Removing Broken pvc material
I get broken vertical pipes quite often and found at ace hardware a small wrench (shape of a T), that at the bottom has a conical shape with sharp edges. You push the tool down into the broken part, and it "scores"/cuts a little bit into the broken part of the pipe and you just twist it out. Works like a charm.
If you have this happen often, you can add two small right angle pieces before the vertical pipe (means getting shorter vertical pipes). The two right angle pieces are left a little loose, so if the lawn mower hits the sprinkler in either of four directions (north, west, east, south), the right angles just twist in or out a bit. Some people add a flexible rubber hose underground. I think it's called a 'funny hose' or something like that. My horizontal pipes aren't deep enough to make that solution very easy to do.
I'm just slowly adding this system as pipes break.
good luck