Nchrp_24-15 Complex Pier Scour and Contraction Scour in Cohesive Soils

National Cooperative Highway Research Program

NCHRP REPORT 24-15

COMPLEX PIER SCOUR AND CONTRACTION SCOUR

IN COHESIVE SOILS

J.-L. Briaud, H.-C. Chen, Y. Li, P. Nurtjahyo, J. Wang

January 2003

Transportation Research Board National Research Council

ACKNOWLEDGEMENTS Special thanks go to the NCHRP group associated with this project for their advice and comments throughout the study: NCHRP Technical Panel Steven P. Smith, (Chair) PBS&J Larry A. Arneson, Federal Highway Administration Daryl J. Greer, Kentucky Transportation Cabinet Robert W. Henthorne, Kansas Department of Transportation Melinda Luna, Lower Colorado River Authority William L. Moore, III, North Carolina Department of Transportation Richard A. Phillips, South Dakota Department of Transportation Mehmet T. Tumay, Louisiana State University FHWA Liaison J. Sterling Jones TRB Liaison Jay Jayaprakash NCHRP Staff Timothy G. Hess Takiyah K. Daniel Special thanks also go to our consultants: Peter Lagasse, Ayres Associates Peter Smith, Parsons Brinkerhoff Quade & Douglas, Inc. Art Parola, Jr. University of Louisville We also wish to acknowledge the help from people at Texas A&M University including John Reed, Bob Randall, Andrew Fawcett, Mike Linger, Richard Gehle, and Josh Reinbolt.

NOMENCLATURE

α Pier attack angle θ Transition angle for bridge contraction ρ Mass density of water γ Unit weight of water ε Roughness coefficient µQ Mean value of daily stream-flow σQ Standard deviation of daily stream-flow #200 Percentage of soil passing No.200 sieve a Width of the cross section of the rectangular pipe in EFA b Length of the cross section of the rectangular pipe in EFA B Pier width B’ Pier projection width B1 Channel upstream width B2 Contracted channel width C Pier center-center spacing CEC Cation exchange capacity CSS Critical shear stress of soil d Scour depth, a random variable and its statistics can be studied in detail to determine the

risk of failure associated with difference choices of the design value of the scour depth D50 Particle size f Friction factor obtained from Moody Chart Fr Froude number g Acceleration due to gravity h Length of soil sample eroded in EFA test H Average water depth upstream bridge piers H1 Average water depth in approaching flow upstream contraction H2 Average water depth in contracted channel HHec Initial average water depth in contracted channel calculated by HEC-RAS L Length of contraction channel Lpier Length of rectangular pier kw Correction factor of water depth for the initial shear stress of pier scour ksh Correction factor of pier shape effect for the initial shear stress of pier scour ksp Correction factor of pier spacing effect for the initial shear stress of pier scour kα Correction factor of pier attack angle effect for the initial shear stress of pier scour kc-R Correction factor of contraction ratio effect for the initial shear stress of contraction scourkc-L Correction factor of contraction length effect for the initial shear stress of contraction

scour kc-H Correction factor of flow water depth effect for the initial shear stress of contraction

scour kc-θ Correction factor of transition angle effect for the initial shear stress of contraction scour Kw Correction factor of water depth for pier scour depth Ksh Correction factor of pier shape effect for pier scour depth Ksp Correction factor of pier spacing effect for pier scour Kα Correction factor of pier attack angle effect for pier scour depth

KL Correction factor of contraction length effect for contraction scour depth Kθ Correction factor of transition angle effect for contraction scour depth KL/Zmax Correction factor of contraction length effect for maximum contraction scour depth KL/unif Correction factor of contraction length effect for uniform contraction scour depth KL/Xmax Correction factor of contraction length effect for location of maximum contraction scour

depth Kθ/Zmax Correction factor of transition angle effect for maximum contraction scour depth Kθ/unif Correction factor of transition angle effect for uniform contraction scour depth Kθ/Xmax Correction factor of transition angle effect for location of maximum contraction scour Lt Life of structure n Manning’s coefficient pH Log Scale Unit of Measure, and is used to express the degree of acidity of a substance. PI Plasticity index Q Daily stream-flow discharge R Level of risk associated with the choice of different design values of scour depth and

project lives Re Reynolds number = VB/v Rh Hydraulic radius S Piers center-center spacing SAR Sodium adsorption ratio Si Initial erodibility SU Undrained shear strength of soil t Time required for soil sample to be eroded in EFA test te Equilibrium time for multi-flood scour depth calculation Tr Return period in risk analysis τ Shear stress on the surface of soil sample τc Critical shear stress of soil τmax Initial shear stress which also is the maximum value during shear stress history τmax(Deep) Initial shear stress which also is the maximum value during shear stress history for pier

sour or contraction scour in deep water case τmax(Circle) Initial shear stress which also is the maximum value during shear stress history for pier

sour or contraction scour in circular pier case τmax(0 degree) Initial shear stress which also is the maximum value during shear stress history for pier

sour or contraction scour in no attack angle case τmax(Cont) Initial shear stress which also is the maximum value during shear stress history for

contraction scour τmax(Single) Initial shear stress which also is the maximum value during shear stress history for pier

sour or contraction scour in single pier case τ(z) Shear stress on the bottom of scour hole at depth z ν Kinematics viscosity of water V Approaching average velocity for pier scour V1 Approaching average velocity for contraction scour V2 Average velocity in the contracted channel Vhec Calculated velocity in the contracted channel by HEC-RAS Xa Location of maximum bed shear stress due to abutment Xc Location of maximum bed shear stress around pier or the abutment (most interested)

Xmax Location of the maximum contraction scour Z Erosion rate

iZ Initial erosion rate Zmax (Cont) Equilibrium maximum contraction scour depth Zmax (Deep) Equilibrium pier scour depth or equilibrium maximum contraction scour depth in deep

water case Zunif(Cont) Equilibrium uniform contraction scour

UNIT CONVERSIONS This report is in SI units. The following conversion table is provided for convenience. The SRICOS-EFA program allows for the use of SI or American customary units. Acceleration 9.81 m/s2=386.22 in./s2=32.185 ft/s2, Paris: g=9.80665 m/s2, London: g = 3.2174 x 101 ft/s2

Area 1 m2 = 1.5500 x 103 in2 = 1.0764 x 101 ft2 = 1.196 yd2 = 106 mm2 = 104 cm2 = 2.471 x 10-4 acres = 3.861 x 10-7 mi2 = 1.0000 x 10-4 hectares

Bending Stiffness

1 kN.m2 = 103 N.m2 =106 kN.mm2 = 2.4198 x 103 lb.ft2 =2.4198 kip.ft2 =3.4845 x 102 kip.in2 = 3.4845 x 105 lb.in2

Coefficient of consolidation

1 m2/s = 3.1557 x 107 m2/yr = 104 cm2/s =6x 105 cm2/min = 3.6 x 107 cm2 /h = 8.64 x 108 cm2/day = 2.628 x 1010 cm2/month = 3.1536 x 1011 cm2/year = 1.550 x 103 in2/s = 4.0734 x 109 in2/month = 1.3392 x 108 in2 /day = 4.8881 x 1010 in2/year = 9.3000 x 105 ft2/day = 2.8288 x 107 ft2/month = 3.3945 x 108 ft2/year

Flow 1 m3/s = 106 cm3/s = 8.64 x 104 m3 /day = 8.64 x 1010 cm3/day = 3.5314 x 101 ft3/s = 3.0511 x 106 ft3/day

Force 10 kN = 2.2481 x 103 lb = 2.2481 kip = 1.1240 t (short ton = 2000 lb) = 1.0197 x 103 kg = 1.0197 x 106 g = 1.0197 T (metric ton= 1000 kg) = 109 dynes = 3.5969 x 104 ounces = 1.022 tl (long ton = 2200 lb)

Force per unit length

1 kN/m = 6.8522 x 101 lb/ft = 6.8522 x 10-2 kip/ft = 3.4261 x 10-2 t/ft = 1.0197 x 102 kg/m = 1.0197 x 10-1 T/m

Length 1 m = 3.9370 x 101 in. = 3.2808 ft = 1.0936 yd = 1010 Angstrom = 106 microns = 103 mm = 102 cm = 10-3 km = 6.2137 x 10-4 mile = 5.3996 x 10-4 nautical mile

Moment or energy

1 kN.m = 7.3756 x l02 lb.ft = 7.3756 x 10-1 kip.ft = 3.6878 x 10-1 t.ft = 1.0197 x 103 g.cm = 1.0197 x 102 kg.m = 1.0197 x 10-1 T.m = 103 N.m = 103 Joule

Moment of inertia

1 m4 = 2.4025 x 106 in4 = 1.1586 x 102 ft4 = 1.4304 yd4 = 108 cm4 = 1012 mm4

Moment per unit length

1 kN.m/m = 2.2481 x 102 lb.ft/ft = 2.2481 x 10-1 kip.ft/ft = 1.1240 x 10-1 t.ft/ft = 1.0197 x 102 kg.m/m = 1.0197 x 10-1 T.m/m

Pressure 100 kPa = 102 kN/m2 = 1.4504 x 101 lb/in.2 = 2.0885 x 103 lb/ft2 = 1.4504 x 10-2 kip/in .2 = 2.0885 kip/ft2 = 1.0443 t/ft2 = 7.5006 x 101 cm of Hg (0 °C) = 1.0197 kg/cm 2 = 1.0197 x 101 T/m2

= 9.8692 x 10-1 Atm = 3.3489 x 101 ft of H2O (60 °F) = 1.0000 bar = 106 dynes/cm2

Temperature °C = 5/9 (°F - 32), °K =°C + 273.15

Time 1 yr. = 12 mo. = 365 day = 8760 hr = 5.256 x 105 min = 3.1536 x 107s

Unit weight, coefficient of subgrade reaction

10 kN/m3 = 6.3659 x 101 lb/ft3 = 3.6840 x 10-2 lb/in.3 = 1.0197 g/cm3 = 1.0197 T/m3 = 1.0197 x 103 kg/m3

Velocity or permeability

1 m/s = 3.6 km/h = 2.2369 mile/h = 6 x 101 m/min = 102 cm/s = 3.15 x 107 m/yr = 1.9685 x 102 ft/min = 3.2808 ft/s = 1.0346 x 108ft/year = 2.8346 x 105 ft/day

Volume 1 m3 = 6.1024 x 104 in.3 = 3.5315 x 101 ft3 = 1.3080 yd3 = 109 mm3 = 106 cm3 = 103 dm3 = 33814.02 ounces = 2113.38 pints (US) = 103 liter = 2.1997 x 102 gallon (UK) = 2.6417 x 102 gallon (US)

Volume loss in a tubing

1 cm3/m/kPa = 8.91 x 10-4 in.3/ft/psf

Reproduced from: Briaud, J.-L., 1992, “The Pressuremeter”, A.A. Balkema Publishers (email: info @ashgate.com) (web - http://balkema.ima.nl)

TABLE OF CONTENTS Page

ACKNOWLEDGEMENTS ......................................................................................................... ii

NOMENCLATURE..................................................................................................................... iii

UNIT CONVERSIONS ............................................................................................................... vi

TABLE OF CONTENTS ........................................................................................................... vii

LIST OF FIGURES ..................................................................................................................... xi

LIST OF TABLES .................................................................................................................... xvii

EXECUTIVE SUMMARY ..................................................................................................... xviii

CHAPTER 1 INTRODUCTION............................................................................................1 1.1. Bridge Scour ..................................................................................................................1 1.2. Soils Classification.........................................................................................................1 1.3. The Problem Addressed.................................................................................................1 1.4. Why Was This Problem Addressed? .............................................................................3 1.5. Approach Selected To Solve The Problem....................................................................3 1.6. Organization Of The Report ..........................................................................................3

CHAPTER 2 ERODIBILITY OF COHESIVE SOILS.......................................................5 2.1. Erodibility: A Definition................................................................................................5 2.2. Erosion Process..............................................................................................................6 2.3. Existing Knowledge On Erodibility Of Cohesive Soils ................................................6 2.4. Erodibility And Correlation To Soil And Rock Properties?..........................................7

CHAPTER 3 EROSION FUNCTION APPARATUS........................................................11 3.1. Concept ........................................................................................................................11 3.2. EFA Test Procedure.....................................................................................................12 3.3. EFA Test Data Reduction ............................................................................................13 3.4. EFA Precision And Typical Results ............................................................................15

CHAPTER 4 THE SRICOS-EFA METHOD FOR CYLINDRICAL PIERS IN DEEP WATER...............................................................................................16

4.1. SRICOS-EFA Method For Constant Velocity And Uniform Soil...............................16 4.2. Small Flood Followed By Big Flood. ..........................................................................17 4.3. Big Flood Followed By Small Flood And General Case.............................................19 4.4. Hard Soil Layer Over Soft Soil Layer. ........................................................................22 4.5. Soft Soil Layer Over Hard Soil Layer and General Case. ...........................................23 4.6. Equivalent Time...........................................................................................................24 4.7. Extended And Simple SRICOS-EFA Method.............................................................26

4.8. Case Histories ..............................................................................................................29 4.9. Predicted And Measured Local Scour For The 8 Bridges ...........................................32 4.10. Conclusions..................................................................................................................38

CHAPTER 5 THE SRICOS-EFA METHOD FOR MAXIMUM SCOUR DEPTH AT COMPLEX PIERS...................................................................40

5.1. Existing Knowledge.....................................................................................................40 5.2. General.........................................................................................................................40 5.3. Flumes And Scour Models...........................................................................................40 5.4. Measuring Equipment..................................................................................................42 5.5. Soils And Soil Bed Preparation ...................................................................................44 5.6. Flume Tests Procedure And Measurement ..................................................................48 5.7. Shallow Water Effect: Flume Tests Results ................................................................48 5.8. Shallow Water Effect On Maximum Pier Scour Depth...............................................49 5.9. Shallow Water Effect On Initial Shear Stress..............................................................52 5.10. Pier Spacing Effect: Flume Tests Results....................................................................54 5.11. Pier Spacing Effect On Maximum Scour Depth..........................................................55 5.12. Pier Spacing Effect On Initial Scour Rate ...................................................................57 5.13. Pier Shape Effect: Flume Test Results.........................................................................58 5.14. Pier Shape Effect On Maximum Scour Depth.............................................................58 5.15. Pier Shape Effect On Initial Scour Rate ......................................................................60 5.16. Pier Shape Effect On Pier Hole Shapes .......................................................................60 5.17. Attack Angle Effect: Flume Tests Results...................................................................62 5.18. Attack Angle Effect On Maximum Scour Depth.........................................................64 5.19. Attack Angle Effect On Initial Scour Rate ..................................................................66 5.20. Attack Angle Effect On Scour Hole Shape..................................................................67 5.21. Maximum Scour Depth Equation For Complex Pier Scour ........................................68

CHAPTER 6 THE SRICOS-EFA METHOD FOR INITIAL SCOUR RATE AT COMPLEX PIERS ........................................................................................71

6.1. General.........................................................................................................................71 6.2. Existing Knowledge On Numerical Simulations For Scour ........................................71 6.3. Numerical Method Used In This Study .......................................................................72 6.4. Verification Of The Numerical Method ......................................................................73 6.5. Shallow Water Effect: Numerical Simulation Results.................................................76 6.6. Shallow Water Eefect On Maximum Shear Stress ......................................................80 6.7. Pier Spacing Effect: Numerical Simulation Results ....................................................81 6.8. Pier Spacing Effect On Maximum Shear Stress ..........................................................83 6.9. Pier Shape Effect: Numerical Simulation Results .......................................................83 6.10. Pier Shape Effect on Maximum Shear Stress ..............................................................86 6.11. Attack Angle Effect: Numerical Simulation Results ...................................................86 6.12. Attack Angle Effect On Maximum Shear Stress .........................................................87 6.13. Maximum Shear Stress Equation For Complex Pier Scour.........................................89

CHAPTER 7 THE SRICOS-EFA METHOD FOR MAXIMUM CONTRACTION SCOUR DEPTH .............................................................90

7.1. Existing Knowledge.....................................................................................................90 7.2. General.........................................................................................................................90 7.3. Flume Tests And Measurements..................................................................................91 7.4. Flume Tests: Flow Observations And Results.............................................................93 7.5. Flume Tests: Scour Observations And Results............................................................95 7.6. Maximum And Uniform Contraction Depths For The Reference Cases...................100 7.7. Location Of Maximum Contraction Depth For The Reference Cases ......................103 7.8. Correction Factors For Transition Angle And Contraction Length...........................105 7.9. SRICOS-EFA method using HEC-RAS generated velocity .....................................108 7.10. Constructing The Complete Contraction Scour Profile .............................................111 7.11. Scour Depth Equations For Contraction Scour..........................................................112

CHAPTER 8 THE SRICOS-EFA METHOD FOR INITIAL SCOUR RATE AT CONTRACTED CHANNELS....................................................................114

8.1. Background................................................................................................................114 8.2. Contraction Ratio Effect: Numerical Simulation Results..........................................114 8.3. Transition Angle Effect: Numerical Simulation Results ...........................................115 8.4. Contracted Length Effect: Numerical Simulation Results.........................................117 8.5. Water Depth Effect: Numerical Simulation Results ..................................................118 8.6. Maximum Shear Stress Equation For Contraction Scour ..........................................121

CHAPTER 9 THE SRICOS-EFA METHOD FOR COMPLEX PIER SCOUR AND CONTRACTION SCOUR IN COHESIVE SOILS ........................126

9.1. Background................................................................................................................126 9.2. The Integrated SRICOS-EFA Method General Principle..........................................126 9.3. The Integrated SRICOS-EFA Method: Step Procedure ............................................127 9.4. Input For The SRICOS-EFA Program.......................................................................134 9.5. The SRICOS-EFA Program.......................................................................................137 9.6. Output Of The SRICOS-EFA Program .....................................................................137

CHAPTER 10 VERIFICATION OF THE SRICOS-EFA METHOD .............................141 10.1. Background................................................................................................................141 10.2. Mueller (1996) Data Base: Pier Scour .......................................................................141 10.3. Froehlich (1988) Database: Pier Scour ......................................................................145 10.4. Gill (1981) Database: Contraction Scour...................................................................146 10.5. Remarks .....................................................................................................................146

CHAPTER 11 FUTURE HYDROGRAPHS & SCOUR RISK ANALYSIS ...................148

11.1. Background................................................................................................................148 11.2. Preparation Of The Future Hydrographs ...................................................................149 11.3. Risk Approach To Scour Predictions.........................................................................151 11.4. Observations On Current Risk Levels .......................................................................152

CHAPTER 12 SCOUR EXAMPLE PROBLEMS .............................................................155

12.1. Example 1: Single Circular Pier With Approaching Constant Velocity....................155

12.1.1. SRICOS-EFA Method Hand-Calculation: ..................................................157 12.1.2. SRICOS-EFA Method Computer-Calculation:...........................................158

12.2. Example 2: Single Rectangular Pier With Attack Angle And Approaching Hydrograph ................................................................................................................160 12.2.1. SRICOS-EFA Method Computer-Calculation:...........................................162

12.3. Exmple 3: Group Rectangular Piers With Attack Angle And Approaching Constant Velocity.......................................................................................................166 12.3.1. SRICOS-EFA Method Hand-Calculation: ..................................................168 12.3.2. SRICOS-EFA method computer-calculation: .............................................170

12.4. example 4: contracted channel with 90° transition angle and approaching constant velocity ........................................................................................................172 12.4.1. SRICOS-EFA method hand-calculation: ....................................................174 12.4.2. SRICOS-EFA Method Computer-Calculation:...........................................175

12.5. Example 5: Contracted Channel With 60� Transition Angle And Approaching Hydrograph ..........................................................................................177 12.5.1. SRICOS-EFA Method Computer-Calculation:...........................................179

12.6. Example 6: Bridge With Group Piers And Contracted Channel With Hydrograph In Contracted Section ............................................................................184 12.6.1. SRICOS-EFA Method Computer-Calculation:...........................................187

CHAPTER 13 CONCLUSIONS AND RECOMMENDATIONS.....................................191 13.1 CONCLUSIONS........................................................................................................191

13.1.1. General ........................................................................................................191 13.1.2. Erodibility Of Cohesive Soils......................................................................191 13.1.3. Erosion Function Apparatus (Efa)...............................................................191 13.1.4. SRICOS-EFA Method For Cylindrical Piers In Deep Water......................192 13.1.5. SRICOS-EFA Method For Maximum Scour Depth At Complex Piers......192 13.1.6. SRICOS-EFA Method For Initial Scour Rate At Complex Piers ...............192 13.1.7. SRICOS-EFA Method For Maximum Contraction Scour Depth................193 13.1.8. SRICOS-EFA Method For Initial Contraction Scour Rate .........................193 13.1.9. SRICOS-EFA Method For Complex Piers Scour And Contraction

Scour In Cohesive Soils...............................................................................194 13.1.10. Verification Of The SRICOS-EFA Method ................................................194 13.1.11. Future Hydrographs And Scour Risk Analysis ...........................................195 13.1.12. Example Problems.......................................................................................195

13.2. RECOMMENDATIONS...........................................................................................195

REFERENCES ........................................................................................................................196

APPENDIX A PHOTOGRAPHS FROM THE FLUME TESTS.....................................201

APPENDIX B FLUME TESTS DATA ...............................................................................219

APPENDIX C DATABASES OF CASE HISTORIES ......................................................236

APPENDIX D SRICOS PROGRAM: USER’S MANUAL...............................................254

LIST OF FIGURES Page Figure 1.1 Typical bridge with Potential Contraction and Pier Scour ......................................2 Figure 2.1 Erodibility Function for a clay and for a sand .........................................................5 Figure 2.2 Critical Shear Stress Versus Mean Soil Grain Diameter .........................................8 Figure 2.3 Erosion properties as a function of water content....................................................9 Figure 2.4 Erosion properties as a function of undrained shear strength ..................................9 Figure 2.5 Erosion properties as a function of plasticity index...............................................10 Figure 2.6 Erosion properties as a function of percent passing sieve #200 ............................10 Figure 3.1 Schematic Diagram and Result of the EFA (Erosion Function Apparatus) ..........11 Figure 3.2 Photographs of the Erosion Function Apparatus (a) General View (b)

Close-up of the Test Section ..................................................................................12 Figure 3.3 Moody Chart (reprinted with permission from Munson et al. 1990).....................14 Figure 3.4 Erosion Function for a soil sample taken near Pier 27E of the Existing

Woodrow Wilson Bridge (2.6 - 3.2 meters depth) : a) Scour Rate vs. Shear Stress, b) Scour Rate vs. Velocity..........................................................................14

Figure 4.1 Example of the SRICOS method for comstant velocity and uniform soil.............18 Figure 4.2 Scour due to a sequence of two flood events (small flood followed by big

flood)......................................................................................................................18 Figure 4.3 Multiflood flume experiment results. a) floods and flood sequence in the

experiments, b) experiment result for flood 1 alone, c) experiment result for flood 2 alone, d) experiment result for the flood 1 and 2 sequence shown in a) and prediction for flood 2...................................................................20

Figure 4.4 Scour due to a sequence of two flood events (big flood followed by small flood)......................................................................................................................21

Figure 4.5 Scour of a two-layer soil (hard layer over soft layer). ...........................................22 Figure 4.6 Scour of a two layer soil (soft layer over hard layer). ...........................................23 Figure 4.7 Velocity hydrographs: a) constant, b) true hydrograph. Both hydrographs

would lead to the same scour depth. ......................................................................25 Figure 4.8 Comparison of scour depth using Extended SRICOS and Simple SRICOS

Methods..................................................................................................................25 Figure 4.9 Examples of Discharged Hydrographs: a) Brazos River at US90A, b) San

Marcos River at SH80, c) Sims Bayou at SH35. ...................................................27 Figure 4.10 Velocity hydrograph and scour depth vs. time curve for Bent 3 of the

Brazos River Bridge at US90A..............................................................................27 Figure 4.11 Velocity hydrograph and scour depth vs. time curve for Bent 3 of the San

Marcos River Bridge at SH80................................................................................28 Figure 4.12 Velocity hydrograph and scour depth vs. time curve for Bent 3 of the Sims

Bayou River Bridge at SH35 .................................................................................28 Figure 4.13 Example of scour calculations by the S-SRICOS method.....................................30 Figure 4.14 Location of Case History Bridges..........................................................................30 Figure 4.15 Erosion Function for San Jacinto River Sample (7.6 m to 8.4 m depth) ...............34 Figure 4.16 Erosion Function for Bedias Creek Sample (6.1 m to 6.9 m depth)......................34 Figure 4.17 Profiles of Navasota River Bridge at SH 7 ............................................................36 Figure 4.18 Profiles of Brazos River Bridge at US 90A...........................................................36

Figure 4.19 Predicted vs Measured Local Scour for the E-SRICOS method ...........................37 Figure 4.20 Predicted vs Measured Local Scour for the S-SRICOS method............................37 Figure 4.21 Velocity Hydrograph and Predicted Scour Depth vs. Time Curve for Pier

1E of the Existing Woodrow Wilson Bridge on the Potomac River in Washington DC......................................................................................................39

Figure 5.1 Parameter Definition for Complex Pier Scour.......................................................41 Figure 5.2 Diagram of the Flume System (not to Scale).........................................................41 Figure 5.3 Pier Models Used in the Complex Pier Scour Tests ..............................................42 Figure 5.4 Abutment Models for Contraction Scour Tests .....................................................43 Figure 5.5 Diagram of the ADV..............................................................................................43 Figure 5.6 Erosion function for the Porcelain clay .................................................................45 Figure 5.7 Erosion function for Gudavalli’s Porcelain clay....................................................46 Figure 5.8 Placement of the clay in the soil tank ....................................................................47 Figure 5.9 Flume tests results for the shallow water cases .....................................................50 Figure 5.10 Influence of shallow water depth on maximum pier scour depth..........................51 Figure 5.11 Correction Factor for Shallow Water Effect on Maximum Pier Scour

Depth......................................................................................................................51 Figure 5.12 Initial scour rate as a function of water depth........................................................53 Figure 5.13 Comparison between scour in shallow and deep waters........................................53 Figure 5.14 Scour Depth versus Time for the Pier Spacing Cases............................................55 Figure 5.15 Correction Factor for Pier Spacing Effect .............................................................56 Figure 5.16 Initial Scour Rate for the Group Pier Tests............................................................57 Figure 5.17 Scour Curves for Groups of Piers in a Line...........................................................57 Figure 5.18- Scour Depth versus Time Curves for Pier Shape Effect Tests..................................59 Figure 5.19 Correction Factor for Pier Shape Effect.................................................................59 Figure 5.20 Initial Scour rates for the Shape Effect Flume Tests .............................................60 Figure 5.21 Shape of the Scour Hole for Different Aspect ratios. ............................................61 Figure 5.22 Scour Curves for Pier of Different Shapes. ...........................................................61 Figure 5.23 Scour Depth versus Time Curves for Attack Angle Tests.....................................63 Figure 5.24 Skewed Pier Definitions ........................................................................................65 Figure 5.25 Attack Angle Effect on Maximum Scour Depth....................................................65 Figure 5.26 initial Scour Rate for the Attack Angle Flume Tests. ............................................66 Figure 5.27 Shape of Scour around a Skewed Pier in a Cohesive Soil (Left: Attack

angle =15°, Right: Attack Angle=30°) ..................................................................67 Figure 5.28 Configuration of the Flume Tests to Verify the Superposition Rule. ....................68 Figure 5.29 Scour Development Curves for the Complex Pier Flume Tests. ...........................69 Figure 6.1 Comparison of bed shear stress distribution around a circular pier between

an experiment by Hjorth (1975) and numerical computations (B=0.075 m, V=0.15 m/s, H=0.1 m) ...........................................................................................74

Figure 6.2 Comparison of bed shear stress distribution around a circular pier between an experiment by Hjorth (1975) and numerical computations (B=0.075 m, V=0.30 m/s, H=0.2 m) ...........................................................................................75

Figure 6.3 Problem definition for water depth effect ..............................................................76 Figure 6.4. Grid System for the Numerical Simulation ...........................................................76 Figure 6.5. Velocity Profile Comparison between Experiment and Numerical

Simulation at the Inlet............................................................................................77

Figure 6.6 Velocity vector around pier for (a) H/B=0.2 and (b) H/B=2 .................................78 Figure 6.7 Initial Bed Shear Stress Distribution (N/m2) around the Pier (H/B=0.2,

V=0.3m/s) ..............................................................................................................79 Figure 6.8 Initial Bed Shear Stress Distribution (N/m2) around the Pier (H/B=2,

V=0.3m/s) ..............................................................................................................79 Figure 6.9. Normalized Pressure (p/ρu2) Contours for H/B=2 on the Riverbed...........................80 Figure 6.10 Relationship between kw ( = τmax/τmax(deep)) and H/B ....................................81 Figure 6.11 Problem Definition of Pier Spacing Effect. ...........................................................81 Figure 6.12 Initial Bed Shear Stress Distribution (N/m2) around the Pier (S/B=1.88,

H=0.38m, V=0.33m/s) ...........................................................................................82 Figure 6.13 Initial Bed Shear Stress Distribution (N/m2) around the Pier (S/B=6,

H=0.38m, V=0.33m/s) ...........................................................................................82 Figure 6.14 Relationship between ksp ( = τmax/τmax(single)) and S/B for deep water

H/B>2) ..................................................................................................................83 Figure 6.15 Problem Definition for the Shape Effect ...............................................................84 Figure 6.16 Velocity Field Around a a Rectangular Pier with L/B = 0.25 ...............................84 Figure 6.17 Velocity Field Around a a Rectangular Pier with L/B = 4 ....................................84 Figure 6.18 Bed shear stress contours (N/m2) around a rectangular pier (L/B=0.25) ..............85 Figure 6.19 Bed shear stress contours (N/m2) around a rectangular pier (L/B=1) ...................85 Figure 6.20 Bed shear stress contours (N/m2) around a rectangular pier (L/B=4) ...................85 Figure 6.21 Relationship between ksh ( = τmax/τmax(circle)) and L/B for deep water

(H/B>2) ..................................................................................................................86 Figure 6.22 Definition of the Angle of Attack Problem............................................................87 Figure 6.26 Relationship between ka ( = τmax/τmax(0 degree)) and α for deep water

(H/B>2) ..................................................................................................................87 Figure 6.23 Bed Shear Stress Contours for an Attack Angle Equal to 15 degree.....................88 Figure 6.24 Bed Shear Stress Contours for Attack Angle Equal to 30 degree..........................88 Figure 6.25 Bed Shear Stress Contours for an Attack Angle Equal to 45 degree.....................88 Figure 7.1 Concepts and Definitions in Contraction Scour.....................................................91 Figure 7.2 Water Surface Elevations along the Channel Centerline in Test 2........................94 Figure 7.3 Velocity Distribution along the Channel Centerline in Test 2...............................94 Figure 7.4 Contraction Scour Profiles along the Channel Centerline as a function of

Time for Test 1 (the numbers in the legend are the elapsed times in hours). ........96 Figure 7.5 Plan view sketch of the contraction scour pattern. ................................................96 Figure 7.6 Maximum Contraction Scour and Hyperbola Model for Test 1 ............................97 Figure 7.7 Uniform Contraction Scour and Hyperbola Model for Test 1...............................97 Figure 7.8 Contraction Scour Profile along the Channel Centerline for Transition

Angle Effect ...........................................................................................................98 Figure 7.9 Contraction Scour Profile along the Channel Centerline for Contraction

Length Effects........................................................................................................98 Figure 7.10 Contraction Scour Profiles along the Channel Centerline for Standard

Tests .......................................................................................................................99 Figure 7.11 Overlapping of Scour for Contraction Scour and Abutment Scour.......................99 Figure 7.12 Correlation Attempt between Contraction Scour Depth and Reynolds

Number ................................................................................................................100 Figure 7.13 Normalized Maximum Contraction Scour Depth versus Froude number ...........101

Figure 7.14 Normalized Uniform Contraction Scour Depth versus Froude number ..............101 Figure 7.15 The Factor β as a Function of the Contraction Ratio. ..........................................103 Figure 7.16 Influence of the Contraction Ratio on the Longitudinal Scour Profile................104 Figure 7.17 Relationship Between Xmax and the Contraction Geometry ................................104 Figure 7.18 Flow around Contraction Inlets ...........................................................................106 Figure 7.19 Transition Angle Effect on Maximum Contraction Scour Depth........................106 Figure 7.20 Transition Angle Effect on Scour Profile and Uniform Contraction Scour.........107 Figure 7.21 Transition Angle Effect on the Location of the Maximum Scour Depth ............107 Figure 7.22 Relationship Between the Nominal Velocity and the HEC-RAS Calculated

Velocity................................................................................................................109 Figure 7.23 Comparison of Water Depth and Velocity between HEC-RAS Simulations

and Measurements for Contraction Test 2. ..........................................................110 Figure 7.24 Generating the Complete Contraction Scour Profile. ..........................................111 Figure 8.1 Grid System for the Simulation in the Case of B2/B1 = 0.25...............................115 Figure 8.2 Initial Bed Shear Stress Distribution (N/m2) for B2/B1=0.25, and

V=0.45m/s............................................................................................................116 Figure 8.3 Initial Bed Shear Stress Distribution (N/m2) for B1/B2=0.50, and

V=0.45m/s............................................................................................................116 Figure 8.4 Initial Bed Shear Stress Distribution (N/m2) for B2/B1=0.75, and

V=0.45m/s............................................................................................................117 Figure 8.5 Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s,

L/(B1-B2)=6.76, and θ =15 degree)......................................................................118 Figure 8.6 Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s,



and L/(B1-B2)=0.25).............................................................................................119 Figure 8.9 Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s,

and L/(B1-B2)=0. 5)..............................................................................................120 Figure 8.10 Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s,

and L/(B1-B2)=1.0)...............................................................................................120 Figure 8.11 Definition of Parameters for Contraction Scour ..................................................121

Figure 8.12 Relationship between Rck − and 2

1

BB

......................................................................122

Figure 8.13 Relationship between θ−ck and 90θ

.....................................................................122

Figure 8.14 Relationship between Lck − and 21 BBL− ............................................................123

Figure 8.15 Distance from the beginning of the fully contracted section to the location of the maximum shear stress along the centerline of the channel, X, as a function of the normalized transition angle, 90θ . .............................................124

Figure 8.16 Distance from the beginning of the fully contracted section to the location of the maximum shear stress along the centerline of the channel, X, as a function of the Contraction Ratio B2/B1. .............................................................125

Figure 9.1 Step I Bridge scour input data and primary calculation......................................127 Figure 9.2 Step II Contraction Scour Calculation and Distribution.....................................128 Figure 9 3 Step III and IV Calculations of Pier Scour and Superposition ............................129 Figure 9.4 Plan View of Complex Pier Scour and Contraction Scour ..................................130 Figure 9.5 Scour Due to a Sequence of Two Flood Events ..................................................133 Figure 9.6 Scour of a Two-Layer Soil System......................................................................133 Figure 9.7 Typical EFA Test Result......................................................................................134 Figure 9.8 Example of Hydrograph transformation for the Pier 1E of the Woodrow

Wilson Bridge on the Potomac River in Washington, D,C. ................................136 Figure 9.9 Flow Chart of the SRICOS-EFA Program ..........................................................138 Figure 9.10 Example of plots generated from a SRICOS-EFA Program Output ...................139 Figure 10.1 SRICOS-EFA Predictions against Mueller (1996) Database ..............................142 Figure 10.2 HEC-18 Predictions against Mueller (1996) Database........................................142 Figure 10.3 SRICOS-EFA Predictions vs. Mueller Database for Various Ranges of D50......143 Figure 10.4 HEC-18 Predictions vs. Mueller Database for Various Ranges of D50 ...............144 Figure 10.5 SRICOS-EFA Predictions against Froehlich (1988) Database............................145 Figure 10.6 HEC-18 Predictions against Froehlich (1988) Database .....................................145 Figure 10.7 SRICOS-EFA Method against Gill (1981) Database ..........................................147 Figure 10.8 HEC-18 Method against Gill (1981) Database....................................................147 Figure 11.1 Woodrow Wilson Measured Hydrograph spiked with a 500-year Flood............148 Figure 11.2 Original Hydrograph & Scour Depth vs. Time near Woodrow Wilson

Bridge Site ...........................................................................................................150 Figure 11.3 Predicted Hydrograph and Scour Depth vs. Time Curve near Woodrow

Wilson Bridge Site (Project time = 75year).........................................................151 Figure 11.4 Probability distribution of scour depth, d, for different lengths of the

project life, Lt .......................................................................................................153 Figure 11.5 Risk associated with different design values of the final scour depth, d,

and different lengths of the project life, Lt...........................................................153 Figure 11.6 Flood-frequency curve for the Potomac River at the Woodrow Wilson

Bridge...................................................................................................................154 Figure 12.1 EFA Results for Soil Layer 1 (Example 1)..........................................................155 Figure 12.2 EFA Results for Soil Layer 2 (Example 1)..........................................................156 Figure 12.3 Plan View of Single Circular Pier Scour Case (Example 1)................................156 Figure 12.4 Scour Depth vs. Time (Example 1)......................................................................159 Figure 12.5 70 Years Future Approaching Hydrograph (Example 2).....................................160 Figure 12.6 EFA Results for Soil Layer 1 (Example 2)..........................................................160 Figure 12.7 EFA Results for Soil Layer 2 (Example 2)..........................................................161 Figure 12.8 Plan View of Single Rectangular Pier Scour Case (Example 2) .........................161 Figure 12.9 Relationship of Discharge vs. Velocity and Discharge vs. Water Depth

(Example 2)..........................................................................................................162 Figure 12.10 Scour Depth Vs Time (Example 2)......................................................................165 Figure 12.11 EFA Results for Soil Layer 1 (Example 3)..........................................................166 Figure 12.12 EFA Results for Soil Layer 2 (Example 3)..........................................................167

Figure 12.13 Plan View of Rectangular Piers Group Scour Case (Example 3)........................167 Figure 12.14 Scour Depth Vs Time (Example 3)......................................................................171 Figure 12.15 EFA Results for Soil Layer 1 (Example 4)..........................................................172 Figure 12.16 EFA Results for Soil Layer 2 (Example 4)..........................................................173 Figure 12.17 Plan View of Contracted Channel Scour Case (Example 4)................................173 Figure 12.18 Maximum Contraction Scour Depth Vs Time (Example 4) ................................176 Figure 12.19 Uniform Contraction Scour Depth Vs Time (Example 4) ...................................176 Figure 12.20 70 Years Future Approaching Hydrograph (Example 5).....................................177 Figure 12.21 EFA Results for Soil Layer 1 (Example 5)..........................................................178 Figure 12.22 EFA Results for Soil Layer 2 (Example 5)..........................................................178 Figure 12.23 Plan View of Contracted Channel Scour Case (Example 5)................................179 Figure 12.24 Relationship of Discharge vs. Velocity and Discharge vs. Water Depth

(Example 5)..........................................................................................................180 Figure 12.25 Maximum Contraction Scour Depth Vs Time (Example 5) ................................183 Figure 12.26 Uniform Contraction Scour Depth Vs Time (Example 5) ...................................183 Figure 12.27 70 Years Future Hydrograph (Example 6)...........................................................184 Figure 12.28 EFA Results for Soil Layer 1 (Example 6)..........................................................185 Figure 12.29 EFA Results for Soil Layer 2 (Example 6)..........................................................185 Figure 12.30 Cross Section View of Approaching Channel (Example 6) ................................186 Figure 12.31 Cross Section View of Bridge (Example 6).........................................................186 Figure 12.32 Relationship of Discharge vs. Velocity and Discharge vs. Water Depth

(Example 6)..........................................................................................................187 Figure 12.33 Bridge Scour Depth Vs Time (Example 6)..........................................................190

LIST OF TABLES Page Table 2.1 Factors influencing the erodibility of cohesive soils ...............................................6 Table 2.2 Database of EFA tests..............................................................................................8 Table 4.1 Properties of the Porcelain Clay for the Flume Experiment. .................................20 Table 4.2 Full Scale Bridges as Case Histories .....................................................................33 Table 4.3 Soil Properties at the Bridge Sites .........................................................................33 Table 5.1 Geotechnical Properties of the Porcelain Clay. .....................................................45 Table 5.2 Properties of the soils used in Gudavalli’s research (Gudavalli, 1997).................46 Table 5.3 Parameters and results for shallow water cases of pier scour................................49 Table 5.4 Parameters and Results for Pier Spacing Flume Tests...........................................54 Table 5.5 Parameters and Results for Pier Shape Effect Flume Tests...................................58 Table 5.6 Parameters and Results for the Attack Angle Effect .............................................62 Table 5.7 Calculations for Isolating the Attack Angle Effect in Pier Scour Depth ...............66 Table 5.8 Transition of the Location of Maximum Scour Depth...........................................67 Table 5.9 Parameters and Results for the Complex Pier Flume Tests...................................68 Table 5.10 Comparison between Calculated and Measured Maximum Pier Scour

Depths ....................................................................................................................70 Table 7.1 Parameters and Results for the Primary Contraction Scour Tests .........................92 Table 7.2 Parameters and Results for the Secondary Contraction Scour Tests .....................92 Table 9.1 Summary of Geometry Factors............................................................................135 Table 9.2 Example of SRICOS-EFA Program Output File .................................................140 Table 11.1 Risk of failure associated with different design values of scour depth and

project lives..........................................................................................................154 Table 12.1 Summary of Data Input (Example 1)...................................................................158 Table 12.2 Summary of Data Input (Example 2)........................................................... 163-164 Table 12.3 Summary of Data Input (Example 3)...................................................................170 Table 12.4 Summary of Data Input (Example 4)...................................................................175 Table 12.5 Summary of Data Input (Example 5)........................................................... 181-182 Table 12.6 Summary of Data Input (Example 6)........................................................... 188-189

EXECUTIVE SUMMARY 1. SCOUR TYPES Bridge scour is the loss of soil by erosion due to flowing water around bridge supports. Bridge scour includes general scour and local scour. General scour is the aggradation or degradation of the riverbed not related to the presence of local obstacles. Aggradation is the gradual and general accumulation of sediments on the river bottom. Degradation is the gradual and general removal of sediments from the riverbed. Local scour is the scour around obstacles to the water flow; it includes pier scour, abutment scour, and contraction scour. Pier scour is the removal of the soil around the foundation of the pier; abutment scour is the removal of the soil around the abutment at the junction between the bridge and the embankment; contraction scour is the removal of the soil from the bottom of the river due to narrowing of the river channel created by the approach embankments for the bridge. 2. SOILS: A DEFINITION Soils can be defined as loosely bound to unbound naturally occurring materials which cover the top few hundred meters of the Earth. By opposition, rock is a strongly bound naturally occurring material found within similar depths or deeper. At the boundary between soils and rocks are intermediate geomaterials. For soils, the classification tests consist of grain size analysis and Atterberg limits. The D50 grain size is the grain size corresponding to 50% of the soil weight passing a sieve of opening equal to D50. The first major division in soils classification is between large-grained soils and fine-grained soils; large-grained soils have D50 larger than 0.075mm while fine-grained soils have D50 smaller than 0.075mm. Large-grained soils include gravels and sands which are identified on the basis of their grain size. Fine grained soils include silts and clays which are identified on the basis of Atterberg Limits. Gravels and sands are typically referred to as cohesionless soils while silts and clays are typically referred to as cohesive soils. 3. THE PROBLEM ADDRESSED This project deals with pier scour and contraction scour in cohesive soils. A previous project performed by the same team of researchers was started in 1990 and was sponsored by the Texas Department of Transportation. It dealt with pier scour in cohesive soils. In the TxDOT project, the piers were cylindrical and the water depth was more than two times the pier diameter (deep water case). In the TxDOT project also, a new apparatus called the EFA (Erosion Function Apparatus) was conceived, built, patented, and commercialized to measure the erodibility of soils. The EFA test gives the erosion function for a soil and became an integral part of the SRICOS method (Scour Rate In COhesive Soils). The SRICOS-EFA method developed at the end of the TxDOT project predicted the scour depth as a function of time when a cylindrical pier founded in a layered soil was subjected to a long-term deep water flow-velocity hydrograph. In this NCHRP project, the SRICOS-EFA method was extended to the case of complex piers and contraction scour. Complex piers refer to piers with various shapes, various flow

attack angles, various spacing between piers, and any water depth. Contraction refers to a narrowing of the flow channel by an embankment with a given encroachment length, a given embankment width, and a given transition angle. 4. WHY WAS THIS PROBLEM ADDRESSED? The reason for solving this problem is that a solution did not exist, that in the absence of a solution the calculations were based on the solution developed for cohesionless soils, and that there was a sense that such an approach was sometimes very conservative and therefore costly. Indeed, overly conservative scour depths lead to foundations which were considered to be deeper than necessary. The major difference between cohesionless soils and cohesive soils is the following. Floods create peak velocities that last a few days. A few days is a length of time which is usually sufficient to generate the maximum scour depth in cohesionless soils. This means that only the peak velocity needs to be used in the calculations of scour depth for cohesionless soils and that such a scour depth is the maximum scour depth for that velocity. The velocities used are typically the 100 year flood velocity and the 500 year flood velocity. In cohesive soils, scour and erosion rates can be 1000 times slower than in cohesionless soils and a few days may generate only a small fraction of the maximum scour depth. Therefore, for cohesive soils, it becomes necessary to consider the rate of erosion and to accumulate the effect of multiple floods. This complicates the problem significantly but this necessary complication is the price one has to pay to get closer to reality. 5. APPROACH SELECTED TO SOLVE THE PROBLEM The approach selected to solve the problem of predicting the scour depth vs. time for complex piers in a contracted channel and for a given velocity hydrograph was based on a combination of review of existing knowledge, flume tests, numerical simulations, fundamental principles in method development, and verification of the method against available data. The review of the existing knowledge avoided duplication of effort and helped in establishing a solid foundation. The flume tests gave the equations for the maximum scour depth and the influence of various factors. The flume tests also gave a calibration basis for the numerical simulations. These numerical simulations were used to generate the equations for the maximum initial shear stress at the initiation of scour. The method was assembled by linking the calculated initial erosion rate (given by the numerical simulation results and the results of the EFA test) to the calculated maximum scour depth (given by the flume tests results) by a hyperbolic model. The multiflood hydrograph and multilayer soil was included through simple accumulation algorithms. Verification was based on comparison to existing databases as well as performing calculations for example cases and evaluating the reasonableness of the results based on experience. 6. ERODIBILITY OF COHESIVE SOILS It is emphasized that erodibility is not an index but a relationship or function between on one hand the water velocity or, better, the shear stress at the water-soil interface and on

the other hand the erosion rate of the soil. Erodibility is represented by this erosion function. Two important parameters help describe the erosion function: the critical shear stress and the initial slope of the erosion function. It is found that, while the critical shear stress of a cohesive soil is not related to its mean grain size, the common range of critical shear stress values for cohesive soils (0.5 N/m2 to 5 N/m2) is comparable to the range obtained in sands. This explains why the maximum scour depth in cohesive soils is comparable to the one obtained in sands. The initial slope of the erosion function can be many times less than the one in sand (e.g.: 1000 times less) and therefore the scour depth can develop very slowly in some cohesive soils. There lies the advantage of developing a method which can predict scour depth as a function of time for a given hydrograph (cohesive soil) rather than a maximum depth of scour for a design flood (sands). This was the goal of this project. It was also found that the critical shear stress and the initial slope were not related to soil properties because the R2 of the regressions were all very low. It is recommended to obtain the erosion function by using the Erosion Function Apparatus. 7. EROSION FUNCTION APPARATUS (EFA) This EFA (http://www.humboldtmfg.com/pdf2/hm4000ds.pdf) was developed in the early nineties to obtain the erosion function. A soil sample is retrieved from the bridge site using an ASTM standard thin wall steel tube (Shelby tube), placing it through a tight fitting opening in the bottom of a rectangular cross section conduit, pushing a small protrusion of soil in the conduit, flowing water over the top of the sample at a chosen velocity, and recording the corresponding erosion rate. This is repeated for several velocities and the erosion function is obtained in that fashion. 8. SRICOS-EFA METHOD FOR CYLINDRICAL PIERS IN DEEP WATER SRICOS stands for Scour Rate In Cohesive Soils. Since the method makes use of the erosion function measured in the EFA, the method is referred to as the SRICOS-EFA method. For a given velocity hydrograph at a bridge, for a given soil exhibiting a multilayered stratigraphy with an erosion function defined for each layer, and for a given cylindrical pier in deep water (water depth larger than 1.6 times the pier diameter), the SRICOS-EFA method (program) gives the scour depth as a function of time for the period covered by the hydrograph. The method is based on the calculation of two basic parameters: the maximum depth of pier scour and the initial rate of scour. The maximum depth of scour is based on an equation obtained from flume tests and the initial rate is based on an equation giving the initial shear stress obtained from numerical simulations. The initial rate of scour is read on the EFA erosion function at the corresponding value of the calculated initial shear stress. A hyperbola is used to connect the initial scour rate to the maximum or asymptotic scour depth and describes the complete scour depth vs. time curve. Robust algorithms are used to incorporate the effect of varying velocities and multilayered soil systems. This earlier method was developed by the authors under TxDOT sponsorship and was verified by satisfactory comparison between predicted scour and measured scour at 8 bridges in Texas.

9. SRICOS-EFA METHOD FOR MAXIMUM SCOUR DEPTH AT COMPLEX PIERS A set of flume experiments were conducted to study the maximum depth of scour for a pier including the effect of shallow water depth, the effect of rectangular shapes, the effect of the angle of attack on rectangular shapes, and the effect of spacing between piers positioned in a row perpendicular to the flow. The proposed equation for the maximum depth of scour is in the form of the equation for the cylindrical pier in deep water with correction factors based on the results of the flume tests.

( ) ( )0.635max 0.18w sp sh eZ Pier in mm K K K R=

where Zmax(Pier) is the maximum depth of pier scour in millimeters, Re is the Reynolds number equal to VB’/ν, V being the mean depth velocity at the location of the pier if the bridge was not there, ν the water viscosity, the K factors take the shallow water depth, the spacing, and the shape into account, the angle of attack being considered through the use of the projected width B’ in the calculation of the Reynolds number. 10. SRICOS-EFA METHOD FOR INITIAL SCOUR RATE AT COMPLEX PIERS A set of numerical simulations were performed to study the maximum shear stress around a pier including the effect of shallow water depth, the effect of rectangular shapes, the effect of the angle of attack on rectangular shapes, and the effect of spacing between piers positioned in a row perpendicular to the flow. The proposed equation for the maximum shear stress is in the form of the equation for the cylindrical pier in deep water with correction factors based on the results of the numerical simulations.

