The only thing that comes to mind is a clay pit. That is where clay is "mined" from. There almost seems to be a mineral or resource connection to many uses of pit. In general useage, one generally hears "dig a hole" more often than "dig a pit" In the Old Testament, when a Prophet was thrown into a pit or dry well it was a repository for trash, chamber pot wastes, etc. So they were thrown into a really nasty place.