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**Lecture 8: Design of Erodible Channels**

25/03/2017 Lecture 8: Design of Erodible Channels CEM001 Hydraulic Structures, Coastal and River Engineering River Engineering Section Dr Md Rowshon Kamal H/P: 1

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**Hydraulic Parameters used in Design of Unlined/Lined Channels**

25/03/2017 Hydraulic Parameters used in Design of Unlined/Lined Channels 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. 2

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**Minimum Permissible Velocity**

25/03/2017 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 3

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**1. Maximum Permissible Velocity Method**

25/03/2017 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 4

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**Maximum Permissible Velocity (m/s) Water carrying colloidal silts**

25/03/2017 Maximum Permissible Velocities Material Maximum Permissible Velocity (m/s) Clear Water Water 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 Coarse gravel 1.22 1.83 5

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**Maximum Permissible Velocities (con’t)**

25/03/2017 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. 6

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25/03/2017 Example 02 Design a trapezoidal channel (side slope 1:2) to carry m3/s on a bed slope of Use Maximum Permissible Velocity Method. Assume the following:- Coarse gravel in water carrying colloidal silt Depth to be greater than 1.0 m Manning’s coefficient n = 0.025 7

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**Answer Ex-02 From Table in slide no 5:**

25/03/2017 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 8

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**Answer Ex-02 From Manning’s formula Cross sectional area**

25/03/2017 1 Answer Ex-02 y b z From Manning’s formula Cross sectional area Wetted perimeter Cross sectional area Wetted perimeter 9

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**Answer Ex-02 Substituting for the side slope, Solve for y and b**

25/03/2017 Answer Ex-02 Substituting for the side slope, Solve for y and b Negative value is not possible Design depth and width 10

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**2. Permissible Tractive Force Method (Shear Stress Method)**

25/03/2017 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. 11

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**Permissible Tractive Forces by USBR**

25/03/2017 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 D75 in mm 12

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**For Fine Cohesive Materials**

25/03/2017 For Fine Cohesive Materials 13

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**Adjustment for Sinuosity**

25/03/2017 Adjustment for Sinuosity Degree of Sinuosity CS Straight channels 1.00 Slightly sinuous 0.90 Moderately sinuous 0.75 Very sinuous 0.60 14

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**Allowable Shear Stresses for a Trapezoidal Channel**

25/03/2017 Allowable Shear Stresses for a Trapezoidal Channel b 1 z y s = ks gyS0 τs and τb - Max Bottom & Side Shear Stresses ks and kb - Depend on y, b, z b = kb gyS0 15

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

25/03/2017 Allowable Shear Stresses for a Trapezoidal Channel (con’t) ks and kb Factors If If Tables need to be used Design Conditions or For bottom For sides or 16

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**Bank Stability in a Trapezoidal Channel**

25/03/2017 Bank Stability in a Trapezoidal Channel Forces acting on the particle: Drag force (FD) Component from weight (Wsinθ) Friction force opposing R (Wcosθtanϕ) W Wsinq q FD Q Wcosq Force normal to the side Sand particle 17

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**Bank Stability in a Trapezoidal Channel (con’t)**

25/03/2017 Bank Stability in a Trapezoidal Channel (con’t) At incipient motion, resultant force, R will be equal to friction force. For side (1) 18

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**Bank Stability in a Trapezoidal Channel (con’t)**

25/03/2017 Bank Stability in a Trapezoidal Channel (con’t) For the bottom θ=0; (2) Combining (1) and (2) gives; 19

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**Bank Stability in a Trapezoidal Channel (con’t)**

25/03/2017 Bank Stability in a Trapezoidal Channel (con’t) For finer materials, θ=0; i.e. Cohesive forces are much greater than the gravity force. 20

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25/03/2017 Example 03 Design a trapezoidal channel to carry 125.0m3/s on a bed slope of 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. 21

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25/03/2017 Question 04 (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 m3/s through country with a bed slope of 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. 22 22

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