\:rf\ T100.I\4 ~t (b H9 199~ DEPARTMENTAL RESEARCH GDOT RESEARCH PROJECT NO. 9411 FINAL REPORT GEORGIA DEPARTMENT OF TRANSPORTATION EFFECT OF COMPOUND "l CHANNEL HYDRAULICS ON \ \ BRIDGE ABUTMENT SCOUR OFFICE OF MATERIALS & RESEARCH RESEARCH AND DEVELOPMENT BRANCH Georgia Department of Transportation Office of Materials and Research GDOT Research Project No. 9411 Final Report EFFECT OF COMPOUND CHANNEL HYDRAULICS ON BRIDGE ABUTMENT SCOUR by Terry W. Sturm, Ph.D., P.E. Associate Professor School of Civil & Environmental Engineering Georgia Institute of Technology Atlanta, GA 30332 April, 1998 The contents of this report reflect the views of the author, who is responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Georgia Department of Transportation or the Federal Highway Administration. This report does not constitute a standard, specification, or regulation. TECHNICAL REPORT STANDARD TITLE PAGE I. Report No. FHWA-GA-98-9411 2. Government Accession No. 4. Title and Subtitle Effect of Compound Channel Hydraulics on Bridge Abutment Scour 7. Author Dr. Terry W. Sturm Associate Professor, School of Civil and Environmental Engineering Georgia Institute of Technology 9. Performing Organization Name and Address Georgia Institute of Technology School of Civil and Environmental Engineering Atlanta, GA 30332-0355 3. Recipient's Catalog No. 5. Report Date Aprill998 6. Performing Organization Code 8. Performing Organiz. Report No. 9411 10. Work Unit No. 11. Contract or Grant No. 12. Sponsoring Agency Name and Address Georgia Department of Transportation No.2 Capitol Square Atlanta, Georgia 30334 13. Type of Report & Period Covered Final 1995-1997 14. Sponsoring Agency Code 15. Supplementary Notes Prepared in cooperation with the U.S. Department of Transportation Federal Highway Administration. 16. Abstract This study examines the effects of compound channel hydraulics on bridge abutment scour where the abutments terminate in wide, roughened floodplains. Water discharge, abutment length, and sediment size were varied to determine their effects on he time development and equilibrium depth of local clear-water scour around abutments that terminate in such floodplains. It is shown that the discharge distribution in the bridge approach channel and its redistribution in the contracted section are important determinants of scour depth. The effects of sediment size are accounted for by the critical velocity at incipient motion. It is demonstrated that scour depth can be related to local values of velocity and depth near the abutment face as well as to approach hydraulic conditions. Based on the experimental results, a dimensionless relationship is proposed for taking into account the effects of time development of scour. A methodology for assessing the expected magnitude of bridge abutment scour is suggested for the purpose of identifying bridges subject to excessive abutment scour in order that remedial action may be taken. Finally, the comparisons of WSPRO results, experimental results, and results from a 2-D numerical turbulence model have shown that WSPRO is adequate for estimating the independent parameters needed for abutment scour prediction, as long as bridge approach hydraulic conditions are utilized as predictor variables. 17. Key Words Compound channel hydraulics, bridge abutment, scour, floodplain 18. Distribution Statement No Restrictions 19. Security Classif. (ofthis report) Unclassified Form DOT 1700.7 (8-69) 20. Security Classif. (of this page) 21. No. of Pages Unclassified 145 22. Price TABLE OF CONTENTS EXECUTIVE SUMMARY ACKNOWLEDGMENTS LIST OF FIGURES LIST OF TABLES LIST OF SYMBOLS CHAPTER 1 - INTRODUCTION Background Research Objectives CHAPTER2- LITERATURE REVIEW Compound Channel Hydraulics Abutment Scour CHAPTER 3 - EXPERIMENTAL INVESTIGATION Introduction Compound Channel and Abutment Geometry Sediment Water Surface Profile and Velocity Measurements Scour Measurements Results Channel Roughness Discharge Distribution Water Surface Profiles Velocity Distributions Time Development of Scour Equilibrium Scour Depths Critical Velocity CHAPTER 4 - ANALYSIS OF RESULTS Equilibrium Scour Depth Alternative Procedure I Page No. ll1 IV v IX XI 1 1 4 7 7 13 21 21 21 23 24 26 28 28 29 31 31 32 32 34 37 37 38 Theoretical Background 38 Correlation of Results 41 Alternative Procedure II 42 Dimensional Analysis 42 Correlation of Results 44 Discussion 45 WSPRO Predictions 47 Time Development Relationship 50 Proposed Procedure for Abutment Scour Prediction 52 Example 54 Solution 54 Limitations 58 CHAPTER 5 - CONCLUSIONS AND RECOMMENDATIONS 61 LITERATURE CITED 65 APPENDIX A- Figures A-1 B - WSPRO Data and Results B-1 II EXECUTIVE SUMMARY This report summarizes experimental work on bridge abutment scour in a compound channel with wide, roughened floodplains. Water discharge, abutment length, and sediment size were varied to determine their effects on the time development and equilibrium depth of local, clear-water scour around abutments that terminate on the floodplain. It is shown that the discharge distribution in the bridge approach channel and its redistribution in the contracted section are very important determinants of scour depth. The effects of sediment size are accounted for by the critical velocity at incipient motion. It is demonstrated that scour depth can be related to local values of velocity and depth near the abutment face as well as to approach hydraulic conditions. Based on the experimental results, a dimensionless relationship is proposed for taking into account the effects of time development of scour. A methodology for assessing the expected magnitude of bridge abutment scour is suggested for the purpose of identifying bridges subject to excessive abutment scour so that remedial action can be taken. Finally, the comparisons ofWSPRO results, experimental results, and results from a 2D numerical turbulence model have shown that WSPRO is adequate for estimating the independent parameters needed for abutment scour prediction as long as bridge approach hydraulic conditions are utilized as predictor variables. 111 ACKNOWLEDGMENTS The contributions of graduate students Bahram Biglari, who completed the twodimensional numerical modeling; Sean Williams, who did much of the early fixed-bed and scour time development measurements; William Blackwood, who measured critical velocities; and Antonis Chrisochoides, who completed the scour and velocity measurements and WSPRO analysis contained herein are gratefully acknowledged. Scott Williams assistance in setting up the experimental flume and constructing the abutments was invaluable. The prior work of graduate students Nazar Janjua and Aftab Sadiq did much to set the framework for the advances made in this project. The author is grateful for the careful and thorough reviews of the final report by the FHWA Regional Office, by the GDOT Bridge Design Office under the supervision of Mr. Paul Liles, State Bridge Engineer, and by Mr. David Jared of the GDOT Materials and Research Office. Mr. Jared provided overall guidance as project engineer, and his patience and support in bringing the project to completion is appreciated. Mr. Lamar Caylor, also of GDOT Materials and Research, greatly encouraged the author's efforts during the project initiation phase. The author also acknowledges the support of the FHWA in a parallel research project with additional related objectives, which is still underway. Mr. Sterling Jones and Mr. Johnny Morris of FHWA made numerous helpful suggestions that improved both the GDOT project and the current FHWA project, which at its completion should augment and enhance the present report. IV LIST OF FIGURES Fig. 3.1. Cross-sections Used in Scour Experiments. Fig. 3.2. Abutment Shapes Used in Scour Experiments. Fig. 3.3. Sediment Grain Size Distributions. Fig. 3.4. Manning's n in the Main Channel and Floodplain for Cross-Section B. Fig. 3.5. Measured and Computed Normal Depth for Cross-Section B. Fig. 3.6. Ratio of Main Channel Discharge to Total Discharge as a Function ofRelative Normal Depth in the Floodplain. Fig. 3.7. Discharge Distribution Factor Mas a Function ofRelative Approach Floodplain Depth. Fig. 3.8. Variation ofMain Channel Discharge Ratio from Approach to Contracted Section with M. Fig. 3.9. Water Surface Profiles for Vertical-Wall Abutments ofVarying Length and Constant Discharge. Fig. 3.10. Water Surface Profiles for Vertical-Wall Abutments of Constant Length and Varying Discharge. Fig. 3. 11. Water Surface Profiles for Spill-Through Abutments of Varying Length and Constant Discharge. Fig. 3.12. Water Surface Profiles for Spill-Through Abutments of Constant Length and Varying Discharge. Fig. 3.13. Variation in Backwater Ratios in Floodplain with Discharge and Abutment Type and Length. Fig. 3.14. Approach Velocity Distributions for Vertical-Wall Abutments ofVarying Length and Constant Discharge. Fig. 3.15. Approach Velocity Distributions for Vertical-Wall Abutment of Constant Length and Varying Discharge. Page No. A-1 A-2 A-3 A-4 A-5 A-6 A-7 A-8 A-9 A-1 0 A-ll A-12 A-13 A-14 A-15 v Fig. 3.16. Approach Velocity Distributions for Spill-Through Abutments ofVarying Length and Constant Discharge. A-16 Fig. 3.17. Approach Velocity Distributions for Spill-Through Abutment of Constant Length and Varying Discharge. A-17 Fig. 3.18. Time Development of Scour Depth for Sediment A with Varying Discharge. A-18 Fig. 3.19. Time Development of Scour Depth for Sediment C with Varying Discharge. A-19 Fig. 3.20. Time Development of Scour Depth for Sediment C with Varying Abutment Length. A-20 Fig. 3.21. Equilibrium Scour Depths for Sediment A with Varying Discharge and Abutment Length. A-21 Fig. 3.22. Equilibrium Scour Depths for Sediments B and C with Varying Discharge and A-22 Abutment Length. Fig. 3.23. Equilibrium Bed Elevation Contours for LjBf= 0.44 (VW) and Q = 3.49 cfs. A-23 Fig. 3.24. Equilibrium Bed Elevation Contours for L/Bf= 0.44 (VW) and Q = 4.00 cfs. A-24 Fig. 3.25. Equilibrium Bed Elevation Contours for LjBf= 0.66 (VW) and Q = 3.51 cfs. A-25 Fig. 3.26. Equilibrium Bed Elevation Contours for LjBf = 0.66 (ST) and Q = 3.50 cfs. A-26 Fig. 3.27. Measured and Calculated Critical Velocities at Incipient Motion. A-27 Fig. 4.1. Definition Sketch for Equilibrium Scour in a Long Contraction in a Compound Channel. A-28 Fig. 4.2. Equilibrium Abutment Scour Relationship Based on Approach and Tailwater Conditions. A-29 Fig. 4.3. Equilibrium Abutment Scour Relationship Based on Local Velocity Near Abutment Face. A-30 Fig. 4.4. Estimate ofRatio of Approach Velocity to Abutment Velocity Based on A-31 Floodplain Flow Depth Near Abutment Face. Fig. 4.5. Estimate of Ratio of Approach Velocity to Abutment Velocity Based on Tailwater Flow Depth. A-32 VI Fig. 4.6. Numerically Predicted Resultant Velocity Distribution at Upstream Face of Bridge by 2D Turbulence Model Applied to Cross-section A Fig. 4.7. Numerically Predicted Velocity Vectors by 2D Turbulence Model Applied to Cross-section A Fig. 4.8. Estimation of Abutment Velocity Based on Relationship Between Alternative I and II Scour Prediction Procedures. Fig. 4.9. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for LJBr =0. 17 and Q=2.0 cfs. Fig. 4.10. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for LJBr=0.33 and Q=2.0 cfs. Fig. 4.11. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for L/Br =0.50 and Q=2.0 cfs. Fig. 4.12. Comparison of Computed and Measured Velocity Distributions in Cross-Section A for LJBr =0.17 and Q=2.0 cfs. Fig. 4.13. Comparison of Computed and Measured Velocity Distributions in Cross-Section A for L/Br =0.33 and Q=2.0 cfs. Fig. 4.14. Comparison of Computed and Measured Velocity Distributions in Cross-Section A for L/Br=0.50 and Q=2.0 cfs. Fig. 4.15. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for L/Br =0. 22 and Q=3.0 cfs. Fig. 4.16. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for L/Br=0.44 and Q=3.0 cfs. Fig. 4.17. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for L/Br=0.66 and Q=3.0 cfs. Fig. 4.18. Comparison of Computed and Measured Velocity Distributions in Cross-Section B forL/Br=0.22 and Q=3.0 cfs. Fig. 4.19. Comparison of Computed and Measured Velocity Distributions in Cross-Section B for L/Br =0.44 and Q=3. 