Frost Penetration Depth (Stefan / Modified Berggren)
How deep frost drives into the ground, by the Stefan / modified-Berggren heat-of-fusion method.
Example
You enter
- Surface freezing index nF = n-factor x air-freezing index (F-days; TM 5-852-6) 2000
- Frozen conductivity kf (BTU/hr-ft-F) 1
- Dry density (pcf) 100
- Water content (percent) 15
- Berggren lambda (0-1, ~0.8) 0.8
You get
- Volumetric latent heat 2,160 BTU/ft^3
- Stefan frost depth (upper bound) 6.67 ft
- Modified Berggren frost depth 5.33 ft
Checked against published worked examples from: Headquarters, Departments of the Army and the Air Force.
Details, formula, and sources
ScopeStefan 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 = SURFACE freezing index (F-days), the air-freezing index times the surface n-factor (TM 5-852-6 tabulates n by surface type) -- entering the raw air index overstates the depth, 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 or tableL = 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.
Source and editionStefan 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.
Free accessThe Stefan/Berggren heat-of-fusion relations are public (Army Corps / FHWA); the freezing index, conductivity, density, water content, and lambda are site and soil values the user supplies, and the code frost line is the adopted table.
What governsEstimate. AHJ and licensed professional govern.
API field namesfreezing_index_f_days, frozen_conductivity_btu, dry_density_pcf, water_content_pct, berggren_lambda, volumetric_latent_heat_btu_ft3, stefan_depth_ft, berggren_depth_ft
- Stefan / Berggren X = sqrt(48 kf FI / L); L = 144 x dry density x water content/100; X_MB = lambda x X_Stefan (lambda 0.6-0.9 from the nomograph)US Army Corps / FHWA
- Physics, not the code line Stefan over-predicts (ignores soil heat capacity); the jurisdictional frost line (IRC Table R301.2 / amendment), the geotech report, and the AHJ set the footing depth; drier soil freezes deeperadopted code / geotechnical practice