Engineering & Science
Clay Primary Consolidation Settlement (Sc) & Terzaghi Time Factor (Tv)
Calculate normally consolidated clay ultimate settlement Sc = (Cc * H0 / (1 + e0)) * LOG10((sigma0 + dsigma) / sigma0) in mm and Terzaghi dimensionless time factor Tv = (cv * t) / Hdr^2.
Predict both how far a saturated clay layer settles—and how fast pore water drains!
Constructing an embankment or mat foundation over saturated normally consolidated soft clay triggers two distinct geotechnical design questions: (1) Ultimate Primary Consolidation Settlement Sc = (Cc * H0 / (1 + e0)) * LOG10((sigma_v0 + delta_sigma) / sigma_v0) driven by compression index Cc, clay thickness H0 (m), initial void ratio e0, and vertical effective stress increase; and (2) Consolidation Rate governed by Karl Terzaghi’s dimensionless Time Factor Tv = (cv * t) / Hdr^2!
Notice the quadratic drainage-path effect in Hdr^2: a 6.0 m clay layer (Cc = 0.35, e0 = 0.95, sigma_v0 = 80 kPa, delta_sigma = 120 kPa) undergoes Sc = 428.6 mm of ultimate settlement. With two-way drainage into both an upper sand blanket and a lower gravel stratum (Hdr = H0 / 2 = 3.0 m at cv = 2.5 m^2/yr over t = 1.5 yr), Terzaghi’s time factor reaches Tv = 0.4167 (~71% primary consolidation); subdividing or installing horizontal permeable sand seams that halve Hdr from 3.0 m to 1.5 m quadruples Tv to 1.6667 (> 98% primary consolidation in the same 1.5 years)!
| Geotechnical Drainage Scenario (H0 = 6 m, Cc = 0.35, e0 = 0.95) | Ultimate Settlement Sc (mm) | Drainage Path Hdr (m) | Terzaghi Time Factor Tv (at 1.5 yr) |
|---|---|---|---|
| Two-Way Top & Bottom Drainage | 428.6 mm | 3.0 m (= H0 / 2) | 0.4167 (~71% U) |
| Halved Drainage Path (Sub-Layer / Drains) | 428.6 mm | 1.5 m | 1.6667 (> 98% U) |
| Zero or Negative Initial Effective Stress | Logarithm Guard | Invalid Stress State | "Invalid Soil Parameters" |
Normally Consolidated Clay Settlement Sc (mm) = ((Cc * H0) / (1 + e0)) * LOG10((sig0 + dsig) / sig0) * 1000
Computes 1D oedometer virgin-compression primary settlement converted from meters to millimeters (* 1000).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 < 0), "Invalid Soil Parameters", ROUND(((B2 * B3) / (1 + B4)) * LOG10((B5 + B6) / B5) * 1000, 1))Terzaghi Dimensionless Consolidation Time Factor Tv = (cv * t) / Hdr^2
Scales coefficient of consolidation cv (m^2/yr) and elapsed time t (yr) against squared longest drainage path Hdr^2 (m^2).
=IF(OR(B7 <= 0, B8 < 0, B9 <= 0), "Invalid Soil Parameters", ROUND((B7 * B8) / (B9 ^ 2), 4))Try the example
Use the original values or change them to test your understanding.