0 cfs. A-33 A-34 A-35 A-36 A-37 A-38 A-39 A-40 A-41 A-42 A-43 A-44 A-45 A-46 Vll Fig. 4.20. Comparisons of Computed and Measured Velocity Distributions in Cross-Section B for L/Br=0.66 and Q=3.0 cfs. Fig. 4.21. Comparisons of Computed and Measured Approach Velocities for Cross-sections A and B. A-47 A-48 Fig. 4.22. Comparisons of Computed and Measured Approach Floodplain Depths for Cross-sections A and B. Fig. 4.23. Comparisons of Computed and Measured Discharge Distribution Factors for Cross-sections A and B. Fig. 4.24. Time Development of Scour Depth for Cross-section B and Sediment A in Dimensionless Form. Fig. 4.25. Time Development of Scour Depth for Cross-section Band Sediment B in Dimensionless Form. Fig. 4.26. Time Development of Scour Depth for Cross-section B and Sediment C in Dimensionless Form. Fig. 4.27. Consolidation of Dimensionless Time Development Data and Least-Square Fits for Sediments A, B, and C. Fig. 4.28. Burdell Creek Cross-section for Estimation of Clear-water Abutment Scour. Fig. 4.29. Design Hydrograph for Burdell Creek. A-49 A-50 A-51 A-52 A-53 A-54 A-55 A-56 V111 LIST OF TABLES Table 3.1. Experimental Parameters Table 4.1. Ranges of Dimensionless Variables in Experimental Relationships Table B.1. WSPRO Input Data File for Burdell Creek- Q100. Table B.2. WSPRO Water Surface Profile Output- Q100. Table B.3. Velocity Distribution from HP Record for Unconstricted Flow at Approach Section Table B.4. Velocity Distribution from HP Record for Constricted Flow at Approach Section Page No. 23 59 B-1 B-2 B-3 B-4 IX THIS PAGE LErr BLANK X LIST OF SYMBOLS 'b pier diameter; floodplain width; main channel width; equilibrium scour depth; theoretical contraction scour depth; scour depth at time t; median sediment size; approach Froude number; Froude number in contracted section near abutment face; g gravitational acceleration; k turbulent kinetic energy in k-E turbulence model; equivalent sand-grain roughness; spiral flow adjustment factor in Chang's method; velocity distribution factor in Chang's method; geometric shape factor for abutment and embankment in Froehlich's equation; embankment skewness factor in Froehlich's equation; flow intensity factor in Melville's method; Ks* abutment shape factor in Melville's method; abutment alignment factor in Melville's method; abutment length; m geometric contraction ratio ofbridge contraction; XI M n Ns Nsc index to the main channel and floodplain discharges calculated by a particular choice of interface (vertical, diagonal, or horizontal) , which was either included or excluded from wetted perimeter. The index was defined as the ratio ofboundary shear force to the streamwise component offluid weight (Radojkovic 1976) as a measure of apparent shear force. If the index is less than unity on the main channel interface, for example, then the apparent shear force resulting from main channel-floodplain interaction resists the fluid motion in the main channel. This modified method was applied to experimental results from the very large compound channel at Hydraulics Research, Wallingford, England. The channel is 184ft long by 33ft wide with a total flow capacity of39 ft3/s. The ratio of floodplain width to main channel half-width varied from 1 to 5.5, and the relative depth (floodplain depth/main channel depth) varied from 0.05 to 0.50. The calculated main channel and floodplain discharges, when multiplied by the square root of the index for each subsection, showed considerable improvement when compared to measured discharges regardless of the choice of interface. The difficulty of the method is in the prediction of the index. A regression equation was proposed for this purpose 9 with the

and the approach Froude number were the most important influences on the dimensionless scour depth. In one series of experiments, clear-water scour was studied by pre-forming the scour hole and determining the flow conditions necessary to just initiate sediment motion in the bottom of the scour hole. In this case, the dimensionless clear-water scour depth was found to be a function of the approach Froude number and the geometric contraction ratio, m. Gill (1972) argued from his experimental results on scour of sand beds around spur dikes that the distinction between clear-water and live-bed scour is unimportant for the design determination of maximum scour depth. He proposed that the maximum scour depth be based on the geometric contraction ratio, m, and on the ratio of sediment size to approach depth, D/y1. Laursen (1960) developed scour-depth relations for bridge abutments that were based on treating the abutment as a limiting case of scour through a long flow constriction. Live-bed scour was considered to be a function only ofL)y1 and the ratio of discharge per unit width in the overbank flow region to discharge per unit width in the scour region. The scour region was assumed to have a constant width of2.75 times the scour depth. In a subsequent analysis of relief-bridge scour (Laursen 1963), which was considered to be a case of clear-water scour, the same approach was taken in relating the abutment scour to that which would take place in a long constriction. The contracted width was assumed to be equal to a scour hole width of2.75 times 14 the scour hole depth. This assumption resulted in an implicit relation for scour depth: (2.1) in which La=abutment length; y1=approach flow depth; d.=maximum scour depth; 1:1=bed shear stress in approach flow; and 1:c=critical shear stress for initiation of sediment motion. In a comprehensive experimental study of the effect of flow depth on clear-water scour around abutments, Tey (1981) held constant the shear stress ratio, 1:/"tc, at a value of0.90 while varying the flow depth and the abutment length and shape. The results showed an increasing scour depth with increasing flow depth but at a decreasing rate as the depth became larger. The length of abutment obstructing the approach flow and the abutment shape were also found to influence the scour depth. Longer abutments and blunter abutment shapes caused deeper scour holes. Froehlich (1989) completed a regression analysis of some 164 laboratory experiments from 11 separate sources on clear-water scour around abutments or spur dikes. His proposed regression equation is: d L o.63 y o.43 __:_ = 0.78Kl K2 (~) Ftu6 (-1) ag-1.87 + 1 y1 y1 d50 (2.2) in which d.=scour depth; y1=approach flow depth; K1=geometric shape factor for abutment and embankment; K2=embankment skewness factor; La=abutment length; F1=approach Froude number; d50=median sediment grain size; and ag=geometric standard deviation ofthe sediment size distribution. Froehlich further proposed that a factor of safety of one should be added to the 15 value of d/y1 obtained from the regression analysis, and it has been included on the right hand side ofEq. 2.2. Currently, HEC-18 recommends the live-bed scour equation obtained by Froehlich's regression analysis of other investigator's results for this case because (2.2) seems to greatly overestimate abutment scour. The live-bed scour equation is given by L o.43 2.27K1 K2 [~] y! F 1 61 + 1 (2.3) with the factor of safety of one included on the right hand side. Melville ( 1992) summarized a large number of experimental results on abutment scour from rectangular channels and proposed a design method for maximum scour depth which depends on empirical correction factors for flow intensity, abutment shape, alignment and length. He classified abutments as short (Ljy1<1) or long (Ljy1>25), and suggested that the maximum clear-water scour depth was 2L. for the former case and 10y1 for the latter. For intermediate abutment lengths, equilibrium scour depth was given by d s = 2 K I K s * K 8 * (y I L a )05 (2.4) in which K1 =flow intensity factor= V1Nc; V1 =approach velocity; Vc =critical velocity for initiation of sediment motion; K, = abutment shape factor; K6* = abutment alignment factor, y1 = approach flow depth; and L. = abutment length. Sturm and Janjua (1993, 1994) conducted a series of experiments in a compound channel consisting of a main channel and floodplain with the abutment terminating in the floodplain, and 16 showed that the approach flow distribution and its readjustment by the abutment in the contracted section is an important factor that should be included in equations for predicting scour depth in natural channels. On the basis of a dimensional analysis and the application of Laursen's ( 1963) analysis of relief bridge scour in a long contraction to compound channels, they proposed a relationship given by d V IV - 5 = 7. 70 [ fJ c - 0.35 ] Yn M (2.5) in which ds =equilibrium scour depth; Yn = approach floodplain flow depth; Vn =approach floodplain flow velocity; Vc =critical velocity; and M =discharge contraction ratio defined as the fraction of the total discharge in the bridge approach section over a width determined by extending the bridge opening upstream to the approach section. Young et al. (1993) developed a regression equation for clear-water as well as live-bed abutment scour using the calculated contraction scour as a nondimensionalizing parameter for the abutment scour depth. Melville and Ettema (1993) reported research results on abutment scour in a compound channel but for the case of an abutment terminating in the main channel rather than on the floodplain. Chang (1996) has applied Laursen's long contraction theory to both clear-water and livebed scour. He has suggested a "velocity adjustment factor" k., to account for the no~uniform velocity distribution in the contracted section, and a "spiral-flow adjustment factor" kf at the abutment toe that depends on the approach Froude number. The value ofk., was based on potential flow theory, and kr was determined from experiments in rectangular laboratory flumes. The resulting scour equation was given by 17 (2.6) in which y2 =flow depth in contracted section after scour; y1 =approach flow depth; q1 =flow rate per unit width in approach section; q2 = flow rate per unit width in contracted section; and 8 = 0. 857 for clear-water scour. Eq. 2. 6 does not include the effect of sediment size on clear-water abutment scour. An equation in HIRE (Richardson et al., 1990) was developed from Corps ofEngineers' field data for scour at the end of spur dikes on the Mississippi River. It is recommended in HEC18 for predicting scour around long abutments with Ljy1 > 25. The equation is given by ds = 4 F o.33 ab Yab (2.7) in which Yab =depth of flow at the abutment; and Fab = Froude number based on the velocity and depth adjacent to the abutment. Time development of scour was studied in Laursen's pioneering research on scour by jets (Sedimentation 1977). Laursen argued that clear-water scour is an asymptotic process in which scour depth increases linearly with the logarithm oftime. Theoretically, equilibrium would never be reached under these circumstances except at infinity, so as a practical matter, some limiting depth of scour is determined in laboratory experiments at large durations when the rate of change in scour depth is very small. A consequence of developing scour equations from laboratory data for this equilibrium condition is that in the field case for small watersheds, the duration of the design discharge may be considerably shorter than the time to reach equilibrium. The result is an 18 overestimate of field scour for a given design event. Most of the research on time development of scour has been done for situations other than abutment scour, e.g. jet scour, pier scour, or hydraulic structure scour. Carstens (1966) has proposed a general method for determining the time development of scour by combining (a) the sediment continuity equation; (b) a sediment pick-up function; and (c) an assumed scour hole shape that is geometrically similar at all times. He showed that the simultaneous solution of these three equations agreed with Laursen's experimental results for time development of scour from a horizontal jet, although the experimental data were used to develop the sediment pickup function. Raudkivi and Ettema (1983) showed from their experimental results on the development of pier scour that dimensionless scour depth (d/b) was linearly proportional to the logarithm of (td50)/b3, in which ds = scour depth; b = cylindrical pier diameter; d50 = median sediment grain diameter; and t =time. Yanmaz and Altinbilek (1991) applied Carstens' method to the problem of time development of scour around bridge piers. The resulting differential equation was solved numerically to obtain a curve of d.lb as function of dimensionless time: (2.8) in which SG = specific gravity of the sediment. The function was linear with the logarithm of dimensionless time up to a large value of time after which it leveled off in agreement with their experimental results. Kothyari et al. (1992) proposed a different approach in which the temporal variation of scour around a bridge pier was calculated in successive time steps governed by: (a) the time required for removal of one sediment grain by the primary vortex; and (b) the resulting 19 gradual decrease of shear stress in the scour hole as it grew larger. Chiew and Melville ( 1996) suggested from their experimental results on scour development around bridge piers an empirical relationship for a dimensionless equilibrium time, t*=Vtjb, as a function ofVNc, in which V =approach velocity; Vc =critical velocity; b =pier diameter; and te = equilibrium time. The equilibrium time was defined as the time at which the rate of increase of scour depth was less than 5% of the pier diameter in 24 hours. The experimental results were then presented as the ratio of scour depth at a given time to equilibrium scour depth (ds/ds) as a function of the ratio of elapsed time to equilibrium time (t/te) for various constant values of(VNc). 