GLOSSARY - 4_0104910041
GLOSSARY (cont.) - 4_0104910042
GLOSSARY (cont.) - 4_0104910043
GLOSSARY (cont.) - 4_0104910044
GLOSSARY (cont.) - 4_0104910045
GLOSSARY (cont.) - 4_0104910046
GLOSSARY (cont.) - 4_0104910047
GLOSSARY (cont.) - 4_0104910048
GLOSSARY (cont.) - 4_0104910049
GLOSSARY (cont.) - 4_0104910050
GLOSSARY (cont.) - 4_0104910051
GLOSSARY (cont.) - 4_0104910052
GLOSSARY (cont.) - 4_0104910053
GLOSSARY (cont.) - 4_0104910054
GLOSSARY (cont.) - 4_0104910055
GLOSSARY (cont.) - 4_0104910056
GLOSSARY (cont.) - 4_0104910057
GLOSSARY (cont.) - 4_0104910058
GLOSSARY (cont.) - 4_0104910059
GLOSSARY (cont.) - 4_0104910060
GLOSSARY (cont.) - 4_0104910061
CLASSIFICATION OF RIVER CROSSINGS AND ENCROACHMENTS
DYNAMICS OF NATURAL RIVERS AND THEIR TRIBUTARIES
Figure 1.1. Geometric properties of bridge crossings
Figure 1.2. Comparison of the 1884 and 1968 Mississippi River Channel near Commerce, Missouri.
Historical Evidence of the Natural Instability of Fluvial Systems
Historical Evidence of the Natural Instability of Fluvial Systems (cont.)
Introduction to River Hydraulics and River Response
Figure 1.3. Sinuosity vs. slope with constant discharge
EFFECTS OF HIGHWAY CONSTRUCTION ON RIVER SYSTEMS
Delayed Response of Rivers to Encroachment
EFFECTS OF RIVER DEVELOPMENT ON HIGHWAY ENCROACHMENTS
EFFECTS OF RIVER DEVELOPMENT ON HIGHWAY ENCROACHMENTS (cont.)
TECHNICAL ASPECTS
Variables Affecting River Behavior
FUTURE TECHNICAL TRENDS
Research Needs
OVERVIEW OF MANUAL CONTENTS
Chapter 3 - Fundamentals of Alluvial Channel Flow
Chapter 5 - River Morphology and River Response
Chapter 8 Data Need and Data Sources
Table 1.1. Commonly Used Engineering Terms in SI and English Units
OPEN CHANNEL FLOW
Definitions - 4_0104910086
THREE BASIC EQUATIONS
Figure 2.1. A river reach as a control volume
Conservation of Mass
Figure 2.2. The control volume for conservation of linear momentum
Conservation of Linear Momentum
Figure 2.3. The streamtube as a control volume
Conservation of Energy
Conservation of Energy (cont.) - 4_0104910094
Conservation of Energy (cont.) - 4_0104910095
HYDROSTATICS
Figure 2.4. Pressure distribution in steady uniform and in steady nonuniform flow
Figure 2.6. Steady uniform flow in a unit width channel
STEADY UNIFORM FLOW
Figure 2.7. Hydraulically smooth boundary
Figure 2.8. Hydraulically rough boundary
Shear Stress, Velocity Distribution, and Average Velocity
Shear Stress, Velocity Distribution, and Average Velocity (cont.)
Figure 2.10. Einstein's multiplication factor X in the logarithmic velocity equations
Other Velocity Equations
Table 2.1. Manning's Roughness Coefficients for Various Boundaries
Table 2.1. Manning's Roughness Coefficients for Various Boundaries (cont.)
Average Boundary Shear Stress
Table 2.2. Adjustment Factors for the Determination of n Values
Figure 2.11. Control volume for steady uniform flow
Relation Between Shear Stress and Velocity
Energy and Momentum Coefficients for Rivers
Energy and Momentum Coefficients for Rivers (cont.) - 4_0104910113
Figure 2.12. Energy and momentum coefficients for a unit width of river
Energy and Momentum Coefficients for Rivers (cont.) - 4_0104910115
Figure 2.14. Definition sketch for small amplitude waves
Gravity Waves
Figure 2.15. Sketch of positive and negative surges
Hydraulic Jump
Figure 2.16. Hydraulic jump characteristics as a function of the upstream Froude number
Figure 2.18. Roll waves or slug flow
Figure 2.19. Transitions in open channel flow
Figure 2.20. Specific energy diagram
Specific Discharge Diagram
Figure 2.21. Changes in water surface resulting from an increase in bed elevation
Figure 2.23. Change in water surface elevation resulting from a change in width
Transitions With Super Critical Flows
Figure 2.24. Flow characteristics over a drop structure (Chow 1959)
Figure 2.25. Nappe profiles for supercritical flow (Ippen 1950)
Transverse Velocity Distribution in Bends
Figure 2.26. Schematic representation of transverse currents in a channel bed
Subcritical Flow in Bends
Supercritical Flow in Bends
GRADUALLY VARIED FLOW
Classification of Flow Profiles
Figure 2.28. Classification of water surface profiles
Table 2.3. Characteristics of Water Surface Profiles
Figure 2.29. Examples of water surface profiles
Figure 2.30. Definition sketch for the standard step method for computation of backwater curves
STREAM GAGING
Figure 2.31. Gaging station well and shelters (from Buchanan and Somers 1968a)
Figure 2.32. Typical float recording gaging station (from Buchanan and Somers 1968a)
Figure 2.34. Stage vs. time hydrograph (Kennedy 1983)
Figure 2.35. Definition sketch of computing area and discharge at a gaging station
Figure 2.36. Stage-discharge relation for Schoharie Creek, New York (Butch 2000)
Figure 2.37. Stage-discharge relation for a sand channel
Backwater Effects on Waterway Openings
Figure 2.38. Three types of backwater effect associated with bridge crossings
Figure 2.39. Submergence of a superstructure
Figure 2.40. Types of flow encountered (HDS 1, Bradley 1978)
HYDRAULICS OF CULVERT FLOW
ROADWAY OVERTOPPING
Figure 2.41. Discharge coefficient for roadway overtopping
Table 2.4. Discharge measurement notes
Table 2.5. Observed Velocity Data
Table 2.6. Velocity Profile Calculations
Shear Stress Analysis - 4_0104910157
Table 2.7. Detailed Computation of Superelevation in Bends
PROBLEM 4 Maximum Stream Constriction Without Causing Backwater (Neglecting Energy Losses) - 4_0104910159
PROBLEM 5 Maximum Water Surface Elevation Upstream of a Grade Control Structure Without Backwater (Neglecting Energy Losses)
Figure 2.43. Sketch of backwater curve over check dam
How much backwater will the dam cause for a flow of 28.37 m3/s if the normal depth for this discharge is 1.52 m and the dam height is 1.22 m?
SOLVED PROBLEMS OPEN CHANNEL FLOW (ENGLISH)
Table 2.8. Discharge measurement notes
Table 2.9. Observed Velocity Data
Table 2.10. Velocity Profile Calculations
Shear Stress Analysis - 4_0104910167
Table 2.11. Detailed Computation of Superelevation in Bends
PROBLEM 4 Maximum Stream Constriction Without Causing Backwater (Neglecting Energy Losses) - 4_0104910169
PROBLEM 5 Maximum Elevation of a Grade Control Structure Without Backwater (Neglecting Energy Losses)
Figure 2.44. Sketch of backwater curve over check dam
How much backwater will the dam cause for a flow of 1000 cfs if the normal depth for this discharge is 5 ft and the dam height is 4.0 ft?
How much backwater will the dam cause for a flow of 1000 cfs if the normal depth for this discharge is 5 ft and the dam height is 4.0 ft? (cont.)
FUNDAMENTALS OF ALLUVIAL CHANNEL FLOW
Particle Shape
Table 3.1. Sediment Grade Scale (Brown 1950)
Fall Velocity - 4_0104910178
Figure 3.1. Drag coefficient CD vs particle Reynolds number Rep for spheres and natural sediments with shape factors Sp equal to 0.3, 0.5, 0.7, and 0.9.
Figure 3.2. Nominal diameter vs. fall velocity (Temperature = 24C)
Sediment Size Distribution
Square-Surface Sample
Figure 3.3. Definition sketches for size-frequency characteristics of sediments
Sediment Size Distribution (cont.)
