DESIGN OF STABLE DESIGN OF STABLE CHANNELSCHANNELS

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Problem of the designgParameters in designDesign of Non-Erodible ChannelsDesign of Non-Erodible ChannelsDesign of Erodible Channels

Th i ibl t ti f h◦ The permissible tractive force approach◦ The regime theory

Problem of the designProblem of the design

Hydraulic engineers concern ;

Problem of the designProblem of the design

y g◦ problem of design◦ maintenance and improvement of channelsIrrigation engineers concern ◦ supply of irrigation water◦ collection of unused water

In such cases the problem is determining ;ShShapeCross sectional areaSlope of the channel Slope of the channel

ParametersParameters in in designdesign

Design of NonDesign of Non--Erodible Erodible ChannelsChannels

Slope stabilitytrapezoidal cross sectionsDesign steps;g p

Manning's n can also be got from Tables or estimated using the Stricklergequation: ◦ n = 0.038 d1/6

A = b d + Z d2 ; P = b + 2 d (1 + Z)1/2A = b d + Z d ; P = b + 2 d (1 + Z)The value of Z is decided, and the value of b is chosen based onthe material for the construction of the channel.The only unknown d is obtained by trial and error to contain they y

design flow. Check flow velocity and add freeboard.

T

d Z D

b

Design of Erodible ChannelsDesign of Erodible ChannelsDesign of Erodible ChannelsDesign of Erodible Channels

The permissible tractive force approach

The regime theory

The permissible tractive force The permissible tractive force approachapproachThe average shear stress on the

boundary of a channel is, given as . 00 RSγτ =However, this shear stress is not uniformly distributed over the boundary

Design procedure for permissible Design procedure for permissible tractive force approachtractive force approachtractive force approachtractive force approachManning roughness coefficient is determined

Side slope is determined

Angle of reponse is selected

Chin, 2006

•Permissible unit tractive force is determined

Permissible tractive force is the maximum unit tractive force that

Permissible unit tractive force for non- cohesive and cohesive soil

Permissible tractive force is the maximum unit tractive force that will not cause erosion

Maximum unit tractive force for various Maximum unit tractive force for various channelschannels

y determined from the equations;◦ C1ySo<זpy p

◦ C2ySo<Kזp

smaller one is takens a e o e s ta e

Using Manning equation channel capacity is determinedis determined.If Qcomputed≠Qdesign

◦ repeat the procedure◦ repeat the procedure

Critical flow conditions is checked and f b d i dd dfreeboard is added.

Example for the tractive forceExample for the tractive forceExample for the tractive forceExample for the tractive forceDesign a trapezoidal channel to carry 20 m³/secSlightly sinuous channel on a slope of 0.0015. The channel is to be excavated in coarsealluvium with a 75-percentile diameter of 2 cm (gravel),Particle is moderately rounded

From the table n=0.025d75= 2 cm.= 0.8 inc α=32’Since the channel is slightly sinuous, the

i f C f h i i correction factor, Cs, for the maximum tractive force

Source : Lane, E.W. Desing of stable channel

Cs=0.90Cs 0.90

The channel slope is selected to be 2:1(H V) Th di l h h id(H:V). The corresponding angle that the sideslope makes with the horizontal, θ, is given by:

Th t ti f ti K (th f ti f th The tractive force ratio, K, (the fraction of the bottom tractive force applied to the channel side) is:side) is:

The permissible tractive force on the bottom of the h l i ti t d f th USBR l t 0 33 lb/ft2 channel is estimated from the USBR plots as 0.33 lb/ft2,

or 15.9 N/m2 for a median particle size of 20 mm. Correcting this permissible force for the sinuousness leads to an allowable shear stress on the bottom of the channel of:

The permissible tractive force on the side of the channel is therefore:

The normal depth of flow can be estimated by assuming that particle motion is incipient (side shear stress equal that particle motion is incipient (side shear stress equal to the permissible tractive force) on the side of thechannel:

Determine channel bottom width using the Manning’s Determine channel bottom width using the Manning s equation:

b results in a minimum real value of 24 2 mb results in a minimum real value of 24.2 mThe actual tractive force on the channel bottom is:

This is less than the maximum permissible tractive force on the channel bottom (14.2 N/m²), and is therefore acceptable from an tractive force aspect.

