Our house came with a concrete porch that was poured in sections right up against the original 160 year old rock wall foundation on the south side up against our bedroom. There is a low spot up against the wall where, in some one's infinite wisdom, there is a 2x? piece of lumber between the house and the slab. Water puddling on this spot has infiltrated and caused settling issues.
Mud jacking isn't going to work, as I am worried that the pressure would heave the rock wall foundation next to it. Replacing the concrete isn't really an option for us right now, so I came up with an alternate solution.
Using a laser level, I determined that the house side was 3/4" lower than the edge of the concrete. So I snapped a chalk line to the lowest point, and cut a kerf into the slab. I used a concrete blade on my circular saw, making a series of full passes towards the house until I achieved a 1" cut on the edge. Since the blade wears away as I am cutting, the cut tapers up automatically to nothing at the low point that I am trying to drain.
So far it is working pretty well. Instead of pooling up near the house, water is drained into the garden bed next to the porch. I may run into issues with the kerf clogging with debris, or cracking in the winter. It will be interesting to see how it performs over the long haul. But for now, at least I have slowed down the erosion and bought us some time without spending a lot of money.