I have a garage floor - the floor in the garage has sunken leaving the area at the exterior foundation wall - Entrance - to sit up higher like a nice ramp which makes a perfect Rain Water collection scoop to wonderfully force the water under the door and into the garage (if anyone wanted to know how that was done - there is your answer.) So I am looking for a way to fix this problem - I thought about grinding and shaving at the Garage Floor to Drive way to even it out with the garage floor and prevent it from acting like a funnel - I have done all kinds of things to seal the door - they have helped reduce the pond in the garage but not end the flow..
When faced with a similar problem I opted to cut the blue part about 4 inches away from the garage slab, break and remove the concrete, and put in a pre fabricated French drain. The cutting was done with an old skilsaw and $15 diamond blade, and busting was with hand tools. About a 1 day project.
I am not an expert, but I’d be concerned with grinding, shaving, or otherwise removing material from actual driveway. It would weaken the slab, which you drive on, I assume, and there is no guarantee that the garage floor won’t sink more over time anyway. That solution seems more like a gypsy-rigging than anything else. But if anything, build up the garage floor inside the door…it will mean a speed bump of sorts, but that is better than removing thickness from the drive, IMO
It is not directly answering the specific question you asked, but since it is the sinking of the garage floor that has been the source of the problem, have you considered having it poly-jacked back to its appropriate height?
How wide is the area that is "scooping" the water? If it's just an inch or two, you could install a "custom door bottom shoe" similar to this:
You just need to make the "skirting" wide enough to cover the scoop, but it will only be as good as the outer seal.