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# EM-1110-2-1601 Hydraulic Design of Flood Control Channels

 Author(s): USACE Publisher: USACE Year: 1991 Link: PDF, USACE Publications Subjects: Channels, Flood control Size: 183 pages, 2.29 MB

This manual presents procedures for the design analysis and criteria of design for improved channels that carry rapid and/or tranquil flows.

Procedures are presented without details of the theory of the hydraulics involved since these details can be found in any of various hydraulic textbooks and publications available to the design engineer. Theories and procedures in design, such as flow in curved channels, flow at bridge piers, flow at confluences, and side drainage inlet structures, that are not covered fully in textbooks are discussed in detail with the aid of Hydraulic Design Criteria (HDC) charts published by the US Army Engineer Waterways Experiment Station (USAEWES).

The charts and other illustrations are included in Appendix B to aid the designer. References to HDC are by HDC chart number. The use of models to develop and verify design details is discussed briefly. Typical calculations are presented to illustrate the principles of design for channels under various conditions of flow. Electronic computer programming techniques are not treated in this manual. However, most of the basic hydraulics presented herein can be adapted for computer use as illustrated in Appendix D.

# HEC-15: Permissible Shear Stress

HEC-15 Section 6.2 – PERMISSIBLE SHEAR STRESS

Values for permissible shear stress for riprap and gravel linings are based on research conducted at laboratory facilities and in the field. The values presented here are judged to be conservative and appropriate for design use. Permissible shear stress is given by the following equation:

 τp = F*.(γs – γ).D50 (6.7)

where,

• τp = permissible shear stress, N/m2 (lb/ft2)
• F* = Shield’s parameter, dimensionless
• γs = specific weight of the stone, N/m3 (lb/ft3)
• γ = specific weight of the water, 9810 N/m3 (62.4 lb/ft3)
• D50 = mean riprap size, m (ft)

Typically, a specific weight of stone of 25,900 N/m3 (165 lb/ft3) is used, but if the available stone is different from this value, the site-specific value should be used.

Recalling Equation 3.2,

τp ≥ SF.τd

and Equation 3.1,

τd = γ.d.So

Equation 6.7 can be written in the form of a sizing equation for D50 as shown below:

 D50 ≥ (SF.d.So)/(F*.(SG – 1)) (6.8)

where,

• d = maximum channel depth, m (ft)
• SG = specific gravity of rock (γs/γ), dimensionless

Changing the inequality sign to an equality gives the minimum stable riprap size for the channel bottom. Additional evaluation for the channel side slope is given in Section 6.3.2.

Equation 6.8 is based on assumptions related to the relative importance of skin friction, form drag, and channel slope. However, skin friction and form drag have been documented to vary resulting in reports of variations in Shield’s parameter by different investigators, for example Gessler (1965), Wang and Shen (1985), and Kilgore and Young (1993). This variation is usually linked to particle Reynolds number as defined below:

 Re = V*.D50/ν (6.9)

where,

• Re = particle Reynolds number, dimensionless
• V* = shear velocity, m/s (ft/s)
• ν = kinematic viscosity, 1.131×10-6 m2/s at 15.5 deg C (1.217×10-5 ft2/s at 60 deg F)

Shear velocity is defined as:

 V* = √(g.d.S) (6.10)

where,

• g = gravitational acceleration, 9.81 m/s2 (32.2 ft/s2)
• d = maximum channel depth, m (ft)
• S = channel slope, m/m (ft/ft)

Higher Reynolds number correlates with a higher Shields parameter as is shown in Table 6.1. For many roadside channel applications, Reynolds number is less than 4×104 and a Shields parameter of 0.047 should be used in Equations 6.7 and 6.8. In cases for a Reynolds number greater than 2×105, for example, with channels on steeper slopes, a Shields parameter of 0.15 should be used. Intermediate values of Shields parameter should be interpolated based on the Reynolds number.

Table 6.1. Selection of Shields’ Parameter and Safety Factor
Reynolds number F* SF
≤ 4×104 0.047 1.0
4×104<Re<2×105 Linear interpolation Linear interpolation
≥ 2×105 0.15 1.5

Higher Reynolds numbers are associated with more turbulent flow and a greater likelihood of lining failure with variations of installation quality. Because of these conditions, it is recommended that the Safety Factor be also increased with Reynolds number as shown in Table 6.1. Depending on site-specific conditions, safety factor may be further increased by the designer, but should not be decreased to values less than those in Table 6.1.

