If you can recall the scene in Gold Finger where the girl is painted in gold and dies, the cause of her death is the same as what compacted soils do to trees. Let me explain:
She died because her skin could not breathe.
Roots need to undertake gaseous exchange. When the soil is compacted this is reduced or stopped. The result, a decline/death of a tree is a result.
Compaction can be caused just by foot traffic, but more commonly it is the storage of materials or the traversing of vehicles /plant. When the ground is damp it's effect is worse.
Air spades can relieve decompaction, but prevention is better than cure. Unfortunately compaction is usually caused when there is a lack of understanding/care about trees, soil and roots.