design channel

7/26/2019 Design Channel

1/22

MODULE 3_____________________________________________________

OPEN CHANNEL DESIGN

Introduction

An open channel is defined as any conveyance system where a liquid is movedunder the influence of gravity in the presence of an air-water interface. Open channel flowoccurs in natural water courses, channels, diversions, and culverts. In all of these cases,the energy source causing the water to move is gravity; water flows down hill. Thischapter will discuss the principles and equations needed to properly analyze and designopen channels used to convey water.

There are two accepted methods of designing open channels; (1) to limit theaverage water velocity, or (2) limit the tractive force (shear stress) on the channel lining.Depth of water and channel slope tend to increase both of these parameters thus causingthe channel lining and the soil under the lining to erode.

The continuity equation

Q AV= (1)

where Q is the discharge in ft3/sec (cfs), A is the channels cross-sectional area of flow in

ft2, and V is the average flow velocity perpendicular to the cross-sectional area in ft/sec or

fps. The cross-sectional area used in equation 1, is the area through which the water isflowing as it moves down a channel, see Figure 3-1.

Figure 3-1. Typical Channel Cross Section.

The velocity of water flowing in an open channel, has been described by Manning'sequation (Chow, 1959) as:

Wetted parameter

Cross-sectional area

F


2/22

Vn

R S=1 2

312

.486 (2)

where V is the average flow velocity in a channel in fps, n is the Mannings roughness

coefficient with units of ft1/6

, R is the hydraulic radius in ft, and S is the channels slope indirection of flow in ft/ft. The Mannings n is obtained from a descriptive statement of thechannel roughness. Typical design Mannings n values are shown in Table 3-1 andFigure 3-3. In both of these presentations the accepted design roughness Manning nvalues are given. Other references such as Chow (1959) and Schwab et al. (1966) showranges of Manning roughness coefficients for most of these conditions. There is nosubstitute for experience in interpreting and selecting values of n.

The parameter called the hydraulic radius, R is defined as:

R A

Wp= (3)

where the cross-sectional area, A and the wetted perimeter, Wpare defined in Figure 3-1.In a crude way the hydraulic radius can be thought of as the depth of flow.

The basic geometric relationships of cross-sectional area, wetted perimeter,hydraulic radius, and top width are given in Figure 3-2 for several common channelshapes. Most channels can be approximated by one of the five geometric shapes shownin Figure 3-2. The area, wetted perimeter, and hydraulic radius formulae are most oftenused in evaluation and design computations. The top width formulae are useful whendesigning a channel. Most of the parameters shown in the sketches and used in the

formulae are self explanatory; d is the water flow depth in feet, D is the total depth of thechannel in feet (D is equal to the flow depth, d plus freeboard) [D = d + F], b is thechannels bottom width in feet, t is the channel top width at the depth of water flow, T isthe channel top width at the channels total depth, D in feet, and z is the side slopeexpressed as a ratio as z(H):1(V). z is shown as being equal to the ratio e/d where e isthe horizontal distance and d is the vertical distance of the sloping side of a channel.

In general, Manning's equation can be used with the continuity equation to; (1)describe and evaluate the capacity and velocity of an existing channel, or (2) to determinethe required channel dimensions so the desired amount of water can be safelytransported.

Channel Freeboard

Freeboard is an unused portion of a structure created to hold or carry water.Freeboard is a way of adding or creating a factor of safety that is built into a water

a. Trapezoidal Cross-SectionCross-Sectional

Area, A

Wetted

Perimeter, Wp

Hydraulic Radius,

R = A/Wp Top Width


3/22

bd zd + 2 b d z+ +2 12 or

b dz+ 2 approximate

bd zd

b d z

+

+ +

2

22 1

or

bd zd

b dz

+

+

2

2

t b dz = + 2

T b Dz = + 2

b. Triangular Cross-SectionCross-Sectional

Area, AWetted

Perimeter, WpHydraulic Radius,

R = A/Wp Top Width

zd2 2 12d z + or

2dzapproximate

zd

d z

2

22 1+

or

d

2

t dz= 2

T Dz= 2

c. Parabolic Cross-Section

Cross-Sectional

Area, A

Wetted

Perimeter, Wp

Hydraulic Radius,

R = A/Wp Top Width

2

3

t d t

d

t+8

3

2

or

t approximate

t d

t d

2

2 215 4. +

or

2

3

d

t A

d=

0 67.

T t D d = ( / ) .0 5

d. Semi-CircularCross-Section

Cross-Sectional

Area, A

Wetted

Perimeter, Wp

Hydraulic Radius,

R = A/Wp Top Width

d2

2

d d

2

t d= 2

e. Rectangular Cross-SectionCross-Sectional

Area, A

Wetted

Perimeter, Wp

Hydraulic Radius,

R = A/Wp Top Width

bd db 2+

db

bd

2+

bt =

bT =

Figure 3-2. Channel cross-section notation and formulas for a. trapezoidal, b. triangular, c. parabolic,d. semi-circular, and e. rectangular channels. Freeboard = D - d. (Adapted from USDA-SCS1972c)

t

D d

d

t

t

dD

e

t

dD d

b

t

e

dD

b


4/22

structure. When a channel is properly designed, most of the channel depth is expected tofill with and carry water when the design discharge occurs.

