You studied the agreement between a rail supported by foam and a free-free modal analysis.

I suggest you study the agreement between a rail supported by rods and a remote displacement supported modal analysis.

This is one step closer to support on sleepers, but is easy to do in the lab and in simulation.

Putting a rail on a wooden sleeper without any other constraint may not be that different to the rods.

If there is a significant difference, then you can no longer use modal analysis. You need to run a full transient analysis that can have frictional contact between the sleeper and the rail.  How do you excite the rail in the lab?  Do you hit it with a hammer?  You will have to have an impact in the transient simulation.  Extracting the data from the simulation will be similar to extracting data off the rail in the lab. How did you determine the frequency and mode shape in the lab?

But in reality, the rail does not rest on the sleeper, there are spikes that hold it down. When are you going to add the spikes?