experience tells me that when mint fills a bottomless bucket the roots escape out of the bottom and come up on the outside. It's very good at forcing its way under and up. If you've got good, thick, solid asphalt you could be OK but you mention 'damage the asphalt further' which suggests otherwise. I would be wary
Nut that's why I take mine out of the container every three or four years, remove the old roots and replant only the newer ones ... that way I keep it under control
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
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experience tells me that when mint fills a bottomless bucket the roots escape out of the bottom and come up on the outside. It's very good at forcing its way under and up. If you've got good, thick, solid asphalt you could be OK but you mention 'damage the asphalt further' which suggests otherwise. I would be wary
In the sticks near Peterborough
Nut
that's why I take mine out of the container every three or four years, remove the old roots and replant only the newer ones ... that way I keep it under control 
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
And in the back yard, I'll cut half of it now and the other half later.
Thank you everyone, you've helved a lot!