The bloody things are heaving the asphalt in an even wider area. It's like some alien thing creeping around under there. But with Roundup they have to expose their leaves for it to work - and it has been raining. Dammit. And I don't apologise for my language.
Proud member of People Who Hate to Kill Wildlife clique
Around here there are people, mostly hispanic, that cut the vines to make decorative wreaths. There is a small business here that makes the wreaths and sells them to craft stores like Hobby Lobby, Michaels, and Ellis Pottery. They were so good at harvesting that the vines became rare and the timber companies had to limit the number of people harvesting vines on their land.
As a kid there was a large wild grape vine in the woods behind our barn. We used to swing on it and play Tarzan. The grapes made wonderful jelly and my mom even made some wine from them once.
Foxtrot-Roundup isn't strong enough to permanently eradicate roots. You need something similar to plant napalm. One type was called something like Triox, and there are some that will kill virtually anything, but you need an expert who can tell you how to get to the roots, and what to use to kill them permanently.
To really get rid of the root under the driveway, then I think the easiest and most permanent solution is digging around where the roots go under the driveway, and putting the stuff on and in (I like the drill holes ides) the root, and then filling it in once the root is permanently destroyed. That way would limit the spread of the weed eradicators, and use the least poison possible.
Sannois, that's a great suggestion-I remember that stuff also. I'm so old I remember my mom running around the lawn with a huge tube of dandelion killer, dispensed by something that looked like a huge syringe. I think it was vitamins for dandelions, because I remember they got bigger instead of dying off.