Schwab et al. (1966) states that all channels should have a minimum freeboard of0.30 feet. A second, often used freeboard concept is to make freeboard a function of theflow velocity and the flow depth. PA-DER (1990) requires that channel freeboard begreater than or equal to

F Vd= 0 075. (4)

where V is the channel flow velocity in fps and d is the depth of water in feet. The bestmethod of determining channel freeboard is to prescribe the larger of these two criteria.

Channel Design Process

Open channels, whose flow is governed by Mannings and the continuity equationscan be evaluated or designed based on two different concepts. Failure of an openchannel can occur as a result of either of two conditions; (1) the channel does not havethe capacity to carry the water it was designed to carry and overbank flooding occurs, and(2) the channel lining does not have the ability to with stand the flow velocities or shearstresses on the channel lining and, therefore, erodes. One method is to determine themaximum permissible velocity of the channel lining and then select the channelsgeometry so that the velocity does not exceed this value. The second method is based onthe shear stress or tractive force acting on the channel lining. Again, based on the liningsability to withstand a tractive force, the channels geometry is selected so the tractive forcedoes not exceed the maximum allowable tractive force. Both of these methods will bepresented. But before these two design approaches are presented, lets take a look atchannel linings and define the design parameters for each lining.

Channel Linings

Open channels are typically distinguished by either their shape (trapezoidal,triangular, parabolic, circular, or rectangular) of their lining. How various shapes affect theflow of water in the channel will be discussed at length during the design section of themodule.

Channel linings can be classified several ways: (1) by the effect the lining has onthe friction or roughness of the channel, (2) by the effect the lining has on preventingchannel erosion, (3) by how quickly the lining will biodegrade and disappear, (4) by howhard and permanent the lining is, and (5) by how much maintenance the lining will need.


5/22

Table 3-1. Mannings roughness coefficients.(Summarized and adapted from Schwab et al.,1966, USDA-SCS, 1972b, and PA-DER, 1990).

T e of Channel and Linin Desi n nRi id Lined Channels

As halt 0.015

Concrete 0.017Concrete rubble 0.024Gabions 0.027Metal, smooth flumes 0.013Metal, corru ated 0.027Plastic lined 0.013Reno Mattress 0.025Shotcrete 0.016Wood, flumes 0.013

Earth Lined Channels Firm loam, fine sand, sand loam, silt loam 0.02Stiff cla , alluvial silts, colloidal 0.025Shales, hard ans, coarse ravels 0.025Graded silt or loam 0.03

Alluvial silt 0.02Earth, strai ht and uniform 0.023Earth bottom, rubble sides 0.030Coarse Gravel 0.030Rock cuts, shale and hard an 0.030Durable rock cuts, a ed and irre ular 0.040Cobbles and shin les 0.035Ston bed, weeds on bank 0.035Strai ht, uniform 0.0225

Windin , slu ish 0.025Natural Stream Channels Clean, strai ht, full sta e, dee ools 0.03Clean, strai ht, full sta e, weeds and stones 0.035Windin , some ools and shoals 0.039Slu ish river reaches, weed , w/ dee ools 0.065Ver weed reaches 0.11

Pi esAsbestos-Cement 0.009Cast Iron 0.012Cla , draina e tile 0.012Concrete 0.015

Corru ated Plastic Draina e i e 0.015Metal, corru ated 0.025Steel, riveted, s iral 0.016Vitrified Sewer i e 0.013


6/22

Mannings Roughness Coefficient, n

For purposes of channel design and channel performance, channel linings are bestdivided into three categories, (1) linings with Mannings roughness coefficients that remainconstant as the flow conditions in the channel change, (2) linings with Mannings

roughness coefficients that change as the depth of flow increases, and (3) linings withMannings roughness coefficients that change with a variety of flow conditions. Each ofthese three types of linings will be addressed separately.

Linings with constant Mannings roughness coefficient. Channel linings that aregenerally considered to have constant roughness coefficients, meaning that Mannings nremains constant as the channels flow depth and velocity change, are summarized inTable 3-1. Most of the linings listed in Table 3-1 are hard linings that have minimal or nobiological components. The exceptions are the natural streams, which, in some cases areconsidered to change as the vegetation in the riparian buffer develops and matures.

Linings with Mannings roughness coefficients that vary with flow depth. Rocks arevaluable channel liners. In areas were velocities are too fast for bare soil or vegetatedlinings, rock placed by itself, as riprap, or placed in wire baskets, as gabions or RenoMattresses, forms a channel lining that will yield very good protection against erosion.

Riprap is a permanent, erosion-resistant ground cover of large, loose, angularstone. Riprap protects the soil surface from the erosive forces of concentrated flow.Riprap slows the velocity of concentrated runoff while enhancing the potential forinfiltration and stabilizes slopes with seepage problems and/or non-cohesive soils.

