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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
rowshon@legendagroup.edu.my
H/P: 0126627589
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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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
School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
Adjustment for Sinuosity
Degree of Sinuosity CS
Straight channels 1.00
Slightly sinuous 0.90
Moderately sinuous 0.75
Very sinuous 0.6014
School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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
School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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
School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
Bank Stability in a Trapezoidal Channel (con’t)
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
Bank Stability in a Trapezoidal Channel (con’t)
For finer materials, θ=0;
cosbc
scK
i.e. Cohesive forces are much greater than the gravity force.
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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
(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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School of Civil Engineering/Linton School of Computing, Information Technology & Engineering
Thank You
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