Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 99
99
Discharge vs. Velocity Discharge vs. Water Depth
4.00 16.0
3.50 14.0
3.00 12.0
Water Depth (m)
Velocity (m/s)
2.50 10.0
2.00 8.0
1.50 6.0
1.00 4.0
0.50 2.0
0.00 0.0
0 5000 10000 15000 20000 25000 0 5000 10000 15000 20000 25000
Discharge (m3/s) Discharge (m3/s)
Figure 12.9. Relationship of discharge versus velocity and discharge versus water depth
(Example 2).
(2) Calculate Reynolds Number Zmax ( Pier ) = 0.18 K w Ksp Ksh R e 0.635
VD 3.36 × 7.3 Zmax = 0.18 × 0.64 × 1.17 × 1.1
Re = = = 2.45 × 10 7
v 10 -6
× (2.45 × 10 7 )
0.635
= 7297 mm
(3) Maximum hydraulic shear stress around the pier is (6) The equation for z (t) is
max = kw ksh ksp k 0.094 V 2
1
-
1 t t ( hrs)
z= =
log R e 10
1 t 1 t ( hrs)
+ +
Z Zmax 15.3 7297
max = 3.9 × 1.15 × 1.33 × 1.636 × 0.094 × 1000
(7) The flood lasts 2 days (48 hours), therefore
2
-
1 1
× 3.36
log( 2 .45 × 10 7)
10 Z = 667 mm or 9.1% of Zmax
= 365.8 N 12.3.2 SRICOS-EFA Method:
m2
Computer Calculation
is read on the EFA curve
(4) The initial rate of scour Z
(Layer 1) at = max Use SRICOS-EFA program Option 1: Complex Pier Scour
= 15.3 mm/hr
Z Results:
After a 2-year period of flood having 3.36 m/sec velocity, the
final pier scour is
(5) The maximum depth of scour Zmax is
Z = 7.1 m
Scour Depth vs. Time (Example 2)
5000
4500
Table 12.3 provides a summary of input data. Figure 12.11
illustrates the scour depth development with time. Figures
Pier Scour Depth (mm)
4000
3500 12.12 through 12.14 provide further information.
3000
2500 12.4 EXAMPLE 4: CONTRACTED CHANNEL
2000
WITH 90-DEGREE TRANSITION ANGLE
AND APPROACHING CONSTANT
1500
VELOCITY
1000
500
Given:
0
Channel geometry: Upstream uncontracted channel width
0 10 20 30 40 50 60 70
B1 = 150 m, contracted channel width
Time (Year)
due to bridge abutment B2 = 50 m, con-
Figure 12.10. Scour depth versus time (Example 2). traction length of channel L: = 30 m
OCR for page 100
100
EFA Result (Layer 1)
20
18
Scour rate Shear stress
16
(mm/hr) (N/m2)
0 1 14
Scour Rate (mm/hr)
1 4 12
2 6
10
3 9
6 30 8
10 100 6
12.5 200
4
16 400
2
0
0 100 200 300 400
2
Shear Stress (N/m )
Figure 12.11. EFA results for Soil Layer 1 (Example 3).
EFA Result (Layer 2)
8
7
Scour rate Shear stress
(mm/hr) (N/m2) 6
0 3
Scour Rate (mm/hr)
0.1 4 5
1 6 4
2 9
4 18.5 3
5 27
2
6 40
6.9 60 1
0
0 10 20 30 40 50 60 70
2
Shear Stress (N/m )
Figure 12.12. EFA results for Soil Layer 2 (Example 3).
Scour Depth vs. Time (Example 3)
8000
7000
Pier Scour Depth (mm)
6000
5000
River Bank River Bank 4000
Flow 20°
B 3000
2000
Lpier 1000
S S
0
0 200 400 600 800
Time (Day)
Figure 12.13. Plan view of rectangular piers group scour
case (Example 3). Figure 12.14. Scour depth versus time (Example 3).
