Pier and Contraction Scour in Cohesive Soils (2004)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

93 CHAPTER 12 SCOUR EXAMPLE PROBLEMS 12.1 EXAMPLE 1: SINGLE CIRCULAR PIER WITH APPROACHING CONSTANT VELOCITY Given: Pier geometry: Pier diameter B = 2.5 m, circular pier Channel geometry: Channel upstream width B1 = 50 m Flow parameters: Water depth H = 3.12 m, Approaching constant velocity V = 3.36 m/sec Angle of attack: 0 degrees EFA result: Layer 1: Thickness 10 m; critical shear stress 2 N/m2 Layer 2: Thickness 20 m; critical shear stress 4 N/m2 Flood period: 2 days for hand calculation 2 years for computer calculation Determine: The magnitude of maximum pier scour depth 12.1.1 SRICOS-EFA Method: Hand Calculation (1) Calculate the K factors for τmax and Zmax: Since the pier in this case is a circular pier, ksh = 1 and Ksh = 1. It is a single pier, so ksp = 1 and Ksp = 1. There is no attack angle of the flow, so kα = 1. (2) Calculate Reynolds Number as (3) Maximum hydraulic shear stress around the pier is τ ραmax . log .= −     =k k k k Vw sh sp eR
0 094 1 1 10 1 109 2 Re = = × = × − Vd v 3 36 2 5 10 8 4 106 6. . . k e e K H B H B w w = + = + = = ( ) = × ( ) = − − ×1 16 1 16 1 109 0 85 0 85 3 122 5 0 916 4 4 3 122 5 0 34 0 34

. . . . . . . . . . (4) The initial rate of scour Z˙ is read on the EFA curve (Layer 1) at τ = τmax Z˙ = 8.6 mm/hr (5) The maximum depth of scour Zmax is Zmax (Pier) = 0.18Kw Ksp Ksh R e0.635 = 0.18 × 0.916 × (8.4 × 106)0.635 = 4112.3mm (6) The equation for z (t) is (7) The flood lasts 2 days (48 hours), therefore Z = 375 mm or 9.1% of Zmax 12.1.2 SRICOS-EFA Method: Computer Calculation Use SRICOS-EFA program Option 1: Complex Pier Scour Results: After a 2-year period of the flood having 3.36 m/s velocity, the final pier scour is Z = 4 m Table 12.1 and Figures 12.1 through 12.3 provide further information. Figure 12.4 illustrates the scour depth develop- ment with time. 12.2 EXAMPLE 2: SINGLE RECTANGULAR PIER WITH ATTACK ANGLE AND APPROACHING HYDROGRAPH Given: Pier geometry: Pier width B = 1.22 m, pier length Lpier = 18 m, rectangular pier z t Z t Z t t = + = ( ) + ( )1 1 8 6 4112 3˙ . .max hrs hrs × × × ×( ) −   = 0 094 1000 3 36 1 8 4 10 1 10 52 28 2 6 2 . . log . . N m

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

95 Scour rate (mm/hr) Shear stress (N/m2) 0 3 0.1 4 1 6 2 9 4 18.5 5 27 6 40 6.9 60 0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 Shear Stress (N/m2) Sc o u r R a te (m m /h r) EFA Result (Layer 2) Flow B 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 200 400 600 800 Ti Scour Depth vs. Time (Example 1) me (Day) Pi er S co u r D ep th (m m ) Figure 12.3. Plan view of single circular pier scour case (Example 1). Figure 12.2. EFA Results for Soil Layer 2 (Example 1). Figure 12.4. Scour depth versus time (Example 1). Channel geometry: Channel upstream width B1 = 50 m Flow parameters: Angle of attack: 20 degrees 70 years predicted hydrograph EFA result: Layer 1: Thickness 10 m; critical shear stress 2 N/m2 Layer 2: Thickness 20 m; critical shear stress 4 N/m2 Time duration: 70 years Determine: The magnitude of maximum pier scour depth 12.2.1 SRICOS-EFA Method: Computer Calculation Since the hydrograph is used in this case as hydrologic data input, the relationship between discharge and velocity and the relationship between discharge and water depth need to be defined. The HEC-RAS program can be a good tool to define these relationships. The following charts present the results obtained from HEC-RAS for this case. Use SRICOS-EFA program Option 1: Complex Pier Scour. Results: After a 70-year period of flood, the final pier scour is Z = 4.7 m Table 12.2 lists data input for this example. Figure 12.5 illus- trates the scour depth development with time. Figures 12.6 through 12.8 provide further information. 12.3 EXAMPLE 3: GROUP RECTANGULAR PIERS WITH ATTACK ANGLE AND APPROACHING CONSTANT VELOCITY Given: Pier geometry: Pier width B = 1.22 m, pier length Lpier = 18 m, rectangular pier, number of piers, N = 3, spacing, S = 18 m Channel geometry: Channel upstream width B1 = 150 m Flow parameters: Water depth H = 3.12 m, Angle of attack: 20 degrees

