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Consolidation Settlement

1-D primary consolidation settlement of a clay layer using e₀, Cc, Cr with NC / OC handling, plus time-rate using Cv and Tv.

Inputs

m
kPa
kPa
kPa
m²/year
years
e.g. 0.9 for 90%
Method & assumptions
  • NC clay (σ'0 + Δσ ≤ σ'p never): S = (Cc·H)/(1+e₀)·log((σ'0+Δσ)/σ'0).
  • OC clay, no exceedance (σ'0+Δσ ≤ σ'p): S = (Cr·H)/(1+e₀)·log((σ'0+Δσ)/σ'0).
  • OC with exceedance: S = (Cr·H)/(1+e₀)·log(σ'p/σ'0) + (Cc·H)/(1+e₀)·log((σ'0+Δσ)/σ'p).
  • Time factor Tv = Cv·t/Hdr²; Hdr = H/2 (double drainage) or H (single).
  • U(Tv) approx: U = √(4Tv/π) for U≤60%, else U = 1 − 10^{(1.781 − 0.933·log(100·(1−U)))} simplified to: Tv = 1.781 − 0.933·log(100·(1−U)) when U>60%.

Results

Stress Path
σ'0 + Δσ
Primary Settlement S
Hdr
Tv at t
Degree of Consolidation U(t)
Settlement at t
Time for U = target

Settlement vs Time

U%TvTime (yr)S(t) (mm)