Riprap is classified as either graded or uniform depending on the range of rock

sizes present in the rock mixture. Graded riprap should contain a mixture of stones thatvary in size from about 0.5D50to 2D50. Uniform riprap contains stones that are all nearlythe same size, D50. Graded riprap is preferred to uniform riprap in erosion andsedimentation control. It is cheaper to install, requiring only that the stones be dumped sothey remain a well-graded mass. Hand or mechanical placement of individual stones islimited to achieving the proper, uniform thickness.

Stone for riprap should consist of fieldstone or rough unhewn quarry stone ofapproximately rectangular shape. The stone should be hard and angular and should notdisintegrate on exposure to water or weathering. Riprap should be placed by end dumping(from a truck) to prevent segregation by sizes. It should never be pushed downhill by adozer or dropped down a chute, because these operations cause segregation of particles.


7/22

1 in

2 in3 in

4 in5 in

6 in8 in

10 in

12 in

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.1 1 10Flow Depth, d (ft)

M

anning'sn

Figure 3-3. Manning's roughness coefficients for riprap lined channels. (Taken from PA-DER, 1990).

In open channels, lined with rock, the Mannings roughness coefficient is greatestat shallow depths of water and decreases as the depth of water increases. Figure 3-3shows that when the depth of water in a rock or riprap lined channel is of the same order

of magnitude as the rock lining (d/D50 1), the friction is very high, i.e. Mannings n = 0.06to 0.07. As the depth of flow increases relative to the rock size (d/D50 > 10, the frictiondecreases and approaches a constant that is dependent on the rock size used in the

lining, i.e. n = 0.025 for D50= 1" rock; n = 0.028 for D50= 2" rock and n = 0.030 for D50= 3"rock. The curves plotted in Figure 3-3 are the solution to the following equation (USDA-NRCS, 1977)

]0.14)/(log6.21[ 5010

61

+

=

Dd

dn (5)


8/22

where d is the depth of flow in the rock-lined channel in feet , D50is the average rockdiameter in feet and n is Manning's roughness coefficient.

According the PADEP (2000), some of the newer temporary erosion blankets alsocreate a situation where Mannings n varies with flow depth, see Table 3-2.

Table 3-2. Mannings roughness coefficients (n) for commonly used temporary channel linings.(PADEP, 2000).

Mannings n

Water Depth Ranges

Lining Type 0 0.5 ft 0.5 2.0 ft >2.0 ft

Jute Net 0.028 0.022 0.019

Curled Wood Mat 0.066 0.035 0.028

Synthetic Mat 0.036 0.025 0.021

Linings with Mannings roughness coefficients that vary with flow depth and

velocity. Vegetation lined channels have roughness coefficients that vary greatlydepending on the type of vegetation and the length of the vegetation.

Table 3-3. Retardance Classifications of Various Grasses. (Adapted from USDA-SCS, 1947).

Retardance Class Cover Condition

A. Very Higha = -0.5

Weeping love grassYellow bluestem ischaemum

Excellent stand, tall (avg 30 in)Excellent stand, tall (avg 36 in)

B. Higha = 2

KudzuBermuda grassNative grass mixture (little blue-stem, bluegama, and other long and short Midwestgrasses.Grass-legume mixture (Timothy, bromegrass)Weeping love grassLespedeza series

AlfalfaBlue Gama

Very dense growth, uncutGood stand, tall (avg 12 in)Good stand, unmowed

Good stand, uncut (avg 20 in)Good stand, tall (avg 13 to 24 in)Good stand, not woody, tall (avg 19 in)Good stand, uncut (avg 11 in)Good stand, uncut (avg 13 in)

C. Moderatea = 5

Crab grassBernuda grassCommon lespedezaGrass-legume mixture-summer (orchard grass,redtop, Italian rye grass, common lespedeza)Centipede grassKentucky bluegrass

Fair stand, uncut (avg 10-48 in)Good stand, Mowed (avg 6 in)Good stand, uncut (avg 11 in)Good stand, uncut (6 to 8 in)

Very dense cover (avg 6 in)Good stand, headed (avg 6-12 in)

D. Lowa = 7

Bermuda grassCommon lespedezaBuffalo grassGrass-legume mixture-summer (orchard grass,

redtop, Italian rye grass, common lespedeza)Lespedeza series

Good stand, cutto 2.5 in heightExcellent stand, uncut (avg 4.5 in)Good stand, uncut (avg 3-6 in)Good stand, uncut (avg 4-5 in)

After cutting to 2-in height, very goodstand before cutting

E. Very Lowa = 11

Bermuda grassBermuda grass

Good stand, cut to 1.5-inch heightBurned stubble


9/22

Table 3-3 shows additional information required to select the retardance classesfor the vegetation. This table also shows the a coefficient needed to apply equation 6,which computes the Mannings roughness coefficient as a function of the flow velocity(fps) and the hydraulic radius (ft) (Schwab et al., 1993)

)]0127.1ln(63.21.2[1

VRan

++

= . (6)

In addition to the difficulties that come from having a roughness coefficient that varies withVR, it is also necessary to account for whether the grass will be maintained at or near aconstant height or left to grow throughout the growing season. As can be seen in Table 3-3, most grasses change retardance classes when they are left to grow. For exampleBermuda grass can be in classes B, C, D, or E depending on how high it is mowed.

