Pile-soil Interaction Convergence

[[email protected]]

Hello Forumers and STKO Team!

Here's an update on my modeling.

I have consulted a few geotechnical professors about the upheaval that occurs at the pile toe during shaking, and they said it's a physically sound response for short piles with a diameter as large as in my model (6m). It's mostly due to the soil around to pile getting pushed and developing shear bands according to the theoretical failure mechanism of piles (mobilized shear wedge at the front of the pile). When this wedge is mobilized soil is mobilized downwards around the pile to the pile toe. Here the soil's only route for expansion and stress relive is to displace into the pile volume where stresses are lower due to prior excavation than in the surrounding soil volume. Another analogy they told me is the tunnel uplifting effects during earthquakes, where a similar mechanism will occur.

For the stability issue I simply had to switch my transient integration method. For the relatively high frequency pile head loading in my tests (2-3Hz) the TRBDF2 method had insufficient numerical damping. The Newmark integration method with gamma=0.7 and beta=0.36 has performed without any issues. The spurious stress oscillations are not present in the model results anymore. I would like to give credit to Amin Rahmani's PhD thesis (Three-dimensional nonlinear analysis of dynamic soil-pile-structure interaction for bridge systems under earthquake shakings) on this parameterization for the Newmark integrator for stable dynamic pile tests in OpenSees.

Hope this comes in handy to some fellow STKO buffs!

Regards,
Bence

[STKO Team]

Good job Bence!
And thanks for the reference and all those valuable notes. For sure they will be useful to other users!
Enjoy your work with STKO!

[miran]

Hi Bence, I am glad to see that you are doing great with your model!

Assuming that you are using some kind of non-linear model for the soil, are you adding any additional material damping?

I have a model that seemingly works fine, but I am not sure if I am adding sufficient or to much damping. This is somewhat important in my case since I am comparing linear and non-linear solutions. I am using the PIMY-model (clay) and I have layered the domain such that I can incorporate the effect from compaction on shear strength and stiffness (i.e. the stiffness increases linearly with depth).

The best solution that I can think of for now is to add purely stiffness-proportional damping using the Rayleigh command. That way I can add more damping when the response is linear, and less damping when the response in non-linear and we have dissipation. Note that I am applying harmonic loading such that I have one particular value for each frequency.

Any tips, advice or references on how to add/estimate proportional damping would be much apricated!

tau_gamma.JPG (131.57 KiB) Viewed 3731 times

[[email protected]]

Hi Miran,

I am not quite sure why you would want to add extra damping to your model. Maybe your modeling goals require this? Let me know in more detail why you are considering the addition of extra material damping.+

In general, equivalent linear models require the description of the degradation of soil’s secant shear modulus and damping with the change of shear strain as well. Whereas the cyclic nonlinear models (such as PIMY) use backbone curves together with a number of rules that govern the unloading and reloading behavior. This mathematical description of the unload-reload behavior results in the hysteresis in the stress-strain graph instead of a constant damping coefficient or a damping curve.

To this end, in general, if you use non-linear soil model like PIMY or PDMY, you should not add additional damping to your model. Except if there is some special reason for this; e.g. if you want to damp out spurious oscillations from boundary effects or you want extremely accurate soil modelling. If you do so, you're modifying the well accepted behavior of the constitutive model. The model itself inherently accounts for damping. At initial high stiffness (small loads) the damping is very low and it increases as the shear strain grows according to the G/Gmax curve which is equivalent to the backbone curve. This curve is automatically generated in STKO (and opensees) through the definition of the yield surfaces according to your usual inputs. However, if you have experimental data on your specific soil type, you can actually input the G/Gmax curve manually and the yield surface generation will be done by opensees according to your newly defined G/Gmax curve instead. By doing this you can increase your rate of stiffness degradation which in response will result in higher damping in the initial parts of your loading history.


