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OCR for page 93

93
CHAPTER 12
SCOUR EXAMPLE PROBLEMS
12.1 EXAMPLE 1: SINGLE CIRCULAR PIER
× 0.094 × 1000 × 3.36 2 -
1 1
WITH APPROACHING
CONSTANT VELOCITY
log(8 .4 × 10 6
) 10
= 52.28 N
Given: m2
Pier geometry: Pier diameter B = 2.5 m, circular pier is read on the EFA curve
Channel geometry: Channel upstream width B1 = 50 m (4) The initial rate of scour Z
Flow parameters: Water depth H = 3.12 m, (Layer 1) at = max
Approaching constant velocity V = = 8.6 mm/hr
Z
3.36 m/sec
Angle of attack: 0 degrees (5) The maximum depth of scour Zmax is
EFA result: Layer 1: Thickness 10 m; critical shear
stress 2 N/m2 Zmax (Pier) = 0.18Kw Ksp Ksh R e
0.635
= 0.18 × 0.916 ×
Layer 2: Thickness 20 m; critical shear (8.4 × 10 )
6 0.635
= 4112.3mm
stress 4 N/m2
Flood period: 2 days for hand calculation (6) The equation for z (t) is
2 years for computer calculation t t ( hrs)
Determine: The magnitude of maximum pier z= =
1
+
t 1 t ( hrs)
scour depth +
Z Z max 8 . 6 4112 .3
(7) The flood lasts 2 days (48 hours), therefore
12.1.1 SRICOS-EFA Method: Hand Calculation
Z = 375 mm or 9.1% of Zmax
(1) Calculate the K factors for max and Zmax:
12.1.2 SRICOS-EFA Method:
H 3.12 Computer Calculation
-4 -4 ×
kw = 1 + 16 e B = 1 + 16 e 2.5 = 1.109
Use SRICOS-EFA program Option 1: Complex Pier Scour
( ) ( )
0.34
0.34 3.12
K w = 0.85 H B = 0.85 × = 0.916
2.5 Results:
After a 2-year period of the flood having 3.36 m/s velocity,
Since the pier in this case is a circular pier, ksh = 1 and the final pier scour is
Ksh = 1.
It is a single pier, so ksp = 1 and Ksp = 1. Z=4m
There is no attack angle of the flow, so k = 1.
Table 12.1 and Figures 12.1 through 12.3 provide further
(2) Calculate Reynolds Number as information. Figure 12.4 illustrates the scour depth develop-
ment with time.
Vd 3.36 × 2.5
Re = = = 8.4 × 10 6
v 10 -6 12.2 EXAMPLE 2: SINGLE RECTANGULAR
PIER WITH ATTACK ANGLE
AND APPROACHING HYDROGRAPH
(3) Maximum hydraulic shear stress around the pier is
Given:
Pier geometry: Pier width B = 1.22 m, pier length
max = kw ksh ksp k 0.094 V 2 - = 1.109
1 1
log R e 10 Lpier = 18 m, rectangular pier

OCR for page 93

94
TABLE 12.1 Summary of data input (Example 1)
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 Channel Width 50
Type of Pier Circular Pier 1
Pier Diameter 2.5
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
Properties of 1st Layer Thickness 10
Critical Shear Stress 2
Number of
Regression Points Shear Stress vs. Scour Rate 8
1, 0
Estimate Initial 2, 0.1
Scour Rate Value of Regression Shear Stress, Scour Rate 4,1
Points 6,2
9, 3
20, 6
40, 8
60, 8.9
Properties of 2nd Layer Thickness 20
Critical Shear Stress 4
Number of
Regression Points Shear Stress vs. Scour Rate 8
3, 0
Estimate Initial 4, 0.1
Scour Rate Value of Regression Shear Stress, Scour Rate 6,1
Points 9,2
18.5, 4
27, 5
40, 6
60, 6.9
EFA Result (Layer 1)
10
9
8
Scour rate Shear stress
7
(mm/hr) (N/m2)
Scour Rate (mm/hr)
0 1 6
0.1 2 5
1 4
4
2 6
3 9 3
6 20
2
8 40
8.9 60 1
0
0 10 20 30 40 50 60 70
Figure 12.1. EFA Results for Soil Layer 1 (Example 1).