Specific Weight
FLOW IN SANDBED CHANNELS
Figure 3.4. Angle of repose of non-cohesive materials
Figure 3.5. Forms of bed roughness in sand channels
Figure 3.6. Relation between water surface and bed configuration
Figure 3.7. Change in velocity with stream power for a sand with D50 = 0.19 mm
Plane Bed Without Sediment Movement
Plane Bed With Movemen
Regime of Flow, Bed Configuration, and Froude Number
Figure 3.8. Relation between regime of flow and depth for bed material with a median size equal to or less than 0.35 mm
RESISTANCE TO FLOW IN ALLUVIAL CHANNELS
Figure 3.10. Relation of depth to discharge for Elkhorn River near Waterloo, Nebraska
Figure 3.11. Apparent kinematic viscosity of water-bentonite dispersions
Figure 3.12. Variation of fall velocity of several sand mixtures with percent bentonite and temperature
Size Gradation
Shape Factor for the Reach and Cross-Section
Figure 3.13. Relation between stream power, median fall diameter, and bed configuration and Manning's n values
Figure 3.14. Change in Manning's n with discharge for Padma River in Bangladesh
Alluvial Processes and Resistance to Flow in Coarse Material Streams
Resistance to Flow
Table 3.3. Typical Sediment Size Distribution for Gravel-Bed Stream
BEGINNING OF MOTION
Theory of Beginning of Motion
Theory of Beginning of Motion (cont.) - 4_0104910208
Theory of Beginning of Motion (cont.) - 4_0104910209
Figure 3.15. Shields Diagram: dimensionless critical shear stress
Figure 3.16. Shields' relation for beginning of motion (after Gessler 1971)
Shields Diagram
Figure 3.17. Comparison of critical shear stress as a function of grain diamete
Equations for Flow and Sediment Variables for Beginning of Motion
Critical Velocity for the Beginning of Bed Material Movement
Critical Size for the Beginning of Bed Material Movement
Table 3.4. Maximum Permissible Velocities Proposed by Fortier and Scobey (1926)
Table 3.5. Nonscour Velocities for Soils (Modified from a report by Keown et al. 1977)
Figure 3.19. Critical velocity as a function of stone size
SEDIMENT DISCHARGE MEASUREMENT
Suspended Sediment Discharge Measurement
Figure 3.21. Schematic sediment and velocity profiles
Figure 3.22b. Suspended sediment sampler-DH48
Figure 3.23. Gage height and suspended sediment concentration hydrograph, Colorado River near San Saba, Texas, May 1-6, 1952
Total Sediment Discharge
Table 3.6. Sand Bed Material Size Distribution
Table 3.7. Sand Size Bed Material Properties
Table 3.8. Gravel Bed Material Size Distribution
Table 3.9. Gravel Bed Material Properties
Figure 3.25. Size distribution curve for pebble count (1,000 mm = 1 m = 3.28 ft).
PROBLEM 3 Resistance to Flow in Alluvial Channels
Manning's n in Cobble Bed Streams - 4_0104910232
PROBLEM 4 Beginning of Motion
Critical Velocity for Beginning of Bed Material Movement
Critical Depth When the Bed Material Movement Would Stop - 4_0104910235
PROBLEM 2 Angle of Repose
Manning's n in Cobble Bed Streams - 4_0104910237
Bed Material Movement Using Shields Figure
Critical Size for Beginning of Bed Material Movement
Critical Depth When the Bed Material Movement Would Stop - 4_0104910240
SEDIMENT TRANSPORT - 4_0104910241
DEFINITIONS - 4_0104910242
GENERAL CONSIDERATIONS
Mode of Sediment Transport
Figure 4.1. Classification of sediment transport in streams (rivers)
Figure 4.2. Sediment transport capacity and supply curves
Figure 4.3. Schematic sediment and velocity profiles
SUSPENDED BED SEDIMENT DISCHARGE
SUSPENDED BED SEDIMENT DISCHARGE (cont.)
Figure 4.4. Graph of suspended sediment distribution (Rouse 1937).
BED SEDIMENT DISCHARGE
BED SEDIMENT DISCHARGE (cont.)
Einstein's Method of Computing Bed Sediment Discharge
Einstein's Method of Computing Bed Sediment Discharge (cont.)
Figure 4.5. Einstein's φ* vs ψ * bed load function (Einstein 1950)
Figure 4.6. Hiding factor (Einstein 1950)
Figure 4.8. Pressure correction (Einstein 1950)
Figure 4.9. Integral I1 in terms of E and Z (Einstein 1950)
Figure 4.10. Integral I2 in terms of E and Z (Einstein 1950)
Figure 4.11. Friction loss due to channel irregularities, as a function of sediment transport
Figure 4.12. Comparison of the Meyer-Peter and Mller and Einstein methods for computing contact load
Figure 4.13. Relation of discharge of sands to mean velocity for six median sizes of bed sands, four depths of flow, and a water temperature of 60F
Figure 4.14. Colby's correction curves for temperature and fine sediment
Relative Influence of Variables
Figure 4.15. Bed-material size effects on bed material transport
Figure 4.17. Effect of kinematic viscosity (temperature) on bed material transport
POWER FUNCTION RELATIONSHIPS
Table 4.1. Coefficient and Exponents of Equation 4.48
Table 4.2. Range of Parameters Equation 4.48 Developed by Simons et al.
Table 4.3. Coefficient and Exponents for Equation 4.50
CONVERSION FACTORS
APPLICATION OF SELECTED SEDIMENT TRANSPORT EQUATIONS
Table 4.4. Summary of Applicability of Selected Sediment Transport Formulas
SEDIMENT TRANSPORTATION ANALYSIS PROCEDURE
Field Measurement
Basic Methods for Sediment Transport Calculations
SOLVED PROBLEMS FOR SEDIMENT TRANSPORT (SI)
Table 4.5. Concentration vs. Elevation Above the Bed
Problem 3 Application of the Einstein Method to Calculate Total Bed-Material Discharge - 4_0104910279
Problem 5 Calculation of Total Bed-Material Discharge Using the Basic Power Function Relationship
Problem 7 Calculate Total Bed-Material Discharge Using Yang's Sand Equation - 4_0104910281
SOLVED PROBLEMS FOR SEDIMENT TRANSPORT (ENGLISH)
Table 4.6. Concentration vs. Elevation Above the Bed
Problem 3 Application of the Einstein Method to Calculate Total Bed-Material Discharge - 4_0104910284
Table 4.7. Bed Material Information for Sample Problem
Figure 4.20. Grain size distribution of bed material
Table 4.8. Hydraulic Calculations for Sample Problem 3. Application of the Einstein Procedure
Table 4.9. Bed-Material Load Calculations for Sample Problem by Applying the Einstein Procedure
Table 4.9. Bed-Material Load Calculations for Sample Problem by Applying the Einstein Procedure (cont.)
Table 4.10. Bed Material Load Calculations for Sample Problem by Applying the Colby Method (Median Diameter)
Table 4.11. Bed Material Discharge Calculations for Sample Problem by Applying the Colby (Individual Size Fraction)
Figure 4.21. Comparison of the Einstein and Colby methods
Problem 6 Calculation of Total Bed-Material Discharge Using the Expanded Power Function Relationship
Problem 7 Calculate Total Bed-Material Discharge Using Yang's Sand Equation - 4_0104910294
RIVER MORPHOLOGY AND RIVER RESPONSE
Floodplain and Delta Formations
Nickpoint Migration and Headcutting
Figure 5.1. Changing slope at fan-head leading to fan-head trenching
VARIABILITY AND CHANGE IN ALLUVIAL RIVERS
VARIABILITY AND CHANGE IN ALLUVIAL RIVERS (cont.)
Figure 5.3. Relationship between flume slope and sinuosity (ratio between channel length and valley length) during flume experiments at constant water discharge
Figure 5.5. Variability of sinuosity between 1765 and 1915 for 24 Mississippi River reaches
Figure 5.6. Mississippi River reaches between Cairo, Illinois and Old River, Louisiana
Differences Between Reaches
Figure 5.8. River Nile between Qena and Cairo showing six reaches of steep valley slope
Figure 5.10. Plot of River Nile sinuosity and valley slope. Numbers represent reaches of Figure 5.9
Classification of River Channels
Figure 5.11. Stream properties for classification (after Brice and Blodgett 1978)
Figure 5.12. Classification of river channels (after Culbertson et al. 1967)
Figure 5.13. Channel classification showing relative stability and types of hazards encountered with each pattern
Straight River Channels
Straight River Channels (cont.)
Figure 5.15. Definition sketch for meanders
Figure 5.16. Empirical relations for meander characteristics (Leopold et al. 1964)
Figure 5.17. Types of multi-channel streams
Figure 5.18a,b. Slope-discharge relationship for braiding or meandering in sandbed streams
Hydraulic Geometry of Alluvial Channels
Hydraulic Geometry of Alluvial Channels (cont.)
Figure 5.19. Variation of discharge at a given river cross section and at points downstream
Table 5.2. At-A-Station and Downstream Hydraulic Geometry Relationships
Dominant Discharge in Alluvial Rivers
River Profiles and Bed Material
General River Response to Change
Figure 5.21. Changes in channel slope in response to an increase in sediment load at Point C.
Figure 5.22. Changes in channel slope in response to a dam at point C
Table 5.4. Change of Variables Induced by Changes in Sediment Discharge, Size of Bed Sediment and Wash Load
Table 5.5. Qualitative Response of Alluvial Channels
River Pattern Thresholds and Response
Table 5.6. Chippewa River Morphology
Figure 5.23. Map of lower Chippewa River. The river is braided below Durand, Wisconsin.
Figure 5.24. Leopold and Wolman's (1957) relation between channel patterns, channel gradient, and bankfull discharge.
River Pattern Thresholds and Response (cont.)