20 CHAPTER3 EXPERIMENTAL INVESTIGATION Introduction Experiments were conducted in a 14 ft wide by 80 ft long flume of fixed slope in the Hydraulics Laboratory ofthe School of Civil and Environmental Engineering at Georgia Tech. Scour depths were measured as a function of discharge, sediment size, and abutment shape and length for two different compound channel cross-sections constructed in the flume at two different fixed slopes. Velocity distributions at the bridge approach section and complete water surface profiles at the beginning and end of scour were measured. The details of the experiments and some typical results are described in this chapter, and the results are analyzed in Chapter 4. Compound Channel and Abutment Geometry Compound channel sections were constructed inside the 14 ft by 80 ft flume and are shown in Fig. 3.1. Cross-section A was constructed for a series of experiments reported by Sadiq (1994) and was also used for a few experiments in this study. Subsequently, cross-section A was replaced by cross-section B for use in this study as well as in a separate FHWA study. Crosssection A had a total width of7.00 ft and a fixed bed slope of0.0050, while cross-section B was 13.83 ft wide with a fixed bed slope of 0. 0022 as shown in Fig. 3. 1. Steel rails on the top of the flume walls were adjusted to serve as a level track for the instrument carriage, which is driven by an electric motor. A pumping system provided the water supply to the flume from a recirculating sump into which the flume discharges. The flume discharge was measured by calibrated bend meters with an uncertainty in discharge of 0.0 1 ft3Is, 21 and the total capacity of the pumping system was approximately 7.00 ft3/s. The tailwater depth in the flume was adjusted with a motor-driven tailgate at the downstream end ofthe flume. The flume entrance included a head tank and a series of stilling devices to remove flow entrance effects. The compound channel section terminated 10 ft upstream of the tailgate in order to provide a sedimentation tank for settling of any sediment scoured from the channel. As a result of the head tank and sedimentation tank, the actual length of the compound channel was approximately 60ft. The main channel bed of cross-section A consisted of concrete having a longitudinal slope of 0. 005 with a standard deviation of 0. 003 ft from the required elevation at any station along the channel. Fine gravel with a mean diameter of3.3 mm and with a geometric standard deviation of 1.3 was used to provide the roughness on the main channel bed and walls. Gravel was affixed to the main channel bed and walls with varnish. Roughness in the floodplain was also provided by gravel of the same size. To prevent movement of the gravel in the floodplain for the uniform-flow experiments, the upper 2-in. layer was stabilized by mixing portland cement in the gravel in a ratio of 1:6 by volume. Water was then added until a reasonable workability was achieved to form a fixed bed consisting predominantly of gravel roughness in the resulting matrix. In the case of cross-section B, a lean concrete mix that utilized the 3.3 mm gravel as aggregate was poured to a constant slope of 0. 0022 with a standard error of 0.005 ft in bed elevation. In both crosssections, the bed surfaces were relatively rough as determined by the protruding grains of gravel. In the case of cross-section A, the bridge abutments were formed by a row of rectangular concrete blocks measuring 0.5 ft high by 0.5 ft wide (in the flow direction) that were fixed to the floor of the flume with cement mortar at Station 32 located 32ft downstream of the flume 22 entrance. The abutments for cross-section B were constructed as a row of concrete blocks poured into custom-built forms to create vertical-wall (VW), spill-through (ST), and wingwall (WW) abutment shapes as shown in Fig. 3.2. The side slopes for the wingwall and spill-through shapes were 2: 1 (horizontal: vertical), and the wingwall angle was 30 degrees as shown in Fig. 3.2. Abutments for cross-section B were located at Station 32. The abutment lengths for both crosssections are summarized in Table 3. 1. The ratio of abutment length La to floodplain width Br in the table indicates the relative length of floodplain obstructed by the abutment. Only the verticalwall abutments are analyzed herein as the worst case, while the effects of abutment shape on scour depth are being studied in a related, current project sponsored by FHWA Table 3.1. Experimental Parameters SHAPE CROSS SECTION LENGTHS La, ft L/Br SED dso mm Vertical-Wall (VW) Vertical-Wall (VW) Spill-Through (ST) Wing-Wall (WW) A 0.50, 1.00, 1.50 0.17, 0.33, 0.50 A 3.3 B 2.62, 5.24, 7.87 0.22, 0.44, 0.66 A,B, 3.3, 2.7, c 1.2 B 3.87, 6.46, 7.87 0.32, 0.54, 0.66 A 3.3 B 5.28, 7.28 0.44, 0.61 A 3.3 Sediment Three sediments having median sediment grain sizes (d50) of3.3, 2.7, and 1.2 mm were used in this research as indicated in Table 3.1 where they are referred to as Sediment A, B, and C, respectively. The measured size distributions of all three sediments are shown in Fig. 3. 3. The geometric standard deviation crg (= [d84/d16] 05) of Sediments A, B, and C was approximately 1.3. 23 Thus, these sediments can be considered to be uniform for the purpose of assessing sediment size effects on abutment scour. Water Surface Profile and Velocity Measurements Both water-surface profiles and velocities were measured in the fixed-bed compound channels just described, first for uniform flow to determine the bed roughness, and then with the abutments in place to obtain the hydraulic conditions at the beginning of scour. In the uniformflow experiments, stations for measuring the water-surface elevations were fixed at 4.00 ft intervals along the length of the channel. The desired discharge was obtained by adjusting the inlet valve, and the tailgate was raised or lowered to achieve the required Ml or M2 profile with no abutments in place. At each station, the water-surface elevation was measured at three points across the cross-section for Cross-section A, and at eight points in the case of Cross-section B. The mean of these elevations was then used to determine the mean elevation of the water surface at each station. The normal depths were determined by taking the mean of the flow depths at a point where both M 1 and M2 water-surface profiles asymptotically approached one another in the upstream direction, which was generally 20 to 30ft downstream of the channel entrance. The relative depth ratio (Yro I y0), in which Yro =normal depth in the floodplain and Yo= corresponding normal depth in the main-channel (see Fig. 3.1), varied between 0.26 and 0.35 for Cross-section A, and from 0. 13 to 0. 32 for Cross-section B. A miniature propeller current meter with a diameter of0.60 in. was used to measure point velocities averaged over 60 seconds. In the uniform flow experiments, Station 32 (32ft downstream of the channel entrance) was selected for measuring the point velocities across the channel cross section because at this station there were negligible entrance effects, and also 24 because the water surface could be adjusted easily to the normal depth at this station. Depth. averaged velocity distributions were obtained from a point velocity measurement at an elevation above the channel bottom of0.37 times the flow depth in each vertical profile in the floodplain, and from six to eight point measurements spaced out over each vertical profile in the main channel. A total of 14 to 19 vertical profiles were measured at a single cross-section to establish the depth-averaged velocity distribution. The resulting measured velocity distributions when integrated over the cross section produced discharges that were within 4 percent of the discharges measured by calibrated bend meters in the flume supply pipes for the uniform flow experimental runs. The separate discharges in the main channel and floodplains were determined from the point velocities by integration. This information was combined with the measured normal depths to determine the separate main channel and floodplain roughnesses in uniform compound channel flow from Manning's equation. Normal depth was also determined with flow in the main channel alone in order to determine the equivalent sand-grain roughness of the main channel. Measurement ofwater-surface profiles and point velocities was also conducted in the fixed-bed channel with the abutments in place. Away from the abutments, the water-surface elevations were measured at stations 4ft apart as in the uniform-flow case. Close to the abutments, water-surface elevations were measured at stations 1 ft to 2ft apart. The depth of flow at the downstream end of the channel was set at the normal depth for each discharge by adjusting the tailgate. With the abutments in place, detailed point velocity measurements were made across the entire channel cross-section at the bridge approach section, which was Station 28 (located 28 ft 25 downstream of the channel entrance) for Cross-section A, and either Station 22 or Station 24 for Cross-section B depending on the abutment length. This station was located in the region where the maximum backwater occurred as well as where the floodplain velocities were not retarded by the abutment. In general, this location varied between 67 and 133 percent of the bridge opening width measured upstream of the bridge. Depth-averaged velocities were determined at 17 to 19 positions across the cross section. This data was used to determine the discharge contraction ratio Mat the beginning of scour as well as the approach velocity and depth upstream of the end of the abutment. Velocity and depth measurements were also made at the downstream face of the abutment. At this location, the depth of flow in the floodplain was very small; therefore, the velocities were measured in the main channel only, but this still allowed the determination of the discharge in the main channel as well as in the floodplain from continuity. Resultant velocities were measured at the upstream face of the bridge for both Crosssections A and B. The resultant velocity direction was determined either by flow visualization or by rotating the velocity meter until a maximum reading was obtained. In the case of Crosssection B, additional resultant velocities were measured in the bridge opening to find the maximum velocity near the face of the abutment. Scour Measurements After the fixed-bed measurements were completed, a movable-bed section was constructed in the vicinity of the abutments. The cement-stabilized floodplain surface was removed between Station 28 and Station 36 for Cross-section A, and between Stations 22 and 42 in the case of Cross-section B. It was replaced by new, clean gravel identical to that in the fixedbed floodplain. The abutments were sealed with cement mortar to the floor of the flume. 26 Scour measurements were made for several discharges at each of the abutment lengths given in Table 3.1. At the start of each experimental scour test, the loose gravel in the movable- bed test section was carefully leveled to the floodplain elevations corresponding to the constant bed slope. Water was then introduced into the channel very gradually from the upstream and downstream ends ofthe flume with the tailgate raised so that the movable bed remained undisturbed. Once the whole channel was flooded, the desired discharge was obtained by adjusting the valve on the main inlet pipe. The tailgate was then lowered slowly until the corresponding normal depth was obtained at the downstream end of the channel. Scour was allowed to continue for 12 to 16 hours for Cross-section A, and for 24 to 36 hours for Crosssection B. After equilibrium had been reached, the water surface profile and the velocity distributions in the approach section and at the downstream face of the abutment were measured in the case of Cross-section B. Then the channel was carefully drained, and the bed elevations throughout the scour and deposition areas were measured with a point gauge having a scale uncertainty of 0. 