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Hydraulics Engineering


Design of Roadside Channels with Flexible Linings
Hydraulic Engineering Circular Number 15, Third Edition

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Table of contents

Technical Report Documentation Page
List of Tables
List of Figures
List of Symbols
Chapter 1: Introduction
1.1 Scope and Applicability
1.2 Background
1.3 Rigid Linings
1.4 Flexible Linings
1.4.1 Long-term Flexible Linings Vegetation Cobble Lining Rock Riprap Wire-Enclosed Riprap Turf Reinforcement
1.4.2 Transitional and Temporary Flexible Linings Bare Soil Gravel Mulch Vegetation (Annual Grass) Open-weave Textile (OWT) Erosion control blanket (ECB)
Chapter 2: Design Concepts
2.1 Open Channel Flow
2.1.1 Type of Flow
2.1.2 Normal Flow Depth
2.1.3 Resistance to Flow
2.2 Shear Stress
2.2.1 Equilibrium Concepts
2.2.2 Applied Shear Stress
2.2.3 Permissible Shear Stress
2.3 Design Parameters
2.3.1 Design Discharge Frequency
2.3.2 Channel Cross Section Geometry
2.3.3 Channel Slope
2.3.4 Freeboard
Chapter 3: General Design Procedure
3.1 Straight Channels
3.2 Side Slope Stability
3.3 Composite Lining Design
3.4 Stability in Bends
3.5 Steep Slope Design
3.6 Maximum Discharge Approach
CHAPTER 4: Vegetative Lining and Bare Soil Design
4.1 Grass Lining Properties
4.2 Manning's Roughness
4.3 Permissible Shear Stress
4.3.1 Effective Shear Stress
4.3.2 Permissible Soil Shear Stress Non-cohesive Soils Cohesive Soils
4.3.3 Permissible Vegetation/Soil Shear Stress
4.4 Maximum Discharge Approach
4.5 Turf Reinforcement with Gravel/Soil Mixture
Chapter 5: Manufactured (RECP) Lining Design
5.1 RECP Properties
5.2 Manning's Roughness
5.3 Permissible Shear Stress
5.3.1 Effective Shear Stress
5.3.2 Permissible RECP/Soil Shear Stress
5.4 Turf Reinforcement with RECPS
5.4.1 Testing Data and Protocols
5.4.2 Turf-Reinforcement Mat Cover Factor
Chapter 6: Riprap, Cobble, and Gravel Lining Design
6.1 Manning's Roughness
6.2 Permissible Shear Stress
6.3 Design Procedure
6.3.1 Basic Design
6.3.2 Side Slopes
6.3.3 Bends
6.4 ADditional Considerations
6.4.1 Freeboard and Slope Changes
6.4.2 Riprap Gradation, Angularity, and Thickness
6.4.3 Riprap Filter Design
Chapter 7: Gabion Lining Design
7.1 Manning's Roughness
7.2 Permissible Shear Stress
7.3 Design Procedure
7.4 Additional Considerations
Appendix A: Metric System, Conversion Factors, and Water Properties
Appendix B: Channel Geometry Equations
Appendix C: Resistance Equations
C.1 General Relationships
C.2 Lining Flow Resistance
C.3 Bathurst Resistance Equation
Appendix D: Riprap Stability on a Steep Slope
Appendix E: Fall-Board Test for Grass Density-Stiffness Parameter, Cs
Appendix F: Shear Stress Relationship for RECPS

