Drainage Trench Conveyance Capacity

[waterboy123]

Hello,

If I have a drainage trench 600mm x 600mm filled with large stones, assuming a porosity of 0.33 and a gradient of 1/200 what is the best way to caculate the conveyance capacity in l/s. In other words what is the maximum flow rate the trench can pass downstream to the outfall.

I would assume using mannings formula with a very high n value wouldn't be suitable?

Thanks

 

[Drew08]

Internet search "riprap intersitial flow". You'll find several references. However, at that shallow gradient, the discharge will be very small.

 

[beej67]

Is it lined, or filled all the way up? For a riprap liner, use Manning's. For it completely full, you're into more complex territory.

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[gbam]

Look into Darcy's equation for sub surface flow. You'll have to come up with the hydraulic conductivity for your specific stone size, gradation and porosity.

 

[waterboy123]

Thanks for the responses. Just to confirm the trench will be filled all the way to the top with stone and lined with a membrane to stop soil ingress. I was hoping I could just use mannings and divide the answer by 3 (the stone creates 33% free space within the trench). I thought it might be Darcy's equation but that might be more complex than I wanted to go :-(

 

[waterboy123]

Please see attachment. The problem with Darcy is I have no way of accessing the delta H, ie the change in water level across the trench. If I new this I could calculate Q and everything would be good in the world.

 

[Drew08]

It's a differential equation where i = dh/dx:

Q=K(dh/dx)By
and, y = h - Sx
or Q = K (dh/dx)B(h - Sx)

B = Width
y = Depth
x = location upstream from the downstream end
S = bottom slope
h = energy head (y + Sx)

The differential equation can be solved using a standard step method, and by varing Q until h = the top of the channel at the upstream end.

 

[cvg]

you cannot solve this with any degree of accuracy given the data you have and Mannings equation is completely out of the question. stick with darcy. a reasonable estimate might be to assume an avg cross sectional area and delta h. solve for a range of hydraulic conductivities to give an estimate of the range of possible flows.

 

[LincolnPE]

No! Manning's is not to be applied to interstitial rock flow! Totally inappropriate!