wet basement issues
Little bit of a long post, but I figured I'd try to anticipate likely questions in advance!
I have a house built in 1927, poured foundation with concrete slab, full basement. The majority of the time, the basement floor is pretty wet. Wetter right after a rain or snowmelt, but stays wet for weeks or months. Really only dry in the dead of winter (live in upstate New York). Most basements on my street are wet also. Soil appears to be "clay-ish": maybe not full-on clay but not loam, hard to dig even where there aren't a lot of rocks in it, which usually there are.
Anyway, the walls of the basement are always dry, but the floor has water coming through it at multiple spots, some of them near the very center of the slab. In places the slab floats a little bit when it gets really wet.
The gutter situation is not perfect by any means, but the lot is so small (only 0.15 acre and the house is 2000sf on 3 levels plus basement) that there is very little room to direct rainwater away from the house without directing it onto neighbor's driveways. Even better, the front yard, which is tiny, sits in a little depression between the front porch and the street, and the back yard, which is ok-sized, is slightly up-grade from the house, so putting water there wouldn't seem to help much.
I did put in a sump pump at one location (I think it might ultimately need 3) but this didn't do a huge amount even though it runs quite frequently. Unfortunately the lowest spot in the basement is right at the foot of the basement stairs, which makes it a lousy spot for a sump pump. The water main pops out of the slab right there too, and I want to keep well away from that... Prior to the pump (and currently) the system drained into the town storm sewer via a drain at the low corner of the basement.
Anyhow, because of all those factors, I've concluded that I have a sub-surface water problem.
So my questions are:
1) Am I right in concluding that I have a subsurface water problem?
2) Based on the internet reading I've done so far, it looks to me like my solution is an interior perimeter French drain system adjacent to (not below!) the footer, with another one or two sump pumps thrown in for good measure. Does that seem right?
3) As I said, quite a lot (most?) of water comes up through the CENTER of the slab, so I was thinking that, in addition to the perimeter drain, I would lay a drain diagonally down the center of the slab. Overkill?
Thanks in advance for your replies, and for your patience in reading this far!