dirt clod, piece
凷 centers on a lump or clod of earth: a solid piece of dirt or soil. The broader sense of a piece or fragment extends naturally from that image.
凷 combines 凵 (a container or pit) with 土 (earth), suggesting a lump of earth or a clod of dirt. The exact historical development is uncertain, but the component combination fits the meaning.
Picture a container 凵 holding a chunk of earth 土: a solid dirt clod. That clod is a piece of the ground.
For カイ, imagine a clod of dirt shaped like a kite: kite -> カイ, and the dirt piece flies up like a kite.