Theoretical considerations for numerical modeling of cantilever embedded walls.

[Sjotroll]

Hi all, please help me understand something.
I'm making numerical calculations of a construction pit with cantilever embedded walls in normally consolidated soil. Let us assume that the largest lateral wall movement will occur at the top of the wall. Now, which constitutive models can/should be used to simulate this situation?

First of all, the question is: which modulus applies in the soil behind the wall - is it the primary loading modulus, or the unloading modulus? By a simplified mental check, a soil element behind the wall will see an increase in deviatoric stress and a decrease in mean stress.
The soil under the excavation is obviously under unloading conditions, and let's say that in all of the analyses this soil is modeled with a linear Mohr-Coulomb model using the unloading modulus.

What model can we use for the top soil?
1) I could use the linear Mohr-Coulomb model with unloading modulus. This, however, gives a deformation trend where the max. lateral deformation is not at the top of the wall, but it complies with the idea that the soil behind the wall is in an unloading state.

2) I could use the linear Mohr-Coulomb model with primary loading modulus. This gives a better looking trend, but only due to the large ratio between the unloading modulus of the bottom soil and the primary loading modulus of the top soil. On top of that, the soil is not really under loading conditions, so a primary loading modulus seems off.

3) I could use the Duncan-Chang model. To simplify, let's assume that the moduli are constant within the soil at rest (not dependent on confining stress). The model then says that the primary loading modulus reduces with increase in mobilized strength (or with axial strain), while the unloading modulus is constant (not strain dependent). This model gives a great looking trend. However, as we saw previously, the soil element behind the wall experiences an increase in deviatoric stress, which means that the Duncan-Chang model thinks it is under primary loading and uses that modulus - which, as I also mentioned previously, show not be correct. If it used the unloading modulus, since it is constant and not depended on strain, the result would probably be equal to the linear Mohr-Coulomb model with unloading modulus. Thus, one of my questions is also: is the unloading modulus really independent of strains?

4) I could use Hardening soil model. This is a little more complicated, but again let us assume that the moduli are independent of confining stress. This model also uses practically the same hyperbolic relationship as the Duncan-Chang model for the primary loading modulus E50. The rest of the used modli (Eoed and Eur) can only be dependent on confining stress, but as mentioned in our case they are constant. The E50 is used when the loading is mostly by deviatoric stress, and Eoed when it is mostly by mean stress, but uses the same Eur for any unloading-reloading. Thanks to the yield surface it uses, it can detect unloading and reloading when the combination of deviatoric and mean stress stays within the surface. According to this, it should be able to detect the unloading that's happening behind the wall, which would then again be equal to using Mohr-Coulomb model with unloading modulus, but instead I get a good looking deformation trend, like with the previous model, but with even larger deformations. The only explanation I could get to is that it doesn't detect unloading, and continues to calculate with the E50 which is reducing according to the hyperbolic relationship. The question here is then: why doesn't the Hardening soil model detect unloading? And if it did, I assume it would be the same as using the Mohr-Coulomb with unloading modulus (which, as previously discussed, doesn't give good trends).

So, what would be an appropriate method of modeling this situation? Am I making some wrong assumptions regarding the lateral deformation trends of cantilever embedded walls, or about any of the models, or perhaps the stress state behind the wall? Perhaps the only thing left that would make sense for me is to lift the assumption of confining-stress-independency and instead make Eur increase with confining stress (~depth), which would make the soil respond softer near the top, and stiffer near the bottom, which should improve the trends - but is this property really so crucial?

Regards

 

[PEinc]

It seems like you are making this a lot more complicated than needed. If this is a design for a real project, you should be looking a cantilevered sheeting design methods and examples readily available in numerous publications. None of what you described is needed or used. If this is for some research project, I don't have an answer for you. Have fun. If you are trying to support soil and an immediately adjacent structure, you probably should not be designing sheeting, especially cantilevered sheeting. Maybe you should underpin the structure.

http://www.PeirceEngineering.com

 

[geotechguy1]

I'm sure buy a book and read it isn't the answer you want but I'd really suggest buying CIRIA 760 and studying it front to back to answer those questions (or other European guidelines if you can find them).

