Frost Penetration Depth (Stefan / Modified Berggren)
How deep frost drives into the ground, by the Stefan / modified-Berggren heat-of-fusion method. Stefan X = sqrt(48 kf FI / L) balances the cold the air delivers against the latent heat of freezing the soil moisture: kf = frozen conductivity (BTU/hr-ft-F), FI = air-freezing index (F-days), L = 144 x dry density x water content/100 (144 BTU/lb is the heat of fusion). A soil at kf 1.0, 100 pcf, 15% water in a 2,000 F-day climate has L 2,160 and a Stefan depth of ~6.7 ft. Stefan over-predicts (it ignores soil heat capacity); the modified-Berggren lambda (~0.6-0.9, off the nomograph) cuts it to ~5.3 ft. CRITICAL: computes the PHYSICS, not the code frost line -- the footing depth is set by the locally adopted frost depth (IRC Table R301.2 / amendment), which this does not replace. A drier soil freezes deeper. A screen; the adopted requirement, the geotech report, and the AHJ govern.
Formula and source
L = 144 x dry_density x water_content/100 (BTU/ft^3); Stefan X = sqrt(48 x kf x FI / L) (ft); modified Berggren X_MB = lambda x X_Stefan, lambda ~0.6-0.9. FI in F-days, kf in BTU/hr-ft-F.
Stefan equation and the modified-Berggren frost-penetration method (US Army Corps of Engineers / FHWA pavement design), by name; the locally adopted frost-depth requirement, the geotechnical report, and the AHJ govern the footing depth.
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