MODELING OF RIVER SYSTEMS
Physical Modeling
Physical Modeling (cont.)
Table 5.7. Scale Ratios for Similitude.
Computer Modeling
Computer Modeling (cont.)
BRI-STARS MODEL (The Bridge Stream Tube Model for Alluvial River Simulation)
FLUVIAL-12
Two-Dimensional Sediment Transport Models
HIGHWAY PROBLEMS RELATED TO GRADATION CHANGES
Changes Due to Human Activities
Natural Causes
Resulting Problems at Highway Crossings
Table 5.8. Channel Response to Changes in Watershed and River Condition
Bank Stability - 4_0104910347
Stability Problems Associated With Channel Relocation
Figure 5.26. Median bank erosion rate in relation to channel width for different types of streams
Figure 5.27. Encroachment on a meandering river
Stability Problems Associated With Channel Relocation (cont.) - 4_0104910351
Stability Problems Associated With Channel Relocation (cont.) - 4_0104910352
Assessment of Stability for Relocated Streams
Estimation of Future Channel Stability and Behavior
Figure 5.28. Erosion index in relation to sinuosity (Brice 1984)
Figure 5.29. Modes of meander loop development.
Assessment Of Degradation
Advances in Predicting Meander Migration
Figure 5.30. Domains of meander behavior
Analysis Options
Figure 5.31. Sinuous point bar stream
Figure 5.32. River channels (After Petersen 1986)
PROBLEM 3 Channel Response to Changes in Watershed Conditions
Figure 5.33. Meandering river sketch (after Petersen 1986)
PROBLEM 5 At-A-Station and Downstream Hydraulic Geometry Relationships (SI)
PROBLEM 5 At-A-Station and Downstream Hydraulic Geometry Relationships (SI) (cont.)
PROBLEM 6 At-A-Station and Downstream Hydraulic Geometry Relationships (English)
PROBLEM 7 Downstream Sediment Size Distribution
Table 5.9. Sediment Size Distribution in the St. Lawrence Seaway
PROBLEM 9 Scale Ratios for Physical Models (English)
RIVER STABILIZATION AND BANK PROTECTION
Table 6.1. Factors Affecting Erosion of River Banks
Bed and Bank Material
Figure 6.1. Typical bank failure surfaces (a) noncohesive, (b) cohesive, (c) composite
Piping of River Banks
RIVER TRAINING AND STABILIZATION
Countermeasures for Channel Instability
Countermeasure Design Guidelines
Protection of Training Works
FLOW CONTROL STRUCTURES
Figure 6.2. Placement of flow control structures relative to channel banks, crossing, and floodplain
Figure 6.3. Perspective of hard point with section detail
Figure 6.4. Retard.
Dikes (Floodplain)
Figure 6.6. Pile dikes (retards would be similar)
Figure 6.8. Typical jetty-field layout
Figure 6.9. Steel jacks
Figure 6.10. Typical guidebank
Figure 6.11. Definition sketch for a vertical drop
Figure 6.12. Flow and scour patterns at a sloping sill
Figure 6.13. Diagram for riprap stability conditions.
Stability Factor Design Methods
Simplified Design Aid For Side Slope Riprap
Figure 6.14. Stability numbers for a 1.5 stability factor for horizontal flow along a side slope
U.S. Army Corps of Engineers Design Equation
U.S. Army Corps of Engineers Design Equation (cont.) - 4_0104910396
U.S. Army Corps of Engineers Design Equation (cont.) - 4_0104910397
Figure 6.15. Suggested gradation for riprap
Riprap Gradation and Thickness
Riprap Placement
Figure 6.16. Tie-in trench to prevent riprap blanket from unraveling
Windrow Revetment
Figure 6.18. Windrow revetment, definition sketch
Riprap Failure Modes
Figure 6.19. Riprap failure models
Table 6.3. Causes of Riprap Failure and Solutions
Bioengineering Countermeasures
Figure 6.20. Rock and wire mattress
Gabions - 4_0104910409
Figure 6.21. Typical sand-cement bag revetment
igure 6.22 Articulated concrete block system
Soil Cement
Figure 6.24. Typical soil-cement bank protection
OVERTOPPING FLOW ON EMBANKMENTS
Figure 6.25. Hydraulic flow zones on an embankment during overtopping flow
Figure 6.26. Definition sketch of variables involved in overtopping flow
Figure 6.27. Definition sketch for application of the momentum equation for embankment overtopping flow
Figure 6.28. Typical embankment erosion pattern with submerged flow
Figure 6.29. Typical embankment erosion pattern with free flow
Erosion Protection in Overtopping Flow
Figure 6.30. Permissible velocities of various protection materials as a function of flow duration
Figure 6.31. Full-scale test of an embankment overtopping protection system under steep-slope, high-velocity flow conditions
ENVIRONMENTAL CONSIDERATIONS - 4_0104910423
Effects of Channelization
SOLVED PROBLEMS FOR STABILITY OF RIPRAP (SI)
Figure. 6.32. Definition sketch for riprap on a channel bed
PROBLEM 3 Stability Factors for Riprap Design - 4_0104910427
PROBLEM 3 Stability Factors for Riprap Design (cont.)
Figure 6.33. Stability factors for various rock sizes on a side slope
PROBLEM 4 Riprap Design on an Abutment
SOLVED PROBLEMS FOR FILTER DESIGN (SI)
Table 6.5. Sizes of Materials
PROBLEM 2 Filter Design - 4_0104910433
Figure 6.35. Gradations of filter blanket for Problem 2 (after Anderson et al. 1968)
Figure. 6.36. Definition sketch for riprap on a channel bed
PROBLEM 2 Riprap Design on Embankment Slopes
PROBLEM 3 Stability Factors for Riprap Design - 4_0104910437
Figure 6.37. Stability factors for various rock sizes on a side slope
Figure 6.38. Safety factors for various side slopes
SOLVED PROBLEMS FOR FILTER DESIGN (ENGLISH)
PROBLEM 1 Filter Design
Table 6.7. Sizes of Materials
PROBLEM 2 Filter Design - 4_0104910443
Figure 6.39. Gradations of filter blanket for Problem 2
SCOUR AT BRIDGES
Bridge Scour Evaluation Program
Figure 7.1. Flow chart for scour and stream stability analysis and countermeasures
TOTAL SCOUR
Figure 7.2. Local scour depth at a pier as a function of time
LONG-TERM BED ELEVATION CHANGES
GENERAL SCOUR
Contraction Scour
Critical Velocity
Live-Bed Contraction Scour
Clear-water Contraction Scour
LOCAL SCOUR AT PIERS
Comparison of Pier Scour Equations
Figure 7.3 Comparison of scour formulas for variable depth ratios (y/a)
Figure 7.5. Comparison of pier scour equations with field measurements
FHWA HEC-18 Equation
Figure 7.6. Common pier shapes
Correction Factor for Bed Material Size
Pier Scour in Cohesive Bed Material
Pier Scour for Other Pier Geometry, Flow Conditions, and Debris
Figure 7.7. Topwidth of scour hole (HEC-18)
Figure 7.8. Schematic representation of abutment scour
Figure 7.9. Comparison of laboratory flow characteristics to field flow conditions
Figure 7.10. Orientation of embankment angle θ to the flow
Figure 7.11. Abutment shape
Froehlich's Live-Bed Scour Equation
SCOUR PROBLEMS
DATA NEEDS AND DATA SOURCES
Aerial and Other Photographs
Climatologic Data
Hydrologic Data - 4_0104910476
CHECKLIST OF DATA NEEDS
Table 8.1. Checklist of Data Needs
Table 8.1. Checklist of Data Needs (cont.)