001 ft. As a practical matter, the uncertainty in the scour depth measurements was about 0.003 ft. In general, bed elevations in the vicinity of the scour hole were measured at some 100 spatial locations from which scour contours could be plotted. Time rate of scour measurements were made for Sediment A and for the vertical-wall abutment for some experiments. For these runs, scour depth was measured from a scale inscribed on a plexiglas block that formed the face of the abutment. The scale could be read from above by the use of a mirror. Only those cases where the maximum scour depth occurred at the upstream comer of the abutment face were suitable for this measurement technique. In general, these cases occurred for the larger discharges for each abutment length. Scour depth measurements were 27 generally taken at times of0.08, 0.17, 0.25, 0.50, 0.75, 1, 2, 4, 8, 16, 24, and 36 hours after the beginning of the experiment. Results Channel Roughness The experimental results for Manning's n in the main channel and floodplain with compound channel flow are shown in Fig. 3.4 for Sediment A First, the value of the equivalent sand-grain roughness in the main channel was determined from the normal depth measurements for flow in the main channel alone (without overbank flow) with the result that~= 0.013 ft (4.0 mm or 1.2 d50). Then the separate discharges were determined in the main channel and floodplain for overbank flow at several discharges as described previously, and the data points are shown in Fig. 3.4 in comparison with Keulegan's equation given by R 116 .0928 (-) n ks (3.1) in which R=hydraulic radius in ft and~= equivalent sand-grain roughness in ft. For the separate flow in the floodplain,~ was found to be 0.013 ft as in main channel flow alone, which is consistent with the fact that the roughness surfaces were identical. In the case of main channel flow, an additional drag due to main channel-floodplain interaction was quantified in terms of (3.2) in which I\nc = effective Manning's n in the main channel with overbank flow; and nK = Keulegan's value for Manning's n in the main channel with~= 0.013 ft and no interaction with the 28 floodplain, i.e. zero contribution of the interface to wetted perimeter. The best-fit value of a was 1.23. In effect, the main channel conveyance was decreased by 23 percent due to the main channel-floodplain interaction. Similar results were found previously for Cross-section A (Sadiq 1994; Sturm and Sadiq 1996) with a=1.19. Shown in Fig. 3.5 are the measured values of normal depth in comparison with the calculated values for Cross-section B using Keulegan's equation and the best-fit values ofk. and a. The standard error in normal depth is 0.0025 ft. While it is true that the values ofManning's n were first calibrated with the same data as in Fig. 3.5, the agreement shown in Fig. 3.5 is indicative ofhow well this calculation approach can reproduce the discharge Q over the full range of experimental values. Also shown in Fig. 3. 5 is the calculated critical depth curve, which is below the normal depth curve, demonstrating that the channel is mild over the experimental range of discharges. Discharge Distribution The purpose of considering floodplain-main channel interaction in developing Manning's n values for compound channel flow is illustrated in Fig. 3.6 in which the ratio of main channel discharge to the total discharge is given as a function of relative depth in the floodplain. In both cross-sections, the calculated discharge distribution agrees well with the measured values. For comparison, the standard WSPRO method of assuming constant Manning's n and no interaction between main channel and floodplain overestimates the relative proportion of main channel discharge as shown in Fig. 3.6 for Cross-section A The correct proportioning of main channel and floodplain discharge is necessary to predict the discharge distribution factor M for which experimental values are given in Fig. 3. 7 as a function of relative floodplain depth in the bridge approach section (indicated by a subscript of 1 29 on the depth). The factor M is defined by (3.3) in which Qmci = discharge in the approach main channel; Qfp1= discharge in the approach floodplain; Qohi = obstructed floodplain discharge over a length equal to the abutment length in the approach cross-section; and Q = total discharge. While the values of M are primarily a function of abutment length and compound channel geometry, Fig. 3. 7 shows that they decrease slowly with increasing relative depth in the approach cross-section. Abutment shape seems to have little influence on M in Fig. 3. 7. Sturm and Janjua (1993) have shown that for small depth changes from the approach section to the bridge section, M represents the ratio of discharge per unit width in the approach floodplain to that in the contracted floodplain in the bridge section, the approach floodplain velocity upstream of the end of the abutment; y0 , the approach depth at the location of VI; and M, the discharge distribution factor, are given in Figs. 4.21, 4.22, and 4.23 for Crosssection A, and for Cross-section B for both the vertical-wall and spill-through abutments. The approach velocity VI is predicted well by WSPRO for Cross-section B as shown in Fig. 4.21 with a mean square deviation between measured and calculated values of about 0.05 ft/s giving a 49 coefficient ofvariation of0.05. The WSPRO comparisons for V1 in Cross-section A are somewhat scattered due to experimental uncertainty, but the 2D numerical turbulence model performs reasonably well for Cross-section A The approach depth Yn is consistently overestimated by WSPRO in both Cross-sections A and Bas shown in Fig. 4.22. The mean percent error is about 12 %. The 2D numerical model slightly underpredicts approach floodplain depths. In Fig. 4.23 it can be observed that the discharge distribution factor M is predicted equally well by WSPRO and the 2D numerical model in Cross-section A; however, WSPRO underestimates M for the smaller values in Cross-section B. This problem is rooted in the differences in velocity distributions noted earlier for this case as well as in the overprediction of yn by WSPRO. The results forM show that at least some of the effect of main channel-floodplain interaction has been accounted for by the adjustment ofManning's n values, but this achieves only the correct split between main channel and floodplain flow, not the correct detailed velocity distribution near the interface. This is a problem with the one-dimensional analysis afforded by WSPRO that can be overcome by a full 2-D numerical model. Time Development Relationship Based on the dimensional analysis result given by Eq. 4.10, time can be added as a variable in the scour development process to produce an expected relationship of the form ~ d =J[ v v ~b, t _c_ ] YJD f' c Ym (4.11) in which d81 is the scour depth at any timet. The influence ofyaJYro in (4.11) has not been included based on the experimental results. The experimental measurements of scour depth with 50 time are presented according to Eq. 4.11 for Sediments A, B, and C in Figs. 4.24, 4.25, and 4.26, respectively. These results for time development of scour include only those cases for which the maximum scour depth developed near the upstream comer of the abutment as discussed previously in Chapter 3. However, the location of the scour hole at the upstream comer occurred for the larger discharges so that the worst cases are included in these results. Close examination of these figures reveals that the choice of dimensionless variables ofEq. 4.11 results in very similar curves for the three different sediment sizes having similar values ofV.JVc. The curves have a functional form that begins with a linear development of scour depth with the logarithm of time followed by an abrupt leveling off to a nearly constant value equal to the equilibrium scour depth that depends only on V.JVc as shown previously in Fig. 4.3. The functional behavior and collapse with respect to sediment size shown in Figs. 4.24, 4.25, and 4.26 suggest the possibility of a universal set oftime development curves that can be applied to field cases provided that the dimensionless variables fall in the same range as in the laboratory experiments. Accordingly, least-squares regression analysis was applied to the data and suggested interpolated curves were developed and plotted as solid lines in Fig. 4.27. Thus, for a given sediment size, which determines Vc; a given abutment velocity v.b, which is determined by the abutment shape, degree of floodplain contraction, and flow velocity distribution; and a given time corresponding to the design flood duration, an estimated depth of scour can be obtained. For example, ifV.JVc = 1.5, approximately 2/3 of the equilibrium scour depth is reached in a flow duration of only about ten percent of the equilibrium time. Figure 4.27 shows very clearly the interplay of time, flow distribution, and sediment size in determining a design value of abutment scour depth. 51 Proposed Procedure for Abutment Scour Prediction As a result of the experimental results on equilibrium depth of clear-water abutment scour in Fig. 4.2 and time development of scour in Fig. 4.27, a prediction procedure that accounts for discharge distribution, sediment size and time can be developed. Based on the extensive comparisons between WSPRO estimations of scour parameters and parameter estimation by a 2D numerical turbulence model, it is assumed that the WSPRO predictions provide a reasonable estimation of the independent parameters for the prediction of clear-water abutment scour. It is further assumed that the abutment velocities to be used in the time development determination in Fig. 4.27 can be obtained from the relationship developed in Fig. 4.8 that depends only on parameters that can be calculated from WSPRO results. The steps in the proposed procedure are: (1) From field data, obtain at least one surveyed cross-section, and preferably three sections (bridge exit, downstream face of the bridge, and bridge approach). Also estimate Manning's n for the floodplains and main channel, and obtain bridge geometry data and sediment size d50. (2) Determine the 100 year and 500 year design discharges based on drainage area and regional frequency estimates (available from NFF in version 6 ofHYDRAIN). (3) Run WSPRO and obtain M, V0 , y0 , and Ym from the results. Also estimate the value of Voc from ymand d50, and the value of V lc from y0 and d50 using Keulegan's equation, Eq. 3.6, which is repeated below: v c JCSG -l)gd50 (4.12) 52 in which SG =specific gravity of the sediment= 2.65; SP =Shields' parameter determined from Shields' diagram for the given sediment size d50 ; andy= flow depth at which critical velocity Vc is to be determined. (4) Calculate the equilibrium depth of abutment scour from the best-fit relationship in Fig. 4.2 modified by a factor of safety FS: ds =8.14 [ qfl - 0.4] + FS }jv M qfDc (4.13) where ~c = Vac yto and Cin = Vn yn The maximum value of d/yto should not be taken any greater than 10 based on the experimental results. In addition, if Vn2:V1c , then maximum clear-water scour occurs so set Vn=V1c . It is recommended that the value of FS = 1.0, which is slightly greater than the standard error of estimate of 0.68 for d/Yto in the best-fit relationship. (5) From the watershed size and a hydrologic estimate oflag time of the watershed, use NFF in HYDRAIN to generate a hydrograph corresponding to the peak design discharge from which a flood duration can be estimated. (6) For the duration obtained from step 5, determine the percent of equilibrium scour depth that will occur from Fig. 4.27. To estimate VaJVc needed in Fig. 4.27, use Fig. 4.8 for which the best-fit relationship is given by V i.TI _3.!!._ = 1 + 1.56 [ __!!p_ - 0.4] Vc M qjDc (4.14) (7) Compare the estimated abutment scour depth with the abutment foundation depth and determine if riprap protection is needed or not. 53 Example A bridge with a 750ft opening length spans Burdell Creek which has a drainage area of 375 mi2. The exit cross-section is shown in Fig. 4.28 with three subsections and their corresponding values of Manning's n. The slope of the stream reach at the bridge site is constant and equal to 0.001 ft/ft. The bridge has a deck elevation of22 ft and a low chord elevation of 18 ft. It is a Type 3 bridge with 2: 1 abutment and embankment slopes, and it is perpendicular to the flow direction (zero skew). There are six bridge piers each with a width of 5 ft. The sediment has a median grain diameter d50 of2.0 mm (0.00656 ft). Estimate the clear-water abutment scour for the 100 year design flood. Solution From HYDRAIN, the NFF (National Flood Frequency) program can be used to estimate the design flood flows. For the given drainage area and for Region 3 in Georgia (coastal plain), the predicted Q100 is 14,000 cfs and Q500 = 20,000 cfs. Calculations are done in this example for QIOO The WSPRO input data file is shown as Table B.1 in App. B for Q100= 14,000 cfs. The program was actually run twice, first to obtain the water surface elevations for both the unconstricted and constricted cases at the approach cross-section, and second, with the HP 2 data records to compute the velocity distribution in the approach section for the unconstricted (undisturbed) water surface elevation of 13.25 ft and the constricted water surface elevation of 13.64 ft. These elevations can be extracted from Table B.2 where the results ofthe water surface profile computations are given. Tables B.3 and B.4 give the results of the velocity distribution computations for the unconstricted and constricted cases, respectively. 