2max

1 1( ) 0.094log 10w sh sp

e

Pier k k k k VRατ ρ

= −

where τmax(Pier) is the maximum shear stress around the pier, Re is the Reynolds number equal to VB/ν, V being the mean depth velocity at the location of the pier if the bridge was not there, ν the water viscosity, B is the pier diameter or pier width, the k factors take shallow water depth, pier shape, pier spacing, and attack angle into account. 11. SRICOS-EFA METHOD FOR MAXIMUM CONTRACTION SCOUR DEPTH A set of flume experiments were conducted to study the depth of scour associated with the contraction of a channel including the effects of the ratio of the contracted channel width over the approach channel width, the contracted channel length, and the transition angle. The proposed equation for the maximum depth of contraction scour is

0.5

max 1 1/311

1.49( ) 1.90 0

c

hecL

VZ Cont K K HgnHgHθ

τρ

= × − ≥

where Zmax(Cont) is the maximum depth of contraction scour, H1 the water depth along the center line of the uncontracted channel after scour has occurred, Vhec the mean depth water velocity at the location of the pier in the contracted channel, τc the critical shear stress of the soil, ρ the mass density of water, g the acceleration due to gravity, n the Manning’s coefficient, and the K factors take the transition and the contracted channel length into account. Note that the parenthesis in the equation is a factored difference between the Froude number and the critical Froude number. Equations are also proposed for the uniform contraction scour depth as well as the location of the scour depths. 12. SRICOS-EFA METHOD FOR INITIAL CONTRACTION SCOUR RATE A set of numerical simulations were performed to study the maximum shear stress around the contraction of a channel including the effects of the ratio of the contracted channel width over the approach channel width, the transition angle, the water depth, and the contracted channel length. The proposed equation for the maximum shear stress is in the form of the equation for the shear stress at the bottom of an open and uncontracted channel with correction factors based on the results of the numerical simulations.

12 2 3

max ( ) c R c c H c L hCont k k k k n V Rθτ γ−

− − − −

=

where τmax(Cont) is the maximum shear stress along the centerline of the contracted channel, γ is the unit weight of water, n the Manning’s coefficient, V the upstream mean depth velocity, Rh the hydraulic radius defined as the cross section area of the flow divided by the wetted perimeter, and the k factors take the contraction ratio, the transition angle, the water depth effect, and the contracted length into account. Equations are also proposed for the location of the maximum shear stress. 13. SRICOS-EFA METHOD FOR COMPLEX PIERS SCOUR AND CONTRACTION SCOUR IN COHESIVE SOILS Once the equations were established, the SRICOS-EFA method was assembled. Care was taken not to simply add complex pier scour and contraction scour to get total pier scour. Instead, advantage was taken of the fact that at the end of the maximum contraction scour, the velocity is at the critical velocity and the maximum pier scour should be calculated using the critical velocity of the soil and not the initial velocity in the contracted channel. In addition, the rules of accumulation due to the hydrograph, and due to the multilayer system developed for the simple pier scour method were adapted for the complex pier and contraction scour method. The superposition and accumulation reasoning lead to the following steps for the SRICOS-EFA method for predicting the scour depth at a complex pier in a contracted channel. This step by step procedure has been automated in a computer program.

1. Collect the input data: velocity and water depth hydrograph, geometry of the pier and of the contracted channel, erosion functions of the soil layers.

2. Calculate the maximum contraction scour depth for the ith velocity in the hydrograph.

3. Calculate the maximum complex pier scour depth using the ith velocity in the hydrograph at the pier location if there is no contraction scour in step 2, or the critical velocity for the soil if there is contraction scour in step 2.

4. Calculate the total pier scour depth as the total of step 2 and step 3. 5. Calculate the initial maximum shear stress for pier scour using the ith velocity in

the hydrograph. 6. Read the initial scour rate corresponding to the initial maximum shear stress of

step 5 on the erosion function of the soil layer corresponding to the current scour depth.

7. Use the results of steps 4 and 6 to construct the hyperbola describing the scour depth vs time curve for the pier.

8. Calculate the equivalent time for the given curve of step 7. The equivalent time is the time required for the ith velocity on the hydrograph to scour the soil to a depth equal to the depth scoured by all the velocities occurring prior to the ith velocity.

9. Read the additional scour generated by the ith velocity starting at the equivalent time and ending at the equivalent time plus the time increment.

10. Repeat steps 2 to 9 for the (i+1)th velocity and so on until the entire hydrograph is consumed.

14. VERIFICATION OF THE SRICOS-EFA METHOD Several full case histories were identified for verification but none could satisfy the requirements necessary to verify the method developed. Some did not have enough details on the observed scour depth, some turned out not to be made of cohesive soil after drilling, some did not have a gauge station nearby. It was decided to compare the maximum scour depth for pier and contraction to existing databases. These databases were mostly in sand however and included those collected by Mueller (pier scour), Froelich (pier scour) and Gill (contraction scour). The comparisons between the predicted and measured scour depths are very satisfactory, although it is not clear whether they should be since the soils were not primarily cohesive. Nevertheless, these comparisons give an indication that the SRICOS-EFA method may not be limited to cohesive soils. Indeed, the fact that the method is based on site specific testing of the erosion function permits incorporating the soil behavior directly into the predictions. 15. FUTURE HYDROGRAPHS AND SCOUR RISK ANALYSIS A novel technique is presented on generating future hydrographs. Indeed, since the SRICOS-EFA method predicts the scour depth as a function of time, it is necessary to input into the program the hydrograph over the design life of the bridge. The proposed technique consists of using a past hydrograph (from a gauge station for example), preparing the frequency distribution plot for the floods within that hydrograph, sampling the distribution randomly and preparing a future hydrograph. This future hydrograph is for the required period and has the same mean and standard deviation as the measured hydrograph. This process is repeated 10,000 times and, for each hydrograph, a final scour depth (the depth reached at the end of the design life of the bridge) is generated. These 10,000 final depths of scour are organized in a frequency distribution plot with a mean

and a standard deviation. That plot can be used to quote a scour depth with a corresponding probability of occurrence, or better, to choose a risk level and quote the corresponding final depth of scour. 16. EXAMPLE PROBLEMS A set of example problems are presented in chapter 12 to help the reader become more familiar with the SRICOS-EFA method. Some examples are done by hand calculations, some of them are done by using the computer program. 17. RECOMMENDATIONS It is recommended that:

1. The proposed method be incorporated in the next version of HEC-18. 2. The SRICOS-EFA method program be transformed into a Windows environment. 3. The project be continued to solve the other major unsolved scour problem in

cohesive soils: abutment scour. 4. A set of short courses be offered across the country to teach the new SRICOS-

EFA method.

CHAPTER 1 INTRODUCTION 1.1. BRIDGE SCOUR Bridge scour is the loss of soil by erosion due to flowing water around bridge supports. Bridge scour includes general scour and local scour. General scour is the aggradation or degradation of the riverbed not related to the presence of local obstacles. Aggradation is the gradual and general accumulation of sediments on the river bottom; one possible scenario is the existence of slope failures upstream leading to the formation of spoils in the river, the erosion of these spoils under higher velocities, followed by transport and deposition under lower velocities at the aggrading location. Degradation is the gradual and general removal of sediments from the riverbed; one possible scenario is the man-made straightening of a river course, a resulting increase in the water velocity and the associated increase in erosion. Local scour is the scour around obstacles in the path of the water flow; it includes pier scour, abutment scour, and contraction scour. Pier scour is the removal of the soil around the foundation of the pier; abutment scour is the removal of the soil around the abutment at the junction between the bridge and the embankment; contraction scour is the removal of the soil from the bottom of the river due to narrowing of the river channel created by the approach embankments for the bridge. 1.2. SOILS CLASSIFICATION Soils can be defined as loosely bound to unbound naturally occurring materials which cover the top few hundred meters of the earth. By opposition, rock is a strongly bound naturally occurring material found within similar depths or deeper. At the boundary between soils and rocks are intermediate geomaterials. Classification tests and mechanical properties help to distinguish between those three types of naturally occurring materials and between different categories of soils. For soils, the classification tests consist of grain size analysis and Atterberg limits (Das, 2001). The D50 grain size is the grain size corresponding to 50% of the soil weight passing a sieve of opening equal to D50. The first major division in soils classification is between large-grained soils and fine-grain soils; large-grained soils have D50 larger than 0.075mm while fine-grained soils have D50 smaller than 0.075mm. Large-grained soils include gravels and sands which are identified on the basis of their grain size. Fine-grained soils include silts and clays which are identified on the basis of Atterberg Limits. Gravels and sands are typically referred to as cohesionless soils while silts and clays are typically referred to as cohesive soils. 1.3. THE PROBLEM ADDRESSED This project deals with pier scour and contraction scour in cohesive soils (Figure 1.1). A previous project performed by the same team of researchers was started in 1990 and was sponsored by the Texas Department of Transportation (Briaud et al., 1999, 2002a and 2002b); it dealt with pier scour in cohesive soils. In the TxDOT project the piers were cylindrical and the water depth was more than two times the pier diameter (deep water

case). As part of the TxDOT project, a new apparatus called the EFA (Erosion Function Apparatus) was conceived, built, patented, and commercialized to measure the erodibility of soils. The EFA test gives the erosion function for a soil which became an integral part of the SRICOS method (Scour Rate In COhesive Soils) to predict the scour depth as a function of time when a cylindrical pier founded in a layered soil is subjected to a long-term deep water flow-velocity hydrograph. In this NCHRP project, the SRICOS-EFA method was extended to the case of complex piers and contraction scour. Complex piers refer to piers with various shapes, various flow attack angles, various spacing between piers, and any water depth. Contraction refers to a narrowing of the flow channel by an embankment with a given encroachment length, a given embankment width, and a given transition angle. The input to the SRICOS-EFA method is the geometry of the piers and of the contraction, the water velocity and the water depth as a function of time over the life of the bridge, and the soil erosion functions for the layers involved in the soil stratigraphy. The output is the scour depth as a function of time during the life of the bridge.

Figure 1.1 – Typical bridge with Potential Contraction and Pier Scour

A

A

A - A

1.4. WHY WAS THIS PROBLEM ADDRESSED? The reason for solving this problem is that a solution did not exist previously, that in the absence of a solution the calculations were based on the solution developed for cohesionless soils, and that there was a sense that such an approach was sometimes very conservative and therefore costly. Indeed, overly conservative scour depths lead to foundations which were considered to be deeper than necessary. The major difference between cohesionless soils and cohesive soils is the following. Floods create peak velocities that last a few days. A few days is a length of time which is usually sufficient to generate the maximum scour depth in cohesionless soils. This means that only the peak velocity needs to be used in the calculations of scour depth for cohesionless soils and that such a scour depth is the maximum scour depth for that velocity. The velocities used are typically the 100 year flood velocity and the 500 year flood velocity. In cohesive soils, scour and erosion rates can be 1000 times slower than in cohesionless soils and a few days may generate only a small fraction of the maximum scour depth. Therefore, for cohesive soils, it becomes necessary to consider the rate of erosion and accumulate the effect of multiple floods. This complicates the problem significantly but this necessary complication is the price one has to pay to get closer to reality. 1.5. APPROACH SELECTED TO SOLVE THE PROBLEM The approach selected to solve the problem of predicting the scour depth vs. time for complex piers in a contracted channel and for a given velocity hydrograph was based on a combination of review of existing knowledge, flume tests, numerical simulations, fundamental principles in method development, and verification of the method against available data. The review of the existing knowledge avoided duplication of effort and helped in establishing a solid foundation. The flume tests gave the equations for the maximum scour depth and the influence of various factors. The flume tests also gave a calibration basis for the numerical simulations. These numerical simulations were used to generate the equations for the maximum initial shear stress at the initiation of scour. The method was assembled by linking the calculated initial erosion rate (given by the numerical simulation results and the results of the EFA test) to the calculated maximum scour depth (given by the flume tests results) by a hyperbolic model. The multiflood hydrograph and multilayer soil was included through simple accumulation algorithms. Verification was based on comparison with existing databases as well as performing calculations for example cases and evaluating the reasonableness of the results based on experience. 1.6. ORGANIZATION OF THE REPORT After a review of the existing knowledge in the beginning chapters, Chapter 5 deals with the case of complex pier scour including the flume tests, the numerical simulations, and the development of the equations. Chapter 6 deals with contraction scour in much the same way as Chapter 5 dealt with complex pier scour. In Chapter 7, a new method is presented to predict future hydrographs. In Chapter 8, the SRICOS-EFA method for complex pier and contraction scour is formulated based on the evidence presented in

previous chapters. An evaluation of the accuracy and precision of the new method is also presented in chapter 8 by comparing predicted and measured data. Examples are worked out and the advantages and limitations of the method are discussed. Conclusions are reached in Chapter 9.

CHAPTER 2 ERODIBILITY OF COHESIVE SOILS 2.1. ERODIBILITY: A DEFINITION Erodibility is a term often used in scour and erosion studies. Erodibility may be thought of as one number which characterizes the rate at which a soil is eroded by the flowing water. With this concept erosion resistant soils would have a low erodibility index and erosion sensitive soils would have a high erodibility index. This concept is not appropriate; indeed the water velocity can vary drastically in rivers from 0 m/s to 5 m/s or more and therefore the erodibility is a not a single number but a relationship between the velocity applied and the corresponding erosion rate experienced by the soils. While this is an improved definition of erodibility, it still presents some problems because water velocity is a vector quantity which varies everywhere in the flow. It is much preferable to quantify the action of the water on the soil by using the shear stress applied by the water on the soil at the water-soil interface. Erodibility is therefore defined here as the relationship between the erosion rate z and the hydraulic shear stress applied τ (Figure 2.1). This relationship is called the erosion function z (τ). The erodibility of a soil or a rock is represented by the erosion function of that soil or rock. Scour Rate vs Velocity

0.01

0.10

1.00

10.00

100.00

Sco

ur

Rat

e(m

m/h

r)

Porcelain Clay PI=16%Su=23.3 Kpa

Vc

Scour Rate vs Velocity

0.01

0.10

1.00

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100.00

1000.00

10000.00

0.1 1.0 10.0 100.0

Velocity (m/s)

Sco

ur

Rat

e(m

m/h

r)

Sand D50 =0.3 mm

Vc

Scour Rate vs Shear Stress

0.01

0.10

1.00

10.00

100.00

Sco

ur

Rat

e(m

m/h

r)

Porcelain Clay PI=16%Su=23.3 Kpa

Si

τc

Scour Rate vs Shear Stress

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.1 1.0 10.0 100.0

Shear Stress (N/m 2)

Sco

ur

Rat

e(m

m/h

r)

Sand D 50 =0.3 mm

Si

τc

Figure 2.1 – Erodibility Function for a clay and for a sand

2.2. EROSION PROCESS Soils are eroded particle by particle in the case of coarse-grained soils (cohesionless soils). In the case of fine-grained soils (cohesive soils), erosion can take place particle by particle but also block of particles by block of particles. The boundaries of these blocks are formed naturally in the soil matrix by micro-fissures due to various phenomena including compression and extension. The resistance to erosion is influenced by the weight of the particles for coarse grained soils and by a combination of weight and electromagnetic and electrostatic interparticle forces for fine grained soils. Observations at the soil water interface on slow motion videotapes indicates that the removal of particle or blocks of particles is by a combination of rolling and plucking action of the water on the soil. 2.3. EXISTING KNOWLEDGE ON ERODIBILITY OF COHESIVE SOILS A complete discussion on the erodibility of cohesive soils and a literature review on that topic can be found in Briaud et al. (1999). The following is a summary of that part of Briaud et al. (1999). The factors influencing the erodibility of cohesive soils according to the literature survey are listed in Table 2.1. Although there are sometimes conflicting findings, the influence of various factors on cohesive soil erodibility is shown in table 2.1 when possible.

Table 2.1: Factors influencing the erodibility of cohesive soils

When this parameter increases Erodibility

Soil water content Soil unit weight decreases

Soil plasticity Index decreases Soil undrained shear strength increases Soil void ratio increases Soil swell increases Soil mean grain size Soil percent passing sieve #200 decreases Soil clay minerals Soil dispersion ratio increases Soil cation exchange capacity Soil sodium absorption ratio increases Soil pH Soil temperature increases Water temperature increases Water chemical composition

The critical shear stress of cohesionless soils is tied to the size of the particles and usually ranges from 0.1 N/m2 to 5 N/m2. The rate of erosion of cohesionless soils above the critical shear stress increases rapidly and can reach tens of thousands of millimeters per hour. The most erodible soils are fine sands and silts with mean grain sizes in the 0.1 mm range (Figure 2.2). The critical shear stress of cohesive soils is not tied to the particle size but rather to a number of factors as listed in Table 2.1. The critical shear stress of cohesive soils however varies within the same range as cohesionless soils (0.1 N/m2 to 5 N/m2) for the most common cases. Since the critical shear stress controls the maximum depth of scour as will be seen later, it is likely that the final depth of scour will be approximately the same in sands and in clays. One major difference between cohesionless and cohesive soils is the rate of erosion beyond the critical shear stress. In cohesive soils, this rate increases slowly and is measured in millimeters per hour. This slow rate makes it advantageous to consider that scour problems are time dependent and to find ways to accumulate the effect of the complete hydrograph rather than to consider a design flood alone. 2.4. ERODIBILITY AND CORRELATION TO SOIL AND ROCK PROPERTIES? There is a critical shear stress τc below which no erosion occurs and above which erosion starts. This concept while practically convenient may not be theoretically simple. Indeed, as seen on Figure 2.1, there is no obvious value for the critical shear stress. In this report the critical shear stress is arbitrarily defined as the shear stress which corresponds to an erosion rate of 1 mm/hr. The critical shear stress is associated with the critical velocity vc. One can also define the initial slope Si = (d z /dτ)i at the origin of the erosion function. Both τc and Si are parameters which help describe the erosion function and therefore the erodibility of a material. In cohesionless soils (sands and gravels), the critical shear stress has been empirically related to the mean grain size D50 (Briaud et al., 2001). τc (N/m2) = D50 (mm) (2.1) For such soils, the erosion rate beyond the critical shear stress is very rapid and one flood is long enough to reach the maximum scour depth. Therefore there is a need to be able to predict the critical shear stress to know if there will be scour or no scour but there is little need to define the erosion function beyond that point because the erosion rate is not sufficiently slow to warrant a time dependent analysis. In cohesive soils (silts, clays) and rocks, equation 2.1 is not applicable (Figure 2.2) and the erosion rate is sufficiently slow that a time rate analysis is warranted. Therefore it is necessary to obtain the complete erosion function. An attempt was made to correlate those parameters, τc and Si, to common soil properties in hope that simple equations could be developed for everyday use. The process consisted of measuring the erosion function on one hand and common soil properties on the other (water content, unit weight, plasticity index, percent passing sieve no. 200, undrained shear strength). This lead to a database of 91 EFA tests (Table 2.2) which was used to perform regression analyses and obtain correlation equations (Figure 2.3 to 2.6). All attempts failed to reach a reasonable R2 value.

Table 2.2 – Database of EFA tests

Woodrow Wilson Bridge (Washington) Tests 1 to 12 South Carolina Bridge Tests 13 to 16 National Geotechnical Experimentation Site (Texas) Tests 17 to 26 Arizona Bridge (NTSB) Test 27 Indonesia samples Tests 28 to 33 Porcelain clay (man-made) Tests 34 to 72 Bedias Creek Bridge (Texas) Tests 73 to 77 Sims Bayou (Texas) Tests 78 to 80 Brazos River Bridge (Texas) Test 81 Navasota River Bridge (Texas) Tests 82 and 83 San Marcos River Bridge (Texas) Tests 84 to 86 San Jacinto River Bridge (Texas) Tests 87 to 89 Trinity River Bridge (Texas) Tests 90 and 91

Figure 2.2 – Critical Shear Stress Versus Mean Soil Grain Diameter

τc vs. wτ c

(Pa)

R2 = 0.0245

0.00

5.00

10.00

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20.00

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30.00

35.00

0.00 20.00 40.00 60.00 80.00 100.00

W (%)

Si vs. w

R2= 0.0928

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100.00

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10000.00

0.00 20.00 40.00 60.00 80.00 100.00

w(%)

S i(m

m/h

r x m

2 /N

)

Figure 2.3 – Erosion properties as a function of water content

R2 = 0.1093

0.00

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0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00

Su(kPa)

τc vs. Su

τ c (P

a)

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Su(kPa)

Si vs. Su

S i(m

m/h

r x m

2 /N

)

Figure 2.4 – Erosion properties as a function of undrained shear strength

R2 = 0.056

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τc vs. PI

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τ c (P

a)

Si vs.PI

R2 = 0.0011

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200.00

0.00 20.00 40.00 60.00 80.00 100.00

PI(kPa)

S i(m

m/h

r x m

2 /N

)

Figure 2.5 – Erosion properties as a function of plasticity index

Si vs.#200

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R^2=0.2077

S i(m

m/h

rxm

2 /N

)τc vs.#200

R = 0.1306

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#200(%)

τ c(P

a)

Figure 2.6 – Erosion properties as a function of percent passing sieve #200 The fact that no relationship could be found in this project between the critical shear stress or the initial slope of the erosion function on one hand and common soil properties on the other seems to be at odds with the accepted idea that different cohesive soils erode at different rates. Indeed if different clays erode at different rates then the erosion function and therefore its parameters should be functions of the soils properties. The likely explanation is that there is a relationship between erodibility and soils properties but that this relationship is quite complicated, involves advanced soil properties, and could not be found within the budget and time of this project. Instead, it was found much easier to develop an apparatus which could measure the erosion function on any sample of cohesive soil from a site. This apparatus was called the Erosion Function Apparatus or EFA.

CHAPTER 3 EROSION FUNCTION APPARATUS 3.1. CONCEPT The EFA or Erosion Function Apparatus (Figures 3.1 and 3.2) (Briaud et al. 1999, 2001) (http://www.humboldtmfg.com/pdf2/hm4000ds.pdf , http://tti.tamu.edu/geotech/scour) was conceived in 1991, designed in 1992, and built in 1993. The sample of soil, fine-grained or not, is taken in the field by pushing an ASTM standard Shelby tube with a 76.2 mm outside diameter (ASTM D1587). One end of the Shelby tube full of soil is placed through a circular opening in the bottom of a rectangular cross section conduit. A snug fit and an O-ring establish a leak proof connection. The cross section of the rectangular conduit is 101.6 mm by 50.8 mm. The conduit is 1.22 m long and has a flow straightener at one end. The water is driven through the conduit by a pump. A valve regulates the flow and a flow meter is used to measure the flow rate. The range of mean flow velocities is 0.1 m/s to 6 m/s. The end of the Shelby tube is held flush with the bottom of the rectangular conduit. A piston at the bottom end of the sampling tube pushes the soil until it protrudes 1 mm into the rectangular conduit at the other end. This 1 mm protrusion of soil is eroded by the water flowing over it.

Figure 3.1 - Schematic Diagram and Result of the EFA (Erosion Function Apparatus)

Figure 3.2 - Photographs of the Erosion Function Apparatus (a) General View (b) Close-up of the Test Section 3.2. EFA TEST PROCEDURE The procedure for the EFA test is as follows. 1. Place the sample in the EFA, fill the conduit with water, and wait one hour. 2. Set the velocity to 0.3 m/s. 3. Push the soil 1 mm into the flow. 4. Record how much time it takes for the 1 mm soil to erode (visual inspection through

plexiglas window)

(a)

(b)

5. When the 1 mm of soil is eroded or after 1 hour of flow whichever comes first, increase the velocity to 0.6 m/s and bring the soil back to a 1 mm protrusion.

6. Repeat step 4. 7. Then repeat steps 5 and 6 for velocities equal to 1 m/s, 1.5 m/s, 2 m/s , 3 m/s, 4.5 m/s,

and 6 m/s. 3.3. EFA TEST DATA REDUCTION The test result consists of the erosion rate z versus shear stress τ curve (Figure 3.1). For each flow velocity v , the erosion rate z (mm/hr) is simply obtained by dividing the length of sample eroded by the time required to do so.

thz = (3.1)

where h is the length of soil sample eroded in a time t. The length h is 1 mm and the time t is the time required for the sample to be eroded flush with the bottom of the pipe (visual inspection through a plexiglass window). After several attempts at measuring the shear stress τ in the apparatus it was found that the best way to obtain τ was by using the Moody Chart (Moody, 1944) for pipe flows.

vfτ ρ81

= 2 (3.2)

Where τ is the shear stress on the wall of the pipe, f is the friction factor obtained from Moody Chart (Figure 3.3), ρ is the mass density of water (1000 kg/m3), and v is the mean flow velocity in the pipe. The friction factor f is a function of the pipe Reynold’s number Re and the pipe roughness ε/D. The Reynold’s number is v D/ν where D is the pipe diameter and ν is the kinematic viscocity of water ( )Catsm 20/10 26− . Since the pipe in the EFA has a rectangular cross section, D is taken as the hydraulic diameter D = 4A/P where A is the cross sectional flow area, P is the wetted perimeter, and the factor 4 is used to ensure that the hydraulic diameter is equal to the diameter for a circular pipe. For a rectangular cross section pipe:

( )baabD += /2 (3.3) where a and b are the dimensions of the sides of the rectangle. The relative roughness ε/D is the ratio of the average height of the roughness elements on the pipe surface over the pipe diameter D. The average height of the roughness elements ε is taken equal to 0.5D50 where D50 is the mean grain size for the soil. The factor 0.5 is used because it is assumed that the top half of the particle protrudes into the flow while the bottom half is buried into the soil mass.

Figure 3.3 - Moody Chart (reprinted with permission from Munson et al. 1990)

Figure 3.4 - Erosion Function for a soil sample taken near Pier 27E of the Existing Woodrow Wilson Bridge (2.6 - 3.2 meters depth) : a) Scour Rate vs. Shear Stress, b) Scour Rate vs. Velocity

(a)

(b)

3.4. EFA PRECISION AND TYPICAL RESULTS If the erosion rate is slow (less that 10 mm/hr) the error on z is estimated at 0.5 mm/hr. If the erosion rate is fast (more than 100 mm/hr) the error on z is estimated at 2 mm/hr. Therefore the relative error on z is estimated to be less than 10%. Comparison between the τc results for the sand and the gravel tested in this study and shown on Figure 2.2 with Shields data indicates a difference of about 10%. Therefore it is estimated that both z and τ are measured with a relative error of about 10%. The z vs. τ curve is the result of a series of tests each of which is performed at a constant velocity. A typical series of 8 velocity tests lasts one working day. Figure 2.1 and Figure 3.4 show examples of EFA tests results.

CHAPTER 4 THE SRICOS-EFA METHOD FOR CYLINDRICAL PIERS IN DEEP WATER Because cohesive soils may scour so much more slowly than cohesionless soils, it is necessary to include the scour rate in the calculations. The SRICOS method was developed for this purpose. 4.1. SRICOS-EFA METHOD FOR CONSTANT VELOCITY AND UNIFORM SOIL The SRICOS method was proposed in 1999 to predict the scour depth z versus time t curve at a cylindrical bridge pier for a constant velocity flow, for a uniform soil, and for a water depth larger than two times the pier diameter. The SRICOS method consists of (Briaud et al., 1999).

1. Collecting Shelby tube samples near the bridge pier, 2. Testing them in the EFA (Erosion Function Apparatus, Briaud et al. 2002) (Figure

3.1) to obtain the erosion rate z (mm/hr) versus hydraulic shear stress τ (N/m²) curve,

3. Calculating the maximum hydraulic shear stress maxτ around the pier before scour starts,

4. Reading the initial erosion rate iz (mm/hr) corresponding to maxτ on the z vs. τ curve,

5. Calculating the maximum depth of scour maxz , 6. Constructing the scour depth z versus time t curve using a hyperbolic model, 7. Reading the scour depth corresponding to the duration of the flood on the z vs. t

curve. The maximum hydraulic shear stress maxτ exerted by the water on the riverbed was obtained by performing a series of three-dimensional numerical simulations of water flowing past a cylindrical pier of diameter B on a flat river bottom and with a large water depth (water depth larger than 2B). The results of several runs lead to the following equation (Briaud et al., 1999):

−=

101

Relog1094.0 2

max vρτ (4.1)

where ρ is the density of water (kg/m³), v is the depth average velocity in the river at the location of the pier if the bridge was not there (it is obtained by performing a hydrologic

analysis with a computer program such as HEC-RAS, 1997), Re is υvB where B is the

pier diameter and υ the kinematic viscosity of water )20/10( 26 Catsm− . The initial rate of scour iz is read on the z vs. τ curve from the EFA test at the value of

maxτ .

The maximum depth of scour maxz was obtained by performing a series of 43 model scale flume tests (36 tests on three different clays and 7 tests in sand) (Briaud et al, 1999). The results of these experiments and a review of other work lead to the following equation which appears to be equally valid for clays and sands:

635.0max Re18.0)( =mmz (4.2)

In equation 4.2, Re has the same definition as in equation 4.1. The regression coefficient for Eq. 4.2 was 0.74. The equation which describes the shape of the scour depth z versus time t curve is:

max

1z

tz

tz

i

+= (4.3)

where iz and maxz have been previously defined, t is time (hours). This hyperbolic equation was chosen because it fits well the curves obtained in the flume tests. Once the duration t of the flood to be simulated is known, the corresponding z value is calculated using equation (4.3). If iz is large as it is in clean fine sands then z is close to maxz even for small t values. But if iz is small as it can be in clays then z may only be a small fraction of maxz . An example of the SRICOS method is shown in Figure 4.1.

The method as described in the previous paragraphs is limited to a constant velocity hydrograph (v = constant), a uniform soil (one z vs. τ curve) and a relatively deep-water depth. In reality, rivers create varying velocity hydrographs and soils are layered. The following describes how SRICOS was extended to include these two features. The case of shallow water flow (water depth over pier diameter < 2), non-circular piers, and flow directions different from the pier main axis are not addressed in this section.

4.2. SMALL FLOOD FOLLOWED BY BIG FLOOD.

For a river, the velocity versus time history over many years is very different from a constant velocity history. In order to investigate the influence of the difference between the two velocity histories or hydrographs on the depth of scour at a bridge pier, the case of a sequence of two different yet constant velocity floods scouring a uniform soil was first considered (Figure 4.2). Flood 1 has a velocity 1v and lasts a time 1t while the subsequent flood 2 has a larger velocity 2v and lasts a time 2t . The scour depth z versus time t curve for flood 1 is described by:

1max1

1z

tz

tz

i

+= (4.4)

Figure 4.1 - Example of the SRICOS method for constant velocity and uniform soil.

Figure 4.2 - Scour due to a sequence of two flood events (small flood followed by big flood).

For flood 2 the z vs. t curve is:

2max2

1z

tz

tz

i

+= (4.5)

After a time 1t , flood 1 creates a scour depth 1z given by equation 4.4 (Point A on Figure 4.2b). This depth 1z would have been created in a shorter time t* by flood 2 because 2v is larger than 1v (point B on Figure 4.2c). This time t* can be found by setting equation 4.4 with 1zz = and 1tt = equal to equation 6 with 1zz = and t = t*.

−+

=

2max1max21

1

2

1*

11zz

ztzz

tt

ii

i

(4.6)

When flood 2 starts, even though the scour depth 1z was due to flood 1 over a time 1t , the situation is identical to having had flood 2 for a time t*. Therefore when flood 2 starts the scour depth vs. time curve proceeds from point B on Figure 4.2c until point C after a time

2t . The z versus t curve for the sequence of flood 1 and 2, follows the path OA on the curve for flood 1 then switches to BC on the curve for flood 2. This is shown as the curve OAC on Figure 4.2d.

A set of two experiments was conducted to investigate this reasoning. For these experiments, a 25mm diameter pipe was placed in the middle of a flume. The pipe was pushed through a 150mm thick deposit of clay made by placing prepared blocks of clay side by side in a tight arrangement. The properties of the clay are listed in Table 4.1. The water depth was 400 mm and the mean flow velocity was smv /3.01 = in flood 1 and smv /4.02 = for flood 2 (Figure 4.3a). The first of the two experiments consisted of setting the velocity equal to 2v for 100 hrs and recording the z versus t curve (Figure 4.3c). The second of the two experiments consisted of setting the velocity equal to 1v for 115 hours (Figure 4.3b) and then switching to 2v for 100 hours (Figure 4.3d). Also shown on Figure 4.3d is the prediction of the portion of the z vs. t curve under the velocity 2v according to the procedure described in Figure 4.3. As can be seen the prediction is very reasonable.

4.3. BIG FLOOD FOLLOWED BY SMALL FLOOD AND GENERAL CASE

Flood 1 has a velocity 1v and lasts 1t (Figure 4.4a). It is followed by flood 2 which has a velocity 2v smaller than 1v and lasts 2t . The scour depth z versus time t curve is given by equation (4.4) for flood 1 and by equation (4.5) for flood 2. After a time 1t , flood 1 creates a scour depth 1z . This depth 1z is compared with 2maxz ; if 1z is larger than 2maxz then, when flood 2 starts, the scour hole is already larger than it can be with flood 2

Table 4.1. Properties of the Porcelain Clay for the Flume Experiment.

Liquid Limit, % 34.4 Shear Strength, kPa(lab vane) 12.5Plastic Limit, % 20.2 Cation Exchange Capacity, (meq/100g) 8.30

Plasticity Index, % 14.1 Sodium Adsorption Ratio 5.00Water Content, % 28.5 Electrical Conductivity, (mmhos/cm) 1.20

Mean Diameter 50D , (mm) 0.0062 pH 6.00Sand Content, % 0.0 Unit Weight (kN/m3) 18.0Silt Content, % 75.0 Specific Gravity 2.61Clay Content, % 25.0

Figure 4.3 - Multiflood flume experiment results. a) floods and flood sequence in the

experiments, b) experiment result for flood 1 alone, c) experiment result for flood 2 alone, d) experiment result for the flood 1 and 2 sequence shown in a) and prediction for flood 2.

therefore flood 2 cannot create additional scour and the scour depth vs. time curve remains flat during flood 2. If 1z is smaller than 2maxz then the procedure followed for the case of a small flood followed by a big flood applies and the combined curve is as shown in Figure 4.4.

Figure 4.4 - Scour due to a sequence of two flood events (big flood followed by small flood).

In the general case the velocity versus time history exhibits many sequences of small floods and big floods. The calculations for scour depth are performed by choosing an increment of time t∆ and breaking the complete velocity versus time history into a series of partial flood events each lasting t∆ . The first two floods in the hydrograph are handled by using the procedure of Figure 4.2 or Figure 4.4 depending on the case. Then the process advances by stepping into time and considering a new “flood 2” and a new t* at each step. The time t∆ is typically one day and a velocity versus time history can be 50 years long. The many steps of calculations are handled with a computer program called SRICOS. The output of the program is the depth of scour versus time curve over the duration of the velocity versus time history.

4.4. HARD SOIL LAYER OVER SOFT SOIL LAYER.

The original SRICOS method (Briaud et al., 1999) was developed for a uniform soil. In order to investigate the influence of the difference between a uniform soil and a more realistic layered soil on the depth of scour at a bridge pier, the case of a two layer soil profile scoured by a constant velocity flood was considered (Figure 4.5). Layer 1 is hard and 1z∆ thick, layer 2 underlays layer 1 and is softer than layer 1. The scour depth z versus time t curve for layer 1 is given by equation (4.4) (Figure 4.5a) and the z vs. t curve for layer 2 is given by equation (4.5) (Figure 4.5b). If 1z∆ is larger than the maximum depth of scour in layer 1, 1maxz , then the scour process is contained in layer 1 and does not reach layer 2. If however the scour depth reaches 1z∆ (Point A on Figure 4.5a), layer 2 starts to be eroded. In this case, even though the scour depth 1z∆ was due to the scour of layer 1 over a time 1t , at that time the situation is identical to having had layer 2 scoured over a time t* (Point B on Figure 4.5b). Therefore, when layer 2 starts being eroded, the scour depth vs. time curve proceeds from point B to point C on Figure 4.5b. The combined curve for the two-layer system is OAC on Figure 4.5c.

Figure 4.5 - Scour of a two-layer soil (hard layer over soft layer).

4.5. SOFT SOIL LAYER OVER HARD SOIL LAYER AND GENERAL CASE.

Layer 1 is soft and 1z∆ thick, layer 2 underlays layer 1 and is harder than layer 1. The scour depth z versus time t curve for layer 1 is given by equation (4.4) (Figure 4.6a) and the z versus t curve for layer 2 is given by equation (4.5) (Figure 4.6b). If 1z∆ is larger than the maximum depth of scour in layer 1, 1maxz , then the scour process is contained in layer 1 and does not reach layer 2. If, however, the scour depth reaches 1z∆ (Point A on Figure 4.6a) layer 2 starts to erode. In this case, even though the scour depth 1z∆ was due to the scour of layer 1 over a time 1t , at that time the situation is identical to having had layer 2 scoured over an equivalent time t* (Point B on Figure 4.6b). Therefore when layer 2 starts being eroded the scour depth vs. time curve proceeds from point B to point C on Figure 4.6b. The combined curve for the two-layer system is OAC on Figure 4.6c.

Figure 4.6 - Scour of a two-layer soil (soft layer over hard layer).

In the general case there may be a series of soil layers with different erosion functions. The computations proceed by stepping forward in time. The time steps are t∆ long, the velocity is the one for the corresponding flood event, and the erosion function ( )tvsz is the one for the soil layer corresponding to the current scour depth (bottom of the scour hole). When t∆ is such that the scour depth proceeds to a new soil layer the computations follow the process described in Figures 4.5 or 4.6 depending on the case. The calculations are handled by the same SRICOS program as the one mentioned for the velocity hydrograph. The output of the program is the scour depth versus time curve for the multilayered soil system and for the complete velocity hydrograph.

4.6. EQUIVALENT TIME

The computer program SRICOS is required to predict the scour depth versus time curve as explained in the preceding section. An attempt was made to simplify the method to the point where only hand calculations would be needed. This requires the consideration of an equivalent uniform soil and an equivalent time for a constant velocity history. The equivalent uniform soil is characterized by an average z versus τ curve over the anticipated scour depth. The equivalent time et is the time required for the maximum velocity in the hydrograph to create the same scour depth as the one created by the complete hydrograph (Figure 4.7). The equivalent time et was obtained for 55 cases generated from 8 bridge sites. For each bridge site, soil samples were collected in Shelby tubes and tested in the EFA to obtain the erosion function τvsz ; then the hydrograph was collected from the nearest gage station and the SRICOS program was used to calculate the scour depth. That scour depth was entered in equation 4.3 together with the corresponding iz and maxz to get et . The iz value was obtained from an average τvsz curve within the final scour depth by reading the z value which corresponded to maxτ obtained from equation 4.1. In equation 4.1 the pier diameter B and the maximum velocity maxv found to exist in the hydrograph over the period considered were used. The

maxz value was obtained from equation 4.2 while using B and maxv for the pier Reynolds number. The hydrograph at each bridge was also divided into shorter period hydrographs and for each period an equivalent time et was calculated. This generated 55 cases (Briaud et al., 2002).

The equivalent time was then correlated to the duration of the hydrograph hydrot , the maximum velocity in the hydrograph maxv , and the initial erosion rate iz . A multiple regression on that data gave the following relationship.

( ) ( )( ) ( )( ) ( )( ) 20.0706.1max

126.0 //73 −= hrmmzsmvyearsthrst ihydroe (4.7) The regression coefficient for equation 4.7 was 0.77. This time et can then be used in equation 4.3 to calculate the scour at the end of the hydrograph. A comparison between the scour depth predicted by the Extended-SRICOS method using the complete hydrograph and the Simple SRICOS method using the equivalent time is shown on Figure 4.8.

Figure 4.7 - Velocity hydrographs: a) constant, b) true hydrograph. Both hydrographs would lead to the same scour depth.

Figure 4.8 - Comparison of scour depth using Extended SRICOS and Simple SRICOS Methods.

4.7. EXTENDED AND SIMPLE SRICOS-EFA METHOD

For final design purposes the Extended SRICOS method (E-SRICOS) is used to predict the scour depth z versus time t over the duration of the design hydrograph. The method proceeds as follows:

1. Calculate the maximum depth of scour maxz for the design velocity by using

equation (4.2). 2. Collect samples at the site within the depth maxz . 3. Test the samples in the EFA to obtain the erosion functions ( )τvsz for the layers

involved. 4. Prepare the flow hydrograph for the bridge. This step may consist in

downloading the discharge hydrograph from a USGS (United States Geological Survey) gage station near the bridge (Figure 4.9). These discharge hydrographs can be found on the Internet at the USGS web site (www.usgs.gov). The discharge hydrograph then needs to be transformed into a velocity hydrograph (Figures 4.10, 4.11, and 4.12). This transformation is performed by using a program such as HEC-RAS (1997) which makes use of the transversed river bottom profile at the bridge site to link the discharge Q )/( 3 sm to the velocity ( )smv / at the anticipated location of the bridge pier.

5. Use the SRICOS program (Kwak et al., 1999) with the following input: the z vs. τ curves for the various layers involved, the velocity hydrograph v vs. t , the pier diameter B, the viscosity of the water υ , and the density of the water wρ . Note that the water depth y is not an input because at this time the solution is limited to a “deep water” condition. This condition is realized when 2y B≥ ; indeed beyond this water depth the scour depth becomes independent of the water depth (Melville & Coleman, 1999, p. 197).

6. The SRICOS program proceeds by a series of time steps; it makes use of the original SRICOS method and of the accumulation algorithms described in Figures 4.2, 4.4, 4.5, and 4.6. The usual time step t∆ is one day because that is the usual reading frequency of the USGS gages. The duration of the hydrograph can vary from a few days to over 100 years.

7. The output of the program is the depth of scour versus time over the period covered by the hydrograph (Figure 4.10, 4.11, and 4.12).

For predicting the future development of a scour hole at a bridge pier over a design life

lifet , one can either develop a synthetic hydrograph much like is done in the case of earthquakes or assume that the hydrograph recorded over the last period equal to lifet will repeat itself. The time required to perform step 3 is about 8 hours per Shelby tube sample because it takes about 8 points to properly describe the erosion function ( )curvevsz τ and, for each point, the water is kept flowing for 1 hour to get a good average z value. The time required to perform all other steps, except for step 2, is about 4 hours for someone who has done it before. In order to reduce these 4 hours to a few minutes a simplified version of SRICOS called S-SRICOS was developed. One must

Figure 4.9 - Examples of Discharged Hydrographs: a) Brazos River at US90A, b) San

Marcos River at SH80, c) Sims Bayou at SH35.

Figure 4.10 - Velocity hydrograph and scour depth vs. time curve for Bent 3 of the

Brazos River Bridge at US90A.

Figure 4.11 - Velocity hydrograph and scour depth vs. time curve for Bent 3 of the San Marcos River Bridge at SH80.

Figure 4.12 - Velocity hydrograph and scour depth vs. time curve for Bent 3 of the Sims

Bayou River Bridge at SH35.

understand that this simplified method is only recommended for preliminary design purposes. If S-SRICOS shows clearly that there is no need for refinement then there is no need for E-SRICOS; if not, one must perform an E-SRICOS analysis.

For preliminary design purposes, the simple SRICOS method (S-SRICOS) can be used. The method proceeds as follows:

1. Calculate the maximum depth of scour maxz for the design velocity maxv by using

equation (4.2). The design velocity is usually the one corresponding to the 100 year flood or the 500 year flood.

2. Collect samples at the site within the depth maxz . 3. Test the samples in the EFA to obtain the erosion function ( )τvsz for the layers

involved. 4. Create a single equivalent erosion function by averaging the erosion functions

within the anticipated depth of scour. 5. Calculate the maximum shear stress maxτ around the pier before scour starts by

using equation (4.1). In equation (4.1) use the pier diameter B and the design velocity maxv

6. Read the erosion rate iz corresponding to maxτ on the equivalent erosion function. 7. Calculate the equivalent time et for a given design life of the bridge hydrot for the

design velocity maxv and for the iz value of step 6 by using equation (4.7). 8. Knowing et , iz , and maxz calculate the scour depth z at the end of the design life

by using equation (4.3).

An example of such calculations is shown in Figure 4.13.

4.8. CASE HISTORIES

In order to evaluate the E-SRICOS and S-SRICOS methods, 8 bridges were selected (Figure 4.14). These bridges all satisfied the following requirements: the predominant soil type was fine-grained soils according to existing borings, the river bottom profiles were measured at two dates separated by at least several years, these river bottom profiles indicated anywhere from 0.05m to 4.57m of scour, a USGS gaging station existed near the bridge, drilling access was relatively easy The Navasota River bridge at SH7 was built in 1956. The main channel bridge has an overall length of 82.8m and consists of 3 continuous steel girder main spans with 4 concrete pan girder approach spans. The foundation type is steel piling down to 5.5m below the channel bed which consists of silty and sandy clay down to the bottom of the piling according to existing borings. Between 1956 and 1996 the peak flood took place in 1992 and generated a measured flow of 1600 sm /3 which corresponds to a HEC-RAS calculated mean approach flow velocity of 3.9 m/s at bent 5 and 2.6 m/s at bent 3. The pier at bent 3 was square with a side equal to 0.36m while the pier at bent 5 was 0.36m

Figure 4.13 - Example of scour calculations by the S-SRICOS method.

Figure 4.14 - Location of Case History Bridges

wide, 8.53m long and had a square nose. The angle between the flow direction and the pier main axis was 5º for bent 5. River bottom profiles exist for 1956 and 1996 and show 0.76m of local scour at bent 3 and 1.8m of total scour at bent 5. At bent 5 the total scour was made up of 1.41m of local scour and 0.39m of contraction scour as explained later.

The Brazos River bridge at US 90A was built in 1965. The bridge has an overall length of 287m and consists of 3 continuous steel girder main spans with 8 prestressed concrete approach spans. The foundation type is concrete piling penetrating 9.1m below the channel bed which consists of sandy clay, clayey sand, and sand down to the bottom of the piling according to existing borings. Between 1965 and 1998 the peak flood occurred in 1966 and generated a measured flow of 2600 sm /3 which corresponds to a HEC-RAS calculated mean approach velocity of 4.2 m/s at bent 3. The pier at bent 3 was 0.91m wide, 8.53m long and had a round nose. The pier was in line with the flow. River bottom profiles exist for 1965 and 1997 and show 4.43m of total scour at bent 3 made up of 2.87m of local scour and 1.56m of combined contraction and general scour as explained later.

The San Jacinto River bridge at US 90 was built in 1988. The bridge is 1472.2m long and has 48 simple prestressed concrete beam spans and 3 continuous steel plate girder spans. The foundation type is concrete piling penetrating 24.4m below the channel bed at bent 43 where the soil consists of clay, silty clay, and sand down to the bottom of the piles according to existing borings. Between 1988 and 1997, the peak flood took place in 1994 and generated a measured flow of 10,000 sm /3 which corresponds to a HEC-RAS calculated mean approach velocity of 3.1m/s at bent 43. The pier at bent 43 was square with a side equal to 0.85m. The angle between the flow direction and the pier main axis was 15º. River bottom profiles exist for 1988 and 1997 and show 3.17m of total scour at bent 43 made up of 1.47m of local scour and 1.70m of combined contraction and general scour as explained later.

The Trinity River bridge at FM 787 was built in 1976. The bridge has three main spans and three approach spans with an overall length of 165.2m. The foundation type is timber piling and the soil is sandy clay to clayey sand. Between 1976 and 1993 the peak flood took place in 1990 and generated a measured flow of 2950 sm /3 which corresponds to a HEC-RAS calculated mean approach flow velocity of 2.0 m/s at bent 3 and 4.05 m/s at bent 4. The piers at bent 3 and 4 were 0.91m wide, 7.3m long, and had a round nose. The angle between the flow direction and the pier main axis was 25º. River bottom profiles exist for 1976 and for 1992 and show 4.57m of total scour at both bent 3 and 4 made up of 2.17m of local scour and 2.40m of contraction and general scour as explained later.

The San Marcos River bridge at SH80 was built in 1939. This 176.2m long bridge has 11 prestressed concrete spans. The soil tested from the site is a low plasticity clay. Between 1939 and 1998 the peak flood occurred in 1992 and generated a measured flow of 1000 sm /3 which corresponds to a HEC-RAS calculated mean approach flow velocity of 1.9 m/s at bent 9. The pier at bent 9 is 0.91m wide, 14.2m long and has a round nose. The pier is in line with the flow. River bottom profiles exist for 1939 and 1998 and show 2.66m of total scour at bent 9 made up of 1.27m of local scour and 1.39m of contraction

and general scour as explained later.

The Sims Bayou bridge at SH35 was built in 1993. This 85.3m long bridge has 5 spans. Each bent rests on 4 drilled concrete shafts. Soil borings indicate mostly clay layers with a significant sand layer about 10m thick starting at a depth of approximately 4m. Between 1993 and 1996 the peak flood occurred in 1994 and generated a measure flow of 200 sm /3 which corresponds to a HEC-RAS calculated mean approach flow velocity of 0.93m/s at bent 3. The pier at bent 3 is circular with a 0.76m diameter. The angle between the flow direction and the pier main axis was 5º. River bottom profiles exist for 1993 and 1995 and indicate 0.05m of local scour at bent 3.

The Bedias Creek bridge at US75 was built in 1947. This 271.9m long bridge has 29 spans and bent 26 is founded on a spread footing. The soil tested from the site varied from low plasticity clay to fine silty sand. Between 1947 and 1996 the peak flood occurred in 1991 and generated a measured flow of 650 sm /3 which corresponds to a HEC-RAS calculated mean approach flow velocity of 2.15 m/s at bent 26. The pier at bent 26 is square with a side of 0.86m. The pier is in line with the flow. River bottom profiles exist for 1947 and 1996 and show 2.13m of total scour at bent 26 made up of 1.35m of local scour and 0.78m of contraction and general scour as explained later.

The Bedias Creek bridge at SH90 was built in 1979. This 73.2m long bridge is founded on 8m long concrete piles embedded in layers of sandy clay and firm gray clay. Between 1979 and 1996 the peak flood occurred in 1991 and generated a measured flow of 650

sm /3 which corresponds to a HEC-RAS calculated mean approach flow velocity of 1.55 m/s at bent 6. The pier at bent 6 was square with a side of 0.38m. The angle between the flow direction and the pier main axis was 5º. River bottom profiles exist for 1979 and 1996 and show 0.61m of local scour at bent 6.

4.9. PREDICTED AND MEASURED LOCAL SCOUR FOR THE 8 BRIDGES The data for all bridges is listed in Tables 4.2 and 4.3. For each bridge the E-SRICOS and the S-SRICOS methods were used to predict the local scour at the chosen bridge pier location. One pier was selected for each bridge except for the Navasota River bridge at SH7 and the Trinity River bridge at FM787 for which two piers were selected. Therefore a total of 10 predictions were made for these 8 bridges. These predictions are not Class A predictions since the measured values were known before the prediction process started. However the predictions were not modified once they were obtained. For each bridge, Shelby tube samples were taken near the bridge pier within a depth at least equal to two pier widths below the pier base. The boring location was chosen to be as close as practically possible to the bridge pier considered. The distance between the pier and the boring varied from 2.9m to 146.3m (Table 4.2). In all instances the boring data available was studied in order to infer the relationship between the soil layers at the pier and at the sampling locations. Shelby tube samples to be tested were selected as the most probable representative samples at the bridge pier. These samples were tested in the EFA and yielded erosion functions τvsz . Figure 4.15 and 4.16 are examples of the

Table 4.2. Full Scale Bridges as Case Histories

Table 4.3. Soil Properties at the Bridge Sites

Figure 4.15 - Erosion Function for San Jacinto River Sample (7.6 m to 8.4 m depth)

Figure 4.16 - Erosion Function for Bedias Creek Sample (6.1 m to 6.9 m depth)

erosion functions obtained. The samples were also analyzed for common soil properties (Table 4.3).