Table 3-4. Maximum permissible velocities for non-vegetated channel linings.(Adapted from USDA-SCS, 1972b and PA-DER, 1990).

1

Channel Linings Maximum PermissibleVelocity

(ft/sec)

Earth Lined Channels

Fine Sand 1.50

Sandy Loam 1.75

Silt Loam (non-colloidal) 2.00

Ordinary Firm Loam, Fine gravel 2.50

Stiff Clay (very colloidal) 3.75

Graded, Loam 3.75

Alluvial Silts (colloidal) 3.75

Graded, Silt 4.0

Coarse Gravel (non-colloidal) 4.0

Cobbles and Shingles 5.0Shales and Hardpans 6.0

Durable Bedrock 8.0

Rolled Erosion Control Products (RECP)

Am. Excelsior Co.; Curlex Net Free 3.0

Am. Excelsior Co.; Straw; 1 net 3.5

Am. Excelsior Co.; Straw; 2 nets 4.5

N. Am. Green; Straw; single net 5.0

Am. Excelsior Co.; Curlex I.73; 1 net 5.0

Geocoir/Dekowe; Straw; RS-1 6.0

N. Am. Green; Straw; double net 6.0


Am. Excelsior Co.; Curlex II.73; 2 nets 7.0N. Am. Green; 70% straw: 30% Coconut; double net 8.0

Geocoir/Dekowe; 400 8.0


Am. Excelsior Co.; Curlex II.98; 2 nets 8.5

N. Am. Green; Polypropylene; double net; Bare soil 9.0

Geocoir/Dekowe; 70% Straw 30% Coconut; RSS/C-3 10.0

1

Company names are used for clarity and do not imply endorsement by NCSU or NC DOT.


10/22

N. Am. Green; Coconut; double net 10.0

Am. Excelsior Co.; Curlex III; 2 nets 10.0

Am. Excelsior Co.; Curlex Enforcer; 2 nets; Bare soil 10.0

Am. Excelsior Co.; Curlex High Velocity; 2 nets 10.0


Geocoir/Dekowe; Poly/Fiber; RSP-5 12.0

Geocoir/Dekowe; Coconut, RSC-4 12.0Geocoir/Dekowe; 900 15.0

N. Am. Green; Polypropylene; double net; Vegetated 16.0

Turf Reinforced Mats (TRM)

North American Green SC250; Bare soil 9.5

North American Green C350; Bare soil 10.5

Profile/Enkamat; 7003, seed w/ bonded fiber matrix (BFM) 12.0

North American Green P550; Bare soil 12.5

Profile/Enkamat II; seed and BFM; Bare 13.0

Profile/Enkamat; 7010, 7018, 7020, seed and hydromulch 14.0

Profile/Enkamat; 7010 7220, seed and BFM; Vege. 14.0

North American Green SC250; Vegetated 15.0

Am. Excelsior Co.; Recyclex 17.0Profile/Enkamat II; seed and BFM; Vege. 19.0

Profile/Enkamat; 7920, seed and BFM; Vege. 19.0

North American Green C350; Vegetated 20.0

Profile/Enkamat; 7010 - 7220, seed and BFM; Bare 20.0

North American Green P550; Vegetated 25.0

Rock Lined Channels

Graded Rock, D50a(inches)

0.75 [Min = No. 8; Max = 1.5] 2.50

1.50 [Min = 1; Max = 3] 4.50

3.00 [Min = 2; Max = 6] 6.50

6.00 [Min = 3; Max = 12] 9.00

9.00 [Min = 5; Max = 18] 11.50

12.00 [Min = 7; Max = 24] 13.0015.00 [Min = 12; Max = 30] 14.50

Reno Mattress, 3 to 6-inch rock, 6 inches thick 13.50



Gabions 22.00

Rigid Lined Channels

Asphalt 7.00

Wood 9.00aD50refers to the median rock size in graded rock.

Maximum Permissible Velocities, Vmax

When designing a channel using the maximum permissible velocity procedure, it isnecessary to have reliable values of Vmaxavailable for use in Mannings equation (V =Vmax). Maximum permissible velocities non-vegetated linings are presented in Table 3-4.

Table 3-5 contains the maximum permissible velocities for vegetative linings.Because these linings are living plants that are rooted in the soil from which the channelwas cut, it is necessary to not only consider the type of vegetation, but also the


11/22

erosiveness of the soil in which the vegetation is growing and the slope of the channel. Inthis table the channels soil is divided into two categories defined by the RUSLEs K-valuefound in Module 2, erosion resistant (K < 0.37) and easily eroded (K > 0.37). Thevalues given in Table 3-5 are for good vegetative stands. If the stand of vegetation usedprovides less than full coverage, the values in Table 3-5 should be decreased accordingly.

