There's a lot of information about DIY gabion walls, but none of the applications that I've seen on YouTube and elsewhere talk about gabion walls as retaining walls.
Really? As a Civil Engineer, I've never seen a gabion wall that wasn't a retaining wall! What else would you use a gabion wall for?
- Given the height, how wide does it need to be? (I'm aiming for a height of 3'.)
3' is pretty much nothing in terms of retaining wall height, assuming you're going from flat ground to flat ground. I haven't done any calculations, and I'm not providing engineering advice here, but I'd be surprised if 1' width wouldn't work. Josh King's advice of 18" wide and 10 degrees inclination sounds pretty sensible to me.
Please note that if you have sloped ground behind/above the wall then this adds more load onto the wall, and it would need to be wider.
- Do I have to worry about drainage?
It's a bunch of rocks with massive gaps between them. Any water behind the wall is going to come through the wall pretty easily unless you put a membrane on the back. Is this ok for you? I guess you might get the ground in front of the wall washed out if you're not careful, so a french drain in front of the wall might be a good idea.
- How do I prevent dirt from infiltrating the basket?
A membrane of some sort.
Overall I don't think I'm not sure I'd do this sort of thing as a DIY project! I know enough about retaining walls to know that I don't know everything I need to! (I design bridges, not retaining walls).
It would probably depend on the location of the wall - i.e. how much damage would it cause if it failed / is anyone likely to be standing next to it if it fails. If it's not critical, I might build it as per above. If it was more critical I'd talk to one of my geotechnical engineering colleagues. (Assuming you don't know any, you can read that as: engage an engineer to design it for me).