For each bridge, the USGS gage data was obtained from the USGS Internet site. This data consisted of a record of discharge Q versus time t over the period of time separating the two river bottom profile observations (Figure 4.9). This discharge hydrograph was transformed into a velocity hydrograph by using the program HEC-RAS (1997) and proceeding as follows. The input to HEC-RAS is the bottom profile of the river cross section (obtained from the Texas DOT records), the mean longitudinal slope of the river at the bridge site (obtained from topographic maps, Table 4.2), and Manning’s roughness coefficient (estimated at 0.035 for all cases after Young et al., 1997). For a given discharge Q, HEC-RAS gives the velocity distribution in the river cross section including the mean approach velocity v at the selected pier location. Many runs of HEC-RAS for different values of Q are used to develop a relationship between Q and v. The relationship (regression equation) is then used to transform the Q-t hydrograph into the v-t hydrograph at the selected pier (Figures 4.10, 4.11, and 4.12).

Then, the program SRICOS (Kwak et al., 2001) was used to predict the scour depth z vs. time t curve. For each bridge, the input consisted of the τvsz curves (erosion functions) for each layer at the bridge pier (e.g. Figure 4.15 and 4.16), the v vs. t record (velocity hydrograph) (e.g. Figures 4.10, 4.11, and 4.12), the pier diameter B, the viscosity of the water υ and the density of the water wρ . The output of the program was the scour depth z vs. time t curve for the selected bridge pier (e.g. Figures 4.10, 4.11, and 4.12) with the predicted local scour depth corresponding to the last value on the curve.

The measured local scour depth was obtained for each case history by analyzing the two bottom profiles of the river cross-section (e.g. Figure 4.17, 4.18). This analysis was necessary to separate the scour components which added to the total scour at the selected pier. The two components were local scour and contraction/general scour. This separation was required because, at this time, SRICOS only predicts the local scour. The contraction/general scour over the period of time separating the two river bottom profiles was calculated as the average scour over the width of the channel. This width was taken as the width corresponding to the mean flow level (width AB on Figure 4.17 and 4.18). Within this width the net area between the two profiles was calculated with scour being positive and aggradation being negative. The net area was then divided by the width AB to obtain an estimate of the mean contraction/general scour. Once this contraction/general scour was obtained it was subtracted from the total scour at the bridge pier to obtain the local scour at the bridge pier. Note that in some instances there was no need to evaluate the contraction/general scour. This is the case of bent 3 for the Navasota Bridge (Figure 4.17). Indeed in this case the bent was in the dry at the time of the field visit (flood plain) and the local scour could be measured directly. Figure 4.19 shows the comparison between E-SRICOS predicted and measured values of local scour at the bridge piers. The precision and accuracy of the method appear reasonably good. On one hand, one would wish to have more than 10 data points; on the other hand, these 10 data points are 10 full scale real situations.

Figure 4.17 - Profiles of Navasota River Bridge at SH 7

Figure 4.18 - Profiles of Brazos River Bridge at US 90A

Figure 4.19 - Predicted vs Measured Local Scour for the E-SRICOS method.

Figure 4.20 - Predicted vs Measured Local Scour for the S-SRICOS method.

The S-SRICOS method was performed next. For each bridge pier the maximum depth of scour maxz was calculated by using equation 4.2. The velocity used for equation 4.2 was the maximum velocity which occurred during the period of time separating the two river bottom profile observations. Then, at each pier an average erosion function ( )curveτvsz within the maximum scour depth was generated. Then, the maximum shear stress maxτ around the pier before scour starts was calculated using equation 4.1 and assuming that the pier was circular (Table 4.2). The initial scour rate iz was read on the average erosion function for that pier (Table 4.2). The equivalent time et was calculated using equation 4.7, using hydrot equal to the time separating the two river bottom profile observations, and maxv equal to the maximum velocity that occurred during hydrot (Table 4.2). Knowing et , iz , and maxz the scour depth accumulated during the period of hydrot was calculated using equation 4.3. Figure 4.20 is a comparison between the measured values of local scour and the predicted values using the S-SRICOS method. The precision and accuracy of the method appear reasonably good. One must keep in mind that the 10 case histories used to evaluate the S-SRICOS method are the same cases which were used to develop that method. Therefore this does not represent an independent evaluation. All the details of the prediction process can be found in Kwak et al. (2001).

Note that E-SRICOS and S-SRICOS described above do not include correction factors for pier shape, skew angle between the flow direction and the pier main axis, shallow water depth effects and multiple pier effect. The following chapter shows how to calculate those factors.

4.10. CONCLUSIONS

The SRICOS method predicts the depth of the local scour hole versus time curve around a bridge pier in a river for a given velocity hydrograph and for a layered soil system (Figure 4.21). The method described in this chapter is limited to cylindrical piers, and water depths larger than two times the pier width. The prediction process makes use of a flood accumulation principle and a layer equivalency principle. These are incorporated in the SRICOS computer program to generate the scour vs. time curve. A simplified version of this method is also described and only requires hand calculations. The simplified method can be used for preliminary design purposes. Both methods are evaluated by comparing predicted scour depths and measured scour depths for 10 piers at 8 full-scale bridges. The precision and accuracy of both methods appear good.

Figure 4.21 - Velocity Hydrograph and Predicted Scour Depth vs. Time Curve for Pier 1E of the Existing Woodrow Wilson Bridge on the Potomac River in Washington DC.

CHAPTER 5 THE SRICOS-EFA METHOD FOR MAXIMUM SCOUR DEPTH AT COMPLEX PIERS 5.1. EXISTING KNOWLEDGE An extensive review of the literature on the topic of pier scour in cohesive soils lead to very few publications. Studies related to the maximum scour depth included those of Hosny, 1995, Ivarson, 1998, and Molinas et al., 1999. Hosny ran a large number of flume tests on prepared samples of clay and sand mixtures. He recommended multiplying factors to include in the HEC-18 equation for the maximum scour depth in cohesionless soils. These factors are based on simple soil properties and lead to maximum scour depths smaller than the cohesionless soil values by 10 to 40%. Ivarson (1998) developed a modification factor K4 for the HEC-18 equation for maximum scour depth in cohesionless soils. The K4 factor is a multiplier in the HEC-18 equation and makes use of the undrained shear strength of the cohesive soil. Molinas et al. (1999) presented a modification of the Hosny (1995) factors. Studies related to numerical simulations were more numerous. 5.2. GENERAL Chapter 4 described a method for cylindrical piers in deep water. This chapter deals with piers which can be rectangular, square, or cylindrical, piers which are attacked by the flow at a non zero angle between the flow direction and the main axis of the pier, piers in shallow water, and the influence of pier spacing. Figure 5.1 shows the definition of the parameters involved with these influencing factors. The approach consisted of using the solution for the case of the cylindrical pier in deep water:

Zmax(mm) = 0.18 Re0.635 (5.1) and developing correction factors to include the effect of the various situations deviating from that case. Since the case of the cylindrical pier in deep water was developed on the basis of two fundamental equations (maximum scour depth and initial maximum shear stress), two sets of correction factors had to be developed. The correction factors for the maximum scour depth were developed on the basis of flume tests while the correction factors for the initial maximum shear stress were developed on the basis of numerical simulations. 5.3. FLUMES AND SCOUR MODELS The in-floor concrete flume, which is 1.5 m wide, 30.48 m long, and 3.48 m deep, was used to conduct the complex pier scour tests, and the wooden flume, which is 0.45 m wide, 36 m long, and 1.22 m deep, was used for the contraction scour tests. These two flumes form a close system (Figure 5.2) and the water is recirculated without any fresh water being added.

B Flow V L

H

B

Flow V

B S

B Pier Spacing Effect

C Pier Shape Effect

A W ater Depth Effect

L

B B’

Flow V

α

D : A ttack Angle Effect

Figure 5.1 – Parameter Definition for Complex Pier Scour.

(1) Tail Gate (4) Soil Tank (7) Computer (10): Pumps (13): Piers

(2) False Bottom (5) Carriage (8) Water Fall (11): Measuring Cadge (14): Mini Pump

(3) Contraction Abutments (6) ADV and Point Gage (9) Switch (12): Screen Wire

Figure 5.2 - Diagram of the Flume System (not to Scale)

(5) (6) ((3)) (1) (2) (4) (7) (14) (8) (9) (10) (11) (12) (13) (13) (2) (4) (4)

0.45m Flume 1.50m Flume

(3)

False Bottoms were designed to make sure that the start and end transitions would not affect the velocity distribution in the test area. For the 1.5 m flume, the slopes of the ramps at the two end of the false bottom are 1:3 (vertical to horizontal) to guarantee a smooth transition. The distance between the two soil tanks is 7.6m to make sure there is no interaction between them. Before starting the scour tests, trial tests were conducted and the velocity distributions were measured along the centerline of the channel to confirm the validity of the design. In the 1.5 m wide flume, the soil tank is 0.6 m deep and 1.5 m long for the front tank and 0.6 m deep and 1.2m long for the rear tank. The false bottom is built with plastic plates and supported by Aluminum frames. The false bottom in the 0.45 m flume was designed for the contraction scour tests. A smooth transition between the uncontracted and contracted channels was constructed. The soil tank is 2.0 m long and 0.3 m deep to provide enough space for both the long contraction flow and the contraction scour hole. This false bottom is made of plywood. Two types of pier models were used in the complex pier scour tests as shown in Figure 5.3. The cylindrical piers were cut from PVC pipes with three different diameters: 273mm, 160mm, and 61mm. The rectangular piers were made of plywood with the same width (61mm) and different length: 61mm, 122mm, 244mm and so on. For piers with projection width B’ larger than 160mm, strutted frames were necessary to fix them and avoid that the piers swayed or be flushed away during scouring. The abutment models were all made of plywood. They are shown in Figure 5.4 including the transition inlets for the contraction scour tests.

Diameter =273mm

61x61

61x122

61x244

61x366

61x488

61x732

Diameter =160mm

Diameter =61mm

Figure 5.3 - Pier Models Used in the Complex Pier Scour Tests

5.4. MEASURING EQUIPMENT

The ADV (Acoustic Doppler Velocimeter, Figure 5.5) uses acoustic techniques to measure the velocity in a remotely sensed volume so that the measured flow is undisturbed by the presence of the probe. An ADV with a velocity range of ±2.5m/s and a resolution of 0.1mm/s, was used to measure the velocity during the tests. The primary use of the ADV was to measure the vertical velocity profile along the water depth around

piers and contractions. The upstream mean depth velocity was the basic velocity recorded for the pier tests. For the contraction tests, the ADV was used to measure the velocity distribution along the centerline of the contracted channel at certain water depths before the scour started and after the scour stopped. In some tests, more extensive velocity measurements were conducted at specific locations. These included the corners of contraction abutments and rectangular piers.

(a) (b) (c) (d) (e)

(f) (g) (h) (i) (a, b, c- Contraction Width; a, d, e, f –transition angle, a, g, h, i-contraction length)

Figure 5.4 - Abutment Models for Contraction Scour Tests

U

V Flow Particle

Response Distance

50mm

Figure 5.5 – Diagram of the ADV

A point gage with a new design was used in this study. Without interrupting the experiments, it is used to measure the water surface elevation, the water depth and the change in scour depth. The point gage is designed based on the fact that air, water, and soil have different electrical conductivity. The point gage system forms a close circuit with a node in the soil or the water and the other one in the air. Once the point gage, which is a needle attached to a vertical ruler, touches the interface between water and air, or water and soil, there is a sudden conductivity change that can be easily read on a voltmeter. When the water is dirty, the maximum scour location can be searched point by point using the point gage. As shown in Figure 5.2, the point gage and ADV are installed in a hanging measurement cage riding on a carriage moving along the longitudinal direction of the flume. In the flume tests, it was found that the presence of piers or contraction abutments had almost no influence on the flow at a distance of one channel width upstream of the obstacle. Therefore the velocity and water depth were determined at this location for each test. In addition, a digital camera was used to record important phenomena during the tests. 5.5. SOILS AND SOIL BED PREPARATION A Porcelain clay was used as the primary soil; sands were also used in several tests for comparison purposes. The predominant mineral of this commercially available Porcelain clay is Kaolinite. Geotechnical tests were conducted according to ASTM standards. The geotechnical properties of the Porcelain clay determined at two different times are summarized in Table 5.1. Vane shear tests were conducted at 3 different locations around the future scour hole after the soil bed was prepared but before the experiment started; the average value is shown in the Table. The erosion properties of the Porcelain were tested by Cao (2001) in the EFA. Two samples were tested separately using tap water. The erosion rate vs. shear stress curve is shown in Figure 5.6. Gudavalli (1997) used three types of clays for his experiments: Porcelain, Armstone, and Bentonite. The properties of these clays are presented here because Gudavalli’s tests were the basis of the original SRICOS method and because these tests are used in this study as well. The geotechnical properties of these soils were measured according to ASTM standards and are given in Table 5.2. The erosion properties of the Porcelain clay were measured in the 0.45m-wide flume. The bed shear stress was varied from 0.118 Pa to 7.92 Pa by changing the flow velocity. The water depth was maintained constant during the experiments. Each test was conducted for a few hours. The bed shear stress was computed by Prandtl’s equation for the velocity versus depth profile obtained by ADV measurements very close to the soil bed. These experiments amounted to running a large scale EFA test. The relationship between erosion rate and shear stress is shown in Figure 5.7.

Table 5.1 - Geotechnical Properties of the Porcelain Clay.

Property Test 1 Test 2 1 Liquid Limit, % 40.23 37.7 2 Plastic Limit, % 19.17 14.4 3 Plastic Index (PI), % 21.06 23.3 4 Bulk Unit Weight ( )/ 3mKN 19.65 24.99 5 Water Content, % 27.35 30.5 6 Shear Strength, KPa 10.7 18.1

0

5

10

15

20

25

30

35

0 10 20 30 40 50Shear Stress (Pa)

Ero

sion

Rat

e (m

m/h

r)

Sample A

Sample B

Figure 5.6 – Erosion function for the Porcelain clay

Table 5.2 - Properties of the soils used in Gudavalli’s research (Gudavalli, 1997)

0

2

4

6

8

10

12

0 2 4 6 8 10Shear Stress (Pa)

Ero

sion

Rat

e(m

m/h

r)

Figure 5.7 – Erosion function for Gudavalli’s Porcelain clay.

S. No. Property Porcelain Armstone Bentonite 1 Liquid Limit, % 34.40 44.20 67.00 2 Plastic Limit, % 20.25 18.39 27.22 3 Plastic Index (PI), % 14.15 25.81 39.78 4 Specific Gravity 2.61 2.59 2.55 5 Water Content, % 28.51 26.18 39.28 6 Sand Content, % ------ 25(grog) ------ 7 Clay Content, % 100 75 100 8 Shear Strength, KPa 12.51 16.57 39.56 9 CEC, (meg/100g) 8.3 10.0 16.1

10 SAR 5.0 2.0 21.0 11 PH 6.0 5.2 8.5 12 Electrical Conductivity (mmhos/cm) 1.2 1.1 1.1 13 Bulk Unit Weight ( )/ 3mKN 18.0 17.89 17.45

The Porcelain Clay was delivered in blocks of 250mm x 180mm x 180mm. Each block was in a sealed bag. The clay was installed block by block in the soil tank, as shown in Figure 5.8. After the completion of one layer, kneading with a 20 lbs concrete block was used to minimize the voids and holes between blocks. The next layer was placed on top of the first one and so on. Once the soil tank was full, the soil surface was leveled by using a straight edge spatula. After each test, the excess water was pumped out, a zone of clay was removed around the scour hole until undisturbed clay was reached, and fresh porcelain clay was placed in the excavated portion. It was critical to remove all the soft film and dry out the excessive water on the old soil surface; otherwise, the old soil and the new soil could not stick tightly together and the new soil could be flushed away in lumps. This requirement was particularly important for the contraction scour tests.

Figure 5.8 – Placement of the clay in the soil tank

5.6. FLUME TESTS PROCEDURE AND MEASUREMENT Complex pier scour tests were conducted in the 1.5 m wide flume and all the tests were done according to the following procedure:

1. Soil bed preparation and pier installation; 2. Vane shear measurements; 3. Initial readings of the soil surface elevation around the piers; 4. Installation of the ADV; 5. Calculations of water volume in the flume and pump rate to get the expected

water depth and velocity; 6. Measurements of the velocity profile and water surface elevation; 7. Measurements of the scour depth at regular time intervals, 8. Empty water, record shape of scour hole and finish the test.

For each test, the primary measurements were the flow velocity, the water depth and the scour depth and the time. Water depth and flow velocity were determined in the middle of the channel 1.5m upstream of the piers. The depth average velocity was calculated from the measured vertical velocity profile and was used as one of the major parameters in the data analysis. The flow velocity was kept constant throughout the experiment. For the measurements of scour depth increment, the point gage was moved around the pier to find the location of maximum scour.

5.7. SHALLOW WATER EFFECT: FLUME TESTS RESULTS

It appears that when the water depth exceeds about 2 times the pier width, the maximum scour depth is practically independent of the water depth. When the water depth becomes shallower than that, there is a reduction in the maximum scour depth. This is attributed to the fact that, as the depth of the scour hole increases, the water looses its eroding energy faster in shallow waters than in deep waters. While extensive studies have been carried out on shallow water effects in sands, corresponding studies in clays are non existent. Gudavalli’s flume tests indicate that in cohesive soils the flow depth has no clear influence on the scour depth when H/B≥1.6 where H is the water depth and B the pier diameter. In this study, a series of pier scour tests with water depths ranging from H/B = 0.2 to H/B = 2.5 were conducted. The cylindrical piers had diameters equal to 273mm and 160mm and were installed in one of the 1.2m x 1.5m x 0.3m soil tanks filled with Porcelain clay. The tests parameters are presented in Table 5.3 and the measured curves of scour depth z(t) vs. time t are plotted in Figure 5.9 for the two different pier sizes. The flume tests were stopped after a time averaging about five days, and then a hyperbola was fitted to the scour depth versus time curve (Briaud et al., 1999, 2001). This technique gave an initial scour rate, iz , (initial slope of the hyperbola) and a maximum scour depth, Zmax, (asymptotic value). The values of the maximum scour depth, Zmax, and initial scour rate,

iz , are shown in Table 5.3.

In the case of very shallow water tests, it was observed that noticeable surface rolling formed due to the roughness of the streambed, which would probably affect the scour depth as mentioned by Ettema (1980). In addition, the velocity in this case becomes more difficult to measure and control due to the limitation of the response distance of the ADV.

Table 5.3 - Parameters and results for shallow water cases of pier scour

Test

No.

H

(mm)

B

(mm)

V

(m/s) H/B

Exp. Duration

(h) iz

(mm/hr)

Zmax

(mm)

Sh-1* 683.00 273.00 0.30 2.502 ----- ---- 112.94

Sh-2 546.00 273.00 0.30 2.000 515.75 1.06 129.62

Sh-3 258.00 273.00 0.30 0.945 262.33 1.57 79.37

Sh-4 137.00 273.00 0.30 0.502 237.42 1.39 57.80

Sh-5 60.00 273.00 0.30 0.220 164.08 1.71 81.30

Sh-6 60.00 273.00 0.30 0.220 111.03 4.49 61.35

Sh-7 25.80 273.00 0.30 0.095 30.50 38.91 35.59

Sh-8 400.00 160.00 0.40 2.500 191.33 1.50 76.92

Sh-9 320.00 160.00 0.40 2.000 129.67 1.82 109.67

Sh-10 170.00 160.00 0.40 1.063 117.17 1.98 77.73

Sh-11 85.00 160.00 0.40 0.531 64.50 2.62 53.48

*: The measured data for test Sh-1 is lost due to the malfunction of computer and Zmax is saved in previous summaries. 5.8. SHALLOW WATER EFFECT ON MAXIMUM PIER SCOUR DEPTH One way to present the data is to plot the relative scour depth Zmax/B vs. relative flow depth H/B (Figure 5.10). Figure 5.10 indicates that in clay much like in sand the relative scour depth, Zmax/B, increases with the relative water depth, H/B until a limiting H/B value. The shallow water correction factor, Kw, is defined as the ratio of the maximum scour depth under shallow water flow to the maximum scour depth under a reference condition where the water depth has no noticeable influence on the maximum scour depth. In this study, the scour depth under the deepest relative water depth, H/B=2.5, was selected as the reference. Therefore the average value of Zmax for test Sh-1 and Sh-8 in Table 5.3 was called Zmax(deep) and was used to normalize the values of Zmax. Figure 5.11 shows the values of Kw = Zmax / Zmax(deep) as a function of H/B.

(Pier: B=0.273m and V=0.3m/s)

0

10

20

30

40

50

60

70

80

0 100 200 300 400 500 600

Time(hr)

Scour Depth (m

)

Sh-2, H/B=2.000 Sh-3, H/B=0.945 Sh-4, H/B=0.502 Sh-5, H/B=0.220 Sh-6, H/B=0.220 Sh-7, H/B=0.095

(Pier: B=0.160m and V=0.4m/s)

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250 Time(hr)

Scour Depth (m

)

Sh-8, H/B=2.500

Sh-9, H/B=2.000

Sh-10, H/B=1.063

Sh-11, H/B=0.531

Figure 5.9 – Flume tests results for the shallow water cases

Zm ax/B = 0.3743(H/B)0.3661

R2 = 0.7517

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5 3.0

H/B

Zm

ax/B

Figure 5.10 - Influence of shallow water depth on maximum pier scour depth

Kw = 0.8493(H/B)0.3385

R2 = 0.7753

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0

H/B

Kw Test

Meville Equ(3.7)

Johnson 0.273/0.3, Equ(3.6A)

0.273/0.3 , Equ(3.6C)

Johnson, 0.16/0.4, Equ(3.6A)

0.16/0.4, Equ(3.6C)

Best Fit of Test

Figure 5.11 - Correction Factor for Shallow Water Effect on Maximum Pier Scour

Depth

In Figure 5.11, the correction factor Kw obtained in the current study on clay is compared with the correction factors recommended for cohesionless soils by Melville and Coleman (1999) and Johnson (1999). Johnson’s correction factor depends on both pier size and velocity, so the label “Johnson 0.273/0.3, Eq. (3.6A)” in the figure represents the correction factor for the condition of B=0.273m and V=0.3m/s following Johnson’s equation. Because Johnson did not provide an equation for very shallow flow, a straight line is used to connect the origin to the shallowest end of the Johnson curves in Figure 5.11. Note also that Johnson’s Kw factor is a correction factor for the HEC-18 equation while that equation already includes a water depth influence so a combined correction factor can be derived. These values correspond to the curves labeled “0.273/0.3, Eq. (3.6C)” and “0.160/0.4, Eq. (3.6C)” with H/B =2.5 as the reference cases for B=0.273m, V=0.3m/s and B=0.160, V=0.4m/s respectively. Figure 5.11 shows that the shallow water effect factor obtained in this study is close to the correction factors for cohesionless soils. By regression, the expression for the proposed cohesive soil correction factor Kw is:

62.1/

62.1/

1

85.034.0

>

<

=BH

BHBH

Kw (5.2)

5.9. SHALLOW WATER EFFECT ON INITIAL SHEAR STRESS For a given scour depth versus time curve, the initial scour rate is the initial slope of that curve. It can be obtained by fitting a hyperbola to the data. These are the rates shown in Table 5.3. The two groups of initial scour rates are plotted in Figure 5.12. Test Sh-8 gave a much higher initial scour rate than the other tests (11 mm/hr), so the large picture does not show its value but the inserted one does. It indicates that the initial scour rate tends to increase as the water depth decreases and that the increase becomes particularly significant when H/B< 0.5. The figure also shows that the scour rates for the larger pier (B=0.273m) are smaller than the rates for the smaller pier (B=0.160m). Since the initial scour rate is directly tied to the initial shear stress through the erosion function, it can be stated that the initial shear stress increases when the water depth decreases and decreases when the pier diameter increases. These trends are opposite to the trends for the maximum scour depth. This means that a pier in shallow water subjected to a constant velocity will scour faster at the beginning but will end up scouring to a shallower maximum depth than the same pier in deep water (Figure 5.13).

0

1

2

3

4

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0

H/B

Ero

sion

Rat

e (m

m/h

r)

V=0.3m/s, B=273mm

V=0.4m/s, B=160mm

0

2

4

6

8

10

12

0 1 2 3

H/B

Eros

ion

Rat

e (m

m/h

r)

Figure 5.12 – Initial scour rate as a function of water depth.

0

30

60

90

0 50 100 150 200 250Time (hr)

Sco

ur D

epth

(mm

)

ABC

For H/B, A>B>C

Figure 5.13 – Comparison between scour in shallow and deep waters

5.10. PIER SPACING EFFECT: FLUME TESTS RESULTS

Pier spacing effect refers to the interaction between piers when they are closely spaced. In this case, the pier scour depth could be increased due to two reasons: (1) the interaction and enhancement of horseshoe vortices at the base of the pier; (2) the acceleration of the flow due to the contraction caused by the piers. Pier spacing effect can be examined for two types of pier installation: (1) in a matrix and (2) in a line. The current study dealt with pier spacing effect when cylindrical piers are uniformly spaced and installed in a single row perpendicular to the flow. For these flume tests, the piers were 0.160m in diameter. The center-to-center distance, C, was called the pier spacing. A distance equal to one pier spacing was kept between the outmost pier and the wall of the flume. Due to the flume width, the maximum number of piers that could be installed was 4 and the corresponding minimum spacing ratio was C/B=1.88. The maximum pier spacing ratio was C/B=4.69 for a single pier. Raudkivi (1991) commented that when the pier spacing is larger than 4, the group pier effect is negligible. The parameters and results for the four pier spacing tests are summarized in Table 5.4. The initial scour rate and maximum scour depth were calculated in the same way as the shallow water cases. The measured scour curves are plotted in Figure 5.14. The maximum scour depth may happen either around the pier or at some intermediate location; its location was searched with the point gage system.

Table 5.4 - Parameters and Results for Pier Spacing Flume Tests

Test

No.

H

(mm)

B

(mm)

V

(m/s) C/B

Time

Lasting

(h)

iz

(mm/hr)

Zmax

(mm)

Gr-1 375.00 160.00 0.33 (1-pier) 4.69 165.00 2.33 165.56

Gr-2 375.00 160.00 0.33 (2-pier) 3.13 122.50 2.83 175.44

Gr-3 375.00 160.00 0.33 (3-pier) 2.34 144.08 5.24 204.08

Gr-4 375.00 160.00 0.33 (4-pier) 1.88 129.83 4.76 250.00

0

40

80

120

160

0 50 100 150 200Time(hr)

Sco

ur D

epth

(mm

)

1-pier, C/B=4.692-pier, C/B=3.133-pier, C/B=2.344-pier, C/B=1.88

Figure 5.14 - Scour Depth versus Time for the Pier Spacing Cases

5.11. PIER SPACING EFFECT ON MAXIMUM SCOUR DEPTH The pier spacing effect on the maximum pier scour depth can be incorporated in the general equation by using a correction factor, Ksp, equal to the ratio of the maximum scour depth of the line of piers over the maximum scour depth of the isolated pier. In this study, the single pier case was the case of the single pier in the 1.5 m wide flume. This case corresponds to a C/B ratio of 4.69 as mentioned previously. Figure 5.15 shows the correction factor. It is observed the difference of maximum scour depth between the single pier and a line of two piers is quite small, which gives some confidence in the use of the C/B ratio of 4.69 as the single pier case. The pier spacing effect obtained in this study for a Porcelain clay is compared on Figure 5.15 with existing recommendations for cohesionless soils. Elliot and Baker (1985) used oblong piers (46mm wide and 150mm long) in his tests on groups of piers. His pier spacing effect is more severe than the others possibly due to the aspect ratio of the piers used. Salim and Jones (1998) conducted flume tests on cylindrical and square piers installed in a matrix in the middle of the channel. Each pier in this group configuration is more affected by other piers than in the case of a single line of piers. This may be the reason why Jones correction factor is more severe than the one found in this study. The test conditions for Raudkivi’s experiments (1991) are very similar to the current study except that only two cylindrical piers were installed in the middle of the flume and the soil was sand. In his tests, the pier spacing effect was examined by varying the distance between the two piers

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

3 .5

4 .0

1 3 5 7

C /B

Ksp

A .J .R a ud k ivi

S te rling Jo ne sK e ith R . E llio t

V e lo c i ty ra tio

P ro je c tio n W id th

P ro je c tio n W id th(K w )M e a sure m e nt

Figure 5.15 - Correction Factor for Pier Spacing Effect

Several attempts were made to find a prediction equation. First, the single equivalent pier concept proposed by Sulim and Jones (1998) was used by adding the widths of all the piers in the row. This was done by using equation 5.1 with the equivalent width. The Ksp curve obtained in such a way is shown under the label “Projection Width” in Figure 5.15. That curve does not fit the measured data well (too conservative). Even after accounting for the water depth effect, the Ksp curve is still too high as shown under the label “ Projection Width (Kw)” in Figure 5.15. This indicates that the single equivalent pier model would overestimate the pier spacing effect at least for piers installed in a row. It was found that the ratio of the width of the channel without the piers over the unobstructed width of the channel with the piers fit the data quite well. This equation is shown in Figure 5.15 under the label “velocity ratio” because the velocity can also be estimated through that ratio. For example, if the flume width is B1, the approaching velocity V1, and there are n piers installed in a row with same diameter B, then the velocity with n piers can be estimated by: ( ) )1/(11 nBBBVVn −= , and the velocity ratio is: )1/(11/ nBBBVVn −= . The equation proposed for Ksp is:

( )nBBBK sp −

=1

1 (5.3)

5.12. PIER SPACING EFFECT ON INITIAL SCOUR RATE The initial scour rate for the pier spacing flume tests are presented in Table 5.4 and plotted in Figure 5.16 where C is the center to center distance and B the pier width. It shows that the initial scour rate tends to increase as the piers become more closely spaced. In summary, both the maximum pier scour depth and the initial scour rate will increase as the piers become more closely spaced. This means that curves such as the ones presented in Figure 5.17 can be expected.

2

3

4

5

6

1 2 3 4 5C /B

Initia

l Sco

ur R

ate

(mm

/hr)

Figure 5.16 - Initial Scour Rate for the Group Pier Tests

Figure 5.17 – Scour Curves for Groups of Piers in a Line

0

30

60

90

120

150

180

0 50 100 150 200Time (hr)

Sco

ur D

epth

(mm

)

ABC

For C/B, A>B>C

For C/B, A>B>C

5.13. PIER SHAPE EFFECT: FLUME TEST RESULTS The shape of a bridge pier can strongly affect the flow pattern around it. In this study, only rectangular piers were considered. Bridge piers are most often installed with the longer side parallel to the major flow direction; therefore, the length over width ratio, L/B, is kept greater than one for all piers in this study. The rectangular pier was installed with a zero degree attack angle in the middle of the soil tank. Major scour always occurred around the four corners of the rectangular pier but only the time history of the maximum scour depth was used in the analysis. The shapes of the scour holes for different rectangular piers were recorded and compared. In addition, cylindrical piers with a diameter equal to the width of the rectangular pier were used as the reference case. Parameters and major results for the flume tests for pier shape effect are summarized in Table 5.5. Again, the maximum scour depth and the initial scour rate were calculated in the same way as in the case of the other flume tests. The scour depth development curves are plotted in Figure 5.18.

Table 5.5 - Parameters and Results for Pier Shape Effect Flume Tests

Test

No.

H

(mm)

B

(mm)

V

(m/s) L/B

Time

Lasting

(h)

iz

(mm/hr)

Zmax

(mm)

Sp-1 375.00 61.00 0.33 Circular 151.92 1.45 68.03

Sp-2 375.00 61.00 0.33 1:1 129.50 5.00 73.53

Sp-3 375.00 61.00 0.33 4:1 124.42 2.05 72.99

Sp-4 375.00 61.00 0.33 8:1 131.58 1.93 74.63

Sp-5 375.00 61.00 0.33 12:1 131.50 1.84 75.19

5.14. PIER SHAPE EFFECT ON MAXIMUM SCOUR DEPTH The cylindrical pier test, SP-1, was chosen as the reference case. The correction factor, Ksp, is the ratio of the maximum scour depth for a given shape over the maximum scour depth for the cylinder (Figure 5.19). The results on Figure 5.19 indicate that there is no noticeable effect on scour depth due to the pier shape. Indeed the correction factor varies from 1:1 to 1:12. This conclusion is consistent with the correction factor for sand listed in HEC-18. Therefore, it is concluded that a pier shape correction factor of 1.1 is a good approximation for the maximum scour depth around rectangular piers in both clay and sand as long as the L/B ratio is larger than 1.The case of L/B smaller than 1 has not been covered in this research project.

0

10

20

30

40

50

60

70

0 50 100 150Time(hr)

Sco

ur D

epth

(mm

)

CircularSquareL/B=12L/B=8L/B=4

Figure 5.18 - Scour Depth versus Time Curves for Pier Shape Effect Tests

0.0

0 .4

0 .8

1 .2

1 .6

2 .0

0 5 10 15L/B

Ksh

HE C -18 , K s h= 1.1 fo r S quare Nos e

Figure 5.19 - Correction Factor for Pier Shape Effect

5.15. PIER SHAPE EFFECT ON INITIAL SCOUR RATE The initial scour rate for the flume tests on the rectangular piers having the same width but different lengths are compared in Figure 5.20. As can be seen, the rectangular piers consistently have larger initial scour rate than the cylindrical pier. The maximum value occurs for the square pier and the difference in rate decreases with the aspect ratio. Dietz (1972) found that the correction factor Ksh decreased from 1.5 to 1.1 when the L/B ratio increased from 1:1 to 5.

0

1

2

3

4

5

6

0 5 10 15L/B

Initi

al S

cour

Rat

e(m

m/h

r)

RectangularCircular

Figure 5.20 – Initial Scour rates for the Shape Effect Flume Tests 5.16. PIER SHAPE EFFECT ON PIER HOLE SHAPES The shape of the scour holes in Tests Sh-2, Sh-4 and Sh-5 are roughly reproduced in Figure 5.21. In that figure, the shadowed areas indicate the contours of the hole and the darker areas the deeper scour zones. It is observed that the relative size of the scour hole produced by the square pier is a much larger than in the other cases. Also in the case of the square pier the scour hole surrounds the entire pier. For piers with aspect ratios, L/B, greater than 4, the scour holes forms around the front face and the scour hole and scour behind the pier is negligible. Figure 5.22 summarizes these observations.

10cm 16cm

5cm3cm

8cm 11cm

10cm

Sh-2: 61mm x 61 mm Sh-4: 61mm x 488mm Sh-5: 61mm x 732mm

7cm 7cm

13cm

r=3cm6cm

Figure 5.21 – Shape of the Scour Hole for Different Aspect ratios.

0

10

20

30

40

50

60

70

80

0 50 100 150 200

T im e(hr)

Sco

ur D

epth

(mm

)

C irc u la rS quare124

Figure 5.22 – Scour Curves for Pier of Different Shapes.

5.17. ATTACK ANGLE EFFECT: FLUME TESTS RESULTS The attack angle α is the angle between the direction of the bridge pier and the direction of the flow. The attack angle effect for pier scour is actually a composite effect and more than one influencing factors are involved. For a given rectangular pier, both the pier shape confronted to the flow and the pier projection width will change with the angle of attack. In addition, due to the change of pier projection width with the attack angle, the water depth effect and pier spacing effect will be affected. To obtain the “pure” attack angle effect, a filtration process is necessary to eliminate the additional influences. When the attack angle effect is examined through rectangular piers, there are two influencing parameters for the pier: one is the attack angle α, the other is aspect ratio L/B. These two independent parameters form a parameter matrix of tests which need to be performed to find the general correction factor. Two perpendicular directions were selected to represent the whole matrix: In the transverse direction, the rectangular pier is kept at L/B = 4 and α is changed from 0° to 90°; in the longitudinal direction, α is kept constant as 45° and the aspect ratio of the pier changes. During the experiments, the scour depths around the four corners of the rectangular pier were measured to find the maximum scour depth. The scour hole shapes for all the cases were also recorded. Parameters and major results for the flume tests for the attack angle effect are summarized in Table 5.6. The scour depth versus time curves are plotted in Figure 5.23. The maximum scour depth and initial scour rate were obtained in the same way as before by using the hyperbola model.

Table 5.6. Parameters and Results for the Attack Angle Effect

Test No.

H (mm)

B (mm)

α (°)

V (m/s) L/B

Time Lasting(h)

iz (mm/hr)

Zmax (mm)

At-1 375.00 61.00 15 0.33 4:1 186.00 1.49 103.09 At-2 375.00 61.00 30 0.33 4:1 211.08 2.37 117.65 At-3 375.00 61.00 45 0.33 4:1 115.17 2.07 151.50 At-4 375.00 61.00 60 0.33 4:1 117.25 2.02 196.08 At-5 375.00 61.00 90 0.33 4:1 117.08 1.88 208.77 At-6 375.00 61.00 45 0.33 1:1 112.67 1.88 147.06 At-7 375.00 61.00 45 0.33 2:1 115.08 2.79 161.29 At-8 375.00 61.00 45 0.33 6:1 115.08 2.28 185.19

(A: Transvers Direction, L/B=4)

0

20

40

60

80

100

120

0 50 100 150 200 250Time (hr)

Sco

ur D

epth

(mm

)a=0a=15a=30a=45a=60a=90

(B: Vertical Direction, a=45)

0

20

40

60

80

100

120

0 50 100 150Time (hr)

Sco

ur D

epth

(mm

)

L/B=1

L/B=2

L/B=4

L/B=6

Figure 5.23 - Scour Depth versus Time Curves for Attack Angle Tests

(A: Transverse Direction, L/B=4)

5.18. ATTACK ANGLE EFFECT ON MAXIMUM SCOUR DEPTH The correction factor, Ka, to account for the attack angle effect on maximum pier scour depth is calculated as the ratio of the maximum scour depth for a given pier and a given attack angle over the maximum scour depth for the same pier and an attack angle equal to zero (reference case). For example, the reference case of test At-2 is Sp-3. If the reference case were not available such as for tests At-7 and At-8, interpolation between existing reference cases was used to calculate the maximum scour depth of the required reference case. The pier projection width, B’, as shown in Figure 5.24, is a widely accepted concept to evaluate the effect of the attack angle:

+=+= αααα cossincossin'

BLBBLB (5.4)

Common scour depth equations for 0° attack angle are of the form: Zmax= f Bn, where n is a constant. If the projection width is equivalent to the pier width, then the correction factor Ka can be calculated as:

n

a BL

ZZK

+== ααα cossin

)0()(

max

max (5.5)

The value of n generally varies from 0.6 to 0.9, and is equal to 0.635 in the SRICOS method for scour depth prediction in cohesive soils. In Figure 5.25, the correction factor obtained in the flume tests is shown together with other solutions using the projection width and with equation 22 in both the transverse and the longitudinal direction. The difference between Ka and Ka’ is linked to the influence of the water depth and pier spacing effect which occur when the angle of attack becomes more severe. In order to examine the pure attack angle effect, the shallow water effect and pier spacing effect need to be eliminated. The proposed equations for shallow water depth and pier spacing are used to isolate the angle of attack effect. The results of the calculations are shown in Table 5.7. The correction factor, Ka’, for pure attack angle effect on scour depth is obtained based on the following relationship:

'a w sp aK K K K= ⋅ ⋅ (5.6) Figure 5.25 shows that when the attack angle is less than 30o, the correction is not significant and that for angles of attack larger than 30o, the correction factor would be overestimated if the correction was not done. Figure 5.25 also shows that using the projection width with the SRICOS exponent of 0.635 leads to a reasonable and often conservative prediction of the correction factor Ka’. Therefore this approach is adopted for the proposed method.

A : Pier Projection W idth B: Flow Pattern and Corner Number

B ⋅cosα L ⋅sinα

B’

L

B

(4) (1) (3) (2)

α

Figure 5.24 – Skewed Pier Definitions

Figure 5.25 - Attack Angle Effect on Maximum Scour Depth

(A: Transverse Direction, L/B=4)

1.0

1.5

2.0

2.5

3.0

3.5

0 30 60 90

Acctack Angle (Degree)

Ka

Mostafa, n=0.8Laursen, n=0.68Richardson, n=0.65SRICOS, n=0.635Ka'Ka

(B: Vertical Direction, Attack Angle =45)

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 4 8 12L/B

Ka

Mostafa, n=0.8Laursen, n=0.68Richardson, n=0.65SRICOS, n=0.635Ka'Ka

Table 5.7 - Calculations for Isolating the Attack Angle Effect in Pier Scour Depth

α (˚) L/B B’

(mm) B’/B Zmax (mm)

Zmax(0)(mm) H/B’ Kw Ksp Ka Ka’

15 4:1 61.00 1.00 72.99 72.99 6.15 1.00 1.00 1.00 1.00 30 4:1 122.07 2.00 103.09 72.99 3.07 1.00 1.00 1.41 1.41 45 4:1 174.83 2.87 117.65 72.99 2.14 1.00 1.02 1.61 1.59 60 4:1 215.67 3.54 151.50 72.99 1.74 1.00 1.05 2.08 1.98 90 4:1 241.81 3.96 196.08 72.99 1.55 0.99 1.08 2.69 2.51 45 1:1 86.27 4.00 208.77 72.99 1.54 0.98 1.09 2.86 2.67 45 2:1 129.40 1.41 147.06 73.53 4.35 1.00 1.00 2.00 2.00 45 6:1 301.93 2.12 161.29 73.20 2.90 1.00 1.00 2.20 2.20

5.19. ATTACK ANGLE EFFECT ON INITIAL SCOUR RATE The initial scour rates for the attack angle flume tests are plotted in Figure 5.26 for both the transverse and vertical direction. In this case, the scour rates show a large scatter. This is because several opposing factors are involved in the initial shear stress or the initial scour rate under a given attack angle condition. Based on the observations in previous sections, the scour rate will decrease with an increase in pier width and flow depth, but increase with an increase in pier contraction and the sharpness of pier corners. Therefore, the relative magnitude of the scour rate under a given attack angle, depends on the balance between these influence factors.

(A: Transverl Direction, L/B=4)

1.0

1.5

2.0

2.5

3.0

0 30 60 90Attack Angle (Degree)

Initi

al R

ate

(mm

/hr)

(B: Vertical Direction, Attack Angle =45)

1.0

1.5

2.0

2.5

3.0

0 2 4 6L/B

Initi

al R

ate

(mm

/hr)

Figure 5.26 – initial Scour Rate for the Attack Angle Flume Tests.

5.20. ATTACK ANGLE EFFECT ON SCOUR HOLE SHAPE The attack angle also strongly affects the shape of the scour hole. If the 4 corners of the rectangular pier are numbered as in Figure 5.24, the location of the maximum scour depth will either happen at corner (1) or corner (3) from test observations. When the attack angle increases, the location of the maximum scour depth gradually moves from corner (1) to corner (3), and this transition is documented in Table 5.8. It is also observed that the scour hole in the tested cohesive soil (Figure 5.27) is much smaller than the scour hole in sands sketched by Raudkivi (1991).

Table 5.8 - Transition of the Location of Maximum Scour Depth

Figure 5.27 – Shape of Scour around a Skewed Pier in a Cohesive Soil (Left: Attack angle =15°, Right: Attack Angle=30°)

Attack Angle (°) Location of the maximum scour depth 0 (1), (4) 0<α<45 (1) 45 (1), (3) 45<α<90 (3) 90 (1), (2), (3), (4)

14cm

7cm

2.5cm

3cm

10cm8cm

6cm

5.5cm

6cm

(4) (4) (1) (1) (3) (3) (2) (2)

5.21. MAXIMUM SCOUR DEPTH EQUATION FOR COMPLEX PIER SCOUR In the previous sections, individual effects on the maximum pier scour depth are studied by flume testing. A series of figures and equations are given to quantify the corresponding correction factors. However, bridge piers are likely to exhibit a combination of these effects and recommendations are needed to combine these effects in the calculations. It is recommended that the correction factors be multiplied in order to represent the combined effect. This is a common approach which implies that the effects are independent, and has been used in many instances before (HEC-18, Melville (1997)).

635.0

max'18.0)(

⋅⋅⋅⋅=

vVBKKKmmZ shspw (5.7)

where: Zmax is the maximum depth of scour (mm), V is depth average velocity at the location of the pier if the pier or bridge was not there (m/s), B’ is the projection width of the pier (m), ν is the kinematic viscosity of water (10E-6 (m2/s) at 20˚C), Kw is correction factor for shallow water effect (equation 5.2), Ksp for pier spacing effect (equation 5.3), and Ksh for pier shape effect (1.1 for rectangular piers), B’ is the pier projection width (equation 5.4 for rectangular pier). Two complex pier flume tests were conducted with the configuration shown in Figure 5.28 where all the individual effects described in previous sections were expected to happen simultaneously. The main parameters and results are summarized in Table 5.9, and the time history of the scour development is plotted in Figure 5.29. The final maximum scour depth was obtained by the Hyperbola model.

(1) (1) 15° 15° (3) (3)

0.5m 0.5m 0.5m

(1) 45° (1) 45° (3) (3)

0.5m 0.5m 0.5m

Figure 5.28 – Configuration of the Flume Tests to Verify the Superposition Rule.

Table 5.9 - Parameters and Results for the Complex Pier Flume Tests

Test

No. H

(mm) V

(mm/s) L

(mm) B

(mm) C

(mm) α (˚)

Time (h)

Zmax (mm)

Cp-1 375 330 244 61 500 15 115.32 175.4

Cp-2 375 330 244 61 500 45 150.67 285.7

0

40

80

120

160

200

0 50 100 150 200

Time (Hr)

Sco

ur D

epth

(mm

)

CP-1CP-2

Figure 5.29 - Scour Development Curves for the Complex Pier Flume Tests. The maximum scour depths for the two tests were calculated according to equation 5.7. The calculations are detailed in Table 5.10 and the measured results are also listed at the bottom of that table. As can be seen (bottom of Table 5.10), the difference between the predictions and the measurements is remarkably small (less than 5%). This tends to indicate that the chosen superposition law works well for complex pier scour predictions.

Table 5.10 – Comparison between Calculated and Measured Maximum Pier Scour Depths

PARAMETERS Cp - 1 Cp - 2 CALCULATION NOTE Primary Inputs B (mm) 61 61 Pier Width L (mm) 244 244 Pier Length H (mm) 375 375 Water Depth α (˚) 15 45 Attack Angle V (mm/s) 330 330 Mean Approaching Velocity C (mm) 500 500 Center to center pier spacing Attack Angle Effect B' (mm) 122.07 215.67 Projection width following Equ.(5.4) Basic Scour Depth Z1 (mm) 151.19 217.01 SRICOS: simple pier Equ. (5.6) Water Depth H/B' 3.07 1.74 Kw 1.00 1.00 Shallow water effect, Equ(5.1) Contraction Effect C/B' 4.10 2.32 Ksp 1.0 1.233 Interpolated from FIG 5.7 Pier Shape Effect Ksh 1.1 1.1 Calculated from FIG 5.11 Composite Effect K 1.16 1.36 K= KwּKspּKsh Final Scour Depth Zcal(mm) 174.63 294.33 Zcal=KּZ1 Comparison Ztest (mm) 175.44 285.71 (Zcal-Ztest)/Ztest (%)

- 0.46 3.02

CHAPTER 6 THE SRICOS-EFA METHOD FOR INITIAL SCOUR RATE AT COMPLEX PIERS 6.1. GENERAL The initial scour rate is an integral part of the SRICOS method because it is one of the two fundamental parameters used to describe the scour depth versus time curve. The other one is the maximum depth of scour which was studied in Chapter 5. The initial rate of scour for a given complex pier scour problem is obtained by first calculating the maximum shear stress τmax existing around the pier before the scour hole develops (flat river bottom) and then reading the initial scour rate on the erosion function obtained in the EFA test. Therefore the problem of obtaining the initial rate of scour is brought back to the problem of obtaining the maximum shear stress around the pier before scour starts. This problem was solved by using numerical simulations and this chapter describes the simulations performed and the associated results. The goal was to develop correction factors for giving τmax for a cylindrical pier in deep water (equation 6.1)

−=

101

Relog1094.0 2

max vρτ (6.1)

These factors include the effects of shallow water depth, pier shape, pier spacing, and angle of attack. 6.2. EXISTING KNOWLEDGE ON NUMERICAL SIMULATIONS FOR SCOUR Hoffman and Booij (1993) applied the Duct-model and the Sustra-model to simulate the development of local scour holes behind the structure. The flow model Duct is based on a parabolic boundary-layer technique using the finite element method, and the SUSTRA model is used to compute the concentration field following the Van Rijn and Meijer’s (1986) approach. The computational model was compared to experimental data. The results (flow velocities, sediment concentration, and bed configurations as a function of time) showed an agreement between both of them. Olsen and Melaaen (1993) simulated scour around a cylinder by using SSIIM, a three-dimensional free-surface flow and transport model. The SSIIM model solves Reynold stresses by the ε−k turbulence model. The authors observed and reported that there is agreement between the pattern of the vortices in front of the cylinder and the model. The application of SSIIM model can be found at http://www.sintef.no/nhl/vass/vassdrag.html. Wei et al. (1997) performed a numerical simulation of the scour process in cohesive soils around cylindrical bridge piers. A multi-block Chimera RANS method was incorporated with a scour rate equation to simulate the scour processes. The scour rate equation linked the scour rate to the streambed shear stress through a linear function. The simulation

captured the important flow features such as the horseshoe vortex ahead of the pier and the flow recirculation behind the pier. A reasonable agreement was found between the progress of the scour depth obtained in the flume experiments and predicted by the numerical model. Wei found that the value of the critical shear stress has a significant influence on the scour process around a cylinder in cohesive soils. The final scour depth and the time necessary to reach it increase with decreasing critical shear stress. Based on a number of parametric runs, he also presented an empirical formula for the maximum streambed shear stress for a cylindrical pier in deep water. Dou (1997) simulated the development of scour holes around piers and abutments at bridge crossings. A stochastic turbulence closure model (Dou, 1980), which includes an isotropic turbulence, was incorporated into a three-dimensional flow model, CCHE3D, developed by the Center for Computational Hydroscience and Engineering at the University of Mississippi. The factors that reflect the secondary flow motion generated by the three-dimensional flow are adopted to modify the sediment transport capacity formula originally developed for estimating general scour. Dou’s study also includes some investigations on sediment incipient movement in local scour including some laboratory experiments. Roulund (2000) presents a comprehensive description on the flow around a circular pier and the development of the scour hole by numerical and experimental study. The numerical model solves the three-dimensional Reynolds averaged Navier-Stokes equations with use of the k-ε (SST) turbulence closure model. The method is based on a full three-dimensional bed load formulation including the effect of gravity. Based on the bed load calculation, the change in bed level with time is calculated from the equation of continuity for the sediments. For the experiments, a video tape was used to observe the scour development from a flat bed to the equilibrium of the scour hole. The evolution of the three-dimensional scour hole with time was obtained by combining the scour profiles from all angles around the pier. 6.3. NUMERICAL METHOD USED IN THIS STUDY In the present study, the three dimensional flow chimera RANS (Reynolds Averaged Navier Stokes) method of Chen et al (1993, 1995a,b,1997) is used. The computational domain is first divided into a number of smaller grid blocks, which allow complex configurations and flow conditions to be modeled efficiently through the judicious selection of different block topology, flow solvers and boundary conditions. The chimera domain decomposition technique was used to connect the overlapped grids together by interpolating information across the block boundaries. The Reynolds stresses were evaluated using two-layer turbulence model of Chen and Patel (1988). The mean flow and turbulence quantities were calculated using the finite-analytical method of Chen, Patel, and Ju (1990). The SIMPLER/PISO pressure-velocity coupling approach of Chen and Patel (1989) and Chen and Korpus (1993) was used to solve for the pressure field. A detailed description of the multiblock and chimera RANS methods is given in Chen and Korpus (1993) and Chen, Chen and Davis (1997). A useful summary of that method can be found in Nurtjahyo (2002). This summary discusses the governing equations including

turbulence modeling (Reynolds-Averaged Navier-Stokes or RANS equations), the boundary conditions on the pier surface, the river bottom, the outer boundaries, and the free water surface. The computer code has the ability to simulate the development of the scour hole around the pier as a function of time. This is done by including an erosion function linking the vertical erosion rate to the shear stress at the interface between the water and the soil. The program then steps into time by adjusting the mesh in the vertical direction after each time step as the scour hole develops. This option is not necessary to obtain the maximum shear stress before scour starts, since in this case the bottom of the river is kept flat. A typical run consists of the following steps:

1. Obtain the information for the problem: water depth, mean depth velocity at the inlet, pier size and pier shape.

2. Calculate the Reynolds Number and Froude Number because they influence the size and distribution of the grid elements.

