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 know a little about 2 subjects. This is one. I'm a landscape architect and two easy examples of how to fix your problem came to mind. BTW...nice drawing.
I HIGHLY RECOMMEND YOU DO THIS...simply get some diamond tip masonry drill bits and drill some holes into your retaining wall about an inch above the ground. Also do the same from the other side of your wall at different levels in your wall, but that's below the ground surface that your retaining.
Doing this is not optional if you want your wall to last through the next rainfall in your area. This is to allow water from any sudden downpours as well as water trapped below the surface to escape, while leaving your yard in place.
The other option that's easily done is called a French drain. This is the most aesthetically pleasing way to move water because the entire drain is buried and cannot be seen. Easily done with the right equipment (varies widely from a mini excavator to a pick and shovel) or neighborhood kid to dig the trench for your pipe to lay in.
The opening to the drain would be where the question mark is on your drawing. And you would have the pipe traveling down the hill and UNDER where your retaining wall will be. Just 3" below the surface of the ground where your wall will be is sufficient to keep it from being pinched or crushed.
Make sure you level out the ground where the first layer of bricks that make up the base of your wall, and bury your pipe 3 inches below that. Cover with dirt. The only things you HAVE TO BE SURE OF is that your pipe must be laid in a straight line, and ALWAYS keep the fall. Meaning don't allow a hump of dirt make your pipe lift more than 1/8 inch or water and sediment will gather there, eventually clogging the drain. It only needs to be as long as about 6 inches at the least past your wall. But you can run it as far as you want. No one will even know its there. You can purchase everything you need at Walmart or your local home improvement store for cheap.
Oh yeah, avoid drilling any holes in the actual mortar/cement you use to hold the bricks in place to prevent weakening the structure. The amount of holes you need depend on the amount of water that comes your direction from other places around you. A 1" hole every 2 to 5 feet above the ground. With smaller holes placed closer together below the surface on other side of wall.
Best Answer
You need a good base for the wall to be stable so I would remove the hardcore and place the footing at least down to original compacted soil.
For the depth of the footing, if you mean the depth of the concrete, 225 mm is good. If you mean how far down in the soil, then either the depth of the footing (225 mm) or provide a decent sized width of footing on the soil retained side. There are two main items to address with the wall, overturning and sliding. The forces are minimal for a 800 mm tall wall assuming no surcharges and it's drained well so no hydrostatic loads. The sliding resistance has to come from somewhere. Some of it is soil friction. Some of it is resistance on the front of the footing from the soil. If the front of the footing is in hardcore then it will not provide much resistance. To increase friction you need weight. To get wait, you have the depth of soil on the retained side. Make the footing wider here by say 400 mm and this should be enough. This will also increase the resistance to overturning.
To get better numbers on sizes and what else to do would require doing a design.