fort
寨 centers on a fortified place: a stockade, stronghold, or military camp. The single given meaning 'fort' captures this idea of a defended enclosure.
寨 combines 宀 (roof/building) with 木 (wood) and an inner element that may represent a barrier or palisade, suggesting a wooden stockade or fort. The exact historical development is uncertain.
Under a roof 宀, wooden logs 木 are stacked with crossbars ハ to form a defensive wall: 寨 is a wooden fort.
For サイ, imagine a fort with a sign that says 'SIGH' because the guards are bored: sigh -> サイ, and the fort stands strong.