3. Generate the grid using a program called GRIDGEN (about 4 days work). 4. The input consists of the Reynolds Number, the Froude Number, the boundary

conditions on all surfaces. The initial condition consists of the velocity profile at the inlet and is automatically generated by the program on the basis of the inlet mean depth velocity and the geometry.

5. Typical runs last 5 hours of CPU time on the Texas A&M University SGI supercomputer when only the bed shear stress is required. The CPU time increases to 20 hours when the scour hole development needs to be simulated.

6. The output consists of the following parameters in the three dimensions: velocity vectors, pressure, bed shear stress, and turbulent kinetic energy.

6.4. VERIFICATION OF THE NUMERICAL METHOD This verification was achieved by comparing the shear stresses predicted by the numerical method to those measured experimentally. The measurements were performed by Hjorth (1975) who investigated the distribution of shear stresses around a circular pier. The experiment was conducted in a rigid boundary flume. Two circular piers were used (diameter 0.05 m and 0.075 m). The study focused on two different velocities (0.15 m/s and 0.20 m/s) and two different depths of approach flow (0.1 m and 0.2 m). The shear stress was measured by using a stationary hot film probe through the bottom of the flume flush with the bottom, then moving the position of the cylinder around the fix probe. In that fashion, Hjorth obtained the shear stress at 35 different locations around the cylinder and created isostress lines by interpolation between the measurements. The numerical method was used to simulate the experiments performed by Hjorth. The output was the distribution of the shear stresses on the flume bottom around the cylinder. The result of the experiment and the numerical simulation for the 0.075 m cylinder are compared on Figures 6.1 and 6.2. The very favorable comparison gave confidence in the validity of the numerical results.

79 111

5

3

3

X/B-1 -0.5 0 0.5

Flow

τ=

(b) Numerical

Figure 6.1 - Comparison of bed shear stress (N/m2) distribution around a circular pier between an experiment by Hjorth (1975) and numerical computations (B=0.075 m, V=0.15 m/s, H=0.1 m)

(a) Experiment (Hjorth, 1975)

τ=

3

5

79

11 1

3

X/B-1 -0.5 0 0.5

Flow

τ=

(b) Numerical

Figure 6.2 - Comparison of bed shear stress (N/m2) distribution around a circular pier between an experiment by Hjorth (1975) and numerical computations (B=0.075 m, V=0.30 m/s, H=0.2 m)

(a) Experiment (Hjorth, 1975)

τ=

6.5. SHALLOW WATER EFFECT: NUMERICAL SIMULATION RESULTS

The objective of this parametric study is to obtain the relationship between the maximum bed shear stress τmax and water depth (Figure 6.3).

Figure 6.3 - Problem definition for water depth effect

One of the flume experiments was chosen to perform the simulation. The cylindrical pier has a diameter equal to 0.273 m was placed vertically in a 1.5 m wide flume. The velocity is constant at 0.3 m/s and four different water depths are simulated: H = 0.546 m (or H/B=2), H = 0.258 m (or H/B=0.95), H = 0.137 m (or H/B=0.5), and H = 0.060 m (or H/B=0.22). The value of Reynolds number based on the diameter is Re=81900 and the Froude number based on the diameter is Fr=0.1833. In order to reduce the amount of CPU time, a half domain is chosen due to symmetric. The grid is divided into 4 blocks as shown in figure 6.4.

Block # 4

Block # 2Block # 1 Block # 3

Figure 6.4. Grid System for the Numerical Simulation

H

B

Flow

The grid is very fine near the pier and riverbed in order to apply the two-layer approach of the turbulence model. A few grid layers are placed within the viscous sub-layer. The first step is to verify that the inlet velocity profile for the numerical simulation matches the experiment. The result is shown in Figure 6.5. In the experiment, the thickness of boundary layer is about 0.06 m for all cases. This observation is also found in Gudavalli’s experiments (1997). The velocity vector around the pier is shown in Figure 6.6 for a shallow-water case and a deep-water case. The difference in velocity field can be observed on the figure especially near the base of the pier where the horseshoe vortex is much stronger in the shallow water case.

Figure 6.5. Velocity Profile Comparison between Experiment and Numerical

Simulation at the Inlet Figure 6.7 and 6.8 show the distribution of shear stress around the pier for different relative water depth equal to H/B = 0.2 and H/B = 2. As can be seen on the figures, the shear stress is higher in the case of the shallow water depth. This is explained as follows. When the water is deep, the velocity profile has the conventional shape shown in Figure 6.5. When the water depth becomes shallow and if the mean depth velocity is kept constant, the velocity profile must curve faster towards the bottom of the profile because of the lack in vertical distance forced by the shallow water condition. This leads to a higher gradient of velocity near the bottom and therefore to a higher shear stress τ since τ is proportional to the velocity gradient. Johnson and Jones (1992) made similar observations on the influence of the pier diameter on the bed shear stress; these observations were based on experiments. Figure 6.9 shows the pressure field induced by the pier. If the pressure field is sufficiently strong, it causes a three-dimensional separation of the boundary layer which in turn rolls up ahead of the pier to form the horseshoe vortex system. A blunt nosed pier, for example, is a pier for which the induced pressure field is sufficiently strong to form the horseshoe vortex system.

0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5

V e lo c ity (m /s )

Dep

th (m

)

F A N SE x p e r im e n t y /D = 2E x p e r im e n t y /D = 1E x p e r im e n t y /D = 0 .5

X

Y

Z

(a). H/B=0.2

X

Y

Z

(b). H/B=2

Figure 6.6 - Velocity vector around pier for (a) H/B=0.2 and (b) H/B=2

Figure 6.7 - Initial Bed Shear Stress Distribution (N/m2) around the Pier (H/B=0.2, V=0.3m/s)

Figure 6.8 - Initial Bed Shear Stress Distribution (N/m2) around the Pier (H/B=2, V=0.3m/s)

4.977.33

0.25

X/B-1 -0.5 0 0.5 1

Flow

0.56 1.03

2.21

0.78

τ =

0.25

0.350.45

0.55

0.650.75

1.05

0.85

0.25

X/B-1 -0.5 0 0.5 1

Flow

τ =

Figure 6.9. Normalized Pressure (p/ρu2) Contours for H/B=2 on the Riverbed

6.6. SHALLOW WATER EEFECT ON MAXIMUM SHEAR STRESS

The maximum shear stress τmax is the maximum shear stress that exists on the river bed just before the scour hole starts to develop. One way to present the data is to plot τmax/τmax(deep) as a function of H/B (Figure 6.10). The parameter τmax(deep) is the value of τmax for the deep water case and is given by equation 6.1. The shallow water correction factor, kw, is the ratio τmax/τmax(deep). The data points on Figure 6.10 correspond to the results of the four numerical simulations. By regression, the equation proposed for the correction factor kw giving the influence of the water depth on the maximum shear stress is:

( )deepττkw

max

max= BH

e4

161−

+= (6.2)

0.160.23

0.09

0.36

-0.37

-0.37 -0.30

-0.43

-0.43

X/D

Y/D

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Pier

Flow

0

1

2

3

4

5

6

7

8

9

0 0.5 1 1.5 2 2.5

H/B

k w

H

B

Figure 6.10 - Relationship between kw ( = τmax/τmax(deep)) and H/B

6.7. PIER SPACING EFFECT: NUMERICAL SIMULATION RESULTS The objective of this parametric study is to obtain the relationship between the maximum bed shear stress τmax and pier spacing (Figure 6.11).

Figure 6.11 - Problem Definition of Pier Spacing Effect.

One of the flume experiments is chosen to perform the numerical simulation. The cylindrical pier has a diameter of 0.16 meter and is placed vertically in a 1.5 meter wide flume. The mean depth approach velocity is 0.33 m/s and the water depth is 0.375 meter. Four different pier spacings are simulated: S/B=6 (in the case of one pile in the flume),

Flow

B

S

S/B=3.12 (in the case of 2 piles), S/B=2.34 (in the case of 3 piles), and S/B=1.88 (in the case of 4 piles). The Reynolds number based on diameter is Re=52800 and the Froude number based on diameter is Fr=0.2634. The velocity between the piles becomes higher due to the decreased spacing and the corresponding shear stress increases. Figures 6.12 and 6.13 show the shear stress distribution for S/B=1.88 and for S/B=6.

0.30

0.47

0.64 0.81

0.98

1.14

1.82

0.98 0.81 0.64 0.47

0.301.31

1.48

X/B

Y/B

-0.5 0 0.50

0.2

0.4

0.6

0.8

1

Flow

Figure 6.12 - Initial Bed Shear Stress Distribution (N/m2) around the Pier (S/B=1.88, H=0.38m, V=0.33m/s)

0.300.40

0.49

0.59 0.69

0.78

0.881.17

X/B

Y/B

-0.5 0 0.50

0.2

0.4

0.6

0.8

1

Figure 6.13 - Initial Bed Shear Stress Distribution (N/m2) around the Pier (S/B=6,

H=0.38m, V=0.33m/s)

Flow

τ =

τ =

6.8. PIER SPACING EFFECT ON MAXIMUM SHEAR STRESS The maximum shear stress τmax is the maximum shear stress that exists on the river bed just before the scour hole starts to develop. One way to present the data is to plot τmax/τmax(single) as a function of S/B (Figure 6.10). The parameter τmax(single) is the value of τmax for the case of a single pier in deep water and is given by equation 6.1. The pier spacing correction factor, ksp, is the ratio τmax/τmax(single). The data points on Figure 6.14 correspond to the results of the four numerical simulations. By regression, the equation proposed for the correction factor ksp giving the influence of the pier spacing on the maximum shear stress is:

( )singlemax

max

ττ

=spk BS

e1.1

51−

+= . (6.3)

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

0 1 2 3 4 5 6 7

S/B

k spB

S

Flow

Figure 6.14 - Relationship between ksp ( = τmax/τmax(single)) and S/B for deep water H/B>2)

6.9. PIER SHAPE EFFECT: NUMERICAL SIMULATION RESULTS The objective of this parametric study is to obtain the relationship between the maximum bed shear stress τmax and the shape of rectangular piers (Figure 6.15). One of the flume experiments is chosen to perform the numerical simulation. A rectangular pier with a width of 0.061 meter was placed vertically in the 1.5 m wide flume. The velocity was constant and equal to 0.33 m/s and the water depth was 0.375 m. Four different pier aspect ratios were simulated: L/B=1, 4, 8, 12. The value of Reynolds number based on the width of the rectangular pier is Re=20130 and Froude number based on the width of the rectangular pier is Fr=0.4267.

Flow L

B

Figure 6.15 - Problem Definition for the Shape Effect

Examples of velocity fields are presented in Figures 6.16 and 6.17 for rectangular piers with aspect ratios equal to 0.25 and 4. Figures 6.18 to 6.19 show the maximum bed shear stress contours around rectangular piers with different aspect ratios: L/B=0.25, 1, and 4. The location of the maximum bed shear stress is at the front corner of the rectangle. It is found that the maximum bed shear stress, τmax, is nearly constant for any aspect ratio above one. The value of τmax increases however when L/B becomes less than one. Figure 6.16 and 6.17 indicate that the flow pattern around the rectangular pier for L/B=0.25 is quite different from the pattern for L/B=4 where the flow is separating at the sharp corner. For L/B=0.25 the flow is allowed to go behind the pier while the flow for L/B=4 follows the side of the pier. In the case of L/B=4, the length of the flow separation is about 1 B from the corner; this may explain that τmax is independent of the pier length for L/B>1. On the contrary, for L/B<1, there is no region of separated flow and the decreasing pressure behind the pile may increase the velocity around the corner.

X/B

Y/B

-1 -0.5 0 0.5 1 1.5

-1

-0.5

0

0.5

1

X/B

Y/B

-1 -0.5 0 0.5 1 1.5-1

-0.5

0

0.5

1

Figure 6.16 – Velocity Field Around Figure 6.17 – Velocity Field Around a Rectangular Pier with L/B = 0.25 a Rectangular Pier with L/B = 4

0.33

0.33

0.67

1.00

1.34

1.68

2.350.33

0.33 0.33

0.33

X/BY

/B-1 -0.5 0 0.5 1 1.5

0

0.5

1

1.5

2

5.10

Figure 6.18 - Bed shear stress contours (N/m2) around a rectangular pier (L/B=0.25)

0.330.33

0.47

0.74

0.881.15

1.34

1.56 0.33

0.33

0.33

0.33

X/B

Y/B

-1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Flow

Figure 6.19 - Bed shear stress contours (N/m2) around a rectangular pier (L/B=1)

0.33

0.42

0.51

0.59 0.68

0.77

0.951.12

1.30

1.56

0.330.33

X/B

Y/B

-1 -0.5 0 0.5 1 1.50

0.5

1

1.5

2

Flow

Figure 6.20 - Bed shear stress contours (N/m2) around a rectangular pier (L/B=4)

Flow

Flow

τ =

τ =

τ =

6.10. PIER SHAPE EEFECT ON MAXIMUM SHEAR STRESS The maximum shear stress τmax is the maximum shear stress that exists on the riverbed just before the scour hole starts to develop. One way to present the data is to plot ksh = τmax/τmax(circle) as a function of L/B (Figure 6.21). The parameter τmax(circle) is the value of τmax for the case of a circular pier in deep water and is given by equation 6.1. The pier spacing correction factor, ksh, is the ratio τmax/τmax(circle). The data points on Figure 6.21 correspond to the results of the seven numerical simulations. The correction factor for shape effect, ksh is given by the following equation which was obtained by regression of the data points on Figure 6.21.

BL

sh ek4

715.1−

+= (6.4)

00.5

11.5

22.5

33.5

44.5

5

0 1 2 3 4 5 6 7 8 9 10 11 12

L/B

k sh

FlowL

B

BL

sh ek4

715.1−

+=

Figure 6.21 - Relationship between ksh ( = τmax/τmax(circle)) and L/B for deep water (H/B>2) 6.11. ATTACK ANGLE EFFECT: NUMERICAL SIMULATION RESULTS The objective of this parametric study is to obtain the relationship between the maximum bed shear stress τmax and the angle of attack α defined as the angle between the flow direction and the pier direction (Figure 6.22). One of the flume experiments is chosen to perform the numerical simulation. A rectangular pier with a width of 0.061 m was placed vertically in a 1.5 m wide flume. The velocity was 0.33 m/s, the aspect ratio of the pier was L/B=4 and the water depth 0.375 m. Four different attack angles were investigated: α = 15, 30, 45, 90 degrees. Based on this data, the value of Reynolds number based on the width of the rectangular pier is Re=20130 and the Froude number based on the width of the rectangular pier is Fr=0.4267.

Figure 6.22 – Definition of the Angle of Attack Problem

The bed shear stress distributions for attack angle 15, 30 and 45 degrees are shown in Figure 6.23 to 6.25. These figures indicate that the value of the maximum bed shear stress tends to increase with the attack angle. They also show that the location of the maximum shear stress moves backward along the side of the pier as the attack angle increases.

6.12. ATTACK ANGLE EEFECT ON MAXIMUM SHEAR STRESS The maximum shear stress τmax is the maximum shear stress that exists on the riverbed just before the scour hole starts to develop. One way to present the data is to plot τmax/τmax(0 degree) as a function of α (Figure 6.26). The parameter τmax(0 degree) is the value of τmax for the case of a pier in line with the flow in deep water and is given by equation 6.1. The attack angle correction factor, ksh, is the ratio τmax/τmax(0 degree). The data points on Figure 6.21 correspond to the results of the five numerical simulations. By regression, the equation proposed for the correction factor ka giving the influence of the attack angle on the maximum bed shear stress is:

( )deg0max

max

ττ

=ak57.0

905.11

+=

α (6.5)

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1 1.2

α/90

k α Flow

L

B

α

57.0

905.11

+=

αak

Figure 6.26 - Relationship between ka ( = τmax/τmax(0 degree)) and α for deep water (H/B>2)

Flow L

B

α

1.361.05

1.55

1.882.11

1.55

1.36

1.05

2.26

1.88

X/B

Y/B

-2 -1 0 1 2 3 4 5 6-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Pier

Flow

Figure 6.23 - Bed Shear Stress (N/m2) Contours for an Attack Angle Equal to 15 degree

0.93

1.11

1.47

0.931.29 1.65

2.00

0.24

0.75

0.75

0.93

1.29

1.832.36

0.24

0.93

2.90

X/B

Y/B

-2 -1 0 1 2 3 4 5 6-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Figure 6.24 - Bed Shear Stress (N/m2) Contours for Attack Angle Equal to 30 degree

3.273.002.52

2.32

2.03

1.611.331.08

0.33

1.08 1.33

1.61 2.52

2.03

0.33

1.33

0.33

0.33

2.52

X/B

Y/B

-2 -1 0 1 2 3 4 5 6-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Pier

Figure 6.25 - Bed Shear Stress (N/m2) Contours for an Attack Angle Equal to 45 degree

τ =

τ =

τ =

Flow

Flow

6.13. MAXIMUM SHEAR STRESS EQUATION FOR COMPLEX PIER SCOUR In the previous sections, individual effects on the maximum shear stress are studied by numerical simulations. A series of figures and equations are given to quantify the corresponding correction factors. However, bridge piers are likely to exhibit a combination of these effects and recommendations are needed to combine these effects in the calculations. It is recommended that the correction factors be multiplied in order to represent the combined effect. This is a common approach which implies that the effects are independent, and has been used in many instances. The proposed equation for calculating the maximum shear stress for a complex pier before the scour process start is

−×=

101

Relog1094.0 2

max Vkkkk ashspw ρτ (6.6)

where • B is the pier width (m), • H is the water depth (m) • V is the upstream velocity (m/s) • ρ is the density of water (kg/m3) • α is the attack angle (in degree)

• Re is the Reynolds number, defined as v

VB=Re

• ν is the kinematic viscosity (m2/s) • wk is the correction factor for the effect of water depth, defined as

( )deepττkw

max

max= . The equation is BH

w ek4

161−

+= .

• spk is the correction factor for the effect of pier spacing, defined as

( )singlemax

max

ττ

=spk . The equation is BS

sp ek1.1

51−

+= .

• shk is the correction factor for the effect of pier shape, defined as

( )circleksh

max

max

ττ

= . The equation is BL

sh ek4

715.1−

+= .

• 1=shk for circular shape. • ak is the correction factor for the effect of attack angle, defined as

( )deg0max

max

ττ

=ak . The equation is 57.0

905.11

+=

αak .

CHAPTER 7 THE SRICOS-EFA METHOD FOR MAXIMUM CONTRACTION SCOUR DEPTH 7.1. EXISTING KNOWLEDGE Contraction scour refers to the lowering of the river bottom due to the narrowing of the flow opening between two abutments or between two bridge piers. In cohesionless soils equations are recommended by HEC-18 (1995) for live bed and clear water contraction scour depths. These equations involve one soil parameters: the mean grain size. The studies on cohesionless soils include those of Straub (1934), Laursen (1960, 1963), Komura (1966), Gill (1981), Lim (1998), Chang (1998), and Smith (1967). For cohesive soils, two methods were found in the literature: Chang and Davis, and Ivarson. They both are empirically based and do not have a time nor stratigraphy component. The studies on contraction scour in cohesive soils are even fewer in numbers than the studies on pier scour in cohesive soils. Chang and Davis (1998) proposed a method to predict clear water contraction scour at bridges. They assume that the maximum scour depth is reached when the critical flow velocity for the bed material is equal to the average velocity of the flow. The critical velocity is defined as the velocity which causes the incipient motion of the bed particles. The method makes use of Neill’s (1973) competent velocity concept which is tied to the mean grain size D50. A series of equations to predict the total depth of flow including the maximum contraction scour depths are proposed. They involve two parameters: the unit discharge at the contraction and the mean grain size. Ivarson et al. (1996) (cited from Ivarson, 1998) developed an equation to predict contraction scour for cohesive soils based on Laursen’s non-cohesive soils contraction scour equation. They set the shear stress in the contracted section equal to the critical shear stress at incipient motion. For cohesive soils, they use the relationship between critical shear stress and unconfined compressive strength (Flaxman, 1963). They propose an equation which includes the following parameters: the undrained shear strength of the soil, the water depth in the approach uncontracted channel, the discharge per unit width in the contracted channel, and Manning’s coefficient in the contracted channel. 7.2. GENERAL This chapter addresses the problem of contraction scour (Figure 7.1). When contraction of the flow occurs and if the bed shear stress exceeds the critical shear stress of the cohesive soils, contraction scour develops and the contraction scour profile looks like the

one shown on Figure 7.1. This profile identifies two separate scour depths: the maximum contraction scour depth zmax which occurs xmax after the beginning of the start of the contracted channel and the uniform scour depth zunif which occurs after that.

H1 V 1

Zma

ZuniXma

V2

L

q

B2 B 1

Turbulence (A

(B

Figure 7.1 - Concepts and Definitions in Contraction Scour. In this chapter a series of flume tests are performed to develop equations to predict the values of zmax, xmax, and zunif in cohesive soils. One of the input is the mean depth velocity of the water. The velocity which controls the contraction scour is the velocity V2 in the contracted channel; this velocity can be estimated by using the velocity in the uncontracted channel and the contraction ratio B2/B1 or by using a program such as HECRAS to obtain V2 directly. These two approaches are developed in the analysis of the flume tests. In the following chapter the contraction scour rate issue is addressed through numerical simulation to obtain the initial shear stress before scour starts. 7.3. FLUME TESTS AND MEASUREMENTS The flume used for the contraction tests was the 0.45 m wide flume because initial tests in the 1.5 m wide flume lead to very large amounts of soil lost. The budget and the schedule did not allow to use such large quantities of soil. The parameters influencing the contraction scour are the mean depth approach velocity V1, the contraction ratio B2/B1, the approach water depth H1, the contraction or abutment transition angle θ, the contraction length L and the soil properties. In this research, a Porcelain clay, as described in Chapter 4, was used for all flume tests and the erosion function of the clay has been described previously in Section 5.5 and Figure 5.6.

The most important parameters are considered to be V1, B2/B1, and H1.and lead to the main part of the equation. The influence of the transition angle θ and the contraction length L are incorporated through correction factors. Therefore the tentative form of the equation to predict the contraction depth Z (Zmax or Zunif) is:

21 1

1

, ,LBZ K K f V HBθ

=

(7.1)

Where, θK and LK are the correction factors for transition angle and contraction length respectively. Based on the above analysis, the flume tests were divided into two parts: the tests run to obtain the function f(V1, B2/B1, H1) called primary tests and the tests run for the correction factors Kθ and KL called secondary tests The contraction geometries were shown in Section 5.3 and in Figure 5.4. The parameters for the tests performed are listed in Table 7.1 (primary tests) and 7.2 (secondary tests). There are 7 primary tests where the contraction scour is generated in a long contracted channel with a 90° transition angle. Among them, the contraction ratio is varied in Tests 1, 2 and 3; the water depth is varied in Tests 4, 5 and 6; and the velocity is varied in Tests 2, 6 and 7. There are two groups of secondary tests: Tests 9,10,11, and Test 2 are for the transition angle effect on contraction scour, and Test 12.13,14 together with Test 2 are for the contraction length effect on contraction scour.

Table 7.1 - Parameters and Results for the Primary Contraction Scour Tests

Test No.

V1 (before) (cm/s)

V1 (after) (cm/s)

V (Hec) (cm/s)

B2/B1 H1

(before)(mm)

H1 (after)(mm)

H (Hec)(mm)

θ(°) L/B1

Zmax (mm)

Zunif (mm)

Xmax(mm)

1 13.8 34.1 103 0.25 297 164.77 170 90 2.932 357.143 227.273 80 2 29 31 67 0.5 171.15 162.03 150 90 3.868 116.279 70.423 285 3 45 45.9 79 0.75 121.6 106.4 100 90 3.38 72.993 47.847 620 4 20.5 20.5 53 0.5 108.2 108.22 100 90 3.38 28.653 11.862 210 5 20.5 20.7 41 0.5 251.4 251.4 240 90 3.38 37.736 19.881 210 6 20.5 20.5 46 0.5 171.76 171.76 160 90 3.38 36.101 13.021 210 7 39 39 84 0.5 174.19 174.19 160 90 3.38 142.857 142.857 210

Table 7.2 - Parameters and Results for the Secondary Contraction Scour Tests

Test No.

V1 (before) (cm/s)

V1 (after) (cm/s)

V (Hec) (cm/s)

B2/B1 H1

(before)(mm)

H1 (after)(mm)

H (Hec)(mm)

θ(°) L/B1

Zmax (mm)

Zunif (mm)

Xmax(mm)

2 29 31 67 0.5 171.15 162.03 150 90 3.868 116.279 70.423 285 9 30 30.2 68 0.5 161 160.21 150 15 3.868 90.909 ----- 785 10 30 30.2 78 0.5 153.6 152 110 45 3.38 128.205 95.234 385 11 30 29.3 69 0.5 166.59 163.25 150 60 3.38 80 41.322 785 12 29 33 75 0.5 172.37 160.5 130 90 0.844 111.11 ----- 85 13 29.2 33 72 0.5 170.54 162.34 140 90 0.25 128.21 ----- 152 14 29.2 34.1 70 0.5 180 164.77 140 90 0.125 208.33 ----- 385

The following measurements were carried out for each flume test: 1. Initial velocity distribution by ADV (Acoustic Doppler Velocimeter): vertical

velocity profile in the middle of the channel at a location of 1.2 m upstream of the contraction, and the longitudinal profile along the centerline of the channel;

2. Initial water surface elevation along the centerline of the channel using the point gage;

3. Contraction scour profile along the centerline of the bottom of the channel, as a function of time, using the point gage;

4. Two abutment scour measurements, as a function of time, using the point gage; 5. Final longitudinal velocity profile along the channel centerline, using the ADV; 6. Final water surface elevation along the channel centerline, using the point gage; 7. Photos of the final scour hole shape, using the digital camera.

7.4. FLUME TESTS: FLOW OBSERVATIONS AND RESULTS The water surface profiles along the channel centerline at the beginning and at the end of Test 2 are plotted in Figure 7.2. The approaching flow of Test 2 is in the subcritical flow regime (all tests were subcritical except Test 1 which was supercritical at the beginning of the test); as a result, there is a drop in water surface elevation in the contracted section. This difference decreases as contraction scour develops. When the equilibrium scour depth profile is reached, the water surface elevation in the contracted section can be considered as level with the water surface elevation in the approach channel. This observation is also mentioned by other researchers (Laursen 1960, Komura 1966). As a result, the contraction scour depth can be simply calculated by subtracting the upstream water depth H1 from the total water depth in the contraction section H2. At equilibrium contraction scour, the contraction scour depth is:

12max )( HequiHZ −= (7.2) In the final profile of the water surface elevation, it is also noticed that the upstream water surface gradually lowers to the downstream water surface. In other words the equilibrium water surface elevation is intermediate between the initial upstream and downstream elevations. The longitudinal velocity profiles along the channel centerline at the beginning and at the end of Test 2 are presented in Figure 7.3. The velocity was measured at a depth of 0.4 H from the water surface with the ADV. As expected, the velocity increases in the contracted channel since the water elevation decreases. As contraction scour deepens, the difference decreases but does not become zero. Instead it was observed that the final value of the velocity in the contracted channel reached the same approximate value for all flume tests on the Porcelain clay. This tends to indicate that contraction scour stops at the critical velocity in the contracted channel no mater what the contraction geometry is.

cVequiV =)(2 (7.3)

0

60

120

180

-1000 -500 0 500 1000 1500X(mm)

Wat

er S

urfa

ce E

leva

tion

(mm

)

BeforeAfterHEC-RAS

Figure 7.2 - Water Surface Elevations along the Channel Centerline in Test 2

0

30

60

90

-1000 -500 0 500 1000 1500

X(mm)

Vel

ocity

(cm

/s)

BeforeAfterHEC-RAS

Figure 7.3 - Velocity Distribution along the Channel Centerline in Test 2

It is also observed that the highest velocity and the lowest water surface elevation in the contracted channel happen at the same approximate location behind the contraction inlet, but this location is different from the maximum contraction scour location as described later. HEC-RAS (Hydraulic Engineering Circular – River Analysis System, 1997) is a widely used program in open channel analysis. It was used with the flume cross section profiles before scour started to predict the quantities measured during the tests. The HEC-RAS outputs are listed in Tables 7.1 and 7.2 and compared with the measured water surface elevation and velocity profiles in Figures 7.2 and 7.3. It is found that HEC-RAS leads to relatively constant values of the water surface elevation and velocity before and after the contraction which is a significant simplification of the measured behavior. It is also noted that the maximum velocity predicted by HEC-RAS in the contracted channel is less than the measured value 7.5. FLUME TESTS: SCOUR OBSERVATIONS AND RESULTS An example of the measurement results is shown in Figure 7.4 for Test 1. Figure 7.5 shows a sketch of the contraction distribution in plan view. The measurement emphasis was placed on obtaining 4 parameters at the equilibrium contraction scour: the maximum contraction scour depth Zmax, the uniform contraction scour depth Zunif, the location of the maximum contraction scour Xmax, and the contraction profile along the channel centerline. The maximum and uniform contraction scour depths at equilibrium are listed in Table 7.1 and 7.2. These values were obtained by fitting the scour depth versus time curve with a hyperbola and using the ordinate of the asymptote as the equilibrium value. The fit between the measured data and the hyperbola was very good as shown on Figure 7.6 and 7.7 for Zmax and Zunif in Test 1. The R2 values were consistently higher than 0.99. The results of tests involving the transition angle and the length of the contraction are shown on Figures 7.8 and 7.9 while Figure 7.10 regroups all the measurements taken for the primary tests (Table 7.1). For the uniform contraction scour depth, the average value of the last four points (over a 0.4 m span) in the contraction scour depth profile was used as the uniform scour value. In addition, it should be noted that for short contraction lengths (Tests 13 and 14), a fully developed uniform contraction did not exist. The location of the maximum contraction scour, Xmax, is measured from the beginning of the fully contracted section. It can be seen that Xmax oscillates at beginning of the test but becomes fixed in the late stages. This value was chosen for Xmax and is the one shown in Tables 7.1 and 7.2. An important observation was noted during the tests: the abutment scour never added itself to the contraction scour. In fact the abutment scour and the contraction scour were of the same order of magnitude. Figure 7.11 shows the different configurations which occurred during the tests. If the combination of contraction ratio and transition angle is small then the contraction scour is down stream from the contraction inlet and the

abutment scour exists by itself at the contraction inlet. If the combination of contraction ratio and transition angle is medium, the abutment scour and the contraction scour occur within the same inlet cross-section but do not overlap. If the combination of contraction ratio and transition angle is severe, the abutment scour and the contraction scour overlap but do not add to each other.

Figure 7.4 - Contraction Scour Profiles along the Channel Centerline as a function of Time for Test 1 (the numbers in the legend are the elapsed times in hours).

S ed im e n t D ep o s itio nB ac k C o n trac tio n S co u r

M ax im u m C o n trac tio n S co u r

A b u tm e n t S c o u r

Figure 7.5 – Plan view sketch of the contraction scour pattern.

0

50

100

150

200

250

300

-300 -100 100 300 500 700 900 1100 1300

X(mm)

Z(x,

t) (m

m)

0.50

4.50

14.25

27.00

40.67

50.00

64.08

77.42

99.08

124.08

148.58FLOW

0

40

80

120

160

200

0 50 100 150 200 250

Time(H)

Z(t)(

mm

)

Measurement

Hyperbola

Figure 7.6 - Maximum Contraction Scour and Hyperbola Model for Test 1

0

50

100

150

200

250

300

0 50 100 150 200 250

Time(H)

Z(t)(

mm

)

Measurement

Hyperbola

Figure 7.7 - Uniform Contraction Scour and Hyperbola Model for Test 1

0

0.25

0.5

0.75

1

-400 0 400 800 1200 1600

Distance X (mm)

Rel

ativ

e S

cour

Dep

th (Z

/Zmax

)

Angle=15

Angle=45

Angle=60

Angle=90

Figure 7.8 - Contraction Scour Profile along the Channel Centerline for

Transition Angle Effect

0

0.25

0.5

0.75

1

-400 0 400 800 1200 1600

Distance X (mm)

Rel

ativ

e S

cour

Dep

th (Z

/Zmax

) L/B2=0.5

L/B2=1

L/B2=1.69

L/B2=6.76

Figure 7.9 - Contraction Scour Profile along the Channel Centerline for

Contraction Length Effect

0

0.2

0.4

0.6

0.8

1

1.2

-500 0 500 1000 1500

Distance X (mm)

Rel

ativ

e S

cour

Dep

th (

Z/Zm

ax)

Figure 7.10 - Contraction Scour Profiles along the Channel Centerline for Standard Tests

Figure 7.11 – Overlapping of scour for contraction scour and abutment scour

Original Bottom

A: Ridge B: Valley C: Plain

is the location of maximum contraction

7.6. MAXIMUM AND UNIFORM CONTRACTION DEPTHS FOR THE REFERENCE CASES The reference case for the development of the basic equation is the case of a 90o transition angle and a long contraction length (L/B2 > 2, Figure 7.5). The maximum depth of contraction scour Zmax is the largest depth which occurs along the contraction scour profile in the center of the contracted channel. The uniform contraction scour depth Zunif is the scour depth which develops in the contracted channel far from the transition zone (Figure 7.1). The Reynolds number (inertia force/gravity force) and the Froude number (inertia force/viscous force) were used as basic correlation parameters. Both Zmax and Zunif were normalized with respect to H1, the upstream water depth. Figure 7.12 shows the attempt to correlate the contraction scour depths to the Reynolds number defined as V1B2/υ; as can be seen, the Reynolds number is not a good predictor of the contraction scour depths. Figure 7.13 and 7.14 show the correlation with the Froude number; although there are only seven points for the correlation, the results are very good. The Froude number was calculated as follows. From simple conservation, we have V1B1H1 = V2B2H2. Because the water depth H2 may not be known for design purposes and because other factors may influence V2, the velocity used for correlation purposes was simply V1B1/B2. As will be seen later, a factor will be needed in front of V1B1/B2 for optimum fit.

V* = V1B1/B2 (7.4) Then the Froude number was calculated as

Fr* = (V1B1/B2)/(gH1)0.5 (7.5)

0.0

0.5

1.0

1.5

2.0

2.5

0 50000 100000 150000 200000

Re=V1B2/n

Z / H

1

Max Contraction

Unif Contraction

Figure 7.12 – Correlation Attempt between Contraction scour depth and Reynolds Number

y = 1.0039x - 0.0013R2 = 0.9885

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5

−

×

× 3/11

2/1

1

1 2138.1

9.1gnHgH

BBV c

ρτ

1

max

HZ

Figure 7.13 – Normalized Maximum Contraction Scour Depth versus Froude number

y = 0.9995x - 4E-06R2 = 0.9558

0

0.3

0.6

0.9

1.2

1.5

0 0.5 1 1.5

−

×

× 3/11

2/1

1

1 2131.1

41.1gnHgH

BBV c

ρτ

1HZunif

Figure 7.14 – Normalized Uniform Contraction Scour Depth versus Froude number

The relationship between the critical shear stress and the critical velocity for an open channel ahs been establsished (Richardson et al., 1995).

τc = (ρgn2Vc2)/(H1)0.33 (7.6)

So the critical Froude number can be written Frc = Vc/(gH1)0.5 = (τc/ρ)0.5/(gnH1)0.33 (7.7)

The contraction scour depths are likely to be proportional to the difference (Fr-Frc). However, as was mentioned before, the velocity used to calculate Fr may require a factor β. The final form of the equation sought was:

Z/H1 = α ( βFr* - Frc) (7.8) The factors α and β were obtained by optimizing the R2 value in the regression on Figures 7.13 and 7.14. The proposed equations are:

−

= 3/11

2/1

1

2

11

1

max

38.190.1

gnHgHBBV

HZ

c

ρτ

(7.9)

−

= 3/11

2/1

1

2

11

1

31.141.1

gnHgHBBV

HZ

c

unif ρτ

(7.10)

where Zmax is the maximum depth of contraction scour, H1 the upstream water depth after scour has occurred, V1 the mean depth upstream velocity after the contraction scour has occurred, B1 the upstream channel width, B2 the contracted channel width, g the acceleration due to gravity, τc the critical shear stress of the soil (obtained from an EFA test), ρ the mass density of water, n the Mannings coefficient. Note that V1 and H1 are the upstream velocity and water depth after contraction scour has occurred. The difference between the V1 and H1 values before and after contraction scour is small in most cases and the correlations were also good when using the values of V1 and H1 before the contraction scour occurs except for Test 1. Test 1 had a very small contraction ratio (B2/B1 = 0.25), and an initial supercritical flow whereas all other tests had larger contraction ratios and an intial subcritical flow. In the case of Test 1, equations 7.9 and 7.10 worked only when using the values of V1 and H1 after contraction scour had occurred. This use of values after scour occurs is consistent with the approach taken by other researchers (Laursen 1960,1963, Komura 1966, Gill 1981, and Lim1998). The value of the β factor is shown as a function of the contraction ratio for all the flume contraction tests on Figure 7.15. An average value of 1.38 was chosen for Zmax and 1.31 for Zunif . Since β should be equal to 1 when B2/B1 is equal to 1 (no contraction), the best fit line on Figure 7.15 should go through that point. It was decided to achieve that results as shown on Figure 5.15. An attempt was made to find a relationship between Zunif and Zmax. The following equation gave a high R2 value:

Zunif/Zmax = 4 Fr where Fr = V1/(gB1)0.5 (7.11)

1

1.1

1.2

1.3

1.4

1.5

1.6

1 1.5 2 2.5 3 3.5 4 4.5

B1/B2

B

B - max - MeasurementB - unif - MeasurementB - max - ProposeB - unif - Propose

Figure 7.15 – The Factor β as a Function of the Contraction Ratio.

7.7. LOCATION OF MAXIMUM CONTRACTION DEPTH FOR THE REFERENCE CASES Knowledge of the location of the maximum contraction scour depth is very important for the design of a bridge. Indeed, the bridge is usually a fairly narrow contraction and the maximum contraction scour depth in this case can be downstream from the bridge site. Based on the flume test observations, the maximum contraction scour generally occurs close to and behind the opening of the contraction. For the primary tests, the data listed in Table 7.1 and 7.2 indicate that Xmax is mostly controlled by the contracted channel width B2 and the contraction ratio B2/B1. The wider the contraction opening is, the bigger the Xmax is (Figure 7.16). Figure 7.17 shows the relationship between Xmax/B2 versus B2/B1. By regression, the best fit equation for Xmax is:

15.025.21

2

2

max +=BB

BX (7.12)

Equation 7.12 indicates that the location of the maximum depth of contraction scour is independent of the velocity and therefore remains constant during the period associated with a hydrograph. This means that an accumulation method such as the SRICOS method can be used to predict the maximum depth of contraction scour after the bridge site has been subjected to a long-term hydrograph.

0

50

100

150

200

250

300-500 0 500 1000 1500

X (mm)

Sco

ur D

epth

(mm

)

B2/B1=0.25B2/B1=0.5B2/B1=0.75

Figure 7.16 - Influence of the Contraction Ratio on the Longitudinal Scour Profile

Xmax/B2= 2.2519(B2/B1) + 0.1457R2 = 0.9999

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

B2/B1

Xm

ax/B

2

Figure 7.17 - Relationship Between Xmax and the Contraction Geometry

7.8. CORRECTION FACTORS FOR TRANSITION ANGLE AND CONTRACTION LENGTH There are 7 secondary tests listed in Table 7.2. Tests 2, 9,10 and 11 are for the transition angle effect, and Tests 2, 12, 13 and 14 are for the contraction length effect. Test 2 is the reference case for both groups and comparisons to Test 2 are used to derive the correction factors for the equations which give Zmax, Zunif and Xmax. A smooth transition angle is generally built to smooth the effect of the approaching flow (Figure 7.18). As can be seen, the approaching flow runs against the abutments and then is guided towards the contracted channel at an angle related to the transition angle θ. The location of the maximum contraction scour depth will be pushed further back from the contraction inlet when the transition angle becomes smoother. Even though the transition angle can change the local flow pattern around the contraction inlet, this influence decreases into the contraction channel, where a uniform flow develops. This indicates that the transition angle may affect the maximum contraction scour but not the uniform contraction scour. Figure 7.19 shows the influence of the transition angle θ on the maximum contraction scour depth Zmax. It can be seen that θ does not have a clear impact on Zmax. This observation is consistent with Komura’s (1977) observation on sands where he stated that a smooth transition angle was not helpful in reducing the scour depth around the abutment inlets. If Test 10 is ignored due to its odd scour profile, the uniform contraction scour depth Zunif is practically independent of the transition angle θ (Figure 7.20) as expected. However, the transition angle has a significant impact on the location of the maximum contraction scour Xmax, as shown in Figure 7.21. Regression analysis of the data leads to the following relationship between the Xmax and θ:

9475.0tan/4793.0)90(

)(

max

max +=°

θθ

XX

(7.13)

Figure 7.18 indicates that Xmax is at (B2/2)/tanθ if the flow follows the prolongation of the transition sides but Equation 7.13 shows that the real location of the maximum contraction scour is further downstream of this estimated point. In a summary, if Test 2, the test with the 90˚ transition angle, is selected as the reference case for the transition angle effect, and the correction factors are calculated as the ratios between the value for θ over the value for 90o, the transition angle effect for contraction scour, in three aspects of Zmax, Zunif and Xmax, is:

+=

=

=

95.0tan/48.0

0.1

0.1

max

max

/

/

/

θθ

θ

θ

X

Z

Z

K

K

K

unif (7.14)

Figure 7.18 - Flow around Contraction Inlets

0

30

60

90

120

150

0 15 30 45 60 75 90

Transition Angle q (Degree)

Zmax

(mm

)

Figure 7.19 - Transition Angle Effect on Maximum Contraction Scour Depth

θ

Transition Angle θ (Degree)

0

0.5

1

-400 0 400 800 1200 1600

Distance X (mm)R

elat

ive

Sco

ur D

epth

(Z/Zm

ax)

Angle=15 Angle=45Angle=60 Angle=90

Figure 7.20 - Transition Angle Effect on Scour Profile and Uniform Contraction scour

y = 0.4621x + 1R2 = 0.9923

0

0.5

1

1.5

2

2.5

3

0 1 2 3 41/Tan(q )

Kq

Test 10

Figure 7.21 - Transition Angle Effect on the Location of the Maximum Scour Depth

1/Tan (θ )

Bridge contractions are often short and the abutments work like a thin wall blocking the flow. The uniform contraction scour depth cannot develop under these conditions. Instead two back contraction scour holes behind the contracted section can develop (Figure 7.5). Further, as shown in Figure 7.9, when the contraction length is between 6.76B2 and 0.5B2, the maximum depth of contraction scour Zmax and the location of that depth Xmax are unaffected by the length of the contracted channel. If the long contraction channel of Test 2 is chosen as the reference case, the correction factors KL for contraction length are:

=

=

=

0.1

0.1

max

max

/

/

/

XL

ZL

ZL

K

voidK

K

unf (7.15)

Test 14 has the shortest contraction length with L/B1 = 0.125. The maximum scour depth is 1.79 times of the scour depth in Test 2, and Xmax is also multiplied at the same time. This situation is very like the “thin wall” pier scour. Therefore, when L/B2 is smaller than 0.25, it is necessary to increase the predicted Zmax and Xmax values. This case has not been evaluated in this research. 7.9. SRICOS-EFA METHOD USING HEC-RAS GENERATED VELOCITY Equations 7.9 and 7.10 proposed to calculate contraction scour depths have a shortcoming: they are developed from tests in rectangular channels. For channels with irregular cross-sections, which is the case in most real situations, some researchers have recommended to use the flow rate ratio Q1/Q2 instead of the contraction ratio B1/B2 to account for the flow contraction (e.g.: Sturm et al., 1997). Here, Q1 is the total flow rate in the approach channel and Q2 is the flow rate in the part of the approach channel limited by two lines representing the extensions of the banks of the contracted channel. The approach which is recommended here, however, is to replace the nominal velocity V1B1/B2 used in equations 7.9 and 7.10 by the velocity VHec obtained by using a program like HEC-RAS. With this approach, the complex geometry of the approach channel can be handled by the program and a more representative velocity can be used. The problem is to find the proper relationship between the HEC-RAS calculated velocity, VHec, and the nominal velocity V1B1/B2. This was done by conducting a series of HEC-RAS analyses to simulate the flow condition in the flume tests, obtaining the resulting velocity, VHec, and correlating it to V1B1/B2. The velocities are listed in Tables 7.1 and 7.2 and the correlation graph is shown in Figure 7.22. Regression analysis gave the following relationship between the two variables:

11

2

1.14HecBV VB

= ⋅ ⋅ (7.16)

In this figure, the point for Test 1 is still outstanding because of the severe backwater effect during that test which exhibited an extreme contraction case ((B2/B1) = 0.25).

y = 1.1352xR2 = 0.8173

30

60

90

120

150

30 60 90 120 150V1(B1/B2)(cm/s)

VH

ec(c

m/s

)

Test 1

Figure 7.22 - Relationship Between the Nominal Velocity and the HEC-RAS Calculated Velocity

Now, it is possible to rewrite equations 7.9 and 7.10 using VHec For maximum contraction scour:

1/ 2

max1/3

1 11

1.491.9

c

HecZ VH gnHgH

τρ

= −

(7.17)

For uniform contraction scour: 1/ 2

1/31 11

1.571.41

c

unif HecZ VH gnHgH

τρ

= −

(7.18)

Users of Equations 7.17 and 7.18 should be aware that the velocity VHec also has its limitations. These limitations are tied to the ability of the program HEC-RAS to simulate the flow at the contraction. As an illustration, the water surfaces and velocity distributions measured and predicted by different means along the centerline of the channel are compared for Test 2 in Figure 7.23. As can be seen, the HEC-RAS generated velocity profile cannot give the peak velocity value in the contracted channel. Instead HEC-RAS gives a step function which parallels the bank contraction profile.

0

60

120

180

-1000 -500 0 500 1000 1500

X(mm)

Wat

er S

urfa

ce E

leva

tion

(mm

)

BeforeAfterHEC-RAS

0

30

60

90

-1000 -500 0 500 1000 1500

X(mm)

Vel

ocity

(cm

/s)

BeforeAfterHEC-RASNominal

Figure 7.23 - Comparison of Water Depth and Velocity between HEC-RAS Simulations and Measurements for Contraction Test 2.

7.10. CONSTRUCTING THE COMPLETE CONTRACTION SCOUR PROFILE Three characteristic dimensions of the contraction scour profile have been determined by the flume tests: Zmax, Zunif and Xmax. Additional information was obtained from the tests in order to develop a procedure to draw the complete contraction scour profile. It was found that the contraction scour hole, much like the pier scour hole, is determined by both the flow and soil strength: In the front part of the scour hole, the flow vortex can generate a steep slope that stresses the soil beyond its shear strength. Therefore it is the soil strength that controls the front slope of the scour. At the back of the scour hole, the slope is usually gentle, slope stability is not a problem. Based on these and other observations, the following steps are recommended to draw the full contraction scour profile (Figure 7.24).

1. Plot the position of the bridge contraction, especially the start point of the full contraction;

2. Calculate Xmax by Equation 7.13, 7.14, and 7.15, and mark the position where the maximum contraction scour happens in the figure;

3. Calculate Zmax by Equation 7.10, 7.14, and 7.15, draw a horizontal line at this depth and extend it 0.5 Zmax on both sides of the location of Zmax (B and C on Figure 106);

4. Plot the starting point A of the contraction scour profile at a distance equal to Zmax from the start point of the full contraction;

5. Connect A and B as the slope of the contraction scour profile before the maximum scour;

6. Calculate Zunif by Equation 7.11, 7.14, and 7.15, draw a line with a upward slope of 1 to 3 from point C to a depth equal to Zunif (D on Figure 106); line CD is the transition from the maximum contraction scour depth to the uniform contraction scour depth.

7. Draw a horizontal line downstream from point D to represent the uniform contraction scour.

A

B CD

Xmax

Zmax

Zmax Zunif 3

1

Contraction

Original Soil Bed

a =Zmax/2

Flow

a a

Figure 7.24 – Generating the Complete Contraction Scour Profile.

7.11. SCOUR DEPTH EQUATIONS FOR CONTRACTION SCOUR The following equations summarize the results obtained in this chapter.

0.51

12

max 11/311

1.38( ) 1.90 0

c

L

BVB

Z Cont K K HgnHgHθ

τρ

= × − ≥

(7.19)

0.5

max 11/311

1.49( ) 1.90 0

c

hecL


τρ

= × − ≥

(7.20)

0.51

12

11/311

1.31( ) 1.41 0

c

unif L

BVB

Z Cont K K HgnHgHθ

τρ

= × − ≥

(7.21)

0.5

11/311

1.57( ) 1.41 0

c

Hecunif L


τρ

= × − ≥

(7.22)

max 2

2 1

2.25 0.15LX BK KB Bθ

= × +

(7.23)

where Zmax(Cont) is the maximum depth of scour along the centerline of the contracted channel, Zunif(Cont) is the uniform depth of scour along the centerline of the contracted channel, Xmax is the distance from the beginning of the fully contracted section to the location of Zmax, V1 is the mean velocity in the approach channel, VHec is the velocity in the contracted channel given by HEC-RAS, B1 is the width of the approach channel, B2 the width of the contracted channel, τc the critical shear stress as given by the EFA, ρ the mass density of water, n Manning’s coefficient, H1 the water depth in the approach channel, Kθ the correction factor for the influence of the transition angle as given by equation 7.24 below, and KL the correction factor for the influence of the contraction length as given by equation 7.25 below.

