Elastic Theory

[nbr1]

When is it not applicable to use elastic theory?
Textbooks offer solutions based on elastic theory but stop short of explaining when it is applicable and not.

 

[dgillette]

That's too broad of a question. Someone could write for a week trying to cover all the "ifs."

 

[rowingengineer]

"When is it not applicable to use elastic theory?"
All of the time, but we just ignore that fact most of the time.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[dgillette]

Rowingengineer - Maybe the question should be "When can we get away with it?"

 

[geotech007]

no any case in geotechnical engineering

 

[rowingengineer]

A quote that best fits from the man Karl Terzaghi:"The major part of the college training of civil engineers consists in the absorption of the laws and rules which apply to relatively simple and well-defined materials, such as steel or concrete. This type of education breeds the illusion that everything connected with engineering should and can be computed on the basis of a priori assumptions. As a consequence, engineers imagined that the future science of foundations would consist in carrying out the following program: Drill a hole into the ground. Send the soil samples obtained from the hole through a laboratory with standardized apparatus served by conscientious human automatons. Collect the figures, introduce them into the equations, and compute the result. Since the thinking was already done by the man who derived the equation, the brains are merely required to secure the contract and to invest the money. The last remnants of this period of unwarranted optimism are still found in attempts to prescribe simple formulas for computing the settlement of buildings or of the safety factor of dams against piping. No such formulas can possibly be obtained except by ignoring a considerable number of vital factors."

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[nbr1]

To clarify:

When would it be appropriate to use elastic theory in settlement calculuation.

Dense Sand?
Soft Clay?
Stiff Clay?

 

[rowingengineer]

It COULD/MAYBE/POSSIBLY/SOMETIMES be appropriate to treat the soil as an elastic material for settlement analysis if the soil profile are similar across the site if you had dense sand over rock for example. Soft clay, well now you playing with fire, and experience/judgment have large inputs here as you will consolidation ect, consolidation can be taken care of with preloading ect, but that is a judgment call by the geotech. Stiff clay, how do you account for variations due to swelling ect, well this all depends on your loadings, so now it is a soil structure related analysis.

we could discuss the soil structure analysis how important are differential settlements....I could go on, but it's lunch time and i'm hungry at the end of the day i would suggest that you get advice from the geo tech on the job and the senior engineer in your firm, there are often times where elastic analysis is more than justified like 90% of concrete pavements. these guys are the ones whom should know wether or not it is good for your site.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[ishvaaag]

Maybe the required precision is that elastic theory is not most of the times the more accurate portrait of what will happen in a soil, but that within such understanding is extremely useful and really the practical way in which we tackle most of the times our calculation tasks, one is tempted to say, even for soils. That this approach is not the more accurate is implied, yet seen technically useful.

Now, almost euclideanly way, things abhorr disturbance and hence allow for themselves to be molested the least when loads are applied to them. This is one way of saying something akin to the principle of the least energy of deformation, a soil and any structure within its constraints will take just the minimum energy of deformation to stay the less disturbed; with the result that this produces (identifies, defines) what between all is the true deformation to happen and final status to have, and, as well, that if you devise some way or mechanism that establishes equilibrium for the case, either it is the true one, or one safer. Seen conversely, finding one actual path to equilibrium, technically feasible, we maybe can't be sure we have found the right one, but we can be sure there is one with equal or less energy of deformation that will be such, and our solution, meeting equilibrium by excess, is safe. The technicalities here would reduce at ensuring to devise a notional mechanism for equilibrium feasible and in accord with extant constraints. A brute simple example would be having a column able to take 100 tons. So we inmediately think it be able to hold 50 tons, there will be a solution at less energy of deformation that provides for the actual equilibrium.

Now, with elastic theory we are in the path to such ways of getting equilibrium; for once most of the times was applied at safety factors getting the more the feasible out of the nonlinear behaviour, say, 2 for steel, 5 wor wood, 10 for cables, 6 for soils and so on. And so our way of thinking is like with beamcolums, or fatigue, at so low axial loads the effect of the axial loads can be dismissed, or never would be meaningful under such level of stress and so on. So we were and are encircling our problems with additional constraints that would allow the simple and general theory of proportionality between force and deformation be able to deliver a solution that if not the true is one safe.

All materials are nonlinear if over a limited amount of the final strain range, and then there is the lack homogeneity in materials of mixes of them, like soils. But through observation and building lookup-tables we have for many cases built methods that making use of the theory of elasticity are well portraited in the literature as useful, never a true statement of what happens, that nobody is really able to ascertain except by theorizations (even if more complex than elastic theory). So we use them with the corrections required, may times to get just relative appraisal of the behaviour respect other cases we previously built etc. Just a tool.

 

[rowingengineer]

well said ishvaaag

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[Ron]

When the material itself has the capability to react loads elastically. Usually only dense sands and rock/sand mixes will come close to behaving elastically.

