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Flow rate into a horizontal bore.

Flow rate into a horizontal bore.

Flow rate into a horizontal bore.

(OP)
This a slightly conceptual question, but it was inspired by a question that a client asked me. Suppose I am excavating a horizontal boring through some silty clay about 5 ft in diameter and 50 feet below ground surface. Let's say the water is about 10 feet below ground surface.

Assuming you know the permeability characteristics of the soil (k, let's say something lke 1x10^-7) is there a way to calculate the flow rate into the boring, asssuming uniform soil and permeability conditions?

A tunneling contractor was telling me some horror stories about doing some deep horizontal bores and how he hit an artesian well and it blew water all over the highway, and I was just curious how fast the water was actually flowing into that hole.

RE: Flow rate into a horizontal bore.

For Q&D, you could probably model it like a well test, if you make the approximation that the pore-water pressure at the crown of the tunnel is the same as at the invert.  That approximation probably introduces no more uncertainty than is in your permeability estimate (bearing in mind that, in general, Kh>>Kv).  At the opposite end of the spectrum, there is the 3D FEM analysis, which would allow you to explicitly include difference between Kh and Kv.

If K is really only 1x10^-7 the inflow would be trivial.  Sand seams would change that considerably.

 

RE: Flow rate into a horizontal bore.

More boundary conditions are required to approach the problem, mostly related to time.  If you were to remove all the clay in an instant and then, just before any reacclimation of pore pressures were to take place, estimate the flow potential under these gradients you'd get some answer.  If you were to remove all the clay, let the tunnel completly fill up with water and then consider how much water you could remove while just keeping the hydraulic grade line above the top of the tunnel, you'd get a different answer.  If you were to keep the hgl just above the invert, a somewhat different answer.

There's a part of me that thinks this a somewhat complicated problem, made very easy using modflow.

p.s., we'd also need to know the tunnel length, unless you just want to address this problem as a unit slice.

f-d

¡papá gordo ain't no madre flaca!

RE: Flow rate into a horizontal bore.

Like dgillette indicated, I would do it as a test well, or similar to a drain system, to rough it out.  If you have the parameters, then it is a quick and easy estimate.  If you hit a confined layer with pressure on it, such as the tunneling contractor, you would have a new analysis on your hands.

RE: Flow rate into a horizontal bore.

Yea, an interstate car wash!

Mike McCann
MMC Engineering

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