How Deep the Frost Goes: A Frost-Penetration Bound for Footings and Posts, and the Climates Where a Shallow Foundation Stops Working

A footing or fence post founded above the depth reached by winter frost can be lifted by the ground it stands in. This study computes an upper bound on frost penetration with the Stefan freezing equation for five stated soils, from dry sand with 5 percent moisture to wet clay with 30 percent moisture, under five stated climate classes with air freezing indices from 200 to 3000 degree-days. A surface factor of 0.9 converts the air index to the index at cleared ground. The bound is deliberately conservative because the calculation omits the sensible heat of the soil, and it should be used as a depth that frost is not expected to exceed, not as a prediction of the depth in a typical winter. Even so, the ordering it produces is instructive. The deepest penetration occurs not in wet ground but in dry sand, whose volumetric latent heat is only 26.7 megajoules per cubic metre: the bound is 1.32 m in the mildest climate class and 5.12 m in the subarctic class. In moist silt the bound is 0.77 m at 200 degree-days, 1.34 m at 600, 1.90 m at 1200, 2.45 m at 2000, and 3.00 m at 3000 degree-days; adding a stated margin of 0.15 m gives footing depths from 0.92 m to 3.15 m in that soil. A separate heave calculation gives the boundary where a shallow foundation stops working. Freezing of pore water in place, before any ice-lens growth, lifts susceptible ground by 0.09 times the volumetric water content times the frozen depth. For moist silt that in-place lift alone passes a stated tolerance of 25 mm once the air freezing index exceeds 329 degree-days, at a frozen depth of 0.99 m; for wet silt the corresponding index is 222 degree-days. At a freezing index of 1200 degree-days, silt-type ground passes the same tolerance at a gravimetric moisture content of only about 5.5 percent. Finally, the study sizes the alternative to digging deeper: horizontal insulation that protects a footing founded at 0.60 m in moist silt. By an equivalent-soil method with a stated factor of 2.0 for edge losses, the specified extruded polystyrene thickness is 10 mm in the mildest climate, 30 mm at 600 degree-days, 50 mm at 1200, 70 mm at 2000, and 100 mm in the subarctic class. The plain conclusion is that in any climate colder than mild maritime, an uninsulated shallow footing in moist silt is founded inside ground that the bound says will freeze and lift; it must be taken deeper, placed on non-susceptible fill, or insulated by the amounts given.