If you want to read more about the non-linear constitutive models and how they handle damping or how they underdamp in low strain and overdamp in high strain regimes you can read this overview (Section 2.4):
https://www.researchgate.net/publicatio ... s_of_Soils

Otherwise you can try to read into the details of the PIMY model. If you find a good reference for this please share it here, I haven't one myself.

In my case additional damping was required for the numerical stability, which is done through the integration method no by "actual" material damping. Some integration methods have inherent numerical damping which account for erroneous very high frequency oscillations. These are not part of the real solution they are generated from rounding errors and other iteration/integration errors (if I am not mistaken, sorry I'm not a big expert on the math here). So, this does not apply to your case in my opinion.

I hope this helps.
Bence

[miran]

First, thank you for the detailed and quick reply!

Initially, I was thinking exactly what you write. Since I am using the PIMY-model in a 3D-domain, the main damping effects, i.e. hysteric damping and radiation damping are accounted for.

At initial high stiffness (small loads) the damping is very low and it increases as the shear strain grows according to the G/Gmax curve which is equivalent to the backbone curve.

The reason why I am considering added material damping is actually what you mention above. Talking to some fellow collogues in geotechnics (I am a structural engineer) and a previous course in geodynamics, I got the impression that field test usually show non-negligible damping even for small strains. This is also briefly discussed in the overview that you posted (section 2.4.1 and 2.4.2).

I am applying a harmonic base displacement to a pile-soil model and evaluating the results in the frequency domain. Results show that the soil response in the upper part of the domain becomes more and more linear as the frequency increases (as expected). Therefore, I was concerned that the system might be somewhat underdamped for high frequency loading. Therefore, by adding purely stiffness proportional damping, I am able to add more damping in the linear domain and less damping in the non-linear domain. I found a recent article (https://www.sciencedirect.com/science/a ... 4AU5l9FHJA) where stiffness-proportional damping was added using the PDMY02 model, but this is not discussed in detail.

I am by no means an expert on the subject, so please correct me if I have misunderstood something. Regardless, I will run a few analysis with and without to see if there are any substantial differences.

These are not part of the real solution they are generated from rounding errors and other iteration/integration errors (if I am not mistaken, sorry I'm not a big expert on the math here). So, this does not apply to your case in my opinion.

I can not see any strange oscillations, so there should be no need for numerical damping in my case.

Otherwise you can try to read into the details of the PIMY model. If you find a good reference for this please share it here, I haven't one myself.

Not a valid reference per se, but perhaps this might be useful: https://datacenterhub.org/resources/714 ... ion_AK.pdf

[[email protected]]

field test usually show non-negligible damping even for small strains.

Yes, I also mentioned that low strain (i.e. high freq. motion) is underdamped and high strain (i.e. low frequency motion) is overdamped. However, this is only an issue when the contributions from the high frequency components are characteristic to your problem. In most cases the consequence of underdamped high frequency waves is small in the overall damage of the soil or soil-pile system. This may be different for machine foundations, for example, and other fatigue prone self-exciting structures such as wind turbines.
All in all, if your goal is to have an extremely high-fidelity soil model or the contribution of high frequency motions is significant to your problem you may add extra stiffness proportional damping.

Therefore, I was concerned that the system might be somewhat underdamped for high frequency loading. Therefore, by adding purely stiffness proportional damping, I am able to add more damping in the linear domain and less damping in the non-linear domain.

If this is done correctly it can counteract underdamping of high frequency motions for sure. But you need exact experimental results and perform FEM model updating in order to optimize this additional damping in a way that it is realistic and physically robust. Handling the overdamping of low frequencey motion is not that easy to solve though, as that would need "negative damping". I do not have any good ideas for that myself.

[miran]

Due to the nature of my problem, and the fact that this is an academic task, I think the best solution in my case is to run a few parametric analysis to highlight potential differences and then neglect the added damping since, as you say, it is very difficult to predict correctly.

Again, thank you for the feedback!

[STKO Team]

You are welcome!