Outside of the United States actual design and analysis is done to optimise things due to cost / capital constraints and insurance requirements. In the US you will find no one knows or understands how to answer any of your questions because historically there has been enough money available to make everything comically conservative; as a result, practitioners in the US frankly don't have the skill set or knowledge for this stuff - US engineers in this space are basically stone masons / technicians copy pasting generic rules of thumb about the embedment depth and section size. Which is a sad state of affairs given that American researchers / engineers in the 50s - 70s were half a century ahead of Europe and the technical work from that era is still ahead of most of what is being done in the UK / Europe but sadly most of the knowledge has been lost.

 

[PEinc]

US engineers in this space are basically stone masons / technicians copy pasting generic rules of thumb about the embedment depth and section size.

OUCH!

http://www.PeirceEngineering.com

 

[Sjotroll]

PEinc:
I don't think this is me complicating, it is a problem of practical value to be able to correctly model deformations of any geotechnical structure. Too many times have I seen numerical modeling where the results seem good, but the theory behind them is shaky. It is imperative to know what is happening in the soil within the problem you are dealing with, and correctly consider that.

geotechguy1:
Why not, I've been reading articles and books to find something, but none get to the core of this problem. I'll check out CIRIA, but I don't have high hopes. I too am from Europe so I am very familiar with their work regarding levees.

 

[EireChch]

I have designed maybe 5 walls use FEM, Plaxis. You obviously have a very good grasp on the model theories, which is great.

But PEinc is right, using Plaxis is over complicating it for the 90% of walls. But maybe you are in the 10%

In my experience, it is not common to apply different soil models for material behind or in front of the wall. Typically one soil model is adopted for all soils. I dont know why you think that HS isnt detecting that the soil is unloading. The model has been proven, against monitored walls, to be very accurate in predicting deflections

Also, retaining walls are typically small strain problems. So Hardening Soil Small strain is used. If you ignore small strain stiffness then you are over estimating deflections.

 

[geotechguy1]

I would think HS-Small should work. The main issue is usually convincing old guys with grey hair to use anything other than linear elastic-perfectly plastic constitutive models.

Duncan Chang is basically American Hardening Soil as you've noted above - not sure if there is a small strain extension to it as well. (In many cases there seem to be parallel bodies of research in the US and UK / Europe that have a whole set of terminology they use for almost exactly the same thing)

FWIW in NZ they like to use linear elastic / beam on spring Wallap models alot for sheet pile walls as part of assessments of effects required by regulatory bodies. As far as I understand (although very little of the actual data gets published) they usually comically overpredict settlements unless someone puts in a sheet pile that's much shorter than it's supposed to be or someone takes a digger and gives the one with the monitoring point on it a nice push outwards.

 

[Sjotroll]

EireChch - This is a question specifically aimed to investigate and understand the difficulties in numerically modelling such a structure, it is not tied to any specific embedded wall design. I am aware of the analytical methods, which I too sometimes use.
Regarding the different models for different soils, there is no reason to keep them all the same, except if you use the most complex of soil models that can adequately predict the behaviour under the different stress paths, and let the software do everything by itself.

EireChch and geotechguy1 - I will have to get a better understanding of the specifics of HSS. I know it considers the initial shear modulus (G0) and a shear modulus reduction curve, but I still have to check how is it incorporated into the model, to be able to comment more on that.

I have stumbled upon an article that talks a bit about how different stress paths lead to different moduli, and mentions that the active stress path, that would be valid behind an embedded wall, the modulus is 1-2 times the primary loading modulus. However, there is no reference for this statement. If anyone is familiar with some research on this topic I'd appreciate some references. This would then explain some things. If the state behind the wall is not conventional "unloading" with a 3-5 time larger modulus, but instead some loading state with a just slightly larger modulus than primary loading, and that is strain dependent (because Eur, as I understand, is never modeled as strain dependent), then the application of the primary loading hyperbolic relationship employed by the Duncan-Chang, HS and HSS, with 1-2 times the primary loading modulus, would indeed give the correct predictions for the wall movement.