List of Tables

2.1 Typical Roughness Coefficients for Selected Linings
2.2 Typical Roughness Coefficients for Riprap, Cobble, and Gravel Linings
2.3 Typical Permissible Shear Stresses for Bare Soil and Stone Linings
4.1 Retardance Classification of Vegetal Covers
4.2 Density-stiffness Coefficient, Cs
4.3 Grass Roughness Coefficient, Cn
4.4 (SI). Grass Roughness Coefficient, Cn, for SCS Retardance Classes
4.4 (CU). Grass Roughness Coefficient, Cn, for SCS Retardance Classes
4.5 Cover Factor Values for Uniform Stands of Grass
4.6 Coefficients for Permissible Soil Shear Stress (USDA, 1987)
4.7 Gravel Gradation Table, Percentages Passing Nominal Size Designations
4.8 Gravel Application Rates for Fine Grain Soils
5.1 Manufactured (RECP) Linings
5.2 Index Tests for RECPs
5.3 Bench-Scale Tests for RECPs
5.4 Standard n value versus Applied Shear
5.5 TRM Protocol Checklist
6.1 Selection of Shields' Parameter and Safety Factor
6.2 Maximum AOS for Geotextile Filters (FHWA, 1998)
A.1 Overview of SI Units
A.2 Relationship of Mass and Weight
A.3 Derived Units With Special Names
A.4 Useful Conversion Factors
A.5 Prefixes
A.6 Physical Properties of Water at Atmospheric Pressure in SI Units
A.7 Physical Properties of Water at Atmospheric Pressure in English Units
A.8 Sediment Particles Grade Scale
A.9 Common Equivalent Hydraulic Units
C.1 Resistance Equation Coefficients
C.2 Relative Roughness Parameters for Vegetation

List of Figures

1.1. Rigid Concrete Channel Lining
1.2. Vegetative Channel Lining
1.3. Cobble Channel Lining
1.4. Riprap Channel Lining
1.5. Wire-Enclosed Riprap
1.6. Installed Wire-Enclosed Riprap
1.7. TRM Profile with Vegetation/Soil/TRM Matrix (Source: ECTC)
1.8. Installed TRM Lining Before Vegetation (Source: ECTC)
1.9. Open Weave Textile Lining
1.10. Installed Open Weave Textile Channel Lining
1.11. Erosion Control Blanket (ECB) Lining (Source: ECTC)
2.1. Typical Distribution of Shear Stress
3.1. Flexible Channel Lining Design Flow Chart
3.2. Composite Lining Design Example
3.3. Shear Stress Distribution in a Channel Bend (Nouh and Townsend, 1979)
3.4. Location Sketch of Flexible Linings for Bend Example
4.1. Cohesive Soil Permissible Shear Stress
6.1. Angle of Repose of Riprap in Terms of Mean Size and Shape of Stone
6.2. Gradations of Granular Filter Blanket for Design Example
C.1a. Relative Roughness Relationships for Excellent Vegetated Conditions
C.1b. Relative Roughness Relationships for Good Vegetated Conditions
C.1c. Relative Roughness Relationships for Poor Vegetated Conditions
C.2. Relationship between Cl and Cs
D.1. Hydraulic Forces Acting on a Riprap Element
E.1. Schematic of the Fall-board Test (after Kouwen, 1988)
F.1. Soil Shear versus Applied Shear to the Manufactured Lining
F.2. Effective Shear on the Soil for Four RECP Linings

List of Symbols

A= Cross-sectional area of flow prism, m2 (ft2)

AOS = Measure of the largest effective opening in an engineering fabric, as measured by the size of a glass bead where five percent or less by weight will pass through the fabric

B = Bottom width of trapezoidal channel, m (ft)

Cf = cover factor

CG = Channel Geometry

D50 = Particle size of gradation, of which 50 percent of the mixture is finer by weight, m (ft)

D85 = Particle size of gradation, of which 85 percent of the mixture is finer by weight, m (ft)

d = Depth of flow in channel for the design flow, m (ft)

da = Average depth of flow in channel, m (ft)

Δd = Change in depth due to super elevation of flow in a bend, m (ft)

dn = Depth of normal or uniform flow, m (ft)

Fd = Drag force in direction of flow

FL = Lift force

Fr = Froude number, ratio of inertial forces to gravitational force in a system

g = gravitational acceleration, m/s2 (ft/s2)

h = Average height of vegetation, mm (in)

Kb = ratio of maximum shear stress in bend to maximum shear stress upstream from bend

