On most of the mines, we plant a building. So there is only one building pulling from that mine. Just like PH/RPH/etc have times remaining until the queue is finish, I suggest we have a time remaining on the mine shaft.
Also, the mine building properties should include the available resources left available.
When we open a mine building properties, it tells us not only the time it takes to mine X quantity of said item (based on level), but it would also show us the time remaining till depleted.