Consolidation Degree from Elapsed Time (Terzaghi)
How far a surcharge or fill has consolidated after a given time.
Example
You enter
- Coefficient of consolidation cv (ft²/day) 0.1
- Drainage path Hdr (ft) 10
- Elapsed time (days) 848
You get
- Time factor Tv 0.848
- Degree of consolidation U 90.0 %
Details, formula, and sources
Tv = cv t / Hdr^2, then U = 100 sqrt(4 Tv/pi) for Tv <= 0.283 else 100 - 10^((1.781-Tv)/0.933). cv 0.1 ft^2/day, Hdr 10 ft, 848 days -> Tv 0.848, U 90%; at 196 days U is only 50% (the decelerating curve, U approaches 100% asymptotically). Hdr is half the layer for double drainage (a 4x time swing). The engineer of record governs.
Tv = cv t / Hdr^2; U = 100 sqrt(4 Tv / pi) for Tv <= 0.283 (U <= 60%), else U = 100 - 10^((1.781 - Tv)/0.933).
Terzaghi one-dimensional consolidation theory (time factor Tv), inverted for U, as compiled in Das, Principles of Geotechnical Engineering, by name.
The Terzaghi time-factor series and the Tv = cv t/Hdr^2 relation are standard published soil-mechanics results.
Estimate. AHJ and licensed professional govern.
Field names used by the API: cv_ft2_day, hdr_ft, t_days, tv, u_percent
- Time factor Tv = cv t / Hdr^2Terzaghi consolidation theory
- Degree of consolidation U = 100 sqrt(4 Tv/pi) (Tv <= 0.283), else 100 - 10^((1.781 - Tv)/0.933)Das, Principles of Geotechnical Engineering
- Drainage path Hdr = full layer (single) or half (double drainage)scope of this tile