Proper backfill for a trench dug below foundation level (within the 45 degree cone of support)
No handy references, (I was taught, as grunt labor, by a licensed civil engineer and former SeaBee, but I don't know which books it might have come from to him, or if any of them are on the web) but backfilling with something like road base (crushed rock including fines so it will pack well) and tamping it very well in thin layers (if you tamp 6" of fill, you only properly compact about 2" of it, so tamping 2" layers 3 times gets a better result.) Tamp with something fairly small - a large plate won't really compact as well (unless you rent a vibratory plate compactor.) If you are tamping by hand and it feels frustratingly slow, you are probably doing it right ;-)

Clay is virtually impossible to get properly compacted back into a trench - in non-bearing applications you generally backfill it and mound it a bit, then come back in  year to fix the settling. Obviously not such a good idea in a bearing application, thus the use of a readily compactable material like road base.