As channel slope increases, the balance of resisting, sliding, and overturning forces is altered slightly. Simons and Senturk (1977) derived a relationship that may be expressed as follows:

 D50 ≥ SF•d•S•Δ/(F*•(SG – 1)) (6.11)

where,

• Δ = function of channel geometry and riprap size.

The parameter Δ can be defined as follows (see HEC-15 Appendix D for the derivation):

 Δ = (K1•(1 + sin(α + β)•tan Φ)/(2•(cosθ•tanΦ  – SF•sinθ•cosβ)) (6.12)

where,

• α = angle of the channel bottom slope
• β = angle between the weight vector and the weight/drag resultant vector in the plane of the side slope
• θ = angle of the channel side slope
• Φ = angle of repose of the riprap.

Finally, β is defined by:

 β = tan-1(cosα/(2•sinθ/(η•tanΦ) + sinα)) (6.13)

where,

• η = stability number.

The stability number is calculated using:

 η = τs/(F*•(Υs – Υ)•D50) (6.14)

Riprap stability on a steep slope depends on forces acting on an individual stone making up the riprap. The primary forces include the average weight of the stones and the lift and drag forces induced by the flow on the stones. On a steep slope, the weight of a stone has a significant component in the direction of flow. Because of this force, a stone within the riprap will tend to move in the flow direction more easily than the same size stone on a milder gradient. As a result, for a given discharge, steep slope channels require larger stones to compensate for larger forces in the flow direction and higher shear stress.

The size of riprap linings increases quickly as discharge and channel gradient increase. Equation 6.11 (not shown) is recommended when channel slope is greater than 10 percent and provides the riprap size for the channel bottom and sides. Equation 6.8 is recommended for slopes less than 5 percent. For slopes between 5 percent and 10 percent, it is recommended that both methods be applied and the larger size used for design. Values for safety factor and Shields parameter are taken from Table 6.1 for both equations.

# Manning’s n For Riprap-Lined Channels

HEC-15 Section 6.1 – MANNING’S ROUGHNESS

Manning’s roughness is a key parameter needed for determining the relationships between depth, velocity, and slope in a channel. However, for gravel and riprap linings, roughness has been shown to be a function of a variety of factors including flow depth, D50, D84, and friction slope, Sf. A partial list of roughness relationships includes Blodgett (1986a), Limerinos (1970), Anderson, et al. (1970), USACE (1994), Bathurst (1985), and Jarrett (1984). For the conditions encountered in roadside and other small channels, the relationships of Blodgett and Bathurst are adopted for this manual.

Blodgett (1986a) proposed a relationship for Manning’s roughness coefficient, n, that is a function of the flow depth and the relative flow depth (da/D50) as follows (Equation 6.1):

 n = α⋅da1/6/(2.25 + 5.23⋅log(da/D50)) (6.1)

where,

• n = Manning’s roughness coefficient, dimensionless
• da = average flow depth in the channel, m (ft)
• D50 = median riprap/gravel size, m (ft)
• α = unit conversion constant, 0.319 (SI) and 0.262 (CU)

Equation 6.1 is applicable for the range of conditions where 1.5 ≤ da/D50 ≤ 185. For small channel applications, relative flow depth should not exceed the upper end of this range.

Some channels may experience conditions below the lower end of this range where protrusion of individual riprap elements into the flow field significantly changes the roughness relationship. This condition may be experienced on steep channels, but also occurs on moderate slopes. The relationship described by Bathurst (1991) addresses these conditions and can be written as follows (See Appendix D for the original form of the equation):

 n = α⋅da1/6 / (√g⋅f(Fr)⋅f(REG)⋅f(CG)) (6.2)

where,

• da = average flow depth in the channel, m (ft)
• g = acceleration due to gravity, 9.81 m/s2 (32.2 ft/s2)
• Fr = Froude number
• REG = roughness element geometry
• CG = channel geometry
• α = unit conversion constant, 1.0 (SI) and 1.49 (CU)

Equation 6.2 is a semi-empirical relationship applicable for the range of conditions where 0.3<da/D50<8.0. The three terms in the denominator represent functions of Froude number, roughness element geometry, and channel geometry given by the following equations:

 f(Fr) = (0.28⋅Fr/b)log(0.755/b) (6.3) f(REG) =13.434⋅(T/D50)0.492b1.025⋅(T/D50)0.118 (6.4) f(CG) = (T/da)-b (6.5)

where,

• T = channel top width, m (ft)
• b = parameter describing the effective roughness concentration.

