I do it similar to Tuck. If it is a 15" main, I use plastic culvert or tile.

Then I use an 18" plastic culvert cut about 6"

 long, cut that circle in half, and that 1/2 covers the 15" joints very nicely.

4" tile might need a 6" tile  1/2 circle for joint.ect.

If main or tile line has all the clay tiles cracked on top( use said 5 places) and collapsing, I might cement the joints because your disturbance to adjoining tiles, might just have them fail next year.

I hate digging down to find a plastic repair from previous tile fix.

Brian