Table 8.2. List of Data Sources
Table 8.2. List of Data Sources (cont.) - 4_0104910481
Table 8.2. List of Data Sources (cont.) - 4_0104910482
CIVIL ENGINEERING DATABASE
GeoRef
DESIGN CONSIDERATIONS FOR HIGHWAY ENCROACHMENTS AND RIVER CROSSINGS
Location of the Crossing or Encroachment
Hydrologic Data - 4_0104910487
Flow Alignment
Site Selection - 4_0104910489
PROCEDURE FOR EVALUATION AND DESIGN OF RIVER CROSSINGS AND ENCROACHMENTS
Figure 9.1. Three-level analysis procedure for river engineering studies
CONCEPTUAL EXAMPLES OF RIVER ENCROACHMENTS
CONCEPTUAL EXAMPLES OF RIVER ENCROACHMENTS (cont.) - 4_0104910493
Table 9.1. River Response to Highway Encroachments and to River Development
CONCEPTUAL EXAMPLES OF RIVER ENCROACHMENTS (Cont.) - 4_0104910495
Table 9.1. River Response to Highway Encroachments and to River Development
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910497
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910498
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910499
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910500
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910501
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910502
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910503
PRACTICAL EXAMPLES OF RIVER ENCROACHMENTS
Figure 9.2. Cimarron River, east of Okeene, Oklahoma (Example 1)
Figure 9.3. Arkansas River, north of Bixby, Oklahoma (Example 2)
Figure 9.4. Washita River, north of Maysville, Oklahoma (Example 3)
Figure 9.5. Beaver River, north of Laverne, Oklahoma (Example 4)
Figure 9.6. Powder River, 40 miles east of Buffalo, Wyoming (Example 5)
Figure 9.7. North Platte River near Guernsey, Wyoming (Example 6)
Figure 9.8. Coal Creek, tributary of Powder River, Wyoming (Example 7)
Figure 9.9b. Channel modifications to South Fork of Deer River at U.S. Highway 51 near Halls, Tennessee (Example 8)
Figure 9.9c. Elevation sketch of U.S. Highway 51 Bridge (Example 8)
Elk Creek at SR-15 Near Jackson, Nebraska (Example 9)
Figure 9.10. Stage trends at Sioux City, Iowa, on the Missouri River (Example 9)
Figure 9.11. Deflector arrangement and alignment problem on I-90 Bridge across Big Elk Creek near Piedmont, North Dakota (Example 10)
Figure 9.12. Plan sketch of channel relocation, Outlet Creek (Example 11)
Figure 9.13. Plan sketch of Nojoqui Creek channel relocation (Example 12)
Figure 9.14. Plan sketch of Turkey Creek channel relocation (Example 13)
Figure 9.15. Case study of sand and gravel mining (Example 14)
Nowood River and Ten Sleep Creek Confluence, Wyoming (Example 15)
Figure 9.16. Nowood River near Ten Sleep, Wyoming (Example 15)
Figure 9.17. Middle Fork Powder River at Kaycee, Wyoming (Example 16)
OVERVIEW EXAMPLES OF DESIGN F0R HIGHWAYS IN THE RIVER ENVIRONMENT
Level 1 - Reconnaissance and Geomorphic Analysis
Figure 10.2. Cross sectional area versus flow depth relation
Figure 10.3. Wetted perimeter versus flow depth relation
Level 2 - Quantitative Engineering Analysis - 4_0104910529
Figure 10.5. Gumbel's method of frequency analysis. Annual floods on Bijou Creek near Wiggins, Colorado
Figure 10.7. Proposed second alternative
Figure 10.9. Proposed fifth alternative
Level 2 - Quantitative Engineering Analysis - 4_0104910533
Table 10.2. Summary of Hydraulic Designs
Table 10.3. Design of Riprap Sizes
Figure 10.10. The sketch of proposed riprap design
Design for Alternatives 4 and 5
Table 10.4. Bank Migration for Alternative 4.
Table 10.7. Size and Filter Design for Riprap at Spur Noses and Spur Shanks
Figure 10.11. Sketch of spur design
OVERVIEW EXAMPLE 2 - RILLITO RIVER
Figure 10.12. Rillito River system vicinity map
Level 1 - Qualitative Geomorphic Analysis
Level 1 - Qualitative Geomorphic Analysis (cont.)
Figure 10.13. Slope-discharge relationship for Rillito River
Figure 10.14. Sketch of Craycroft Road crossing
Level 2 - Engineering Geomorphic Analysis
Figure 10.15. Sabino Canyon Road crossing site
Table 10.8. Rillito River Near Tucson, Arizona Log-Pearson Type III Frequency Analysis by USGS
Figure 10.17. Log-normal frequency analysis for Rillito River near Tucson
Figure 10.19. 100-year flood design hydrographs
Figure 10.21. Rillito-Pantano-Tanque Verde bed sediment distribution
Riparian Vegetation
Engineering Geomorphology
Table 10.9. Equilibrium Slope Calculations, Dominant Discharge
Results of Analysis
Figure 10.22. Bed elevation change of Rillito-Tanque Verde System (Tanque Verde flooding).
Figure 10.24. Alternative I for Craycroft Road Bridge crossing
Figure 10.25. Alternative II for Craycroft Road Bridge crossing
Table 10.10. Low Chord and Total Scour Requirements at Craycroft Road
Figure 10.26. Alternative III for Craycroft Road Bridge crossing
BRI-STARS SEDIMENT TRANSPORT MODELING EXAMPLE
Figure 10.27. General plan view of Sabino Canyon Road crossing for alternative II, III, and IV (II Shown).
Figure 10.28. Cross section of proposed bridge
Level 2 - Hydraulic Engineering Analysis
Figure 10.29. Equal conveyance tubes of approach section
Figure 10.31. Velocity distribution at bridge crossing
Figure 10.32. Plot of total scour for example problem
Figure 10.33. Revised plot of total scour for example problem
Figure 10.34. Three-day hydrograph for BRI-STARS analysis
Figure 10.36 Comparison cross-sections from BRI-STARS
Figure 10.37. BRI-STARS model profiles for steady-state run
REFERENCES - 4_0104910573
REFERENCES (cont.) - 4_0104910574
REFERENCES (cont.) - 4_0104910575
REFERENCES (cont.) - 4_0104910576
REFERENCES (cont.) - 4_0104910577
REFERENCES (cont.) - 4_0104910578
REFERENCES (cont.) - 4_0104910579
REFERENCES (cont.) - 4_0104910580
REFERENCES (cont.) - 4_0104910581
REFERENCES (cont.) - 4_0104910582
REFERENCES (cont.) - 4_0104910583
REFERENCES (cont.) - 4_0104910584
REFERENCES (cont.) - 4_0104910585
REFERENCES (cont.) - 4_0104910586
REFERENCES (cont.) - 4_0104910587
REFERENCES (cont.) - 4_0104910588
REFERENCES (cont.) - 4_0104910589
REFERENCES (cont.) - 4_0104910590
REFERENCES (cont.) - 4_0104910591
REFERENCES (cont.) - 4_0104910592
REFERENCES (cont.) - 4_0104910593
REFERENCES (cont.) - 4_0104910594
REFERENCES (cont.) - 4_0104910595
REFERENCES (cont.) - 4_0104910596
REFERENCES (cont.) - 4_0104910597
REFERENCES (cont.) - 4_0104910598
REFERENCES (cont.) - 4_0104910599
REFERENCES (cont.) - 4_0104910600
APPENDIX A. Metric System, Conversion Factors, and Water Properties
Table A.1. Overview of SI Units.
Table A.3. Derived Units With Special Names
Table A.4. Useful Conversion Factors
Table A.4. Useful Conversion Factors (cont.)
Table A6. Physical Properties of Water at Atmospheric Pressure in SI Units
Table A7. Physical Properties of Water at Atmospheric Pressure in English Units
Table A8. Sediment Particles Grade Scale
Table A9. Common Equivalent Hydraulic Units
APPENDIX B. Analysis of Selected Sediment Transport Relationships
EVALUATION OF SELECTED SEDIMENT TRANSPORT EQUATIONS
Table B.1a. Field Data
Table B.1b. Laboratory Data
Table B3. Summary of Ten Sediment Transport Relations
Analysis of Sediment Transport Relations
Figure B.1. Predicted versus measured total bed-material transport considering four classifications of size of bed materials
Figure B.1. Predicted versus measured total bed-material transport considering four classifications of size of bed materials (cont.) - 4_0104910618
Figure B.1. Predicted versus measured total bed-material transport considering four classifications of size of bed materials (cont.) - 4_0104910619
Figure B.1. Predicted versus measured total bed-material transport considering four classifications of size of bed materials (cont.) - 4_0104910620
Figure B.2. Comparison Cppm computed and measured for three river sets
Figure B.2. Comparison Cppm computed and measured for three river sets (cont.) - 4_0104910622
Figure B.2. Comparison Cppm computed and measured for three river sets (cont.) - 4_0104910623
Medium to very coarse sand-bed rivers (0.250 mm < D50 < 2.00 mm)
Table B.4. Summary of Applicability of Selected Sediment Transport Relations
Table B.5. Coefficient and Exponents of Equation B.3
Figure B.3. Relation of unit sediment discharge qs from measured and computed results using Equation B.5 for 2503 sets of field data
Table B.7. Range of Data Utilized by Posada to Develop Equation B.5
LAURSEN AND MODIFIED LAURSEN EQUATIONS
Figure B.4. Comparison of measured qs and computed qs using Posada and Kodoatie equations for various river-bed materials, data from Group 1
Figure B.5. Comparison of measured qs and computed qs using Posada and Kodoatie equations for various river-bed materials, data from Group 2
Figure B.6. Modifications of Laursen's (1958) Graph
Figure B.7. Plotting V*/ωi and f(V*/ωi) for data from Group 1 with Laursen's Equation
Table B.11. Value of "a" in Equation B.10 for Various Sizes of Bed Material.
