Analytic solution for dynamic geotechnical problem

[awa5114]

Unfortunately I have not received assistance for this problem in the geotechnical forum so I am now asking it here. I am responsible for validating an FEM model of the following problem:

Loading: 1 kPa downward (constant)
Const. model for soil medium: Mohr-Coulomb
Analysis: Dynamic
duration: 1 second
state variables: Displacement, Velocity and acceleration

I have 2 numerical packages that I am using. One of them is Plaxis2D. The results I am getting from both are drastically different. I have checked everything: From geometry to mesh size to material parameters and it all corresponds for the two numerical packages. Of course one would expect for there to be a difference but in my opinion this is too different.

I would like to explore options outside the current two programs I am using. Namely analytic closed form solutions. A baseline to compare with. Something to give me an idea what the displacement, velocity and acceleration would need to be without requiring high level math that would take months to implement. Anyone have any ideas? Thanks.

 

[whitwas]

I don't have any idea about an analytical solution. It sounds next to impossible for a plastic dynamic model. But here are some suggestions for comparing the FEA solutions:

Just because each program has the same mesh doesn't mean they'll have similar results. You still have to check for mesh convergence independently with each program. An example of where that's particularly dramatic is linear 4-node quadrilateral elements having full vs reduced integration.

Ways to isolate the problem:

Try simplifying it until either the solutions match or it's so simple you can do an easier hand-calc that you already know.

If it's doing plastic deformation, can you reduce the load so there's only elastic behaviour and see if the results then match?

Check if the wavelengths/periods of the oscillations match. That could show if the problem is the material or the boundary conditions.

 

[IRstuff]

Please refrain from double posting. Your other posting was barely 3 hrs ago.

TTFN (ta ta for now)
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[gravityandinertia]

To validate an FEM analysis the following needs to happen:

Materials need to be ensured that they are correct
Load needs to be ensured that it is correct
Solver needs to be ensured that it is solving correctly

To check the material, you can setup a simpler model that you know has a closed form analytic solution in the software, compare them and make sure everything is fine.
After the material is checked, again setup a problem that has a well-defined solution for your given loading parameters, this may mean changing the material to keep it in the plastic range.
As for checking the solver, I would first see if they have validation examples that they used and if there is anything validated against your type of example, if not, you'll have to create your own. This may be doing research to find a thesis or dissertation where someone calculated something similar analytically then setting it up in the software and seeing if the values match. This isn't totally valid because it's possible that the thesis calculated wrong values, and it was missed by the reviewers. However, if you can find one that has both an analytic solution and FEM solution, you can use it to determine whether your FEM software is working appropriately.

All that aside, if you can't do that, perhaps you could consult (possibly for a fee) with a Professor who has research interests in soil dynamics or seismic engineering. He would like have the skills to do the analytic derivation you are looking for.

 

[IDS]

The most obvious source of different results is differences in the starting conditions, which will greatly affect the initial failure stresses for a Mohr-Coulomb material.

Why not do a linear dynamic analysis with your two programs. For a 1 kPa pressure the behaviour should be very close to linear anyway.



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[ThomasH]

Based on the information you provide it is diffucult to quess what can be the problem. But I assume that the loading is dynamic and perhaps harmonic (a sinus function). You also say that the results differ, but I don't understand how. And what type of software is the second option, general och specialized?

Nevertheless, Plaxis is a geotechnical software and I think that it assumes that the boundary does not reflect the wave from a dynamic load. I experienced this in a project a few years ago. When I instead used a general software the vibrations increased with time, basically backgrund "noise" due to reflections. The boundary so the longer duration we used for the analysis the higher the vibrations were. We did one solution in Plaxis 2D and the other in Nastran (3d solid model). The Nastran model required more work but at the end it worked. There was nothing wrong with Plaxis 2d but in our case the vibrations were transfered in a 3d volume and Plaxis 3d was not up to the task.

Good Luck

Thomas