Elastic Settlement as a Separate Quantity in Settlement Analysis 3

[ScarpShooter]

I have often wondered why there is a convention to include elastic settlement as a separate value in addition to consolidation (primary & secondary) settlement. It seems to me that when you run an oedometer test you have an initial stress and void ratio and a final stress and void ratio. This should be all you need to estimate settlement? Wouldn't the addition of an extra elastic settlement amount, which I imagine is calculated extraneous to the oedometer test data, change your void ratio to something other than what is measured in your test? How can this be justified if the oedometer test fundamentally represents the relationship for a change in void ratio with a change in stress?

Part of my frustration with elastic settlement is that it seems like there is never really good input data (other than loading conditions). Why not run an oedometer test on a remolded coarse-grained (sand) sample? Wouldn't this also give you a volume change/stress relationship from which a modulus value could be calculated even though the void ratio/log time plot from the test wouldn't be worth much? Maybe even better (two birds with one stone) is to use void ratio/stress data from a series of specimens being prepared for a direct shear test (maybe unlikely that the shear test normal loads are in the same range as the consolidation loads of interest, but for arguments sake). Regardless, it seems like you could get a modulus out of that data for elastic settlement calcs?

I'm thinking that the approach of using actual lab test data as opposed to taking a conservative tabular value from some reference is superior but I just haven't seen this called out as a good idea anywhere and found myself in this forum today. Thanks in advance.

 

[oldestguy]

To answer your question in some respects examine the graphic plot of the test and explain that the test does not reflect elastic behavior also.

 

[Ron]

You are trying to equate and compare two distinctly different parameters.

Consolidation is a process by which soil grains are reoriented and relocated to fill voids, thus decreasing overall soil matrix volume.

Elastic settlement is a different type of process in that the soil grains are compressed and elastically deformed....not re-oriented or otherwise moved to fill voids. Elastic settlement has little to do with a void ratio change.

 

[ScarpShooter]

Ron, I see where you are coming from. I think it might take the discussion in a somewhat different direction but I have the following thoughts.

Regardless of whether the deformation from a load results in a change in void ratio or an elastic deformation, the volume change measured in the oedometer test captures both phenomena because they both have adequate time to develop in the test. True elastic deformation, the kind I believe you are referring to, in soils is likely very minimal as the individual soil grains have very high moduli values 10^6 psi vs applied stress levels often in the 10^1 psi range.

In soil mechanics practice it is common to calculate settlement in a cohesionless soil using an elastic deformation analysis (usually rigid or flexible foundation over elastic half-space). The elastic modulus used in this analysis will vary depending on the in-situ density of the soil. This is simply an approximation of the actual soil behavior where the actual deformation is due mostly to the rearrangement of soil grains. As we know, the elastic modulus of the individual soil particles will not change whether the particles are in a loose or dense configuration. I think that the important thing for me, and maybe others, to realize is that this settlement analysis using the elastic half space and a moduli value representative of the bulk soil condition with collapsible voids is not the same as elastic soil deformation due to compression of the individual soil grains (the kind you speak of).

 

[Okiryu]

It is an interesting post. But, I agree with Ron. Elastic settlement does not consider volumetric strains. Also, settlement analysis will depend on site conditions. For example, if you have saturated clays with large loadings; i.e. embankments, you can considered the elastic settlement as zero, so in this particular case, you just need to be concern of consolidation settlements.

 

[fattdad]

calculating elastic properties of a sand in an odometer doesn't make sense. To some extent, we need to evaluate the influence of load on all soil layers. You are correct on clay, the consolidation (i.e., as related to dissipation of excess pore pressures) trumps elastic theory. Don't convince yourself that elastic response is not important though!

In the odometer you will also obtain the coefficient of secondary compression for clay and organic materials. Elastic theory in geotechnical practice has a different term for the same thing though. We call that, "C-sub-t," which ranges from 1.1 to 1.5 depending on whether you are looking at the creep response for 10 or 50 years. Sort of a parallel to secondary compression. However, again, we can't measure it in an odometer.

I would accept elastic theory in a clay though if I knew there was no chance of exceeding the preconsolidation pressure, the soil was not saturated, and there was some basis for the assignment of modulus. So, you have a point for one aspect of our field, but it's not universal.

f-d

ípapß gordo ainÆt no madre flaca!

 

[Okiryu]

f-d, some time ago I read the attached paper from Professor Paul Mayne at Georgia Tech. At page 11, second paragraph, just below figure 7, he indicates: "....Calculations of total displacements due to drained primary consolidation are best handled by either the classical evaluation of elastic stress distributions beneath surface foundations coupled with e-logσv' data, or elasticity theory using displacement influence factors and appropriate moduli." So, I emailed him to ask if does this means that elastic settlements analysis can be also used in lieu of consolidation settlement analysis? , he answered:

"The short answer is that when you use consolidation theory, you also use elastic theory to calculate the stress distributions with depth. The stresses are used to position where you are on the e-log sv’ curves. An alternate (used more so outside the USA) is to represent consolidation data as “constrained modulus” (See Lambe & Whitman 1979).

Otherwise, the (same) elastic theory can be used to obtain displacement influence factors – here, the stresses attenuated with depth are represented as strains

All things equivalent, you would get same answer, either using stresses or strains.

For the case study in the Piedmont geology, the coefficient of consolidation is high (sandy silt) and the time it took to build the dorm hi-rise (12 months) was essentially all drained settlements. That is, it consolidated quickly as the building was constructed (slowly)."

I just wanted to share this with the forum as I thought it is related to the OP's discussion...In addition, I also apply what you have indicated in your last paragraph from your above reply...

