We have many raised beds, all built up and modified each and every year since 2002.
In 2012 they were roughly 3 courses of garden ties, maybe 9″ deep.
That is not enough. Preferred depth is at least 12″ to give more soil to work with, better ability for water retention, more room for roots to grow, easier access to sit on the edge and weed, etc.
So this spring we added another courses to the various raised veg beds. We are now sitting at 12-13″ for each one and in a few days will start adding a lot of dirt to top them off. Garden mix dirt. We’ve already added bags and bags of composted sheep manure (0.5, 0.5, 0.5), 15kgs apiece, at a rate of between 1 bag/25ft^2 to 1 bag/50ft^2.