Hi San: This would be highly nonlinear due both to contacts and the elastomer, but you can start "linear" in the sense that the basic simulation package can model the contact side of it - then progress to nonlinear rubber model with large deformation. It will show the rubber deformation up to the point where the elements do not get too distorted - but that's about all.
Take baby-steps (no insult intended):
1) Get the contacts to operate correctly. Try placing the floor directly up against the tire so that it initially contacts some of the tire surfaces. Then define "no-penetration" contact sets between the floor and a tread or two. Do not create more than a few contact sets at a time since it can take a long time to converge depending on the number of contact surfaces and mesh density, and you won't know where issues might arise. Next, instead of a force on the floor component, try a finite displacement value upward, such as 1/4", to start. It sounds a bit crazy since no actual "forces" are applied but the algorithm actually runs a bit smoother with non-zero displacements applied (as compared to forces). You can help stabilize the analysis a bit more by applying a pressure to the inside surfaces of the tire to stiffen-up the structure. You may need to turn on the "large displacement" option, but try it with the "small displacement" option, first - the goal at this point is to get the contact sets to function correctly. Use a coarse mesh as an initial trial.
Once that's running, go back and add a few more contact sets, modify the finite displacement value to a higher number than 1/4" - perhaps 3/8" or 1/2" and observe if more contact surfaces are actually engaging.
When you get all that running smoothly and the deformation looks realistic, then you can proceed to a finer (smaller element sized) mesh, and a nonlinear material description for the rubber.