+=

=

=

95.0tan/48.0

0.1

0.1

max

max

/

/

/

θθ

θ

θ

X

Z

Z

K

K

K

unif (7.24)

=

=

=

0.1

0.1

max

max

/

/

/

XL

ZL

ZL

K

voidK

K

unf (7.25)

CHAPTER 8 THE SRICOS-EFA METHOD FOR INITIAL SCOUR RATE AT CONTRACTED CHANNELS

8.1. BACKGROUND The existing knowledge on numerical methods for scour studies has been presented at the beginning of Chapter 6 (section 6.2) and the existing knowledge on contraction scour in cohesive soils has been presented at the beginning of Chapter 7 (section 7.1). The initial scour rate is an integral part of the SRICOS method to predict contraction scour as a function of time because it is one of the two fundamental parameters used to describe the scour depth versus time curve. The other one is the maximum depth of contraction scour which was studied in Chapter 7. The initial rate of scour for a given contraction scour problem is obtained by first calculating the maximum shear stress τmax existing in the contracted channel before the scour starts (flat river bottom) and then reading the initial scour rate on the erosion function obtained in the EFA test. Therefore the problem of obtaining the initial rate of contraction scour is brought back to the problem of obtaining the maximum shear stress in the contracted channel before scour starts. This problem was solved by numerical simulations using the Chimera RANS method. This method was described in Section 6.3 and a verification of its reliability was presented in Section 6.4. This chapter describes the simulations performed and the associated results. The goal was to develop an equation for the maximum shear stress τmax existing in the contraction zone. The equation for the maximum shear stress τmax at the bottom of an open channel without contraction is given by (Munson et al., 1990):

31

22max

−= hRVnγτ (8.1)

where γ is the unit weight of water, n is Manning’s roughness coefficient, V is the mean depth velocity, and Rh is the hydraulic radius defined as the cross section area of the flow divided by the wetted perimeter. The equation obtained for the contracted channel case should collapse to the open channel case when the contraction ratio B2/B1 becomes equal to 1. The objective of the numerical simulations was to obtain correction factors which would introduce the effect of the contraction ratio, the transition angle, and the length of the contracted zone. 8.2. CONTRACTION RATIO EFFECT: NUMERICAL SIMULATION RESULTS One of the flume experiments is chosen to perform the numerical simulation. The width of the flume used is 0.45 m. The upstream flow is a steady flow with a velocity V1 of 0.45 m/s and the upstream water depth H is 0.12m. Three different contraction ratios are chosen: B2/B1 = 0.25, 0.5, and 0.75. In order to reduce the CPU time, a half domain is

used based on the symmetry of the problem. For numerical purposes, the characteristic length B is defined as half of the flume width. Based on this definition, the value of Reynolds number ( νVB=Re ) is 101250 and Froude number ( gBVFr = ) is 0.303. The grid is made of four blocks as shown in Figure 8.1.

-0.4

-0.2

0

Z/(0.5B1)

-2

0

2

4

6

8

X/(0.5B1)0

0.250.5

0.751

Y/(0.5B1)

X Y

Z

Block 2

Block 1

Block 3Block 4

Center of the channel

Figure 8.1 - Grid System for the Simulation in the Case of B2/B1 = 0.25.

The bed shear stress contours around the abutment and in the contracted zone are shown in Figures 8.2 to 8.4. The maximum bed shear stress is found around the abutment but the maximum contraction bed shear stress τmax is found along the centerline of the channel in the contracted section. As expected, it is found that the magnitude of τmax increases when the contraction ratio (B2/B1) decreases. It is also observed that the distance Xmax between the beginning of the fully contracted section and the location of τmax increases when the contraction ratio (B2/B1) increases. 8.3. TRANSITION ANGLE EFFECT: NUMERICAL SIMULATION RESULTS Again, one of the flume experiments is chosen to perform the numerical simulation. The width of the flume used is 0.45 m. The upstream flow is a steady flow with a velocity of 0.45 m/s, the contracted length L is such that L/(B1-B2)=6.76 and the water depth is 0.12 m. Four different transition angles are chosen for the simulations: α = 15, 30, 45, and 90 degrees. The width (B1-B2) is chosen as the characteristic length B. Then, Reynolds number is 101250 and Froude number is 0.303.

0.912.11

3.31

4.516.92 8.12 6.92

5.714.51

0.91

8.50

9.32

X/(0.5B1)

Y/(0.5B1)

-1 -0.5 0 0.50

0.25

0.5

0.75

1

Abutment

Flow

Center of channel

Figure 8.2 - Initial Bed Shear Stress Distribution (N/m2) for B2/B1=0.25, and V=0.45m/s.

0.91

1.70

2.493.29

3.29

4.08

2.491.70

0.91

1.25

3.11

X/(0.5B1)

Y/(0.5B1)

-1 -0.5 0 0.50

0.25

0.5

0.75

1

AbutmentFlow

Center of channel

Figure 8.3 - Initial Bed Shear Stress Distribution (N/m2) for B1/B2=0.50, and V=0.45m/s.

τ =

τ =

0.91

2.18

1.291.54 1.78 2.03

2.33

2.66

3.00

1.78

2.03

1.290.91

1.54

X/(0.5B1)

Y/(0.5B1)

-1 -0.5 0 0.50

0.25

0.5

0.75

1

Abutment

Flow

Center of channel

Figure 8.4 - Initial Bed Shear Stress Distribution (N/m2) for B2/B1=0.75, and V=0.45m/s. The bed shear stress contours around the abutment and in the contracted zone are shown in Figures 8.5 to 8.7. As can be seen, the magnitude of the maximum bed shear stress τmax along the center of the channel in the contracted section increases when the transition angle θ increases. However the transition angle does not have a major influence on τmax. It is also observed that the distance xmax between the beginning of the fully contracted section and the location of τmax increases when θ increases 8.4. CONTRACTED LENGTH EFFECT: NUMERICAL SIMULATION RESULTs Again, one of the flume experiments is chosen to perform the numerical simulation. The width of the flume used is 0.45 m. The upstream flow is a steady flow with a velocity of 0.45 m/s, the contraction channel ratio (B2/B1) is equal to 0.5, the transition angle is 90o and the water depth is 0.12 m. Four different contraction length are simulated: L/(B1-B2)=0.25, 0.5, 1.0 and 6.76. The difference (B1-B2) is chosen as the characteristic length B. Then, Reynolds number is 101250 and Froude number is 0.303. The initial bed shear stress distribution around the contracted zone is shown in Figures114 to 116 for various contraction lengths. As can be seen the maximum bed shear stress along the center of the channel in the contracted section is the same for all the contraction lengths. At the same time, the location of the maximum bed shear stress is not influenced by the contraction length. Therefore τmax and xmax are independent of the contraction length and there is no need for any correction factors for contraction length. It was discovered later that in the case of very thin contraction length (L/(B1-B2) < 0.33) the maximum shear stress within the contracted length is smaller than the maximum shear stress due to the contraction. The reason is that the maximum shear stress occurs downstream from the contraction. The correction factor will reflect this finding at very small values of the contracted length (L/(B1/B2) < 0.33) (section 8.6).

τ =

8.5. WATER DEPTH EFFECT: NUMERICAL SIMULATION RESULTS It was found that the water depth had no influence on the magnitude or the location of the maximum bed shear stress for the contraction problem. In fact the water depth is already included in the equation through the hydraulic radius of equation 8.1. .

1.68

1.68

0.91

1.06

1.22

1.371.52

1.68

1.99

2.45

1.83

X/(B1-B2)

Y/(B1-B2)

-3 -2 -1 0 1 20

0.25

0.5

0.75

1

AbutmentFlow

Center of channel

Figure 8.5 - Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s,

L/(B1-B2)=6.76, and θ =15 degree)

0.91

1.101.49

1.872.06

1.87

2.06

2.25

1.681.49

3.17

X/(B1-B2)

Y/(B1-B2)

-3 -2 -1 0 1 20

0.25

0.5

0.75

1

Abutment

Center of channel

Flow

Figure 8.6 - Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s,

L/(B1-B2)=6.76, and θ =30 degree)

τ =

τ =

0.91

1.36

1.82 2.02

2.27

2.27

2.02

2.62

3.76

X/(B1-B2)

Y/(B1-B2)

-3 -2 -1 0 1 20

0.25

0.5

0.75

1

Center of channel

FlowAbutment

Figure 8.7 - Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s, L/(B1-B2)=6.76, and θ =45 degree)

0.911.44

1.972.49 3.02

0.911.97

3.02

3.25

3.25

4.04

3.443.75

X/(B1-B2)

Y/(B1-B2)

-1 -0.5 0 0.50

0.25

0.5

0.75

1

Flow

Center of channel

Abutment

Figure 8.8 - Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s, and

L/(B1-B2)=0.25)

τ =

τ =

3.27

0.91

1.582.49

4.08

2.491.58

0.91

3.47

3.27

3.133.02

2.83

3.02

3.13

1.22

2.052.83

X/(B1-B2)

Y/(B1-B2)

-1 -0.5 0 0.50

0.25

0.5

0.75

1

AbutmentFlow

Center of channel

Figure 8.9 - Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s, and

L/(B1-B2)=0. 5)

0.91

1.55

2.06 2.71

4.05

3.25

3.51

2.061.55

0.91

1.13

3.03 3.253.03

2.71

3.34

3.81

X/(B1-B2)

Y/(B1-B2)

-1 -0.5 0 0.50

0.25

0.5

0.75

1Center of channel

Flow Abutment

Figure 8.10 - Initial Bed Shear Stress (N/m2) Distribution for B2/B1=0.5, V=0.45 m/s, and L/(B1-B2)=1.0)

τ =

τ =

8.6. MAXIMUM SHEAR STRESS EQUATION FOR CONTRACTION SCOUR

The influence of four parameters on the maximum shear stress and its location near a channel contraction was investigated by numerical simulation. These factors are: the contraction ratio (B2/B1), the transition angle (θ), the length of contraction (L), and the water depth (H). Figure 8.11 describes the problem definition for abutment and contraction scour. In this figure, B1 is the width of channel, B2 is the width of contracted section, L is the length of abutment, θ is the transition angle, Xa is the location of maximum bed shear stress due to the abutment, Xmax is a normalized distance which gives the location of the maximum bed shear stress along the centerline of the channel ( ( )21max BBXX −= ) where X is the actual distance to τmax.

Figure 8.11 - Definition of Parameters for Contraction Scour

It was found (for certain θ and 21 BB ) that the influence of L on Xmax and τmax was negligible. In the case of θ = 90 degree and 21 BB = 2, the value of Xmax was about 0.35 for ( )21 BBL − varying from 0.25 to 6.76. For engineering design, what we are interested in is scouring around the pier or the abutment and along the contracted section. For small ratios of L/(B1-B2) (less than 0.33) the maximum shear stress τmax is past the contracted location and the shear stress of interest is located at Xc from the beginning of the fully contracted channel. The correction factor for a given influencing parameter is defined as the ratio of the τmax value including that parameter to the τmax value for the case of the open channel without any contraction. The results of the numerical simulations were used to plot the shear stress as a function of each influencing parameter. Regressions were then used to obtain the best-fit equation to describe the influence of each parameter. Figure 8.12 shows the variation of the correction factor kc-R for the influence of the contraction ratio B2/B1. Figure 8.13 shows the correction factor kc-θ for the influence of the transition angle θ. Figure 8.14 shows the correction factor kc-L for the influence of the contracted length L. The correction factor kc-H for the water depth influence was found to be equal to 1.

B 1

B 2

θ

L

X a

X m ax

X cX

Y

F lo w

B 1

B 2

θ

L

X a

X m ax

X cX

Y

F lo w

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

B 1/B 2

k c-R

B2

B1

θ L

751

2

1380620.

Rc BB..k

+=−

Figure 8.12 - Relationship between Rck − and2

1

BB

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.2 0.4 0.6 0.8 1 1.2

θ /90

k c -θ B2

B1

θ L

5.1

909.01

+=−

θθck

Figure 8.13 - Relationship between θ−ck and

90θ

0.6

0.7

0.8

0.9

1

1.1

1.2

0 1 2 3 4 5 6 7L/(B1-B2)

kc-L

B2

B1

θ L

<

−

−

−

+

≥

−

−

− 350981361770

35012

2121

.kfor,BB

L.BB

L..

.kfor,

kLc

Lc

Lc

Figure 8.14 - Relationship between Lck − and

21 BBL−

The proposed equation for calculating the maximum shear stress within the contracted length of a channel along its centerline is:

31

22max

−

−−−−= hLcHccRc RVnkkkk γτ θ (8.2) where

• γ is the unit weight of water (kN/m3) • n is Manning’s roughness coefficient (s/m1/3) • V is the upstream mean depth velocity (m/s) • θ is the contraction transition angle (in degrees) (Figure 8.13) • hR is the hydraulic radius defined as the cross section area of the flow divided by

the wetted perimeter (m). • Rck − is the correction factor for the contraction ratio, given by

• 75.1

2

138.062.0

+=− B

Bk Rc (Figure 8.12)

• θ−ck is the correction factor for the contraction transition angle, given by

• 5.1

909.01

+=−

θθck (Figure 8.13).

• Lck − is the correction factor for the contraction length, given by

•

<

−

−

−

+

≥

=−

−

− 35.0,98.136.177.0

35.0,12

2121Lc

Lc

Lc kforBB

LBB

L

kfor

k (Fig.8.14)

• Hck − is the correction factor for the contraction water depth. Since the water depth has a has negligible influence, then 1≈−Hck . The influence of the water depth H is in hR .

Note that the last part of the equation ( )33.022 −

hRVnγ is the formula for the bed shear stress in an open channel (equation 8.2). Equation 8.2 is consistent with the open channel case since all correction factors collapse to 1 when the parameter corresponds to the open channel case. In other words when 21 BB =1, θ =0, and ( ) LBB 21 − =0, then Rck − = 1,

Lck − = 1, θ−ck = 1. Figure 8.15 and 8.16 give the location of the maximum shear stress along the centerline of the contracted channel. Figure 8.15 shows the influence of the transition angle while Figure 8.16 shows the influence of the contraction ratio.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.2 0.4 0.6 0.8 1 1.2

θ/90

X/(B1-B2)

B2

B1

θ L

−−

+

=−

110

4209021

1

340

.

.

e

.BB

Xθ

Figure 8.15 – Distance from the beginning of the fully contracted section to the location of the maximum shear stress along the centerline of the channel, X, as a function of the

normalized transition angle, 90θ .

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

B2/B1

X/(B1-B2)

B2

B1

θ L

3

1

2

2

1

2

1

2

21

762481730

+

−

=

− BB.

BB.

BB.

BBX

Figure 8.16 - Distance from the beginning of the fully contracted section to

the location of the maximum shear stress along the centerline of the channel, X, as a function of the Contraction Ratio B2/B1.

CHAPTER 9 THE SRICOS-EFA METHOD FOR COMPLEX PIER SCOUR AND CONTRACTION SCOUR IN COHESIVE SOILS

9.1. BACKGROUND The SRICOS-EFA method for complex pier and contraction scour can be used to handle the complex pier problem alone or contraction scour alone. It can also handle the combined case of complex pier scour and contraction scour (integrated SRICOS-EFA method). Abutment scour is not included in this project but will be added later. A method exists in HEC 18 to predict bridge scour under the combined influence of contraction scour, pier scour, and abutment scour. This method consists of calculating the individual scour depth independently and simply adding them up. Engineers have often stated that the results obtained in such a way are too conservative. The SRICOS-EFA integrated method is not just adding the complex pier scour and the contraction scour. The method considers the time factor, the soil properties and, most importantly, the interaction between the contraction scour and the pier scour. In following sections, the principle, the accumulation algorithm, and the step-by-step procedure for the SRICOS-EFA integrated method is presented. 9.2. THE INTEGRATED SRICOS-EFA METHOD GENERAL PRINCIPLE In the integrated SRICOS-EFA method for calculating bridge scour, the scour process is separated into two imaginary steps: (1) calculation of the total contraction scour, (2) calculation of pier scour. The contraction scour is assumed to happen first and without considering pier scour. This does not mean that the piers are not influencing the contraction scour; indeed the piers are considered in the contraction scour calculations because their total projection width is added to the abutment projection width to calculate the total contraction ratio. The contraction scour is calculated in this fashion for a given hydrograph. Then, the pier scour is calculated. There are two options for the pier scour calculations:

1. If the contraction scour calculations indicate that there is no contraction scour at the bridge site, then the pier scour is calculated by following the SRICOS-EFA complex pier scour calculation procedure. In this case, HEC-RAS, for example, can be used to calculate the water depth and the velocity in the contracted section after removing the piers obstructing the flow. The removal of the piers is necessary because the velocity used for pier scour calculations is the mean depth velocity at the location of the pier if the pier was not there.

2. If the calculations indicate that contraction scour occurs at the bridge site, then the pier scour calculations are made using the critical velocity, not the actual velocity, because when contraction scour has stopped (Zmax(Cont) is reached), the velocity in the contracted section is the critical velocity Vc. The value of Vc can be

obtained from the EFA tests for cohesive soils or from the equations presented in HEC-18 for cohesionless soils. The water depth for the pier scour calculations is the water depth in the contracted section after the contraction scour has occurred. The bottom profile of the river after scour has occurred is obtained by adding the contraction scour and the pier scour.

This approach is valid for the maximum scour depth calculations. For the time stepping process, the maximum scour depth is not reached at each step but the maximum scour depth is calculated as part of each step and used to calculate the partial scour depth. Therefore the above technique is included in each time step. The other parameter calculated at each time step is the initial maximum shear stress; this shear stress is used to read the initial scour rate on the erosion function obtained form the EFA tests. Both parameters, Zmax and iZ , are used to generate the scour depth versus time curve and the actual scour depth is read on that curve at the value equal to the time step. The details of that procedure are presented in the next section. 9.3. THE INTEGRATED SRICOS-EFA METHOD: STEP PROCEDURE Step I: Input Data Collection (Figure 9.1) Water: flow (mean velocity V1, and water depth H1) upstream of the bridge where

the flow is not noticeably influenced by the existence of bridge contraction and piers.

Geometry: bridge contraction parameters and pier geometry. total Contraction Ratio: B2/B1= (w1+w2+w3+w4)/B1 (9.1) Soil: critical shear stress and erosion function. All the parameters are defined in Figure 9.1.

Figure 9.1 - Step I - Bridge scour input data and primary calculation

B1

w1 w2 w3 w4

V1 H1

I I

(A): Plan View

(B): Cross Section at Bridge (I-I)

H1

Step II: Maximum Contraction Scour Calculation (Figure 9.2) Based on the upstream flow conditions, on the soil properties and on the total bridge contraction ratio calculated in Step I, the maximum contraction scour can be calculated directly by Equation 9.2:

0.51

12

max 11/311

1.38( ) 1.90 0

c

L

BVB

Z Cont K K HgnHgHθ

τρ

= × − ≥

(9.2)

Zmax(cont) (m) is the maximum contraction scour, Kθ is the factor for the influence of the transition angle (Kθ is equal to1), KL is the factor for the influence of the length of the contracted channel (KL is equal to 1), V1 (m/s) is the velocity in the uncontracted channel, B1 (m) is the width of the uncontracted channel in meters, B2 (m) is the width of the contracted channel as defined in Equation 9.1 and Figure 9.1, g (m/s2) is the acceleration due to gravity, H1 (m) is the water depth in the uncontracted channel, τc (kN/m2) is the critical shear stress of the soil obtained in the EFA, ρ is the mass density of water (kg/m3), and n is the Manning’s coefficient (s/m1/3). The engineers may prefer to calculate the velocity Vhec in the contracted channel with a width B2 as calculated according to Equation 9.1 and Figure 9.1 by using a program like HEC-RAS. In this case, the engineer needs to use Equation 9.3.

0.5

max 11/311

1.49( ) 1.90 0

c

hecL


τρ

= × − ≥

(9.3)

Where, VHec is the maximum velocity in the middle of the contracted channel (m/s). If the value of the maximum contraction scour Zmax(cont) is negative, the flow and contraction is not severe enough to cause any contraction scour and the maximum contraction scour is zero. If there is contraction scour, the shear stress reached on the river bottom at the time of maximum contraction scour Zmax(cont) is the critical shear stress of the soil τc and scour at the bridge site is as shown in Figure 9.2.

Figure 9.2 - Step II - Contraction Scour Calculation and Distribution

H1

Zmax(Cont)

Step III: Pier Scour Calculation

1. If Step II leads to no contraction scour, the pier scour is calculated by using the velocity V and water depth H at the location of the pier in the contracted channel assuming that the bridge piers are not there. The velocity Vhec and water depth can be calculated directly by using a program like HEC-RAS.

2. If Step II leads to a maximum contraction scour depth Zmax(Cont), then the maximum pier scour depth is calculated by using the critical velocity Vc for the soil and the water depth H2 including the contraction scour depth. These are:

( )ContZHH max12 += (9.4)

( )

( )

=

>==

0

0

max

max2

31

2

ContZV

ContZgnHVV

hec

cC ρ

τ (9.5)

where H1 is the water depth in the contracted channel before contraction scour starts (m). Then the maximum pier scour depth Zmax(pier) can be calculated by using equation 9.6:

( ) 635.0max 18.0 eshspw RKKKPierZ = (9.6)

Where Kw is the correction factor for pier scour water depth, given by: For H/B ≤ 1.6 Kw = 0.85 (H/B) 0.34 (9.7)

For H/B > 1.6 Kw = 1 Ksp is the correction factor for the pier spacing effect on the pier scour depth, when n piers of diameter B are installed in a row, given by:

( )nBBBK sp −

=1

1 (9.8)

Ksh is the correction factor for pier shape effect on pier scour. Ksh is equal to 1.1 for rectangular piers with length to width ratios larger than 1. Re is the Reynolds number:

Re = VB’/ν (9.9) where V is the mean depth average velocity at the location of the pier if the pier is not there when there is no contraction scour, or the critical velocity Vc (equation 9.5) of the bed material if contraction scour occurs, B’ is the pier diameter or projected width (Lsinα +Bcosα), B and L are the pier width and length respectively, α is the attack angle and ν is the kinematic viscosity of water.

Figure 9.3: - Step III and IV – Calculations of Pier Scour and Superposition

Zmax

H1

Zmax (Cont) Zmax (Pier)

Step IV: Total Maximum Bridge Scour Calculation: The maximum bridge scour is (Figure 9.3):

)()( maxmaxmax PierZContZZ += (9.10) Step V: Maximum Shear Stress around the Bridge Pier (Figure 9.4) In the calculations of the initial development of the scour depth, the maximum shear stress τmax is needed. This maximum shear stress is the one that exists around the bridge pier since the pier is the design concern. This step describes how to obtain τmax. Figure 9.4 gives the parameters definition.

Figure 9.4 - Plan View of Complex Pier Scour and Contraction Scour In the case of an uncontracted channel (no abutments), the maximum bed shear stress τmax around the pier is given by:

2max 1

1 10.094log 10w sh sp

e

k k k k VRατ ρ

= ⋅ −

(9.11)

Where ρ is the water mass density (kg/m3), V1 is the mean depth velocity in the approach uncontracted channel (m/sec), Re is the Reynolds number based (V1B/ν) where B (m) is the pier diameter or pier projected width, ν is the kinematic viscosity of the water (m2/s), and kw, ksh, ksp, kα are the correction factors for water depth, shape, pier spacing, and attack angle, respectively.

( )deepττkw

max

max= = 4

1 16HBe

−+ (9.12)

( )singlemax

max

ττ

=spk1.1

1 5SBe

−= + (9.13)

V1 V2

L

B2 B1

( )circleksh

max

max

ττ

=4

1.15 7LBe

−= + (9.14)

1=shk for circular shape

( )deg0max

max

ττ

=ak0.57

1 1.590α = +

(9.15)

where H is the water depth, B is the pier diameter or projected width, S is the pier center to center spacing, L is the pier length, and α is the angle between the direction of the flow and the main direction of the pier. In the case of a contracted channel (Figure 9.4), the maximum bed shear stress around pier is given by Equation (9.11) except that the velocity in the contracted section V2 is used instead of the approach velocity V1. The equation is:

2max 2

1 10.094log Re 10w sh spk k k k Vατ ρ

= −

(9.16)

Where 2V (m/s) is the mean depth velocity in the contracted channel at the location of the pier without the presence of the pier. The velocity V2 can be obtained from HEC-RAS or from mass conservation for a rectangular channel

=

2

112 14.1

BBVV (9.17)

Step VI: Time History of the Bridge Scour This part of the method proceeds like the original SRICOS-EFA method, which has been described in Step III. The initial shear stress τmax around the pier is calculated from equation (9.16) and the corresponding initial erosion rate iZ is obtained from the erosion function (measured in the EFA), the maximum scour depth due to contraction scour and pier scour is calculated from Equation (9.10). With these two quantities defining the tangent to the origin and the asymptotic value of the scour depth versus time curve, a hyperbola is defined to describe the entire curve.

max

( ) 1i

tZ t tZ Z

=+

(9.18)

where Z(t) is the scour depth due to a flood, t is the flood duration, iZ is the initial erosion rate, Zmax is the maximum scour depth due to the flood (equation 9.10). In the case of a complete hydrograph and of a multi-layer soil system, the accumulation algorithms are as follows. • Multi-flood System The hydrograph of a river indicates how the velocity varies with time. The fundamental basis of the accumulation algorithms is that the velocity histogram is a step function with a constant velocity value for each time step. When this time step is taken as one day, the gauge station value is constant for that day because only daily records are kept. The case

of a sequence of two different constant velocity floods scouring a uniform soil is considered (Figure 9.5). Flood 1 has velocity V1 and lasts a time t1 while flood 2 has a velocity V2 and lasts a time t2. After flood 1, a scour depth Z1 is reached at time t1 (Point A on Figure 9.5b) and can be calculated as follows:

11

1

1 max1

1i

tZ tZ Z

=+

(9.19)

For flood 2, the scour depth will be: 2

22

2 max 2

1i

tZ tZ Z

=+

(9.20)

The scour depth Z1 also could have be created by flood 2 in a time te (Point B on Figure 9.5c). The time te is called the equivalent time. The time te can be obtained by using Equations 9.19 and 9.20 with Z2 = Z1 and t2 = te.

1

21 2

1 max1 max 2

1 1ei

ii

ttZ t ZZ Z Z

=

+ −

(9.21)

When flood 2 starts, even though the scour depth Z1 was due to flood 1 over a time t1, the situation is equivalent to having had flood 2 for a time te. Therefore when flood 2 starts the scour depth versus time curve proceeds from point B on Figure 9.5c until point C after a time t2. The Z versus t curve for the sequence of flood 1 and 2 follows the path OA on the curve for flood 1 then switches to BC on the curve for flood 2. This is shown as the curve OAC on Figure 9.5d. The procedure described above is for the case of a velocity V1 followed by a velocity V2 higher than V1. In the opposite case, where V2 is less than V1, flood 1 creates a scour depth Z1 after a time t1. This depth is compared with Zmax2 due to flood 2. If Z1 is larger than Zmax2, it means that when flood 2 starts the scour hole is already deeper than the maximum scour depth that flood 2 can create. Hence, flood 2 cannot create any additional scour and the scour depth versus time curve remains flat during flood 2. If Z1 is less than Zmax2, the procedure of Figure 9.5d should be followed. In the general case, the complete velocity hydrograph is divided into a series of partial flood events, each lasting ∆t. The scour depth due to floods 1 and 2 in the hydrograph will be handled by following the procedure of Figure 9.5d. At this point the situation is reduced to a single flood 2 which lasts te. Then the process will consider flood 3 as a new “flood 2” and will repeat the procedure of Figure 9.5d applied to flood 2 lasting te2 and flood 3. Therefore the process advances with only two floods to be considered: the previous flood with its equivalent time and the new “flood 2”. The time step ∆t is typically one day and the velocity hydrograph can be 70 years long. • Multi-layer System In the multi-flood system analysis, the soil is assumed to be uniform. In reality, the soil involves different layers and the layer characteristics can vary significantly with depth. It

Figure 9.5 - Scour Due to a Sequence of Two Flood Events

Figure 9.6 - Scour of a Two-Layer Soil System

is necessary to have an accumulation process which can handle the case of a multi-layer system. Consider the case of a first layer with a thickness equal to 1Z∆ and a second layer with a thickness equal to 2Z∆ . The river bed is subjected to a constant velocity V (Figure 9.6a). The scour depth Z versus time t curves for Layer 1 and Layer 2 are given by Equations 9.19 and 9.20 (Figure 9.6b, Figure 9.6c). If the thickness of Layer 1 1Z∆ is larger than the maximum scour depth Zmax1, given by Equation (9.10), then the scour process only involves Layer 1. This case is the case of a uniform soil. On the other hand, if the maximum scour depth Zmax1 exceeds the thickness 1Z∆ , then Layer 2 will also be involved in the scour process. In this case, the scour depth 1Z∆ (Point A on Figure 9.6b) in layer 1 is reached after a time t1; at that time, the situation is equivalent to having had Layer 2 scoured over an equivalent time te (Point B on Figure 9.6c). Therefore when Layer 2 starts to be eroded, the scour depth versus time curve proceeds from Point B to Point C on Figure 9.6c. The combined scour process for the two-layer system corresponds to the path OAC on Figure 9.6d. In reality, there may be a series of soil layers with different erosion functions. The computations proceed by stepping forward in time. The time steps are t∆ long, the velocity is the one for the corresponding flood event, and the erosion function ( z vs τ ) is the one for the soil layer corresponding to the current scour depth (bottom of the scour hole). When t∆ is such that the scour depth enters a new soil layer, the computations follow the process described in Figure 9.6d. 9.4. INPUT FOR THE SRICOS-EFA PROGRAM The input includes parameters for the soil, the water, and the geometry of the problem. Soil properties: In the SRICOS-EFA method, the soil properties at the bridge site are represented by the soil erosion function which is a measure of the erodibility of the soil. The soil erosion function is the relationship between the erosion rate z of the soil and the hydraulic shear stress τ applied on the bottom of riverbed. It is obtained by performing an EFA test on the soil sample (Briaud et al. (2002)). The erosion function (Figure 9.7) is needed for each layer within the potential scour depth at the bridge site.

Shear Stress (N/m2)0 10 20 30 40 50 60 70 80

Scou

r Rat

e (m

m/h

r)

0

5

10

15

20

τc = 7 N/m2

Figure 9.7 - Typical EFA Test Result

Hydrologic data: The water flow is represented by the velocity hydrograph. This hydrograph can be obtained from a nearby gauge station. The hydrograph should last as long as the required period of prediction. Furthermore, if the hydrograph obtained from the gauge station does not contain a 100-year flood, it can be spiked artificially to include such a large event if required by design. The hydrograph is typically in the form of discharge as a function of time. Because the input for scour calculations is the velocity and not the discharge, it is necessary to transform the discharge data at the gauge station into velocity data at the bridge site. This can be done by using a program such as HEC-RAS (Hydrologic Center’s River Analysis System, HEC-RAS, 1997), which was developed by US Army Corps of Engineers. In order to run HEC-RAS, several geographical features are necessary such as: the average slope of channel bed, the channel cross-section, and the roughness coefficient of the riverbed. Figures 9.8 show the discharge hydrograph, the discharge versus velocity curve (HEC-RAS results), and the mean depth velocity at one of the piers versus time (velocity hydrograph) for the Woodrow Wilson Bridge on the Potomac River in Washington DC between 1960 and 1998. Geometry: The geometry includes the channel geometry and the bridge geometry. The channel and bridge geometry are used for contraction scour evaluation including the determination of the contraction ratio. The piers size, shape, spacing, and angle of attack are used for pier scour calculations.

Table 9.1 - Summary of Geometry Factors

Bridge Geometric Factors Channel Geometric Factors

Bridge contraction ratio Channel contraction ratio Bridge opening Bridge contraction length Channel contraction length

Type, shape

Attack angle

Channel water depth

Size, length, width (diameter) Manning coefficient

Pier spacing Channel Hydraulic radius

Bridge piers

Number of piers

Channel characteristics

Soil stratigraphy

W o o d r o w W ils o n B r id g e H y d r o g r a p h y(fr o m 1 9 6 0 to 1 9 9 8 )

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 9 6 0 1 9 6 3 1 9 6 6 1 9 6 9 1 9 7 2 1 9 7 5 1 9 7 8 1 9 8 1 1 9 8 4 1 9 8 7 1 9 9 0 1 9 9 3 1 9 9 6 1 9 9 9

Y e a r

Dis

char

ge (m

3 /sec

)

R e la tio ns hip o f D is c ha rg e a nd V e lo c ity(W o o do w W ils o n B ridg e a t Pie r 1 E )

0 .0 0

0 .5 0

1 .0 0

1 .5 0

2 .0 0

2 .5 0

3 .0 0

3 .5 0

4 .0 0

0 5 0 0 0 1 0 0 0 0 1 5 0 0 0 2 0 0 0 0 2 5 0 0 0

D i s c har g e (m 3 /s )

Vel

ocity

(m/s

)

W o o d ro w W ils o n B r id g e F lo w V e lo c ity C h a rt(fro m 1 9 6 0 to 1 9 9 8 )

0

0 .5

1

1 .5

2

2 .5

3

1 9 6 0 1 9 6 3 1 9 6 6 1 9 6 8 1 9 7 1 1 9 7 4 1 9 7 7 1 9 8 0 1 9 8 3 1 9 8 5 1 9 8 8 1 9 9 1 1 9 9 4 1 9 9 7

Y e a r

Vel

ocity

(m/s

ec)

Figure 9.8: Example of Hydrograph transformation for the Pier 1E of the Woodrow

Wilson Bridge on the Potomac River in Washington, D,C.

9.5. THE SRICOS-EFA PROGRAM The SRICOS-EFA program automates the SRICOS-EFA method. The first version of the program was solving the problem of a cylindrical pier in deep water (Kwak, 1999, Kwak et al., 2001). In this study the program was extended to predict complex pier scour and contraction including the superposition of both scour modes. Using the input described in the previous section, the program automates the calculations of all the parameters: transformation of discharge into velocities, maximum shear stress, initial slope of the scour rate vs. shear stress curve, maximum scour depth, and so on. Then it proceeds with the techniques described to handle multi-flood and multi-layer systems. The program was written in FORTRAN by using Visual FORTRAN 5.0. The flow chart of the program in Figure 9.9 gives an overall view of the SRICOS-EFA method including all the equations. As it can be seen, there is one branch to handle complex pier scour alone, one branch to handle contraction scour alone, and one branch to handle the concurrent occurrence of complex pier scour and contraction scour. The SRICOS-EFA program is a user friendly, interactive code that guides the user through a step-by-step data input procedure except velocity or discharge data. This program however is not in the windows environment and needs to be implemented in such an environment for easier use. For the hydrograph, the number of velocity or discharge data points can be at least several tens of thousands for the time duration corresponding to the design life of bridges and if the velocity data is given on a daily basis. The velocity or discharge data should be prepared in the format of an ASCII file or a text document before running the program. The input data can be either in the Metric System or the U.S. Customary System; the output can also be in either system. The User’s Manual for SRICOS-EFA is presented in Appendix D. 9.6. OUTPUT OF THE SRICOS-EFA PROGRAM Once the program finishes all of the computations successfully, the output file is automatically created. The output file includes the following columns: time, flow velocity, water depth, shear stress, maximum scour depth (pier, contraction, or total), and instantaneous scour depth (pier, contraction, or total). The first few days of a typical output file of the program are shown in Table 9.2. For this example the critical shear stress was 4 N/m2; as can be seen no scour occurred until the velocity was high enough to overcome the critical shear stress on day 11. The format of the output file is a text file. This file can be used to plot a number of figures (Figure 9.10). The most commonly plotted curves are water velocity vs. time, water depth vs. time, shear stress vs. time, and scour depth vs. time. The scour depth versus time curve indicates if the final scour depth Zfinal (scour depth at the end of the hydrograph) is close to the maximum scour depth for the biggest flood in the hydrograph Zmax(max) or not. Typically in sand the answer is yes but in low erodibility clays the difference is significant enough to warrant the analysis in the first place. Kwak et al. (2001) showed the results of a parametric analysis indicating the most important parameters in the prediction process.

Figure 9.9 – Flow Chart of the SRICOS-EFA Program Woodrow Wilson Bridge Flow Velocity Chart

(from 1960 to 1998)

0

0.5

1

1.5

2

2.5

3

1960 1963 1966 1968 1971 1974 1977 1980 1983 1985 1988 1991 1994 1997

Year

Vel

ocity

(m/s

ec)

Scour Depth Vs Time

0

1000

2000

3000

4000

5000

6000

7000

1960 1965 1970 1975 1980 1985 1990 1995

Time (year)

Scou

r D

epth

(mm

)

Figure 9.10 – Example of plots generated from a SRICOS-EFA Program Output.

Table 9.2 - Example of SRICOS-EFA Program Output File

CHAPTER 10 VERIFICATION OF THE SRICOS-EFA METHOD

10.1. BACKGROUND The SRICOS-EFA method for complex pier and contraction scour in cohesive soils was developed on the basis of flume tests for the maximum scour depth equations and numerical simulations for the maximum initial shear stress equations. As with any new method, there is a need to verify the method against other measurements. These measurements should preferably be full scale case histories. For this project, the case histories had to satisfy the following site requirements:

1. Channel contraction exists 2. A bridge with piers in the water exists 3. A gauge station exists giving the hydrograph over a period of time T 4. The soil is cohesive 5. The site can be accessed with a drill rig 6. The river bed cross section was documented at the beginning and at the end of the

same period of time T as the hydrograph. A survey of the US DOTs was conducted and many sites were collected. Upon further review, it was found that none of the sites had the requirements necessary for evaluating the method. Since, after much time, effort, and money was spent trying to find such sites, and after realizing that this avenue could not be pursued, it was decided to look in the literature for existing data associated with the topic of complex pier and contraction scour. The following databases were found:

1. Mueller (1996) for complex pier scour 2. Froehlich (1988) for complex pier scour 3. Gill (1981) for contraction scour

These databases were for primarily for cohesionless soils but it was felt that it would be useful to compare the SRICOS-EFA method to cohesionless soils measurements. The following gives a brief description of the databases and shows the comparisons between measured and predicted scour depth. Note that since the data pertains to cohesionless soils, the comparison is limited to evaluating the equations for the maximum scour depth Zmax(complex pier and contraction). 10.2. MUELLER (1996) DATA BASE: PIER SCOUR The Mueller Database was obtained from the report FHWA-RD-95-184 entitled “Channel Scour at Bridges in the United States”. More than 380 pier scour measurements were collected at 56 bridge sites in Alaska, Arkansas, Colorado, Delaware, Georgia, Illinois, Indiana, Louisiana, Maryland, Mississippi, Montana, New York, Ohio, and Virginia. Figure 10.1 shows the comparison between the complex pier scour depth calculated by the SRICOS-EFA method and the measurements in the database. The

equation used was the SRICOS equation for the maximum pier scour depth. Figure 10.2 shows the predictions by the HEC-18 equation compared to the measurements for the same database. Both SRICOS and HEC 18 appear to be conservative with less scatter in the SRICOS predictions.

K Factors Approach (Mueller Database)

0

2

4

6

8

10

0 2 4 6 8 10

Measured Scour Depth (m)

Pred

icte

d Sc

our

Dep

th (m

)

Figure 10.1 – SRICOS-EFA Predictions against Mueller (1996) Database

HEC-18 Method (Mueller Database)

0

2

4

6

8

10

0 2 4 6 8 10


Pred

icte

d Sc

our

Dep

th (m

)

Figure 10.2 - HEC-18 Predictions against Mueller (1996) Database

In order to investigate the influence of D50 on the match between SRICOS-EFA predictions and measurements, the database was divided in three D50 categories. Figures 10.3 show the results. It appears that there are no obvious trends to be observed. ( )

0

2

4

6

8

0 2 4 6 8


Pred

icte

d Sc

our

Dep

th (m

)

D50 (0.075mm~4.75 mm)

( )

0

2

4

6

8

0 2 4 6 8


Pred

icte

d Sc

our

Dep

th (m

)

D50 (4.75mm~75mm

( )

0

2

4

6

8

0 2 4 6 8


Pred

icte

d Sc

our

Dep

th (m

)

D50 (75mm~300mm)

Figure 10.3 – SRICOS-EFA Predictions vs. Mueller Database for Various Ranges of D50

The same approach was taken for the HEC-18 predictions and Figure 10.4 shows the results. Again it appears that there is no major trend to be observed.

0

2

4

6

8

10

0 2 4 6 8 10Measured Scour Depth (m)

Pred

icte

d Sc

our

Dep

th (m

)

D50 (0.075mm~4.75 mm)

0

2

4

6

8

10

0 2 4 6 8 10Measured Scour Depth (m)

Pred

icte

d Sc

our

Dep

th (m

)

D50 (4.75mm~75mm)

0

2

4

6

8

0 2 4 6 8Measured Scour Depth (m)

Pred

icte

d Sc

our

Dep

th (m

)

D50 (75mm~300mm)

Figure 10.4 – HEC-18 Predictions vs. Mueller Database for Various Ranges of D50

10.3. FROEHLICH (1988) DATABASE: PIER SCOUR The Froehlich database was obtained from an ASCE report entitled “Analysis of Onsite Measurements of Scour at Piers”. In the Froehlich database, there are 79 pier scour measurement points, 50 cases for round–nosed pier, 9 cases for square-nosed pier and 20 cases for sharp-nosed pier. Figure 10.5 shows the comparison between the complex pier scour depth calculated by the SRICOS-EFA method and the measurements in the database. The equation used was the SRICOS equation for the maximum pier scour depth. Figure 10.6 shows the HEC-18 equation compared with the same database. With this database HEC-18 appears to be more conservative than SRICOS.

K Factors Approach (Froehlich Database)

0

1

10

100

0.1 1 10 100Measured Scour Depth (m)

Pred

icte

d Sc

our

Dep

th (m

)

Figure 10.5 - SRICOS-EFA Predictions against Froehlich (1988) Database

HEC-18 Method (Froehlich Database)

0

1

10

100

0.1 1 10 100Measured Scour Depth (m)

Pred

icte

d Sc

our

Dep

th (m

)

Figure 10.6 - HEC-18 Predictions against Froehlich (1988) Database

10.4. GILL (1981) DATABASE: CONTRACTION SCOUR The Gill database was obtained from the Journal of the Hydraulic Division of ASCE in an article entitled “Bed Erosion in Rectangular Long Contraction”. Gill (1981) ran some contraction tests on sand in the laboratory. The experiments were conducted in a rectangular steel channel, which was 11.4 m in length, 0.76 m in width and 0.46 m in depth. There were two sizes of contracted sections in the channel. In the first series of experiments, the effective length of the contraction was 1.83 m, excluding the upstream (inlet) and downstream (outlet) transitions, each 0.46 m long. In the second series of experiments, the effective length of the contraction was 2.44 m with transitions each 0.46 m long. The width of the contracted section was 0.5 m. Two types of nearly uniform sand were used in the experiments. The average size of the coarse sand, D50, was 1.53 mm while D50 of the fine sand was 0.92 mm. The angle of transition at the contraction was approximately 15°. The scour depth was obtained by averaging several depth readings taken along the centerline of the channel. According to the location of the measurements, the scour depth measured by Gill was the uniform scour depth in this study. The Gill (1981) database was therefore used to verify the uniform contraction scour equation Zunif, not Zmax. The SRICOS-EFA method calls for a value of the critical velocity Vc measured in the EFA. Since this data was not available in Gill’s database, the expression recommended in HEC-18 was used.

31

5061

19.6 DyVC = (10.1) where Vc is the critical velocity of the bed material, m/s; y is the water depth in the upstream flow, m; and D50 is the particle corresponding to 50% passing by weight, m. Figure 10.7 shows the comparison between the uniform contraction scour depth calculated by the SRICOS-EFA method and the measurements in the database. Figure 10.8 shows the HEC-18 equation compared with the same database. As can be seen the SRICOS method is reasonably good while the HEC-18 method is severely under predicting. 10.5. REMARKS While it would have been preferable to find a number of full scale case histories, at least the comparison to databases obtained primarily on cohesionless soils gave an idea of how the SRICOS-EFA method fits with the HEC-18 method. Note that the comparison is only based on the maximum depth of scour values and does not involve the scour rate which is the major difference between the current HEC-18 method and the SRICOS-EFA method. Overall it is found that the performance of the SRICOS-EFA method is similar to the HEC-18 method except for the contraction scour depth where the SRICOS–EFA method is much closer to the measurements.

SRICOS-EFA Method (Gill Database)

05

10152025303540455055

0 5 10 15 20 25 30 35 40 45 50 55

Measured Scour Depth (mm)

Pred

icte

d Sc

our

Dep

th (m

m)

Figure 10.7 - SRICOS-EFA Method against Gill (1981) Database

HEC-18 Method (Gill Database)

05

10152025303540455055

0 5 10 15 20 25 30 35 40 45 50 55

Measured Scour Depth (mm)

Pred

icte

d Sc

our

Dep

th (m

m)

Figure 10.8 - HEC-18 Method against Gill (1981) Database

CHAPTER 11 FUTURE HYDROGRAPHS & SCOUR RISK ANALYSIS 11.1. BACKGROUND Since the SRICOS-EFA method predicts the scour depth as a function of time, one of the input is the velocity versus time curve or hydrograph at the foundation location. This hydrograph should cover the period over which the scour depth must be predicted. A typical bridge is designed for 75 years. Therefore the design for a new bridge requires the knowledge of the hydrograph from the year of construction until that year plus 75 years. The question is: how can one obtain the future hydrograph covering that long period of time? This requires predicting the future over a 75-year period! One solution is to use a hydrograph recorded at a nearby gauge station over the last 75 years and assume that the future hydrograph will be equal to the past hydrograph. If the gauge is not at the future bridge location, the discharge can be multiplied by the ratio of the drainage area at the bridge site over the drainage area at the gauge site. If the record at the gauge station is not 75 years long, one can simply repeat the recorded hydrograph until it covers the 75-year period. If the recorded hydrograph does not include the design flood (100 year flood or 500 year flood), one can spike the hydrograph with one or more of those floods before running the SRICOS program (Figure 11.1).

Hydrograph (Add 500year flood)

0

3000

6000

9000

12000

15000

18000

1960 1970 1980 1990 2000

Time (Year)

Stre

amflo

w (m

3 /s)

Scour Depth Vs. Time (Add 500year flood)

0

2

4

6

8

10

12

1960 1970 1980 1990 2000

Time (Year)

Scou

r Dep

th (m

)

(a) Hydrograph (b) Scour Depth Vs. Time Curve

Figure 11.1 – Woodrow Wilson Measured Hydrograph spiked with a 500-year Flood

Another solution is to use the new technique which is presented here. This technique consists of using a past hydrograph, preparing the frequency distribution plot for the

floods within that hydrograph, sampling the distribution randomly and preparing a future hydrograph, for the required period, which has the same mean and standard deviation as the measured hydrograph. This process is repeated 10,000 times and, for each hydrograph, a final scour depth (the depth reached after 75 years of flow) is generated. These 10,000 final depths of scour are organized in a frequency distribution plot with a mean and a standard deviation. That plot can be used to quote a scour depth with a corresponding probability of occurrence, or better, to choose a risk level and quote the corresponding final depth of scour. 11.2. PREPARATION OF THE FUTURE HYDROGRAPHS The SRICOS-EFA method determines the scour depth at the end of the bridge life as a progressive process driven by a given sequence of daily stream-flow values throughout the life, Lt, of the structure. The randomness of the hydrologic forcing suggests combining the scour model with some hydrological and statistical analyses. If the stream-flow sequence (or hydrograph) is modeled as a stochastic process, it is possible to set up a Monte Carlo procedure sampling from that process different realizations of the hydrograph (of length Lt), and estimating (SRICOS-EFA method) for each of them the scour depth, d, at the end of the bridge life. Thus, d is regarded as a random variable and its statistics can be studied in detail to determine the risk of failure associated with different choices of the design value of the scour depth. The modeling of daily stream-flow, Q, can be tackled using different approaches (e.g., Bras and Rodriguez-Iturbe, 1986; Montanari et al., 1997; 2000) corresponding to different levels of complexity. A first simple analysis suggested here considers Q as a random, uncorrelated variable. A suitable distribution is fitted to the data and the hydrographs are then generated as series of values sampled from such a distribution. Ongoing research is also applying other stochastic models to account for both the autocorrelation and the memory of the process and is assessing whether the temporal structure (i.e. both autocorrelation and memory) of the stream-flow sequences is able to affect the statistical properties of the scour-depth probability distribution. The theoretical distribution used to model daily stream-flow observations needs to be defined only for positive values of Q, to have a positive skewness, and to be able to provide an accurate representation of the extreme values (i.e. good fit at the upper tail of the distribution). As expected, the extreme values are found to greatly affect the scour depth estimates and an imprecise modeling of stream-flow maxima could easily lead to unrealistic estimations of the scour depth statistics. Logarithmic transformations are frequently used to study stream-flow extremes (e.g., Chow et al., 1988; Benjamin and Cornell, 1970); therefore, a log-normal distribution can be a good candidate for modeling the daily stream-flows. The method of moments is used to determine the parameters of the distribution. As such, Q is expressed as the exponential of a normally distributed random variable, y, with mean

+

= 2

2

121

Q

Q

Qy Log

µσ

µµ (11.1)

and standard deviation

+=

2

1Q

Qy Log

µσ

σ (11.2)

with µQ and σQ being the mean and the standard deviation of daily streamflow, respectively. In the case of the Woodrow Wilson Bridge, stream-flow data is available at the Little Falls station (USGS #01646500) on the Potomac River, approximately 13 km upstream from the bridge. Correction of the measured stream flow is applied by multiplying the values by the drainage area ratio. The correction is of the order of 3%. Figure 11.2 shows the original hydrograph and the corresponding prediction of scour depth history using the SRICOS-EFA method. The mean and standard deviation of Q in the period of record 1931-2000 are µQ=327 m3s-1, and σQ=467 m3s-1, respectively, while the maximum discharge in the 70-year-long record was 12,056 m3s-1. Synthetic hydrographs of the same length generated by sampling from a lognormal distribution of mean µQ and standard deviation σQ have on the average a maximum value of about 12,000 m3s-1,

Original Hydrograph

0

3000

6000

9000

12000

15000

18000

1930 1940 1950 1960 1970 1980 1990 2000

Time (Year)

Stre

amflo

w (m

3 /s)

Original Scour Depth vs. Time

0

2

4

6

8

10

12

1930 1940 1950 1960 1970 1980 1990 2000

Time (Year)

Scou

r Dep

th (m

)

(a) Hydrograph (b) Scour Depth vs. Time

Figure 11.2 - Original Hydrograph & Scour Depth vs. Time near Woodrow Wilson Bridge Site

suggesting that such a distribution gives an adequate representation of the extrema. Figure 11.3 shows an example of a generated future hydrograph and the associated scour depth history as predicted by the SRICOS-EFA method.