54 Now the scour parameters can be calculated from the WSPRO results. The value ofM(K) from Table B.2 is 0.189, which by definition gives M = 1- M(K) = 0.811. For consistency with current FHWA methodology, the unconstricted and constricted floodplain depths and velocities are determined by the procedure given in HEC-18 for Froehlich's equation. First for the constricted case, the abutment length is determined from Table B.2 by La = LEWBRDG - LEWAPPR = 937 - 173 = 764ft (4.15) Then from Table B.4 the blocked flow in the approach section up to X STA. 937 is 1.97 streamtubes by interpolation. Therefore, the blocked flow Qn is (1.97/20)*14,000 = 1379 cfs since each of the 20 streamtubes carries 1/20 of the total flow. Also, the blocked flow area An is 659 + .97*506 = 1150 ft?. Now we can calculate Vn = Qn/An = 1379/1150 = 1.20 ft/s, and Yn = An/La = 1150/764 = 1.50 ft. In a similar way, the value ofy10 is found for the equivalent blocked flow area in the unconstricted cross section from Table B.3 to be 1.17 ft. The critical velocities for coarse sediments are determined by substituting into Eq. 4.12. First, for the constricted approach section in the floodplain, we have for a depth of 1.50 ft: v 1 = v(2.65 -1)(32.2)(.00656)(0.035)*5.75*10g(12 .2)(1. 50) = 2.0ft/s c 2*0.00656 (4.16) in which the Shields parameter was taken to be 0.035 for this sediment size (Julien 1996). In a similar manner, the value of Yeo for an unconstricted floodplain depth of 1.17 ft is 1. 93 ftls. Because Vn < Ve1, it is apparent that we have clear-water scour. 55 To compute the scour depth, substitute into Eq. 4. 13 to obtain ds = 8.17 [ (1.20)(1.50) - 0.4] + 1.0 = 5.5 y fO (0.81 )(2.0)(1.17) (4.17) Finally, the scour depth is 5.5*1.17 = 6.4 ft. The NFF program can be used to develop a design flood hydrograph. Assuming that the watershed is 30 miles long with a lag time of 15 hours, the resulting hydrograph can be computed and is shown in Fig. 4.29. As a conservative assumption, the flood duration is estimated as the time required for a constant discharge equal to the peak discharge to give the same volume of direct runoff as the original hydrograph. This results in a duration of 16 hrs. The critical velocity at the toe of the abutment is computed from a depth equal to the water surface elevation in the bridge opening, which is 12.47 ft (Table B.2) minus the ground elevation at the toe (10.35 ft) to give Yab = 2.12 ft. Then using Eq. 4.12 again for consistency, the critical velocity Vc = 2.1 ft/s, and Vc tl Ym= (2.1)(16)(3600) I (1.17) = 1.0 x 105. From Eq. 4.14, VaJVc = 1.54, and Fig. 4.27 indicates that more than 90 percent of the equilibrium scour will occur over the flood duration of 16 hours. Under these circumstances, the reduction in scour due to equilibrium not being reached is small so that the final result for clear-water abutment scour depth is left at the value of 6.4 ft that was previously estimated. Because scour holes can develop as a result of several floods over time, the time analysis proposed herein is intended as a judgment factor in reducing the estimated scour only when (a) the estimated scour is significantly higher than actually observed on an existing bridge; or (b) the watershed is so small that only a small fraction of equilibrium scour is reached in a typical design 56 flood. It is strongly recommended that a whole range of discharges be considered and that the percent of equilibrium scour be investigated in each case. Fig. 4.27 provides for the first time a method for estimating percent of equilibrium scour for floods of differing magnitude, and it should greatly enhance the engineer's judgment in making a final evaluation for scour susceptibility. It should be noted that the estimated equilibrium scour has been determined for a verticalwall abutment and could be further reduced by a shape factor for a spill-through abutment currently recommended by HEC-18 to be 0.55. However, the results currently being obtained under the FHWA contract do not support such a large reduction for very long abutments, and so for the time being the worst case of the vertical-wall abutment is assumed. In addition, the estimated scour could be increased by a skewness factor for abutments not perpendicular to the flow as recommended by HEC-18, but for this example, the skewness factor was taken to be 1.0 for a perpendicular abutment. Finally, for purposes of comparison, it is reasonable to calculate the abutment scour for this case using Froehlich's live-bed scour equation or the HIRE equation as recommended by HEC-18. Substituting into Froehlich's equation given previously as Eq. 2.3, and using the values ofL3, Yn, and Vn already determined, we have 5._ = (2.27)(1.0)(1.0)( 764 )0.43 ( 1.20 )0.61 + 1 = 12.3 Yn 1.50 J(32.2)(1.50) (4.18) so that ds = (12.3)(1.5) = 18.4 ft. (Froehlich's clear-water abutment scour equation gives a value ofds =39ft!) 57 For the HIRE equation, which is recommended by HEC-18 for long abutments, the value ofyab is taken to be 2.12 ft as determined previously from the water surface elevation in the bridge section. However, the value ofVab is estimated to be equal to 3.2 ft/s as determined from Fig. 4.8 or Eq. 4.14 developed in this research. It is not recommended to use WSPRO results from the bridge section to estimate Vab because conveyance ratios cannot predict the local acceleration occurring near the abutment face. Now substituting into the HIRE equation given by Eq. 2. 9, we have ds = (4.0)( 3 2 . 113 ) = 2.9 Y ab J(32.2)(2.12) (4.19) from which ds = (2.9)(2.12) = 6.2 ft. This estimated scour depth is in much better agreement with the one predicted from the results of this research (6.4 ft), but the agreement is partly due to the choice of sediment size for this example. Much more extensive field testing is required to verify the relationships developed herein. Limitations The experimental results developed herein are for the case of clear-water abutment scour and should not be applied at the present time for abutment lengths and cross-sections that produce M values less than about 0.5, or for abutments that approach the bank of the main channel. The ranges of variables covered in the experiments reported herein are given in Table 4.1. If the livebed scour case occurs, then it is recommended that Vn be set equal to Vnc for maximum clearwater scour. In any case, the value of d/y10 without the factor of safety should not exceed a maximum value of 10, which was obtained both from these experimental results and those of 58 Melville (1992). Additional experiments are currently underway under the sponsorship ofFHWA to consider the case of the abutment terminating at the edge of the main channel, the case oflivebed scour, and the effect of abutment shape. These results may require some minor modification of the proposed scour prediction procedure but they are certain to enhance it. Some bridge scour data for the Georgia flood of 1994 was reviewed, but this data was collected for the purpose of closing bridges during the flood. It is not detailed enough for field verification of the proposed scour prediction procedure, so additional research is suggested in Chapter 5. Nevertheless, the field example problem that has been presented should assist the engineer in implementing the results of this research. Table 4.1- Range of Dimensionless Variables in Experimental Relationships Variable M Yr/Vflc Vrr/Vft)c YtofYo L/Br Qn/(MqmJ Range 0.60-0.95 0.4-0.8 0.5-1.0 0.6-1.0 0.17-0.66 0.4-1.6 59 THIS PAGE LEFT BLAHK 60 CHAPTERS CONCLUSIONS AND RECOMMENDATIONS It is concluded that the experimental results and methodology developed from this research can be utilized to estimate the depth of abutment scour and protect those bridges that may be scour susceptible. It has been determined over a much wider range of variables than was previously available that the effects of discharge distribution, sediment size, and time development on scour depth can be predicted from the relationships given in Figures 4.2, 4.8, and 4.27. The comparisons ofWSPRO results, experimental results, and results from a 2D numerical turbulence model have shown that the results from WSPRO are adequate for estimating the independent parameters needed for abutment scour prediction so long as bridge approach hydraulic conditions are used as predictor variables. It is recommended that the proposed procedure for abutment scour estimation be used alongside current FHWA procedures subject to the limitations on ranges of dimensionless variables given in Table 4.1. Full implementation of the proposed procedure should await completion of the present FHWA research for the case of the abutment approaching the banks of the main channel and for the case oflive-bed scour. In addition, it is strongly recommended that verification of the proposed procedure with field data be undertaken to develop confidence in its use. It is recommended that further research be conducted to advance to the next level of confidence in abutment scour predictions in the field in order to protect bridges that are subject to scour and possible failure. Suggested areas for further research are: 61 a. A well planned, detailed field study of a bridge subject to abutment scour in cooperation with the USGS is needed. The bridge should be instrumented and scour determined over a three year period with detailed field measurements of velocity and bed elevation changes. If resources are available, it is further recommended that more than one bridge be instrumented to allow for different regions in Georgia such as wide, heavily vegetated river floodplains as well as tidal zones in estuaries. b. A laboratory model of the instrumented field bridge should be constructed and tested to compare scour predictions based on the laboratory data with those actually measured in the field. c. Numerical model results from both WSPRO and FESWMS should be compared with the field data to determine their performance in an actual field case with respect to estimation of scour-prediction parameters. d. A laboratory study of scour countermeasures is needed in order to design the most efficient abutment scour protection schemes. The study should consider (a) the extent, size, and placement of riprap at abutments; (b) the effectiveness of spur dikes; and (c) procedures for using rock riprap to repair an ongoing abutment scour problem. e. The next level of research needed in order to refine equations for abutment scour prediction is the application of a 3D numerical model combined with 3D velocity measurements in the scour-hole area as the scour hole develops with time. Such a 3D model could also enhance the proposed field and scour countermeasure 62 studies. f. 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Q) a.. - - - - - - I I-t- I +- - .___ - 1--- -1- I- _I_ I I L _ L _I_ L l_ I I __ i __ _I_ _I_ I_ _!_ I -~- I - - 1- I - r - r r -~- -t - + - 1- -+ -j - I I J _j _ J _ l _ I_ 1 ------- 1 - 1- -I I I - - r - T ~- -~- ~ ~- 20 - - - - - - -t -1 - I I L- - - - - ~--- -1- - ~- 1- -1- - I- - - I- - -+ - _j_ - 1- -+ ---! - I L _____ o _;___~~~-j___j____L_.L__j.---J......""'!'!~=----_L_ ___J_ __L_ _[__L___L__u 0.1 1 10 Sieve Size, mm i ~ Sediment A ....... Sediment B ...... Sediment C I Fig. 3. 3. Sediment Grain Size Distributions. A-3 0.10 _j - L ~- - -:-- I - - i - - I- ' - - - - - - ' -- - MAIN CHANNEL ,- : - - - -T ks=0.013 ft r ~ _______ I__ _ l ~ -_I_ - - I I_ - - - - - - - l SIGMA=1.23 --<0 .T.."._" . -< (/) ~ c ! l_ - I- L - - - - - - _I_ ' .... l J - I- - I- - -- L J - i - l - ., ...."'-<- I I ' I j_ - - _j - _I_~- _I_. _j _I - - - - - - - l I - - I- I _I_ - - I- - - _j - l - - II I _j - l - - I_ FLOODPLAIN - - - - - - -~- ks=0.013 ft -,- - - - - - - T I I I II -,- ' ' - -r - I I - ---, - r -~- I 0.01 1 10 100 Rlks Fig. 3. 