OCR for page 101
101
TABLE 12.4 Summary of data input (Example 4)
Input Unit SI 1
Output Unit SI 1
First Date of Analysis 01-01-2003
Last Date of Analysis 01-01-2005
No. Of Input Data 730
Upstream Uncontracted Channel Width 150
Contracted Channel Width 50
Contraction Length of Channel 30
Transition Angle of Channel 90
Manning's Coefficient 0.02
Average Hydraulic Radius 2.77
Time Step Hours 24
Type of Hydrologic Input Velocity 2
Number of Regression Points Velocity vs. Water Depth 1
Values of Regression Points Velocity, Water Depth 3.36, 3.12
No. of Layers 2
st
Properties of 1 Layer Thickness 15
Critical Shear Stress 2
Number of Regression
Points Shear Stress vs. Scour Rate 8
1, 0
4, 1
Estimate Initial 6,2
Scour Rate Value of Regression Shear Stress, Scour Rate 9,3
Points 6, 30
100, 10
200, 12.5
400, 16
Properties of 2nd Layer Thickness 20
Critical Shear Stress 4
Number of Regression
Points Shear Stress vs. Scour Rate 8
3, 0
4, 0.1
Estimate Initial 6,1
Scour Rate Value of Regression Shear Stress, Scour Rate 9,2
Points 18.5, 4
27, 5
40, 6
60, 6.9
Abutment 12.4.1 SRICOS-EFA Method: Hand Calculation
transition angle: 90 degrees
Flow parameters: Water depth H = 3.12 m, (1) Calculate the K factors for max:
Approaching constant velocity V = kw 1
3.36 m/sec
B 1.75
( )
1.75
kR = 0.62 + 0.38 1 = 0.62 + 0.38
Manning 150
= 3.2
Coefficient: 0.02 B2 50
EFA result: Layer 1: Thickness 15 m; critical shear
(90
) (90
90)
1.5 1.5
stress 2 N/m2 k = 1 + 0.9 = 1 + 0.9 = 1.9
Layer 2: Thickness 20 m; critical shear
stress 4 N/m2 L 30
Since = = 0.3 < 0.35, so
Flood period: 2 days for hand calculation ( B1 - B2 ) 100
2 years for computer calculation
L 2
kL = 0.77 + 1.36
L
- 1.98
Determine: The magnitude of maximum contrac-
1
tion scour depth B1 - B2 B1 - B2
OCR for page 102
102
EFA Result (Layer 1)
20
18
Scour rate Shear stress 16
(mm/hr) (N/m2)
0 1 14
Scour Rate (mm/hr)
1 4 12
2 6
10
3 9
6 30 8
10 100 6
12.5 200
4
16 400
2
0
0 100 200 300 400
2
Shear Stress (N/m )
Figure 12.15. EFA results for Soil Layer 1 (Example 4).
(2) Calculate hydraulic radius of contracted section 0.5
1.38V1 1 C
B
B2
Zmax (Cont ) = 1.9 - 1
A 3.12 × 50 gH
Rh = = = 2.77 m gnH 3
P 2 × 3.12 + 50
H = 13.98 m
(3) Maximum hydraulic shear stress in contraction chan-
0.5
1.31V1 1 C
B
nel is
B2 -
Zmax (Unif ) = 1.41 1
gH
1 gnH 3
max = kR kL kw k n 2 V 2 R h - 3 = 3.2 × 1.9 × 9810
H = 9.81 m
1
-
× 0.02 × 3.36 × 2.77
2 2 3 = 191.8 N (6) The equation for z (t) is
m2
is read on the EFA curve at t t ( hrs)
(4) The initial rate of scour Z z= =
= max 1 t 1 t ( hrs)
+ Zmax 12.2 + 13980
Z
= 12.2 mm/hr
Z t t ( hrs)
z= =
1 t 1 t ( hrs)
(5) The maximum depth of scour Zmax is + Zmax 12.2 + 9810
Z
EFA Result (Layer 2)
8
7
Scour rate Shear stress
(mm/hr) (N/m2) 6
Scour Rate (mm/hr)
0 3 5
0.1 4
1 6 4
2 9
3
4 18.5
5 27 2
6 40
6.9 60 1
0
0 10 20 30 40 50 60 70
2
Shear Stress (N/m )
Figure 12.16. EFA results for Soil Layer 2 (Example 4).