Figure B.8. Proposed graph by Kodoatie using Equation B.10
Medium to Very Coarse Sand-Bed Rivers
Very Fine to Fine Sand-Bed Rivers
RANGE OF DATA FOR VALIDATION
Bed Material Size
River Size
APPENDIX C. Index
APPENDIX C. Index (cont.) - 4_0104910642
APPENDIX C. Index (cont.) - 4_0104910643
APPENDIX C. Index (cont.) - 4_0104910644
APPENDIX C. Index (cont.) - 4_0104910645
APPENDIX C. Index (cont.) - 4_0104910646
4_010491
GLOSSARY (cont.) - 4_0104910042
GLOSSARY (cont.) - 4_0104910043
GLOSSARY (cont.) - 4_0104910044
GLOSSARY (cont.) - 4_0104910045
GLOSSARY (cont.) - 4_0104910046
GLOSSARY (cont.) - 4_0104910047
GLOSSARY (cont.) - 4_0104910048
GLOSSARY (cont.) - 4_0104910049
GLOSSARY (cont.) - 4_0104910050
GLOSSARY (cont.) - 4_0104910051
GLOSSARY (cont.) - 4_0104910052
GLOSSARY (cont.) - 4_0104910053
GLOSSARY (cont.) - 4_0104910054
GLOSSARY (cont.) - 4_0104910055
GLOSSARY (cont.) - 4_0104910056
GLOSSARY (cont.) - 4_0104910057
GLOSSARY (cont.) - 4_0104910058
GLOSSARY (cont.) - 4_0104910059
GLOSSARY (cont.) - 4_0104910060
GLOSSARY (cont.) - 4_0104910061
CLASSIFICATION OF RIVER CROSSINGS AND ENCROACHMENTS
DYNAMICS OF NATURAL RIVERS AND THEIR TRIBUTARIES
Figure 1.1. Geometric properties of bridge crossings
Figure 1.2. Comparison of the 1884 and 1968 Mississippi River Channel near Commerce, Missouri.
Historical Evidence of the Natural Instability of Fluvial Systems
Historical Evidence of the Natural Instability of Fluvial Systems (cont.)
Introduction to River Hydraulics and River Response
Figure 1.3. Sinuosity vs. slope with constant discharge
EFFECTS OF HIGHWAY CONSTRUCTION ON RIVER SYSTEMS
Delayed Response of Rivers to Encroachment
EFFECTS OF RIVER DEVELOPMENT ON HIGHWAY ENCROACHMENTS
EFFECTS OF RIVER DEVELOPMENT ON HIGHWAY ENCROACHMENTS (cont.)
TECHNICAL ASPECTS
Variables Affecting River Behavior
FUTURE TECHNICAL TRENDS
Research Needs
OVERVIEW OF MANUAL CONTENTS
Chapter 3 - Fundamentals of Alluvial Channel Flow
Chapter 5 - River Morphology and River Response
Chapter 8 Data Need and Data Sources
Table 1.1. Commonly Used Engineering Terms in SI and English Units
OPEN CHANNEL FLOW
Definitions - 4_0104910086
THREE BASIC EQUATIONS
Figure 2.1. A river reach as a control volume
Conservation of Mass
Figure 2.2. The control volume for conservation of linear momentum
Conservation of Linear Momentum
Figure 2.3. The streamtube as a control volume
Conservation of Energy
Conservation of Energy (cont.) - 4_0104910094
Conservation of Energy (cont.) - 4_0104910095
HYDROSTATICS
Figure 2.4. Pressure distribution in steady uniform and in steady nonuniform flow
Figure 2.6. Steady uniform flow in a unit width channel
STEADY UNIFORM FLOW
Figure 2.7. Hydraulically smooth boundary
Figure 2.8. Hydraulically rough boundary
Shear Stress, Velocity Distribution, and Average Velocity
Shear Stress, Velocity Distribution, and Average Velocity (cont.)
Figure 2.10. Einstein's multiplication factor X in the logarithmic velocity equations
Other Velocity Equations
Table 2.1. Manning's Roughness Coefficients for Various Boundaries
Table 2.1. Manning's Roughness Coefficients for Various Boundaries (cont.)
Average Boundary Shear Stress
Table 2.2. Adjustment Factors for the Determination of n Values
Figure 2.11. Control volume for steady uniform flow
Relation Between Shear Stress and Velocity
Energy and Momentum Coefficients for Rivers
Energy and Momentum Coefficients for Rivers (cont.) - 4_0104910113
Figure 2.12. Energy and momentum coefficients for a unit width of river
Energy and Momentum Coefficients for Rivers (cont.) - 4_0104910115
Figure 2.14. Definition sketch for small amplitude waves
Gravity Waves
Figure 2.15. Sketch of positive and negative surges
Hydraulic Jump
Figure 2.16. Hydraulic jump characteristics as a function of the upstream Froude number
Figure 2.18. Roll waves or slug flow
Figure 2.19. Transitions in open channel flow
Figure 2.20. Specific energy diagram
Specific Discharge Diagram
Figure 2.21. Changes in water surface resulting from an increase in bed elevation
Figure 2.23. Change in water surface elevation resulting from a change in width
Transitions With Super Critical Flows
Figure 2.24. Flow characteristics over a drop structure (Chow 1959)
Figure 2.25. Nappe profiles for supercritical flow (Ippen 1950)
Transverse Velocity Distribution in Bends
Figure 2.26. Schematic representation of transverse currents in a channel bed
Subcritical Flow in Bends
Supercritical Flow in Bends
GRADUALLY VARIED FLOW
Classification of Flow Profiles
Figure 2.28. Classification of water surface profiles
Table 2.3. Characteristics of Water Surface Profiles
Figure 2.29. Examples of water surface profiles
Figure 2.30. Definition sketch for the standard step method for computation of backwater curves
STREAM GAGING
Figure 2.31. Gaging station well and shelters (from Buchanan and Somers 1968a)
Figure 2.32. Typical float recording gaging station (from Buchanan and Somers 1968a)
Figure 2.34. Stage vs. time hydrograph (Kennedy 1983)
Figure 2.35. Definition sketch of computing area and discharge at a gaging station
Figure 2.36. Stage-discharge relation for Schoharie Creek, New York (Butch 2000)
Figure 2.37. Stage-discharge relation for a sand channel
Backwater Effects on Waterway Openings
Figure 2.38. Three types of backwater effect associated with bridge crossings
Figure 2.39. Submergence of a superstructure
Figure 2.40. Types of flow encountered (HDS 1, Bradley 1978)
HYDRAULICS OF CULVERT FLOW
ROADWAY OVERTOPPING
Figure 2.41. Discharge coefficient for roadway overtopping
Table 2.4. Discharge measurement notes
Table 2.5. Observed Velocity Data
Table 2.6. Velocity Profile Calculations
Shear Stress Analysis - 4_0104910157
Table 2.7. Detailed Computation of Superelevation in Bends
PROBLEM 4 Maximum Stream Constriction Without Causing Backwater (Neglecting Energy Losses) - 4_0104910159
PROBLEM 5 Maximum Water Surface Elevation Upstream of a Grade Control Structure Without Backwater (Neglecting Energy Losses)
Figure 2.43. Sketch of backwater curve over check dam
How much backwater will the dam cause for a flow of 28.37 m3/s if the normal depth for this discharge is 1.52 m and the dam height is 1.22 m?
SOLVED PROBLEMS OPEN CHANNEL FLOW (ENGLISH)
Table 2.8. Discharge measurement notes
Table 2.9. Observed Velocity Data
Table 2.10. Velocity Profile Calculations
Shear Stress Analysis - 4_0104910167
Table 2.11. Detailed Computation of Superelevation in Bends
PROBLEM 4 Maximum Stream Constriction Without Causing Backwater (Neglecting Energy Losses) - 4_0104910169
PROBLEM 5 Maximum Elevation of a Grade Control Structure Without Backwater (Neglecting Energy Losses)
Figure 2.44. Sketch of backwater curve over check dam
How much backwater will the dam cause for a flow of 1000 cfs if the normal depth for this discharge is 5 ft and the dam height is 4.0 ft?
How much backwater will the dam cause for a flow of 1000 cfs if the normal depth for this discharge is 5 ft and the dam height is 4.0 ft? (cont.)
FUNDAMENTALS OF ALLUVIAL CHANNEL FLOW
Particle Shape
Table 3.1. Sediment Grade Scale (Brown 1950)
Fall Velocity - 4_0104910178
Figure 3.1. Drag coefficient CD vs particle Reynolds number Rep for spheres and natural sediments with shape factors Sp equal to 0.3, 0.5, 0.7, and 0.9.
Figure 3.2. Nominal diameter vs. fall velocity (Temperature = 24C)
Sediment Size Distribution
Square-Surface Sample
Figure 3.3. Definition sketches for size-frequency characteristics of sediments
Sediment Size Distribution (cont.)
