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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering

Lecture 8: Design of Erodible Channels

CEM001 Hydraulic Structures, Coastal and River Engineering

River Engineering Section

Dr Md Rowshon Kamal

[email protected]

H/P: 0126627589

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1. Channel must carry design flow/discharge (Qd).

2. Velocity in the channel must not be high to cause scour.

3. Velocity in the channel must not be low to cause deposition.

Hydraulic Parameters used in Design of Unlined/Lined Channels

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Minimum Permissible Velocity

This is the lowest velocity which prevents both sedimentation (deposition) and vegetation growth.

Recommendations by French (1985)• Prevent from sedimentation – 0.61~0.91m/s• Prevent from growth of vegetation – 0.76m/s

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1. Maximum Permissible Velocity Method

This is one of the methods we use to design a channel.

Special committee on Irrigation Hydraulics (ASCE) formed this method.

Design criteria: Mean Flow Velocity < Max. Permissible Velocity

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Maximum Permissible Velocities

MaterialMaximum Permissible Velocity (m/s)

Clear WaterWater carrying colloidal silts

Fine sand, non colloidal

0.46 0.76

Alluvial silt, non colloidal

0.61 1.07

Stiff clay, very colloidal

1.14 1.52

Fine gravel 0.76 1.52

Coarse gravel 1.22 1.835


Maximum Permissible Velocities (con’t)

Above values will be changed if;

1. Reduce values by 25% for sinuous (meandering) channels.

2. Increase by 0.15 m/s for depths greater than 0.91m.

3. Reduce by 0.15 m/s if channel carries abrasive material.

4. Increase by 0.3 – 0.6 m/s for channels with high silt load.

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Example 02Design a trapezoidal channel (side slope 1:2) to carry 125.0 m3/s on a bed slope of 0.001. Use Maximum Permissible Velocity Method.

Assume the following:- Coarse gravel in water carrying colloidal siltDepth to be greater than 1.0 m Manning’s coefficient n = 0.025

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Answer Ex-02

From Table in slide no 5:

Corresponding allowable velocity = 1.83m/s This may be increased by 0.15m/s because channel depth assumed to be greater than 1.0m,

Modified allowable velocity = 1.98m/s

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Answer Ex-02

From Manning’s formulan

SRV

A

Q 2/10

3/2

mS

VnR 96.1

001.0

025.098.12/3

2/1

2/3

2/10

Cross sectional area213.63

98.1

125m

V

QA

Wetted perimeter mR

AP 31.32

96.1

13.63

)( zybyA Cross sectional area

212 zybP Wetted perimeter

y

b

1

z

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Answer Ex-02

Substituting for the side slope, 2z

)2(13.63 yby

yb 5231.32

013.6331.32472.2 2 yy

my 4.2 my 6.10

mb 5.21 mb 3.15 Negative value is not possible

Design depth and width my 4.2 mb 5.21

Solve for y and b

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2. Permissible Tractive Force Method (Shear Stress Method)

Most rational and widely used method.

Based on the consideration of equilibrium of particle resting on the bed with drag and lifting forces balanced by the submerged weight of particle.

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Permissible Tractive Forces by USBR

USBR recommends the following values for boundary shear stresses:

Course non-cohesive material (D > 5.0mm)

Fine non-cohesive materials (Refer Example 2.4 – Next page please!)

Cohesive sediments – Not covered by USBR

7575.0 Dbc 2/mN D75 in mm

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For Fine Cohesive MaterialsGraph of 0/g against d from Shields Diagram

0.00001

0.00010

0.00100

0.01000

0.01 0.10 1.00 10.00 100.00

Particle Diameter, d, (mm)

0/ g

= R

S (

m)

USBR VALUES FOR FINE NON- COHESIVE SEDIMENTS

AMOUNT OF SUSPENDED SEDIMENT

HIGH

LOW

MED

SHIELDS' FUNCTION

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Adjustment for Sinuosity

Degree of Sinuosity CS

Straight channels 1.00

Slightly sinuous 0.90

Moderately sinuous 0.75

Very sinuous 0.6014


Allowable Shear Stresses for a Trapezoidal Channel

b = kb gyS0

s = ks gyS0

b

1z

y

τs and τb - Max Bottom & Side Shear Stresses

ks and kb - Depend on y, b, z 15


Allowable Shear Stresses for a Trapezoidal Channel (con’t)

ks and kb Factors

97.0bkIf

If

75.0sk4y

b

4y

b Tables need to be used

Design Conditionsbcb

scs

For bottom

For sidesor

or bcb yy

scs yy 16


Bank Stability in a Trapezoidal Channel

W

Wsin

FDQ

Wcos

Force normal to the side

222 sin WR

s

Forces acting on the particle:1.Drag force (FD) 2.Component from weight (Wsinθ)3.Friction force opposing R

(Wcosθtanϕ)

Sand particle

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Bank Stability in a Trapezoidal Channel (con’t)

At incipient motion, resultant force, R will be equal to friction force.

2222 sintancos scWW

)sintan(cos 22222 Wsc

2/1

2

2

tan

tan1tancos

Wsc (1)For side

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For the bottom θ=0;

tanW

bc

2/1

2

2

sin

sin1

bc

scK

Combining (1) and (2) gives;

(2)

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For finer materials, θ=0;

cosbc

scK

i.e. Cohesive forces are much greater than the gravity force.

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Example 03

Design a trapezoidal channel to carry 125.0m3/s on a bed slope of 0.001. The channel is to be excavated in coarse alluvium, containing moderately angular stones with d75 of 50.0mm. The angle of friction for this material is 40º, which is also its angle of repose.

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(i) Define the terms maximum and minimum permissible velocities.

(ii) A river 30.0 m wide and 4.0 m deep and of a regular rectangular cross-section carries a discharge of 350.0 m3/s through country with a bed slope of 0.0003. If the bed material is coarse alluvium having a D50 size of 10.0 mm and specific gravity s = 2.65, estimate the total transport load using the Ackers and White formula.

Question 04

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Thank You

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