Predicted Hydrograph (75year)

0

3000

6000

9000

12000

15000

18000

0 15 30 45 60 75

Time (Year)

Stre

amflo

w (m

3 /s)

Predicted Scour Depth Vs. Time

0

2

4

6

8

10

12

0 15 30 45 60 75

Time (Year)Sc

our D

epth

(m)

(a) Hydrograph (b) Scour Depth vs. Time

Figure 11.3 - Predicted Hydrograph and Scour Depth vs. Time Curve near Woodrow

Wilson Bridge Site (Project time = 75year) 11.3. RISK APPROACH TO SCOUR PREDICTIONS Many equally possible future hydrographs such as the one in Figure 11.3 are generated by the random sampling process. For each hydrograph, the SRICOS program generates a scour depth history including a final depth of scour, d, at the end of the project life. These values of the final depth of scour can be organized in a frequency distribution. Figure 11.4 shows the probability distributions obtained for the example of the Woodrow Wilson bridge at the end of a chosen bridge life, Lt. This analysis can be used to estimate the level of risk, R, associated with the choice of different design values of scour depth and project lives. By definition, the risk level is the probability that the design conditions are exceeded in the course of the life of the structure. Thus, from the probability distribution of d (Figure 11.4) it is possible to determine the cumulative distribution function (CDF) of d (Figure 11.5). The risk is then estimated as the probability of exceedence (Figure 11.5). Table 11.1 reports the risk level associated with different project lives and design values of d. It is observed that R is a non-linear function of d and Lt. This analysis provides a statistical framework that can be used in a cost-benefit study of bridge foundation design. Commonly accepted methods of scour analysis in cohesionless soils refer to a single peak-flow value selected on the basis of its return period, Tr, as well as of the associated

level of risk. Such an approach does not account for the contribution to bridge scour due to smaller (and more frequent) floods. The SRICOS-EFA method can be used to include the effect of the entire hydrograph. The Monte Carlo procedure outlined in this section represents a possible new probabilistic approach to scour analysis. Ongoing research is developing an extended version of this approach using different stochastic hydrologic models able to account for the daily-flow distribution, and for the autocorrelation of the stream-flow series. This study will show whether the scour depth is sensitive to the temporal structure of stream-flow sequences and will indicate the level of detail that is necessary to include in the hydrologic stochastic model. 11.4. OBSERVATIONS ON CURRENT RISK LEVELS A direct comparison between the risk results obtained here with the SRICOS method (Table 11.1) and traditional approaches based on single peak-flow values is not easy. Nevertheless, an example is provided here. The peak flow value associated with a given return period can be determined through a flood-frequency analysis (e.g., Chow et al., 1988; pp 375-378). Figure 11.6 shows the result of such an analysis for the Woodrow Wilson measured hydrograph. As can be seen on that figure, the 100 year flood has a discharge of 12,600 m3/s and the 500 year flood has a value of 16,600 m3/s. If the design life of the bridge is Lt, the probability of exceedence or risk R for a flood having a return period Tr is given by:

R = 1 – (1 – 1/Tr)Lt (11.3) If the design life of the bridge is 75 years, the probability that the flood with a return period of 100 year will be exceeded during the 75 year design life is 53% according to equation 11.3. The risk that the 100 year flood will be exceeded during the 75 years is 53% or about one chance out of two. For the 500 year flood, and for the same 75 year design life, the risk is 14% or one chance in about 7. Even if a bridge designed for a 100 or 500 year flood experiences a 1000 year flood, this bridge may not collapse. Indeed collapse of the bridge is based on a different criterion than just exceedence of the design flood. There are numerous inherent redundancies in the design of a bridge and many design parameters have to be exceeded before collapse occurs. Nevertheless, the risk level associated with the floods used in everyday design appears very high compared to risk levels in other disciplines within Civil Engineering. For example the structural engineers have based their codes on a risk level of about 0.1%. The geotechnical engineers probably operate at about 1%. The scour engineers seem to operate at a much higher risk level. This is particularly worrisome since there is no factor of safety on the depth of scour passed on from the scour engineer to the geotechnical engineer for him to calculate the pile length. One useful approach in this respect is to conduct a sensitivity analysis by varying the input parameters and monitoring the impact of the parameter variation on the final scour depth. This would help in realizing how important each parameter is and give a range of scour depth values. Note that the proposed method is a prediction method not a design method. Indeed the equations were derived from a number of best-fit regressions against the experimental data. The proposed method becomes a design method when a factor of

safety is added. The recommended factor of safety is 1.5. In other words, the predicted final depth of scour should be multiplied by 1. 5 before it becomes a design scour depth.

0

0.1

0.2

0.3

0.4

0.5

5 7.5 10 12.5 15d (m)

p(d)

Lt=50yearLt=75yearLt=100yearLt=150year

Figure 11.4 - Probability distribution of scour depth, d, for different lengths of the

project life, Lt

0.01

0.1

1

10

100

5 7.5 10 12.5 15

d (m)

R(d

) (%

)

Lt=50yearLt=75yearLt=100yearLt=150year

Figure 11.5 - Risk associated with different design values of the final scour depth,

d, and different lengths of the project life, Lt

Table 11.1 - Risk of failure associated with different design values of scour depth and project lives

Design value of Project Life Scour depth (m) 50 yrs 75 yrs 100 yrs 150 yrs

6.5 42% 74% 91% 99.8% 7.0 25% 48% 70% 93% 7.5 14% 27% 40% 65%

Flood-frequency curve based on Original Hydrograph(1931-1999)

y = -2491.6Ln(x) + 12629R2 = 0.9563

0

5000

10000

15000

20000

0.1110100

Percent probability of exceedance in X years

Stre

amflo

w (m

3 /sec

)

100year flood: 12629m3/s500year flood: 16639m3/s

Figure 11.6 - Flood-frequency curve for the Potomac River at the Woodrow Wilson Bridge

CHAPTER 12 SCOUR EXAMPLE PROBLEMS 12.1. EXAMPLE 1: SINGLE CIRCULAR PIER WITH APPROACHING CONSTANT VELOCITY Given: Pier geometry: Pier diameter B = 2.5m, circular pier Channel geometry: Channel upstream width B1 = 50m Flow parameters: Water depth H = 3.12m,

Approaching constant velocity V = 3.36m/sec Angle of attack: 0 degree

EFA result: Layer 1: Thickness 10m; Critical shear stress 2 N/m2

Figure 12.1 – EFA Results for Soil Layer 1 (Example 1)

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

EFA Result (Layer 1)

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50 60 70Shear Stress (N/m2)

Scou

r R

ate

(mm

/hr)

Layer 2: Thickness 20m; Critical shear stress 4 N/m2

Figure 12.2 – EFA Results for Soil Layer 2 (Example 1) Flood period: 2 days for hand-calculation 2 years for computer-calculation Determine: The magnitude of maximum pier scour depth.

Figure 12.3 – Plan View of Single Circular Pier Scour Case (Example 1)

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

Flow

B


0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70

Shear Stress (N/m2)Sc

our

Rat

e (m

m/h

r)

12.1.1. SRICOS-EFA METHOD HAND-CALCULATION: (1) Calculate the K factors for τmax and Zmax:

109.1161161 5.212.344=⋅+=⋅+=

×−−eek B

H

w

( ) 916.05.2

12.385.085.034.0

34.0=

×== B

HKw

Since in this case, the pier is a circular pier, so 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’s number 6

6 104.810

5.236.3Re ×=×

== −νVD

(3) Maximum hydraulic shear stress around the pier is:

( ) 2622

max 28.52101

104.8log136.31000094.0109.1

101

log1094.0 m

NR

Vkkkke

spshw =

−

××××=

−⋅= ρτ α

(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: ( ) ( ) mmRKKKPierZ eshspw 3.4112104.8916.018.018.0 635.06635.0

max =×××== (6) The equation for z (t) is:

( )( )

3.41126.811

max

hrsthrst

Zt

Z

tz+

=+

=

(7) The flood lasts 2 days (48 hrs), 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

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 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


Regression Points Shear Stress vs. Scour Rate 8 Estimate Initial

Scour Rate



3, 0 4, 0.1 6,1 9,2

18.5, 4 27, 5 40, 6

60, 6.9

Results: After two years period of the flood having 3.36m/sec velocity, the final pier scour is: Z = 4 m The following figure illustrates the scour depth development with time.

Figure 12.4 – Scour Depth vs. Time (Example 1)

Scour Depth vs. Time (Example 1)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 200 400 600 800

Time (Day)

Pier

Sco

ur D

epth

(mm

)

12.2. EXAMPLE 2: SINGLE RECTANGULAR PIER WITH ATTACK ANGLE AND APPROACHING HYDROGRAPH Given: Pier geometry: Pier width B = 1.22m, pier length Lpier = 18m, rectangular pier Channel geometry: Channel upstream width B1 = 50m Flow parameters: Angle of attack: 20 degree

70 years predicted hygrograph

Figure 12.5 – 70 Years Future Approaching Hydrograph (Example 2)



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 70Shear Stress (N/m2)

Scou

r R

ate

(mm

/hr)

Future Hydrograph

0

2000

4000

6000

8000

10000

12000

14000

0 10 20 30 40 50 60 70Time (Year)

Dis

char

ge (m

3 /sec

)


Figure 12.7 – EFA Results for Soil Layer 2 (Example 2) Time duration: 70 years Determine: The magnitude of maximum pier scour depth.

Figure 12.8 – Plan View of Single Rectangular Pier Scour Case (Example 2)

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

Flow 20°

B

Lpier


0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70

Shear Stress (N/m2)

Scou

r R

ate

(mm

/hr)

12.2.1. SRICOS-EFA METHOD COMPUTER-CALCULATION: Since in this case we use the hydrograph as hydrologic data input, the relationship

between the discharge and velocity and the relationship between discharge and water

depth need to be defined. The program titled as River Analysis System (HEC-RAS) can

be the one of the good tools to find the relationships. The following charts are the results

obtained from HEC-RAS for this case.

Figure 12.9 – Relationship of Discharge vs. Velocity and Discharge vs. Water Depth (Example 2)

Discharge vs. Velocity

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 5000 10000 15000 20000 25000Discharge (m3/s)

Vel

ocity

(m/s

)

Discharge vs. Water Depth

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0 5000 10000 15000 20000 25000Discharge (m3/s)

Wat

er D

epth

(m)





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


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


Regression Points Shear Stress vs. Scour Rate 8

Estimate Initial

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


Regression Points Shear Stress vs. Scour Rate 8

Estimate Initial

Scour Rate



3, 0 4, 0.1 6,1 9,2

18.5, 4 27, 5 40, 6

60, 6.9 Results: After 70 years period of the flood, the final pier scour is: Z = 4.7m The following figure illustrates the scour depth development with time.

Figure 12.10 – Scour Depth Vs Time (Example 2)


0500

100015002000250030003500400045005000

0 10 20 30 40 50 60 70

Time (Year)

Pier

Sco

ur D

epth

(mm

)

12.3. EXMPLE 3: GROUP RECTANGULAR PIERS WITH ATTACK ANGLE AND APPROACHING CONSTANT VELOCITY Given: Pier geometry: Pier width B = 1.22m, pier length Lpier = 18m, rectangular pier,

number of piers, N = 3, spacing, S = 18m Channel geometry: Channel upstream width B1 = 150m Flow parameters: Water depth H = 3.12m,

Angle of attack: 20 degree Approaching constant velocity V = 3.36m/sec



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 400Shear Stress (N/m2)

Scou

r R

ate

(mm

/hr)



Flood period: 2 days for hand-calculation 2 years for computer-calculation Determine: The magnitude of maximum pier scour depth.

Figure 12.13 – Plan View of Rectangular Piers Group Scour Case (Example 3)

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

our

Rat

e (m

m/h

r)

Flow

River Bank River Bank

Lpier

B

S S

Flow 20°

12.3.1. SRICOS-EFA METHOD HAND-CALCULATION: (1) Calculate the K factors for τmax and Zmax:

9.3161161 3.712.344=⋅+=⋅+=

×−−eek B

H

w

( ) 637.03.7

12.385.085.034.0

34.0=

×== B

HKw

Here B is the projected width of pier. mWLB pier 3.720cos22.120sin18cossin 00 =×+×=+= αα

Since in this case, the pier is a rectangular pier, so

15.1715.1 22.1184

=×+=−eksh

Ksh = 1.1 (from HEC-18) Since there are 3 piers, so in this case the effect of group pier exists.

33.15151 3.7181.11.1

=+=+=

−

−

eek Ds

sp

17.13.7*3150

150

1

1 =−

=−

=nBB

BKsp

There is attack angle of the flow, so

636.190205.11

905.11

57.057.0

=

+=

+=α

αk

(2) Calculate Reynolds’s number 7

6 1045.210

3.736.3Re ×=×

== −νVD

(3) Maximum hydraulic shear stress around the pier is:

( ) 272

max

2max

8.365101

1045.2log136.31000094.0636.133.115.19.3

101

log1094.0

mN

RVkkkk

espshw

=

−

×××××××=

−⋅=

τ

ρτ α

(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: ( )

( ) mmZ

RKKKPierZ eshspw

72971045.21.117.164.018.0

18.0635.07

max

635.0max

=×××××=

=

(6) The equation for z (t) is: ( )

( )72973.15

11

max

hrsthrst

Zt

Z

tz+

=+

=

(7) The flood lasts 2 days (48 hrs), therefore Z = 667 mm or 9.1% of Zmax






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



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


Estimate Initial

Scour Rate



3, 0 4, 0.1 6,1 9,2

18.5, 4 27, 5 40, 6

60, 6.9

Results: After two years period of the flood having 3.36m/sec velocity, the final pier scour is: Z = 7.1 m The following figure illustrates the scour depth development with time.

Figure 12.14 – Scour Depth Vs Time (Example 3)


0

1000

2000

3000

4000

5000

6000

7000

8000

0 200 400 600 800

Time (Day)

Pier

Sco

ur D

epth

(mm

)

12.4. EXAMPLE 4: CONTRACTED CHANNEL WITH 90° TRANSITION ANGLE AND APPROACHING CONSTANT VELOCITY Given: Channel geometry: Upstream uncontracted channel width B1=150 m,

contracted channel width due to bridge abutment B2 = 50m, contraction length of channel L: = 30 m

Abutment transition angle: 90 degree Flow parameters: Water depth H = 3.12m,

Approaching constant velocity V = 3.36m/sec Manning coefficient: 0.02 EFA result: Layer 1: Thickness 15m; Critical shear stress 2 N/m2


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 400Shear Stress (N/m2)

Scou

r R

ate

(mm

/hr)


Figure 12.16 – EFA Results for Soil Layer 2 (Example 4) Flood period: 2 days for hand-calculation 2 years for computer-calculation Determine: The magnitude of maximum contraction scour depth.

Figure 12.17 – Plan View of Contracted Channel Scour Case (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

B2

B1

Bridge Abutment Bridge Abutment

90°

V1


0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70

Shear Stress (N/m2)

Scou

r R

ate

(mm

/hr)

River Bank River Bank Flow

L

12.4.1. SRICOS-EFA METHOD HAND-CALCULATION: (1) Calculate the K factors for τmax:

1≈wk

2.350

15038.062.038.062.075.175.1

2

1 =

+=

+=

BBkR

9.190909.01

909.01

5.15.1

=

+=

+=θ

θk

Since ( ) 35.03.010030

21

<==− BBL , so

198.136.177.02

2121

≈

−

−

−

+=BBL

BBLkL

(2) Calculate Hydraulic radius of contracted section

mPARh 77.2

5012.325012.3

=+×

×==

(3) Maximum hydraulic shear stress in contraction channel is:

231

2231

22max 8.19177.236.302.098109.12.3 m

NRVnkkkk hwLR =×××××=⋅=−−γτ θ

(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:

( ) mHgnHgH

BBV

ContZ

C

98.1338.1

9.131

5.0

2

11

max =•

−

=ρτ

( ) mHgnHgH

BBV

UnifZ

C

81.931.1

41.131

5.0

2

11

max =•

−

=ρτ

(6) The equation for z (t) is: ( )

( )139802.12

11

max

hrsthrst

Zt

Z

tz+

=+

= ( )( )98102.12

11

max

hrsthrst

Zt

Z

tz+

=+

=

(7) The flood lasts 2 days (48 hrs), therefore ZCont = 562 mm or 4% of Zmax(Cont) ZUnif = 553 mm or 5.6% of Zmax(Cont)


Use SRICOS-EFA program option 2: Contraction Scour





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



Estimate Initial

Scour Rate



1, 0 4, 1 6,2 9,3

6, 30 100, 10

200, 12.5 400, 16



Estimate Initial

Scour Rate



3, 0 4, 0.1 6,1 9,2

18.5, 4 27, 5 40, 6

60, 6.9

Results: After two years period of the flood having 3.36m/sec velocity, the final contraction scours are: Z (Cont) = 13.14 m Z (Unif) = 9.39 m The following figure illustrates the scour depth development with time.

Figure 12.18 – Maximum Contraction Scour Depth Vs Time (Example 4)

Figure 12.19 – Uniform Contraction Scour Depth Vs Time (Example 4)

Uniform Contraction Scour Depth vs. Time (Example 4)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 200 400 600 800Time (Day)

Pier

Sco

ur D

epth

(mm

)

Maximum Contraction Scour Depth vs. Time (Example 4)

0

2000

4000

6000

8000

10000

12000

14000

0 200 400 600 800Time (Day)

Pier

Sco

ur D

epth

(mm

)

12.5. EXAMPLE 5: CONTRACTED CHANNEL WITH 60° TRANSITION ANGLE AND APPROACHING HYDROGRAPH Given: Channel geometry: Upstream uncontracted channel width B1=150, contracted

channel width due to bridge abutment B2 = 50m, Contraction length of channel L: = 30 m

Abutment transition angle: 60 degree Flow parameters: 70 years predicted hygrograph

Figure 12.20 – 70 Years Future Approaching Hydrograph (Example 5) Manning coefficient: 0.02 Hydraulic Radius: 2.72 m

Future Hydrograph

0

2000

4000

6000

8000

10000

12000

14000

0 10 20 30 40 50 60 70Time (Year)

Dis

char

ge (m

3 /sec

)


Figure 12.21 – EFA Results for Soil Layer 1 (Example 5) Layer 2: Thickness 20m; Critical shear stress 4 N/m2

Figure 12.22 – EFA Results for Soil Layer 2 (Example 5) Flood period: 70 years Determine: The magnitude of maximum contraction scour depth.

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

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)

Scou

r R

ate

(mm

/hr)


0

2

4

6

8

10

12

14

16

18

20

0 100 200 300 400Shear Stress (N/m2)

Scou

r R

ate

(mm

/hr)

Figure 12.23 – Plan View of Contracted Channel Scour Case (Example 5)






B2

B1

Bridge Abutment Bridge Abutment

60°

V1 River Bank River Bank Flow

L


Discharge vs. Velocity

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 5000 10000 15000 20000 25000Discharge (m3/s)

Vel

ocity

(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 25000Discharge (m3/s)

Wat

er D

epth

(m)

Use SRICOS-EFA program option 2: Contraction Scour





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


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





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



Estimate Initial

Scour Rate



1, 0 4, 1 6,2 9,3

6, 30 100, 10

200, 12.5 400, 16



Estimate Initial

Scour Rate



3, 0 4, 0.1 6,1 9,2

18.5, 4 27, 5 40, 6

60, 6.9 Results: After 70 years period of the flood, the final contraction scours are: Z (Cont) = 8.8 m Z (Unif) = 6.6 m The following figure illustrates the scour depth development with time.

Figure 12.25 – Maximum Contraction Scour Depth Vs Time (Example 5)

Figure 12.26 – Uniform Contraction Scour Depth Vs Time (Example 5)

Maximum Contraction Scour Depth vs. Time (Example 5)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 10 20 30 40 50 60 70Time (Year)

Pier

Sco

ur D

epth

(mm

)

Uniform Contraction Scour Depth vs. Time (Example 5)

0

1000

2000

3000

4000

5000

6000

7000

0 10 20 30 40 50 60 70Time (Year)

Pier

Sco

ur D

epth

(mm

)

12.6. EXAMPLE 6: BRIDGE WITH GROUP PIERS AND CONTRACTED CHANNEL WITH HYDROGRAPH IN CONTRACTED SECTION Given: Pier geometry: Pier width B = 1.52m, pier length Lpier = 12.19m,

rectangular pier, number of piers, N = 6, spacing, S = 30 m Channel geometry: Upstream uncontracted channel width B1=725m, contracted

channel width due to bridge abutment B2 = 122m, Contraction length of channel L: = 40 m

Abutment transition angle: 90 degree Flow parameters: 70 years predicted hydrograph

Figure 12.27 – 70 Years Future Hydrograph (Example 6)

Manning coefficient: 0.0146 Hydraulic radius: 2.62 m

Future Hydrograph

0

2000

4000

6000

8000

10000

12000

14000

0 10 20 30 40 50 60 70Time (Year)

Dis

char

ge (m

3 /sec

)


Figure 12.28 – EFA Results for Soil Layer 1 (Example 6) Layer 2: Thickness 20m; Critical shear stress 4 N/m2

Figure 12.29 – EFA Results for Soil Layer 2 (Example 6) Flood period: 70 years Determine: The magnitude of maximum bridge scour depth.

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

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)

Scou

r R

ate

(mm

/hr)


0

2

4

6

8

10

12

14

16

18

20

0 100 200 300 400Shear Stress (N/m2)

Scou

r R

ate

(mm

/hr)

Figure 12.30 – Cross Section View of Approaching Channel (Example 6)

Ele

vatio

n, M

eter

s

0

Distance, Meters 350300 450400

30 m1

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)

Left Overbank Main Channel Right Overbank

Approach Cross Section

0 100 200 300 500 600 700 8004000

1

3

2

4

5

6

7

8

Distance, Meters

Elev

atio

n, M

eter

s








0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0 5000 10000 15000 20000 25000Discharge (m3/s)

Wat

er D

epth

(m)

Discharge vs. Velocity (Contracted Section)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0 5000 10000 15000 20000 25000Discharge (m3/s)

Vel

ocity

(m/s)

Use SRICOS-EFA program option 3: Bridge Scour





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


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





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



Estimate Initial

Scour Rate



1, 0 4, 1 6,2 9,3

6, 30 100, 10

200, 12.5 400, 16



Estimate Initial

Scour Rate



3, 0 4, 0.1 6,1 9,2

18.5, 4 27, 5 40, 6

60, 6.9 Results: After 70 years period of the flood, in this case the occurred maximum final bridge scour is: Z = 6.2m The following figure illustrates the scour depth development with time.

Figure 12.33 – Bridge Scour Depth Vs Time (Example 6)


0

1000

2000

3000

4000

5000

6000

7000

0 10 20 30 40 50 60 70

Time (Year)

Pier

Sco

ur D

epth

(mm

)

CHAPTER 13 CONCLUSIONS AND RECOMMENDATIONS 13.1 CONCLUSIONS 13.1.1. General The topic addressed is the prediction of the scour depth around a bridge pier founded in cohesive soils and subjected to water flow. The scour components considered are complex pier scour and contraction scour. The proposed method is based on 42 useful flume tests, and 49 useful numerical simulations. It is a further development of the method formulated earlier for simple pier scour (cylindrical pier in deep water). 13.1.2. Erodibility of cohesive soils It is emphasized that erodibility is not an index but a relationship or function between on one hand the water velocity or, better, the shear stress at the water-soil interface and on the other hand the erosion rate of the soil. Erodibility is represented by this erosion function. Two important parameters help describe the erosion function: the critical shear stress and the initial slope of the erosion function. It is found that, while the critical shear stress of a cohesive soil is not related to its mean grain size, the common range of critical shear stress values for cohesive soils (0.5 N/m2 to 5 N/m2) is comparable to the range obtained in sands. This explains why the maximum scour depth in cohesive soils is comparable to the one obtained in sands. The initial slope of the erosion function can be many times less than the one in sand (e.g.: 1000 times less) and therefore the scour depth can develop very slowly in some cohesive soils. There lies the advantage of developing a method which can predict scour depth as a function of time for a given hydrograph (cohesive soil) rather than a maximum depth of scour for a design flood (sands). This was the goal of this project. It was also found that the critical shear stress and the initial slope were not related to soil properties because the R2 of the regressions were all very low. It is recommended to obtain the erosion function by using the Erosion Function Apparatus. 13.1.3. Erosion function apparatus (EFA) This EFA (http://www.humboldtmfg.com/pdf2/hm4000ds.pdf) was developed in the early nineties to obtain the erosion function. A soil sample is retrieved from the bridge site using an ASTM standard thin wall steel tube ( Shelby tube), placing it through a tight fitting opening in the bottom of a rectangular cross section conduit, pushing a small protrusion of soil in the conduit, flowing water over the top of the sample at a chosen velocity, and recording the corresponding erosion rate. This is repeated for several velocities and the erosion function is obtained in that fashion.

13.1.4. SRICOS-EFA method for cylindrical piers in deep water SRICOS stands for Scour Rate In Cohesive Soils. Since the method makes use of the erosion function measured in the EFA, the method is referred to as the SRICOS-EFA method. For a given velocity hydrograph at a bridge, for a given soil multilayered stratigraphy with an erosion function defined for each layer, and for a given cylindrical pier in deep water (water depth larger than 1.6 times the pier diameter), the SRICOS-EFA method (program) gives the scour depth as a function of time for the period covered by the hydrograph. The method is based on the calculation of two basic parameters: the maximum depth of pier scour and the initial rate of scour. The maximum depth of scour is based on an equation obtained from flume tests and the initial rate is based on an equation giving the initial shear stress obtained from numerical simulations. The initial rate of scour is read on the EFA erosion function at the corresponding value of the calculated shear stress. A hyperbola is used to connect the initial scour rate to the maximum or asymptotic scour depth and describes the complete scour depth vs. time curve. Robust algorithms are used to incorporate the effect of varying velocities and multilayered soil systems. This earlier method was developed by the authors under TxDOT sponsorship and was verified by satisfactory comparison between predicted scour and measured scour at 8 bridges in Texas. 13.1.5. SRICOS-EFA method for maximum scour depth at complex piers A set of flume experiments were conducted to study the maximum depth of scour for a pier including the effect of shallow water depth, the effect of rectangular shapes, the effect of the angle of attack on rectangular shapes, and the effect of spacing between piers positioned in a row perpendicularly to the flow. The proposed equation for the maximum depth of scour is in the form of the equation for the cylindrical pier in deep water with correction factors based on the results of the flume tests.

( ) ( )0.635max 0.18w sp sh eZ Pier in mm K K K R=

where Zmax(Pier) is the maximum depth of pier scour in millimeters, Re is the Reynolds number equal to VB’/ν, V (m/s) being the mean depth velocity at the location of the pier if the bridge was not there, the K factors take the shallow water depth, the spacing, and the shape into account, the angle of attack being considered through the use of the projected width B’ (m) in the calculation of the Reynolds number. 13.1.6. SRICOS-EFA method for initial scour rate at complex piers A set of numerical simulations were performed to study the maximum shear stress around a pier including the effect of shallow water depth, the effect of rectangular shapes, the effect of the angle of attack on rectangular shapes, and the effect of spacing between piers positioned in a row perpendicularly to the flow. The proposed equation for the maximum shear stress is in the form of the equation for the cylindrical pier in deep water with correction factors based on the results of the numerical simulations.

2max

1 1( ) 0.094log 10w sh sp

e

Pier k k k k VRατ ρ

= −

where τmax(Pier) (kN/m2) is the maximum shear stress around the pier, Re is the Reynolds number equal to VB/ν, V (m/s) being the mean depth velocity at the location of the pier if the bridge was not there, B (m) is the pier diameter or pier width, ρ (kg/m3) is the mass density of water, the k factors take the shallow water depth, the pier shape, the pier spacing, and the attack angle into account. 13.1.7. SRICOS-EFA method for maximum contraction scour depth A set of flume experiments were conducted to study the depth of scour associated with the contraction of a channel including the effects of the ratio of the contracted channel width over the approach channel width, the contracted channel length, and the transition angle. The proposed equation for the maximum depth of contraction scour is

0.5

max 1 1/311

1.49( ) 1.90 0

c

hecL


τρ

= × − ≥

where Zmax(Cont) (m) is the maximum depth of contraction scour, H1 (m) the water depth along the center line of the uncontracted channel after scour has occurred, Vhec (m/s) the mean depth water velocity at the location of the pier in the contracted channel, τc (N/m2) the critical shear stress of the soil, ρ (kg/m3) the mass density of water, g (m/s2) the acceleration due to gravity, n the Manning’s coefficient (s/m1/3), and the K factors take the transition and the contracted channel length into account. Note that the parenthesis in the equation is a factored difference between the Froude number and the critical Froude number. Equations are also proposed for the uniform contraction scour depth as well as the location of the scour depths. 13.1.8. SRICOS-EFA method for initial contraction scour rate A set of numerical simulations were performed to study the maximum shear stress around the contraction of a channel including the effects of the ratio of the contracted channel width over the approach channel width, the transition angle, the water depth, and the contracted channel length. The proposed equation for the maximum shear stress is in the form of the equation for the shear stress at the bottom of an open and uncontracted channel with correction factors based on the results of the numerical simulations.

12 2 3

max ( ) c R c c H c L hCont k k k k n V Rθτ γ−

− − − −

=

where τmax(Cont) (N/m2) is the maximum shear stress along the centerline of the contracted channel, γ is the unit weight of water (kN/m3), n the Manning’s coefficient (s/m1/3) , V (m/s) the upstream mean depth velocity, Rh (m) the hydraulic radius defined as the cross section area of the flow divided by the wetted perimeter, and the k factors take the contraction ratio, the transition angle, the water depth effect, and the contracted

length into account. Equations are also proposed for the location of the maximum shear stress. 13.1.9. SRICOS-EFA method for complex piers scour and contraction scour in cohesive soils Once the equations were established, the SRICOS-EFA method was assembled. Care was taken not to simply add complex pier scour and contraction scour to get total pier scour. Instead, advantage was taken of the fact that at the end of the maximum contraction scour, the velocity is at the critical velocity and the maximum pier scour should be calculated using the critical velocity of the soil and not the initial velocity in the contracted channel. In addition, the rules of accumulation due to the hydrograph, and due to the multiplayer system developed for the simple pier scour method were adapted for the complex pier and contraction scour method. The superposition and accumulation reasoning lead to the following steps for the SRICOS-EFA method for predicting the soucr depth at a complex pier in a contracted channel. This step by step procedure has been automated in a computer program.

1. Collect the input data: velocity and water depth hydrograph, geometry of the pier and of the contracted channel, erosion functions of the soil layers.

2. Calculate the maximum contraction scour depth for the ith velocity in the hydrograph.

3. Calculate the maximum complex pier scour depth using the ith velocity in the hydrograph at the pier location if there is no contraction scour in step 2, or the critical velocity for the soil if there is contraction scour in step 2.

4. Calculate the total pier scour depth as the total of step 2 and step 3. 5. Calculate the initial maximum shear stress for pier scour using the ith velocity in

the hydrograph. 6. Read the initial scour rate corresponding to the initial maximum shear stress of

step 5 on the erosion function of the soil layer corresponding to the current scour depth.

7. Use the results of steps 4 and 6 to construct the hyperbola describing the scour depth vs time for the pier.

8. Calculate the equivalent time for the given curve of step 7. The equivalent time is the time required for the ith velocity on the hydrograph to scour the soil to a depth equal to the depth scoured by all the velocities occurring prior to the ith velocity.

9. Read the additional scour generated by the ith velocity starting at the equivalent time and ending at the equivalent time plus the time increment.

10. Repeat steps 2 to 9 for the (i+1)th velocity and so on until the entire hydrograph is consumed.

13.1.10. Verification of the SRICOS-EFA method Several full case histories were identified for verification but none could satisfy the requirements necessary to verify the method developed. Some did not have enough details on the observed scour depth, some turned out not to be made of cohesive soil after drilling, some did not have a gauge station nearby. It was decided to compare the

maximum scour depth for pier and contraction to existing databases. These databases were mostly in sand however and included those collected by Mueller (pier scour), Froelich (pier scour) and Gill (contraction scour). The comparisons between the predicted and measured scour depths are very satisfactory although it is not clear whether they should be or not since the soils were not primarily cohesive. Nevertheless, these comparisons give an indication that the SRICOS-EFA method may not be limited to cohesive soils. Indeed, the fact that the method is based on site specific testing of the erosion function permits incorporating the soil behavior directly in the predictions. 13.1.11. Future hydrographs and scour risk analysis A novel technique is presented on generating future hydrographs. Indeed, since the SRICOS-EFA method predicts the scour depth as a function of time, it is necessary to input into the program the hydrograph over the design life of the bridge. The proposed technique consists of using a past hydrograph (from a gauge station for example), preparing the frequency distribution plot for the floods within that hydrograph, sampling the distribution randomly and preparing a future hydrograph, for the required period, which has the same mean and standard deviation as the measured hydrograph. This process is repeated 10,000 times and, for each hydrograph, a final scour depth (the depth reached at the end of the design life of the bridge) is generated. These 10,000 final depths of scour are organized in a frequency distribution plot with a mean and a standard deviation. That plot can be used to quote a scour depth with a corresponding probability of occurrence, or better, to choose a risk level and quote the corresponding final depth of scour. 13.1.12. Example Problems A set of example problems are presented to help the reader become more familiar with the SRICOS-EFA method. Some examples are done by hand calculations, some of them are using the computer program. 13.2 RECOMMENDATIONS It is recommended that:

1. the proposed method be incorporated in the next version of HEC-18. 2. the SRICOS-EFA method program be transformed into a Windows environment. 3. the project be continued to solve the last major unsolved scour problem in

cohesive soils: abutment scour. 4. a set of short courses be offered across the country to teach the new method and

the corresponding program.

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APPENDIX A PHOTOGRAHS FROM THE FLUME TESTS

Figure A1 Flow Pattern around Pier under Shallow Water Condition

Figure A2 Pier Scour Hole under Shallow Water Condition – Front View

Figure A3 Pier Scour Hole under Shallow Water Condition – Back View

Figure A4 Pier Scour Hole in Sand under Shallow Water Condition

Figure A5 Scour Hole of Test Gr-1

Figure A6 Scour Hole of Test Gr-2

Figure A7 Flow Pattern around Pier Group in Test Gr-3

Figure A8 Scour Hole of Test Gr-3 – Back View

Figure A9 Scour Hole of Test Gr-3 – Top View

Figure A10 Scour Hole of Test Gr-3 – Back View (Large Scale)

Figure A11 Flow Pattern around Pier Group in Test Gr-4

Figure A12 Scour Hole in Test Sh-3

Figure A13 Flow Pattern around Rectangular Pier in Test Sh-5

Figure A14 Scour Hole in Test At-1 – Back View

Figure A15 Scour Hole in Test At-1 – Front View

Figure A16 Scour Hole in Test At-6 – Front View

Figure A17 Scour Hole in Test At-6 – Back View

Figure A18 Scour Hole in Test At-3

Figure A19 Scour Hole in Test At-8

Figure A20 Scour Hole Contour in Test Cp-1

Figure A21 Scour Hole in Test Cp-2

Figure A22 Scour Hole in Contraction Scour Test 1


Figure A24 Scour Hole in Contraction Scour Test 2 - Overview

Figure A25 Flow Pattern in Contraction Scour Test 2



Figure A30 Scour Hole in Contraction Scour Test 13 – Top View

Figure A31 Scour Hole in Contraction Scour Test 13 – Back View


APPENDIX B FLUME TESTS DATA

MEASURED SCOUR DEPTH AS A FUCNTION OF TIME Table B.1 Measured Scour Depth as a Function of Time in Shallow Water Effect

Test Sh-2 Test Sh-3 Test Sh-4 Test Sh-5 Test Sh-6 Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.08 1.52 1.00 1.00 1.08 1.82 1.00 0.91 3.03 9.12 3.08 2.43 2.00 2.22 3.08 4.26 3.17 2.43 6.78 12.77 5.92 4.86 4.00 2.52 7.17 7.60 6.17 6.69 16.78 18.24 9.92 6.08 10.00 3.43 12.25 10.34 10.83 10.94 28.12 23.41 21.58 10.03 15.00 6.99 21.50 20.67 21.67 22.80 39.95 27.06 27.08 11.55 22.00 6.99 28.33 22.80 27.50 28.88 61.62 31.92 34.08 13.07 28.83 7.30 35.00 27.66 33.08 33.14 86.28 39.52 46.00 15.20 33.58 14.90 47.75 29.79 46.92 40.13 111.03 44.99 52.25 17.02 42.50 18.85 52.75 32.22 58.50 45.90 59.92 18.24 48.58 22.19 58.75 32.83 70.00 49.25 70.58 21.28 56.25 24.32 69.42 35.26 82.08 51.07 84.58 23.41 63.17 26.75 75.33 37.39 92.17 55.33 92.92 24.02 68.83 27.97 83.25 39.82 105.92 56.85 101.75 26.75 78.50 34.96 93.42 42.26 118.00 57.15 133.58 34.35 83.08 37.39 102.83 43.78 127.50 58.37 157.83 38.61 90.33 43.86 121.50 44.38 140.33 59.58 181.58 41.95 94.83 46.30 144.50 45.60 149.58 62.93 205.75 44.99 100.33 46.30 167.83 45.90 164.08 62.93 228.33 47.73 105.58 50.86 193.83 46.51 242.25 50.16 112.08 52.98 216.58 48.64 255.67 52.59 118.92 55.42 237.42 48.94 272.75 54.11 127.83 56.33 250.00 296.00 57.46 142.83 58.76 309.75 59.58 149.50 59.98 324.58 60.19 167.00 61.19 347.50 62.02 177.08 61.50 368.75 65.36 189.92 62.10 392.17 66.27 201.00 62.71 417.92 67.79 220.67 64.23 439.83 69.92 238.08 65.45 464.25 71.44 262.33 66.06 494.25 72.35 515.75 74.18

Table B.1 (Cont.) Measured Scour Depth as a Function of Time in Shallow Water Effect

Test Sh-7 Test Sh-8 Test Sh-9 Test Sh-10 Test Sh-11 Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.75 13.68 1.75 3.04 8.50 12.77 4.33 8.82 1.42 3.65 3.00 19.15 7.00 9.12 12.17 15.81 7.08 12.16 4.67 10.03 6.67 22.19 10.25 13.68 19.83 21.89 9.67 18.24 7.83 14.59 13.25 22.80 21.33 24.32 31.08 29.49 20.83 24.32 19.50 24.93 21.67 31.92 27.83 28.88 38.50 35.57 26.67 27.97 24.75 30.40 30.50 33.44 32.83 31.92 44.33 43.17 33.50 32.83 31.83 33.44 45.33 34.96 55.50 51.38 45.58 37.09 43.33 34.05 56.67 38.00 65.50 56.24 57.17 44.99 52.33 39.52 69.83 41.95 79.25 59.89 69.17 45.30 64.58 41.04 80.67 43.17 89.50 63.54 78.00 48.03 93.42 47.12 104.50 68.40 93.25 51.68 106.42 50.16 115.75 71.14 105.92 53.20 118.00 53.20 129.67 73.57 117.17 56.54 142.00 54.72 165.42 60.80 191.33 63.84

Table B.2 Measured Scour Depth as a Function of Time in Pie Spacing Effect

Test Gr-1 Test Gr-2 Test Gr-3 Test Gr-4 Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.17 7.60 4.33 10.64 3.33 11.25 4.00 17.02 5.92 11.25 6.25 16.72 4.67 12.16 7.83 31.01 10.75 22.50 11.50 25.84 14.75 30.40 19.25 54.72 22.17 41.95 22.33 42.56 25.67 62.32 29.33 75.39 33.67 55.63 36.00 72.96 39.00 92.72 43.92 92.72 45.67 60.80 48.92 83.60 50.83 114.00 61.08 115.52 58.42 71.44 59.50 88.16 66.25 139.84 80.67 138.93 75.33 85.12 81.42 101.84 92.83 153.52 108.08 152.91 99.50 94.85 107.00 109.44 118.58 155.04 129.83 161.12 130.50 106.40 122.50 114.00 144.08 156.56 165.00 118.56

Table B.3 Measured Scour Depth as a Function of Time in Pie Shape Effect

Test Sp-1 Test Sp-2 Test Sp-3 Test Sp-4 Test Sp-5 Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.08 2.43 3.78 3.04 3.50 6.69 2.50 4.56 2.42 3.04 4.83 5.17 7.92 10.03 7.50 13.07 6.58 10.64 6.67 6.08 14.50 16.11 19.13 31.92 18.00 24.93 17.50 25.84 17.42 17.63 23.83 25.23 29.58 48.03 31.00 31.92 28.58 30.70 28.75 28.88 48.67 29.79 43.75 57.76 49.50 40.13 42.67 36.48 42.50 39.52 76.00 41.95 62.25 57.76 71.67 51.68 65.33 47.12 65.42 48.03 103.00 50.46 80.50 63.23 96.25 54.72 87.42 53.20 87.25 51.68 128.75 50.46 108.08 64.75 124.42 55.63 107.75 55.02 107.92 54.72 151.92 50.46 129.50 66.27 131.58 57.15 131.50 56.54

Table B.4 Measured Scour Depth as a Function of Time in Attack Angle Effect

Test At-1 Test At-2 Test At-3 Test At-4 Test At-5 Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.50 6.69 3.58 4.56 3.50 3.04 2.58 2.43 3.42 4.86 7.50 13.07 7.25 7.60 8.50 12.16 5.25 7.90 8.58 13.98 18.00 24.93 18.17 13.68 13.33 20.37 15.58 29.79 19.00 32.22 31.00 31.92 30.83 25.23 25.75 34.35 29.08 60.19 31.75 49.86 49.50 40.13 49.67 44.08 36.58 39.22 46.25 77.52 43.92 65.06 71.67 51.68 71.50 55.63 55.08 45.30 70.17 97.28 57.50 71.14 96.25 54.72 96.50 63.23 78.50 50.46 78.58 83.60 124.42 55.63 124.33 67.79 104.17 54.72 145.75 73.57 170.00 72.96 186.00 76.30 211.08 78.13

Table B.4 (Cont.) Measured Scour Depth as a Function of Time in Attack Angle Effect

Test At-6 Test At-7 Test At-8 Test At-9

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.50 3.04 1.83 1.52 2.50 3.34 2.50 3.65 8.50 12.16 5.83 10.64 5.33 12.16 5.33 11.25 19.08 32.53 17.67 26.45 15.50 34.05 15.50 29.79 31.58 51.98 29.92 40.74 29.25 55.02 29.25 49.25 44.17 60.80 43.92 51.68 46.08 70.22 46.08 65.36 57.42 72.05 64.08 66.58 70.25 91.81 70.25 92.00 78.75 94.24 88.00 79.04 115.08 107.01 116.00 108.00 117.08 102.75 112.67 86.64

Table B.5 Measured Scour Depth as a Function of Time in Complex Pier Installation

Test Cp-1 Test Cp-2 Time (Hr)

Scour (mm)

Time (Hr)

Scour (mm)

0.00 0.00 0.00 0.00 2.33 5.17 2.08 9.12 6.42 17.94 6.67 25.84 11.58 25.54 16.25 47.12 22.33 43.78 31.08 72.35 34.75 59.89 42.00 87.55 48.83 73.57 51.00 100.62 70.92 88.77 64.67 115.52 118.32 111.57 78.75 127.07 94.92 139.23 116.83 158.08 150.67 182.4

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8 -7

0.0

0.0

0.0

0.0

5.5

29.8

45

.6

60.8

74

.2

85.7

12

6.2

166.

3 18

5.7

-20.

0 0.

0 0.

0 3.

6 51

.7

75.1

85

.1

91.2

10

2.4

182.

4 20

0.6

214.

3 23

4.7

30.0

0.

0 10

.3

30.4

66

.9

93.6

10

7.3

125.

2 15

7.5

188.

5 20

4.3

227.

1 24

3.8

80.0

0.

0 8.

2 15

.8

65.7

99

.4

120.

1 14

6.2

164.

8 18

7.0

206.

7 23

1.0

250.

5 13

0.0

0.0

9.1

22.8

43

.5

89.4

12

8.3

149.

6 16

8.7

189.

4 20

9.8

228.

6 24

9.3

180.

0 0.

0 0.

9 12

.5

51.7

84

.5

123.

4 13

8.6

160.

2 17

9.4

194.

6 21

8.0

246.

2 23

0.0

0.0

0.0

14.6

49

.6

85.7

12

0.7

134.

4 15

8.1

173.

9 19

3.6

224.

4 24

1.4

280.

0 0.

0 2.

4 19

.5

59.3

96

.7

123.

1 13

6.2

147.

7 17

2.7

190.

3 21

1.3

234.

1 33

0.0

0.0

6.1

22.8

64

.4

97.9

12

7.7

134.

4 15

0.5

168.

1 17

9.4

197.

3 21

1.3

380.

0 0.

0 1.

5 16

.7

60.8

84

.5

119.

8 13

7.7

151.

7 15

9.6

174.

8 18

9.1

203.

1 48

0.0

0.0

6.1

19.8

65

.4

85.7

10

3.4

124.

6 14

3.5

149.

0 15

2.6

162.

9 17

6.3

580.

0 0.

0 7.

6 20

.4

62.0

99

.4

113.

1 12

3.1

140.

8 14

6.5

150.

5 16

7.2

167.

2 78

0.0

0.0

0.6

12.2

48

.0

65.7

86

.6

102.

8 12

4.0

139.

8 15

8.1

161.

7 16

9.9

980.

0 0.

0 6.

7 19

.5

46.8

72

.0

90.9

99

.4

116.

1 13

5.3

154.

4 15

8.1

176.

3 11

80.0

0.

0 12

.2

25.8

51

.7

74.5

95

.5

100.

3 11

7.0

130.

1 14

8.0

149.

6 16

7.8

Tab

le B

.7

Mea

sure

d Sc

our D

epth

as a

Fun

ctio

n of

Tim

e an

d Lo

catio

n X

in C

ontra

ctio

n Sc

our T

est 2

(T

he O

rigin

of X

is th

e be

ginn

ing

of fu

ll co

ntra

ctio

n)

C

ontra

ctio

n Sc

our

Abu

tmen

t Sco

ur

T

ime(

Hr)

X

(mm

) 0.

00

1.42

5.

58

8.92

21

.17

34.5

044

.33

57.5

0 72

.67

95.5

8 12

3.17

-315

.0

0.0

2.4

3.3

3.3

3.3

3.3

3.3

3.3

3.3

3.3

3.3

-215

.0

0.0

1.8

2.4

2.4

2.4

2.4

2.4

2.4

2.4

2.4

2.4

-115

.0

0.0

0.0

0.3

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

-65.

0 0.

0 0.

3 1.

2 3.

0 3.

0 12

.2

3.0

3.0

4.6

5.8

5.8

-15.

0 0.

0 0.

9 2.

7 7.

0 13

.4

15.5

17

.0

28.9

48

.9

52.0

64

.8

35.0

0.

0 0.

0 7.

9 12

.2

27.7

35

.9

45.0

61

.1

76.3

84

.5

92.7

85

.0

0.0

0.3

7.3

13.1

29

.5

41.3

51

.7

63.5

77

.8

91.5

93

.3

135.

0 0.

0 2.

4 10

.3

15.5

30

.1

40.7

45

.3

55.3

65

.4

86.6

90

.6

185.

0 0.

0 2.

7 13

.4

17.3

25

.5

31.3

39

.5

42.9

62

.0

66.9

77

.8

235.

0 0.

0 4.

0 9.

1 14

.6

22.8

28

.9

30.7

39

.5

86.3

86

.9

96.1

28

5.0

0.0

5.8

14.3

17

.3

27.4

36

.2

44.7

60

.8

77.8

89

.4

96.7

33

5.0

0.0

5.8

10.9

16

.1

30.7

45

.9

54.1

56

.5

70.5

81

.2

91.2

38

5.0

0.0

8.5

11.6

18

.5

31.0

45

.0

54.1

58

.4

61.7

70

.5

80.9

43

5.0

0.0

9.4

9.7

13.1

27

.7

43.5

51

.4

52.6

55

.3

60.2

68

.7

485.

0 0.

0 8.

2 8.

5 14

.6

25.8

42

.3

47.1

51

.1

58.1

61

.1

74.8

58

5.0

0.0

10.9

12

.5

15.8

30

.7

47.4

54

.1

55.6

65

.1

66.0

73

.3

785.

0 0.

0 15

.2

18.8

20

.1

25.5

38

.9

42.6

45

.0

48.9

50

.5

50.8

98

5.0

0.0

11.6

17

.0

18.5

30

.7

39.8

42

.9

45.3

55

.0

58.1

67

.8

1185

.0

0.0

10.9

15

.5

21.3

38

.3

47.4

52

.0

55.0

64

.1

64.4

71

.1

1385

.0

0.0

13.1

14

.6

18.5

25

.2

34.4

42

.3

48.9

48

.9

49.6

50

.2

Left

0.0

9.4

26.1

00

37.4

52

.0

61.1

68

.4

71.7

77

.8

83.9

88

.5

Rig

ht

0.0

12.5

26

.1

39.8

54

.4

75.7

85

.4

94.5

98

.2

109.

7 11

1.6

Tab

le B

.8

Mea

sure

d Sc

our D

epth

as a

Fun

ctio

n of

Tim

e an

d Lo

catio

n X

in C

ontra

ctio

n Sc

our T

est 3

(T

he O

rigin

of X

is th

e be

ginn

ing

of fu

ll co

ntra

ctio

n)

C

ontra

ctio

n Sc

our

A

butm

ent S

cour

T

ime(

Hr)

X

(mm

) 0.

00

6.00

8.83

19.4

233

.25

43.5

867

.17

93.1

711

5.67

148.

5018

8.67

237.

42

-180

.0

0.0

5.5

7.6

11.6

-1

30.0

0.

0

11

.6

13.7

15

.5

-80.

0 0.

0

19

.8

19.8

22

.2

0.0

0.0

5.5

5.5

10.0

12

.8

14.0

14

.6

20.1

20

.1

20.7

23

.7

26.8

70

.0

0.0

4.3

7.0

11.6

19

.2

22.5

23

.7

24.3

24

.6

29.8

33

.7

35.6

12

0.0

0.0

5.5

10.0

16

.7

21.6

26

.8

29.8

30

.4

31.9

32

.8

39.5

41

.6

170.

0 0.

0 6.

7 10

.0

17.6

24

.9

28.0

29

.8

30.4

31

.0

32.2

41

.3

44.1

22

0.0

0.0

5.2

10.0

18

.2

24.9

24

.9

34.0

36

.2

38.3

44

.1

45.9

50

.5

270.

0 0.

0 4.

9 9.

