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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 99
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).

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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

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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).