demolition, break, destroy
壞 centers on forceful destruction: breaking something apart, demolishing a structure, or ruining an object so it no longer functions.
壞 combines 土 (earth/ground) with 褱, which likely contributes the sound and carries a sense of breaking or ruining. The character expresses destruction, especially of earthen structures.
The left side is earth 土, and the right side 褱 looks like a complicated structure being pulled apart. Picture an earthen wall crumbling into rubble: 壞 is demolition.
For カイ, imagine a wrecking ball crying out 'KAI!' as it smashes into an earthen wall: the sound 'KAI' cues カイ while the wall breaks apart.