96 Input Unit SI 1 Output Unit SI 1 First Date of Analysis 01-01-2003 Last Date of Analysis 01-01-2073 No. Of Input Data 25569 Upstream Channel Width 50 Type of Pier Pier Width Pier Length Attack Angle Number of Piers Rectangular Pier 2 1.22 18 20 1 Time Step Hours 24 Type of Hydrologic Input Discharge 1 Number of Regression Points Discharge vs. Velocity 8 Values of Regression Points Discharge, Velocity 1.42, 0 14, 0.02 141, 0.16 566, 0.49 1415, 0.87 5663, 1.75 13592, 2.97 19821, 3.56 Number of Regression Points Discharge vs. Water Depth 8 Input Hydrologic Data Values of Regression Points Discharge, Water Depth 1.42, 3.86 14, 4.18 141, 5.02 566, 6.18 1415, 7.83 5663, 11.33 13592, 13.15 19821, 14.19 No. Of Layers 2 Thickness 10 Properties of 1st Layer Critical Shear Stress 2 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 1, 0 2, 0.1 4,1 6,2 9, 3 20, 6 40, 8 60, 8.9 Thickness 20 Properties of 2nd Layer Critical Shear Stress 4 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 3, 0 4, 0.1 6,1 9,2 18.5, 4 27, 5 40, 6 60, 6.9 TABLE 12.2 Summary of data input (Example 2)

97 Layer 2: Thickness 20 m; critical shear stress 4 N/m2 Flood period: 2 days for hand calculation 2 years for computer calculation Determine: The magnitude of maximum pier scour depth 12.3.1 SRICOS-EFA Method: Hand Calculation (1) Calculate the K factors for τmax and Zmax as follows: Here, B is the projected width of pier. B = Lpier sin α + W cos α = 18 × sin 20° + 1.22 × cos 20° = 7.3 m k e e K H B H B w w = + = + = = ( ) = × ( ) = − − ×1 16 1 16 3 9 0 85 0 85 3 127 3 0 637 4 4 3 127 3 0 34 0 34

. . . . . . . . . . Scour rate (mm/hr) Shear stress (N/m2) 0 1 0.1 2 1 4 2 6 3 9 6 20 8 40 8.9 60 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 70 Sh EFA Result (Layer 1) ear Stress (N/m2) Sc o u r R a te (m m /h r) Scour rate (mm/hr) Shear stress (N/m2) 0 3 0.1 4 1 6 2 9 4 18.5 5 27 6 40 6.9 60 0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 Shear Stress (N/m2) Sc o u r R a te (m m /h r) EFA Result (Layer 2) 0 2000 4000 6000 8000 10000 12000 14000 0 10 20 30 40 50 60 70 Ti Future Hydrograph me (Year) D isc ha rg e (m 3 /s ec ) Figure 12.5. Seventy years future approaching hydrograph (Example 2). Figure 12.7. EFA results for Soil Layer 2 (Example 2). Figure 12.6. EFA results for Soil Layer 1 (Example 2). Approaching constant velocity V = 3.36 m/sec EFA result: Layer 1: Thickness 10 m; critical shear stress 2 N/m2