Some clays may appear to act elastically, but in fact they are not, so I wouldn't consider using elastic theory for settlement of clays.

 

[BigH]

An interesting discussion to date. Is elastic theory correct? - no. Is it used? - yes. and why? Because there is very little choice unless one goes into particulate theory (see M.E. Harr).
There are two ways to use elastic theory, in my view. First - as has been discussed above, is for small strains when the load-deformation curve can be approximated as linear for a reasonable amount of strain. Steel - that is linear for a "long way." Concrete - also linear for a bit of a way, but the modulus of elasticity at the onset differs from the secant modulus (say half way up the load-deformation curve) to the modulus near the peak - in other words, the modulus is a function of strain. I would suggest that this could be modeled (although not to the accuracy that one would expect as a structural engineer, say). Settlement computations using the modulus values are used in basically cohesionless materials - Bowles and others lay this out. There are correction factors to be applied for depths of embedments, etc. for clays - so long as one is on the recompression path, it is reasonable but, of course, one must use consolidation theory for soft to stiff clays that extend beyond the preconsolidation pressure. (but use elastic theory for immediate settlements.)
But for all those saying that elastic theory doesn't hold - I would, secondly, query as to how they figure out stresses from a load applied to a footing or an embankment with depth - say one has a footing at the surface and has two strata below. Of course, one wants to know the pressure on the surface and within, say, the second layer which is a soft clay - it is the pressure within the soft clay that will cause the consolidation of the clay. Also, say the upper layer is a bit overconsolidated and hence stiffer. For those that "don't" use elastic theory - how does one estimate the pressures in both layers? Bousinesq? Westergaard? - whoa, are these not all solutions based on a continuum elastic half-space? Sure are! For the stiffer layer one estimates the ratio of stiffness and applies a layer correction factor for the stresses - two layer theory - three layer theory - pavement structures with 4 to 5 layers.
Yes, we use elastic theory - for settlements because the strains, typically, as factors of safety that have been traditionally used, are low enough to suggest that the initial tangent modulus is generally valid for the range of loading. For pressure values within the soil substrata because how else would we estimate them? As I noted earlier - we could use particulate theory; but I've only ever seen it in Harr's book.
Similar arguments are made for the shear modulus - what is needed in vibration amplitude estimations and seismic design - and let's not forget that the cross-hole seismic tests for shear wave velocities are also used to estimate "E" values . . .
It was a good lunch hour . . .

 

[rowingengineer]

Big H,
Was wondering when/if you would join the discussion.
I think we can all agree that elastic theory is used often to estimate the pressure distribution within soil substrata, as for settlement analysis as you have noted there are corrections required based on test/experience required to fudge the results for clay, But I would also use a varying soil profile to model the effects of volume change due to moisture effects.

Now let’s up the stakes and discuss sites with soils with uncompacted fill or similar (aka highly changing stiffness across the site), would you use elastic theory to estimate settlement? Ok I’m being sadistic, but the point I make is while we use these analysis procedures we use them where and if appropriate, sometimes you need to adjust the site condition such that your analysis methods can be justified, aka preloading, re-compacting ect. Sometimes you need to understand that the elastic model is only an approximation of settlement and then you need to judge as best as you can the differential effects ect.

In summing up: assuming that elastic analysis can be directly applied to soil substructure is not always justified; this is the point that must be stressed to someone learning the trade.


Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[ishvaaag]

Wellm there are aristo-pigs that even love ***clean*** water. The look-up table goes on...

http://mw2.google.com/mw-panoramio/photos/medium/5157990.jpg

http://mw2.google.com/mw-panoramio/photos/medium/16543142.jpg

 

[rowingengineer]

Nice play ishvaaag

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[nbr1]

Thanks Big H.

The comments answer my question.

Regards,

 

[Ron]

I agree that BigH's comments are excellent. Consider one other thing....Elastic theory actually works when you can predict the parameters for its application.

As an example, we limit the vertical strain in pavement subgrades to prevent rutting. If elastic theory were not present and working, we would have significantly more pavement rutting than we do.

Pavements are truly designed using elastic parameters. To extend this to a foundation requires a bit of thought....Do we know the elastic parameters of each of the materials? Can we determine those parameters accurately through laboratory testing?

If you look at the stress-strain curve in a cyclic triaxial test, you can clearly see the elastic influence. That's where BigH's explanation is clearly on target.

 

[fattdad]

Elastic theory is appropriate for soils that are overconsolidated and not prone to secondary consolidation. For non-linear behavoir, hyperbolic modulus can help (stain-softening). If any part of the newly-applied load results in virgin consolidation, elastic theory isn't correct.

Yes, it approximates real life, but not too bad.

Obtaining representative values is the biggest hurdle.

f-d

¡papá gordo ain’t no madre flaca!