4. Manning's n in the Main Channel and Floodplain for Cross-Section B A-4 0.80 ~------- ' i ' 0.75- .:= 0.70 >. I Iaw.-. 0.65 0 0.60 0.55 . / // / 0. 50 '-._j___..L..._.L..._...C___c_~__L._.~..L__..._____.c--'----'-___L__~-'----'~--'-_L__j__~L......_l.__L.--'-~ 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Q,cfs , - CALC. NORMAL DEPTH i - - - CRITICAL DEPTH I MEASURED NORMAL DEPTH I I I ' Fig. 3.5. Measured and Computed Normal Depth for Cross-section B. A-5 0.5 ~~~ 0.4 ~ 0.3 ~ --------~-- 1 0.2 i 0.1 0.0 ~~-L- ~1__~--'-~--~L~--"~ ____] 0.0 0.1 0.2 0.3 ... ~-L-~ 0.4 L____L______l~__L__ ~ _l________!__ ~~-~_j_- ___j_~J____ --"- _ __j 0.5 0.6 0.7 0.8 0.9 1.0 QIQ m e 1 MEAS., XSECT. A .A MEAS., XSECT. B II - CALC.; n VARIABLE; A & B - - - CALC.; n CONSTANT; A Fig. 3.6. Ratio ofMain Channel Discharge to Total Discharge as a Function ofRelative Normal Depth in the Floodplain A-6 1.0 c - ,- - - - - 0.8 ! I 0.6 ~ I 0.4 i- 0.2 l.. ! _ _ X-SECTION A - - - - - - X-SECTION 8 0.0 0.1 0.2 0.3 0.4 ~1 I y1 ; -~ VW; La/Bf=0.22 -.s VW; La/Bf=0.44 -G VW; La/Bf=0.66 1-~ ST; La/Bf=0.32 - ST; La/Bf=0.52 - ST; La/Bf=0.66 I ~ VW; La/Bf=0.17 --- VW; La/Bf=0.33 ~ VW; La/Bf=0.50 Fig. 3.7. Discharge Distribution Factor Mas a Function of Relative Approach Floodplain Depth A-7 1.0 ~,~~~~~~~~~--~--~---, 0.9 0.8 0.7 0.6 0.5 ~-~-~'--L~~- -----".-~~----"~~~.L__---' 0.5 0.6 0.7 0.9 1.0 Fig. 3.8. Variation ofMain Channel Discharge Ratio from Approach Section to Contracted Section with M. A-8 CROSS-SECTION B ABUTMENT VW; Q=3.0 cfs 0.85 ,~~~~~~~ ---~-~~...-----~--~-~-~-- 0. 80 - - - - - - - ~ - - - - - - - + - - - - - - - + I ABUTMENT - - - - - 4 - - - - - - - ~- - - - - - - 0.75 -- - - - - - - - - - T--- - - - - "T ' ' - - - - - I --- ---- - ----- - .::=_ 0.70 :_-- ----- ~I -- ~-! --- ~ - ~ ~ t~ a~.. 0.65 rf -------,'_ -- I I ' ' I ---- - -- ----- - ------ I - - - - - I - - - - - - - - -~ - - - ::: L_- :- - -,- --: a.6a r~ -------~I --- ----+i - - - - - - -- ~I I - - - - - - - -: - - - - - - -1 ~ ' I I 11 I I 11-- --i- -- - :-- ' --~ 0 1 0 20 30 40 50 60 X-STATION, ft ~ La/Bf=0.22 ___.__ La/Bf=0.44 ~ ~a/Bf=0.66_] Fig. 3.9. Water Surface Profiles for Vertical Wall Abutments of Varying Length and Constant Discharge. A-9 CROSS-SECTION 8 ABUTMENT VW; La/Bf=0.44 0.85 ---------------;1..,.-i----------~ : :: ____ ~ :::: ___ ::: :::) ~UTME:NT: :: ~ ___ :- ~ I I I I ~ ~ ~-~:~=~ ;_ _ _ _: I I r- - ---- -,------ __ ________ I 0.70 I I i ~- ---.~- - - - - - - ~ - - - - - - ~ - - - - - - - 0.65 0. 60 ~ - - - - - - - : - - - - - - - : - - - - - - - : _____:_______ -:_______ i I I I 1 I 0.55 I _____ : ______ : __ __ : u~ I I -~ 0.50 r ' I I 0 1 0 I ' 20 I I I , I 30 I I ' I ' I I I I I I 40 50 I __c___j 60 X-STATION, ft i --- Q=2.5 cfs --.- Q=3.0 cfs --a-- Q=3.5 cfs 1 ----------' Fig. 3.10. Water Surface Profiles for Vertical Wall Abutments of Constant Length and Varying Discharge. A-10 CROSS-SECTION B ABUTMENT ST; 0=3.0 cfs :::: ~-------~------~----_-_-_~__-___+_________________+_:i~i~1------------~-,-~---------~--~-:------------~-.- 0.75 i' ' ~ ~- ~ ~ ~ ~ - - - - - - r - - - I I -- - - - - - - - - - l ABUTMENT I - - - - - 1 - - -- - - - - - - - - - -- - I ! ! I I I i \ I t-- --- -- ------ ~ 0.70 ~- I -- -=----._..1. I '_---- ~------- ~------- -~ f--:-- : : -- ----- - ---- Q.. O W 0.65 f~ ------~ ~ I .....- I : I [ ~I , I I 1 - - - - - - - -1 - - - - - - - - t 0.60 ~ - - - - - - - ~ - - - - - - - +- - - - - - - I I I - - - - - - - -, - - - - - - - -~ ! o.55 f r - - - - - - - I ~ - - - - - - - I ~ - - - - - - - I ~ L 0.50 : :1 ~~~~~~~~~~~~~-_J~~~~~~~~ 0 10 20 30 40 50 60 X-STATION, ft /-e- La/Bf=0.32--.- La/Bf=0.54 -a- La/Bf=~:_66_j Fig. 3.11. Water Surface Profiles for Spill-Through Abutments of Varying Length and Constant Discharge. A-ll CROSS-SECTION B ABUTMENT ST; La/Bf=0.54 0.80 0.75 ------------ .;:= I 0.70 ID... ~ 0.65 0.60 0. 50 '----'----'----'---"-- '~~~~ ..l.__c__..L..._"--.L._L.b.~ 0 10 20 30 40 50 60 X-STATION, ft I -e- 0=2.5 cfs -.- 0=3.0 cfs -a- 0=3.5 cfs I L___----------------------------------~----_j Fig. 3.12. Water Surface Profiles for Spill-Through Abutments of Constant Length and Varying Discharge. A-12 1.0,--- CROSS-SECTION 8 0.8 y Iy fO f1 0.6 0.4 0.2 0. 0 L _ '_ 0.0 _ _ J __ ! ___i_ _-'----~---'---~-___c---'------L--------'--------'---- 1.0 2.0 3.0 4.0 5.0 6.0 Q,cfs )', VW; La=2.62 ft z VW; La=5.24 ft + VW; La=7.86 ft o ST; La=3.86 ft ST; La=6.47 ft - ST; La=7.78 ft - VW (Exp. Fit) - ST (Exp. Fit) - - - - - - - - - - - -----1 Fig. 3.13. Variation ofBackwater Ratios in Floodplain with Discharge and Abutment Type and Length. A-13 CROSS-SECTION B ABUTMENT VW: Q=3.0 cfs 2.0 1.6 ~ 1.2 : - - - - - - - - - -4 - - -- - - ,_ - ~. - -! --- j r _._- 1-- 0 !------ I~. tI =-~----=I t=~--~-' cc--- I J I /-J g w > 0 .8 i~.>-----~-=-=-'~--_-__-___.,I. --~~--~.+-.-------~-I ---I -- ~~-~---------I~ I' I 1 ~--- 0.4 !Y' - . - - - - I- - - - - ' I - -- - - -' - - - - ! .. - - - - ,_ - - - - - - ,- - - - - - . iI I I I i 0. 0 L______L_ _ j __ _L.___L.... 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 TRANSVERSE STATION, ft I -e-- NO ABUTMENT --&-- La/Bf=0.22 ---- La/Bf=0.44 __.__ La/Bf=0.66 l Fig. 3.14. Approach Velocity Distributions for Vertical Wall Abutments of Varying Length and Constant Discharge. A-14 CROSS-SECTION B ABUTMENT VW; La/Bf=0.44 2.0 ~------------------------------------------------------------- 1.6 f i r------ I r - - - - - - ~------ r - - - - - -~------ -~------ -~-- I I I I I (/) 1.2 ~ i I ~------ ~------ ~------ L - - - - - - 1- - - - - - - 1 - - - - - - -1- ~ I I I ' i I I I 0~ 0.8t~.~~ ~ ~ : ~- : ~- : -- I ---- / 1I1 > ..--------, I I i I I ~ ' I I I I I I I I I 0.4 ~- - - - - - r - - - - - - r I I I I I - - : - - - - - - :- - -- - - - -:- - - - - - -:- - - - - - -~ ~ o.o L~--~-~-"----~ I I 0.0 2.0 4.0 6.0 8.0 10.0 TRANSVERSE STATION, ft : ___j 12.0 14.0 1--- I = = = Q 2.5 cfs -..- Q 3.0 cfs -a-- Q 3.5 cfs ____________________________ _j Fig. 3.15. Approach Velocity Distributions for Vertical Wall Abutments of Constant Length and Varying Discharge. A-15 CROSS-SECTION B ABUTMENT ST: 0=3.0 cfs 2.0 ----------------------------------------- ---------- 1.6 - - - - - - r - - - - - - ~------ r - - - - - - 1 - - - - - - -~------ -~-- ~ - 1.2 - - - - - - ~ i-- - - - - -- - 1- - - - - - - L - - - - - -I_ - - - - >- I I I I I - 1- - - - - - - 1- I ... I- --=--------- ------- ; --- 0 L~ -~ I ~ r~~---~-~~~~---:------- > 0.8 I / I ' ~ I _ ____________..- -.-.-.-. ---....::..-=---=----==~-- ~-~-~: 0.4 I~ I ~------- c ! I I - - - - -~------- r - - - - - - -~- -- I - - - -~------ -~------- I r 0.0 l 0.0 2.0 . _ L __ _ L __ __ J __ ___,_ _ ___L__ _ __c_ _ _ _ _ _ _, 4.0 6.0 8.0 10.0 12.0 14.0 TRANSVERSE STATION, ft ' --- NO ABUTMENT ___..,._ La/Bf=0.32 ----- La/Bf=0.54 __._ La/Bf=0.66 Fig. 3. 16. Approach Velocity Distributions for Spill-Through Abutments of Varying Length and Constant Discharge. A-16 CROSS-SECTION 8 ABUTMENT ST: La/Bf=0.54 2.0 ~--------------------------------------------------------------- I i 1.6 ~------ ~------ ~------ ~------ :-------:-------:-------I f I I I I I en >--~ ! ' ' 1.2 1- ______ L __ . ___ L - - - - I - -L - - - ' - - - I_ - - - - I - - 1- - - - - - : - J_ - 1- - - -~I I 0 0 _J w 0.8 -I =i:=:=====~.c=-=--~~-~--=-=----=----- :- - - - - - I > I I 1- -----' -- ! 0.4 I I I I I I - - - r - - - - - - ~-- - - - : - - - - - - - : - - - - - - - : - - - - - - -~ f o.o L_______L___L____L_____ I i 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 TRANSVERSE STATION, ft = = = ~ Q 2.5 cfs ....._ Q 3.0 cfs --- Q 3.5 cfs I Fig. 3. 17. Approach Velocity Distributions for Spill-Through Abutments of Constant Length and Varying Discharge. A-17 CROSS-SECTION B ABUTMENT VW; SEDIMENT A 1.0 ,--------------------------------------------------------- 0.8 I !:L 0.6 w 0 60::: 0.4 0 (f) 0.2 - - - - - - - - - - - T- - - - - - - - - - - I - - - - - - - - - - - I - - - - - - - - - - - I I I 1e X I ::::X - - - - - - - - - - - L - - - - - - - - - - - -- -l - - - - - - - - _:x__-- - 1 - - - - - - - - - - - I e e I X X i X X I. I X - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - I - - - - - - - - - - - X X x I I - - - - - - ~ - - - - - - - - - - - ~ - - - - - - - - 0 0 L ______ -'-----'----~-L-LLLLI --------"----'--__L__L_L_LL.LL___"---'--_J__J_-'---L_L_L[__ ____j__L__l___j__L_L_L__Lj 1 10 100 1000 10000 TIME, min. [ La=2.62 ft, 0=4.0 cfs x La=2.62 ft, 0=4.5 cfs La=2.62 ft, 0=5.0 cfs Fig. 3.18. Time Development of Scour Depth for Sediment A with Varying Discharge. A-18 CROSS-SECTION B ABUTMENT VW; SEDIMENT C 1.0 i 0.8 Ir - - - - - - - - - - - - - - - - - - ~----------- -~------------ I b= 0.6 w 0 6a::: 0.4 0 (f) I - - - - - - - - - - - ~----------- ~----------- - 1 - - - - - - - - - - - - ' XX X XX I X I : I I --= ________ _ - - - - - - - - - - - .'.. - - __ - - _X _X__ _I _______ -.- --. IIIII _ I X X I. -I . . :I; I 0.2 L ----X------ -- - - - - ~ - - - - - - - - - - - I - - - - - - 0. 0 I : L~-~_j_____j_______l___._..L.~..--.l--- __ .._ __l___L~~.L_L.l_..LJ._~_ _L_____J________j____j_j__J______L__l___L__~____J-'---.l..__L__L_j_JJ 1 10 100 1000 10000 TIME, min. I La=2.62 ft, 0=2.0 cfs x La=2.62 ft, 0=2.5 cfs La=2.62 ft, 0=3.0 cfs I Fig. 3. 19. Time Development of Scour Depth for Sediment C with Varying Discharge. A-19 CROSS-SECTION 8 ABUTMENT VW; SEDIMENT C 1.0 0.8 - - - - - - - - - ~ - - ---- - -i---- -- -- I. f----~~ I b= 0.6 w 0 60::: 0.4 0 (/') X I X -II1--------.-.----..--------- - - - - - - - - - - - 4- . - - - - - ;;:_-- X I. I XX I I 0.2 :I-- - - - - - - - - - - -.i - - - - - - - - - - - - I - - - - - - - - - - - - ,i- - - - - - - - - - - - IJt 0' 0 c____"-- - -'---'----"-~.__u_L_____~ -~~< ~ ~L-'-'-'-'-L 1 10 100 TIME, min. 1000 10000 La=2.62 ft, 0=2.0 cfs x La=5.24 ft, 0=2.0 cfs La=7.91 ft, 0=2.0 cfs / Fig. 3.20. Time Development of Scour Depth for Sediment C with Varying Abutment Length. A-20 CROSS-SECTION B ABUTMENT VW; SEDIMENT A ds ,ft 1.0 ~~~~-----------------------------------------------------------, I A 0.8 0.6 0.4 - - - - - - 1 - - - - - - - - - - - - - -. .- - - - - - -~------ -~------------- I A - - - - - - ~- - - I I e - -- - 1-- - - -I - - - - - - -1-- - - - - - -I- - - - - - -I - - - - - ... ...... ..I - - - - - - - - - !- - - - - - - I- - - - - - - I- - - - - I- - - - - - I- - - - - - - I - - - - - - i I ...... I I I I I : 0.2 ~ - - - - - - ~ - f L o.o ---'--~_L _____l_ I -- - t- -A- - - - - i- - - - - - - r- - - - - -- --~- -- - - - - -~ - - I I ! ____ _________[_ ____,______]__ -----'-----' I : j ___L__ _____cL___ _...L__ _ _ _ L _ _ __L__ _ _ _ 0 1 2 3 4 5 6 7 Q, cfs 1 La=2.62 ft La=5.24 ft La=7.86 ft 1 ------------------------~-.-....J Fig. 3.21. Equilibrium Scour Depths for Sediment A with Varying Discharge and Abutment Length. A-21 CROSS-SECTION B ABUTMENT VW; SEDIMENTS B & C 1.0 0.8 0.6 ~ - - - - - - ~------ 1 - - - - - - - ! - - - - - - - 1 - - - - - - - 1 - - - - - - - 1 - - - - - - I I G 12:; I _ _ _ _ _ _ i_ _ _ _ _ _ _e_ _[]_ _ _ _ _ I _ _ _ _ _ _ _ I _ _ _ _ _ _ _ I _ _ _ _ _ _ _ I _ _ _ _ _ _ ,G ------,-------I-- 0.4 I ' 8--- -I~------ -!~------ -~I - I -------,------ .L 0.2 ,_. - - - - - e - - - - - - - - - - - - - - - - - - - - - - - _,_------~-------I--- I 0.0 0 --~----'----------.L--~- 1 2 3 4 5 6 7 Q, cfs r I .0. La=2.62 ft; SED B G La=5.24 ft;SED B D La=-7.86 ft; SED B I ... La=2.62 ft; SED C La=5.24 ft; SED C I La=7.86 ft; SED C j Fig. 3.22. Equilibrium Scour Depths for Sediments B and C with Varying Discharge and Abutment Length. A-22 40. : <( I f- w N (/) >< 31. 30. []--!C...,.....,-i--'-;"-T--'~,.....r-:ri--.,.-,----r-r--r--i'-r-r"+-+-'-r-"i-T'>r-t"+"'-i-"'r"'-i~ 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Z- STA. (ft) 9.0 10.0 11.0 12.0 13.0 Fig. 3.23. Equilibrium Bed Elevation Contours for La/Bf= 0.44 (VW) and Q = 3.49 cfs. Elevation (ft) 1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 = Q 3.49 cfs X 32. 3 0. 0 -+-r...,....,.....,.-,-T-'!--,--,i-T--,-,-,.,--,-,-.,-'-rT-rT"1"'..,.,-" 0.0 11.0 12.0 Fig. 3.24. Equilibrium Bed Elevation Contours for La/Bf= 0.44 (VW) and Q = 4.00 cfs. Elevation (ft) 1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 Q =4.00 cfs 40.0 39.0 38.0 37.0 ~ ~ I <( f- 36.0 N (f) Vl X 35.0 34.0 33.0 32.0 31.0 Elevation (ft) 1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 = Q 3.51 cfs Fig. 3.25. Equilibrium Bed Elevation Contours for La/Bf= 0.66 (VW) and Q = 3.51 cfs. 42.0 39. ~ 36.0 ;J> <{ I f- N 0' x(/) 33. 32. 31. 30. Fig. 3.26. Equilibrium Bed Elevation Contours for La/Bf= 0.66 (ST) and Q = 3.50 cfs. Elevation (ft) 1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 Q = 3.50 cfs 10 ------N sc 1 0.01 : VW-SEDA i D ST-SEDA I I ~ LAURSEN (SP=.039) e VW-SED 8 .