Settlement question 6

[lhosuna]

I'm trying to set up a work sheet on Excel to calculate the settlement for rectangular footings. One step requires for me to read the influence value from NAVFAC DM-7 Figure 4 "Influence Value for Vertical Stress Beneath a Corner of a Uniformly Loaded Rectangular Area (Boussinesq Case) page 7.1-168 and I was wondering if any of you guys know where can I find the formulas to recreate those curves or to find the influence value "I" directly without having to read the values from the chart as it is very cumbersome. Any help will be really appreciated. Thanks in advance!

Luis

 

[BigH]

Poulos and Davis' "Elastic Solutions to Soil and Rock Mechanics," Wiley Publishers, 1975. I understand it is out of print now, but if you are near a university, you should be able to find the text. Also, many of the Indian geotechnical texts spend a lot of pages with stresses - and you might find the equations in one of them.

 

[CarlB]

Some formulas here:

http://www.usace.army.mil/publications/eng-manuals/em1110-1-1904/a-c.pdf

 

[PSlem]

download a curve matching program from the internet and type a table with values and let it give you a polynomial.

 

[Panars]

Since there are two variables in the equation, curve fitting is not a simple proposition. The equation is readily available from many sources anyway.

The Boussinesq equation for the vertical stress beneath a corner of a rectangular loaded area is :

This is in terms of B and L in place of X and Y, as given in NAVFAC.

 

[fattdad]

What about the equation for the center of a loaded rectangular area? I think it's great Panars provided this equation, but wonder whether a settlement evaluation should also consider the behavoir of the soils beneath the center of the footing. . . .

f-d

¡papá gordo ain’t no madre flaca!

 

[BigH]

fattdad - as you, I know, are well aware divide the footing into 4 equal rectangular parts - common at the centre of the overall footing rectangle. Then determine the stresses at the corner and multiply by 4. Bousinesque is for flexible footings - most footings aren't really flexible so, in fact, you actually need to determine the stresses under a rigid footing. You can use the correction factor as found in Bowles (and others) for rigid footings compared to flexible. Steel tank bottoms, on the other hand are flexible. Stresses beyond the confines of the rigid footing would be flexible.

 

[Gimbli]

I think Das book has something about it

 

[Mccoy]

Best recent work on the specific subject (influence coefficient and spreadsheet), as far as I know, is the following:

Approximate displacement influence factors for elastic shallow foundations, Mayne and Poulos, JGGE, ASCE, june 1999

 

[GeoPerson]

The boussinesq equation as mentioned above is not true when (mn)^2 > m2+n^2+1 due the term tan^-1 is (-), see Bowles 1988 for references. It took me a while to figure the equation out. You need to minus pi and change arctan to arcsin. Also use the PDF from CarlB above (the army corp. of engineering) for strip footing (L>9B). Good Luck.