Siberian elm roots

I have a few Siberian elms on my property which make a wonderful windbreak and shade tree, but unfortunately their roots are preventing me from growing anything. I built a few raised beds, which were quickly filled with their fine roots, taking all the water and nutrients away from my vegetables.  I then poured a 4" deep concrete pad and put my raised bed on that which lasted a year before they found an almost imperceptible crack which the roots forced open and again sucked the water away.
I'm not giving up, so my plan is now to rent a ditch witch, dig a trench and line it with something impervious to the roots.
My question is, does anyone know how deep their lateral roots are, so I know how deep to dig?

I don't have a direct answer but Siberian elm is a common shelter belt tree in fields around here and it is advised that every couple years a farmer should take a single cultivator blade and run it 18 to 24 inches down on each side of the row to keep the roots from stealing nutrients and water from the main crop.

I know this isnt a permanent solution but may be one of the simplest.