43
0.61
12
'
2.27 1.0
r
dL
KK F
yy
⎛⎞
=+
⎜⎟
⎝⎠

84. 84
Froehlich Equation
•K
2
= correction factor for angle of embankment to flow
θ
0.43
0.61
12
'
2.27 1.0
r
dL
KK F
yy
⎛⎞
=+
⎜⎟
⎝⎠

85. 85
Froehlich Equation
•K
2
= correction factor for angle of embankment to flow
•Where
•2= angle between channel bank and abutment
•2is > 90 degrees of embankment points upstream
•2is < 90 degrees if embankment points downstream
0.13
2
90
Kθ
⎛⎞
=
⎜⎟
⎝⎠
0.43
0.61
12
'
2.27 1.0
r
dL
KK F
yy
⎛⎞
=+
⎜⎟
⎝⎠

86. 86
Check Method
U.S. Bureau of Reclamation

87. 87
Check Method
U.S. Bureau of Reclamation
• Provides method to compute scour at:
– Channel bends
–Piers
– Grade-control structures
– Vertical rock banks or walls
• May not be as conservative as
previous approaches

88. 88
Check Method
U.S. Bureau of Reclamation
• Computes scour depth by applying an
adjustment to the average of three
regime equations
– Neil equation (1973)
– Modified Lacey Equation (1930)
– Blench equation (1969)

89. 89
Neil Equation
• Where
–y
n
= scour depth below design flow level (L)
–y
bf
= average bank-full flow depth (L)
–q
d
= design flow discharge per unit width (L
2
/T)
–q
bf
= bankfull flow discharge per unit width (L
2
/T)
– m = exponent varying from 0.67 for sand and 0.85 for
coarse gravel
m
d
nbf
bf
q
yy
q
⎛⎞
=⎜⎟
⎜⎟
⎝⎠

90. 90
Neil Equation
• Obtain field measurements of an incised reach
• Compute bank-full discharge and associated hydraulics
• Determine scour depth
m
d
nbf
bf
q
yy
q
⎛⎞
=⎜⎟
⎜⎟
⎝⎠

91. 91
Modified Lacey Equation
• Where
–y
L
= mean depth at design discharge (L)
– Q = design discharge (L
3
/T)
–
f
= Lacey’s silt factor = 1.76 D
50
0.5
–D
50
= median size of bed material (must be in mm!)
3.3
0.47
L
Q
y
f
⎛⎞
=
⎜⎟
⎝⎠

92. 92
Blench Equation
• Where
–y
B
= depth for zero bed sediment transport (L)
–q
d
= design discharge per unit width (L
2
/T)
–F
bo
= Blench’szero bed factor
0.67
0.33
d
B
bo
q
y
F
=

93. 93
Blench Equation
F
bo
= Blench’s zero bed factor
0.67
0.33
d
B
bo
q
y
F
=

94. 94
Check Method
U.S. Bureau of Reclamation
• Computes scour depth by applying an
adjustment to the average of three
regime equations
– Neil equation (1973)
– Modified Lacey Equation (1930)
– Blench equation (1969)
• Adjust as follows…

95. 95
Check Method
U.S. Bureau of Reclamation
•Where
–d
N
, d
L
, d
B
= depth of scour from Neil, Lacey and Blench equations,
respectively
–K
N
, K
L
, K
B
= adjustment coefficients for each equation
NNN L
LL
BbB
dKy
dKy
dKy
= =
=

96. 96
Check Method
U.S. Bureau of Reclamation
K
N
, K
L
, K
B
0.75 – 1.25 1.50 0.4 - 0.7 Small dam or grade control
0.50 – 1.00 - 1.00 Nose of Piers
- 1.25 - Vertical rock bank or wall
- 1.00 - Right-angle bend
0.60 0.75 0.70 Severe bend
0.60 0.5 0.60 Moderate bend
0.60 0.25 0.50 Straight reach (wandering thalweg)
Bend ScourBlench-K
B
Lacey-K
L
Neil-K
N
Condition

97. 97
Check Method
U.S. Bureau of Reclamation
• Average values and compare to results of previous
methods
• Appropriate level of conservatism??
NNN L
LL
BbB
dKy
dKy
dKy
= =
=

98. 98
REFERENCES
1. Lane, E.W. 1955. Design of stable channels. Transactions
of the American Society of Civil Engineers. 120: 1234-
1260
2. U.S. Department of Transportation, Federal Highway
Administration. 1988. Design of Roadside Channel with
Flexable Linings. Hydraulic Engineering Circular No. 15.
Publication No. FHWA-IP-87-7.
3. Richardson, E.V. and S.R. Davis. U.S. Department of
Transportation, Federal Highway Administration, 1995.
Evaluating Scour at Bridges, Hydraulic Engineering
Circular No. 18. Publication No. FHWA-IP-90-017.
4. U.S. Department of Transportation, Federal Highway
Administration. 1990. Highways in the River Environment.
5. Thorne, C.R., R.D. Hey and M.D. Newson. 1997. Applied
Fluvial Geomorphology for River Engineering and
Management. John Wiley and Sons, Inc. New York, N.Y.

99. 99
REFERENCES
6. Maynord, S. 1996. Toe Scour Estimation on Stabilized
Bendways. Journal of Hydraulic Engineering, American
Society of Civil Engineers, Vol. 122, No.8.
7. U.S. Department of Transportation, Federal Highway
Administration. 1955a. Stream Stability at Highway
Structures. Hydraulic Engineering Circular No. 20.
8. Laursen, E.M. and Flick, M.W. 1983. Final Report,
Predicting Scour at Bridges: Questions Not Fully
Answered – Scour at Sill Structures, Report ATTI-83-6,
Arizona Department of Transportation.
9. Simons, D.B and Senturk, F. 1992. Sediemnt Transport
Technology, Water Resources Publications, Littleton, CO.
10. Bureau of Reclamation, Sediment and River Hydraulics
Section. 1884. Computing Degradation and Local Scour,
Technical Guideline for Bureau of Reclamation, Denver,
CO.