Terzaghi boundary porosity 1

[Jordan2]

Dear Friends,
I have some doubt about the definition of the effective stress proposed by Terzaghi and reported in the book Underground Excavation in Rock (Hoek & Brown, 1980):
s'=s-(1-nb)u
where s'=effective stress; s=total stress; u=pore pressure and nb=boundary porosity.
Evidently the formula should adequate the concept of effective stress to low porosity material, but (maybe I am wrong) it seems to me that there is some problem. In fact, if I consider a very porous material, nb should be high and then the equation tends to s'=s, that is the opposite I expected. Do you have perhaps the original reference? Am I wrong to interpret the "boundary" porosity as the effective porosity (i.e. referred to interconnetted pores)?
Thank you in advance for your help/suggestion?

 

[jdonville]

Jordan2,

While I haven't seen this relation before, it would tend to make sense to me in terms of the traditional definition of porosity, where I understand porosity to be

Volume of Voids / Total Volume of Soil Specimen (not just solids)

which implies a spectrum of possible values from 1 (totally fluid, no soil particles) to 0 (totally solid, no fluids).

The limit on porosity, then, is what is the minimum amount of soil you need to still call it a soil, rather than a suspension of fine soil solids in some fluid (air, water, etc.).

Jeff

 

[Jordan2]

Hi Jeff,
thank you for your answer.
Conceptually I agree with you, nevertheless, speaking of common soils, I do not understand why for a very porous soil the cited equation tends to give s=s'.
Where am I wrong?
Jordan

 

[dgillette]

I wonder if this is misquoted in H&B. It doesn't make sense to me either. The typical S'=S-u is based on approximately zero contact area on a wavy plane through the soil (boundary porosity approximately equal to 1). (I think the boundary porosity of a soil would refer to contact area, rather than to volume.)

Looks to me like it should be S'=S-nb*u. Anybody got Theoretical Soil Mechanics handy? I MIGHT be able to find the ASTM proceedings that far back.

On the other hand, maybe all three of us are too dense to see it.

 

[Jordan2]

I have written also to Ted Brown and he answered that the boundary porosity should be in effect the ratio B/A, where B is the solid to solid contact area and A the total area. Therefore, for a material with very low porosity, the boundary porosity would tend to 1, etc. It is a strange definition and it would be interesting to get the original Terzaghi paper..
Thank you for your contribute.
Giordano

 

[jdonville]

Jordan2,

Thanks for bringing the question to our attention. I would be interested in haring back from you on what you learn.

Jeff