98 Since in this case, the pier is a rectangular pier, so Since there are three piers in this case, the effect of a group pier exists. There is attack angle of the flow, so kα α = + ( ) = + ( ) =1 1 5 90 1 1 5 2090 1 6360 57 0 57. . .. . k e e K B B nB S D sp sp = + = + = = − = − = −( ) −( )1 5 1 5 1 33 150 150 3 7 3 1 17 1 1 1 1187 3 1 1 . . . . * . . k esh = + × = −1 15 7 1 154 18 1 22 . . . Flow 20° B Lpier Figure 12.8. Plan view of single rectangular pier scour case (Example 2). Input Unit SI 1 Output Unit SI 1 First Date of Analysis 01-01-1998 Last Date of Analysis 01-01-2000 No. Of Input Data 730 Upstream Channel Width 150 Type of Pier Pier Width Pier Length Attack angle Number of piers Pier spacing Rectangular Pier 2 1.22 18 20 3 18 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 Thickness 10 Properties of 1st Layer Critical Shear Stress 2 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 1, 0 4, 1 6,2 9,3 6, 30 100, 10 200, 12.5 400, 16 Thickness 20 Properties of 2nd Layer Critical Shear Stress 4 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 3, 0 4, 0.1 6,1 9,2 18.5, 4 27, 5 40, 6 60, 6.9 TABLE 12.3 Summary of data input (Example 3)

99 (6) The equation for z (t) is (7) The flood lasts 2 days (48 hours), therefore Z = 667 mm or 9.1% of Zmax 12.3.2 SRICOS-EFA Method: Computer Calculation Use SRICOS-EFA program Option 1: Complex Pier Scour Results: After a 2-year period of flood having 3.36 m/sec velocity, the final pier scour is Z = 7.1 m Table 12.3 provides a summary of input data. Figure 12.11 illustrates the scour depth development with time. Figures 12.12 through 12.14 provide further information. 12.4 EXAMPLE 4: CONTRACTED CHANNEL WITH 90-DEGREE TRANSITION ANGLE AND APPROACHING CONSTANT VELOCITY Given: Channel geometry: Upstream uncontracted channel width B1 = 150 m, contracted channel width due to bridge abutment B2 = 50 m, con- traction length of channel L: = 30 m z t Z t Z t t = + = ( ) + ( )1 1 15 3 7297˙ .max hrs hrs Z Pier K K K Z max . max . . . . . . . ( ) = = × × × × ×( ) = 0 18 0 18 0 64 1 17 1 1 2 45 10 7297 0 635 7 0 635 w sp sh eR mm 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 0 5000 10000 15000 20000 25000 Discharge (m3/s) V el oc ity (m /s) 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 0 5000 10000 15000 20000 25000 Discharge (m3/s) Discharge vs. Velocity Discharge vs. Water Depth W at er D ep th (m ) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 10 20 30 40 50 60 70 Ti Scour Depth vs. Time (Example 2) me (Year) Pi er Sc o u r D ep th (m m ) Figure 12.10. Scour depth versus time (Example 2). Figure 12.9. Relationship of discharge versus velocity and discharge versus water depth (Example 2). (2) Calculate Reynolds Number (3) Maximum hydraulic shear stress around the pier is (4) The initial rate of scour Z˙ is read on the EFA curve (Layer 1) at τ = τmax Z˙ = 15.3 mm/hr (5) The maximum depth of scour Zmax is τmax . . . . . . log . . = × × × × × × ×( ) −     = 3 9 1 15 1 33 1 636 0 094 1000 3 36 1 2 45 10 1 10 365 8 2 7 2 N m τ ραmax . log= −    k k k k Vw sh sp eR
0 094 1 1 10 2 Re = = × = × − VD v 3 36 7 3 10 2 45 106 7. . .