7 17

.6

25.2

28

.3

34.0

40

.7

41.0

47

.1

48.0

50

.8

320.

0 0.

0 4.

6 9.

4 17

.6

25.2

29

.2

36.8

38

.3

39.2

44

.4

45.6

48

.0

420.

0 0.

0 6.

7 11

.6

17.6

27

.1

32.2

39

.8

41.0

43

.2

45.0

48

.0

50.5

62

0.0

0.0

5.5

8.5

18.2

27

.4

33.1

39

.2

46.2

54

.1

55.3

56

.2

58.7

82

0.0

0.0

1.5

2.7

9.1

17.6

22

.8

35.9

43

.5

46.2

48

.6

50.2

52

.6

1020

.0

0.0

0.9

2.1

8.5

12.2

14

.6

25.5

43

.5

44.7

45

.0

45.3

46

.2

Ave

rage

0.

00

0.00

0.

00

0.00

0.

00

0.00

0.

00

0.00

0.

00

0.00

0.

00

0.00

Tab

le B

.9

Mea

sure

d Sc

our D

epth

as a

Fun

ctio

n of

Tim

e an

d Lo

catio

n X

in C

ontra

ctio

n Sc

our T

est 4

(T

he O

rigin

of X

is th

e be

ginn

ing

of fu

ll co

ntra

ctio

n)

C

ontra

ctio

n Sc

our

Abu

tmen

t Sco

ur

T

ime(

Hr)

X

(mm

) 0.

00

4.75

10

.25

20.0

0 31

.25

45.7

556

.17

76.9

2 10

3.50

168.

33

-290

.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-190

.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-140

.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-90.

0 0.

0 0.

0 0.

6 0.

6 3.

0 3.

0 3.

0 3.

0 3.

0 3.

0 -4

0.0

0.0

0.3

3.6

3.6

3.6

4.3

4.3

4.3

5.5

7.3

10.0

0.

0 1.

2 3.

3 3.

3 4.

0 4.

0 4.

6 4.

6 4.

6 6.

4 60

.0

0.0

1.8

3.3

4.9

5.2

5.2

5.8

5.8

5.8

6.4

110.

0 0.

0 2.

1 3.

3 4.

3 4.

3 4.

9 5.

8 5.

8 6.

1 6.

1 16

0.0

0.0

9.1

13.4

14

.3

15.2

18

.2

18.2

18

.2

18.2

18

.2

210.

0 0.

0 7.

6 15

.8

21.3

23

.4

25.8

25

.8

26.1

26

.1

27.7

26

0.0

0.0

7.6

17.3

19

.5

22.5

25

.2

25.2

26

.1

26.1

26

.1

310.

0 0.

0 4.

0 10

.6

12.8

15

.2

17.3

17

.3

19.8

19

.8

19.8

36

0.0

0.0

6.4

8.8

13.7

15

.8

16.7

16

.7

17.3

17

.3

17.3

41

0.0

0.0

5.2

11.6

20

.1

21.9

23

.1

23.1

24

.3

24.3

24

.3

510.

0 0.

0 10

.6

16.1

21

.3

22.2

22

.2

22.2

24

.9

24.9

24

.9

610.

0 0.

0 4.

0 8.

2 11

.9

14.0

16

.1

16.1

18

.2

18.2

18

.2

710.

0 0.

0 3.

6 7.

3 9.

4 11

.2

11.9

11

.9

14.3

14

.3

14.3

91

0.0

0.0

1.8

7.3

10.0

12

.5

13.7

13

.7

14.3

14

.3

14.3

11

10.0

0.

0 2.

4 8.

5 9.

1 11

.2

11.2

11

.2

11.6

11

.6

11.6

13

10.0

0.

0 1.

2 3.

3 3.

6 4.

6 4.

9 4.

9 4.

9 4.

9 4.

9

Left

0.0

12.8

24

.3

33.4

51

.7

58.4

64

.1

67.5

68

.4

71.4

R

ight

0.

0 17

.6

28.0

40

.4

48.6

56

.2

59.6

68

.4

69.9

73

.0

Tab

le B

.10

Mea

sure

d Sc

our D

epth

as a

Fun

ctio

n of

Tim

e an

d Lo

catio

n X

in C

ontra

ctio

n Sc

our T

est 5

(T

he O

rigin

of X

is th

e be

ginn

ing

of fu

ll co

ntra

ctio

n, a

nd T

est 5

was

run

afte

r Tes

t 4 w

ithou

t ren

ewin

g th

e te

st)

C

ontra

ctio

n Sc

our

Abu

tmen

t Sco

ur

T

ime(

Hr)

X

(mm

) 16

8.33

174.

5819

4.66

216.

66

247.

50

277.

08

-290

.0

0.0

0.0

0.0

0.3

0.3

0.3

-190

.0

0.0

0.0

0.0

0.0

0.0

0.0

-140

.0

0.0

0.0

0.0

0.9

1.8

1.8

-90.

0 3.

0 3.

0 3.

0 4.

6 4.

6 6.

1 -4

0.0

7.3

7.3

7.3

10.3

11

.6

13.1

10

.0

6.4

6.4

6.4

6.7

8.2

10.0

60

.0

6.4

6.4

9.1

10.0

11

.9

13.1

11

0.0

6.1

6.7

10.3

11

.2

12.8

13

.4

160.

0 18

.2

20.7

23

.7

23.7

23

.7

26.4

21

0.0

27.7

27

.7

29.5

29

.5

29.5

30

.4

260.

0 26

.1

26.1

27

.1

27.1

27

.1

28.0

31

0.0

19.8

20

.1

20.4

20

.7

22.2

23

.4

360.

0 17

.3

22.8

22

.8

22.8

22

.8

28.0

41

0.0

24.3

24

.6

25.8

26

.8

28.3

29

.5

510.

0 24

.9

29.2

29

.8

29.8

30

.4

31.6

61

0.0

18.2

17

.9

20.7

22

.8

23.4

24

.3

710.

0 14

.3

17.0

17

.0

17.0

17

.0

17.9

91

0.0

14.3

15

.5

17.6

18

.5

18.5

18

.5

1110

.0

11.6

11

.9

11.9

11

.9

11.9

14

.6

1310

.0

4.9

4.9

4.9

4.9

4.9

5.8

Left

71.4

73

.0

73.6

75

.4

80.0

82

.7

Rig

ht

73.0

73

.6

77.8

80

.0

80.6

85

.1

Tab

le B

.11

Mea

sure

d Sc

our D

epth

as a

Fun

ctio

n of

Tim

e an

d Lo

catio

n X

in C

ontra

ctio

n Sc

our T

est 6

(T

he O

rigin

of X

is th

e be

ginn

ing

of fu

ll co

ntra

ctio

n, a

nd T

est 7

was

run

afte

r Tes

t 6 w

ithou

t ren

ewin

g th

e te

st)

C

ontra

ctio

n Sc

our

Abu

tmen

t Sco

ur

T

ime(

Hr)

X

(mm

) 0.

00

1.17

7.

75

18.0

0 32

.00

43.4

256

.00

80.5

8 10

4.00

120.

92

-290

.0

0.0

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

-190

.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-140

.0

0.0

0.3

0.3

0.9

1.5

1.5

1.5

6.1

6.1

6.1

-90.

0 0.

0 1.

8 1.

8 2.

4 2.

4 3.

0 3.

0 6.

7 6.

7 12

.2

-40.

0 0.

0 0.

6 1.

5 5.

5 8.

2 10

.3

10.3

10

.6

12.2

15

.2

10.0

0.

0 1.

8 2.

4 5.

5 8.

5 8.

5 9.

1 9.

7 10

.6

13.7

60

.0

0.0

3.3

4.6

12.2

14

.0

14.0

14

.6

14.9

16

.1

16.1

11

0.0

0.0

3.6

7.0

8.5

12.5

14

.3

17.3

18

.2

19.2

19

.8

160.

0 0.

0 0.

6 4.

6 6.

7 13

.4

14.3

16

.7

21.3

21

.9

27.4

21

0.0

0.0

0.0

2.1

8.2

14.9

21

.3

21.9

26

.4

27.4

28

.0

260.

0 0.

0 0.

6 4.

6 7.

3 13

.1

19.2

22

.8

24.3

26

.8

27.4

31

0.0

0.0

2.4

3.3

6.7

8.2

10.3

12

.2

15.2

16

.7

17.3

36

0.0

0.0

5.5

5.5

7.3

9.1

11.6

13

.4

14.9

17

.3

17.3

41

0.0

0.0

2.4

4.6

6.7

7.9

11.2

13

.1

14.6

16

.1

16.1

51

0.0

0.0

6.7

8.2

9.1

9.4

12.5

13

.1

13.1

13

.7

13.7

61

0.0

0.0

5.5

5.5

6.7

9.4

11.6

12

.8

14.3

16

.7

16.7

71

0.0

0.0

5.5

6.7

6.7

9.1

9.7

10.9

13

.7

14.3

14

.3

910.

0 0.

0 4.

6 4.

6 4.

6 4.

6 6.

4 7.

0 7.

0 8.

2 8.

2 11

10.0

0.

0 4.

0 4.

6 4.

6 6.

4 7.

3 7.

6 7.

6 9.

1 9.

1 13

10.0

0.

0 5.

5 7.

6 9.

1 9.

4 10

.0

10.6

10

.6

12.2

12

.2

Left

0.0

1.2

8.5

25.8

34

.4

48.3

56

.5

65.4

71

.4

0.0

Rig

ht

0.0

3.0

9.4

17.3

35

.6

48.6

53

.2

62.0

67

.8

0.0

Tab

le B

.12

Mea

sure

d Sc

our D

epth

as a

Fun

ctio

n of

Tim

e an

d Lo

catio

n X

in C

ontra

ctio

n Sc

our T

est 7

(T

he O

rigin

of X

is th

e be

ginn

ing

of fu

ll co

ntra

ctio

n)

C

ontra

ctio

n Sc

our

Abu

tmen

t Sco

ur

T

ime(

Hr)

X

(mm

) 25

.00

33.3

345

.25

68.7

5 79

.33

93.0

010

3.08

12

5.67

151.

5817

5.50

-290

.0

0.9

0.9

0.9

1.8

1.8

3.0

3.0

10.6

10

.6

11.6

-1

90.0

0.

0 0.

0 6.

1 6.

1 7.

0 8.

5 15

.2

19.8

19

.8

20.1

-1

40.0

6.

1 15

.2

19.8

24

.3

24.3

24

.3

24.3

23

.7

51.7

67

.5

-90.

0 12

.2

21.3

29

.2

25.5

28

.6

31.3

40

.4

52.0

66

.0

79.0

-4

0.0

15.2

20

.4

28.6

24

.3

30.4

39

.5

57.8

66

.3

83.9

91

.8

10.0

13

.7

15.8

24

.0

26.8

42

.6

48.6

63

.8

71.7

80

.9

90.3

60

.0

16.1

17

.3

27.1

34

.0

42.6

53

.2

66.9

75

.1

82.7

90

.6

110.

0 19

.8

21.9

30

.4

40.1

42

.0

60.5

72

.4

77.5

85

.1

90.6

16

0.0

27.4

32

.2

43.2

50

.8

57.8

61

.7

76.6

85

.1

92.4

95

.2

210.

0 28

.0

34.7

48

.0

57.8

66

.6

69.0

80

.6

88.2

89

.1

95.2

26

0.0

27.4

34

.7

51.7

56

.5

74.5

76

.0

88.2

88

.8

90.0

92

.7

310.

0 17

.3

25.5

35

.6

46.2

51

.4

61.4

73

.0

79.0

80

.3

85.7

36

0.0

17.3

30

.4

37.1

46

.2

53.8

63

.2

76.9

78

.1

79.0

84

.2

410.

0 16

.1

23.4

35

.6

50.8

57

.2

66.3

73

.0

82.1

83

.6

87.6

51

0.0

13.7

22

.8

35.6

51

.7

59.6

66

.0

71.4

78

.7

81.5

85

.1

610.

0 16

.7

21.9

34

.7

42.9

57

.2

64.1

71

.4

83.6

83

.9

88.2

71

0.0

14.3

26

.8

36.8

46

.8

55.3

60

.8

72.0

86

.6

86.6

90

.3

910.

0 8.

2 22

.5

35.9

46

.8

51.1

53

.8

59.6

79

.0

79.0

81

.5

1110

.0

9.1

18.2

31

.0

44.4

48

.3

55.3

58

.1

69.9

74

.5

76.6

13

10.0

12

.2

23.7

36

.5

48.6

53

.8

55.9

63

.2

73.0

75

.1

76.0

Left

76.0

97

.6

107.

9 12

3.1

126.

5 12

9.2

131.

9 13

8.3

147.

4 76

.0

Rig

ht

69.9

91

.2

105.

8 13

0.1

133.

2 13

9.8

140.

8 14

2.9

154.

4 69

.9

Table B.11 Measured Scour Depth as a Function of Time and Location X in Contraction Scour Test 9

(The Origin of X is the beginning of full contraction)

Contraction Scour

Abutment Scour

Time(Hr)

X(mm) 0.00 29.42 42.83 53.08 72.75 96.50 116.67 144.42

-315.0 0.0 0.6 0.6 0.6 0.6 0.6 0.6 0.6 -215.0 0.0 2.7 2.7 2.7 2.7 2.7 4.6 4.6 -115.0 0.0 5.5 6.4 6.4 6.4 6.4 6.4 7.6 -15.0 0.0 6.1 6.7 6.7 7.0 7.0 7.6 7.6 35.0 0.0 7.9 7.9 7.9 7.9 7.9 9.1 9.1 85.0 0.0 7.3 7.9 7.9 8.5 8.5 10.6 10.6 135.0 0.0 11.2 11.2 11.2 11.9 11.9 13.4 13.4 185.0 0.0 14.0 14.0 14.0 15.8 15.8 16.7 16.7 235.0 0.0 12.2 13.7 13.7 14.3 14.3 16.1 18.8 285.0 0.0 17.3 17.3 17.3 17.6 17.6 19.8 21.3 335.0 0.0 17.6 17.6 17.6 18.8 18.8 26.4 27.4 385.0 0.0 20.4 21.0 21.3 22.5 23.4 32.8 34.0 435.0 0.0 22.8 22.8 27.4 28.9 31.6 33.4 36.5 485.0 0.0 18.8 23.4 23.7 26.8 30.1 33.7 33.7 535.0 0.0 18.8 21.3 22.5 23.7 23.7 30.4 36.5 585.0 0.0 18.2 20.1 20.7 21.0 21.0 21.6 22.8 685.0 0.0 12.2 12.8 13.1 13.1 56.2 56.2 56.2 785.0 0.0 12.2 27.4 48.6 50.8 53.2 65.1 72.0 885.0 0.0 22.8 28.9 35.6 36.5 41.0 41.0 41.0 985.0 0.0 12.2 35.0 40.1 40.7 42.6 44.1 44.1

1085.0 0.0 37.7 45.6 48.9 49.2 49.2 49.9 49.9 1185.0 0.0 12.2 27.4 28.9 30.1 31.9 36.2 36.5 1285.0 0.0 28.0 35.6 36.5 36.5 36.5 39.5 39.5 1385.0 0.0 12.2 26.4 29.8 32.8 49.6 53.2 57.8 1485.0 0.0 30.1 38.9 47.7 51.1 53.8 57.8 61.4

Left 0.0 27.1 31.3 32.5 39.5 46.8 48.3 48.9 Right 0.0 35.6 37.1 49.2 51.7 52.3 53.2 53.2

Tab

le B

.12

Mea

sure

d Sc

our D

epth

as a

Fun

ctio

n of

Tim

e an

d Lo

catio

n X

in C

ontra

ctio

n Sc

our T

est 1

1 (T

he O

rigin

of X

is th

e be

ginn

ing

of fu

ll co

ntra

ctio

n)

C

ontra

ctio

n Sc

our

A

butm

ent S

cour

T

ime(

Hr)

X

(mm

) 0.

00

5.33

9.50

21.6

731

.75

49.0

069

.50

91.5

810

4.00

122.

2514

5.00

-215

.0

0.0

1.5

1.5

2.1

3.0

3.0

3.0

3.0

3.0

3.0

3.0

-115

.0

0.0

0.6

1.2

2.4

3.0

4.0

4.6

5.5

6.1

6.1

6.1

-15.

0 0.

0 0.

6 1.

2 4.

6 4.

6 6.

7 6.

7 6.

7 7.

6 7.

6 7.

6 35

.0

0.0

0.0

0.3

1.5

1.5

3.0

3.0

3.0

3.0

3.0

3.0

85.0

0.

0 0.

6 0.

9 6.

1 7.

6 9.

1 11

.9

24.9

32

.8

37.1

42

.6

135.

0 0.

0 5.

8 9.

1 10

.0

10.3

10

.6

28.3

38

.6

42.6

46

.2

46.2

18

5.0

0.0

8.2

12.2

13

.4

16.7

16

.7

36.2

43

.2

48.6

51

.1

53.2

23

5.0

0.0

12.2

16

.4

28.9

39

.5

46.5

54

.1

57.8

58

.1

58.4

60

.8

285.

0 0.

0 14

.6

21.3

33

.4

42.0

49

.2

56.2

57

.8

58.1

58

.4

58.4

33

5.0

0.0

13.7

18

.8

31.0

45

.0

45.0

52

.3

54.7

55

.3

55.3

55

.3

385.

0 0.

0 12

.2

17.3

26

.8

32.5

35

.6

39.8

42

.0

43.5

45

.0

45.0

43

5.0

0.0

9.1

11.9

21

.3

32.8

33

.4

39.5

42

.6

44.7

46

.2

46.2

48

5.0

0.0

7.6

11.2

19

.8

27.4

30

.4

31.9

37

.1

37.1

39

.5

39.5

53

5.0

0.0

7.0

8.5

13.7

24

.3

30.4

32

.8

36.5

41

.3

42.6

42

.6

585.

0 0.

0 4.

9 7.

0 9.

7 16

.7

29.8

31

.6

34.0

36

.2

36.5

36

.5

685.

0 0.

0 4.

0 9.

4 11

.6

16.1

18

.2

24.3

38

.6

45.9

48

.6

50.8

78

5.0

0.0

7.6

10.0

14

.3

26.8

42

.6

53.8

61

.1

65.4

66

.9

66.9

88

5.0

0.0

8.5

13.7

17

.6

26.4

34

.0

44.7

53

.2

53.8

53

.8

54.7

98

5.0

0.0

6.7

9.1

12.5

19

.8

29.5

38

.9

42.6

43

.8

44.7

44

.7

1085

.0

0.0

6.1

8.8

12.2

21

.3

31.0

38

.0

42.0

42

.0

42.0

42

.0

1185

.0

0.0

4.0

8.8

17.3

27

.4

31.3

36

.5

37.4

39

.5

41.0

41

.0

1285

.0

0.0

7.0

9.7

13.7

19

.8

23.4

26

.4

27.4

31

.0

33.4

33

.4

1385

.0

0.0

7.3

9.7

11.6

21

.3

29.8

32

.8

36.5

36

.5

36.5

36

.5

1485

.0

0.0

8.8

10.6

12

.8

18.2

21

.3

22.8

27

.4

28.9

28

.9

28.9

Left

0.0

12.2

22

.5

43.2

55

.9

63.2

75

.1

88.2

88

.8

93.6

94

.2

Rig

ht

0.0

18.8

30

.4

49.2

58

.7

67.2

83

.6

97.0

10

0.3

102.

1 10

2.8

Tab

le B

.12

Mea

sure

d Sc

our D

epth

as a

Fun

ctio

n of

Tim

e an

d Lo

catio

n X

in C

ontra

ctio

n Sc

our T

est 1

2 (T

he O

rigin

of X

is th

e be

ginn

ing

of fu

ll co

ntra

ctio

n)

C

ontra

ctio

n Sc

our

A

butm

ent S

cour

T

ime(

Hr)

X

(mm

) 0.

00

1.08

4.

58

10.0

8 20

.92

31.4

244

.83

54.7

5 78

.67

105.

2014

5.50

-215

.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-115

.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-65.

0 0.

0 5.

2 3.

0 4.

9 5.

2 4.

9 5.

8 7.

3 22

.8

48.6

55

.9

-15.

0 0.

0 2.

7 3.

6 7.

9 12

.2

15.5

53

.2

61.7

72

.0

76.0

77

.5

35.0

0.

0 3.

0 12

.2

20.1

40

.4

48.0

60

.2

67.8

80

.9

85.1

86

.6

85.0

0.

0 5.

5 13

.1

24.3

45

.3

49.9

57

.8

66.3

82

.1

88.2

97

.3

135.

0 0.

0 6.

1 14

.0

31.9

48

.9

59.0

70

.5

72.0

83

.6

85.4

88

.2

185.

0 0.

0 9.

1 23

.7

32.8

52

.3

66.0

76

.3

78.7

83

.0

83.6

85

.1

235.

0 0.

0 10

.6

18.2

32

.5

43.2

58

.1

67.8

73

.0

77.5

84

.5

86.0

28

5.0

0.0

5.2

12.8

25

.8

38.9

47

.7

57.8

63

.8

75.4

76

.0

78.4

33

5.0

0.0

5.2

9.1

23.1

36

.5

46.8

57

.8

62.6

80

.3

82.1

83

.6

385.

0 0.

0 3.

0 8.

5 20

.7

38.0

47

.7

60.2

67

.8

73.0

74

.2

77.2

43

5.0

0.0

1.5

8.5

24.3

43

.2

53.5

65

.1

65.4

71

.4

75.1

79

.0

485.

0 0.

0 1.

5 5.

5 20

.4

36.8

53

.8

63.8

66

.3

66.9

68

.1

74.5

53

5.0

0.0

0.0

4.3

16.1

32

.8

45.0

53

.5

57.8

62

.6

65.4

70

.8

585.

0 0.

0 0.

0 4.

3 14

.6

34.7

46

.5

50.5

55

.6

61.7

61

.7

69.0

68

5.0

0.0

0.0

4.0

10.0

25

.8

29.2

35

.6

38.9

42

.9

47.7

51

.4

785.

0 0.

0 0.

0 11

.6

17.3

21

.3

26.4

27

.4

30.7

39

.2

39.2

43

.2

885.

0 0.

0 0.

0 13

.7

21.0

34

.0

34.0

41

.6

45.3

45

.3

48.6

50

.8

985.

0 0.

0 0.

0 13

.7

23.7

32

.2

35.9

39

.2

40.4

40

.4

44.1

45

.0

1085

.0

0.0

0.0

20.4

26

.4

36.2

38

.0

39.8

39

.5

43.2

43

.2

43.2

11

85.0

0.

0 0.

0 18

.5

23.4

34

.4

41.6

42

.6

44.1

45

.6

46.5

46

.5

1285

.0

0.0

0.0

21.3

28

.9

36.5

38

.6

41.3

43

.2

43.2

43

.2

43.2

13

85.0

0.

0 0.

0 24

.3

32.8

35

.3

38.9

40

.1

41.6

41

.6

41.6

41

.6

Left

0.0

6.1

21.0

36

.5

56.2

73

.0

85.1

95

.5

102.

4 11

1.6

112.

5R

ight

0.

0 6.

1 21

.3

48.6

60

.8

73.3

95

.5

105.

5

Tab

le B

.12

Mea

sure

d Sc

our D

epth

as a

Fun

ctio

n of

Tim

e an

d Lo

catio

n X

in C

ontra

ctio

n Sc

our T

est 1

3 (T

he O

rigin

of X

is th

e be

ginn

ing

of fu

ll co

ntra

ctio

n)

C

ontra

ctio

n Sc

our

A

butm

ent S

cour

T

ime(

Hr)

X

(mm

) 0.

00

2.25

7.

00

10.5

0 23

.00

33.4

244

.92

58.0

8 70

.17

82.0

0 92

.67

102.

5012

5.08

152.

25

-215

.0

0.0

0.0

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

-115

.0

0.0

0.0

0.3

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

-65.

0 0.

0 0.

6 0.

6 2.

1 4.

3 4.

3 4.

3 4.

3 4.

3 4.

3 57

.8

54.1

60

.8

65.7

-1

5.0

0.0

0.6

0.6

6.7

10.0

14

.3

17.6

17

.6

29.5

45

.3

51.7

55

.6

59.6

65

.7

35.0

0.

0 5.

8 6.

1 10

.9

24.3

32

.8

43.5

50

.8

51.7

67

.8

72.7

90

.0

97.9

10

0.3

85.0

0.

0 1.

5 5.

5 13

.4

35.0

45

.6

55.3

60

.8

72.4

81

.5

82.1

90

.0

93.9

97

.3

135.

0 0.

0 2.

1 4.

9 13

.1

44.7

59

.9

68.4

73

.0

78.1

86

.9

88.8

91

.2

93.9

96

.4

185.

0 0.

0 0.

6 8.

2 18

.2

42.9

60

.2

69.0

73

.3

77.8

83

.6

86.0

88

.8

91.5

93

.6

235.

0 0.

0 1.

5 3.

0 10

.9

40.7

53

.2

62.9

66

.6

72.4

75

.1

76.6

77

.5

80.0

82

.7

285.

0 0.

0 3.

0 6.

1 13

.1

36.2

48

.6

59.0

62

.9

65.4

69

.6

75.4

78

.1

81.2

84

.5

335.

0 0.

0 3.

0 4.

0 12

.8

32.2

43

.8

56.2

62

.6

69.0

72

.4

73.9

78

.7

81.8

83

.9

385.

0 0.

0 4.

3 5.

8 11

.6

29.5

41

.3

50.8

57

.8

65.1

72

.0

82.1

78

.1

82.7

83

.6

435.

0 0.

0 4.

3 5.

8 12

.2

28.3

40

.7

47.7

56

.8

64.1

72

.0

73.0

75

.4

80.3

83

.3

485.

0 0.

0 4.

6 6.

1 13

.4

27.1

38

.0

47.4

52

.9

62.6

69

.0

69.6

71

.4

73.9

80

.6

585.

0 0.

0 3.

6 10

.3

10.0

25

.8

31.6

37

.1

47.7

52

.6

64.4

66

.9

67.5

67

.5

67.5

68

5.0

0.0

3.0

6.1

8.2

18.8

30

.1

35.9

40

.4

44.1

45

.6

51.7

51

.1

52.6

55

.6

785.

0 0.

0 1.

2 4.

9 4.

6 15

.8

22.8

30

.7

37.1

43

.2

44.7

47

.7

48.6

49

.9

49.9

88

5.0

0.0

0.9

4.6

6.7

16.7

23

.7

31.9

34

.4

34.4

38

.0

38.0

42

.6

43.8

44

.7

985.

0 0.

0 1.

5 3.

0 4.

9 16

.7

23.1

31

.3

32.8

32

.8

33.4

33

.4

33.4

34

.7

35.6

Left

0.0

8.2

23.1

32

.5

53.2

63

.2

70.2

81

.2

89.1

93

.0

93.9

95

.5

102.

8 10

6.4

Rig

ht

0.0

8.5

24.3

34

.0

53.2

62

.3

67.8

75

.7

78.4

88

.2

88.2

91

.2

96.1

10

7.0

T

able

B.1

2 M

easu

red

Scou

r Dep

th a

s a F

unct

ion

of T

ime

and

Loca

tion

X in

Con

tract

ion

Scou

r Tes

t 14

(The

Orig

in o

f X is

the

begi

nnin

g of

full

cont

ract

ion)

Con

tract

ion

Scou

r

Abu

tmen

t Sco

ur

T

ime(

Hr)

X

(mm

) 0.

00

0.83

3.

75

15.0

8 28

.75

40.5

852

.58

61.8

3 16

8.08

194.

50

-215

.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-115

.0

0.0

0.0

0.0

2.1

3.0

3.0

3.0

4.6

6.1

6.1

-65.

0 0.

0 0.

3 0.

6 1.

2 3.

0 4.

6 4.

6 4.

6 61

.7

61.7

-1

5.0

0.0

1.8

2.4

4.3

6.4

7.6

25.8

28

.3

71.7

72

.4

35.0

0.

0 1.

8 3.

0 16

.7

24.3

38

.6

54.1

59

.3

89.7

10

0.6

85.0

0.

0 0.

3 5.

5 22

.8

39.5

57

.8

71.7

75

.4

129.

2 13

7.7

135.

0 0.

0 0.

9 6.

4 39

.2

52.3

67

.5

76.9

80

.3

141.

4 14

7.4

185.

0 0.

0 2.

1 7.

0 42

.9

59.3

71

.4

79.0

85

.1

147.

7 15

2.3

235.

0 0.

0 0.

3 7.

6 42

.6

66.9

79

.6

82.7

84

.5

148.

0 15

5.6

285.

0 0.

0 0.

0 10

.6

44.7

64

.4

80.6

89

.7

94.5

14

7.7

155.

6 33

5.0

0.0

0.0

11.9

39

.5

63.8

78

.7

87.6

93

.6

152.

3 15

6.9

385.

0 0.

0 0.

0 8.

8 39

.2

62.6

75

.7

82.4

89

.1

155.

6 15

9.6

485.

0 0.

0 0.

0 6.

4 31

.3

53.8

66

.3

72.4

81

.2

153.

5 15

7.5

585.

0 0.

0 2.

1 7.

0 28

.9

54.1

76

.0

90.9

98

.8

138.

3 14

2.3

685.

0 0.

0 3.

0 11

.9

39.8

60

.5

73.6

92

.7

102.

8 12

1.6

130.

7 78

5.0

0.0

3.0

11.9

36

.5

56.2

69

.9

79.0

89

.7

114.

9 11

7.0

885.

0 0.

0 3.

0 11

.9

36.5

50

.5

60.2

66

.3

69.9

95

.2

96.7

98

5.0

0.0

3.0

11.9

19

.8

39.2

55

.0

59.6

66

.6

83.6

87

.6

Left

0.0

0.6

19.2

53

.8

66.6

79

.0

93.3

97

.9

158.

7 16

1.7

Rig

ht

0.0

0.6

12.8

44

.7

72.0

76

.6

86.3

93

.9

146.

5 14

9.6

APPENDIX C

DATABASES OF CASE HISTORIES

Tab

le C

1 –

MU

EL

LE

R (1

996)

Dat

abas

e

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 1

SS

1.52

6.

10

1.52

0

5.79

3020

895

3.8

1.00

1

0.9

2.11

0.

91.

001.

100.

262.

71

0.76

2

SS

1.52

6.

10

1.52

0

5.33

4647

531

3.5

1.00

1

0.9

2.77

0.

91.

001.

100.

423.

23

0.61

3

SS

1.52

6.

10

1.52

0

4.11

3950

402

2.7

1.00

1

0.9

2.50

0.

91.

001.

100.

412.

90

0.76

4

SS

1.52

6.

10

1.52

0

6.55

4415

155

4.3

1.00

1

0.9

2.69

0.

91.

001.

100.

363.

24

0.61

5

SS

1.52

6.

10

1.52

0

3.35

3253

272

2.2

1.00

1

0.9

2.21

0.

91.

001.

100.

372.

60

0.61

6

SS

1.52

6.

10

1.52

0

5.18

5344

661

3.4

1.00

1

0.9

3.03

0.

91.

001.

100.

493.

41

0.61

7

SS

1.52

6.

10

1.52

0

4.11

2323

766

2.7

1.00

1

0.9

1.79

0.

91.

001.

100.

242.

31

1.52

8

SS

1.52

6.

10

1.52

0

5.33

4415

155

3.5

1.00

1

0.9

2.69

0.

91.

001.

100.

403.

16

1.52

9

SS

1.83

8.

84

1.83

0

5.49

6692

445

3.0

1.00

1

0.9

3.50

0.

91.

001.

100.

503.

94

1.07

10

R

S 1.

52

11.2

5 1.

52

0 2.

1323

2376

61.

4 0.

95

1 1.

0 1.

89

1 1.

001.

100.

332.

35

0.61

11

R

S 1.

52

11.2

5 1.

52

0 0.

9114

4073

50.

6 0.

71

1 1.

0 1.

05

1 1.

001.

100.

321.

71

0.46

12

R

S 1.

52

11.2

5 1.

52

0 1.

9823

7024

11.

3 0.

93

1 1.

0 1.

87

1 1.

001.

100.

352.

35

0.61

13

R

S 1.

52

11.2

5 1.

52

0 0.

9114

8721

00.

6 0.

71

1 1.

0 1.

07

1 1.

001.

100.

331.

73

0.61

14

R

S 1.

52

11.2

5 1.

52

0 1.

2274

3605

0.

8 0.

79

1 1.

0 0.

76

1 1.

001.

100.

141.

34

0.30

15

R

S 1.

52

11.2

5 1.

52

0 3.

0524

1671

62.

0 1.

00

1 1.

0 2.

03

1 1.

001.

100.

292.

51

0.91

16

R

S 1.

52

11.2

5 1.

52

0 1.

8316

7311

11.

2 0.

90

1 1.

0 1.

46

1 1.

001.

100.

262.

00

0.46

17

R

S 1.

52

11.2

5 1.

52

0 1.

5211

6188

31.

0 0.

85

1 1.

0 1.

09

1 1.

001.

100.

201.

67

0.30

18

R

S 1.

52

11.2

5 1.

52

0 3.

2030

2089

52.

1 1.

00

1 1.

0 2.

34

1 1.

001.

100.

352.

78

1.22

19

R

S 1.

52

11.2

5 1.

52

0 2.

4417

6606

21.

6 1.

00

1 1.

0 1.

66

1 1.

001.

100.

242.

13

0.61

20

R

S 1.

52

11.2

5 1.

52

0 1.

2213

4778

40.

8 0.

79

1 1.

0 1.

11

1 1.

001.

100.

261.

72

0.30

21

R

S 1.

52

11.2

5 1.

52

0 3.

0527

4204

32.

0 1.

00

1 1.

0 2.

20

1 1.

001.

100.

332.

65

1.37

22

R

S 1.

52

11.2

5 1.

52

0 2.

2917

1958

71.

5 0.

98

1 1.

0 1.

60

1 1.

001.

100.

242.

09

0.76

23

R

S 1.

52

11.2

5 1.

52

0 0.

4641

8278

0.

3 0.

56

1 1.

0 0.

38

1 1.

001.

100.

130.

91

0.76

24

R

S 1.

52

11.2

5 1.

52

0 2.

5931

6032

11.

7 1.

00

1 1.

0 2.

41

1 1.

001.

100.

412.

75

1.07

25

R

S 1.

52

11.2

5 1.

52

0 1.

5217

1958

71.

0 0.

85

1 1.

0 1.

39

1 1.

001.

100.

291.

97

0.46

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 26

R

S 1.

52

11.2

5 1.

52

0 0.

6123

2377

0.

4 0.

62

1 1.

0 0.

29

1 1.

001.

100.

060.

74

1.22

27

R

S 1.

52

11.2

5 1.

52

0 3.

0527

8851

92.

0 1.

00

1 1.

0 2.

23

1 1.

001.

100.

332.

67

1.83

28

R

S 1.

52

11.2

5 1.

52

0 1.

9814

8721

01.

3 0.

93

1 1.

0 1.

39

1 1.

001.

100.

221.

92

0.76

29

R

S 1.

22

6.40

1.

22

0 2.

2920

0773

31.

9 1.

00

1 1.

0 1.

81

1 1.

001.

100.

352.

12

1.31

30

R

S 1.

22

6.40

1.

22

0 2.

2920

0773

31.

9 1.

00

1 1.

0 1.

81

1 1.

001.

100.

352.

12

0.46

31

R

S 1.

22

6.40

1.

22

0 0.

6481

7965

0.

5 0.

68

1 1.

0 0.

70

1 1.

001.

100.

271.

21

0.30

32

R

S 1.

22

6.40

1.

22

0 0.

6481

7965

0.

5 0.

68

1 1.

0 0.

70

1 1.

001.

100.

271.

21

0.30

33

R

S 1.

22

6.40

1.

22

0 1.

0412

2694

80.

9 0.

80

1 1.

0 1.

06

1 1.

001.

100.

321.

54

0.30

34

R

S 1.

22

6.40

1.

22

0 1.

0412

2694

80.

9 0.

80

1 1.

0 1.

06

1 1.

001.

100.

321.

54

0.34

35

R

S 0.

91

10.2

1 0.

91

0 5.

1228

1640

5.

6 1.

00

1 1.

0 0.

52

1 1.

001.

100.

040.

95

0.43

36

R

S 0.

91

10.2

1 0.

91

0 5.

9469

7130

6.

5 1.

00

1 1.

0 0.

92

1 1.

001.

100.

101.

44

1.04

37

R

S 0.

91

13.1

1 0.

91

0 5.

0911

7117

85.

6 1.

00

1 1.

0 1.

28

1 1.

001.

100.

181.

76

0.67

38

SS

4.

27

16.4

6 4.

27

0 11

.58

1093

0993

2.7

1.00

1

0.9

4.77

0.

91.

001.

100.

246.

49

3.72

39

SS

4.

27

16.4

6 4.

27

0 12

.25

1093

0993

2.9

1.00

1

0.9

4.77

0.

91.

001.

100.

236.

54

0.91

40

SS

4.

27

16.4

6 4.

27

0 9.

4289

7903

02.

2 1.

00

1 0.

9 4.

21

0.9

1.00

1.10

0.22

5.80

3.

47

41

SS

4.27

16

.46

4.27

0

9.39

8979

030

2.2

1.00

1

0.9

4.21

0.

91.

001.

100.

225.

80

1.13

42

SS

4.

27

16.4

6 4.

27

0 11

.95

1353

3611

2.8

1.00

1

0.9

5.47

0.

91.

001.

100.

297.

14

6.98

43

SS

4.

27

16.4

6 4.

27

0 12

.62

1353

3611

3.0

1.00

1

0.9

5.47

0.

91.

001.

100.

287.

20

5.18

44

SS

4.

27

16.4

6 4.

27

0 9.

7812

3624

332.

3 1.

00

1 0.

9 5.

16

0.9

1.00

1.10

0.30

6.69

7.

65

45

SS

4.27

16

.46

4.27

0

9.78

1236

2433

2.3

1.00

1

0.9

5.16

0.

91.

001.

100.

306.

69

5.64

46

R

S 4.

27

12.1

9 4.

27

0 11

.67

1067

0732

2.7

1.00

1

1.0

5.22

1

1.00

1.10

0.23

7.14

4.

39

47

RS

4.27

12

.19

4.27

0

11.7

310

6707

322.

8 1.

00

1 1.

0 5.

22

1 1.

001.

100.

237.

15

3.93

48

R

S 4.

27

12.1

9 4.

27

0 10

.82

1093

0993

2.5

1.00

1

1.0

5.31

1

1.00

1.10

0.25

7.15

3.

29

49

RS

4.27

12

.19

4.27

0

11.2

810

9309

932.

6 1.

00

1 1.

0 5.

31

1 1.

001.

100.

247.

19

2.07

50

R

S 4.

27

12.1

9 4.

27

0 9.

3389

7903

02.

2 1.

00

1 1.

0 4.

68

1 1.

001.

100.

226.

44

3.84

51

R

S 4.

27

12.1

9 4.

27

0 9.

2789

7903

02.

2 1.

00

1 1.

0 4.

68

1 1.

001.

100.

226.

43

4.18

52

R

S 4.

27

12.1

9 4.

27

0 11

.73

1275

2826

2.8

1.00

1

1.0

5.85

1

1.00

1.10

0.28

7.72

4.

75

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 53

R

S 4.

27

12.1

9 4.

27

0 12

.04

1275

2826

2.8

1.00

1

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54

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15

56

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75

57

RS

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64

58

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80

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62

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65

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US

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73

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US

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67

77

CS

2.44

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44

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0

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1

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1

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25

78

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2.44

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44

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0

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095

1.1

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1

1.0

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1

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0.

98

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 79

C

S 2.

44

2.44

2.

44

0 3.

9352

0523

51.

6 1.

00

1 1.

0 3.

31

1 1.

001.

100.

344.

01

0.88

80

C

S 2.

44

2.44

2.

44

0 2.

6545

3599

01.

1 0.

87

1 1.

0 2.

65

1 1.

001.

100.

363.

58

0.88

81

C

S 2.

44

2.44

2.

44

0 2.

9051

6061

91.

2 0.

90

1 1.

0 2.

97

1 1.

001.

100.

403.

83

1.19

82

C

S 2.

44

2.44

2.

44

0 2.

6555

0267

71.

1 0.

87

1 1.

0 3.

00

1 1.

001.

100.

443.

89

1.95

83

C

S 2.

44

2.44

2.

44

0 3.

0542

6829

31.

3 0.

92

1 1.

0 2.

68

1 1.

001.

100.

323.

55

1.43

84

C

S 2.

44

2.44

2.

44

0 3.

1148

7061

31.

3 0.

92

1 1.

0 2.

93

1 1.

001.

100.

363.

77

1.37

85

SS

0.

94

10.3

6 0.

94

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6523

0517

52.

8 1.

00

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9 1.

78

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0.48

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0.

76

86

SS

0.94

10

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0

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1

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0.

91.

001.

100.

501.

96

0.70

87

SS

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94

10.3

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94

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00

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30

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0.

58

88

SS

0.98

10

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559

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100.

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94

0.49

89

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94

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94

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5 1.

00

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55

90

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0.98

10

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53

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91

SS

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94

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4 1.

00

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09

92

SS

0.94

10

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241.

34

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93

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94

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94

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001.

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731.

41

0.37

95

SS

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04

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04

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4613

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4 0.

64

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9 0.

83

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0.

52

96

SS

1.04

10

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0.40

1327

335

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91.

001.

100.

651.

22

0.46

97

SS

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04

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04

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30.

4 0.

61

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9 0.

90

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0.

98

98

SS

1.04

10

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831.

23

1.04

99

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04

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04

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30.

4 0.

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07

100

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91.

001.

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761.

15

0.49

10

1 SS

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04

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04

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1279

0080

0.

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41

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9 0.

37

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30

102

SS

1.04

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67

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91.

001.

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520.

79

0.37

10

3 R

S 1.

52

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52

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1.

1 0.

89

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86

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121.

40

0.00

10

4 R

S 1.

52

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7940

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23.

8 1.

00

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82

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100.

353.

41

0.61

10

5 R

S 1.

52

14.6

3 1.

52

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7834

3917

32.

5 1.

00

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55

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001.

100.

373.

01

0.27

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 10

6 R

S 1.

52

14.6

3 1.

52

0 2.

5925

0966

71.

7 1.

00

1 1.

0 2.

08

1 1.

001.

100.

332.

49

0.00

10

7 R

S 1.

52

14.6

3 1.

52

0 2.

0411

6188

31.

3 0.

94

1 1.

0 1.

20

1 1.

001.

100.

171.

73

0.00

10

8 R

S 1.

52

14.6

3 1.

52

0 8.

0848

7990

85.

3 1.

00

1 1.

0 3.

18

1 1.

001.

100.

363.

87

1.19

10

9 R

S 1.

52

14.6

3 1.

52

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4341

3630

33.

6 1.

00

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86

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100.

373.

42

0.58

11

0 R

S 1.

52

14.6

3 1.

52

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6030

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4 1.

00

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34

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332.

82

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11

1 R

S 1.

52

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6 0.

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00

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2 R

S 1.

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00

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08

1.31

11

3 R

S 1.

52

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00

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98

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393.

54

0.58

11

4 R

S 1.

52

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93

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5 R

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6 R

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24

1.19

11

7 R

S 1.

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423.

69

0.70

11

8 R

S 1.

52

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00

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05

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11

9 R

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73

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12

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32

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22

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12

2 R

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85

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12

3 R

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32

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4 R

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12

5 R

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6 R

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7 R

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8 R

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9 R

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97

0.94

13

1 R

S 1.

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93

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2 R

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95

0.30

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 13

3 R

S 0.

98

10.8

5 0.

98

0 1.

9511

6002

42.

0 1.

00

1 1.

0 1.

28

1 1.

001.

100.

271.

56

0.55

13

4 R

S 0.

76

7.41

0.

76

0 2.

5610

6893

23.

4 1.

00

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0 1.

21

1 1.

001.

100.

281.

48

0.18

13

5 R

S 0.

76

7.41

0.

76

0 2.

3211

1540

73.

0 1.

00

1 1.

0 1.

25

1 1.

001.

100.

311.

49

0.82

13

6 R

S 0.

76

7.41

0.

76

0 1.

7185

9793

2.

2 1.

00

1 1.

0 1.

06

1 1.

001.

100.

281.

28

0.21

13

7 R

S 0.

76

11.3

7 0.

76

0 1.

6558

0941

2.

2 1.

00

1 1.

0 0.

82

1 1.

001.

100.

191.

07

0.76

13

8 R

S 0.

76

11.3

7 0.

76

0 3.

1797

5982

4.

2 1.

00

1 1.

0 1.

14

1 1.

001.

100.

231.

47

0.67

13

9 R

S 0.

76

11.3

7 0.

76

0 1.

4918

5901

2.

0 1.

00

1 1.

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40

1 1.

001.

100.

060.

65

0.15

14

0 R

S 0.

76

11.3

7 0.

76

0 3.

1151

1228

4.

1 1.

00

1 1.

0 0.

76

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001.

100.

121.

11

0.15

14

1 R

S 1.

13

11.8

9 1.

13

0 1.

5517

8837

01.

4 0.

95

1 1.

0 1.

59

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001.

100.

411.

88

0.40

14

2 R

S 1.

13

11.8

9 1.

13

0 2.

8724

0742

12.

5 1.

00

1 1.

0 2.

03

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001.

100.

402.

32

0.73

14

3 R

S 1.

13

11.8

9 1.

13

0 3.

0820

2911

22.

7 1.

00

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82

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001.

100.

332.

18

0.49

14

4 R

S 1.

31

11.8

9 1.

31

0 2.

0421

9828

21.

6 0.

99

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89

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001.

100.

372.

21

0.73

14

5 R

S 1.

34

11.8

9 1.

34

0 3.

2028

6287

92.

4 1.

00

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27

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100.

382.

64

0.91

14

6 R

S 1.

37

11.8

9 1.

37

0 3.

3827

1880

62.

5 1.

00

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19

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001.

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342.

62

0.98

14

7 R

S 0.

76

9.60

0.

76

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2355

7704

2.

9 1.

00

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0 0.

80

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001.

100.

161.

10

0.40

14

8 R

S 0.

76

9.60

0.

76

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7769

7130

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6 1.

00

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0 0.

92

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100.

181.

25

0.43

14

9 R

S 0.

91

10.6

7 0.

91

0 6.

4648

2414

7.

1 1.

00

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001.

100.

071.

24

0.98

15

0 R

S 0.

91

10.6

7 0.

91

0 5.

0028

1640

5.

5 1.

00

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0 0.

52

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001.

100.

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95

0.91

15

1 R

S 0.

91

10.6

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5 1.

00

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58

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03

0.49

15

2 R

S 0.

91

10.6

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91

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3336

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8 1.

00

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61

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051.

07

0.91

15

3 R

S 0.

91

10.6

7 0.

91

0 5.

1528

4429

5.

6 1.

00

1 1.

0 0.

52

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001.

100.

040.

96

0.61

15

4 R

S 0.

91

10.6

7 0.

91

0 4.

7526

4909

5.

2 1.

00

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0 0.

50

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100.

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92

0.55

15

5 R

S 0.

91

10.6

7 0.

91

0 5.

5243

5009

6.

0 1.

00

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68

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001.

100.

061.

16

0.49

15

6 R

S 0.

91

10.6

7 0.

91

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6137

6450

6.

1 1.

00

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0 0.

62

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001.

100.

061.

09

0.61

15

7 R

S 0.

91

10.6

7 0.

91

0 5.

7647

4048

6.

3 1.

00

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72

1 1.

001.

100.

071.

21

0.70

15

8 R

S 0.

91

10.6

7 0.

91

0 8.

7512

7156

59.

6 1.

00

1 1.

0 1.

35

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001.

100.

151.

96

1.52

15

9 R

S 0.

91

10.6

7 0.

91

0 7.

3288

1172

8.

0 1.

00

1 1.

0 1.

07

1 1.

001.

100.

111.

64

0.76

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 16

0 R

S 0.

91

10.6

7 0.

91

0 4.

9488

6749

5.

4 1.

00

1 1.

0 1.

08

1 1.

001.

100.

141.

56

1.37

16

1 R

S 0.

91

10.6

7 0.

91

0 6.

9592

3000

7.

6 1.

00

1 1.

0 1.

10

1 1.

001.

100.

121.

66

1.07

16

2 R

S 0.

91

10.6

7 0.

91

0 6.

7183

9344

7.

3 1.

00

1 1.

0 1.

04

1 1.

001.

100.

111.

58

1.37

16

3 R

S 0.

91

10.6

7 0.

91

0 6.

4979

1939

7.

1 1.

00

1 1.

0 1.

00

1 1.

001.

100.

111.

54

1.65

16

4 R

S 0.

91

10.6

7 0.

91

0 6.

6185

8864

7.

2 1.

00

1 1.

0 1.

05

1 1.

001.

100.

121.

60

1.28

16

5 R

S 0.

91

10.6

7 0.

91

0 7.

5093

1365

8.

2 1.

00

1 1.

0 1.

11

1 1.

001.

100.

121.

68

1.22

16

6 R

S 0.

91

10.6

7 0.

91

0 7.

4489

7903

8.

1 1.

00

1 1.

0 1.

09

1 1.

001.

100.

111.

65

1.07

16

7 R

S 0.

91

10.6

7 0.

91

0 7.

5690

9057

8.

3 1.

00

1 1.

0 1.

09

1 1.

001.

100.

121.

66

1.10

16

8 R

S 0.

91

10.6

7 0.

91

0 8.

0252

1453

8.

8 1.

00

1 1.

0 0.

77

1 1.

001.

100.

061.

32

0.91

16

9 R

S 0.

91

10.6

7 0.

91

0 5.

9434

8565

6.

5 1.

00

1 1.

0 0.

59

1 1.

001.

100.

051.

07

0.46

17

0 R

S 0.

91

10.6

7 0.

91

0 6.

1033

4622

6.

7 1.

00

1 1.

0 0.

58

1 1.

001.

100.

051.

05

0.61

17

1 R

S 0.

91

10.6

7 0.

91

0 5.

7322

8659

6.

3 1.

00

1 1.

0 0.

46

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001.

100.

030.

89

0.37

17

2 R

S 0.

91

10.6

7 0.

91

0 5.

6429

8372

6.

2 1.

00

1 1.

0 0.

54

1 1.

001.

100.

040.

99

0.46

17

3 R

S 0.

91

10.6

7 0.

91

0 5.

8826

4909

6.

4 1.

00

1 1.

0 0.

50

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001.

100.

040.

95

0.40

17

4 R

S 0.

91

10.6

7 0.

91

0 6.

3432

3468

6.

9 1.

00

1 1.

0 0.

57

1 1.

001.

100.

041.

04

0.46

17

5 R

S 0.

91

10.6

7 0.

91

0 6.

4030

1160

7.

0 1.

00

1 1.

0 0.

54

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001.

100.

041.

01

0.46

17

6 R

S 0.

91

10.6

7 0.

91

0 7.

1330

1160

7.

8 1.

00

1 1.

0 0.

54

1 1.

