Influence factor for stress increase

There is an influence factor to determine the stress below a corner of a rectangular area which is derived from Boussinesq's equation. The format is several functions of m and n, then an arctan. There is a modifier for when the arctan portion of this equation is negative. Does anyone know what the modifier is? I know this is vague but I am hoping that I have included enough information that someone familiar with the topic would be able to understand.

Thanks.

SS

scottiesei said:

There is an influence factor to determine the stress below a corner of a rectangular area which is derived from Boussinesq's equation. The format is several functions of m and n, then an arctan. There is a modifier for when the arctan portion of this equation is negative. Does anyone know what the modifier is? I know this is vague but I am hoping that I have included enough information that someone familiar with the topic would be able to understand.Thanks.

SS

Click to expand...

I know which formula you are talking about. I usually refer to my Das text, but the argument of that term is too complex to write out. I noted the same formula in NAVFAC 7.01 - they use (x,y) convention instead of (m,n). There is a chart including terms to orient yourself wrt the loading condition. I pasted the imaged page below - it is the 3rd diagram.



Please confirm this is what you needed or if you need a better image/formulae.

JR

That's the one, but I am looking for a modifier for when arctan is less than 0 due to certain x and y values.

scottiesei said:

That's the one, but I am looking for a modifier for when arctan is less than 0 due to certain x and y values.

Click to expand...

scottie,

Are you reviewing a geotech report? I thought you were structural?

I have seen a number of different 'expressions' for the solution. Remembering that the equation is based on elastic solutions for soil (medium) there are other possible solutions. I came across a variant of the solution based on Poulos and Davis' book of Elastic Solutions for Soil and Rock Mechanics from Page 54:

Iσz = 1/(2π)*[arctan(m*n/sqrt(m²+n²+1)) + {m*n/sqrt(m²+n²+1)}*{1/(1+m²) + 1/(1+n²)}]

where Iσz = influence coefficient

m = B/z

n = L/z

B = half breadth of foundation

L = half length of foundation

z = depth

There is still an arctan function in the expression, but it is limited to part of the expression - maybe this will help with the 'negative' results. I recall seeing just a polynomial expansion of the solution somewhere - I will see if I can find it for you this evening. I have to run to class + another late afternoon meeting.

JR

Mitchell and Gardner (1967), Schmertmann (1970) developed a correlation between the Nf(standard penetration number) and the elastic modulus of the soil. This is all in the Das book, but for the "negative" influence factor, I think this must be over my head because I am looking at the consolidation settlement calculation and I'm seeing that the table will never yield an influence factor less than zero. What are you calculating?

McEngr said:

Mitchell and Gardner (1967), Schmertmann (1970) developed a correlation between the Nf(standard penetration number) and the elastic modulus of the soil. This is all in the Das book, but for the "negative" influence factor, I think this must be over my head because I am looking at the consolidation settlement calculation and I'm seeing that the table will never yield an influence factor less than zero. What are you calculating?

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Sorry scottie, I'll do some more reading... I have to read more carefully what you're asking. )

This is for a grad project, real pita

Scottie,

In my Das book, it says that within the arctan expression, you must use a "Pie - 2mn*SQRT(..." in leau of "2mn*SQRT(..." when the arctan expression is negative.

Is that what you're after?

McEngr

That's the one!!!! I can not get correct values from the second equation using the pi modifier????

maybe spot me and try a few to match the chart????

scottiesei said:

maybe spot me and try a few to match the chart????

Click to expand...

I'll see if I can do this for "fun" on my lunch break. Us westcoasters don't have our fudgepump sandwiches until 3 o'clock eastcoast time .

:bananalama:

http://www.marchetti-dmt.it/docfiles/boussinesq.doc

This equation appears to work. I am going to run a few more to be sure. I think Das's is jacked up. I called and no eratta, blah!

scottiesei said:

http://www.marchetti-dmt.it/docfiles/boussinesq.doc
This equation appears to work. I am going to run a few more to be sure. I think Das's is jacked up. I called and no eratta, blah!

Click to expand...

Cool !! I noticed that the equation is the same reference as what I posted above (Poulous, page 54) - it seems I got the multiplier on the outside of the paranthesis incorrect though. I might have just transcribed it long ago incorrectly. However, please double check that formula because the analytical solution method is done in POLAR COORDINATE SYSTEM. The (m,n) convention is a conversion to RECTANGULAR COORDINATES - my recollection is that the pi() term falls out. I will see if I have anything that confirms/denies.

My understanding is that is the go-to book as long as you KNOW the medium is behaving in a elastic mode.

FYI - Das follows Terzaghi which is the classical foundation of soil mechanics. Terzaghi, considered the father of geotechnical engineering, basically took what he new about materials mechanics and applied it soil medium. It sounds simple, but is actually quite powerful.

JR