I did some Plaxis modelling of vibrated stone columns. I found it very interesting and a great introduction to numerical modelling. I would make sure you have an expert at hand who knows plaxis as you can get stuck on one little thing and it can take weeks to figure it out. It could be as simple as one little box not being ticked.
I would also advise that you have a field case to compare it too. I had field load tests of stone columns at a site and i used the site investigation to develop my soil model. My results compared reasonably well with the field load tests.
You can use an "imaginary" soil model, lots of researchers have done that but I think that having a real site to compare it too was a nice touch. Just my personal opinion though.....
Although not foundation engineering, I have been always curious to see how deformations for slopes and retaining structures can be calculated. Typically, analysis for these structures are based on factors of safety against failure. It may be interesting to see also some numerical analysis to address deformations of these structures.
Here's a few ideas:
1. Numerical analyses of self-driving piling.
2. Gram-Schmidt orthogonalization of expansion characteristics derived from highly expansive fat sands
3. Multivariable fast Fourier transforms of rat droppings in deep pier excavations.
4. Steady-state distribution characterized by elliptic PDEs for seepage under a hog lot.
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