Specific Weight
FLOW IN SANDBED CHANNELS
Figure 3.4. Angle of repose of non-cohesive materials
Figure 3.5. Forms of bed roughness in sand channels
Figure 3.6. Relation between water surface and bed configuration
Figure 3.7. Change in velocity with stream power for a sand with D50 = 0.19 mm
Plane Bed Without Sediment Movement
Plane Bed With Movemen
Regime of Flow, Bed Configuration, and Froude Number
Figure 3.8. Relation between regime of flow and depth for bed material with a median size equal to or less than 0.35 mm
RESISTANCE TO FLOW IN ALLUVIAL CHANNELS
Figure 3.10. Relation of depth to discharge for Elkhorn River near Waterloo, Nebraska
Figure 3.11. Apparent kinematic viscosity of water-bentonite dispersions
Figure 3.12. Variation of fall velocity of several sand mixtures with percent bentonite and temperature
Size Gradation
Shape Factor for the Reach and Cross-Section
Figure 3.13. Relation between stream power, median fall diameter, and bed configuration and Manning's n values
Figure 3.14. Change in Manning's n with discharge for Padma River in Bangladesh
Alluvial Processes and Resistance to Flow in Coarse Material Streams
Resistance to Flow
Table 3.3. Typical Sediment Size Distribution for Gravel-Bed Stream
BEGINNING OF MOTION
Theory of Beginning of Motion
Theory of Beginning of Motion (cont.) - 4_0104910208
Theory of Beginning of Motion (cont.) - 4_0104910209
Figure 3.15. Shields Diagram: dimensionless critical shear stress
Figure 3.16. Shields' relation for beginning of motion (after Gessler 1971)
Shields Diagram
Figure 3.17. Comparison of critical shear stress as a function of grain diamete
Equations for Flow and Sediment Variables for Beginning of Motion
Critical Velocity for the Beginning of Bed Material Movement
Critical Size for the Beginning of Bed Material Movement
Table 3.4. Maximum Permissible Velocities Proposed by Fortier and Scobey (1926)
Table 3.5. Nonscour Velocities for Soils (Modified from a report by Keown et al. 1977)
Figure 3.19. Critical velocity as a function of stone size
SEDIMENT DISCHARGE MEASUREMENT
Suspended Sediment Discharge Measurement
Figure 3.21. Schematic sediment and velocity profiles
Figure 3.22b. Suspended sediment sampler-DH48
Figure 3.23. Gage height and suspended sediment concentration hydrograph, Colorado River near San Saba, Texas, May 1-6, 1952
Total Sediment Discharge
Table 3.6. Sand Bed Material Size Distribution
Table 3.7. Sand Size Bed Material Properties
Table 3.8. Gravel Bed Material Size Distribution
Table 3.9. Gravel Bed Material Properties
Figure 3.25. Size distribution curve for pebble count (1,000 mm = 1 m = 3.28 ft).
PROBLEM 3 Resistance to Flow in Alluvial Channels
Manning's n in Cobble Bed Streams - 4_0104910232
PROBLEM 4 Beginning of Motion
Critical Velocity for Beginning of Bed Material Movement
Critical Depth When the Bed Material Movement Would Stop - 4_0104910235
PROBLEM 2 Angle of Repose
Manning's n in Cobble Bed Streams - 4_0104910237
Bed Material Movement Using Shields Figure
Critical Size for Beginning of Bed Material Movement
Critical Depth When the Bed Material Movement Would Stop - 4_0104910240
SEDIMENT TRANSPORT - 4_0104910241
DEFINITIONS - 4_0104910242
GENERAL CONSIDERATIONS
Mode of Sediment Transport
Figure 4.1. Classification of sediment transport in streams (rivers)
Figure 4.2. Sediment transport capacity and supply curves
Figure 4.3. Schematic sediment and velocity profiles
SUSPENDED BED SEDIMENT DISCHARGE
SUSPENDED BED SEDIMENT DISCHARGE (cont.)
Figure 4.4. Graph of suspended sediment distribution (Rouse 1937).
BED SEDIMENT DISCHARGE
BED SEDIMENT DISCHARGE (cont.)
Einstein's Method of Computing Bed Sediment Discharge
Einstein's Method of Computing Bed Sediment Discharge (cont.)
Figure 4.5. Einstein's φ* vs ψ * bed load function (Einstein 1950)
Figure 4.6. Hiding factor (Einstein 1950)
Figure 4.8. Pressure correction (Einstein 1950)
Figure 4.9. Integral I1 in terms of E and Z (Einstein 1950)
Figure 4.10. Integral I2 in terms of E and Z (Einstein 1950)
Figure 4.11. Friction loss due to channel irregularities, as a function of sediment transport
Figure 4.12. Comparison of the Meyer-Peter and Mller and Einstein methods for computing contact load
Figure 4.13. Relation of discharge of sands to mean velocity for six median sizes of bed sands, four depths of flow, and a water temperature of 60F
Figure 4.14. Colby's correction curves for temperature and fine sediment
Relative Influence of Variables
Figure 4.15. Bed-material size effects on bed material transport
Figure 4.17. Effect of kinematic viscosity (temperature) on bed material transport
POWER FUNCTION RELATIONSHIPS
Table 4.1. Coefficient and Exponents of Equation 4.48
Table 4.2. Range of Parameters Equation 4.48 Developed by Simons et al.
Table 4.3. Coefficient and Exponents for Equation 4.50
CONVERSION FACTORS
APPLICATION OF SELECTED SEDIMENT TRANSPORT EQUATIONS
Table 4.4. Summary of Applicability of Selected Sediment Transport Formulas
SEDIMENT TRANSPORTATION ANALYSIS PROCEDURE
Field Measurement
Basic Methods for Sediment Transport Calculations
SOLVED PROBLEMS FOR SEDIMENT TRANSPORT (SI)
Table 4.5. Concentration vs. Elevation Above the Bed
Problem 3 Application of the Einstein Method to Calculate Total Bed-Material Discharge - 4_0104910279
Problem 5 Calculation of Total Bed-Material Discharge Using the Basic Power Function Relationship
Problem 7 Calculate Total Bed-Material Discharge Using Yang's Sand Equation - 4_0104910281
SOLVED PROBLEMS FOR SEDIMENT TRANSPORT (ENGLISH)
Table 4.6. Concentration vs. Elevation Above the Bed
Problem 3 Application of the Einstein Method to Calculate Total Bed-Material Discharge - 4_0104910284
Table 4.7. Bed Material Information for Sample Problem
Figure 4.20. Grain size distribution of bed material
Table 4.8. Hydraulic Calculations for Sample Problem 3. Application of the Einstein Procedure
Table 4.9. Bed-Material Load Calculations for Sample Problem by Applying the Einstein Procedure
Table 4.9. Bed-Material Load Calculations for Sample Problem by Applying the Einstein Procedure (cont.)
Table 4.10. Bed Material Load Calculations for Sample Problem by Applying the Colby Method (Median Diameter)
Table 4.11. Bed Material Discharge Calculations for Sample Problem by Applying the Colby (Individual Size Fraction)
Figure 4.21. Comparison of the Einstein and Colby methods
Problem 6 Calculation of Total Bed-Material Discharge Using the Expanded Power Function Relationship
Problem 7 Calculate Total Bed-Material Discharge Using Yang's Sand Equation - 4_0104910294
RIVER MORPHOLOGY AND RIVER RESPONSE
Floodplain and Delta Formations
Nickpoint Migration and Headcutting
Figure 5.1. Changing slope at fan-head leading to fan-head trenching
VARIABILITY AND CHANGE IN ALLUVIAL RIVERS
VARIABILITY AND CHANGE IN ALLUVIAL RIVERS (cont.)
Figure 5.3. Relationship between flume slope and sinuosity (ratio between channel length and valley length) during flume experiments at constant water discharge
Figure 5.5. Variability of sinuosity between 1765 and 1915 for 24 Mississippi River reaches
Figure 5.6. Mississippi River reaches between Cairo, Illinois and Old River, Louisiana
Differences Between Reaches
Figure 5.8. River Nile between Qena and Cairo showing six reaches of steep valley slope
Figure 5.10. Plot of River Nile sinuosity and valley slope. Numbers represent reaches of Figure 5.9
Classification of River Channels
Figure 5.11. Stream properties for classification (after Brice and Blodgett 1978)
Figure 5.12. Classification of river channels (after Culbertson et al. 1967)
Figure 5.13. Channel classification showing relative stability and types of hazards encountered with each pattern
Straight River Channels
Straight River Channels (cont.)
Figure 5.15. Definition sketch for meanders
Figure 5.16. Empirical relations for meander characteristics (Leopold et al. 1964)
Figure 5.17. Types of multi-channel streams
Figure 5.18a,b. Slope-discharge relationship for braiding or meandering in sandbed streams
Hydraulic Geometry of Alluvial Channels
Hydraulic Geometry of Alluvial Channels (cont.)
Figure 5.19. Variation of discharge at a given river cross section and at points downstream
Table 5.2. At-A-Station and Downstream Hydraulic Geometry Relationships
Dominant Discharge in Alluvial Rivers
River Profiles and Bed Material
General River Response to Change
Figure 5.21. Changes in channel slope in response to an increase in sediment load at Point C.
Figure 5.22. Changes in channel slope in response to a dam at point C
Table 5.4. Change of Variables Induced by Changes in Sediment Discharge, Size of Bed Sediment and Wash Load
Table 5.5. Qualitative Response of Alluvial Channels
River Pattern Thresholds and Response
Table 5.6. Chippewa River Morphology
Figure 5.23. Map of lower Chippewa River. The river is braided below Durand, Wisconsin.
Figure 5.24. Leopold and Wolman's (1957) relation between channel patterns, channel gradient, and bankfull discharge.
River Pattern Thresholds and Response (cont.)
MODELING OF RIVER SYSTEMS
Physical Modeling
Physical Modeling (cont.)