Table 3-5. Maximum permissible velocities for vegetation lined channels. (Modified from Ree, 1949and PA-DER, 1990).

Maximum Permissible Velocities

Erosion Resistant Soils Easily Eroded Soils

K < 0.37 K > 0.37

(percent slope) (percent slope)

0-5 5-10 Over 10 0-5 5-10 Over 10

Cover fps fps fps fps fps fps

Bermuda Grass 8 7 6 6 5 4

Buffalo Grass

Kentucky Bluegrass

Smooth Bromegrass 7 6 5 5 4 3Blue Grama

Tall Fescue

Grass Mixture 5 4 NRa 4 3 NR

Reed Canarygrass 5 4 NR 4 3 NR

Lespedeza

Weeping Lovegrass

Red Top

Kudzu 3.5 NR NR 2.5 NR NR

Alfalfa

Red Fescue

Crabgrass

Annuals for TemporaryProtection

3.5 NR NR 2.5 NR NR

Sudangrass 3.5 NR NR 2.5 NR NRaNot Recommeded.

Maximum Allowable Shear Stress or Tractive Force, all

Maximum allowable tractive force is a measure of the shear stress exerted by theflowing water on the channel lining. If the actual shear stress, in lbs/ft2, exceeds themaximum allowable shear stress or tractive force, the flowing water will erode thechannel, usually at its deepest depth. Maximum allowable tractive forces for non-cohesive

soils smaller than 6.35 mm (sands and gravels) are given in Figure 3-4. Allowable tractiveforces for a wide variety of channel linings are shown in Table 3-6. The dimensions for theNorth Carolina rock classification are given in Table 3-7. Suggested products for use incontrolling erosion on side slopes are given in Table 3-8.


12/22

Figure 3-4. Allowable tractive forces for non-cohesive soils; D75< 6.35 mm or 0.25 inches

(Adapted from USDA-SCS, 1964).

Finally, it is important to note that the tractive force, or shear stress in a channeldoes not remain constant across the entire channel. Figure 3-6 shows how the shearstress changes across a trapezoidal channel. The important thing to keep in mind is thatshear stress is almost always maximum at the point in the channel where the depth offlow is the greatest.

Table 3-6. Allowable Tractive Forces and Mannings n Values for Various Channel Linings(PADEP, 2000).

1

Channel Lining Category Lining Type

AllowableTractive

Force, (lbs/ft

2)

Unlined Erodible Soils (K > 0.37) Silts, Fine Medium Sands 0.03

Coarse Sands 0.04

Very Coarse Sands 0.05

Fine Gravel 0.10

Erosion Resistant Soils (K < 0.37) Sandy loam 0.02

Gravely, Stony, Channery loam 0.05

Stony or Channery silt loam 0.07

Loam 0.07

Sandy clay loam 0.10

Silt loam 0.12

Silty clay loam 0.18

Clay loam 0.25Shale & Hardpan 1.00

Durable Bedrock 2.00

RECP Jute Netting 0.45


Profile; Futerra 1.00

Am. Excelsior Co.; Curlex Net Free 1.00

Am. Excelsior Co.; Straw; 1 net 1.25


Allowable Tractive Force; D75< 6.35 mm

0.01

0.10

1.00

0.1 1.0 10.0

Median Particle Size (D50) mm

AllowabeTractiveForce(lbs/ft2)

Clear Water

Low Content

High Content


13/22

E. Coast Ero. Blank.; Straw/Coir, 2 Jutenets

1.35

Am. Excelsior Co.; Straw; 2 nets 1.50

N. Am. Green; Straw; single net 1.55


E. Coast Ero. Blank.; Straw, 1 net 1.55

E. Coast Ero. Blank.; Coir, 2 Jute nets 1.63Am. Excelsior Co.; Curlex I.98; 1 net 1.65


N. Am. Green; Straw; double net 1.75

E. Coast Ero. Blank.; Excelsior, 1 net 1.80

Geocoir/Dekowe; 70% Straw 30% Coconut;RSS/C-3

1.85

N. Am. Green; 70% straw: 30% Coconut;double net

2.00

N. Am. Green; Polypropylene; double net;Bare soil

2.00


Geocoir/Dekowe; Poly/Fiber; RSP-5 2.00

Geocoir/Dekowe; Coconut, RSC-4 2.00E. Coast Ero. Blank.; Excelsior, 2 nets 2.00

E. Coast Ero. Blank.; Straw, Jute net 2.10

E. Coast Ero. Blank.; Straw, 2 nets 2.10

N. Am. Green; Coconut; double net 2.25

Am. Excelsior Co.; Curlex III; 2 nets 2.30

Am. Excelsior Co.; Curlex Enforcer; 2 nets;Bare soil

2.30

E. Coast Ero. Blank.; Straw/Coir, 2 nets 2.60

Am. Excelsior Co.; Curlex High Velocity; 2nets

3.00


E. Coast Ero. Blank.; Coir, 2 nets 3.20

E. Coast Ero. Blank.; Polypropylene, 2 nets 3.21Geocoir/Dekowe; 700 4.46


N. Am. Green; Polypropylene; double net;Vegetated

8.00

Turf Reinforced Mats (TRM) North Am. Green SC250; Bare soil 2.50

North Am. Green C350; Bare soil 3.00

North Am. Green P550; Bare soil 3.25

E. Coast Ero. Blank.; Coir, 3 nets 3.50

Profile/Enkamat; 7003, seed w/ bondedfiber matrix (BFM)

5.00

Profile/Enkamat; 7010, seed andhydromulch

6.00

Profile/Enkamat; 7010 7220, seed andBFM; Vege.

