Void under cracked garage floor slab

[austin]

This is a basement 2-car garage at grade level. The other 3 sides of the house are back filled with sand to about 2/3 the height of the cinder block foundation. Winter temperatures here go to -20 to -30. The concrete floor is cracked in several areas, especially near the garage doors door. When I purchased the house, the gravel driveway sloped toward the garage. I regraded it a couple of years ago to slope away from the house. I want to repair the cracks, so I began by digging out the area in front of the garage door. Please see the uploaded photos. There were 2" x 1' rigid polystyrene foam lying vertically against the front of the slab and horizontally in front of and below the bottom edge of the slab. The edges/joints of the foam wasn't sealed, so water could get in behind it. There doesn't appear to be a French drain, unless it's under the foam, but that wouldn't seem to make sense to me. I haven't finished digging it all out yet, but it looks like I'm going to find a similar picture all along the front of the garage. What do I do about all this?! It will have to be a quick DIY fix because it will soon be winter here. We're look at a few days now of above freezing temperatures, so I hoping I'll be able to get it done now.

[austin]

I dug out the rest of the area in front of the garage. It looks like the void is only in the corner shown in the photo in the previous post. The rest seems to be pretty well compacted and in contact with the underside of the slab. So I'm thinking I'll: (1) pack this void with concrete and tap it in best I can; (2) patch the horizontal and vertical cracks with hydraulic cement, then smooth out the surface with a layer of poly cement; (3) spray expanding foam into the 3/8" horizontal space between the slab and the concrete floor; (4) add 2" exterior rigid polystyrene foam on the vertical face of the concrete pad and floor.; (5) add a French drain across the front of the garage.

What do you think about my plan?At what depth should the bottom of the drain pipe be - above or below the underside of the concrete slab? What should be the horizontal distance of the drain pipe from the front face of the concrete slab?