100 Scour rate (mm/hr) Shear stress (N/m2) 0 1 1 4 2 6 3 9 6 30 10 100 12.5 200 16 400 0 2 4 6 8 10 12 14 16 18 20 0 100 200 300 400 Sh EFA Result (Layer 1) ear Stress (N/m2) Sc o u r R a te (m m /h r ) Scour rate (mm/hr) Shear stress (N/m2) 0 3 0.1 4 1 6 2 9 4 18.5 5 27 6 40 6.9 60 0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 Shear Stress (N/m2) Sc o u r R a te (m m /h r) EFA Result (Layer 2) River Bank River Bank Lpier B S S Flow 20° 0 1000 2000 3000 4000 5000 6000 7000 8000 0 200 400 600 800 Ti Scour Depth vs. Time (Example 3) me (Day) Pi er S co u r D ep th (m m ) Figure 12.11. EFA results for Soil Layer 1 (Example 3). Figure 12.12. EFA results for Soil Layer 2 (Example 3). Figure 12.13. Plan view of rectangular piers group scour case (Example 3). Figure 12.14. Scour depth versus time (Example 3).

Abutment transition angle: 90 degrees Flow parameters: Water depth H = 3.12 m, Approaching constant velocity V = 3.36 m/sec Manning Coefficient: 0.02 EFA result: Layer 1: Thickness 15 m; critical shear stress 2 N/m2 Layer 2: Thickness 20 m; critical shear stress 4 N/m2 Flood period: 2 days for hand calculation 2 years for computer calculation Determine: The magnitude of maximum contrac- tion scour depth 101 12.4.1 SRICOS-EFA Method: Hand Calculation (1) Calculate the K factors for τmax: k k B B k L B B k L B B w R L Since so ≈ = +   = + ( ) = = + ( ) = + ( ) = −( ) = = < = + −  1 0 62 0 38 0 62 0 38 15050 3 2 1 0 9 90 1 0 9 90 90 1 9 30 100 0 3 0 35 0 77 1 36 1 2 1 75 1 75 1 5 1 5 1 2 1 2 . . . . . . . . . . , . . . . . . θ θ  − −  ≈1 98 11 2 2 . L B B 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 Contraction Length of Channel Transition Angle of Channel Manning’s Coefficient Average Hydraulic Radius 50 30 90 0.02 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 Thickness 15 Properties of 1st Layer Critical Shear Stress 2 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 1, 0 4, 1 6,2 9,3 6, 30 100, 10 200, 12.5 400, 16 Thickness 20 Properties of 2nd Layer Critical Shear Stress 4 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 3, 0 4, 0.1 6,1 9,2 18.5, 4 27, 5 40, 6 60, 6.9 TABLE 12.4 Summary of data input (Example 4)

102 Scour rate (mm/hr) Shear stress (N/m2) 0 1 1 4 2 6 3 9 6 30 10 100 12.5 200 16 400 0 2 4 6 8 10 12 14 16 18 20 0 100 200 300 400 Sh EFA Result (Layer 1) ear Stress (N/m2) Sc o u r R a te (m m /h r ) Figure 12.15. EFA results for Soil Layer 1 (Example 4). Scour rate (mm/hr) Shear stress (N/m2) 0 3 0.1 4 1 6 2 9 4 18.5 5 27 6 40 6.9 60 0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 She EFA Result (Layer 2) ar Stress (N/m2) Sc o u r R a te (m m /h r) Figure 12.16. EFA results for Soil Layer 2 (Example 4). (2) Calculate hydraulic radius of contracted section (3) Maximum hydraulic shear stress in contraction chan- nel is (4) The initial rate of scour Z˙ is read on the EFA curve at τ = τmax Z˙ = 12.2 mm/hr (5) The maximum depth of scour Zmax is τ γθmax . . . . . . = = × × × × × = − − k k k k n V N R L w hR m
2 2 1 3 2 2 1 3 2 3 2 1 9 9810 0 02 3 36 2 77 191 8 R A Ph m= = × × + = 3 12 50 2 3 12 50 2 77 . . . (6) The equation for z (t) is z t Z t Z t t z t Z t Z t t = + = ( ) + ( ) = + = ( ) + ( ) 1 1 12 2 13980 1 1 12 2 9810 ˙ . ˙ . max max hrs hrs hrs hrs Z V B B gH gnH H m Z V B B gH gnH H m C C max . max . . . . . . . Cont Unif ( ) =     −           = ( ) =     −           = 1 9 1 38 13 98 1 41 1 31 9 81 1 1 2 0 5 1 3 1 1 2 0 5 1 3 τ ρ τ ρ

