Answer: This is a difficult question to answer because it depends on the situation. Tree roots can sometimes run beneath pavement without damaging it. However, the area closer to the trunk is subject to heaving when the trees grows larger in diameter and the flare at the base of the tree expands. This is why we so often see heaved up, cracking or broken sidewalks next to street trees.
Trees also need room for their roots to grow, in part to help anchor the tree but also to allow it to take up ample water and nutrients so it can stay healthy and thrive. Trees usually have a root system that extends at least twice as far as the branches, so this is a wide area. Paving requires compaction of the soil and usually involves extensive disturbance of the surrounding soil, so it may be that the site is not really suited to a tree.
Sometimes, rather than plant a tree or even a large shrub next to pavement, it can be better to plant a vine on a fence/trellis or possibly use pergola type structure if you need shade. Your local county extension and/or professional nursery staff should be able to help you analyze the site and determine whether or not a tree would be a viable planting in the long term, and depending on the growing site (eg sun, shade, soil type, wind exposure) suggest which trees to try.
Also, I should mention -- in case you are planting on the berm, that some towns have a street tree commission and require that only certain trees be planted in the space between the sidewalk and street, so you may need to check into that as well.
Good luck with your project!
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