smash, break, crush, familiar, popular
砕 centers on breaking something into pieces: smashing, crushing, or shattering. The extended sense of 'familiar' or 'popular' comes from the idea of breaking down formality or barriers, making something approachable.
砕 is the modern simplified form of 碎. The older form combines 石 (stone) with 卒, which likely contributed the sound and the idea of breaking into small pieces. The modern 卆 is a simplified replacement for 卒.
A stone 石 on the left and a simplified 卆 on the right: imagine a stone being smashed into fragments by a sudden impact, breaking it down into familiar, small pieces.
For サイ, picture a sigh of relief as a formal barrier is smashed: sigh -> サイ, and the situation becomes more familiar and popular.
pulverization; pulverisation
to break (into pieces); to smash; to crush; to shatter; to grind (into powder); to pound
to break (into pieces); to be broken; to be smashed
honorable death; death without surrender; honorable defeat
crushing (into pieces); smashing; cracking; breaking up
pyroclastic flow
to smash; to break (into pieces); to shatter; to crush
crushed stone; macadam
collapsing in the middle of a bout
ice breaking
to crunch; to masticate
blasting
making one's best exertions
coffee grinder; coffee mill
crushing
grinder; crusher
large pyroclastic flow
take a chance; go for broke; nothing ventured, nothing gained
to take great pains; to make every effort; to rack one's brains
mill; grinding mill