So, my idea is to cut them the rest of the way through in the area of the puddles so the water can then drain. I'm thinking about 10 ft or so is all I need in total and I'm thinking about using a circular saw with either a diamond blade or else one of those abrasive saw blades that also say they will cut concrete. The difference is the diamond blade is $40, while the abrasive ones are $6. I obviously don't care if it takes a bit longer with the abrasive blade, but I don't want to have to go through 4 blades and have it take 3 hours either. I think we can assume the remaining concrete is about 2" thick.
Any thoughts? Anyone do anything similar with one of the abrasive type blades? Thanks.