Drainage pipe causing mini sinkhole in yard

They stopped the pipe in the middle of your yard underground? That’s weird...certainly not a good idea.

You just need to extend the drainage to an area better suited for it to drain like the street or a rock base and then fix the low spot in your yard with new compacted dirt.

Should I put fill dirt (thick, clayish dirt) where it empties? This one site is saying don’t fill with gravel because the water will just trickle down trough the gravel and create cavity underneath it.

Ok, here’s what I’m thinking now:

Put stones in a bag made of landscape fabric and place the stones on the area where it empties. My question is whether I should mix in or put a layer of fill dirt underneath the stones to make the area directly underneath the stones more supportive and less porous so it doesn’t create a cavity underneath the stones?

Intuitively, it would seem to me you just might want to consider enlarging that “dry well” area to increase the area where water drains into the subsoil. You did say you were having a great deal of rain recently. I don’t see where adding soil to the bottom of the basin where you add the stones will achieve what you want to prevent, but I’m not a civil engineer.

Another suggestion, couple years ago when correcting some lawn drainage issues in my own yard in southern Louisiana, I came across some great extension resource materials from Penn State U. on this topic. Just google Penn State Cooperative Extension Service and search for lawn drainage, etc. Pretty sure they had a water resources division in their extension program with a good bit of info on lawn water management, including videos. Don’t hesitate to contact your county university extension agent to help direct you to this information and ask the same questions you are posing here, that’s what their employed to do, and of course they are going to be more knowledgeable of your area, soils than we can be.

I would look into burying a small plastic dry well similar to this one
LINK