Constrained Modulus Vs Young's Modulus

[cbosy]

When would one be used rather than the other? Say the depth to rock is 100 ft (H) and the footing is 25 ft wide (B), I would use the Young's Modulus. If B=100 ft and H=25 ft, I would use the constrained modulus. Does anyone have any references or guidance when to choose between the two when considering varying B's and H's?

 

[BigH]

Might wish to download from link below:

http://ceprofs.tamu.edu/briaud/Intro to Moduli/Intro to Moduli.pdf

 

[Mccoy]

Good link, BigH, I'm going and read it first thning tomorrow morning.

I also found very interesting the following article, with correct conversion formulae from E to Ed:

Approximate Displacement Influence Factors for Elastic Shallow Foundations
J. Geotech. and Geoenvir. Engrg., Volume 125, Issue 6, pp. 453-460 (June 1999)

Paul W. Mayne

Member, ASCE,
Harry G. Poulos

Fellow, ASCE 1Assoc. Prof., School of Civ. and Envir. Engrg., Georgia Inst. of Technol., Atlanta, GA 30332-0355. E-mail: pmayne@ce.gatech.edu 2Sr. Prin., Coffey Partners Int. Pty. Ltd., 12 Waterloo Rd., North Ryde NSW, Australia 2113. E-mail: harrpoulos@syd.coffey.com.au
Displacement influence factors for calculating the magnitudes of drained and undrained settlements of shallow foundations are approximated by simple numerical integration of elastic stress distributions within a spreadsheet. Influence factors for circular foundations resting on soils having homogeneous (constant modulus with depth) to Gibson-type (linearly increasing modulus) profiles with finite layer thicknesses are obtained by summing the unit strains from incremental vertical and radial stress changes. The effects of foundation rigidity and embedment are addressed by approximate modifier terms obtained from prior finite-element studies. Results are compared with closed-form analytical and rigorous numerical solutions, where available. A new solution for Gibson soil of finite thickness is presented.

 

[dgillette]

A suggestion: When you put in an email address, such as above, put it in as:

smith'at'jones.com

or something like that, rather than:

smith@jones.com.

I'm told by my IT-guy neighbor that the spammers have programs that hunt around the web looking for addresses. Help to minimize Paul and Harry's spam load.

BTW - Regardless of what you may have heard, I have NEVER advocated the death penalty for spammers. Flogging should suffice.

 

[cbosy]

Can you fax me the page with the conversion?
Chris Bosy, 312-922-0201.
TX

 

[BigH]

dgillette - good point on the email addies - the site frowns heavily on this too. I have my opinions on metting out justice to spammers; malicious spammers and identity thieves - let's say it is a sliding scale and I don't like others using my "self" for their own gain. Cheers.

 

[Mccoy]

Sorry for the glitch folks,
but those are cut & pasted addresses from another webpage so already prone to spamming.
Maybe the moderator may transform or erase them.

cbosy, page 7, equation (1) of following link should do:

http://casehistories.geoengineer.org/volume/volume1/issue1/IJGCH_1_1_3.pdf

 

[cbosy]

Mayne's paper indicates that due to the small Poisson's ratio, the difference between the two is so small that it can practically be neglected. Clyde Baker was a forensic investigator on the project addressed in Mayne's paper and said during a talk up here in Chicago that the original engineers plugged a Compression Index that was one tenth of the real value into their computer program and nobody manually checked it, if my memory serves me correctly.

 

[BigH]

cbosy - good point!! One reason that one should always do, as a minimum, a back of the envelope calc to see what the correct ball-park values might be!

 

[Mccoy]

Mayne's paper indicates that due to the small Poisson's ratio, the difference between the two is so small that it can practically be neglected

That's an interesting development from recent research, although it is underlined in Fang's 1990 treatise that nu is most sensitive to water content.

As a matter of fact, the D' and E' symbols refer to drained conditions.

If undrained conditions in saturated soil occur usually a nu = 0.5 is indicated, with the result that the D/E ratio reaches infinity!!!

A nu = 0.4 doubles the ratio D/E
A nu = 0.45 almost quadruples it


I'll have to look the other article up, at a first sight the relationship seemed a little different. I'll let you know.

Clyde Baker was a forensic investigator on the project addressed in Mayne's paper and said during a talk up here in Chicago that the original engineers plugged a Compression Index that was one tenth of the real value into their computer program and nobody manually checked it, if my memory serves me correctly.

One factor of magnitude only depends from a final zero, after all!
Weird nobody checked though, since E or Ed was pretty low (8 MPa) and the slab was pretty much loaded (up to 200 KPa).
I mean, those values should sure trigger an alarm ring into a geotech's brain!

 

[dgillette]

They don't trigger an alarm in my brain because, like most Americans, I have to stop and figure out what they mean in English units, like tonnes per square furlong or something. ;-)

But seriously, folks, I think undrained D/E of saturated material can't really approach infinity because D is limited by the bulk modulus of the pore fluid. We often model it as an elastic solid with very high nu (~0.47 - 0.49), but that's a useful fiction. It's a porous solid with fairly low nu, filled with a liquid (whose compressibility varies greatly if there are small bubbles of undissolved air).

 

[Mccoy]

cbosy,
the formula indicated in the ASCE paper is identical to the the one in the web article. In the ASCE paper some plots with nu = 0.5 are indicated, but in reality it's a 0.49.

dgillette,
conversions are terrible both ways indeed

what value of nu would you use in a saturated clay?

I undertstand there is no unique answer, a function of OCR as well.
Also, when nu approches 0.5, D/E is a tad too sensitive to the choice, so it becomes no easy job

I was reading Tomlinson (and here I'm definitely feeling a from BigH) where it's related that the ratio of immediate settlements to consolidation settlements are diferent for different OCR's.

With some juggling, we should be able to guess if the D/E ratio is in the ballpark....

 

[BigH]

Another convert, McCoy? Good on you!

 

[Mccoy]

BigH,
I never told you but Tomlinson was one of the first geotech books I read and I've always thought it's very practical and sensible. The author has worked a lot in the field so he knows the everyday problems and, most important of all, his explanations range from the simple one-floor masonry structures to the complex buoyancy rafts and caissons foundations.

We're both in the Tomlinson fans club !