It depends.
A GTX1070 is somewhat comparable to aGTX980ti.
I find that with a GTX980ti, I get a steady 60fps in civ 4 and civ5 and skyrim on a 4k monitor.
Very few 4k monitors can go faster than 60hz.
Because of the density of a 4k panel, you can lower the aa which is one of the most resource heavy settings.
A graphics card will last as long as it does the job.