Table 5.7. Scale Ratios for Similitude.
Computer Modeling
Computer Modeling (cont.)
BRI-STARS MODEL (The Bridge Stream Tube Model for Alluvial River Simulation)
FLUVIAL-12
Two-Dimensional Sediment Transport Models
HIGHWAY PROBLEMS RELATED TO GRADATION CHANGES
Changes Due to Human Activities
Natural Causes
Resulting Problems at Highway Crossings
Table 5.8. Channel Response to Changes in Watershed and River Condition
Bank Stability - 4_0104910347
Stability Problems Associated With Channel Relocation
Figure 5.26. Median bank erosion rate in relation to channel width for different types of streams
Figure 5.27. Encroachment on a meandering river
Stability Problems Associated With Channel Relocation (cont.) - 4_0104910351
Stability Problems Associated With Channel Relocation (cont.) - 4_0104910352
Assessment of Stability for Relocated Streams
Estimation of Future Channel Stability and Behavior
Figure 5.28. Erosion index in relation to sinuosity (Brice 1984)
Figure 5.29. Modes of meander loop development.
Assessment Of Degradation
Advances in Predicting Meander Migration
Figure 5.30. Domains of meander behavior
Analysis Options
Figure 5.31. Sinuous point bar stream
Figure 5.32. River channels (After Petersen 1986)
PROBLEM 3 Channel Response to Changes in Watershed Conditions
Figure 5.33. Meandering river sketch (after Petersen 1986)
PROBLEM 5 At-A-Station and Downstream Hydraulic Geometry Relationships (SI)
PROBLEM 5 At-A-Station and Downstream Hydraulic Geometry Relationships (SI) (cont.)
PROBLEM 6 At-A-Station and Downstream Hydraulic Geometry Relationships (English)
PROBLEM 7 Downstream Sediment Size Distribution
Table 5.9. Sediment Size Distribution in the St. Lawrence Seaway
PROBLEM 9 Scale Ratios for Physical Models (English)
RIVER STABILIZATION AND BANK PROTECTION
Table 6.1. Factors Affecting Erosion of River Banks
Bed and Bank Material
Figure 6.1. Typical bank failure surfaces (a) noncohesive, (b) cohesive, (c) composite
Piping of River Banks
RIVER TRAINING AND STABILIZATION
Countermeasures for Channel Instability
Countermeasure Design Guidelines
Protection of Training Works
FLOW CONTROL STRUCTURES
Figure 6.2. Placement of flow control structures relative to channel banks, crossing, and floodplain
Figure 6.3. Perspective of hard point with section detail
Figure 6.4. Retard.
Dikes (Floodplain)
Figure 6.6. Pile dikes (retards would be similar)
Figure 6.8. Typical jetty-field layout
Figure 6.9. Steel jacks
Figure 6.10. Typical guidebank
Figure 6.11. Definition sketch for a vertical drop
Figure 6.12. Flow and scour patterns at a sloping sill
Figure 6.13. Diagram for riprap stability conditions.
Stability Factor Design Methods
Simplified Design Aid For Side Slope Riprap
Figure 6.14. Stability numbers for a 1.5 stability factor for horizontal flow along a side slope
U.S. Army Corps of Engineers Design Equation
U.S. Army Corps of Engineers Design Equation (cont.) - 4_0104910396
U.S. Army Corps of Engineers Design Equation (cont.) - 4_0104910397
Figure 6.15. Suggested gradation for riprap
Riprap Gradation and Thickness
Riprap Placement
Figure 6.16. Tie-in trench to prevent riprap blanket from unraveling
Windrow Revetment
Figure 6.18. Windrow revetment, definition sketch
Riprap Failure Modes
Figure 6.19. Riprap failure models
Table 6.3. Causes of Riprap Failure and Solutions
Bioengineering Countermeasures
Figure 6.20. Rock and wire mattress
Gabions - 4_0104910409
Figure 6.21. Typical sand-cement bag revetment
igure 6.22 Articulated concrete block system
Soil Cement
Figure 6.24. Typical soil-cement bank protection
OVERTOPPING FLOW ON EMBANKMENTS
Figure 6.25. Hydraulic flow zones on an embankment during overtopping flow
Figure 6.26. Definition sketch of variables involved in overtopping flow
Figure 6.27. Definition sketch for application of the momentum equation for embankment overtopping flow
Figure 6.28. Typical embankment erosion pattern with submerged flow
Figure 6.29. Typical embankment erosion pattern with free flow
Erosion Protection in Overtopping Flow
Figure 6.30. Permissible velocities of various protection materials as a function of flow duration
Figure 6.31. Full-scale test of an embankment overtopping protection system under steep-slope, high-velocity flow conditions
ENVIRONMENTAL CONSIDERATIONS - 4_0104910423
Effects of Channelization
SOLVED PROBLEMS FOR STABILITY OF RIPRAP (SI)
Figure. 6.32. Definition sketch for riprap on a channel bed
PROBLEM 3 Stability Factors for Riprap Design - 4_0104910427
PROBLEM 3 Stability Factors for Riprap Design (cont.)
Figure 6.33. Stability factors for various rock sizes on a side slope
PROBLEM 4 Riprap Design on an Abutment
SOLVED PROBLEMS FOR FILTER DESIGN (SI)
Table 6.5. Sizes of Materials
PROBLEM 2 Filter Design - 4_0104910433
Figure 6.35. Gradations of filter blanket for Problem 2 (after Anderson et al. 1968)
Figure. 6.36. Definition sketch for riprap on a channel bed
PROBLEM 2 Riprap Design on Embankment Slopes
PROBLEM 3 Stability Factors for Riprap Design - 4_0104910437
Figure 6.37. Stability factors for various rock sizes on a side slope
Figure 6.38. Safety factors for various side slopes
SOLVED PROBLEMS FOR FILTER DESIGN (ENGLISH)
PROBLEM 1 Filter Design
Table 6.7. Sizes of Materials
PROBLEM 2 Filter Design - 4_0104910443
Figure 6.39. Gradations of filter blanket for Problem 2
SCOUR AT BRIDGES
Bridge Scour Evaluation Program
Figure 7.1. Flow chart for scour and stream stability analysis and countermeasures
TOTAL SCOUR
Figure 7.2. Local scour depth at a pier as a function of time
LONG-TERM BED ELEVATION CHANGES
GENERAL SCOUR
Contraction Scour
Critical Velocity
Live-Bed Contraction Scour
Clear-water Contraction Scour
LOCAL SCOUR AT PIERS
Comparison of Pier Scour Equations
Figure 7.3 Comparison of scour formulas for variable depth ratios (y/a)
Figure 7.5. Comparison of pier scour equations with field measurements
FHWA HEC-18 Equation
Figure 7.6. Common pier shapes
Correction Factor for Bed Material Size
Pier Scour in Cohesive Bed Material
Pier Scour for Other Pier Geometry, Flow Conditions, and Debris
Figure 7.7. Topwidth of scour hole (HEC-18)
Figure 7.8. Schematic representation of abutment scour
Figure 7.9. Comparison of laboratory flow characteristics to field flow conditions
Figure 7.10. Orientation of embankment angle θ to the flow
Figure 7.11. Abutment shape
Froehlich's Live-Bed Scour Equation
SCOUR PROBLEMS
DATA NEEDS AND DATA SOURCES
Aerial and Other Photographs
Climatologic Data
Hydrologic Data - 4_0104910476
CHECKLIST OF DATA NEEDS
Table 8.1. Checklist of Data Needs
Table 8.1. Checklist of Data Needs (cont.)
