Consolidation of Soil Notes

Last reviewed 16 Sept 2026 · 6 min read

What consolidation is

When load is applied to a saturated clay, water cannot escape quickly because permeability is very low. The load is first carried by excess pore water pressure; as water slowly drains, the load transfers to the soil skeleton, effective stress increases and the soil compresses. This time-dependent volume reduction due to expulsion of pore water is consolidation.

Total settlement of a foundation on clay:

S = S_{i} + S_{c} + S_{s}

$S_{i}$ = immediate (elastic) settlement — distortion at constant volume.
$S_{c}$ = primary consolidation settlement — expulsion of pore water (this chapter).
$S_{s}$ = secondary compression — creep of the skeleton after excess pore pressure has dissipated.

Spring–piston analogy (Terzaghi)

A cylinder full of water with a spring (soil skeleton) and a piston with a small valve (low permeability):

Instant of loading ( $t = 0$ ): water carries the whole load; excess pore pressure $Δ u = Δ σ$ ; spring stress unchanged.
During drainage: water escapes through the valve; load gradually shifts to the spring; $Δ u$ falls, $Δ σ^{'}$ rises.
End of consolidation: $Δ u = 0$ ; the spring carries the full load; $Δ σ^{'} = Δ σ$ .

Oedometer (consolidation) test

An undisturbed specimen (typically 60–75 mm diameter, 20–25 mm thick) is confined laterally in a ring between porous stones (one-dimensional compression, drainage top and bottom). Loads are applied in stages (each usually doubled, held about 24 hours) and dial readings recorded with time. Results give void ratio $e$ at the end of each stage.

Compressibility parameters

FormulaCompressibility

Coefficient of compressibility: $a_{v} = - \frac{Δ e}{Δ σ ^{'}}$ (m²/kN)
Coefficient of volume compressibility: $m_{v} = \frac{a _{v}}{1 + e _{0}} = \frac{Δ H / H}{Δ σ ^{'}}$ (m²/kN)
Compression index (slope of the virgin line on $e$ –log σ′): $C_{c} = \frac{e _{1} - e _{2}}{lo g _{10} ( σ _{2}^{'} / σ _{1}^{'} )}$
Swelling / recompression index $C_{s}$ (or $C_{r}$ ): slope of unloading–reloading line, typically $C_{c} /5$ to $C_{c} /10$ .
Skempton's empirical relations: $C_{c} = 0.009 (w_{L} - 10)$ (undisturbed clays of low–medium sensitivity); $C_{c} = 0.007 (w_{L} - 10)$ (remoulded).

Normally consolidated and over-consolidated clays

Preconsolidation pressure $σ_{p}^{'}$ (or $σ_{c}^{'}$ ) — the maximum effective stress the soil has experienced in its history. Found from the $e$ –log σ′ curve by Casagrande's graphical construction (point of maximum curvature, horizontal line, tangent, bisector, intersection with the extended virgin line).
Normally consolidated (NC): present effective stress $σ_{0}^{'} = σ_{p}^{'}$ — soil is on the virgin line; highly compressible.
Over-consolidated (OC): $σ_{0}^{'} < σ_{p}^{'}$ (past erosion, desiccation, lowered water table, glacial load); much less compressible for stresses below $σ_{p}^{'}$ .
Under-consolidated: still consolidating under its own recent weight ( $σ_{0}^{'}$ less than the final value).

Over-consolidation ratio O C R = \frac{σ _{p}^{'}}{σ _{0}^{'}}

Consolidation settlement

FormulaPrimary consolidation settlement of a layer of thickness H

Normally consolidated:

S_{c} = \frac{C _{c} H}{1 + e _{0}} lo g_{10} \frac{σ _{0}^{'} + Δ σ}{σ _{0}^{'}}

Over-consolidated, final stress ≤ $σ_{p}^{'}$ :

S_{c} = \frac{C _{s} H}{1 + e _{0}} lo g_{10} \frac{σ _{0}^{'} + Δ σ}{σ _{0}^{'}}

Over-consolidated, final stress > $σ_{p}^{'}$ :

S_{c} = \frac{C _{s} H}{1 + e _{0}} lo g_{10} \frac{σ _{p}^{'}}{σ _{0}^{'}} + \frac{C _{c} H}{1 + e _{0}} lo g_{10} \frac{σ _{0}^{'} + Δ σ}{σ _{p}^{'}}

Using $m_{v}$ : $S_{c} = m_{v} Δ σ H$ (for a small stress range).

$σ_{0}^{'}$ and $Δ σ$ are taken at the middle of the layer (thick layers are divided into sub-layers).

Downloaded from civilgyantests.com · Not for resale. Verify every code clause and date against the official source.

Consolidation of Soil