K1 = ratio of channel side shear to bottom shear stress

K2 = tractive force ratio

ks = roughness height, mm (in)

l = Moment arms of forces acting on riprap in a channel

Lp = protected length downstream from bend, m (ft)

MEI = Stiffness factor, N·m2 (lb·ft2)

n = Manning's roughness coefficient

ne = composite channel lining equivalent Manning's n

P = Wetted perimeter of flow prism, m (ft)

PL = Wetted perimeter of low-flow channel, m (ft)

PC = Point on curve

PT = Point on tangent

Q = Discharge, flow rate, m3/s (ft3/s)

R = Hydraulic radius, A/P, m (ft)

RC = Mean radius of channel center line, m (ft)

REG = Roughness element geometry

So = Average channel gradient

Sf = Energy (friction) gradient

SF = Safety factor

S50 = Mean value of the short axis lengths of the roughness element, m (ft)

T = Channel top width (water surface), m (ft)

V = Mean channel velocity, m/s (ft/s)

V* = Shear velocity, m/s (ft/s)

WS = Weight of riprap element, N (lb)

Y50 = Mean value of the average of the long and median axes of the roughness element, m (ft)

Z = Side slope; cotangent of angle measured from horizontal, Z = tan-1θ

α = Unit conversion constant for SI and CU; equation specific

αc = Angle of channel bottom slope

β = Angle between weight vector and the resultant in the plane of the side slope

γ = Unit weight of water, N/m3 (lb/ft3)

δ = Angle between the drag vector and resultant in the plane of the side slope

θ = Angle of side slope (bank) measured from horizontal

φ = Angle of repose of coarse, noncohesive material, degrees

η = Stability number

η' = Stability number for side slopes

σ = Bed material gradation

τb = Shear stress in a bend, N/m2 (lb/ft2)

τd = Shear stress in channel at maximum depth, d, N/m2 (lb/ft2)

τl = Shear stress on a RECP that results in 12.5 mm (0.5 in) of erosion in 30 minutes

τo = Mean boundary shear stress, N/m2 (lb/ft2)

τp = Permissible shear stress, N/m2 (lb/ft2)

τs = Shear stress on sides of channel, N/m2 (lb/ft2)


Angle of Repose: Angle of slope formed by particulate material under the critical equilibrium condition of incipient motion.

Apparent Opening Size (AOS): Measure of the largest effective opening in an engineering fabric, as measured by the size of a glass bead where five percent or less by weight will pass through the fabric (formerly called the equivalent opening size, EOS).

Compaction: The closing of pore spaces among the particles of soil and rock, generally caused by running heavy equipment over the soil during construction.

Customary Units (CU): Foot-pound system of units often referred to as English units.

Depth of Flow: Vertical distance from the bottom of a channel to the water surface, also referred to as the maximum depth of flow.

Design Discharge: Discharge at a specific location defined by an appropriate return period to be used for design purposes.

Engineering Fabric: Permeable textile (or filter fabric) used below riprap to prevent piping and permit natural seepage to occur.

Erosion Control Blanket (ECB): A degradable material, composed primarily of processed natural organic materials, manufactured or fabricated into rolls designed to reduce soil erosion and assist in the growth, establishment and protection of vegetation.

Filter Blanket: One or more layers of graded noncohesive material placed below riprap to prevent soil piping and permit natural seepage to occur.

Freeboard: Vertical distance from the water surface to the top of the channel at design condition.

Gabion: Compartmented rectangular containers made of galvanized steel hexagonal wire mesh and filled with stone.

Hydraulic Radius: Flow area divided by wetted perimeter.

Hydraulic Resistance: Resistance encountered by water as it moves through a channel, commonly described by Manning's n.

Hydrostatic Pressure: Pressure exerted at a depth below the water surface for flow at constant velocity or at rest.

Incipient Motion: Conditions at that point in time when any increase in factors responsible for particle movement causes motion.

Lining, Composite: Combination of lining materials in a given cross section (e.g., riprap in low-flow channel and vegetated side slopes).