&. VW-SED C L UNIFORM-SED C - - - PAROLA -LAURSEN (SP=0.035) - KEULEGAN (SP=0.047) Fig. 3.27. Measured and Calculated Critical Velocities at Incipient Motion. A-27 '1 Bl A L APPROACH i ;or v, ,2 BRIDGE ~ ABUTMENT B._) PLAN ====> Q FLOODPLAIN '--------------- -- --~lc'__--- SEC. A-A tJY SEC. B-B Fig. 4. 1. Definition Sketch for Equilibrium Scour in a Long Contraction in a Compound Channel. A-28 10 .~------------------------------------------~,---- 9 [SYMBOL ~FILL 8 ~ None rf Solid 7 Dots d50, mm 3.3 2.7 1.2 I Best Fit 5 4 ______L 3 ~..;:;& Janjua, 1994 c:=~ l '-.........__ 2 ""/ cZ 1 :z 0 ~~~--~~~--~----~--~~--~~--~~--~~--~~ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 qf/ (M qfOc) SYMBOL SHAPE r XSECT. 8: i :z La/Bf = 0.22 6 0.44 XSECT. A: i c La/Bf=0.17 v 0.33 D 0.66 EB 0.50 Fig. 4.2. Equilibrium Abutment Scour Relationship Based on Approach and Tailwater Conditions. A-29 10 9 r L 8 k i8est Fit ~---~ ~- d/Ym 7 6 5 SYMBOL 4 FILL d50, mm None 3.3 3 Solid 2.7 2 Dots 1.2 1 0 0.0 0.5 1.0 1.5 2.0 (V IV)- 1 ab c SYMBOL SHAPE XSECT. B: I :z: La/Bf=0.22 L- La/Bf=0.44 o La/Bf=0.66 I XSECT. A: I c La/Bf=0.17 v La/Bf=0.33 EB La/Bf=0.50 I Fig. 4.3. Equilibrium Abutment Scour Relationship Based on Local Velocity Near Abutment Face_ A-30 1.0 -- - - - - - I - - - - I - -I - - - - Ii I I I I -- - - ~-- -, - - ~ ~--- ~- ~ ~- ~- 4 ~-- ~- ~-- 4 ~ ~I----~~-- - 1 - - - ~-- ~- ~- ~i - - - - - - - - - - - - - - - - - iii;-, - ~ ~ ~ ~ ~ ~- I ~ ~ ~ ~ I ~ ~ ~ -~ ~ ~ ~~ ~ I i I I I i ~ r ~ - r - -~ - - , , 1 1 -------- ---t--------'----- _,_ 6-- -1--- _,_- -I , ul 1 1 -- r--- -1- I I I ~ ~ ~ ~ ~ ~ ~ - ... - --- - - - - - - - - _I - - - - - -: I I I I ~I- -~- ~ -~ - -:- :- -:- ; I I . I I I I :~.- -~- ---: ---: --:~ -~: --I I -~-----_I_--- _ I - - - _ I _ - - L - - L - _I-- r - - r - - - - - - - - - - - - - - - ~-------- T - - - - - - , - - - - -~--- - , - - - -~-- I I I I 0.1 L _ _ __ 0.1 I I I I L---~--~-----L-~1 ~J 1.0 I ... XSECTION B 0/W) XSECTION B (ST) 6 XSECTION A 0/W) I Fig. 4.4. Estimate ofRatio of Approach Velocity to Abutment Velocity Based on Floodplain Flow Depth Near Abutment Face. A-31 1.0 - - - - - - ~- - - - - - - - - I_ - - - :_ - - J - - _l _ _ '_ _ - - - ~ - - - - - - - - ~ - - - - - - 1- - - - - 1- - - - ~ - - 4 - - 4 - - ~ - :- :- :- -~ - - - - I I I I I I -- - - -- - -- ,- - - ~ - ~ - V/V 1 ab -: :- ~ - - - --- - -- - ~ - - - - - --- - --- - - - - -- -- - I I I I I r - - - - - - - - - - - - - - -', - IBEST FIT)2= 0.77 ( - ~ .D._ I_ I I ~-~-I -I - I ~- - - I I - --III-III - - I - - : ~--- 1 "' . : L-------,---~--' 1--,~ I I ---------~--------~-- __ --~-L------~--~--L- I~ - - - - - -- - - I - - - - - -- ~- - - - - 1- - - - 'I - - -- -r i 0.1 i L_________ _ 0.1 _ _j _ __ _ I ______]__ - ________[__ _ ____j__ I I ______l_ ! j _ _ l _ _ _ L _ ____ 1.0 My ly to t1 .a. XSECTION B 0/W) XSECTION B (ST) Leo. XSECTION A 0/W) ] Fig. 4.5. Estimate ofRatio of Approach Velocity to Abutment Velocity Based on Tailwater Flow Depth. A-32 3.5 ~---,Sia.:---c3c:-2---------------------------, 3.5 3.0 ~ ~ i-2.5 - ] >" 2.0- Q = 2.02 cfs; lA = 0.5 ft -!-3.0 -;-2.5 .-~ " -2.0 Ui Transverse Distance, ft (a) :-Computed Velocity X Exp. Velocity (Sadiq 1994) - - WSE -BED 3.5 . . , - - - - S l a . : c - - : : - : 3 2 = - - - - - - - - - - - - - - - - - - - - - - 3.5 3.0- ~ ig- 2.5 -;- u> 2.0- Q = 3.83 cfs; lA- 0.5 ft I -;-3.0 0 2 3 4 6 7 Transverse Distance, ft (b) -Computed Velocity x Exp. Velocity (Sadiq 1994) 1-WSE -BED 3.5 - - - - - - - - - - - - - - - - - - - - - - - - 3 . 5 Sla. 32 Q = 2.02 cfs; lA ~ 1.5 ft 0 2 4 6 Transverse Distance, ft . - Computed Velocity X Exp. Velocity (Sadiq 1994) (c) -WSE -BED Fig. 4.6. Numerically Predicted Resultant Velocities at Upstream Face of Bridge by 2D Turbulence Model Applied to Cross-section A. A-33 3.5 3.0 -c::: 2.5 '-" >- 8 s c 2.0 0"' u ~ 1.5 ~"' 1.0 0.5 0.0 28 Velocity Vector Distribution Q = 2.89 cfs, 12 in. Abutment, Exp. 53 . _______ _.. __--t....., _,_...._...._...,..,. ---- --- --------_ -- . -.. ------------- ----.~..-_:....-$:::; .. t .. e _..._..:::; _,....,..,,..,/~ ~- -- --- -- __ -------- _,....,....,.......//~-- ,....,.......,....,,....,~- ,....,....,......,...............-::; -- ---- ----...... ////, ...... -- :::~ ...... /// // .~- -..--~-- :-::--:-:-- :-::---~ ----- -- -~~~- ---- ----- -- ;;~ :::::: -- --- ----- --- -- .;.... ~ ~ ~ ..- :~:::; ~ ~ ..~ :..:....:.. ~:~ ~ :::;::;~~!!.~~ ~:::: :.___.-/.-.;-,,.;-,;--I..-__...f,,~,,,, -- ---- .---. .- . . ~~~ ~~~~ ~ ~ :::::-;;:: ~8::::;ts::-:-;::::::::--:~o: ........ .:.:.:.:- .. ...... ":~.~.~~...~:.....-.:.~.:.:....:.-.:....:.:..:...::.i:-.:.-.::...:..-:...:..:::.:::.::::.:-::.::.:::..:...-:...:....:..:.~:::: ~ ~ ~ 29 30 31 32 33 34 35 36 37 38 Longitudinal Distance X (ft ) Fig. 4.7. Numerically Predicted Velocity Vectors by 2D Turbulence Model Applied to Cross-section A. A-34 10.00 - - - - - - - - - - - - , - - - - - - - - - - - - - - - - - - - , (V IV)- 1 ab c 1.00 r L__ 0.10 .L. 0.1 I I --~~~~~~ 1.0 [q I (M q )] - 0.4 f1 fOe 6 CROSS-SECTION A A. CROSS-SECTION B ~---------------~----------- ------~----- - - - - - - - - - - - ' Fig. 4.8. Estimate of Abutment Velocity Based on Relationship Between Alternative I and II Scour Prediction Procedures. 10.0 A-35 CROSS-SECTION A ABUTMENT VW; La/Bf=0.17; Q = 2.02 cfs 0.85 ----------------------------------------------------------~ 0.80 - - - - - - - ~------- ~------- ~------- _ : _ - - - - - - - I 0.75 I 0.70 I - - - - - - - ~------- ~------- ~------- - 1 - - - - - - - - I 11 I I ~ - --- - - - ~ :~- - -- -: -~- - -- - - - - - - -- -- 1-- 0w... 0 0.65 --------- I / I iI , I -III ~----- 1 ~~ ' _ _ _ _ _ __ _ _ I 1 _ _ _ _ _ _ _ _ I , 0.60 ~--=~~~.;;..<......;_......;;____.,...;;;;,.~---...J+.<.'.......~ / ~-~ -cQ-,~-~- ~ -c-x~_ --.....,c~ ;i---:.,:-: -~3.,><_..I~1 ..t.; _.~ij;'-- -~ 'J I 'J lJ T I I 0.55 l -------:-------:- ------~ -I- -----: ------ - i- - - - - - - -I 0. 50 LLL.L..L..L.L..L...L...L...L..L..L...L...L.~ .L.L_L_l_ ' -"---'...L..L....L..L...L..~..l_j_LL.L.L.L..L.L..L.L..L.L..L.L..L.L..L..L.L...L..L...L..L...L LL.L..L.J 0 10 20 30 40 50 60 X-STATION, ft ' - BIGLARI (NUMERICAL) c SADIQ (MEASURED) x WSPRO Fig. 4.9. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for La/Bf= 0.17 and Q = 2.0 cfs. A-36 CROSS-SECTION A ABUTMENT VW; La/Bf=0.33; Q= 2.01 cfs 0.85 r ' 0.80 - - - - - - - L - - - - - - - ~ - - - - - - - ~ - - - - - - - ~ - - - - - - - ~- - - - - - - 0.75 :.:: I 0.70 Ia.-.. w 0.65 0 0.60 0.55 II - - - - - - - ~ - - - - - - - + - - - - - - - 4 -rr - - - - - ~ - - - - - - - ~ - - - - - - - i I I I -----. -:-------' .------ i~f----. ~---- .. -J_------ i ' I : ! ' I I - - -- - - - - I - - - - - - - T - - - - - -X- .::L - - -- - - - I - - - - - - - -1 - - - - - - - CJ,__'--..J G IG I :or:: X 1A I - - - - - - - ~- - - - - - - l - - - - - - - J I I - - - - - J - - - - - - - _I - - - - - - - - I 0. 50 L_j_L__L_._c__~___j_L_.L..L_l_L_L_-'--'--'---L-L~L..L..l___L_L_L-L_L_i_U.'--.LJ____J_L_~___l___j__~_L_L__l___L_l___l_t__l___L_l___L_L~ 0 10 20 30 40 50 60 X-STATION, ft - BIGLARI (NUMERICAL) o SADIQ (MEASURED) X WSPRO Fig. 4.10. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for La/Bf-=0.33 and Q=2.0 cfs. A-37 0.85 CROSS-SECTION A ABUTMENT VW; LaBf=0.50; Q=2.02 cfs 0.80 ~ - - - - - - - ~ - - - - - - - ~ - - - - - - - ~ - - - - - - - ~ - - - - - - - -:- - - - - - - e - 0.75 -- - - - - - ~ - - - - - - - ~ - - - - - - - ~ -n - - - - - I ~ - - - - - - - -: - - - - - - - -i' ....... ' I I 0.70 - - - - - ~- - - - - - 1-- 0w... 0 0.65 ----- T-------; / I 0.60 ~-:------- -~ / I 0.55 - - --- -- ~ - ----- ~ -- -----~-If-----~--- ---- ~------- 0. 50 ___L_.L_L_j_.L_L__L_L_l_l___L_j_L_.L_L_~__L. I '! I I _L_j_L_L_j__L_.L_L_L_L_.LUJ_L_L_.L_.L_.L_.L_.L_.L_.L_.L_L_L_L_L_j__L_.L_.L__L_L_~--"-__J__j_____L . ;' 0 10 20 30 40 50 60 X-STATION, ft '~ - BIGLARI (NUMERICAL) o SADIQ (MEASURED) x WSPRO ----- I -.-J Fig. 4.11. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for La/Bf= 0.50 and Q = 2.0 cfs. A-38 CROSS-SECTION A: APPROACH ABUTMENT VW; La/Bf=0.17; Q = 2.02 cfs 3.5 6. 0 ~,-------;-----,-------,---~----;---------,-------,- 3.0 _ _ _ _ _ _ ! _ _ _ _ _ _ l _ _ _ _ _ _ I_ _ _ _ _ _ ~ _ _ _ _ _ _ 1 _ _ _ _ _ _ ;_ _ _ _ _ _ I I 5.0 ~ 2.5 ~ - - 1 - - - - - - ~-----_I_----- ~ 2.0 1- g 0 1.5 ----- -~------ I ~------ - - - - - - T - - - - - - ,- - - - - - 3.0 > w I >: { X ' 1....__ _X_..__X ___..A.1_~...,..,..~2.0 1.0 - - - - - -~------------- ~-------------I------------ 0. 0 c_____c__ ..L__~---___j___.L__....J.__~_J._______j_ 0 1 2 3 4 _ _ l __ 5 TRANSVERSE STATION ,ft _ _ _ L __ _ _ _ l __ 6 0. 0 _L____L 7 ! - BIGLARI SADIQ ~ WSE -BED X WSPRO I Fig. 4.12. Comparison of Computed and Measured Velocity Distributions in Cross-section A for La/Bf= 0.17 and Q = 2.0 cfs. A-39 CROSS-SECTION A: APPROACH ABUTMENT VW; La/Bf=0.33; Q=2.01 cfs 3.0 I I I I ------~------I------~-------~-------------~------ 5.0 z 2.5 -- _;_----- l-- __ I __ 0 4.0 ~ I ~ 2.0 - - - - - - 1 - - - - - - ~------ 1- ---1------ w _J 0 3.0 w 0 _J 1.5 > w 1.0 ---t--- -- - 1- - -- - - - I ~ I I - - 1 - - - - - - - 1 - - - - - - T - - - - - -~----X- 2.0 0 m w ~ w 0 5 1==:::;;:;::::;;:;::!;;;;;;;:;::;;:;::::;;:;:::::;;;;;;::;;:;::~:;-=-:::--::-=----::-;!xI::;;:;::::;;:;::;;;;;;:I:::::::;;:;::::;;:;::::::::!:::;;:;::::;;:;::~ 1.0 ~ . 1 0. 0 L_~-- _ 0. 0 ______j __L__ _ _ ____________j__ _ _ _l _ __ _ _c _ __ _ _____j_ _ ____l__ _ 0 1 2 3 4 5 6 7 TRANSVERSE STATION, ft r I - BIGLARI SADIQ - WSE -BED X WSPRO I _ _ _ _ _ _ _ _j Fig. 4.13. Comparison of Computed and Measured Velocity Distributions in Cross-section A for La/Bf=0.33 and Q=2.0 cfs. A-40 CROSS-SECTION A: APPROACH ABUTMENT VW; La/Bf=0.50; 0=2.02 cfs 3.5 6. 0 ,---------------,---~------,--------,------,---~-----, - x - - - -.- - - e- - Te- - - - - - - -.- - -e - - ~- - -.- x - w en 0.5 ~==:::::r::====::::::::====:r;-------=---~::.::::==:::::c====::r:::==~ 1.0 s I 0.0 I ------+----~----+----+-------+----:1-----, 0 1 2 3 4 5 TRANSVERSE STATION, ft - Biglari SADIQ - WSE__-_-:__B_E_D___x_W_SPRO] 1 Fig. 4.14. Comparison of Computed and Measured Velocity Distributions in Cross-section A for La/Bf= 0_50 and Q = 2.0 cfs A-41 CROSS-SECTION 8 ABUTMENT VW; La/Bf=0.22; Q=3.0 cfs 0.85 0.80 _______ L _______ ~ _______ ~ ________I ________ I_______ _ _______ _______ _______ -n _____ 0.75 ~ ~ ~ -1- ______ -I- ______ _ I i I I I I r ; :T .---, ~ I 0.70 r------- ~--- ---- i------- ~ -~~----- ,------- -!-------- 1o._- w 0.65 0 : --li --li-' ~-- : : I' : Tx ~.-;; -.- rr~. ~. : I ~- r 1- l--- 0.60 ~ ~ ~ ~ ~ ~- ~-- ~ ~-- ~ ~ ~-- ~ ~ ~- ~- -~---- ~-- ~~-----~~~I l 0.55 I r - ----- ----: ~ - ---- -~J- --- -i- - - ! --- - 0. 50 l__LJ~_L_L__LJ_L_LJ_~__j__L...LJ_L...L...C....L.L_...L...L._L...L...L...L_L~L_L_J_...LJ_.L..C..-'___L__L...L...L._L_L_J__J_J__L_L__'--l_L_L..j_..L..l.....L.J 0 1 0 20 30 40 50 60 X-STATION, ft MEASURED DEPTH - NORMAL DEPTH X WSPRO Fig. 4.15. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for La!Bf= 0.22 and Q = 3.0 cfs. A-42 CROSS-SECTION 8 ABUTMENT VW; La/Bf=0.44; Q=3.0 cfs 0.85 ~--------------~---------~ r------- ------- ------- rr o.8o I I ~ ~ I I I _jl- - - - - - - -:- - - - - - - -:- - - - - - - - t- I I o. 75 fIf --- - -- - I ~ - --- --- ~ ---- --- i ~ -n------:I --------:I- ------ - ~ t , ! I1 I i ~ II , , . I 0.70 ~------- + - - - - - - - - - t - - - - - - - 4 -~ - - - - - -~------- - 1 - - - - - - - - I r I , . I I, I , t:L 0.65 - - - - - w If < /: .: ! I -.-- - - . - - i - - - - - - - "l - 0 1 ' 1 I X 1 ~X: 0.60 t --- "" l ---:i -------:Ii --------:1i -----:- -~-~l---e..I -- - ----:II- ------ -I1 I -' --------: -:--- ----:------ - 0 . 5 : 5 [-. - -c~----: :------- I I -~I:----- I I : _i 050 i ' -->--L-L.L_L_U_L I i I I I 0 1 0 20 30 40 50 60 X- STATION, ft I MEASURED DEPTH - NORMAL DEPTH X WSPRO Fig. 4.16. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for La/Bf=0.44 and Q=3.0 cfs. A-43 CROSS-SECTION B ABUTMENT VW; La/Bf=0.66; Q=3.0 cfs 0.85 0.80 I I ~ ~ ~ ~ ~ ~ ~ L ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~ ~ ~ ~ ~ ~ ~ ~~~ ~ ~ ~ ~ ~ ~ ~ I MEASURED DEPTH - NORMAL DEPTH x WSPRO Fig. 4.17. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for La/Bf= 0.66 and Q = 3.0 cfs. A-44 CROSS-SECTION 8: APPROACH ABUTMENT VW; La/Bf=0.22; Q=3.0 cfs 2.0 1.6 X ~ : I , I I I - -- - - - :,..._ - - - - - - r- - - - - - - !-- - - - - - - i- - - - - - - 1- - - - - - - 1- - ->~- ~- I U) ~ >-- 1-- 0 0uj 1.2 0.8 L- - - - - - L - - I ~ I -~ . , - _ - - - ' ; - -I~- -- - -- ,""' -- - -L - ' - :- - - -v " -- - - :_ - ~: - : - I~- - - -/ -- - .- I_ x I I - 1- - - -- x ' -- - .- I_ ::>< - II~- - - - - - .I.I ~ - I_ - - - xl - II~- - - - - -- X- > 0.4 ~- - -~ - - - - r -- - - - - - ~ - - - - - - - ~- - - - - - 1- - - - - - - !- - - r 0' 0 l___L__~_..L_......J__~"--L---~~_ _L_.____~_l____L__o _t____L___L_~~ _L_.....L.___L.