Concrete – Is it possible to create a 4“x4” channel through concrete using acid

You can't just slap down new concrete. It will never bond. Some options:

1) They make bonding agents for this. Not sure how well they work.

2) vinyl patching compound. Probably your best bet for damages stairs. Not as good as new concrete, but might hold you over for a while.

3) Epoxy. probably the best for small repairs. I use it quite a bit for small cracks and pits.

Without seeing pictures, I'm guessing #2 is maybe what you want to try first.

Cut both sides of the channel with the concrete saw and break and clear out the concrete between the cuts using a jackhammer with a wide chisel bit, don't mess around with a hammer drill. Both tools are readily available at most tool rental places and should make relatively fast work of these cuts. Make sure you get a saw that can do the depth of cut that you want.

If you are a little more adventurous and or experienced with a jackhammer you could do a shallower cut or skip the concrete saw altogether. It won't make as clean of an edge, but will be much faster, and depending on your circumstances it can be good enough and be covered when pouring the new concrete to refill the trench.

You'll want to do a wet cut with the saw to keep the dust down and cool the blade.

Depending on the amount of rebar you are anticipating you may want an abrasive blade (better for rebar) rather than a normal diamond concrete cutting blade (will cut rebar but will wear down the blade if cutting a lot of it). Depending on the rental place you may need to buy your own blade.

You might also want to consider making the cut wider than 2". This will give you room to work if you need to make up joints or otherwise manipulate the pipe and will also allow you to put some horizontal rebar into the remaining concrete (this is where you use the hammer drill) to better tie your new concrete back into the existing structure.