Lining, Flexible: Lining material with the capacity to adjust to settlement typically constructed of a porous material that allows infiltration and exfiltration.

Lining, Long-term: Lining designed for long-term use. Although many flexible linings do have limited functional life spans, their durability is compatible with the service life of the drainageway.

Lining, Rigid: Lining material with no capacity to adjust to settlement constructed of nonporous material with smooth finish that provides a large conveyance capacity (e.g. concrete, soil cement).

Lining, Temporary: Lining designed for an interim condition, typically serving the needs of construction sequencing. Temporary linings will be removed.

Lining, Transitional: Lining designed for an interim condition, typically to assist in development of a permanent vegetative lining. Transitional linings will not be removed.

Normal Depth: Depth of a uniform channel flow.

Open Weave Textile (OWT): A temporary degradable ECB composed of natural or polymer yarns woven into a matrix used to provide erosion control and facilitate vegetation establishment.

Permeability: Property of a soil that enables water or air to move through it.

Retardance Classification: Qualitative description of the resistance to flow offered by various types of vegetation.

Riprap: Broken rock, cobbles, or boulders placed on side slopes or in channels for protection against the action of water.

Rolled Erosion Control Product (RECP): A temporary degradable or long-term non-degradable material manufactured or fabricated into rolls designed to reduce soil erosion and assist in the growth, establishment, and protection of vegetation.

Rundown: Steep, generally short, conveyance channel used adjacent to bridge abutments or other embankment locations.

Roadside Channel: Stabilized drainageway used to collect water from the roadway and adjacent areas and to deliver it to an inlet or main drainageway.

Shear Stress: Stress developed on the wetted area of the channel for a given hydraulic conditions that acts in the direction of the flow; stress is force per unit wetted area.

Shear Stress, Permissible: Force at which the channel lining will fail.

Side Slope: Slope of the sides of a channel defined as the run corresponding to a unit rise; represented by Z as in 1:Z (vertical:horizontal).

Superelevation: Local increase in water surface on the outside of a bend.

System International (SI): Meter kilogram second system of units often referred to as metric units.

Tractive Force: Force developed due to the shear stress acting on the perimeter of a channel section that acts in the direction of flow on the channel bottom; equals the shear stress on the channel section multiplied by the wetted channel area.

Turf Reinforcement Mat (TRM):A non-degradable RECP composed of UV stabilized synthetic fibers, filaments, netting and/or wire mesh processed into a three-dimensional matrix. TRMs provide sufficient thickness, strength and void space to permit soil filling and establishment of grass roots within the matrix.

Uniform flow: The flow condition where the rate of head loss due to friction is equal to bottom slope of the channel, that is, Sf = So, where Sf is the friction slope and So is the bottom slope.

Velocity, Mean: Discharge divided by the area of flow.

Velocity, Permissible: Mean velocity that will not cause serious erosion of the channel.


First Edition

Mr. Jerome M. Normann of Federal Highway Administration wrote the first edition of this Hydraulic Engineering Circular. FHWA reviewers included Frank Johnson, Dennis Richards and Albert Lowe of the Hydraulics Branch. The manual was dated October 1975.

Second Edition

Dr. Y. H. Chen and Mr. G. K. Cotton of Simons, Li & Associates wrote the second edition of this Hydraulic Engineering Circular. It was published as report number FHWA-IP-87-7 dated April 1988 under contract number DTFH61-84-C-00055. The FHWA project managers were John M. Kurdziel and Thomas Krylowski. Philip L. Thompson, Dennis L. Richards, and J. Sterling Jones were FHWA technical assistants

Third Edition

Mr. Roger T. Kilgore and Mr. George K. Cotton wrote this third edition of this Hydraulic Engineering Circular. The authors appreciate guidance of FHWA technical project manager, Mr. Dan Ghere and the technical review comments of Jorge Pagan, Joe Krolak, Brian Beucler, Sterling Jones, and Philip Thompson.

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Updated: 09/22/2014

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