Scrape away the soil around the broken fence post with a mattock so the extent of the concrete footing can be seen.
Dig a trench around the circumference of the concrete using a pointed shovel. Make one pass around the concrete to expose it to a depth of 6 or 8 inches with a trench of the same width.
Place the tip of the rockbar against the concrete at the bottom of the trench on one side and lay it down until it contacts the surface of the soil. Apply pressure so the tip of the rockbar digs into the concrete and pry up with the rockbar to attempt to lift the post and concrete out of the ground. Repeat the process in several locations on all sides of the concrete to see if it can be dislodged.
Use a sledgehammer to break the concrete off of the post and remove the rubble from the hole. Once the post is partially exposed, strike it with the sledgehammer on all sides to loosen it in the hole.
Dig the first trench an additional 6 to 8 inches wide and then dig down against the concrete another 6 to 8 inches on all sides.
Continue the combination of prying with the rock bar and hitting the post with a sledgehammer until it can be removed. Depending on the depth of the post, it may be necessary to continue digging the hole wider and deeper, but eventually even the biggest, deepest post can be removed with this technique.
Return the excavated soil to the hole once the post has been removed.