Soils with a significant clay or loam component are much more compactable than sandy soils. Once compacted, soils are very slow to “de-compact” naturally. Mulching, air tilling, plug aeration, and deep or shallow tillage of the soil can mitigate soil compaction to a certain degree. Some trees, such as those found in swampy conditions in their native habitat, can be quite tolerant of compacted soils and, as the roots grow, they will also loosen compacted soils.
Some state Extension programs have good online resources for tree selection that include trees for compacted soils. Virginia Tech and Cornell University are two examples. Many species that are listed as tolerant of wet sites should also tolerate some soil compaction. There are many factors to consider when choosing the most appropriate tree for a given site. The specific species will vary by the region of the country where you live. Contact your local state forestry service or Extension agent for more information.