(7) The flood lasts 2 days (48 hours), therefore Z(Cont) = 562 mm or 4% of Zmax(Cont) Z(Unif) = 553 mm or 5.6% of Zmax(Cont) 12.4.2 SRICOS-EFA Method: Computer Calculation Use SRICOS-EFA program Option 2: Contraction Scour. Results: After a 2-year period of flood having 3.36 m/sec velocity, the final contraction scours are Z(Cont) = 13.14 m Z(Unif) = 9.39 m Table 12.4 and Figures 12.15 through 12.19 provide a sum- mary of input data and illustrate the results. 12.5 EXAMPLE 5: CONTRACTED CHANNEL WITH 60-DEGREE TRANSITION ANGLE AND APPROACHING HYDROGRAPH Given: Channel geometry: Upstream uncontracted channel width B1 = 150, contracted channel width due to bridge abutment B2 = 50 m, contrac- tion length of channel L: = 30 m Abutment transition angle: 60 degrees Flow parameters: 70 years predicted hygrograph Manning Coefficient: 0.02 Hydraulic Radius: 2.72 m EFA result: Layer 1: Thickness 10 m; critical shear stress 2 N/m2 Layer 2: Thickness 20 m; critical shear stress 4 N/m2 103 B2 B1 Bridge Abutment Bridge Abutment 90° V1 River Bank River Bank Flow L 0 2000 4000 6000 8000 10000 12000 14000 0 200 400 600 800 Ti Maximum Contraction Scour Depth vs. Time (Example 4) me (Day) Pi er S co u r D ep th (m m ) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 200 400 600 800 Ti Uniform Contraction Scour Depth vs. Time (Example 4) me (Day) Pi er S co u r D ep th (m m ) Figure 12.17. Plan view of contracted channel scour case (Example 4). Figure 12.18. Maximum contraction scour depth versus time (Example 4). Figure 12.19. Uniform contraction scour depth versus time (Example 4). Flood period: 70 years Determine: The magnitude of maximum contrac- tion scour depth 12.5.1 SRICOS-EFA Method: Computer Calculation Since the hydrograph is used in this case as hydrologic data input, the relationship between the discharge and veloc- ity and the relationship between discharge and water depth need to be defined. The HEC-RAS program can be a good tool to define these relationships. The following charts pre- sent the results obtained from HEC-RAS for this case. Use SRICOS-EFA program Option 2: Contraction Scour. Results: After a 70-year period of flood, the final contraction scours are Z(Cont) = 8.8 m Z(Unif) = 6.6 m

104 Input Unit SI 1 Output Unit SI 1 First Date of Analysis 01-01-2003 Last Date of Analysis 01-01-2073 No. Of Input Data 25569 Upstream Uncontracted Channel Width 150 Contracted Channel Width Contraction Length of Channel Transition Angle of Channel Manning’s Coefficient Average Hydraulic Radius 50 30 60 0.02 2.77 Time Step Hours 24 Type of Hydrologic Input Discharge 1 Number of Regression Points Discharge vs. Velocity 8 Values of Regression Points Discharge, Velocity 1.42, 0 14, 0.02 141, 0.16 566, 0.49 1415, 0.87 5663, 1.75 13592, 2.97 19821, 3.56 Number of Regression Points Discharge vs. Water Depth 8 Input Hydrologic Data Values of Regression Points Discharge, Water Depth 1.42, 3.86 14, 4.18 141, 5.02 566, 6.18 1415, 7.83 5663, 11.33 13592, 13.15 19821, 14.19 No. Of Layers 2 Thickness 10 Properties of 1st Layer Critical Shear Stress 2 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 1, 0 4, 1 6,2 9,3 6, 30 100, 10 200, 12.5 400, 16 Thickness 20 Properties of 2nd Layer Critical Shear Stress 4 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 3, 0 4, 0.1 6,1 9,2 18.5, 4 27, 5 40, 6 60, 6.9 TABLE 12.5 Summary of data input (Example 5)

