Backsplit Basement Floor Leak

The basement of my backsplit consists of two concrete boxes offset vertically about 3'. A concrete stairway connects the two boxes in the middle (ie far from any exterior walls). After extensive rain, we get a leak at the bottom of the stairs. Previous owners have tried a bunch of quick fixes which I have now chipped/scrapped/sanded away. The concrete in the whole floor is very soft and crumbles to sand on the surface. The concrete in the leak area contains voids, and seems to be discoloured brown and/or mixed with beach sand (no beaches nearby!).
The lot has been graded away from the foundation and the downspouts routed away from the house. Obviously, can't get at the exterior of the leak area without tunneling.
Current plan is to chisel along the seam, apply silicate sealer and hydraulic cement, then top coat with patching mix.
Any comments, suggestions, warnings?
TIA, Chris
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Chris wrote:

and have had interior walls in my basement leak too. snipped-for-privacy@pauloman.com
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