The parameter b describes the relationship between effective roughness concentration and relative submergence of the roughness bed. This relationship is given by:

 b = 1.14⋅(D50/T)0.453(da/D50)0.814 (6.6)

Equations 6.1 and 6.2 both apply in the overlapping range of 1.5 ≤ da/D50 ≤ 8. For consistency and ease of application over the widest range of potential design situations, use of the Blodgett equation (6.1) is recommended when 1.5 ≤ da/D50. The Bathurst equation (6.2) is recommended for 0.3<da/D50<1.5.

As a practical problem, both Equations 6.1 and 6.2 require depth to estimate n while n is needed to determine depth setting up an iterative process.

# Trapezoidal Channel: Manning’s n

Caltrans Highway Design Manual

Commonly accepted values for Manning’s roughness coefficient are provided in Table 866.3A. The tabulated values take into account deterioration of the channel lining surface, distortion of the grade line due to unequal settlement, construction joints and normal surface irregularities. These average values should be modified to satisfy any foreseeable abnormal conditions (Reference: Caltrans Highway Design Manual Index 866.3(3)).

Table 866.3A Average Values for Manning’s n
Type of Channel n value
Unlined Channels:
Clay Loam 0.023
Sand 0.020
Gravel 0.030
Rock 0.040
Lined Channels:
Portland Cement Concrete 0.014
Sand 0.020
Gravel 0.030
Rock 0.040
Lined Channels:
Portland Cement Concrete 0.014
Air Blown Mortar (troweled) 0.012
Air Blown Mortar (untroweled) 0.016
Air Blown Mortar (roughened) 0.025
Asphalt Concrete 0.016 – 0.018
Sacked Concrete 0.025
Pavement and Gutters:
Portland Cement Concrete 0.013 – 0.015
Hot Mix Asphalt Concrete 0.016 – 0.018
Depressed Medians:
Earth (without growth) 0.016 – 0.025
Earth (with growth) 0.05
Gravel (d50 = 1 in. flow depth < 6 in.) 0.040
Gravel (d50 = 2 in. flow depth < 6 in.) 0.056
NOTES:
For additional values of n, see HEC No. 15, Tables 2.1 and 2.2, and “Introduction to Highway Hydraulics”, Hydraulic Design Series No. 4, FHWA Table 14. (No such table. Table B-2 provides n values.)

HEC-15

Section 2.1.3 Resistance to Flow

For rigid channel lining types, Manning’s roughness coefficient, n, is approximately constant. However, for very shallow flows the roughness coefficient will increase slightly. (Very shallow is defined where the height of the roughness is about one-tenth of the flow depth or more.)

For a riprap lining, the flow depth in small channels may be only a few times greater than the diameter of the mean riprap size. In this case, use of a constant n value is not acceptable and consideration of the shallow flow depth should be made by using a higher n value.

Tables 2.1 and 2.2 provide typical examples of n values of various lining materials. Table 2.1 summarizes linings for which the n value is dependent on flow depth as well as the specific properties of the material. Values for rolled erosion control products (RECPs) are presented to give a rough estimate of roughness for the three different classes of products. Although there is a wide range of RECPs available, jute net, curled wood mat, and synthetic mat are examples of open-weave textiles, erosion control blankets, and turf reinforcement mats, respectively. Chapter 5 contains more detail on roughness for RECPs.

Table 2.2 presents typical values for the stone linings: riprap, cobbles, and gravels. These are highly depth-dependent for roadside channel applications. More in-depth lining-specific information on roughness is provided in Chapter 6. Roughness guidance for vegetative and gabion mattress linings is in Chapters 4 and 7, respectively.

Table 2.1. Typical Roughness Coefficients for Selected Linings
Manning’s n1
Lining Category2 Lining Type Maximum Typical Minimum
Rigid Concrete 0.015 0.013 0.011
Grouted Riprap 0.040 0.030 0.028
Stone Masonry 0.042 0.032 0.030
Soil Cement 0.025 0.022 0.020
Asphalt 0.018 0.016 0.016
Unlined Bare Soil 0.025 0.020 0.016
Rock Cut (smooth, uniform) 0.045 0.035 0.025
RECP Open-weave textile 0.028 0.025 0.022
Erosion control blankets 0.045 0.035 0.028
Turf reinforement mat 0.036 0.030 0.024
1Based on data from Kouwen, et al. (1980), Cox, et al. (1970), McWhorter, et al. (1968) and Thibodeaux (1968).
2Minimum value accounts for grain roughness. Typical and maximum values incorporate varying degrees of form roughness.

