Plumbing – put concrete over PVC pipe

You can use the Sharkbite or Gatorbite connectors as a junction for copper and PVC. Sharkbite and Gatorbite connectors are "snap together" connectors available at Lowes or HomeDepot, you can put copper in one side and PVC in another.

There is a concrete that I have used, and it is regular concrete, and perhaps it can have gravel in it, but the type I have installed did not use any gravel/aggregate. Dry pack is what I have learned to know it by, and stone setters use it for building walls and laying flagstone sidewalks. I have used it for shower bases over PVC liner and coated it with Redguard for waterproofing. That is where I learned that it took on water real fast. I was to dampen the dry pack slab I set 2 days before. What water I poured on to move around just fell into the concrete, did not stand at all. I even had a decent troweled surface.

The mix is the same, just add enough water to get the concrete to form a ball when compressed in your hand, and I mean just enough, too much will screw it up.

This may be worth a shot, but be careful, this may clog too from atmospheric dirt, decayed debris settling in etc.

The pipe since it is covered with concrete can be black corrugated drain tile or perforated sch 35 set in a gravel bed. Holes in the pipe are slits in the black drain tile and gravel size will not matter. In the Sch 35 the holes are larger so you do not want to use a small gravel there, #57 crushed stone or something larger than 3/4" washed gravel depending on your area. You may want to consider using a different type of area drain. The way you describe "shower drain", sound like it get clogged pretty easily. Replacing the drain you have with something that has a much larger grate or trap included that allows debris to collect, but not clog, may do you well too.