The DOD actually funded a scale model test back in the late 50's or early 60's that used conventional explosives. It worked and did not fly apart and had no significant erosion of the dome.
But, it didn't generate temperatures nearly as hot as a nuke would.
Why am I not surprised? I once read about someone placing a jet engine on a car just for kicks. It took them a while to figure this out after they wondered what made the big splat on the side of a mountain.