Governing Equations:
Consolidation settlement is the vertical compression of a saturated soil layer due to expulsion of pore water under sustained loading. It is usually evaluated for clayey soils, where dissipation of excess pore water pressure governs settlement over time.
The classical one-dimensional consolidation method is the most widely adopted, based on oedometer test results. The procedure is summarised as follows:
1. Determine initial soil state
From site investigation and laboratory testing (Oedometer):
Initial void ratio, eo
Preconsolidation pressure, σ′c
Compression index, Cc (for virgin compression)
Recompression index, Cr (for unloading–reloading)
Thickness of compressible layer, H
2. Compute stress increment
For applied footing or embankment load:
Calculate initial effective vertical stress at representative depth (e.g., mid-depth of the clay layer): σ′o = γ′·z (where γ′ is the effective unit weight).
Calculate stress increase at the same depth due to applied load (Δσv) using Boussinesq, Westergaard, or elastic solutions.
Final effective stress: σ′f = σ′o + Δσv.
3. Settlement formula
If σ′f < σ′c:
\[
S_c = \frac{C_r \cdot H}{1 + e_0} \log_{10}\left(\frac{\sigma'_f}{\sigma'_0}\right)
\]
If σ′f > σ′c:
\[
S_c = \frac{C_r \cdot H}{1 + e_0} \log_{10}\left(\frac{\sigma'_c}{\sigma'_0}\right)
+ \frac{C_c \cdot H}{1 + e_0} \log_{10}\left(\frac{\sigma'_f}{\sigma'_c}\right)
\]
This gives the ultimate consolidation settlement.