Table 2.2. Typical Roughness Coefficients for Riprap, Cobble, and Gravel Linings
Manning’s n for Selected Flow Depths1
Lining Category Lining Type 0.15 m (0.5 ft) 0.50 m (1.6 ft) 1.0 m (3.3 ft)
Gravel Mulch D50 = 25 mm (1 in.) 0.040 0.033 0.031
D50 = 50 mm (2 in.) 0.056 0.042 0.038
Cobbles D50 = 0.1 m (0.33 ft) 2 0.055 0.047
Rock Riprap D50 = 0.15 m (0.5 ft) 2 0.069 0.056
D50 = 0.1 m (0.33 ft) 2 2 0.080
1Based on Equation 6.1 (Blodgett and McConaughy, 1985). Manning’s n estimated assuming a trapezoidal channel with 1:3 side slopes and 0.6 m (2 ft) bottom width.
2Shallow relative depth (average depth to D50 ratio less than 1.5) requires use of Equation 6.2 (Bathurst, et al., 1981) and is slope-dependent. See Section 6.1.

# HDS-4 Introduction To Highway Hydraulics

 Author(s): James D. Schall, Everett V. Richardson, and Johnny L. Morris Publisher: FHWA Year: 2008 Links: PDF Subjects: Hydrology, hydraulics, highway drainage, open channels, roadside ditches, pavement drainage, inlets, conduits, culverts, storm drains, energy dissipators

Hydraulic Design Series No. 4 provides an introduction to highway hydraulics. Hydrologic techniques presented concentrate on methods suitable to small areas, since many components of highway drainage (culverts, storm drains, ditches, etc.) service primarily small areas. A brief review of fundamental hydraulic concepts is provided, including continuity, energy, momentum, hydrostatics, weir flow and orifice flow.

The document then presents open channel flow principles and design applications, followed by a parallel discussion of closed conduit principles and design applications. Open channel applications include discussion of stable channel design and pavement drainage. Closed conduit applications include culvert and storm drain design. Examples are provided to help illustrate important concepts. An overview of energy dissipators is provided and the document concludes with a brief discussion of construction, maintenance and economic issues.

As the title suggests, Hydraulic Design Series No. 4 provides only an introduction to the design of highway drainage facilities and should be particularly useful for designers and engineers without extensive drainage training or experience. More detailed information on each topic discussed is provided by other Hydraulic Design Series and Hydraulic Engineering Circulars.

This publication is an update of the third edition. Revisions were necessary to reflect new information given in the third edition of HEC-14 (Hydraulic Design of Energy Dissipators for Culverts and Channels), the third edition of HEC-15 (Design of Roadside Channels with Flexible Linings), and the third edition HEC-22 (Urban Drainage Design Manual).

# HEC-15 Design of Roadside Channels, 3rd Ed

 Author(s): Kilgore RT, Cotton GK Publisher: FHWA Year: 2005 Links: PDF Subjects: channel lining, channel stabilization, tractive force, resistance, permissible shear stress, vegetation, riprap, manufactured linings, RECP, gabions

Flexible linings provide a means of stabilizing roadside channels. Flexible linings are able to conform to changes in channel shape while maintaining overall lining integrity. Long-term flexible linings such as riprap, gravel, or vegetation (reinforced with synthetic mats or unreinforced) are suitable for a range of hydraulic conditions. Unreinforced vegetation and many transitional and temporary linings are suited to hydraulic conditions with moderate shear stresses.

Design procedures are given for four major categories of flexible lining: vegetative linings; manufactured linings (RECPs); riprap, cobble, gravel linings; and gabion mattress linings. Design procedures for composite linings, bends, and steep slopes are also provided. The design procedures are based on the concept of maximum permissible tractive force. Methods for determination of hydraulic resistance applied shear stress as well as permissible shear stress for individual linings and lining types are presented.

This edition includes updated methodologies for vegetated and manufactured lining design that addresses the wide range of commercial products now on the market. This edition also includes a unified design approach for riprap integrating alternative methods for estimating hydraulic resistance and the steep slope procedures. Other minor updates and corrections have been made. This edition has been prepared using dual units.