I am removing soil down to the footing/ slab level near the corner of a basement. The basement wall will have a new sliding door which will exit onto a new brick paver patio. 4 ft. retaining walls will be located 3 ft. from each door jamb to create a level patio. Since the job is in southern N.Y. state I am concerned about frost heave. I would rather not excavate and underpin the footings because I am afraid this may cause more problems (cracking, etc.) than it will solve. Does anyone have a better solution? I was thinking of pouring a new concrete frost wall 1 ft. away from the existing wall. This wall would extend down 3 ft. below grade. The patio just outside the step down from the door would receive 3″ rigid insulation with 4″ slab over (essentially butted up to the existing house footing). My theory is that this would prevent frost from spreading to the soil below the footings.
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Interesting problem. Obviously, drainage is key here. If the soil does not saturate, it will not heave.
There was something on shallow foundations in FHB #107. Might be pertinent...
http://www.taunton.com/store/pages/fh_toc_107.asp
FROST-PROTECTED SHALLOW FOUNDATIONS
In general, your theory is right. The foam will prevent frost from penetrating. You also want to keep water from saying in the underlying soils.
I would dig the footing for the buttress walls below the house footings and make sure the soil between them - under the patio - is a load bearing soil, not clay or loam but gravel or stone, and lay drains into it to lead to daylight. Then compact that base and then place the foam and slab. You'll need to do an elevation drawing to be sure the finished brick and adjacent footings end up at the right elevation.
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Repeat after me: Frost heaves require 1) Freezing Temperatures AND 2) Water AND 3) Fine Grained Soils. Eliminate any one and you can't have frost heaves.
You have focused on minimizing the depth to which freezing temps will reach (as Piffin points out, that will help). It also minimizes the depth that summer heat will reach. It keeps the soils temps closer to the local deep soil temperature (50-51F, I'd estimate). Dark concrete/pavers (if it seees any sun) will help a bit more in summer than they hurt in winter.
I'd overexcavate under the foam level and put in a foot of NFS (non-frost-susceptible) soil - pea gravel, coarse sand, crushed rock, or a mixture. No clay and no silt. So to the extent that freezing temps get through the foam, there won't be susceptible soils immediately underneath.
Piffin's, "lay drains into it to lead to daylight" is good but I'd also slope the concrete and brick on the high end of the range (at least 1/4" per foot) to minimize water infiltration.
Belt, suspenders, and cumberbund if you eliminate water, find-grained soils, and temps <32F.