Broken clay drainage pipe
With rain water only it is much easier. I am guessing that is 4” inside diameter clay pipe, I would excavate a bit more and cut the bell on the left or dig back to the next section. With both ends open purchase some flexible drainage pipe (commonly used for a French drain). Split the flex and put it over the clay and then cover the end where it is split with plastic. Then backfill and it will be fine for as long as the clay holds up. This is a small job and a heavy duty garbage bag wrapped around the split at rack end will work to keep dirt out. So you cut the end of the flex put it over the clay at each end then cover with the plastic trash wrapping snug at each end or opening. Backfilling with gravel is best but the dirt that was removed can be used for backfill, 

If this was for sewer my answer would be much different but rain water it could be even something solid over the break then plastic to keep the dirt out , I have had patches like this last for quite a few years when another section failed and I replaced the entire line.