6.0-8.0

Profile/Enkamat; 7010 - 7220, seed andBFM; Bare

6.7-11.2


7.00

North Am. Green SC250; Vegetated 8.00


8.00


14/22

Profile/Enkamat II; seed and BFM; Vege. 8.00

Profile/Enkamat; 7920, seed and BFM;Vege.

8.00

North Am. Green C350; Vegetated 10.0

Profile/Enkamat II; seed and BFM; Bare 10.0

Am. Excelsior Co.; Recyclex 10.0+

North Am. Green P550; Vegetated 12.5Grass Liners Class D; a = 7 0.60

Class C; a = 5 1.00

Class B; a = 2 2.10

Aggregate & Riprap #57 0.25

(See Table 3-7) #5 0.50

Class A 1.00

Class B 2.00

Class 1 3.00

Class 2 4.00

Reno Mattress & Gabion 8.35

Concrete 100.

Table 3-7. Aggregate and Riprap gradation.

Graded Rock Size (in)

Class or # Maximum D50 Minimum

#57 1 No. 8

#5 1 3/4 3/8

A 6 4 2

B 12 8 5

1 17 10 5

2 23 14 9


15/22

Figure 3-5. Channel lining selection guide.

Table 3-8. Permissible Shear Stress of Various RECPs. (Adapted from Table 6.17a NCDENR (2006))1

Category Product TypeMax. Permissible

Shear Stress (lbs/ft2)

SlopesUp to

RECP N. Am. Green; Straw; 1 net 1.55 3:1

Am. Excelsior Co.; Curlex Net Free 1.00 3:1Am. Excelsior Co.; Straw; 1 net 1.25 3:1

Geocoir/Dekowe; Straw; RS-1 0.83 3:1

N. Am. Green; Straw; 2 nets 1.75 2:1

Am. Excelsior Co.; Curlex I.73; 1 net 1.55 2:1

Am. Excelsior Co.; Curlex I.98; 1 net 1.65 2:1

Am. Excelsior Co.; Straw; 2 nets 1.50 2:1

Geocoir/Dekowe; Straw; RS-2 1.25 2:1

Geocoir/Dekowe; 70% Straw 30%Coconut; RSS/C-3

1.85 2:1

Geocoir/Dekowe; Poly/Fiber; RSP-5 2.00 2:1

Geocoir/Dekowe; Coconut, RSC-4 2.00 2:1

Am. Excelsior Co.; Curlex II.73; 2 nets 1.75 1.5:1

Am. Excelsior Co.; Curlex II.98; 2 nets 2.0 1.5:1Am. Excelsior Co.; Straw/Coconut; 2nets

1.5:1

N. Am. Green; 70% straw: 30% Coir; 2nets

2.00 1:1

N. Am. Green; Coconut; 2 nets 2.25 1:1

Am. Excelsior Co.; Curlex III; 2 nets 2.3 1:1

N. Am. Green; Polypropylene; 2 nets;Bare soil

2.0 1:1

N. Am. Green; Polypropylene; 2 nets;Vegetated

8.0 1:1

Am. Excelsior Co.; Coconut; 2 nets 1:1

Am. Excelsior Co.; Curlex Enforcer; 2nets

0.75:1

Am. Excelsior Co.; Curlex High Velocity;2 nets

3.0 0.75:1

TRM Profile/Enka; 7003, Vege. 5.0 3.5:1

Profile/Enka; 7010, 7210, 7910, Vege. 6.0 2:1

Profile/Enka; 7220, 7020, Vege. 8.0 1.5:1

Profile/Enkamat II 8.0 1:1

Profile/Enka; 7520, Vege. 8.0 0.5:1

Am. Excelsior Co.; Recyclex 10.0+ 0.5:1

NCDENR Specs

Degradable RECPs Nets and Mulch 0.1 0.2 20:1

(Unvegetated) Coir Mesh 0.4 3.0 3:1

Blanket Single Net 1.55 2.0 2:1Blanket Double net 1.65 3.0 1:1

Nondegradable Unvegetated 2 4 1:1

Turf Reinforced Mats Partially Vegetated 4 6 >1:1

Fully Vegetated 5 - 10 >1:1


16/22

Selecting Channel Linings

Applying the maximum permissible velocity, Vmax criteria to channel liningselection is difficult, requiring that the lining be chosen before the channel is designed.The maximum allowable tractive force, can however be applied quite easily to channellining selection. Tractive force, is a measure of the frictional resistance to flow in achannel and is the weight of the water in the channel on the channel bottom times thechannel slope or

