Question

A trapezoidal channel is to be designed through a silty clay alluvium on a slope of 0.0035 ft/ft. The angle of repose of the material is 35° and the Manning coefficient is 0.025. If the channel is to be designed to carry a maximum discharge of 700 cfs at a depth of 4.9 ft, determine if rip-rap will be required, and, if so, compute the stone size for both the bed and sides.

Answer 1

Sol:- Information Provided in the Question:-

Trapezoidal Channel Designed by Silty Clay

Having Slope (S) = 0.0035 ft/ft

Angle of Repose = 35o

Mannings Coefficient (n) = 0.025

Discharge (Q) = 700 cfs

Depth = 4.9 ft

Now the Rip - Rap required ( to prevent the scouring of Soil particle lying on the channel bed) The Size of stone required can be determined as follows:

Using Shield' s Theory

< Shear strength of particle

Here R = hydraulic radius of channel

Ss = Specific gravity of soil Particle

Let us assume Ss = 2.56

d = diameter of particle

Then putting all values :

R < (d /10.825 x S)

Here to determine the Hydraulic Radius of channel, We use Mannings Equation

700 / Bx 4.9 = ( 1/0.025) R 2/3 (0.0035)1/2   ( Here B = width of channel}

60.368/B = R 2/3

take unit width ( As nothing is given in question) then

R = 469.040 ft

The for  R < (d /10.825 x S)

469.040 < (d /10.825 x 0.0035)

Size (d) = 17.7556 ft ( required for Bed of Channel)

Note : Value of size of particle seems to be large because we have taken unit width but if we increase the width of channel then value will decrease ultimately

=> Now to prevent scouring of soil particles lying on Channel Sides

we use   

Here = ( for very small values)

=

Then   

after solving we get,

d (Size of stone) = 13.3139 ft  ( required for Side of Channel)

Note : Value of size of particle seems to be large because we have taken unit width but if we increase the width of channel then value will decrease ultimately