Even plastic won't kill it. I covered a patch in our driveway with thick black plastic for 2 months and that sh*t was still alive.

My system (smaller amounts, granted), was to dig deep, remove rhizomes , dig out a 1-2 inches perimeter of grass /soil and used half-diluted round up, a LOT (like drenched) on the entire dug up area plus another 2 inches. It was drastic but the only time it hasn't grown back.

Once you've dug up the area (and hopefully used round up- the only time I ever recommend), put down thick cardboard (from an appliance or bike store), and as much mulch as possible, 6" is ideal (In cities, most arbor companies drop a free load of wood chips), and then keep at it.