you will have to tunnel as suggested earlier by Dick. Your best bet is to call in a boring contractor and discuss methods and issues with him to get a better feel. some of the issues that you need to start defining are:
1) allowable settlement of the tracks and monitoring requirements for it
2) action plan if the tracks do subside
3) how deep to groundwater?
4) type of tunnel to construct ie: concrete box, steel arch, shotcrete lined, other?
5) if you are in expansive clay, will your subgrade expand once you remove the load? If so, how will you mitigate the effect on the railroad above?
6) will grouting be require to stabilize the ground before tunneling? Will grouting be required to fill voids behind the lining?
7) Can you jack a culvert through the embankment instead of constructing a tunnel?