RS = . (7)

In this equation is the average shear stress acting on the channel lining across thewidth of the channel. In a wide channel with a rectangular cross-section, the depth canbe assumed to equal the hydraulic radius, d = R. If we substitute the depth into equation7, we get an expression of shear stress that is a function of flow depth and slope as

dS = . (8)

In a channel with a rectangular cross-section, the tractive force is nearly constant, seeFigure 3-5. In channels having cross-sections where the depth is not constant, themaximum tractive force occurs where the depth of flow is greatest. Thus, if is set equalto the maximum allowable shear stress (from one of the above tables or figures),equation 8 can be solved for, what is the maximum allowable flow depth, dmaxas

Sd all

=max (9)

Figure 3-6. How tractive force varies in a trapezoidal channel.


17/22

Where S is the channel slope in feet/foot and is the unit weight of water (62.4 lbs/ft3).

In most cases, where channel linings are to be chosen, it is better to solve equation 9for the maximum shear stress, which occurs at the point of maximum flow depth as

Sdmaxmax = . (10)

By comparing the maximum shear stress from equation 10 with the maximum allowableshear stresses from the tables and figures above a channel lining can be selected. Thefollowing example will show the procedure.

Table 3-9. North Carolina DOT guidelines for selecting channel linings.

Channel Slope (%) Recommended Channel Lining

0.0 to 1.5 Seed and mulch

>1.5 to 5.0 Temporary liners

>5.0 Turf Reinforced Mats or Hard

In North Carolina, DOT has a rule of thumb to assist in selecting road ditch linings.These guidelines are shown in Table 3-9. The following example will show that the NCDOT guidelines are consistent with meeting the allowable shear stress limitations.

Example 1. A proposed triangular road ditch channel has 2:1 side slopes,a slope of 3%, and the road will be serviced by an 18-inch culvert; thedesign depth of flow in the proposed road ditch is generally about thesame depth as the diameter of the culvert. Select a suitable channel liningfor this channel.

Solution:Since the road is serviced by an 18-inch culvert, it is safe toassume that the maximum flow depth in the ditch will be about 18 inchesor 1.5 feet. From equation 10 compute the maximum shear stress in thischannel as

2

max /9.1)02.0)(5.1)(4.62( ftlbs==

Now look on the tables and figures above and select a channel lining thathas a maximum allowable shear stress that is >1.9 lbs/ft2. Table 3-8shows that a double-sided non-degradable RECP without vegetationmaybe okay (actually this channel pushes the upper limits of when such a

liner is expected to do the job of controlling erosion. This is consistent withthe guidelines in Table 3-9. It should be noted that for slopes greater thanthe 2% used in this example, temporary liners are going to be subjected toexcessive shear stresses and will be expected to fail.

If this example is re-worked using a ditch slope of 1%, the maximum shearstress in the channel will be just less than 1.0 lbs/ft2, which is probablyokay for seed and mulch. If, with the flatter slope, we also assume a


18/22

smaller culvert, say 12-inch, then the shear stresses are more reasonablefor the seed and mulch application.

It is hard to understand how channel slope relates or controls depth offlow.

North American Green Software

A procedure, not greatly different from the one developed above for trapezoidalchannels has been developed and published by North American Green, Inc (Lancasterand Nelsen, 2002). This software package is available from North American Green, Incand you are encouraged to go to http://www.nagreen.com/software/ and download thesoftware package named ECMDS version 4.2 onto your own computer.

Sizing Pipes for Open Channel Flow

Though circular channels obey the continuity and Mannings equations, the

geometry of circular channels is much more complex. Therefore, it is suggested that youuse Figure 3-7 for sizing pipes that have relatively smooth linings such as clay orconcrete pipe or corrugated plastic pipe with the smooth inner lining. For corrugatedplastic pipe, Figure 3-8 is appropriate. In both of these figures the pipe slope, in %, islocated on the x-axis and the pipe discharge, in gpm, is located on the y-axis. The solidsloping lines (low on the left and rising toward the right) represent each pipe (diametershown below the line) flowing full.


19/22

40,000

30,000

20,000

10,000

5,000

4,000

3,000

2,000

1,000

500

400

300

200

100

50

40

30

DISCHARGE(G

PM)

ACRES DRAINED

DRAINAGE COEFF.

.1 .2 .3 .4 .5 1.0 2.0 3.0 4.0 5.0 10 1/4 1/2 1 3/8 3/4

SLOPE IN FEET PER 100 FEET (%)

Based on Mannings n=0.0108

8000

5000

4000

3000

2000

1000

500

400

300

200

100

50

40

30

20

10

4000

3000

2000

1000

500

400

300

200

100

50

40

30

20

10

5

4

3

2000

1000

500

400

300

200

100

50

40

30

20

10

5

4

3

2

1

5000

4000

3000

2000

1000

500

400

300

200

100

50

40

30

20

10

5

4

2000

1000

500

400

300

200

100

50

40

30

20

10

5

4

3

2

V=20

V=15

V=12

V=10V=

9

V=7

V=8

V=6

V

=5

V=4

V=3

V=2

V=1

48

42

36

30

24

18

16

14

12

10

8

6

5

4

Figure 3-7. Pipe sizing chart for clay, concrete and corrugated plastic pipe with a smooth

inner liner (Jarrett, 2000).


