Frost Depth
Modified Berggren Preliminary estimateEstimate design frost penetration depth from the site air-freezing index and soil thermal properties. Pick an Alaska community to prefill the climate inputs.
Results update as you type. These are educational estimates — confirm against the governing code and a licensed engineer before design use.
Method & references
The design depth of frost penetration is estimated with the Modified Berggren equation, a correction of the Stefan solution for one-dimensional freezing:
X = λ · √( 48 · k · F / L )
- X — frost penetration depth (ft)
- k — soil thermal conductivity (Btu/ft·hr·°F)
- F — surface freezing index (°F·days)
- L — volumetric latent heat of fusion = 144 · γd · (w/100) (Btu/ft³)
- λ — dimensionless correction coefficient (≈0.6–1.0)
The coefficient λ depends on the thermal ratio α = vo/vs and the fusion parameter μ = (c/L)·vs. This tool estimates λ with a smooth approximation to the Aldrich & Paynter chart; for final design, read λ from the published chart. Setting λ = 1 recovers the Stefan equation (a conservative upper bound).
References: Aldrich & Paynter (1953); U.S. Army Corps of Engineers / CRREL frost-design guidance; Andersland & Ladanyi, Frozen Ground Engineering.