105 Table 12.5 and Figures 12.20 through 12.26 provide a sum- mary of input data and illustrate the results. 12.6 EXAMPLE 6: BRIDGE WITH GROUP PIERS AND CONTRACTED CHANNEL WITH HYDROGRAPH IN CONTRACTED SECTION Given: Pier geometry: Pier width B = 1.52 m, pier length Lpier = 12.19 m, rectangular pier, num- ber of piers, N = 6, spacing, S = 30 m Channel geometry: Upstream uncontracted channel width B1 = 725 m, contracted channel width due to bridge abutment B2 = 122 m, Contraction length of channel L: = 40 m 0 2000 4000 6000 8000 10000 12000 14000 0 10 20 30 40 50 60 70 Ti Future Hydrograph me (Year) D isc ha rg e (m 3 /s ec ) Figure 12.20. Seventy years future approaching hydrograph (Example 5). Scour rate (mm/hr) Shear stress (N/m2) 0 3 0.1 4 1 6 2 9 4 18.5 5 27 6 40 6.9 60 0 1 2 3 4 5 6 7 8 01 02 03 04 05 06 07 0 Sh EFA Result (Layer 2) ear Stress (N/m2) Sc ou r R at e (m m/ hr ) Figure 12.22. EFA results for Soil Layer 2 (Example 5). Scour rate (mm/hr) Shear stress (N/m2) 0 1 1 4 2 6 3 9 6 30 10 100 12.5 200 16 400 0 2 4 6 8 10 12 14 16 18 20 01 00 2003 00 400 Sh EFA Result (Layer 1) ear Stress (N/m2) Sc ou r R at e (m m /h r) Figure 12.21. EFA results for Soil Layer 1 (Example 5).

106 Abutment transition angle: 90 degrees Flow parameters: 70 years predicted hydrograph Manning Coefficient: 0.0146 Hydraulic radius: 2.62 m EFA result: Layer 1: Thickness 15 m; critical shear stress 2 N/m2 Layer 2: Thickness 20 m; critical shear stress 4 N/m2 Flood period: 70 years Determine: The magnitude of maximum bridge scour depth 12.6.1 SRICOS-EFA Method: Computer Calculation Since the hydrograph is used in this case as hydrologic data input, the relationship between the discharge and B2 B1 Bridge Abutment Bridge Abutment 60° V1 River Bank River Bank Flow L 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 05 0001 0000 150002 0000 25000 Discharge (m3/s) V el oc ity (m /s) 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 05 0001 0000 150002 0000 25000 Di Discharge vs. Velocity Discharge vs. Water Depth scharge (m3/s) W at er D ep th (m ) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Maximum Contraction Scour Depth vs. Time (Example 5) Pi er S co ur D ep th (m m) 0 1000 2000 3000 4000 5000 6000 7000 Uniform Contraction Scour Depth vs. Time (Example 5) Pi er S co ur D ep th (m m ) Figure 12.23. Plan view of contracted channel scour case (Example 5). Figure 12.24. Relationship of discharge versus velocity and discharge versus water depth (Example 5). Figure 12.25. Maximum contraction scour depth versus time (Example 5). Figure 12.26. Uniform contraction scour depth versus time (Example 5).

