Can I convince you to not do this ?
Honestly not trying to be an ass.
Please, please - Get a quote from a company that builds retaining walls.
The quote will cost very little or nothing.
You will be shocked at the cost, and not in a good way.
The quantity of material needed to build the wall, will amaze you.
Please get a quote or two first.
I promise you, you will not regret it.
Block walls work in compression, heavy things directly on top of them is fine.
Side to side, their goal in life is to tip over, and they are damn good at it.
Blocks work because they are tied to very solid, heavy things at the top and bottom that run the length of the wall, and have regular supports at a right angle to the length of the brick.
A 1' deep pile of soil, behind a 4' block wall, 1 block long, weighs 500 pounds.
The path of least resistance is to knock over the wall.
Blocks, attached with mortar, to the soil behind the wall about as strong as a 2x10 resting on its edge.
The question is more one of how many yards of concrete will you need to build the footing.
I think you're asking about width, and not depth. I'd simply excavate an inch or three under the sidewalk and fill it with your substrate, then set the wall tight to the sidewalk.
If this is not possible, build the base as wide as is practically feasible and compact it well. It's unlikely that you'll have problems with a three-course wall.
Best Answer
The depth of your 'foundation' should be 4" compacted crushed gravel plus one row of your CMU (concrete modular units). Behind that wall and sitting below the gravel is a perforated 4" pipe wrapped in landscape fabric and back filled with drain rock. Daylight down slope and there should be a down slope so you control the surface water. Do not drain onto your neighbor's property. I've always had to install a simple drywell; a pit with landscape fabric, drainrock (rounded cobble) another layer of landscape fabric then covered with a thin layer of drainrock. The size of the pit is determined by the surcharge behind you wall and the length of your wall and your area or zone.
Make sure each of your walls are no more than 3' or you shall be eligible for permit fines if they find out. One wall no more than 4'. Check your codes. Behind the two walls make sure you slope the soil away from the wall about a foot or so down into a little 'swale' to collect surface water and drain towards that drywell pit as well...so bigger pit: Say 4'X6'X3'? Or more?
Do you have enough depth to your property you could make at least 4 maybe 6' bed between the walls with a mini swale such as the one I described behind the top wall? If you want to plant that first wall you should put as much space as you are able. Install perf drain pipe behind both walls. How much surcharge is behind those walls or slope? Send a picture. Drainage will make or break your all your work. I am not kidding. I am glad you are doing a cap. I don't know if you've already selected your cmu but I would suggest as a profession to use ONLY grey with a light grey or concrete cap. The wall should be 30 % dark grey to make it look more natural. That cap should be a very light concrete color. Any color will LOOK DIY. Reds, browns will look like your wall is dirty or has a very nasty infection. Just some tried and true tips from a licensed
landscape architect and construction install project manager...blah blah blah. Dove grey is the only color I ever use for architectural structures in the landscape. Comes from my background in Japanese garden design principles. Gravel, concrete, decks, pergolas, arbors and garden walls are always dove grey to allow your plants to be the focus, not say, the fire engine red fence? Grins.
UPDATE: Glad you gave more information. Wish I could just draw you a section, I'm sure I could but dissed learning CAD, I learned to design by paper.
It has always been a no no to use your home's foundation drain as well as storm sewers to direct excess water. Perhaps your codes are different but the reason for that is you do not want to encourage MORE water to travel to any foundation or concrete. Water is pretty destructive. I've had a hard time with the rules for not being able to use the storm drains. That is why I love dry wells. Check your codes but it isn't a good idea to ever encourage water to drain towards your home's foundation even if it is into a pipe.
Then I need to know the distance between your wall (the radius is it based on your CMU's for a curvature)? Is there a scale I could use or did I miss that? I am disturbed there is a slope between you and your home. That means water is not only draining through the soil towards your wall but towards your home's foundation. Do you know there is a decent foundation perimeter drain? Do you have a basement? Do you know if your foundation has asphalt emulsion between soil and concrete? Is there a drain in your basement if so where does that go? And this sump pump. Now that really worries me. Tell me more about this pump; where is it, what is its purpose, how often do you have to use it? Sump pump just tells me a band aid is in place to cover up a problem that you might be exacerbating? Also, that perf pipe should be on the same level as the bottom of your gravel foundation, not an inch or two above. It might not be a big deal if I knew more but if you've not installed this pipe try to do so. Back fill is NOT soil, it should be drainrock. You want to encourage water to go towards the pipe that allows excess water to flow en mass to a proper spot. What will the elevation of the patio at the foot of your wall be? Why 2 walls that close to your home. Shoot. I need more information. How about a picture of the area, excavation in relation to your home's foundation? Get back to me, okay? This could be a beautiful addition to your home and if done correctly will add big value to your home. What planting do you imagine above that wall. Is it really going to take two walls to accommodate that slope? Pictures. I'd rather do this on site but am learning to try being 'virtual'...