Check for subcritical flow

which indicates desirable subcritical flow (Fr < 1)

The regime theoryThe regime theory

Brief information about Kennedy, Lindleyy yLacey, Blenchand Simons and Albertson approacha S o s a be tso app oacUSACE approach

Regime theory , empirical approachDeveloped in IndiapA canal said to be in regime if…

Kennedy and Lindley , correlation between v and y

v= kyn

k=0.84

n=0.64 (?)

Later improvement done by Lacey,p y y,

Silt factor (relation d) .

..

..

The difference between Kennedy’s and Lacey’s theory is that Kennedy considered the depth of flow (d) as y p ( )significant variable and Lacey considered the Hydraulic radius (R) as the significant variable

In this field more development has been done

Blench (2 equations for the silt factor)

Data should cover wider variety of bed and bank conditions

Remedy (large extend)

In the United States, Simons and Albertson (1963) continued regime development by combining data from canal studies in India and north America

Criticism about the method1. data comes from limited range of 1. data comes from limited range of conditions

2. f depends on only d factor, h b di i ?what about sediment concentration?

3. what is the channel slope Indian data?

Several investigators have studied the relationship Several investigators have studied the relationship between surface width, flow depth and velocity for an alluvial stream one of them is Leopold and Moddockwhich was discussed in the coursewhich was discussed in the course

The USACE (1994) provides guidance on channel The USACE (1994) provides guidance on channel design. Their recommendation is to use locally or regionally developed equations for channel design. H h thi i t ibl F ll i fi However, when this is not possible, Following figures can be used to provide rough estimates for top width, depth, and slope of a channel given the channel-forming discharge and bed material.

Top Width as Function of Discharge (USACE(USACE,1994)

Depth as Function of Discharge (from USACE 1994)USACE, 1994)

Slope as Function of Discharge (USACE, 1994)1994)

USACE Regime Chart LimitationsUSACE Regime Chart Limitations

The charts are more compatible with single-h l d l t ithchannel sand or gravel systems with

relatively low bed material transport.

If bed material transport is high, the slopes may be too low and the depths may be too hi h high.

The use of all three charts does not permit The use of all three charts does not permit explicit selection of roughness and allowablevelocity or shear stress.

To concludeTo concludeTo concludeTo conclude• Regime equations are strictly valid for one discharge

conditionconditionIn other words;

Sustained discharge (irrigation channel)Dominant discharge (alluvial stream)Dominant discharge (alluvial stream)

Tractive force theory consist resistance law and sediment transport law are applicable not only stable channels but also transport law are applicable not only stable channels but also varying discharge

Therefore tractive force method is more generalg

However, incomplete knowledge of resistance to flow and mechanics of sediment transport tractive force method may p ynot give accurate design.

ReferencesReferencesReferencesReferencesMechanics of sediment transportation and alluvial stream problems R J Garde K G Ranga Raju Edition: 3stream problems, R. J. Garde, K. G. Ranga Raju, Edition: 3Yanmaz, A. M. 2006. "Applied Water Resources Engineering", Third Edition, METU Press Publishing CompanyCompanyLane, E. W. “ Design of stable channels” traction of American Society of Civil Engineers, v.120, p. 1234-79 (for the charts)( o t c a ts)Demonstration Erosion Control Design Manual, U.S. Army, Engineer Research and Development Center, Vicksburg, Mississippig, ppSediment Transport Technology, Proceedings, State of Hydraulic Works, Technical Research Department, volume2

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