20/22

DRAINAGE COEFF..1 .2 .3 .4 .5 1.0 2.0 3.0 4.0 5.0 10 1/4 1/2 1 3/8 3/4

SLOPE IN FEET PER 100 FEET (%)

Based on Mannings n=0.015

10,000

5,000

4,000

3,000

2,000

1,000

500

400

50

5

DISCHARGE(G

PM)

300

200

100

40

30

20

10

ACRES DRAINED

V=12V=

10

V=8

V=7

V=6

V=5

V=4

V=3

V=2

18

15

12

10

5

4

3

2

6

8

1500

1000

500

400

300

200

100

50

40

30

20

10

5

4

3

2

900

500

400

300

200

100

50

40

30

20

10

5

4

3

2

1

.6

400

300

200

100

50

40

30

20

10

5

4

3

2

1

.5

.4

.3

1000

500

400

300

200

100

50

40

30

20

10

5

4

3

2

1

400

300

200

100

50

40

30

20

10

5

4

3

2

1

.5

.4

500

600

V=1

V=.5

Figure 3-8. Pipe sizing chart for corrugated plastic pipe. (Jarrett, 2000).


21/22

Flow Regimes

Water flowing in an open channel will exist in either the subcritical or supercriticalregime. Briefly, most natural streams are subcritical meaning that the energy due to thedepth of flow (potential energy) is greater than the kinetic energy of motion (velocity).

Occasionally, in steep channel reaches the flow may become supercritical. This meansthat the kinetic energy of flow is greater than the depth energy.

Why is it important that you be aware of whether the flow in your channels is sub orsuper critical? Because if your channel has supercritical flow, the water MUST go througha hydraulic jump before it can return to subcritical flow. A hydraulic jump is a big energydissipater, which has the potential to erode large quantities of soil into the stream.

A channel can easily be checked to determine if the design flow will be sub or supercritical by computing the Froude Number as

3

2

gAtQFr = (11)

Where Q is the flow rate in the channel (in cfs), t is the top width of flow in the channel (infeet), g is the acceleration of gravity (as 32.2 ft/sec2), and A is the cross-sectional area offlow (in ft2).

When the Froude Number is less than 1.0, the flow is subcritical; just the way youwant it. When the Froude Number is greater than 1.0, the flow is supercritical, and you willneed to design an energy dissipater to protect the channel where the slope decreasesand the flow will change to subcritical. If the Froude Number equals 1.0 the flow is critical.

This is so rare we need not worry about it. Table 3-10 shows how key channel flowparameters are affected by flow regimes.

Table 3-10. Relationship between key channel flow parameters and flow regime.

Flow Regimes

Parameters Subcritical Critical Supercritical

Velocity < Vc = Vc >Vc

Depth > dc = dc < dc

Slope < Sc = Sc > Sc

Regime Changes

As discussed earlier, when subcritical flow passes through a transition the flowdepth will decrease. Conversely, when supercritical flow passes through a transition theflow depth will increase. In many cases, the transition is so great that the flow after thetransition has not just changed in depth, but has also been transformed into a differentflow regime. For instance, when water flowing in a diversion, having a 1% slope, passesthrough a slope change (transition) into a channel of conveyance, having an 8% slope,the flow depth will not only decrease, but may also change from subcritical to supercritical


22/22

flow. The only correct way to determine whether a regime change has (or will) occur is tocheck the Froude Number before and after the transition.

Subcritical to Supercritical Flow.

The transition from subcritical (Fr< 1.0) to supercritical (Fr> 1.0) flow is a smooth,seldom noticed transition. The flow depth simply drops from a subcritical depth to asupercritical depth as the flow velocity increases. As long as the channel lining(s) are ableto withstand the flow velocities, there is nothing to worry about. No special lining orchannel protection is generally needed.

Supercritical to Subcritical Flow.

The transition from supercritical (Fr> 1.0) to subcritical (Fr< 1.0) flow is, however,a very different situation. This regime change occurs by passing the water through whatis called a 'hydraulic jump' where the depth of flow suddenly changes, often with white

water, from the supercritical depth to what appears to be the subcritical depth. Thepurpose of white-water rafting is to ride these hydraulic jumps and experience the thrill ofthe sudden depth change. In addition to a sudden depth change and white water (if thechange in Froude Number is great) there is also a large amount of energy lost ordissipated onto the channel bottom at the point of the hydraulic jump. Therefore, anyportion of a channel that experiences a hydraulic jump must be carefully protected with achannel lining that can withstand the elevated turbulence and velocities associated with ahydraulic jump. Channel linings such as riprap, gabions or other durable material must beused to line these channel portions.

design channel

Documents