107 Input Unit SI 1 Output Unit SI 1 First Date of Analysis 01-01-2003 Last Date of Analysis 01-01-2073 No. Of Input Data 25569 Type of Pier Pier Width Pier Length Attack angle Number of piers Pier spacing Rectangular Pier 2 1.52 12.19 0 6 30 Upstreamed Uncontracted Channel Width 725 Contracted Channel Width Contraction Length of Channel Transition Angle of Channel Manning’s Coefficient Average Hydraulic Radius 122 40 90 0.0146 2.62 Time Step Hours 24 Type of Hydrologic Input Discharge 1 Type of Velocity Velocity in contracted section 2 Number of Regression Points Discharge vs. Velocity 8 Values of Regression Points Discharge, Velocity 1.42, 0 14, 0.02 141, 0.16 566, 0.49 1415, 0.90 5663, 2.50 12375, 4.20 19821, 5.60 Number of Regression Points Discharge vs. Water Depth 8 Input Hydrologic Data Values of Regression Points Discharge, Water Depth 1.42, 3.86 14, 4.18 141, 5.02 566, 6.18 1415, 7.83 5663, 11.33 13592, 13.15 19821, 14.19 No. Of Layers 2 Thickness 15 Properties of 1st Layer Critical Shear Stress 2 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 1, 0 4, 1 6,2 9,3 6, 30 100, 10 200, 12.5 400, 16 Thickness 20 Properties of 2nd Layer Critical Shear Stress 4 Number of Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial Scour Rate Value of Regression Points Shear Stress, Scour Rate 3, 0 4, 0.1 6,1 9,2 18.5, 4 27, 5 40, 6 60, 6.9 TABLE 12.6 Summary of data input (Example 6)

108 0 2000 4000 6000 8000 10000 12000 14000 0 10 20 30 40 50 60 70 Ti Future Hydrograph me (Year) D isc ha rg e (m 3 /s ec ) Scour rate (mm/hr) Shear stress (N/m2) 0 1 1 4 2 6 3 9 6 30 10 100 12.5 200 16 400 0 2 4 6 8 10 12 14 16 18 20 0 100 200 300 400 Sh EFA Result (Layer 1) ear Stress (N/m2) Sc ou r R at e (m m /h r) Scour rate (mm/hr) Shear stress (N/m2) 0 3 0.1 4 1 6 2 9 4 18.5 5 27 6 40 6.9 60 0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 Sh EFA Result (Layer 2) ear Stress (N/m2) Sc ou r R at e (m m/ hr ) velocity and the relationship between discharge and water depth need to be defined. The HEC-RAS program can be a good tool to define these relationships. The follow- ing charts present the results obtained from HEC-RAS for this case. Use SRICOS-EFA program Option 3: Bridge Scour. Results: After a 70-year period of flood, in this case the maximum final bridge scour is Z = 6.2 m Table 12.6 and Figures 12.27 through 12.33 provide a sum- mary of input data and illustrate the results. Figure 12.27. Seventy years future hydrograph (Example 6). Figure 12.28. EFA results for Soil Layer 1 (Example 6). Figure 12.29. EFA results for Soil Layer 2 (Example 6).

109 Left Overbank Main Channel Right Overbank Approach Cross Section 0 100 200 300 500 600 700 800400 0 1 3 2 4 5 6 7 8 Distance, Meters El ev at io n, M et er s Figure 12.30. Cross-section view of approaching channel (Example 6). El ev at io n, M et er s 0 Distance, Meters 350300 450400 30 m 1 30 m30 m 2 3 30 m30 m Bridge Cross Section7 5 4 6 8 Figure 12.31. Cross-section view of bridge (Example 6).

110 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 0 5000 10000 15000 20000 25000 Discharge (m3/s) 0.00 1.00 2.00 3.00 4.00 5.00 6.00 0 5000 10000 15000 20000 25000 Di Discharge vs. Water Depth Discharge vs. Velocity (Contracted Section) scharge (m3/s) V el oc ity (m /s) 0 1000 2000 3000 4000 5000 6000 7000 0 10 20 30 40 50 60 70 Ti Scour Depth vs. Time (Example 6) me (Year) Pi er S co ur D ep th (m m ) Figure 12.32. Relationship of discharge versus velocity and discharge versus water depth (Example 6). Figure 12.33. Bridge scour depth versus time (Example 6).