__j____L---'~ 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 TRANSVERSE STATION, ft ' MEASURED VELOCITY x WSPRO Fig. 4.18. Comparison of Computed and Measured Velocity Distributions in Cross-section B for La/Bf= 0.22 and Q = 3.0 cfs. A-45 CROSS-SECTION 8: APPROACH ABUTMENT VW; La/Bf=0.44; 0=3.0 cfs 2.0 ~--------------------------- l I I 1.6 [- - e ! ~ ~ ~ ~ ~ II~ ~ ~ - - ~ ~ t,~ ~ ~ ~ ~ ~ ~ II~ - I ~ ~ ~ ~ ~ ,- ~ ~ ~ ~ ~ ~!! ~ ~ ~ ~ ~ ~ ~II ~ ~ ~ ~ ~ ~ 1.2 1- 0 0 _j > w I I ' I i I --- i------- 1----- ---I------ -1- I X r 0. 4 rI I ~ ~ ~ ~ ~ ~r I I I I I ~ ~ ~ ~ ~ ~ !~ ~ .. ~ ~ ~ ~ I~ ~ ~ ~ ~ ~ ~ I~ ~ ~ ~ ~ ~ ~I~ ~ ~ ~ ~ ~ ~I~ ~ ~ ~ ~ ~ r o. o L--'---'---'-"-----'-----'---.L..--L___L____L___j__J______L___j___L__L____L___L____j_..L..__C--.L.___j__-'----~ 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 TRANSVERSE STATION, ft ' MEASURED VELOCITY x WSPRO l Fig. 4. 19. Comparison of Computed and Measured Velocity Distributions in Cross-section B for La/Bf=0.44 and Q=3.0 cfs. A-46 CROSS-SECTION 8: APPROACH ABUTMENT VW; La/Bf=0.66; Q=3.0 cfs 2.0 ~----~------~------~------~----~------~------- 1.6 - - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - - ~ >-- 1.2 1- 0 0u:l 0.8 > I I I I i I l l I ~ _ _ _ _ _ _ I_ _ _ _ _ ~- _ I_ _ _ _ _ _ _ I_ _ _ _ _ _ _ I_ _ _ _ _ _ _ ~~- _ _ _ _ _ _ I__ _e_ _ ._ _ I 1 X I X e I I I I I ~ I :-:x:- -I I i I I >- - - - - -;:: - :- x- - ~c - ;Y:- - ; :- - ;-;::_- - 7- I ! -7 - -~ - -x - -x :-:;,: - - - - I : ~ I I : 0.4 Ir ~------ ~~------ 1 - - - ~ I 1 X i' - I -~--- ~------- ! - - - - - - - - r - - - - - - - t - - - - - - I I I I I 0.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 TRANSVERSE STATION, ft MEASURED VELOCITY x WSPRO Fig. 4.20. Comparison of Computed and Measured Velocity Distributions in Cross-section B for La/Bf= 0.66 and Q = 3.0 cfs. A-47 2.0 1.5 en ~ 'I- >...-- 0 w f- 1.0 :5 :::> 0 _J <( 0 0.5 I I ID L I I -~~~. ~DL ~ .A. /'-' , - - - - - - - -c~ll/_ - - - - - - - - .._ - 41 I I I ~~~ ... : I ~ 'D- - - - - - - -.761/ - - - - - - - - --I - - - - - - - - - I T - - - - - - - - - / ' IL 1 w:PRO: xs-A; vw 120: XS-A; VW I D I WSPRO: XS-8; vw I I WSPRO: XS-8; ST 0.0 t 1/ ___ l'~. _____j _ _L___..l......__!__-.---.L...,.~ 0.0 0.5 1.0 MEASURED V1, ft/s 1.5 2.0 Fig. 4.21. Comparison of Computed and Measured Approach Velocities for Cross-sections A and B. A-48 0.40: 0.30 D - - - - - - - - - 1 - - - - - - - - - ~- - - - - - - - - r-::-~------- 1 ~ .>..--- 0w~ 0.20 '~ ---. I WSPRO: XS-A; vw D /. I I ,. 12: : ~- ~~- W~PRO: :- - - - - --- - , o& J21 - . - - - - !. - . - - - - - - - I I I XS-A;VW XS-8; vw ::J 0 _.J <( 0 0.10 .,Q : s:l ~v/ I I I I 1 Q~ : : II - - - - - - - - - ~~- - - - - - - - - ~ - - - - - - - - T - - - - - - - - - WSPRO: XS-8; ST , , ' I 0.00 I l'--.. _ _ _ _L. _ __ _ j _ __~-----_L_~- 0.00 0.10 0.20 MEASURED yf1, ft I .J_____j ___L_._ _ 0.30 0.40 Fig. 4.22. Comparison of Computed and Measured Approach Floodplain Depths for Cross-sections A and B. A-49 1.0 0.8 ~ 6J 0.6 ~ ::::> 0 ~ 0.4 0 ' ~:~ ; . '\L / : ; ~ :y. .. - - - - -. - - - - - - _, ; - - - - - - .J : - - - - :. ~I ./tt:J.I I _" - - -- - '// ; ./....If._ I - - - -~-- I - - ~ I /- ,. ---- - I T - - - - - - - ./ 21 ?D1e 1 I I I [] I I - - - - l - - - - - - - T- - - - - - - D lu WSPRO: XS-A; VW A 20: XS-A; VW D WSPRO: XS-B; VW WSPRO: XS-B; ST 0.2 L-- i ~ I - - - - - I - - - - - - - -I - - - - - - - I I 0. 0 "'~-~ ~.~._J_.L_ __ -'----L_ 0.0 0.2 0.4 0.6 0.8 1.0 MEASURED M Fig. 4.23. Comparison of Computed and Measured Discharge Distribution Factors for Cross-sections A and B. A-50 CROSS-SECTION B SEDIMENT A: All Abutment Lengths 10.0 -------------------------------------------------------- 9.0 dst I Ym I 8.0 ' 7 . o L i r 6.0 ~ 5.0 ~ 4.0 3.0 . .... ... ... ~~+ ~ 2.0 1.0 ~ o. o L_____~ --~--'-~~-~ -~-Ll. ~ - -----1".. ___j____l___j...........J_L____l__Lj_ _ _____________..___ __j __;__L_.l__L_L_ i I ---'------'---'---'--~ 1.0E+03 1.0E+04 1.0E+06 1.0E+07 Vr=1.23 z Vr=1.26 Vr=1.29 6 Vr=1.51 + Vr=1.58 Y Vr=1.86l 1 Fig. 4.24. Time Development of Scour Depth for Cross-section B and Sediment A in Dimensionless Form. A-51 CROSS-SECTION 8 SEDIMENT 8: All Abutment Lengths 10.0 ------------------------------------------------ 9.0. d I y 8.0 ~ st fO 7.0 : 6.0 ~. 5.0 c- .... .... .... .... 4.0 : 3.0 ~ 2.0 . 1.0 ' ,.,. ...... .A. X ,X/- X -.. yx 0. 0 i L_________j_______j- __.L__.i_____._l____._L___L_j____l____ _ _ _ _ l___ _____L__ _____L________L_j___L___l___]~_ _____L__ __J___l_______l___.L_l--L.L....__ 1.0E+03 1.0E+04 1.0E+05 1.0E+06 ~ t/ yfO 1.0E+07 Vr=1.24 x Vr =1.32 Vr=1.35 .& Vr=1.61 j Fig. 4.25. Time Development of Scour Depth for Cross-section B and Sediment B in Dimensionless Form. A-52 CROSS-SECTION 8 SEDIMENT C: All Abutment Lengths 10.0 --------------------------------------~~~-~YY~.-.__V_r_=_V_a_b/_V_c__ d Iy st fO 9.0 r- a.o r 1 t I 7.0 r I 6.0 r 5.0 l4.0 f 3.0 + ,:::,. + + ~ 2.0 i 1.0 ~ o.o L-----'---'----'--'--'--'-Ll__--'-_____L_"--'---'.--'-LLJ_---'---'----L___l_L_L..L.L.L_-'------''---'-"--'--'-LLJ 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 Vet/ yfO .., - I I I Vr=1.52 z Vr=1.59 Vr=1.79 !'c. Vr=1.90 I I + Vr=2.02 Vr=2.23 X Vr=2.45 [81 Vr=2.55 I --------------~---- Fig. 4.26. Time Development of Scour Depth for Cross-section B and Sediment C in Dimensionless Form. A-53 10.0 ------------------------------------==~--------~ SYMBOL L,' --~~- 2.50 d Iy st fO 9.0 ' FILL d50 mm " - - - - - - -- - - -1I 3-.~- ~ ~ 8.0 r-N-on_e___ r- - - - - - - - --- + - -- - -- - - - - - ___________ t Solid 2.7 7.0 r Dots 1.2 f j ' 6.0 ~ - - - - - - - - - - r - - - - - ~ 1.0E+04 1.0E+06 1.0E+07 SYMBOL SHAPE ; Li Vr=1.25 c Vr=1.50 D Vr=2.0 z Vr=2.5 - BEST FIT I Fig. 4.27. Consolidation ofDimensionless Time Development Data and Least-Squares Fits for Sediments A, B, andC . A-54 BURDELL CREEK D.A. = 375 SQ. MI. 25 --------------------------------------------------~ I I f EXIT SECTION ! 20 I i I I I I---------,---------'------- I I I I ! -- T--------- I---------; I ' ' f-- r\1 1 ' I ' ' I I I ~I 2 -.--A u_ ~ , i : I i ~15 ""\, ---- :-~~0~;2- ~1-n-~~-~~~~-~~-0-;3~-: ~ 10 l . --~~-~~~-------- b~- -! w I I I~ .,. I ' ---------;- -------- f I I \ ;: 1 ! 5 r---------~- -- --- ---~- --~.-I- ~ I w 0 ~-~---~L- ________l__________ _ J _ _ __ _j _ _ _~ 0 500 1000 1500 TRANSVERSE STATION, FT 2000 2500 Fig. 4.28. Burdell Creek Cross-section for Estimation of Clear-water Abutment Scour. A-55 BURDELL CREEK D.A. =375 SQ. MI.; 0100; TL =15 HRS 20000 ~I----------------~----------~----~----~--~ 18000 ' - - - - - I - - - - - - - - - - - ' - - - - - ' - - - - - I - - - - - -~ - - - - - - - - - - - - 16000 ~ ~ ~ -1 r - - - - - - - - - - T - - - - - T - - - - - , - - - - - - - - - - - - - - - -1- - - - - I I I I I I I 14000 I I I i - - - - - t- - - - - - + - - - __.._ - - - - - -+ - - - - - -j - - - - - -j - - - - - -I - - - - - - I I . I I I I I I ! 12000 _ _ _ _ _ L ___ - - L ) - ' - - - ~- - - - J - - - - - ~-----~------I------~ .\~~: ~ (/) LL 0 10000 a : : ..:. f. :::/.:. :. ;: . : : . : . : . : :: ... : :: ... : : 8000 I J I I I I I I I 6000 I I I I - - - - - I - - - - I - - - - - T- I I I I - - I - - - - . ; I - - - - - -1 - - - - - -r - - - : 4000 --- - - ,_I ' I ~ - - - I , ~ - -- - - I I ~- - - - - I ~ - -- ' -:- I I I. I I - - -----~~- - - - - -- - - 2000 ~-~- ~ ~ ~- i - - - - - - - - - - - - T - - - - -- -f - - - - - ----- -- - 0 0 5 10 15 20 25 30 35 40 TIME, HRS Fig. 4.29. Design Hydrograph for Burdell Creek. A-56 APPENDIX B. WSPRO DATA AND RESULTS Table B.l - WSPRO Input Data File for Burdell Creek - QlOO. *F SI 0 T1 ABUTMENT SCOUR EXAMPLE * Q 14000 SK 0.001 * XS EXIT 750 0.0 0.5 0.0 0.001 GR 0, 19 100, 15 200, 11 500, 10.75 900, 10 1100, 9.0 GR 1215, 5.5 1250, 4.9 1300, 3.05 1350, 4.85 1385, 5.1 GR 1500, 9.0 1700, 10 2100, 10.75 2400, 11 2500, 15 GR 2600, 19 N 0.042 0.032 0.042 SA 1100 1500 * XS FULV 1500 0.0 0.5 0.0 * BR BRDG 1500 * 0.0 0.5 0.0 * BL 0 750 1100 1500 BC 18 CD 3 50 2 22 0.0 0.0 0.0 AB 2 2 PD 0 5.65 30 6 N 0.042 0.032 0.042 SA 1100 1500 * xs APPR 2300 0.0 0.5 0.0 * HP 2 APPR 13.25 0 13.25 14000 HP 2 APPR 13.64 0 13.64 14000 * DA BRDG 1 1 * * 14000 1 * EX 0 ER B-1 Table B.2 - WSPRO Water Surface Profile Output for Burdell Creek - QlOO ************************* W S P R 0 *************************** Federal Highway Administration U. S. Geological Survey Model for Water-Surface Profile Computations. Input Units: English I Output Units: English *---------------------------------------------------------------* ABUTMENT SCOUR EXAMPLE WSEL VHD EGEL HF CRWS HO Q v FR # AREA K SF SRDL LEW FLEN REW ALPHA ERR Section: EXIT Header Type: XS SRD: 750.000 Section: FULV Header Type: FV S RD : 1 5 0 0 . 0 0 0 11.696 .268 11. 964 ****** 9.447 ****** 14000.000 2.965 .504 4721.088 ********* 442473.00 ********* ****** 1. 960 182.604 2417.396 ****** 12.449 12.716 10.197 . 267 14000.000 4728.060 .750 2.961 443183.70 .000 .502 .0010 750.000 182.526 750.000 2417.474 1. 959 .003 <<< The Preceding Data Reflect The "Unconstricted" Profile >>> Section: APPR Header Type: AS SRD: 2300.000 13.250 13.517 10.997 .267 14000.000 4730.357 .798 2.960 443418.00 .000 .502 .0010 800.000 182.500 800.000 2417.500 1. 959 .003 <<< The Preceding Data Reflect The "Unconstricted" Profile >>> <<< The Following Data Reflect The "Constricted" Profile >>> <<< Beginning Bridge/Culvert Hydraulic Computations >>> Section: BRDG Header Type: BR SRD: 1500.000 WSEL VHD Q AREA SRDL LEW EGEL HF v K FLEN REW CRWS HO FR # SF ALPHA ERR --------- ------ ---------- ---------- --------- --------- 12.470 .470 14000.000 3038.370 750.000 936.685 12.940 .921 4.608 386306.30 750.000 1663.315 10.668 .055 .474 ****** 1. 424 -.004 Specific Bridge Information c Bridge Type 3 Flow Type 1 ------ Pier/Pile Code 0 .8380 --------------------------- ------ P/A PFELEV BLEN XLAB XRAB -------- -------- -------- -------- .067 18.000 750.000 940.750 1659.250 -------- -------- -------- -------- Section: APPR Header Type: AS SRD: 2300.000 WSEL VHD Q AREA SRDL LEW EGEL HF v K FLEN REW CRWS HO FR # SF ALPHA ERR --------- ------ ---------- ---------- --------- --------- 13. 635 .186 14000.000 5595.480 750.000 172.865 13.822 .780 2.502 536819.40 776.571 2427.135 10.997 .100 .387 .0010 1. 914 -. 017 Approach Section APPR Flow Contraction Information M( G ) M( K ) KQ XLKQ XRKQ OTEL .675 .189 438924.8 938.577 1661.368 13.635 B-2 Table B.3 - Velocity Distribution from HP Record for Unconstricted Flow at Approach Section - QlOO. ************************* W S P R 0 *************************** Federal Highway Administration U. S. Geological Survey Model for Water-Surface Profile Computations. Input Units: English I Output Units: English *---------------------------------------------------------------* ABUTMENT SCOUR EXAMPLE *** Beginning Velocity Distribution For Header Record APPR *** SRD Location: 2300.000 Header Record Number 4 Water Surface Elevation: 13.250 Element # 1 Flow: 14000.000 Velocity: 2.96 Hydraulic Depth: 2.116 Cross-Section Area: 4730.38 Conveyance: 443419.90 Bank Stations -> Left: 182.500 Right: 2417.500 X STA. A( I V( I D( I 182.5 803.7 628.6 1.11 1. 01 1045.3 454.8 1. 54 1. 88 1141.7 279.4 2.51 2.90 1181. 9 184.1 3.80 4.58 1209.7 156.0 4.49 5.62 X STA. A( I V( I D( I 1209.7 1232.9 146.1 4.79 6.30 1253.5 138.2 5.07 6.69 1271.9 133.4 5.25 7.27 1288.1 128.5 5.45 7.91 1302.5 121.2 5.77 8.46 X STA. A( I V( I D( I 1302.5 1317.4 124.2 5.64 8.29 1333.9 127.1 5.51 7.73 1352.7 133.8 5.23 7.10 1373.2 138.2 5.07 6.76 1394.8 141.8 4.94 6.55 X STA. A( I V( I D( I 1394.8 1421.9 157.2 4.45 5.81 1458.5 172.9 4.05 4.73 1558.5 290.7 2.41 2.91 1799.0 449.8 1. 56 1. 87 2417.5 624.5 1.12 1. 01 B-3 Table B.4 -Velocity Distribution from HP Record for Constricted Flow at Approach Section - QlOO. ************************* W S P R 0 *************************** Federal Highway Administration U. S. Geological Survey Model for Water-Surface Profile Computations. Input Units: English I Output Units: English *---------------------------------------------------------------* ABUTMENT SCOUR EXAMPLE *** Beginning Velocity Distribution For Header Record APPR *** SRD Location: 2300.000 Header Record Number 4 Water Surface Elevation: 13.640 Element # 1 Flow: 14000.000 Velocity: 2.50 Hydraulic Depth: 2.487 Cross-Section Area: 5605.83 Conveyance: 537996.80 Bank Stations -> Left: 172.750 Right: 2427.250 X STA. A( I V( I D( I 172.7 684.7 658.8 1. 06 1. 29 945.3 506.4 1. 38 1. 94 1101. 6 423.1 1. 65 2.71 1161.2 241.3 2.90 4.05 1195. 4 187.3 3.74 5.47 X STA. A( I V( I D( I 1195. 4 1223.0 176.6 3.96 6.40 1246.6 163.5 4.28 6.93 1268.0 159.7 4.38 7.47 1286.0 147.8 4.74 8.19 1302.5 144.8 4.83 8.81 X STA. A( I V( I D( I 1302.5 1319.1 143.9 4.87 8.65 1338.0 151.0 4.64 8.01 1359.2 156.4 4.48 7.35 1382.3 163.7 4.28 7.09 1407.8 169.5 4.13 6.64 X STA. A( I V( I D( I 1407.8 1441.5 190.1 3.68 5.64 1497.0 229.2 3.05 4.13 1658.1 435.6 1. 61 2.70 1917.6 502.4 1. 39 1. 94 2427.3 655.0 1. 07 1. 29 B-~