 

[bdbd]

Hello,

Of course consolidation can be predicted with elastic theory if you use the correct E value. Lambe and Whitman's chapter 32.6 gives example for this. You can use drained elastic modulus to calculate total settlement and subtract the undrained settlement (elastic as we called it) which we calculated with undrained elastic modulus.

At this point, correlations like E'=0.6Eu becomes meaningless. (I think Poulos, Carter & Small, 2000?)

Why?

Because elastic settlement is around 0.1.-0.3 of the consolidation settlement. So, if consolidation settlement is x, then total settlement is 1.3x. Using elastic theory we can estimate E'=0.8Eu or something close. Difference between E' and Eu should be small since it is usually like this.

Last point: I understood what SkarpShooter meant. I didn't think it before. He says that since we load our samples in oedometer, we are probably seeing elastic settlement too. We observe both elastic and consolidaton settlement during oedometer. However, SkarpShooter, you should be aware that, we use mv or cc after initial settlement. Remember the consolidation curve, initial settlement already occured between 0 and first loading. So, based on this, I might choose not to calculate cr from 0 to first loading, since it may include elastic settlement too.

 

[Ron]

fattdad....years ago we had a contract in our geotech lab to do multiple consolidation tests on clean sands for a Coal Fired Power Plant. We did dozens of them. Each one took minutes to complete as compared to multiple days/weeks for a typical test! I have no idea what the designers did with the data. The tests were dictated by our contract work scope, not by our geotechnical engineering staff, otherwise we would have used cyclic triaxial tests to get modulus data.

 

[geotechguy1]

I'm still not following why the elastic settlement isn't captured in the 1-D Oedometer test. If elastic settlement occurs near-instantaneously under load, then how can it not be captured in the 1-D Oedometer test, unless no load is applied? In which case, there would be no consolidation measured in the test either, and you would just have a big lump of confused clay sitting in the lab wondering why it was there.

 

[ScarpShooter]

Thinking about this more and more, my personal conclusions is that students, when they learn settlement evaluation, don't learn, or aren't taught, to parse the difference between elastic settlement and the theory of elasticity. My conclusion, although not explicitly stated in my soil mechanics textbook, is that the elastic settlement referenced in the very beginning of the chapter, is very small and due to stresses on the individual soil grains, quartz or what have you. The applicable moduli for this settlement is likely on the order of millions of psi so for most practical soil mechanics stress levels it is almost nothing. The rest of the chapter goes on to talk about settlement based on the theory of elasticity and also consolidation theory. The main thing though is that the referenced moduli values for the settlement based on the theory of elasticity are often orders of magnitude less than the moduli for the parents material of the individual soils grains. I think the main reason that the theory of elasticity has been used is that it provides a relatively simple and reasonable approximation to describe the stress distribution in the soil. It also makes sense that if you are approximating stress levels using the theory that you might as well extend the basic hooke's law equation to calculate settlement magnitudes at any point in your stress distribution. The shortfalls are however that despite being called "Theory of elasticity" the settlement is definitely not elastic because physically you are getting the rearrangement of soil grains in addition to that much smaller elastic component. Once compressed, they are not going to revert back to a less dense state (think what happens in DDC). So I guess it just needs to be understood that despite being based on the theory of elasticity, there are definitely some simplifying assumptions that make the application of the theory reasonable for compression loads due to buildings, embankments, etc. but that its not truly elastic response.

 

[Okiryu]

Elastic settlements may be more critical than consolidation settlements for some situations. For example, for overconsolidated clays, elastic settlements may be larger. That is my experience with my overconsolidated medium stiff clays.

For normally and underconsolidated clays, you may need to calculate both, but as you now, the time that takes to consolidation settlements to happen is normally more critical.

 

[geotechguy1]

Does elastic settlement occur in a 1D Oedometer, and if not, why not?

 

[fattdad]

You can use oedometer to derive constrained modulus. That and poisson's ratio and you can derive elastic modulus.

Modulus derived a such may be mixing intent; however. You just want total change in height? Sure, use it! You want to know if the dissipation of pore pressures has an influence on the change in height? Modulus won't help.

f-d

ípapß gordo ainÆt no madre flaca!

 

[Okiryu]

f-d, have you ever used he constrained modulus to calculate elastic settlements?

 

[ScarpShooter]

Correct me if I am wrong f-d, but I think that the important thing here is that constrained modulus used in such a way as you suggest would give you the total settlement. It would not be additive with some separate analysis considering consolidation.

 

[fattdad]

I'm just saying there's a calculation that can be obtained via the oedometer.

I'd agree that such use would negate the Cc, Cr approach.

I've never used constrained modulus for settlement.

For me, modulus settlements (i.e., "Immediate settlement") occurs quickly and unlikely to affect the completed works. Follow-up deformation is what I'd more likely consider - i.e., what happens in the decades after the, "Immediate settlement" is complete. This returns to the earlier post on Ct.

f-d

ípapß gordo ainÆt no madre flaca!

 

[Okiryu]

ScarpShooter, based on Mayne's paper posted above, I think you are right. If you use the constrained modulus, you are capturing also the consolidation settlement (that is my interpretation of the paper).

 

[geotechguy1]

The constrained modulus and some of the Mayne papers discussed here are referenced in the canadian foundation engineering manual, although they never explicitly state you don't need to add consolidation in as a seperate quantity if you use an appropriate modulus value.

Interestingly this is what my firm has been doing, but no one could remember why.

 

[Okiryu]

This is interesting because if you use a typical Poisson ratio of 0.33, you will get that the constrained modulus is almost 1.5 times the elastic modulus. Meaning that if you use the constrained moduluscin elastic settlements calculations it will give you less settlement values even though the consolidation settlement is included.