Table 8.2. List of Data Sources
Table 8.2. List of Data Sources (cont.) - 4_0104910481
Table 8.2. List of Data Sources (cont.) - 4_0104910482
CIVIL ENGINEERING DATABASE
GeoRef
DESIGN CONSIDERATIONS FOR HIGHWAY ENCROACHMENTS AND RIVER CROSSINGS
Location of the Crossing or Encroachment
Hydrologic Data - 4_0104910487
Flow Alignment
Site Selection - 4_0104910489
PROCEDURE FOR EVALUATION AND DESIGN OF RIVER CROSSINGS AND ENCROACHMENTS
Figure 9.1. Three-level analysis procedure for river engineering studies
CONCEPTUAL EXAMPLES OF RIVER ENCROACHMENTS
CONCEPTUAL EXAMPLES OF RIVER ENCROACHMENTS (cont.) - 4_0104910493
Table 9.1. River Response to Highway Encroachments and to River Development
CONCEPTUAL EXAMPLES OF RIVER ENCROACHMENTS (Cont.) - 4_0104910495
Table 9.1. River Response to Highway Encroachments and to River Development
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910497
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910498
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910499
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910500
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910501
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910502
Table 9.1. River Response to Highway Encroachments and to River Development (continued) - 4_0104910503
PRACTICAL EXAMPLES OF RIVER ENCROACHMENTS
Figure 9.2. Cimarron River, east of Okeene, Oklahoma (Example 1)
Figure 9.3. Arkansas River, north of Bixby, Oklahoma (Example 2)
Figure 9.4. Washita River, north of Maysville, Oklahoma (Example 3)
Figure 9.5. Beaver River, north of Laverne, Oklahoma (Example 4)
Figure 9.6. Powder River, 40 miles east of Buffalo, Wyoming (Example 5)
Figure 9.7. North Platte River near Guernsey, Wyoming (Example 6)
Figure 9.8. Coal Creek, tributary of Powder River, Wyoming (Example 7)
Figure 9.9b. Channel modifications to South Fork of Deer River at U.S. Highway 51 near Halls, Tennessee (Example 8)
Figure 9.9c. Elevation sketch of U.S. Highway 51 Bridge (Example 8)
Elk Creek at SR-15 Near Jackson, Nebraska (Example 9)
Figure 9.10. Stage trends at Sioux City, Iowa, on the Missouri River (Example 9)
Figure 9.11. Deflector arrangement and alignment problem on I-90 Bridge across Big Elk Creek near Piedmont, North Dakota (Example 10)
Figure 9.12. Plan sketch of channel relocation, Outlet Creek (Example 11)
Figure 9.13. Plan sketch of Nojoqui Creek channel relocation (Example 12)
Figure 9.14. Plan sketch of Turkey Creek channel relocation (Example 13)
Figure 9.15. Case study of sand and gravel mining (Example 14)
Nowood River and Ten Sleep Creek Confluence, Wyoming (Example 15)
Figure 9.16. Nowood River near Ten Sleep, Wyoming (Example 15)
Figure 9.17. Middle Fork Powder River at Kaycee, Wyoming (Example 16)
OVERVIEW EXAMPLES OF DESIGN F0R HIGHWAYS IN THE RIVER ENVIRONMENT
Level 1 - Reconnaissance and Geomorphic Analysis
Figure 10.2. Cross sectional area versus flow depth relation
Figure 10.3. Wetted perimeter versus flow depth relation
Level 2 - Quantitative Engineering Analysis - 4_0104910529
Figure 10.5. Gumbel's method of frequency analysis. Annual floods on Bijou Creek near Wiggins, Colorado
Figure 10.7. Proposed second alternative
Figure 10.9. Proposed fifth alternative
Level 2 - Quantitative Engineering Analysis - 4_0104910533
Table 10.2. Summary of Hydraulic Designs
Table 10.3. Design of Riprap Sizes
Figure 10.10. The sketch of proposed riprap design
Design for Alternatives 4 and 5
Table 10.4. Bank Migration for Alternative 4.
Table 10.7. Size and Filter Design for Riprap at Spur Noses and Spur Shanks
Figure 10.11. Sketch of spur design
OVERVIEW EXAMPLE 2 - RILLITO RIVER
Figure 10.12. Rillito River system vicinity map
Level 1 - Qualitative Geomorphic Analysis
Level 1 - Qualitative Geomorphic Analysis (cont.)
Figure 10.13. Slope-discharge relationship for Rillito River
Figure 10.14. Sketch of Craycroft Road crossing
Level 2 - Engineering Geomorphic Analysis
Figure 10.15. Sabino Canyon Road crossing site
Table 10.8. Rillito River Near Tucson, Arizona Log-Pearson Type III Frequency Analysis by USGS
Figure 10.17. Log-normal frequency analysis for Rillito River near Tucson
Figure 10.19. 100-year flood design hydrographs
Figure 10.21. Rillito-Pantano-Tanque Verde bed sediment distribution
Riparian Vegetation
Engineering Geomorphology
Table 10.9. Equilibrium Slope Calculations, Dominant Discharge
Results of Analysis
Figure 10.22. Bed elevation change of Rillito-Tanque Verde System (Tanque Verde flooding).
Figure 10.24. Alternative I for Craycroft Road Bridge crossing
Figure 10.25. Alternative II for Craycroft Road Bridge crossing
Table 10.10. Low Chord and Total Scour Requirements at Craycroft Road
Figure 10.26. Alternative III for Craycroft Road Bridge crossing
BRI-STARS SEDIMENT TRANSPORT MODELING EXAMPLE
Figure 10.27. General plan view of Sabino Canyon Road crossing for alternative II, III, and IV (II Shown).
Figure 10.28. Cross section of proposed bridge
Level 2 - Hydraulic Engineering Analysis
Figure 10.29. Equal conveyance tubes of approach section
Figure 10.31. Velocity distribution at bridge crossing
Figure 10.32. Plot of total scour for example problem
Figure 10.33. Revised plot of total scour for example problem
Figure 10.34. Three-day hydrograph for BRI-STARS analysis
Figure 10.36 Comparison cross-sections from BRI-STARS
Figure 10.37. BRI-STARS model profiles for steady-state run
REFERENCES - 4_0104910573
REFERENCES (cont.) - 4_0104910574
REFERENCES (cont.) - 4_0104910575
REFERENCES (cont.) - 4_0104910576
REFERENCES (cont.) - 4_0104910577
REFERENCES (cont.) - 4_0104910578
REFERENCES (cont.) - 4_0104910579
REFERENCES (cont.) - 4_0104910580
REFERENCES (cont.) - 4_0104910581
REFERENCES (cont.) - 4_0104910582
REFERENCES (cont.) - 4_0104910583
REFERENCES (cont.) - 4_0104910584
REFERENCES (cont.) - 4_0104910585
REFERENCES (cont.) - 4_0104910586
REFERENCES (cont.) - 4_0104910587
REFERENCES (cont.) - 4_0104910588
REFERENCES (cont.) - 4_0104910589
REFERENCES (cont.) - 4_0104910590
REFERENCES (cont.) - 4_0104910591
REFERENCES (cont.) - 4_0104910592
REFERENCES (cont.) - 4_0104910593
REFERENCES (cont.) - 4_0104910594
REFERENCES (cont.) - 4_0104910595
REFERENCES (cont.) - 4_0104910596
REFERENCES (cont.) - 4_0104910597
REFERENCES (cont.) - 4_0104910598
REFERENCES (cont.) - 4_0104910599
REFERENCES (cont.) - 4_0104910600
APPENDIX A. Metric System, Conversion Factors, and Water Properties
Table A.1. Overview of SI Units.
Table A.3. Derived Units With Special Names
Table A.4. Useful Conversion Factors
Table A.4. Useful Conversion Factors (cont.)
Table A6. Physical Properties of Water at Atmospheric Pressure in SI Units
Table A7. Physical Properties of Water at Atmospheric Pressure in English Units
Table A8. Sediment Particles Grade Scale
Table A9. Common Equivalent Hydraulic Units
APPENDIX B. Analysis of Selected Sediment Transport Relationships
EVALUATION OF SELECTED SEDIMENT TRANSPORT EQUATIONS
Table B.1a. Field Data
Table B.1b. Laboratory Data
Table B3. Summary of Ten Sediment Transport Relations
Analysis of Sediment Transport Relations
Figure B.1. Predicted versus measured total bed-material transport considering four classifications of size of bed materials
Figure B.1. Predicted versus measured total bed-material transport considering four classifications of size of bed materials (cont.) - 4_0104910618
Figure B.1. Predicted versus measured total bed-material transport considering four classifications of size of bed materials (cont.) - 4_0104910619
Figure B.1. Predicted versus measured total bed-material transport considering four classifications of size of bed materials (cont.) - 4_0104910620
Figure B.2. Comparison Cppm computed and measured for three river sets
Figure B.2. Comparison Cppm computed and measured for three river sets (cont.) - 4_0104910622
Figure B.2. Comparison Cppm computed and measured for three river sets (cont.) - 4_0104910623
Medium to very coarse sand-bed rivers (0.250 mm < D50 < 2.00 mm)
Table B.4. Summary of Applicability of Selected Sediment Transport Relations
Table B.5. Coefficient and Exponents of Equation B.3
Figure B.3. Relation of unit sediment discharge qs from measured and computed results using Equation B.5 for 2503 sets of field data
Table B.7. Range of Data Utilized by Posada to Develop Equation B.5
LAURSEN AND MODIFIED LAURSEN EQUATIONS
Figure B.4. Comparison of measured qs and computed qs using Posada and Kodoatie equations for various river-bed materials, data from Group 1
Figure B.5. Comparison of measured qs and computed qs using Posada and Kodoatie equations for various river-bed materials, data from Group 2
Figure B.6. Modifications of Laursen's (1958) Graph
Figure B.7. Plotting V*/ωi and f(V*/ωi) for data from Group 1 with Laursen's Equation
Table B.11. Value of "a" in Equation B.10 for Various Sizes of Bed Material.
Figure B.8. Proposed graph by Kodoatie using Equation B.10
Medium to Very Coarse Sand-Bed Rivers
Very Fine to Fine Sand-Bed Rivers
RANGE OF DATA FOR VALIDATION
Bed Material Size
River Size
APPENDIX C. Index
APPENDIX C. Index (cont.) - 4_0104910642
APPENDIX C. Index (cont.) - 4_0104910643
APPENDIX C. Index (cont.) - 4_0104910644
APPENDIX C. Index (cont.) - 4_0104910645
APPENDIX C. Index (cont.) - 4_0104910646
4_010491
