Pressure Dissipation through soil 2

[Dirtguy4587]

I am faced with a problem that I don't know the answer to. I am trying to determine how pressure dissipates through a soil, not with respect to time, but with respect to distance.

Say, for example, a soil with an initial pore pressure, is injected with a higher pressure at a point source (i.e. a well). Given that you know the permeability (k), is it possible to determine a steady state relationship between that additional pressure, and the distance required to return to the original pressure?

Anyone have any thoughts on this?

 

[msucog]

just curious here but: what in the world are you trying to do? (i'm actually trying to get my brain wrapped around your question and scenario)

 

[Dirtguy4587]

I'm trying to determine how excess pore pressure will dissipate as a function of distance. If I have a thin soil layer with an initial pore pressure, and I then increase that pore pressure at a point source (like an injection well), how far away from the well will the pressure dissipate back to the original condition? Another way of wording it is how do I determine head loss through a soil?

 

[oldestguy]

This is in the category of flow net design and use.

Look up the basics of flow nets and very likely you will be able to solve your question.

It takes a soil mechanics text that goes into considerable detail on theoretical aspects.

Once such book is "Foundation Engineering for difficult Subsoil" conditions by Leonardo Zeevaert Printed by Van Nostrand Reinhold Co.

You probably start off with changing your excess pore pressure to a hydraulic head and go from there.

 

[BigH]

Also Cedergren's book on Seepage and Flow Nets.

 

[fattdad]

Flow nets relate to steady state pore pressure distribution only. The rate of pore pressure dissipation with respect to time depened on Cv or Mv, which are dependant on the state of stress.

I may have to think on this. . .

f-d

¡papá gordo ain’t no madre flaca!

 

[msquared48]

Kinda sounds like an orifice or wier condition with a head that is decreasing with time asthe water exits the orifice.

Big difference here is that the orifice can flow any direction out of a hemispherical shape.

Mike McCann
MMC Engineering

 

[fattdad]

One more thing on flow nets: They are independent on permeability. Fundamentally, Cv and Mv are dependent on permeability and related directly to the rate of pore pressure dissipation over time. As a flow net is independent on permeability, there can be no flow net solution to your problem (i.e., if you are concerned with the matter of stress dissipation over time).

I'm not saying I have the solution, I'm just thinking through the problem. . .

f-d

¡papá gordo ain’t no madre flaca!

 

[LCruiser]

They are only independent of permeability if homogeneous, which we know never really happens.

P.S. qualify "original pressure"

 

[Dirtguy4587]

Original pressure = hydrostatic, assuming the ground water table is at ground surface.

I'm only trying to calibrate myself to some modelling that was done (by someone else). For my purposes, I am assuming a homogeneous sand layer, approximately 2m thick at a depth of 30 m. Therefore the initial pore pressure is approx. 295 kPa. In this case, I have a well injecting up to 1200 kPa.

I guess the distance is also time dependant; the more time the pressure is applied, the further the pressure front will advance.

 

[fattdad]

Model it as an injection well and use Theis equations (or the graphical solution), perhaps. . . ?

f-d

¡papá gordo ain’t no madre flaca!

 

[muuddfun]

You might look at Dewatering and Groundwater Control from the Army Corps, TM 5-818-5.

 

[msucog]

i'm picturing the drawdown effect...except in reverse. i vaguely recall toying with something like this idea back in college and just manipulated the drawdown equations (don't remember by whom but it was in either my foundations book by das or in my water resources book). i think it involved double integrals but it's hard to recall those days...my brain didn't start functioning properly until i got in to the real world.

 

[fattdad]

Any steady state drawdown equations can work in reverse. Just use negative values for "Q". I'd hope the steady state condition could be reasonably evaluated without needing to drag out my calculus book (not that I could that is. . .)

f-d

¡papá gordo ain’t no madre flaca!

 

[Dirtguy4587]

Thanks - if I absolutely have to, I'll dig into the calculus, but I'll see if I can avoid it first.

 

[DRC1]

If you are only looking at pressure at distance and a constant injection pressure and no sink, I would assume that a Bousinessiq solution would work. It really is a pressure in an elastic half space question, not really a hydraulic problem.

 

[fattdad]

DRC1's point is well taken. My advice is related to pressure in the form of excess pore pressure (i.e., hydraulic head). If you are applying earth pressure, that in turn affects the pore pressure, then that is a different problem. For the former, you'd look at flow nets and well equations. For the latter, you'd have to look at the change in stress with radial distance (i.e., that would develop after the dissipation of excess pore pressure) and relate that to excess pore pressure at the first instance and then consider the time to dissipate this excess pore pressure. I think that problem would be best addressed using funny elephants - oops, finite elements. And, it would be funamentally related to Mv, Cv, k (which are all inter-related).

Confused. . . . (well, I kind of am confused if you aren't)?

f-d

¡papá gordo ain’t no madre flaca!

 

[Dirtguy4587]

Yes, I am confused, to a point. I think I will do a finite element analysis (using SEEP/W) to see what happens in a steady state condition.

 

[civilperson]

The dissipation is a function of time, not distance per se. Initially the excess pore pressure gradient will be extreme and go to normal in a short distance. Over time, the gradient will flatten to effect farther out. The rate of change of the gradient is a function of void ratio and permeability of the soils. Steady state will be achieved when the gradient is unchanging, (assuming a constant increase in pressure at the source).

 

[fattdad]

The rate of change is also related to the state of stress. If the soil is overconsolidated and the increase stress is lower than the pre-consolidation pressure, then the pressure dissipation can occur more redily (i.e., again this relates to Cv, which is also a function of Pp).

I suggested finite elements related to transient pore pressure dissipation with respect to earth pressures. Seep/W cannot address that.

f-d

¡papá gordo ain’t no madre flaca!