001.

100.

041.

03

0.91

17

7 R

S 0.

88

9.75

0.

88

0 4.

2775

4759

4.

8 1.

00

1 1.

0 0.

97

1 1.

001.

100.

131.

41

0.27

17

8 R

S 0.

88

9.75

0.

88

0 4.

3969

0065

5.

0 1.

00

1 1.

0 0.

92

1 1.

001.

100.

121.

36

0.24

17

9 R

S 0.

88

9.75

0.

88

0 4.

5181

6757

5.

1 1.

00

1 1.

0 1.

02

1 1.

001.

100.

141.

47

0.27

18

0 R

S 0.

88

9.75

0.

88

0 4.

2775

7455

4.

8 1.

00

1 1.

0 0.

97

1 1.

001.

100.

131.

41

0.34

18

1 R

S 0.

88

9.75

0.

88

0 4.

3976

0150

5.

0 1.

00

1 1.

0 0.

98

1 1.

001.

100.

131.

42

0.49

18

2 R

S 0.

88

9.75

0.

88

0 4.

6389

4929

5.

2 1.

00

1 1.

0 1.

08

1 1.

001.

100.

151.

54

0.43

18

3 R

S 0.

88

9.75

0.

88

0 4.

3684

6408

4.

9 1.

00

1 1.

0 1.

05

1 1.

001.

100.

151.

49

0.43

18

4 R

S 0.

88

9.75

0.

88

0 4.

6390

3015

5.

2 1.

00

1 1.

0 1.

09

1 1.

001.

100.

151.

54

0.55

18

5 R

S 0.

88

9.75

0.

88

0 4.

6384

3713

5.

2 1.

00

1 1.

0 1.

04

1 1.

001.

100.

141.

50

0.46

18

6 R

S 0.

88

9.75

0.

88

0 4.

6987

3364

5.

3 1.

00

1 1.

0 1.

07

1 1.

001.

100.

151.

52

0.40

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 18

7 R

S 0.

88

9.75

0.

88

0 4.

7280

0584

5.

3 1.

00

1 1.

0 1.

01

1 1.

001.

100.

131.

47

0.34

18

8 R

S 0.

88

9.75

0.

88

0 4.

8870

6239

5.

5 1.

00

1 1.

0 0.

93

1 1.

001.

100.

121.

40

0.46

18

9 R

S 0.

88

9.75

0.

88

0 5.

0387

8755

5.

7 1.

00

1 1.

0 1.

07

1 1.

001.

100.

141.

54

0.37

19

0 R

S 0.

88

9.75

0.

88

0 4.

7992

1884

5.

4 1.

00

1 1.

0 1.

10

1 1.

001.

100.

151.

56

0.37

19

1 R

S 0.

88

9.75

0.

88

0 4.

4881

6757

5.

1 1.

00

1 1.

0 1.

02

1 1.

001.

100.

141.

47

0.37

19

2 R

S 0.

88

9.75

0.

88

0 5.

0399

4665

5.

7 1.

00

1 1.

0 1.

16

1 1.

001.

100.

161.

63

0.40

19

3 R

S 0.

88

9.75

0.

88

0 5.

0988

4146

5.

8 1.

00

1 1.

0 1.

07

1 1.

001.

100.

141.

55

0.55

19

4 R

S 0.

88

9.75

0.

88

0 4.

8598

6578

5.

5 1.

00

1 1.

0 1.

15

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001.

100.

161.

61

0.61

19

5 R

S 0.

88

9.75

0.

88

0 5.

1592

9971

5.

8 1.

00

1 1.

0 1.

11

1 1.

001.

100.

151.

58

0.61

19

6 R

S 0.

88

9.75

0.

88

0 4.

6995

9622

5.

3 1.

00

1 1.

0 1.

13

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001.

100.

161.

59

0.61

19

7 R

S 0.

76

13.1

1 0.

76

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7148

7991

3.

6 1.

00

1 1.

0 0.

74

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001.

100.

121.

07

0.76

19

8 R

S 0.

98

25.3

0 0.

98

0 6.

2515

5859

66.

4 1.

00

1 1.

0 1.

54

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001.

100.

202.

08

1.07

19

9 R

S 0.

98

25.3

0 0.

98

0 7.

9218

3224

38.

1 1.

00

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71

1 1.

001.

100.

212.

30

1.22

20

0 R

S 0.

98

25.3

0 0.

98

0 5.

8212

8494

96.

0 1.

00

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36

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001.

100.

171.

89

0.82

20

1 R

S 0.

98

25.3

0 0.

98

0 9.

3021

1481

39.

5 1.

00

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87

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001.

100.

232.

50

1.07

20

2 R

S 0.

98

25.3

0 0.

98

0 8.

3816

2403

38.

6 1.

00

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58

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001.

100.

182.

20

1.52

20

3 R

S 0.

61

12.5

0 0.

61

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4634

2058

0.

8 0.

77

1 1.

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45

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001.

100.

260.

68

0.24

20

4 R

S 0.

61

12.5

0 0.

61

0 0.

6794

8096

1.

1 0.

88

1 1.

0 0.

99

1 1.

001.

100.

611.

12

0.18

20

5 R

S 0.

61

12.5

0 0.

61

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6897

0405

2.

8 1.

00

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14

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001.

100.

391.

28

0.49

20

6 R

S 0.

61

12.5

0 0.

61

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2275

2900

2.

0 1.

00

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0 0.

97

1 1.

001.

100.

361.

10

0.30

20

7 R

S 0.

61

12.5

0 0.

61

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5298

7136

2.

5 1.

00

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15

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001.

100.

421.

27

0.37

20

8 R

S 0.

61

12.5

0 0.

61

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6215

8016

14.

3 1.

00

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0 1.

55

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100.

511.

67

0.76

20

9 R

S 0.

69

8.53

0.

69

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7144

9649

2.

5 1.

00

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0 0.

70

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001.

100.

160.

94

0.40

21

0 R

S 0.

69

8.53

0.

69

0 1.

8047

0563

2.

6 1.

00

1 1.

0 0.

72

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001.

100.

160.

97

0.37

21

1 R

S 0.

69

8.53

0.

69

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5543

9192

2.

3 1.

00

1 1.

0 0.

69

1 1.

001.

100.

160.

92

0.21

21

2 R

S 0.

69

8.53

0.

69

0 0.

8826

3515

1.

3 0.

93

1 1.

0 0.

46

1 1.

001.

100.

130.

69

0.40

21

3 R

S 0.

69

8.53

0.

69

0 1.

4035

5536

2.

0 1.

00

1 1.

0 0.

60

1 1.

001.

100.

140.

83

0.43

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 21

4 R

S 0.

69

8.53

0.

69

0 1.

6235

9719

2.

4 1.

00

1 1.

0 0.

61

1 1.

001.

100.

130.

85

0.37

21

5 R

S 0.

69

8.53

0.

69

0 0.

9812

9666

1.

4 0.

96

1 1.

0 0.

30

1 1.

001.

100.

060.

51

0.55

21

6 R

S 0.

69

8.53

0.

69

0 0.

8822

1687

1.

3 0.

93

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63

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08

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50.

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46

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 24

4 SS

0.

53

7.09

5.

22

43

1.40

5095

275

0.3

0.54

1

0.9

1.60

0.

94.

151.

100.

263.

46

0.67

24

5 SS

0.

53

7.09

2.

92

20

1.31

4101

565

0.4

0.65

1

0.9

1.66

0.

92.

861.

100.

392.

77

0.91

24

6 SS

0.

53

7.09

5.

22

43

1.01

5413

730

0.2

0.49

1

0.9

1.48

0.

94.

151.

100.

333.

39

0.49

24

7 Q

S 0.

29

7.32

3.

47

26

1.01

2747

781

0.3

0.56

1

1.1

1.36

1.

13.

261.

100.

251.

95

0.61

24

8 Q

S 0.

29

7.32

3.

47

26

1.01

2747

781

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0.56

1

1.1

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13.

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100.

251.

95

0.58

24

9 Q

S 0.

29

7.32

2.

17

15

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494

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1

1.1

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12.

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100.

291.

31

0.21

25

0 Q

S 0.

29

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17

15

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1

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291.

31

0.43

25

1 Q

S 0.

29

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47

26

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13.

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22

0.15

25

2 Q

S 0.

29

7.32

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47

26

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13.

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342.

22

0.46

25

3 Q

S 0.

29

7.32

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05

14

1.01

2375

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1

1.1

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12.

411.

100.

371.

70

0.30

25

4 Q

S 0.

29

7.32

2.

05

14

1.01

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1

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12.

411.

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371.

70

0.34

25

5 Q

S 0.

29

7.32

2.

77

20

0.34

2283

109

0.1

0.41

1

1.1

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1.

12.

861.

100.

451.

50

0.30

25

6 Q

S 0.

29

7.32

2.

77

20

0.34

2283

109

0.1

0.41

1

1.1

0.89

1.

12.

861.

100.

451.

50

0.00

25

7 Q

S 0.

29

7.32

3.

12

23

1.31

3714

833

0.4

0.63

1

1.1

1.86

1.

13.

071.

100.

332.

27

0.18

25

8 Q

S 0.

29

7.32

3.

12

23

1.31

3714

833

0.4

0.63

1

1.1

1.86

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13.

071.

100.

332.

27

0.34

25

9 Q

S 0.

29

7.32

2.

29

16

0.34

2308

278

0.1

0.44

1

1.1

0.96

1.

12.

571.

100.

551.

47

0.37

26

0 Q

S 0.

29

7.32

2.

29

16

0.34

2308

278

0.1

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1

1.1

0.96

1.

12.

571.

100.

551.

47

0.24

26

1 Q

S 0.

29

7.32

2.

29

16

1.86

2867

861

0.8

0.79

1

1.1

1.97

1.

12.

571.

100.

292.

03

0.64

26

2 Q

S 0.

29

7.32

2.

29

16

1.86

2867

861

0.8

0.79

1

1.1

1.97

1.

12.

571.

100.

292.

03

0.49

26

3 Q

S 0.

29

7.32

1.

68

11

0.43

1894

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0.3

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12.

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551.

34

0.55

26

4 Q

S 0.

29

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11

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1

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12.

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100.

551.

34

0.40

26

5 Q

S 0.

29

7.32

2.

29

16

2.65

2727

965

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1

1.1

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1.

12.

571.

100.

232.

09

0.73

26

6 Q

S 0.

29

7.32

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29

16

2.65

2727

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1

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12.

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232.

09

0.76

26

7 Q

S 0.

29

7.32

1.

30

8 0.

5214

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80.

4 0.

62

1 1.

1 1.

00

1.1

1.89

1.10

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1.19

0.

52

268

QS

0.29

7.

32

1.30

8

0.52

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928

0.4

0.62

1

1.1

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1.

11.

891.

100.

491.

19

0.40

26

9 Q

S 0.

29

7.32

2.

05

14

2.80

3250

508

1.4

0.95

1

1.1

2.55

1.

12.

411.

100.

302.

24

0.40

27

0 Q

S 0.

29

7.32

2.

05

14

2.80

3250

508

1.4

0.95

1

1.1

2.55

1.

12.

411.

100.

302.

24

0.40

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 27

1 Q

S 0.

29

7.32

1.

93

13

0.67

2174

180

0.3

0.59

1

1.1

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1.

12.

331.

100.

441.

54

0.52

27

2 Q

S 0.

29

7.32

1.

93

13

0.67

2174

180

0.3

0.59

1

1.1

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1.

12.

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100.

441.

54

0.37

27

3 Q

S 0.

29

7.32

1.

68

11

2.87

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12.

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251.

85

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27

4 Q

S 0.

29

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68

11

2.87

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1

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1.

12.

161.

100.

251.

85

0.61

27

5 R

S 1.

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52

12

2.10

2538

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0.8

0.80

1

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1

1.60

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2.72

0.

64

276

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40

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72

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27

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74

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27

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74

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49

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37

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28

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1

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1

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285

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286

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22

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28

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98

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288

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17

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4431

62.

6 1.

00

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21

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19

289

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15

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5

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0.

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100.

503.

87

1.13

29

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31

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7 0.

77

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41

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0.

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291

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52

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29

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30.

5 0.

69

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9 1.

73

0.9

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0.

98

293

SS

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15

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5

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0.8

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0.

91.

571.

100.

433.

39

0.79

29

4 SS

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31

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63

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50.

6 0.

73

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9 2.

08

0.9

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1.10

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3.17

0.

91

295

SS

1.31

15

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5

1.92

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097

0.7

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1

0.9

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0.

91.

571.

100.

493.

44

0.85

29

6 SS

1.

31

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4 2.

63

5 1.

2529

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20.

5 0.

66

1 0.

9 1.

36

0.9

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0.

91

297

SS

1.04

11

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1.66

3

1.46

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144

0.9

0.81

1

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2.14

0.

91.

361.

100.

682.

66

0.24

Pi

er D

ata

Flow

Dat

a SR

ICO

S-EF

A K

Fac

tors

App

roac

h H

EC-1

8 M

etho

d Te

st

No.

Pi

er

Type

Pi

er

Wid

th

Pier

Le

ngth

B

A

ttack

Ang

le

H

Re

H/B

K

w

Ksp

K

sh

Z max

K

1K

2 K

3 F r

H

EC-1

8

Mea

sure

d Pi

er

Scou

r

(m

) (m

) (m

) (d

egre

e)(m

)

D

epth

(m

)

(m

) (m

) 29

8 SS

1.

04

11.9

8 1.

66

3 1.

0125

8408

70.

6 0.

72

1 0.

9 1.

37

0.9

1.36

1.10

0.49

2.04

0.

37

299

SS

1.04

11

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1.66

3

1.04

3141

439

0.6

0.72

1

0.9

1.57

0.

91.

361.

100.

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23

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30

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04

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4 1.

66

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6853

8115

61.

0 0.

85

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9 2.

59

0.9

1.36

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68

301

SS

1.04

12

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3553

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30

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04

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37

303

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30

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8 2.

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5312

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02

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41

0.15

R

efer

ence

: D

.S. M

uelle

r, 19

96, “

Chan

nel S

cour

at B

ridg

es in

the

Uni

ted

Stat

es”,

FH

WA-

RD-9

5-18

4, F

eder

al H

ighw

ay A

dmin

istra

tion,

VA,

USA

N

ote

B:

pier

pro

ject

ed w

idth

; K

2: co

rrec

tion

fact

or fo

r ang

le o

f atta

ck o

f flo

w fr

om H

EC-1

8 Q

S: S

quar

e si

ngle

C

S: C

ylin

der s

ingl

e K

3: co

rrec

tion

fact

or fo

r bed

con

ditio

n fr

om H

EC-1

8 R

e: R

eyno

lds n

umbe

r F r

: fro

ude

num

ber

Ksh

: pie

r sha

pe e

ffec

t on

Zmax

for S

RIC

OS-

EFA

met

hod

RS:

Rou

nd si

ngle

H

: A

ppro

chin

g flo

w d

epth

K

sp: p

ier s

paci

ng e

ffec

t on

Zmax

for S

RIC

OS-

EFA

met

hod

SS:

Shar

p si

ngle

K

1: co

rrec

tion

fact

or fo

r pie

r sha

pe

from

HEC

-18

Kw: w

ater

dep

th e

ffec

t on

Zmax

for S

RIC

OS-

EFA

met

hod

Zm

ax: t

he p

redi

cted

max

imum

scou

r dep

th

T

able

C2

– FR

OE

HL

ICH

(198

8) D

atab

ase

Pier

Dat

a A

ppro

ach

Flow

Dat

a B

ed M

ater

ial

SRIC

OS-

EFA

Met

hod

H

EC-1

8 M

etho

d

Test

N

o.

Type

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de

Wid

th

(m)

Leng

th

(m)

Dep

th

(m)

Vel

ocity

(m/s

) A

ttack

Ang

leD

50

(mm

) H

(m

) H

/BK

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sh

Re

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F r

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-18

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Mea

sure

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our

Dep

th

(m)

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14

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84

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250

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181.

01.

01.

0 82

8000

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450.

135

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30

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28

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250

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2600

00

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01.

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50

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3

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92

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39

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43

1.57

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860.

3 3.

660.

248

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9.47

1.

74

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50

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65

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6 3.

140.

069

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80

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85

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96

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90

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312

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21.

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58

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3 1.

52

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5.

80

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00

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821.

01.

00.

9 30

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0 2.

110.

262

0.9

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1.1

2.71

0.

76

7 3

1.52

6.

10

4.10

2.

59

0 70

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1.

52

2.70

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0.9

3936

800

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80.

91.

01.

12.

90

0.76

8

3 1.

52

6.10

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40

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0

70.0

00

1.52

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241.

01.

00.

9 32

3760

0 2.

210.

369

0.9

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2.60

0.

61

9 3

1.52

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10

5.30

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05

0 70

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1.

52

3.49

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4636

000

2.77

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91.

01.

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22

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10

3

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10

6.60

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90

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52

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000

2.68

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00.

91.

01.

13.

24

0.61

11

3

1.52

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10

5.20

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51

0 70

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52

3.42

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0.9

5335

200

3.03

0.49

10.

91.

01.

13.

41

0.61

12

3

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60

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67

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500

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061.

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9 66

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470.

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82

13

2 1.

52

11.5

8 1.

20

0.49

0

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52

0.79

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00

0.76

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31.

01.

01.

11.

33

0.30

14

2

1.52

11

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1.50

0.

76

0 0.

500

1.52

0.

990.

81.

01.

0 11

5520

0 1.

080.

198

1.0

1.0

1.1

1.66

0.

30

15

2 1.

52

11.5

8 1.

20

0.88

0

0.50

0 1.

52

0.79

0.8

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1.0

1337

600

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61.

01.

01.

11.

71

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16

2

1.52

11

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0.50

0.

27

0 0.

500

1.52

0.

330.

61.

01.

0 41

0400

0.

380.

122

1.0

1.0

1.1

0.92

0.

76

17

2 1.

52

11.5

8 0.

60

0.15

0

0.50

0 1.

52

0.39

0.6

1.0

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2280

00

0.28

0.06

21.

01.

01.

10.

73

1.22

18

2

1.52

11

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2.10

1.

52

0 1.

600

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1.

380.

91.

01.

0 23

1040

0 1.

880.

335

1.0

1.0

1.1

2.34

0.

61

19

2 1.

52

11.5

8 2.

00

1.55

0

1.60

0 1.

52

1.32

0.9

1.0

1.0

2356

000

1.87

0.35

01.

01.

01.

12.

34

0.61

20

2

1.52

11

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3.00

1.

58

0 1.

600

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971.

01.

01.

0 24

0160

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030.

291

1.0

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91

21

2 1.

52

11.5

8 3.

20

1.98

0

1.60

0 1.

52

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1.0

1.0

1.0

3009

600

2.34

0.35

31.

01.

01.

12.

77

1.22

22

2

1.52

11

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3.00

1.

80

0 1.

600

1.52

1.

971.

01.

01.

0 27

3600

0 2.

200.

332

1.0

1.0

1.1

2.64

1.

37

23

2 1.

52

11.5

8 2.

60

2.07

0

1.60

0 1.

52

1.71

1.0

1.0

1.0

3146

400

2.41

0.41

01.

01.

01.

12.

75

1.07

24

2

1.52

11

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3.00

1.

83

0 1.

600

1.52

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971.

01.

01.

0 27

8160

0 2.

230.

337

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1.1

2.66

1.

83

25

2 1.

52

11.5

8 0.

90

0.94

0

1.60

0 1.

52

0.59

0.7

1.0

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1428

800

1.04

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61.

01.

01.

11.

70

0.46

26

2

1.52

11

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0.90

0.

98

0 1.

600

1.52

0.

590.

71.

01.

0 14

8960

0 1.

060.

330

1.0

1.0

1.1

1.73

0.

61

Pier

Dat

a A

ppro

ach

Flow

Dat

a B

ed M

ater

ial

SRIC

OS-

EFA

Met

hod

H

EC-1

8 M

etho

d

Test

N

o.

Type

co

de

Wid

th

(m)

Leng

th

(m)

Dep

th

(m)

Vel

ocity

(m/s

) A

ttack

Ang

leD

50

(mm

) H

(m

) H

/BK

wK

spK

sh

Re

Z max

(m)

F r

K1

K2

K3

HEC

-18

(m)

Mea

sure

dSc

our

Dep

th

(m)

27

2 1.

52

11.5

8 1.

80

1.10

0

1.60

0 1.

52

1.18

0.9

1.0

1.0

1672

000

1.45

0.26

21.

01.

01.

11.

99

0.46

28

2

1.52

11

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2.40

1.

16

0 1.

600

1.52

1.

581.

01.

01.

0 17

6320

0 1.

650.

239

1.0

1.0

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2.12

0.

61

29

2 1.

52

11.5

8 2.

30

1.13

0

1.60

0 1.

52

1.51

1.0

1.0

1.0

1717

600

1.60

0.23

81.

01.

01.

12.

08

0.76

30

2

1.52

11

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1.50

1.

13

0 1.

600

1.52

0.

990.

81.

01.

0 17

1760

0 1.

390.

295

1.0

1.0

1.1

1.97

0.

46

31

2 1.

52

11.5

8 2.

00

0.98

0

1.60

0 1.

52

1.32

0.9

1.0

1.0

1489

600

1.40

0.22

11.

01.

01.

11.

92

0.76

33

3

4.60

4.

60

3.70

2.

90

0 90

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4.

60

0.80

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1.0

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1334

0000

4.

280.

481

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1.0

1.1

6.16

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50

34

3 4.

60

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60

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0

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00

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91.

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9 16

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3

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60

1.50

0.

61

0 90

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60

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91.

01.

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46

4.58

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81.

05.

61.

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41

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05.

61.

116

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2

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00

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2

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0 15

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30

Pier

Dat

a A

ppro

ach

Flow

Dat

a B

ed M

ater

ial

SRIC

OS-

EFA

Met

hod

H

EC-1

8 M

etho

d

Test

N

o.

Type

co

de

Wid

th

(m)

Leng

th

(m)

Dep

th

(m)

Vel

ocity

(m/s

) A

ttack

Ang

leD

50

(mm

) H

(m

) H

/BK

wK

spK

sh

Re

Z max

(m)

F r

K1

K2

K3

HEC

-18

(m)

Mea

sure

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our

Dep

th

(m)

59

2 1.

50

1.50

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00

2.69

0

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00

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001.

01.

01.

0 40

3500

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820.

496

1.0

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30

60

2 1.

50

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50

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671.

01.

01.

0 38

1000

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720.

513

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80

61

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50

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40

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94.

81.

14.

54

0.65

R

efer

ence

Fr

oehl

ich

D.C

. (19

88),

"Ana

lysi

s of O

nsite

Mea

sure

men

t of S

cour

at P

iers

", P

roce

edin

gs o

f ASC

E Na

tiona

l Hyd

raul

ic E

ngin

eeri

ng C

onfe

renc

e, C

olor

ado

Spri

ngs,

Colo

rado

Not

e:

1: S

quar

e-no

sed;

H

: App

roch

ing

flow

dep

th

2:

R

ound

-nos

ed;

K1:

corr

ectio

n fa

ctor

for p

ier s

hape

from

HEC

-18

Ksp

: pie

r spa

cing

eff

ect o

n Zm

ax fo

r SR

ICO

S-EF

A

met

hod

3:

Shar

p-no

sed;

K

2: co

rrec

tion

fact

or fo

r ang

le o

f atta

ck o

f flo

w fr

om H

EC-1

8 K

w: w

ater

dep

th e

ffec

t on

Zmax

for S

RIC

OS-

EFA

m

etho

d B

: pi

er p

roje

cted

wid

th;

K3:

corr

ectio

n fa

ctor

for b

ed c

ondi

tion

from

HEC

-18

Re:

Rey

nold

s num

ber

F r:

frou

de n

umbe

r K

sh: p

ier s

hape

eff

ect o

n Zm

ax fo

r SR

ICO

S-EF

A m

etho

d Z

max

: the

pre

dict

ed m

axim

um sc

our d

epth

Tab

le C

3 –

Gill

(198

1) C

ontr

actio

n Sc

our

Dat

abas

e Te

st N

o. D

1(m

m)

Q (m

3 /s)

D2(

mm

) B

1(m

) B

2(m

) Sa

nd

D50

(mm

)τc

/τ1

B1/B

2 n

Vc(m

/s)

V1(

m/s

)M

easu

red

(mm

) SR

ICO

S-EF

A (m

m)

HEC

-18

(mm

)

1 67

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504

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76

0.50

1.

53

1.51

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52

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444

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29

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2

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6 10

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0.

76

0.50

1.

53

1.40

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52

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0.

30

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1.47

3

80.5

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11

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76

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53

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52

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32

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4

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13

1.10

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76

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1.

53

1.26

1.

52

0.01

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0.

36

50.3

0 40

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6 5

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48

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50

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8 8.

12

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33

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50

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60

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39

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06

8 68

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65

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76

0.50

1.

53

1.49

1.

52

0.01

444

0.39

0.

32

29.2

0 28

.40

5.67

9

74.1

0 0.

0196

10

6.70

0.

76

0.50

1.

53

1.37

1.

52

0.01

444

0.41

0.

35

32.6

0 34

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11.7

3 10

83

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0.02

10

118.

90

0.76

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50

1.53

1.

22

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0.

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37

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64

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50

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82

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50

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1.

51

1.52

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7 0.

30

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16

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13

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0 0.

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10

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0.

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0.

92

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1.

52

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327

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0.

32

32.0

0 29

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16.9

4 14

38

.70

0.00

71

48.8

0 0.

76

0.50

0.

92

2.55

1.

52

0.01

327

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0.

24

10.1

0 8.

86

2.86

15

43

.60

0.00

94

67.1

0 0.

76

0.50

0.

92

1.34

1.

52

0.01

327

0.33

0.

28

23.5

0 21

.85

9.13

16

53

.30

0.01

22

82.3

0 0.

76

0.50

0.

92

1.08

1.

52

0.01

327

0.31

0.

30

29.0

0 30

.11

12.8

7 17

54

.30

0.01

33

88.4

0 0.

76

0.50

0.

92

1.00

1.

52

0.01

327

0.32

0.

32

34.1

0 33

.95

17.1

4 18

27

.40

0.00

51

39.6

0 0.

76

0.50

0.

92

1.52

1.

52

0.01

327

0.30

0.

25

12.2

0 14

.06

3.99

R

efer

ence

: G

ill M

.A. (

1981

), "B

ed E

rosio

n in

Rec

tang

ular

Lon

g C

ontra

ctio

n", A

SCE

Jour

nal o

f Hyd

raul

ic D

ivisi

on, V

ol. 1

07, n

. HY3

, 273

-284

. N

ote:

B

1:

wid

th o

f nor

mal

cha

nnel

D

50:

diam

eter

whi

ch 5

0% o

f the

bed

mat

eria

l siz

e ar

e sm

alle

r V

c:

criti

cal v

eloc

ity fo

r D50

bed

mat

eria

l si

ze

B2:

w

idth

of c

ontra

cted

cha

nnel

n:

m

anni

ng c

oeff

icie

nt

τ 1:

bed

shea

r stre

ss in

the

norm

al c

hann

el

D1:

flow

dep

th in

nor

mal

cha

nnel

Q

: di

scha

rge

τ c:

critc

al sh

ear s

tress

of b

ed m

ater

ial

D2:

flow

dep

th in

con

tract

ed c

hann

el

V1:

flow

vel

ocity

in n

orm

al c

hann

el

APPENDIX D

SRICOS PROGRAM: USER’S MANUAL

SRICOS-EFA PROGRAM: USER’S MANUAL INTRODUCTION The SRICOS-EFA method can be used to handle complex pier scour alone, contraction scour alone, and the superposition of complex pier scour and contraction scour (integrated SRICOS-EFA method). The SRICOS-EFA program is associated with the SRICOS-EFA method and includes all the procedures. It automates the calculations of all the parameters such as maximum initial shear stress, initial scour rate, maximum scour depth, and transformation of the discharge into velocity. It automates also the computations to handle multi-flood and multi-layer systems. The program was written in Fortran by using visual Fortran 5.0. The input data can be either in the Metric System or the U.S. Customary System; the output data can be in either system as well. The output of the SRICOS-EFA program are curves showing the flow velocity vs. time, maximum shear stress vs. time and scour depth versus time. In order to run the SRICOS-EFA program, the following data sets are required: 1. EFA results or erosion function: scour rate z versus hydraulic shear stress τ , 2. Hydrologic data such as a discharge hydrograph or velocity data over time, 3. Bridge geometry, channel geometry, 4. Channel hydraulic information: channel hydraulic radius and Manning Coefficient. 5. Soil stratigraphy. STARTING THE SRICOS PROGRAM

The SRICOS-EFA program should be executed from the directory occupied by the program’s files by typing ‘SRICOS-EFA’ at the DOS prompt or double-clicking ‘SRICOS-EFA.EXE’ in the window environment. The SRICOS-EFA program is a user friendly, interactive code that guides the user through a step-by-step data input procedure except for the velocity or discharge data. The velocity or discharge input can represent several thousands of data points if the duration of the scour analysis is several years with daily readings. The velocity or discharge data should be prepared in the format of an ASCII file or a text document before running the program. STEPS OF DATA INPUT After starting the program, the logo of SRICOS shows up, and then the data input procedures proceed: • COMPLEX PIER SCOUR PLEASE ENTER (1) - User decides the type of scour calculation. Press ‘1’ to calculate complex pier scour

only. • CONTRACTION SCOUR PLEASE ENTER (2)

- User decides the type of scour calculation. Press ‘2’ to calculate contraction scour only.

• BRIDGE SCOUR PLEASE ENTER (3) - User decides the type of scour calculation. Press ‘3’ to calculate bridge scour, which

is used to calculate the scour depth when complex pier scour and contraction scour occur at the same time.

COMPLEX PIER SCOUR If user decides to calculate complex pier scour only (press ‘1’), then the data input proceeds as follows. • UNIT OF INPUT DATA – SI UNIT (1) OR ENGLISH UNIT (2) • User decides the unit of input data. Press ‘1’ to use SI unit or ‘2’ to use English unit. • UNIT OF OUTPUT DATA – SI UNIT (1) OR ENGLISH UNIT (2) • User decides the unit of output data. Press ‘1’ to use SI unit or ‘2’ for English unit. • FIRST DATE OF ANALYSIS – FORMAT(MM/DD/YYYY) • Input the first date of analysis, for example, 01/01/1999. • LAST DATE OF ANALYSIS – FORMAT(MM/DD/YYYY) • Input the last date of analysis, for example, 12/31/1999. • THE NUMBER OF INPUT (HYDROLOGIC) DATA AS INTEGER • Input the number of discharges or velocities as an integer number for the duration of

the analysis. These hydrologic data basically have the same time step. • CHANNEL UPSTREAM WIDTH AS REAL – UNIT [(m) OR (ft)] • Input the width of channel as a real number in meters if the unit of input data is SI

unit, or in feet if the unit of input data is English unit. • TYPE OF PIER –CIRCULAR PIER (1) OR RECTANGULAR PIER (2) • Input the type of the bridge piers. Press ‘1’ for circular pier or ‘2’ for rectangular

pier. If the pier is a circular pier, please press ‘1’, then the program will ask user to input: • PIER DIAMETER AS REAL – UNIT [(m) OR (ft)] - Input the diameter of the pier as a real number in meters if the unit of input data is SI

unit, or in feet if the unit of input data is English unit. If the pier is a rectangular pier, the program will ask user to input: • PIER WIDTH AS REAL – UNIT [(m) OR (ft)] - Input the pier width as a real number in meters if the unit of input data is SI unit, or

in feet if the unit of input data is English unit. • PIER LENGTH AS REAL – UNIT [(m) OR (ft)] - Input the pier length as a real number in meters if the unit of input data is SI unit, or

in feet if the unit of input data is English unit. • ATTACK ANGLE OF FLOW AS REAL – UNIT [(DEGREE)]

- Input the angle of attack of flow, which is only valid for rectangular pier since for a circular pier the angle of attack is always 0.

• NUMBER OF PIERS AS INTEGER - If it is a single pier case, please enter ‘1’. For a group of in line piers perpendicular to

the flow, please input the number of piers as integer and the program will ask the spacing of the piers in the next step.

• SPACING OF PIERS AS REAL – UNIT [(m) OR (ft)] - Input the spacing of the piers as a real number in meters if the unit of input data is SI

unit, or in feet if the unit of input data is English unit. • TIME STEP, dt AS REAL – UNIT [hrs] - Input the time step in hours as a real number. • TYPE OF INPUT (HYDROLOGIC) DATA – DISCHARGE (1) OR VELOCITY (2) - User decides the type of hydrologic data. In the actual calculations within the

program, the velocity data are used. If user has velocity data, press ‘2’. Otherwise, if user has no velocity data but only discharge data, press ‘1’ to use discharge data. Several sub-procedures are necessary to transform the discharge data to velocity data. User should input a sufficient number of points to describe the velocity to discharge relationship.

• TRANSFORM DISCHARGE DATA TO VELOCITY DATA: - DEFINED BY USER (HEC-RAS output)

• THE NUMBER OF REGRESSION POINTS AS INTEGER - FOR TRANSFORMING DISCHARGE DATA TO VELOCITY DATA

- Input the number of regression points representing the relationship between velocity data and discharge data.

• VALUES OF REGRESSION POINTS AS REAL - FOR TRANFORMING DISCHARGE DATA TO VELOCITY DATA - FORMAT [DISCHARGE (I) VELOCITY(2)] - UNIT [(CMS) OR (CFS) (m3/s) OR (ft3/s)]

- Input the values of regression points (discharge and velocity) as real numbers. If the unit of input data is SI unit, the units of discharge and velocity are (CMS) and (m/s), respectively. Otherwise, they are (CFS) and (ft/s). For example, if the unit system of input data is SI unit and the number of points is 3, 5.0 0.2 50.0 0.8 100.0 1.2 The values of the first column represent discharges and the unit is (CMS). The values of the second column represent velocities and the unit is (m/s).

• DEFINE RELATIONSHIP BETWEEN DISCHARGE AND WATER DEPTH - DEFINED BY USER (HEC-RAS output)

• THE NUMBER OF REGRESSION POINTS AS INTEGER - FOR DEFINING DISCHARGE DATA AND WATER DEPTH

- Input the number of regression points representing the relationship between discharge data and water depth.

• VALUES OF REGRESSION POINTS AS REAL - FOR TRANFORMING DISCHARGE DATA TO WATER DEPTH - FORMAT [DISCHARGE (I) WATER DEPTH(2)] - UNIT [(CMS) OR (CFS) (m) OR (ft)]

- Input the values of regression points (discharge and water depth) as real numbers. If the unit of input data is SI unit, the units of discharge and water depth are (CMS) and (m), respectively. Otherwise, they are (CFS) and (ft).

If input hydrologic data is velocity, the program will only ask user to define the relationship between velocity and water depth. • DEFINE RELATIONSHIP BETWEEN VELOCITY AND WATER DEPTH

- DEFINED BY USER (HEC-RAS output) • THE NUMBER OF REGRESSION POINTS AS INTEGER

- FOR DEFINING VELOCITY DATA AND WATER DEPTH - Input the number of regression points representing the relationship between velocity

data and water depth. • VALUES OF REGRESSION POINTS AS REAL

- FOR TRANFORMING VELOCITY DATA TO WATER DEPTH - FORMAT [VELOCITY (I) WATER DEPTH(2)] - UNIT [(m/s) OR (ft/s) (m) OR (ft)]

- Input the values of the regression points (velocity and water depth) as real numbers. If the unit of the input data is SI unit, the units of velocity and water depth are (m/s) and (m), respectively. Otherwise, they are (ft/s) and (ft).

• THE NUMBER OF LAYERS AS INTEGER - Input the number of soil layers as an integer number. • PROPERTIES OF 1st LAYER

- FORMAT [THICHNESS CRITICAL SHEAR STRESS] - UNIT [ (m) OR (ft) (N/m2) ]

- Input thickness of the layer and the critical shear stress. User should repeat this input as many time as the number of layers.

• ESTIMATE INITIAL SCOUR RATE – 1st LAYER - DEFINED BY USER

• THE NUMBER OF REGRESSION POINTS AS INTEGER: - FOR DEFINING DISCHARGE DATA AND WATER DEPTH

- Input the regression points for the relationship between the scour rate z and the hydraulic shear stresses τ , which is the result of the EFA test. Basically, it is the same procedure as in the step above, ‘TRANSFORM DISCHARGE DATA TO VELOCITY DATA’.

• FILE NAME OF INPUT

- Input the file name of hydrologic data such as discharges or velocities. This file should be in the directory occupied by the program files.

• FILE NAME OF CALCULATION RESULT ONLY - Input a file name for calculation result only. This file will include the results only

such as time t, velocity v, shear stress τ , maximum scour depth maxz , and scour depth z for each time step.

• FILE NAME OF OUTPUT - Input a file name for output. CONTRACTION SCOUR If user decides to calculate contraction scour only (press ‘2’), then the following data input proceeds as follows. • UNIT OF INPUT DATA – SI UNIT (1) OR ENGLISH UNIT (2) - User decides the unit of input data. Press ‘1’ to use SI unit or ‘2’ to use English unit. • UNIT OF OUTPUT DATA – SI UNIT (1) OR ENGLISH UNIT (2) - User decides the unit of output. Press ‘1’ to use SI unit or ‘2’ to use English unit. • FIRST DATE OF ANALYSIS – FORMAT(MM/DD/YYYY) - Input the first date of analysis, for example, 01/01/1999. • LAST DATE OF ANALYSIS – FORMAT(MM/DD/YYYY) - Input the last date of analysis, for example, 12/31/1999. • THE NUMBER OF INPUT (HYDROLOGIC) DATA AS INTEGER - Input the number of discharges or velocities as an integer number for the duration of

analysis. These hydrologic data basically have the same time step. • UPSTREAM UNCONTRACTED CHANNEL WIDTH AS REAL – UNIT [(m) OR (ft)] - Input the width of uncontracted channel as a real number in meters if the unit of

input data is SI unit, or in feet if the unit of input data is English unit. • CONTRACTED CHANNEL WIDTH AS REAL – UNIT [(m) OR (ft)] - Input the width of the contracted channel as a real number in meters if the unit of

input data is SI unit, or in feet if the unit of input data is English unit. • CONTRACTION LENGTH OF CHANNEL – UNIT [(m) OR (ft)] - Input the length of the contraction channel as a real number in meters if the unit of

input data is SI unit, or in feet if the unit of input data is English unit. • TRANSITION ANGLE OF CHANNEL AS REAL – UNIT [(DEGREE)] - Input the transition angle of the channel as a real number in degree. • MANNING COEFFICIENT OF CHANNEL AS REAL - Input the average Manning’s coefficient of the channel. • AVERAGE RIVER HYDRAULIC RADIUS AS REAL – UNIT [(m) OR (ft)] - Input the average river hydraulic radius of the contraction section as a real number in

meters if the unit of input data is SI unit, or in feet if the unit of input data is English unit. The hydraulic radius can be calculated as the area of the flow cross section divided by the wetted perimeter of the channel.

• TIME STEP, dt AS REAL – UNIT [hrs] - Input the time step in hours as a real number. • TYPE OF INPUT (HYDROLOGIC) DATA – DISCHARGE (1) OR VELOCITY (2) - User decides the type of hydrologic data. In the actual calculations within the

program, the velocity data are used. If user has velocity data, press ‘2’. Otherwise, if user has no velocity data but discharge data, then press ‘1’ to use the discharge data, several sub-procedures are necessary to transform the discharge data into velocity data. User should input a sufficient number of points to define the relationship.

• TRANSFORM DISCHARGE DATA TO VELOCITY DATA: - DEFINED BY USER (HEC-RAS output)



• VALUES OF REGRESSION POINTS AS REAL - FOR TRANFORMING DISCHARGE DATA TO VELOCITY DATA - FORMAT [DISCHARGE(I) VELOCITY(I)] - UNIT [(CMS) OR (CFS) (m/s) OR (ft/s)]

- Input the values of regression points (discharge and velocity) as real numbers. If the unit of input data is SI unit, the units of discharge and velocity are (CMS) and (m/s), respectively. Otherwise, they are (CFS) and (ft/s). For example, if the unit system of input data is SI unit and the number of points is 3, 5.0 0.2 50.0 0.8 100.0 1.2 The values of the first column represent discharges and the unit is (CMS). Similarly the values of the second column represent velocities and the unit is (m/s).

• DEFINE RELATIONSHIP BETWEEN DISCHARGE AND WATER DEPTH - DEFINED BY USER (HEC-RAS output)




- Input the values of the regression points (discharge and water depth) as real numbers. If the unit of input data is SI unit, the units of discharge and water depth are (CMS) and (m), respectively. Otherwise, they are (CFS) and (ft).

If input hydrologic data is velocity, the program will only ask user to define the relationship between velocity and water depth only. • DEFINE RELATIONSHIP BETWEEN VELOCITY AND WATER DEPTH

- DEFINED BY USER (HEC-RAS output) • THE NUMBER OF REGRESSION POINTS AS INTEGER

- FOR DEFINING VELOCITY DATA AND WATER DEPTH - Input the number of regression points representing the relationship between velocity

data and water depth. • VALUES OF REGRESSION POINTS AS REAL

- FOR TRANFORMING VELOCITY DATA TO WATER DEPTH - FORMAT [VELOCITY (I) WATER DEPTH(2)] - UNIT [(m/s) OR (ft/s) (m) OR (ft)]

- Input the values of regression points (velocity and water depth) as real numbers. If the unit of input data is SI unit, the units of velocity and water depth are (m/s) and (m), respectively. Otherwise, they are (ft/s) and (ft).



- Input thickness of the layer and the critical shear stress. User should repeat this input as many times as the number of layers.


• THE NUMBER OF REGRESSION POINTS AS INTEGER: - FOR DEFINING DISCHARGE DATA AND WATER DEPTH

- Input the regression points for the relationship between the scour rate z and the hydraulic shear stresses τ , which is the result of EFA test. Basically, it is the same procedure as the one described in the above step, ‘TRANSFORM DISCHARGE DATA TO VELOCITY DATA’.

• FILE NAME OF INPUT - Input the file name of hydrologic data (discharges or velocities). This file should be

in the directory occupied by the program files. • FILE NAME OF CALCULATION RESULT ONLY - Input a file name for calculation result only. This file will include the results only

such as time t, velocity v, shear stress τ , maximum scour depth maxz , and scour depth z for each time step.

• FILE NAME OF OUTPUT - Input a file name for output.

BRIDGE SCOUR If user decides to calculate bridge scour (press ‘3’), then data input procedures are followed. • UNIT OF INPUT DATA – SI UNIT (1) OR ENGLISH UNIT (2) - User decides the unit of input data. Press ‘1’ to use SI unit or ‘2’ to use English unit. • UNIT OF OUTPUT DATA – SI UNIT (1) OR ENGLISH UNIT (2) - User decides the unit of output. Press ‘1’ to use SI unit or ‘2’ to use English unit. • FIRST DATE OF ANALYSIS – FORMAT(MM/DD/YYYY) - Input the first date of analysis, for example, 01/01/1999. • LAST DATE OF ANALYSIS – FORMAT(MM/DD/YYYY) - Input the last date of analysis, for example, 12/31/1999. • THE NUMBER OF INPUT (HYDROLOGIC) DATA AS INTEGER - Input the number of discharges or velocities as an integer number for the duration of

analysis. These hydrologic data basically have the same time step. • TYPE OF PIER –CIRCULAR PIER (1) OR RECTANGULAR PIER (2) - Input the type of the bridge piers. Press ‘1’ for circular pier or press ‘2’ for

rectangular pier. If the pier is circular pier, please press ‘1’, then the program will ask user to input: • PIER DIAMETER AS REAL – UNIT [(m) OR (ft)] - Input the diameter of the pier as a real number in meter if the unit of input data is SI

unit, or in foot if the unit of input data is English unit. If the pier is rectangular pier, the program will ask user to input: • PIER WIDTH AS REAL – UNIT [(m) OR (ft)] - Input the pier width as a real number in meter if the unit of input data is SI unit, or in

foot if the unit of input data is English unit. • PIER LENGTH AS REAL – UNIT [(m) OR (ft)] - Input the pier length as a real number in meter if the unit of input data is SI unit, or in

foot if the unit of input data is English unit. • ATTACK ANGLE OF FLOW AS REAL – UNIT [(DEGREE)] - Input the angle of attack of flow, which is only valid for rectangular pier since

circular pier the angle of attack is always 0. • NUMBER OF PIERS AS INTEGER - If it is single pier case, please enter ‘1’. If group piers, please input the number of

piers as integer and the program will ask the spacing of the piers in next step. • SPACING OF PIERS AS REAL – UNIT [(m) OR (ft)] - Input the spacing of the piers as a real number in meter if the unit of input data is SI

unit, or in foot if the unit of input data is English unit.

• UPSTREAM UNCONTRACTED CHANNEL WIDTH AS REAL – UNIT [(m) OR (ft)]

- Input the width of uncontracted channel as a real number in meter if the unit of input data is SI unit, or in foot if the unit of input data is English unit.

• CONTRACTED CHANNEL WIDTH AS REAL – UNIT [(m) OR (ft)] - Input the width of the contracted channel as a real number in meter if the unit of

input data is SI unit, or in foot if the unit of input data is English unit. • CONTRACTION LENGTH OF CHANNEL – UNIT [(m) OR (ft)] - Input the length of the contraction channel as a real number in meter if the unit of

input data is SI unit, or in foot if the unit of input data is English unit. • TRANSITION ANGLE OF CHANNEL AS REAL – UNIT [(DEGREE)] - Input the transition angle of channel as a real number in degree. • MANNING COEFFICIENT OF CHANNEL AS REAL - Input the average manning coefficient of channel. • AVERAGE RIVER HYDRAULIC RADIUS AS REAL – UNIT [(m) OR (ft)] - Input the average river hydraulic radius corresponding to the contraction section as a

real number in meter if the unit of input data is SI unit, or in foot if the unit of input data is English unit. The hydraulic radius can calculated as the area of the flow cross section divided by the wetted perimeter of the channel.

• TIME STEP, dt AS REAL – UNIT [hrs] - Input the time step in hours as a real number. • TYPE OF INPUT (HYDROLOGIC) DATA – DISCHARGE (1) OR VELOCITY (2) - User decides the type of hydrologic data. In actual calculation of this program, the

velocity data are used. If user has velocity data, press ‘2’. Otherwise, if user has no velocity data but discharge data, and press ‘1’ to use discharge data, several sub-procedures are necessary to transform the discharge data to velocity data. User should input sufficient points representing the relationship.

• TRANSFORM DISCHARGE DATA TO VELOCITY DATA: - DEFINED BY USER

• TRANSFORM DISCHARGE DATA TO APPROACHING (1) OR CONTRACTED VELOCITY (2):

- Input the type of velocity. Press ‘1’ for transforming the discharge data to the upstream approaching velocity. Press ‘2’ for transforming the discharge data to the velocity in contracted section. The actual velocity data is used in the program will be the velocity in the contracted section. The program will automatically transform the approaching velocity to contracted velocity by using the following equation, which is obtained from HEC-RAS:

=

2

112 14.1

BB

VV

Where V2 is the velocity in the contracted channel with no piers, V1 is the approaching velocity, B1 is the width of uncontracted channel, B2 is the width of contracted channel.

Please noted that this equation only valid when it is rectangular channel. So the author recommends it is better for the user to define the relationship between the discharge and the velocity in contracted section directly.



• VALUES OF REGRESSION POINTS AS REAL - FOR TRANFORMING DISCHARGE DATA TO VELOCITY DATA - FORMAT [DISCHARGE (I) VELOCITY(I)] - UNIT [(CMS) OR (CFS) (m/s) OR (ft/s)]

- Input the values of regression points (discharge and velocity) as real numbers. If the unit of input data is SI unit, the units of discharge and velocity are (CMS) and (m/s), respectively. Otherwise, they are (CFS) and (ft/s). For example, if the unit system of input data is SI unit and the number of points is 3, 5.0 0.2 50.0 0.8 100.0 1.2 The values of the first column represent discharges and the unit is (CMS). Similarly the values of the second column represent velocities and the unit is (m/s).

• DEFINE RELATIONSHIP BETWEEN DISCHARGE AND WATER DEPTH - DEFINED BY USER




- Input the values of regression points (discharge and water depth) as real numbers. If the unit of input data is SI unit, the units of discharge and water depth are (CMS) and (m), respectively. Otherwise, they are (CFS) and (ft).

If input hydrologic data is velocity, the program will only ask user to define the relationship between velocity and water depth only. • DEFINE RELATIONSHIP BETWEEN VELOCITY AND WATER DEPTH

- DEFINED BY USER • TYPE OF VELOCITY DATA -APPROACHING VELOCITY (1) OR CONTRACTED

VELOCITY (2): - Input the type of velocity. Press ‘1’ for the upstream approaching velocity. Press ‘2’

for the velocity data in contracted section. The actual velocity data is used in the

program will be the velocity in the contracted section. The program will automatically transform the approaching velocity to contracted velocity by using the following equation, which is obtained from HEC-RAS:

=

2

112 14.1

BB

VV

Where V2 is the velocity in the contracted channel with no piers, V1 is the approaching velocity, B1 is the width of uncontracted channel, B2 is the width of contracted channel.

Please noted that this equation only valid when it is rectangular channel. So the author recommends it is better for the user to find and input the velocity in contracted section directly.

• THE NUMBER OF REGRESSION POINTS AS INTEGER - FOR DEFINING VELOCITY DATA AND WATER DEPTH

- Input the number of regression points representing the relationship between velocity data and water depth.

• VALUES OF REGRESSION POINTS AS REAL - FOR TRANFORMING VELOCITY DATA TO WATER DEPTH - FORMAT [VELOCITY (I) WATER DEPTH(2)] - UNIT [(m/s) OR (ft/s) (m) OR (ft)]

- Input the values of regression points (velocity and water depth) as real numbers. If the unit of input data is SI unit, the units of velocity and water depth are (m/s) and (m), respectively. Otherwise, they are (ft/s) and (ft).



- Input thickness of the layer and the critical shear stress. User should repeat this input as many as the number of layers.


• THE NUMBE OF REGRESSION POINTS AS INTEGER: - FOR DEFINING DISCHARGE DATA AND WATER DEPTH

- Input the regression points for the relationship between the scour rate z and the hydraulic shear stresses τ , which is the result of EFA test. Basically, it is the same procedures with above step, ‘TRANSFORM DISCHARGE DATA TO VELOCITY DATA’.

• FILE NAME OF INPUT - Input the file name of hydrologic data such as discharges or velocities. This file

should be in the directory occupied by the program files. • FILE NAME OF CALCULATION RESULT ONLY

- Input a file name for calculation result only. This file would include the results only such as time t, velocity v, shear stress τ , maximum scour depth maxz , and scour depth z for each time step.

• FILE NAME OF OUTPUT - Input a file name for output.

Nchrp_24-15 Complex Pier Scour and Contraction Scour in Cohesive Soils

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Transcript of Nchrp_24-15 Complex Pier Scour and Contraction Scour in Cohesive Soils