blocked, separated, to prevent
閡 centers on obstruction or separation: something is blocked, kept apart, or prevented from proceeding.
閡 combines 門 (gate) with 亥, which likely contributes the sound. The gate suggests a barrier, fitting the meaning of blocking or preventing passage.
A gate 門 with a boar-like shape 亥 inside: imagine a wild boar blocking the gate, preventing anyone from passing.
For カイ, picture a kite (カイト) caught in the gate, blocking the way: kite -> カイ, and the gate is blocked.